-------
'-
Table
2.1
202
2.3
2.4
5.1
5.2
5.3
5.4
5.5
Aol
Col
Co2
C03
C04
C.5
C.6
LIST OF TABLES
Various Correlation Relations for Jet Trajectory Data.
Independent Dimensionless Parameters
Range of Parameters. . .
. . . .
. . . .
. . . .
Overall Percent Coverage
. . . . .
. . . . . .
. . . "
Turbulence Scale
. . . .
. . . . .
. . . .
Overall Density Distribution at Plane A-A.
. . . . . .
Data from Shawnee Boiler
. . . . .
. . . . .
. . . . .
Example of Shawnee Data Supplied by O.A.P.
Overall Percent Coverage
. . . . . .
Various Correlation Relations for Jet Trajectory Data.
Dimensionless Parameters Obtained in Solid-Gas
Suspension Studies. . . . . . . . . . . . .
. . . .
A Comparison of Scaling Techniques
. . . .
Summary of Dimensionless Groups Obtained by Two
Techniques. . . . . . . . . . . . . . .
Independent Dimensionless Parameters
. . . .
. . . . .
Independent Variables.
. . . .
. . . .
. . . . .
Range of Parameters.
. . . .
. . . . . .
. 0 . .
iv
Page
2-3
2-6
2-7
2-14
5.-13
5-34
5-46
5..-4.7
5-50
A-4
C-3
C-5
C-28
C-31
C.-34
C-3.'5
-------
Figure
2.1
2.2
3.1
3.2
3.3
3.4a
3.4b
3.4c
3.4d
3.4e
3.5
3.6
3.7
3.8a
3.8b
3.9a
3.9b
3.10
3.11
3.12
3.13a
3.13b
3.14
4.1
4.2
LIST OF FIGURES
Trajectory Data 12" x 12" Duct. . . .
. . . . . . . . .
Concentration Profile Along Centerline of 12" x 12"
Due t . . . . . . . . . . . . . . . . . . . . . 0 . ., .,
Centrifugal Fan Output
. . . .
. . . . 0 0 .
Lead-in Duct
. . . . . .
. . . .
Square Duct
. . . . .
.....
. . . . . .
Shawnee Model
. . . . . . . .
. . . "
Shawnee System.
. .. . . .
............
Location of Data Acquisition Points in Plane A-A.
Photograph of Shawnee Model System. .
......
Photographs of Shawnee Model. . . .
.....
. . . . .,
Turbulence Generators, Screens, etc. .
. . . .
., . . ., .
Filter System
.. . . . . .
. . . . . .
......
Pitot Tube. . . .
.....
........
Solid-Gas Feed System
" . " " . " " .
. . . . . . . . .
Photograph of Feeder System
.....
o " l1li " 0 "
Isokinetic Probe System
.. " . " .
" " " "
. . . "
Photograph of Isokinetic Sampling Probe System
" . ., ., .,
Isokinetic Probe Holder
. " . . . "
.....00
Photograph of Hot Wire Probe System
" . . " " "
" " . .
Full Size Representation of Optical Probe
. . . . " " "
Photograph of Optical Concentration Probe
.......
Optical Concentration Probe Circuit Diagram
. . " " . 0
Schematic of Laser Ve10cimeter . .
. . . . . . .
. 0 " "
Photograph of 12 in. x 12 in. Duct with Laser
. " . " .
Trajectory Photographs
" . . . " "
...........
v
Page
2-10
2~12
3-2
3~4
3~6
3-7
3~7
3-8
3-8
3-9
3-11
3-12
3-12
3~14
3-15
3-18
3...18
3-19
3-19
3-21
3-23
3-23
3-25
4-6
4-6
-------
Figure
5.1
5.2
5.3
5.4
5.5
5.6
5.7
5.8
5.9
5.10
5.11
5.12
5.13
5.14
5.15
5.16
5.17
5.18
5.19
5.20
5.21
LIST OF FIGURES (Continued)
Trajectory Data 12" x 12" Duct. . . 0 . 0 0 0 . .
Trajectory Comparison of a Single Particle with a
Homogeneous Jet . . . . . . . . . . . . .
Page
5-3
5-5
Concentration Profile Along Centerline of 12" x 12"
Due to. . . . . .. . . . .. 0 .. . . . .. . .. . 0 .
Velocity and Intensity - Screens - Plane A-A
5-7
. . . . . .
5-8
Velocity and Intensity - 2" Grid - Plane A-A
5-9
. . . . . .
5-10
Velocity and Intensity - Vortex Generator - Plane A-A
Velocity and Intensity - Open Box - Plane A-A
Shawnee Model Plane A-A - 2" Grid (Concentration
Profiles) ...... . . . . . . . . . . . .
Shawnee Model Plane A-A - Screens (Concentration
Profi les) . . . . . . . . . . . . . . .
Normalized Density Distribution - Shawnee Model
Plane A-A (2" Grid, L-1) . . . . . . . . . . .
Normalized Density Distribution - Shawnee Model
Plane A-A (2" Grid, L-2) . 0 . . . . . . . . .
Normalized Density Distribution - Shawnee Model
Plane A-A (2" Grid, L-3) . . . . . . . . . . .
. . . . .
5-11
. . . . 5-21
. . . . 5-22
o . . . 5-23
. . . . 5-24-
. . . 5-26
Shawnee Model Plane A-A (Concentration Profiles, L-2) .5-28
Shawnee Model Plane A-A (Concen tra tion Profiles, L-2) 5-30
Shawnee Model Plane A-A (Concentration Profiles, L-2) 5-<31
Normalized Density Distribution - Shawnee Model
Plane A-A (Vortex Generator, L-2) . . . . . .
Normalized Density Distribution - Shawnee Model
Plane A-A (Open Box, L-2) ... 0 . . . 0 . 0
Penetration Profiles - Shawnee Model Plane A-A
Shawnee Model Position Y-Y Concentration Profiles
Shawnee Model Plane Y-Y Data Acquisition Points
. . . .
5-<32
. . . ..
5-33
.. .. .. .. ..
5-37
5-40
.. .. .. ..
5-41
Velocity Profile and Intensity at Plane Y-Y of Model,
Velocity Profile at Plane B-B Shawnee Boiler. 0 . . .
vi
5-42
-------
Figure
5.22
5.23
5.24
5.25
5.26
A.l
Col
C.2
LIST OF FIGURES (Continued)
Shawnee Model Plane Y-Y Concentration Profiles.
. . . .
Shawnee Model Plane Y-Y Concentration Profiles. .
Normalized Mass Flow Rates, mpo/~p = C, Plane A-A,
Injection Level 1 . 0 . . .~o . 0 . 0 0 0 . . 0
Normalized Mass Flow Rates, mp./mp = C, Plane A-A,
Injection Level 2 . . . . o~. . . . 0 . 0 0 . .
Normalized Mass Flow Rates, ~./~ = C, Plane A-A,
Injection Level 3 0 0 . 0 .~o . 0 0 . . .
Effects of Plume Temperature on Trajectory for Two
Velocity Ratios. . 0 . . 0 . 0 0 . . . . 0 0 0 . . .
Coordinate System - Fractional Analysis
. . 0 . .
System Definition for Integral Approach
........
vii
Page
5-43
5~44
5-52
5-53
5-54
A-9
C-7
C-l5
-------
NOMENCLATURE
Cl' C2
Dp
,....
Dp
Dpw
f, fo
~
mp'
~
mSi
-;-
ffip
~
Re
a
particle radius
A
area
constants
d
nozzle diameter
D
duct width
eddy diffusivity of gas in gas/solids fluid
turbulent diffusivity of particles
diffusivity of particles at wall
F
time constant for momentum transfer between particles and gas
total friction factors (with solids/gas alone)
g
gravitational constant
I
intensity, vi /Uo
effectiveness parameter
L
duct length
m
mass of particle
local particulate mass flow rate
local theoretical particulate mass flow rate to satisfy
stoichiometry
mean particulate mass flow rate averaged over all ~Pi's
total particulate mass flow rate through cross section
p
pressure
q
electric charge per particle
r
vector representing spatial location in duct
Reynolds number
s
surface area of control volume
viii
-------
Up
U
v, w
Vp' Wp
v'
v
x, y, z
x'
y'
Eo
A
p
V
f
fo
~j
fp
Jp
fpo
l"
t
time
u
gas turbulence velocity in x direction
u
gas velocity in x direction
particle velocity in x direction
time averaged gas velocity in x direction
gas velocities in y and z directions, respectively
particle velocities in y and z directions, respectively
RMS turbulence velocity at x = 0
volume
spatial coordinates
distance downstream from injection point
penetration distance of jet
permittivity of free space
scale of turbulence at x = 0
viscosity
kinematic viscosity
density
gas density in duct
jet mixture density
density of particulate phase
material density of particles
particulate cloud density at x = 0
shear stress
ix
-------
ABSTRACT
This study was undertaken to model the geometry and flow conditions
of the Shawnee Unit 10 Boiler during the dry limestone injection process.
The basic goal was to determine the penetration and dispersion character-
is tics of the limestone injection into the Shawnee boiler with the aid of
a model.
A cold-gas model was selected to simplify the instrumentation
and measurement problems.
The model was scaled geometrically with a scale factor of 12.5 to 1.
The combustion gases and the solid-gas injection flow conditions in the
boiler were simulated by keeping the values of the relevant dimensionless
parameters for the model as close as possible to those of the full scale
Shawnee unit.
The dimensionless parameters were identified by nondimen-
siona1izing the governing conservation equations and boundary conditions
associated with solid-gas flow.
However, a lack of information on the
turbulence characteristics in the full scale boiler prevented a matching
of the turbulence intensity and dimensionless turbulence scale.
As a
result model experiments were repeated over a range of values for those
two parameters to yield information on the effect of turbulence on dis-
persion in the model.
At present it is not known if this range of values
bracketed the operating conditions of the full scale system.
Since full scale limestone distribution results were available, a
comparison of these data with those of the model was made.
The degree of
dispersion of the limestone was characterized by a percent coverage value
which in effect is the fraction of complete mixing of the limestone and
S02 at Plane A-A.
Percent coverage values were calculated for the Shawnee boi.1er for
each of the three injection levels.
The same was done for the model at
x
-------
one turbulence level and then additional tests were conducted at a fixed
injection level under various turbulence conditions.
The variation in
dispersion with injection level followed the same pattern for both the
model and full scale system with the lower rear injection providing the
largest percent coverage and the front, the smallest.
At each injection
level the model and full scale system fractional coverage values deviated
by approximately ten to twenty percent.
A qualitative comparison of the
distribution of the limestone across Plane A-A for each system was also
made.
Here, as might be expected, point by point agreement between the
model and full scale system-was not as close as were the overall coverage
values.
Nevertheless, the low and high limestone concentration locations
generally tended to be similar which is consistent with the relatively
good agreement in overall percent coverage values.
This suggests that
the Shawnee model used in this study was an adequate representation of
the full scale unit.
xi
-------
1.0
INTRODUCTION
This study was undertaken to better understand the penetration and
dispersion characteristics associated with the limestone injection tech-
nique for removing sulfur oxides from the combustion gases of a coal-fired
power plant boiler.
The fundamental assumption underlying this investiga-
tion was that a necessary condition for removal of the sulfur oxides is a
uniform distribution of the limestone with respect to the S02 in the com-
bustion gases in the region where the temperature range for chemical reac-
tion between the S02 and the limestone occurs.
The main objective of this
study was to develop a scale model which would simulate the limestone dis-
persion characteristics of the full scale Shawnee system.
The original plan for achieving the goal of scaling the limestone
dispersion was essentially composed of two parts.
The first was to iden-
tify, through analysis, the important flow parameters associated with the
injection technique.
This was to be coupled with single and multiple noz-
zle experiments to provide a more basic understanding of the relationships
among the flow variables as they affect the penetration and dispersion
phenomenon.
The plan was to use the results from this portion of the pro-
gram to aid in effecting the second half of the program.'~e second half
consisted of the design, fabrication, and operation of an experimental pro-
gram which utilized a scale model of the No. 10 Shawnee steam plant boiler
section located in Paducah, Kentucky.
Both the geometry and flow condi-
tions were to be modeled as closely as possible so that the results would
be useful in evaluating the full scale Shawnee system.
The following dis-
cussion summarizes the major tasks required to complete this study.
1-1
-------
2.0
SUMMARY
2.1
Introduction
The following discussion lists the major steps that were taken during
this study to determine the dispersion characteristics in the Shawnee sys-
tern.
These include the literature survey, the fractional analysis to iden-
tify the experimental parameters, the experimental program and the conc1u-
sions.
In general, the original scope of work proposed for this investi.ga-
tion was met although additions and deletions to this plan were made duri.ng
the course of the study.
2.2
Literature Review
The literature review initiated prior to the start of the contract
continued throughout the duration of the study.
A variety of injection
studies have been reported in the literature and range from the deflection
of liquid jets injected normal to an air stream to the spreading of a free
solid-gas jet.
The literature survey was broken into several categories for conven-
ience.
The following is a list of these categories which were covered i.n
the study and were felt to be related to the limestone injection problem:
1.
Injection of a gas jet into a transverse gas stream
2.
Injection of a liquid jet into a transverse gas stream
3.
Free and cof1owing jets (single and two phase)
4.
Stack emissions
5.
Transport of particles in a turbulent flow field
Appendix B is a bibliography including the five above categories.
However, it was found that none of the reported studies have considered
either of the following aspects related to limestone injection:
2-1
-------
1.
Solid-gas jet injected into a transverse stream
2.
The effects of ambient turbulence conditions on the
dispersion of the jet
Nevertheless, all of the five listed categories do provide some over-
lap with the limestone injection problem.
In particular, category (1), the
gas jet into a transverse stream most closely resembles the present prob-
1em.
Jet trajectories have been determined experimentally both by monitor-
ing a tracer gas mixed with the injectant gas and by measuring the tempera-
ture profile along the plume of a heated injectan~ g~s.
The penetration
equations resulting from these experimental studies are shown on the
accompanying chart, Table 2.1.
The last four equations in Table 2.1 strongly suggest that the dynamic
pressure ratio (~jVj2/~ oUo2) may be an importar..t dimensionless parameter
for jet injection problems.
However, results from the literature do not
indicate whether these relationships hold for a solid-gas jet.
If it is
shown that the solid-gas jet can be treated as a homogeneous mixture then
these relationships should be valid.
Conversely, if it were experimentally
demonstrated that these relationships are valid for the jet then it would
be assumed that the jet behaves as a homogeneous mixture and that the
dynamic pressure ratio (with the mixture density represented by S j) is a
jet trajectory parameter for scaling purposes.
2.3
Fractional Analysis
In the beginning of this study the experimental work and the analysis
for identifying the dimensionless parameters were carried out in a somewhat
parallel effort.
However, early in the program first priority was assi.gned
to the fractional analysis or the nondimensiona1ization of the governing
2-2
-------
AUTHOR (8)
Callaghan and
Ruggeri (4)
Weiland and
Trass (5)
Patrick (3)
N
I
u.>
*
8handorov
*
Ivanov
Norgren and
Humenik (8)
PENETRATION EQUATION
~ '= C3'1 (~r"«J (1)'~
*: ~(fit ~rx:~ dFrl
Blowing air into duct
ci.:= . S "'6' = ,''2. 5
~:. ,~6 0= .10
C = dimensionless coefficient
Author notes that powers vary
with changes in d
Sucking air through duct
0(:: . 6'1 ~ :.. ,22
~:. .1/ & = ,56
.33 ~ n L .3'2
*Referenced in Abromovich (9)
All of the above references are listed in Appendix A.
Table 2.1.
Note: The units of
this equation do not
check.
Various Correlation Relations for Jet Trajectory Data
-------
flow equations.
This was necessary since a well planned experimental
effort requires prior knowledge of the relevant dimensionless parameters.
Prior to the initiation of this program it was decided that an
entirely analytical approach to the limestone dispersion problem would not
be a good one.
As a result a combined experimental and analytical approach
was selected.
Here the conservation of mass and momentum equations along
with the boundary conditions were nondimensionalized with the characteris.-
tic values of the system.
This partial analysis with the resulting dimen-
sionless parameters or 'p! groups was then used as the starting point for an
experimental program.
The departure from further analytical effort at this
point was due to the complex interactions be~ween the particles and the
turbulent stream.
This makes a solution to the governing equations
impossible to conceive of at this time.
The identification of the dimensionless parameters served the two
basic aims of this study.
First, the parameters were needed to plan exper-
iments related to the penetration and dispersion of a single jet.
Here the
parameters were varied to determine the relative effect of each on the
penetration and dispersion.
These parameters were also used in design.:i:ng
a scale model of the Shawnee system.
In modeling, the values of the param-
eters for both the full size system and the model are kept the same or as
close as possible in order to preserve the similarity between the two sys-
terns.
Ideally, with this arrangement, the governing equations for both
the full sized Shawnee system and the model are identical.
In effect then,
the experimental results for the model will be equally valid for the full
scale system in that the results are a form of solution of the governing
equations in a physical rather than mathematical form.
2-4
-------
The significant groups obtained by a fractional analysis of the
Shawnee boiler are shown in the first column of the dimensionless parameter
chart, Table 2.2.
In scaling the Shawnee boiler
it is desirable to sat-
isfy as many of these dimensionless terms as is possible.
Prior to con-
structing the model, the terms which could be. scaled were identified.
Before this was done the dimensionless parameters were rewritten since sev-
eral of the groups were included within each other.
It was desirable to
break these groups into a set of independent dimensionless parameters.
This is shown in column 2 of the same chart.
A linear geometric scaling was used, so that the first dimensionless
term is automatically satisfied.
The injection nozzle size was also scaled
linearly, preserving the ratio (d/D) in a number of terms.
The next chart
(Table 2.3) provides the actual ranges for these independent dimensionless
parameters for both the Shawnee boiler and the model.
These numerical
results demonstrate that 111 and iT4 are scaled within the limits indicated
by the Shawnee operating conditions.
The effect of not satisfying 1T 5
exactly cannot be ascertained without further experimentation.
However,
since there is only a factor of three difference (rather than several
orders of magnitude difference) between the scaling parameter the effect is
not expected to be large.
Forlf 2 and\{3 it was known in advance that the turbulence data for
the Shawnee would be difficult to obtain.
Therefore, the operational con-
ditions of the model included a wide range of turbulence conditions.
In
this manner it was hoped that it would be possible to bracket the values
for the actual boiler conditions.
2-5
-------
N
i
0\
From Equation (19) Independent Dimensionless Terms Descriptive Term
~~ d same: 110 = ~ ~ 11':. d Geometric Sca le
D 0 D
~UoD same~ 1l=- ~900 b Reynolds Number
~ ' ,}.A.
Vi I
TT-=)[ Turbulence
Uo same: Z. Uo
Parameter
A same: 1\3 -::. % Turbulence
D Parameter
"Z.d '- ~~QT;)2- Dynamic Pressure
£,.\JJ rewritten:
~
~oU~ if tl4 - ~. Ratio
- RU~
~ NbdJ(~)~) TIs-AT, Particle Inter-
rewritten: action Parameter
TIS:' if8t
PjVJ'c\'1- (nJt scaled) TIfo~ ';~ Vi Mass Flux Ratio
fb t10 rt ~ 1J1)
Ta'i::le 202.
Independent Dimensionless Parameters
-------
N
I
.......
Shawnee Group Model
4.1 x 105 L IT L.. 6. 5 x 105 Tli = Re.: Yt 5.21 x 105 f:"IT, b 5.69 x 105
- ,- 135 ~ 114 ~ 465 1\= ~ VJ' 209 'TT4' 331
~U~
ITS': 2. 18 x 10 7 -- ~{)L. IT 5' ':. 6
115= ~(QJ 6.7 x 10
Table 2.3. Range of Parameters
-------
2.4
Initial Experimentation
The initial small scale experiments were designed to ascertain whether
or not the dynamic pressure ratio was a valid pi group. Two small scale
ducts (2" x 3" and 6" x I") were used to investigate this relationship. In
addition to the experiments a digital program was written to calculate the
trajectory of individual particles injected into a transverse stream.
The
preliminary results of the small duct experiments indicated that the injec-
tion path was much closer to the trajectory predictions of the homogeneous
jet studies outlined on the chart than the computerized predictions for
individual particles.
The small scale experiments were also useful in determining the
requirements necessary for the injection feed system.
In addition, some
experimentation with illuminating the jet plume for photographic purposes
was accomplished with these apparatus.
2.5
Square Duct Experiments
The larger 12" x 12" duct was designed and built as the smaller exper'.'
iments were being phased out.
Incorporated into this design were the tag
filter system to handle the heavier dust loading and the improved closed
feed system.
This pressurized feed system enabled the mass flow rates of
the air and solids as well as the mean injection velocity to be measured.
The duct was designed to provide more carefully controlled conditions with
which to study single nozzle injection experiments.
In addition, it was
utilized to make final modifications and checks of the auxiliary equipment
and instrumentation that were to be incorporated into the Shawnee model
tests.
2-8
-------
During the course of checking out these subsystems, the feed system
was modified until a reliable, steady feed rate of solids was achieved.
In
addition the capabilities of the blower were determined and both pitot tube
and hot wire measurements of the duct velocities were obtained.
Some effort
was also put into developing the optical concentration probe with this duct
system.
Dust deposition on the optical surfaces proved to be a problem and
due to time limitations its development was terminated although the progno-
sis for its successful completion was good.
Finally, the substitute iso-
kinetic probe technique for obtaining concentration measurements was checked
out with the same duct.
Because of the substantial improvements in the
injection system, the trajectory studies were repeated for comparison witll
the preliminary data obtained using the small ducts.
The experiments per-.
formed using this improved hardware substantiated the trends indicated by
the small scale ducts (Figure 2.1).
Therefore, further design considera-
tions for the Shawnee model included the dynamic pressure ratio (SjVj2/
SoU02) to scale the injection trajectory phenomena.
These trajectory tests were run in a horizontal duct, hence, the
question arose as to the applicability of these results to the case of
injection into a vertical boiler.
The relative importance: of!-it=he'8ravi-
tational to the inertial terms for the injection procest; is indicated by
the Froude number (gL/u02),
This dimensionless group was calculated and
the value was in a range indicating that the orientation of the gravita-
tional field is not significant to the injection process.
Experiments were also run with this test section in order to determine
the effects of the ambient turbulence on the jet trajectory and disper-
sion.
Unfortunately, there was insufficient time for any extensive exper-
imentation on this aspect of the study since the 12" x 12" duct had to be
2-9
-------
N
I
t-'
o
,
32
Do= 60 ft/sec
(II;, : 321 ftlsee
. ~ s>~o= 5.32
~
.--
~
~
/'
24
--
- Patrick
d = 1/8"
/""
/'
'1j
-..
/'
Experimental Data
-
:>-,
t::
o
-.-I
.j.I
tU
H
.j.I
-------
dismantled and replaced by the Shawnee model.
The only results parameter-
izing turbulence obtained are shown in Figure 2.2.
These results have not
been substantiated by further testing and at this time can only be con-
sidered as preliminary data.
2.6
Shawnee Model Results
Upon completion of the fabrication of the Shawnee model, it rep1ac.ed
the 12" x 12" duct.
All three injection levels were studied with the
improved feeder system allowing all of the nozzles at any given level to
be used.
The turbulence parameters obtained from the fractional analysis
were a dimensionless turbulence scale and intensity.
These were systemat..
i.cally varied by using several different turbulence producing devices.
These devices were selected to cover a wide range of eddy sizes as well as
turbulence intensities.
The concentration profiles were then compared fo1'
the various turbulence conditions.
The results indicated that the most significant effect on the concen-
tration profile at Plane A-A was the distance from the injection plane to
Plane A-A.
Hence, it was found that the lower rear injection plane pro-
duced a signi.fi.cantly higher degree of dispersion than the other two i.nje(~-
tion planes.
The turbulence intensity was also found to play some part ln
the dispersion phenomenon.
It appears from the present data that an
increase in dispersi.on occurs wi.th an i.ncrease i.n turbulence intensity.
However, increasing the inte~sity from three to ten percent (a factor of
three) only resulted in an improvement in the dispersion of the order of
ten percent.
2-11
-------
,-...
CI)
'0
s::
o
to)
-------
2.7
Comparison of Model and Full Scale Results
The data in this model study are compared with the data provided by
the a.A.p. and the specific tests used for comparison are listed in Table
5.3.
The data from both studies were used to calculate the fraction (or
percent) of uniform coverage for each of the three injection levels.
Unfortunately, it will not be possible to compare these data on an equi.v-
alent basis since exact modeling was not maintained.
Several types of
deviations from exact modeling occurred.
First the turbulence level in
the Shawnee boiler is unknown and hence could not be matched with any model
turbulence.
Furthermore, the dynamic pressure ratio for the front injec-
tion in the Shawnee boiler was approximately 50 percent greater than this
ratio at the other two levels while the dynamic pressure ratio was kept
constant for all three levels in the model experiments.
Also the excess
air was varied in the Shawnee boiler experiments whereas the duct mass flow
rate was kept the same throughout the testing in the model.
Finally, no
specific information was made available on the variati.ons, if any, between
the injection mass flow rates for each of the nozzles at Shawnee.
Any
significant variations of this type would also influence the dispersi.on
r.haracteristics.
Table 2.4 gives the average percent coverage for each of the three
injection levels based on the experiments listed in Table 5.3.
The model
coverage for the two-i.nch grid are presented along with the Shawnee calcu.-
lations for all three levels.
The most general observation that can be
made is that the results from the model are consistent with those from the
full scale system.
In particular both systems found the same relative
standing for the three injection levels with regard to fractional coverage.
Furthermore, the magnitudes of the coverage values at each level for each
system were reasonably close together.
However, it should be noted that
2-13
-------
Table 2.4.
Overall Percent Coverage
Model
(2" Grid)
Shawnee*
Levell
66
70.9
Level 2
85
74
Level 3
49.1
63.2
*These values averaged over all experiments listed in Table 5.3.
2-14
-------
the variations between levels in the model were not as great as those in
the Shawnee boiler.
However, the dynamic pressure ratios for the model
and full scale system differed by 50 percent for the front injection level
which may have contributed to this discrepancy.
Thus, in summary it is felt that the agreement between the model and
full scale coverage values is due to the modeling efforts.
In particular,
the values. of the dimensionless parameters for the model were kept as
close as possible to those of the full scale boiler as was indicated in
Table 2.3.
At the same time it is recognized that modeling was not com-
plete and the above stated deviations from exact modeling are the likely
causes of differences in the percent coverage values.
2-15
-------
3.0
EXPERIMENTAL EQUIPMENT AND INSTRUMENTATION
3.1
Introduction
The experimental program was performed using a system designed specif-
ica11y for this study.
The total apparatus requirements include the main
air flow system, the solid-gas feed system, and the instrumentation neces-
sary for monitoring the process and obtaining the concentration data.
The main air flow system contains three components, which are:
(1)
the blower, (2) the two test sections, and (3) the filter.
The solid-gas
feed system, which performs the function of mixing the solid phase with
the air and injecting it into the test sections, completes the list of
equipment necessary to obtain the flow and injection process.
There are five major instrumentation components.
These are:
(1) a
pitot tube, (2) an isokinetic sampling system, (3) a hot wire probe, (4)
an optical concentration probe, and (5) a laser veloci.meter.
At the ter-
mination of data acquisition, development of the last two instruments was
:::'.ot complete and they were not used.
Each of the flow system components
and the instrumentation components are described s~parate1y below.
3.2
The Blower
The blower system is composed of three parts; a fan, a D.C. motor,
and a D.C. generator.
The fan is a centrifugal type made by American
Blower Inc. and is connected in line to a General Electric D.C. motor.
The power for this motor is supplied by a General Electric speed varia tor
unit which is used to regulate the output of the fan.
The operational
envelope of this blower system is shown in Figure 3.1.
3-1
-------
8
6
Q) ........
1-1 1-1
=' Q)
CI.I +J
CI.I ~
Q) :3 4
1-1
Pol CI.I
w Q)
I .-I ..c
N ~ CJ
+J s::
0 H
H '-"
2
o
o
2
4
6
8
Flow Rate (1000 CFM)
Figure 3,1.
Centrifugal Fan Output
-------
3.3
Test Sections
3.3.A
Straight Test Section
The straight test section used for this experiment has a square cross
,
section twelve inches to a side and is ~de with transparent materials.
The top and bottom portions are one and one-half inch thick pieces of plexi-
glass, respectively.
The sides are one-quarter inch thick white plate
glass.
These transparent materials were selected for observing and
photographing the process.
The lead-in duct upstream of the test section is constructed of ga1-
vanized sheet metal.
This conduit contains a convergent transi.tion sec-
tion (to match the blower outlet to the 12-inch square duct) and a straight
12-inch square section which is six feet long.
A flow straightener has
been placed in the duct immediately behind the convergent section.
This
flow straightener i.8 made of a number of one inch LD. by six inc.h long
seamless steel tubes whi.ch were fastened together forming 1:1 square packing
of parallel tubes which fi11 the enti.re cross sectlon.
This was done to
eliminate the flow angulation induced by the fan,
A turbulence generat:tng
,
grid is placed a short di.stance upstream of the test section when increased
duct turbulence is desired,
The turbulence generating devi.ce is a grid of
one inch rods placed on two ir.ch centers and mounted in a wooden frame.
Figure 3,2 shows the dimensions of this lead-in duct as well as the
locations of the flow straightener and turbulence generating grid.
This test section contains a single injection port.
The solid-gas jet
is injected through a 1/8 inch nozzle placed in the top section of the duct
with the axis normal to it,
The isokinetic concentration measurements are
3-3
-------
Flow Straightener
1--- I 1-'
I I I I
Air from I Turbulence ------I I
:"> I Generating
1 Grid I I
VJ Blower I I LJ
I L___, .[
.po.
77 \.
96"
I~ 36"
Figure 3.2. Lead-in Duct
-------
r-
made at a test plane two feet downstream of the nozzle as is shown in
Figure 3.3.
The test section terminates inside the filter system box
eliminating the need for a special exhaust duct.
3.3.B
Shawnee Test Section
The Shawnee model test section is a scaled down version of one side of
boiler number ten at the Shawnee Power Station near Paducah, Kentucky.
A
ratio of 12.5:1 has been used in scaling the model to the boiler.
The model
is constructed of wood with glass si.des (1/4 inch thick white plate glass).
This makes visual observation and photography of the plume possible.
The
wood section is made of plywood with two inch by four inch framing to
. stiffen the structure.
Fi.gure 3.4 shows the details of this test section.
For the Shawnee model, a flexible plastic duct connects the fan to a
"stagnation" box immediately under the test section.
The air proceeds
upwards through a seri.es of screens or turbulence generating devi.ces which
are used to control flow conditions i.n the test section.
Two types of
fine mesh screens are used to smooth the flow and reduce the turbulence
intensity.
Both a large grid and cylindrical vortex generators are used
to promote turbulence.
These turbulence conditions were produced by remov-
i.ng the stagnation box face plate and slidi.ng the appropriate turbulence
frames into or out of the box.
The entire set of frames included four
frames with fine mesh (wi.ndow type) screens, one frame with one inch
wooden dowels on two inch centers, and one with vortex generating cans.
The four turbulence conditions created in this study were obtained in the
following manner.
1.
Turbulence reduction screens -- all four screen frames in place.
3-5
-------
Pitot Tube
W
I
0'\
I-
12"
Nozzle
Injection
-j~
!
24"
72"
Sample Plane
47
Figure 3.3.
Square Duct
Air to
Fil ter
-:->'
~I
-------
W
I
.....
Injection
Level 3
Superheater
A
Uo
t
I
I Turbulence
I Control
I Devices
I
Figure 3.4a.
y
Injection Level 1
Injection Level 2
Shawnee Model
A
Front
B
B
U
R
N
E
R
S
Figure 3.4b.
C
Upper Rear
Lower Rear
Shawnee System
C
-------
1-
~ 12" :-:1
N VJ .po VI 0\
+ + + + + td
+ + + + + (')
+ + + + + t]
+ + + + + t%j
+ + + + + "
-------
-~
Figure 3.4e.
Photographs of Shawnee Model
3-9
-------
2.
Two inch grid -- three screen frames and the two inch grid, with
the grid in the top slot.
3.
Vortex generator -- one screen and the vortex generating frame
in the higher position.
4.
Open box -- all devices removed.
These devices are shown in Figure 3.5.
The air then passes through the
test section where it makes a sweeping turn and proceeds through a series
of rods which are scaled to the first bank of superheater tubes at Shawnee.
The air is then ducted back down and into the filter.
As in the Shawnee half boiler, there are a total of eight nozzle loca-
tions for the Shawnee model.
There are two levels at which there are three
nozzles across the duct and a third level with two nozzle locations.
The
injection nozzles are scaled linearly with the boiler dimensions and cor-
responding1y are 5/32 inch in diameter.
Figure 3.4b is a schematic of
the Shawnee boiler for comparison with the Shawnee model of Figure 3.4a.
3.4
Fil ter
The filter system was buH t at West Virginia University specifically
for this project.
In house construction was necessary to assure fit into
the available lab space and because it cost considerably less than an
equivalent commercially available unit.
The filter contains 96 cylinci'rical. cloth- filters which are suspended
over a large collection box (Figure 3.6).
The filter bags and the perfo-
rated receiving sheets were purchased from the Pangborn Corporation.
Access to the box for purposes of removing dust is provided for by a
'bolt-on lid.
3-10
-------
VJ
I
I-'
I-'
Figure 3.5.
Turbulence Generators, Screens, etc.
-------
F IL TER SYS TEM
Figure 3.6
l~tiC .pressure
I
I
1
Total Pressure
PITOT TUBE
Figure 3.7
3-12
-------
3.5
Soli.d-Gas Feed System
For this study, it was necessary to have a steady and consistent jet
i.ssuing into the main stream, hence, it was essential that the feeder expel
the solid phase at a constant rate.
It was also necessary that the system
be completely closed so that the air and solid mass flow rates can be mon-
ltored and controlled.
The feed system designed and built for this project
satisfies these requirements.
The essentials of the present feed system are shown in Figure 3.8a.
This feed system has a combination vibration and stirring action in the
hopper section to assure a smooth flow of the solid phase.
At the base of
the hopper the air is mixed with the solid phase.
This two-phase flow
then p:r.oceeds through a screw chamber, which further enhances mi.xing.
After
the solid-gas flow exits from the screw chamber it is directed into a mani-
f<..\ld block.
The block divides the flow into two or three streams depending
upon the number of nozzles being utili.zed.
A block with three exit ports
18 used for feeding the three nozzles at injection levels one and two.
A
mar:i fold block with two exit paths is used for injection at level three
as
whll as for penetration studies.
The hopper was designed to hold approximately five pounds of dry pow-
de:r..
The cylindrical portion of the hopper is constructed of seamless
aluminum tubi.ng with five inch LD. by si.x inch a.D. and is about seven and
one-half inc.h long.
The lower portion, also aluminum, has a short cyli.n-
drieal section with a truncated conical section below.
The apex angle of
thi.s conical section is 60 degrees.
The exit port at the bottom of the
hopper is 1/2 inch I.D.
3-13
-------
Stirring Mechanism
VJ
I
t-'
.po
Axis of -t
Rota tiona 1 r
Vibration
of Hopper
Flexible Connector
SOLID-GAS FEED SYSTEM
Figure 3.8a
K
o
T
A
M
E
T
E
R
Air
-------
l-
I
I
,
I
I
I
\
Figure 3.8b.
Photograph of Feeder System
3-15
-------
The stirring mechanism rotates on a double sealed (pressure sealed)
bearing installed in the lid.
It is driven through a flexible shaft by a
combination tIlotor and reduction gear box (Janette Manufacturing Company
Model SU30).
The final drive operates at 24 RPM.
In addition to the stirring mechanism, the hopper is also vibrated to
facilitate the flow of the solid phase.
The axis of vibration passes
through the cylindrical portion of the hopper, six and one-half inches from
the top.
A small crank (1/16 inch throw) and split journal bearing were
constructed for the purpose of vibrating the hopper.
The connecting rod is
attached to the base of the conical section, which moves the full di.stance
of the crank throw.
The crank is driven by the same motor which is used
to dri.ve the screw.
The motor is a Dayton Model 5K-070 (1/10 hp at 1000
RP'M) .
The hopper is connected to the screw housing by a flexible hose,
allowing the hopper to vibrate while the screw remains fixed.
The screw
is a one inch wood auger bit, which rotates in an aluminum screw housing.
The horizontal distance between the inlet (from the hopper) and outlet (to
the mani.fold block) i.s two inches.
306
Pi tot Tube
A two-element pitot tube is used in conjunction with an inclined
manometer to give direct readings of the dynamic head.
The pUot tube is
stainless steel with an inner copper tube.
There is a stagnation hole at
the tip and a series of static pressure pin holes (Figure 3.7) are located
1/2 inch from the tip.
3-16
-------
3.7
Isokinetic Sampling Probe
The isokinetic sampling probe is a complete system in itself.
It con-
sists of the probe protruding into the flow (probe body), a solids collec:-
tion filter, a rotameter and a vacuum pump.
The schematic, Figure 3.9a,
shows the flow path and locations of the various parts of the system.
The vacuum pump used is the Precision Scientific Company Model 75
driven through a V-belt by a General Electric 1/3 hp motor.
Air is drawn
thr.ough the probe body, the filter, the rotameter, the by-pass valve, and
f:i.na lly i.n to the pump.
The probe body is constructed of 1/8 inch copper tubing reinforced
over the straight portion with a section of 1/4 inch copper tubing.
The
probe holder (Figure 3.10) with two degrees of freedom allows the probe to
be moved to any location in a gi.ven plane.
In line with the probe is a
two-pi.ece filter made to be quick.1y taken apart for insertion or removal of
the filt.er paper.
The paper filters are 4.7 ern diameter discs.
The by~pass valve is used to control the intake rate of the probe.
Re~~.e, it is possible to match the velocity at the probe tip to the duct
''(7elocity i.n the vJ.ci.n:i.ty of the probe.
:L8
Hot Wi.re Probe
The hot wire probe 1.8 used for measuring velocity by relating the
veloc:i.ty of a fluid over the probe wire to the convective heat transfer.
Because of the rapid response of the electronic circuitry of the probe to
changes in velocity, it is the prime method of measuring turbulence prop-
erties.
There are two principle types of hot wire probes available; these
3-17
-------
1'---
-
fl
t
Fil ter
;/
Probe Body
.
.
R
o
T
A
M
E
T
E
R
By-Pass
Valve
~
Vacuum
I
Pump
Figure 3.9a.
Isokinetic Probe System
Figure 3.9b.
Photograph of Isokinetic Sampling Probe System
3-18
-------
Figure 3.10.
Isokinetic Probe Holder
Figure 3.11.
Photograph of Hot Wire Probe System
3-19
-------
are the constant-current and constant-temperature probes.
The constant-
temperature type probe has been used for this experiment.
The particular unit used is the DISA 55D05 battery operated CTA (con-
stant temperature amplifier) and the DISA 55D15 linearizer.
The linearizer
has a small D.C. voltage gauge which indicates mean velocity but it was
necessary to use a separate root mean square voltmeter for determining tur-
bulence intensity.
The Hewlett-Packard 3400A RMS voltmeter was used to
obtain the A.C. component (Figure 3.11).
A probe body for the hot wire was
constructed to fit the isokinetic probe holder so that the duct cross sec-
tion would be traversed in the same manner with this probe as with the
isokinetic probe.
3,9
Optical Concentration Probe
An optical concentration probe is desirable in order to obtain instan-
tane~us as well as average values of solid concentration at a point.
The
isokinetic probe reported in Section 3.7 can perform only the latter func-
tion.
This probe is basically a modification of existing probes reported
by 800 (1) and Ehmen (2).
This particular design arose over the need
for an i.nplace measurement with a capability for low concentrati.on measure-
ments and a small probe head.
The probe described in this section has been
bui.lt and operated successfully.
It has responded to low concentrations
of smoke, however, operating in a particulate environment has caused par-
tic Ie deposition on the optical surfaces.
It is anticipated that this
problem could be overcome yielding an attractive two-phase flow instrument.
In Figure 3.12 a full-sized sketch of the existing probe is shown and
gives an indication of the compactness of such a probe.
This figure does
3-20
-------
W
I
N
t-'
Reference
Photocell
~J
,
cp
Front View
Reference Photocell
Primary Photocell
Primary Photocell
Two-Phase
Figure 3.12.
i
Flow ~ Secondary Air Flows
'\
Steel~;f;J7~(/!;i/!!r
Brass Inserts
Mirror
Cutaway Side View
Full Size Representation of Optical Probe
-------
not detail the secondary air flow for preventing dust buildup on the
optical surfaces or the electrical connections, both of which are conducted
down the center of the support rod.
The reference photocell is adjacent
to the primary (source) photocell and receives light directly from the
light source through a channel.
The reasons for having two photocells and
placing them so close to each other are:
(1) variations in light bulb
intensity would not effect the zero reference positions since both cells
would be reacting to the same change, and (2) photocells are temperature
sensitive, hence, the close proximity lessens any significant temperature
effects.
The circuit diagram is presented in Figure 3.l3b.
The power supply
is the Kepco ABC 40-0.5N.
The differential amplifier is a Tektroni.x 1A 7-.A
used in conjunction with a Tektronix .547 scope.
3.10
Laser Velocimeter
The velocity of the gaseous phase of the solid-gas injection can be
calculated, knowing the air mass flow rate through the feed system and the
pressure at the nozzle exit,
There is no correspondingly simple way of
calculating the velocity of the solid phase, which very likely has a slip
velocity relative to the gaseous phase.
The laser velocimeter is an i:nst:ru-
ment which would directly measure the velocity of the solid phase and yet
in no way interfere with the injection process.
The velocity of the par-
ticles is determined by detecting the Doppler shift of the lase:r light
scattered from the moving stream of particles.
A laser velocimeter has been constructed and operated successfully
in a bench arrangement, measuring the velocity of a rotating ground glass
3-22
-------
I~
It, .
Figure 3.13a.
Photograph of Optical Concentration Probe
+
PI P2
Power
Supply
RI R2
30 volts
RI' R2 500K fl Potentiometers
PI' P2 Photocells
Differential
Amplifier
Figure 3.13b.
Circuit Diagram
OPTICAL CONCENTRATION PROBE
3-23
-------
. -
disc.
Figure 3.14 shows the configuration of the light path for this
setup.
The laser used is the five mw Spectra Physics stabilite Model 20
with a Spectra Physics 256 exciter.
The light is picked up by an RCA
8344
photomultiplier tube with a grid bias supplied by a Fluke 412B
high voltage power supply.
The output from the tube is processed through
a Keithley Instruments 104 wideband amplifier into a Tektronix 3L10 spec-
trum analyzer used in conjunction with the 561A oscilloscope.
The spec-
tru.m analyzer indi.cates the beat frequency which results from combining
two waves of different frequency, that is, light directly from laser and
light reflected from the particles which experiences a Doppler shift.
This beat frequency can then be related to the particulate velocity.
The optical alignment of the necessary mirrors and lenses requires
sensitive adjustment capabiliti.es.
Time did not permit the fabrication of
a portable opti.ca1 bench for achieving this sensitivity.
However, it is
felt that such an arrangement is entirely feasible as other somewhat sim-
ilar applications of the laser ve10cimeter have been reported as bei.ng
successful.
3-24
-------
First
Surface
Mirror
W
I
N
V1
Natural ~~sity Filter
7;;;/
~;/)~
,,~i ~ I Scattered
~I/ll Light
Beam Splitter
Figure 3.14.
1
Laser
-- --
/' ""
"
,><;
'-...... ./
---
Scattering Volume
Approximately .05 rom x .1 rom
Schematic of Laser Ve10cimeter
-------
4.0
TEST PROCEDURES
4.1
Introduction
In this chapter, the operation of the experimental program will be
discussed in detail.
Separate sections will be devoted to discussion of
the operation of each of the two test sections as well as operation of the
feed system, isokinetic probe, and hot wire probe.
During the course of the experimental program, operational techniques
improved as expected.
Appreciable changes can be noted in certain aspects
of the test procedure when comparing early square duct experiments to the
final Shawnee model experiments.
As an example the problem of bridging of
powder in the feeder hopper was not entirely eliminated until the Shawnee
model was operational.
In addition, since most of the data were taken with
ths Shawnee model, test procedures discussed will reflect those employed
with the model experiments.
For the reasons outlined above, the data obtained from the twelve
in~h by twelve inch duct are not considered as reliable as those obtained
for the Shawnee model.
4.2
Feed System
The hopper is loaded and the feeder is operated until empty for each
ccmcentration data measurement obtained and at the end of each run the air
flow rate is increased to help remove any particulate deposition which
occurs during a run.
It has been found that if the feeder was stopped
during the injection process or deposition allowed to build, blockages
would be formed in the lines.
4-1
-------
The hopper lid must be removed before loading.
Since the stirring
mechanism is driven with a flexible cable, the attachment of the stirring
. mechanism to the lid does not present any problems for filling the hopper.
A predetermined amount of powder is loaded into the hopper thl8n tb.,," lid is
replaced and secured.
The feeder air line valve is opened at the same time that the motors
driving the stirring mechanism, the screw, and the crank for vibrat:ing the
hopper are turned on.
Pressure adjustments are made at the rotameter to
maintain it at a constant value for each run.
The value for thi.s pressu:J::e
is determi.ned by calibrating the feed system to match Shawnee dynfamic
pressure ratios.
The method of calibration is as follows.
A known mass of powder is
placed in the hopper.
The feed system is turned on, the pressure held ~on-
stant, and the rotameter value monitored.
One observer moni.tors the injec'-
tion nozzles and uses a stop watch to observe the length of time ne~essary
to empty the hopper.
In this way the flow rate of the powder can be dete:r:-
mined.
The ai.r mass flow rate and, hence, nozzle velocity is cah.',ul.att'!Q
usi.ng the rotame,ter and pressure data.
A sample ~alculati.on of the d.ynam.ic
pressure ratio is shown below:
Powder 2. 5311F
Time 38.6 sec. = 0.64,:2 nrl.n.
Press
29}Q = 5.58
26
cu.ft./min.
V. = 231 ft./sec.
J
Roto
.
m=
2.5311F
.642 min.
= 3.934Flmin.
'pj = .0752#/cu.£t. + 3. 931F/min.
5.58 eu.ft./min.
Dynamic Pressure Ratio = mX~) 2 =
= .782iF/cu.ft.
[.7821"l231J 2 = 274
L.0752 4.5
4-2
-------
Once the feed system is calibrated, it is necessary only to monitor
the pressure for normal operation.
Calibration runs made at different
times for the same operating conditions indicate a variation on the order
of t seven percent.
4.3
Isokinetic Probe
The operation of the isokinetic probe is relatively simple once the
tip velocity can be related to rotameter readings (Figure 3.9).
Since ca1-
ibration curves for rotameters do not give negative pressure correction
curves, it was necessary to calibrate the rotameter to the system.
A
Rockwell 250 dry gas meter was used for this purpose.
By adjusting the
by-pass valve on the vacuum pump, it is possible to vary the flow through
the system (rotameter and dry gas meter).
Once the system is calibrated to
the rotameter, it i.s necessary only to choose the correct rotameter setting
for a given duct position.
The operation of the probe is as follows.
First, the vacuum pump is
turned on and remains so for the entire operation.
Then the filter paper
is placed in the holder and the two halves of the holder are fastened
together in the operating position.
The probe is adjusted in the holder
until the tip is at the proper location in the duct.
The probe tip is then
rotated 180 degrees from the orientation for data sampling.
The by-pass
valve is adjusted until the rotameter is at the proper setting.
The feed
system is turned on and when the injection appears to have reached its
steady state operating condition, the probe tip is rotated to the predeter-
mined orientation for sampling.
At the end of the sampling time period,
the probe is rotated 180 degrees once again.
The filter paper is removed,
4-3
-------
a new one installed and the probe is again ready to operate.
In order to determine the amount of dust injected into the probe when
in the nonoperating position (rotated 180 degrees), special tests were run.
The probe was positioned in an area of high concentration (a'bout 70 ~12C
sec.) and the procedure outlined in the previous paragraph was followed
except that the probe was not rotated into the flow.
The results gave an
i.ndication of the intake of powder collected prior to and immediately f01,-
lowing the sampling period while powder was still being injected i,:>rlbJ the
system.
These tests were run for about 20 seconds each.
In each case,
less than six mg was collected.
Hence, it was concluded that the i~take
of powder prior to and after the test period was a small fracti.on of that
obtained during the sampling period.
4.4
Hot Wire Probe
The procedure for setting up the hot wire probe is standard and OVlt-
lined step by step in the manuals accompanyi.ng the unit.
Dnree the c.:Jm-
ponents are assembled and the unit calibrated, the amplifie'i' resistantr:€ is
adjusted to match that of the hot wire probe.
Then the gain is adjusted 80
that the output voltage corresponding to the maximum duct Vt::lo~ity is
within the range of the 1i.nearizer (less than three volts).
The output
voltage from the linearizer i.s shaped to be di.rectly proport:i.um.al t.o the
velocity normal to the wire.
Therefore, it is only necessary to obtain the
voltage corresponding to a single known velocity i.n order to l~ali'!:;'.rat:e t28
probe over the entire operational range.
This was done by usi.ng the pitot
tube.
4-4
-------
The turbulent fluctuations are also picked up with the hot wire probe.
These fluctuations are measured with respect to the mean velocity and are
put on a root mean square meter. The value read is 1f~2 or the square
root of the mean value of the fluctuating component of velocity squared.
The ratio of this value to the mean velocity tio'
,
tT/uo' is defined as
the intensity.
The intensity as well as the mean velocity can be obtained
in thi.s manner at any location in the plane of measurement.
4.5
Straight Test Section
Two types of experiments were performed using the straight duct.
The
first was the acquisition of data for the trajectory i.n the vicinity of
the nozzle exit.
The second set of experiments were conducted to ascertai.n
the effects of turbulence for a single injection condition.
The operation of the main duct and the feed system are the same for
both experiments.
First, the blower system is turned on and the air veloc-
ity is monitored using a pitot tube set at the center of the duct one foot
upstream of the injection nozzle.
The blower is adjusted to the proper
velocity as indicated by the pitot tube and maintained at that level
throughout the test, where periodic adjustment of the blower was necessary
due to dust buildup in the bag filter system.
Then the feed system hopper
was filled and preparations for operation of the feed system were performed
as outlined in Section 4.2.
From thIs point on the operations were different for the two experi-
ments.
In the experiment to obtain the trajectory, a laser beam was used
to illuminate about a ten-inch portion of the plume.
The laser was placed
on the floor, Figure 4.1, since the bottom of the duct is 2.2 feet above
the floor level.
The light was directed through a cylindrical lens which
4-5
-------
I
Figure 4.1.
Photograph of 12 in x 12 in Duct with Laser
.p-
I
0\
Figure 4.2.
Trajectory Photographs
-------
spread the light in a vertical plane (much like an open fan).
The light,
after passing through the lens, was reflected off a first surface mirror,
at an angle of 45 degrees, straight up into the duct such that the plane
of the light was coincident with the jet centerline and parallel to the
duct walls.
In this way, the portion of the duct from the nozzle to a dis-
tance of about ten inches downstream was illuminated by a thin sheet of
light.
Although no measurements were made, visual observations indicated
that thickness of this fan of light was on the order of 1/32 inch.
Hence,
it was possible to observe a thi.n slice of the jet plume.
A thin sheet of clear plastic was taped to the side of the duct, and
the experiment proceeded.
One observer traced the shape of the plume on
the plastic sheet.
This process was repeated for a number of different
dynamic pressure rati.os.
These ratios were obtained by varying the main
duct velocity.
This was found to be preferable to varying the feed system
operating condition.
Because of the concentrated i.~tensity characteristics of the laser
light there was sufficient light for photographic work.
However, it was
necessary to blacken the interior surface of the far side glass wall and
to perform a number of other alterations to eliminate reflection and .other
undesirably illuminated surfaces.
The photographi.c results are shown in
Figure 4.2.
The isokineti.c probe was used to obtain the profile of the injected
plume at a point two feet downstream of injection for the experimental work
related to testing the effects of variations in turbulence.
For the fir s t
flow condition, only the flow straighteners were placed in the duct.
This
corresponded to the "quiescent" condition.
For the second condition, the
4-7
-------
turbulence generating grid was placed about half a foot downstream of the
flow straighteners.
The average velocity (as measured by the pitot tube)
was kept the same for both cases as was the feed system operating condition.
The isokinetic data was taken along the vertical center axis of the duct.
That is, at points two inches, four inches, six inches, eight inches, and
ten inches from the top of the duct and at a position two feet dOW!lstream
of the injection point.
The actual operation of the system is a combination of Secti.ons 4..2
and 4.3.
The feed system is turned on and monitored.
When the mass flow
rate out of the injection nozzle reaches the steady state condition, the
probe was rotated to the sampling position for 15 seconds and then turned
back.
This process was repeated for both turbulence conditions at all the
required pr~be locations.
4.6
Shawnee Test Section
The bulk of the Shawnee model experimental program has been devoted t~
obtaining concentration profiles at Section A-A by injec.ting at the. th:ree
different levels corresponding to those used at Shawnee and for fuu:r d:!.f=
ferent types of duct turbulence.
For a11 nine testconditioIls, the dt::~t
mean velocity and the dynamic pressure ratio of the injection prorc:e:B(~ were
held constant.
In addition, experiments were performed to study pe'c.'.etra-
tion, injection superposition at Plane A-A, and dispersion at Se(.~tlo!! B-B.
For a11 of these tests the i~okinetic probe was used to obtai.n the
concentration profiles.
The blower was turned on and set at the scaled operati.ng condi.tion.
This corresponded to a dynamic head of .430 inches of water (45 ft./sec.)
4-8
-------
at Section A-A.
It was necessary to check and reset the blower approxi-
mately every four runs to maintain this level.
The next steps were to pre-
pare the isokinetic probe and the feed system for operation.
One observer
started the feed system and the other operated the isokinetic probe.
This
process was repeated from 50 to 90 times to obtain a single concentration
profile at Plane A-A for each of the four turbulence conditions and injec-
tion pos i tions .
There were a possible total of 55 sampling points for each
condition although all were not used for any given set of turbulence and
injection conditions.
For each of these conditions, the intensity of turbulence was meas-
ured using the hot wire probe.
It was necessary to do this only once for
each condition since the turbulence generated by these devices remains
constant so long as the flow velocity is not changed.
For the superposition tests, the nozzles at injection level
2
were
utilized along with the turbulence reducing screens.
One nozzle was left
in place, and the other two were removed and inserted into the exhaust
section.
In thi.s manner the feeder was operating under identical condi-
tions (1. e., feeding three nozzles) as in the previous tests.
Data were
obtained for each of the three nozzle positions at level 2. ,
The penetrati.on tests were performed using the two nozzle-manifold.
One nozzle injected into the exhaust portion of the test section, and the
other was placed in the center nozzle position of injection level 2.
Three different feeder operating conditions were utilized.
Duct condi-
tions were maintained with the turbulence reduction screens at the Shawnee
model duct velocity (45 ft./sec.).
As for the previously mentioned Shawnee
model tests, the concentration data were obtained with the isokinetic probe
at Plane A-A.
4-9
-------
Duri.ng the final portion of the experimental test program, a limited
amount of concentration data were obtained for model Section Y-Y.
For
these data, all three nozzles at injection level 2 were utilized.
Two di£-
ferent duct turbulence conditions were used; one with the turbulence
reduction screens and the other with the vortex generator.
This concluded the Shawnee model test program.
Over 750 data points
were obtained during this program.
Each of these required operational
procedures outlined at the beginning of the section and detailed in
Sections 4.4 and 4.5.
4-10
-------
5.0
EXPERIMENTAL RESULTS AND DISCUSSION
5.1
Introduction
This section will present the experimental results and their inter-
pretation.
As with previous sections of this study, the data from the
twelve-inch duct will be treated separately from those from the Shawnee
model.
The twelve-inch duct results include single jet trajectory data as
well as downstream concentration profiles for two different turbulence
condi tions .
Most of the Shawnee model experiments were conducted to
obtain concentration profiles at Plane A-A for each of the three injection
levels .
These experiments were run with one injection level operating at
any given time which corresponds to the limestone distribution study at
Shawnee conducted early in 1971.
For the model experiments a range of
turbulence conditions was studied.
In addition, some concentration data
were taken at Plane Y-Y (close to B-B) to compare with the data taken at
Plane A-A.
5.2
Penetration and Concentration Results for Twelve-Inch Duct
5.2.1
Introduction
The twelve-inch straight duct experiments were planned i.n order to
aid in the design of the Shawnee model experiments.
In particular, it was
designed to handle the dual roles of providing an experimental arrange-
ment for the study of a single solid-gas jet and to serve as a checkout
facility for the various components that were eventually utilized in the
Shawnee model system.
The twelve-inch straight duct was oriented horizon-
tally even though the real system and the scale model are oriented
5-1
-------
vertically.
But, as is shown in Appendix C, gravitation effects are not
significant to the injection and dispersion phenomena.
Therefore, the
orientation of. this duct will not have an effect on the applicability of
the data so obtained.
Hence, the experiments with this test section
supplement those with the Shawnee model.
The original plan was to spend more than half the time allocated to
the straight duct experiments for single jet trajectory and dispersion
tests.
The remaining time was to be used experimenting to determine the
effects of multijet injection and injection angle on dispersion.
H~-
ever, during the course of the study it was necessary to devote more time
than planned to the feeder and concentration probe development.
Conse-
quently, the experimental single solid-gas jet experiments were reduced
in number which significantly limited the quantitative conclusions that
were drawn.
Nevertheless, trajectory data were obtained for a solid-gas
jet which were compared with existing gas jet correlations.
In addition,
qualitative information on the effect of increased turbulence intensity
and scale on the downstream concentration profile was obtained.
No'work
was done in the straight duct for multiple injection or for variation in
injection angle.
5.2.2
Trajectory Results
The trajectory data were obtained by visual observation.
Here, as
mentioned earlier, the laser beam was optically transformed into a ver-
tical plane of light which sliced through the solid-gas plume providing
good illumination.
The plume envelope was then traced onto transparent
plastic sheet attached to the face of the duct.
The solid curves in
Figure 5.1 represent the centerline value of the measured envelope of the
5-2
-------
24
'C
-
-
>.
s::
0 16
'M
+J
IV
!-I
+J
QJ
s::
QJ
p..,
VI 8
I
W
32
Vo:' 60 ft/see
.
/'
/
..-/'
} ~ = _321 ft/see
91>0 - 5.32
~
./""
/""
Experimental Data
--
Patrick
d = 1/8"
'1 \J.; -= 160 ft/see
- - - - -_....-:.-- f'~= 1.37
--
---------- 1~=- 98ft/see
J ~~: 1.6
.-C)---
o
8
Figure 5.1.
16
24
32
40
48
Downstream Position x'/d
Trajectory Data 12" x 12" Duct
-------
plume.
The dotted ~urves represent the correlation obtained by Patrick
(3) for a gas jet study.
The experimenta~ values of )OJ from this study
treat the solid-gas flow as a homogeneous mixture.
The value of fj in
for the jet which is
Patrick's correlation corresponds to a gas density
different from that of the transverse stream.
Nevertheless, agreement
between Patrick's prediction and the two-phase jet is significantly better
than that between single particle trajectories and the same two-phase jet.
Figure 5.2 shows the trajectory paths as predicted by Patrick's equation
along with the numerical solution for a single particle.
Unfortunately,
conclusions drawn from such few results would be premature.
Independent
variables such as particle size, particle density, and free stream turbu-
1ence were not parameterized.
In addition, the geometrical centerline of
the plume may not represent the true centerline of the plume.
In fact,
the ideal method for determining the jet trajectory would be to take
concentration profile measurements at various downstream locations.
In summary, while the limited number of trajectory curves for the
solid-gas jet are in fair ~greement with Patrick's correlation, the flow
regime considered here was too narrow to endorse that correlation for a
solid-gas jet.
Before doing so, it would be necessary to conduct a sys-
tematic study over a range of values for the dimensionless parameters
obtained in Section 3.
5.2.3
Concentration Profile Measurements
Several experiments were also conducted to compare the effect of tur-
bulence intensity on the distribution of particulate in the duct.
This
was done by obtaining concentration data both for the relatively quiet
flow in the duct approximately ten feet downstream from the flow
5-4
-------
10
U = 50 ft/sec
o
v. = 23.5 ft/sec
J
8
~ = 1.5
A
S>p = 2000
"t:I 6 ~
-
-
~
s::
0
.r-!
+J
IJ1 ~
, 1-1
IJ1 +J
CLJ 4
s::
CLJ
~
2
Patrick
o
0 8 16 32 40 48 56 64 72
Downstream Position y' /d
Figure 5.2. Trajectory Comparison of a Single Particle With a Homogeneous Jet
-------
straighteners and for a more turbulent condition produced by a grid.
Figure 5.3 shows the two concentration profiles along a vertical axis
through the center of the duct two feet downstream of the point of injec-
tion.
As expected, the more turbulent condition increased the dispersion.
5.3
Shawnee Model Experiments
5.3.1
Introduction
The primary goal of this portion of the experimental program was to
operate the model after the full-size Shawnee system.
Appendix C dis-
cusses the fractional analysis and details the required fluid properties
and flow variables necessary to keep the dimensionless pi groups the same
for both the full-scale system and the Shawnee model.
The experiments
were carried out meeting these requirements as nearly as possible.
As
mentioned earlier, the turbulence parameters were undefined in the Sha~ee
boiler and as a result it was necessary to experiment over a range of
turbulence conditions with the intent of learning what effects these con-
ditions have on dispersion.
The resulting concentration profiles at
Plane A-A are presented along with comparisons and conclusions as to the
effects of the various turbulence conditions and injection levels on the
concentration profiles.
5.3.2
Turbulence Conditions in the Shawnee MOdel
5.3.2.1
Introduction
Various devices for promoting turbulence were tried in this program
and
are
described', below.
'Measurements. -of. :the
turbulence- inten-
sity in Plane A-A were obtained for each device and are presented in
Figures 5.4, 5, 6 and 7.
The turbulence scale was not measured so that
5-6
-------
60
,
~== 192
u=- 74 ft/sec
()
y. = 270 ft/sec
------0.... J
/" -0--- Quiescent Flow
/ \ -0-- Turbulent Flow
"'"' / \
CI)
'i:I
!:J J \
0
CJ 40
Q)
CJ)
LI"'\ / \
r-4
~ ~
o .~ I
.~
.j.J 'i:I
I\J Q)
1-1 .j.J \
.j.J CJ
~ Q)
Q) r-4
CJ r-4 \
~ 0
0 u
U
1-1 \
Q)
'i:I
~ 20 \
Pol
'H \
0
~ ~
~
\
\
"
"
~
0
8 40
I
Penetration Distance L
d
Figure 5.3. Concentration Profile Along Centerline
of 12" x 12" Duct
5-7
-------
60
50
40 .2
u
<11
co
- >.
4.J 4.J
~ '.-1
.. 30 r .15 co
s::
>. <11
4.J 4.J
'.-1 s::
U H
o
r-I
~
20 .10
10
.05
"
......
'-
-
-
...... --- -- ---
---
o
o
2
3
4
5
6
Lateral Position
Figure 5.4.
Velocity and Intensity - Screens -
Plane A-A
5-8
-------
60
50
-0
40 .2
CJ
Q)
I1J
- >-
~
I.H ~
30 .15 'H
.. I1J
>- ~
~ Q)
'H ~
U ~
o H
~
Q)
:>
20 .10
10
.05
-0--
--
---
--
o
2
3
4
5
o
6
Lateral Position
Figure 5.5.
Velocity and Intensity - 2" Grid -
Plane A-A
5-9
-------
60
50
40 .2
CJ
Q)
tI)
- :>.
.j.J
~ .j.J
'r-!
.. 30 .15 tI)
:>. !::
Q)
.j.J .j.J
'r-! !::
CJ
0 H
~
Q)
~
20 .10
10
-0-
.05
o
o
2
3
4
5
6
Lateral Position
Figure 5.6.
Velocity and Intensity - Vortex Generator -
Plane A-A
5-10
-------
60
50
-0
40 .2
0
Q)
!f.I
-
~ :>-.
\i-I ~
~ 30 .15 .~
!f.I
:>-. !::
~ Q)
.~ ~
o !::
o H
......
Q)
:>
20 - .10
------
--
--... -
--
10 .05
o
o
2
3
4
5
6
Lateral Position
Figure 5.7.
Velocity and Intensity - Open Box -
Plane A-A
5-11
-------
approximate values, as suggested by the literature, were assigned to each
condition.
The following sections consider each condition separately
presenting both the measured values of intensity and a discussion of the
resulting turbulence scale.
5.3.2.2
Fine Wire Screens
Eight wire screens placed in series upstream of the injection ports
provided the least turbulent condition.
As shown by Dryden, et al. (4),
the turbulence intensity is reduced as more screens are added.
This flow
condition was used to obtain a reference condition with Which to compare
the concentration results from the more turbulent flow situations.
Fig-
ure 5.4 shows the velocity profile in the north-south direction through
the center of the model as well as the turbulence intensity.
The veloc-
ity measurements were time averaged values at each point.
The measure-
ments of the velocity profile in the east-west direction show little var-
iation in velocity in that direction.
As can be seen in Figure 5.3 the
turbulence intensity did not exceed seven percent with the fine wire
screens.
Some indication of the scale of turbulence can be obtained from
studies where screens were used to reduce blower turbulence in wind tun-
nels.
Dryden and Batchelor and Townsend (5, 6) present data for the
scale of turbulence as a function of the distance downstream of the
screens for different mesh screens.
The screen solidities for these
studies do not match those of this study but should be close enough for
making a rough estimate of the scale.
Table 5.1 gives the values of the
scale at Plane A-A based on both Dryden's and Batchelor and Townsend's
results.
5-12
-------
Author Screens 2" Grid
Dryden ( 4) 0.4 in.
Batchelor & Townsend ( 5) 0.896 in.
Batchelor & Townsend ( 6) .185 in.
Tab le 5. 1.
Turbulence Scale
5-13
-------
5.3.2.3
Two- Inch Grid
This configuration consisted of six wire screens in series upstream of
the two-inch grid.
Here the two-inch grid replaced the top set of screens.
This grid was used to obtain a significantly larger scale of turbulence.
Figure 5.5 shows the mean velocity profile in the north-south direction, as
well as the turbulence intensity, in the same direction at Plane A-A.
The scale can be estimated in the same manner as was done for the wi.re
screens and Table 5.1 also includes these values.
5.3.2.4
Vortex Generators
This technique was employed to somewhat resemble the flow conditions
in the boiler although the flow direction at the Shawnee burners is at
right angles to its direction at Plane A-A whereas the main duct flow is
in line with vortex generators in the model.
However, the basic reason
for using this technique was to produce a swirling motion approximately
scaled to the size representative of the swirls in the Shawnee boiler at
the secondary air exit.
It should be noted that the swirls produced are
of an entirely different nature than the near isotropic turbulence pro-'
duced by the grids.
In fact, characteri.zing the swirls as turbulence
could be misleading.
Nevertheless, it is expected that the phenomenon of
mixing produced by them is somewhat analogous to that produced in a
turbulent field.
There is a180 some question as to whether or not the swirling motion
remains intact after combustion takes place.
Although a more thorough
investigation into this question is required, indications in the litera-
ture are that the swirls do remain intact and that cold gas studies of
this motion are a reasonably close approximation to the actual combustion
5-14
-------
conditions.
As a result, it is felt that this turbulence promoting tech-
nique, of the four techniques used in this study, most closely resembles
the actual fluid motion at Shawnee.
Figure 5.6 shows the mean velocity profile in the north-south direc-
tion with this configuration and the turbulence intensity in the same
direction.
As can be seen, the intensity values are greater than either
of the two grid generating devices.
The burners which produce the swirl
in the Shawnee system are approximately 30 inches in diameter.
In the
scaled down version, this would correspond in a diameter slightly less
than three inches.
The vortex generators used in this study produce vor-
tices in the neighborhood of two to four inches which is based on the size
of the tubes and vanes.
Although no measurements of the achieved size of
the swirls were made, it is felt that the size of the model vortices are
scaled reasonably close to those values determined from the scaling
equations.
5.3.2.5
Open Box - No Barriers
A final set of experiments was conducted without any generating
devices present.
It was felt that intensity produced by the fan should be
greater in this case and that effect on distribution would provide addi-
tiona1 knowledge.
However, no indications of the turbulence scale are
readily available with this arrangement.
As a result, it remains an
unknown since a good estimate could not be made.
Figure 5.7 shows the north-south mean velocity profile and the north-
south intensity profile.
Here, the intensity level was found to be
approximately fifty percent greater than that of the vortex generators.
5-15
-------
5.3.3
Measurements of Concentration Profile at Plane A-A
5.3.3.1
Introduction
Concentration profile measurements at Plane A~,A were made for a11
three injection levels with the screens and with the two-inch grid.
How-
ever, only injection level two was used for the other turbulence genarat-
ing arrangements.
Nevertheless, it is believed that the results do show
the comparative effects of a varying turbulence level on the dispersi
-------
is presented with the raw data and is in the same form as the data TVA has
provided from the Shawnee experiments.
Here, profiles are either shown in
the east-west direction (transverse) for a fixed distance from the nose
(lateral position) or in the north-south direction (lateral) for a fixed
distance from the east or west wall (transverse position).
This technique,
more qualitati.ve in nat.ure, tends to emphasize the heavier concentrations
i.n the vicinity of the jets (east-west profiles) as well as the concentra-
tion distribution in the direction of the jet axes (north-south profiles).
In these cases, the data have been taken directly from Appendix D.
A second technique which is more useful for a quantitati.ve assessment
of the degree of uniformity of the solid-phase employs isodensity plots of
Section A-A.
This is an effective representation for showing the inf1u-
ence of nozzle location and turbulence on the dispersion of the jet.
For
these charts a normalized density is uti.lized.
A perfect distribution
would result in a uniform value of 1.0 for the normalized density values
in these charts.
For example, if a stoichiometric mass of powder were
i.njected i.nto the model, the normalized density plots would indicate the
local fraction of a stoichiometric mixture.
5.3.3.2.2
Definitions
The coneentration profiles and the isodensity plots are different
representations of the same data which in the raw form are in terms of
mass collected or injected per unit time.
Although some uniformity may
have been achieved by placing all of the data in terms of density, it was
felt that. this would -not '-'aid in. data.'!i.nterpretation..and. hence.it was not.done.
The concentration profiles are in fact plots of the mass of powder
collected in 20 seconds at each isokinetic probe location as a function of
5-17
-------
the collection location.
Sample collection points were located in both
Planes A-A and Y-Y.
The isodensity graphs can be thought of as constant density contours.
The density values are normalized so that these dimensionless density val-
ues are a measure of the degree of dispersion.
The normalized density ~ N
is defined as
~N=
~Pi
gP
(5.1)
where ~ Pi = local particle density as measured with the probe at location i.
fp. =
~
(mp)i probe
V A
probe probe
(5.2)
and
~ =
p
average particle density in Plane A-A as measured by total feed
rate through the nozzles
s =
p
(~) feeder
V A
duct duct
(.5 .3)
Thus, S N is the ratio of the local density to the theoretically unifor~
density in Plane A-A.
Hence, if complete dispersion were to occur, ~N
would have the value one at every point in Plane A-A.
The isodE:!~.sity
graphs indicate the regions that are heavy in parti.culate (~N > 1) and
those with less than the mean value C) N L 1). The values of S' N can be
determined directly from the measured mass flow rate collected in the
probe and that injected through the nozzle.
This can be shown by combin-
ing equations (1) and (2) with equation (3) which defines ~N.
Here
5-18
-------
9N ~
(Mp)~~
Vf'~ Af~1C
( ~r\EaEe.
\/Dl)(:T AtlLJCT
-
lM~~fc:.Q~ Arxx:r
(Mr)~Q.. A~
(5.4)
where Vprobe tip is matched properly to Vduct.
5.3.3.2.3
Data Accuracy
It is necessary to establish the accuracy of both the mass collected
per unit time with the probe as used in the concentration profiles and the
isodensity contours.
This was done by comparing the value of the total
soad mass flux determi.ned by measuring the mass flow rate from the feeder
injected through the nozzles to the mass flux as obtained by estimating
the total mass flux from 55 collection poi.nts in Plane A-A.
Measuring the
total mass flow rate injected through the nozzles and dividi.ng it by the
cross-sectional area of the duct gi.ves (~) feeder/Aduct.
hand, the average mass flow rate per uni.t area can also be obtained by
On the other
averaging the mass flow rate per unit area over a number of samples col-
lected with the },sokinetic probe.
Here this mean value is obtained by
.
\'Y\f
AflltO¥£
':::
~ ~
t"\ ,,~\
C~r )n ~g D~~
A.f~o~
(5.5 )
The value of M, the number of collection points in Plane A-A, was 55.
Thus, if the isokinetic sampling was exact then
( mp )FeE!)~R
A 1>uc.1"
:.
--r-
fY'\p
A~o'f!
(5. 6 )
Evaluation of the data for the two-inch grid and the screens showed
that the difference between the two mass flux values was approximately
six percent.
Since this difference could either be due to feed rate
5-19
-------
inaccuracies or collection errors, it will be assumed that the six percent
error is the overall error in the values of both the concentrati.on pro-
files and the isodensity contours.
It is also of interest to note that
with this identity in equation (5.4) that 'pN can be written as
IN ::
(ffir) l
~p
(5.7)
5.3.3.3
Effect on Distance from Injection to Plane A-A
5.3.3.3.1
Concentration Profile
Figure 5.8 shows the concentration profile in the transverse direc-
tion at position 4 for each of the three i.njection levels.
These data
were all taken with the two-inch grid configuration.
From a qualitative
viewpoint, it is found that injection from level 2 which is farthest fr.om
Plane A-A resulted in the most uniform distribution in the transverse
direction.
Figure 5.9 compares the profiles in the lateral direction for
each of the levels with screens being used in each case.
Agai.n the same
general trend results.
That is, injection level 2 produces the most uni~
form dispersion of the three levels.
One can observe from both f.i.gure::3
that an injection at L-3 results in a slightly more uniform pattern than
L-l, but as stated earlier, they are on opposite walls and do not have
the same number of nozzles.
However, both figures do illustrate that L-2
definitely results in a more uniform profile than L-l where L-2 is
approximately 30 percent further from Plane A-A than is L-l.
5.3.3.3.2
Isodensity Contours
A comparison of injection levels 1, 2
and 3 (Figures 5.10, 5.11 and
5-20
-------
120
Inje~tion Level 1. 2, 3 ---1
2 \
- --....... 2" Grid ----- 3 \
...... Lateral Position 4 I
100
I / '\ / \
\ / \
I \ /
I \
I \
,-.. 80
(J
(!)
to \ ''I
0 ,
N \ \
~ -
0 "C
'r-! (!)
.u .u I \
co (J
~ (!) 60
VI .u ~
I ~ ~ \
N (!) 0
t-' (J U
Ci
0 ~
u (!) \
"C
~
P-4
~ 40
........ I
J
I
20
\
.......
'"
....-"
o
L
J
I
H
G
F
E
D
r'
v
B
Transverse Position
CONCENTRATION PROFILE
Figure 5.8.
Shawnee Model Plane A-A - 2" Grid
-------
1-
120
100
\
Scre8ns.
Transverse Inj ec tion Symbol
Position Level
,-... 80
0 0
Q) G 1
(/)
0 C 2 0
N E 3 \l
~ -
0 "C
or-! Q)
.j.J .j.J
co CJ
1-1 Q) 60
.j.J .-I
~ .-I
VI Q) 0
i tJ U
N ~
N 0 1-1
U Q)
i
p.,
~ 40
'-"
20
o
<:,
2
:3
4
.5
6
Lateral P0sition
Figu.r~ 5.9,
Shawne'8 Mvdal
) .a11e A-A - SCr6~!1B
-------
Injection Level 1 - 2" Grid
2
3
4
In
I
N
~ 5
6
L
K
J
I
H
G
F
E
D
c
B
Nose
Figure 5.10.
Normalized Density Distribution - Shawnee Model Plane A-A
-------
Injection Level 2 - 2" Grid
I.J1
I
N
.po
L
I
H
K
J
Nose
.75
G
F
E
D
c
B
Figure 5. 11.
Normalized Density Distribution - Shawnee Model Plane A-A
2
3
4
5
6
-------
5.12, respectively) for the two-inch grid turbulence generator provides
a good indication of the effect of location on dispersion.
It was found
that with injection level 1 each jet maintains its own identity.
The peak
values for the normalized density range from 3.2 to 4.6.
More than 63
percent of the volumetric flow at A-A has a density of less than 1. O.
For
17 percent of the plane, the concentration is greater than 2.0.
Simple
\.:alculations show that 71 percent of the dust is contained within 37 per-
cent of the fluid passing through Plane A-A.
Hence, dispersion is
relatively poor in thi.s case.
For injection level 2, there is significant dispersion when compared
with that of level 1.
Note that the peaks are consistently about 30 per-
cent less.
As with injection levell, more than half, 59 percent, of the
two=phase fluid passing Plane A-A has a normalized density of less than
La.
The major difference between injection levels 1 and 2 is the over-
all uni.formity of solid distri.bution across the duct.
The peak concen-
trations for level 2 are lower with a correspondingly smaller density
gradient: across the duct.
Less data were obtained for i.njection level 3, but it can be seen
that this case raprest:!nts the poorest di.spersion of the three.
Nearly 80
pt-JT.'cent of the solid phase is contai.ned with.i.n 30 percent of the flui.d.
For this injection level, the peaks are well defi.ned and concentration
drop-off is quite rapi.d at the b.:»undary.
5.3.3.3.3
Summary
The differences between the dispersion of the plumes injected at
level 1 and 2 can be explai.ned by the increased path length to Plane A-A.
The centerline path for injection level 1 is about 25 in., that for 2 is
5=25
-------
Injection Level 3 - 2" Grid
\J1
I
N
0"'1
-+- 5.7
\ "
, "
" /
~ --- ~ .---
L
K
J
I
.5
+ 5.8
\
'- " /
,'-- "
....... ./
---
H
G
'E
B
F
D
c
Nose
Figure 5,12.
Normalized Density Di.stribution - Shawnee Madel Plane A-A
2
3
4
5
6
-------
37 i.n.
Hence, significantly greater dispersion could be expected for level
2 as has been the case.
The explanation for the difference in dispersion when comparing levels
2 and 3 is less certain.
The path length for injection at level 3 is
nearly the same as that for injection levell, hence, the dispersion :i.s not
due to path length alone.
One possible explanation is that the differencE!
is a result of the nose impinging on the flow.
This would cause a veloc-
:;,ty gradient and acceleration of the flow which may induce greater
di.spdX'sion.
5,3,3,4
Effect of Turbulence on Dispersion at Plane A-A
5.3,3.4.1
Introduction
This discussion will consider the trend of dispersion with increased
turbul8nce intensity.
The details of the four levels of turbulence con-
sld~red here are discussed in Section 5,3,2.
The effect of turbul~nce on
diFpersIon can only be fully dIscussed with respect to injection level 2
where all fOThr turbulence levels were used.
The p'revious section covered
the effect of i!:jection level on dispersion and it :i.8 felt that the gen-
Hral trend of :i.mpro\'ed dispersion with distance from the sampling plane
will hold fl!)r all turbulence levels in this study,
Thus, it is expected
that the degree of d1.l3persion at level 2 should be greater than that at
If.Nels land 3 for all four tu:rbulence levels,
Again, the discussion
w:tll bt:! bI"oken into two parts, one with the profiles and the other with
the isodensity contours.
5.3.3.4.2
Concentration Profiles
Figure 5.13 illustrates the effect of turbulence on the concentra-
tion profile in the transverse direction for injection level 2 at lateral
5-27
-------
120
Injection Level 2
Lateral Position 4
Grid
- -- -- Screen
--- Vortex
--- - Open
100
-""'" 80
y
(j)
tf.j
0
N
P -
0 '"d
''''; (j)
~ ~
Ct! tJ
1-1 (j} 60
.+oJ ,.....;
VI S:: .-!
I
-------
positions 3 and 4.
As can be seen, the profiles corresponding to the
screens, two-inch grid, and vortex generators are not significantly dif-
ferent.
However, the open box profile is flatter than the other three.
This trend was observed at all of the lateral positions.
The turbulence
intensity for the open box is greater than that for the other three tur-
bulence conditions and the results are consistent with the expectation
that increased turbulence intensity does promote dispersion.
Figures
5.14 and 5.15 indicate that the same trend occurs in the lateral direc-
tion.
In particular the profiles for the open box appear to be flatter
than the others.
However, variations among the other three profiles are
not as apparent and this is reflected in the more quantitative
evaluation below.
5.3.3.4.3
Isodensity Contours
The contour maps for the vortex generators and the open box system
are represented by Figures 5.16 and 5.17.
Figure 5.1.1 corresponds to the
two-inch grid data.
Again all three fi.gures are based on data obtained
for injection level 2.
Table 5.2 presents this data in a tabulated form
for all of the conditions represented with normalized density'distribu-
ti.on charts.
The cross se~tion of the duct is divided into two parts.
The percentage of cross-sectional area which has a soUd density greater
than the mean density and that which has a density less than the mean.
In terms of the normalized density contours this represents the percent
area with the normalized distribution greater than unity (column 1) and
less than unity (column 4), respectively.
These are noted as % G.T. 1.0
and % L.T. 1.0, respectively in Table 5.2.
The column immediately fol-
lowing these columns indicates the percent of the entire injected solid
5-29
-------
120
100
Injection Level 2
Transverse G
80 ~' Position
,,-...
(J
<11
(/)
0
N Open
~ -
0 "t:I ---- Vortex
...-1 <11
~ ~ - -.- Screens
1\1 (J
VI ~ <11 60 -~-=---2" Grid
I ~ ...-I
W ~ ...-I
0 <11 0
(J u
~ ~
0
U <11
i
0
~
~ 40
'-"
20
o
2
3
4
5
6
Lateral Position
Figure 5 0 .40
Shawnee/ioeel Pane A=A
-------
.20
100
Injection Level 2
Transverse C
80 Position
,-..
()
(U
(/J
0
N ---- 2" Grid
~ -
0 't:I - - - Screens
tr-! Qj
..., ...,
co CJ -- --- Vortex
lJ1 !-! (U 60
I ..., .-! Open
\.J.) ~ ...-I
t-' (U 0
0 t)
~
0 !-I
t) QI
't:I
~
0
p...
~ 40
'-"
20
o
2 3 4 5 6
Lateral Position
Figure 5.15. Shawnee Model Plane A-A
-------
Injection Level 2 - Vortex Generator
2
B \, 3
1.5 8 \
\\
VI 2.0 \ \ 4
I I J
VJ
N 1.5 I}
1.5
~I 5
1.0
/ 6
L
K
J
I
H
G
F
E
D
c
B
Nose
Figure: 5.16.
Normalized Density Distribution - Shawnee Model Plane A-A
-------
Injection Level 2 - Open Box
VI
I
W
W
1.0
.75
L
K
G
E
B
c
F
D
I
H
J
Nose
Figure 5.17.
Normalized Density Distribution - Shawnee Model Plane A-A
2
3
4
5
6
-------
Average Average
% G. T. % of Solid Density % L.T. %. of Solid Density Overall
1.0 Within in Area 1.0 Within in Area Percent
(A) A Included (B) B Included Coverage
by A by B
Leve 1 1 37 71 1.92 63 ,29 .46 66
2" Grid
Level 2 41 56 1.36 59 44 .747 85
2" Grid
Le.ve 1 3 27.6 78.5 2.84 72.4 21.5 .297 49.1
2" Grid
Level 2 34 46.5 1.36 66 53.5 .8ll 87.5
Vortex
Level 2 38 46 1.21 62 54 .871 92
-
Open
,
Table 5.2.
Overall Density Distribution at Plane A-A
5-34
-------
mass crossing these respective areas.
The sum of these columns (2 and
5)
will always be
100 percent.
Columns 3 and 6 represent the nor-
malized average density in these two portions of cross section A-A.
The last column of Table 5.2 represents a method of assigning a
quantitative value to the density distribution for the various condi-
tions.
The rationalizat.ion behi.nd this determination is as follows.
Assume that a stoichiometric mass of powder is injected into the duct.
The regions where the normalized density is greater than one results in
a complete reacti.on eliminati.ng all the 802.
In the regi.on where the
normalized density distribution is less than one there is complete
reae.tion, but of course s:tnce there is a deficiency of the solid in this
area some of the 802 does not react.
For example, the open box case has
38 percent of the area with an excess of 100 percent of stoichiometric
mixture and the remaining 62 percent has an 87.1 percent average
coverage.
Thus, the overall percent coverage is calculated as
overall percent coverage = 38 + 87.1 (.62) = 85 percent.
Note that th:i.s i.ndiiCates that r:ange of coverage when comparing the two-
"
inch grid to the open box at level 2 is 85 to 92 percent or a 7.6 per-
cent increase when going fr.:>m the two-inch grid to the open box.
How-
e'ver, when comparing level 1 with level 2 for the two.-i.nch grid there
is an increase from 66 percent to 85 percent which corresponds to an
increase of 22.3 percent.
Thus, it appears that within the limits of
this particular study that the i.nfluence of i.njection level upon
dispersion was greater than the level of turbulence.
This type of calculation appears to be a reasonable one for
assigning a quality number to the dispersion characteristics for the
5-35
-------
various injection levels and turbulence conditions.
Nevertheless, it
should be emphasized that these figures do not represent the expected
percent removal of S02 but only the upper limit of what could be ren~ved
if no other limiting factors to complete reaction were present.
5.3.3.5
Effect of Dynamic Pressure Ratio
A limited number of tests were run in the Shawnee model to corre-
lat~ the trajectory dependence upon the dynamic pressure ratio.
This
was necessary for a number of reasons.
The primary reason was that the
data obtained from the twelve-inch duct did not establish the depende~ce
of trajectory upon the dynamic pressure ratio with complete assurance.
Secondly, the twelve-inch duct trajectory data were obtained by visual
i.nspection of the plume rather than by more exact measurements of the
concentration profile.
A third reason for this series of runs was that
the Shawnee model has a much more complex flow pattern than the strai.ght
duct.
The projection of the nose in ,the boiler might be expected to
exaggerate the trajectory phenomena and perhaps emphasize some sc:condary
effect not previously noticed.
The center nozzle at level 2 was used
for these experiments.
Normalized concentration profiles far three different dynami.>; pres.-
sure ratias are shown an Figure 5.18.
It is immediately obvious that the
penetration dOles increase with increasing dynamic pressure ratio.
Anather aspect which can be identified from these limited tests is that
dispersian appears ta increase with an increase af dynamic pressure rati.o.
This points ta the passibility that dispersion may be dependent upon
either the dynamic pressure ratia ar the path lengt~ of the plume
centerline.
5-36
-------
(/)
QJ
.-I
.,-1
44
o
J.1
Pot
s::1
o
.,-1
+J
IU
J.1
+J
~
QJ
o
s::1
o ,
C) .
,
~
QJ
to:!
.,-1
.-I
m
I-!
o
Z
3/4
1/2
Tr4 = 305
TT 4 = 250
1
lT4 = 210
Dyr.'la::n:i.c Pressure Ratio TI4 =
9.V.2
-J] ]
Q u 2
00 0
Injecti.on Level 2 ~-
2
3
4
Lateral Posi.tion
5
6
Figure 5.18.
Penetration Profiles - Shawnee Model Plane A-A
5-37
-------
Interesting results are obtained by assuming that the trajectory
equation can be written in the form
i - [~.,. \t,2. ]~.&. (~) K3
d - k, ~c Uo"L d
(5 . 8 )
This form corresponds to the experimentally determined trajectory corre-
lations for a homogeneous jet as shown in the last four equations of Table
2.1.
For the three penetration profiles obtained in these model boiler
texts x'/d is a constant, so that the penetration equation can be written
~' - * [~. V.2. ] "'z..
--~ J
d -go Uo~
(5.9)
Comparing the three trajectories by considering the point of highest
concentration to be the jet centerline it is possible to determine K*, k2
and check these values.
It was found that the data best correlated to
K* = 18.6
and
k2 = O. 371.
The dependence of penetration upon the dynamic pressure ratio cornpares
very favorably with the equations of Table 2.1 where the value of k2 v'ar-.
ies between 0.392 and 0.45.
This is also consi.stent with the 12-inch duct
results which indicate that the solid-gas jet trajectory may be repre.e
sented by a homogeneous jet injected into a transverse stream of a
different density.
5.3.4
Concentration Profiles at Plane Y-Y
Because of the location of the sampling port on the model, Plane Y-Y
was sampled instead of the plane equivalent to B-B.
Since both are close
5-38
-------
together, no significant differences in concentration results would be
expected.
The basic purpose for this portion of the investigation was to
probe for any significant or unexpected results.
Figure 5.19 is a plot of
the concentration profile along a vertical axis through the center of the
duct at Plane Y-Y.
The data for screens and the vortex generators indi-
cate an appreciable reducti.on in solid loading away from the top surface
of the model.
Figure 5.20 shows the data acquisition points in Plane Y-Y.
It should be noted from Figure 5.21 that for nearly eight inches below the
top, the velocity profile is nearly flat.
This means that mass flow rate
of air is nearly uniform over this portion while the particle loadi.ng i.s
reduced by a factor of four.
Further, since nearly 80 percent of the total mass flow rate of air
passes through the top eight inches of Plane Y-Y, this indicates a some-
what less than uniform dispersion at Plane Y-Y.
In addition some data
were taken in the transverse direction both two inches and six inches
below the top surface.
These results are shown in Figures 5.22 and 5.23.
Here, only one side of the centerline was probed but indicatious are that
the distribution is of the same order of uniformity in thi.s direction as
in Plane A-A.
In summary, the concentrati.on profile measurement.s in Plane Y-Y show
a relatively uniform distribution in the transverse direction but an
uneven one in the vertical direction.
This distribution would probably
yield an overall percent coverage in the range of 50 to 75 percent
(although this has not been calculated and demonstrated to be the actual
case) .
It appears that the heavier dust loading near the top is due to
the 90 degree turn that fluid makes before entering the superheater
section of the model boiler.
5-39
-------
\J1
I
~
o
t::
o
'M
~
CO
H
~
t::
Q)
o
t::
o
o
,
Injection Level 2
Vortex Generator l:::.
Screens 0
Duct Centerline
-
,J
0
~~
~~
()
0 ~~
C )
(> ~~
()
0 ~~
~~
~ J. !).
~
50
,......, 40
-u
Q)
{IJ
o
N
........
'tj
Q)
~
~ 30
~
~
o
o
H
Q)
'tj
~
p..,
20
~
'-"
10
o
Top
2 4 6 8 10
Lateral Position
Figure 5.19. Shawnee Model Position y-y
Concentration Profiles
-------
o
I
2 2" ~
4 4"
,
6 6" t
8 8"
I
10 lO"t
12
14
16
18
20
-12"
-10"
-8"
~6"
-4"
-2"
o
211
4"
6"
8"
10"
12"
Data Acquis:i..t:i..on Points
Figure 5.20.
Shawnee Model Plane Y-Y
Data Acquisition Points
5-41
-------
p..
0 8
H
8
0 '"'
1-1 CIJ
~
-------
;-., 40
o
Q)
en
a
N
>:: -
0 't:!
.!""'!: (j)
~ ~
to 0
I-i Q) 30
~ .....
s:: .....
CL' 0
0 CJ
V1 s::
0 I-i
I t) Q)
.po 't:!
UJ :3
0
p..
~ 20
.......
60
Injection Level 2
Vortex Generator 6
Screens 0
Lateral Position 6"
-
~
~ 0
i
0
A ~ 6 6
~ 0
s~
:
50
10
o
o 2 4 6 8 10
Transverse Position
Figure 5.22. Shawnee Model Plane y-y
-------
VI
I
~
~
60
s::
o
.~
+J
cu
H
+J
s::
Q)
()
s::
o
u
Injection Level 2
Screens
Lateral Position 2"
o
0
0
~~ 0
0
(~
(~
0
0
0 4 6 8 10
50
"'"' 40
()
Q)
CI)
o
N
-
~
Q)
+J
()
~ 30
.-I
o
U
H
Q)
~
~
P-<
~ 2
'-'
1
o
Transverse Position
Figure 5.23,
Shawnee Model Plane Y-Y
-------
5.4
Comparison with Shawnee Results
This study presents one of those unusual situations where the results
of the model experiments are preceded by those for the full scale operation.
As it turns out, the model results have proven to be consistent with those
from the Shawnee boiler.
Here both the magni tude of the degree of di,sper-
sion and the trend in these values with injection location for the model
compare favorably with those from the full scale system.
However, it is
necessary to reemphasi.ze that for several reasons exact modeling was not
carried out in this study.
Thus, some discussion of the effects of the
deviations from exact mode1i.ng on the comparative results will also follow.
5.4.1
Data from Shawnee Boiler
The O.A. P. has provided dust distribution data from the limestone d1.s-
persion studies :i.n the Shawnee boiler.
These data were collee.ted during
the period from December 1970 through January 1971.
The data included east
and west side results as well as a11 three injection locations.
Table 5.3
lists the test numbers and dates of thuse data which were used for com-
par:i,son with the model data.
5.4.2
Basis £01' Comparison of Data
Table 5.4 provides an example of the type of data that was given by
t.he O.A.P.
As can be seen from this table the velocity profile is not UD.i.~
form whereas the model velocity profile was nearly uniform (see Figure 5.5).
Hence, even though the parts per million values for the S02 were listed as
uniform for all 24 locations, the mass flow rate at each of these locations
varied from point to point.
As a result the theoretical values of the mass
flow rate of CaO needed for stoichi.ometry for each location varied propor-
tionate1y to the S02 mass flow rates.
In the model study the required CaO
5-.45
-------
Table 5.3. Data from 8hawnee Boiler
Test 8ide Injection Location Date
8601 E&W Upper Rear 12/8/70
8603 E " " 12/10/70
8604 W " " "
8602 E&W " " "
8604 E&W " "
8901 E&W " " 1/5/71
8902 E&W " " "
8601 E&W Lower Rear 12/3/70
8603 E&W " " "
8601 E&W " " 12/4/70
8607 E&W " " "
8901 E&W " " "
8902 E " " "
8903 W " " "
8602 E&W Front 12/11/70
8601 E&W " 12/16/70
8604 E&W " "
5-46
-------
Table 5.4.
Examp 1e 0 f the Shawnee Da ta Supp lied by the O.A. P.
Tennessee Valley Authority - Division of Power Production
Sulfur Oxide Removal from Power Plant Stack Gas
Full-Scale Limestone Injection Tests at Shawnee Unit 10
Test No. S601
Date:
December 16, 1970
(The following is a partial representation of a given test data sheet)
Test Conditions
Unit Load, MW
Boiler Load, MLBS/HR
Coal Rate, LBS/HR
Limestone Rate, LBS/LBCOAL
Injection Velocity, FT/SEC
Injection Angle, Degrees
Injection Elevation
Limestone Type, BCR NO.
Particle Size, Microns
Stoichiometry
Coal Type, Contract No.
Excess Air, Percent -
Samp ling
Location
WEST
19.0
Limestone Distribution Index
S02 CAO GR LDG VELOCITY
PPM GRNS/CUFT FT/SEC
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
2120.
2120.
2120.
2120.
2120.
2120.
2120.
2120.
2120.
2120.
2120.
2120.
2120.
2120.
2120.
2120.
2120.
2120.
2120.
2120.
2120.
2120.
2120.
2120.
0.07
0.15
0.46
0.99
0.29
0.41
0.24
0.42
2.95
7.31
8.14
2.61
3.45
2.55
3.28
3.09
4.02
2.72
0.72
0.91
0.85
2.15
0.29
0.18
59.9
68.7
64.5
57.7
38.2
74.1
63.6
72.7
71.9
67.0
69.2
74.8
41.4
47.0
44.9
45.2
52.5
54.3
37.6
35.1
28.9
32.5
40.8
27.0
5-47
143
1000
121600.
0.157
193
o
FRONT
2061
4.7
1.88
81T10
EAST
S02 CAO
CUFT/SEC GRNS/SEC
(mpi)
0.0245
0.0277
0.0268
0.0240
0.0181
0.0339
0.0313
0.0274
0.0289
0.0245
0.0250
0.0289
0.0167
0.0184
0.0173
0.0172
0.0198
0.0207
0.0161
0.0148
0.0120
0.0133
0.0170
0.0128
1.
2.
6.
11.
2.
7.
4.
5.
40.
85.
96.
36.
27.
22.
27.
25.
38.
27.
6.
6.
5.
13.
2.
1.
18.0
THEORET CAO
GRNS/SEC
(mSi)
2.3.
26.
26.
23.
17.
32.
30.
26.
28.
23.
24.
28.
16.
18.
17.
16.
19.
20.
15.
14.
11.
13.
16.
12.
-------
mass flow rate was assumed to be uniform across Plane A-A since the
velocity profile was nearly uniform.
The calculations of the percent coverage of powder was based on the
assumption that the total mass flow rate of CaO was equal to the amount
required for complete removal of S02 with uniform coverage.
The total
mass flow rate of particulate is labeled as Hr.
The actual mass flow rate
.
of particulate at any location (i) is termed mpi (see Equation 5.7) and
~s' is the theoretical mass flow rate at location (i) for a stoichiometric
~
mixture.
In order to determine the percent coverage it is assumed that
all of the CaO passing through location (i) will satisfy the local stoi-
chiometry condition with the S02 whenever mSi ';> ffipi'
On the other hand,
whenever ~Pi >
mSi it is assumed that the excess (mpi - mSi) leaves the
boiler without reacting and that only the difference, ms., will be avail-
~
able for combination with the S02'
Thus, the total fraction of CaO that
satisfies the condition for stoichiometry is
Friction
I~i\
I
(ms. > mp,)
~ ~
+ L mSi
\
\ (mPi > m-i)
(5.10)
=
.
MT
The formula was used to determine the degree of coverage for both the
model and Shawnee boiler data.
The model calculations were somewhat sim-
plified since it was assumed that mSi = mp was the same for all locations
in Plane A-A.
Although this dispersion model does not represent the chem-
ical process it does provide a very acceptable method for comparing disper-
sion data.
The description above is a loose argument to indicate the logic
behind this criterion and give a physical meaning to the value of the
"overall percent coverage" term.
5-48
-------
5.4.3
Quantitative Comparison of Results
. .
The values of ffi-. and ms. were obtained from the full scale Shawnee
p~ ~
data listed in Table 5.3 and Table 5.5 gives the results of the percent
coverage calculations for the experiments listed.
Note that the tests are
categorized according to nozzle location.
Table 5.5 compares the average
values of the percent coverage for the three nozzle locations of the Shawnee
experiments with the model values with the two-inch grid turbulence from
Table 5.2.
Thus, although the turbulence conditions probably were not
matched, the pattern of the highest degree of coverage with the lower rear
i.njection level, followed by the upper rear injection level and last with
the front injection level was obtained for both the model and the full
scale boiler.
In addition the magnitude variation between the model and
full scale system at each of the rear injection levels was less than ten
percent.
The front inject:i.on variation was near 25 percent but the dynami.c
pressure ratio was 50 percent greater for the full scale system than for
the model.
5.4.4
Graphical Comparison of Results
While the quantitatiqe results of the model appear to be consistent
with the results of the Shawnee boiler, one cannot use overall averages
alone as conclusive proof of good model:i.ng.
As a result a point by point
comparison as well as the overall percent coverage must be considered to
help support the vali.dity of the modeling process.
Isodensity contour
diagrams obtained for the model as well as the Shawnee experiments will be
used for this purpose.
The Shawnee contour lines represent fixed values
of the ratio of the mass flow rate to the mean value of the mass flow rate
for the entire duct.
The isodensity lines from the model can also be
considered the same way since from Equation 5.7
5-49
-------
Table 5.5.
Overall Percent Coverage
Model Shawnee*
(2" Grid)
Levell 66 70.9
Leve 1 2 85 74
Level 3 49.1 63.2
*These values averaged over all experiments
listed in Table 5.3.
5-50
-------
~ - alpi
N-:;-
alp
alpi
Thus, each continuous curve represents a constant value of =--
.
in the
nip
contour diagrams.
Figures 5.24, 5.25 and 5.26 show both a model and full scale contour
diagram for each of the injection configurations.
It is sugges ted here tha t there are s imilari ties even though the indi.-
vidual contour lines are not coincident when comparing the model and full
scale diagrams.
In fact the well defined high ratio areas in the model
located along the nozzle's axis do not appear in the Shawnee boiler diagrams.
However, what might be construed as barely discernab1e traces of such pat-
terns can be found in the Shawnee diagrams.
The mass flow ratios are
higher in these vicinities whether or not these are in fact traces of such
patterns.
Furthermore, the outer envelopes with much lower ratios are
similar for both the model and full scale figures.
Thus, in a gross sense
the high and low areas are generally in the same correspondi.ng locations.
5.4.5
Discussion of Comparisons
At this time it does not appear to be possible to pinpoint the reasons
for the apparent quantitative and quaUtative differences in the two 5Y8-
tems.
As stated earlier the turbulence level in the full scale boiler is
unknown and was probably not similar to the model turbulence.
Also the
model velocity profile was uniform and the Shawnee profile was not.
In
addition, the mean velocity varied by as much as 20 percent in the Shawnee
experiments listed in Table 5.3 whereas the model mean velocity was kept
constant.
Furthermore, the dynamic pressure ratio for the front injection
5-51
-------
.__..__._,--_._.~_.
- ~ 1.0
---,/-- ~
1.5
2.0
~
-
--- 1. 0
~
.5 .75 --
-----
.5
Nose
Shawnee Boiler - Test:
S602, East, 12-10-70
Nose
Shawnee Model - 2" Grid
Figure 5. 24.
mpi
Normalized mass flow rates, ~ =C, Plane A-A, Injection Levell
mp
5-52
-------
\
.5
Nose
Shawnee Boiler - Test:
5601, West, 12-4-70
.75
Nose
Shawnee Model - 2" Grid
Figure 5.25.
lTIpi
Normalized mass flow rates, ~= C, Plane A~A, Injection Level 2
~
5-53
-------
---
----
- .75
Nose
Shawnee Boiler - Test:
S602, East, 12-12-70
~....--....,
"
2.0
.5
+5.7
\ I
\. \ / I
" " / //
" --,/ /
- ,..
---
+5.8
\ /
\. /
",- ..."../
.......--- -----
Nose
Shawnee Model - 2" Grid
Figure 5.26.
'.
mpi
Normalized mass flow rates, ~= C, Plane A-A, Injection Level 3
Ihp
5-54
-------
was 50 percent greater than for the other two Shawnee injection levels.
Another possible factor are vari.ations in the nozzle to nozzle injection
velocity and mass flow rate.
The model experiments indicated that care
had to be taken to prevent clogging in the lines as well as in the manifold
which distributed the flow from the main feeder.
Since no information has
been made available on the operational characteristi.cs of the nozzle dis-
tribution system at Shawnee, this is only mentioned as a possible source of
differences.
In summary there were test variations in the flow character-
is tics in the relatively complex Shawnee system whereas the model condi-
tions were easily held constant from test to test.
As a result exact
modeling comparisons cannot be made.
Nevertheless, results seem to indi-
cate that the model does serve as an experimental approximation to the
solid-gas flow phenomenon in the Shawnee boiler.
5~55
-------
6.0
RECOMMENDATIONS FOR FUTURE WORK
It should be mentioned that the following recommendations are made in
light of the fact that EPA has indicated that no additional effort will be
placed into the dry limestone process.
As a result any suggestions for
study to improve the efficiency of the mixing process in the Shawnee boiler
may be somewhat academic.
Nevertheless, they will be presented in keeping
with the original intent of this dispersion study.
However, in additi.on,
recommendations of a more general nature which could broaden the techno-
logical base for understanding the dispersion of injected solids wi.ll be
presented.
6.1
Recommendations to Improve Technological Understanding of Injection
and Dispersi~n
The following recommendations are predicated on the assumptions that
the two-phase injection process is common to many engineering applications
I
i
and that it is not well understood.
In particular, the i.njection of a
solid-gas jet perpendicular to or at some angle to a cross stream of a
single phase fluid cannot be accurately described at the present ti.me.
The dry limestone process is one current example of a situati.on where lack
of injection and dispersion desi.gn i.nformati.on was a definite handicap
during an ongoing program.
In the future si.milar situations more than
likely will arise, some perhaps within the domain of O.A.P., where two-
phase injection and dispersi.on information will be needed.
Thus, it is
recommended that a parametric study of the injection phenomena be made
with a single nozzle in a straight duct.
Here an experimental program
could be designed with the dimensionless parameters obtained in this study.
Such a study would detail the relative importance of the various
6-1
-------
dimensionless groups to injection and dispersion.
By doing so one would
have both the individual as well as the composite effect of such variables
as turbulence, particle size, and injection velocity on the penetration
and distribution.
Table 2.2 outlines the dimensionless parameters that
would be considered in this recommended program.
A closely related topic to the basic dispersion study is the develop-
ment of an optical concentration probe where the reading is taken directly
in the flow situation (see Section 3.9).
The ability to read instantaneous
concentration values would provide a much firmer basis for evaluating the
distribution of powder in a duct.
The readings in this study were time
averaged over 20 seconds, those at Shawnee over five minutes so that the
possibility remains that pulsations of the order of a second or two could
easily go undetected but could have some significance in a meaningful def-
inition of dust distribution.
Thus, it is recommended that effort be given
to the further development of a probe similar to the one built for this
study or to developing a new one with the above stated capability.
6.2
Recommendations -- Related Directly to Shawnee System
1.
Acquire additional data with Shawnee Model where needed
a.
Study effects of turbulence at Plane A-A for Levels land 3
b.
Study effects of turbulence at Plane Y-Y
c.
Measure turbulence scale at Plane A-A with dual hot wire
system
2.
Consider techniques for improving dispersion in Shawnee Model
At present only straight nozzles, at three or four fixed
injection levels have been tried at Shawnee.
Also the dynami.c
pressure ratio was not changed appreciably.
A planned model
6-2
-------
program would be instituted to vary nozzle angle, vary nozzle
patterns and number, introduce several types of nozzle swirl and
also parameterize the dynamic pressure ratio as well as the other
pi groups.
Such information would indicate the trends of disper-
sion with each of the nozzle variables as well as with other
variables included in the dimensionless parameters.
This informa-
tion should indicate the optimum i.njection configurati.on for
dispersion and penetration.
3.
Conduct investigation to determine turbulence conditions in
Shawnee boiler -- incorporate into model
Perform detailed literature search of swirl flow and flame
turbulence in order to arrive at best estimate of turbulence
environment in the Shawnee boiler.
These conditions would then
be simulated with the Shawnee model.
Then a comparison with the
new dispersion data could be made with the present turbulent data
from the model.
6-3
-------
REFERENCES
1.
Soo, S. L., Trezek, G. J., Dimick, R. C., and Hohnstreither, G. F.
"Concentration and Mass Flow Distribution in a Gas-Solid Suspension,"
Ind. Eng. Chem. Fundamentals, V. 3, 1964, pp. 98-106.
2.
Ehmen, E. E. "An Improved Fiber Optic Probe for Low Particulate
Concentrations," M. S. Thesis, U. of Illinois, 1969.
3.
Patrick, M. A. "Experimental Investigation of the Mixing and Pen-
etration of a Round Turbulent Jet Injected Perpendicularly i.nto a
Transverse Stream," Trans. Instn. Chem. Engrs., Vol. 45, 1967, pp.
T16-T31.
4.
Dryden, H. L., Schubauer, G. B., Mock, W. C., and Skramstad, H. K.
"Measurements of Intensity and Scale of Wind-Tunnel Turbulence and
Their Relation to the Critical Reynolds Number of Spheres," NBS
Report No. 581, 1937, p. 109.
5.
Batchelor, G. K., and Townsend, A. A. "Decay of Isotropic
Turbulence in the Initial Period," Proc. Roy. Soc. London, Series
A, Vol. 193, 1948, p. 539.
6.
"Decay of Turbulence in the
Series A, Vol. 194, 1949,
Batchelor, G. K., and Townsend, A. A.
Final Period," Proc. Roy. Soc. London,
p. 5270
R-1
-------
APPENDIX A
LITERATURE REVIEW
A. I
Introduction
The present problem requires an understanding of two interdependent
phenomena; that is, the injection and the dispersion of a two-phase jet.
The first portion is the study of the trajectory of the solid-gas jet
injected into a transverse stream.
The second part of the problem is the
dispersion of the solid phase following this injection.
The literature
review, started early in this study, covered both of these areas.
To
date, no reports of similar work have been found in the literature with
the exception of a preliminary study at Babcock and Wilcox, Pfeifer (1),
on limestone injection.
For that study, a scale model was built and
tested but an orderly scaling procedure was not utilized in desi.gning the
mode I .
Because there have been no directly comparable studies, it has
been necessary to review the literature of related subjects.
These stud-
ies include analyses of jet injections for a vari.ety of configurations.
In addition to studies of injection phenomena, the area of stati.stical
turbulence as related to the dispersion of particles has also been
searched.
Hence, the results of the literature search have been catego-
rized into the subjects of jet injections and particle transport i.n
turbulent flow.
A.2
Jet Injection Studies
The variety of injection studies researched have included a range
from those concerned with the deflection of liquid jets injected normal
A-I
-------
to a gas stream to those involving the spreading of a free solid-gas jet.
Of these, some have considered the effects of shear induced turbulence at
the boundary of the jet with respect to mass and momentum transfer.
How-
ever, none of the work reviewed have considered either of the two
following situations:
1)
Solid-gas jet injected into transverse gas stream
2)
Effect of ambient turbulent conditions on dispersion of a jet.
For convenience, the jet injection review will be divided into the fo1-
lowing subject a~eas, each of which is related to some facet of the
present study.
1.
Injection of a gas jet into a transverse gas stream.
2.
Injection of a liquid jet into a transverse stream.
3.
Free and coflowing jets (single and two-phase).
4.
Stack emission.
Appendix B is a bibliography which is divided in a similar manner so that
there is a bibliography associated with each topic.
A.2.1
Injection of a Gas Jet Into a Transverse Gas Stream
The topic of jet penetration into a transverse flow has been given a
reasonable amount of attention in the literature.
Results are usually
correlated to the densities and velocities of the jet and transverse flow.
This is generally accomplished by forming dimensionless groups and cor-
relating the experimental data (location of the jet centerline) to these
groups.
The form for these dimensionless groups varies from worker to
worker but essentially the injection penetration is expressed in terms of
one of the three functional relations listed below
A-2
-------
{ (' ( Xl ~. 0 ~)
d = "t d ) t ) f'.w~'} U 0
(A-I)
2-
~=t(f)~~o~)
(A-2)
~I ~(~ f' ~.'1.)
-- - rJ.~
d- d)~
(A-3 )
Keffer and Baines (2) argue that the jet Reynolds number does not have
an appreciable effect in the jet problem and consequently neglect it.
The
second equation, like the first, is often used to correlate the data and
appears to have the advantage of being easier to correlate since the den-
sities and velocities are combined into a single grouping.
Patrick (3)
used the second approach and demonstrated that the constants and powers in
a correlation equation containing these groups are only valid over partic-
ular ranges of dynamic pressure ratio, SjVl/ SoU02.
few of the empirically derived correlation equations as reported in the
Table 2.1 lists a
literature.
All neglect jet Reynolds number.
Some are correlations along
the lines of equation (1), the others equation (2).
References (4-8) fall
into the group most closely associated with equation (1) and references
(3, 9) with equation (2).
Keffer and Baines demonstrate a more reduced
form for their jet centerline data, equation (3), which closely parallels
the form of equation (2).
Here the dimensionless penetration is related
to the dynamic pressure ratio and distance along the jet centerline rather
than along the duct.
A semianalytical approach for gas jets has also been performed by
several authors including Abramovich (9), Wooler (10), and Braun and
Goldstein (11).
In all three, some aspect of the analysis requires
experimental information.
Abramovich's approach requires the value of a
drag coefficient for the crosswind flow normal to the jet.
Nevertheless,
A-3
-------
>
I
.po
AUTHOR(S) PENETRATION EQUATION
Callaghan and y ,31 (£.)57 (Yi}'ff (X) .lb C = dimensionless coefficient
Ruggeri (4) ci=C -rt =\1 d Author notes that powers vary
with changes in d
~ ~ K, ( ~J'(itl X)' d !i-I Note: The units of
Weiland and this equation do not
check.
Trass (5) Blowing air into duct Sucking air through duct
0( = \ S '6' =: . 2.!) 0(-= .U1 ~ = .2'2..
~: .6b b"= .10 ~-=.11 ~ -= .56
Patrick (3) ~:( £i Vi)''f2S(:&)t"\ .33~ n ~ .3<6
Po Vo d
Shandorov * Y' ={PJ Vj7.. )0392 (A')'3~1.
d 9~ -q:- d
* ~=(~r"'(f)333
Ivanov cJ ~ Uo
Norgren and ~ "- .~1(~)'IJ(~J5"~')'~2
Humenik (8)
*Referenced in Abromovich (9)
Table A.I.
Various Correlation Relations for Jet Trajectory Data
-------
Abramovich found that his solution compared favorably with the experimen-
tal results of Shandorov and Ivanov (see Abramovich).
Woo1er and Braun
and Goldstein also required trajectory information in order to complete
their analyses.
As with the other experimental results, these studies
were based on a gas phase jet and crosswind.
Consequently, results may
not apply to a solid-gas jet.
To summarize, the relationships described above correspond to gas jets
injected into gas crossf10ws where JPj is the homogeneous jet density.
Hence, the use of any of these equations to predict the trajectory of a
solid-gas jet would be questionable until it was ascertained whether or
not the jet behaved like a homogeneous fluid.
If this were the case, then
the mixture density of the solid-gas flow at the nozzle would be treated
as the representative density, j>j, of the jet.
A.2.2
Injection of a Liquid Jet Into a Transverse Gas Stream
Only the most general aspects of this phenomena appear to be applica-
b1e to the solid-gas jet.
The liquid jet is by nature a single phase jet
rather than a two-phase one.
Breakup into a two-phase jet occurs at some
distance (determined by the flow conditions and physical properties) away
from the nozzle.
As a result, forces on the jet prior to breakup are
entirely different from that for a solid-gas jet.
Here, dimensionless num-
bers such as the Weber number and Bond number corne into play since surface
tension forces must be considered in a liquid jet.
Liquid jet studies
range from free jets to jets issuing into crosswinds.
Most studies have
been primarily concerned with the degree of liquid breakup although a few
have studied the jet trajectory.
Povine11i (12) did develop a correlation
equation for the jet trajectory utilizing the concept of the dynamic
A-5
-------
pressure ratio.
However, he replaced the crosswind velocity and distance
downstream with the time that the liquid was exposed to the crosswind.
This, however, makes the equations difficult to use since time is not as
convenient an independent variable as is distance downstream.
Clark (13)
considers the breakup of a liquid jet but not its penetration distance.
However, he also uses the dynamic .pressure ratio to correlate data where
the relative velocity of the gas with respect to the liquid replaces the
normally used crosswind velocity.
Other references examined (14, 15)
yielded little information with respect to the correlation of trajectory
curves.
A.2.3
Free and Coflowing Jets (Single and Two-Phase)
The geometry of these problems makes these the simplest of the two-
phase injection problems and although there are no exact solutions, phe-
nomenological mass and momentum transfer relations give quite satisfactory
results.
Trajectory information cannot be obtained from studies in this
category, but the dispersion of particles may have many similarities
between these types of injected flows and transversely injected flows.
Hence. it may be possible to compare results from the crosswind-jet prob-
lem with the coaxial jet at some distance downstream from the injection
poi.nt.
One study which appears to closely resemble that of the proposed one
was made by Goldschmidt and Eskinazi (16).
They used a plane jet with a
li.quid aerosol and measured the turbulent Schmidt eddy diffusivity across
the plume.
Here the turbulence was generated at the jet-free stream
interface.
However, the turbulent scale and intensity of the free stream
were not considered nor were the drop size and density parameterized.
A-6
-------
Csanady (17) investigating the dispersal of effluents in lakes did touch
upon the influence of lake turbulence on the effective eddy diffusivity.
Indications were that the diffusivity increased as the intensity increased.
Although the effect of turbulence scale was discussed, no measurements were
made.
Other two-phase jet studies have considered fringe problems which are
inherent in two-phase injections.
In studies by Soo (18) and Lee and Soo
(19) the effects of particulate electrostatic charge was treated.
In these
papers the charge was induced on the particles to control distribution and
collection of the dust.
Doughman and Lewis (20) found that the particle
plume boundary moved further from the plume axis as the smallest particles
in a given distribution were decreased in size.
Laats (21) investigated
the effect of particle loading on free jet dynamics and found the effect
of the solid phase on the transverse mass process.
Kusui (22) found that
the performance of a water jets was dependent upon the surface roughness
of the nozzle's inner wall.
These studies are mentioned basically to
point out that although many of these fine points were not considered in
the present study, such studies may be required at some future date in
order to interpret results or improve the design of the present injection
equipment.
A.2.4
Stack Emission
Considerable work has been done in this area over a period of more
than forty years.
This work has included both simple analytic studies and
many experimental investigations.
Major emphasis has been placed on obtain-
ing equations to predict plume trajectory and particulate deposition from
the plume.
In a paper by Bryant and Cowdrey (23), model plume trajectories
A-7
-------
were studied resulting in curves of trajectory showing the effects of var-
ious temperature differences between the plume and ambient, Figure 2.1.
The interest here is limited to those portions of the curves where the
trajectory is indistinguishable from the curve with no temperature dif-
ference.
This is the portion of the curves where inertial effects pre-
dominate and gravity (thermal buoyancy) effects have not yet become
signifi.cant.
If considerations are included for the natural turbulence associated
with wind, then this class of problem and the present study have a great
deal in common.
Bosanquet (24) noticed that large scale eddies (size of
plume diameter or larger) contribute to plume meandering but only the
smaller eddies contribute to turbulent dispersion.
Qualitatively, this
would seem reasonable, unfortunately, no papers have been found in this
group which have tried to correlate measured turbulence parameters
(intensity and scale) to plume trajectory and dispersion data.
A.3
Transport of Particles in Turbulent Flow Field
Another subject area of direct interest to this experimental program
1.8 the dispersion of a solid phase as a result of turbulent motions of t.he
carrier fluid.
In particular, the dispersion of the jet plume downstream
of the injection point should be similar to that associated with a single
particle in a turbulent stream.
The literature contains studies of the
transport of particles in a turbulent flow field as well as equations of
motion utilizing the continuum concept of a gas phase and a particle cloud.
Appendix B contains a bibliography associated with this area of the
literature review.
A-8
-------
>
I
\0
"C
......
-
>.
~
o
'.-1
.j.J'
cu
~
.j.J
Q)
~
Q)
P-I
16
12
8
4
t10 == 4.0
I
I
o
o
4
8
Downstream Position x'/d
2000
1500
1000.
500
00
12
16
"C
......
-
>.
s::
o
..-1
.j.J
cu
~
.j.J
Q)
s::
Q)
P-I
16
12
Vj -
Vo-
2000
1500
1000
~o -
#-
,. :;.....----
/
1.0
8
4
o
16
o
4
12
8
Downstream Position x'/d
Exit Temperature in CO Above Ambient
Figure A.1.
Effects of Plume Temperature on Trajectory for Two Velocity Ratios
-------
One aspect of particular interest is the result obtained by analyzing
the equation for an accelerating particle in an accelerating fluid (some-
times referred to as the Oseen, Basset, Boussinesq equation).
By nondimen-
siona1izing this equation and sizing the various terms (Appendix C) a
dimensionless group is obtained which relates the particle dynamics to
those of the fluid (the forcing function)
1fD =[~,J [~][kJ
(4.)
This is a term which appears in papers by Ahmadi (25), Soo (26), and
Householder and Goldschmidt (27) and has been used to correlate turbulent
dispersion data.
Another aspect of two-phase turbulent motion are the studies in two-
phase statistical turbulence.
This is essentially an extension of the
theories developed by Taylor, Von Karman, Kolmogoroff, etc. (a collection
of these papers is contained in reference
(28».
The addition of solid
particles does require additional rigor in order to account for the i.nter-
action between the solid phase and the carrier fluid.
Since Tchen's (29)
pap~r on this subject in 1947, a good deal of work has been done both of
an analytical and experimental nature.
Of the many papers available on
thi.s subject, those by Friedlander (30), Liu (31), and 800, Ihrig, and E1
Kouh (32) are of particular interest.
The first two papers present rela-
tionships for the statistical behavior of the solid phase, in particular,
statistical relationships for turbulent slip velocity and dispersion of
the solid phase.
It is worth noting that though their respective
. \.''-.'
approaches to the problem are different, the resulting equations for
A-lO
-------
turbulent dispersion of the particles are e~sentially the same.
In the
final paper referred to, the authors experimentally determined the effects
of solid particles on the stream turbulence characteristics.
They also
obtained some information on the turbulent behavior of the particle phase
as a result of the stream turbulence where the correlation term used was
thelnr D term noted above.
A-ll
-------
A.4
References
1.
Pfeifer, W. A. "Jet Penetration and Distribution Studies - Lime-
stone Injection Model," Babcock and Wilcox Research and Development
Divi.sion Report, Ref. LR-69-6071-0l-l, 1969.
2.
Keffer, J. F., and Baines, W. D. "The Round Turbulent Jet in a
Crosswind," J. Fluid Mech., 1963, V. 8, p. 481.
3.
Patrick, M. A. "Experimental Investigation of the Mixing and Pe;r:.-
etration of a Round Turbulent Jet Injected Perpendicularly into a
Transverse Stream," Trans. Instn. Chern. Engrs., Vol. 45, 1967, ppo
T16-T3l.
4.
Callaghan, Eo, and Ruggeri, R. S. "A General Correlation of Tem-
perature Profiles Downstream of a Heated-Air Jet Directed Perpen-
dicularly to an Air Stream," NACA Tech. Note 2466.
5.
Weiland, R. H., and Trass, O. "Jet Penetration in Turbulent
Streams," Canadian J. of Chern. Engr., V. 47, A~gust 1969, Technical
Note, pp. 443-444.
6.
Pratte, B. D., and Baines, W. D. "Profiles of the Round Turbulent
Jet in a Cross Flow," Journal of the Hydrualics Divisi.on, V. 92,
1967, p. 53.
7.
Carlson, C. W., Hsu, J. J., and Meyers, C. A. "The Penetration and
Mixing of Air Jets Directed Perpendicular to a Stream," ASME Paper
68-WA/GT-6.
8.
Norgren, C. T., and Humenik, F. M. "Dilution-Jet Mixing Study for
Gas-Turbine Combustors," NASA TN D-4695.
9.
Abromovich, G. N.
The Theory of Turbulent Jets, MIT Press, 1963.
10.
Wooler, P. T. "Flow of a Circular Jet into a Cross Flow," J. of
Aircraft, V. 6, N. 3, 1969, pp. 283-284.
11.
Braun, W., and Goldstein, M. E. "Analysis of the Mixing Region for
a Two Dimensional Jet Injected at an Angle to a Moving Stream,"
NASA TN D-5531, 1969.
12.
Povine11i, F. P. "Displacement of Disintegrating Liquid Jets in
Cross flow," NASA TN D-4334.
13.
Clark, B. J. "Breakup of a Liquid Jet in a Transverse Flow of
Gas," NASA TN D-2424.
14.
Adelberg, M. "Breakup Rate and Penetration of a Liquid Jet in a
Gas Stream," AIM J., V. 5, N. 8, August 1967, pp. 1408-1415.
15.
Catton, 1., Hill, D. E., and McRae, R. P. "Study of Liquid Jet
Penetration in a Hypersonic Stream," AIM Journal, V. 6, 1968, po
2084.
A-12
-------
16.
Goldschmidt, V., and Eskinazi, S. "Two Phase Turbulent Flow in a
Plane Jet," J. Applied Mech., December 1966, pp. 735-747.
17.
Csanady, G. T. "Dispersal of Effluents in the Great Lakes," Water
Research, V. 4, 1970, p. 79-114.
18.
Soo, S. L. "E1ectrohydrodynamic Jets," Proceedings of the 11th
Midwestern Mechanics Conference, 1969.
19.
Lee, Y. N., and Soo, S. L. "Effects of Electrostatic Charges on
Dust Particles in a Jet," Presented at Air Pollution Control
Association Meeting, 1970.
20.
Doughman, E., and Lewis, C. H. "Radial Lag of Solid Particles in
De1aval Nozzles," AIAA Journal, V. 3, 1965, p. 169.
21.
Laats, M. K. "Experimental Study of the Dynamics of an Air-Dust
Jet," Inzhenerno-Fizicheskii Zhurna1, V. 10, N. 1, 1966, pp. 11-15.
22.
Kusui, T. "Liquid Jet Flow Into Still Gas," Bulletin of JSME, V.
12, 1969, p. 1062.
23.
Bryant, L. W., and Cowdrey, C. F. "Effects of Velocity and Tem-
perature of Discharge on the Shape of Smoke Plumes From a Chimney;
Experiments and Wind Tunnel," Instn. of Mech. Engr., Proceedings,
Vol. 169, 1955, pp. 371-399.
24.
Bosanquet, C. H. "The Rise of a Hot Waste Gas Plume," J. Inst. of
Fuel, V. 30, No. 197, 1957, p. 322.
25.
Ahmadi, G. "Analytical Predictions of Turbulent Dispersion of
Finite Size Particles," Ph.D. Thesis, 1970, Purdue.
26.
Soo, S. L. "Statistical Properties of Momentum Transfer in a Two-
Phase Flow," J. of Chern. Engr. Science, V. 5, 1956, pp.57-67.
27.
Householder, M. K., and Goldschmidt, V. W. "Turbulent Diffusion
and Schmidt Number of Particles," J. of Engr. Mech. Div., Vol. 95,
December 1969, pp. 1345-1367.
28.
Friedlander, S. K., and Topper, L. (Editors). Turbulence, Classic
Papers on Statistical Theory, Interscience Publishers, 1961,
29.
Tchen, C. M. "Mean Value and Correlation Problems Connected with
the Motion of Small Particles Suspended in a Turbulent Fluid," The
Hague, M. Nishoff, 1947.
30.
Friedlander, S. K. "Behavior of Suspended Particles in a Turbulent
Fluid," A.I.Ch.E.J., V. 3, September 1957, pp. 381-385.
31.
Liu, V. C. "Turbulent Dispersion of Dynamic Particles," Journal of
Meteorology, V. 13, August 1956, pp. 399-405.
32.
Soo, S. L., Ihrig, H. K., and El Kouh, A. F. "Experimental Deter-
mination of Statistical Properties of Two-Phase Turbulent Motions,"
J. of Basic Engr., September 1960, pp. 609-621.
A-13
-------
APPENDIX B - BIBLIOGRAPHY
1.
Injection of a Gas Jet into a Transverse Stream
Abromovich, G. N.
The Theory of Turbulent Jets, MIT Press, 1963.
Analysis of a Jet in a Subsonic Crosswind NASA Sp-2l8, Proceedings
of a Symposium at Langley Research Center, September 9 and 10, 1969.
Callaghan, E., and Ruggeri, R. S. "A General Correlation of Tem-
perature Profiles Downstream of a Heated-Air Jet Directed Perpen-
dicularly to an Air Stream," NACA Tech. Note 2466.
Carlson, C. W., Hsu, J. J., and Meyers, C. A. "The Penetration and
Mixing of Air Jets Directed Perpendicular to a Stream," ASME Paper
68-WA/GT-6.
Keffer, J. F., and Baines, W. D. "The Round Turbulent Jet in a
Crosswind," J. Fluid Mech., 1963, V. 8, p. 481.
Krzywoblocki, M. Z. "Jets-Review of Literature," Jet Propulsion,
Sept. 1956, pp. 760-779.
Patri.ck, M. A. "Experimental Investigation of the Mixing and Pen-
etration of a Round Turbulent Jet Injected Perpendicularly into a
Transverse Stream," Trans. Instn. Chem. Engrs., Vol. 45, 1967, pp.
T-16-T31.
Platten, J. L., and Keffer, J. F.
ASME Paper 71-APM-SS.
"Deflected Turbulent Jet Flows,"
P'ratte, B. D., and Baines, W. D. "Profiles of the Round Turbulent
Jet in a Cross Flow," Journal of the Hydraulics Division, V. 92,
1967, p. 53.
Weiland, R. H., and Trass, o. "Jet Penetration in Turbulent
Streams," Canadian J. of Chem. Engr., V. 47, August 1969, Technical
Note, pp. 443-444.
Woo1er, P. T. "Flow of a Circular Jet into a Cross Flow," J. of
Aircraft, V. 6, N. 3, 1969, pp. 283-284.
2.
Injection of a Liquid Jet into a Transverse Gas Stream
Adelberg, M. "Breakup Rate and Penetration of a Liquid Jet in a
Gas Stream," AIAA J., V. 5, N. 8, August 1967, pp. 1408-1415.
Catton, 1., Hill, D. E., and McRae, R. P. "Study of Liquid Jet
Penetration in a Hypersonic Stream," AIAA Journal, V. 6, 1968, p.
2084.
B-1
-------
Clark, B. J. "Breakup of a Liquid Jet in a Transverse Flow of Gas,"
NASA TN D-2424.
Norgren, C. T., and Humenik, F. M. "Dilution-Jet Mixing Study for
Gas-Turbine Combustors," NASA TN D-4695.
Povinelli, F. P. "Displacement of Disintegrating Liquid Jets in
Crossflow," NASA TN D-4334.
3.
Free and Coflowing Jet (Single and Two-Phase)
Abromovich, G. N.
(Already cited).
Braun, W., and Goldstein, M. E. "Analysis of the Mixing Region for a
Two Dimensional Jet Injected at an Angle to a Moving Stream," NASA TN
D-553l, 1969.
Forstall, W., Jr., and Shapiro, A. H. "Momentum and Mass Transfer in
Coaxial Gas Jets," J. Applied Mech., 1950, V. 72, p. 339.
Goldschmidt, V., and Eskinazi, S. "Two-Phase Turbulent Flow in a Plane
Jet," J. Applied Mech., December 1966, pp. 735-747.
",'
Kusui, T. "Liquid Jet Flow Into Still Gas," Bulletin of JSME, V. U,
1969, p. 1062.
Latts, M. K. "Experimental Study of the Dynamics of an Air-Dust Jet,"
Inzhenerno-Fizicheskii Zhurnal, V. 10, N. 1, 1966, pp. 11-15.
Lee, Y. N., and Soo, S. L. "Effects of Electrostatic Charges on Dust
Particles in a Jet," Presented at Air Pollution Control Association
Meeting, 1970.
Maczyski, J. F. "A Round Jet in an Ambient Coaxial Stream," J. of
Fluid Mech., V. 13, 1962, pp. 597-608.
Mikhail, S. "Mixing of Coaxial Streams in a Closed Conduit," J. of
Mech. Engr. Sci., V. 2, N. 1, p. 59.
Pai, S. 1.
Fluid Dynamics of Jets, Van Nostrand Co. Inc., 1954..
Pai, S. 1. "Unsteady Three-Dimensional Laminar Jet Mixing of a Com-
pressible Fluid," AIAA J., V. 3, N. 4, Apri1l965.
Schetz, J. A.
1382.
"Unified Analysis of Turbulent Jet Mixing," NASA CR-
Singer, H. A. "Jet Mixing of a Two-Phase Stream with a Surrounding
Fluid Stream," Ph.D. Thesis, U.S.C., 1970.
B-2
-------
Sco~ S. L. "E1ectrohydrodynamic Jets," Proceedings of the 11th
Midwestern Mechanics Conf., 1969.
4.
Sta~k Emissi.on
Bosanquet, C. H. "The Rise of a Hot Waste Gas Plume," J. lnst. of
Fuel, V. 30, No. 197, 1957, p. 322.
Bosanquet, C. H., Carey ~ W. V., and Halton, E. M. "Dust Deposition
From Chimney Stacks," 1. Mech. Engr., 1950 ~ p. 355.
I:sryari t, L. W., and Cowdrey, C. F. "Effects of Ve loci ty and Tem-
perature of Discharge on the Shape of Smoke Plumes From a Funnel
or Chimney; Experiments in a Wind Tunnel," Instn. of Mech. Engr.~
Pro~eedings, Vol. 169, 1955, pp. 371-399.
Minutes of the Symposium on Plume Behavior~ Air and Water Pol1ut.
Int. J., 1966, Vol. 10~ p. 393.
Moore, D. J. "Physical Aspects of Plume Models," Air and Water
Po1lut. Int. J., 1960, Vol. 10~ p. 411.
Pasquill, F.
Atmospheric Diffusion, Van Nostrand, 1962.
Priestley, C. H. B. "A Working Theory of the Bent Over Plume of
Hot Gas," Q. J. R. Met. Soc., V. 82, p. 165.
Scorer, R. S. "The Behavior of Chimney Plumes," Int. J. Air Poll.,
1959, V. 1, p. 198.
Soo, S. L. "Effect of Simultaneous Diffusion and Fallout from
Plumes of Stack and Jet Engines," Presented at Air Pollution
Control Association Meeting, 1970.
Suttcm, o. G. "The Dispersion of Hot Gases in the Atmosphere,"
J. of Meteorology, V. 7, N. 5, 10/50, p. 307.
5.
Two-Phase Turbulent Motion
Ahmadi., G. "Analytical Predictions of Turbulent Dispersion of
Finite Size Particles, Ph.D. Thesis, 1970, Purdue.
Baw, P. S. H., and Peskin, R. L. "Some Aspects of Gas-Solid
Suspension Turbulence," ASME Paper No. 71-FE-15.
Boothroyd, R. G. "Turbulence Characteristics of Gaseous Phase in
a Duct Flow of a Suspension of Fine Particles," Trans. Inst. Chern.
Engr., V. 45, 1967, pp. T297-T310.
B-3
-------
Brodkey, R. S.
1967.
The Phenomena of Fluid Motions, Addison Wesley,
Friedlander, S. K. "Behavior of Suspended Particles in a Turbulent
Fluid," A.I.Ch.E.J., V. 3, September 1957, pp. 381-385.
Hit'lze, J. O. "Momentum and Mechanical En~rgy Balance Equation for
a Flowing Homogeneous Suspension with Slip Between the Two Phases,"
Appli.ed Science Res., V. 11, pp. 33-46.
Hinze, J. O.
Turbulence, McGraw-Hill, 1959.
Hjelmfelt, A. T., and Mockros, L. F. "Motion of Discrete Partid.E\i:!
in a Turbulent Fluid," Applied Science Res., V. 16, p. 149.
Householder, M. K., and Goldschmidt, V. W. "Turbulent Diffusion
and Schmidt Number of Particles," J. of Engr. Mech. Div., Vol. 95,
December 1969, pp. 1345-1366.
Liu, V. C. "Turbulent Dispersion of Dynamic Particles," Journal
of Meteorology, V. 13, August 1956, pp. 399-405.
Peskin, R. L. "Statistical Effects Resulting from the Presence
of Many Particles in Motion in an Ideal Fluid," Heat Trans. & Fl.
Mech. Inst., 1960.
Shirazi, A. A. "On the Motion of Small Particles in a Turbulent
Fluid Field," Ph.D. Thesis, Univ. of Illinois, 1967.
Soo, S. L.
1967.
Fluid Dynamics of Multiphase Systems, Ginn Blai.sdell,
Soo, S. L. "Fully Developed Turbulent Pipe Flow of a Gas-Solid
Suspension," I & EC Fundamentals, Vol. 1, 1962, p. 33.
800, S. L. "Statistical Properties of Momentum Transfer i.n a Two-
Phase Flow," J. of Chern. Engr. Science, V. 5, 1956.
Soo, S. 1., Ihrig, H. K., and.El Kouh, A. F. "Experi.mental Deter-
mi..nation of Statistical Properties of Two-Phase Turbulent Mot:i.ons~"
J. of Basi~ Engr., September 1960, pp. 609-621.
Stukel, J. J., and Soo, S. L. "Turbulent Flow of a Suspension into
a Channel," Power Technology, Vol. 2, No.5, June 1969, pp. 278-
289.
Tchen, C. M. "Mean Value and Correlation Problems Connected with
the Motion of Small Particles Suspended in a Turbulent Fluid," The
Hague, M. Nishoff, 1947.
Wallace, J. P. "A Study of the Fluid Turbulence Energy Spectrum in
a Gas Solid Suspension," Ph.D. Thesis, Rutgers, 1966.
B-4
-------
6.
Flame Studies
Chigier, N. A. "Pressure, Velocity, and Turbulence Measurements in
Flames~" Presented at the ASME Fluids Engr. Div. Conf., Pgh., Pa.,
May 1971.
Gunther, R., and Simon, H.
12th Symp. on Comb., 1969, p. 1069.
Gross, R. A.
19.56, p. 716.
"Flame Generated Turbulence," Jet Propulsion, V. 26,
Putnam, A. A. "Swirl Burning," Presented to American Flame Research
Committee, Jan. 1967.
Karlovitz, B., Denniston, D. W., and Wells, F. E. ":j:nvestigation of
Turbulent Flames," The Journal of Chemical Physics, V. 19, 1951, p.
541-547.
7.
Additional Bibliography
Batchelor, G. K., and Townsend, A. A. "Decay of Isotropic Turbu-
lence in the Initial Period," Proc. Roy. Soc. London, Series A,
Vol. 193, 1948, p. 539.
Bat~helor, G. K., and Townsend, A. A. "Decay of Turbulence in the
Final Period," Proc. Roy. Soc. London, Series A, Vol. 194, 1949,
p. 527.
Boothroyd, R. G. "Similarity i.n Gas-Borne Flowing Particle Sus-
p~::!RioJ:!s," Journal of Engineering for Industry, No. 68-MH-ll, May
1963, pp. 303-313.
Cheng, L., and Soo, S. L.
J. Applied Physics, V. 41, N. 2, 1970.
C8a~~ady, G. T. "Dispersal of Effluents in the Great Lakes," Wate!."
Research, V. 4, Pergamon Press, 1970, pp. 79-114.
Doughman, E., and Lewis, C. H. "Radial Lag of Solid Particles in
Delaval Nozzles," AIM Journal, V. 3, 1965, p. 169.
Dryden, H. L., Schubauer, G. B., Mock, W. C., and Skramstad, H. K.
"Measurements of Intensity and Scale of Wind-Tunnel Turbulence and
Their Re la tion to .the Cri tical Reynolds Number of Spheres," NBS
Report No. 581, 1937, p. 109.
B-5
-------
[-
Friedlander, S. K., and Topper, L. (Editors). Turbulence, Classic
Papers on Statistical Theory, Intersicence Publishers,.. .1961.
Hinze, J. O.
Turbulence, McGraw-Hill Publishing Company, 19590
K1ein~ S. J.
Similitude and Approximation Theory, McGraw-Hill, 1965.
01dshue, J. Yo "Mixing," Indust. Engr. Chem., V. 60, N. 11, November
1968, pp. 24-35.
Peskin, R. L. "Some Effects of Particle-Particle and Particle-Fluid
Interaction in a Two-Phase Flow System," Ph.D. Thesis, Princeton Univ.,
1959.
Pfeifer, W. A. "Jet Penetration and Dispersion Study," Babcock &
W1.1cox Co., Research Center, Alliance, Ohio, October 1968.
Rose, H. E., and Barnacle, H. E. "Flow of Suspensions of Non-Cohesive
Spherical Particles in Pipes - No. I," The Engineer, Vol. 203, June 14,
1957, pp. 898-901.
Rose, H. Eo, and Barnacle, H. E "Flow of Suspensions of Non-Cohesive
Spherical Particles in Pipes - No. II," The Engineer, Vol. 203, June
21, 1957, pp. 939-9410
Rudinger, G. "Addition of Heated Solid Particles to a Gas Flowing in
a Pipe," A8ME Paper No. 71-FE-22.
800, S. L., Trejek, G. J., Dimick, R. C., and Hohnstrither, G. F.
"Concentration and Mass Flow Distribution in a Gas Solid SuspensioIl.~"
Ind. Engr. Chem. Qtr1y., V. 3, 1964.
Soo~ S. 1., and Tung, S. K. "Gravity Effect in Pipe Flow Suspension~,"
Presented at the Symposium on Flow, Pittsburgh, May 1971.
Thring, M. W.
The Science of Flames and Furnaces, Wiley & Sons~ 1962.
Vogt, E. G., and White, R. R. "Friction in the Flow of Suspensions,"
Industrial and Engineering Chemistry, Vol. 40, No.9, September 1948,
pp. 1731-1738.
B-6
-------
APPENJ;>IX C
C.O
FRACTIONAL ANALYSIS
C.l
Introduction
The solid-gas jet penetration and dispersion phenomenon is quite com-
plex and a relatively new area of study, thus, it was felt that the most
reasonable approach was to combine a theoretical and an experimental pro-
gram.
The first step was to develop a partial or fractional analysis of
the governing equations for a solid-gas suspension.
This analysis includes
thp. nondimensionalization of the conservation of mass and momentum equa~
tioes which yield a set of dimensionless parameters which characterize the
phys:i.cal phenomena.
These parameters are then used to provide the ration-
ale for an experimental program.
The jet experiments and modeling of the
Shawnee boiler were based on a set of dimensionless parameters obtained in
this manner.
The term fractional analysis encompasses three basic techniques, which
arA 1) dimensional analysis, 2) similitude, and 3) nondimensionalization of
the governi.ng equa ti.ont3.
All three have been employed at one time or
amJ1thet.' in soUd-gas suspension studies.
Although no such study reported
in the literature was found to be directly applicable to this investiga-
ti.02, there was some overlap.
Most of the studies surveyed fell into
ei.ther a dimension.al analysis category or one where the governing
equations were nondimensionalized.
C.2
Previous Work
The following discussion covers some solid-gas flow studies where a
C-I
-------
dependent variable such as pressure drop or eddy diffusivity are corre-
lated to a set of dimensionless groups.
Table C.l summarizes the results
of a selected group of investigations.
As can be seen, these studies
were primarily concerned with frictional losses in flows through tubes and
ducts.
Although none included jet injection, it is felt that at some
point downstream of the injection point, the flow characteristics wi.ll not
differ appreciably from the solid-gas suspension studies listed in Table
C.l.
This table indicates that although the important variables are com-
mon to all of the studies, there are some differences in the resulting
sets of dimensionless parameters.
Thus, one given study may consider the
Reynolds number as an independent dimensionless parameter whereas another
indicates that Reynolds number by itself does not adequately correlate
the data.
This discussion is not intended to explain the individual dif-
ferences in frictional loss studies of two-phase suspensions, but to point
out these differences in order to illustrate the general form of the
results which have been obtained with fractional analysis.
It is interesting to note that only Soo (1) and Soo, et ale (2)
include both the scale and intensity of turbulence as characteristic
values in the analyses.
However, in some flows these turbulence values
are dependent upon the geometry and mean velocity and therefore do not
appear as independent variables.
Stuckel and Soo (3) as well as Boothroyd
(4) include a dimensionless group which is related to the electrostatic
charge of the particulate phase.
The importance of this term will vary
with experimental conditions and is generally neglected as a first order
approximation.
In summary, Table C.l lists the various dimensionless parameters
C-2
-------
("')
I
W
. -
References Dimensionless Parameters Comments
p f"'(2ss. - reD ~ )M~Q-)\J~)
Vogt, E. G., and Dr~ - Q..,) f
White, R. R. (5) =- f (~) ~ )1\~/11,)~03) Pipe Flow
Soo, S. L. (1) ~p -= F (~~O).k >i)
Ct. 0.. \ ~) Stream Flow
Momentum - F (n\ 1T2.D )P1\3 ) ~
-
. Transfer
~ - (Q."l.)T' ~ ')
Soo, S. L., Ihrig, H. Dp - F ",u-::7C
K., and E1 Kouh, A. ::. F ( 17; n;z. ) Pipe Flow
F. (2)
ni 77S
........ . W1. ~ et+
Stucke1, J. J. and Dp - EP pt
- F ( Uo ) VV\ EcDP- )
Soo, S. L. (3) ~c::O Inlet of Channel
- f ( .TI£ ~CLY' ~~o.~ ')
- 1T.) Mt: E:.o ~'&.
Boothroyd, R. G. (4) ~-~ - ( U~ P W\ 'Y2..~ t 1M 6... ~;a:-
- ~ - S;o - f --v-) ~ ) "if ~R(l ) a ~~
r "- ) Pipe Flow
~ L ().....,~
=- f ( rr.- ) TIo )#f )~p) (Eo 02-)
Boothroyd, R. G. (6) ~ - (~ ~ l 'a ) YY\ ~ )
(7, 8) ~ F (1To ) ~ ) 'IT£- ) 110 Pi?e Flow
q
-
Table C.l.
D:LmensionltP.88 Param~te1"s Obtai:':led in Solid=Gas
Suspensio~ Studies
-------
obtained by a number of different analyses.
All were concerned with
solid-gas suspensions and none include jet injection.
Nevertheless, it is
to be expected that similar parameters would be found in the solid-gas jet
injection study in addition to those parameters which specifically
characterize the jet.
C.3
Fractional Analysis of Solid-Gas Jet Inj~ction
Several goals of this study dictated the need for a fractional anal-
ysis of a solid-gas jet.
As sta.ted" el1tlier>the complex.it¥:. 0 fl.'. this 'p:t'ob lem
in addition to a lack of prior work strongly suggested an experimental pro-
gram to provide insight into the basic fluid mechanics of the solid-gas
jet interaction.
Furthermore, by merely listing the variables which could
influence both the jet penetration and the concentration of particulate
downstream from the injection point, it appears that a "brute force" exper-
imental approach. of systematically changing these variables would be dif-
ficult .
The dependent variables, e.g., penetration or concentration of
the solid phase, labeled 0 for simplicity will be influenced by the
following i.ndependent variables.
cp = c? (~ So> ~~~. J fp ) Uo) \/J. ) \J' ) LJ D)d) Ow) -A-)jA )
C-l
In order to reduce the experimental effort, it was decided to utilize
some aspect of fractional analysis.
Kline (9) cites the three possible
approaches listed above and discusses the advantages and disadvantages of
each.
Table C.2 summarizes the rationale of this discussion.
In agreement with Table C.2, the next step was to make a choice
between the differential formulation and the integral formulation of the
governi.ng equations.
In either case, it was felt that the overall system
c-4
-------
C':)
I
VI
Method Power Rigor Accuracy Simplicity Input
Dimensional Least Least Least Intermediate Least
Analysis
Method of Intermediate Intermediate Intermediate Greatest Intermediate
S imil i tude
Systematic Use Far Greater Much Better Greatest Most Greatest
of Differential Than Others Than Others Complicated
Equations
POWER - The amount of output information achievable
RIGOR - The accuracy inherent in the method
ACCURACY - The percentage of correct answers achieved in practice
SIMPLICITY - The effort and knowledge required for use
IN¥JT ~ The amount of infDrmation required to utilize the method
Tabl-e Co~o
(Refe:l:'e;:,:,-;if:; Klin8 (9;).
A Compari8~n of Scaling Techniques
-------
boundaries should include both the solid-gas jet and the solid-gas suspen-
sion within the duct downstream of the nozzle.
As was mentioned above,
this was one of the major points of departure from existing studies which
either consider a jet alone or a solid-gas suspension by itself.
Since
the literature generally indicated that the differential formulation was
more widely used, it was selected for the first approach.
The resulting
dimensionless parameters agreed well with those from the solid-gas suspen-
sion analyses.
However, the basic dimensionless parameter of a jet, the
dynami.c pressure ratio of the jet to the duct, was missing.
At this
point, the uncertainty in the analyses coupled with what appeared to be
the omission of this experimentally proven parameter, motivated the inte-
gral approach.
This technique did produce the dynamic pressure ratio as
well as all of the other dimensionless parameters found by the differen-
tial equation approach.
Because of the good agreement between the two
approaches, it is felt that all of the dimensionless parameters were iden-
tified.
The fact that the integral technique produced a dynamic pressure
ratio while the other did not only lies in the more complete description
of the boundary conditions with the integral approach.
C.3.l
Nondimensionalization of the Governing Differential Equations for
Multiphase Flow
To properly describe a flow problem, one must write both the conserva-
tion equations and the boundary conditions.
Thus, it is necessary to
define the domain of interest.
For this approach, the overall system
includes a plane perpendicular to duct axis upstream of the injection
point to a parallel plane a sufficient distance L from the injection point.
The duct walls provide the remaining surfaces for this system.
Figure C.l
C-6
-------
~v
v
(J
I
")J
j
A
R
D
o
Figu.re C.l.
C~~rdinate System - Fra~tlonal AnalY8is
-------
illustrates this domain., The conservation equations are written in the
differential form for an arbitrary location within the system.
Thus, the
jet itself now is treated as a boundary condition where the mass crosses
the system boundary at the injection point.
Then once the jet has spread
across the entire duct cross section, the flow could be treated as a con-
ventional two-phase suspension.
It should be noted that another technique
for analyzing a jet is to treat it separately, writing the conservation
equation specifically for the jet.
However, for this technique defining
both the boundaries and the boundary conditions would be quite difficult.
It is anticipated that both of these approaches should yield the same
dimensionless groups.
For this portion of the study the particle motion is represented by
a particle cloud having the properties of a continuum.
The governing equa-
tions therefore include the conservation of mass and momentum for both the
gas and the particle cloud and are treated in a manner outlined by 800
(10).
As a first approximation for analysis of this problem the energy
equation has been omitted.
This seems to be a reasonable assumption
si.nce the dispersion phenomenon is dominated by the inertial effects of
the mainstream and jet fluid motion.
That is, the heat transfer and
related energy phenomena will be controlled by the various velocities
where the effects of these processes on the velocity are negligible except
through the dependence of S upon temperature.
Therefore, it is necessary
to use mean values of the properties for the modeling process which would
account for thermal gradients without explicitly treating the energy
equation.
A number of simplifying assumptions are made in the analysis of four
C-8
-------
mass and momentum equations.
The first is that all time variations in
velocity are associated with the turbulence conditions and that the mean
velocities are time independent.
In addition, the fluid can be treated as
incompressible.
The instantaneous component of velocity at any point can
be written
U(r:t:)=-lJ(yt) + u..(~t.)
C-2
A reference velocity is chosen to be the time averaged (mean) velocity at
a reference x = 0 and is written as Uo.
Conservation Equations
Since the momentum equations for all three directions would yield the
same dimensionless groups, only the momentum equations will be written for
the x direction.
The continuity equations in orthogonal Cartesian coordi-
nates for the gaseous phase and the particle cloud are, respectively,
-;;)~u + Q;). ~ y + ~=O
-
Q)X "d(1 -r
and ~ + og~~ + ~+- d~PWi' ::. 0
~~ ~)( ~a- ---~
C<3
c-4
The momentum equations in the x direction for the gas phase and the
particle cloud, respectively, are
s~u +SU~+~V~U 1-rwillL =..-?1
~t ~X o~ ~t c)x
+ )i(~~~ +~~ +~~F~p(Ll-U,)
~ +-IL~...V ~ +Wp:>~P=F(U-LJ~
"d-t. \...Lf a.1. f ~ ;;l~ . f J
C-3
C-6
800 (10) labels the term Km as the effectiveness which is a measure of
the transfer of momentum of the mass motion of the particle cloud to the
gas.
In a dilute suspension ~ tends towards zero. When the interparticle
C-9
-------
spacing is of the order of ten times the particle diameter, the value of
Km is close to zero, (see Soo (6».
In the most closely packed region of
flow in this problem, i.e., the nozzle exit, the density is still small
enough to neglect ~.
The body force term shown in equation C-6 includes the assumption
that the particle Reynolds number (~oCt(U - Up)~) is small enough that
the force on a particle can be described by Stokes drag law.
This is
described in detail in references (7) and (10).
Nondimensionalization of the Equations
The equations are nondimensionalized by transforming the variables to
dimensionless variables.
The transformation is accomplished by dividing
each variable by some value of that variable which characterizes that par-
ticular aspect of the problem.
The following transformations are used in
this study.
X~_L
- L
u~- ~
~ - "D
1..
Zt_-
-D
U* - ..u..
- Uo
V~ - y:
- llc
)
\ ..1*- '1:L
V" - Uti
C-7
~ U"
Uf :. -- )
U()
'\j '*' - \If>
r-C4 )
w. ~- ':!:if
f - Uo
.o~- ~p
~f - 'fo
"P
~:=~~ )
* -1:
t == J...../IJI
C-IO
-------
Figure C.2 shows the coordinate system and the duct dimensions.
Replacing the variables with the transformed quantities in equation C-7
results in the following dimensionless conservation equations.
Conservation of mass-gas
d s*U"
d. X.
l (~ ,,?"'V*
+ D d-~"
d ~'It.""*)-
+ "If-O
d~
Conservation of mass-cloud
(IJ/\(L\ ~j>D* d~P*U: L (~~"/' + -;)~;~'If;)= 0
~) A..) ..;>t! + d XII + D d 'PJ. ":;> 1..
Conservation of momentum-gas (x direction)
(Jf!)(1.) ~ + U"~
Ub A dt.~ d-X*
+- 1:.. (V~ d1J. 4-W ~)
t:::> ~d'" .:2~'"
__dP
- ~
.' D (It \:J'U ~ (~ \ ( L \ (:lrJ~
-+ -c. ~Ul)b) a~Z + $~UcPJ 0) ~z.
+~~) -J<",(~X~)Cll~U;)
Conservation of momentum-cloud (x direction)
(.\i)(L J :>11/ +- U. :lU~ -+- L (\l -- ;). U: -4- \N .. d-.Ll: \
U~ .A-J ~'l~ p ';;).~ 1::::> P O>'d'lt P d~~
=(~(ITE) (LJ~-~-)
C-8
C-9
C-IO
C-ll)
Thus, the dimensionless variables obtained from the conservation equations
are
(u* V~ Wif U *" V * W. X p* P *)
) ) ) F".) P ) p.) ) )p
and the dimensionless parameters are
(LID) io Uo D 1ft) FD/Uc) \J'/Uo ) J\.- /L ')
C-ll
-------
where the term F (800 (10)) is
,/fA-
~~Z,
'f7
As can be seen, there are eight equations (six momentum and two continuity
C\
F= -
z.
C-12
equations) and eight dimensionless variables so that the number of equa-
tions is sufficient.
Finally, the application of the boundary conditions
is required to complete the solution.
Boundary Conditions
In considering the boundary conditions for the gas, the usual no-slip
condition at the walls is assumed as well as assuming the normal components
of the velocity at the walls to be zero.
However, at the y-z plane for x =
0, the mean velocity is Uo and the density is ~o with the turbulence asso-
ciated with this flow characterized by v' and--A-, the root mean square of
the fluctuating velocity and the scale of turbulence, respectively.
The
velocity components normal to the walls are considered to be zero with the
exception of the injection point where the velocity is Vj'
density at this location is 3p = ~p, jet.
The cloud
Because of the geometry of the problem, it is not expected that the
boundary layer effects would be significant.
Even if considered, the
boundary layer thickness would be negligibly small compared to the duct
dimensions so that potential flow boundary conditions are applicable for
both the gas and the cloud (i.e., velocity at wall is tangent to same).
At this point it is necessary to obtain the boundary conditions for
the conservation of mass and momentum equations.
The momentum equations
are examined first and here
u = Uo
at x = 0
in the y-z plane
and
v = W = 0 at x = 0
in the y-z plane
C-13
C-12
-------
~ -
In addition for the particle phase
Up = Vp = Wp = 0 at x = 0 in the y-z plane
but
Vp = V = Vj at the nozzle exit where it is assumed that the gas
and particulate velocities of the jet are the same.
In the dimensionless form these boundary conditions are
* * *
Up = Vp = Wp = 0 at x = 0 in the y-z plane
V* = W* = 0 at x = 0 in the y-z plane
C-14
and
V* = Vj/Uo at nozzle exit
*
Vp = Vj/Uo at nozzle exit.
It is convenient to add the two conservation of mass equations which
gives
C~;:)(l)
::If/+ ~ tf)
d t*
-t-
w:u; 1-~\J~)
'dX"
+ l' f~ (~'\J;-r~\') T ;;> (~;w~Vt~~~\=-a
D\~~~ d~ )
Here, the
dimensionless boundary conditions for c3p * + ~*) are
Sp * + <5 * = S* = 1 at x = 0 in the y-z plane
C-15
and
to * 0 * ~ * ~ * ~ "+ f ," ~ .
~p +) = ~p,j + Ja,j =,)P,l-s>o a'J=~
at nozzle exit.
Dimensionless Parameters
Hence, the two additional dimensionless parameters Vj/Uo and
result from the application of the boundary conditions.
~j / ~ 0
C-13
-------
It should be noted here that isotropic turbulence has been assumed as a
first approximation where u'
= v' = w' .
In summary then, one can express the dimensionless density at a fixed
point, i, in space as
~: :. ~~ +-~: = ~ (L/DJ \J'/Uo ).A/L) foUc)D~) FD/Uo)t-/~) ~/Uo)
C-16
The term FD/Uo in equation C-16 can be rewritten as
£I2. =- (£4\( V-I D\
Wo 'IT -J UO A)
which upon multiplying and dividing by like terms can be again rewritten
. . (t: A) ( \r I D \ =- (C,).1. A) ( \(, D \
\)' UI) A) \:~ a} Llo.l\. )
~ c,( 1&) (~) (~ )(~~~)
C-17
In summary, equation C-16 gives the dimensionless parameters which can
affect the cloud density.
For a comprehensive understanding of the solid-
gas jet into a turbulent crosswind, the effect of each group on the parti-
cle cloud at a point must be known.
However, in a model study such as the
scale model of the Shawnee boiler, it is not necessary to ascertain the
effect of each of the dimensionless parameters but only to assure that
C-14
-------
they are the same for both the model and full-scale systems.
C.3.2
Nondimensionalization of the Governing Integral Equations
As an independent check, another approach was utilized to obtai.::: t:2e
applicable dimensionless parameters.
For this approach the analysis is
divided into three parts.
First, the continuity and momentum equations
are expressed in integral form and integrated over the entire control v'o1.=
ume.
The final part of this approach is the analysis of a single partil~le
in a turbulent flow field.
In this manner the parameters related to
i.nteraction of the solid phase and the ambient turbulence are obtained.
The integral approach outlined in the following pages is significa~tly
different from that outlined in section C.3.l.
However, more significant
than the differences between the two approaches to obtain the appli~ab1.e
dimensionless parameters, is the similarity of the results obtai.!led.
The
results of these two approaches complement one another but i.n no way arc
contradictory.
The system being analyzed is shown in Figure C.2.
The appropriate
inlet and outlet parameters are also shown on the figure.
r---------l
I I
I I
r ..d
I .&..&-..&-
~
I rr.& ~
I ~-.;;::
~
I ~~
I l
I ~ I fj')j )Aj
l- - L - J Figure C.2.
t po,Q"Ao C-15
~
Fe IVe ,Ae
System Definition
for Integral
Approach
-------
Continuity Equation
The continuity equation for the entire control volume is obtained
from the Lagrangian integral formulation.
M '- ~~~ p~~
V~)
C-18
The time rate of change
;: JU~~ ~d\l = 0
Vrt)
where' Vol(t) defines the volume boundary of the closed system and can be
d
cH: M
C-19
related to Vol by the Jacobian of the transformation
o
Jt ~r~ p Cf\loL
V~)
-
dV~) -;. J\t) Malo
&)~~?1~\ ~ = J~fLJip~pitJJJIl
Va.c \ - '101.0
&: It.) :: 'oV J(t)
~ t\1 ~ )\\ LftP ~ PV/D VJ d\{
V~)
C-20
The intergrand can be written
cftf + p\JI;V :: ~p + VIe (~V)
Integrating over the control volume and using the divergence theorem
))~~f + ~ 9V"Y1 ds ~O
Vc .Y. Sc."
Assuming a steady state operating condition the first term is zero.
C-2l
The
second term integrated over the closed surface of the control volume is
zero except at the inlets and outlet where
C-16
-------
foUoAo + ~j v jAj - pe V eAe = O. C-22
Factoring out poUoAo and equating the model to the full sized system, the
dimensionless terms are
YJ'~Aj
,-
~ UbA~
and
~ Ve.Ae
~ U-A,()
Momentum Equation
A twofold procedure will be used for examining the momentum equation.
The momentum equation will be expressed in integral form without uti1i.zing
the i.dentity obtained from the continuity equation.
This is necessary in
order to maintain the independence of the two equations, since it may not
be possible to satisfy the constraints of both the continuity and momentum
equations.
The second aspect of the analysis of the momentum equation is
the nondimensionalization of the integrand.
The parameters obtained from
this procedure are required in order to obtain similarity of the i.nteri.or
flow patterns between the model and the actual system.
The momentum of a closed system is
Mo~ ~ ~)) pVd\(~
~~~)
The rate of change of this property is
C~23
directly proportional to the sum of
a11 forces acting on the system
at)\( rVclV6c - ~ F
~)
The term on the left is operated on in exactly the same manner (equation
C~24
C-20)) as was done for the continuity equation.
--'"
The argrment »\1 is sub-
sti.tuted for .p of the previous case yielding
~\C jll pI! ell{
'IJf)
OL
)J~[at(fV) + pV y/oV]dV,,-
~J.~)
C-25
C-17
-------
or in terms of the partial derivative with respect to time the integrand
can be rewritten
~~ + V/Q~V~V)
C-25a
where
~~
V: V is a tensor product.
The summation over all forces include both body and surface forces
acting on the system.
Body forces include those resulting from magnetic
fields (on ferrous materials), electric fields (on charged particles and
ions) and gravitational fields.
The most important is the last and so the
other body forces will be neglected
-
tIS
= - )~\ ?9lLc\~L
VcW
normal and shear, are expressed in terms of
C-26
The combined surface forces,
the gradient of the stress tensor
~
- )~~ \]Iol? d~~
VJt.)
obtained from numerous
C-27
The stress tensor 1P can be
sources and will be
given here for completeness with one limiting assumption.
For this anal-
ysis it will be assumed that,~, the viscosity is constant throughout the
control volume.
In the real system this is not the case since~ is tem-
perature dependent.
However, by choosing a representative value for vis-
cosity this variation is taken into account.
Using this assumption the
stress tensor can be written
C-18
-------
~
~ -=
Z:
1P -ll~ ~j~ +\k~
lL [- P - ~)A VI. V -t SM 9x u) -+ ~ T~ -t- Ik ~
II ~ .. !JL-P- ~,M ?OV" 2,;4 ~v 1 "~"Se
II ttX 4 j 1.'j?; + It<.\.- p- ~? \lOV -+ ~ ~i: w]
--
2 =
>(
R -
'j -
where
P = static pressure
'~j:: ~[~V~SxVJ
~~ :. ~l ~=lu .~w)
L~~ = ~ L~V ~~W]
Using these relations (equations C-25, C-26 and C-27) momentum equation
C-24, can be written for the control volume as
~l ~pV -t \f,(PdV~) + ~9 ~ - -
.v. - ax ~ - ~ ~ - ~ Fi1d\loL - 0
For an infinitesmal volume the integrand of the equation above must he
C-.28
equal to zero.
In treating this integrand the equation is separated ir.to
its steady state and turbulent components.
Each of these components is
nondimensionalized in order to obtain the scaling parameters associated
wi th each.
For this process the )( component of the momentum equation will
'be used.
This component will give the same dimensionless groups as the
other two components, but will have an additional group which is associated
wlth the gravitational effects.
.
The [component of the momentum integrand ,is
~ pU -+ \Jj oCp'JU) -+ pcj ~ ~ P
I a - ,"",;2-.,.,
- "3;M ~ ,\¥oV + J'l J/ u
=- 0
C-l9
-------
The turbulent and steady state components of the velocity vector are
~ ~ --.:...
V-= \j + 'u
-
- -
U It ~ V j -+ Wl~ -+ \A~ +-Vj ;- U,) IR-.
C-29
Density and viscosity are assumed not to have variations related to
turbulence.
The momentum equation can now be ~itten
&(PU) + "VIo(~V 0) + f3 + ~? - ~)-l~peV)
+)A \II'V + ~'pu. -+ \iro{pV~) + ~o(PvU)
+ \¥oCfiFu.) + ~-r - ~?~xJVfaV-) -tjA- \lj"'-U
C-30
-
o
By performing a time averaging procedure on this equation we obtain the
steady
state momentum equation.
~(pO) -t 9Io(pVO) -tf~ + ~p - ~"M~(\1oV)
~ \IIi-V -t 'J o\p V u.)
C..3l
-:0
This last term is usually referred to as the Reynolds stress.
It is the
interaction term between the steady state and turbulent components of the
momentum equation.
In other words the steady state flow is not completely
independent of the ambient turbulence condition.
Subtracting C-3l from C-30 the turbulent component is
~(p~) ,. ~a~VlA) -+ vyc(pvU) + ~oCfU-U) - Weg?V~)
C-32
"0 .1 d (-\ '" L
;- dX-p - 3P &\,,¥aV) +)J VI U = 0
Nondimensionalization
Separate scale components are used for nondimensionalizing equations
C-3l and C-32.
The characteristic scales for C-3Lare the dimensions related
to duct size.
The characteristic length for equation C-32 is the size of the
C-20
-------
turbulent eddies, ~ .
For equation C-3l the following nondimensionalization groups are used
L
t: ltT
X,:: L x+
~ ~ D 'jot
p:r :po Tt F'
~~ Uov-+
'J::. t \71+
\//= tL ~)(t + ~ ~ ~~ ~IR~ ~~
C-33
9 -= 9C1 p+
- ,,-
v= V 1ft
u..::. v' u."t
\l~ ~iJ2. '
i.. = D i.-t
Subst.ituting these terms into C-3l
~(p~u~) ~ '1~ o(p+V~[f) of ~ pt 'T ~ p+
_1 ~ ~ 71 .If\jt\ v+)
5) Sf' bVo aX\, )
A. \]t'U-+ 4 C~Ml.\7/" (p"';:jt lA~)
po lJJo ,UuJ
C-34
:.
o
By e~amining the nondimensional coefficients we obtain four groups.
Th8se
are
L gl
- I ---;:.
\) Uo
~
\ PoLUo I and
I
V
Uo
Performing a similar analysis of the turbulent portion of the mome~-
tum equati.on different scale factors are used for time, length and veloc-
ity.
These scale factors are the ones most closely associated with thA
turbulent condition
l = 1\.l+
'J/= * 'J/
i" ''C) d IL ';;}
"VI =- fJ. ~ * j ~ + Kae
--p ':. ~o V,1.-pI"
1\ - scale of turbulence
lJ' ::A.(v~' -
t=~'L
X =- 1\X+
R.M.S. turbulent velocity
17-= lJ"V-t
y ::. A "d+
L.t :. v' u-r
C-2l
-------
Substituting into C-32 one finds that
~(p-tlA+) ~ ~, \]+0 (y-tV+U+) + ~I \1+0 (p1-1J+5-t-)
T \/t"o (ptV+U+) - V/t.(PT1rU+) ... $-x..t ?+
+ ~:J\ \it7.. ~+
- 1 ~
3 Po v1\
~ (v;to iJ--r)
:: 0
There are two dimensionless groups associated with this differential
equation
Uo
Vi
and
~ lfl\
~
The first was obtained previously.
The second term can be rewritten in
terms of the main duct Reynolds number and intensity of turbulence
S?,:) v:A =
~
P~L (-&')(1)
In summary nondimensionalizing the integrand of the control volume momen-
turn equation results in five dimensionless groups.
These groups can be
reduced to five independent parameters
L 0oLUo Vi 1\
-IJ"L.- \- )-r->
D~ UbL
and
.~
Uo
By scaling these five parameters or the most significant of the five orig-
inal groups will result in the successful momentum scaling of the system.
This scaling includes both s~eady state and turbulence considerations and
is therefore a completely general statement.
Boundary Conditions
The boundary conditions are included by integrating over the entire
control volume.
Applying the divergence theorem to equation C-28
C-22
-------
1-
~~\l~PY) + 9~~ - '1oieJ cf\(
\Jt~ kh -(-- \
. +'j}fpVVOln}c,\S
~.'l
~ 0
C-35
The second term is identically zero except at the inlets and outlet.
Assumlng co>nstant properties across these areas the second term is
~ 'pV(Vol~) dS - Pe'iC:A~ + ~JV:/tj - ,?otiAou.
s.;:~\
The fi.rst term of equation C-35 may be written
fbU"~L{ \\\~(?0) . \ 5>. i ..... Jd~ 1
\{.\(
where the large scale nondimensionalization procedure is utilized. This
tarm mai:;::tains a similarity condition between the model and the full
siz~d system as long as the five parameters are satisfied.
Substi.tuti:r:g
these last two relati.onships into equation C-35
fbD:L: t \\\ l~(p~~) + \-.~+ u. -+
'ill ~'\.A
..... e e. j
po ()L
, . . J dV:
+ 2J~~t ~
~UQ~
_~1L1
L1.. J
= 0
The term ir.side the large brackets must be zero.
More exactly, ea~h ~om-
pOtient of the vector within the bracket must be zero.
Sin~e the integr.al
term has already been scaled then the remaining groups are those ne«:f:!8sar.y
to scale the boundary conditions.
~\VlA'
~ '.J ~ )
Pu \J: L:
geV:Ae.
~-()~C- )
and
&
t:
C-23
-------
C.3.2.l
Motion of a Single Particle in a Turbulent Stream
To determine the interaction of turbulence and particle motion asso-
ciated with this problem, a single particle in a turbulent field will be
rigorously analyzed.
A number of authors point out that for certain lim-
iting conditions the turbulent dispersion of a dilute solid phase is very
closely related to the dynamics of a single particle in an accelerating
flow field.
The flow about such a particle has been obtained analytically
through the work of Oseen, Basset, and Boussinesq.
These equations were
later modified by Tchen (11) in order to obtain a form applicable to a
particle caught up in a turbulent eddy.
The limitations on the
applicability of this equation to turbulent dispersion are
1.
Particle spherical and so small that its relative motion gives
rise to resistance according to Stokes' law.
2.
Particle small when compared with smallest wavelength of
turbulence.
3.
Dispersion effect of shear flow is negligible.
These limitations are taken directly from Soo (10).
There are additional
implied constraints which are considered (and discussed at some length)
by Hinze (12).
The equation for an accelerating particle in an infinite accelerating
fluid is determined to be
~ 110: (PI" +~)~ Vr = 6TT(;tjA(V-Vp) + ZTTC3FJtV
t
T6Q7-Q~r (~(V(~)-~(f)] d~
JO J tVt-~ I (r
-<$) ?f
C-36
A good deal of insight may be gained from this equation with just a
general acknowledgment of the turbulent field in which it is flowing.
It
C-24
-------
is possible to nondimensionalize the turbulent portion of this equation
using R.M.S. turbulent velocity and a representative length scale.
Thi~
r..ondimensionalization gives certain relevant information when the vari.ous
dimeI'.:si.onless coefficients are sized and compared.
First, equation C-36 is written in terms of the mean and turbulence
terms.
The turbulent portion of the equation is:
d -"'
dt up =-
,..,. -I A. -\
i~(~+~)(U--?jp) "i(~'!) ~iJ
t.
+1 ~ fi.AfTJ~(v~)-4!!ld~
2 Q. It 'Vff -00 ~t -~ I (f
C~.37
Using the nondimensionalization procedure as outlined previously, equation
C~,37 is transformed to obtain
~(....+) -
dt vP -
i [¥%1(~..!)tv+- 'if+) .. i (~ ~irA<1f+1
~
-t <1 r ~ ]~ ..l (.& 4-1)-\ r ~(=U-1 7)- ~ ~()
2 lQ'1r' ~ ~ 2..L l\ji-vC c. \.
C..,38
A ~~wnber of authors have disregarded this last term ar..d thiB l~an b~
IOhown to be reasonable by sizing the various coefficientg of e1.uat::i.0Zl C<38.
For a ~olid particle (sp gr ~
2.5) in air
"-
2t :::0(\(5))80 that
Po
",... -
~+l ~ S1
Jo ~ 'po
C-25
-------
By the constraint on the relative size of the particle compared with that
of the turbulence scale
~ » 1.0
Finally, in order to satisfy the Stokes' flow constraint
Q~' ~ O( 1.0)
Now we can compare the first term with the second and it is apparent that
the first term is larger by a factor of
if L\
en}"' Q
» 1.0
The first term is larger than the third by a factor of this term to the
one-half power.
Now the dynamic equation for the particle flow subject to the
constraints outlined earlier can be written as
~(lt) :
~ V ~ R (Vi -l:fc't)
2. CAV' \..\ Pr p
C-39
This dimensionless group is exactly the same as was obtained from the
previous analysis (equation C-35) using a gas and particle cloud approxima-
tion.
As was stated earlier, the same results should be obtained irrespec-
tive of the approach used.
Of course, these results are not new or unique,
and a number of authors have used this term in correlating turbulent dis-
persion data.
The results of these correlations can be seen in papers by
Householder and Goldschmidt (13), Ahmadi (14), and Soo (15).
C.3.3
Summary of the Dimensional Analysis
It has been found that the nondimensionalization of the governing
equations in the differential form (section C.3.l) or in the integral form
coupled with the equation of motion for a single particle in a turbulent
C-26
-------
fLe1d (section c.3.2) yield results which are nearly the same.
A discus-
sion of these results follows along with Table C.3 which summarizes the
dimensionless groups obtained with each approach.
The first four dimensionless groups in Table C.3 have the same f~rm
for each approach but differ in the characteristic value for l~ngth that
is used.
Since geometric similarity is to be maintained, Le., LID 1.[$
constant, it is arbitrary as to which length is selected.
The fifth
group, with both techniques, is obtained from the equation of m.otiQ)::i of
the particles.
The resulting group in the left-hand column includes in
it the term on the right-hand side.
The additional terms in the left-hand
column arise from the use of different characteristic values in nOD.dim.~n=
sionalization.
However, since these additional terms are the third alld
fourth dimensionless groups, the final term in each column will be the
same.
The sixth tenn was included in the integral approach al~d relat~s the
gravity to i.nert1.a forces, 1.. e., the Froude number.
It is expe~ted that
this number would have also been obtained with differential :equaU,m
apprl>8ch i.f the body force term were not assumed tu be negligi.ble.
HlYWm
ever. when the effect of gravity is evaluated by determining t2E\ slip
veloci.ty of a particle as a resu1 t of the gravitational forces, th8
assumption of the first analysis is shown to be reasonable.
Therefor'?',
this term was not retained for further design considerations.
Group 7, which only appears in the second column, is a r~itaratio~
of Group 1 since Ao is proportional to D2.
Group 7 therefore is equal to
Group 1 squared.
Groups 8 and 9 at first glance might appear to indicate a signif:i.~ant
C-27
-------
Section C.3.l Sec t ion C. 3. 2
1 L L
D D
2 gUoD ~
"u..
. .
3 V-' Y
-
UD Uo
4 -A: ~
L 1-
5 PP... \) ~o 12 ~A~
Ut) -Gillo ~ (L V-tl. 0.... ~
6 ~
U~
7 Ao
L'2..
8 i. ~
i- Uo
2-
9 'V.J -~ VJ Aj
- ~ U: L z.
U't)
Table C.3.
Summary of DimensionleSs Groups Obtained by Two Techniques
C-28
-------
difference between the two approaches, but further analysis shows that
this is not the case.
In the first app:t'oach when the term LID was obta:i.x:ed.
it was assumed that this also applied to scaling the jet ulilzzle.
For tJ1P.
!'Iee.ond approaC'.h this was not assumed, and hence Aj IL2 appears in lines 8
and 9.
However, "to.m.en complete geometric scaling is sati.sfied (i::.!clud:l.:'1g
the nozzle size) the last two lines become
£:
,?\)
.H~~
~~tb
and
V:
11
'"L
.Pi Vi
90 001.
The two groups in the second column are combinations of the two gr<)up~ in
the first column.
From both analyses there are two groups obtained which
udate wi.th the boundary conditions at the jet inlet to those s.t t:~~e main
du~t inl~t (see Fi.gure C.2).
The difference is that terms of the s8,~,1nd
column combine the density and velocity ratios into the dynami.c prB8~~~2.
ratio and a mass flow ratio.
The dynamic pressura ratio has bee~~ 8:ti.~'jif(i
to DH a significant parameter in papers reviewed in the lit2rature of j~~
inj~
-------
the dimensionless terms contained in Table C.3 as is possible.
Prior to
constructing the model, these dimensionless parameters were rewritten.
Table C.4 summarizes the dimensionless ratios from Table C.3 and the
rewritten set of independent dimensionless parameters.
Here the original
parameters are listed along with the independent parameters within each
group.
The following discussion outlines the steps in doing so term by
term.
C.4.l
Geometric Scale
The term LID is maintained by preserving the geometric similarity
between the Shawnee system and the model.
Hence, all dimensions were
scaled linearly.
In addition, the term diD which appears within several
of the dimensionless groups was also selected to preserve geometric scale.
Thus, the nozzle diameter is also scaled linearly.
C.4.2
Reynolds Number
The flow Reynolds number was used for determining the scale factor
for sizing the model with respect to the Shawnee system.
The limit for
sizi.ng the duct was based upon the output characteristics of the existing
blower system and filter.
This 'led to the selection of 12.5 as the value
for scaling the Shawnee system.
C.4.3
Turbulence Intensity Parameter, TI 2' and Turbulence Scale Paramete.r,
TT3
It has not been possible to obtain turbulence information for the
Shawnee sys tem.
It was therefore necessary to operate the model under as
wide a range of the turbulence parameters, 11 2 and TT 3' as is possi.b Ie.
In this way it was hoped that the scaled turbulence conditions of the
C-30
-------
(')
I
W
I-'
-
From Equation (19) Indepe:'lder..t Dime~3icn1ess Terms Db~~r.iptive Term
L ~ d same: Tb=~ E} IT: = t Geometric S!:ale
\:) D
j>o1bD same: 11::::. foUo t) Reynolds Number
.)J I ,;U
Jl' J['
"00 same: T\z. = Do Turbulence
Parameter
% -q-i\. Turbulence
same: :3 - 1)
Parameter
,8,£7.J' rewritten: 114 ~ (nc:)'- Dynamic Pressure
po U~ t)'t n~~ Ratio
4 -~ '00
~~~J(~) (!) TTs/fli Particle Inter-
rewritten: 1 (8)' action Parameter
'ITs =
:Pj '
-------
Shawnee boiler would be bracketed by those of the model.
C.4.4
Dynamic Pressure Ratio
In order to satisfy both the dynamic pressure ratio and mass flow
ratio scaling factors, it would be necessary to scale JPj/JP~ and Vj/Uo
(same as dynamic pressure ratio and mass ratio).
This would have requi.red
the jet dust loading to be a factor of five greater than the model feed
system was capable of attaining.
Therefore, it was necessary to choose
between modeling to dynamic pressure ratio or the mass ratio.
Based upon
the results of previous authors in the field of jet trajectory studies
(Table A.l), the dynamic pressure ratio was chosen as the preferable scal-
ing term.
As shown in Table C.4, the dynamic pressure ratio when separated
into independent dimensionless groups results in an independent parameter,
TT4'
C.4.5
FD/Uo
The dimensionless term, FD/Uo' includes the Reynolds number, Trl.
No generality is lost in factoring out1Tl since the overall functional
dependence on this term is maintained.
The grouping that is left is a
term which scales the particle size and density of the two systems,lT 5'
C.5
Summary
With the guidelines stated above the model was scaled to five of the
six dimensionless parameters obtained through the dimensional analysis of
Section C.3.
Since two of these five dimensionless groups are dependent
upon the others, the groups were first separated into independent dimen-
sionless groups.
As was stated previously, the geometric scale factor of
C-32
-------
12.5 was selected for modeling the Shawnee system.
It was not possi.ble to
hold all the variables constant during operation for both the Shawnee ~ys-
tern and the model.
Table C.5 either lists the values or range of va1.u.~1s
for the independent variables shown in Table C.6 for both the Shawnee
boiler and the scale model.
These were the values used for sizing the
nondimensio~al parameters.
The range of values obtained for three of the five independe::1t pi's
for bath the Shawnee system and model are shown in Table C.6.
The valu8s
in this table show that 1T 1 and IT 4 for the model are within the opera-
tiona1 range of the Shawnee system.
The term-rT;, a single valued func-
tion, was matched as closely as was possible.
Finally, the turbulence
parameters,1T 2 and 113, for the model will hopefully bracket the values
for the Shawnee system.
C-33
-------
(")
I
VJ
.p.
ShaWl1.ee
T = 211 0° F
.po = 0.01435 {Fm/ ft3
)A = .1245 ¥Fm/ft-hr
~ = 2.41 x 10-3 ft2/see
43 ft/ see ~ Uo ~ 68 ft/ see
~ = 150 {Fm/ ft3
~ ~ ~ . 73 ¥Fm/ ft3
V. = 130 ft/see
J
a ~ 16 microns
.53 {Fm/ ft3
'I
D
Model
T = 760 F
Po=
fA=
\/=
.0752 {Fm/ft3
.0406 {Fm/ ft -hr
1.5 x 10-4 ft2/see
42.5 ft/see ~ Uo ~ 46 ft/see
,S'p = 167 {Fm/ft3
. 663 {Fm/ ft3 ~ ~j ~ .782 {Fm/ ft3
224 ft/see ~ Vj ~ 245 ft/see
a = 5 microns
D/12.5
Table C.5.
Independent Variables
-------
('")
I
VJ
I.rI
Shawnee Group Model
4.1 x 105 ~ r.T1 ~ 6. 5 x 105 TT, ~ ~ =- ~ 5.21 x 105 £. TI, ~5.. 69 x 105
1..
135 ~ TI4 "465 1\: ~ 209 ~ ~~ 331
~lJo
TTs- = 2.18 x 107 ~ D 1. 6. 7 x 106
lTs = ~) TIS"::.
Table C.6.
Range of Parameters
-------
C .6
References
1.
Soo, S. L, "Fully Developed Turbulent Pipe Flow of a Gas-Solid
Suspension," I & EC Fundamentals, Vol. 1, 1962, p. 33.
2.
800, S. L" Ihrig, H, K., and E1 Kouh, A. F. "Experimental Deter..
mination of Statistical Properties of Two-Phase Turbulent Motions,"
J, of Basic Engr., September 1960, pp. 609-621.
3,
Stukel, J. J., and Soo, S. L. "Turbulent Flow of a Suspension into
a Channel," Power Technology, Vol. 2, No.5, June 1969, pp. 278...289.
4.
Boothroyd, R. G., "Similarity in Gas-Borne Flowing Particle Suspen-
si.ems," Journal of Engineering for Industry, No. 68-MH-ll, May 1969,
pp. 303-313.
5.
Vogt, E. G., and White, R. R. "Friction in the Flow of Suspen-
sions," Industrial and Engineering Chemistry, Vol. 40, No. 9~
September 1948, pp. 1731-1738.
6.
Boothroyd, R. G. "Turbulence Characteristics of the Gaseous Phase
in Duct Flow of a Suspension of Fine Particles," Trans. Instn. Chem.
Engrs., Vol. 45, 1967, pp. T297-T310.
7.
Rose, H. E., and Barnacle, H. E. "Flow of Suspensions of Non-
Cohesive Spherical Particles in Pipes - No. I," The Engineer, Vol.
203, June 14, 1957, pp. 898-901.
8.
Rose, H. E., and Barnacle, H. E. "Flow of Suspensions of Non-
Cohesive Spherical Particles in Pipes - No. II," The Engineer, Vol.
203, June 21, 1957, pp. 939-941.
9.
Kline, S. J.
1965.
Similitude and Approximation Theory, McGraw-Hill,
10.
Soo, S. L. Fluid Dynamics of Multiphase Systems, Blaisdell
Publishing Company, 1967.
11.
Tchen, C. M. "Mean Value and Correlation Problems Connected wi.th
the Motion of Small Particles Suspended in a Turbulent Flu:id~" The
Hauge~ M. Nishoff, 1947.
12.
Turbulence, McGraw-Hill Publishing Company, 1959.
Hinze, J. O.
13.
Householder,M. K., and Goldschmidt, V. W. "Turbulent Diffusion
and Schmidt Number of Particles," J. of Engr. Mech. Div., Vol. 95,
December 1969, pp. 1345-1367.
14.
Ahmadi, G. "Analytical Predictions 9f Turbulent Dispersion of
Finite Size Particles," Ph.D. Thesis, 1970, Purdue.
15.
Soo, S. L. "Statistical Properties of Momentum Transfer in a Two-
Phase Flow," J. of Chem. Engr. Science, V. 5, 1956.
c-36
-------
APPENDIX D
D-l
-------
....... 8
CJ
Q.I
11)
a
N
s=:-
.0 't:J
.... Q.I
~~
III CJ
~ Q.I 6
~.....
S::"'"
Q.I 0
CJ CJ
s::
0 ~
t:j CJ Q.I
I 1
N 0
0.
W 4
'-"
.20
10
- . I
'
Injection Level 1
Turbulence Reduction Screens
Lateral Position 3
0 -
0
~
o.
~ -
4
.
0
4
4
~
H
4 4
0
C
4~
4
0 4
2
L
I
E
D
C
B
H
G
F
K
J
Transverse Position
Shawnee Model Plane A-A
CONCENTRATION PROFILE
-------
""'
CJ
QI
en
o
N
c::-
o'U
~ QI
~~
111 CJ
1-4 QI
~ .....
C::.....
QI 0
CJ CJ
c::
o 1-4
~ U QI
I 'U
UJ ~
c:1.
~
'-"
.2C
. I ~
'
(I
H Injection Levell
Turbulence Reduction Screens
Lateral Position 4 U
- ~
0
4 U
c ~
0
po
c
C
H
4
-
-
~
I
0
c h
. 4 )
~ 4 '
100
80
60
40
20
o
L
F
E
c
B
H
G
D
K
J
I
Transverse Position
Shawnee Model Plane A-A
CONCENTRATION PROFILE
. ..-...
. .
-------
"""'
(J
Q)
III
o
N
C::........
O"CJ
..-1 CIJ
4J4J
CO (J
~ CIJ
4J~
C::""
CIJ 0
(J (J
c::
o ~
t;j U CIJ
"t:I
I ~
~
g.
f
-
.2C
-
- I
Injection Level 1
Turbulence Reduction Screens
Lateral Position 5
-
j
( c
c
j
C
'"
~
0
0 0 0
p c 8 0
c
4~ ~
(
c
( c
.
.
100
80
60
40
20
o
L
G
E
c
B
H
F
D
J
.r
K
Transverse Position
Shawnee Model Plane A-A
CONCENTRATION PROFILE
-------
......
U
41
a:a
o
N
c::-
O"t3
orof 41
4.J4.J
CO U
J.I Q)
4.J .-I
c::.-I
41 0
U U
c::
0 J.I
t:1 041
"t3
I ~
VI
Po
f
'-'
.2(
i I '
Injection Level 1
Turbulence Reduction Screens
Lateral Position 2 0
- 6 D
I ~
It
4
I U .
~ C
C C
100
80
60
40
20
o
L
I
H
G
E
K
J
F
D
C
B
Transverse Position
Shawnee Model Plane A-A
CONCENTRATION PROFILE
~ -;....
-------
"'"'
u
Q)
{O
o
N
~-
O'1:j
o.-f Q)
4.14.1
to U
J.I Q)
4.1 ~
~~
Q) 0
U U
~
o J.I
t::::I U Q)
I i
0\ 0
0.
r
-
120
I . I '
Injection Level 1
.. 211 Grid
Lateral Position 2
-
I~
4
4~
I~ ~ 4 C C
100
80
60
40
20
o
L
G
E
D
.1
H
F
C
K
J
B
Transverse Position
Shawnee Model Plane A-A
CONCENTRATION PROFILE
-------
-
CJ
~
aI
.0
N
t:-
o~
'" ~
.&.1.&.1
to CJ
J.4 ~
.&.1M
t:M
~ 0
CJ CJ
t:
0 J.4
t:;I U~
~
I ~
......
0-
f
'-'
120
.
. I
.,
Injection Level 1
.. 21t Grid
Lateral Position 3
C
c~
..
c c c
c>
H
~~
H
4 4 ~
100
80
60
40
20
o
L
I
G
F
E
D
K
H
c
J
B
Transverse Position
Shawnee Model Plane A-A
CONCENTRATION PROFILE
-------
.....
(J
(\)
II)
o
N
s::-
0""
." (\)
~~
C\1 (J
J.f (\)
~~
s::~
(\) 0
(J 0
s::
0 J.f
I::;j U (\)
""
I ~
00
Q..
~
-
120
I I 0'
j j. 1
Injection Level
" 2" Grid' C
C Lateral Position 4
U
4
u
~I
j
j~ 4~
c~
j
~
j
ro
100
80
60
40
20
o
L
K
I
H
J
G
F
E
D
c
B
Transverse Position
Shawnee Model Plane A-A
CONCENTRATION PROFILE
-------
-
u
G)
CD
o
N
c::-
0'0
""G)
~~
!II U
$.I G)
~ .....
C::"'"
G) 0
U U
c::
o $.I
t::I UG)
I 1
1.0
Q.
?f
-
.20
10
- i I
"
Injection Level 1
.. 2" Grid
Lateral Position 5
0
0
~8
C.
j
c
0
c
4 .
c
C
~
C
H ~ ~
80
60
40
20
o
L
G
E
D
c
H
F
B
K
J
I
Transverse Position
Shawnee Model Plane A-A
CONCENTRATION PROFILE
-------
--- 8
u
-------
.......
u
G)
(/)
o
N
c::-
O~
.... Q)
~~
tU U
J.I G)
~~
c::~
G) 0
U U
c::
~ 0 J.I
I U G)
...... ~
...... ~
Q.
if
-
.2C
I '
Injection Level 2
2" Grid
Lateral Position 2
>
ct
~ 4> c
c
. 4~ C
4
100
80
60
40
20
o
L
K
J
I
H
G
F
E
D
C
B
Transverse Position
Shawnee Model Plane A-A
CONCENTRATION PROFILE
-------
........
U
41
{,Q
o
N
s::-
0'0
~4I
.u.u
CO U
,., 41
.u..-l
s::..-I
41 0
U U
s::
t:;I 0,.,
U4I
I '0
..... ~
N
r:l.
~
-
.2(
6
- I I
,
Injection Level 2
.. 2" Grid.
Lateral Position 3
0 -
0
U
n
. 4
I»
~~
0 4
.4
8
I»
0
I:'
~
j.
0
10
8
4
2
L
K
I
J
H
G
F
E
D
C
B
Transverse Position
Shawnee Model Plane A-A
CONCENTRATION PROFILE
-------
"'"'
o
ell
CO
o
N
c::-
0'0
..-I ell
~~
C\I 0
,.. ell
~~
c::~
ell 0
o 0
c::
t:::1 0,..
c.J ell
I 't:I
..... ~
W
Q.
~
.....,
.20
- I I
'
Injection Level 2
2" Grid'
Lateral Position 4
4
4
n
4
a u
4 ) 4
~
U
U
t 4
~
100
80
60
40
20
o
L
H
G
F
E
D
C
K
J
I
B
Transverse Position
Shawnee Model Plane A-A
CONCENTRATION PROFILE
-------
......
CJ
Q)
to
0
N
t:-
o~
.r-I Q)
.u.u
QI CJ
$.I Q) 6
.u ~
t:~
Q) 0
CJ CJ
t:
t::;j 0 $.I
U Q)
I ~
..... g
.J:-o
Q.
tf 4
'-"
120
10
i I
,
Injection Level 2
2" Grid
Lateral Position 5
0 -
0
I>
0
.
. 0 .
.
0
4~ .~
4~
C
c~
U
0 It
c
,
0
8
2
L
K
I
H
G
J
F
D
c
E
B
Transverse Position
Shawnee Model Plane A-A
CONCENTRATION PROFILE
-------
"'"' 8
u
CIJ
fI.I
0
N
t::-
o~
'" CIJ
.j.J.j.J
CIS U
$.4 CIJ 6
.j.J.-4
t::.-4
CIJ 0
U u
t::
t;j 0 $.4
I U CIJ
... ~
VI ~
(:I.
W 4
'-'
10
- I ;
,
Injection Level 2
.. 2" Grid'
Lateral Position 6
0 -
0
0
0
0 l
0 ~
~~ I ~
4~ I~
. I . I»
o
.20
2
L
K
J
I
H
G
F
E
D
c
B
Transverse Position
Shawnee Model Plane A-A
CONCENTRATION PROFILE
-------
-
CJ
GI
en
o
N
c-
0'0
.,-4 GI
..........
111 CJ
/0.4 GI
..... ..-I
C..-l
QJ 0
CJ CJ
C
t:1 0 /0.4
c.J QJ
I l
t-'
0\
0-
?f
-
.2 )
- i j
Injection Level 2
Turbulence Reduction Screens
Lateral Position 2
-
"
0 4:t
.
0 t 0 C 4
100
80
60
40
20
o
L
C
E
D
H
G
F
B
K
J
I
Transverse Position
Shawnee Model Plane A-A
CONCENTRATION PROFILE
-------
-
(J
Q)
!lJ
o
N
d-
O."
-rot Q)
........
CO (J
$.4 Q)
.... .-I
d.-l
Q) 0
(J (J
d
t:I 0 $.4
(.) Q)
I ."
.... g
......
Po
W
...,
.2(
- I I
Injection Level 2
Turbulence Reduction Screens
Lateral Position 3
-
j
C
0
,
,
> 4)
CC) U
~ 4)
4 ~
I
4 4
~
j
4
100
80
60
40
20
o
L
K
J
I
H
G
F
E
D
C
B
Transverse Position
Shawnee Model Plane A-A
CONCENTRATION PROFILE
-------
-
CJ
Q)
co
o
N
s::-
0."
.r-I Q)
.IoJ.IoJ
CIS CJ
J.4 Q)
.IoJP'"'I
S::P'"'I
Q) 0
CJ CJ
s::
t:::I 0 J.4
U Q)
I ."
t-' ~
00
Q.
if
.....,
\
\
i
.20
I I '
Injection Level 2
Turbulence Reduction Screens
Lateral Position 4
U
4>
»
4 4
C
U
CI~ 4
c ~~
« C) 4 4
C 4
4 4
4
100
80
60
40
20
o
L
G
F
E
D
C
I
H
B
K
J
Transverse Position
Shawnee Model Plane A-A
CONCENTRATION PROFILE
-------
.......
u
ctI
II)
o
N
1::-
o~
0.-4 ctI
.u.u
1\1 U
... ctI
.u ~
I::~
ctI 0
U U
I::
t:::I 0...
CJ ctI
I ~
I-' ~
\0
p..
if
.....,
.20
I I I ,
Injection Level 2
Turbulence Reduction Screens
Lateral Position 5
-
II>
~~
c ~
~ CI'
. 4 C~
C ~ j i
I I
I ~
~
4 ~ It
100
80
60
40
20
o
L
K
H
G
J
I
F
E
D
C
B
Transverse Position
Shawnee Model Plane A-A
CONCENTRATION PROFILE
-------
""'
(J
GI
(/J
o
N
~-
0'0
'r! GI
.j.J.j.J
to (J
k GI
.j.JM
~M
CO 0
(J (J
~
t:;j 0 k
U GI
I '0
N ~
o
Q.
!1f
-
.20
I I -
Injection Level 2
Vortex Generator
Lateral Position 3
-
U
-
C) 0
0 4~
4~
'"
C~
., , ,
100
80
60
40
20
o
L
K
H
G
F
E
D
C
J
I
B
Transverse Position
Shawnee Model Plane A-A
CONCENTRATION PROFILE
-------
"......
o
0
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100
80
60
40
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B
K
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Transverse Position
Shawnee Model Plane A-A
CONCENTRATION PROFILE
-------
......
CJ
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Injection Level 2
Vortex Generator
Lateral Position 5
-
4
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100
80
60
40
20
o
L
K
I
J
H
G
F
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D
C
B
Transverse Position
Shawnee Model Plane A-A
CONCENTRATION PROFILE
-------
-
o
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Injection Level 2
.. Open Box
,
Lateral Position 3
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0
100
80
60
40
20
o
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B
Transverse Position
Shawnee Model Plane A-A
CONCENTRATION PROFILE
-------
-
U
GI
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N
c::-
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Injection Level 2
Open Box
Lateral Position 4
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,
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10
80
60
40
20
o
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J
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H
K
Transverse Position
Shawnee Model Plane A-A
CONCENTRATION PROFILE
-------
......
U
GJ
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Injection Level 2
.. Open Box
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Lateral Position 5
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100
80
60
40
20
o
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H
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B
K
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Transverse Position
Shawnee Model Plane A-A
CONCENTRATION PROFILE
-------
--- 8
(J
GJ
II)
0
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c-
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Injection Level 3
Turbulence Reduction Screens
Lateral Position 3
0 -
0
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0
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2
L
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H
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Transverse Position
Shawnee Model Plane A-A
CONCENTRATION PROFILE
-------
.2 )
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U
QI
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80
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Injection Level 3
Turbulence Reduction Screens
Lateral Position 4
-
.
C
4
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100
60
20
o
L
K
J
I
H
G
F
E
D
c
B
Transverse Position
Shawnee Model Plane A-A
CONCENTRATION PROFILE
-------
.20
2
I I
Injection Level 3
Turbulence Reduction Screens 4~
- Lateral Position
5
0 .
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Transverse Position
Shawnee Model Plane A-A
CONCENTRATION PROFILE
-------
....... 8
()
-------
- 8
CJ
CIJ
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Injection Level 3
2" Grid
Lateral Position 4
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B
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Transverse Position
Shawnee Model Plane A-A
CONCENTRATION PROFILE
-------
-
C.I
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c:-
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Injection Level 3
.. 2" Grid <>
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Lateral Position 5
-
U c
-
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I~
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100
80
60
40
20
o
L
K
I
H
G
F
E
J
D
C
B
Transverse Position
Shawnee Model Plane A-A
CONCENTRATION PROFILE
-------
.,---
WEST VIRGINIA BOARD OF REGENTS
FOR HIGHER EDUCATION, 1969170
John E. Amos, President. Charleston
Earle T. Andrews, I'ice-president
Berkeley Springs
Amos A. Bolen, Secretary, Huntington
Dr. Forrest L. Blair, Walker
David B. Dalzell. MoundsviIle
Mrs. Elizabeth H. Gilmore, Charleston
Edward H. Greene, Huntington
Albert M. Morgan, Morgantown
Okey L. Patteson, Mount Hope
Rex M. Smith, ex officio, Charleston
Dr. Prince B. Woodard, Chancellor, Charleston
-------