EPA-600/2-76-225
August 1976
Environmental Protection Technology Series
VAStt
Industrial Environmental Research Laboratory
Office of Research ami Development
U.S. Environmental Protection Agency
Research Triangle Park, North Carolina 27711
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EPA-600/2-76-22 5
August 1976
FLUIDIZED VORTEX
INCINERATION
OF WASTE
by
Jack P. Holraan and Richard A. Razgaitis
Southern Methodist University
Civil and Mechanical Engineering Department
Dallas, Texas 75275
Grant No. R801078
ROAPNo. 21AQQ
Program Element No. 1AB013
EPA Project Officer: James D. Kilgroe
Industrial Environmental Research Laboratory
Office of Energy, Minerals, and Industry
Research Triangle Park, NC 27711
Prepared for
U.S. ENVIRONMENTAL PROTECTION AGENCY
Office of Research and Development
Washington, DC 20460
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ABSTRACT
An alternative concept of incineration utilizing fluidized wastes
in a confined vortex flow with simultaneous heat recovery was experi-
mentally investigated. The apparatus consisted -of a vortex tube five-
feet in length and O.U800 feet in internal diameter which was cooled
in five one-foot sections by water flowing through refrigeration tubing
spirally wound and soldered to the exterior of the tube. The vortex
was generated by means of two tangential air-inlets located at a radius
of 0.638 feet from the centerline of the tube in a sandwich-like
structure 0.312 feet high and 1.50 feet in diameter attached to the
base of the vortex tube. No transition section was used.
The vortex incinerator was operated using propane/air, sawdust/
propane/air, and sawdust/air. The principal data investigation was
performed using propane/air at air fuel ratios and total mass flow rates
(in units of pounds per hour) in three combinations: 15 and 125; 20 and
220; 20 and 280.
Radial temperature profiles and heat transfer to the wall of the
vortex tube were measured as a function of air/fuel ratio, vertical
position (in five discrete steps), total gas flow rate, and inlet-outlet
configurations. The temperature profiles at the entrance to the tube
demonstrated a peak of approximately l800°F at a radius ratio of one-half;
at the exit of the vortex tube the location of the maximum temperature
had shifted to the centerline and the temperature had decreased to less
than 1000°F. Total energy recovery rates varied from 8U,000 to 152,000
Btu/hour depending upon propane flow rate and inlet-outlet configuration
at recovery efficiencies (defined as the ratio of the heat recovered to
iii
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the maximum possible) of 5!+ to 70 percent. Maximum energy fluxes
experienced were approximately on the order of 37,000 Btu/hour-square
foot.
Application of the helicoidal flow-model, axial velocity inde-
pendent of radius (slug flow) and tangential velocity linearly dependent
upon radius (solid-body rotation), developed the following correlation:
St Pr = 0.117 Re ~* for fiuid properties evaluated at the film
•«v X
temperature. The characteristic length used in the definition of the
Reynolds number was the equivalent flat-plate length of the surface of
the vortex tube obtained by calculating the path length of the flow-
helix in terms of axial position. The characteristic velocity used in
both the Stanton and Reynolds numbers was the estimated velocity vector
near the wall of the vortex tube based upon the assumption of perfect
conversion of the injected angular momentum flux to a solid-body rotation
profile .
This correlation is approximately four-times that predicted for
the Colburn j-Factor using the Reynolds analogy for fluid friction for
turbulent flow past a flat plate.
iv
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TABLE OF CONTENTS
Page
ABSTRACT ill
TABLE OF CONTENTS V
LIST OF TABLES VJli
LIST OF ILLUSTRATIONS Xi
Chapter
I. INTRODUCTION 1
Backround of Research Problem 1
Three societal needs 1
Resource and energy production potential
of solid wastes 3
Schemes for energy recovery from solid
wastes 6
Recent operating experience with waste
heat recovery incinerators 10
Literature Survey of "Swirling Flows" 14
Classification of subject field 14
Outline of survey 16
Literature common to vortex flows 26
Literature survey of free vortex flows ... 31
Literature survey of confined vortex
flows 43
Literature survey of rotating flows 73
Literature survey of curved flows 80
Scope, Significance, and Objective of
Research Investigation 93
II. EXPERIMENTAL APPARATUS AND PROCEDURE 95
Experimental Apparatus 95
Vortex chamber 95
Furnace column/heat recovery system 100
Separator , • • 106
Exhaust stack/sampling equipment 110
Fluidizer 116
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Air/propane supply system 119
Instrumentation and calibration 121
Procedure 122
III. RESULTS AND DISCUSSION 125
Independent Variables Investigated 125
Heat Recovery/Vortex Gas Temperature-
Profile Data 129
Effect of exit configuration and condition . . 129
Effect of inlet configuration and condition. . 138
Discussion of Heat Recovery Data 143
Discussion of Vortex Gas Temperature-
Profile Data 154
Wall Temperature Data 158
Orsat Data 160
Slagging Effects 161
Sawdust as Fuel/Stack Sampling Results 162
IV. DATA ANALYSIS AND ANALYTICAL INVESTIGATIONS ... 165
Philosophy of Approach 165
Heat Recovery Efficiency 166
Energy Balance 172
Radiation loss 174
Free convection loss 178
Conduction loss 181
Total energy loss 183
Determination of Convective Heat Transfer
Component 185
Conduction flux component 186
Radiation flux component 188
Convection flux component 199
Nusselt Number Correlation 201
Evaluation of donvection Conductance 201
Mean Nusselt number correlation 202
Length Nusselt number correlation 205
Stanton Number Correlation 208
Concept 208
Characterization of swirl Intensity 210
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Calculation of mean axial velocity 214
Calculation of inlet air velocity 216
Calculation of free-stream velocity 217
Equivalent flat plate length 218
Entry length effect upon convection
conductance 219
Calculation of Colburn j-factor 220
Chemical reaction effect 222
APPENDICES
A. EQUIPMENT CALIBRATION 228
B. DATA REDUCTION PROCEDURE 238
C. CALCULATION OF AVERAGE TEMPERATURE 241
D. REYNOLDS NUMBER CALCULATIONS 247
E. ASSESSMENT OF RADIATION AND CONDUCTION ERROR .... 255
F. THERMOCHEMISTRY CALCULATIONS 263
G. CONFIGURATION FACTOR CALCULATIONS 270
H. NUSSELT NUMBER CALCULATIONS 278
I. STANTON NUMBER CALCULATIONS 282
J. LEAST-SQUARES CURVE-FIT CALCULATION 286
REFERENCES 289
vii
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LIST OF TABLES
Table
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
Distinguishing Characteristics of the Three
Types of Swirling Flows
Geometric Classification of Swirling Flows ....
Thermodynamic Classification of Swirling Flows . .
Summary of Principal Investigations of Swirl
Tape Flow
Summary of Operating Conditions
Independent Variables Investigated ...
Configuration 1 Heat Recovery Data
Mean, Standard Deviation, and Standard Deviation
of the Mean of the Heat Recovery Data
Configuration 1 Vortex Gas Temperature Profiles . .
Configuration 2 Vortex Gas Temperature Profiles . .
Configuration 3 Vortex Gas Temperature Profiles . .
Inlet Configuration Effect Upon Heat Recovery . . .
Vortex Gas Temperatures for 3 Inlet
Furnace Column Wall Temperature vs. Furnace
Vortex Chamber /Copper Plate Temperatures
Orsat Data
Pag!
17
18
20
88
126
127
131
132
133
135
136
137
139
141
142
1 SQ
x jy
160
161
viii
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Table Page
20 Radiation Loss from Vortex Chamber 176
21 Summary of Energy Losses from System 184
22 Energy Balance Table 184
23 Conduction Flux to Each Section 188
24 External Radiation Flux to Each Section .... 190
25 Internal Plate Radiation Flux to
Each Section 192
26 External Radiation Flux Loss from Each
Section 193
27 Radiation Flux from Copper Base Plate to
Each Section 194
28 Calculation of Radiation Flux from Vortex
Gas to Each Section 198
29 Calculation of Total Radiation Flux to
Each Section 200
30 Convection Flux at Each Section 202
31 Evaluation of Convection Conductance 204
32 Gas Constant of Products 215
33 Mean Axial Velocity 216
34 Inlet Air Velocity 217
35 Swirl Parameter Calculation 218
A-l Honeywell Recoder Calibration 229
C-l Average Vortex Gas Temperature at Station 1 . . 242
C-2 Average Vortex Gas Temperature at Station 2 . . 243
C-3 Average Vortex Gas Temperature at Station 3 . . 244
C-4 Average Vortex Gas Temperature at Station 4 . . 245
C-5 Average Vortex Gas Temperature at Station 5 . . 246
D-l Axial Reynolds Number Calculation for 3
Exit Configurations 249
ix
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Table Page
D-2 Axial Reynolds Number Calculation for 3
Inlet Configurations 249
D-3 Exit Reynolds Number Calculation 251
D-4 Inlet Reynolds Number Calculation 251
D-5 Length Reynolds Number Calculation 253
D-6 Free-Stream Reynolds Number Calculation . . . 254
F-l Molar Coefficients of the Theoretical
Chemical Reaction Based Upon the
Measured Air/Fuel Ratio 264
F-2 Theoretical Enthalpy of Combustion at 77°F . . 265
F-3 Sensible Enthalpy of Reactants 267
F-4 Sensible Enthalpy of Products/ Net
Enthalpy of Reaction 268
F-5 Net Enthalpy of Reaction at the Exit 269
G-l Numerical Integration Results for
Configuration Factor 274
G-2 Configuration Factor from Vortex Chamber
to Each Furnace Column Section 274
H-l Mean Nusselt Number Calculation 280
H-2 Length Nusselt Number Calculation ...... 281
1-1 Calculation of Colburn j-Factor 283
1-2 Calculation of Modified Colburn j-Factor . . . 285
x
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LIST OF ILLUSTRATIONS
Figure Page
1 Chigier Swirl Generators 33
2 Two Fundamental Geometries 45
3 Swirl Generators 92
4 Overall Configuration of Vortex Incinerator . . 96
5 Vortex Combustion Chamber 98
*
6 Vortex Combustion Chamber and Furnace Column . . 101
7 Furnace Column Cooling Water Schematic 103
8 Furnace Column 104
9 Thermocouple Locations 107
10 Gas Temperature Measurement System 108
11 Separator 109
12 Collar Ill
13 Separator (Exit Orifice Removed) 112
14 Exhaust Stack, Separator, and Furnace Column . . 114
15 "Staksamplr" Installation 115
16 Fluidizer Motor/Drive Shaft 118
17 Sawdust Mixture 120
18 Total Heat Recovery Rate vs. Axial
Reynolds Number 145
19 Total Heat Recovered per Pound of Propane
vs. Axial Reynolds Number 145
20 Total Heat Recovery Rate vs. Axial Reynolds
Number 147
xi
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Figure Page
21 Total Heat Recovered per Pound of Propane
vs. Axial Reynolds Number .......... 147
22 Total Heat Recovered per Pound of Propane
vs. Exit Reynolds Number .......... 148
23 Total Heat Recovered per Pound of Propane
vs. Inlet Reynolds Number .......... 148
24 Heat Flux Recovered vs. Length Reynolds
Number ................... 151
25 Heat Flux Recovered per Unit Flow Rate of
Propane vs. Length Reynolds Number ..... 153
26 Vortex Gas Temperature Profiles for
Configuration 2 ............... 155
27 Vortex Gas Temperature Profiles for
Condition 8 ................. 156
28 Absolute and Practical Efficiency vs. Axial
Reynolds Number ............... 168
29 Comparison of Incinerator Efficiency vs.
Available Heat with Broido Curve ...... 171
30 Conduction Heat Transfer Schematic ...... 187
31 Mean Nusselt Number vs. Axial Reynolds
Number ................... 206
32 Length Nusselt Number vs. Length
Reynolds Number ............... 207
33 Colburn j -Factor vs. Free-Stream
Reynolds Number ............... 221
34 Modified Colburn j -Factor vs, Free-Stream
Reynolds Number ............... 225
35 Modified Colburn j -Factor vsi. Free-Stream
Reynolds Number ............... 226
A-l Daystrom Recorder Calibration ......... 230
A-2 Air Rotameter No. 1 Calibration ........ 235
A-3 Air Rotameter No. 2 Calibration ........ 236
D-l Absolute Viscosity of Flue Gas as 1 Atm. . . . 248
xii
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Figure Page
(•
E-l Comparison of Shielded and Un-Shietded
Thermocouple Data 257
E-2 Aspirated Thermocouple . 258
E-3 Comparison of Aspirated and Sheathed
Thermocouple Data 259
G-l Configuration Factor Geometry 271
G-2 Configuration Factor Equation 273
G-3 Internal Radiation Transfer Schematic 276
H-l Thermal Conductivity of Flue Gas 279
xiii
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CHAPTER I
INTRODUCTION
Background of Research Problem
Three Societal Needs
There are three fundamental societal needs which have drawn a
great deal of attention in the last several years: the production and
availability of energy, the ever-diminishing supply of inorganic re-
sources, and the disposal of wastes. The process of satisfying these
needs has created a relatively new problem area broadly referred to as
pollution. Concern for the impact of these four problem areas has re-
cently resulted in an incredible number of legislative acts and execu-
tive orders at all levels of government. In-the last five years, the
United States Congress alone has produced the National Environmental
Policy Act of 1969, the Clean Air Act as Ammended in 1970, the Solid
Waste Disposal Act of 1970, the National Materials Policy Act of 1970,
the Water Resources Planning Act as Ammended in 1971, the Federal Water
Pollution Control Act as Ammended in 1972, the Marine Protection, Re-
search, and Sanctuaries Act of 1972, and the Noise Control Act of 1972
[1]*.
In the last several years the methods of waste disposal have
been reexamined in light of the opportunities to recover inorganic
* Numbers in brackets refer to References listed after the Appendices.
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resources and produce energy thus using the means to meet one of the
aforementioned societal needs to mitigate the remaining two as well.
The potential of energy from wastes, particulary solid wastes, was
the fundamental motivation for this study.
Energy Requirements
In the past 30 years, the United States has consumed more energy
than all of mankind in all previous history 12]. We presently require
one-third of the world's energy production and by 1980 our annual con-
sumption for all uses will be on the order of 100 quadrillion Btu (i.e.
10 Btu) [3] which is equivalent to 50 million barrels of oil per day
(based upon a calorific value of 130,000 Btu per gallon). If all the
proven reserves of the Alaskan North Slope Field (approximately 10 bil-
lion barrels) were dedicated to our nation's energy needs in 1980, we
would run out in mid-July of that year.
Furthermore, as the sources of new energy become scarcer, they
will naturally become more expensive. Typical estimates are for a
doubling in unit cost in the next 10 years [4].
The Magnitude of Solid Waste
The solid waste production statistics for the United States are
absolutely staggering. A 1968 estimate [5] of the total generation of
solid waste put the figure at 7.12 trillion pounds annually (roughly 10
million tons per day or more than 90 pounds per person per day). Of
this total 4.20 trillion pounds came from agricultural and animal
wastes, 2.20 trillion pounds from mining and mineral processing wastes,
and 720 billion pounds from residential, commercial, industrial, and
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institutional sources. Due to the lack of any complete measurements,
the amount of solid wastes actually collected by U. S. municipalities
is a topic of some debate. Cohan [6] gives this figure as 539 billion
pounds per year, while Regan [7] and Stabenow [8] suggest 400 billion
pounds, Niessen [9] 380 billion, and still another source [10] quotes
270 billion. A figure of 5 pounds per person per day is a commonly
noted rule-of-thumb for municipally collected solid wastes. These
figures are just for the United States, which comprises only 6% of the
world's population.
As overwhelming as these figures are for current collection and
disposal needs, they will be even larger in the future. Not only is
the population steadily increasing, but it appears that we are becoming
continuously more productive of solid wastes. The magnitude of the
disposal problem is expected to more than double in the next 25 years
[11].
Resource and Energy Production Potential
of Solid Wastes
The usual terminology for solid waste (i.e. refuse, garbage,
trash, and even the work "wastes" itself) implies a substance of little
or no value. This could not be further from the truth. Not only does
this "waste" possess significant heating value (on the order of 10 mil-
lion Btu per ton 16]) but it is a veritable mine field of both ferrous
and non-ferrous metals (including, for instance, 48 billion cans annu-
ally) , glass (28 billion bottles annually), as well as a wide assortment
of organic materials (100 million tires, 60 billion pounds of paper,
and 8 billion pounds of plastic annually) 112]. It has been estimated
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that typical municipal waste with a moisture content of 25% contains
inorganic materials worth between $2.35 and $7.20 per ton in addition
to its organic materials whose worth (principally in terms of heating
value) is between $3.40 and $11.40 per ton suggesting a total value of
between $5.75 and $18.60 in each ton 112]. This means that the annual
value of collected municipal wastes is between $1 billion and $3 billion
based upon 400 billion pounds per year; yet, it currently costs about
$1 billion to dispose of this material in addition to the $3.4 billion
expended for collection [12].
Dr. Lesher of the National Center for Resource Recovery, Inc.
(NCRR) has cited 1973 as the pivotal year in having swung the economic
balance in favor of resource recovery [13]. He points out that the
first large scale resource recovery system just began construction in
1974 (in New Orleans) and by 1976 the estimate is for 15 such systems
under construction with a majority of U. S. cities practicing resource
recovery by 1984. Russell Train, administrator of the Environmental
Protection Agency, has stated: "It is significant that 7% of the iron,
8% of the aluminum, 20% of the tin, and 14% of the paper consumed annu-
ally could be met by materials recycled from solid waste generated in
urban areas." [14]
The solid wastes of municipalities is also valuable in terms of
its heating value. The energy content of urban refuse has been esti-
mated at 4,000 Btu per pound by Stabenow [8] and 6,200 Btu per pound by
Engdahl [15J with various other estimates between these figures [6, 7,
10]; these values are based upon the wastes as collected without either
air or magnetic classification. Murray Jll] estimates that when the
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70% light fraction is separated its energy content is approximately
7,000 Btu per pound.
Stabenow [8], using 400 billion pounds of 4,000 Btu per pound
wastes per year, points out that this has the energy equivalent of
687,000 barrels per day of 152,000 Btu per gallon oil which is the
typical capacity of a 120,000 ton tanker. Other sources, [10], using
annual production figures of 272 billion pounds of 5,3000 Btu per
pound wastes, point out that this could be used to generate approxi-
mately 136 billion kilowatt-hours of electricity (about 11% of the annual
U. S. total) which would otherwise require 100 billion pounds of coal
or 10 billion gallons of oil. For just the New York City area alone,
recent estimates 116] point out that the 22 billion pounds of wastes
produced per year there could generate approximately 20% of the base
electrical load of the same metropolitan area if it is efficiently
incinerated with waste heat recovery- Typically, however, refuse in-
cineration processes consume about 75 cents-worth or electrical energy
per ton [17].
In addition to energy recovery from urban wastes there is even
greater potential for conservation by utilizing the wastes of animals
and feedlots, agricultural crops, forest slaeh, as well as from indus-
trial sources not collected by municipalities. Several years ago
Engdahl [18] identified 17 industrial wastes suitable for incineration
with heat recovery. Hescheles [19] has presented an even more exten-
sive list of wastes from petroleum, pulp and paper, metal, chemical,
food, and furniture industries. Recently, data has become available
for the heating value of this wide variety of potential "fuels" (see
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[20], for instance).
A 1974 book published by the National Center for Resource Re-
covery entitled Resource Recovery from Municipal Solid Waste [21], con-
tains a wealth of additional information regarding the possibilities
of using one of our country's critical needs—the economic and non-
deleterious disposal of its solid wastes—to contribute to the solution
of the other two previously-mentioned needs (energy and inorganic re-
sources).
Schemes for Energy Recovery
from Solid Wastes
The selection of the optimum method or methods for the utiliza-
tion of the energy content of municipal solid wastes is an extremely
complicated one. Although this study is directed toward the concept of
incineration by means of vortex combustion with simultaneous waste heat
recovery, it is useful to briefly consider recent proposals for other
possible concepts.
Pyrolysis
One of the most novel energy recovery proposals is documented by
Finney [12] wherein one barrel of synthetic fuel oil roughly equivalent
to a No. 6 oil is produced from a single ton of raw, wet municipal
garbage by means of a proprietary pyrolysis process of the Garrett
Research and Development Company. A 200 ton per day facility using
this process is currently being constructed for the city of San Diego
from which each ton of waste will provide $1.40 of salvageable magnetic
metals, $0.72 of high purity mixed-color glass cullet, and one barrel
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of synthetic crude which will be sold to the San Diego Gas and Electric
Company as a boiler fuel for $2.32. This plant should begin operation
in 1975. Garrett estimates that for metropolitan areas of population
exceeding 800,000 (of which there are currently 49 such areas in the
U. S.) this process can produce a profit without any charge for the
waste collection service. Even for populations on the order of 200,000
they estimate that this process would only require about the same
charge as that of the most inexpensive landfill operations (about $2.50
per ton).
Combustible gas can also be produced from a pyrolysis process
using municipal wastes. Bailie [22] has developed a process, using the
wastes in the form of a fluidized bed, which is capable of producing
12,600 standard cubic feet (SCF) of 435 Btu per SCF gas per ton.
Digestion
The use of digestion to produce a combustible gas is a very old
technique and it has found wide use in countries not known for their
advanced technological societies (in Taiwan, for instance, it is claimed
that 20 pigs provide the total energy needs for a family of 8 [23]).
Recent improvements in the use of methane digestion have demonstrated
that one ton of shredded municipal wastes can yield about 100 SCF of
975 Btu per SCF gas after four days of digestion [23].
Incineration
The combustion of solid wastes to provide warmth and for cooking
requirements dates from antiquity. The advent of municipal incineration,
where the dispersed wastes of a society are collected and burned in a
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central facility, is however, of comparatively recent origin. The
first such incinerator appeared in 1874 in Nottingham, England (where
it was called a "destructor") and by the 1920's they were commonly used
to generate steam and produce power without the need of any auxiliary
fuel [24]. In the United States, the first municipal incinerator is
reported to have been built on Governor's Island in New York in 1885.
In 1903, an experimental facility demonstrated that steam could be
efficiently produced from the incineration of wastes and shortly there-
after a large number of full-scale plants were built (called "crema-
tories") which used the community's waste to provide the community's
energy. During the second decade of this century virtually all inciner-
ators constructed were designed for the production of steam [24].
Starting in the 1930's an interesting change took place. While
the Europeans continued the development of steam-from-wastes incinera-
tors, the concept fell into disfavor in the United States. By 1966,
this process had become the rule in Europe and the exception here and
led Eberhardt [25] to say:
American and European incineration starts from two different
prerequisites. In America, volume reduction of the refuse is
strived for, in Europe the aim is to completely burn out the
refuse, to utilize the waste heat, and to minimize air pollu-
tion as far as possible through the use of expensive flue-gas
cleaning equipment.
At the 1966 National Incinerator Conference two of the presented papers
quantitatively outlined this contrast. Rogus [26] reported upon his
visit to 13 modern incinerators in 7 countries with a detailed descrip-
tion of 3 of the facilities (Dusseldorf, Rotterdam, and Vienna); all
13 of these incinerators utilized the heat of combustion for the pro-
duction of steam. Stephenson [27], on the other hand, presented data
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on 205 U. S. incinerators all constructed since 1945. Only 43 of these
incinerators put the waste heat to any use at all and only 5 of these
utilized the heat for the production of electric power (24 used it for
building heat and/or hot water, 6 used it for sewage sludge drying,
while the remaining 8 used it in a variety of other ways). This led
Stephenson to conclude: "Waste-heat utilization can seldom be justi-
fied." [27]
The two principal advantages of incineration, which has led to
its wide-spread use, are very efficient volume reduction (about 94%
reduction for "slagging" incinerators 128] and 97.5% for "bonfire-ash"
incinerators 129]) and simplicity of operation (although the advent of
stringent air pollution restrictions has negated this latter advantage
somewhat). The disadvantages are the cost of operation (roughly twice
that of simple dumping) and the resultant air pollution. Surprisingly,
odor does not seem to be a problem as long as the furnace temperature
is above 1500°F (although in some cases it can be as low as 1000°F) [30]
Shredding of the wastes prior to incineration almost miraculously pro-
duces a homogeneous, grayish material which is esthetically inoffensive
and virtually odorfree [31]. In addition, shredding greatly enhances
the combustion efficiency of incinerators by permitting suspension-
firing of the wastes rather than the conventional and less-efficient
stoker-firing. Using waste heat boilers with incinerators also tends
to diminish the air pollution problems. With no heat removal it is
necessary to inject large quantities of excess air or water to suffi-
ciently cool the flue gas temperature so that it may be treated by
electrostatic precipitators. The presence of heat recovery coils
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10
eliminates this requirement and greatly diminishes (approximately by a
factor of 5 [32]) the gas volume requiring clean-up. Also, municipal
refuse is inherently low in sulfur content (the light fraction typically
contains about 0.2% sulfur [11J , which is about one-tenth that of
coal [10]) and thus tends to aid the achievement of pollution control
standards when burned in combination with conventional fuels.
A recent analysis of 11 methods utilizing energy from wastes,
concluded that the best mode was the use of wastes as a supplemental
boiler fuel [11]. The principal difficulty has been associated with
the fouling and corrosion of the boiler and/or furnace wall surfaces,
although recent work in this area has indicated that this can be mini-
mized by a combination of increased boiler tube spacing, metal tempera-
ture control, furnace dew point control, and the prevention of a locally
reducing atmosphere within the combustion chamber (see [7, 20, 33, 34],
for instance). The use of waste in combination with other fuels also
tends to minimize the corrosion/fouling problem.
There is a very large number of reference works available on the
related subjects of incineration and air pollution. Several of these
have been included in the list of References [35-43].
Recent Operating Experiences with
Waste Heat Recovery
Incinerators
In Appendix A of the recent NCRR publication already cited [21]
a list of 33 resource recovery systems and their experiences is pre-
sented; some of these systems include heat recovery. Typical performance
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11
of 60-70% thermal efficiency and 1-3% pounds of steam per pound of
waste has been realized 144-47]; this means that each ton of waste
could produce $1.50 to $5.00 of electrical energy based upon a 25%
cycle efficiency and an electrical value of 10 mils per kilowatt-hour
[45]. Although there continues to be interest in stoker-fired config-
urations (see [47] for work with "briquettes" and [2] for "cubettes")
most of the effort appears to be directed toward suspension-firing con-
figurations. A brief description of some of the more-recent, successful
energy recovery schemes follows.
In France, the Issy-les-Moulineaux Plant located in southwest
Paris has used refuse collected in Paris to generate 9,000 kilowatts of
electrical energy 148] and has been in operation since 1965. Even the
outlet steam from the generating turbine is sold to the Compagnie
Parisienne de Chauffage Urbain for use in district heating while the
residue remaining in the incinerator is sold for use in road construc-
tion. In 1969 another plant began operation (called the "Ivry" Plant)
which has an annual capacity of 600,000 tons of refuse and is used to
drive a 64,000 kilowatt generator 149]. In England a new refuse power
facility has just been recently constructed that is used to produce
25,000 to 35,000 kilowatts of electrical energy [50].
In the United States the Union Electric Company's experiment
with its Meramec Plant serving the city of St. Louis has recently re-
ceived a great deal of attention. There a facility designed to use
coal as the fuel has been supplemented (about 10% based upon heating
value) with municipally collected wastes. In this manner the incin-
eration of approximately 10 tons per hour of refuse aids in the operation
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12
of a 125,000 kolowatt boiler [51]. The refuse preparation consists of
shredding to a 1%-inch particle size and magnetic separation prior to
ingestion into a tangentially-fired furnace. Wisely [52] concludes on
the basis of the St. Louis experience that, "almost all powerplant
boilers designed to burn pulverized coal as fuel should be adaptable
to permit the firing of refuse as supplementary fuel."
In Chicago, the Southwest Incinerator has been burning 1200 tons
per day of refuse (nominally) and generating steam for sale to private
customers on a contractual basis since 1962 [53]. The success of this
plant led to the construction (completed in 1971) of the largest incin-
erator of its kind in the United States—the Chicago Northwest Incin-
erator [8]. This incinerator uses a water-wall configuration and is
capable of handling 1600 tons per day of refuse. It will produce
250,000 pounds per hour of steam for sale to neighboring industries.
With the addition of this incinerator, Chicago becomes the first major
city in the United States that has the capability of incinerating all
its municipal refuse [54].
In Maryland the Dickerson Plant has been designed to use coal
and oil as the primary fuels in conjunction with municipal refuse and
sewage sludge. The fuel nozzles are located in the eight windboxes (it
has a divided rectangular-furnace configuration) with tangential firing
producing a single flame envelope with apparently large recirculation
zones and very efficient combustion [55]. The energy liberated is
used to generate 1,700,000 kilowatts of electrical energy for the
Washington, D. C. area.
In Nashville the energy from refuse will be used to provide
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13
steam and chilled water to 24 buildings initially (scheduled for com-
pletion in 1974) and eliminate 50% of the cities landfill requirements.
Ultimately they expect to use three-fourths of the city's wastes and
serve 38 buildings. 156]
In Menlo Park, California an unconventional energy recovery
technique is being developed by the Combustion Power Company. The
municipal wastes are burned in a fluidized bed configuration incinera-
tor and then are used directly to drive a specially designed gas turbine
obviating the need for steam entirely. [57]
Industries are also rapidly developing energy recovery facili-
ties. The Spaulding Fibre Plant in New York replaced their coal-fired
boilers with 5 heat-recovery incinerators one of which is designed to
use 60 tons per day of 8,000 to 10,000 Btu per pound solid wastes (the
other four incinerators are designed for fumes and liquid wastes) [58].
Mockridge [59] has reported upon package boilers that have been de-
veloped for industrial use that are capable of delivering 15,000 to
250,000 pounds of steam per hour (at 1000 pounds per square inch and
925°F). He points out how they can be used for energy recovery in the
furniture industry where sawdust production rates can reach 7,000
pounds per hour.
This rapid development of energy recovery schemes has led many
(e.g. [6]) to predict a parallel development t6 the use of pulverized
coal which in its 40-year history has come to be the primary power
generation fuel. It is interesting to speculate what might-have-been
but for the forty-year hiatus of the energy-recovery philosophy in the
United States.
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Literature Survey of "Swirling Flows"
Classification of Subject-Field
Fluid-Dynamic Classification
Any survey of this subject must first of all cope with the
problem of ill-defined terminology. This problem is especially acute
because the subject of swirling or vortex flows has been studied from
widely different perspectives (wing theory, cylconic separation, Ranque-
Hilsch effect, tornado modeling, etc.). As a result, investigators
have come from widely different backgrounds each with their own ter-
minology and symbol-convention. In addition, there are subject-areas
that appear to be entirely unrelated to the study of vortex flow but
which are, in fact, pertinent; the study of flow past concave walls
and in helical tubing would be two such examples.
The term "swirling flows" has been selected to represent that
class of fluid flows with a significant global vorticity (defined as
the curl of the velocity vector) which results in a significant inter-
action with the stream function. The term "global" is necessary since
localized vorticity effects are present in virtually all fluid flows.
The term "vortex flows" is reserved for configurations which result in
a significant region of flow for which the product of tangential velo-
city and radius from the centerline is nearly constant (often termed a
"circulation preserving" region in the literature although it actually
is a region of zero circulation). Due to the effects of viscosity this
condition can never hold true at either a physical boundary or the axis
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15
of such a flow. The term "rotating flows" is used for that category
of swirling flows for which the global vorticity is generated by either
externally or internally rotating boundaries. These flows are charac-
terized by regions of constant fluid angular velocity (if the flow is
permitted to become fully-developed) in contrast to constant circula-
tion (i.e. circulation preserving). Rotating flows are further dis-
tinguishable in that they are generated by a rotating boundary in con-
trast to vortex flows which are generated "fluid-dynamically" by means
of tangential injection or inlet vanes or even by the decay of fluid
flowing initially in solid-body rotation. The third category of swirl-
ing flows is referred to here as "curved flows". These flows are dis-
tinguished by a stationary boundary causing a continual bending of the
local velocity vector. They differ from vortex flows in that the vec-
tor turning process continues throughout the entire flow not just as
the initial generation mechanism. The distinguishing characteristics
of these three types of swirling flows are presented in Table 1.
Geometric Classification
Within each type of swirling flow there have been widely differ-
ent geometrical configurations studied. Each different kind of physi-
cal boundary causes a unique flow pattern which is usually not similar
to that obtained with a different configuration. A classification
scheme for these different geometries is presented in Table 2.
Thermo-Dynamic Classification
A final classification requirement is necessary because the
presence or absence of heat transfer in a swirling flow can be just as
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16
significant as the effect of its geometry or flow-type. There are two
kinds (referred to here as "Classes") of heat transfer boundary condi-
tions for a system: adiabatic or diabatic. Within each class it is
also pertinent to specify whether the fluid is reacting or inert. In
addition, there is a special condition that occurs in confined vortex
flows wherein a non-isothermal flow is produced even for inert fluids
flowing in an adiabatic system; this is as a result of an energy sepa-
ration process, which is adiabatic, and is to be carefully distinguished
from an energy transfer process, which is diabatic. Also it should be
noted that class A2 and D2 flow fields are significantly more complex
because of the presence of specie gradients and radiation effects.
These two Classes of heat transfer conditions are defined in Table 3.
Outline of Survey
Survey Philosophy
Any serious attempt to survey the entire field of swirling flows
would easily result in 5,000 citations for literature published in the
past 25 years alone. It is clearly necessary to not only exclude
certain aspects of swirling flows from the survey but also to be se-
lective within those areas deemed most-pertinent.
Areas excluded from this survey would include geophysical flows
of large time scales (i.e. oceanographic and atmospheric motions which
are rotating flows), swirling flows generated by aircraft (these are
free vortex flows), flows which are driven by bouyancy forces (such as
the thermosiphon), flows of conducting fluids, boiling or condensing
flows, astrophysical applications of vortex flow, and those flows which
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TABLE 1
DISTINGUISHING CHARACTERISTICS OF THE
THREE TYPES OF SWIRLING FLOWS
Type 1: Vortex Flow
(1) The tangential velocity varies with the
inverse first power of the radius (cir-
culation preserving) over a significant
portion of the flow field.
(2) There is a core of fluid rotating in
solid body motion (constant angular
velocity).
(3) The tangential velocity decays with
respect to length.
(4) Boundaries, when present, serve only to
retard the adjacent fluid layers through
viscous action.
Type 2: Rotating Flow (1)
(2)
(3)
(4)
There is no region that can be charac-
terized as being circulation preserving.
If the configuration permits the attain-
ment of fully-developed flow, the tangen-
tial velocity will vary linearly with
the radius (i.e. solid body rotation).
The tangential velocity will increase
with respect to axial length until the
flow is fully-developed and then will
remain constant.
Boundaries are always present and act to
generate the rotating motion through the
action of viscosity (hence, the boundary
velocity always exceeds the fluid velo-
city) .
Type 3: Curved Flow
(1) The tangential velocity is not a simple
function of radius anywhere in the flow
field due to the superposition of complex
secondary flows.
(2) There is no decay in velocity components
with respect to length of boundary.
(3) The boundary, although not itself rota-
ting, generates the rotating motion as a
result of the fluid dynamic reaction to
the continual rotation of the local vel-
ocity vector by the walls of the geometry.
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18
TABLE 2
GEOMETRIC CLASSIFICATION OF SWIRLING FLOWS
Type 1: Vortex Flow
A. Free Vortex Flow
1. No Boundary Interaction
a. Origin of Flow is an Aircraft
b. Origin of Flow is Geophysically Generated
c. Origin of Flow is a Swirl Generator
2. With a Boundary Interaction
a. Tornado, Hurricane, et. al. Modeling
b. Vortex Breakdown Phenomenon
B. Confined Vortex Flow
1. Fundamental Studies
a. Vortex Generator Studies
b. Vortex Tube Studies
2. Practical Devices
a. Ranque-Hilsch Tube
b. Cyclone Separator
c. Fluidic Devices
d. Containment/Stabilization Configurations
e. Nozzles/Diffusers
f. Cyclonic Combustion Chamber
g. Tangentially-Fired Combustion Chamber
Type 2: Rotating Flow
A. External Rotating Flow
1. With an Otherwise Quiescent Fluid
2. With an Imposed Free-Stream Velocity
B. Internal Rotating Flow
1. Simple Rotating Tube
2. Tube with Centerline Inserts
a. Small Diameter Inner Tubes
b. Axi-Symmetric Bodies of Revolution
3. Ducts with Vortex Generators on Internal Walls
a. Spiral Wire
b. Trips
4. Annular Tube
5. Shrouded Rotating and Corotating Disks
a. Without a Source Flow
b. With a Source Flow
Type 3: Curved Flow
A. Boundary Layer Flow Past Concave/Convex Walls
B. Flow Through Helically-Formed Tubes
C. Flow Through Tubes with Axially-Mounted Swirl Generators
1. Swirl Tape
2. Helical Vane
3. Spiral Brush
4. Wire Coil
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19
are investigated from the perspective of pure mathematics.
The survey will be selective in emphasizing Class D conditions
(i.e. heat transfer) since that is the primary focus of this investi-
gation. However, Class A flows will also be cited when the results
appear to be relevant. The emphasis of the survey will be to give some
indication of the earliest work, the most significant papers in the
development of the particular flow-type, and the most recent results
available.
The primary reason for the prolific publication record on the
subject of swirling flows is that it remains very much an unsolved
science. Even for the simplest thermodynamic class (i.e. Class Al)
insuperable analytical difficulties arise for almost any problem of
practical engineering interest. Even the usual analytical technique of
fluid mechanics—boundary-layer analysis—becomes much more unmanage-
able. For a Class Al/confined vortex flow, for instance, instead of
the usual viscous boundary layer we find instead a boundary layer "pair"
wherein a second layer (usually called the "inertial" layer) arises
purely as a result of the fluid rotation. For a Class Dl flow it is
necessary to consider a thermal boundary layer in addition to the afore-
mentioned two with even a fourth boundary layer for Class D2 flows (the
mass specie concentration layer). In addition, data for most turbulent
flows (i.e. those of practical interest) indicate that the exchange
coefficients of the flow field are highly anisotropic and non-homo-
geneous. The net result is that the analytical solutions available in
the literature are almost exclusively of the "bits and pieces" variety
and are usually applicable only to very simplistic boundary conditions.
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TABLE 3
THERMODYNAMIC CLASSIFICATION
OF SWIRLING FLOWS
Class A: Adiabatic Systems
1. Isothermal Fluid
2. Exothermically
Reacting Gas
3. Non-Isothermal,
Non-Reacting Gas
Approximately isothermal flow
field with adiabatic boundaries.
Thermal energy is released by
means of an exothermic reaction
but this energy is not trans-
mitted across the boundaries.
A non-isothermal flow field which
originates as a result of energy
separation and not because of heat
transfer or chemical reaction.
Class D: Diabatic Systems
1. Non-Reacting
Fluid
2. Exothermically
Reacting Gas
Heat transfer is present at the
boundaries as a result of a differ-
ence in thermal energy between the
inert fluid and the walls.
The released thermal energy of
chemical reaction is transported
across the system boundaries.
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21
In March 1974 issue of the Journal of Fluids Engineering. Dr.
Joshua Swithenbank 160], a well-known professor and consultant in the
area of combustion, commented on the limitations of our current know-
ledge of combustion processes. His remarks are appropriate in that they
delimit what one can hope to expect in any literature search in the
turbulent combustion area even without the presence of swirl:
... It is widely thought thay we understand the indus-
trial combustion processes, and it is this myth which I wish
to explode. . . .
. . . we do not even know the turbulence level nor its
distribution in any industrial combustor* We have no satis-
factory theory which accounts for turbulent flame speeds in
gaseous systems . . . our predictions of convective heat trans-
fer to combustor walls are, to say the least, inaccurate, while
the true effects of the unsteady gas temperatures on radiant
heat transfer are a long way from comprehension.
. . . burners incorporating particle separation could be
designed using confined vortex flow, however there is no
theoretical method of predicting these flow patterns nor any
meaningful measurements in confined vortex systems since the
presence of probes modifies the flow field.
Many of the practical problems of turbulent flow are not
even defined . . . the rate of growth, agglomeration, and
burnout of soot is not understood, and in fact the rates of
most pertinent reactions are not known within a factor of two.
... we cannot fundamentally predict the combustion efficiency
or even the limits of operation of any practical combustor. . . .
It is not surprising, then, that the most extensive survey of Class A2
or D2 flows provides principally empirical correlations for special
geometries.
Basic Theory of Swirling Flows
Swirling flow has been a subject of scientific interest for at
least four centuries. Da Vinci recorded a number of observations on
vortices which are available in publications of his papers. Newton
applied his considerable analytical prowess to rotating spheres of
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22
liquid in attempting to explain the oblateness of the earth. In the
nineteenth century, Helmholtz, Kelvin, and Rayleigh (among others)
achieved noteriety, in part, for their work on rotating flows. Helm-
holtz developed three famous theorems on the transmission of vorticity
in fluids which are now known by his name. Rayleigh published a very
famous work in 1917 161] that is still widely quoted in regard to the
stability criteria for a rotating fluid. In 1916 Proudman [62] predicted
that a rotating fluid could maintain a two-dimensional column of fluid
within a fluid; this phenomenon was demonstrated in the now famous ex-
periment of Taylor 163] in 1921.
Perhaps the first analytical effort to determine heat transfer
in a swirling flow was due to von Karman 164] who in 1921 developed one
of the classic solutions of the Navier-Stokes Equations—that of a
flow field induced by a rotating disk.
One of the earliest books available that provided an extensive
treatment of the subject of swirling flows was Lamb's classic work [65].
He included a chapter on "vortex motion" as well as one on "rotating
masses of liquids." Goldstein [66] also included this subject in his
edited work. In more recent times, Truesdell [67] has published a
widely cited work on the kinematics of vorticity, Batchellor [68] has
treated rotating flows in addition to vorticity transport, and Owczarek
[69] has discussed the effect of fluid rotation on the development of
flow instabilities and transition from laminar to turbulent flow.
It appears that Greenspan [70] in 1968 published the first book
that dealt solely with the topic of swirling flow. His work is con-
cerned with the motion of an incompressible, viscous fluid rotating
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23
either in a container or an unbounded environment with geophysical
flows as the primary application in mind. Like all the previously-
mentioned books, his treatment is restricted to adiabatic, isothermal
conditions (i. e. Clas Al). A very extensive bibliography of 312 cita-
tions is included in Professor Greenspan's book.
More recently (1971), Murthy [71] has written a monograph with
the purpose of providing a survey of swirling flows from a theoretical
viewpoint oriented primarily toward non-geophysical applications (he
has included a bibliography of 220 references). Frequent reference will
be made to this work. Murthy brings out many of the sources of diffi-
culty in analyzing swirling flows some of which are summarized below:
(1) The use of a scalar eddy viscosity has had very limited success
in correlating experimental data (Page 34).
(2) Although a boundary layer develops as for simple linear flows
the casual and sustaining mechanism is much more sophisticated (Page
35).
(3) A large number of additional dimensionless parameters are
necessary due to the fluid rotation but even these do not fully de-
fine the flow field; specifically, he writes: "It may be remarked
here that the use of such dimensionless parameters as similarity
parameters for confined vortex flows is beset with a great number
of difficulties. Such difficulties arise because changes in the
geometrical configurations cannot simply be accounted for by changes
in the geometrical non-dimensional parameters based upon character-
istic lengths. Rotating fluid flows, as stated in the introduction,
involve curious wave motions, instabilities and transition (from
laminar to turbulent state). The occurrence of such phenomena is
not subject to simple scaling laws. Even in the absence of such
processes, the influence of wall boundary layers presents consider-
able difficulties particularly in regions where the swirl is intro-
duced into the flow. Lastly, apart from such uncertainties in the
initial conditions, the exit conditions from a system are not in
general subject to similarity considerations." (Page 38, italics
mine)
(4) The analogy that can sometimes be invoked for linear flows
between the transport of heat and vorticity is not possible when
the flow has a component of tangential (i.e. circumferential) velo-
city (Page 185).
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24
The quote given above (3) is especially significant because it indicates
the difficulty in using the results available in the literature since
the geometry is rarely ever similar let alone identical. This has led
Dr. Erich Soehngen; whose work with vortex flows has spanned 3 decades,
to recently comment, "Experimental vortex flows are like their maker,
each is one-of-a-kind." [72]
Heat Transfer Aspects
Heat transfer augmentation is a subject of much current re-
search as the need continues for higher heat flux densities in smaller
volumes. Bergles in two recent surveys on the subject 173, 74] classi-
fies swirling flow as one of about a dozen ways that higher heat trans-
fer rates can be achieved. He identifies 5 kinds of Swirling Flow
heat transfer configurations:
(1) coiled wires/spiral fins
(2) stationary propellers
(3) coiled (or helical) tubes
(4) inlet vortex generators
(5) swirl tapes
Of these five, the coiled wires/spiral fins are treated as surface
roughness effects since they produce only a slight fluid rotation, the
stationary propellers are dismissed as being ineffective, the inlet
vortex generators are noted to be the subject of limited research (he
gives only two citations for single-phase flows), and only the helical
tubes and swirl tapes are surveyed in any depth. It should be noted
that this latter category (helically-coiled tubes and swirl tapes) is
characterized by a non-decaying swirl-level in contrast to the sta-
tionary propeller or inlet vortex generator configurations. All five
of these swirl flow heat transfer augmentation concepts are for confined
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25
or internal geometrical configurations without rotating boundaries
(i.e. Types 1A or 3 in Table 2).
Kreith [75] has reviewed the state of heat transfer in what he
terms rotating flow (basically Types 2A and 2B in Table 2). He in-
cludes a limited discussion on swirl tape flow (Type 3C1) among the
193 references he cites. Kreith also includes a very pertinent caveat:
"...new and unexpected phenomena may occur when operating conditions
are extended beyond the ranges of the variables for which experimental
data are available."
Eckert 176] has edited a recent survey of heat transfer litera-
ture for the 17 year period from 1953 through 1969 that includes heat
transfer references for confined vortex flow and curved flow under the
heading of "Channel Flow" (a total of 63 such references) and for rota-
ting flow under the heading of "Convection from Rotating Surfaces"
(183 references). In addition, more-recent bibliographies and surveys
appear periodically in the International Journal of Heat and Mass
Transfer.
A detailed discussion of the pertinent results of these citations
will be deferred to the appropriate subsections to follow.
Aspects of Data Interpretation and Application
There are two aspects of data interpretation and application
which are pertinent to the study here that are widely debated in the
literature. Tlie first deals with the applicability of isothermal data
to the prediction or interpretation of conflagrant flow fields. The
question arises because of the difficulty of obtaining data in a com-
bustion environment and thus there is a great temptation to utilize the
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26
abundant data available with Class Al flows for Class A2 or D2 flows.
There is not yet a consensus for the validity of this concept and in
the course of the survey the various divergent viewpoints and opinions
will be noted.
The second aspect of data application debated in the literature
is the validity of any data obtained by the use of probes, however small,
inserted into the flow field. Although it is agreed that some disturb-
ance of the flow field is inherently present as with almost any measure-
ment system, it is not at all clear whether the peculiar nature of
swirling flows is sufficiently insensitive to these devices that mean-
ingful data can be obtained. The divergent opinions expressed in the
literature will be discussed in the course of the survey for this issue
also.
Literature Common to Vortex Flows
Vortex "Cores"
The subject of vortex "cores", sometimes called "concentrated
vortex cores," is concerned specifically with the structure of the inner
portion of a vortex flow wherein the effects of viscosity prevent the
circulation from being preserved (otherwise an infinite tangential
velocity would need to occur at the axis). There is a wide body of
literature on this subject although most of it is directed toward
either atmospheric vortex cores (i.e. whirls, dust devils, tornadoes,
whirlwinds, waterspouts, typhoons, hurricanes, willy-willies, etc.) or
aerodynamic vortex cores (i.e. the trailing vortex pair always present
as a result of induced lift from a finite wing).
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27
An early survey of the structure of vortex cores was given by
Gartshore {77, 78] while Hall 179] has more recently summarized the
state of knowledge on the subject. Hall begins his survey of the axi-
symmetric core of a spiraling fluid of high vorticity by presenting the
complete equations of motion for a viscous, heat-conducting, compressible
fluid; then he quickly notes that: "The above equations are couple,
elliptic, and highly non-linear, and can not at present be solved with-
out drastic simplification." There are three usual procedures, he
points out, by which analytical results can be achieved:
(1) make use of quasi-cylindrical assumptions to transform the
equation from an elliptic-type to a parabolic-type, or
(2) simply linearize the equations by dropping every non-linear
term, or
C3) apply similarity transforms, which apply only to special
boundary conditions, that permit the reduction of the partial
differential equations to simply ordinary differential equations.
Hall then discusses in some detail the application of vortex core
theory to the explanation of the Ranque-Hilsch Effect.
Kuchemann [80] and Riley [81] have recently reported on inter-
national conferences that have been devoted exclusively to papers on
vortex cores.
Morton [82] has surveyed the area of vortex cores from a geo-
physical-application viewpoint. Howard [83], Lighthill [84], and
Carrier [85] are three widely-quoted reference papers on the subject of
geophysical motions that are helpful in explaining how such vortex cores
can develop. The study of fire whirls has received considerable recent
attention, see Etnmons 186] and Lee 187], and is of interest here because
the combustion phenomenon present greatly influences the flow. Emmons
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28
points out the somewhat paradoxical result that fire whirls, together
with tornadoes, achieve their violence primarily because turbulence is
suppressed by the centrifugal forces present as a result of the rota-
ting flow field. In fact, he indicates that it is entirely possible
to laminarize a whirl flame due to the stabilizing effect of rotation.
As will be discussed later this is in contrast to the experience of
free vortex flames. Emmons summarizes the extent of knowledge about
fire whirls as "very crude."
Vortex core literature from the aerodynamic perspective is so
abundant that no attempt will be made to survey it here. Ruchemann [88]
has written a survey article on the subject with an extensive biblio-
graphy. A recent NASA report by Baldwin and Chigier I89] presents a
computer program for the prediction of vortex decay from aircraft. The
subject of aerodynamic vortex cores has, in fact, almost become a fluid-
dynamic field to itself even to the extent of short courses devoted ex-
clusively to this area [90].
Vortex "Waves"
One of the interesting features of swirling flows is their capa-
city to sustain wave motion even for completely incompressible fluids.
Perhaps the most well-known standing wave motion is that of the previous-
ly-mentioned Taylor-Proudman Column but there are a great many other
examples (see Batchellor I68] for some unusual photographs). A de-
tailed survey of this subject is outside the scope of this investigation
and reference is made only to the books of Lyttleton 191] and Chandra-
sekhar [92J on the general subject of hydrodynamic stability and to
Chapters 3 and 4 of Murthy [71] where a survey of this topic is available.
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29
Vortex "Breakdown"
It is experimentally observed that under certain circumstances
a vortex whose structure and velocity profiles has been changing gradu-
ally and uniformly with respect to its length abruptly forms a stagna-
tion point at its axis with an associated reversed flow "bubble" that
causes the streamlines to diverge suddenly. This phenomenon has come
to be known as "vortex breakdown" although some investigators prefer
the term "vortex jump". According to Murthy Q71], page 121) this un-
usual feature was observed almost two centuries ago; however, careful
observation and investigation of vortex breakdowns, at least insofar
as the literature reveals, has only been done in the past 15 years or
so. Harvey 193] reported one of the earliest investigations on this
subject; his results were purely visual. More recently, Maxworthy
194] has developed an apparatus that can produce the breakdown under a
variety of conditions although it is primarily an end-wall interaction
effect in his experiments. Because the occurrence of a breakdown is
associated with a large region of sensitive, low-velocity flow, experi-
ments have been hampered by the effect of measuring devices on the flow
to be measured. However, within the past several years, the use of
laser anemometry has been reported [95] which should provide much more
useful data in the near future.
Explanations and interpretations of the breakdown phenomenon
have been hotly debated in the literature. Hall 196], in a recent
survey of the subject, has classified all the postulated theories into
three camps:
(1) the separation theory—which explains the breakdown as a
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30
rotating flow equivalent of two-dimensional, axial flow separation
(a viewpoint championed by Hall himself [97]),
(2) the hydrodynamic instability theory—which explains the event
in terms of a standing wave (see Ludwieg [98]), and
(3) the critical state theory—which takes the perspective that
breakdown (usually called a "jump" by this group) is a finite
transition between conjugate states much like a hydraulic jump in
open channel flow (see Benjamin [99-101] and Bossel [102-104]).
Although no completely satisfactory theory exists as yet, it is
still possible to summarize the circumstances under which breakdown
usually occurs:
(1) A high value of swirl is essential. Hall [96] claims that the
swirl angle (defined as the arctangent of the ratio of the tangential
velocity to the axial velocity) must be greater than 40 degrees up-
stream of a breakdown; this means that the tangential velocity must
be greater than 0.84 times the axial velocity.
(2) The axial pressure gradient can determine both the existence and
location of the breakdown [102]. It appears that an adverse pressure
gradient is not essential as Hall [96] reports that breakdown can
occur in a simple tube for which there is a favorable gradient for
values of swirl just below the breakdown value. Bossel [104] points
out that for low values of swirl it is possible to have a large
divergence for the outer streamtube contour, but at higher swirls a
very small increase in streamtube radius can cause stagnation at the
axis or a very small decrease in radius can cause accleration at the
axis. It would seem, then, that breakdown would occur much more
readily in unconfined vortex flows where the spread of the vortex jet
is unconstrained than it would for confined vortex flows where the
development of side-wall boundary layer would tend to diminish the
radius of the vortex contour.
(3) When breakdown occurs, the influence of downstream disturbances
becomes very pronounced [102] much in the manner of a hydraulic jump
or a normal shock. This increased downstream-influence effect was
explained by Lewelllen (1105], pages 101, 102) as follows:
In a confined vortex, breakdown may be expected to occur at varying
positions along the axis as a function of swirl. For small values
of swirl breakdown will not occur anywhere. For moderate values
of swirl which permit the flow at the minimum exhaust cross section
to still be slightly supercritical, breakdown should occur downstream
of this cross section as flow expands, and becomes less supercriti-
cal (increasing its maximum swirl angle). As the swirl is increased,
breakdown will move upstream toward the minimum exhaust cross section.
When the swirl is sufficiently large for the breakdown to move up-
stream of the exhaust the flow becomes subcritical all along the
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31
axis and the breakdown must jump to the wall opposite the exhaust
where it is associated with the eruption of the end wall boundary
layer.
This statement by Lewellen will be discussed more thoroughly in
Chapters 3 and 4.
(4) The breakdown is ar essentially inviscid phenomenon with the
Reynolds number and Mach number playing only a minor role. {102]
(5) Rotation in the recirculation bubble may be reversed. [102]
(6) The breakdown may be either axisymmetric or spiral 'n ch&iacter
CI105], page 95).
The form ~>c voitax breakdown discussed to this poir t is essen-
tially of a steady flow nature. Unsteady vortex cores and vortex
bubblas have also been observed 1106, 107]. Not only can the vortex
core take on a spiral shape but it can precess as well. It is thought
that this phenomenon is related to the occurrence of the vortex
whistle.
In Murthy [71] a connected account of the subject of vortex
breakdown is presented. It appears that very little work has been done
for non-isothermal flows in regard to the breakdown; further mention
of this will be made in the subsection on vortex flames to follow.
Literature Survey of Free Vortex Flows
Isothermal Jets
The use of swirl with isothermal jets in practical Devices dates
back many years. Wotring .{108] obtained a patent for using swirl to
atomize oil for a burner in 1940. Through the years a wide variety of
swirl atomizer configurations have been developed and reported in the
literature; among the more recent are Nolan 1109] who has reported on
the use of such, an atomizer to inject sewage sludge in a heat recovery
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32
incinerator, and Herman [110] who has presented a somewhat novel con-
figuration for the use with liquid fuels which he terms a "swirl cup".
Due to its limited application to the study here, no further mention
is made of swirl atomizers.
Swirl jets can be generated in a variety of ways. Ullrich Illl]
used tangential inlets and vanes, Rose 1112] a pipe rotating at 9500
revolutions per minute, Gore [113] a rotating perforated plate, Chigier
[114] an annular chamber shown in Figure la (taken from [114]) with
both orifice-exits and diverging channels, and Chigier [115] with what
has come to be known as a "swirl generator". This swirl generator per-
mits the mixing of any combination of tangential and axial air flow
rates and is shown in Figure Ib (taken from [115]).
As a result of the swirl imposed upon a jet, tangential, axial,
and radial velocity components are produced together with axial and
radial pressure gradients. These gradients enhance jet mixing and
produce a wider jet for the same length than for the case without
swirl (or with reduced swirl).
There has been a modest production of theoretical examinations
of swirl jets although until recently they have been strictly for laminar
flows and usually only for very weak (in terms of intensity) swirls.
Loitsyanskii [116] and Gortler [117] were two of the earliest efforts
along this line. Steiger [118, 119] extended their analysis to permit
moderate and strong swirls. These analyses predict that the tangential
velocity of the jet will decay with the inverse square of the coordinate
along the jet while the tangential and radial velocities will tend to
decay with the inverse first power. Therefore, if the swirl ratio is
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33
A-A
Twgwttlit
t
••*
1
•Ir
'1
- - • • — -- -
•til
60 cm
,1
u
^~"
—
L. Jurat •«•
(a) Annular Swirl Generator
(b) Orifice Swirl Generator
Figure 1. Chigier Swirl Generators (taken from [114, 115] )
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34
defined as the ratio of the local tangential to axial velocity compo-
nents, this would decay as the inverse first power also. These ana-
lyses have been extended to turbulent flows by means of a great many
simplifying assumptions. Shao-Lin 1120] assumed similar profiles for
the axial and tangential velocity together with an assumed jet entrain-
ment velocity to obtain a close-form solution using the mixing-length
theory. This was extended by Chigier 1121, 115] who reduced the equa-
tions to functions of three empirically determined decay constants
without the need for any entrainment velocity assumption. These decay
constants are a function of the magnitude of swirl and have been ex-
perimentally examined by Chigier also [115].
Recent experimental work has been devoted to trying to obtain
double-velocity correlations using hot-wire equipment 1122, 123] to
permit a better understanding of the turbulence structure of these
jets. Lilley [124, 125] has developed a program that uses axial and
tangential velocity profile data to infer the radial-axial and radial-
tangential shear coefficients for small values of swirl. He has found
that the shear stress, the turbulent intensity, and the rate of entrain-
ment increase for increasing values of swirl in the near-jet region; in
the far region (usually defined to be about 15 exit orifice diameters
downstream), however, he has found that the shear stresses are actually
lower than for the case of no swirl. From this he has concluded that
the model of an isotropic, uniform mixing-length is appropriate only
for very small swirls.
The restriction of small swirl values in the analytical schemes
attempted is a result of the formation of vortex bubbles or recirculation
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35
zones for values above a critical number. These zones have been observed
and documented by a number of sources 1114, 115, 122J and are the source
of insuperable analytical difficulties. It is the presence of this
bubble, however, that makes swirl such an attractive feature for flames,
a point to be discussed in the next subsection.
The primary correlating variable that has been reported is common-
ly referred to as the "swirl number" with the symbol "S". It was de-
fined originally by Chigier I114J as the ratio G./G R, where G, is the
9 x cp
axial flux of angular momentum, G is the axial flux of linear momentum,
X
and R is the outer radius at the orifice exit. The value of S is
found by integrating the axial and tangential velocity profile data for
r (radius from the jet centerline) from zero to infinity at each axial
station of the jet. The data appears to indicate that both G, and G
are conserved with respect to jet length and hence S is also conserved.
If the tangential velocity varies according to some known function of
jet radius, and if the axial velocity can be similarly described, it
is then possible to compute the value of swirl a priori. However, the
only apparent success at this procedure was noted by Chigier [115] for
the assumption of solid body rotation and uniform axial velocity at
the orifice exit and even this success was limited to very small values
of swirl (about 0.20 maximum) indicating that the exit flow is not so
simply described.
The use of this swirl number has been successful in correlating
the Chigier decay constants and the onset of recalculation. Chigier
J115J has demonstrated that a recirculation zone can be expected to
occur for swirl values greater than 0.64 (a magnitude which-he calls
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36
"very strong swirl"). However, he also cautions (1114], page 789):
...these distributions showed that the basic nondimensional
characteristics of swirling jats, i.e., pressures in swirl
generator, exit profiles, minimum pressure, maximum reverse-
flow velocity, and length of the internal vortex, were largely
determined by the ratio of the momenta. It became clear,
however, that the shape of the nozzle as well as the method of
introduction of the tangential air can also influence the be-
havior of the jets. It cannot therefore be claimed that the
ratio G
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37
University of Illinois in the period 1949-1952, however there are no
published papers during this period. The first known paper on this
effect was by Hottel 1126] in 1953. He was concerned about the possi-
bility of modeling the conflagrant flow with an isothermal one. On the
basis of qualitative observation Hottel concluded, "Combustion runs
indicated no significant change from cold flow in the volume occupied
by the fixed-vortex core." He explained the recirculation zone and the
resulting shortened flame length as due to an adverse axial pressure
gradient that must be present due to vortex decay. For his configura-
tion, however, he concluded that no recirculation actually occurred.
Pistor 1127] also examined a swirl flame in a ducted system and
found, as Hottel had, that the flame formed an annulus with the unburn-
ed gases on the exterior. Albright 1128] then published extensive
results for swirl flames in free jets, straight ducts, and diverging
ducts. For the ducted configurations, Albright also found hollow flames
with the unburned gases on the exterior even though his apparatus
produced much higher superficial velocities (up to 700 feet per second)
and, apparently, a recirculation region. He found that the effect of
swirl was to stabilize the flame whether it was a free jet or a con-
fined one, but he found the effect more pronounced for the confined
configurations. In fact, he was able to produce stable flames 20 inches
long in only a half-inch diameter tube. Albright attributed this to the
phenomenon of recirculation but the only evidence he offerred was that
for conflagrant flows the core gas temperatures were lower than at the
flame-annulus boundary which he explained by the hypothesis of rela-
tively cool recirculation gases mixing with the products of combustion.
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38
It should be noted that in his configuration the fuel (natural gas)
was admitted only axially while the swirl was provided by supplying
the air tangentially-
The continuation of this work was published a year later by
Albright J129] for a larger diameter tube (2 inches) and a less intense
vortex. For this work he measured velocity profiles by means of a
1/16-inch diameter pitot probe for both isothermal and conflagrant
conditions and noted that although recirculation was observed for the
air-only condition at the axis, no such pattern was found for the com-
bustion condition. This led him to conclude contra Hottel 1126], "The
differences in the flow patterns . . . were probably caused primarily
by heat release in the gases. Angular momentum was, however, unaffected
by combustion." He makes no mention of the possible disturbance of
the effect he is trying to measure by the device he is using to measure
it. Kenny 1130] continued this work on the same apparatus using pro-
(f.
pane to determine combustion efficiency as a function of degree of
swirl and duct length by means of a quenching-gas analysis device lo-
cated at the duct exit. Drake [131] found that there was an optimum
value of swirl to maximize combustion-completeness. Kerr 1132, 133]
presented correlations for combustion efficiency in an actual furnace
installation as a function of a single, non-dimensional parameter char-
acterizing the intensity of swirl.
The results of this early work may be summarized as follows:
(1) The presence of swirl tends to stabilize flames for both free
and confined configuratibns.
(2) The flame front forms an annulus {identified by the location of
maximum temperature isotherms) with the unburned gases on the
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39
exterior and the products of combustion in the core region.
(3) For ducted configurations the flame front does not quite touch
the wall and somewhat surprisingly does not appreciably heat the
walls either (hence these flame systems were essentially adiabatic).
(4) When the apparatus was used under isothermal conditions re-
circulation zones (usually only at the core region) were observed
that apparently were not present under combustion conditions.
(5) Two crucial questions were unresolved: how valid is it to
interpret conflagrant flows by results observed with isothermal flows?
and is it possible to insert probes into the vortex flow field and
obtain uncorrupted, meaningful data particularly when recirculation
is present or eminent?
It is this last pair of questions that remain to be answered to this
day.
There has been a great deal of work done on the subject of
vortex flames in recent years spurned by its widespread use in commer-
cial furnaces. Much of it has been done under the sponsorship of the
International Flame Research Foundation. Chigier [134] has measured
the decay of the axial and tangential velocity components for a vortex
flame (from a combination of propane, butane, and air) and found it (the
decay) to be slower than for an isothermal jet. Chigier, in this paper,
made all the usual observations regarding these flames: they are
shorter, more turbulent, and become stabilized closer to the exit ori-
fice all as a result of swirl; Professor Emmons, in his recorded
comments of the paper 1134], pointed out how these contradict all the
maxims of what is known about fire whirls (see [86, 87]) which evidence
lengthened flames and reduced turbulence (even to the point of laminari-
zation). Although unable to convince Dr. Chigier, Professor Emmons
reasoned that the difference could be accounted for by noting that for
a fire whirl, which has a rotating core with a free vortex surrounding,
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40
the radial gradient of angular momentum is either positive or zero
everywhere and hence from Rayleigh's stability criterion [61] the flow
field is stable, whereas the vortex flame, which is characterized by a
rotating flow field exiting into a stationary air mass, possesses a
strong negative radial gradient of angular momentum at the jet boundary
and is therefore unstable because of the same criterion and hence tur-
bulence tends to be promoted rather than suppressed. He, Emmons, readily
admitted, however, that "There are in fact so many effects present that
it is impossible to solve the Navier-Stokes Equations in either case..."
Chervinsky [135], on the basis of his data, also concluded that
an increase in the value of swirl resulted in an increased flame width,
decreased flame length, increased decay rates of all velocity compo-
nents, and increased turbulent intensity; he explained all these effects
in terms of an increased eddy viscosity and spatial variation of the
turbulent Prandtl Number.
This discrepancy in the effect of fluid rotation on flame length
was apparently resolved by Beer [136] with his experiments for an axial
jet exiting into a rotating cylindrical flow. The rotation tends to
exert a stabilizing effect because of centrifugal forces even for iso-
thermal conditions, but when combustion is also present the density
stratification causes an additional stabilizing influence. Hence, he
concludes that this configuration could well lead to a laminarized flow
and confirms the observations of Emmons.
Analytical attempts to model swirl flames have been greatly im-
peded by their need to begin with the aero-chemical dynamics of high
vorticity flames 1137], Beer and Chigier, in a recent (1972) book on
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41
the subject of combustion aerodynamics concluded that ". . .the theory
is not yet able to predict flame stability." Q138] , page 130). Thus,
as noted by Dr. Swithenbank 160], the turbulent swirl-flame is as yet
unsolved.
The debate continues as to the validity of using isothermal
results for combustion processes. Syred [139] has recently commented
". . .for the modeling of swirl combustors it has been common practice
to extrapolate isothermal experiments to combustion conditions. Although
there are similarities it now appears that certain fundamental differences
may arise depending upon the type of burner and mode of entry." (italics
mine) But, Chigier, in a paper published not only in the same era but
in the same volume of the same journal [140], claimed that it is permis-
sible to compare isothermal and combustion condition processes even
when recirculation is present because "the gasdynamic and chemokinetic
processes become decoupled" since, he reasons, the chemical energy
release is much less than the turbulent energy of the flow and hence has
a negligible effect on the turbulent flow field.
The debate on the effects of inserted probes, however, may soon
reach a resolution. The development of laser anemometry for velocity
measurement in flames began about 1971 (see, for instance, [141-143], and
meaningful data should be forthcoming soon.
In the two years since the publication of Beer and Chigier's
book J138J, a number of advances in analytical techniques have been
published. Rubel 1144, 145] has used a simple scalar eddy viscosity
model with a potential core formulation to accurately predict the be-
havior of swirling flames in the far-jet region for weak swirl inten-
sities. He has found that the enhanced mixing present at the jet
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42
boundary as a result of swirl could result in as much as a 25% re-
duction in nitrogen oxide formation because of the early cessation of
NO producing reactions. Since he invoked the boundary layer approxi-
mations, his analysis can not be extended to either the near jet re-
gion or to cases with strong swirls.
Lilley, in a wholesale assault on the problem [146-149], has
been able to achieve the following:
(1) He has extended his work for isothermal swirling jets to con-
flagrant ones for the invoked boundary layer assumptions and restric-
tions of weak swirl, thus enabling the calculation (via a computer
program) of the two significant shear stress components of the stress
tensor, the radial component of the turbulent enthalpy flux vector,
and the radial component of each turbulent chemical specie flux
vector from experimental mean distributions of tangential and axial
velocity components, temperature distribution, and mass specie dis-
tributions.
(2) He has utilized his program with the limited distribution data
available to show that the turbulent stress distribution is aniso-
tropic, inhomogeneous, and a function of the degree of swirl.
(3) The results of his program tend to confirm the suspicion that
conflagrant flows are very different from isothermal ones. Speci-
fically, he writes, "In particular, the turbulent viscosity was found
to be highly nonisotropic, the r6 component being an order of magni-
tude less than the rz component. The variation of normalized urz
with swirl was found to be the opposite of that found in the iso-
thermal case, indication that the effect of the combustion was far
more than just a density change." (1146], pages 186, 187, italics
mine—where 8 is the tangential coordinate, z the axial coordinate,
and y the viscosity).
(4) In a very recent paper [148] he has incorporated a nonisotropic
mixing-length and energy-length turbulence model together with an
eddy-break-up turbulence controlled reaction model (all previous
work, including that of Rubel, employed the Arrhenius Model), together
with the usual boundary layer assumptions (thus restricting the analy-
sis to weak swirls) in a finite difference computation scheme that
appears to accurately portray a vortex flame albeit a weak one.
Hacker [150] has recently published a proposed blow-off model
for strongly swirling flows in terms of the ratio of tangential velo-
city to axial velocity which he calls the swirl parameter. However, he
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43
claims that, "The presence of the reverse flow region is in all respects
identical to the reverse flow region observed in cold swirling flows".
It is interesting that this comment and the one by Lilley (given on the
preceeding page) were made only a month apart in the same journal.
Literature Survey of Confined Vortex Flows
Fundamental Studies
The literature survey of confined vortex flows is separated into
two broad categories: fundamental studies and practical devices. Al-
though it is sometimes difficult to classify a particular paper into
one of the other of these categories, if the work is of a general nature
not specifically for a restricted geometry it has been classified as a
fundamental study; on the other hand if the work is directed pri-
marily to understanding how a particular device operates or how it
might be optimized, it has been classified under that device in the
category of practical devices.
Two basic kinds of geometries have been investigated in the area
of fundamental studies. One of them has come to be known in the liter-
ature as the "bath-tub" vortex problem; this terminology is unfortunate
in that it implies the draining of a liquid with swirl and the associa-
ted free surface problem (see, for instance, Dergarabedian [151] or
Sibulkin [152]). Since the literature on this configuration is
devoted to single-phase fluids without a free surface it will be re-
ferred to as a "vortex chamber" here. A sketch of this geometry, taken
from Lewellen [105], is shown in Figure 2a.
The second geometry for which a body of literature exists also
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44
has a terminology-difficulty—specifically, no name at all. It is
shown in Figure 2b (taken from Murthy 171]) and is referred to here as
a "vortex tube" although it is not to be confused with a Ranque-Hilsch
Tube which operates under a very different fluid-dynamic environment.
As is apparent from a comparison of Figures 2a and 2b, the vortex tube
can be thought of as a vortex chamber with a relatively large exit ori-
fice connected to a long cylindrical tube. In both devices the swirling
motion may be generated in a variety of ways (tangential entry, inlet
vanes, stationary propellers, etc.) the vortex tube is distinguished by
the presence of vortex decay with respect to length.
The vortex chamber configuration has been extensively studied
for more than 20 years and the literature contains hundreds of papers,
many of them purely analytical, on the flow field for this geometry.
The vortex tube, on the other hand, has had rather limited study (with
the exception of the Ranque-Hilsch Tube device which bears some geo-
metrical similarity) especially along analytical lines. Since the
object of this study would be classed in the vortex tube category, it
is pertinent to ask : to what extent may vortex chamber analysis be
utilized ? The answer may be given by identifying the distinguishing
characteristics of these two geometries:
(1) Length to Diameter Ratio: For the vortex chamber this is of
order 1 whereas in the vortex tube it is of order 10.
(2) Decay: Only for the vortex tube, since the tangentially-in-
jected fluid is supplied over the entire length of the vortex chamber.
(3) Exit Boundary Condition: For the vortex chamber the ratio of
the chamber diameter to the exit orifice is of order 10 and is a
significant controlling factor; in the vortex tube there are really
two exits, the chamber exit and the tube exit, both of which are of
realatively large diameter. It is also important to note that for
-------
(a) Vortex Chamber (taken from [ 105] )
exit to k
..^.
exit I
geometry
transition
section
cylindrical
"tube
-.^y.. Supply
ru~ sonic nozzle
v— static pressure tap
Togs!.
VOrtfiX £• flow iniectlon
CnamDer(ang|e ad|USlable)
(b) Vortex Tube (taken from [?l] )
Figure 2. Two Fundamental Geometries
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46
the vortex chamber the flow field is governed by a free expansion
of the fluid out the exit orifice whereas in the vortex tube the
flow exiting the chamber is constrained by the tube.
(4) Transition Section: vortex tubes have been constructed using
a variety of transition sections whereas the vortex chamber has used
the abrupt, end-plate-like configuration exclusively.
The conclusion of this comparison must be that the results of vortex
chamber analysis are of limited applicability to vortex tube flow. In
fact, as will be discussed subsequently, many of the results available
for vortex tube flow are difficult to interpret because of variations
in injection schemes, transition sections, length-to-diameter ratios,
etc.
Vortex Chamber Studies
This geometry as shown in Figure 2a has become the classic
geometry for confined vortex flows in the sense that virtually all the
analytical approaches have adopted it as the object of investigation.
Perhaps the very first investigators to do so were Einstein and Li [153]
in 1951 in what has come to be the classic paper in the field as evi-
denced by the hundreds of times it has been cited since its publication.
There are two principal problem areas that are the object of most
of the papers: the effects of the exit boundary conditions and the end
wall boundary layers. Donaldson in a series of publications ([154-156],
among many others) has developed a complete family of similarity solu-
tions to the Navier-Stokes equations. The primary difficulty with the
result, aside from being restricted to weak swirls, is that the required
form of the boundary conditions do not appear to be capable of being
satisfied by the geometry of Figure 2a (some have suggested a rotating,
perforated pipe open at both ends through which the tangentially
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47
admitted air exits). Lewellen 1157] has extended Donaldson's work to
include the case of strong circulation.
The end wall boundary layer has been examined by a plethora of
papers with the usual progression of initially laminar-only analysis
to turbulent flow analysis. Rosenzweig J158] has demonstrated that this
end wall boundary layer is the dominant force in determining the axial
velocity distribution even though it represents a small fraction of
the total internal volume. Rott [159], in a survey paper, points out
that it is this end wall boundary layer with its unique role of pro-
viding a strong interaction between the region of highly viscous flow
and the outer region that makes rotating flows so much more complicated
than simple linear flows. He also points out that this interaction is
crucial to the understanding of tornadoes since the boundary layer
"feeds" the observed high velocity core (where velocities as high as
700 feet per second have been observed). This boundary layer interac-
tion phenomenon was recently extended by Serrin 1160] to show how it
can create the down drafts that can occassionally occur in tornado
cores. This interaction remains the fertile ground of very recent re-
search (see, for instance Chi 1161] for a mixing length theory appli-
cation and Hoffman [162] for an account of radial inflow effects) and
it is certain to be the subject of much future work as well.
In general, the tangential velocity distribution inside a vortex
chamber has been found to take the form of a Rankine vortex: solid body
rotation from the center line axis to the point of maximum tangential
velocity and near-free-vortex flow from then until near the outer
boundary or vortex generating mechanism, gmithson [163], in a recent
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48
survey of velocity profiles, concluded that the velocity profile out-
side the core region can be expressed as vr = c, where v is the tan-
gential velocity, r the radius from the centerline, c a constant, and
n an experimentally determined constant which may vary in value from
/
0.2 to 0.8 depending on how the vortex has been generated; he has
also stated what has been found by many others: namely that the radius
at which the maximum tangential velocity occurs is located at a value of
r "slightly less" than the exit orifice radius.
An extensive monograph, more than 200 pages with more than 400
references, was published on the subject of vortex chamber analysis in
1971 by Lewellen 1105]. In this work he traces the complete development
of literature on the subject (as can be inferred from his bibliography)
with the purpose of applying the results to fluidic devices and con-
tainment configurations for nuclear rockets both of which tend to have
geometries similar to the vortex chamber. Since this publication,
numerous other papers have appeared of which several have already been
cited [160-163].
It is very important to note that all of the literature cited in
this subsection as well as the vast majority of Lewellen's bibliography
are restricted to adiabatic, isothermal flows (i.e. Class Al). The few
papers considered by Lewellen that were not of this class were for the
nuclear rocket configuration which will be discussed in an appropriate
subsection to follow.
Vortex Tube Studies
In contrast to the case for the vortex chamber geometry, rela-
tively little literature exists for the vortex tube. Perhaps the
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49
reason is that most of the effort has been directed toward practical .
configurations, such as the cyclone separator and the Ranqxie-Hilsch
Tube, rather than the development of a baseline apparatus for which the
effects of swirl can be systematically examined. The results for cyclone
separator studies must be excluded here (to be discussed in a later
subsection) because the flow pattern is so vastly different due to the
fact that the exit tube is usually of a re-entrant type and it is located
at the same end of the chamber as the tangential inlet. The Ranque-
Hilsch Tube results are not appropriate here, since the objective of such
a device is energy separation it is characterized by a pair of flow
exits (at the same end for a uniflow type and at opposite ends for a
counterflow type) with very complex secondary and'back flows occuring
throughout the length of the tube; also, because the degree of tempera-
ture separation is a strong function of the inlet tangential velocity,
virtually all of the devices investigated have extremely high tangential
velocities (tangential Mach numbers of order 1) and thus compressibility
effects are very pronounced.
The literature on the category of vortex tube studies can be
surveyed in two groups: adiabatic systems for which the primary ob-
jective is either an analytical expression or experimental data for
vortex decay (i.e. decrease in angular momentum with axial length) as
a function of a Reynolds number and a parameter characterizing the
level of swirl and diabatic systems for which an additional result is
sought—that of a heat transfer correlation (usually in terms of
Nusselt number) also as a function of these two dimensionless parameters.
Since the objectives of these groups are different they will be surveyed
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50
separately.
One of the earliest works for adiabatic vortex decay was done by
Talbot I164J in 1954 for laminar flow. He generated the swirl by the
use of a section of rotating pipe, which of course resulted in solid
body rotation, then permitting the tangential velocity component to
decay as the flow was confined in a stationary cylindrical pipe. Both
his analysis and experiments were restricted to the laminar regime.
This work is cited here under the category of confined vortex flows
instead of internal rotating flows because in the absence of the rota-
ting pipe the flow pattern is observed to develop into a Rankine vortex
wherein the solid body rotation region becomes confined to an ever-
decreasing radius with the development of an annulus corresponding to
a potential vortex. Laufer 1165] in a NACA report did much the same
thing for turbulent flows.
More recently, Thompson [166] has done both a theoretical and
experimental study of free and confined vortex flows. For the confined
vortex experiments he used a tube 5.72 inches in diameter and 30 inches
long through which air was induced and swirl generated by the use of
inlet vanes. There was no transition section connecting the vortex
generator with the tube and the exit configuration consisted of a 1.25
inch diameter hole in an end plate. The length of the vortex chamber
was 1 inch. Thompson noted that without the exit orifice in place,
the flow pattern was one of solid body rotation over almost the entire
cross-section whereas when it was installed there developed a potential
flow region in the outer regions of the tube thus indicating the entire
flow field can be sensitive to the exit boundary conditions. He noted
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51
complex axial velocity profiles with an annular region of reversed flow.
Musolf 1167] and Kreith 1168] presented data and analysis respec-
tively on vortex decay. Kreith assumed that the Reynolds shear stress
could be related to the velocity field by means of an eddy diffusivity
that was neither a function of radius nor axial length. With this and
several additional assumptions he was able to obtain a linear equation
for the tangential velocity which compared favorably with the data
available for axial distances up to 20 diameters. He noted that the
swirl decays to approximately 10 to 20% of its original value in 50
diameters with the higher decay rate occuring for the lower Reynolds
number. The data used for comparison was obtained by Musolf using a
swirl tape (i.e. a twisted band of metal which is inserted into a simple
cylindrical tube usually extending across the entire cross-section thus
forcing the flow on a complex spiral path) at an inlet section with
decay taking place in a simple tube.
Youssef [169] presented extensive data that were taken using air
in a tube 12 inches in diameter and 184 inches long in which the swirl
was generated by means of inlet vanes. Velocity profiles were obtained
through the use of a 5 hole pressure probe. Lavin [170] used a geometry
of a 3 inch diameter, 30 inch long tube to obtain similar data only at
much higher velocities (the axial Mach number varied from 0.3 to 2.0).
The swirl was induced by means of vanes located at a 30 inch radius and
a complex transition section was used in which a shaped-plug insert was
designed to aid in turning the flow from radially inward to an axial
direction. One of Lavin1s observations was especially noteworthy:
... if the swirl ratio is sufficiently large, stagnation regions
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52
and regions of reversed flow can be formed near the entrance
section. At flows with large Reynolds number this occurred when
the ratio of maximum tangential velocity to the average axial
velocity was in excess of four. When the Reynolds number was very
small, this phenomenon was not noticed. (page 145)
Baker 1171] obtained swirl decay data for two geometries one
with a diameter of 5.75 inches and length of 270 inches using water
and one with a diameter of 1.18 inches and length of 120 inches using
liquid hydrocarbons. He found that the decay of swirl was exponential
in which the angular momentum flux at any point downstream of a known
•TV
angular momentum flux could be determined by multiplying the upstream
flux by the quantity exp(-pAx/D) where 3 is a decay parameter found to
be a function of the axial Reynolds number, Ax is the axial distance
between the two points, and D is the pipe diameter. Typical values of
(3 were 0.02 for Reynolds numbers (based upon mean axial velocity and
pipe diameter) of 2 x 10 and 0.04 for Reynolds numbers of 1.25 x 10 .
Thus he found that the decay increased for decreasing Reynolds number
as has already been noted from earlier studies.
Wolf 1172] and Rochino [173], in related papers, presented data
and analysis for the flow of air in a 3 inch tube of 216 inch length for
which the swirl was induced by means of inlet guide vanes. The degree
of swirl was quite strong, in contrast to most of the results, with
swirl angles (defined as the arc tangent of the ratio of tangential
velocity to axial velocity) of 60 degrees—which implies that the
tangential velocity exceeded the axial velocity by a factor of approxi-
mately 1.7. The-ir results may be summarized as, follows:
(1) The radius at which the maximum tangential velocity was found,
separated the regions of solid body rotation and.potential flow. This
location moved radially inward with Increasing axial distance (i.e.
as a result of vortex decay) thus making more of the pipe area of the
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53
free vortex type.
(2) The distribution of axial velocity as a function of radius
remained relatively unchanged with respect to length. This was
attributed to the presence of an adverse pressure gradient at the
axis and a favorable one at the wall, a combination which tended to
hinder the development of the axial profile.
(3) The decay parameter (see Baker above) was found to vary as 140
times the axial Reynolds number to the minus 017 power—thus indi-
cating that decay increased with decreasing Reynolds number. When
this result was compared with an analytical expression developed by
Dreith [16g]3the turbulent Prandtl number was predicted to be equal
to 8.32 Re ' where Re is the axial Reynolds number.
(4) Hot wire probes showed that the turbulent intensity was high at
the axis(and relatively independent of length) and diminishing as the
wall was approached in contrast to linear flows and thus showing that
the turbulence structure is a strong function of radial position.
(5) Analytical predictions for decay could be obtained by using
Taylor's modified vorticity transport theorem and Karman's similarity
hypothesis. Two equations were presented for eddy viscosity as a
function of radius: one for the region up to 0.9 of the pipe radius
and the other for th& annular area near the wall.
Recently, Yajnik [174] has presented the first part of his results for
an inlet vane vortex tube of 100 diameters length. He has examined the
turbulent law of the wall for weak swirls and found that the logarith-
mic variation was still valid although the thickness of the region so
described was both a function of the swirl and the axial Reynolds
number. He used a swirl parameter analogous to Chigier [114] only the
upper limit on the integral is the pipe radius rather than infinity.
Yajnik has also shown that for appropriately defined scales of axial
velocity and angular velocity this awirl parameter reduces to the in-
verse of the Rossby number. The original apparatus used by Yajnik did
not include a transition section between the vortex chamber and the
cylindrical tube but apparently cons.is.ted of an abrupt contraction.
This configuration caused an unsteadiness to be observed which-was only
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eliminated by designing a transition section fairing described by a
cubic curve. Yajnik noted that for values of swirl exceeding 0.155
(a very small value) flow reversal occurred*a flow regime he has chosen
to avoid; hence, his results are restricted to very weak swirl levels.
In a very recent paper (July 1974), Love [175] has attempted to
explain the increased pressure drop noted with swirl flows with respect
to linear flows by accounting for the acceleration of an annular region
of the pipe due to the stagnant or reversed flow region observed in the
core region. The effect of the accelerated flow together with the
effect of swirl decay is claimed to explain the increased friction fac-
tor noted. His predictions agree fairly well with that of Youssef and
Baker.
The subject of swirl decay has been examined by a large number of
recent Soviet papers, among them: Filippov [176], Gostinets [177],
Liane [178], Veske [179], and Nurste [180]. Of particular interest
here, Gostinets found that, "the turbulent swirled flow of liquid in
the greater part of the pipecross section is actually close to helical
and the vortex lines in it coincide with the streamline. The establish-
ment of this fact confirms the possibility of using a model of a helical
flow of an ideal liquid for calculating certain effects of real rotating
flows". This point will be pursued further in Chapter 4. Also, Liane
found an annular reversed flow in contrast to the core or axial reversed
flow observed by several U. S. investigators Calthough Thompson [166]
also reported an annular reversed flow region).
None of the investigators cited in this discussion of vortex
decay of adiabatic confined vortex flows has dealt with- the problem of
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55
flow perturbation by the use of inserted pressure probes. This effect
is one possible explanation for the varying observations noted for
regions of reversed flow. Also, a close comparison of results between
apparatus' shows a significant variation in decay rates, velocity pro-
files, etc. It is entirely possible that this is a result of the lack
of geometric scaling, as noted earlier in citing a quote by Murthy [71].
Among the earliest work examining heat transfer characteristics
for vortex tubes were two papers by Gambill and Greene [181, 182].
Greene 1182] reported "heat transfer coefficients one to two hundred
per cent larger than that calculated for linear turbulent flow at the
same pumping power". Blum 1183] has also demonstrated a markedly im-
proved heat transfer performance although diminished by vortex decay
effects.
Virtually every additional paper on this subject (beside the three
just mentioned) can be classed in one of two groups: work carried out
at the Aerospace Research Laboratories using a heated inner cylinder
and an adiabatic outer cylinder (often called the boundary condition
of the "second kind") with air swirled initially either by vanes or
tangential nozzles and work documented in recent Societ publications
for a wide variety of configurations and boundary conditions.
The Aerospace Research Laboratories' (ARL) interest in confined
vortex flow heat transfer stems from the prospect of stabilizing a long
arc and transferring the contained electrical energy to the vortex
flow. This concept was presented at the First Plasma Arc Seminar by
Andrada 1184]. Because of the operational difficulties of using the
arc discharge to obtain data, the ARL work has similuated this energy
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56
addition through the use of an inner cylindrical tube which is heated
via electric resistance. Scambos 1185] presented the results of the
first such simulation. His apparatus was similar to that used by
Moore [186] and Holman [187] who were concerned with isothermal effects.
Scambos observed that there was a reversed flow region that surrounded
the inner cylinder and caused, he concluded, the observed increase in
heat transfer coefficient with respect to length contrary to the
usual trend. McKelvey [188] examining basically the same concept
(but with a vortex tube of smaller length to diameter ratio) found that
the Nusselt number was augmented by the vortex effect but not to the
degree observed by Scambos; McKelvey also noted an increase in heat
transfer coefficient with respect to length-, and he also explained it
on the basis of a reversed flow cell. Kelsey [189] examined the re-
versed flow cell in detail and concluded that it was not due to the
heat addition process but apparently was a characteristic of the geo-
metry. The only observable change in the flow field as a result of
the heat addition process was a changed total temperature profile.
Loosley [190] using an apparatus of even smaller length to diameter
ratio and with two different diameter insert tubes found no evidence of
a reversed flow region and was able to correlate mean Nusselt numbers
with the Reynolds number (based upon hydraulic diameter) and Prandtl
number. He did his experiments with, inner cylinder diameters of one
and two inches (vortex tube diameter was 4 inches) and found very little
change in the correlation equation indicating that the heat transfer
process was not sensitive to the annular gap. This work was continued
by Talcott [191], Palanek 1192], and Murthy [193, 194, 71] to account
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57
for the effect of inlet injection angle i.e. swirl intensity, in addi-
tion to axial Reynolds number. In these studies J191-194] the heat
tranfer coefficient was found to be essentially independent of length,
in contrast to earlier work. This led Murthy 1193] to conclude, "In a
study of this type, one should be forewarned that the conclusions drawn
in the discussion will apply largely to the configuration under inves-
tigation." (page 10)
In the Soviet literature, Alimov 1195] presents one of the
earlier papers that is available in the United States. He used a
tangential slot generator and concluded that the heat transfer could
be correlated by the ratios of the areas of the tube cross-section and
the slots. Migay 1196] used a vane swirl generator with a relatively
long tube. He concluded that the JStusselt number ratio of vortex to
linear flow was approximately equal to the square root of the friction
factor ratio for vortex to linear flow. He noted that "the initial
swirl distribution has an appreciable effect on the heat transfer and
friction characteristics." Bol'shakov {197] examined a configuration
where tangential nozzles were distributed along the entire length of a
cylindrical tube, thus obviating the need for a swirl generator, with
the perspective of developing a gas-liquid heat exchanger. Koval'nogov
[198] examined the effect of vortex decay and different tangential
velocity distributions Cas a function of radius) upon Nusselt number.
The various velocity distributions were obtained by means of inlet pro-
pellers of various blading laws. He used a heated outer tube with cool
swirling water. He has continued this investigation in a more recent
publication 1199] which does not appear to be available in the United
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58
States. Sudaver {200] examined the flow of air swirled by means of
inlet vanes flowing through an annular channel with the outer cylinder
heated. Borisenko 1201] also used an annular channel but with, the inner
cylinder heated. Bukhman I2Q2J used a hot gas geometry to develop both
local and mean Nusselt numbers but he made no attempt to correlate his
results to the intensity of swirl employed. Schchukin 1203] has used
inlet vanes to examine heat transfer coefficients as a function of
axial length in a paper not yet available in U. S. literature.
Theoretical attainments are decidedly meager for vortex heat
transfer with decay effects. Kharitonov 1204] and Ghil J205] have
presented recent attempts but the analysis currently available is
limited to providing coarse interpretations of the available data.
Many of the results of the papers cited in this subsection
1181-203] will be referred to again in more specific detail in Chapter
IV.
Practical Devices
The objective of this section is to present a broad overview of
the literature of confined vortex flows that have been oriented pri-
marily to the analysis or optimization of practical devices. Since
vortex flows have been applied to an exceedingly wide variety of devices
only the literature for the seven most-common types are presented here
(as listed under 1B2 in Table 2).
Ranque-Hilsch Tube
One of the most-remarkable fluid-dynamic results of a confined
vortex flow is usually termed the ftanque-Hilsch. Effect after its
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59
original discoverer (Georges Joseph Ranque) and its re-discoverer
(Rudolf Hilsch). In 1931, Ranque read a paper before the Societe
Francaise de Physique (French Society of Physics) wherein he reported
that it was possible to obtain a hot and cold stream of air out of an
adiabatic pipe with a single inlet stream of ambient air; the response
of the society was apparently something less than enthusiastic. In
that same year Ranque applied for a French, patent and in 1932, after
it was issued, he applied for a United States patent as well. In 1933
his paper became available in the literature [206] and in 1934 his
TJ. S. patent was granted 1207]. Ranque then assigned the patent rights
to a small company that he had formed—La Giration Des Fluides (or
Whirl-Gas) of Montlucon. Despite these events his invention remained
virtually unknown and in the period 1934 to 1944 no further mention of
the device was made in the Societe1s Journal.
After the .end of World War II, when TJ. S. scientists were sent
to Germany to examine the work of the German intelligentsia, it was
found that Rudolf Hilsch, a physicist at the University of Erlangen, had
been working on an operating model of Ranque's device from whose paper
[206] he got the original idea. Hilsch then published his results in
1946 [208] one month before it was referred to in a brief article by
Milton [209] in a U. S. journal (Milton had been one of the scientists
sent to Germany and had observed Hilsch's work). From this year on there
has been a veritable explosion of papers on the subject. Further de-
tails on the early history of this device can be found in Fulton [210].
This proliferation of literature is attested to by the fact that
by 1951 a bibliography of literature on the subject was publishable [214],
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60
In 1957, Westley [212] published the details of the practical perfor-
mance parameters of the Ranque-Hilsch Tube which Lewellen [105] cited
in 1971 as "one of the best sources of data for determining optimum
performance of the tube".
There was a large number of early systematic experimental studies
of the tube; among the more well-known were: Eckert [213, 214],
Hartnett [215], Keyes [216], Schowalter [217], and Savino [218]. The
theory of operation of the tube has also been the subject of a great
many papers from Kassner's [219] in 1948 through Deissler [220, 221],
Lay [222, 223], Sibulkin [224-226], and even in recent times with
Linderstrom-Lang [227]. Despite this effort by investigators, Lewellen
([105], page 182) concluded that "the detailed prediction of the
three-dimensional flow pattern in a highly turbulent vortex tube is
still beyond the state of the art. Since the energy separation de-
pends upon this flow pattern it is to be expected that the numerous
attempts to predict the performance of a Ranque-Hilsch Tube, although
each contributing to the understanding on the tube, have not met with
complete success." Hall [79] even went further by saying, "the com-
plexity of the flow in a Ranque-Hilsch Tube has made the accurate
prediction of performance virtually impossible."
Even the data for the velocity profiles in these tubes is sub-
ject to strong suspicion. Reynolds [228] in commenting on the use of
one-sixteenth inch diameter probes used by Sibulkin to obtain data
used to substantiate his theory, said:
...the introduction of such pressure and temperature probes into
the vortex produced large changes in the fields within the tube.
These changes were not .lust local ones; large disturbances occurred
throughout the tube...However, all the measurements made in vortex
tubes until now have relied upon instruments of somewhat similar
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design and of about the same size as those used here. All the
data must be equally suspect. (italics mine)
Holman [187] has found that the flow field was "significantly" dis-
turbed by the introduction of probes of this size. Timm [229] has
published a recent survey of the velocity profile data that is avail-
able for the tube flow.
Recent literature reveals that investigation of the Ranque-
Hilsch tube continues unabated with new geometries (see Gulyaev [230]
for the use of a diverging tube which he claims improves the refri-
geration capacity by 25%) as well as new thermodynamic boundary condi-
tions (see Martynov [231] for predictions of "more effective" perfor-
mance for a diabatic tube).
A number of literature surveys strictly on the subject of Ranque-
Hilsch tubes are available. In addition to Curley already cited,
Westley [232] included 116 references in 1954, a bibliography which was
updated by Dobratz [233] in 1964. Lewellen [105] includes in his
bibliography the papers published since Dobratz1 survey on the subject.
Both the theory and the data obtained for this device are not
pertinent to this investigation. Not only'is the geometry fundamen-
tally different (relatively short tubes with a pair of exits) but the
very high-velocity flow field and adiabatic boundary conditions are in
contradistinction to that used here.
Cyclone Separator
The cyclone separator is unquestionably the most practical
application of confined vortex flow characteristics as it is widely-
used in industry to separate particulate on the order of several mi-
crons in diameter from flue gas streams. Lewellen [105] claims that
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a German Patent had been issued in 1855 for such a device that looks
very similar to those used today. The secondary flows characteristic
of swirling flow play an important role in the particulate separation.
By shaping the bottom of the separator into a conical form, the boundary
layer formed on the walls, which contains most of the particulate to be
separated, will tend to flow inward and downward because of the imposed
radial pressure gradient and thus can be collected at the bottom of the
separator without being reinjected into the air stream.
Ter Linden [234] gave an early account of the velocity distri-
bution inside a separator and noted that the solid body rotation core
extended to approximately 0.6 of the exit radius of the re-entrant pipe;
this same figure has been reported by many others (e.g. [235]). Davies
1236], in a survey paper on separation techniques, detailed the collec-
tion efficiency of a cyclone separator in comparison to alternate
techniques (settling tanks, scrubbers, etc.). He pointed out that
desirable operating characteristics required a geometry that included
r
a high inlet velocity, small exit radius, large height to radius ratio,
and a ratio of external radius to outlet radius of nearly one.
Smith [237, 238] has presented detailed analytical and experi-
mental results for the cyclone separator. He showed by means of sta-
bility analysis that the boundary layer on the outer wall of the cyclone
is unstable to a radially inward displacement, explaining the dust
streaks that are sometimes found on the walls of operating separators.
In his experimental work he found that in addition to the expected
turbulent and laminar regimes that it was possible to produce a peri-
odic regime. An apparent axiom for vortex flows is that the unexpected
should be expected.
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The Aerospace Research Laboratories has recently become inter-
ested in examining new configurations of cyclone separators, which they
have termed "reverse-flow" chambers. Two of many reports on the opera-
tion of such a device were given by Fiorino [239] and Poplawski [240].
The objective is that through the use of new geometries better utilizing
the inherent secondary flows and with very high inlet velocities
(tangential Mach numbers exceeding one), sub-micron separation can be
achieved.
Despite the cyclone's long history, it is still the topic of
continued research (see, for instance, [241]). Two books on the sub-
ject that are often quoted for design information are Reitema [242]
and Bradley [243]. Recently, fluid-dynamic separation principles have
also been applied to gas centrifuges whose purpose is the enrichment
of nuclear fuels.
Fluidic Devices
As with many applications of fluid dynamics, fluidic devices
have undergone a history of early development and interest followed by
a long dormant period and now have experienced a recent revival.
Thoma [244] is usually credited with having invented the first use of
vortex flow in a fluidic device, having obtained a patent for his
vortex in 1928. The original idea was simply that the use of a small
control jet oriented tangentially at the periphery of a short cylin-
drical chamber could greatly reduce a much larger flow rate by con-
verting much of the linear flow energy into a vortex. Shortly there-
after, Heim [245] used this principle to develop a vortex diode.
For the next thirty years of its history, the literature is very
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meager. Starting in about 1960, however, there has been an exponential
growth in research and publications on the subject. Mayer [246], in
a survey article, gives a partial list of fluidic devices that operate
upon some principle of vortex flow: vortex diode, swirl atomizer,
vortex air thermometer, storm diverter, vortex combustor, vortex ampli-
fier, vortex valve, and negative vortex oscillator. Lewellen [105]
has expanded this list as well as provided an updated bibliography in
his 1971 monograph.
Vortex fluidics has been the subject of a great many disser-
tations, among them Lawley [247] and Lea [248] of this institution,
and can be found as the research subject of at least one article in
almost any current journal related to controls (see, for instance,
[249]).
These devices are operated under isothermal conditions in
(usually) small, sandwich-like chambers. The small flow areas suggest
that their flow patterns are strongly influenced by end wall boundary
layer effects. Due to the many different purposes to which they are
put, there is rarely any geometry which may be termed "usual" and as a
result it is very difficult to translate the results, for a vortex
structure obtained from data for one apparatus to another. The usual
procedure is to completely ignore the internal flow dynamics, because
of its hopelessly complex nature, and instead concentrate on obtaining
macroscopic performance characteristics. Perhaps the most common of
these characteristics is presented as a graph of the total flow through
a vortex modulator as a function of the control flow (usually expressed
in terms of the turn down ratio).
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Containment/Stabilization
The earliest work in this area is usually attributed to
Schoenherr [250] who in 1909 documented the stabilizing influence of a
vortex flow upon a long arc discharge. Schoenherr was developing a
process to synthesize nitric acid for which he needed a stabilized high
temperature source. The stabilizing effect of vortex flow upon flames
dates from about 1950 and has already been discussed at some length
[126-130].
In the last 15 years a new application of this characteristic
of vortex flow has become of great interest. This application is
commonly referred to as "containment". It originally arose in connec-
tion with the development of a nuclear rocket,wherein the vortex flow
of a gas such as hydrogen would contain the fissionable material in an
annular volume while simultaneously being heated and accelerated by
the energy of release. The first apparent mention of this concept in
unclassified literature was by Grey [251] in 1959, although it is
claimed to be the idea of Kerrebrock who proposed it in classified
literature in 1958; in 1959, Kerrebrock [252] presented the concept
at a conference in technically couched terms. Of interest here is
that he noted a fundamental difference in velocity profiles which
occurred because of the heat addition process—specifically, "Heat
addition, through its effect on the gas temperature would provide a
means for establishing a quite different variation of the tangential
Mach number with radius than is found for any adiabatic flow". Later,
in 1961, Kerrebrock [253] was much more direct in his application of
vortex containment (it is interesting to note the difference in the
titles of his papers.)
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Very early in the investigation it was recognized that the
apparent maximum tangential velocity achievable for confined vortex
flows, i.e. a Mach number of approximately 1.5, would not be sufficient
to achieve adequate containment. Lewellen [254] posed this problem in
1960 noting that the only other logical alternative, that of generating
the vortex by rotating the tube walls, is also severely limited (here
by structural considerations), has suggested using magnet hydrodynamic
forces to augment the intensity of swirl. R. G. Ragsdale and J. M.
Kendall each authored a large number of early publications on this
subject. In [255] Ragsdale included a bibliography of the early
literature on containment. Kendall [256] in a Jet Propulsion Laboratory
report, examined the fluid dynamic reasons for bounds on the contain-
ment parameter (defined as the ratio of the tangential Mach number
squared to the radial Reynolds number); he concluded that the end wall
boundary layer was the most likely cause, especially in view of the
rather short chambers being investigated (length to diameter ratio of
order one).
In the past 5 years the interest in containment has expanded
to include a vortex reactor [257], a control scheme permitting the
same chamber to be used for both subsonic and supersonic combustion
[258], and for use in electric propulsion rockets [259]. Murthy [259]
in his survey paper includes 155 references on the subject of vortex
stabilization and confinement in addition to the following caution:
"the use of immersed probes is open to question on account of the
disturbance introduced into the flow."
Despite the interest in containing an energy releasing volume,
virtually all the data available is for isothermal operation, although
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ARL, in their study of containment, have utilized a heated cylindrical
rod at the axis to simulate a stabilized arc (this literature has
already been discussed [184-194]).
Nozzles/Diffusers
Vortex flow has been found to offer enhanced performance for
both nozzles and diffusers. Guderley in a series of papers [260-262]
has shown that swirl in a Laval nozzle can be advantageous with respect
to fuel consumption as a result of increased effectiveness of the
nozzle. This question has also been recently examined by Boerner [263].
The effect of swirl upon improving the performance of a diverging,
conical diffuser has been reported by So [264]. So found 5 distinct
flow regimes for different intensities of swirl, giving some indication
of the complexity of flow present in such arrangements. Chow [265]
has discussed the general effect of non-uniform cross-section channels
upon swirl flow in a recent paper.
Usually the diffuser investigations are for isothermal flows
only while the nozzle investigations, because they involve propellant
exhaust gases, are for non-isothermal and diabatic flows. The objective
of the diabatic boundary for the nozzle flows is not, however, heat
recovery (as is the case in the present study) but merely the protection
of the nozzle wall; hence, the amount of heat transfer at the wall in
comparison to the energy content of the gas stream is very small.
Cyclonic Combustion Chamber
Cyclonic combustion, as distinguished from tangentially-fired
combustion, dates from the 1940's and is almost the exclusive means
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of burning low grade coal (in crushed, but not pulverized, form).
The distinguishing features arid early history of these two kinds of
vortex combustion is presented in a number of reference works [266-
268]. Discussion of the tangentially-fired combustion chamber will
be deferred to the next subsection.
Perhaps the earliest paper on vortex combustion is due to Hurley
[269] who reported its use in 1931. By 1943 a patent had been issued
to Vroom [270] for:
A pulverized fuel burner comprising a burner tube having an open
outlet end adapted to connect with a combustion chamber, means
including an inlet port in the peripheral wall of said burner
tube supplying to said burner tube in a direction tangential to
the inner surface thereof a stream of pulverized fuel suspended
in carrier air, means causing said suspended fuel to advance
helically in a peripheral layer in said burner tube to the outlet
end thereof, a central axial air admission means including an
air register admitting a secondary air stream at the inlet
end of said burner tube out of the main path of the peripherally
rotating layer of fuel, said air register having peripheral doors
to impart a rotary motion to said secondary air stream, and means
preventing direct contact between at least the main portion of
the rotating stream of secondary air and the main portion of said
fuel stream at the inlet end of said burner tube.
Parmale [271] received a patent for a modified form of cyclonic com-
bustion chamber in which all the air and fuel was introduced tangen-
tially with a slight backward (with respect to the outlet) component.
The original design, development, and commercial fruition of
cyclonic combustion was described in a series of papers by Brunnert
[272], Gilg [273], and Schroeder [274]. The abundance of unusable
low-grade, Central Illinois coal led Babcock and Wilcox Company to
develop a combustion chamber that would trap the high ash content of
these coals. They found by orienting a cylindrical combustion chamber
(originally only one foot in diameter ) in a horizontal fashion with a
slight favorable slope (usually about 5 degrees) and by injecting the
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air and suspended crushed coal that a liquid slag formed on the bottom
of the chamber which was highly scrubbed by the tangential gases; this
slag acted as a trap for the ash suspended in the tangential stream
thus preventing its being passed to the boiler-tube section and then to
the atmosphere. The slight slope to the chamber permitted a means of
continually collecting the molten slag. The first full-scale use of
such a chamber was at the Calument Station of the Commonwealth Edison
System in September 1944; this chamber had an 8-foot diameter and an
11-foot length with a 5 degree slope. It was found that the same power
generation capacity could be obtained with a. furnace requiring 25%
less floor area, 33% less volume, and 22% less weight. The operating
temperature of the combustion chamber was on the order of 3000 degrees
Fahrenheit; thus, although the chamber walls were water cooled, a
negligible fraction of the heat of combustion was in fact recovered
through these walls as is typical of these devices. The hot exhaust
gases must be routed through the usual boiler tubes to achieve the
rated steam capacity- Flushed with these early successes, a number of
other configurations were attempted, among them a vertical furnace
where the tangential impetus occurred at the top with a slight down-
ward component and then exhausted through a re-entrant nozzle also at
the top. This configuration was apparently not very successful
(although it occasionally reappears in the literature [275]) and vir-
tually every cyclonic combustion chamber currently in use (currently
about 600 in the United States and Europe) closely resembles its first
ancestor. An early book detailing the performance of cyclone com-
bustion chambers in comparison to the alternatives was written by
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Smith and Stinson [276]. They quote a typical capability of 50,000
British Thermal Units (Btu) per hour per cubic foot based upon the
total furnace volume and 500,000 Btu per hour per cubic foot based
upon the volume of the cyclone chamber itself.
This concept of vortex combustion has also been successfully
demonstrated with natural gas and oil as the fuel although the method
does not appear competitive with alternative techniques. Garner [277]
and Stone [278] have reported on two early such demonstrations. Garner
in particular noted that the pressure at the axis of the combustion
f
chamber was sub-atmospheric and suggested that flow reversal might be
the explanation. Recently, Dumoutet [279] has observed such recircu-
lation patterns and in fact found that they were substantially different
for a gas as the fuel than for crushed coal. Seidl [280] in a rela-
tively old paper noted that for crushed coal the velocity profile
outside the solid body rotating core could be described by vrn = c
where v is the tangential velocity, r the radius, c a constant, and n,
an experimentally observed constant, of about 0.5. He explained this
value of n by suggesting that the coarse dust of the coal had an
"altered" viscosity which prevented the development of a free vortex
region (for which the value of n would have been 1.0). For calculation
purposes he suggested using solid body rotation (i.e. n = -1.0) for the
core region and constant velocity (i.e. n = 0.0) for the outer annulus
region since this closely approximated the measured profile. Recently,
however, Kalishevskii [281] has reported on observations of a peripheral
reversed flow region.
Continued research on improving the cyclonic combustion process
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is being reported in the literature, particularly in Soviet journals
(see, for instance, [282-284]). Mills [285] has also recently re-
ported on the use of waste wood in a cyclone furnace (Cycloburner,
Tradename of Energex, Ltd.). This was a refractory chamber of 3-foot
diameter, 6-foot length which developed heat releases of up to 800,000
Btu per hour per cubic foot. Once again the primary heat recovery was
external to the burner.
In addition to power generation, vortex combustion has recently
become of interest for use in turbojet combustors [286, 287]. Osgerby
[288] has written a survey paper on the subject of turbine combustion
modelling that includes vortex combustion configurations. He includes
more than 100 references in his review.
Tangentially-Fired Combustion Chamber
There are two broad classes of coal firing: grate/stoker and
suspension. Of the suspension class there are four sub-classes: ver-
I
tical firing, impact firing, horizontal firing, and corner or tangen-
tial firing [289]. It is this later subclass that is of interest here.
Tangentially firing pulverized coal pre-dates the 1920's when corner
nozzles were used in square, vertical, refractory furnaces. The effect
of vortex combustion was observed early to enhance the turbulence level
of the chamber and resulted in more efficient combustion. Starting in
about 1925, water cooling all or most of the furnace chamber walls be-
came structurally necessary in order to achieve the large furnace sizes
desired [290] and today virtually all such furnaces are water-walled.
But, as was the case for the cyclone combustion chamber, the degree of
heat recovered by the wall cooling water is negligible in comparison to
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72
the heat of combustion and virtually all the heat-recovery process
takes place external to the combustion chamber. Hence the temperature
of the chamber tends to be very high with only a slight radial variation
due to the cool, confining walls.
This combustion chamber configuration is by far the most common
for use with pulverized coal. Nozzles are customarily located in each
of the four corners of the square or rectangular chamber and are
distributed along the height of the chamber as well. The nozzles are
sometimes oriented such that the incoming suspension of coal and air
has a small downward velocity component as well as a tangential one.
Photographs of the vortex flame typically show a hot, annular turbulent
flame with a relatively cool core. The injection scheme together with
the combustion process tends to make the flame extremely turbulent and
intense and undoubtedly causes very complex velocity profiles as the
conflagrant gas spirals down and then up out of the chamber.
A comprehensive survey of the literature on this subject would
easily result in hundreds of citations that would still shed very
little light on the subject of this investigation. Instead, a brief
survey of the literature on the use of tangentially-fired combustion
chambers for the incineration of waste products will be presented.
The U. S. Bureau of Mines has sponsored a series of experimental
research programs on the use of tangentially-fired chambers to incin-
erate wastes. The typical configuration involves the waste being fed
in from the bottom (by means of stokers or on a charge basis) with only
the air being injected tangentially. The results of these efforts
have been reported by Corey [291-293], Weintraub [294], and Schwartz
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73
[295] among others. The results of this series of papers may be
summarized by noting that the use of tangentially-over-fired air was
capable of significantly increasing the burning rate in a manner
correlatable with the Reynolds number of the injection nozzles. There
is an optimum such Reynolds number (usually stated as 35,000 based upon
the diameter of the nozzle and the tangential velocity) in terms of
maximum burning rate. Again, like all the previous work in this area,
heat recovery at the walls of the combustion chamber was not the objec-
tive and was in fact avoided and, as a result, there is no experimental
data for Nusselt number (for instance) as a function of inlet Reynolds
number and geometry.
Literature Survey of Rotating Flows
Heat Transfer Surveys Available
A complete bibliography of the literature on the subject of
heat transfer from rotating surfaces for the period through 1959 has
already been cited—Eckert's monograph in the series Progress in Heat
and Mass Transfer [76]. This bibliography has been continually updated
in selected issues of the International Journal of Heat and Mass Transfer
so that a relatively current body of literature is readily available
to a researcher in the field.
Dorfman [296] published one of the earliest surveys on this
subject in 1963. Kreith [75], already cited, updated this book in 1968
in the series Advances in Heat Transfer, providing 193 references.
Dorfman [297] has very recently provided another update, including 242
references.
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74
Despite these extensive surveys and the intense interest in the field,
there are fewer than ten papers available on the heat transfer be-
tween an internally flowing fluid and a confining tube wall which is
rotating about its own axis. It is this configuration that would be
most closely similar to that under study here.
External Rotating Flow
Since this type of swirling flow is really not applicable to
the present investigation, no attempt will be made to survey the liter-
ature available. A few citations will be included for the most recent
work in this area in the interest of completeness.
Cham and Head in a series of recent papers [298-300] have de-
veloped an integral-profile technique for use on isothermal, turbulent
boundary layers forming on a variety of rotating surfaces. Chin [301]
has examined the problem of simultaneous mass and momentum transfer
on a rotating hemispherical electrode. Koosinlin [302] in contrast to
Cham, has used a finite difference technique to predict the flow field
surrounding rotating free disks, cylinders, cones, etc. This technique
is essentially that used by Lilley [125] for isothermal swirling jets.
Recent heat transfer research has been reported for a variety
of configurations. Johnson [303] found that the heat transfer from a
cylinder to a normal air stream could be increased approximately 15%
by the use of vortex generators. Eisele [304] claims to have presented
the first research on the heat transfer from a flat plate rotating as
a propeller. Eastop [305] has correlated the heat transfer from a
rotating sphere in an air stream solely in terms of a flow Reynolds
number and a rotational Reynolds number. Koosinlin, Launder, and
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75
Sharma in a series of papers [306-308] have extended their finite
difference analytical technique to predict heat transfer as well as
momentum transfer with a variety of rotating surfaces. They have de-
fined a local swirling flow Richardson number that has been used to
obtain a mixing length (via a linear relationship) to generate what
are apparently accurate models of the actual external rotating flow
heat transfer processes. At present their results are still restricted
to small swirls (i.e. low values of rotational Reynolds number).
Internally Rotating Flow
There is a vast literature on internally rotating isothermal
flows since many geophysical flows can be modeled by such geometries.
Also, various unusual phenomena occur relating to vortex breakdown,
such as the Taylor-Proudmann column, for this geometry that are widely
reported. Only the most recent literature—that published within the
last five years—will be cited here.
Bien [309] has examined a cylinder with one end wall fixed and
the other rotating with a Helium-Neon laser anemometer using water as
the working fluid. His experiment was interesting in that it showed
the development of the Karman profile by the rotating disk and the
Bodewadt profile by the stationary one. Carrier [310] has examined
the flow over a rigid body locating in a rotating container by means
of the modified Oseen method. Wagner [311] has modeled the radial
passages in centrifugal pumps and compressors by means of a pipe ro-
tating about an axis perpendicular to its centerline for both laminar
and turbulent flow. His theory predicted and his experiments confirmed
the presence of longitudinal vortices for this flow field. In an
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76
attempt to model air cooled multiple disk pumps and compressors,
P.akke [312] presented hot-wire data obtained for a source flow between
two rotating disks under a wide combination of disk speeds and source
flow rates. He found that the flow tended to be stabilized as a result
of centrifugal forces. Moore [313, 314] has examined the flow field
surrounding the impeller of a centrifugal compressor and has noted the
presence of: a potential flow region, top and bottom wall boundary
layers, corner flows, and sidewall boundary layers. Huppert [315]
has studied the flow field about an obstacle located on the bottom
of a cylinder rotating about its vertical axis. He has explained how
the observed streamline displacement around the obstacle is dependent
upon the side walls through the Influence of the Rossby number. Benton
[316] has presented a survey paper on what he calls the "spin-up"
problem. This is the change of a homogeneous fluid which is initially
rotating as a solid body to a step change in the angular velocity of the
rotating, confining cylinder. He has noted the development of three
boundary layers—each of which is a function of the Ekman number but
to a different power.
For diabatic conditions for internally rotating flows there are
a large number of papers for configurations vastly different from that
of interest here. Miyazaki [317], in a recent paper, has presented
results obtained by rotating a rectangular tube about an axis other than
its own axis of symmetry. This kind of a problem is usually classed
as a special case of a thermosiphon as the flow field is greatly in-
fluenced by the heat transfer process through the bouyancy forces.
The configuration of parallel disks within a casing is also the subject
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77
of recent research (see, for instance [318-320]) and is important to
the design of cooling systems for gas turbines and compressors. Hammond
1321] has summarized some of the literature available on the subject
of rotary heat exchangers (sometimes called rotary regenerators).
Heat transfer in annular tube configurations has also been the
subject of much research. The literature is very difficult to
classify as there are a large number of possible operating conditions:
one or both tubes rotating, heat transfer from the fluid to one or both
of the tubes, heat transfer from one or both of the tubes to the
fluid, and various relative gap thicknesses. Bjorklund 1322] provided
some of the earliest results for 4 values of annular gap and several
combinations of cylinder rotation rates. For the inner cylinder only
rotating he found that he could correlate the observed Nusselt number
in terms of the Taylor number (which is essentially a rotational Reynolds
number) only. One of the complications of annular configurations is
the possiblity of the formation of Taylor vortices; Haas 1323] has
examined their effect upon heat transfer to a liquid flowing through
the annulus. Zmeykov [324] has published recently some of the Soviet
research for this configuration. Sharman [325] has examined the con-
figuration for a heated outer cylinder and a cooled inner cylinder with
air flowing in the gap. Scott [326] used an adiabatic, rotating inner
wall with a heated, stationary outer wall to measure the turbulent trans-
port properties, eddy diffusivities of momentum and heat, which were
found to be functions of the swirl distribution (i.e. they varied as
the flow developed down the rotating annulus). Citations of additional
work with annular, rotating flows can be found in the surveys of Kreith
[75] and Dorfman [296, 197].
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78
As previously mentioned, the research in the area of simple
rotating tubes is much more limited than other geometries, and may
be summarized as follows:
(1) Water as the working fluid without entry-length effects—
Kuo [327] and Pattenden [328, 329]
(2) Air as the working fluid without entry-length effects—
Briggs [330] and Cannon [331]
(3) Air as the working fluid including entry-length effects—
Buznik [332-334]
Kuo [327] has presented data for a variety of rotating configu-
rations: full as well as partially-full tubes and with and without
inserts (either an annulus or a paddle system). The length to diameter
ratio of the rotating tube was 8.0. Heat was supplied to the system
by stationary Nichrome wires located parallel to the tube axis near the
walls. He was able to correlate the measured Nusselt number in terms
of the axial and rotational Reynolds numbers with the general result
that Nusselt number increased with Reynolds number although it did so
in steps on log-log paper. He attributed this to a transition phenomena
from a region where the effects of gravitation are significant to a
region where centrifugal effects are significant. It is interesting to
note that the data for partially filled tubes indicated a higher Nusselt
number than for the full-tube case.
Pattenden [328, 329] used a configuration similar to a single-
pass, counter-flow heat exchanger only with the separating tube being
rotated. He concluded from his experiments that "very high heat transfer
coefficients can be obtained." Kreith [75] however, has concluded that
Pattenden1s experiments were of "limited accuracy" (page 241).
Briggs [330] has reported on extensive data taken with air being
heated by the rotating tube. The principal effect of the tube's
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79
rotation was concluded to be a delay in transition from laminar to
turbulent flow for, "Once fully established turbulent flow is attained
the effect of rotation, at least for the range of variables considered
is small." This result is in contrast with that reported above by Kuo
and by Pattenden. Briggs was able to correlate his data for Nusselt
number in terms of the axial Reynolds number and the number of revo-
lutions per minute of the tube (investigated for the values of 0, 1900,
and 3400 RPM). For Reynolds numbers exceeding about 20,000 the Stanton
number was essentially independent of the speed of rotation. Briggs did
not analyze any entry length effect (the length to diameter ratio of
his apparatus was 56.5).
Cannon [331] has extended Briggs' work using essentially the
same apparatus. Although he too did not account for entry-length effects,
he has included both the case of the rotating air being heated as well
as cooled (which he found to have only a minimal effect upon the ob-
served Nusselt number suggesting that the flow field was essentially
independent of thermal boundary conditions). Cannon's principal con-
clusion was that the effect of rotation was only to delay transition from
laminar to turbulent flow because of its stabilizing influence on the
wall boundary layer, specifically, "As the tube rotational speed is in-
creased, with the through-flow velocity constant, the effect is to
stabilize and make less frequent the bursts of turbulence. If rotational
velocity is sufficiently high, the bursts disappear entirely."
Buznik in a series of papers reported in Soviet journals [332-
334] has examined the entry-length effects upon heat transfer from a hot
rotating tube to cool air flowing through it. He has used an apparatus
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80
with a length to diameter ratio of 16.25, capable of rotational speeds
of up to 1170 revolutions per minute. He was able to correlate his
data by using a Stanton number as a function of the two Reynolds num-
bers (axial and rotational) and the non-dimensional axial distance from
the start of the test section. As found earlier by the work of Briggs
and Cannon, the effect of rotation was to diminish the heat transfer
coefficient from that obtained for purely linear flow.
The results of Briggs, Cannon, and Buznik will be compared to
that obtained for this study in Chapter 4.
Literature Survey of Curved Flows
Flow Past Concave/Convex Walls
Since many of the characteristics of swirling flow inside sta-
tionary tubes can be analyzed as flow past concave surfaces, it is
pertinent to examine the state of knowledge and literature on this
subject. Gortler [335], in what has become a classic paper, predicted
in 1940 that the laminar flow past a concave surface is unstable to
the formation of longitudinal vortices which have since become known
by his name (this work was later translated and published as a NASA
report in 1954 [336]). Some time later, Gortler [337] demonstrated
the analogy between instabilities caused by centrifugal body forces
originating because of flow past a concave wall and by the bouyant
forces originating in a thermally stratified boundary layer. Tani
[338] showed the existence of a longitudinal vortex structure in a
turbulent flow as well as for a laminar one.
Kreith in a series of papers [339-340] has shown both
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81
analytically and experimentally that flow past a concave
wall enhances heat transfer (with respect to a flat wall) and flow past
a convex wall inhibits heat transfer. He has demonstrated that the
Nusselt number ratio for that obtained in a concave flow to that for a
convex flow is approximately equal to the square-root of the ratio of
wall shear stress for a concave flow to that of a convex flow. As
noted in the subsection on vortex tube studies, Migay [196] made a
similar observation for the Nusselt number ratio obtained with swirl
to that obtained without swirl.
The actual fluid-dynamic cause of the enhancement is a subject
of some debate. One line of reasoning explains the effect as a result
of increased radial turbulent fluctuations at a concave wall (see,
for instance, [342]). The alternative explanation accounts for the
increased heat transfer by the presence of a vortex structure (see
[343]). Schultz-Grunow [344] has shown for a laminar flow that by
accounting for streamline curvature by using a higher order boundary
layer approximation than that usually employed, it is possible to obtain
an expression where the Nusselt number is equal to 0.5 3 u x/V where
U is the free stream velocity, x the distance along the wall, v the
o
kinematic viscosity, and 3 a non-dimensional function of the Prandtl
number. For a flat plate 3 is known to be equal to 0.664Pr ' where
Pr is the Prandtl number. Schultz-Grunow has shown that 3 is equal to
0.692Pr°'355 for flow past a concave wall and 0.632Pr ' for a con-
vex wall. Thus there appears to be sound analytical basis for increased
heat transfer for concave walls at least for laminar flows.
Persen has examined the effect of longitudinal vortices on heat
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82
transfer in series of papers and reports [345-351]. His analysis
as relevant to this study, has concluded that the presence of longi-
tudinal vortices can not account for the increased heat transfer
observed (he quotes an increase of "70 to 80%", although he does not
cite a source) with the principal effect of the vortex structure
being the more rapid development of the boundary layer when compared
to a simple linear flow.
Recent data by Ellis [352] for the turbulence in a curved duct
(with a 15 inch radius of curvature) has shown that the flow behavior
is distinctly different than for the case of a plane wall. The tur-
bulence intensity is amplified for flows past concave walls with in-
creased rates of boundary layer growth and larger measured values of
friction factor. Data for heat transfer in a simply curved duct are
limited. Shchukin [353] has presented data for heat transfer as a
function of length of the channel (of fixed curvature) for laminar
flows.
A very extensive survey on the state of knowledge on the effect
of streamline curvature upon turbulent flows has recently been pre-
pared by Bradshaw [354], This monograph includes more than 300
references of work in this area. The conclusions of this reference
as pertinent to the present investigation may be summarized as follows:
(1) The changes in the flow produced by streamline curvature are
both large and, to a degree, surprising. "These changes are usually
an order of magnitude more important that normal pressure gradients
and other explicit terms appearing in the mean-motion equations for
curved flows". (page 1)
(2) The effect of curvature upon friction factor and heat transfer
coefficient is about 10 times greater in turbulent flows than in
laminar flows which implies that the change in the Reynolds stress
term must be a factor of 10 greater than the change in the viscous
term. However, at present there does not appear to be any reasonable
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83
explanation as to how this could occur leading to the conclusion
that curvature must change the very structure of the turbulent flow.
(3) Knowledge of curvature effects upon the flow field properties
is still so minimal that heat transfer predictions are not yet
achievable for turbulent flows. In particular, "Some apology is
necessary for the neglect of heat transfer in this review. Quite
simply, the uncertainty of the behaviour of the Reynolds analogy
factor and the turbulent Prandtl number is so great even in plane
flows that a discussion of the effect of streamline curvature on
these quantities would be premature". (page 52)
(4) On the subject of data and interpretations of confined vortex
flows, he writes:
There seems to be little detailed information on the decay of
pre-swirl in a simple pipe flow: any device for generating strong
swirl will cause large changes in the axial velocity profile, whose
return to full development will be inseparable from the decay of
the swirl .... it is frequently unclear whether experiments on
vortex flows in tubes are supposed to relate to classical vortices
surrounded by an irrotational flow, to fully-turbulent pipe flow
initially near a state of solid-body rotation, or to some unhappy
compromise between the two. . . . Unfortunately it is not possible
to classify experiments by the swirl generator used: the use of a
twisted tape or rotating grid implies a rough approximation to
solid-body rotation, but with a vortex tube with radial entry, of
the type originally intended to generate a classical vortex with
W~l/r outside the core, can be used by design or accident to pro-
duce almost any swirl distribution. (page 64, where W is the
tangential velocity and r the radius from the centerline, italics
mine).
(5) On the subject of conflagrant, swirling flows, Bradshaw notes:
Swirling flames are an example of the class of flows in which a
qualitative consideration of curvature effects is helpful in under-
standing the phenomena but which are rather too complicated to
yield quantitative data for general use: turbulence measurements
are difficult and numerical experiments may show up discrepancies
other than those directly attributable to curvature effects.
(page 65).
Bradshaw includes in his report a detailed history of the devel-
opment of the theory of curved flow back to the time of Rayleigh's
paper [61]. He concludes this section with the following observation:
"The history of research on the effects of streamline curvature on
turbulence is an object lesson in the effects of poor communication".
(page 24)
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84
Flow Through Helically-Formed Tubes
The problem of predicting the heat transfer through helically
coiled tubes has been examined by a large number of investigators
starting with Grindley [355] in 1908. From the beginning, the presence
of secondary flows as a result of the curving geometry has been noted
as the agent of the observed heat transfer enhancement. Eustice
[356, 357] expanded upon the work of Grindley in 1910 and 1911. Some-
what later, 1925, Jeschke [358] published the first complete set of
data for the flow through coiled tubing. About this same time Dean
[359, 360], in his study of the flow characteristics in refrigeration
tubing, found a non-dimensional grouping of flow variables—now known
as the Dean number—that correlated the observed results. The classic
work in this field, however, was done by White [361, 362] in 1929 and
1932 and was used by designers of heat transfer equipment as the author-
itative work on the subject for nearly three decades.
McAdams in his reference work on heat transfer [363] has
suggested a simple correlation for the average heat transfer coeffi-
cient for coiled tubes in terms of the result for simple linear tubes:
a multiplying factor of 1 + 3.5/R, where R in the curvature ratio
defined as the radius of curvature of the tubing coil (to the center-
line of the tube) divided by the radius of the tube. Although sim-
plistic, later research has basically supported this result.
Ito [364] has examined the turbulent regime for helical-flow
to obtain an empirical law for friction factor supported by some
theoretical considerations. He found that the critical Reynolds
number (defined as the transition point from laminar to turbulent flow)
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85
could be correlated by the following expression: 2000/R0'32 where
R is once again the curvature ratio. This shows that for a decrease
in the curvature ratio, i.e. a more tightly wrapped coil, the transi-
tion from laminar to turbulent flow is delayed much in the manner of
the effect of rotating a tube with an axial throughflow.
Seban [365] has extended Ito's work to include heat transfer
effects upon friction factor as well as to obtain a Nusselt number
correlation. Seban has shown that Ito's friction factor correlation
can be used for non-isothermal flow if the fluid properties are evalu-
ated at the mean film temperature. For the Nusselt number, Seban
recommends the following relation: f Re Pr * /8, where f is the
friction factor determined by Ito's correlation, re is the Reynolds
number based upon mean velocity and pipe diameter, and Pr is the
Prandtl number of the fluid. Seban has noted that his expression
yields very similar results to the simple correlation suggested by
McAdams. In addition to causing a delay in transition to higher
Reynolds numbers, Seban has also found that the tube curvature causes
a significant peripheral variation in Nusselt number (by a factor of
about 2 to 4 larger on the outside radius than on the inside radius).
This result is consistent with what was noted as observed heat transfer
enhancement for flow past concave walls and inhibition for flow past
convex walls.
Rogers [366] has extended Seban's work and, although supportive
of his conclusions, has suggested two alternative correlations for
Nusselt number: one based upon evaluating the fluid properties at
the film temperature and the other at the bulk temperature. Mori [367]
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86
has performed an analytical study for high Dean numbers (usually
defined as the ratio of the Reynolds number to the square root of the
curvature ratio) using a boundary layer/potential flow analysis that
appears to be valid only for fluids with Prandtl number about 1. He
quotes a 50% heat transfer increase over that obtainable with a simple
straight tube with a curvature ratio of 20.
Kalb in several papers [368, 369] has examined the flow from a
theoretical standpoint for two boundary conditions: constant axial
heat flow with uniform peripheral wall temperature and for the case of
uniform wall temperature. Patankar [370] has recently developed a
numerical, finite-difference procedure to obtain predictions of
laminar flow in helically coiled pipes. He notes that the principal
effect of the curvature is to cause secondary flows which in turn
result in a departure from Poiseuille flow. But he cautions, "further
work is required to develop turbulent flow predictions".
This particular configuration has such wide spread application
to industrial equipment that new studies and geometries are continually
being reported in the literature (see [371, 372] for several recent
Soviet papers). It appears, however, that the correlations currently
available for both heat transfer and friction factor are sufficient
to predict the performance of virtually any such flow with physical
dimensions of practical interest.
Flow Through Tubes with Axially-Mounted
Swirl Generators
The most common means of generating a swirling flow for con-
fined applications is through the use of inserts of various sorts.
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87
The most common insert is fabricated by simply twisting a metal tape
and pulling it through a pipe; this configuration is usually referred
to as a swirl tape flow.
The use of swirl tapes to augment heat transfer dates back at
least to the work of Royds [373] in 1921. Sometime later, in 1931,
Colburn [374] also examined the effect of internally twisted tapes along
with stationary propellers. Since that time, data has been obtained
by a large number of investigators [375-389] for a variety of fluids,
pitch-ratios of tape twist, and thermodynamic boundary conditions. A
summary of this work is presented in Table 4, taken from Bergles [73].
Not included in this table are data obtained for boiling (see, for
example, [390, 391]) or for data obtained with other effects combined
(see [392] where the effects of wall roughness and swirling flow pro-
duced by the swirl tape were found to be roughly additive in augmenting
heat transfer).
One of the earliest attempts at explaining the observed heat
transfer enhancement was by Kreith and Margolis in an early pair
of papers [379-380]. They noted that it was possible to obtain a
four-fold increase in Nusselt number and they attributed this increase
to four effects:
(1) fin-like character: the presence of the internal metal tape
attached to the tube wall acts much like an internal rib or fin and
would act to augment the heat transfer regardless of any swirling
velocity.
(2) wall curvature: as noted in the subsection on concave/convex
flows, Kreith has presented analyses to show that heat transfer is
augmented simply by passing a concave wall without a swirling velocity.
(3) Centrifugal force field: when the heat flow is from larger to
smaller radii the body force field acting on the density gradient aids
-------
TABLE 1*
SUMMARY OF PRINCIPAL INVESTIGATIONS
OF SWIRL TAPE FLOW
Investigator
Royds [373]
Colburn [37**]
Siegel [375]
Evans [376]
Koch [377]
Judd [378]
Kreith [380]
Greene [392]
Gambill [383]
Ibragimov [381*]
Smithberg [385]
Gambill [386]
Seymour [387]
Lopina [388]
Thorsen [389]
Fluid
Air
Air
Water
Non- luminous gases
Air
Isopropylated Santowax
Air, Water
Water
Water
Water, liquid metals
Air, Water
Ethylene glycol
Air
Water
Air
Inside
Diameter
(inch)
2.625
2.625
0.527
3.00
1.97 .
O.W
0.53
0.89
0.136 - 0.25
0.1+73
1.382
0.136 - 0.25
0.87
0.191*
0.587
Tape
Pitch*
Below 10
2.67 - 3.05
(axial core)
2.81*
2.9 - 5-9
2.1*5 -11.0
2.6 - 7.3
2.58 - 7-3
0.28 - 1.12
(axial core)
2.30 -12.03
2.12 - 1*.57
1.81 - °°
2.30 -12.03
1.8 -ll*.0
2.1*8 - 9-2
1.58 - u.o
Tape
fit
Loose
Loose
Snug
Loose
Unknown
Snug
Snug
Unknown
Tight
Tight
Snug
Tight
Tight
Tight
Snug
Heating
X
X
X
X
X
X
X
X
X
3.
X
X
Cooling
X
X
X
X
X
X
X
X
Pressure
drop
X
X
X
X
X
X
X
X
X
X
X
X
X
CD
00
Defined as distance per 180° of twist.
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89
convection (and, of course, vice versa when the heat flow is in the
other direction).
(A) roughness character: the presence of the swirl tape causes
an added turbulence level to the flow field much like wall rough-
ness elements which tends to enhance the heat transfer.
Smithberg and Landis [385] were the first to attempt a detailed
correlation of the data available, including their own, with an ana-
lytical model of some sort. Their study was limited to low heat
transfer rates and low wall to fluid temperature differences. They
used a flow field model of a forced vortex flow in the core region
superposed on an essentially uniform axial flow, a combination they
termed as "helicoidal." This model was then used to predict the
friction factor by summing the effects of the axial flow, the tangen-
tial flow, and the momentum deficit due to vortex core mixing. Then
by means of the Colburn analogy they were able to predict the heat
transfer coefficient. This work was then extended by Throsen and
Landis [389] for high heat transfer rates and large temperature differ-
ences in the radial direction. They were able to develop a diabatic
friction factor correlation in terms of the friction factor for flow
through a straight pipe that was valid for both heating and cooling,
and two Nusselt number correlations (one for fluid heating and one for
fluid cooling) that were functions of the Reynolds number and the
Grashof number. Bergles [74] in assessing the worth of these two
papers has concluded: "their semi-analytical prediction method appears
to account for all of their observed variation in hg with the swirl
flow of air subjected to large radial temperature gradients". (hg
defined as the heat transfer coefficient for swirling flow).
-------
90
Lopina and Bergles [388] developed a correlation based upon the pre-
mise that the observed heat transfer is due to the simple sum of
three effects: turbulent flow in a spiral channel, centrifugal con-
vection upon a density gradient, and the fin-effect. Their assumption
and calculations agrees well with the data for fluid heating but for
cooling a better prediction is obtained simply by neglecting the
centrifugal convection effect rather than by trying to make it inhibi-
tive of the heat transfer. Thus they sum three terms to predict the
Nusselt number for fluid heating and two terms for fluid cooling.
Recently there has been literature published for swirl-generating
inserts other than swirl tapes. Gutstein [393] in an extensive mono-
graph has investigated a family of inserts: helical vanes with and
without a centerbody and a wire-wrapped plug. Sketches of these geo-
metries together with the swirl tape and the wire coil are presented in
Figure 3, taken from his report. The distinguishing feature between
the swirl tape configuration and the helical vane configuration is that
in the latter case there is a single helical flow passage which would
appear to be more amenable to analysis and would, perhaps, be charac-
terized by a smaller pressure drop. The analytical model presented
for the prediction of the measured Stanton number provided an excellent
correlation for the helical vane configuration. However, when compared
to the swirl tape data available in the literature, the correlating
equation underpredicted the observed heat transfer.
In a configuration similar to Gutstein1s, Seban and Hunsbedt
[394] have obtained additional data supportive of his results. Their
correlation used a "straightened-out" length of the flow channel based
upon the known helix angle.
-------
91
Klaczak [395] has recently reported on the use of spiral and helical
turbulators to enhance the heat transfer in a tube. These configura-
tions have not been examined in detail here since their effect is
primarily through artificially increasing the wall roughness as there
is very little induced swirl. Megerlin [396] has used spiral brush
inserts to obtain heat transfer coefficients 5 times empty tube values.
These data also include the effect of heat transfer enhancement due to
entry-length effects (the length to diameter ratio of the apparatus
was 9-5) whereas the data is usually available only in terms of mean
Nusselt numbers obtained from fully developed flow in relatively long
tubes.
Klepper [397] in a recent paper claims to present the first
data for Nusselt number as a function of tube length in a decaying
swirl flow generated by swirl tapes. All the other data reported in
subsection (i.e. [373-397]) is for geometries in which the swirl gen-
erator, usually tapes, extends through out the entire heat transfer
length; in addition, all the data but that of Megerlin appears to be
obtained for sufficiently long tubes that any entry-length effect
present has been minimized. Klepper, on the other hand, has examined
sections for which the tube contains a length of swirl tape followed
by an extended section that is only a simple tube. He has obtained
data and a correlation under these combined effects of entry-length
and swirl decay. The local Nusselt number is correlated to be equal
to 0.023 Re°*8Pr°'4(T /T, )~°'5^9> where Re is the Reynolds number,
w b J. /
Pr the Prandtl number, T /Tfe the temperature ratio of the wall to the
bulk fluid and il) is the "Reynolds number modulus" for which he gives
' 1
-------
92
L. . y _ J
Twisted tape insert
Wire coil insert
"cb
Helical vane insert
I "afc.
T
Helical vane - without - centerbody insert
Wire-wrapped plug insert
Figure 3. Swirl Generators (taken from Gutstein [393] )
-------
93
an expression that, is a function of Reynolds number only, and i|'9 is
the entry length factor which is given as a function of distance from
the trailing edge of the swirl tape.
Further reference will be made to the data available for swirl
tape heat transfer, particularly the work of Klepper, in Chapter IV.
Scope, Significance, and Objective
of Research Investigation
In the area of incineration there appears to be three primary
needs worthy of investigation:
(1) A dependable, clean, and Inherently efficient incinerator
concept that would dispose of solid wastes without unacceptable
pollution levels.
(2) An incinerator configuration that would not require the usual
complement of stack devices to meet air quality standards.
(3) A device that would efficiently recover the energy liberated by
combustion.
The incineration configuration to be examined in this research
effort is anticipated to meet these three requirements. The concept
is that of a vortex furnace wherein the solid waste is used as fuel,
augmented as necessary by auxiliary fuels, and fed to the furnace in
a fluidized state carried by the feed air. The auxiliary fuel is
utilized to maintain the combustion process at a sufficiently high
temperature to insure the complete odor-free pyrolysis of the waste
material.
The vortex can be effectively generated by supplying the air
and fuel into a vortex chamber through tangentially opposing ports.
The attached vortex tube would be a water-walled furnace column from
which a significant fraction of the chemical energy liberated can be
-------
94
recovered. The outlet of the vortex tube would be connected to an
enlarged section whose purpose would be to trap any unburned parti-
culate much as a cyclone separator.
There are a number of unknown factors that would determine the
performance of such an incinerator concept:
(1) Heat transfer from a confined, conflagrant vortex flow has
never been examined in the literature and thus the amount of heat
recovery as a function of vortex tube length (or, in this case,
furnace column height) is at present both unknown and unknowable.
(2) Heat transfer under the conditions of vortex decay with entry-
length effect has not been examined for swirl generation by means
of tangential jets and thus its prediction is not yet possible.
(3) Gas temperature profiles in regions of confined, conflagrant
vortex flow with significant heat recovery have never been reported
in the literature.
The overall objective of this research effort was to obtain
the data and correlations necessary for these unknown factors that
would permit the prediction of the performance capability of a full-
size incinerator utilizing this concept of vortex combustion with
simultaneous heat recovery.
To this end, a laboratory-size incinerator has been designed,
constructed, instrumented, and operated to obtain the first body of
data for this concept. The configuration of the apparatus is described
in detail in Chapter II, the results of the data in Chapter III, and
the suggested correlations for heat transfer in a conflagrant, vortex
flow are given in Chapter IV.
-------
CHAPTER II
EXPERIMENTAL APPARATUS MD PROCEDURE
Experimental Apparatus
In order to achieve the outlined research objectives, a working
model of a fluidized, vortex incinerator was fabricated and assembled
within a separate four-foot concrete structure directly adjoining the
Thermal/Fluid Sciences Laboratory. This structure effectively isolated
the incinerator in a near-adiabatic enclosure as well as acted as a
safety chamber in the event of a structural failure during operation.
The controls for the operation of the incinerator were all located with-
in the laboratory itself.
Figure k illustrates the overall configuration of the vortex
incinerator installation.
Vortex Chamber
The vortex incinerator has two primary requirements essential for
operation: an arrangement for the generation of the vortex and a com-
bustion zone within which the flame front can be stabilized. As noted
in the literature survey, there are a variety of means used to generate
a vortex flow. The use of inlet vanes in conjunction with an induced
flow scheme was rejected because the blower required would need to operate
in a high temperature environment and thus necessitate a relatively ex-
pensive installation. Swirl tapes, helical vanes, etc., were also
95
-------
96
FOUR-INCH DIAMETER
STACK INSERT PIPE
29'
FLOW —
STRAIGHT-
ENERS
Butterfly,
Damper
EXHAUST
STACK
Separator
Furnace
Column
Thermocouple •
Vortex -
Chamber
70"
Sampling^ *T
Probe 19"
6.5'
A
Umbilical
Cord
64"
41
Water
•4.5"
II" Staksampler
Figure ;4. Overall Configuration of Vortex Incinerator
-------
97
rejected from consideration because: (l) manufacturing restrictions
greatly limit the intensity of swirl that can be generated with these
devices (it is not usually possible to obtain a tangential velocity com-
ponent exceeding the mean axial velocity component), (2) the high tempe-
rature environment anticipated in a conflagrant flow would require sophis-
ticated cooling techniques to maintain structural integrity of these
devices, and (3) because these generation devices introduce an unT
necessary uncertainty in the quantification of swirl level in that by
their very nature it is only possible to specify the twist ratio whereas
the degree of swirl experienced by the fluid motion is unknown. Since a
large reciprocating air compressor and an associated storage pressure-
vessel was . available in the laboratory complex, the. decision was made
tangential air inlets to generate the vortex flow.
Due to the intense mixing and turbulence anticipated, it was also
decided to use the vortex chamber as the combustion zone as well by intro-
ducing the fuel into the same area as the inlet air. A schematic of the
vortex chamber is given in Figure 5-
The side walls of the chamber were constructed of one-eighth inch
sheet steel rolled to an eighteen-inch diameter. The top and the bottom
of the chamber were made of three-eighths inch steel plate; grooves
(0.150 inch) were cut in the plates to permit insertion of the side walls.
These seams were then welded. The two air inlets, made of 1%-inch/
schedule UO pipe, were welded to the side walls at opposite corners of
the chamber as shown in Figure 5. A hole (5-76 inch diameter) was cut
in the top plate and a 0.2 inch deep inset was cut around this edge to
provide an opening and a supporting base for the furnace column. The
-------
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Figure 5. Vortex Combustion Chamber
-------
99
complete vortex chamber was mounted atop a steel table (workbench height)
that had been constructed in the four-by-eight structure.
Fluidized wastes entered the chamber through one of the air inlets
whereas the auxiliary fuel (propane was chosen) was supplied through a
pair of one-half inch stainless steel tubes mounted in the bottom plate
with Conax fittings (see Figure 5). These jets were located near the
walls in order to insure that the entering refuse would be immediately
exposed to the flame for ignition. The height of the jets with respect
to the bottom plate was not found to have a significant effect upon the
incinerator performance. It was necessary, however, to install reducers
within the stainless steel tubes because of instabilities introduced
into the propane feed system by pressure variations in the combustion
chamber; apparently without the reducers this was a dynamically unstable
system.
The initial propane inlet configuration was a single inlet located
in the center of the bottom plate. In this position a very stable flame,
more or less confined to the center of the chamber, was stretched verti-
cally in a narrow, cylindrical shape (approximately 2 inches in diameter)
through most of the furnace column much in the manner of that reported
by Albright [128, 129J. As a result, most of the entering refuse escaped
ignition, since the core of this flame was comparatively quiescent, and
was collected unburned. For this reason, the configuration was changed
to that described in the preceeding paragraph.
The three-quarter inch hole remaining in the center of the bottom
plate was then used as a drain line (to remove trapped water after rains)
and as a slag collector during slagging tests. The bottom plate acquired
a convex shape (when viewed from above) after several runs which permitted
-------
100
any liquids to collect above the central hole.
A small hole (one-eighth inch MPT) was tapped in the side wall of
the chamber to provide a means of starting the incinerator. A separate
propane tank (the standard size used for portable hand-torches) was used
for this purpose by means of an attached section of copper tubing that
was crimped off at the end except for a very small hole; when ignited,
a flame of approximately six inches in length could be provided by this
arrangement.
Various additional one-eighth inch WPT ports were provided in the
top plate of the chamber permitting the insertion of Honeywell MegopaK
Thermocouple Assemblies.
Figure 6 is a photograph of the vortex combustion chamber as
installed with the furnace column attached.
Furnace Column/Heat Recovery System
Since the primary objective of this investigation was to assess
the heat transfer capability of the vortex incineration concept, it was
necessary to design a heat removal scheme that would enable the recovery
of an economically significant fraction of the heat of combustion. This
component is a combination cylindrical tube attached to a vortex genera-
tor (see Figure 2b) and a heat sink and is referred to here as a "furnace
column".
The basic objectives in its design were to make the column long (to
allow enough residence time to remove a reasonable amount of thermal
energy), of small diameter (to maximize vortex velocities and hence maxi-
mize convection coefficient), and to use a good conductor (so that energy
transmitted to the interior wall by the hot gases would be readily trans-
mitted through the column's wall to the heat recovery medium). In
-------
Sec. 1 Cooling
Water Inlp.t
"
rFurnace Column
Sec. 1
Coo ling
Water
/ Outlet
......
a
......
Inlet ~ . Inlet
Air Air
Sec. 2
/' Cooling
Water
Outlet
Figure 6.
Vortex Combustion Chamber and Furnace Column
-------
102
addition, the size of the column was restricted to that available off-the-
shelf at reasonable cost. As a result af these considerations, the furnace
column was selected to be a six-foot long copper tube with an inside
diameter of 5.76 inches and a three-sixteenths-inch wall thickness.
Water was chosen as the heat recovery medium and the system was
designed to insure that boiling would not occur (again, in order to
maximize heat transfer). As a result, the column was divided into one-
foot sections with each section cooled by a separate water supply. Only
five feet of the column was actually cooled; the remaining one foot
extended inside the separator. In a full-size, commerical installation
these cooling coils could—and probably should—be located inside the
furnace column to maximize heat recovery. Due to the relatively small
diameter of this column it was not possible to install the coils inter-
nally. The cooling water flowed through one-quarter inch (outside dia-
meter) copper refrigeration tubing that was wrapped spirally around the
furnace column at a rate of approximately sixteen turns per foot (this
corresponds to approximately a nine-sixteenths-inch gap between adjacent
tubing). The flow direction was selected to achieve a slight counter-
flow effect. To facilitate removal of the column, each section of cooling
coil terminated in a six-inch leader which was connected to the water
system with a Swagelok union. Figure 7 is a schematic of a typical one-
foot section of cooling coil and Figure 8 is a photograph of the in-
stalled furnace column.
*
The five water supply lines were fed by a single two-horsepower
pump that acted as a booster pump to a main city water supply line.
The discharge pressure was approximately 125 psig and the total flow to
-------
WATER SUPPLY TO OTHER
STATIONS
INLET_
WATER"
I'
16 TURNS
(5
MANIFOLD
FLOWMETER
THERMOCOUPLE
FURNACE COLUMN
MIXER
k5/ OUTLET
"WATER
u
©
DISCHARGE
o
LO
Figure 7. Furnace Column Cooling Water Schematic (Typical Section)
-------
Furnace Column
Fluidizing Auger ~
'i"
Combustion Chamber
Figure 8.
Furnace Column
'- Inlet
Air
t-'
o
~
-------
105
all five sections was approximately 2l+0 gallons per hour (nominally
60 gph went to the bottom section and with k$ gph supplied to each of
the other four sections). The discharge water from each section was
routed to a mixing chamber where its temperature was measured and then
it was simply discharged.
Initially the cooling coils were thought to be amenable to attach-
ment to the column by means of silver solder. However, the copper fur-
nace column was such a good heat conductor that the silver simply would
not melt (its melting point is about 1200°F). It was then necessary to
use lead-tin solder (melting point ^00°F) which worked satisfactorily.
There was some a priori concern that the column would heat up to the
solder's melting point during operation, but by insulating it from the
very hot vortex chamber, and by insuring an adequate flow rate of water,
this problem never materialized.
An eight inch square copper plate (with a 5-76 inch hole), one-
quarter of an inch thick (hereafter referred to as the "copper base
plate") was then silver-soldered to the base of the furnace column.
This base was in turn attached to the top of the vortex combustion chamber
with a one-eighth-inch thick asbestos separating gasket (to minimize gas
leakage and conduction heat transfer from the hot vortex chamber).
At the midpoint of each one-foot section, a one-eighth inch tap
was provided between the refrigeration tubing. MegopaK thermocouples
were then installed permitting the measurement of the gas temperature at
five different vertical stations (6, 18, 30, k2, and 51* inches above the
vortex chamber) as well as at various radial positions at each station;
thus each "station" is located at the mid-point of each respective
-------
106
"section". Figure 9 illustrates the location of these thermocouple taps
and Figure 10 the method of obtaining temperature measurements as a
function of radial position. Static pressure taps were also installed
at various points along the column although it became exceedingly diffi-
cult to obtain any reliable data (due to condensation) and hence they
were not used further.
An additional tap was also provided for installation of an aspi-
rated thermocouple. This device will be discussed further in Appendix E.
Separator
One of the advantages of using vortex flow in an incineration
concept is that it provides a ready means of separating particulate
matter. The separator designed for this incinerator is illustrated in
Figure 11.
The entrapment of particulate is achieved by providing a cylindri-
cal section approximately one-foot high with an inside diameter of eighteen
inches rather than the 5-76 inch diameter of the furnace column. At
the bottom of the separator an annular trough three inches wide and three
inches deep was provided to prevent the separated particulate from being
picked-up and reintroduced into the primary flow pattern. A 1% -inch
diameter port was installed in the bottom of this trough to permit con-
tinuous ash removal (via a suction pump) in the event it became necessary.
Because of the small volumes of refuse incinerated by this apparatus, this
port was never utilized; only occasional emptying of the trough was neces-
sary and this was done simply by removing the separator itself, and dumping
the accumulated particulate.
The separator was constructed of 16 gauge galvanized steel and
-------
107
72.5
72'
-a
•o-
SEPARATOR
FURNACE
COLUMN
Copppr
Base Platp
VortPX Chamber
Top Plate
EXHAUST
STACK
r
o
Station 5
12'
12'
12'
Station 4
Station 3
Station 2
12'
Station 1
Figure 9. Thermocouple Locations
-------
108
Honeywell MegopaK
Chrome1-Alumel
Thermocouple
Furnace
Column
Wall
CD
Figure 10. Gas Temperature Measurement System
-------
109
EXHAUST
STACK
ASH
TROUGH
FURNACE
COLUMN
Figure 11. Separator
-------
110
was attached to the furnace column by means of the collar shown in
Figure 12. The collar was bolted directly to the bottom of the sepa-
rator and then the entire assembly was slipped over the furnace column
and locked into place by tightening the five-sixteenths inch bolt provided
in the collar. In addition, the separator was also supported by a 1
inch angle-iron frame that was built up from the table. This arrangement
can be seen in Figure 13.
A ten-inch coupling (visible in Figure 13) was welded to the top
of the separator to provide for attachment of the exhaust stack. The
stack slipped over this fitting and could be removed easily. Ridges on
the coupling made the connection nearly air-tight although Carey MW-50
insulating cement was also used on this and all other connections.
Inside this coupling, and atop the separator, mounting bolts were
provided so that exit sections of various diameters could be used in the
incinerator's operation. Three different diameters were used: 6, h, and
2 inches. These orifice sections resembled a top hat although both ends
were, of course, open. Figure 13 is a photograph of one of these orifices
as it is being installed (it is barely visible in the upper right-hand
corner of the picture). Use of these three orifices constituted one of
the independent variables investigated.
Exhaust Stack/Sampling Equipment
The exhaust stack was constructed from a single, spiral tube of 20
gauge galvanized steel, ten inches in diameter and fourteen feet high.
It was attached directly atop the separator to the coupling provided and
it ended a safe distance above the roof of the laboratory.
A butterfly damper was installed in the stack approximately thirty
-------
Ill
Separator
Attachment—
Taps (four)
\
Furnace
Column
Figure 12. Collar
-------
Angle-Iron Support
>-'
>-'
N
Top of Separator
Figure 13.
Separator and Exhaust Stack Coupling (Exit Orifice Removed)
-------
113
inches above the separator. Its original purpose was to provide a means
Of assessing the performance of the incinerator under various back pres-
sures. However, the use of the damper was awkward and the resulting
charges in back pressure did not appear to be adequately reproducible,
and, since the effect was observed to be minimal, it was left in the full
open position for all the data taken.
A photograph of the exhaust stack together with the separator and
the top of the furnace column is shown in Figure 14.
A commercially manufactured sample train—Research Appliance Corpo-
ration "Staksamplr" Model 23^3—was installed on the roof of the labora-
tory to isokinetically sample the stack. The installation was done to
conform to the requirements given in Specifications for Incinerator
Testing at Federal Facilities [398, 399]- Figure 15 is a photograph of
the actual installation.
In order to satisfy the requirements of the Staksamplr two modifi-
cations to the exhaust stack were necessary. First, flow straighteners
were installed (see Figure k) that would convert the vortex flow into a
simple axial flow; these straighteners consisted of a bank of half-inch,
thin-wall, aluminum tubes six inches long. Second, a four-inch diameter
insert pipe was installed (also illustrated in Figure h) to provide stack
velocities high enough (17 feet per second minimum) to permit the sample
to operate isokinetically; the top of the stack was plugged except for the
four-inch opening thus effectively reducing the flow diameter from ten
inches to four. It should be noted that virtually all the temperature and
heat transfer data presented in Chapter III were obtained with this insert
removed; it was installed primarily for the sampling efforts. However,
-------
114
But terfly
Damper
Figure 14.
Exhaust Stack, Separator, and Furnace Column
Exhaust
Stack
eparator
Furnace
Column
-------
.~'t
t-'
t-'
Ln
Figure
15.
"Staksarnp1r"
Installation
-------
116
since an orifice was always used at the separator exit, the operating
performance of the incinerator was not noticeably affected by its presence
or absence.
Fluidizer
In order to operate this apparatus as an incinerator, some method
of ingesting the refuse was necessary. The most convenient means of
doing this was to fluidize the refuse in one of the air supply lines to
the vortex chamber. The use of the word "fluidized" should be distin-
guished from its use by chemical engineers with respect to fluidized beds;
the objective here was not to mobilize the refuse en masse, but merely
to use the air as a carrier for the fuel much as in an automobile carbure-
tor. In a full-size commerical incinerator it would be feasible to provide
separate ports where the refuse, truly "fluidized," could be ingested.
The device designed to accomplish this objective is visible in
Figure 8. It should be noted that the refuse was. fluidized into only one
of the two air lines; however, the turbulence level in the vortex com-
bustion chamber was sufficient that no uneven burning effects were detected.
The fluidizer was constructed from a plexiglass tube four-feet
long and six-inches in diameter which was mounted vertically as shown in
Figure 8. This tube acted as a hopper whereby a charge of refuse could
be stored. The refuse was injected to the three foot horizontal section
of plexiglass by means of a reducer/tee section which was machined from a
single block of plexiglass. All joints were fused with acetone.
Plexiglass was chosen so that feed rates could be determined (to
insure a uniform rate of ingestion) and also to provide a means of de-
tecting clogging as different kinds of refuse were tested.
-------
117
Initially it had been hoped that simple gravity feed in conjunction
with the venturi effect would be sufficient to cause the refuse to leave
the hopper. These attempts, however, were unsuccessful as the natural
packing of the refuse prevented any significant amount of the material
from dropping through the tee section. Even pressurizing the hopper did
not measurably improve the situation. Finally an earth auger driven at
5^ revolutions per minute by an electric motor providing 0.308 foot-pounds
of torque achieved the desired results, although stirring rods (attached
to the auger) were necessary to prevent the auger from simply boring out
a cavity in the refuse. The drive shaft consisted of a five-sixteenths
steel rod which was inserted through the lid sealing the top of the hopper.
These components are shown in the photograph given as Figure 16. Thus
the operating procedure required charging the hopper with refuse, sealing
the lid, and then attaching the motor prior to each data run. Sealing
the top of the hopper was necessary because it was discovered that non-
uniform feed rates would result because of the changing height of the
refuse column when the lid was left off.
Initially it had been hoped that a variety of products would serve
as refuse: shredded computer cards, shredded leaves, shredded newsprint,
digested paper, sawdust, wood chips, grass clippings, potato peelings,
etc. Several difficulties were encountered as many of these substances
were tried but the principal problem was that of the effect of scale.
Specifically, because this incinerator was not full-size, various dimen-
sions were, naturally, restricted; one of these dimensions—air inlet
diameter—proved to be crucial here. The inside diameter of the air inlet
pipe was 1.6 inches; this dimension in turn limited the maximum diameter
of the outlet of the fluidizing hopper. This situation prevented most of
-------
118
i!!I
II
Figure 16.
Fluidizer Motor/Drive Shaft
Motor
Shaft
Pressur-
ization
Line
(Not
used)
Hopper
-------
119
the previously mentioned materials from being fluidized. With the
shredding facilities available (a Sears Lawn and Garden Shredder) the
newsprint, cards, etc., could never be made small enough to work. As a
result, all the refuse data was taken using a mixture of woodchips,
sawdust and wood shavings which was obtained by sweeping a local cabi-
net maker's floor; when the term "refuse" or "sawdust" is used through-
out this report it refers to this mixture. Figure 17 is a photograph of
this "sawdust".
When the sawdust mixture was used, the hopper was capable of
holding about four pounds and the motor/auger caused it to be ingested at
a rate of about thirty-five pounds per hour. This permitted approximately
five minutes of operation per charge—which turned out to be very limiting
when stack sampling was attempted.
Air/Propane Supply System
The air supply system necessary to drive the vortex (as well as
oxidize the fuel) was provided by a UOOO cubic foot storage tank which was
pressurized to approximately 150 psig prior to each run. This supply was
divided into two separate lines each with its own regulating valve.
Propane was selected as the fuel since it was readily available
in one-hundred pound tanks. The propane was filtered and regulated prior
to being supplied to the combustion chamber.
The use of propane was necessary for two reasons. First, some means
of igniting the refuse initially was required; in the case of low heating
value refuse (or wet refuse), auxiliary fuel such as propane would also
be necessary to maintain combustion (although this was not the problem
here). Second, because of the inconvenience of the use of the refuse and
-------
~¥-..;;';..
~;. -<}""~~. :.00
Figure
17.
Sawdust Mixture
"
> .
>-"
N
o
-------
121
the associated short operating times, propane alone as the fuel was used
to assess the performance of the incinerator. Thus all the quantitative
data presented in Chapter 3 (heat recovery, heat transfer, and tempera-
/
ture profiles) was obtained using propane as the sole fuel.
Instrumentation and Calibration
Temperature data were obtained using 2J chromel-alumel and 8 copper-
t
constantan thermocouples. All of the thermocouples together with the
associated extension, wire was purchased from Honeywell, Inc.
Sixteen of the chromel-alumel thermocouples were of the MegopaK-Type
•
(Model No. 2K2M13-G-6-5-T, one-eighth-inch outside diameter, 3C)U stainless
steel sheath material, integral measuring junction, compression fitting
attachment, and Quick Konnect electrical connection); the remaining eleven
chromel-alumel thermocouples (used to obtain furnace column wall tempera-
tures) were fabricated from bulk thermocouple wire. All the eopper-con-
stantan thermocouples were also of the MegopaK-Type (Model Ho. 2T2M13-G6-
5-T, similar in all respects to the chromel-alumel assemblies except for
calibration-type).
These data were permanently recorded on either of two multichannel
strip charts or on a twenty-four channel digital recorder. Details of the
recording equipment and the calibration procedure are presented in Ap-
pendix A.
The temperature of the inlet air and propane was measured ("to
determine mass flow) and also of the five inlet and outlet cooling water
lines (to determine heat recovery). In addition, the furnace column
wall temperature was measured at eleven locations while the combustion
gas temperature measured at five stations (see Figure 9) for thirteen
radial positions. Various additional temperature measurements were made
-------
122
in the vortex combustion chamber, the separator, and the exhaust stack.
Manometers were used to measure the inlet pressure of the two air
supply lines and the propane supply'line. Together with the tempera-
ture data this permitted a determination of the density.
Eight Fisher and Porter Rotameters were used to determine the
flow rate of the two air supplies, the propane supply, and the five cool-
ing water supplies. The water and propane flow meters were calibrated
using a simple weight-change procedure.
The calibration procedure and results for these measurements are
also presented in Appendix A.
Procedure
The start-up procedure for the operation of the vortex incinerator
was very straight-forward. First, the air storage tank pressure was
checked to ascertain whether an adequate supply of compressed air was
available, if the pressure was below approximately 100 psig, the Ingersoll-
Rand reciprocating air compressor was activated until the tank was pres-
surized to approximately 200 psig. Next, the cooling water supply valve
was opened and the boost pump energized. After a wait of several minutes
a steady-state, bubble-free flow of water was established in the cooling
system as observed through the glass tubes in the rotameters. Then one of
the two tangential air supply valves was cracked open to provide a slight
flow of air. The propane starter tank with the crimped-off copper line
(.as already described in the subsection on the vortex chamber) was ignited
and positioned on the steel table so that a six-inch flame would extend
past the open one-eigth inch NPT port on the side of the vortex chamber.
Next the main propane supply valve was cracked open resulting in a slight
-------
123
vacuum within the vortex chamber which in turn sucked in the pilot flame
from the portable propane tank and thus ignited the incinerator. The
air and propane supply valve were then brought open in steps until each
of the rotameters were indicating 30$ of full-scale. This operating
condition is one of three that were examined in detail and is referred
to as Condition 3 in Chapters III and IV. Once steady-state combustion
had been confirmed, the pilot propane tank was shut-off and the WPT port
plugged.
The strip chart recorder-motors were then started (their electronic
sections were usually left on overnight) and the incinerator temperatures
were monitored for the attainment of steady state conditions. This
usually required about thirty minutes. Once the incinerator was fully
warmed-up, only about ten minutes was required to stabilize the tempera-
tures as various changes in operating conditions were imposed.
Once steady-state operation was confirmed for the flow conditions
to be examined, data were recorded and a run number assigned. The data
customarily recorded for a run were as follows:
(l) The flow rates of
(a) each of the two tangential air supplies,
(b) of the propane supply, and
(c) of each of the five cooling water supplies;
(2) the total pressure of
(a) each air supply line, and
(b) the propane supply line;
(3} the temperatures of
Ca) the air supply,
(.b) the propane supply,
-------
Cc) the water inlet supply
Cd) each of the five cooling water outlet lines, and
(e) the furnace column wall and vortex gas as it was
instrumented at the time;
the barometric pressure.
The radial temperature profiles of the conflagrant, vortex flow
were obtained at the 5 vertical stations by positioning the sheathed
thermocouples at thirteen different insertion depths. This was done by
using dial calipers to measure dimension B on Figure 10. Since di-
mensions A and C were known, the penetration depth, D, could be readily
determined. The radial positions examined together with the data is
presented in Chapter III.
To facilitate data reduction, two programs were written for the
Monroe Desk Calculator Model l655> card-punched, and de-bugged thus
assuring an error-free algorithm. The details of these programs are
given in Appendix B.
-------
CHAPTER III
RESULTS AND DISCUSSION
Independent Variables Investigated
There were four variables selected as independent whose influence
on heat transfer and temperature profiles was examined:
(l) air/fuel ratio,
(2) total mass flow rate,
(3) exit orifice diameter,
(U) inlet air-line diameter.
The incinerator has operated successfully at air/fuel ratios
from 15-3 to 33-5 and total mass flow rates from 60 to 355 pounds per
hour in thirty different combinations; these combinations are henceforth
referred to as Conditions. A complete tabulation of these 30 Conditions
is given in Table 5. It was decided to examine the effect of air/fuel
ratio and mass flow rate by taking data for three of these thirty combi-
nations; these were Conditions 3, 8, and 12. Condition 3 is very close
to stoichiometric (slightly fuel rich), whereas Conditions 8 and 12 both
represent an excess-air state (approximately 130$ of theoretical). The
nominal flow rates and air fuel ratios for these three Conditions is given
in Table 6.
The third independent variable, the effect of exit orifice diameter,
was examined by taking data with three different-sized exit sections (as
described in Chapter II): 2, U, and 6-inch diameters. These are referred
125
-------
126
TABLE 5
SUMMARY OF OPERATING CONDITIONS
Condition
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
- 24
25
26
27
28
29
30
Air Flow Rate
(Ibm/hr)
77.4
119.7
119.7
167.0
267.0
167.1
220.4
216.5
216.6
216.8
354.9
276.5
276.2
347.2
60.2
78.8
78.8
98.6
119.6
131.3
143.5
143.5
143.5
143.6
155.9
168.9
182.4
195.0
207.9
221.5
Propane Flow Rate
(Ibm/hr)
3.88
5.19
7.83
5.20
7.84
10.55
7.83
10.45
13.17
6.48
10.45
13.36
16.19
13.39
3.92
3.92
.5.24
5.25
5.25
5.25
5.25
6.58
7.93
9.30
5.23
5.24
7.92
7.93
7.92
7.92
Air/ fuel Ratio
19.9
23.1
15.3
32.2
21.3
15.8
28.1
20.7
16.4
33.5
26.6
20.7
17.1
25.9
15.3
20.1
15.0
18.8
22.8
25.0
27.3
21.8
18.0
15.4
29.8
32.3
23.0
24.6
26.2
28.0
-------
127
TABLE 6
INDEPENDENT VARIABLES INVESTIGATED
Mass Flow Rate and Air/Fuel Ratio
Condition Air/Fuel
3 15
8 20
12 20
Exit Configuration
1
2
3
Inlet Configuration
A
B
C
Ratio Propane Flow Rate Total Flow Rate
(Ibm/hr) (Ibm/hr)
7.9 125
10.5 220
13.3 280
Exit Configuration
Exit Diameter Exit Velocity Ratio
(inches)
2 9.00
, 4 2.25
6 1.00
Inlet Configuration
Inlet Area Inlet Velocity Ratio
(sq. ft.)
0.00418 3.36
0.00616 2.28
0.00140 1.00
-------
128
to as exit Configurations 1, 2, and 3 respectively. For simple axial
flow, ConriRurutJon 1 should cause an exit velocity 9 times that of
Configuration 3 based upon continuity considerations (when at the same
temperature). In addition, the> presence of different exit diameters could
cause a change in the distribution of the solid-body rotation and potential-
vortex regions as described by Thompson [166]. It is also possible that
the change in the exit diameter could be the cause of a ,drastic alteration
of the flow field in the manner described by Lewellen [1051 and quoted in
Chapter I, wherein the flow could be made to experience a "jump" at the
bottom plate of the vortex chamber for one exit Configuration whereas
remain supercritical throughout the furnace column with a breakdown in the
exhaust stack for another exit Configuration. The exit Configurations
examined are also summarized in Table 6.
The fourth independent variable, the effect of inlet-air-line dia-
meter, was examined by installing sleeves of different internal diameters
in the tangential air supply-lines attached to the vortex chamber. The
effect of the sleeves was to increase the vortex velocity at the same mass
flow rate. Without any sleeve, the inside diameter of each supply line
was 1.602 inches which corresponds to an area of 0.01^0 square feet; this
arrangement is referred to as inlet Configuration C. The largest internal-
diameter sleeve used had a bore of 1-1/16 inches (flow area of 0.006l6
square feet) and is referred to as Configuration B. The smallest sleeve
diameter that was successfully utilized was- 7/8 inches (flow area O.OOUlS
square feet) and is designated Configuration A. Two smaller diameter sleeves
were fabricated (1/2 and 3/h inch), but it was not possible to ignite the
air/propane mixture with, the high inlet velocities generated (velocity ratios
of 10-3 and U.6, respectively, with respect to Configuration C). Based upon
-------
129
the continuity relation Configuration A has an inlet velocity 3.36 times that or
C while B has a velocity of 2.28 times C. The geometry and velocity
characteristics of the three inlet Configurations are also summarized
in Table 5.
Whenever data is presented without a specification of the exit and
inlet Configuration it should be presumed to be 3-C (i.e. exit Configuration
3 and inlet Configuration C).
Heat Recovery/Vortex Gas Temperature-Profile Data
Since the demonstration of efficient heat recovery at sufficiently
high gas temperatures was the major objective of the investigation, these
data constitute the primary achievement of the experimental phase. There
are two heat recovery rates of interest: the total heat recovery rate
which is obtained by summing the rates recovered at each of the five
cooling-coil sections, and the heat flux recovered as a function of furnace
column height (or, equivalently, vortex tube length) which is obtained by
dividing the heat recovered at each section by the area of each section
(1.508 square feet).
Effect of Exit Configuration and Condition
Since it was desired to examine the effect of three exit Configu-
rations and three Conditions there were nine possible operating combinations.
Thus, in order to obtain a thirteen-point radial temperature profile of
the vortex gas, at the five selected vertical locations identified in
Figure 9 (called Stations), it was necessary to perform thirteen runs
for each of the nine operating combinations or a total of 117 runs. In
addition to obtaining the temperature profile data, heat recovery rates
-------
130 .
were determined for each of these runs yielding 13 data points for each
operating combination (although, due to equipment failures of one sort or
another, the average number of data points actually reduced to obtain heat
recovery rates was between 11 and 12 for each combination). The flow rate
and associated heat recovery data for Conditions 3, 8, and 12 for exit
Configuration 1 are presented in Table 7; there are 13 points for Condition
3, 12 for Condition 8, and 11 for Condition 12. The data for exit configu-
ration 2 is given in Table 8 and for exit Configuration 3 in Table 9- All
these data are for inlet Configuration C. Since a reasonable number of
data points were available for the same Condition and Configuration, it was
possible to perform a statistical analysis to obtain the mean, the standard
deviation, and the standard deviation of the mean. These results are given
in Table 10 for all 9 combinations of heat recovery data.
The temperature profiles of the vortex gas obtained in these 117
runs are presented in Tables 11 (for Configuration 1-C), 12 (for Configuration
2-C), and 13 (for Configuration 3-C) for each Station.
If the velocity profiles were known, it would be possible to obtain
the mixed-mean temperature (sometimes also called the mixing-cup tempera-
ture or the bulk temperature) defined ([1|00]> page 105) by the following
relation:
r
T = -.^ U T r dr (l)
U A
:C
However, since these data would be exceedingly difficult to obtain as well
as of dubious value due to the disturbance effect of the inserted probes,
a calculated or assumed profile is necessary to perform the above integration.
As indicated in Chapter I, there does not yet exist an analytical means
-------
131
TABLE 7
CONFIGURATION 1 HEAT RECOVERY DATA
Flow Rate
A1r
119.7
117.9
116.8
116.5
115.5
116.5
116.4
116.7
117.2
116.1
115.9
116.8
116.3
216.5
216.0
215.6
213.5
214.0
214.3
214.3
214.9
213.5
212.8
215.3
213.5
276.5
273.8
275.8
274.0
274.9
274.8
274.9
273.3
272.5
275.6
273.2
(Ibm/hr)
C3H8
7.83
7.86
7.83
7.84
7.70
7.83
7.89
7.88
7.89
7.80
7.74
7.84
7.86
10.45
10.52
10.55
10.50
10.51
10.60
10.59
10.59
10.44
10.40
10.52
10.54
13.36
13.17
13.32
13.26
13.37
13.35
13.34
13.17
13.22
13.32
13.25
Air/
Fuel
Ratio
15.29
15.00
14.92
14.86
15.00
14.88
14.75
14.81
14.85
14.88
14.97
14.90
14.80
20.72
20.52
20.44
20.33
20.36
20.22
20.24
20.29
20.45
20.46
20.47
20.26
20.70
20.79
20.71
20.66
20.56
20.58
20.61
20.75
20.61
20.69
20.62
Heat
Sec. 1
20,120
16,170
19,760
19,410
17,050
18,920
19,620
22,040
21 ,880
20,670
20,530
21,150
22,430
28,030
25,150
30,190
29,470
27,880
29,440
31 ,280
30,780
29,340
29,820
31,640
33,420
32,340
34,140
33,530
33,060
35,390
35,190
36,790
34,100
35,080
36,260
36,510
Flux Recovered
Sec. 2
12,380
9,950
12,160
12,930
10,780
12,930
14,300
15,010
13,890
13,170
13,030
14,400
14,370
15,260
12,610
16,800
15,570
14,610
15,640
17,190
16,700
15,700
15,990
17,430
18,200
18,800
19,240
19,770
19,160
21,300
20.820
21,900
20,360
20,780
21,540
21,540
Sec. 3
9,290
9,510
9,730
9,730
8,400
8,620
10,390
9,290
9,510
8,850
8,960
9,290
9,400
11,940
11,500
11,500
11,720
11,050
12,270
12,390
11,940
11,140
11,610
11,940
11,940
14,380
14,600
15,040
14,600
15,590
13,270
16,580
15,700
15,150
15,?60
15,700
(Btu/hr-ft2)
Sec. 4
6,630
7,080
7,080
7,080
5,970
6,630
7,960
7,080
7,300
6,630
6,630
7,300
7,080
9,730
9,290
9,290
9,290
• 8,630
9,730
9,730
9,290
8,960
9,180
9,290
9,510
11,500
10,840
11,500
11,050
12,160
11,940
13,160
12,610
12,270
12,390
12,390
Sec. 5
6,190
6,410
6,510
6,410
5,530
5,970
7,520
6,410
6,520
6,190
5,860
6,740
6,630
9,290
9,100
9,200
9,290
8,400
9,510
9,510
9,510
8,960
9,190
9,290
9,400
11,500
10,990
11,500
11,050
12,160
12,160
12,940
11,940
11,940
12,160
12,490
Total Heat
Recovered
(Btu/hr)
82,350
74,070
83,300
83,780
71,980
80,030
90,160
90,220
89,120
83,710
82,960
88,790
90,340
111,970
102,020
116,090
113,610
106,420
115,500
120,790
117,960
111,740
114,290
120,020
124,360
133,490
135,430
137,740
134,090
145,670
140,820
152,870
1-12,820
143,590
147,200
148,730
-------
TABLE 8
CONFIGURATION 2 HEAT RECOVERY DATA
Flow Rate
Air
115.5
115.5
115.0
115.7
115.5
115.3
113.9
113.7
115.5
115.5
115.5
115.0
207.6
205.8
205.8
207.4
205.8
205.8
205.8
205.8
207.6
206.6
206.0
205.8
264.2
261.3
260.2
264.2
261.5
262.6
261.3
261.3
264.2
264.3
261.3
261.1
(Ibm/hr)
C3H8
7.92
7.88
7.85
7.88
7.84
7.86
7.90
7.87
7.89
7.87
7.85
7.81
10.65
10.57
10.50
10.58
10.51
10.52
10.62
10.59
10.59
10.57
10.54
10.49
13.41
13.33
13.24
13.32
13.22
13.20
13.39
13.34
13.35
13.34
13.27
13.24
Air/
Fuel
Ratio
14.58
14.66
14.65
14.68
14.73
14.67
14.42
14.45
14.64
14.68
14.71
14.72
19.49
19.47
19.60
19.60
19.58
19.56
19.38
19.43
19.60
19.55
19.54
19.62
19.70
19.60
19.65
19.83
19.78
19.89
19.51
19.59
19.79
19.81
19.69
19.72
Heat
Sec. 1
24,340
24,880
24,340
24,340
23,110
23,650
23,290
23,290
23,630
23,790
24,520
24,140
32,220
34,370
30,960
32,220
31,410
31 ,060
30,710
31,730
31,140
31,940
32,310
31,580
35,620
38,300
35,620
36,870
36,350
37,060
35,800
37,240
36,050
36,300
38,480
35,760
Flux Recovered
Sec. 2
14,280
16,870
15,250
15,090
14,490
15,010
15,970
14,760
14,920
14,920
16,630
16,430
19,850
18,880
16,820
18,440
20,360
17,190
20,090
19,560
17,120
17,540
19,810
18,280
20,940
24,690
23,350
21,550
23,960
21,060
23,240
24,320
21,270
23,720
24,950
23,350
Sec. 3
11,130
11,540
11,130
10,900
10,780
10,940
10,410
11,380
10,760
10,810
11,250
11,370
13,800
13,800
12,710
13,290
13,170
13,310
12,590
13,080
12,840
13,090
12,840
13,220
15,850
16,020
16,020
16,170
16,460
15,980
15,600
15,730
15,400
15,810
16,110
15,440
(Btu/hr-ft2
Sec. 4
7,960
8,180
8,180
8,400
7,410
7,850
7,960
7,850
8,070
7,960
8,400
8,180
10,440
10,610
9,950
10,440
10,390
9,990
9,770
10,280
9,730
9,990
10,220
10,170
12,380
12,940
12,490
13,160
13,270
12,600
12,380
12,720
12,500
12,160
12,720
11,830
)
Sec. 5
7,850
7,740
7,410
7,850
7,850
7,410
6,970
7,300
7,520
7,190
7,740
7,740
9,990
10,660
10,060
10,390
10,170
9,950
9,770
9,990
9,730
10,390
10,500
9,770
13,160
13,050
13,160
13,270
13,420
12,600
12,600
12,720
12,500
12,380
12,600
12,160
Total Heat
Recovered
(Btu/hr)
98,860
104,370
100,000
100,400
95,970
97,810
97,420
97,390
97,870
97,520
103,360
102,330
130,140
133,190
121,390
127,850
128,930
122,900
125,060
127,640
121,480
125,090
129,200
125,190
147,710
158,340
151,760
152,340
156,020
149,740
150,230
154,920
147,360
151,360
158,130
148,600
-------
133
TABLE 9
CONFIGURATION 3 HEAT RECOVERY DATA
Flow Rate
Air
114.2
114.0
113.8
114.5
116.8
116.8
116.8
114.6
115.5
115.5
115.5
115.5
113.7
205.3
209.6
204.9
205.8
208.5
205.4
209.0
204.4
208.5
206.2
207.6
205.8
205.8
260.2
259.7
258.8
265.1
260.1
262.0
260.2
262.4
264.2
261.3
259.8
(Ibm/hr)
C3H8
7.81
7.82
7.71
7.74
7.88
7.85
7.89
7.85
7.89
7.82
7.94
7.88
7.82
10.51
10.50
10.34
10.35
10.58
10.54
10.58
10.50
10.56
10.50
10.68
10.60
10.53
13.23
13.22
13.01
13.38
13.28
13.36
13.17
13.22
13.46
13.34
13.28
Air/
Fuel
Ratio
14.62
14.58
14.76
14.79
14.82
14.88
14.80
14.60
14.64
14.77
14.55
14.66
14.54
19.53
19.96
19.82
19.88
19.71
19.49
19.75
19.47
19.74
19.64
19.44
19.42
19.54
19.67
19.64
19.89
19.81
19.59
19.60
19.76
19.85
19.63
19.59
19.56
Heat
Sec. 1
23,830
23,450
24,000
22,590
24,350
23,430
24,520
23,450
23,800
22,140
22,570
23,120
21 ,350
31 ,540
30,790
31,760
3U760
32,700
31 ,000
32,220
31,140
31,860
31,130
31,710
31 ,760
30,560
35,920
34,940
37,760
37,670
35,910
37,050
35,800
36,870
36,470
36,050
35,370
Flux Recovered
Sec. 2
15,090
14,640
15,330
15,330
16,700
15,650
16,090
15,890
16,100
14,920
15,160
15,850
14,300
18,440
17,670
18,440
17,240
17,770
15,650
16,900
15,940
17,430
17,120
17,850
17,670
16,940
21,460
20,820
23,720
22,010
20,780
22,030
21,060
21,780
21,810
21,080
20,450
Sec. 3
10,170
10,590
10.540
10,540
11,420
11,370
11,420
11,300
11,180
10,640
10,810
11,260
10,340
12,830
12,340
12,210
12,330
12,950
12,350
12,950
12,590
13,070
12,840
12,960
13,310
12,830
15,610
15,370
15,980
16,140
15,410
16,220
15,490
16,220
15,890
15,770
15,490
(Btu/hr-ft2
Sec. 4
7,410
7,630
7,520
7,410
8,400
8,620
8,180
8,400
8,400
7,960
7,960
8,400
7,630
9,840
9,180
9,730
9,400
10,440
9,620
10,440
9,780
10,500
10,220
10,280
10,440
10,060
11,940
11,940
11,940
12,830
12,160
13,050
12,610
13,050
12,830
11,500
12,500
)
Sec. 5
7,080
6,970
6,970
6,860
7,740
7,960
7,740
7,520
7,960
6,860
7,300
7,960
6,970
9,840
9,400
9,510
9,400
10,280
9,330
10,280
10,060
10,500
10,060
10,280
10,280
9,780
12,160
12,160
12,160
12,830
12,380
13,270
12,610
13,270
13,050
11,500
12,500
Total Heat
Recovered
(Btu/hr)
95,880
95,430
97,050
94,600
103,460
101,080
102,470
100,370
101,700
94,280
96,210
100,420
91,370
124,390
119,700
123,130
120,840
126,880
117,550
124,850
121,410
125,710
122,710
125,290
125,860
120,900
146,410
143,610
153,150
153,030
145,730
153,240
147,140
152,590
150,880
144,620
145,230
-------
TABLE 10
MEAN, STANDARD DEVIATION,AND STANDARD DEVIATION OF THE MEAN OF THE HEAT RECOVERY DATA
Configuration , Condition
1 . 7 1 T -
- ; ^ 1 A """'
I
c =
8
J
i
! 12
i
cm=
x =
Flow Rate (Ibm/hr)
Air C,H0
o o
116.79 7.830
1.06 O.C55
0.29 0.016
214.52 10.518
o = 1.15 0.053
V
x =
.a =
anf
2 3 i x =
i C =
8
i
1
12
;
3 ' 1
i
! 8
i
12
i
!
°nf
x =
a =
am=
x =
a =
°m=
x =
am=
>T =
0 ~
CRT
x =
a =
am"
0.33 0.018
274.48 13.285
1.23 0.074
0.37 0.022 -
115.13 7.858
0.66 0.029
0.19 0.008
205.32 10.561
0.77 0.050
0.22 0.014
262.29 13.304
1.52 0.058
0.44 0.020
115.17 7.838
1.14 0.063
0.32 0.017
206.68 10.521
1.73 0.093
0.48 0.026
261.26 13.268
1.99 0.121
0.60 0.036
Air/
Fuel
Ratio
14.916
0.135
0.037
20.397
0.143
0.041
20.662
0.073
0.022
14". 6 33
0.101
0.029
19.535
0.076
0.022
19.713
0.112
0.032
14.693
0.114
0.032
19.645
0.178
0.049
19.690
0.117
0.035
p
Heat Flux Recovered (Btu/hr-ft )
Sec. 1 Sec. 2 Sec. 3 Sec. 4 Sec. 5
19,981 13,023 9,305 6,953 6-375
1,843 1,464 520 476 480
511 406 144 132 133
29,703 15,975 11,745 9,327 9,221
2,101 1,471 408 326 310
607 425 118 94 89
34,763 20,474 15,079 11,983 11,894
1,455 1,085 869 698 592
439 327 252 210 178
23,943 15,385 11,033 8,033 7,548
552 868 325 271 293
162 251 94 78 85
31,804 18,662 13,145 10,165 10,114
969 1,276 382 281 309
280 368 110 81 89
36,621 23,033 15,883 12,596 12,802
9S2 1,453 309 406 397
286 420 89 117 114
23,277 15,465 10,891 7,994 7,375
908 664 448 434 450
252 184 124 120 125
31,533 17,389 12,735 9,995 9,923
593 735 339 436 406
164 204 94 121 113
35,346 21,545 15,781 12,395 12,535
907 899 327 526 544
273 271 99 159 164
Total Heat
Recovered
(Btu/hr)
83,908
5,980
1,659
114,564
6,169
1,781
142,041
6,363
1,919
99,442
2.675
772
126,505
3,623
1,046
152,209
3,841
1,109
98,025
3,753
1,041
123,017
2,791
774
148,694
3,875
1,168
-------
135
TABLE 11
CONFIGURATION 1
VORTEX GAS TEMPERATURE PROFILES
Condition
3
-
8
12
Distance from
Wall
no i i
(inches)
0
0.25
0.50
0.75
1.00
1.25
1.50
1.75
2.00
2.25
2.50
2.75
2.88
0
0.25
0.50
0.75
1.00
1.25
1.50 '
1.75
2.00
2.25
2.50
2.75
2.88
0
0.25
0.50
0.75
1.00
1.25
1.50
1.75
2.00
2.25
2.50
2.75
2.88
Radius
Ratio
r\Q v i \J
r/rwall
1.000
0.913
0.826
0.740
0.653
0.566
0.479
0.392
0.306
0.219
0.132
0.045
0.000
1.000
0.913
0.826
0.740
0.653
0.566
0.479
0.392
0.306
0.219
0.132
0.045
0.000
1.000
0.913
0.826
0.740
0.653
0.566
0.479
0.392
0.306
0.219
0.132
0.045 '
0.000
Vortex Gas Temperatures (°F)
Sta. 1
139
803
1424
1587
1681
1699
1712
1699
1654
1609
1578
1538
1573
173
998
1569
1706
1772
1794
1799
1794
1767
1726
1708
1663
1645
186
1107
1667
1790
1850
1873
1873
1850
1841
1808
1776
1740
1731
Sta. 2
165
854
1222
1346
1433
1468
1481
1468
1428
1394
1394
1364
1359
186
1048
1368
1490
1560
1600
1591
1578
1547
1529
1547
1538
1490
265
1158
1699
1587
1609
1699
1690
1654
1645
1632
1654
1645
1600
Sta. 3
139
532
1014
1103
1196
1226
1245
1226
1205
1218
1226
1188
1175
169
875
1192
1286
1351
1368
1359
1365
1346
1359
1415
1415
1376
296
998
1312
1415
1463
1481
1472
1450
1459
1481
1534
1534
1499
Sta. 4
104
386
743
913
977
1019
1052
1044
1023
1048
1078
1057
1040
156
501
930
1090
1158
1184
1188
1184
1158
1184
1256
1295
1269
139
731
1124
1226
1273
1299
1260
1286
1290
1316
1381
1420
1407
Sta. 5
99
323
576
692
829
867
896
901
884
909
943
947
922
156
422
778
964
1036
1057
1057
1052
1027
1052
1133
1201
1166
130
701
989
1107
1162
1175
1171
1149
1154
1192
1260
1338
1312
-------
136
TABLE 12
CONFIGURATION 2
VORTEX GAS TEMPERATURE PROFILES
Condition
3
r
-
8
12
Distance from
Wall
(inches)
0
0.25
0.50
0.75
1.00
1.25
1.50
1.75
2.00
2.25
2.50
2.75
2.88
0
0.25
0.50
0.75
1.00
1.25
1.50 '
1.75
2.00
2.25
2.50
2.75
2.88
0
0.25
0.50
0.75
1.00
1.25
1.50
1.75
2.00
2.25
2.50
2.75
2.88
Radius
Ratio
r/rwall
1.000
0.913
0.826
0.740
0.653
0.566
0.479
0.392
0.306
0.219
0.132
0.045
0.000
1.000
0.913
0.826
0.740
0.653
0.566
0.479
0.392
0.306 .
0.219
0.132
0.045
0.000
1.000
0.913
0.826
0.740
0.653
0.566
0.479
0.392
0.306
0.219
0.132
0.045
0.000
Vortex Gas Temperatures (°F)
Sta. 1
160
1006
1485
1645
1694
1717
1712
1721
1699
1672
1627
1569
1543
191
1162
1582
1717
1753
1772
1772
1767
1744
• 1721
1690
1632
1600
208
1265
1663
1785
1818
1836
1841
1832
1818
1794
1767
1721
1690
Sta. 2
136
888
1196
1329
1424
1468
1499
1494
1468
1450
1424
1398
1368
238
1002
1303
1428
1512
1560
1573
1569
1538
1520
1503
1481
1446
300
1112
1411
1534
1614
1659
1672
1650
1627
1600
1591
1565
1525
Sta. 3
121
684
968
1078
1188
1226
1235
1239
1243
1239
1231
1196
1171
130
824
1107
1231
1316
1342
1338
1338
1338
1355
1351
1321
1290
191
930
1222
1351
1415
1433
1441
1437
1454
1468
1463
1437
1411
Sta. 4
104
462
752
901
981
1023
1052
1069
1078
1090
-1082
1065
1044
117
680
913
1065
1133
1166
1175
1179
1184
1209
1213
1201
1179
147
. 786
1040
1171
1235
1265
1290
1286
1299
1321
1329
1312
1290
Sta. 5
104
426
641
778
854
888
922
934
943
951
955
951
939
117
580
837
968
1031
1057
1052
1057
1061
1078
1099
1103
1094
143
688
960
1078
1137
1158
1171
1162
1179
1196
1222
1222
1213
-------
137
TABLE 13
CONFIGURATION 3
VORTEX GAS TEMPERATURE PROFILES
Condition
3
8
12
Distance from
Mali
no I 'I
(Inches)
0
0.25
0.50
0.75
1.00
1.25
1.50
1.75
2.00
2.25
2.50
2.75
2.88
0
0.25
0.50
0.75
1.00
1.25
1.50 '
1.75
2.00
2.25
2.50
2.75
2.88
0
0.25
0.50
0.75
1.00
1.25
1.50
1.75
2.00
2.25
2.50
2.75
2.88
Radius
Ratio
r\u LIU
r/rwall
1.000
0.913
0.826
0.740
0.653
0.566
0.479
0.392
0.306
0.219
0.132
0.045
0.000
1.000
0.913
0.826
0.740
0.653
0.566
0.479
0.392
0.306 -
0.219
0.132
0.045
0.000
1.000
0.913
0.826
0.740
0.653
0.566
0.479
0.392
0.306
0.219
0.132
0.015
0.000
Vortex Gas Temperatures (°F)
Sta. 1
156
960
1446
1663
1717
1726
1721
1712
1699
1636
1573
1529
1547
191
1100
1520
1703
1776
1762
1749
1740
1726
1681
1627
1569
1582
203
1200
1600
1772
1836
1836
1818
1799
1790
1755
1694
1654
1659
Sta. 2
147
840
1154
1342
1441
1485
1494
1472
1450
1389
1372
1364
1381
156
1000
1282
1415
1525
1547
1556
1529
1520
1481
1476
1441
1468
296
1110
1402
1538
.1618
1645
1636
1605
1582
1570
1551
1538
1556
Sta. 3
121
680
972
1082
1158
1201
1222
1218
1222
1175
1175
1166
1184
130
825
1112
1231
1299
1303
1303
1299
1312
1286
1290
1256
1278
191
930
1209
1329
1394
1411
1407
1389
1411
1410
1394
1381
1394
Sta. 4
104
500
795
913
989
1031
1061
1061
1061
1031
1027
1031
1036
117
680
913
1040
1116
1133
1158
1149
1154
1158
1158
1137
1158
139
780
1023
1145
1222
1252
1269
1252
1256
1260
1260
1265
1282
Sta. 5
104
420
684
803
862
905
930
930
926
888
888
892
905
121
550
807
917
993
1019
1036
1031
1027
1014
1014
1010
1031
139
650
930
1040
1107
1137
1149
1133
1133
1125
1124
1141
1162
-------
138
of predicting the velocity field in confined vortex; even the limited
data available is often contradictory which suggests that the flow is
disturbed significantly by the measuring probe or is extremely sensitive
to the geometry of the vortex apparatus or both. The results of Wolf
[172J and Rochino 1173], already reported in Chapter I, indicate that
the axial profile does not tend to develop with respect to length as is
characteristic of simple linear flows. Thus the profile can be expected
to remain relatively flat for all axial stations (except very near the
wall). Thus, there appears to be a reasonable basis to assume that the
axial velocity is simply a constant with respect to both radius and length
providing, of course, flow reversal does not occur. This assumption—
which is frequently made (see [388] for instance) is often termed the
"slug^flow" model— permits removing the velocity from inside the integral
in Equation (.1) where it cancels the mean velocity factor in the denomi-
nator. The temperature obtained by means of this assumption is referred
to here as the "average" temperature at each furnace column station since it
represents the result of a simple temperature-area average. The details
of the calculation procedure are presented in Appendix C with the results
given in Table lU; the data termed "Average Furnace Column Temperature" are
obtained simply by finding the mean of the five average temperatures (one
for each Station) available for each Configuration/Condition combination.
Effect of Inlet Configuration and Condition
The heat recovery and temperature data obtained for the three inlet
Configurations investigated utilized exit Configuration 3 exclusively (as
the exit configuration data was for inlet Configuration C exclusively).
The expected result of the use of the insert sleeves (i.e. inlet Configu-
rations A and B) was that of higher heat transfer rates and higher
-------
TABLE 14
AVERAGE VORTEX GAS TEMPERATURES
Configuration
Condition
Vortex Gas Temperature (°F)
Sta. 1
1
2
3
8
12
3
3
o
12
3
o
12
I
1
1363
1480
1560
1424
1500
1572
1413
1474
1543
Sta. 2
1201
1333
1459
1205
1299
1397
1192
1280
1384
Sta. 3
976
1152
1269
991
1108
1211
978
1092
1190
Sta, 4
Sta. 5
792
940
1074
811
-
954
1058
822
937
1037
658
828
977
710
859
964
716
826
931
Average
Furnace
Column
Temperature (°F)
928
1147
1263
1028
1144
1240
1024
1122
1217
LO
VO
-------
vortex gas temperatures due to the higher inlet air velocities and increased
mixing. However, the data showed that just the opposite occurred leading
one to reaffirm "expect the unexpected". The reason for this anomalous
behavior is that, apparently, a change in the location of the combustion
process took place. The sleeves, in addition to increasing the tangential
velocity, also decreased the static pressure of the vortex chamber as a
result of Bernoulli's Principle. This lowered pressure caused the com-
bustion process to occur much lower in the vortex chamber/furnace column
apparatus and was observable by the noticeably-increased radiation from
the walls of the uncooled vortex chamber. This effect was so pronounced
that it caused the wood supports of the steel table on which the incinerator
rests to ignite. Thus, although the combustion intensity and heat transfer
were probably enhanced because of the sleeves, the effect of the lowered
pressure caused the heat transfer to take place at a point where no heat
recovery capacity had been provided; thus the losses from the system were
greatly increased and the observed heat recovery and gas temperatures
diminished.
As a result, the data are not particularly useful in correlating
the effect of the sleeves upon heat transfer, and only one set of data
was obtained for the nine combinations of inlet Configuration and Con-
dition; these data are presented in Table 15. Also, because only one set
of data was obtained, no temperature profiles were measured. The gas
temperature was, however, measured at one radial position for each station
and this is given as Table l6» These data confirm the early explanation
for diminished heat transfer in that they show a much cooler gas flowing
through the furnace column for increasing inlet tangential velocity.
-------
TABLE 15
INLET CONFIGURATION EFFECT UPON HEAT RECOVERY
Inlet
Configuration
i
C
B
A
!
Condition
3
8
12
3
8
12
3
8
12
Flow Rate (Ibm/hr)
Air C3Hg
115.2 7.96
208.4 10.69
268.0 13.45
116.0 7.93
208.0 10.66
266.4 13.46
115.5 7.86
1 208.6 10.54
i 268.3 13.27
Air/
Fuel
Ratio
14.47
19.49
19.93
14.63
19.51
19.79
14.69
19.79
20.22
Heat Flux Data - Btu/Hr-ft2
Sec. 1 Sec. 2 Sec. 3 Sec. 4 Sec. 5
19,350 13,980 10,060 7,450 6,640
28,570 15,920 11,700 9,290 9,390
33,080 19,480 12,460 11,190 11,170
16,740 13,780 9,120 6,750 5,710
30,690 16,110 11,530 9,500 9,030
35,540 20,560 14,780 11,300 11,280
16,230 12,800 8,270 5,720 4,650
26,940 15,360 10,410 8,350 7,380
33,370 19,860 11,920 9,740 9,420
Total Heat
Recovery
Btu/hr
86,680
112,900
131,770
78,570
115,900
140,940
71,890
103,210
127,140
-------
TABLE 16
VORTEX GAS TEMPERATURES* FOR 3 INLET CONFIGURATIONS
Configuration
A
8
C
Condition
3
8
12
3
8
12
3
8
12
Temperature (°F)
Sta. 1
1331
1567
1654
1415
1658
1763
1678
1715
1751
Sta. 2
1101
1355
1512
1201
1490
1658
1518
1594
1667
Sta. 3
854
1107
1276
945
1241
1433
1260
1377
1461
Sta. 4
658
896
1097
742
1029
1224
1070
1152
1252
Sta. 5
559
739
934
639
905
1097
926
1044
1129
* All these data were measured at 1.25 Inches from the furnace column wall.
-------
A comparison of the data presented in Tables 10 and 15 for the
same inlet /exit Configuration (C-3) reveals a small discrepancy. Since
these data were obtained for identical Configurations and Conditions it
would be expected that recovery rates should be nearly equal (at least
within a standard deviation as given in Table 10); however, the data
taken during the inlet Configuration investigation is approximately 10$
lower than that observed for the exit Configuration investigation. Al-
though this difference is not great, it appears to be consistent and not
easily explainable. Two possible explanations are suggested: (l) due
to the elapsed time between data taking periods (about one year) it is
possible that there has been a slight aging effect (corrosion in the
water tubes, carbon build-up on the inside walls of the furnace column,
etc.), and/or, (2) the fuel provided in the one-hundred pound supply-
tanks, although claimed to be propane (_C H ) , may in fact be "watered-
down" by the dealer (who carries other fuels such as LUG) with lower
heating-value hydrocarbons as a result of the scarcity and high cost of
C3H8-
Discussion of Heat Recovery Data
The objective of any investigation of the effect of independent
variables upon a dependent variable is to develop a correlation relation.
The usual means of expressing the mass flow rate independent variable is
through the use of a Reynolds number. The difficulty here is that there
are many possible definitions of Reynolds number. The usual form of inter-
nal-flow Reynolds number is given by
D
-------
Dili
•whiTo U it: l-he average axial velocity, D the tube diameter, and m the
axial flow rate all in consistent units.
The second form given in Equation (.2) will be used here since the
total mass flow rate of air plus propane is known and will be referred
to as the "axial Reynolds number". The absolute viscosity is somewhat
difficult to determine since it is both a function of temperature and gas
composition and there is no simple expression available that can account
for these two effects. Maxwell [Uoi], however, has obtained data for the
absolute viscosity of "flue gas" as a function of flue-gas temperature.
He has found that it is relatively insensitive to the percentage of excess
air and is thus approximately only a function of the temperature. The
calculation of the axial Reynolds number, using [1+01] to find the viscosity
for the average furnace column temperature, is given in Appendix D.
The total heat recovery rate and the total heat recovered per pound
of propane as a function of the axial Reynolds number evaluated at the
average furnace column temperature is presented in Figures 18 and 19 for
the data given in Tables 7-9 (i.e. exit Configuration/Condition effect).
It should be noted that the heat recovery data cannot be expressed directly
in terms of Nusselt or Stanton numbers because it includes the effects of
radiation and conduction. To determine the convective portion of the heat
recovered requires further analysis and will be performed in Chapter IV.
On these figures, the left-most group of 3 data parts are for Condition 3,
the middle group for Condition 8, and the right group for Condition 12.
What should be noted from Figure 19 is that the heat recovery rate is
relatively insensitive to the average axial Reynolds number when expressed
on a per pound of propane basis. For Configurations 2 and 3 there is an
approximate linear degradation in heat recovery with increasing Reynolds
-------
11*5
160
120
100
u 60
60
40
20
Exit
Conf. Symbol
2-— A
3— -O
-3
Axial Reynolds Number x 10
Figure 18. Total Heat Recovery Rate vs. Axial Reynolds Number
14
12
4J
A
10
I8
a.
Exit
Conf. Symbol
,2-— A
3 ..... a
10"
Figure 19. Total Heal.
Axl«l Reynolds Number x
<••(. Ri-covi-rrd pt-r Pniitul nf rrnpani. vn. Axlnl RiynuMn
-------
number although the change is only about 10% for a doubling in Reynolds
number. This trend is explainable because of the shorter residence times
within the furnace column for the higher Reynolds numbers. It is also
significant to note that the data of Configuration 1 is substantially
(i.e. about 20%) lower than the Configuration 2/3 data; this would
suggest that an entirely different flow field has resulted
for the change from a four-inch exit diameter to a two-inch diameter.
The total heat recovery rate data for the three inlet Configurations
are given in Figures 20 and 21. The. measured recovery rate for
the smallest sleeve is considerably below that for no sleeve but the
large sleeve (Configuration B) does yield a higher rate at the largest
Reynolds numbers. These data are difficult to interpret—as noted earlier—
because of the increased energy losses from the uncooled vortex chamber.
There are two other Reynolds numbers that can be meaningfully
defined: the "exit Reynolds number" where D in Equation (2) represents
the diameter of the exit orifice and the viscosity is evaluated at the
average temperature at the exit section and the "inlet Reynolds number"
where D is the inlet air-line diameter and the viscosity is found from
air-property tables using the measured inlet air. temperature. These
calculations are also performed in Appendix D.
The total heat recovery rate as a function of exit Reynolds number,
for the exit-effect investigation, is presented in Figure 22 while the
recovery rate as a function of inlet Reynolds number, for the inlet-
effect investigation, is given in Figure 23.
Figure 22 suggests a cause for the observed decreased heat recovery
rates obtained with exit Configuration 1 seen in Figures 18 and 19: namely,
that exit Reynolds number is higher than any of the Configuration 2/3
-------
160
140
120
I 100
o
«-«
K
60
-
z
&
20
Inlet
Conf. Symbol
A—-O
B A
c—n
12 34567
Axial Reynolds Number x 10
Figure 20. Total Heat Recovery Rate vs. Axial Reynolds Number
14
9
to
1*S
«
o 10
16
Inlet
Conf. Symbol
A O
B A
C O
Axial Reynolds Number x 10
-3
Figure 21. Total Heat Recovered per Found of Propane vs. Axial Reynolds Number
-------
14
5 12
2 10
X
EU
»H
O
Tl
I «
ikS
Exit L ,
Conf. Symbol
I O
2—A
3-D
12
16
20
24
28
Exit Reynolds Number x 10
Figure 22. Total Heat Recovered per Found of Propane vs. Exit Reynolds Number
14
^\
flO
fC
-------
data. Note also, for Configuration 2/Condition 12 and Configuration I/
Condition 3 the exit Reynolds numbers are nearly equal and despite the
differences in geometry, flow rate, and air/fuel ratio, the heat re-
covered per pound of propane is nearly equal as well. By comparing
Figures 19 and 22 the following can be concluded:
(l) If the heat recovery rate per pound of propane were independent
of the exit geometry, then the data for the three Configurations
investigated should fall nearly on a common line. This is true,
however, only for the Configuration 2/3 data; this suggests that
for the larger exit diameters—on the order of the furnace column
diameter (5-76 inches)—the effect of the exit Configuration is
small.
(2) Since Figure 19 has shown that there is, in fact, an exit
Configuration effect for the 2-inch diameter exit, then a plot
of heat recovery rate per pound of propane versus an appropriate
dimensionless parameter representing the exit diameter change
(and the exit Reynolds number is one such parameter) should
reveal that Configurations 2/3 are operating in approximately
the same flow regime with Configuration 1 in a distinctly dif-
ferent regime. This is precisely demonstrated by Figure 22.
The total heat recovery rate is given as a function of the inlet
Reynolds number in Figure 23- Again this graph tends to explain the
earlier graph for which the axial Reynolds number was used for the ab-
cissa. Configuration A is operating at the highest inlet Reynolds number
and thus the lowest recovery rates (in comparison with Configuration C).
Configuration B does not, however, follow the pattern and instead shows
a peak in heat recovery rate at an inlet Reynolds number of approximately
35,000. Corey [291] reported a tangential inlet Reynolds number of 15,000
as optimum in his tangential-overfire studies of solid waste incineration;
although his configuration and objectives were very different, it is in-
teresting to note a comparable value of Reynolds number.
In order to assess the entry-length/vortex-decay effects associated
with heat transfer from a confined vortex it is necessary to examine the
heat flux recovered as a function of furnace column height (or, equiva-
-------
150
lently, vortex -tube length). These data have already been given in
tabular form in Table 10. In order to present these results graphically
it is desirable to obtain yet another Reynolds number : the "length
Reynolds number" defined by
m L **• m L
L D
which is simply equal to the axial Reynolds number defined in Equation
(2) multiplied by the length-to-diameter ratio of each heat recovery
section (i.e. L equals one-foot, two-feet, etc., where D is the furnace
column diameter in feet, O.U800). These calculations are presented
in Appendix D.
The heat flux data for each of the five furnace column sections is
presented as a function of the length Reynolds number for the nine combi-
nations of exit Configuration and Condition in Figure 2k. It is clear
that there is a very pronounced effect of length Reynolds number upon
the local heat flux although there are a number of causes:
Cl) the radiation flux density is the highest at the lowest sections
because of the larger radiation view factor with respect to the
radiating flame and the vortex chamber walls,
(2) the conduction heat transfer component is the largest at the
bottom section because the furnace column is separated from the
very hot vortex chamber by only a one-eighth-inch asbestos gasket,
(3) the largest gas temperature occurs at the lowest sections thus
causing a greater potential for heat transfer,
(k). the flow is undeveloped both fluid-dynamically and thermally
and thus there is an entry-length enhancement effect, and
(.5) the vortex strength is at its maximum value at the lowest
sections since it has had the least opportunity to decay for
those locations.
It should also be noted that the Condition 12 data indicate higher heat
fluxes at comparable Reynolds numbers than the Condition 3/8 data but it
-------
40
35
30
20
15
10
Configuration 1
Symbol
_l_
_l_
246
Length Reynolds Number x 10
Configuration 2
Configuration 3
10
-3
2 4 6
Length Reynolds Number x
10
2468
Length Reynolds Number x 10"3
10
Figure 24. Heat Flux Recovered vs. Length Reynolds Number
-------
is only because the ordinate is given on a per unit time basis rather than
on a per unit of mass of propane basis, because Condition 12 has the
highest propane flow rates and thus the greatest rates of enthalpy addition,
it should evidence the highest heat recovery fluxes on a per unit time basis.
One final observation regarding Figure 2k should be made. The
effectiveness of each additional one-foot cooling section diminishes ex-
ponentially—at least for the first four sections. It is clear, then,
that greatly increasing the length of the furnace column would not result
in marked improvement in total heat recovery. What is not clear is
whether the leveling-off between sections k and 5 is due to the total
decay of the vortex, the attainment of fully-developed flow, or the effect
of the exit boundary conditions (or some combination of all three effects).
To examine the combustion/recovery efficiency of each cooling
section, it is necessary to examine the local heat flux on a per unit
mass of propane basis. This result is given in Figure 25- Since there
are five flux data points available for each combination of Configuration
and Condition (and there are 9 such combinations) this figure presents
U5 data points. It is interesting to note that all of the Condition 8/12
data (triangles and squares) fall in a fairly narrow band regardless of
the exit Configuration with the data for Configuration 1 congregated on
the low side of the band and the data for Configuration 3 on the high
side- For length Reynolds numbers exceeding 60,000 the heat flux> remains
2
almost .exactly constant 'at about 900 Btu/ft -Ibm C"H0: " ,
3 o
Every data point for Condition 3 lies entirely outside the band
of the Condition 8/12 data. This effect is examined in detail in Chapter
IY where Nusselt and Stanton numbers are calculated and the effects of
radiation, conduction, and different mixed-mean temperatures are accounted
-------
es
4J
c
n)
o
4i
I
1.5
e
ED
p
01
O.
•8 *
0.9
0.8
0.7
0.6
T T
Condition Symbol
3 o
8 A
12 o
_L
•I T
Note; Darkened symbols represent Configuration 1 data
Open symbols represent Configuration 2 data
Half-darkened Configuration 3 data
A
A
D
B
±
JL
m
_L
_L
J L
8 9 10
15 20 30 40
Length Reynolds Number x 10
50
60 70 80 90 100
u;
Figure 25. Heat Flux Recovered per Unit Flow Rate of Propane vs. Length Reynolds Number
-------
for. Although the level and slope of the Condition 3 data
is considerably different from that of Condition 8/12, the data
suggest the existence of a similar constant heat flux region at approxi-
2
mately the same level (900 Btu/ft -Ibm C Hg) and length Reynolds number.
Discussion of Vortex Gas Temperature-Profile Data
In order to assess the effect of changing Condition upon the
radial temperature profile data, the data for Configuration 2 from
Table 12 are given in Figure 26; the data for Configurations 1 and 3
illustrate similar results and are, therefore, not also graphically
presented. Several observations should be noted:
(.1) The temperature profiles reveal an almost linear decrease in
temperature with increasing furnace column height (Station) at a
given radius ratio as a result of the heat removal process.
(.2) The radial profiles show a peak temperature at a radius ratio
of approximately 0.5 for Stations 1 and 2 for all three Conditions,
but at the higher Stations the peak appears to shift inward nearing
the centerline for Station 5-
(3) The primary effect of Condition is simply to increase the
temperature level of the gas with the same approximate profile
shape despite the fact that there is both a change in air/fuel
ratio and mass flow rate. The increase in temperature is to be
expected since the energy addition rate increases with increasing
condition (higher flow rates of propane) faster than the energy
removal rate increases (since the cooling-water system is unchanged).
To illustrate the effect of exit Configuration at the same Con-
dition, some of the data of Tables 11, 12, and 13 are presented in Figure
27. The following can be noted:
(l) The data for Configuration 2/3 are similar and portray analogous
behavior to that described previously for Figure 26; the temperature-
level at Stations 1 and 2 are nearly equal although at the higher
Stations, Configuration 3 data show that the gas'is appreciably cooler
than for Configuration 2.
(2) The profiles obtained for Configuration 1 are noticeably different
from any of the other profiles for Stations 3-5 with a sharp peak lo-
cated near the centerline; the data for Stations 1 and 2 show similar
-------
2000
1600
? noo r
800 r
400 I-
1.0
0.6 0.4
Radius Ratio
0.2
0 1.0
0.8
0.6 0.4 _
Radluf Ratio
0.2
VJ1
Figure 26. Vortex Gas Temperature Profiles for Configuration 2
-------
2000
Configuration 2
Station I
0.8
0.6 0.4
Radius Ratio
C.S 0.4
Radius Ratio
0.6 0.4
Radius Ratio
Figure 27. Vortex Gas Temperature Profiles for Configuration 8
-------
157
shapes, to the comparable Configuration 2/3 profiles.
(3) The temperature levels for all three Configurations are very
nearly equal and suggest that the effect of changing exit diameter
is not large.
The presence of an annular peak in the temperature profile sug-
gests that combustion is occurring in an annular region as observed by
others Il26, 128-130]. The temperature decreases toward the centerline
because of radiant energy lost from the hot gases to the cool walls and
it decreases toward the walls because of convective heat transfer. Thus
the absence of an annular peak for Stations 3-5 would imply that com-
bustion is complete and only energy removal processes are occurring.
Visual observation confirms the implication that flame front is confined
to approximately the bottom one-foot section of furnace column.
These temperature profile data were obtained using Honeywell
MegopaK, sheathed, chromel-alumel thermocouples. They are subject to
two principal errors: radiation error and conduction error.
The radiation error present is due to the fact that the thermo-
couple sensing-tip "sees" a relatively cool furnace column wall and
thus there is a net radiant energy loss resulting in a temperature
reading that is also too low. The severity of this effect is extremely
difficult to assess because the vortex gas separating the tip of the
thermocouple and the wall is both emitting and absorbing; thus, for
measurements near the centerline of the furnace column, the measuring
junction is to some degree shielded from the wall by the presence of
the high temperature annular flame. Near the wall, however, the absence
of a flame permits the maximum radiation exchange. Therefore, the maxi-
mum radiation' error .occurs for radius ratios near one. In Appendix E an
estimate of the radiation present in Tables 11-lU is given.
-------
158
Wall Temperature Data
Because of the difficulty In obtaining accurate readings of the
wall temperature using the MegopaK-type thermocouple, separate thermo-
couples were fabricated and bonded into a hollowed-out cavity on the
exterior furnace of the column wall between the cooling water tubing at
6-inch intervals for a total of 11 vertical positions.
The temperature data obtained with these thermocouples is not as
useful as was hoped because of a sensitive dependence upon the water inlet-
temperature which, in Dallas, can be as high as 90°F in August and as
cool as 50°F in January. Thus the wall temperature of the furnace column
would be expected to shift by approximately the same amount as the shift
in water temperature.
The data for Configuration 3-C for two different water inlet
temperatures is presented in Table 17 as a function of Condition and
furnace column height. It is clear that the wall temperature is affected
principally by the water temperature although for the same inlet tempera-
ture there is a marked increase with increasing Condition.
Two additional wall temperature measurements were also made: the
top plate of the vortex chamber and the top of the copper base plate of
the furnace column. This latter location differs from that of the 0-foot
location for the furnace column wall temperature data given in Table 17
in that it is located on top of the horizontal plate that is directly atop
the asbestos gasket (separating the vortex chamber from the furnace column)
whereas the 0-foot thermocouple is mounted on the cylindrical portion of
the furnace column near the copper plate but between the cooling water
tube-spiral (see Figure 30). These data are necessary to determine the
-------
TABLE 17
FURNACE COLUMN WALL TEMPERATURE vs. FURNACE COLUMN HEIGHT
Condition
3
8
12
3
8
12
Water Inlet
Temperature
(°F)
82
62
0 %
256 154
298 171
330 186
N.O.* 138
N.O. 148
N.O. 161
1
145
158
169
124
127
140
U
134
141
152
112
114
125
Furnace
2
X
126
134
141
103
107
114
Column
2%
123
128
137
N.O.*
N.O.
N.O.
Height
3
119
126
134
92
101
109
(ft)
3%
117
124
130
92
98
105
4
115
121
128
90
96
103
4%
114
121
130
90
96
105
5
114
126
134
92
101
109
vn
MD
Thermocouple was not operative at the time.
-------
i6o
conduction heat transfer from the hot yortex chamber to the relatively-
cool furnace column. The data obtained for Conditions 3, 8, and 12 for
Configuration 3-C are summarized below:
TABLE 18
VORTEX CHAMBER/COPPER PLATE TEMPERATURES
Vortex Chamber Top
Plate Temperature (°F)
Furnace Column
Copper Base Plate
Temperature (°F)
Condition
3 8
1001 1060
^92 555
12
1088
573
These data will be used in Chapter IV to calculate the conduction heat
transfer component of the heat recovered at each cooling water section.
Orsat Data
An Orsat sample and analysis was obtained for Conditions 3, 8, and
12 for Configuration 3-C using a Model lo. 39-5^7 Burrell Gas Analysis
Apparatus according to the instructions of the manufacturer [U02]. The
gas samples were taken from a tap located just above the separator. The
volumetric results of the analysis on a dry products basis, are summarized
in the following table:
-------
161
TABLE 19
ORSAT DATA
..
Propane Flow Rate (ibm/hr)
Air /Fuel Ratio
Percent Stoichiometric Air
Percent C0?
Percent 0
Percent CO
Condition
3
7.83
15.3
98.0
10.0
6.0
0.75
8 12
10.1+5 13.36
20.7 20.7
132. h 132. U
9-2 9-6
7.6 7-6
O.l 0.2
Slagging Effects
Since one of the principal problems of incinerators is coping
with, the slag that is invariably created by burning wastes, the effect
of slagging on this incinerator concept was investigated by using alumi-
num, in various forms, and fluidizing it in one of the inlet air supplies,
Forms of aluminum tried were:
(l) metal lathe-generated "curly-cues"
(2) milling machine-generated "slivers"
(3) aluminum foil sheet squares
(k) aluminum foil balls
(5) aluminum shot (about pea-size)
All forms of the aluminum "slag" were successfully ingested into
the vortex chamber, although only the shot was used in large quantities
(about 20 pounds). As might be expected, the less dense forms of
-------
162
aluminum (slivers, curly-cues, and squares) occasionally exited the
furnace column without melting and were subsequently trapped in the
separator. The other forms of aluminum (balls and shot) appeared to
be too dense to be carried out of the vortex chamber at the air veloci-
ties being used (maximum of approximately 100 feet/second). In no in-
stance did slag form on the inside cool wall of the furnace column.
To collect the slag, the natural concave shape of the bottom of
the vortex combustion chamber was utilized together with a collecting
tank attached to a hole in the bottom-center of the chamber as des-
cribed in Chapter II.
Unfortunately, the aluminum shot unexpectedly piled up on the
floor of the chamber without melting as was anticipated although, in-
itially, a small amount did melt and flow. The problem was caused by
the shallowness of the vortex chamber (approximately 3-7 inches high)
that permitted the cool inlet air to blow over the aluminum shot and
thus keep it relatively cool despite being in contact with the hot
chamber wall. It appears, however, that this problem could be solved
by making the chamber sufficiently high (perhaps a foot or so) with the
air inlets still near the top so that the ingested aluminum could always
be maintained above its melting temperature as a result of contact with
the hot chamber walls and the hot combustion gases. By liquefying the
slag, the concave shape of the chamber floor would permit collection
simply by using gravity feed.
Sawdust as Fuel/Stack Sampling Results
Sawdust was used as fuel in the operation of this incinerator on
approximately fifteen occasions. Most of these runs were concerned with
-------
16
determining the qualitative performance and feasibility of the fluidizing
system.
Once an effective fluidizing system was developed (rotating
auger with stirrers) feed rates were determined. The hopper would hold
almost exactly four pounds of sawdust mixture when it was lightly packed.
At the fixed motor rotation speed (5U rpm), this charge would be ingested
in about six minutes and forty-five seconds—which corresponds to a feed
rate of approximately 35 pounds per hour. The feed rate was relatively
uniform (after a starting transient) with the varying sawdust height in
the hopper until the sawdust level reached the top of the tee/contraction
section. This meant that approximately uniform conditions could be anti-
cipated for a period of five to six minutes.
Sawdust was ingested into the incinerator in two modes: in con-
junction with propane and as the sole fuel (after warm-up and ignition using
propane). The incinerator operated successfully in both modes. With the
sawdust/propane combination it was always possible to adjust the air flow
rate so that the exhaust stack was visually clear.
Quantitative data were very difficult to obtain due to the short
feed times for the hopper capacity. A Configuration 3/Condition 8 base-
line run was performed to determine total heat recovery with a result of
118,200 Btu/hr. Then the sawdust feed motor was turned on and data taken;
it should be noted that the air/propane settings were not changed result-
ing in a somewhat more fuel-rich condition than before. The resulting
heat recovery rate immediately after the sawdust ingestion began was
136,900 Btu/hour or an increase of 18,700 Btu/hour which corresponds to
53k Btu/pound of sawdust. However, the heat recovery rate steadily de-
creased with time until near the end of the five-minute period it was
-------
virtually identical to the propane-only figure. This decrease occurred
despite what -was a fairly uniform feed rate. Since the usual procedure
was to allow a minimum of ten minutes of operation for the removal of
transients when changing from one Condition to another, it is difficult
to interpret this result.
Originally, it had been hoped that the Staksamplr could be used
to quantitatively assess the efficiency of combustion and the performance
of the separator. The specifications for its use dictate a thirty min-
ute sample of typical operation and it was thought that even though the
sawdust capacity of the hopper was limited to about five minutes, the
requirement could still be fulfilled by doing it in six steps. As it
turned out this was not practical. Due to the small scale of operation
any momentary burst of sawdust from the hopper would result in an equally
momentary black cloud. These bursts would occur at the beginning and
end of each hopper load as well as on one or two occasions in between
as a result of the fact that the mixture was not homogeneous and the
slow feed rates. Thus, each sample taken resulted in a black piece of
filter paper at the end of the first five-minute sequence even though for
99 percent of the time the exhaust was clear.
As a result of these difficulties it was concluded that a commercial
stack sampling procedure is just not feasible for a laboratory-size
apparatus because of scale effects. What is needed is a much simpler
procedure that would require sample times only on the order of fifteen to
thirty seconds.
-------
CHAPTER IV
DATA ANALYSIS AND ANALYTICAL INVESTIGATIONS
Philosophy of Approach
Purely analytical attempts at finding the fluid velocity, the
temperature profiles, or heat transfer rates encounter incredible compli-
cations because of the many effects present. From the very nature of a
vortex flow With an axial velocity component, three dimensional consider-
ations are essential. Also, because the walls are of a non-refractory
nature due to the heat recovery system, severe radial temperature
gradients are present which require consideration of variable-property
effects. In addition, as is apparent from the Reynolds number calcu-
lations presented in Appendix D, the flow stream is fully turbulent.
Further, there is the added consideration of combustion effects; not only
does this result in an energy addition but there are also mass specie
concentration effects, gas radiation and absorption effects, and finite-
rate combustion chemistry effects.
As noted in the survey of the available literature (presented in
Chapter I), no solution exists for this flow field. The analytical
efforts presented in this Chapter have been directed primarily toward
both gleaning from the data the maximum amount of information possible
and developing a correlation relation between heat transfer and Reynolds
number. The models employed are necessarily quasi-simplistic and must
rely upon the data for their sustenance.
-------
166
Heat Recovery Efficiency
Although the data for heat recovery have already been presented in
Chapter III, it is important to assess the performance demonstrated by
this laboratory-sized incinerator in terms of some useful benchmarks.
What is in view here is not the amount of heat transfer but the quality
of heat transfer.
The significance of these heat recovery data can best be displayed
by expressing the results in terms of the theoretically achievable values
by calculating recovery "efficiencies". There are two obvious possi-
bilities for a theoretical standard:
(l) the "absolute" theoretical standard corresponding to a furnace
column of infinite height for which the exhaust gas temperature
would be 77°F with water appearing as a liquid in the products, and
(2) the "practical" theoretical standard for which the theoretical
heat recovery is based upon measured furnace column exit temperatures
with water assumed to appear as a vapor in the products.
Since both of these standards represent useful concepts, the data
will be presented in terms of each.
It is first necessary to calculate the theoretical enthalpy of
combustion based upon the known air/fuel ratio; the procedure for doing
this is presented in virtually every thermodynamics textbook (see, for
instance, Wark [U03] Chapters lU and 15). For the theoretical standard,
the sensible enthalpy of the products need not be calculated since they
are taken to be at the reaction temperature (77°F). The sensible enthalpy
of the reactants together with the sensible enthalpy of the products re-
quired for the practical standard can be found by means of known property
tables such as the JANAF Thermochemical Tables [UoU, ^05] for the measured
average gas temperature. These calculations are performed in Appendix F.
-------
IfVf
The absolute efficiency can now be found by ratioing the actual
heat recovered per pound of propane (available from Table 10) to the "let
Enthalpy of Combustion" given in Table F-3. The practical efficiency is
found by using the "Net Enthalpy of Reaction at the Exit" given in Table
F-5 as the standard to ratio with the heat recovery data. These two
efficiencies, so calculated, are presented in Figure 28 as a function of
the average axial Reynolds number (calculated in Table D-l and used in
Figures 18 and 19) of the furnace column.
Several observations can be noted from the graphs given as Figure
28. First, the relatively high efficiency levels of the incinerator
indicate that the heat recovery concept of vortex heat transfer is ef-
fective even for the modest length-to-diameter ratio used in this apparatus
(slightly greater than 10). The maximum efficiency on an absolute basis
was 70$ while values in excess of 80$ were obtained for practical effi>
ciencies. It is relevent to note that the efficiency of simple boilers—
whose sole objective is to recover heat—is often quoted ([268, k06] for
example) to be on the order of 85$ on an absolute standard. In comparison,
the heat recovery performance of this model incinerator is considered to
be highly satisfactory.
Several additions observations can be made:
(l) The absolute efficiency decreases with increasing mean axial
Reynolds number of the furnace column. Since this trend is also pre-
sent for the practical efficiency curve (with the exception of
Configuration l) it can be concluded that this efficiency degradation
is not due entirely to increased sensible enthalpy loss in the flue
gas as a result of higher mean axial velocities (although this effect
does play a significant role).
(2) The change in slope of the efficiency curves at the middle value
of Reynolds number (which represents Condition 8) could be a result of
an air/fuel ratio effect. By extending a straight line beyond the
Condition 8 and 12 data it is clear that the Condition 3 data lie
-------
168
1UO
90
80
70
60
3')
20
10
"Absolute" KffIclvncv
Exit
Can (
I
2
3
o
A
2 4 6 8
Axial Reynolds Number x 10"
"Practical" Efficiency
Exit
Conf. Svmbol
2
3
10 0 2 4 6 8
Axial Reynolds Number x 1
10
Flgnrp 28. Absolute «nd Practical Efficiency vs. Axial Reynolds Number
-------
1.69
above this line for all six possibilities which is expected since
Condition 3 is near-stoichiometric. If this is in fact the case,
then the degredation of recovery efficiency observed is due in
part to the increase in air/fuel ratio and in part because of the
increase in Reynolds number with the latter factor the most-pre-
dominant .
(3) The effect of the exit Configuration is small for the change
from the four to the six-inch exit diameter. A dramatic change
occurs, however, for the change from the four to the two-inch diameter
This suggests a fundamental change in the operating characteristics
of the incinerator, perhaps as a result of a vortex breakdown. The
middle-sized exit diameter (Configuration 2) actually demonstrates
a higher recovery efficiency than either the size larger or the size
smaller for all eighteen data points. On the basis of Thompson [l66]
and others it is known that a reduced exit orifice size increases
the region of free vortex flow and thus increases the maximum tan-
gential velocity experienced. Thus it is expected that the smaller
exit diameters would cause a higher heat transfer rate due to a
higher velocity gradient (although in this configuration the effect
of the intervening separator between the end of the furnace column
and the actual exit orifice is unclear). This is exactly what the
data show for the change from Configuration 3 to 2. However, for
the change from 2 to 1 an abrupt decrease is observed, suggesting
the likelihood of a breakdown or vortex jump.
It should also be noted that these recovery efficiencies have
been obtained without any attempt at optimizing the performance
either in terms of determining an optimum Condition/Configuration
or in attempting hardward modifications. In particular, since no
attempt to recover heat from the vortex chamber has been made, a
marked improvement in these efficiencies can be expected as a result
of an installation of an additional cooling coil. It is predicted
that recovery efficiencies on the order of 80% on the absolute basis
(90$ on the practical) can be obtained as a result of this single
modification.
For many years a great many investigators have attempted to
correlate furnace heat recovery in terms of some universal parameter on
a basis that would be applicable to all types and configurations. Hudson
[407] proposed one of the earliest such correlations in 1890. His was a
purely empirical equation that related absolute furnace efficiency in
terms of air/fuel ratio and a quantity that has come to be known as the
"available heat"; the available heat is defined as the net enthalpy of
combustion (see Appendix F) divided by the radiant wall surface area.
-------
170
Broido [Uo8] presented in 1925 what has become a widely-known curve
correlating efficiency with available heat. In that same year, Orrok
[^09J suggested a modification of Hudson's correlation (now referred to
as a Hudson-Orrok equation) and Wohlenberg [UlO-Ul2j presented the first
of his several papers attempting to ground the subject on a firmer theo-
retical basis. Hurvich [Ul3J has given an equation for a modified Boltz-
mann number in terms of an experimentally determined coefficient accounting
for the fraction of the total heat transferred via radiation, for coal-
fired furnaces. Konokov [^lU] has approached the same question with some-
what different assumptions. Greyson [Ul5] has presented a survey of
these correlations with suggested modifications together with a compendium
of data from various boiler furnaces in operation in the United States.
All of the above relations have been developed with the large,
typical power generation furnace in mind. These devices are character-
ized by large furnace volumes of extremely high-temperature gas with a
relatively low velocity and small wall area. As a result, radiation
heat transfer is predominant in the furnace chamber area in contrast to
the case in view here- Hence, these correlations generally do not
agree with the results of this investigation.
However, if the total heat recovery data of Table 10 are plotted
as a function of the available heat and compared with the classic Broido
curve there is remarkably close agreement. These results are given in
Figure 29 for. absolute efficiency in terms of two available heats: one
based upon the internal area of the furnace column (7.5UO square feet)
and the other using the total internal area of the furnace column plus
the vortex chamber (12.36 square feet). The Broido curve was obtained
-------
171
100
90
80
70
60
o
e
50
w
0)
S
30
20
10
BROIDO CURVE
Note: Solid data based upon radiant area of
furnace column only.
Open data based upon radiant area of
furnace column plus vortex cbamber.
Configuration Symbol
I o
2 A
3 a
JL
_L
J_
_L
4 8 12 16 20 24 28
Available Heat (Btu x 10'3/hr-ft2 of radiant surface)
32
36
Figure 29. Comparison of Incinerator Efficiency vs. Available Heat With Broido Curve
-------
from Reference [^08] (page 1132) which- was presented for available heats
2
from 10,000 to 250,000 Btu/hr-ft ; the good agreement shown in Figure 29
is especially surprising because only the very lowest portion of the
Broido curve applies to heat rates measured for this incinerator.
The lowest available heat data presented by Greyson [^15] corre-
sponds to the maximum shown in Figure 29- This point was taken from
measurements made at the Willow Island Station (which is a pulverized
coal furnace) and demonstrated approximately the same absolute efficiency
as was achieved with the vortex incinerator—namely, 55$-
A final basis of comparison for the heat recovery performance is
the total heat recovery rate (in Btu/hour) per furnace volume (in cubic
•3
feet); the volume of the vortex chamber alone is 0.5508 ft and that of
the vortex chamber plus the furnace column is l.ij-56 ft . Thus the heat
recovery data of Table 10 ranged from a low of 57,700 Btu/hr-ft (for
Configuration I/Condition 3 using the total volume of the vortex chamber
•j
plus the furnace column) to a high of 276,300 Btu/hr-ft (for Configuration
2/Condition 12 using just the volume of the vortex chamber).
Energy Balance
There are three energy fluxes that comprise the energy balance of
the incinerator: the total heat recovery rate, the enthalpy rate associ-
ated with the internal energy of the flue gas leaving the furnace column,
and the over-all energy losses from the system. The total heat recovery
rates are given in Table 10 and the gas enthalpy rates in Table F-5. The
calculation of the energy losses from the system is presented in this
section.
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173
The sources of energy loss are as follows:
(l) radiation from the vortex chamber that does not reach the
exterior of the furnace column,
(2) free convection from the vortex chamber,
(3) conduction from the vortex chamber through its supporting
pins to the steel table (the conduction to the furnace column
is not a loss from the system),
(k) radiation from the furnace column/copper base plate,
(5) free convection from the furnace column/copper base plate,
(6) conduction from the furnace column to the separator.
Also, the actual enthalpy of reaction is somewhat less than the
theoretical value calculated in Table F-5. This is because of two effects;
the Second Law of Thermodynamics which limits the degree of completion
of any reaction (usually expressed in terms of the attainment of the
minimum of the Gibbs function) and the incompleteness of combustion that
results from the imperfect mixing that occurs in all combustors. The
Orsat data given in Chapter III, however, demonstrates that the actual
chemical energy released is very close to the theoretical values already
calculated in Appendix F.
Although the energy recovered and released are known to relatively
high precision, the calculation of the energy losses from the incinerator
can only be, at best, a reasonable approximation. Many of the material
properties (such as surface emissivity) can only be estimated and a number
of assumptions are necessary to obtain any result whatever due to the
complicated geometry, heat transfer processes, and absence of data in
some cases. As a result, no distinction will be made for Configuration
in the calculations since both the heat recovery data and the sensible
enthalpy calculations show that the effect is small. Also, although the
calculations are performed to the nearlest 100 Btu/hour, it should be
-------
ITU
noted that two significant digits is about the best accuracy that can be
obtained.
Radiation Loss
From the Vortex Chamber
The radiation loss from the vortex chamber will be calculated in
/ '
three components due to the difference in surroundings: the radiation
from the top plate, from the side walls, and from the bottom plate.
A portion of the radiant energy emitted from the top plate of the
vortex chamber strikes the external wall of the furnace column and hence
is not a loss from the system. The remainder of the radiant energy is
exchanged principally with the concrete walls of the enclosure of the
incinerator. A calculation of the configuration factor (sometimes re-
ferred to as the "view" factor of the "angle" factor) is necessary to
account for the latter fraction. The numerical integration procedure to
find this factor is presented in Appendix G; the result appropriate here
is the factor of 0.138 from the top plate square annulus to the entire
furnace column—thus the configuration factor to the concrete enclosure
is 0.862. The top plate must be viewed as a square annulus because the
copper base plate of the furnace column is located on the top-center of
the vortex chamber and this plate is at a comparatively low temperature.
The area of this annulus is simply the area of the top plate (19 inches
square) less the area of the copper base plate (8 inches square) and is
equal to 2.06 square feet.
The emissivity of the plate can be estimated to be 0.80 (taken
from [kl6] "sheet steel with strong, rough oxide layer"). The temperature
of the concrete walls (which act as an approximate diffuse, gray enclosure)
-------
175
can be estimated to be 70°F (530°R) although it is obvious that this
value was dependent upon the time of operation of the incinerator as
well as the seasons of the year. The final quantity required before
the calculation of the radiation exchange between the top plate and the
enclosure is the temperature of the plate itself. These data were given
in Table 18 and are as follows: 1^6l, 1520, and 15^8°R for Conditions
3, 8, and 12. Although the plate was not at a uniform temperature, these
data were taken at a location away from both the hottest and the coolest
area and so will be taken to represent the temperature of an equivalent
isothermal plate; to do otherwise would unduly complicate the calculation.
The equation for the heat exchange between an object and its en-
closure (for the diffuse, gray assumption) is given by ([Ul6], page 263):
qR = a A e F (T^ - TeS (U)
The results of the calculation (in Btu/hour) for Conditions 3, 8, and 12
are as follows: 10,900; 12,800; and 13,800 Btu/hour for Conditions 3, 8,
and 12 respectively.
The radiation loss from the side-walls of the vortex chamber can
be readily calculated since the configuration factor is 1.0 because the
furnace column is not viewable. The emissivity, wall, and enclosure
temperatures will be assumed to be the same as that used above. The side
wall area is 1.865 square feet. Again using Equation (k) results in the
following loss rates in Btu/hour for Conditions 3, 8, and 12: 11,^00;
13,500; and lU,500.
The radiation loss from the bottom plate of the vortex chamber is
complicated somewhat by the fact that the steel table underneath the
-------
176
has a square hole (7-5 inches square) and two round holes (2-75 inches
in diameter). Thus, there is a total area of O.U73 square feet that
views the concrete floor, whereas the remaining area (2.03 square feet)
views the steel table which is located approximately h-inch below and
parallel to the bottom plate. For the area that views the concrete
floor, the radiation loss may be calculated in exactly the same manner
as given above using Equation (U). The resulting loss rates are: 2900,
3^00, and 3700 Btu/hour for Conditions 3, 8, and 12.
The radiation loss for that portion of the plate that views the
steel supporting table can be estimated by treating the table as a flat
radiation shield of the same approximate emissivity and thus the radiation
rate equation can be expressed as ([Ul6], page 26^):
0.5 a A (T - T )
(5)
l/e + 1/e - 1
Using the same temperatures and emissivity as before (the table is assumed
to have the same emissivity as the vortex chamber—namely 0.80) results
in radiation rates of 5200, 6100, and 6600 Btu/hour for Conditions 3, 8,
and 12.
Thus the total radiation loss from the vortex chamber can be found
from summing these four separately calculated rates and is tabulated below:
TABLE 20
RADIATION LOSS FROM VORTEX CHAMBER (Btu/hour)
Condition
3
8
12
From the
Top Plate
10,900
12,800
13,800
From the
Side Wall
11,1*00
13,500
1^,500
From the Bottom Plate
To Floor
2,900
3,1*00
3,700
To Table
5,200
6,100
6,600
Total
30,UOO
35,800
38,600
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177
From the Furnace Column/Copper Base Plate
In addition to the radiation loss from the vortex chamber just
calculated, there is a loss from the furnace column via radiation because
it is relatively warm with respect to the concrete enclosure. There are
two radiating areas that must be considered: the cylindrical portion of
the column and the copper base plate.
The configuration factor from the cylindrical tube of the furnace
column to the concrete enclosure can-be found directly from Table G-l:
since the factor from the cylinder to the top plate of the vortex chamber
is 0.0232, the factor to the enclosure must be 0.9768. The radiating
area is simply the circumference (6.h inches' to the outside of the cooling-
water tubing) times pi times the height (5 feet) or 8.38 square feet. The
emissivity will be taken:,to be 0.78 ([Ul6], for "plate, heated long time,
covered with thick oxide layer"). The temperature of the furnace column
wall has been tabulated in Table 17- Because the total radiation loss
from the furnace column walls is relatively small, it is sufficiently pre-
cise to choose an equivalent isothermal column temperature rather than calcu-
late the loss in sections. Since most of the heat recovery data was ob-
tained for relatively warm water inlet temperatures, the higher wall'tempera-
tures given in Table 17 will be used. The equivalent temperature point
to be used will be that for the one-foot height; a low location was se-
lected because of the strongly non-linear relationship of emitted energy
with wall temperature (thus a simple area-average would have predicted too
low a radiation loss). Once again using Equation (k) results in the follow-
ing radiation loss rates in Btu/hour: 600, 700, 800 for Conditions 3, 8,
and 12.
-------
178
The radiation loss from the copper base plate requires a
determination of the configuration factor that views the concrete
enclosure. From Table G-l the factor from the base plate to the entire
cylinder is given to be 0.155; thus the factor to the enclosure must be
0.8^5. The temperature of the base plate was given in Table 18 C952,
1015, and 1033°K for Conditions 3, 8, and 12}. The area of the base
plate is 0.263 square feet. Thus the radiation loss from the copper
base plate is: 200, 300, and 300 Btu/hour for Conditions 3, 8, and 12.
Thus the total radiation loss from the furnace column is 800, 1000,
and 1100 Btu/hour for Conditions 3, 8, and 12.
Free Convection Loss
From the Vortex Chamber
Since these losses are approximately an order of magnitude smaller
than that given in Table 20, the calculation procedure is only intended
to provide a gross estimate. Because the walls of the vortex chamber are
oriented differently, the calculation for the free, convection losses from
the top, sides, and bottom will be performed separately.
The calculation procedure will follow that given in Chapter 7 of
Eeference [J+16] using 70°F as the ambient air temperature. The vortex
wall temperature will be assumed to be that given in Table 18. Knowing
these two temperatures permits calculating the film temperature and thus
all the required fluid properties (the volume coefficient of expansion,
the density, the absolute viscosity, the thermal conductivity, and the
Prandtl number). The Grashof number, defined by the following equation,
may then also be found:
Gr - P2 § 3 AT L3 (6)
-------
179
where L here is the length of the plate (approximately 19/12 feet). By
forming the products of the Grashof and Prandtl numbers the equation
for the free convection conductance may- be found from Table 7-1 of
Beference IUl6]; this product, for Conditions 3, 8, and 12, is as
Q Q Q
follows: 3.UU x 10 , 3.26 x 10 , and 3.l6 x 10.
'From Beference IUl6], the convection conductance can then be
found from:
h = O.lU (k/L) (Gr Pr)0'333 (7)
p
This calculation results in values of h of 1.57 Btu/hr-ft -°F for all
three Conditions. The convection rate may now be found from the
defining equation for convection conductance:
q = h AT (8)
Performing this calculation results in the following convection
losses in Btu/hour for Conditions 3, 8, and 12: 3000, 3200, and 3300.
The procedure for determining the convection losses from the side-
walls of the vortex chamber is the same as that given for the top plate
only now the length, L, is the height of the sides (0.312 feet). This
results in three new products of Grashof-Prandtl numbers: 2.6^ x 10 ,
2.50 x 10 , and 2.1*3 x 10 . The associated convection conductance
equation is now given by:
h = 0.5^ (k/L) (Gr Pr)0'250 (9)
This calculation yields values of convection conductance of: 1.77> 1-78,
and 1.78. Using Equation (5) to find the convection loss in Btu/hour
-------
180
for Conditions 3, 8, and 12 yields; 2^00, 2600, and 2700.
The convection loss from the bottom plate is a much more
complicated calculation since the steel table greatly affects the flow
field induced by thermal bouyancy effects. It is known that for
narrow, horizontal gaps with the top plate heated, the formation of
free convection currents is inhibited. Since the steel table is
positioned only about a half-inch below the bottom plate of the vortex
chamber, it is assumed that the free convection losses from this sur-
face are so small as not to warrant inclusion.
Thus the total convection loss from the vortex chamber is:
5^00, 5800, and 6000 Btu/hour for Conditions 3, 8, and 12.
Prom the Furnace Column/Copper Base Plate
There are two surfaces from which free convection losses occur
from the furnace column: the cylindrical tube and the copper base
plate.
The length of the equivalent plate for the copper base plate will
be taken to be 6 inches instead of 8 inches because of the effect of
the furnace column located at its center. Using the temperature data
of Table 18 and JO°F ambient air results in Prandtl number/Grashof
. l± o
number products in the laminar range (i.e. between 10 and 10 ).
According to McAdams 1363] the convection conductance for air with an
upward facing heated plate is given by:
h ;= 0.27 (AT/L)0'250 (.10)
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181
Substituting the appropriate values yields convection conductances
of: 1.U6, 1.51, and 1.52 for Conditions 3, 8, and 12. Using these
values in Equation C8) for a surface area of 0.263 square feet results
in loss rates of: 200, 200, and 200 Btu/hour for conditions 3, 8, and
12.
The free convection loss from the furnace column, if calculated
in the manner given above, would be on the order of 200 Btu/hour.
However, since the air flowing upward along the furnace column has been
heated by the vortex chamber top plate and the copper base plate, it is
no longer valid to assume a TO°F ambient temperature. Since the ambient
temperature is probably very near the wall temperature and the magni-
tudes involved are very small anyway, the convection losses from the
furnace column cylindrical portion will be ignored.
Conduction Loss
From the Vortex Chamber
There are two conduction heat transfer rates associated with the
vortex chamber: the conduction through the asbestos gasket to the
furnace column and the conduction through the four supporting pins to
the steel table. Since the former does not constitute a heat transfer
component leaving the system it need not be evaluated here.
The vortex chamber is supported by four steel bolts of length
0.75 inches and diameter 0.325 inches. The heat transfer area is
0.00230 square feet and the length is 0.625 feet. The thermal conductivity
of 0.5$ carbon steel at 752°F is 2k Btu/hr-ft-0? IUl6]. The conduction
-------
182
heat transfer can be evaluated directly for the Fourier Law for
constant thermal conductivity and a uniform temperature gradient:
q = k A (AT/L) (11)
The temperature of the steel table is estimated to be 275°F> 300°F,
and 325°F for Conditions 3, 8, and 12. Using this estimate together
with the measured plate temperature data to determine AT the conduction
rate is determined to be as follows (Btu/hour): 200, 300, and 300 for
Conditions 3, 8, and 12.
The conduction across the top gap can be estimated by using the
thermal conductivity of air at the film temperature (approximately 0.03
Btu/hr-ft-°F) and the area of the bottom plate (2.51 square feet). The
heat transfer length used is 0.5 inches since the plate has a significant
sag, the average separation distance from the top of the steel table is
less than the 0.75 inches that the four corners are supported. The
calculated conduction heat transfer is 500, 600, and 600 Btu/hour for
Conditions 3, 8, and 12 across the film gap.
Thus, the total conduction heat transfer from the vortex
chamber bottom plate is 700, 900, and 900 Btu/hour for Conditions 3, 8,
and 12.
From the Furnace Column
The only possible conduction loss from the furnace column would
be up to the separator through the attachment collar. However, because
the separator is uncooled, its temperature has been measured to be
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183
several degrees above the wall temperature at the top of the furnace
column. Thus the conduction heat transfer component is very small
(.because of the small temperature difference) and would represent an
energy addition to the system and not a loss. In any case it is
neglected.
Total Energy Losses
The calculations of this section are summarized in Table 21.
By summing the losses from the vortex chamber and furnace column for
the three modes of heat transfer it is seen that the energy leakage
rate is: 37,500; 1*3,700; and k6,QoO Btu/hour for Conditions 3, 8,
and 12.
The energy recovered from the system has been measured and
tabulated in Table 10. Since the energy losses were calculated on the
basis of mean values for all three Configurations, it is necessary
also to use the mean for each Condition of this data given in this
table. This averaging must also be performed on the final component
of the energy balance: the net enthalpy of reaction at the exit
given in Table F-5. Since this value is given in terms of Btu/pound
^
C HO, it must be multiplied by the average propane flow rate for
each condition as found from Table 10.
The results of these calculations together with the results of
Table 21 are given in Table 22.
-------
18U
TABLE 21
SUMMARY OF ENERGY LOSSES FROM SYSTEM
(Btu/hour)
Vortex Chamber:
Furnace Column:
Radiation
Convection
Conduction
Total
Radiation
Convection
Conduction
Total
Total
Condition
3
30,400
5,400
700
36,500
800
200
0
1,000
37,500
8
35,800
5,800
900
42,500
1,000
200
0
1,200
43,700
12
38,600
6,000
900
45,500
1,100
200
0
1,300
46,800
TABLE 22
ENERGY BALANCE TABLE
Mean Energy Recovery
Rate (Btu/hr)
Calculated Energy Loss
Rate (Btu/hr)
Predicted Rate of Energy
Leaving the System
(Btu/hr)
Net Enthalpy of Reaction
Within the System
(Btu/hr)
Percent of Net Enthalpy
of Reaction Unaccounted
For
Condition
3 8 12
93,800 121,400 147,600
37,500 43,700 46,800
131,300 165,100 194,400
125,300 168,600 202,700
+4.8 -2.1 -4.1
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185
Table 22 shows that the system (vortex chamber/furnace column)
balances very well for all three Conditions. Apparently the loss analysis
has overpredicted the, true loss rate since for Condition 3 the total energy
rate leaving the system exceeds that entering.
Several important conclusions can be made from this balance:
(l) The incinerator system has been properly identified with all
the associated energy rate satisfactorily measured and/or computed.
(2) The sensible enthalpy of products at the exit, which is used to
find the net enthalpy of reaction (which represents the net energy
into the system), is accurately found on the basis of enthalpy
calculations for the theoretical products using the JANAF Tables [Ho^,
U05] and the average temperature found by the area average method
of Appendix C. This implies that the average temperature so calcu-
lated is in fact the true mixed-mean temperature.
(3) The implication that the average temperature at the exit of the
furnace column is the true mixed-mean temperature confirms that the
temperature data as measured with the sheathed,MegopaK thermocouple
is not greatly in error due to conduction and radiation effects, and
that the assumption of a uniform axial velocity profile at that point
in the furnace column is an adequate assumption.
(k) The credence so given to the temperature profile data at the top
of the furnace column is very important since the maximum radiation
error would be expected at that location due to the absence of a
shielding effect since no flame occurs that high in the column. Since
the conduction error would not be substantially different for any of
;,';the Stations» it is expected .then that' the temperature data given in
Tables 11 through 13 is, in fact, accurate.
Determination of Convective Heat Transfer Component
As noted in Chapter III, the heat recovery fluxes presented in
Tables 7 through 10 included the effectsoof conduction heat transfer from
the hot vortex chamber top plate and of radiation from the vortex chamber
as well as from the hot vortex gas itself. In order to determine a
Nusselt number (or Stanton number) it is necessary to evaluate these two
components of heat flux and subtract them from the known total flux to
find the convection-only component. These calculations are presented in
this section.
-------
186
Conduction Flux Component
A schematic illustrating the conduction heat transfer path is
given as Figure 30. The data obtained from the two thermocouples shown
in this figure have been presented in Table 18.
The conduction heat transfer rate can be computed using Fourier's
Law based upon a constant thermal conductivity and a uniform temperature
gradient; this equation has been presented as Equation (ll). The thermal
conductivity used will be simply that of the asbestos gasket (approxi-
mately 0.096 Btu/hr-ft-°F) since the conductivity of the copper base plate
is so high in comparison thfet its effect in determining the total thermal
resistance may be neglected. The heat transfer area is simply the area
of the base plate (6^ sqaiare inches) less the area of the furnace column
opening (26.06 square inches) or 0.263 square feet. The heat transfer
length (L in Equation H-8) is the thickness of the gasket which is 1/8-
inch or 0.010** feet.
The results of this calculation in Btu/hour for Conditions 3, 8,
arid 12 are: 12^0, 1230, and 1260. As can be seen by comparing this rate
with the flux recovered at the bottom furnace column section, the con-
duction component of heat transfer is small; it is also interesting to
note that the variation in the calculated heat transfer for these three
Conditions is less than 2.%.
In addition, because there is a wall temperature gradient with
respect to furnace column height, there is a conduction heat transfer
component from section to section. Since this value is quite small, only
a very approximate calculation will be performed.
The same Fourier Law equation can be used as was used for the
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187
TOP VIEW
COPPER BASE PLATE
FURNACE COLUMN
(5.76" I.D.)
END VIEW (CUT)
COPPKR BASE
PLATE
(8"x8"xV)
TOP PLATE
OF VOKTEX
CHAMBER
ASBESTOS
GASKET
(1/8 ")
VT" 7~7 ? S S / /—"7~~r~1*v •
FURNACE
COLUMN
'(3/16 " WALL)^
THERMOCOUPLES
V
0 FT.
VORTEX
/vxi y CHAMBER
•'/• /7/////777A
V
Figure 30. Conduction Heat Transfer Schematic
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188
vortex chamber/copper base plate calculation—Equation (ll). Now the heat
transfer area is the annular area of the furnace column (the cross-
sectional area of the furnace column vail) which is 0.02ll3 square feet.
The thermal conductivity of copper is approximately 220 Btu/hr-ft-°F.
The temperature gradient, AT/L, will be computed by using the wall tempera-
ture difference between mid-points of cooling-water sections for AT and
the length is then one-foot. The data for a water inlet temperature of
82°F will be used.
The net conduction rate into any given section can simply be deter-
mined by subtracting the outlet conduction rate from the inlet conduction
2
rate. This quentity is then converted to a flux (units of Btu/hr-ft )
by dividing by the surface area of each section (1.508 square feet). The
results of this calculation procedure is presented in Table 23-
TABLE 23
CONDUCTION FLUX TO EACH SECTION (Btu/hr-ft2)
''
Section
1
2
3
1+
5
Condition
3
750
30
20
10
0
8
710
60
30
10
30
12
710
70
30
20
30
Radiation Flux Component
There are three primary sources of radiant energy that supply an
energy flux to each of the furnace column sections: the vortex chamber
walls (the top plate via exterior radiation and the bottom plate via
-------
189
interior radiation), the copper base plate, and the vortex gas itself
(principally water and carbon dioxide molecules). In addition, the
furnace column itself radiates to the concrete enclosure and this consti-
tutes a loss to the system. Each of these components are calculated in
this subsection.
Vortex Chamber Walls
First, the radiation flux that originates externally due to the
vortex chamber top plate will be calculated. In Appendix G, the proce-
dure and results of the necessary configuration factor calculation to
each furnace column section was presented; again the top plate must be
treated as a square annulus because a relatively cool copper base plate
sits atop this surface. These factors are given in Table G-2. The e-
missivity will again be taken as 0.80, the area as 2.06 square feet, and
the wall temperature as given in Table 18 (lU6l, 1520, and 15^8°R for
Conditions 3, 8, and 12, respectively). The temperature of the furnace
column is taken to be the recorded wall temperature data given in Table
IT at the midpoint of each section for the higher water inlet temperature
(since most of the heat recovery data was obtained for this water inlet
temperature). The results of this calculation is given in Table 2^ below
(the heat rate is converted to a flux by dividing by the area of each
section—1.508 square feet):
-------
190
TABLE 2k
EXTERNAL RADIATION FLUX TO EACH. SECTION (Btu/hr-ft )
Section
1
2
3
k
5
Condition
3
980
110
30
10
10
8
1150
130
ko
10
10
12
12l*0
lllO
Uo
10
10
Thus the total radiation energy transfer to the furnace column
from the vortex chamber top plate is 1720, 2020, and 2170 Btu/hour
for Conditions 3, 8, and 12, respectively.
In addition to the above calculation, the vortex chamber bottom
plate also radiates to each furnace column section internally. The
effect of this radiation is much more difficult to calculate since sepa-
rating the plate and the column sections is an absorbing/emitting medium.
However, since the vortex bottom plate is significantly cooler than the
vortex gas (about 1000°F compared to 1800°F) its radiant energy is con-
centrated in a relatively long-wavelength band, and thus, it is not signi-
ficantly affected by the absorption/emission phenomena present in the hot
gas; this assumption permits the calculation of the plate and gas radi-
ation rates separately and then simply adding them to find the total
internal radiation rate to each furnace column section.
The emissivity of the plate will be taken as 0.80 as before. The
plate temperature is somewhat higher than the data given in Table 18 since
there is a temperature drop across the thickness of the plate. Using the
-------
191
conduction path as the plate thickness (0.031 feet), the heat transfer
area as the plate thickness (0.031 feet), the heat transfer area as the
area of the bottom plate (2.5 square feet), the thermal conductivity of
the plate as 20 Btu/hr-ft-°F ([h±6] for 0.5$ carbon steel at 1112°F), and
the calculated heat rate out the bottom plate due to radiation and con-
duction that was performed in the previous section (which yielded 8800,
IQliOO, and 11200 Btu/hour for Conditions 3, 8, and 12), and substituting
into the Fourier Law, Equation (ll), results in estimated temperature
drops across the bottom plate of approximately 6°F for all three Conditions.
Since this value is less than the uncertainty in the original temperature
measurement, the effect of the temperature drop across the bottom plate
will be neglected.
The configuration factors from the bottom plate (which is viewed as
a disk located at the base of the furnace column, the same area as the
cross-sectional area—namely, 0.181 square feet) to each of the furnace
column sections have been calculated in Appendix G and are as follows:
0.9^8, 0.01*91, 0.0025*1, 0.00013, and 0.00000 for sections 1.through
5, respectively. In addition, because the bottom section can view more
of the vortex chamber cavity because it can "see around the corner" the
effective emissivity of the bottom plate is greater than 0.80 taken as
its surface property; since the maximum value of effective emissivity would
be 1.0 (for the assumption that the vortex chamber cavity is acting as a
black body radiator), a reasonable estimate of 0.95 will be used for
furnace column section 1 only (the remaining sections will use 0.80).
The furnace column wall temperature used in this calculation will
be the mid-height temperature of each section as given in Table IT for
the 82°F water inlet temperature.
-------
192
Substitution of these values into Equation (k) results in the
radiation rate from the vortex chamber bottom plate to each furnace column
section; this rate is converted to a flux by dividing by the area of each
section (1-508 square feet) and is tabulated in Table 25:
TABLE 25
INTERNAL PLATE RADIATION FLUX TO EACH SECTION
(Btu/hr-ft2)
Section
1
2
3
U
5
Condition
3
820
ho
0
0
0
8
960
ko
0
0
0
12
10UO
50
0
0
0
Furnace Column/Copper Base Plate
The radiation loss from the furnace column can be found in the same
manner as in the previous calculations. The radiating wall temperature
will again be chosen as the mid-height data for the 82°F water inlet
temperature tabulated in Table 17- The emissivity of the copper will
again be taken to be 0-78. The enclosure will be assumed to be diffuse,
gray at 70°F. The external radiation area of each section will be based
upon the diameter to the outside of the copper refrigeration tubing (i.e.
3.20 inches) and results in 1.676 square feet. The. configuration factors
from each furnace column section to the copper base plate/vortex chamber
top plate can be found from Table G-l; however, since the largest factor—
-------
193
that of section 1 to the top plate—is only 0.0232 (thus implying that
the factor to the enclosure is 0.9768), the configuration factor for
each furnace column section will "be taken as 1.0.
Using these values in Equation (h) results in the following calcu-
lated radiation flux loss from each furnace column section (where the rate
has been converted to a flux by dividing by 1.508 since all the flux cal-
culations have been normalized on the inside surface area of each furnace
column section):
TABLE 26
EXTERNAL RADIATION FLUX LOSS FROM EACH SECTION
(Btu/hr-ft2)
Section
1
2
3
U
5
Condition
3
90
70
50
50
Uo
8
120
80
60
60
50
12
lUo
90
70
60
60
In addition to 'the just-calculated radiation loss from each furnace
column section, the copper base plate located at the bottom of the furnace
column acts as a radiant energy source to each section in addition to the
conduction transfer calculated in an earlier subsection. The emissivity
of the base plate will be taken as 0-78 as has been done for all the
copper surfaces. The temperature of the plate has been given in Table 18.
The temperature of each furnace column section will be taken as before.
-------
The radiating area of the base plate is 0.263 square feet. The
configuration factors from the plate to each section have been found in
Appendix G: 0.15*1, 0.001, 0, 0, and 0 for sections 1 through 5
respectively.
Substitution in Equation (k) and dividing by 1.508 to get a flux
results in the following:
TABLE 27
RADIATION FLUX FROM COPPER BASE PLATE TO EACH SECTION
(Btu/hr-ft2)
Section
1
2
3
U
5
Condition
3
20
0
0
0
0
8
30
0
0
0
0
12
30
0
0
0
0
Conflagrant Vortex Gas
The calculation of the effective emittance of the conflagrant
vortex gas and the associated radiation flux is considerably more difficult
than any of the previous calculations. The estimate of the radiation load
in industrial furnaces has been examined for many years without complete
success. In addition to the papers of Hudson, Orrok, Broido, Wohlenberg
and others [UOT-^15] previously cited, additional, more-recent work is
noted: the work of Myers [Ul7] who attempted to account for the effect
of furnace-wall fouling upon radiation transfer for a pulverized coal
plant, Yagi [Ul8] who has examined radiation from the viewpoint of indivi-
dual soot particles by adding the flux due to the soot to that due to the
-------
195
gaa which he claims to be valid for optically thin gases, Beer [hl9] who
has recently updated the state of knowledge for the prediction of
radiation from flames in furnaces, Brovkin [1*20] who has assessed the
error caused by treating a non-isothermal radiating gas by a model using
a set of isothermal zones, and Edwards [U21] who has presented a very
detailed and thorough treatment of the subject for those cases where the
mole fraction composition is known throughout the volume.
The method of analysis adopted here is that given by Siegel and
Howell [U22] in Chapter 17 of their book—namely, the mean beam
length technique. This approach is warranted here because the radiation
component of the total heat transfer process is relatively small.
Although it is customary to increase the calculated gas emittance by some
rule-of-thumb factor to account for chemiluminescent effects (see [k23]
page 2-60) this procedure will not be adopted here because of the absence
of soot and the small amounts of carbon liberated by the reaction pro-
cess.
In Table 17-1 of Reference [^22], mean beam lengths corrected for
finite optical thicknesses are given for various geometries of gas volume.
For a cylinder of infinite height radiating to its convex bounding sur-
face the length is given to be 0-95D where D is the cylinder diameter;
for the furnace column this results in a mean beam length of 0.1*56 feet.
Although the furnace column is not particularly long in comparison to its
diameter (about a factor of 10), the beam length is not very sensitive to
the relative length as long as the cylinder in question is not so short
such that end effects are important—this point is usually taken to be
when the cylinder height is less than or equal to its diameter. Further,
-------
196
the emittance which is determined on the basis of this beam length
estimate is not very sensitive to changes in the value of beam length.
For these reasons the value of 0.^56 feet will be used for the mean
beam length.
In keeping with the previous calculations for radiation and
conduction flux to each section, no distinction will be made for exit
Configuration. Since the temperature profiles of Configuration 3 were
noted to be of a value intermediate between Configurations 1 and 2, they
will be used in the determination of the gas emittance and the calcula-
tion of the radiation flux.
The component pressures of the radiant constituents in the
conflagrant vortex gas can be estimated using the ideal gas approximation
from the ratio of the molal coefficient to the total number of moles of
product; the pressure of the gaseous products will be assumed to be one
atmosphere (this value is nearly independent of Condition since the
change in velocities is so small that the total and static pressures are
virtually identical) and the reaction will be assumed complete at each
section. Using the coefficients given in Table F-l for Configuration 3
for the theoretical reaction results in partial pressures (in units of
atmospheres) for carbon dioxide of 0.0971, 0.09^0, and 0.0939 for Conditions
3, 8, and 12, and for water vapor 0.1622, 0.125*1, and 0.1251 for these
same Conditions. Water vapor and carbon dioxide are the two principal
radiating molecules present in the theoretical products (although carbon
monoxide also radiates, it is present in such small concentrations that
it does not warrant inclusion in this analysis).
By forming the products of the partial pressure and the mean beam
length for both of these molecules and using the average temperature
-------
197
data given in Table lU for each Station and Condition the emissivities
of carbon dioxide and water vapor can be found from Figures 17-11 and
17-13 of Reference [U22]. Next the band overlap correction (Ae) may be
found using Figure 17-15 of this same reference (it turns out to be
negligible for all cases). Finally, the pressure correction coefficients
and CH Q) may be found from Figures 17-12 and IJ-lU; the correction
coefficient for carbon dioxide is 1.0 for all Conditions and the
coefficient for water vapor is l.lU for Condition 3 and 1.08 for Condi-
tions 8 and 12.
The emittance of the vortex gas is now found through the use of
Equation 17-62 of References [422]:
The heat flux to each of the furnace column sections may now be
found using:
q = a (e T - a T ) (13)
g g g w'
where a is the absorptance of the gas for the radiation emitted from the
o
wall and is evaluated at the wall temperature. Since the wall temperature
is very small with respect to the gas temperature, this term will be
ignored.
The calculations of the emissivities of carbon dioxide and water
vapor, the gas emittance, and the radiation flux to each section are
presented in Table 28.
Summary of Radiation Flux Calculations
The net radiation flux to each section can now be estimated by
summing the components due to five sources: the vortex chamber top
-------
198
TABLE 28
CALCULATION OF RADIATION FLUX FROM VORTEX GAS TO EACH SECTION
Section
1
2
3
4
5
Average Temperature (°R)
Emissivity of C02
Emissivity of HgO
Emittance of Vortex Gas
Radiation Flux (Btu/hr-ft2)
Average Temperature (°R)
Emissivity of C02
Emissivity of fLO
Emittance of Vortex Gas
Radiation Flux (Btu/hr-ft2)
Average Temperature (°R)
Emissivity of C02
Emissivity of H20
Emittance of Vortex Gas
Radiation Flux (Btu/hr-ft2)
Average Temperature (°R)
Emissivity of C02
Emissivity of H20
Emittance of Vortex Gas
Radiation Flux (Btu/hr-ft2)
Average Temperature (°R)
Emissivity of C02
Emissivity of H20
Emittance of Vortex Gas
Radiation Flux (Btu/hr-ft2)
Condition
3
1873
0.060
0.048
0.115
2430
1652
0.061
0.055
0.124
1580
1438
0.059
0.062
0.130
950
1282
0.057
0.069
0.136
630
1176
0.055
0.072
0.137
450
8
1934
0.058
0.036
0.097
2330
1740
0.060
0.041
0.104
1630
1552
0.060
0.048
0.112
1110
1397
0.059
0.051
0.114
740
1286
0.056
0.055
0.115
540
12
2003
0.057
0.035
0.095
2620
1844
0.059
0.039
0.101
2000
1650
0.060
0.045
0.109
1380
1497
0.060
0.049
0.113
970
1391
0.058
0.051
0.113
730
-------
199
plate, vortex chamber bottom plate, the furnace column (a loss to the
system), the copper base plate, and the vortex gas.
This calculation is given in Table 29.
Convection Flux Component
In the preceeding subsections the energy fluxes to each section
attributable to conduction and radiation have been estimated. In Table
10 the total energy flux recovered at each section has been given on
the basis of recorded data. The question that remains is as follows:
Can the convection flux component be assumed to be that quantity that
remains as a result of subtracting the conduction and radiation sources
to each section from the total known to be present?
The difficulty in answering this question is that there can be a
significant interaction between these heat flux modes: in particular,
the interaction between radiation and convection at a surface. This
subject has been the topic of a large number of papers, among them
are the works of Viskanta [k2k], Macken [1*25], and Bratis [1*26]. Despite
the many efforts in the field, the state of knowledge is still incomplete
(for instance the work of Bratis [U26], although extremely recent, is
restricted to laminar flows of a free convection boundary layer along a
vertical flat plate being irradiated by a high temperature parallel
flat plate). Fortunately, the effect of radiation is small upon the
Navier-Stokes equation; Viskanta [h2h] writes in connection with
Rosseland's radiation pressure tensor term that it is, "ordinarily
negligible in engineering applications even at moderately high tempera-
tures." The principal effect appears.in the energy equation in a manner
uncoupled from the equation of motion. Thus the procedure adopted here
-------
200
TABLE 29
CALCULATION OF TOTAL RADIATION FLUX TO EACH SECTION
(Btu/hr-ft2)
Section
1
2
3
'
4
5
External Vortex Plate
Internal Vortex Plate
Column Loss
Copper Base Plate
Vortex Gas
Total
External Vortex Plate
Internal Vortex Plate
Column Loss
Copper Base Plate
Vortex Gas
Total
External Vortex Plate
Internal Vortex Plate
Column Loss
Copper Base Plate
Vortex Gas
Total
External Vortex Plate
Internal Vortex Plate
Column Loss
Copper Base Plate
Vortex Gas
Total
External Vortex Plate
Internal Vortex Plate
Column Loss
Copper Base Plate
Vortex Gas
Total
Condition
3
980
820
(90)
20
2430
4160
no
40
(70) '
0
1580
1660
30
0
(50)
0
950
930
10
0
(50)
0
630
590
10
0
(40)
0
450
420
8
1150
960
(120)
30
2330
4350
130
40
(80)
0
1630
1720
40
0
(60)
0
1110
1090
10
0
(60)
0
740
690
10
0
(50)
0
540
500
12
1240
1040
(140)
30
2620
4790
140
50
(90)
0
2000
2100
40
0
(70)
0
1380
1350
10
0
(60)
0
970
920
10
0
(60)
0
730
680
-------
201
is one in which the components are assumed to be merely additive and
so the convection flux can be found by subtracting the radiation and
conduction fluxes from the total heat recovery flux.
The results of this subtraction procedure are given in Table 30.
Because of the uncertainty associated with the calculations of the
radiation flux and since the calculations were performed independent of
Configuration, these results are given only to three significant
figures.
Nusselt Number Correlation
Evaluation of Convection Conductance
The convection conductance, h, is defined by Equation (8) where
the AT is usually taken as the temperature difference between the mixed-
mean temperature and the wall temperature. Since the velocities present
in this incinerator are relatively low, the difference between the
adiabatic wall temperature and the measured wall temperature is
negligible. Because the wall temperature data of Table 17 is particularly
sensitive to water inlet temperature, the wall temperature used in
formulating AT will be that measured a radius ratio of 0.0 for the vortex
gas (as given in Tables 11-13). The average temperature of Table lU will
be used for the mixed-mean temperature.
The results of this calculation is given in Table 31 for convection
conductance for each Station/Configuration/Condition combination. The
mean convection conductance has been found by dividing the total convec-
tive heat recovery rate by the average temperature difference for all
five Stations for each combination of Configuration/Condition.
-------
TABLE 30
CONVECTION FLUX AT EACH STATION
Configuration
1
]
3
• Condition
3
8
12
3
8
12
3
8
12
_
Convection Heat Flux (Btu/hr-ft )
Sec. 1
15,000
24,600
29,300
19,000
26,700
31,100
18,400
26,500
30,800
Sec. 2
11,300
14,200
18,300
13,700
16,900
20,900
13,800
15,600
19,400
Sec. 3
8,360
10,600
13,700
10,100
12,000
14,500
9,940
11,600
14,400
Sec. 4
6,360
8,630
11,000
7,430
9,470
11,700
7,390
9,300
11,500
Sec. 5
5,960
8,690
11,200
7,130
9,580
12,100
6,960
9,390
11,800
Total
Convection
Rate
(Btu/nr)
71,000
101,000
126,000
86,500
113,000
136,000
85,200
109,000
133,000
ro
o
IV)
-------
203
Mean Nusselt Number Correlation
The mean Nusselt number is defined here by the following
equation:
% = h D / k
where h is defined to be the mean convection conductance as calculated
in Table 31, D is the diameter of the furnace column (O.WO feet), and
k is the thermal conductivity evaluated at the average furnace column
gas temperature as given in Table lU. The calculation of this latter
quantity is complicated by the fact that the conductivity is both a
function of the gas temperature as well as composition. However, Maxwell
[itOl] has measured the thermal conductivity of "flue gas" which he
found to be insensitive to the degree of excess air and a function only
of temperature similar to what was used for the viscosity in Appendix D.
The details of the calculation procedure are given in Appendix H.
Correlations for Nusselt number are typically given as functions
of both Reynolds and Prandtl numbers for simple axial flow inside a tube.
The well-known Dittus-Boelter equation for turbulent flow in a smooth
tube with cool walls is as follows (taken from page 176 of Reference
NuD = 0.023 Re°'8 Pr°'3 (15)
where the fluid properties are evaluated at the mixed-mean temperature.
When the mixed-mean and wall temperatures are significantly
different, the Dittus-Boelter equation is usually modified as follows
(sometimes known as the Sieder-Tate relation, taken from page 178 of
Reference [Ul6]):
— 0.8 _ 0.333 / / xO.lU
Nn = 0.027 Re^ Pr JJ (y/y )
D D w
-------
TABLE 31
EVALUATION OF CONVECTION CONDUCTANCE
(Btu/hr-ft2-°F)
Configuration
1
2
3
Condition
3
8
12
3
8
12
3
8
12
Sec. 1
12.3
18.8
21.3
15.0
20.4
22.8
14.6
20.7
23.0
Local
Sec.
10.9
12.4
15.3
12.8
15.9
19.1
13.2
13.9
17.8
Convection Conductance
2 Sec. 3
10.0
10.8
14.1
11.6
12.3
14.2
11.6
12.1
14.4
Sec. 4
9.24
11.0
11.8
10.5
11.3
12.8
10.3
11.3
12.8
Sec. 5
10.7
12.9
13.2
11.8
12.9
14.7
11.4
13.3
14.9
Mean
Convection
Conductance
11.0
13.7
15.7
12.7
15.2
17.3
12.6
14.8
17.2
O
-------
205
where all fluid properties are evaluated at the mixed-mean temperature
except y which is evaluated at the wall temperature.
The mean Nusselt number found in Appendix H together with the
Seider-Tate relation are graphed at a function of the axial Reynolds
number in Figure 31 •
Length Nusselt Number Correlation
Just as a length Reynolds number was defined in Chapter III, a
similar length Nusselt number can be defined using a characteristic
length, L (equal to one-foot for the bottom furnace column section,
two-feet, for the next section, and so on), instead of the furnace column
diameter D.
NuL = \L = NuD (L/D) (17)
The convection conductance, h, used in this Nusselt number is the local
value as given in Table 30 for each furnace column section.
This calculation is performed in Appendix H and the results are
presented in Figure 32 as a function of the length Reynolds number found
in Table D-5-
Nusselt has suggested the following correlation for heat transfer
in the entry-length section of a tube (taken from [4l6] page 178):
NuD = 0.036 Re°'8prO. 333 (L/D)-0. 055
By substituting Equation (17) for NuD and Equation (3) for ReD the
following form of Nusselt 's Equation can be found:
NUT = 0.036 Re?'8 Pr°-333
L L
The Prandtl number has been evaluated using air property tables
for the U5 average vortex gas temperatures tabulated in Table lU. The
-------
206
M
-------
207
H
V
to
n,
40
30
20
10
9
8
7
6
5
4
1
0.9
0.8
0.7
0.6
0.5
0.4
T 1 1 1
Note: Darkened symbols represent Configuration 1 data
Open symbols represent Configuration 2 data
Half-Darkened Configuration 3 data
Cond it ion Symbo1
3 O
8 A
12 D
8
Prediction of
Equation (20
for Conditions
3, 8, & 12
A8.
i
A
A
J L
J 1 L
4 5 6 7 8 10 20
Length Reynolds Number x 10*3
40
60
100
Figure 32. Length Nusselt Number vs. Length Reynolds Number
-------
208
variation is very small and the Prandtl number raised to the 0.333 power
is equal to 0.881 plus or minus 0.25$ for all the data. Substituting
this value into Equation (19) results In:
NuT = 0.0317 ReT°'8 (L/D)' (20)
L Li
The predicted length Nusselt number of this equation has been
included in Figure 32. The calculation for each Condition was per-
formed using the mean of the length Reynolds number given in Table D-5
for the three exit Configuration values available for each Condition/
Station.
The restrictions usually imposed upon the Wusselt correlation
are for length-to-diameter ratios greater than 10. Since the length-
to-diameter ratio of the furnace column is only 10. U2 it is not
surprising that the slope of the data for the lower sections in the
furnace column differs from that predicted. However, at the higher
sections the slope of the data is almost exactly parallel to the pre-
diction curve except for the very last section. The level of the Husselt
number measured is much higher than the prediction (by a factor of
approximately 7)-
Stanton Humber Correlation
Concept
The Nusselt number correlation attempted in the previous subsection
did not adequately represent the level of the data, although the slope
is of the correct order.
The concept to be developed here stems from viewing the swirling
flow within the furnace column as an external flow problem rather than an
-------
209
entry-length section of an internal flow field. The furnace
column walls are replaced by an equivalent flat plate by un-
wrapping the column in what has come to be known as the
"helicoidal model."
The Stanton number is defined as:
St = h / (p cp ¥) (21)
where W is defined to be the free-stream velocity. The convection
conductance used in the above equation is the local value as given in
Table 31 for each section.
The Stanton number is usually correlated in the following
manner:
P/^
St Pr /J = J = function (Re ) (22)
X
where j is the Colburn j-Factor (defined as given) and Re is the
x
length Reynolds number defined as:
Re = p W x / y (23)
X
where x is the distance along the surface which is the distance from the
leading edge of the equivalent flat plate in this case. To avoid con-
fusion with the length Reynolds number defined in Equation (3)—which is
based upon the mean axial velocity and the furnace column height—this
Reynolds number will be referred to as the free-stream Reynolds number
(since it is based upon the free-stream velocity and the equivalent flat
plate distance).
Thus, in order to develop a plot of the Colburn j-Factor as a
function of the free-stream Reynolds number, the free-stream velocity
must be determined and the equivalent flat plate distance found.
-------
210
Characterization of Swirl Intensity
There are many possible definitions of dimensionless parameters
that would characterize the intensity of swirl present in the flow
field. The one chosen here is defined in terms of the following:
(1) the axial flux of angular momentum, K
(2) the axial flux of axial momentum, I
(3) and the wall radius of the furnace column, R.
In terms of these quantities, the swirl parameter S is defined as:
S = K / (I R) (2*0
The axial flux of angular momentum is equal to the following:
K = 2ir p U V r dr (25)
•'o
where U is the axial velocity, V the tangential velocity, and r the
distance from the centerline of the furnace column. If the density is
independent of the radius and the two assumptions that constitute the
helicoidal model are made—namely, slug flow (i.e. U is also independent
of r) and solid-body rotation (therefore V is equal to a constant times
the radius)—then the axial flux of angular momentum can be expressed as
follows:
K = m V R / 2 (26)
w
where m is the total mass flow rate, V the tangential velocity at the
w
furnace column wall (in reality the velocity must be evaluated a short
distance from the wall because the no-slip condition of continuum flow
requires that the velocity at a solid surface be identically zero), and
R the radius of the furnace column wall (0.2^0 feet).
-------
211
The axial flux of axial momentum is equal to the following:
fR 2 fR
I = 2ir p U r dr + 2ir p r dr (27)
'o JQ
where p is the static pressure expressed in units of psfg. By making
the assumptions of density independent of radius, slug flow, and
negligible contribution of the pressure integral term, this expression
can be reduced to:
I = m U (28) „
where m is the total flow rate and U is the mean axial velocity.
Thus for the assumptions of density independent of radius and
helicoidal flow, the swirl parameter can be expressed as follows:
S = 0.5 V / U (29)
w
Greenspan [70] has defined the Rossby number as the ratio of the
inertia forces (a characteristic velocity) to the coriolis forces (the
product of the angular velocity and a characteristic length). If U is
taken to be the characteristic velocity, R the characteristic length,
and the quantity V /R as the angular velocity then the Rossby number is
w
simply the following:
Ro = U / V (30)
w
Thus, in terms of these assumptions the swirl parameter is simply
the inverse of twice the Rossby number:
S = 1 / 2 Ro (31)
If the effect of pressure integral of Equation (27) is taken into
account using Bernoulli's Law to relate the static pressure in terms of
-------
212
the tangential velocity and assuming that the total pressure is
simply atmospheric pressure, then the following result for the swirl
parameter is obtained:
0.5 V / U
"^ — •— '
s = £ —^ (32)
1 - 0.25 (V / U)
w
Other authors have defined the swirl parameter somewhat differ-
ently. Persen [3^6] has defined it as the ratio of the maximum
tangential velocity divided by the mean axial velocity; he called this
expression the "vortex strength." Love [175] has defined a "local
vorticity characteristic" as one-half the circulation evaluated at the
wall times the wall radius divided by the axial volumetric through-flow.
If the assumption of helicoidal flow is made, then Love's definition
reduces to simply two times the result of Equation (29). Lewellen [105]
has defined an "interaction parameter between the circulation and the
stream function" as the circulation times the wall radius divided by the
mass flow rate divided by the density; when the helicoidal assumptions
are substituted and the circulation is evaluated at the wall the result
is four times that given for the swirl parameter in Equation (30).
Murthy's result [71] is similar to that used by Love. Chigier [11^,115],
Lilley [121 ], and Yajnik [17**] used definitions of swirl intensity that
would result in the same equation as developed here for the same
assumptions. However, if the pressure integral term is ignored, then all
the swirl parameter definitions reduce to essentially the same result,
differing only by a factor of 2 or k. The {justification for ignoring the
pressure integral term can be seen by comparing Equations (29) and (32).
For tangential velocities equal to or greater than twice the mean axial
-------
213
velocity, the swirl parameter found by Equation (32) — which includes
the effect of the pressure integral term — is undefined becoming infinite
for values twice the mean axial velocity and negative for larger tangential
velocities. Equation (29) will be used here.
The free-stream velocity to be used in the Stanton number
definition is defined to be:
w = ( u + V (33)
By eliminating the tangential velocity through the use of Equation (29),
the free-stream velocity can be expressed as a function of the mean
axial velocity and the swirl parameter:
¥ = U ( 1 + 1* S2 )% (3>0
Using Equations (26) and (29) to eliminate V and solving for
w
S results in the following expression:
S = K / m U R (35)
The axial flux of angular momentum, K, can be approximated by
assuming that its value at the tangential inlet air-line is the value
at the start of the furnace column. This assumption is termed the per-
fect conversion assumption since it assumes that the angular momentum
injected into the vortex chamber is not dissipated in the contraction
of the flow field as it enters the bottom of the furnace column. By
employing this assumption, K can be found directly from the following
equation:
K = m V R (36)
a a a
-------
where the subscript a designates conditions at the air inlet section.
Thus in is the flow rate of the air only (m is the flow rate of the air
a
plus the propane), V is the velocity of the air in the inlet air pipe,
£1.
and R is the radius of the centerline of the inlet air pipe with res-
a
pect to the centerline of the furnace column (which can be found to be
0.638 feet from Figure 5)- Thus, S can be expressed as follows:
[APR 1 fval
1 + AFRj [u J
s • 2-« [T^J [f| (3T>
where AFR is the air/fuel ratio, and the values for R and R have been
substituted to obtain the factor 2.66.
Calculation of Mean Axial Velocity
The mean axial velocity is found from the use of the continuity
relationship:
U = m / ( p Ac ) (1*2)
The mass flow rate in the above equation is the total of the air and
propane flow rates given in Table 10, the area is the area of the furnace
column (O.l8l square feet), and the density is the mean density of the
products of reaction evaluated at the average gas temperature.
By assuming that the perfect gas law holds for the reaction pro-
ducts, the mean axial velocity can be related directly to the average
gas temperature:
U = (m Rg Tm) / (p Ac) (US)
.where R is the gas constant of the products of combustion and p is the
o
pressure of the gas (which is assumed to be atmospheric throughout
these calculations).
-------
215
If the reaction is assumed to be complete at the first furnace
column section, then the gas constant can be found from Table F-l and
the following relation:
*
R =
B
t. M.
i i
s
i
(MO
where R is the universal gas constant (15^5 ft-lbf/l"fam-°E), x. the mole
fraction of each product constituent, M. the molecular weight of each
constituent, and E. the gas constant of each constituent. Performing
the calculation indicated above results in the following values of R :
TABLE 32
GAS CONSTANT OF PRODUCTS
(ft-lbf/lbm- R)
Configuration
1
2
3
Condition
3
55-13
55-36
55-31
8
5^-35
5^.38
5^.38
12
5^.34
5>*. 38
5^.38
• 1. !• <**-~*-~~ 1.
Since the angular momentum flux is being evaluated based upon
conditions at the bottom of the furnace column, the mean axial velocity
will also be evaluated at that section. Thus the average gas tempera-
ture as given in Table lU for Station 1 will be used in-Equation (U3).
The results of the calculation for the mean axial velocity are as
follows:
-------
216
TABLE 33
MEAN AXIAL VELOCITY
(ft/sec)
Configuration
1
2
3
Condition
3
9-08
9-30
9.2U
8
17.2
' 16.8
16.6
12
22.9
22.1
21.?
Calculation of Inlet Air Velocity
The inlet air velocity may be found using the equation of
continuity and the perfect gas law similar to the procedure used to find
the mean axial velocity. The pressure measured in the inlet air supply-
line is the total pressure whereas the static pressure is required to
determine the density in the perfect gas law; however, by assuming that
the total and static pressures are equal, and using Bernoulli's Equation
for incompressible flow to find the velocity and thus the difference
between static and total-pressure, the validity of the original assumption
can be substantiated.
Using the total air flow rate (for both inlet air lines) given in
Table 10, and twice the area of each inlet line (0,OlUo square feet)
together with the density calculated as outlined above, the velocity in
the inlet air-line can be calculated. The results are tabulated below:
-------
217
TABLE 3k
INLET AIR VELOCITY
(ft/sec)
Configuration
1
2
3
Condition
3
13.9
13.6
13-7
8
20.9 •
20.1
20.3
12
23.3
22.5
22.6
Calculation of Free-Stream Velocity
By substituting the calculated values of mean axial velocity and
inlet air velocity together with the tabulated values of air/fuel ratio
(from Table 10) the swirl parameter can be found from Equation (37).
Use of Equations (33) and (29) then permit the determination of the
free-stream velocity and the tangential velocity.
These results are presented in the following table:
-------
TABLE 35
SWIRL PARAMETER CALCULATION
Configuration
1
2
3
Condition
3
8
12
3
8
12
3
8
12
S
3.82
3.08
2.58
3.6U
3.03
2.58
3.69
3-10
2.6k
¥
(ft/sec)
69-9
107
120
68. U
103
116
68.9
10U
116
V
w
(ft/sec)
69. U
106
118
67.7
102
lilt
68.2
103
115
Equivalent Flat Plate Length
In order to determine an equivalent flat plate length x for each
furnace column section (given in terms of length L) some assumption is
necessary. The one made here is that the helix pitch of the equivalent
plate is determined by the ratios of the tangential to axial velocities via:
x = L ( V / U ) = 2LS
w
-------
The heat flux recovered at each section will be ascribed to the
mid-height of that section; thus the value of L for the first section is
0.50 feet, the second 1.50 feet and so on. Therefore the entire five-
foot high furnace column is approximately equivalent to a 30-foot flat
plate, the precise value dependent upon Configuration and Condition.
The free-stream Reynolds number may now be found using Equation (23)
together with the values of W and x found in this section. These
calculations are performed in Appendix D, and the results tabulated in
Table D-6.
Entry Length Effect Upon Convection Conductance
The convection conductances calculated in Table 31 were obtained
by using the convective heat flux measured for each furnace column
section. Thus they are mean convection conductances with respect to the
height of each section. Since the Stanton number correlation obtained in
this section is to be evaluated as a function of the free-stream Reynolds
number evaluated at the mid-point of each section, this mean value needs
to be adjusted so that it too reflects the local value at the mid-height
point.
To do this it is necessary to know how the convection conductance
varies with respect to x and hence L. For simple linear flows past a
flat plate this variation is to the minus one-fifth power, and this relation
will be used to evaluate h , defined as the convection conductance at the
x
mid-height of each section. If $ is defined as the ratio of h to h (which
J\-
is the mean conductance over the whole section), and if the variation of
C\ 9
h is assumed to be as x , then (3 can be expressed as follows:
-------
220
0.80 (x - x, )
0.8 0.8
xt - xb
where x is the equivalent flat plate distance at the mid-height of each
section, x at the top of the section, x at the bottom of the section.
"C D
Performing the above calculation for each section and Configuration/
Condition results in the following values which are dependent only upon
section: 0.919, 0.995, 0.998, 0.999S and 0-999 for sections 1 through
5 respectively.
Calculation of Colburn j-Factor
2/3
All the quantities necessary to form the product St Pr have
J\.
been defined where St indicates that the convection conductance to be
x
used is h as defined above.
x
This calculation is presented in Appendix I with all the fluid
properties evaluated at the film temperature which is defined to be the
mean of the average fluid temperature and the wall temperature.
The j-Factor is graphed as a function of Re as calculated in
X
Table D-6, in Figure 33- The least-squares curve-fit calculation has been
performed in Appendix J in accordance with the procedure outlined in
Reference
On the basis of the Reynolds analogy, the Colburn j-Factor for
turbulent flow past a flat plate is given as (from [^l6] page 153):
St Pr2/3 = 0.0288 Re~°'2° (U?)
x x
The prediction of this equation is given in Figure 33.
-------
i i
I I i I i
Least-Square*
Curve-Flc
•0288
fie-O.
1.0
0.9
0.8
0.2
Note: Darkened symbol* represent Configuration 1 data
Open symbols represent Configuration 2 data
Half-Darkened Configuration 3 data
Condition Symbol
I o
2 A
3 a
Prediction of
Equation (47)*
«.* 0.5 0.6 0.8 1.0 1.5 2
Free-Stream Reynolds Number x 10"*
IX)
ru
10
Figure 33. Colburn J-Factor v«. Free-Stream Reynolds Number
-------
222
Chtiiti-icHi Reaction Ei'i'ocL
The proceeding form of the Stanton number is that usually specified
for non-reacting flows for which the thermodynamic driving potential is,
in fact, the difference in temperature between the mixed-mean temperature
and the wall temperature. However, in the present "instance a chemical
reaction process is occuring simultaneous with the convective/radiative
heat transfer process. The question remains then: is the above tempera-
ture difference still the appropriate thermodynamic driving potential
upon which the convection conductance and hence the Stanton number should
be normalized?
This problem—usually termed "heat transfer in chemically reacting
flows"—has been dealt with in a number of papers. Bartz [i+28] examined
the turbulent heat transfer from a rocket combustion gas to a cooled
nozzle wall. Chung [^29] in a review work, has documented the state of
knowledge for laminar reacting boundary layers noting, "for very few
published works exist for turbulent non-equillibrium boundary layers."
He identified the key parameter as the gas phase Damkohler number. For
vanishing Damkohler number, the reaction rates are much slower than the
transport rates and the condition is usually termed as "chemically
frozen flows." For infinite values of Damkohler number just the reverse
is true with the reaction rate dominating the transport rate; this case
is usually referred to as "local chemical equillibrium flows." Because
the maximum velocities experienced in this vortex flow are relatively
small (on the order of 100 feet per second) this later state is assumed
to hold true.
Chung [1+30 ] has shown that for the case of infinite Damkohler
-------
number, the "total enthalpy difference ia basically the driving potential
for heat transfer in a chemically reacting flow." If the kinetic energy
of the flow field is negligible with respect to the chemical enthalpy
(which is the case here) then this driving potential is simply the
difference between the net enthalpy of reaction (which is the sum of the
chemical enthalpies and the sensible enthalpy) evaluated at the mixed-
mean temperature and at the wall temperature.
Conolly [431] has presented a means for accounting for an "equili-
brium Prandtl number" in terms of the frozen Prandtl number and the Lewis
number thereby accounting for diffusion effects upon the energy transport
process. However, by assuming that the Lewis number for the gas is approxi-
mately one (which is a reasonable assumption for most gases) then equili-
brium Prandtl number reduces to the frozen Prandtl number.
In general, the heat transfer process in the presence of flames is
extremely complicated and has not been solved even for relatively simple
cases. Emmons [432] in a recent survey paper has identified 16 significant
dimensionless parameters (not including geometrical ones) that governing
the heat transfer process in fires. The approach utilized here is to account
for the effect of chemical reaction by defining an enthalpy potential.
Thus, the Stanton number can be expressed as follows:
St = 3 <1 /pWAH (48)
x conv
where 3 has been defined in Equation (46), q Qnv is the convective heat
transfer flux as given in Table 30, p the gas density evaluated at the film
temperature, W the free-stream velocity (given in Table 35), and AH the
enthalpy potential for heat transfer.
-------
22k
The enthalpy potential is expressed here in the following manner:
AH = AHc + H* - H*
where AH is the net enthalpy of combustion (defined in Appendix F and
calculated in Table F-3), H* is the sensible enthalpy of the products
(determinable from the JANAF Tables [kok, ^05] as a function of product's
temperature) and H* is the sensible enthalpy of the reactants (similarly
a function of the temperature).
If the flow field is assumed to be such that the reactants are
heated to the mixed-mean temperature and the products are generated at the
wall temperature, then the quantity H* is evaluated at the average tempe-
rature as tabulated in Table lU and the quantity H* is evaluated at the
gas temperature at the wall as given in Tables 11-13-
The Stanton number obtained using this value of enthalpy potential
is called the "modified Stanton number" here. Multiplying this Stanton
number by the Prandtl number raised to the 2/3 power results in the modi-
fied Colburn j -Factor. These calculations are given in Table 1-2 and
graphically presented as a function of the free-stream Reynolds number in
\v
Figure 3^- The least-squares line is calculated in Appendix J.
In Figure 35 the same data as given in Figure 3^ is presented with
the exception of the 9 data-points at section 5 (the top-most section of
the furnace column). Two least-squares lines are shown: one through the
data of sections 1 and 2 (the bottom two sections) and one for sections 2
through 1|. These equations are calculated in Appendix J.
Also shown in Figure 35 is the prediction of the Colburn j -Factor for
laminar flows which is given by (taken from page 153 of Reference
-------
2.0
Prediction of
Equation (47)
Note: Darkened symbols represent Configuration 1 data
Open symbols represent Configuration 2 data
Half-Darkened Configuration 3 data
Condition Symbol
0.2
0.2
0.3
ro
7 8 9 10
Free-Stream Reynolds Number x 10"
Figure 34. Modified Colburn J-Factor vs. Free-Stream Reynolds Number
-------
2.0
o
1-4
X
u
o
u
u
m
b.
*
«-»
c
u
a
ji
o
u
Prediction of
Equation (4?)
Condition Symbol
Prediction of
Equation (50)
Note: Darkened symbols represent Configuration 1 data
Open syn>>ols represent Configuration 2 data
Half-Darkened Configuration 3 data
IV)
ro
ON
Free-Stream Reynolds Number x 10"
F'gur<' J5. Modified Colburn j-Factor vs. Fr««-Stre«™ Reynolds Number
-------
227
St Pr2/3 = 0.332 Re ~°'5° (50)
x x w '
The data of sections 1 and 2 agrees with the slope of the turbulent
flow prediction, Equation (^T)» whereas the slope of the data for sections
2 through k more closely agrees with the laminar flow prediction given
above. This change in slope is also present in Figure 33 although the
effect is not as dramatic.
There are three likely causes of the slope change:
(l) vortex decay,
(2) entry-length effects, and
(3) chemical reaction variation.
This latter effect would alter the formulation of the enthalpy potential
equation as given in Equation (^9) for each section. Since the slope
change seen in Figure 35 is much larger than that of Figure 33, the change
in the chemical reaction process with respect to furnace column height is
the most-likely cause of this effect.
-------
228
APPENDIX A
EQUIPMENT CALIBRATION
Temperature Measurement
Three different temperature measuring devices were used for data
recording during the experimental phase of this investigation:
(1) A Honeywell Model No. Y153X82-C-II-III-13, 2i|-channel, 0 to 50
millivolt strip-chart recorder compensated for chromel-alumel thermo-
couple material (Type T).
(2) A Daystrom Model No. 6702, 12-channel, minus 100 to plus 150 degrees
Fahrenheit strip-chart recorder compensated for copper-constantan thermo-
couple -material (Type T).
(3) A Hewlet-Packard Model No. 680, single-channel, 0 to 100 volts in
ten calibrated spans (only the 0 to 50 millivolt span was used) strip-
chart recorder.
(k) A Hewlet-Packard 2^-channel digital recording system consisting
of the following:
(a) a Model No. 2901A input Scanner,
(b) a Model No. 2^02A Integrating Digital Voltmeter, and
(c) a Model No. 5050B Digital Recorder.
The two Hewlett-Packard recorders were not compensated for a specific ther-
mocouple material or reference temperature and required the use of an ice-
bath together with an insulated junction box.
The Honeywell and Daystrom strip-chart recorders, items" 1 and 2 in
the above list, were calibrated with a Leeds and Northrup Millivolt Po-
tentiometer (Model Number 8686-2, Serial Number 17892^9) in accordance
with the procedure given in Reference [^33]• The results of the calibration
are given in Table A-l for the Honeywell recorder for two of its 2k
channels and Figure A-l for the Daystrom recorder for one of its 12 channels.
-------
229
TABLE A-l
HONEYWELL RECORDER CALIBRATION (Serial No. D 1168326002)
Channel
Number
6
=12
Potentiometer
Input (mv)
0
5
10
15
20
25
30
35
40
45
46
47
0
1
2
3
4
5
10
15
20
25
30
35
40
45
46
47
Recorder
Output (mv)
0.0
5.0
10.0
15.0
20.0
25.0
30.0
35.0
.40.0
44.9
45.9
46.9
0.1
1.0
2.0
3.0
4.0
5.0
10.0
15.0
20.0
25.0
30.0
35.0
40.0
44.9
46.0
46.9
Reference
Temperature (°F)
69.2
68.0
-------
230
150
130
NO
0)
3
2
90
70
01
H
T>
41
1 50
30
I I I I I I \
I T
30 50 70 90 110
True Temperature (°F)
130
150
Figure A-l. Daystrom Recorder Calibration (Serial No. 17219-1)
-------
231
The Hewlett-Packard strip-chart recorder, item 3, was calibrated
using a Honeywell Rubicon Potentiometer (Model Number 27^5, Serial Number
115587)- Use of the internal adjustments accessible on the recorder
always made it possible to obtain a linear, accurate (within the pen-
width) indication of the input voltage; hence, no calibration curve is
presented for this recorder.
The Hewlett-Packard digital recording system, item It, included a
self-contained calibration device which was used to check the accuracy
of the measurement system. Since the calibration never deviated more
than one one-thousandth of a millivolt, no correction was applied to the
data obtained with this device.
Two types of thermocouple materials were used: chromel-alumel
(Type K) and copper-constantan (Type T). All the Type T data were
measured exclusively on the Daystrom recorder, whereas the Type K were
measured on all of the other three recorders. All thermocouple materials
were purchased from Honeywell, Inc. The stated accuracy [U3^J of the
thermocouples were as follows:
(l) copper-constantan: ±1%°F in the range used.
(2) chromel-alumel: ±U°F for temperatures below 530°F, and
±0-75/2 of the actual temperature recorded for
temperatures above 530°F.
The stated accuracy [k3h] of the standard grade extension wire were as
follows:
(l) copper-constantan: ±1%°F, or
±0.75$ of the temperature difference between
the connection heat and the reference junction,
whichever is less.
-------
(2) chroinel-alumel: ±U°F, or
±2.5% of the temperature difference between the
connection heat and the reference junction,
whichever is less.
For the Honeywell and Daystrom strip-chart recorders the reference junction
temperature was approximately room temperature- The maximum connection
head temperature experienced was approximately 110°F. Thus for these
recorders the limits of error for the extension wire were ±0.30°F for
the copper-constantan and ±1.0°F for the chromel-alumel. However, most
of the thermocouples were located sufficiently far from the incinerator
that the connection head temperature was very nearly that of the reference
temperature. For the two Hewlett-Packard recorders the junction tempera-
ture was 32°F; thus the limits of error for the extension wire for these
recorders were ("based upon the maximum connection head temperature of
110°F) ±0.60°F for the copper-constantan and ±2.0°F for the chromel-alumel.
End-to-end calibration checks for the entire temperature measuring
system, thermocouple/extension wire/recorder, were performed using an ice-
bath and boiling water together with a highly-accurate Mercury thermometer.
In addition, intermediate temperature points were also checked by using a
variac with a resistance-heated container of water. The results of this
calibration indicated that the temperature could be measured within approxi-
mately ±0.5°F over this range.
Pressure Measurement
In addition to the barometric pressure, three system pressure
measurements were also made: each of the two air supply lines and the
propane supply line- These pressure measurements were made just upstream
-------
233
of the. flow control valve and the rotameter in such a fashion as to obtain
the total pressure.
The two air pressures were measured on a Meriam Instrument Company
mercury manometer (Type ¥, Model Humber 33KA35, Serial Number T20133) of
range 0 to 100 inches. The propane pressure was measured with a U-type
Meriam Instrument Company water manometer (Model Number 10AA25) of'range
0 to 30 inches.
The barometric pressure was obtained from a Precision Thermo, and
Inst. Company of Philadelphia precision barometer located within the
laboratory.
Flow Measurement
Eight rotameters were utilized to measure the required flow rates:
one for each air supply (two), one for the propane supply, and one for each
cooling water section(five). All of these flow meters were series 10A3000
Glass Tube Indicating Rotameters manufactured by the Fisher and Porter
Company of Warminster, Pennsylvania. The specified [*i35] accuracy and
repeatability were ±2% and 0.25$ of full-scale, respectively.
The two air flow meters were rated for 4l.O SCFM (standard cubic
feet per minute) of air at STP (standard temperature and pressure—here
taken to be 70°F and ik.J psi) at 100$ of scale. These rotameters were
accurate to within ±0.82 SCFM and repeatable to within ±0.1025 SCFM.
These devices were calibrated against a square-edged orifice of rated
accuracy ±0.5$. The calibration procedure consisted of setting the control
valve to provide the desired reading on the rotameter, then measuring the
temperature and pressure of the air stream, with the system described in
the preceeding Chapter II; the scale reading in percent was converted to
-------
SCFM using the pressure and temperature data according to the procedure
outlined by the manufacturer [^36]. At the same time, the pressure drop
•across the square-edged orifice, the pressure, and the temperature were
used in accordance with standard procedures [U37J to obtain the actual
flow rate in cubic feet per minute. Thus it was possible to develop a
calibration curve which would yield actual flow rate in cubic feet per
minute from the calculated flow rate (in SCFM) by means of the known
scale reading (in %) and the measured pressure and temperature. These
calibrations, for air flow meters number 1 and 2, are given as Figures
A-2 and A-3.
The propane flow meter was rated for It.6 SCFM of air at STP: thus
its stated accuracy and repeatability was ±0.092 and ±0.0115 SCFM of air,
respectively. Since, the propane was supplied in one-hundred pound tanks,
it was more convenient to calibrate the rotameter by a weight-change
procedure using a standard beam-balance scale. The calculated flow rate
(including the specific gravity correction) in accordance with the manu-
facturer's specification [^36] was found to agree to within \.% of the
measured weight change; as a result, no calibration curve was used.
Each water flow rate rotameter was rated for 1-52 GPM (gallons per
minute) of water at STP; thus, the stated accuracy and repeatability was
±0.030lt and ±0.00376 GPM of water, respectively. Each of the five rota-
meters were calibrated by means of a weight change procedure which entailed
collecting the water through-flow in portable tanks and obtaining the tare
weight on a beam-balance scale. The water flow was achieved by means of
the boost pump described in Chapter II on the city water supply line. Due
to transients in water pressure, there were inevitable momentary drop-offs
in flow rate. This flow disturbance together with the start-up and shut-
-------
235
60
50
40
1 30
3
§ 20
ctf
u
o
<
10
0
0
I
I
I
10 20 30 40
Calculated Flow Rate (SCFM)
50
60
Figure A-2. Air Rotaraeter No. 1 Calibration
-------
236
50
40
I 30
C 20
i-4
3
o
10
0
I • I
0
10 20 30 40
Calculated Flow Rate (SCIM)
50 60
Figure A-3. Air Rotameter No. 2 Calibration
-------
237
down Lr/i.n:; i onU; .•uiuociu'tod with this procedure resulted in a somewhat
|OW«.T li-vel ol' confidence in the calibration obtained, although the
degree of agreement was within the stated accuracy of the rotameter over
the range of interest (approximately ^5 to 70$ of full-scale). In addition,
since in the actual operation of the incinerator these same momentary
drop-offs in flow could be expected to occur, even an absolutely precise
calibration curve could not account for these effects. Hence it was
decided that the predicted flow rates using the observed percent of full-
scale reading would be used without further modification to obtain the
water flow rate. The water flow rate in gallons per hour was thus obtained
from the rotameter reading in percent by multiplying by a factor of 0.912.
-------
238
APPENDIX B
DATA REDUCTION PROCEDURE
General Procedure
Due to the large number of data runs that required reduction, it
became both expedient and necessary to develop a data analysis algorithm.
Available in the laboratory was a Monroe Model 1655 Electronic Programmable
Display Calculator together with a card reader that provided a programming
capability of 126 steps [^-38]. Once the programs had been written, de-
bugged, and punched-out then all future operations required only that the
cards be fed into the reader and stored in the machine's internal memory
pripr to each data reduction session.
The data was supplied through the key-board to the operating program
with the results presented in the electronic display.
Heat Recovery Program
The heat recovery program was designed to utilize the cooling water
temperature and flow rate data to determine the heat transferred to each
section of cooling water and the total heat recovered in all five cooling
sections. The basis of the program was the following equation:
q = m c AT (B-l)
where q is the heat transfer rate in Btu/hour, m the water flow rate in
pounds per hour, c the specific heat at constant pressure (the value of
1.0 was used for all the calculations), and AT the temperature difference
-------
239
of the water outlet temperature ininus the inlet temperature.
The program was designed so that the water inlet temperature,
which was common to all five cooling-water lines, was loaded first. Then
in sequence each cooling-coil section's outlet temperature and flow rate
in gallons per hour (obtained by multiplying the rotameter percent reading
by the factor 0.912) were loaded. The program then provides the heat
transferred to each section and the total of all five sections in units of
Btu per hour. To obtain the heat flux recovered at each section it was
then only necessary to divide each section's heat recovery rate by the
area of each section (1.508 square feet).
Flow Rate Program
The purpose of the flow rate program was to utilize the rotameter
percent full-scale data for the two air and one propane control valve
settings to obtain the actual mass flow rate for each of these quantities.
The required input was the rotameter reading, the pressure, and the tempera-
ture of each flow supply and the barometric pressure. The program pro-
ceeds in the following fashion. It utilizes the rotameter reading in per-
cent (defined as D), the rated rotameter capacity in SCFM (defined as C,
which is equal to 1*1.0 for the air rotameters and k.6 for the propane
rotameter), and the pressure and temperature of the flowing gas. Three
correction factors are required as follows:
(l) the specific gravity correction factor (defined as H) which is
equal to the square root of the specific gravity of the gas to the
specific gravity of air(thus it is equal to 1.00 for air and 1.22
for propane),
(2) the pressure correction factor (defined as I) which is equal to
the square root of the ratio of 1*1.7 to the actual flowing gas pressure
in pounds per square inch absolute, and
-------
2kO
(3) Ihe temperature correction-factor (defined as J) which is equal to
the square root of the ratio of the actual flowing gas temperature in
degrees Rankirie to the standard temperature (530°R).
The predicted flow rate according to rotameter theory [^36] is
then:
SCFM =DxC/(HxIxJ) (B-2)
At this point in the program there is a halt and the above calculated
value is corrected by the calibration curves given in Figures A-2 and A-3
(for propane, the calculated value is uncorrected). After the correction
is inserted into the program, the actual flow rate in pounds per hour is
computed directly by using the equation of state together with the con-
tinuity equation.
The air/fuel ratio is obtained simply by dividing the total flow
rate of the two air supplies by the flow rate of the propane.
-------
APPENDIX C
CALCULATION OF AVERAGE TEMPERATURE
The concept of mixed-mean temperature is commonly used [kOO] to
correlate convective heat transfer coefficient for internal flows. This
temperature is defined by Equation (l) given in Chapter III — but for
the assumption of uniform axial profile, it can be written in the follow-
ing form:
Tm = / j Trdr (C-l)
c J o
The justification of the assumption of a uniform axial profile has been
presented in Chapter III. The temperature so obtained will be called the
"average" gas temperature since it represents a simple area-average of
the temperature data presented in Tables 11-13.
This average is obtained in the following fashion:
(l) the temperature data for two adjoining radii (say at 0.25 and
0.50 inches from the wall) are averaged, then
(2) the area of the annulus bounded by these two radii is calculated
(for these radii it would be 3-936 square inches), then
(3) the product of the averaged temperature and its respective annular
area is formed;
this procedure is continued for all twelve annuli, then the twelve
temperature-area products are summed and the total is divided by the
total area of the cross-section (26.058 square inches) yielding the
"average" temperature .
The results of this calculation procedure are presented in Tables
C-l through C-5 for each of the five thermocouple stations and for each
combination of Exit Configuration and Condition.
-------
TABLE C-l
AVERAGE VORTEX GAS TEMPERATURE AT STATION 1
Distance
From Wall
(inches)
0.00
0.25
0.50
0.75
1.00
1.25
1.50
K75
2.00
2.25
2.50
2.75
2.88
Annular
Area
(sq. in.)
4.328
3.935
3.542
3.149
2.757
2.366
1.971
1.579
1.186
0.793
0.401
0.053
Sum of Temperature-
Area Products
Average Temperature (°F)
Average
for
Cond. 3
471
1114
1506
1634
1690
1706
1706
1676 .
1632
1594
1558
1556
35,507
1363
Annular Temperature
Configuration 1
Cond. 8 Cond. 12
586
1284
1638
1739
1783
1796
1796
1780
1746
1717
1686
1654
38,571
1480
646
1387
1728
1820
1862
1873
1862
1846
1824
1792
1758
1736
40,631
1560
Average
for
Cond. 3
583
1246
1565
1670'
1706
1714
1716
1710
1686
1650
1598
1556
37,093
1424
Annular Temperature
Configuration 2
Cond.
676
1372
1650
1735
1762
1772
1770
1756
1732
1706
1661
1616
39,096
1500
8 Cond. 12
736
1464
1724
1802
1827
1838
1836
1825
1806
1780
1744
1706
40,949
1572
Average
for
Cond. 3
558
1203
1554
1690
1722
1724
1716
1706
1668
1604
1551
1538
36,824
1413
Annular Temperature
Configuration 3
Cond.
646
1310
1612
1740
1769
1756
1744
1733
1704
1654
1598
1576
38,398
1474
8 Cond. 12
702
1400
.
1686
1804
1836
1827
1808
1794
1772
1724
1674
1656
40,201
1543
ro
-p-
ro
-------
TABLE C-2
AVERAGE VORTEX GAS TEMPERATURE AT STATION 2
Distance
From Wall
(inches)
0.00
0.25
0.50
0.75
1.00
1.25
1.50
1.75
2.00
2.25
2.50
2.75
2.88
Annular
Area
(sq. in.)
4.328
3.935
3.542
3.149
2.757
2.366
1 .971
1.579
1.186
0.793
0.401
0.053
Sum of Temperature-
Area Products
Average Temperature (°F)
Average
for
Cond. 3
510
1038
1284
1390
1450
1474
1474
1448
1411
1394
1379
1362
31,293
1201
Annular Temperature
Configuration 1
Cond. 8 Cond. 12
617
1208
1429
1525
1580
1596
1584
1562
1538
1538
1542
1514
34,744
1333
712
1428
1643
1598
1654
1694
1672
1650
1638
1643
1650
1622
38,007
1459
Average
for
Cond. 3
512
1042
1262
1376
1446
1484
1496 '
1481
1459
1437
1411
1383
31 ,406
1205
Annular Temperature
Configuration 2
Cond.
620
1152
1366
1470
1536
1566
1571
1554
1529
1512
1492
1464
33,856
1299
8 Cond. 12
706
1262
1472
1574
•
1636
1666
1661
1638
1614
1596
1578
1545
36,393
1397
Average
for
Cond. 3
494
997
1248
1392
1463
1490
1483
1461
1420
1380
1368
1372
31,048
1192
Annular Tempera turo
Configuration 3
Cond.
578
1141
1348
1470
1536
1552
1542
1524
1500
1478
1458
1454
33,355
1280
8 Cond. 12
703
1256
1470
1578
1632
1640
•
1620
1594
1576
1560
1544
1547
36,051
1384
re
-tr-
U!
-------
TABLE C-3
AVERAGE VORTEX GAS TEMPERATURE AT STATION 3
Distance
From Wall
(i ncheO
0.00
0.25
0.50
0.75
1.00
1.25
1.50
1.75
2.00
2.25
2.50
2.75
2.88
Annular
Area
fco in )
\3H* in./
4.328
3.935
3.542
3.149
2.757
2.366
1.971
1.579
1.186
0.793
0.401
0.053
Sum of Temperature-
Area Products
Average Temperature (°F)
Average
for
Cond. 3
336
773
1058
1150
1211
1236
1236
1216 ;
1212
1222
1207
1182
25,432
976
Annular Temperature
Configuration 1
Cond, 8
522
1034
1239
1318
1360
1364
1362
1356
1352
1387
1415
1396
30,009
1152
Cond. 12
647
1155
1364
1439
1472
1476
1461
1454
1470
1508
1534
1516
33,061
1269
Average
for
Cond. 3
402
826
1023
1133
1207
1230
1237
1241
1241
1235
1214
1184
25,812
991
Annular Temperature
Configuration 2
Cond. 8
477
966
1169
1274
1329
1340
1338
1338
1346
1353
1336
1306
28,871
1108
Cond. 12
560
1076
1286
1383
1424
1437
.1439
1446
1461
1466
1450
1424
31,558
1211
Average
for
Cond. 3
400
826
1027
1120
1180
1212
1220
1220
1198
1175
1170
1175
25,477
978
Annular Temperature
Configuration 3
Cond.
478
968
1172
1265
1301
1303
1301
1306
1299
1288
1273
1267
28,443
1092
8 Cond. 12
560
1070
1269
1362
1402
1409
1398
1400
1410
1402
1388
1388
30,994
.1190
ro
-------
TABLE C-4
AVERAGE VORTEX GAS TEMPERATURE AT STATION 4
Distance
From Wall
(inches)
0.00
0.25
0.50
0.75
1.00
1.25
1.50
1.75
2.00
2.25
2.50
2.75
2.88
Annular
Area
(sq. in.)
4.328
3.935
3.542
3.149
2.757
2.366
1.971
1.579
1.186
0.793
0.401
0.053
'
^ — - — — •
Sum of Temperature-
Area Products
•-- - — - •- " ~™'
Average Temperature (°F)
Average
for
Cond. 3
245
564
828
945
998
1036
1048
1034
1036
1063
1068
1048
20,641
792
Annular Temperature
Configuration 1
Cond. 8
328
716
1010
1124
1171
1186
1186
1171
1171
1220
1276
1282
24,505
940
Cond. 12
435
928
1175
1250
1286
1280
1273
1288
1303
1348
1400
1414
27,997
1074
Average
for
Cond. 3
283
607
826
941
1002
1038
1060
1074
1084
1086
1074
1054
21,133
811
Annular Temperature
Configuration 2
Cond.
398
796
989
1099
1150
1170
1177
1182
1196
1211
1207
1190
24,866
954
8 Cond. 12
466
913
1106
1203
1250
1278
1288
1292
1310
1325
1320
1301
27,562
^f**iimm*ti~i*i*imiMitii**m**m*i^*tiiim**iii**m***
1058
Average
for
Cond. 3
302
648
854
951
1010
1046
1061
1061
1046
1029
1029
1034
21,422
WWB«*MIMPW*allW«WIWWMW4IW-
822
Annular Temperature
Configuration 3
Cond.
398
796
976
1078
1124
1146
1154
1152
1156
1158
1148
1148
24,417
937
8 Cond. 12
460
902
*
1084
1184
1237
1260
1260
1254
1258
1260
1262
1274
27,023
1037
ro
-------
TABLE C-5
AVERAGE VORTEX GAS TEMPERATURE AT STATION 5
Distance
From Wall
(i nches)
0.00
0.25
0.50
0.75
1.00
1.25
1.50
1.75
2.00
2.25
2.50
2.75
2.88
Annular
Area
ten in }
4.328
3.935
3.542
3.149
2.757
2.366
1.971
1.579
1.186
0.793
0.401
0.053
Sum of Temperature-
Area Products
Average Temperature (°F)
Average
for
Cond. 3
211
450
634
760
848
882
898
892
896
926
945
934
17,148
658
Annular Temperature
Configuration 1
Cond. 8
289
600
871
1000
1046
1057
1054
1040
1040
1092
1167
1184
21,576
828
Cond. 12
416
845
1048
1134
1168
1173
1160
1152
1173
1226
1299
1325
25,459
977
Average
for
Cond. 3
265
534
710
816"
871
905
928
938
947
953
953
945
18,492
710
Annular Temperature
Configuration 2
Cond. 8 Cond. 12
348
708
902
1000
1044
1054
1054
1059
1070
1088
1101
1098
22,384
859
416
824
1019
1108
1148
1164
1166
1170
1188
1209
1222
1218
25,124
964
Average
for
Cond. 3
262
552
744
832
884
918
930
928
907
888
890
898
18,650
716
Annular Temperature
Configuration 3
Cond.
336
678
862
955
1006
1028
1034
1029
1020
1014
1012
1020
21,522
826
8 Cond. 12
394
790
985
1074
1122
1143
1141 .
1133
1129
1124
1132
1152
24,261
931
ro
-P-
ON
-------
APPENDIX D
REYNOLDS NUMBER CALCULATIONS
There are many possible definitions of Reynolds number because of
the many choices available of characteristic dimension, characteristic
velocity, and temperature at which fluid properties are evaluated. The
absolute viscosity of the vortex gas is evaluated as a function of gas
temperature using the flue gas viscosity curve of Maxwell ([l*0lj, page
191) which is given as Figure D-l.
Axial Reynolds Number
For the axial Reynolds number, the quantity D in Equation (2)
given in Chapter III is the furnace column diameter, O.U800 feet. This
Reynolds number must be calculated separately for the exit and inlet
Configuration investigations because the total mass flow rates varied
slightly as well as the vortex gas temperature.
The axial Reynolds number for the exit Configuration investigation
is presented in Table D-l where the absolute viscosity has been evaluated
at the average furnace column temperature which is obtained by finding
the mean of the five Station average temperatures.
The axial Reynolds number for the inlet Configuration investigation
is presented in Table D-2. Since temperature profiles were not available
for these data, the average of the temperature measurements given in
Table l6 was used to evaluate viscosity.
-------
0.14
0.12
0.10
.c
3 0.08
t>
V
.u
3
i—<
O
0.06
0.04
0.02
200
400
ro
-P-
co
600
1400
800 1000 1200
Temperature (°F)
Figure D-l. Absolute Viscosity of Flue Gas at 1 Atm.
1600
1800
2000
-------
TABLE D-l
AXIAL REYNOLDS NUMBER CALCULATION FOR 3 EXIT CONFIGURATIONS
Exit
Configuration
1
2
•
3
Condition
3
8
12
3
8
12
3
8
12
• i ......... i . »,.
Average
Furnace
Column
Gas Temperature
(°F)
988
1147
1268
1028
1144
1240
1024
1122
1217
-*--- • i ii i
Absolute
Viscosity
(Ibm/hr-ft)
0.0859
0.091S
0.0958
0.0871
0.0912
0.0949
0.0869
0.0908
0.0939
Total Flow
Rate
(Ibm/hr)
124.6
225.0
287.8
123.0
216.9
275.6
123.0
217.2
274.5
Axial
f
Reynolds
Number
3850
6220
7970
3750
6310
7700
3760
6350
7760
TABLE D-2
AXIAL REYNOLDS NUMBER CALCULATION FOR 3 INLET CONFIGURATIONS
Inlet
Configuration
A
B
C
Condition
3
8
12
3
8
12
3
8
12
•
Average*
Furnace
Column Gas
Temperature
(°F)
901
1133
1295
988
1265
1435
1290
137C
1452
Absolute
Viscosity
(Ibm/hr-ft)
0.0823 '
0.0911
0.0968
0.0859
0.0959
0.1016
0.0167
o.owa
0.1022
Total Flow
Rate
(Ibm/hr)
123.1
219.0
281.5
123.9
218,7
279.9
123.4
219.2
281.6
Axial
Reynolds
Number
3970
6380
7710
3830
6050
7310
3380
5830
7310
*Th1s av<;ra<|o w,n nht;i1n«:'l by ftn'JImi tho nipan of the twpc-rature rfsto at th<>
five '.UUon-. at \.?'i Inchi:'. from tho wall.
-------
250
Exit Reynolds Number
In order to assess the effect of changing the exit orifice dia-
meter (exit Configurations. 1-3) it is useful to formulate a Reynolds
number based upon the total flow rate and the orifice diameter with the
viscosity evaluated at the average gas temperature at Station 5 (presumed
to be approximately the same as the temperature at the exit orifice
location) using the flue gas curve given as Figure D-l. The Reynolds
number so calculated is referred to as the "exit Reynolds number"'.' The
calculation procedure and the results are given in Table D-3-
Inlet Reynolds Number
To assess the inlet Configuration effect, an "inlet Reynolds
number" analogous to that described in the preceeding paragraph is also
defined. Here the characteristic dimension is the bore of the inlet
air-line and the viscosity is found from tables available for the pro-
perties of air ([U39J» page 555) as a function of the measured air tempera-
ture at the Inlet. This calculation is given in Table D-U.
Length Reynolds Number
In order to assess entry-length effects, the Reynolds number can be
calculated using furnace column height as the characteristic dimension
instead of a diameter. The resulting equation is given as Equation (3)
in Chapter III. Since there are five discrete heat transfer sections
(i.e. cooling-water sections) there are five discrete values of L: 1, 2,
3, U, and 5 feet. The Reynolds number so obtained is referred to here as
the "length Reynolds number" and as is apparent from Equation (3) is equal
to the axial Reynolds number times the local value of L divided by the
-------
251
TABLE 0-3
EXIT REYNOLDS NUMBER CALCULATION
Exit
Configuration
1
2
3
Exit Orifice
Diameter
(ft)
0.1667
0.3333
0.5000
Condition
3
8
12
3
8
12
3
8
12
Average Gas
Temperature
at Station 5
(°F)
658
828
977
710
859
' 964
716
826
931
Absolute
Viscosity
(Ibm/hr-ft)
0.0718
0.0795
0.0853
0.0743
0.0808
0.0848
0.0745
0.0794
0.0836
Total
Flow Rate
(ltxn/hr)
124.6
225.0
287.8
123.0
216.9
275.6
123.0
217.2
274.5
Exit
Reynolds
Number
13,260
21 .620
25,780
6,320
10,250
12,410
4,200
6,970
8,360
' TABLE D-4
INLET REYNOLDS NUMBER CALCULATION
1 . ., -1 1 1 ' —
Inlet
Configuration
A
B
C
- -____ i - ...
Inlet
Air-Line
Diameter
(feet)
0.07292
0.08854
0.1335
Condition
3
8
12
3
8
12
3
8
12
Average
A1r Inlet
Temperature
(°F)
67.0
68.5
66.0
68.2
71.0
70.0
68.8
70.2
6B.5
Absolute
Viscosity
(Ibm/hr-ft)
0.04384
0.04393
0.04377
0.04391
0.04409
0.04403
0.04395
0.04104
0.04193
Average
Air Flow
Rate
(Ibm/hr)
57.58
104.2
134.0
58.01
104.0
133.2
57.77
101.3
134.2
Inlet
Reynolds
Number
22,930
41 ,420
53,460
19,000
33,920
43,500
12,540
22, MO
29,140
-------
252
furnace column diameter (D). However, since the length Reynolds number
is intended to be a local parameter with respect to furnace column height,
the property of absolute viscosity should be evaluated at the local average
temperature (given in Tables 11-13 for each of the five Stations which are
located at the mid-heights of each respective furnace column section).
This calculation is presented in Table D-5.
Free-Stream Reynolds Number
The free-stream Reynolds number has been defined by Equation (23)
in Chapter IV. The values of free-stream velocity have been presented
in Table 35- The equivalent flat-plate distances for the mid-height of
each furnace column section can be found from using Equation (^5) with the
tabulated values of swirl parameter given in Table 35- The value of L
used in this equation is the mid-height of each section since the equiva-
lent flat-plate distance sought is at this point. The fluid properties
are evaluated at the film temperature which is defined as the mean of the
average temperature (given in Table Lh) and the gas temperature at the wall
(given in Tables 11-13). The viscosity is evaluated using Figure D-l and
the density using the perfect gas law for gas constants given in Table 32.
-------
253
TABLE D-5
LENGTH REYNOLDS NUMBER CALCULATION
Configuration
1
2
3
Condition
3
8
12
3
8
12
3
8
12
Furnace
Column
Section
1
2
3
4
5
1
2
3
4
5
1
2
3
4
5
1
2
3
4
5
1
2
3
4
5
1
2
3
4
5
1
2
3
4
5
1
2
3
4
5
1
2
3
4
5
I/O
2.08
4.17
6.25
8.33
10.42
2.08
4.17
6.25
8.33
10.42
2.08
4:i7
6.25
8.33
10.42
2.08
4.17
6.25
8.33
10.42
2.08
4.17
6.25
8.33
10.42
2.08
4.17
6.25
8.33
10.42
2.08
4.17
6.25
8.33
10.42
2.08
4.17
6.25
8.33
10.42
2.08
4.17
6.25
8.33
10.42
Average
Gas
Temperature
(°F)
1363
1201
976
792
658
1480
1333
1152
940
828
1560
1459
1269
1074
977
1424
1205
991
811
710
1500
1299
1108
954
859
1572
1397
1211
1058
964
1413
1192
978
822
716
1474
1280
1092
937
826
1543
1384
1190
1037
931
Absolute
Viscosity
(Ibm/hr-ft)
0.0993
0.0937
0.0854
0.0778
0.0719
0.1032
0.0982
0.0919
0.0838
0.0794
0.1058
0.1026
0.0960
0.0890
0.0853
0.1014
0.0938
0.0860
0.0788
0.0741
0.1037
0.0970
0.0902
0.0844
0.0808
0.1062
0.1003
0.0940
0.0883
0.0848
0.1009
0.0932
0.0853
0.0792
0.0745
0.1030
0.0963
0.0897
0.0838
0.0794
0.1052
0.0999
0.0931
0.0876
0.0837
Local Axial
Reynolds
Number
3330
3530
3870
4250
4600
5780
6080
6490
7120
7520
7220
7440
7950
8580
8950
3220
3480
3790
4140
4400
5550
5930
6380
6820
7120
6880
7290
7780
8280
8620
3230
3500
3830
4120
4380
5590
5980
6420
6880
7260
6920
7290
7820
8310
8700
Length
Reynolds
Number
6,930
14,720
24,190
35,400
47,900
12,000
25,400
40,600
59,300
78,400
15,000
31 ,000
49,700
71,500
93,300
6,700
14,500
23,700
34,500
45,800
11,500
24,700
39,900
56,800
74,2,00
14,300
30,400
48,600
69,000
89,800
6,720
14,600
23,900
34,300
45,600
11,600
24,900
40,100
57,300
75,600
14,400
30,400
48,900
69,200
90,700
-------
TABLE D-6
FREE-STREAM REYNOLDS NUMBER CALCULATION
Configuration
1
2
3
Condition
3
8
12
3
8
12
3
8
12
Furnace
Column
Section
1
2
3
4
5
1
2
3
4
5
1
2
3
4
5
" 1
2
3
4
5
1
2
3
4
5
1
2
3
4
5
1
2
3
4
5
1
2
3
4
5
1
2
3
4
5
Equivalent
Flat-Plate
Distance
(ft)
3.82
11.5
19.1
26.7
34.4
3.08
9.24
15.4
21.6
27.7
2.58
7.74
12.9
18.1
23.2
3.64
10.9
18.2
25.5
. 32.8
3.03
9.09
15.2
21.2
27.3
2.58
7.74
12.9
18.1
23.2
3.69
11.1
18.5
25.8
33.2
3.10
9.30
15.5
21.7
27.9
2.64
7.92
13.2
18.5
23.8
Film
Temperature
(°F)
751
683
558
448
378
826
780
660
548
492
873
862
782
606
554
792
671
556
458
407
846
769
619
536
488
890
849
701
603
554
785
670
550
463
410
833
718
611
527
474
873
840
691
588
535
Gas
Density,
(lbm/fr)
0.0317
0.0336
0.0377
0.0423
0.0458
0.0303
0.0314
0.0348
0.0386
0.0409
0.0292
0.0295
0.0314
0.0365
0.0384
0.0305
0.0338
0.0376
0.0416
0.0441
0.0298
0.0317
0.0361
0.0391
0.0411
0.0288
0.0297
0.0335
0.0366
0.0384
0.0307
0.0339
0.0379
0.0415
0.0440
0.0301
0.0330
0.0363
0.0394
0.0417
0.0292
0.0299
0.0338
0.-0371
0.0391
Absolute
Viscosity
(Ibm/hr-ft)
0.0760
0.0730
0.0672
0.0621
0.0587
0.0794
0.0774
0'.0721
0.0668
0.0640
0.0812
0.0809
0.0776
0.0695
0.0670
0.0780
0.0727
0.0670
0.0623
0.0600
0.0800
0.0768
0.0698
0.0661
0.0639
0.0819
0.0802
0.0737
0.0693
0.0670
0.0785
0.0712
0.0669
0.0628
0.0601
0.0797
0.0744
0.0697
0.0658
0.0634
0.0813
0.0798
0.0736
0.0686
0.0662
Free-Stream
Reynolds
Number
x 10"5
4.01
13.3
27. 0
45.8
67.5
4.53
14.4
28.6
48.1
68.2
4.01
12.2
22.5
41.1
57.4
3.50
12.5
25.2
41.9
59.4
4.19
13.9
29.1
46.5
65.1
3.79
12.0
24.5
39.9
55.5
3.58
13.1
26.0
42.3
60.3
4.38
15.4
30.2
48.6
68.7
3.96
12.4
25.3
41.8
58.7
-------
255
APPENDIX E
ASSESSMENT OF RADIATION AND CONDUCTION ERROR
Because the walls of the furnace column are water-cooled there is
a large temperature difference between the measuring tip of the
sheathed thermocouples used to obtain the data given in Tables 11-lU and
the wall. This temperature difference causes two errors: radiation
error and conduction error.
Radiation Error
The first attempt to assess the extent of the radiation error was
»
through the use of a radiation shield fabricated and installed on a
single sheathed thermocouple. The shield was made from a three-eighths
inch diameter steel tube, six inches long. The tube was attached to the
Megopak thermocouple by means of six machine screws arranged in the form
of two sets of three "spokes" each that were screwed in through tapped
holes in the shield until they pinched the sheath. The thermocouple it-
self was installed at Station 2 and had a 90 degree bend so that the
shielded portion was vertical (permitting it to measure the temperature
at a unique distance from the wall) with the measuring tip located
exactly midway between Stations 1 and 2 (i.e. exactly one foot above the
vortex chamber).
This thermocouple/shield was then used to measure the gas temperature
at Conditions 3, 8, and 12 at each of three radii for Configuration 3-C.
The shield was then removed and the same thermocouple was used to obtain
-------
256
unshielded data to permit a direct comparison. These data are given in
I'M^ure l'J-1.
These data suggest a maximum radiation error of about 90°F and
this occurs at a distance of 1.5 inches from the furnace column wall.
At Conditions 8 and 12 at a radius of 0.5 inches there is an anomalous
result in that the shielded data fall above the unshielded data; although
this shift is only approximately UO°F, it is not readily explainable.
These data would also tend to suggest that there exists an annular-like
flame front in that the radiation error at a radius of 1.5 inches from
the wall is greater than at either 0.5 inches or 2.88 inches.
To examine this radiation error correction further, an aspirated
thermocouple was obtained from ARI Industries, Inc. The manufacturer's
specification control drawing {4Uo] is given as Figure E-2. A Millipore
•f
pump (model 0211 lubricated pump manufactured by Gast Manufacturing
Corporation) was used to provide the necessary suction. Once again the
data were taken at Conditions 3, 8, and 12 and at several radii. Because
the aspirated thermocouple was larger (%-inch NPT required) than the
nominal spacing between the cooling-water tubing, it was necessary to
install the thermocouple where a larger than normal gap was available.
Fortunately such a point was available at the approximate height of the
Station 1 thermocouple (i.e. 6 inches above the vortex chamber). The
results of the aspirated thermocouple investigation are given in Figure E-3;
the data of Table 13 has also been included on this figure to provide a
comparison.
The clear result of the aspirated data is that there is an
extremely large temperature difference due (presumably) to radiation error
(the peak temperature also has shifted inward). However, the energy
-------
257
2000
1800
1600 -
1400
1800
a
f
01
H
o
X
01
1600
1400
2 12QQ
.1 l
Condition 8
Note: Dashed data are for thermocouple
with radiation shield installed.
Solid data are for thermocouple
with radiation shield removed.
1800
1600 -
1400 -
1200
1.0
0.8
0.6 0.4
Radius Ratio
0.2
Figure E-l. Comparison of Shielded and Un-Shielded Thermocouple Data
-------
1-1
(5
>
01
•o
o.
H
:r
o
O
c
•o
B
*•
re
Flexible Stoinless Steei Tuoe
over Lead Wire.
This portion it outside
vessel or duct.
" NP1
1-5/16"Typ.
Direction of Flow of Pressure H
Mating connector available as Aft!
Type BMK (for ISA Cal. K)
(Supplied as on extra)
_ Adjustable Adaptor
Stainless Steel
P/N PTM-WA
(Order as an ex Ira)
APPLICATION:
This probe wos designed for use in accurately measuring the temperature of goses moving (
either low o* nigh velocity. Examples of installation wiuld be:
T-1006-"L" KB APPLICATION
ISA Col. K
S/N
A. Tall pipes c*~ jet engines.
B. Boilers
C. Flue stacks ond checkers-
D. High temperature wind tunnels.
E. Kilns
Thermocouple Insert Removable and Replaceable
Head Detail A
NOTES-
1. Temperature Range: 0-1300° F, Intermittent »o 2 '50° F
2. Moch Range: 0 to Supersonic
3. Service Media: Oxidizing or Reducing Gases.
4. Flov/ Angle Range: *• 60° with no change in performance characteristics.
5. Standard Ihermocoupie is Cai. K (Chromel-P, Alumel). Other calibra-
tions available on special order.
6. Construction: Welded inconel.
7. Vibration & Shock: The transducer will meet or exceed the vibration ond
shock specification or MIL-E-5272C.
9. For operation at temperatees 'f. excess of 2000° F, refer to ARi Catalog
8. t wherein are desciibed 'hermocouples for operation to 4000° F. A
high temperature (to 3000° F) modification of this thermocouple is des-
cribed (T-1006-2 and T-1006-c).
9. Standard lengths of "L" are 16" and 24"
The unit operates on the principle of arfifical.y acceieraring the gas over the sensing ther-
mocoupie. The acceleration is accomplished by having the entrance pressure , H, higher
than the exit pressure by M%. When the entrance pressure Is at or be!ow atmosphere
pressure, love r values of "p" car, be obtained by a suction pump or steam ejection. Detail
of design ond performance ore based on NASA TN 3755. By aspiration feither by the
pressure differentia! between the process and the ambient pressures or by a suction pump)
the ability of the sensing thermocouple re accurately obtain rr^e rote! lemperolure is neg-
ligibly Influenced cy the velocity o' me gas, the difference in temperature berween the
thermocouple and the wails, flow direction and rapid clxingts in gos fe.-nperatures.
REVISIONS
THERMOCOUPLE PROBE, ASPIRATING
FOR HIGH TEMPERATURE GASES
a STANDARD »«o HMM.H ^«,MtM Nn
KOUOH'.flS* 0« PrtMUffiO.
IUNFACC* 'O BC
HiocmCHEt •-«.». —
T-1Q06
HBV.
A
ro
VJ1
CO
-------
259
2400
2000
1600
Cu
o
(U
I
H
01
3
1200
800
400 -
1.0
Note: Darkened symbols are
for aspirated thermo-
couple data.
Open symbols are for
data from Table 13.
All data are for
Configuration 3-C.
Condition Symbol
3 O
8 A
12 a
JL
0.8
0.6 0.4
Radius Ratio
0.2
Figure E-3. Comparison of Aspirated and Sheathed Thermocouple Data
-------
260
balance calculation performed in Chapter IV shows that the temperature
measured vith sheathed thermocouples is in fact correct. The difficulty
with all aspirated thermocouples is that one can never be sure where the
gas being measured has come from because of the suction pump. This is
especially the case in a vortex flow where recirculation zones and a
low pressure core could interact in dramatic ways with this instrument.
In particular, it is entirely possible that the suction pump alters the
flow field such that the actual temperature being measured is not that
of the vortex at Station 1 but of the very hot gases from the vortex
chamber which were being drawn into the thermocouple inadvertantly.
Thus, it is believed that the radiation error is small as shown
by the shielded thermocouple data and the energy balance (see Chapter IV),
Conduction Error
The conduction error will be estimated by using the equation of
temperature for a long fin given in Eeference [kl6] (page 32):
T - T e"m
1 - e
where T is the actual vortex gas temperature, T the measured gas
temperature, T the temperature at the b'ase of the thermocouple, x the
distance from the base to the measuring tip of the thermocouple, and m
defined by
m = (h P / k A )^ (E-2)
where h is the convection conductance from the gas to the thermocouple
tube, k is the effective thermal conductivity of the tube, P is the
perimeter of the tube, and A is the cross-sectional area of the tube.
The diameter of the measuring tube is 1/8 inches; thus the ratio
of P over A is 381* ft~ . The effective thermal conductivity can be
-------
261
estimated by analogy to a parallel resistance electrical circuit since
Uie crotis-section is composed of asbestos insulation, metal sheathing,
the actual thermocouple wire, and the insulation of the thermocouple
wire. By combining the insulation with the asbestos and the wire with
the sheathing, the following relation may be written for the effective
thermal conductivity:
k = (*A)asb/Atot * sheath/Atot
From the manufacturer's specifications [^3^] the ratio of the asbestos
to the total area is 0.^93, and the ratio of the sheath to the total
area is 0.507. From Reference [hl6] the conductivity of the asbestos
insulation can be estimated to be 0.093 Btu/hr-ft-°F (for loosely packed
asbestos at 210°F) and that of the sheath as 10 Btu/hr-ft-°F (for SS 304
at HOO°F). Substitution of these values into Equation (E-3) results in
an effective conductivity of 5.12 Btu/hr-ft-°F.
The convection conductance for the flow past the thermocouple
tube can be estimated by empirical expressions for heat transfer for air
cross-flowing cylinders (page 196 [Ul6]). The Reynolds number of the
flow is as follows:
Re n = W D/V (E-U)
cyl
where W is the free-stream velocity, D the diameter of the cylinder, and
V the kinematic viscosity evaluated at the film temperature. From Table 35,
it is seen that the free-stream velocity is on the order of 100 feet per
2
second. For air at 200°F, the kinematic viscosity is 0.86U ft /hour.
Thus the Reynolds number for the cylinder is approximately ^3^0. From
Table 6-1 of Reference [Ul6], this implies that the convection conductance
is given by the following:
-------
h = 0.683 Re Pr1/3 kf /D (E-5)
where k is the thermal conductivity of air evaluated, at the film
temperature, and Pr is the Prandtl number similarly found. Performing
2
the above calculation results in a predicted value of h of 52 Btu/hr-ft -°F.
Therefore the value of m defined by Equation (E-2) may be
determined as follows:
m = (52) (3810 / (5.12) = 62.5 (E-6)
The conduction error will be evaluated for the worst-case position
that of a distance of 0.25 inches from the wall. The actual value of x
to be used in Equation (E-l) is, however, somewhat larger than simply the
penetration depth of the thermocouple tube because the tube is mounted in
a compression fitting which in turn is held in place in the vortex
chamber wall by a one- eighth- inch MPT adapter. Thus the point of actual
wall contact with the thermocouple tube is effectively further removed
from the tip than simply the penetration distance. Since the length of
the compression/NPT fitting is 1.25 inches, the value of x is estimated
to be equal to 1.50 inches for a 0.25 inch- penetration. Substitution
into Equation (E-l) yields the following:
Ttrue = V " (U'05 X W~k) Tv (E~T)
Thus for a measured gas temperature of 1200°F at 0.25 inches from
the wall with a wall temperature of 200°F, the true temperature is
estimated as 1199- 9°F indicating that the conduction error is in fact
negligible.
For increasing penetration depths this error decreases to even
smaller values.
-------
APPENDIX F
THERMOCHEMISTBY CALCULATIONS
Enthalpy of Combustion
The enthalpy of combustion can be determined from the tabulated
values of enthalpy of formation once a chemical reaction can be written
for the process. The reactants are known quite precisely because they
are supplied to the system at a measured ratio: propane (C HQ) and "air"
(approximately 0? + 3. 76 N?). The products are not so known and some
assumptions must be made. It will be assumed that the only products
formed are: C0?, HO, ¥ , 0 (for those reactions with excess air), and
CO (for those reactions with deficient air). At the temperatures
measured in the furnace column the assumption of no formation of nitrogen-
oxide molecules (or other more-complicated molecules) is well justified.
The basic chemical equation is as follows:
x(02 + 3.76N2) t yC02 + z02 + uCO
(F-l)
The value of x can be determined from the air/fuel ratio from the known
molecular weights of propane (U4.09) and "air" (28.97):
x = APR (UU. 09/28. 97) = 1-522 AFR (F-2)
The results of the specie balance for the nine combinations of exit
Configuration and Conditions are given in Table F-l.
-------
TABLE F-l
MOLAR COEFFICIENTS OF THE THEORETICAL CHEMICAL REATION BASED UPON THE MEASURED AIR/FUEL RATIO
Configuration
1
2
3
Condition
3
8
12
3
8
12
3
8
12
Reactants
C3H8 (02+3.76N2)
1 4.769
1 6.521
1 6.606
1 4.678
1 6.245
1 6.302
1 4.697
1 6.281
1 6.295
.Products
co2
2.537
3.0
3.0
2.356
3.0
3.0
2.394
3.0
3.0
°2
0
1.521
1.606
0
1.245
1.302
0
1.281
1.295
CO H20 N2
0.463 4 17.930
0 4 24.519
0 4 24.839
0.644 4 17.589
0 4 23.481
0 4 23.696
0.606 4 17.661
0 4 23.617
0 4 23.669
ro
-------
265
The theoretical enthalpy of combustion at 77°F for all the
Condition 8 and 12 data is the same since it is independent of the
degree of excess air. The Condition 3 enthalpy of combustion is, however,
dependent upon the air/fuel ratio because of its influence upon the
formation of carbon monoxide as seen in Table F-l. The theoretical
enthalpy can be calculated from the following expression:
AH
c,7T
AVProd
(F-l)
where AH^y is the enthalpy of combustion, AHf the enthalpy of formation,
and vi are the coefficients of the reaction. Using the values tabulated
in Wark [U03] for the enthalpies of formation, the resulting enthalpies
of combustion are as follows:
TABLE F-2
THEORETICAL ENTHALPY OF COMBUSTION AT 77°F
(Btu/lbm C_HR)
Configuration
1
2
3
Condition
3
18,666
18,166
18,271
8
19,9^
19, 9 UU
19,9^
12
19,9^
19,9^
19, 9 UU
Sensible Enthalpy of Reactants
Since the enthalpy of combustion has been evaluated at the
reference state (77°F), it is necessary to account for the sensible
enthalpy change associated with the reactants when they are not supplied
at that temperature. The mean supply temperature of the reactants has
-------
266
been measured, so the JANAF Tables [UoU, U05] can be used together with the
molar coefficients of Table F-l to calculate the sensible enthalpy of the
reactants. The net enthalpy of combustion is defined as the sum of the
enthalpy of combustion as calculated in Equation (F-l) and the enthalpy
of the reactants as follows:
AHcnet,77 = AHc,77 + Hreac(Tsupply ' 77) ^
*
where H designates the sensible enthalpy.
These calculations for sensible enthalpy of reactants and net
enthalpy of combustion are presented in Table F-3.
Sensible Enthalpy of Products
A similar procedure to that followed to find the sensible
enthalpy of the reactants can be used for the products. The temperature
at which the sensible enthalpy of each products is evaluated is the
average temperature of the vortex gas at that station (given in Table
The net enthalpy of reaction is then defined as follows:
AH = AH . - H _(T - 77) (F-3)
R cnet prod m
These calculations are performed in Table F-U.
Net Enthalpy of Reaction at the Exit
Since each of the Station thermocouples is located at the mid- point
of each respective cooling-water section, the net enthalpy of reaction
calculated at Station 5 in Table F-U is not quite equal to the net
enthalpy of reaction available for the entire furnace column due to the
six inches of cooling section remaining above Station 5- This can be
accounted for satisfactorily by subtracting one-half of the enthalpy
difference between Stations h and 5 from the value at Station 5. This
-------
TABLE F-3
SENSIBLE ENTHALPY OF REACTANTS
Configuration
1
2
3
Condition
3
8
12
3
8
12
3
8
12
Propane
Supply Sensible
Temperature Enthalpy *
(°F) (Btu/lbm C3H8)
60.0 -3
66.3 -2
57.8 -3
55.7 -4
55.0 -4
54.7 -4
58.6 -3
58.0 -3
55.1 -4
Air
Supply Sensible
Temperature Enthalpy*
(°F) (Btu/lbm C3H8)
74.1 -10
74.4 -12
76.4 - 3
70.8 -21
73.0 -18
74.2 -13
. 73.0 -14
75.3 - 1
77.8 + 4
Sensible
Enthalpy*
of Reactants
{ Btu/lbm C3H8)
-13
-14
- 6
-25
-22
-17
-17
- 4
0
Net Enthalpy of
Combustion **
(Btu/lbm C3Hg)
18,653
19,930
19,938
18,141
19,922
19,927
18,254
19,940
19,944
ON
—J
* Taken with respect to 77°F
** Obtained from Equation (F-2)
-------
TABLE F-4
SENSIBLE ENTHALPY OF PRODUCTS/NET ENTHALPY OF REACTION
Configuration
1
2
3
Condition
3
8
12
3
i
8
12
3
8
12
Station
1
2
3
4
5
1
2
3
4
5
1
2
3
4
5
1
2
3
4
5
1
2
3
4
5
1
2
3
4
5
1
2
3
4
5
1
2
3
4
5
1
2
3
4
5
Average
Gas Temperature.
(°F)
1363
1201
976
792
658
1480
1333
1152
940
828
1560
1459
1269
1074
977
1424
1205
991
811
710
1500
1299
1108
954
859
1572
1397
1211
1058
964
1413
1192
978
822
716
1474
1280
1092
937
826
1543
1384
1190
1037
931
Sensible
Enthalpy of
Products
(Btu/lbmC3Hg)
5808
5020
3949
3100
2496
8368
7418
6271
4962
4284
8994
8329
7092
5855
5247
6011
4957
3955
3136
2687
8181
6935
5774
4859
4304
8706
7600
6448
5520
4944
5977
4912
3909
3197
2723
. 8060
6852
5708
4783
4133
8512
7510
6313
5388
4757
Net Enthalpy of
Reaction*
(Btu/lbmC3Hg)
12,845
13,633
14,704
15,553
16,157
11,562
12,512
13,659
14,968
15,646
10,944
11,609
12,846
14,083
14,691
12,130
13,184
14,186
15,005
15,454
11,741
12,987
14,148
15,063
15,618
11,221
12,327
13,479
14,407
14,983
12,277
13,342
14,345
15,057
15,531
11,880
13,088
14,232
15,157
15,807
11,432
12,434
13,631
14,556
15,187
Obtained from Equation (F-3)
-------
269
approximation essentially assumes that the heat flux for the top 6-inch
portion of the fifth cooling-water section is approximately that of the
portion between Stations U and 5. Figure 2k shows that this is a
reasonable assumption.
The results of this calculation procedure is tabulated below:
TABLE F-5
1ET ENTHALPY OF BEACTION AT THE EXIT
Configuration
1
2
3
Condition
3
8
12
3
8
12
3
8
12
Sensible Enthalpy
of Products at
Exit (Btu/lbm C,Hj
3 o
2191*
39^5
1*9^3
21*62
1*027
1*656
2U86
3803
1*1*1*2
Net Enthalpy of
Reaction at Exit
(Btu/lbm CLHj
0 O
16,1*59
15,985
1^,995
15,679
15,896
15,271
15,768
16,132
15,503
-------
270
APPENDIX G
CONFIGURATION FACTOR CALCULATIONS
External Factors
There are two external configuration factor calculations required:
factors from the copper base plate to each furnace column section, and
factors from the square annulus formed by the area of the vortex chamber
top plate less the copper base plate to each furnace column section. The
geometry is shown in Figure G-l where one-eighth of the copper base plate
is shown as area A and one-eighth of the vortex chamber top plate as area
A?; each section of furnace column is shown by letters A through E
(thus section 1 is designated A, 2 as B, etc.). This figure has been
taken from a report by Tripp, Hwang, and Crank [UUl]. In this reference
a procedure is presented that permits the calculation of configuration
factors from a cylinder to a perpendicular right triangle positioned at
its base. In order to determine the needed factor for the square annulus,
a series of calculations must be performed: the configuration factors
must be found from the furnace column to the smaller triangle (A on
Figure G-l) which represents the copper base plate, then the factors
from the furnace column to the larger triangle (A ) need to be found, and
finally by means of configuration factor algebra the factor between the
furnace column and the square annulus can be found. Once this factor is
known, further use of configuration algebra can readily yield the inverse
of this factor. Similarly, the factors from the copper base plate to the
furnace column sections may also be found.
-------
271
FURNACE
COLUMN
SMALL TRIANGLE
REPRESENTS ONE-
EIGHTH OF FURNACE
COLUMN COPPER BASE
RELEVANT DIMENSIONS:
= L = 9.45 INCHES
L[ = L' = 4.0 INCHES
R = 3.20 INCHES
(to outside of cooling
water tubing)
LARGE TRIANGLE
REPRESENTS ONE-
EIGHTH OF VORTEX
CHAMBER TOP PLATE
Figure G-l. Configuration Factor Geometry (taken from [441])
-------
The report by Trip provided a series of graphs for readily
determining these factors based upon the known values of H, R, L , and
L (defined in Figure G-l). Unfortunately, the ranges of these
variables presented in their graphs does not include the physical
dimensions of this furnace column/vortex chamber; since the authors
were concerned with modeling people on floors, they used short cylinders
on large plates whereas the geometry here is one of a relatively long
cylinder standing on a small plate. As a result it was necessary to
numerically integrate their equation for the configuration factor. The
equation used is given in Figure G-2 which is page 19 of their report
[Ma].
The numerical integration was performed using a Three-Eights
Simpson's Rule on a CDC 6000 computer. The results of this program are
given in Table G-l for the configuration factor for furnace column
heights of from one to five sections to each of the triangles (one
representing the copper base plate and the other the vortex chamber top
plate ) .
To convert these results so that the factor from the square
annulus to the various furnace column section can be found, it is first
necessary to perform the following subtraction:
= 0. 0052k - 0.00103
= 0.00*121
which follows from configuration factor algebra where F represents the
configuration factor, with the subscripts (A-E) representing the total
furnace column area of all five sections (i.e. section A to section E),
-------
273
Radiation Shape Factor Between a Finite Cylinder and a Plane Surface
Case I: The finite cylinder is perpendicular to a right triangle.
Shape factors for this case, in
which one base of the cylinder lies
in the same plane as the triangle, and
the center line of the cylinder is
normal to the triangle and passes
through the apex of one of the acute
angles of the triangle, Fig. 11, were
obtained by integrating, partially,
Equation (2) to the form
FIG II
^jB^Tc2
can
-1 1 f. -1
I a + i
- W2 -fr (g -t- 1) (a - I) -1 I (a - 1) (V!2 4- (a +
•, tan I
.|{H2 + (a + l)2)(w2 + (a - I)2} -\J (a + i)(w2 + (a -
I)2)
ada
(cH-l) (q-l)
tan"
(a+1)z) (w2 + (a-l)2) 'vj (a-n) (w2+(a-l)2)
sec ii
(7)
B = L /R, C ° L /R, W = H/R, a «=
Equation (7) was Integrated by the authors to a further extent (see
?pcndlx III); however, for purposes of computation, through the use of•the
>!-H 650 Computer, it was decided to use Equation (7) to obtain the numerical
'*'ue» of the'shape factors. These values are presented in Figs. 5a to 5e,
*"n8 the parameters U = H/L. and V - 1!/L2 instead of B » I^/R and C = L2/R.
Figure G-2. Configuration Factor Equation (page 19 of [441])
-------
27 U
TABLE G-l
NUMERICAL INTEGRATION RESULTS FOR CONFIGURATION FACTOR
TRIANGLE*
1
2-
CYLINDER*
A
A+B
A+B+C
A+B+C+D
A+B+C+D+E
A
A+B
A+B+C
A+B+C+D
A+B+C+D+E
CONFIGURATION FACTOR
FROM CYLINDER
TO TRIANGLE
0.00511
0.00257
0.00172
0.00129
0.00103
0.0232
0.0127
0.00864
0.00653
0.00524
FROM TRIANGLE
TO CYLINDER
0.154
0.155
0.155
0.155
0.155
0.125
0.137
0.139
0.140
0.141
*See Figure G-l for definition of these areas.
TABLE G-2
CONFIGURATION FACTOR FROM VORTEX CHAMBER TO
EACH FURNACE COLUMN SECTION
From Cylinder to
Area 2-1*
From Area 2-1* to
Cylinder
From Area 2-1* to
each Cylinder Section
Cylinder Sections*
A-E
0.00421
0.138
A-D
0.00524
0.137
A-C
0.00692
0.136
A-B
0.0101
0.132
A
0.0181
0.119
Cylinder Sections*
E
0.001
D
0.001
C
0.004
B
0.013
A
0.119
*See Figure G-l for definition of these areas
-------
275
uubricrJ pi I. ropronunlintf tr imi^.I.e A , and HU"b.';<:rij>t V. triangle A all
defined in Figure G-l. Similar calculations are required to find the
configuration factor for sections A through D to the area formed by
subtracting A from A . To convert these five factors so that they
represent the energy fraction leaving the top plate and striking the
appropriate furnace column section requires use of the reciprocity
relation as follows:
F(2-lHA-E) = F(A-E)-K2-1) IS(A-E) ' S(2-1)J (G"2)
= 0.001*21 (8.38/0.256)
= 0.138
vhere S,._E\ represents the area of furnace column sections A through E
and S,,j_jx represents the area of the trapezoid formed by subtracting A
from A . A summary of this calculation procedure is given in Table G-2.
The configuration factors from the copper base plate to each
furnace column section can be found directly from Table G-l by simple
subtraction. Since the factor to areas A plus B is 0.155 and that to A
only is 0.15^9 the factor to B only must be 0.001. Likewise it can be
seen that to three decimal places the factor to each of the remaining
furnace column sections is zero.
The configuration factors from the vortex chamber bottom plate can
be found somewhat more directly. A schematic of this internal radiation
path is presented in Figure G-3.
The factor from the vortex chamber cavity to the bottom section is
very difficult to calculate due to the fact that the bottom portion of
the furnace column walls can "see around the corner".
-------
NOTE: Drawing is
scale
COOLING
WATER TUBES
FURNACE :
"COLUMN
TOP OF THE
BOTTOM ONE-FOOT
COOLING WATER
SECTION
WALL TEMPERATURE
THERMOCOUPLES
VORTEX CHAMBER
BOTTOM PLATE
Figure G»3. Internal Radiation Transfer Schematic
-------
277
The cavity, therefore, resembles (.to a degree) a black body radiator.
Since the vortex-wall emissivity has been estimated to be 0.80, it appears
to be a reasonable estimate to account for this enhanced configuration
factor to the bottom one-foot section of furnace column by taking the
effective emissivity to be 0.95. The radiating area is the furnace
column area which is O.lSlO square feet.
The configuration factor from section to section can now be
calculated using equations presented by Siegel and Howell ([k22], page
787):
2 J
- - k (R2/Rnr I (G-3)
where
X = 1 + (1 + Rg^l (G-^
and where R is defined as the ratio of r /fl and R as r /H where r
is the radius of the top disk, r the' bottom disk, and H the separation
distance. For the configuration under investigation here r and r? are
equal and are 2.88 inches, H is the height of each furnace column section
which is 12 inches. By substituting these values in the above equations
yields a configuration factor of 0.05179 from the disk at the bottom of
the furnace column to the disk separating furnace column section 1 from
2; thus the factor from the bottom disk to the furnace column wall of
section 1 is 0.9^821.
Continuing in a similar manner results in configuration factors
from the bottom disk to sections 2 through 5 as follows: 0.0^91, 0.002514:
0.00013, and 0.00000.
-------
278
APPENDIX- H
NUSSELT NUMBER CALCULATIONS
Mean Nusselt Number
The mean Nusselt number has been defined in Chapter IV by Equation
(ih) in terms of the mean convection conductance given in Table 31, the
furnace column diameter, and the thermal conductivity evaluated at the
average furnace column gas temperature (found in Table 1*0.
The thermal conductivity will be evaluated as a function of tempera-
ture using Maxwell's curve [Uoi] which he found to be relatively inde-
pendent of the degree of excess air and thus only a function of temperature.
A graph of the conductivity versus gas temperature is given as Figure H-l.
The calculation of mean Nusselt number is given in Table H-l.
Local Nusselt Number
The local Nusselt number may be found in an analogous calculation
to that performed for the mean Nusselt number above. The local value of
convection conductance is used (given in Table 31) and the thermal con-
ductivity relation given in Figure H-l is evaluated at the local average
gas temperature (from Table lU).
The results of this calculation is given in Table H-2.
-------
0.07
ro
-q
vo
200 400 600 800 1000 1200
Temperature (°F)
1400
1600
1800
2000
Figure fi-1. Thermal Conductivity of Flue Gas
-------
280
TABLE H-l
MEAN NUSSELT NUMBER CALCULATION
Exit
Configuration
1
2
•
3
Condition
3
8
12
3
8
12
3
8
12
Average
Furnace
Column
Gas Temperature
(°F)
988
1147
1268
' 1028
1144
1240
1024
1122
1217
Thermal
Conductivity
(Btu/hr-ft-°F)
0.0312
0.0343
0.0367
0.0319
0.0342
0.0362
0.0318
0.0338
0.0358
Mean
Convection
Conductance
(Btu/hr-ft2-°F)
11.0
13.7
15.7
12.7
15.2
17.3
12.6
14.8
17.2
Mean
Nusselt
Number
169
192
205
191
213
229
190
210
231
-------
281
TABLE H-2
LENGTH NUSSELT NUMBER CALCULATION
Configuration
1
2
3
V
Condition
3
8
"
12
3
8
12
3
8
w
12
1 Ih
Furnace
Column
Section
1
2
3
4
5
1
2
3
4
5
1
2
3
4
5
1
2
3
4
5
1
2
3
4
5
1
2
3
4
5
1
2
3
4
5
1
2
3
v
4
5
1
2
3
4
5
L/D
2.08
4.17
6.25
8.33
10.42
2.08
4.17
6.25
8.33
10.42
2.08
4.17
6.25
8.33
10.42
2.08
4.17
6.25
8.33
10.42
2.08
4.17
6.25
8.33
10.42
2.08
4.17
6.25
8.33
10.42
2.08
4.17
6.25
8.33
10.42
2.08
4.17
6.25
8.33
10.42
2.08
4.17
6.25
8.33
10.42
Average
Gas
Temperature
(°F)
1363
1201
976
792
658
1480
1333
1152
940
828
1560
1459
1269
1074
977
1424
1205
991
811
710
1500
1299
1108
954
859
1572
1397
1211
1058
964
1413
1192
978
822
716
1474
1280
1092
937
826
1543
1384
1190
1037
931
Thermal
Conductivity
(Btu/hr-ft-°F)
0.0386
0.0354
0.0308
0.0272
0.0245
G.0409
0.0381
0.0344
0.0302
0.0278
0.0424
0.0405
0.0367
0.0328
0.0309
0.0398
0.0354
0.0312
0.0276
0.0255
0.0412
0.0373
0.0335
0.0304
0.0285
0.0427
0.0393
0.0355
0.0325
•0.0307
0.0396
0.0353
0.0309
0.0278
0.0256
0.0407
0.0369
0.0332
0.0301
0.0278
0.0422
0.0391
0.0352
0.0321
0.0299
Axial
Nusselt
Number
153
148
156
163
210
221
156
151
175
223
241
181
184
173
205
181
173
178
183
222
238
205
176
178
217
256
233
192
189
230
177
179
180
178
214
244
181
175
180
230
262
219
196
192
239
Length
Nusselt
Number
318
617
975
1360
2190
460
651
944
1460
2320
501
755
1150
1440
2140
376
721
1113
1520
2310
495
855
1100
1480
2260
532
972
1200
1570
2400
368
746
1125
1480
2230
508
755
1094
1500
2400
545
913
1225
1600
2490
-------
282
APPENDIX I
STANTON NUMBER CALCULATIONS
The Stanton number has been defined in Chapter IV by Equations
(21)-- and (1*8) in terms of the free-stream 'velocity W. The calculation of
the free-stream velocity has been presented in Table 35 for the 9 combi-
nations of Configuration/Condition.
The fluid properties are evaluated at the film temperature, defined
as the mean of the average gas temperature (Table iH) and the gas tempera-
ture at the wall (Tables 11-13)» in accordance with the usual procedure.
The density is calculated by means of the perfect gas law for the assump-
tion of atmospheric pressure throughout the vortex chamber using the gas
constants calculated in Table 32. The specific heat at constant pressure
i
is evaluated from air property tables (Reference [1*39] page 565) for the
film temperature.
Colburn J-Factor
The Colburn j-Factor is defined as the product of the Stanton number
and the Prandtl number raised to the two-thirds power. The Prandtl number
is evaluated at the film temperature using air property tables [1*39].
The results of this calculation are given in Table 1-1. The
density used in the calculation was taken from Table D-6. The film tempera-
ture at which the specific heat and Prandtl number were evaluated is also
given in Table D-6.
-------
283
TABLE 1-1
CALCULATION OF COLBURN j-FACTOR
Configuration
1
•
2
3
Condition
3
3
12
3
8
12
3
8
12
Furnace
Column
Section
1
2
3
4
5
1
2
3
4
5
1
2
3
4
5.
1
2
3
4
5
1
2
3
4
5
1
2
3
4
5
1
2
3
4
5
1
2
3
4
5
1
2
3
4
5
Convection
Conductance
(Btu/lbm-ft2-°F)
11.3
10.8
10.0
9.24
10.7
17.3
12.3
10.8
11.0
12.9
19.6
15.2
14.1
11.8
13.2
13.8
12.7
11.6
10.5
11.8
18.7
15.8
12.3
11.3
12.9
21.0
19.0
14.2
12.8
14.7
13.4
13.1
11.6
10.3
11.4
19.0
13.8
12.1
11.3
13.3
21.1
17.7
14.4
12.8
14.9
Specific
Heat
(Btu/lbm°F)
0.255
0.253
0.249
0.246
0.245
0.258
0.256
0.253
0.249
0.248
0.259
0.259
0.256
0.251
0.249
0.257
0.253
0.249
0.247
0.245
0.258
0.256
0.251
0.249
0.247
0.260
0.259
0.254
0.251
0.249
0.257
0.253
0.249
0.247
0.245
0.258
0.254
0.251
0.249
0.247
0.259
0.258
0.253
0.250
0.249
Stanton
Number
x 103
5.56
5.05
4.23
3.53
3.79
5.75
3.97
3.18
2.97
3.30
6.00
4.61
4.06
2.98
3.20
7.15
6.03
5.03
4.15
4.44
6.56
5.25
•• 3.66
3.13
3.43
6.72
5.91
4.00
3.34
3.68
6.85
6.16
4.96
4.05
4.26
6.53
4.40
3.55
3.08
3.45
6.68
5.49
4.03
3.30
3.66
Colburn
j- Factor
x 103
4.31
3.92
3.28
2.73
2.94
4.47
3.08
2.47
2.30
2.55
4.67
3.59
3.16
2.31
2.47
5.56
4.67
3.89
3.21
3.44
5.10
4.08
2.83
2.42
2.65
5.23
4.60
3.10
2.58
2.85
5.32
4.77
3.84
3.14
3.30
5.08
3.41
2.75
2.38
2.67
5.20
4.27
3.13
2.56
2.83
-------
28U
Modified Colburn J-Factor
The modified Colburn j-Factor is defined by using the Stanton
number obtained from Equation (48). The calculation procedure is identi-
cal to that for the usual Colburn j-Factor with the exception that a
calculation is required for the enthalpy potential instead of the specific
heat.
The enthalpy potential has been defined in Equation (49) in terms
of the net enthalpy of combustion (given in Table F-3) and the sensibly
enthalpies of the reactants (evaluated at the average gas temperature)
and the products (evaluated at the wall gas temperature).
The calculation of the enthalpy potential together with the result
for the modified Colburn j-Factor is given in Table 1-2.
-------
TABLE 1-2
CALCULATION OF MODIFIED COLBURN j-FACTOR
Configuration
1.
2
3
•
Condition
3
8
.
12
3
8
12
3
8
•
12
.
Furnace
Column
Section
1
2
3
4
5
1
2
3
4
5
1
2
3
4
5
1
2
3
4
5
1
2
3
4
5
1
2
3
4
5
1
2
3
4
5
1
2
3
4
5
1
2
3
4
5
Enthalpy
Potential
(Btu/lbm products)
1484.7
1433.7
1380.2
1341.4
1301.3
1268.2
1224.1
1179.3
1126.3
1097.0
1276.1
1227.6
1167.3
1155.3
1131.7
1477.6
1432.6
1363.1
1334.7
1308.8
1307.7
1240.1
1216.3
1178.6
1153.8
1315.4
1242.9
1220.3
1190.7
1166.6
1485.3
1427.2
1376.7
1340.4
1313.2
1296.3
1251.9
1207.8
1170.0
1140.0
1310.5
1242.9
1216.5
1188.9
1160.9
Modified
Col burn .
Factor x 10
1.17
9.28
6.37
4.45
3.97
15.3
9.54
6.69
5.15
5.02
16.7
11.6
8.63
6.03
5.96
15.7
11.4
7.99
5.43
5.01
17.0
11.5
7.36
5.54
5.44
18.1
13.5
8.48
6.42
6.46
15.0
11.4
7.67
5.35
4.85
16.7
10.0
7.05
5.38
5.27
17.7
12.4
8.37
6.24
6.22
-------
286
APPENDIX J
LEAST-SQUARES CURVE-FIT CALCULATION
•I
The calculation of a least-squares curve-fit to data is performed
in accordance with the procedure outline in Reference [U27]-
The equation for the Colburn j-Factor can be written in terms of
the free-stream Reynolds number and two constants to be determined from
the data:
St Pr2'3 = a Re b (j-l)
xx ^ '
The constants a and b can be determined from N data points by
summing each ith data point as follows:
1 2 ~ 1 U
In a = —— -—- (J-2)
TVT K" —• / T/" \ ^i
N K - K K^
b = * -±-| (J-3)
where
K, = 2 in |st Pr2'3) (J-10
i X
K = Z In2 (Re ) (J-5)
£--. • JF**
\
K_ = Z In (St Pr2/3). ln(Re ) (J-6)
K
:, = Z In (Re ) (J-7)
^* • ^^
-------
Performing the above calculations upon the free-stream Reynolds
number values tabulated in Table D-6 (N = 1*5) results in the following:
K = 9559
K
:h = 65U.U
Similarly using the values given in Table 1-1 results in:
KX = -255-7
K3 = -3729
Substituting these values into Equations (J-2) and (J-3) results in the
following correlation for all Stations/Configurations/Conditions of the
Colburn j -Factor given in Table 1-1:
St Pr2/3 = 0.117 Re '-- (J-8)
X -X.
Using the same procedure to find the least-squares fit for the
modified Colburn j -Factor first for Stations 1 and 2 only and then for
Stations 2, 3, and k only for all Configurations and Conditions results
in the following :
For Stations 1+2 (N = 18)
K-L = -119-2
K2 = 328U
K3 = -1611
K^ = 2U2.9
(St Pr2/3) = 0.0683 Re -°-29° (J-9)
1-2
-------
288
For Stations 2 + 3 + 4 (N = 2?)
= 5861
K = -2852
K^ = 397-6
(St Pr2/3) = 3.39Re~°'5T° (J-10)
x 2-4 X
For all Stations/Configurations/Conditions for the modified Colburn
j-Factor using Equations (J-l) through (J-7) results in the following:
For Stations 1+2+3+4+5 (N =
KX = -319-3
K2 = 9559
K = -4662
(St Pr2/3) = O.ll88 Re " (J-ll)
x 1-5 x
-------
289
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TECHNICAL REPORT DATA
(Please read Instructions on the reverse before completing}
1 HtPORT NO.
EPA-600/2-76-225
3. HECIPItNTS ACCESSION NO.
4. TITLE ANDSUBTITLE
FLUIDIZED VORTEX INCINERATION OF WASTE
5. REPORT DATE
August 1976
6. PERFORMING ORGANIZATION CODE
7. AUTHOH(S)
Jack P. Holman and Richard A. Razgaitis
8. PERFORMING ORGANIZATION REPORT NO.
9. PERFORMING OR3ANIZATION NAME AND ADDRESS
Southern Methodist University
Civil and Mechanical Engineering Department
Dallas, Texas 75275
10. PROGRAM ELEMENT NO.
1AB013; ROAP 21AQQ
11. CONTRACT/GRANT NO.
Grant R801078
12. SPONSORING AGENCY NAME AND ADDRESS
EPA, Office of Research and Development
Industrial Environmental Research Laboratory
Research Triangle Park, NC 27711
13. TYPE OF REPORT AND PERIOD COVERED
Final; 5/70-8/74
14. SPONSORING AGENCY CODE
EPA-ORD
15. SUPPLEMENTARY NOTES project officer for this report is J.D. Kilgroe, Mail Drop 61,
Ext 2851.
6. ABSTRACT
The report gives results of an experimental investigation of an incineration
concept utilizing fluidized wastes in a confined vortex flow with simultaneous heat
recovery. The incinerator consisted of a vortex combustion chamber and a cooled
vertical furnace column 5 feet long and half a foot in diameter. (No transition section
was used.) The vortex incinerator was operated using propane, sawdust/propane, and
sawdust. The principal experiments were performed using propane at air/fuel ratios
and total mass flow rates (in Ibs per hour) in three combinations: 15 and 125, 20 and
220, and 20 and 280. Radial temperature profiles and heat transfer to the wall of the
vortex tube were measured as a function of air/fuel ratio, vertical position, total
gas flow rate, and inlet/outlet configurations. Tube entrance temperature profiles
demonstrated a peak of approximately 1800 F at a radius ratio of 0. 5; at the tube
exit, the maximum temperature shifted to the centerline and decreased to less than
1000 F. Total energy recovery rates varied from 84,000 to 152,000 Btu/hr and energy
recovery efficiencies varied from 54 to 70%. Maximum energy fluxes experienced
were on the order of 37,000 Btu/hr-sq ft. A helicoidal flow-model correlation was
developed which was about 4 times that predicted for the Colburn j-Factor using the
Reynolds analogy for fluid friction for turbulent flow past a flat plate.
KEY WORDS AND DOCUMENT ANALYSIS
DESCRIPTOFtS
b.lDENTIFIERS/OPEN ENDED TERMS
c. COSATI Field/Group
Air Pollution
Tluidizing
Waste Disposal
ncinerators
feat Recovery
Propane
Sawdust
Air Pollution Control
Stationary Sources
Fluidized Vortex Incin-
erator
Fluidized Wastes
13B 11L
07A,13H
15E
13M, 13A
07C
DISTRIBUTION STATEMENT
Unlimited
19. SECURITY CLASS (This Report)
Unclassified
21. NO. OF PAGES
337
20. SECURITY CLASS (Thispage}
Unclassified
22. PRICE
EPA Form 2230-1 (9-73)
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