310830-3-F
APTD-1375
Annual Progress Report No. 3
(Final)
Kinetics of Oxidation and Quenching
of Combustibles in Exhaust Systems
of Gasoline Engines
D. J. PATTERSON, R. H. KADLEC
B. CARNAHAN
H. A. LORD
J. J. MARTIN
W. MIRSKY
E. SONDREAL
PERIOD: February 24, 1971 to August 22, 1972
1971 - 1972
This project is under the technical supervision of the:
Coordinating Research Council
APRAC-CAPE 8-68 Steering Committee
and is work performed by the:
Departments of Mechanical and Chemical Engineering
The University of Michigan
Ann Arbor, Michigan
Under Contract No, CAPE-8-68(1-68)-CRC
and Contract No. CPA-22-69-51-HEW
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ANNUAL PROGRI~SS HEPOg'[' NO.3
(final)
KINETICS OF OXIDATION AND QUENCHING OF COMBUSTIBLES IN
EXHAUST SYSTEMS OF GASOLINE ENGINES
D. J.
Patterson, R. H. Kadlec
B. carnahan
H. A. Lord
J. J. Martin
W. Mirsky
E. A. Sondreal
PER IOD :
February 24, 1971 to August 22, 1972
1971 - 1972
This project is under the technical supervision of the:
Coordinating Research Council
APRAC-CAPE 8-68 Steering Committee
and is work performed by the:
Departments
of Mechanical and Chemical
The University of Michigan
Ann Arbor, Michigan
Engineering
Under Contract No. CAPE-8-68(1-68)-CRC
. and Contract No. CPA-22-68-51-HEW
-------
1.-
ACKNOWLEDGMENTS
We wish to thank the APRAC-CAPE 8-68 project group, Dr.
P. R. Ryason, Chairman, who on behalf of the Coordinating Re-
search Council guided the progress of this work and made many
helpful suggestions. Their names are listed in the Distribu-
tion List at the end of this report. There is little doubt
that the cooperative efforts of industry and The University
of Michigan in this applied research area produced a syner-
gistic effect.
Further, we wish to acknowledge the assistance of the
numerous students who worked on the project. Their diligence
and attention to detail were a significant factor in the suc-
cess of this effort.
iii
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TABLE OF CONTENTS
Pa.g~
LIST OF TABLES viii
LIST OF FIGURES X
ABSTRACT xviii
INTRODUCTION 1
COMPREHENSIVE SUMMARY 2
MAJOR CONCLUSIONS 6
AREAS FOR FUTURE WORK 8
DETAILED PROGRESS - PHASE I
MULTI CYLINDER AND SINGLE CYLINDER ENGINE
MOUNTED REACTOR EXPERIMENTAL EVALUATIONS
A.
MULTICYLINDER CONVENTIONAL REACTOR
1-
2.
Objectives
Experimental System
a. Engine-reactor system
b. Instrumentation
Experimental Results
. B.. Warm-up limita.tions on reaction
b. Mixing limitations to steady performance.
c. Reactor combustion luminosity
11
11
11
11
14
14
16
25
42
3.
B.
SINGLE MULTICYLINDER EXPERIMENTAL REACTOR STUDY
1-
2.
3.
Objectives
Experimental Apparatus
Experimental Results
a. Summary of CO oxidation rate
b. Summary of HC oxidation rate
c. Summary of H2 oxidation rate
49
49
49
51
51
57
58
results
results
results
C.
REFERENCES FOR PHASE I
64
iv
'"
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FOREWORD
TABLE OF CONTENTS (Continued)
DETAILED PROGRESS - PHASE II
COMPUTER MODEL DEVELOPMENT
INTRODUCTION TO THE THERMAL REACTOR PROBLEM
MODEL BUILDING AND PARAMETER EVALUATION FOR STATIONARY STATE OPERATION
I.
Mixing Coupled with Reaction
A. Review on mixing in chemical reactor design
B. The pattern of flow micromixing simulation
C. Simplified mixing simulations
General Parameter Ev~luation
A. Simulations run on mixing with instantaneous reaction
B. Coupled mixing and kinetics at steady flow: param-
eter study on "MICROMIX II"
II.
SIMULATIONS ON STATIONARY STATE REACTOR OPERATION:
COMPARISON WITH EXPERIMENTAL STUDIES.
III.
IV.
V.
Estimates of the Coalescence Parameter, 1m
Simulations on the Kinetics Test Reactor
Simulations on the DuPont Model V Re8.ctor
A. Maximum conversions for instantaneous reaction--
. "MIX ONLY POF"
B. Comparison dilution ratio on changes in air
C. Approach to a high temperature limit on conversion
of carbon monoxide
D. Sensitivity to residence time distribution and
micromixedness (1m)
MODELING REACTOR OPERATION DURING WARM-UP
VII.
VI.
Model Building for Unsteady State Operation
A. Key features and assumptions
:8. Reactor parts temperature simulation
C. . Solutions for multiple oxidations in a "CSTR"
Base Case Warm-Up Simulations for the DuPont Model V Reactor
A. Warm-up without reaction-thermal parameter evalua tion
B. Warm-up with lightoff
v
Page
69
71
dl
81
82
8)
99
108
108
121
140
140
144
150
150
153
157
166
172
172
172
173
177
186
186
191
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VIII.
TABLE OF CONTENTS (Continued)
Variations on the Base Case Warm-Up
A. Design and operation
B. Lightoff a.t time zero
C. Summary on ignition effects
Simulation
CONCLUSIONS AND USE OF RESULTS
IX.
X.
APPENDIX A.
APPENDIX B.
APPENDIX C.
Summary and Conclusions
Use of Results
MIXING AND REACTOR THEORY
1.
2.
3.
Mixing in Reactor Design
Theory of an Idealized Turbulent Mixer
Selection of a Model Type for Exhaust Reactor Simulation
MOMENTS OF THE CONCENTRATION DISTRIBUTION FOR CURL'S
RANDOM COALESCENCE MODEL APPLIED TO A REACTION VELOCITY.
OF ORDER ~, r = -kc~
DANCKWERTS' "J" FACTOR FOR STIRRED TANKS IN SERIES AT
1m = 00
REFERENCES FOR PHASE II
NOMENCLATURE FOR PHASE II
DETAILED PROGRESS - PHASE III
SPECIAL INSTRUMENTATION DEVELOPMENT AND MEASUREMENTS
A.
SUBTRACTIVE COLUMN HYDROCARBON ANALYSIS
1.
2.
3.
Purpose
Equipment
Experimental Verifica.tion
A. Gas chromatographic comparison
B.Calibration gas comparison
Conclusions
4.
vi
Page
195
195
200
202
207
207
212
214
214
221
.224
230
234
237
241
249
249
249
251
251
253
253
\.
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TABLE OF CONTENTS (Concluded)
Page
1-
2.
3.
4.
~.
Purpose
Sampling Technique
Gas Chromatograph Operation
Data Analysis
Conclusion
255
255
255
255
2':/(
259
B.
GAS CHROMATOGRAPHIC STUDIES OF EXHAUST ACETYLENE
C.
MEASUREMENT OF INSTANTANEOUS ENGINE EXHAUST VELOCITY
AND TEMPERATURE
1-
2.
The Measurement of Engine Exhaust Velocity
The Attempted Measurement of Instantaneous Exhaust
Temperature
265
265
273
. DISTRIBUTION LIST
280
I .
vii
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Table
III.
VII.
. VII I.
XI.
XII.
III. .
LIST OF TABLES
PHASE I
I. Chevrolet Engine Characteristics
II.
DuPont Type V Reactor Characteristics
qas Analysis Techniques
IV.
Multicylinder Engine-Reactor Performance
V.
Warm-Up Test Results
VI.
Range of Parameters (Carbon Monoxide Oxidation)
Regression Program Results) CO Oxidation Rates
Comparison of Experimental CO Oxidation Rates with Two Wall
Materials and Two Sparger Tubes
IX.
Range of Parameters (Hydrocarbon Oxidation)
X.
Hydrocarbon Oxidation Regression Results
Hange of Parameters (Hydrogen Oxidation)
Hydrogen Oxidation Regression Results
PHASE II
I.
Conversions of "A" for Mixing with Instantaneous Reaction of
Separate Reactant Streams in '~" Equal Size Cell-Wise Stirred
Tanks in Series
II.
Conditions for Testing Parameters of MICROMIX II
Comparison of High Temperature Experimental Conversion
"MIXONLY POF" Simulations of Mixing with Instantaneous
Rea.ction
with
IV.
Time to Lic;htoff for Variations to the DuPont Model V Base
Case
viii
Page
12
12
15
16
24
51
53
55
57
59
59
61
117
122
152
196
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Table
III.
LIST OF TABLES (Concluded)
Page
PHASE III
I.
Substractive Column--G~C. Comparisons
252
II.
256
FID and Subtractive Column Analyses
Hexane Equivalent of Components Determined by GC Analysis
258
IV.
Corrected Olefin Content of Samples
260
V.
Engine Specifications
272
ix
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Figure
LIST OF FIGURES
PHASE I
1.
DuPont type V reactor mounted on the Chevrolet ))0 in.)
engine for test.
2.
Type V duPont exhaust manifold reactor.
).
DuPont Model V exhaust manifold reactor showing thermocouple
locations.
4.
Hydrocarbon, CO, and NO emissions as well as reactor center-
line gas temperature and outer skin temperature versus time
for a 70°F cold start.
).
Torque, bsfc and air/fuel ratio provided to the engine as a
function of time.
lJ.
Hydrocarbon, CO, a.nd
ditions of 1200 rpm,
no air injection.
NO emissions versus time for ellgine con-
30 BHP, MET spark, 17:1 a.ir/fuel ratio,
7.
Reactor temperatures versus time.
8.
Torque, bsfc and air/fuel ratio provided to the engine as a
function of time.
9.
J:'xhaust emissions with duPont reactors as a function of air-
injection fraction.
10.
Extent of' reaction vs. reactor temperature.
11.
Conditions similar to Figure 10 except higher CO and H2 reac':"
tor input.
12.
Conditions similar to Figure 11 except air injection fra.ction
doubled to F = 0.2.
13-
Air injection manifold pressure minus exhaust port pressure
versus crankangle.
14.
Mass flow through air injection tube for cylinder number L
x
pa.ge
13
13
17
113
19
21
22
23
26
27
29
30
32
33
-------
Figur e
LIST OF FIGURES (Continued)
15.
Conditions similar to Figure 12
lean enough to provide the same
out air injection.
except the engine is run
reactor mixture ratio with-
16.
Effect of reactor temperature on the concentration of 02, HC,
and CO in the exhaust of a lean running engine, 1% = 10,000
ppm.
17.
Extent of reaction vs. reactor temperature.
18.
Same as Figure 17, except air injection fraction increased
to approximately 0.15.
19.
Effect of air injection fraction on CO conversion and reac-
tor temperature.
20.
Same as Figure 19 for hydrocarbon conversion.
21.
Chevrolet 350 in.3 engine, 1200rpm, 30 hp, 12.5:1 air-fuel
ratio, air injection fraction .22, reactor temperature ap-
proximately 1650°F.
22.
Repeatability of light emission.
23.
Location of light emission peaks with respect to cycle ef-
fects for cylinders 1, 3, 5, and 7.
24.
Repeatability of light emission.
25.
Repeatability of light emission.
26.
Spectrogram of luminous blue flame appearing in exhaust gas
reactor .'
27.
Two-tank experimental reactor system schematic.
28.
Predicted rates for CO oxidation for a mixture containing
1% CO, 1% 02' and 500 ppm NO.
29.
Conversions of hydrogen corrected to 20 lb exhaust/hr and
.006 mole fraction hydrogen entering, rH2 = 12,660
e-52,000/RT. ' ,
xi
Page
. 35
\.
30
38
39
40
41
43
43
44
46
46
47
50
54
63
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Figure
LIST OF FIGURES (Continued)
PHASE II
1.
Schematic of exhaust flow from one cylinder through a thermal
reactor exhaust system.
2.
Characteristic variation in cyclic exhaust flow from a single
cylinder spark ignition engine.
3.
Combined normalized flow for cylinders 1, 3, 5, and 7 of a
V-8 engine.
4.
Characteristic variation in cyclic mass flow through air in-
jection tube during a 7200 engine cycle.
5.
Assumed variation in cyclic exhaust temperature based ,on coin-
cidence with measured peak flow.
6.
Characteristic variation in cyclic hydrocarbon concentration.
7.
Illustrative module network for simulation "MMPOF. II
8.
Schematic on the compiling of the inlet cell roster.
9.
Flow and mixing in non-ideal stirred tank modules within
"MICROMIX PATTERN OF FLOW. II
10.
Flow and mixing in non-ideal plug flow modules within 'MICRO-
MIX PATTERN OF FLOW. II
11.
Mole fraction integration showing dise,ppearance of species.
12.
Mixing with instantaneous reaction, A+B -+ 2C.
13.
The effect of a small number of cells in
conversion for a stirred-tank'simulation
stantaneous reaction, A + 1/2B -+ c.
the reactor, Nc, on
of mixing with in-
14.
The effect of a small number of cells in the
the conversion for a stirred-tank simulation
instantaneous reaction, A + 1/2B -+ C.
reactor,Nc' on
of mixing with
15.
Stirred-tank mixing with instantaneous reaction, A +1/2B -+ C.
xii
Page
72
'7)
76
77
79
80
89
91
93
95
97
104 '
105
106
109
-------
Figure
LIST OF FIGURES (Continued)
16.
Stirred-tank mixing with instantaneous reaction, A + 1/2B -+ C.
17.
Effect of feed stoichiometric ratio, SR, on stirred-tank cell
mixing with instantaneous reaction, A + 1/2B -+ C.
18.
Effect of dilution, ratio (stream 2/stream 1) on stirred-tank
cell mixing with instantaneous reaction, A + 1/2B -+ C.
19.
Plug-flow cell mixing with instantaneous reaction, A:'- 1/2B -+ C.
20.
Effect of feed stoichiometric ratio on plug flow cell mixing
with instantaneous reaction, A + 1/2B -+ C.
21.
Effect of dilution ratio, DR, on plug-flow mixing with instan-
taneous reaction, A + 1/2B -+ C.
22.
Mixing with instantaneous reaction for "n" equal size cell-
wise stirred tanks.
23.
Danckwerts' "J" factor far cell-wise mixed stirred tanks in
series.
24.
Influence of Danckwerts' "J" on fraction "A" converted for
instantaneous reaction of "A" in cell-wise mixed tanks in
series.
25.
Comparison of stirred-tank conversion for zero order and .269
order CO kinetics at Im = 00.
26.
Material and energy balance curves for coupled reaction and
mixing, 1m = 1 to 00, in a cell-wise mixed stirred tank at
dilution ratio, DR = .1.
27.
Material and energy balance curves for coupled reaction and
mixing, Im = 1 to 00, in a cell-wise mixed stirred tank at
dilution ratio, DR = .25.
28.
Material and energy balance curves for coupled reaction and
mixing, Im = ~ to 00, in a cell-wise mixed stirred tank at
dilution ratio, DR = .50.
xiii
Page
110
111
112
113
114
115
118
119
120
123
124
125
126
-------
.
. Figure
LIST OF FIGURES (Continued)
29.
Material and energy balance curves for coupledreactlon and
mixing, 1m = 1 to 00, in a cell-wise mixed stirred tank at
dilution ratio, DR = 1.
30.
Material and energy balance curves for coupled reaction and
mixing, 1m = 1 to .00, in a cell-wise mixed stirred tank at a
feed stoichiometric ratio (B:A), SR = 1.
31.
Material and energy balance curves for coupled reaction and
. .
mixing, 1m = 1 to 00, in a cell-wise mixed stirred tank at a
feed stoichiometric ratio (B:A),SR = 2.
32.
Material and energy balance curves for coupled reaction and
mixing, 1m = 1 to 00, in a cell-wise mixed stirred tank at a
feed stoichiometric ratio (B:A), SR = 5.
33.
Material and energy balance curves for coupled reaction and
mixing, 1m = 1 to 00, in a cell-wise mixed stirred tank at a
feed stoichiometric ratio (B:A), SR = 15. .
34.
Material and energy balance curves for coupled reaction and
mixing, 1m = I to 00, in a cell-wise mixed stirred tank at
activation energy, E = 10,000 cal/g mole. .
3).
Material and energy balance curves for coupled reaction and
mixing, 1m = 1 to 00, in a cell-wise mixed stirred tank at
activation energy, E = 50,000 cal/g mole.
36.
Material and energy balance curves for coupled reaction and
mixing, 1m = 1 to 00, in a cell-wise mixed stirred tank for
first order reaction.
37.
Material and
mixing, 1m =
second order
energy balance curves for coupled reaction and
1 to 00,. in a cell-wise mixed stirred tank for
reaction.
38.
Material and energy balance curves for coupled reaction and
mixing, 1m = 1 to 00, in a cell-wise mixed stirred tank at a
mean residence time, T = .002 sec at 1500°F.
39.
Material and energy balance curves for coupled reaction and
mixing, 1m = 1 to 00, in a cell-wise mixed stirred ta.nk at a.
mean residence time, T = .150 sec at 1500°F.
xiv
Page
127
129 .
130
131
132
134
135
136
137
138
139
-------
Figure
LIST OF FIGURES .( Continued)
40.
Simulation of CO conversions in the kinetic test reactor.
41.
Experimental conversions from kinetics test data plotted on
the cell-wise mixing simulation of Figure 40.
42.
The effect of mixing parameter (1m) on hydrogen conversion.
43.
Patterns of flow run to simulate the DuPont Model V reactor.
44.
Stirred-tank simulation of the effect of air injection frac-
tion at a mixing parameter value of 1m = 8.
45.
Simulation of the effect of air injection fraction using the
pattern of cell flow shown in Figure 43~
46.
Simulation of the approach to high-temperature mixing-limited
conversion for CO using a stirred tank cell mixing model.
47.
Simulation of the approach to high-temperature conversion for
CO using the cell pattern of flow shown in Figure 43.
48.
Simulation of the approach to high-temperature conversion for
CO using the cell pattern. of flow shown' in Figure 43.
49.
Cell mixed plug flow simulation.
50.
Residence time distribution for the simulation shown in
Figure 47 and item 2, Figure 43.
)1.
The effect of inlet exhaust temperature span (cyclic) on
conversion.
)2.
Simulation of a half reactor assuming symmetry.
53.
Sensitivity of simulation conversions to the mixing param-
eter, 1m'
54.
Comparison of the stirred tank-with-plug-flow simulation
with cell-wise stirred tanks in series.
55.
Thermal conductance network for the DuPont Model V reactor
with external insulation.
xv
Page
14)
146
147
151
154
155
159
160
161
162
163
167
168
169
171
174
-------
Figure
62.
63.
64.
65.
66.
67.
LIST OF FIGURES (Continued)
56.
Conversions of carbon monoxide corrected to 30 lb exhaust/hr
and .02 mole fraction CO entering.
57.
Conversions of hydrocarbon corrected to 20 lb exhaust/hr and
400 ppm hydrocarbon entering.
58.
Simulated steady-state heat loss measured as drop in exhaust
temperature.
59.
Steady-state metal temperature profiles.
60.
Warm-up of the DuPont Model V.
61.
Comparison of experimental and typical simulated warm-up for
the DuPont Model V reactor.
Simulation of lightoff for the DuPont Model V reactor.
Deviations in time to lightoff for variations to the DuPont
Model V base case.
Approach to immediate lightoff.
Simulated lightoff for insulated empty can.
Warm-up simula.tion of inlet properties reQuired to achieve
immediate ignition with stoichiometric air at 100°F.
A summary of typical ignition beha.vior for a. zero order CSTR
simulation.
PHASE III
1. Flow schematic of University of Michigan subtractive column-
flame ionization hydrocarbon analysis system.
2. Results for samples without after-reaction.
3. Results for samples with after-reaction.
4. Results for samples without after-reaction.
xvi
pa.ge
184
185
187
188
189
192
194
199
201
203
204
205
250
261
262
263
-------
Figure
LIST OF FIGURES (Concluded)
5.
Results for samples with after-reaction.
6.
Schematic diagram of laser-schlieren optical system.
7.
Streak schlieren photograph showing the start of the exhaust
process.
8.
Exhaust velocity measurement system.
9.
Electrical schematic.
10.
Velocity as a function of crankangle.
11.
Exhaust gas velocity vs. crankangle.
12.
Photodiode amplifier circuit.
13.
Dimensions of Hewlett-Packard pin photodiode 5082-4205.
14.
Spark circuit.
15.
Speed of sound in exhaust gas as a function of temperature
and equivalence ratio.
16.
Photodiode signals from velocity of sound measurements in
room air at 72°F.
17.
Photodiode signals with expanded time scale.
18.
Photodiode signals showing repeatability.
xvii
Page
264
266
267
268
269
270
271
274
274
275
276
277
277
277
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ABSTRACT
A comprehensive analytical and experimental study of thermal reactors
has been made. The findings have been incorporated into a computer model
capable of simulating reactor performance both during warm-up and ste~dy-
state operation. Arbitrary reactor configurations may be explored in re-
gard to the steady-state and warm-up extent of oxidation of hydrocarbons,
carbon monoxide, and hydrogen with perfect or imperfect mixing and the
detrimental effects of heat losses. Reactor size, shape, and material as
well as start-up temperature may be explored for their effect on reactor
lightoff time with various levels of exhaust HC, CO, and H2'
This experimental and analytical program focused on the Chevrolet 350
in.3 engine--duPont Model V reactor combination. Experimental and calcula-
ted results are presented and compared where possible. Analytical models
for the duPont reactor were developed each of which treated the exhaust
ports, core, and annulus differently. . An experimental techGique was de-
veloped which permits an assessment of the completeness of mixing between
exhaust and injected air within a thermal reactor and is expected to be
useful as a design aid.
In addition to oxidation results for CO, H2, and hydrocarbons as a
whole, measurements were made to determine any changes in nitric oxide,
aldehydes and olefin, paraffin, and aromatic class proportion affected by
the thermal reactor at selected operating conditions. Finally separate
studies were conducted in a stirred tank reactor to determine global oxi-
dation kinetics for exhaust CO, HC, and H2 to be used in the computer sim-
ulation.
Results of this study are incorporated in three annual progress reports
to the Coordinating Research Council of which this report is the third and
final. Cor~uter programs are included on microfiche cards in the pocket
on the inside back cover of this report. Limited additional copies of these
reports are available from:
Coordinating Research Council, Inc.
30 Rockefeller Plnza
New York, New York 10020
xviii
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!-
INTRODUCTION
This exhaust thermal reactor program, which has been conducted within the
Departments of Mechanical and Chemical Engineering at The University of Michi-
gan over a three-year period has had the following broad objectives:
'To quantify the effects that the various chemical and physical processes
have on emission characteristics of exhaust thermal reactors installed
on selected typical engines operating at various conditions on a dyna-
mometer test stand.
'To obtain concentration measurements of pertinent chemical species and
classes at the entrance to, within, and at the exit from thermal reac-
tors, and, from this data to determine gross chemical reaction rates.
'To obtain information which will be helpful in predicting the design of
gasoline engine exhaust reactors.
'To develop a computer model for the thermal reactors.
The program has been divided into three phases of study.
These were:
Phase I. Multicylinder and Single Cylinder Engine Mounted Reactor Experi-
mental Evaluations.
Phase II. Computer Model Development.
Phase III. Special Instrumentation Develo~ment and Measurements.
This report details progress made primarily during the third and final
year of the program. In some cases information contained in prior annual re-
ports has been included to improve readability. In other cases reference is
made to the First and Second Annual Progress Reports for additional details.
Below are the comprehensive summary and major conclusions of the program.
1
-------
COMPREHENSIVE SUMMARY
PHASE I.
MULTI CYLINDER AND SINGLE CYLINDER ENGINE MOUNTED
REACTOR EXPERIMENTAL EVALUATIONS
A Chevrolet 350 in.3 engine was procured and baseline performance and
emission data obtained. Variables included mixture ratio, ignition timing,
speed, and load. Subsequently a pair of duPont Model V thermal reactors \"ere
installed on the engine and evaluated for emission reduction performance.
Studies were made to determine fa9tors which limited conversion of hydro-
gen, carbon monoxide, and hydrocarbons in the reactor during both warm-up and
steady-state operation. Variables explored were mixture ratio, spark timing,
and air injection quantity. For a given flowrate (residence time) oxidation.
of these compounds was found to depend on temperature, exhaust feed composi-
tion, air injection quantity, and mixing. Conversions between 0 and 100% were
.observed for hydrogen, 0 and 98% for hydrocarbons, and 0 to 95% for CO. In
every case. CO was the most difficult specie to oxidize because of its rela-
tively slow reaction rate. It was a common observation that above l600°F con-
version was a maximum and no additional oxidation of any specie measured oc-
curred as temperature increased. On the other hand, below l200°F conversion
was nil. On the average, nitric oxide concentration was not affected by the
Model V reactor even though its concentration was found to correlate with
CO and HC global oxidation rates determined in a separate study described
later. This apparent paradox may be explained, at least in part, by the glo- .
bal rate assumptions themselves.
Variations in composition and temperatures within the reactor show that
maximum .conversion was undoubtedly mixing limited during hot steady operation.
Exper.iments in which the air was injected steadily using a critical flow ori-
fice strengthened the mixing limitation conclusion. Low conversion during
warm-up suggested that the reactor was primarily rate limited during this mode
of opera ti on.
I.
Under certain nonoptimum conditions of air injection and temperature,
olefin and aldehyde compounds emitted from the reactor increased even though
total hydrocarbons decreased. This increase was relative to the emissions
without the after-reaction afforded by the thermal reactor when the injected
air was terminated. The aldehyde increase was deemed potentially serious. A
tenfold increase was observed in one test. Olefin increase was typically
20-30% under these nonoptimum conditions.
Our conclusion is that under warmed up conditions and especially as the
reactor temperature approaches l600°F, maximum conversion is mixing limited.
Thus mixing simulation must be a key aspect in any steady-state simulation
2
-------
model. In contrast, during warm-up when temperatures are below 1200°F, reac-
tors are rate limited as a result of heat transfer from the hot exhaust gas
to the cold reactor surfaces. Future reactor designs should stress improved
mixing and reduced thermal inertia and heat loss.
Concurrently with the multicylinder engine study, a single cylinder CFR
engine-reactor study was undertaken to determine gross hydrocarbon, carbon.
monoxide, and hydrogen oxidation kinetics in actual engine exhaust under the
controlled conditions possible with a single cylinder engine and reactor. The
rate expressions determined were used in the computer models developed in.
Phase II.
The single cylinder thermal reactor was designed to be a continuously
stirred tank reactor (CSTR). A helium tracer hot-wire anemometer technique
was employed to assess residence time distribution. It indicated design
changes needed to approach CSTR behavior. Rate equations were formulated
which correlated CO oxidation rate with CO and 02 concentrations in one case
and with CO and 02 and NO concentrations in the other; the latter providing
a slightly better correlation. Reaction order was low, about 1/4 in either
case. Hydrocarbon oxidation rate was correlated with hydrocarbon, oxygen,
and nitric oxide concentration in one case, and additionally with CO in the
other, the latter providing a significant improvement. Reaction order was
between one and two in these hydrocarbon correlations. Hydrogen oxidation
data were quite scattered and a zero-order rate expression was selected to
predict the observed resu~ts. Water vapor was not included in these oxidation
correlations since water vapor concentration is relatively high and constant
in engine exhaust. A near zero-order dependence is the result in the global
correlations.
PHASE II.
COMPUTER MODEL DEVELOPMENT
The simulation efforts have been divided into two main areas of reactor
performance: steady operation and warm-up. The primary goal of the steady
operation effort has been the correct implementation of mixing imperfections
whereas the primary goal of the warm-up study has been to describe the start-
up of a cold reactor.
The warm-up simulation consisted of a program termed IRTEIvIP" which ac-
cepted warm-up of an arbitrary number of metal surfaces in a reactor and which
accepted values of gas temperature from a simple stirred tank kinetics pro-
gram. This approach assumes that conversion during warm-up is reaction rate
(temperature) limited rather than mixing limited. Warm-up simulations have
been run using steady-state reactor inputs. For the warm-up computations,
steady mass averaged reactor exhaust inputs were found to yield results vir-
tually identical to those obtained with staggered pulsed inputs characteristic
of single or multicylinder gasoline engine exhaust. To speed computation, the
3
-------
rate data of Phase I were fitted with zero-order expressions. This did not
affect the predicted time to light off, but did give a more abrupt light off
than observed experimentally. Reasonable correlation with the results of
Phase I were obtained. It must be noted that all warm-up runs, both experi-
mental and calculated, were made with a constant (or nearly ~o in the experi-
mental runs) fuel-air ratio. Thus warm-up rates and light off times do not
reflect conventional cold start choked engine operation. Choked operation
would be expected to accelerate the warm-up process. Rather, our results are
closer to simulating a hot start where the choke is off.
The simulation of steady-state performance encompassed several programs
depending on the sophistication desired. Initially a program termed "EXHAUST'"
was developed. It predicted the performance of a stirred tank reactor and
was capable of accepting staggered pulse-type exhaust inputs. Studies in
Phase I soon suggested that steady performance was mixing limited. Conse-
quently, this aspect was added to the simulation. Since both macromixing
(residence time distribution) and micromixing (localized reactant segregation)
are important, our simulations have included both. .
The first generation of programs incorporating mixing limitations assumed
a perfectly macromixed reactor with imperfect micromixing. Three levels of
capability were developed using a random coalescence mixing model. The most
complicated was MICROMIX I which treated the (batch) kinetics occurring in a
single packet or cell with generality and employed multiple-step integration.
A more economical model to run, MICROMIX'II was restricted to combustion re-
actions and used a single step integration for updating projections. The
simplest and fastest was MIXONLY (several versions), which assumed very fast
reactions which go to completion. Here, conversion was limited by mixing only.
The second generation of programs dealt in addition with imperfect macro-
mixing. Initially efforts were aimed at developing a generalized program in
which an arbitrary residence time distribution could be entered to simulate a
particular reactor configuration. For this work a model for a micromixed
limited plug-flow reactor was developed "MMPF." This general approach was
subsequently abandoned in favor of a pattern of flow (POF) model which simu-
lated the reactor with a series and parallel combination of stirred tank and
plug~flow elements. The patterns of flow model used with one of the micro-
mixing programs and appropriate rate expressions is the final package recom-
mended for simulating real steady reactor performance. The degree of micro-
mixing may vary from element to element. The program may be used with stag-
gered pulsed inputs and these effects become more significant as the residence
time distribution departs from that for a stirred tank.
~.
-------
PHASE III.
SPECIAL INSTRUMENTATION DEVELOPMENT AND MEASUREMENTS
A.
Gas Analysis
Several gas analysis instruments and procedures were constructed or de-
veloped in the course of this program. These were:
1.
Hydrocarbon class analysis by subtractive columns~discussed herein
in Detailed Progress - Phase III.
2.
Hydrogen concentration by thermal conductivity-discussed in the
Second Annual Progress Report.
3.
Aldehyde analysis by DNPH.
l.t.
Light hydrocarbon identification by gas chromatogra.ph-discussed
herein in Detailed Progress - Phase III.
As indicated, numerous experimental
above instrumentation were included
Reports as well as in this report. .
results and procedural details for the
in the First and Second Annual Progress
B.
Exhaust Velocity Measurement
A laser-schlieren technique has been developed to measure instantaneous
exhaust gas velocity. Successful results were obtained by photographing the.
schlieren image of an exhaust stream eddy passing through the exhaust pipe.
Results from a firing single cylinder CFR engine at 600 and 1000 rpm, wot,
showed instantaneous exhaust velocity reached about 200 ft/sec with flow re-
versals reaching 60 ft/sec midway through the exhaust process. Similar ef-
forts to measure instantaneous exhaust temperature by detecting the passage
of spark-induced pressure waves did not prove successful.
5
-------
MAJOR CONCLUSIONS
Although the automotive-type thermal reactor is similar to classical
chemical reactor models, a number of imPortant differences arise. These are:
(1) the staggered pulse-type segregated feed, (2). the numerous reacting
species in the feed stream, (3) the importance of transient low temperature
rate limited operation, and (4) imperfect mixing within the reactor. There-
fore, the complete reactor simulation must not only account for the effects
of temperature, composition, reaction rate, residence time, and heat loss,
but also provide for the above four additional factors. In addition the simu-
lation must provide for a description of the often complex reactor and heat
transfer geometry required in multicylinder engine applications. The experi-
mental and analytical results of this study have shown that:
1. Under steady warmed up conditions, oxidation of exhaust combustibles
can be predicted reasonably ~ell by the simulation as temperature, feed com-
position, and residence time change. The simulation is most useful for deter-
mining directions for design modifications.
2. Peak conversions of exhaust hydrocarbons and carbon monoxide can
reach 95% in the duPont Model V reactor. Conversion is ultimately precluded
from being complete by imperfect mixing. Both theoretical and experimental
results support this conclusion.
3. The simulation has shown that the character of the pulsed staggered
exhaust inputs to the reactor can greatly affect oxidation of combustibles for
reactors which are not well macromixed.
)~. 'rhe simulation results show virtually
exhaust port. This arises from segregation of
the port and the short residence time there.
no oxidation occurring in the
injection air and exhaust in
I
5. Experimental results showed that reactive hydrocarbons and aldehydes
mayor may not be largely eliminated in a thermal reactor and, in fact may be
. increased under certain nonoptimum conditions, even while total hydrocarbons
have decreased. .
6. For air-injected reactors, a mixing volume followed by a plug-flow
element is expected to be an effective reactor configuration.
7. Experimental time to light off may be predicted reasonably well by
a simulation at least for the unchoked constant mixture ratio cases explored.
n.
I\apid react.or w:J,rm-up i:::; enhancer] b.v:
6
-------
a.
Low thermal inertia of reactor parts and minimum heat losses.
b.
Maximization of exhaust gas temperature through, for example,
retarding engine spark timing.
c.
Maximization of exhaust combustibles through severe engine
choking at start-up and thereafter.
d.
Diversion of cool injected air until reactor temperature reaches
l200°F, a typical light-off temperature. This last conclusion
applies to an unchoked or lightly choked engine.
9. Results from the stirred tank experimental reactor operating on ac-
tual exhaust have yielded reaction orders for exhaust combustibles which are
considerably lower than literature values.
10. A reasonable estimate of mixing intensity
data. Reactor and engine dimensions, together with
yield upper and lower bounds on mixing intensity.
can be made from design
flowrate information,
11. The extent of conversion at high reactor temperatures is recommended
as a design aid to indicate the thoroughness of mixing of exhaust and injected
air within the reactor. Retarding the spark at a fixed mixture ratio and air
injection quantity, the approach used in Phase I of this report may be used
. .
to increase reactor temperature for this mixing assessment.
.,
7
'. ,
-------
AREAS FOR FUTURE WORK
Results obtained thus far suggest the following areas for future study:
1.
Further verification of the model with other reactor designs.
.)
,-.
Effect of severe choking or hot-spot ignition on warm-up time for
an experimental engine reactor system.
:3.
Effect of fuel hydrogen to carbon ratio on warm-up.
l~.
Optimization of reactor warm-up through programmed changes in engine
operating variables.
,- .
).
Reactor performance and optimization for Wankel engines.
8
\
,
-------
DETAILED"PROGRESS - PHASE I
MULTICYLINDER AND SINGLE CYLINDER ENGINE MOUNTED REACTOR
EXPERIMENTAL EVALUATIONS "
""
9
-------
A.
MULTICYLINDER CONVENTIONAL REACTOR
1.
Objecti ves
The overall objectives of the multicylinder engine reactor study were:
(1) to determine the emission characteristics of a typical engine-reactor
system operating at various conditions on a dynamometer test stand during both
warm-up and steady state operation; (2) to determine concentrations of perti-
nent chemical species and classes entering, within, and exiting the reactor;
(3) to explore factors which limit thermal reactor performance; and (4) to
obtain thermal reactor data against whith the computer mode could be tested.
2.
Experimental System
8..
ENGINE-REACTOR SYSTEM
A production Chevrolet 350 in.3 v-8 engine with duPont Model V exhaust
reactors was used for the multicylinder work. Selected engine characteristics
,are listed in Table 'I. The engine was installed with the vehicle exhaust
system.
The duPont Model V reactor is shown in Figure 1. It is mounted in place
of the production exhaust ,manifold. One reactor is used for each bank of the
engine. Figure 2 shows a schematic of the type V reactor. The reactor con-
sists of an outer shell in which is mounted a tubular core and a radiation
shield to insulate the hot core from the cooler outer shell. Air is injected
into each exhaust port counter to the exhaust flow. The exhaust gas-air
mixture is swept into the reactor core during the exhaust stroke as the arrows
suggest. When conditions are favorable vigorous chemical reactions occur
which convert hydrocarbon and carbon monoxide compounds to carbon dioxide and
water vapor. The hot gases still reacting then flow around ,the radiation
shield into the exhaust system. References 1-5 describe the reactors and
their performance on vehicles in more detail. Key characteristics are listed
in Table II.
In our tests, stainless steel quench coils were installed in each entrance
port of the reactor. These provide cooling of the exhaust and suppression of
exhaust after-reaction. The composition of the cooled mixed unreacted gases
leaving the exhaust reactor has been used as a measure of the reactor input.
F.tlch coil was made from a 4-'ft length of 1/8 in. stainless steel tubing
I'
\
, ')-.} .~ J'\, r\
11
-------
TABLE I
CHEVROLET ENGINE CHARACTERISTICS
Model year
Displacement
Compression ratio
No; of cylinders
Bore
S tr oke
Con. rod length
Firing order
Fuel specification
Carburetion
Emission control
.Rated power
Rated torque
Exhaust opening.
Exhaust closing
Intake opening
Intake closing
Left exhaust manifold
Right exhaust mainfold
Exhaust port volume
TABLE II
1969
350 in.3
9.0:1
8
4.0 in.
3.48 in.
5.7 in.
1-8-4- 3-6- 5-7-2
regular
Rochester 2-bbl
AIR
255 BHP at 4200 rpm
365 lb ft at 1600 rpm
66° BBC
32° ATC
16 ° BTC
70° ABC 3
13 lb/64.6 in.
13.25 lb/73 in.3
3.66 in.3/cyl
DuPONT TYPE V REACTOR CHARACTERISTICS
Year received
Overall length
Overall diameter (exc. port)
Overall internal vol) flange-to-flange
Inner core volume
\AI e igh t
Primary material
Maximum recommended core temperature*
1969
21.37'5 in.
'5.'5 in.
.259 in.3/reactor
60 in.3jreactor
26 lb/reactor
310 stainless
. 1750°F
-)(°Materialsare available which permit higher temperature
operation.
,r
12
-------
Figure 1. DuPont type V reactor mounted on the Chevrolet 350 in.3 engine
for test in Room 243 of the Automotive Engineering Laboratory.
..EXHAUST GAS:l r- fOU:; SHELL
\~/~\~/ ~
- ~--- ¥ 'a.. ---G--+ _/
-
RADIATION
SHIELD
CORE
TO EXHAUST SYSTEM
-
Figure 2. Type V duPont exhaust manifold reactor.
Figure courtesy duPont Corporation.
.
-------
through which cold water at 65 psi circulated.
drop could be obtained with the coils.
Typically a 2000 temperature
An engine change required for optimum reactor operation involved mod-
'ifying the intake manifold heating system. The conventional exhaust gas cross-
over passage entrances were blocked. Instead, hot water was routed to the
'crossover. This conserved reactor energy while providing manifold heat. An
intake manifold properly modified was supplied by duPont.
One of the reactors was modified to accept quartz windows at the center
of each end of the reactor. This provided a straight optical path through the
hot core. One window was large enough (1-3/4 in. dia) to allow a visual in-
spection of the combustion process. The other window was smaller (3/4 in. dia).
Additional photographs of the reactor were included in the First Annual Progress
Report. " '
b.
INSTRUMENTATION
(1 )
Engine
Engine power was measured by a Westinghouse 200 hp electric dynamometer.
Fuel flow was measured by a General Motors displacement-type burette system. ,
Fuel-air ratio was controlled by pressurization or evacuation of the carburetor
float bowl. Air flow was measured by a 1000 CFM Meriam laminar flowmeter. A
large tank was mounted above the engine to minimize pulsation effects. Mercury
manometers were used to measure the intake and exhuast system average pressures.
Continuous gas sampling taps were installed at each port, at the exhaust wye,
and at the tailpipe. Various thermocouples measured engine and reactor local
temperatures. .
(2)
Gas Analysis
Gas analyses were made with, a variety c>f instrumentl3.tion. Table III
lists this equipment. The'02 analyzer as well as nondispersive'IR analyzers
for CO, C02' NO, and HC have been incorporated into a large semi portable cart.
Additional details of the gas analysis system including schematics are included
in the First and Second Annual Progress Reports.ll,18
3.
Experimental Results
In the course of this investigation a variety of experimental data have
been gathered on the Chevrolet 3~0 in.3 engine and the duPont Model V reactor.
14
-------
Specie
Carbon monoxide
Carbon dioxide
Nitric oxide
Hydrocarbon
Hydrocarbon
02
Aldehydes
Hydrocarbon
classes
Individual
hydrocarbons
Hydrogen
TABLE III
GAS ANALYSIS TECHNIQUES
Technique
NDIR1,2
NDIR1,2
NDIR1,3
NDIRl
FID4
Amperometr:lc
DNPH'5
Subtracti ve
column plus FID
Gas chromatograph
Thermal conductivity
Manufacturer
Range
O-lCP/o
0-1'7fl/o
0-4000 ppm
0-1000 ppm
0-3000 ppm
0- '5% or 0-2'5%
Beckman Inst. Model 315A
Beckman Inst. Model 315A
Beckman Inst. Model 31'5A
Beckman Inst. Model 31'5A
Beckman Inst. Model l09A
Beckman Inst. Model 71'5
Wet chemical and Bausch
& Lomb Spectronic
20 spectrophotometer
Homemade--after Sigsby (Ref. 6)
(see also Ref. 11, p. 27 and
Phase III of this report)
Perkin-Elmer 800 (see Phase III
of this report)
Homemade (discussed in
Ref. 12, p. 8'5)
0-'7fl/o
l.
2.
3.
4.
:;.
NDIR - Nondispersive infrared.
Orsat used as check of calibration gases.
Modified Saltzman used as check of calibration gases (Ref. 10)
FID - Flame ionization detector.
DNPH - Dinitrophenylhydrazone wet chemical. method--colorimetric
(Refs. 7-9)
procedure
Table IV summarizes the work performed during the first and second year, and
where discussions can be located.
The present report contains data and analyses for work performed during
the final year. The topics covered herein are:
.warm-up limitations on reaction
.mixing limitations to steady performance
.reactor combustion luminosity
In some cases the data have been corrected for the dilution effect of air
injection. This correction was made based on a dry exhaust carbon balance with
and without air injection. Emission results corrected for dilution are so
. des igna ted.
1'5
-------
TABLE IV
MULTICYLINDER ENGINE-REACTOR PERFORMANCE
Type of Test
Baseline engine performance and emissions
Varying air/fuel ratio, spark timing,
speed, and load
steady-state engine-reactor performance
Hydrocarbon and carbon monoxide
oxidation, hysteresis effects
Nitric oxide emission
Aldehyde emission
Reactor mixing
Air injection distribution
a.
WARM-UP LIMITATIONS ON REACTION
Annual Report
Reference
1st, pp. 4-8
2nd, pp. 8-10
2nd, p. 10
2nd, pp.lO-ll
2nd, pp. 11-13
2nd, p. 13
Warm-up is an important mode of thermal reactor performance because of the
emphasis on cold start in Federal vehicle exhaust emission procedures. In
order to simulate warm-up on our dynamometer tests, the engine was allowed to
cool overnight (16 hr) to room temperature (about 70°F). For each test the
engine mixture ratio, throttle, and spark settings were established the after-
noon proceeding the test. They were adjusted to give 30 BHP at 1200 rpm for
the warmed-up engine. Twelve tests were run with various mixture ratios,spark
tiniings, loads, and air injection rates (see Table V). Because relatively
constant mixture ratios were used results do not reflect conventional choked
engine operation.
In order to measure reactor gas and metal temperatures during warm-up,
thermocouples were installed in the right-hand reactor; . Four chromel/alumel
immersion-type thermocouples were attached to the reactor inner surfaces. These
had a sheath diameter of 1/16 in. and a response time of approximately 1/4 sec.
A fifth identical but shielded couple was installed to measure gas temperature.
. .
Three additional couples were attached to measure the outer skin temperature
of the outer skin temperature of the reactor. The thermocouple locations are
shown in Figure 3.
16
-------
, -
. 654321 7 B
~,l
-------
~ 1200
a..
a..
6
:z
1000
~ 800
«
x
4J
::c
~
~ 600
'l>, - t-'
())
V)
z
a
co
a:::
5400
a
a:::
Q
>-
:r::
e 200
u-
o
4
1600
U-
1200 0
4J
a:::
::J
I-
«
, a:::
800 ~
~
4J
I-
400
25
Figure 4. Hydrocarbon, CO, and NO emissions as well as reactor centerline gas tem~e~ature and o~~er skin
temperature versus time for a 10°F cold start. Engine conditions were set at 1200 rpm, 30 BJP, MET s)ark
12. S: , air/fue, ratio, air in, ection fraction of 0.3.
REACTOR CENTERLI NE
-----CII:IIII::IIIII------
. GAS TEMPERATURE
3
c /;
~ I<
~2 I
a.. I
8 ,
I'
REACTOR OUTER
---
--
,..,"------ CASING TEMPERATURE
~",
-","""
.----"--'
---
o
5
10
TIME. min
-------
140
;1::
- 13C i- .. O. 7
.c
LJ
.:::>
0'
Q::
0
I-- 120 - e:::
0.6 :r:
. I
a..
:r:
co
. ~..,. -
r-o 0 ~
\0 0.5 co
I-- -'
:::> .CO
~
11
e:::
-------
about 5 min and stabilization was not achieved until nearly 12 min. Hydro-
carbon reduction preceded CO reduction in time. The observed 'fariations in
NO were thought to arise from the slight variations in mixture ratio shown
in Figure 5. These emission results are typical of all rich mixture operation
with air injected. As Table V shows time to light off decreased as mixture
ratio was richened or as reactor input temperature was increased by retarding
the timing. Low reaction rate during reactor warm-up severely limits oxidation.
It was typical observation that little reaction occurred until gas temperature
reached 1200°F.
. Figure 6 shows emissions for a similar test run at 17:1 air/fuel ratio
without air injection. This mixture ratio was selected to give the same.
reactor product distribution as the preceeding test at 12. '5: 1; namely,. the
products of a 12;'5:1 engine air/fuel ratio plus 30% air injection. Figure 7
shows the temperature results. No light off occurred on this test. It is
noteworthy that even though reactor temperature rose to 1350°F, relatively
little hydrocarbon oxidation occurred. The result is typical of lean operation.
Light off does not occur since the heat release of a few hundred ppm hydrocar-
bons is very small.
Figures 5 and 8 show the engine
for these rich and lean tests. This
and excessive heat loss to the walls
engine is fully warmed up.
torque and BSFC as the engine warmed up
result can be attributed to high friction
of the combustion chamber before the
One final observation is that reactor skin temperature reached 500-600°F
in these tests. This was a typical temperature for the duPont reactor. Tem-
. .
peratures this high on such large surfaces may pose a serious problem with
respect to evaporative losses and hot fuel handling.
Table V summarized results from several additional tests including those
discussed in detail already. From these results and the original data, one
concludes:
1.
The richer the carburetion the shorter the light off time.
377, 378, 302, 306.
Runs 308,
2.
Retarding the spark which increases reactor inlet gas temperature
shortens light off time. Runs 382, 387.
3.
The half life for HC disappearance is always shorter than that for
CO.
4.
Hydrocarbon light off can occur without CO light off.
Run 303.
The light off times observed in this study are very long compared to light off
times in vehicle mounted engines which may be only a. few seconds. The b/"sic
20
-------
2000 -6 NO AIR INJECTION
0.50 6- ~ AIF '" 17
~ 1800 /
Q.. 6/ ~------ .
Q..
-6 NO
~. 1600 0.40 / 6-
~
1400 ~ I
z
LU 6
u /
LU 1200 ffi O. 30
z
- 0 0 HC
::r:
0
LJ.... 0 0
0 5 10 15 20 25 30 35
TIME, MINUTES
Figure 6. Hydrocarbon, CO, and NO emissions versus time for engine conditions of 1200 rpm, 30 BHF, MET
spark, 17:1 air/fuel ratio, no air injection. The products in the reactor reflect the same air/fuel ratio
as the former test at 12.5:1 with 0.3 air injection fraction.
-------
1600
1400
u...
V)
LU 1200
LU
a::::
<.:)
LU 1000
Q
LU
a:::: 800
::;:)
I-
i\)
-------
19 140 0.9
0 NO AIR INJECTION
A/F!:! 17
18 120 ~6 6
0.8 - -6- -6:-------0-------.:oRQUE
0:= 6_6.
a :I 6'" 0
I- ~/ O~. . A/F
I- u.. ~.
co
u.. => ...J 0
0 ....0-0/
J\) e:::: e::::
\>I
-------
TABLE V
WAIDIr-UP TEST RESULTS
Reactor * Ligr-" t Dff Air Spark . Harmed HC Disappearance, CO Disappearance,
Run Engine, Centerline Time, Injection Up, half life, mini half life, mini
No. A/F Adv. .
Temp , of min Fraction hp final level, ppm final level, %
301 12.5 1650 15 .36 MET 30 11/15 19/0.2
302 12.5 1650 8 .36 MET 30 9/4.5 ND/ND
303 12.5 1300 NE .60 MET 15 14.8/390 .NE/l.75
304 12.5. 1750 8 .2 MET 47 9/42 10/0.4
306 12.3 1540 6 .3 MET 30 7/20 9/0.35
I\)
.j::""" 11/ND
307 17.l 1325 FfE .0 20° 30 NE/ND
retard
377 13.0 1740 14 .3 ViET 30 ND/ND 17/0.32
378 13.0 1780 14 .3 MBT 31 ND/ND 18/0.4
380 13.8 1575 22 .3 MET 30 10/20 23/0.45
382 13.1 1730 4 .3 200 30 2.3/52 3.3/0.25
retard
385 13.1 1660 16 .3 MET 30 12/26 15/0.4
387 14.3 1520 ~o .43 200 30 2/28 3.5/0.28
retard
. :.."E - no change. evident 1'::0 - no data
*Stabilized
-------
difference is that. in the vehicle the choke provides
tially. Our warm-up results are a better simulation
the choke is off.
a very rich mixture ini-
for a hot start in which
Our conclusion is that when adequate oxygen is present, low reaction rate
primarily limits conversion of HC, CO, and H2 during warm-up.
b.
MIXING LIMITATIONS TO STEADY PERFORlf~NCE
The Second Annual Progress Report contained curves of emission concentra-
tion versus air injection fraction. Figure 9 .reproduces a typical curve for
rich engine operation. Emission values were corrected for air injection using
an exhaust carbon balance with and without air injection. Note that even under
optimum conditions, carbon monoxide and hydrocarbon emissions are not neces-
sarily zero. In such tests, the reactor operating point is a balance between
the extent of reaction as determined by reaction rate, residence time and
mixing and the temperature rise due to oxidation. References 13 and.14 develop
the theory. The lack of complete combustion at the highest temperature was
concluded to ariSe from incomplete micromixing of exhaust combustibles and
oxyge n.
To explore the effect of incomplete mixing on extent of reaction, tests
were run in which the spark was retarded while keeping fixed all other variables
including mixture ratio, throttle, and speed. This served to heat up the
reactor gases to a.point where reaction rate was no longer a limit to conversion
and any unconverted carbon monoxide, hydrocarbons, or hydrogen was deemed to .
result from incomplete mixing. As a design aid the extent of imperfect mixing
. .
may be judged by the conversion efficiency plataeu attained at the highest.
temperature. . Theoretical support for the existence of a mixing limited plateau
is included in Detailed Progress - Phase II.
( 1)
Rich Carburetion Plus Air Injection
For rich reactor studies, air was injected into the engine exhaust port.
A production Chevrolet air manifold was used and supplied with shop air. Long
high volume lines were used to simulate the low pressure system typical of a
vehicle.
Figure 10 shows extent of conversion of HC, CO, and H2 as a function of
reactor temperature. Input CO was 1.91%. Reactor temperature was varied by
changing the spark timing. Initially the reactor was warmed to l640°F by
retarding the spark to 10° BTC. The spark was then advanced incrementally to
cool the reactor. Maximum advance in this test was 30° BTC which was MBT
Reactor input was taken to be the well mixed CO, HC and H2 concentration emitted
from the reactor at 30° spark advance with cooling coils. in the exhaust to
25
-------
~
o
ci 5.0
u
8 4.0
~
frl
a:: 3.0
0::
o
u 2.0 .
I~--.-
Figure 9.
fraction.
)0 fueL
~
a.
a.
o
o
.2
.4
.6
.8
F
7.0
6.0
1600
1500-
lL.
o
-
REACTOR TEMP.
1400 a!
:!:
w
1300 t-
a::
o
1200 t;
.«
w
1100 a:: .
o
o
.2 .4 .6
. AI R I NJECTION FRACTION, F
.8
Exhaust emissions with duPont reactors as a function of air-injection
1200 rpm, 30 hp, 12.5:1 air/fuel ra.tio, MET spa.rk of 33°. Indolene
26
'~, it
-------
1.0
o 0.8
w.
I-
a:::
w
~ 0.6
o
u
z
Q 0.4
I-
u
«
a:::
La.. 0.2
o 1200
HC
14° 12"10° -SPARK
16° ADVANCE
Nominel Reactor Input
HC 820 ppm
CO i,91 %
CO2 13.57%
O2 0.65%
H2 0.52%
. rhair = 217lbm/hr
rhfuel = 16.5Ibm/hr
Air Injee. Free. ~ 0.1
30° 25° 1400 1500 1600 1700
REACTOR TEMPERATURE, of
H2
Figure 10. Extent of reaction vs. reactor temperature. Engine condi-
tions 1200 rpm, 30 hp at 30° BTC spark timing. Total engine air flow
217 lbm/hr and fuel flow 16.5 lbm/hr. Air injection fraction approxi-
mately 0.1.
27
-------
suppress after-reaction. Extent of conversion is defined as one minus the
ratio of emitted to input specie concentration. Of significance is the extent
of reaction at the highest temperature where it is reasonable to assume the
reactor is not kinetically limited but only mixing limited. In this test the
experimental limit of conversion was 82% for CO, 95% for HC and 100% for
hydrogen.
Figure 11 shows similar resul ts for richer engine operation, 2.8% CO
input to the reactor but with the same air injection fraction. With more CO
the extent of conversion curves were shifted to the right with respect to
temperature. CO conversion was only 75% and HC 93% complete in the limit in
spite of the fact that the overall reactor mixture ratio was slightly leaner
than chemically correct. Hydrogen was reacted completely. .
Fi~ure 12 shows results for operating conditions similar to Figure 11 but
with twice as much air injection. An increase in air quantity increased reac-
tion rate and shifted the extent of reaction curves to the left and upward.
CO conversion was 93%, HC was 97% and H2 was 100% complete. One can conclude
that when mixing is poor, flooding the reactor with excess air will always
help conversion if the temperature is maintained at a given level.. Poorly
mixed reactors are expected to require more air and more spark retard to
achieve a given level of performance. .
The difference between the extent of conversion for CO and H2 at the limit
is thought to arise from the fact that because of a higher reaction rate, the
hydrogen is consumed prior to the CO, closer to the reactor entrance. As a
result the hydrogen reacts in a more oxygen enriched environment and thus
reacts more completely. Note that the reported extent of conversion for hydro-
.carbons is inaccurate. This is because spark timing affects HC concentration
emitted from the cylinder and the HC concentration at each retarded timing
without after reaction was not obtained. Thus the extend of conversion for
HC with retarded timing is overestimated since it is based on the high quenched
value. If one makes the reasonable assumption that the HC emitted from the
cylinder decreased by less than a factor of two due to spark retard over the
range of this experiment then the true fraction HC unconverted is no more than
twice the observed value and for the data of Figures 10, 11, and 12. the CO
oxidation is not only apparently less complete but is actually less complete.
than the HC oxidation.
Consequently of the three choices, incomplete carbon monoxide oxidation is
. the most reliable indicator of poor mixing in a rich thermal reactor for the
type of experiment described herein. As a more general conclusion, the spark
retard method is recommended for assessing the goodness of mixing in a rich
thermal reactor with CO conversion as an indicator.
28
-------
1.0
c 0.8
w
......
a::
w
~ 0.6
o
u
z
52 0.4
~
u
-------
1.0'
c 0.8
LJJ
....
a::
LJJ
>
z 0.6
o
u
z
o
.... 0.4
u
-------
( 2)
Air Injection Flow Characteristics
The lack of mixing between combustibles and air may be thought of as
arising from two sources, incomplete micro- and macromixing. r,ommonly air
and exhaust do not enter the reactor at the same time and the exhaust compo-
sition varies during the cycle. This reactant segregation naturally results
from the exhaust and air injection flow characteristics of reciprocating en-
gines. A high degree of micromixing within the reactor is required to homog-
enize the reactants and achieve complete combustion. The incomplete micromixing
is one cause of reactor inefficiency. The other source of incomplete mixing
arises from the patterns of flow within the reactor coupled with the segregated
input. Depending on the residence time distribution within the reactor, it
may not be possible for various elements of gas to intermix in spite of a high
level of micromixing. This effect, termed incomplete macromixing, is most
evident for a plug flow reactor. Reactants which enter early are precluded
from mixing with those entering later.
The segregation of air and exhaust arise from the unsteady exhaust flow
characteristic of reciprocating engines and the air flow variations of low
pressure continuous air injection systems. 'The exhaust volume flow variations
are indicated by the exhaust velocity variations measured in Phase III, and
shown in Figure 28 of that section.
One measurement was made of the variation in velocity of the injected air
in the air injection tube under running conditions. For this a hot-wire
anemometer was installed in the air injection tube for cylinder 1. The wire
was located about 5 in. from the discharge end of the tube. A 0.0002-in.
diameter tungsten wire was employed. The instantaneous pressure difference
between the air injection manifold and exhaust port was also measured ( A
Statham strain gage transducer with a range of ~ 5 psi peak to peak was used.)
Figure 13 shows the pressure difference between the air injection manifold
and the exhaust port as a function of crank angle. Figure 14 shows the calcu-
lated mass flow based on the velocity measurements made by the hot wire
anemometer. Constant air density was as summed.
As a result of the blowdown process in cylinder 1, Figures 13 and 14
show a pressure ahd flow reversal occurred in the air injection tube. Some
slowing of the air flow appeared to occur also as a result of rapid explusion
of exhaust gas when the pistion velocity reached its maximum value. Some flow
perturbation is noted as well from events in other cylinders. In these situ- .
ations the air is diverted to the other three exhaust ports. These measurements
show that the air injection flow lagged the engine events by about 4"5°.
Indicated on Figure 14 are the measured average value of air injection
flow (computed from one-eighth of the known air and fuel flow to the engine
and air injection fraction) and the integrated average of Figure 14. Their
difference is about 10%.
31
-------
3
#1
EXH. OPENS t
~7
3
t
~ #1 MAXIMUM PISTON VELOCITY
5
+
7
+
2
~3
C) --L-
:I: 0
Z 180 270 360 450 540 720
CL. -I CRANK ANGLE
\J.I
-------
3
a:
x
.......
:E
m 2
....J
-
\>I 3:
\>I 9
LL
en I
en
ct
:E
/ MEASURED AVERAGE / CYLI NOER
/ /AVERAGE OF THIS CURVE
o
I
450
540
630
720
TOC
270
360
CRANK ANGLE.
90
180
Figure 14. Mass flow through air injection tube for cylinder number 1.
. 350 CID Chevrolet, 1200 rpm, 30 hp, MBT spark, air injection fraction
0.3.
-------
The variatibns in air injection flow and particularly the slowing or
reversal of air flow just when exhaust flow is maximum is a major factor leading
to segregation of oxygen and combustibles. For optimum reactor performance
the ratio of air flow to exhaust flow should be nearly constant at each crank
angle. .
(3)
Lean Carburetion~No Injection
Figure 15 shows the extent of conversion for a lean engine without air
injection. Exhaust CO was very low (less than 3000ppm and difficult to
measure with NDIR analyzer of this experiment) and H2 was zero. The conditions
were chosen such that the reactor air-fuel ratio was the same as that of
Figure 12 where air was added to a rich mixture exhaust. Compared to Figure
12, the HC entent of conversion curve was shifted to the right but reached the
same limiting conversion of 97%. With lean operation, it was anticipated that
the conversion would be complete since without air injection, oxygen is well
mixed with the exhaust. Perhaps the result can be attributed to imperfect.
mixing arising in this case from a uniformly distributed oxygen quantity being
mixed with a nonuniform hydrocarbon emission pr~file whose span may be a factor.
of 10. The hydrocarbon containing boundary layer is expected to be quite rich
in hydrocarbons since a portion of its contents arises from the evaporation
of liquid droplets which impinge and collect on combustion chamber surfaces
and deposits. Consequently even a lean reactor may benefit from air injection
especially if it is timed to coincide with the end of the exhaust stroke where
HC concentration is high.
A very interesting result of this lean reactor experiment is shown in
Figure 16. . Plotted on a semilog scale are the CO, HC. and oxygen conc.entra-
tions. The oxygen in the exhaust was 2.6'5%. The oxygen value plotted in
Figure 16 is the actual oxygen reading minus 2.0')0/0 excess. 02 not required for
complete combustion of the emitted CO and HC. Plotting in this way amplifies
the fluctuations in oxygen.
The low temperature (975°F1 points were measured with exhaust cooling
coils turned on to suppress after-reaction and are assumed to be the reactor
input. As reactor temperature was increased. CO emission first increased and
then decreased. The CO increase is thought to arise from the HC oxidation in
which CO is an intermediate. HC oxidation proceeded more rapidly above 1300°F.
but the CO was not rapidly oxidized to C02 until a temperature above 1400°F
was reached in the reactor. . .
The partial oxidation of unburned hydrocarbons to CO in the exhaust may
be one source of the exhaust CO commonly found in lean running engines. Two
other sources are mixture maldistribution and slow atom recombination reactions
during expansion leading to nonequilibrium CO concentration. Normally maldis-
tribution masks the other effects.
34
-------
1.0
~ 0.8
.-
a::
w
>
5 0.6
u
z
o
~ 0.4
u .
«
IX:
Ii.
0.2
o
HC
1200
Nominal Reactor Input
HC 630ppm
CO 0.10%
CO2 13.29%
H2 0.0%
O2 2.650/0
mair = 205 Ibm/hr
mfuel =13.8 Ibm/hr
No Air Injection
1300 1400 1500. 1600
REACTOR TEMPERATURE~ of
1700
Figure 15. Conditions similar to Figure 12 except the engine is run lean
enough to provide the same reactor mixture ratio without air injection.
35
-------
10,000
x,
..........
--
----------~-~
\ *
->Ht-~02
IQOO
E
Q.
Q.
..
Z
0
-
I-
«
0::
~
Z
L.&J
U
Z
0
u
100
. r Quenched Exhaust [J
. """
. ,,-
. ,".
,,'
,,""
.,.,.""
.,.,.-
.,.,.
0--
co
0-------
--
--
-.....
.......,
, .
......
HC
NOTE:
0: represents total oxygen
minus oxygen not needed
for total conversion.
10900
1000
1100 1200 1300 1400 1500 1600
REACTOR TEMPERATURE, OF
1700
Figure 16. Effect of reactor temperature on the concentration of 02' HC,
and CO in the exhaust of a lean running engine, 10/0 ::: 10,000 ppm. oxidation
of HC leaves CO as a product at the lower temperatures. Engine conditions of
Figure l~. . .
36
-------
( 4)
Rich carburetion Plus Critical Flow Air Injection
A critical flow air injection system was incorporated by installing a
small orifice in the air injection line about ~ in. the discharge from point. .
Orifice size was adjusted until each cylinder received the same air quantity.
The shop supply was used to supply the high pressure air required. The
purpose was to improve the mixing of air and exhaust by injecting air at a
constant rate. Obviously this was a partial step since the instantaneous
exhaust flow variations were unchanged.
Tests were run to explore conversion gains possible with the better
mixing provided by the critical flow system. Figure 17 shows the fraction
converted as a function of reactor temperature for the critical flow' system
at an engine operating condition of 3% exhaust CO and about 0.09 air injection
fraction. Maximum conversion was H2 100%, HC 93%, and CO 86% This may be
compared to the low pressure air injection results in Figure 11 where maximum
conversions were 100%, 93%, and 75%. respectively, for a similar mixture' ratio
and air injection fraction. CO oxidation was signifi~antly improved with
critical flow air injection. At temperatures between 13000 and l~OO°F, H2
oxidation was significantly improved with critical flow injection and HC
oxidation was improved slightly.
Figure 18 shows similar results at a 5~~ increased air injection quantity
of F = .15. In the limit conversion was H2 100%, HC 98%, and CO 96%. These
data may be compared to Figure 12 which shows data for F = .2. These maximum
conversions were 100%, 97%, and 9)%, respectively. Normally an air injection
fraction of 0.2 would be expected to provide better oxidation than one of 0.15.
However, critical flow injection yielded better results at the lower air
quantity. In this test, it was impossible to stop light of.f by advancing the
spark (to 39°).
Figures 19 and 20 show additional comparisions with and without critical
flow air injection as air injection fraction was varied. The limitations of
our critical flow system precluded air fractions greater than 0.375. Note
. that with the critical flow system light off occurred at a lower air injectiQn
fraction and produced a higher temperature (less dilution), and yielded more
complete oxidation. Tn this comparison minimum CO was reduced from about 0.4%
to 0.2%, a ~rJ1/o improvement. Minimum HC emissions were also reduced from about
30 to 20-2~ ppm.
These results further demonstrate that incomplete mixing of air and
exhaust limits peak reactor conversion in the duPont reactor. The critical
flow air system increased the unformity of the instantaneous ratio of air to
exhaust by making the air rate constant. Of course the exhaust flow rate
remained variable so only an improvement was made in reactant segregation.
Some form of timed air distribution is required. to achieve perfect uniformity
of instantaneous air to exhaust ratio. Favorable results with timed air
3.7
-------
-.
"
o .6
LU
~
0::
LU
>
Z
o
u 4
z'
o
~
U
-------
1.0
300 270 220 190
H2 390. 36°
.8 HC
CO
0
LLJ
I-
~ .6
z
0
u
z
0
1-.
U
c:(
Q::
u..
u..
u..
0
a:::
-
c:(
I
1300
. --- -- -----
NOMINAL INPUT
HC 700 PPM
CO 3. 0%
C02 13.0%
02 . O. 5%
~2 1. 04%.
l\"a i r = 215 Ibm Ih r
Mfuel = in 8 Ibm/h r
1400 1500 1600 1700
REACTOR TEMP£RATUR~ of
1800
..- -~-_.~
. .
Figure 18. Same as Figure 17, except air injection fraction
increased to approximately 0.15.
39
)".
-------
1600.
1500
,
'\
\
L.L..
o
u.J
a:::
::::>
r-
< 1400
a:::
u.J
a..
~
u.J
r-
a:::
2 1300
u
<
u.J
a:::
\~
\ \
\ ,
\ \ .
\ ,.
"
'\
,
,~
.~~
0---0 Without "critical flow" air inj.
. lPe With "critical flow" ai r in j.
~
- ....~
3.0
,
~
\
\\
, \
, \
, \
\ \
\ \
\\
, ,
\'
0..0
..~~
~'I
I '
. I
I I .
/ I
. I .,
I~
a
u
8 2.0
r-
u
u.J
a:::
~
a
u 1.0
00
O. 2 O. 4 0.6 O. 8
A IR INJECTION FRACTION, of
1.0
Figure 19. Effect of air injection fraction on CO conversion and
reactor temperature. The conventional air injection system is
compared to an experimental critical flow system. Engine
conditions same as for Figure 17.
40
-'"
-------
800
V')
z
a
ca
~ 500
u
a
0::
o
>-
. :::I:
8 400
I-
U
LJ.J
0::
0::
a
u
300
200
100
900
Slight Misfire
Detected
0---.0 Without 'Icritical flow" air inj.
... With "critical flow" air inj.
o .
o
,r
II
II
II
"
II
/,/
II
,',i
j/
/ I
/ I
/ "
.....0
Q2 Q4 Q6 Q8
AIR INJECTION FRACTION, F
1.0
Figure 20., Same as Figu:re 19 for hydrocarbon conversion. .
, ,
,
\ .
~ "~I
,.' .
. ',,<,,
41
-------
. l~
injection on a vehicle have been reported by Glass. The incentive is a lower
air requirement for light off, higher reactor temperature, and b~tter conversion
of exhaust combustibles. It is antipated that mixing limitations will be
more evident with Wankel engine thermal reactor thermal reactor systems, since
the higher exhaust temperature of the Wankel will minimize kinetic limitations
to complete conversion.
c.
REACTOR COMBUSTION LuMINOSITY
( 1)
General
. 11
As described in the First Annual Progress Report, page 3, one duPont
reactor used in this study was modified to accept quartz windows at either
end. During operation where extensive carbon monoxide was oxidized, a bluish-
gray light was observed in the reactor core. Studies were made to determine
the intensity versus time of the light and also its spectrum. Overall bright-
ness as a function of time was measured with an IP-21photomultiplier. The
light emission spectrum was measured with a home made spectrometer with the
. .
assistance of Dr. Joseph Harrington of the Ford Motor Company Scientific
Laboratory. .
( 2)
Photomultipier Results
Overall reactor brightness was measured with. the IP-21
tube. The phototube was located about 18 in. from the rear
reactor and was closest to cylinder 7.
photomultiplier
of the left-hand
To the eye the flame in
a strong sensitivity to blue
angstroms.
the reactor appeared blqe-gray. The IP-21 has
light, its maximum response being at 4000 + ~OO
The upper trace of Figure 21 shows the output of the phototube as a func-
tion of time. The lower trace shows timing marks 4~o apart. As each cylinder
exhausts two light peaks arise. The first and largest corresponds to blowdown.
The second corresponds to the maximum piston velocity. At both times, rela-
tively large amounts of gas enter the reactor. Referring to Figure 21, the
left-most peak is blowdown for cylinder 7: The next peak is blowdown for
cylinder 1. Note that this has a double hump. One hump is the blowdown for
cylinder 1 and the other corresponds to the maximum piston velocity for cylinder
7.. Double humps are evident for cylinders 3 and 7 as well. The second hump
for 5 is nearly masked by the blowdown from 7.
The uneven spacing of the
opening. The location of the
shown in Figure 23. The large
pulses reflects the order of exhaust valve
peaks with respect to the cycle events is
peak from each cylinder occurs slightly after
42
-------
i
I
I
l
L
- ~ ~;i£"
CYL :tt:1
o
TDC 180
I 1
3600 5400 7200
I I I
>-
-
"en
~!
-
-'=
0'
..J
Peak -I
Cyl -7
I
-3
-3
I
-4
-5
3
Figure 21. Chevrolet 350 in. engine, 1200 rpm, 30 hp, 12.5:1 air-fuel ratio,
air injection fraction .22, reactor temperature approximately l650°F. Upper
trace: Light emission as function of time. Lower trace: 45° timing marks.
I
Pea k -I
Cyl -7
I
-2
-I
I
-3
-3
I
-4
-5
I
-5
-7
Figure 22.
Repeatability of light emission.
43
~
:,
- ..-. - .....
~-------- -'-~ -~-~-
-------
'.
CYL~ .CYL* CYL# CYL#=
1 3 5 7
0
PEAK #1 = r
CJ)
:::> 100
-------
bottom center.' The
temperature between
the photomultiplier
variations in
cylinders and
tube.
height reflect both variations in exhaust
the location of the port with respect to
Figures 22 and 24 show data repeatibility. Differences in light emission
from cycle-to-cycle for a given cylinder primarily reflect differences in gas
temperature at the end of expansion. Temperature variations result from
combustion variations in the cylinder. Figure 24 shows an often observed
phenomena of growing and diminishing overall light intensity. On this photo-
graph there are two brighter regions: The frequency of these brighter regions
,appears to be about 2 cps which is near the surge frequency of a vehicle:
Note that the light signal from cylinder 1 disappears during the low-intensity
period. Cylinder 1 is the second bltp after the TDC timing mark which is on
the lower trace. Cylinder ~ was generally the highest in this run. For this
test the photomultiplier was mounted in front of the engine, recording iight
emitted from the large front window in the reactor.
Figure 2'5 shows additional data similar to Figure 22. The second bright
region during the exhaust of cylinders 1 and 3 is very evident. Note also
that cycles with lower peak light intensities began emitting later in time.
Cylinders which emit strongly tended to be strong each cycle.
Upon starting the engine, there is no light. After a minute 'br so, an
occasional flicker is noted. The flicker frequency gradually increases in an
apparently erratic manner until a relatively steady light is obtained. Even
at steady state however, there is a perceptible flicker. This arises fron
the uneven frequency of exhaust valve opening which leads to one brighter and
one darker period per two revolutions of the crankshaft. At 1200 rpm, the
test condition, this leads to a 10 cps flicker which is easily detected with
the eye.
(3 )
Spectral Studies
A spectrum of the light emission was obtained from the spectrograph.
Calibration was made with a mercury lamp. Figure 26 shows a typical result.
Maximum intensity was near 4000 angstroms. It was surprising to find that all
the detectible lines were lead or lead oxide. Perhaps engines running on
unleaded fuel do not have the high intensity luminous reactions observed in
these tests. Running for 20 hr on unleaded gasoline did not diminish the
light emitted from our reactor. Perhaps too much lead had accumulated in the
engine and reactor to be eliminated in this short time.
4'5
-------
["
~
-
.-
f/)
~
C'
':J
2 CPS
I
TOC
CYL #1
Figure 24.
Repeatability of light emission.
Exhaust from
cylinder 7
I
TOC
CYL" I
Figure 25. Repeatability of light emission.
Timing marks on lower trace are 90° apart.
46
[
\.
~ t_~ ,--
J
.' :",~.""
~\
-------
1_-
. PbO 3264 A
PbO 3342
PbO 3402
PbO 3486
PbO 3594
Pb 3683
PbO 3805
PbO 3878
Pb 4058
PbO 41 56
PbO 4229
PbO 43 1 7
Pb04410
PbO 4554
PbO 4658
PbO 48 1 7
~
.~
_Hg 2967 A
Hg 3126/3132
Hg 3650
- Hg 4047
-Hg 4078
- Hg 4358
Figure 26. Spectrogram of luminous blue flame appearing in exhaust
gas reactor. Chevrolet 350 in.3 engine, leaded fuel, 1200 rpm, 30
hp, 12.5:1 air fuel ratio, air injection fraction approximately 0.3.
.,
47
-------
( 4)
Summary
The following observations have been made regarding light emission:
( a)
Illumination varies directly with the rate of gas input to the
reactor.
(b)
There are marked cycle-to-cycle and cylinder-to-cylinder differences
in light emission.
( c)
To an extent cylinder-to-cylinder differences repeat.
( d)
During warm up illumination rises slowly and in an intermittent
manner.
(e)
Spectral lines observed were those of lead and lead oxide.
( f)
Maximum intensity was near 4000 angstroms.
)If)
-------
B.
SINGLE CYLIND~R EXPERIMENTAL REACTOR STUDY
1.
Objecti ves
The objectives of the eA~erimental reactor study were: (1) to obtain
data on the chemical kinetics of the oxidation of carbon monoxide, hydrogen,
and hydrocarbons in internal. combustion engine exhaust; and (2) to determine
from this data gross kinetic rate equations which can be used in modeling
thermal exhaust reactors.
2.
Experimental Apparatus
The experimental reactor system is sketched in Figure 27. The exhaust
gas inlet was attached directly to the exhaust port of a propane fueled single
cylinder CFR variable compression ratio engine. Hot exhaust gas passed from
the exhaust port through a perforated exhaust inlet tube and into a 1350 in.3
surge and mixing tank and then through a sparger tube and into the 59.5 in.)
reactor. The high-velocity jets generated by the sparger tube kept the reac-
tor well stirred. Reactor mixing was discussed in detail in the Second Annual
Progress Report. Air was injected into the reactor inlet , tube after passing
through a bank of heaters. A bypass loop was incorporated to permit the reac-
tor residence time to be varied without changing engine conditions. The two
tanks and ~onnecting piping were made of Hastelloy-X and similar high-tempera-'
ture alloys and the reactor was operated at temperatures up to about lBoo°F.
Gas samples were withdrawn at the reactor inlet and outlet through water
cooled sampling probes. Gas temperatures were measured with shielded thermo-
couples in the surge tank, at the reactor inlet, at three locations inside the
reactor, and at the bypass flowmet.er. One of the thermocouples inside the
reactor was movable and was used to obtain temperature profiles along the
len~th of the reactor. The reactor wall temperature was measured at one loca-
tion on the outside of the cylindrical surface. Temperature nonuniformities
and wall.effects were discussed in the Second Annual Progress Report. Surge
tank and reactor pressures were measured with mercury manometers. Propane and
air flowrates to the engine and injection air flowrate \>lere measured \..,.i th
critical flow orifices, and injection air temperature with a shielded thermo-
couple. F'lowrate through the reactor was measured by using the calibrated
sparger tubes as square-edged orifices.
49
-------
AIR HEATER
..J'
J
SA:\IPLI;:\G.
TAP
MIXING AND
SURGE TANK
THf~R:\10-
COCPLE
I
THLR?\'lOCOCPLE
METER
HEAT
EXCHANGER
AIR
IN
STIRRED
TANK
REACTOR
SA :VIPLI),"G
TAP
BYPASS LOOP
VE:'-1TURI
THERMO-
COUPLE
Figure 27. Two-tank experimental reactor system schematic.
-------
:C:xhau:;(; WJ.S composition was cont.roll('(l mainly by, ad.justing fucl/nil' rat.io and,
spark timinr:, while temperature war; i~ont.rollccl b.V adjusting spark timing Hnd
compres[don ratio, and by passing cooling air through the heat exchanger at
the surge tank entrance. Injection air flowrate was controlled by adjusting
the pressure upstream' of the critical flow orifice, and its temperature Ivas
controlled by adjusting the power to the air heaters with a variable trans-
former.
3.
Experimental Results
a.
SUMMARY OF CO OXIDATION RATE RESULTS
( 1)
Range of Parameters
The range of parameters for which CO oxidation has been studied in the
two-tank reactor system is give~ in Table VI. Output values of 0.1 to 5% co
and .2 to 8% 02 were observed in the multicylinder reactor study, Phase I. '
TABLE VI
RANGE OF PARAMETERS
(Carbon Monoxide Oxidation)
CO Conversion
Temperature
Mean residence time
Volume fraction CO
- in
- out
Volume fraction 02
Wall materials
20 to 8CP/o
1130 to 1525 of
74 to,240 msec
0~5 to 2.3%
o.:~ to 1. 6%
0.6 to 4.5%
Hastelloy-X
Copper
(;-?)
Regression Results
A linear regression was used to find the best fit values for the con-
stants in the equations
)1
-------
.en l'
CO
==
E
.en K - - + A £n P + B .en PO
RT CO. 2
( 1)
.en rCO
E
.en K - - + A £n P + B .en P02. + Cin P
RT CO NO
(;n
\vhere l' == rate of disappearance of CO in lb-moles/sec-in.3,
CO
R ~ gas constant in cal/gm-moleOK,
T == temperature in oK, and
P
x
-
partial pressure of species x in psia.
Regressions for each equation have been performed over the entire range of
temperatures and over two ranges, above and below 1000oK, respectively, re-
sulting in six separate correlations. Inclusion of all data in the regression
for the parameters in. Eq. (1) and all data where the NO concentration was mea-
sured in the regression for Eq. (2) result in the best fit values given in
Table VII. Tolerances represent one unit of standard error. ' . The apparent
activation energy and reaction order with respect to CO are seen to be highest
in the higher temperature range. To illustrate the variation of the predicted
rate with temperature, the different expressions are plotted in Figure 28 for
a mixture containing 1% CO, 1% 02' and 500 ppm NO by volume.
Using the best fit values of E, A, B, and Cdetermined by the regression
program, an experimental value of the logarithm of the preexponential constant
K was determined for each data point, and a comparison of rates with the dif-
ferent sparger tubes and with and without a copper sleeve in the reactor was
made by comparihg mean values and standard deviations of the distributions of
.en K for the different subsets of data. The characteristics of the sparger
'tubes as well as the copper sleeve experiment are detailed in the Second An-
nual Progress Report.12
Table VIII contains a summary of the data analyzed in this way. (Sparger
tube #2 was the one having the smaller holes.) Since K, rather than .en K, is
directly used in the rate calculation, the results have also been tabulated in
terms of K. The items denoted "mean* K" "std. dev.* K" do not represent true
means and standard deviations of the distribution of values for K, but are
simply antilogarithms of values determined from the logarithmic distribution.
The Second Annual Progress Report also incluoes a detailed comparison of these
CO ox:idation I'esults with othen; in published literature. ..
The equations in Table VIr
tion rates in thermal reactors.
improves the correlation.
maybe used to predict carbon monoxide oxida-
Where NO concentration is known its addition
52
-------
TABLE VII
REGRESSION PRCGP.Al,1 RESULTS, eo OXIDATION RJI.TES
in reo
= in K - E/RT + A in Peo + B In P02
Ten:pere.ture
Range (FO)
113C to 1340
13hc to 1525
1130 to 1525
l';::. of
Runs
70
87
1~7
),
in K E A ~f,ultiple Cor-
cal/gm-mo1e B relation Coef.
-2.23 28,7C5 1 2,441 . 310 1 . 073 -. 006 1 . c-84 C. 851
4.55 42,915 1 2,907 . 326 :t .064 -. 058 1 .062 c.853
-2. 68 28,198 1 1,111 . 269 1 .050 -.031 1 .053 C.913
,£n rco = in K - E/RT + A in PCO + B .en P02 + C .en PNC
'V Tempere.tCJ.re No. e>f E Multiple Cor-
\.>I
j,n K A B e
Range (FO) Runs call gm-m::;le ::relation Coef.
1130 to 1340 50 - 3. 69 26,087:t 2,765 . 109 :t . 105 .027:t. 095 . 048 1 . 065 0.849
1340 to 1525 80 7.06 45,821 1 3,593 .:;861 .096 -.051:t .064 . 145 1 . 062 O. 83B
1130 to 1525 130 -1.43 29,126 1 1, 644 . 198 :t . 067 -.003 1 .055 . 144 1 .046 c.897
-------
-/5
-16
in r 0
C .
-/7
-18
-16
~17
In l'
co
-18
-19
= 1170 exp (-45,821) p.386 -.051 .145'.
RT co PO,., PNO'
<
.240 exp (-29,126) p.198 p-.003 p.144
RT CO 02 NO
r
CO
= 0.25.. (-26,087) .108 .027 .048
. exp RT. PCO . Po PNO
2
reo = 95.0 exp (-4~:15) p~~26 p~~058
- 0690 (.28,198). p.269 p-.031
-. exp RT CO 02
= .1075 exp (-28,705) p.310 -.006
RT. CO PO.
2
0.45
0.50
10001 RT
0.55
Figure 28. Predicted rates for CO oxidation for a mixture
. -
containing 1% CO, 1% 02, and 500 ppm NO.
54
1-~/"
,-"
-------
TABLE VIII
COMPARISON OF EXPERIMENTAL CO OXIDATION RATES WITH TWO WALL MATERIALS AND TWO SPARGER TUBES
Ln K = Ln rCO + E/RT - A Ln PCO - B Ln P02
Temperatures belovrl000oK
E = 28,705 A = .310 B = -.O~
No. of min. max. mean std. dev. min. max. mean* std. dev.*
Data Set Runs Ln K Ln K ~n K Ln K K K K K
Sparger Tube #1 48 -2.96 -1. 73 '-2.218 .266 .0)20 ..L775 ,.109') .0292
(without Cu insert)
Sparger Tube #1 13 -2.75 -1. 57 -2.194 .289 .0642 .208 .H20 .052'(
with Cu insert
Sparger Tube #2 9 -2.85 -1. 78 -2.364 .350 .0579 .169 .0943 .0337
(without Cu insert)
All runs 70 -2.96 -1. 57 -2.232 .282 .0520 .208 .1075 .0306
Temperatures above 10000K
E = 42,915 A = .326 B = -.058
No. of min. max. mean std. dev. min. max. mean* std. dev.*
Data Set Runs In K Ln K Ln K Ln K K K K K
Sparger Tube #1 57 3.93 5.05 4.537 .278 51.0 166 93.5 26.2
(without Cu insert)
Sparger Tube #1 19 4.18 5.30 4.707 .245 65.5 201 111. 27.5
with Cu insert
Sparger Tube #2 11 ,4.00 4.71 4.376 .320 54.5 111 80.0 26.5
(without Cu insert)
All runs 87 3.93 5.30 4.554 .250 51.0 201 95.0 24.5
All Temperatures
E = 28,199 A = .269 B = -.031
No. of min. max. mean std. dev. min. max. mean* std. ,jev."
Data Set Runs Ln K Ln K Ln K LnK K K K K
Sparger Tube #1 105 -3.37 -2.11 -2.671 .280 .0345 .1215 .~95 .0197
(without Cu insert)
Sparger Tube #1 32 -3.28 -1. 97 -2.578 326 .0378 .140 .0762 .0253
wi.th Cu insert'
Sparger Tube 112 20 -3.34 -2.17 -2.858 .324 .0355 .1145 .0577 .0240
(without Cu insert)
All runs 157 -3.34 -1. 97 '-2.676 .306 .0355 .140 .0690 .0214
)5
-------
TABLE VIII (Concluded)
In K = In rCO + E/RT - A In PCO - B tn P02 - C In PNO
Temperatures below 10000K
E = 26,087 A = .108 B = .027 c = .048
No. of min. max. mean std. dev. min. max. mean* std. dev.*
Data Set Runs In K tn K in K in K K K K K
Sparger Tube #1 28 -4.00 . -3.34 -3.649 .181 .0184 .03;6. .0261 .0047
(without Cu insert)
Sparger Tube #1 13 -4.13 -3.13 -3.708 .350 .0161 .0439 .0247 .0088
with Cu insert.
Sparger Tube #2 9 -4.27 -:3.23 -3.763 .306 .0140 .0397 .0232 .007)
(without Cu insert)
All runs 50 -4.27. -3.13 :-3.685 .255 .0140 .0439 .0252 .0064
Temperatures above 10000K
E = 45,821 A = . 386 B = -.051 C = .145
No. of min. max. mean std. .dev. min. max. mean* std. dev.*
Data Set Runs In K in K in K In K K K K K
Sparger Tube #1 50 6.46 7.50 7.011 .249 640 1810 1110 282
(without Cu insert)
Sparger Tube #1 19 6.79 7.80 7.239 .)00 890 2440 1390 425
with Cu insert
Sparger Tube #2 11 6.68 7.25 6.957 .222 800 1410 1060 235
(without Cu insert)
All runs 80 6.46 7.80 7.058 .275 640 2440 1170 320
All Temperatures
E = 29,126 A = .198 B = -.003 C = .144
No. of min. max. mean std.. dev. min. max. mean* std. dev.*
Data Set Runs In K in K In K in K K K K K
Sparger Tube #1 78 -2.03 -0.93 -1. 437 .2)2 .1315 .395 .238 .0605
(without CU insert)
Sparger Tube #1 32 -2.12 -0.81 -1.339 .366 .120 .445 .262 .098
with Cu insert
Sparger Tube #2 20 -2.04 -0.90 -1. 540 .309 .1305 .407 .215 .067
(without Cu insert)
All runs 130 -2.12 -0.81 -1.429 .297 .120 .445 .240 .067
56
-------
.
-. . - . .- - ----- -- -"- --- ---.
b.
SUMMARY OF HC OXIDATION RATE RESULTS
( 1)
Range of Parameters
The range of par.ameters for which HC oxidation has been studied is given
in Table IX. During normal operation output values of 0 to 800 parts per
million C6 were observed in the multicylinder reactor study of Phase I.
TABLE IX
RANGE OF PARAMETERS
(HYdrocarbon Oxidation)
. HYdrocarbon conversion
20 to 8CP/o
Temperature
1090 to 1308°F
Mean residence time
110 to 250 millisec
HYdrocarbon concentration -in
-out
(Total hydrocarbons as n-hexane,
~~asured by flame ionization de-
t~t~) .
35 to 260
8 to 150
Fraction paraffins -in
-out
. 42 to. 66
.23 to .85
Fraction olefins
-in
-out
. 34 to. 58
. 15 to . 77
Fraction aromatics -in
-out
'" 0
~ 0
Oxygen concentration
o. 3 to 4. Y/o
NO concentration
3 to 850 ppm
Sparger tubes
#2 only
Wall materials
Hastelloy X only
'J(
-------
(2)
Regression Re?ults
A linear regression was used to find the best fit values for the con-
stants in the equations
.en r HC
==
E
.en K - RT + A .en PHC + B En Po
2.
+ C .en P
NO
( 3)
in r HC
E
.en K - -- + A .en P + B .en P + C .en P + D .en PCO (4)
RT HC 02 NO
where rHC == rate of disappearance of HC in lb-moles/sec-in.3.
meters are the same as in the CO oxidation equations. .
The other para-
Regression for each equation was performed over the range of temperature
1090o-1309°F. The regression result for Eq. (3) is shown in Table X. Tol-
erances are one unit bf standard error. The scatter is clearly greater than
that for the CO data. The regression results for Eq. (4) are shown also in
Table X. A significant improvement was made by including CO concentration.
The multiple regression coefficient was 0.893 for Eq. (4) compared to 0.763
for Eq. (3). Equation (4) results reflect an additional 29 runs in which CO
was added (13 runs) and H2 added (16 runs) to the exhaust gas. The objective
was to change the ratio of B2. to CO in the reactor feed. This ratio tends
to be fixed in engine exhaust for.a particular fuel. In so far as Eq. (3) is
concerned, these 29 runs yielded data which fell within the range of para-
meters given in Table ~ As a point of interest the reaction order for CO in
Eq. (4) was. 376 for just the 29 runs as opposed to .512 for all 105 runs.
Equation (4) is believed to reasonably represent the trends in the hydrocarbon
oxidation data and is recommended for use in estimating oxidation in thermal
reactors.
c.
SUMMARY OF I? OXIDATION RATE RESULTS
( 1)
Range of Parameters
. The range of parameters for which B2 oxidation has been studied is given
in Table XI. During normal operation output values of 0 to 2% H2 were ob-
served in the multicylinder reactor study of Phase I.
)8
-------
TABLE X
HYDROCARBON OXIDATION REGRESSION RESULTS
1m r HC
=
E; .
,En K - - + A .en P + B .en P + C .en PNO (76 runs)
. RTllC 02
Multiple correlation coefficient
=
.763
.en K = .33C
E = 30,)33:! }1,.171
A =
H =
C =
.433 i . 106
. 3 3; ~ :!: . 0)18
. 33) :!: .038
min ,En K -1. 242 min K = .289
max .en K = +1. 245 max K = 3.48
mean .en K = o. 336 mean* K = 1.40
stddev .en K = .410 std dev* K = .591
.en r HC
E; . )
.en K - - + A .en PHC + B .en P + C .en P + D .en CO (105 runs
RT 02 NO
Multiple correlation coefficient
=
.893
. .en K = . 175
E = 29,836:!: 2,0~6
A =
B =
C
D =
. 238 :!: . 06~
. 537 :t . 082
.415 :t . 040
. 51? :1: . 12 3
TABLE XI
RANGE OF PARAMETERS
(~ydrogen Oxidation)
No. of data points
}~ydrogen conversion
Temperature
Mean residence time
HYdrogen concentration
-in
-out
,53
20 to 8Cf/o
1090 to 1)80°F
110 to 250 millisec
O. 2 to 1. 5%
0.1 to i.CP/o
0.3 to 4.3%
3 to 840 ppm
#2 only
. Hastelloy X only
Oxygen concentration
NO concentration
Sparger tubes.
Wall materials
)9
-------
(2)
RegressiaG Results
A linear regression was used to find the best fit values for the con-
stants in the equations
.en I' H
2
=
.en K - E/RT + A .en PH + B .en Po
2 2
(5)
.{n I'
H0
in K - E/RT + A .en
PH
2
+ B in P + C p,n P
02 NO
(6 )
.en I' H
2
in K - E/RT + A .en P + B .en Po + D .en Peo
H2 2
( 7)
where rH2 = rate of disappearance of H2 in lb-moles/sec-in.3.
tel'S are as defined previously.
Other parame-
Regression for each equation was performed over the range of. temperature
l090-l380°F. The regression results are shown in Table XII. In general none
of the equations correlate the data particularly well, the multiple correla-
tion coefficient being about 0.59 for the first two and 0.49 for the third.
Moreover the reaction orders are close to zero in every case except for CO.
The doped data gave. approximately a zero order with respect to eo, while all
data taken together indicated an or.der of about l/2, but in both cases the
overall correlation coefficient was very low. rhus within the temperature
range in which intermediate H2 conversion was observed, little success was
experienced in correlating observed rates with an equation of the desired for~
It was observed that below about llOO°F appreciable ~ .conversion (2CJ!/o or more)
almost never occurred, while above about l300°F fairly complete conversion
(8l~k or more) almost always occurred. It was also observed that whenever ap-
preciable CO conversion occurred (above ;2CfJk) the hydrogen was nearly complete-
ly oxidized (above 8CJ!/o conversion with very few exceptions), but nearly com-
plete H2 conversion also occurred in many cases .with very little CO conversion.
The equations in Table XII not only failed to correlate the data very
well within the llOO°F to l300°F temperature range, but in conflict with .the
observations above did not indicate substantially different rates at (for ex-
ample) l050°F and l350°F (runs in which conversion of H2 was less than 20% or
more than 80% were not included in the data regressed). Thus this equation
very definitely should not be used in predicting rates outside the llOO°F to
l300°F temperature range, and is of little value even in this range. It is .
therefore not recommended for use in modeling thermal exhaust reactors.
60
If
-------
TABLE XII
HYDROGEN OXIDATION REGRESSION RESULTS
. E
.en r =.en K - - + A .en PH + B .en P
H2 RT 2 02
Multiple Correlation Coefficient
=
.583
.en K =
-8.688
A = .0258 1 .1343
B = -.0609 1 .1505
min K = .0000499
max K = .000462
E = 17,804 1 4433
min .en K .= -9.905
max .en K = -7.694
mean .en K = -8.688
mean* K
= .000172
std. dev. .en K =
.505
std. dev.* K =
.000088
.enr
H2
=
E
.en K - - + A .en P + B .en p' + C .en P
RT H2 02 NO
Multiple Correlation Coefficient =
.594
.en K =
-5.236 .
A =
B =
C
=
.118 :!: .164
.0375 1 .1812
.0861 1 0882
min K = .00147
max K = .0142
E = 22~299 1 6393
min .en K = -6.534
max .en K = -4.258
mean .en K = -5.236
std. dev. .en K =
.500
mean* K = .00540
std. dev.* K = .00279
(In r =
.' If
: :
E:
Un K -R1 + A £n PH + B £n Po
~!. 2
+ Den Pea
Multiple Correlation Coefficient
= .489
.En K =
-15.?
A= -.333 i .160 .
B = -. 154 i . 122
E =. 6335i 2497
D = +.526 i .216
61
~
.',
-------
In consequence of t,he failure of the above equations tb predict hydrogen
oxidation results, a zero-order reaction was assumed (in line with the regres-
sion results) with activation energy and preexponential term adjusted to pre-
dict virtually zero conversion below 1100°F and virtually complete conversion
above 1300°F, behavior in line with the observed effect of temperature.
For a reaction, in which temperature alol1e determines the rate, the ex-
tent of conversion is:
Conversion
x
=
kV -E/RT
mC e ;
o
where
r
=
ke-E/RT l'S rate f t' lb 1 / '
o reac lon, mo es cu In.
SE7C;
V is reactor volume, cu in.,
m isflowrate, lb mOles/see,
and
C is entering concentration, mole fraction.
o
Using this expression, experimental data in X versusT can be
the same flowrate ill and entering concentration Co by a simple
dure. In Figure 29 ttie data for hydrogen are shown corrected
and Co = o. &fa ~. '
corrected to
ratioing proce-
to 20 lb mass/hr
The correction of conversions does not alter the scatter in relation to
temperature, however, it does redistribute the conversions so that a slope
for conversion versus temperature can be identified. This slope, discounting
the scatter, suggests that conversion would proceed from 0 to 1 in approxi-
mately 130°F. To reduce this observation to an analytical expression, the
points (X,T) = (.2,1195) and (.8,1280) were fit to the zero-order conversion
equation. This gave k = 12,660 and an activation energy E =52,000 cal/g-mole.
The final equation is: ' ,
rH
2
=
66 -52, OOO/RT / ' "
12, 0 e , lb moles cu l~' sec
(8)
In the absence of better data, Eq. (8) may be us,ed to predict hydrogen oxida-
tion in thermal reactors.
62
-------
1.0 0
00
0
0.9 0 0
0 00
o
0.8 <:) 0
o 0
LLJ 0
~
a:: 0.7 0
LLJ
> 0
Z <:)
0 0.6 <:) 00
U
Z 0
l.LJ 0 0
I C) 0
I 0 0.5
0:: 0 0
o
o 0 0
>- 0 . 0. <:)
::I: 0.4 0 0 0
Z 00 0
0 0 0 0
-
~ 0.3 0 0
U 0
« 00 0
0:: 0
LL. 0
0.2 0
0 <:) 0
0 0
0.1
0.0
1000
1100
1200 1300 1400 .
TEMPERATURE, of
1500
1600
Figure 29. Conve~sions of hydrogen corrected to 20 lb exha\}st/hr and
.006 mole fraction hydrogen entering, rH2 = 12,660e-52,000jRT.
63
-------
,-
'I
C.
REFERENCES FOR PHASE I
1.
Cantwell, E. N., et a1., "A Progress Report on the Development of Exhaust
.Manifold Reactors," SAE paper 690139, Ja.nuary 1969.
2.
Cant'\ifell, E. N., et a1., "Recent Development in Exhaust Manifold Reactor
Systems," Inst. of Mech. Eng. Preprint ADP13 (B) /70, May 1970.
3.
Cantwell, E. N., and' J. J.
Solution to the Automotive
Assoc., April 1970.
Mikita, "Exhaust Manifold Thermal Reactors-A
Emission Problem," 68th Annual. Nat. Pet. Ref.
4.
Cantwell, E. N., and A. J. Pahnke (DuPont), "Design Factors Affecting the
Performance of Exhaust Manifold Reactors," SAE paper 650527, 1965.
5.
Blenk, M. H.' and R. G. E. Franks, "Math Modeling of an Exhaust Reactor,"
SAE paper 710607, 1971.
Klosterman, D. L. and J. E. Sigsby, "Application of
niques to the Analysis of Automotive Exhaust," Env.
April 1967, p. 309. .
6.
Subtractive Tech-
ScL Tech., !, No.4,
7.
Oberdorfer, P. E., "Determination of Aldehydes in Automobile Exhaust
Gas," SAE paper 670123, January 1967.
U. S. Bureau of Mines, "Procedures for Determining Exhaust Carbonyls as
~~, 4-Dinitrophenylhydrazones," APHAC Project CAPE-11-68, Final Report,
19(8. .
n.
Papa, L. J., "Colorimetric Determination of Carbonyl Compounds in Automo..-
. ti ve Exhaust as 2, 4-Dini trophenylhydrozones," Env. ScL Tech., }, No.4,
April 1969, p. 397.
9.
10.
Saltzman, B. E., Analytical Chemistry, 32, p. 135, 1960.
11.
Patterson, D. J., et a1.,
tibles in Exhaust Systems
No.1 to CRC, 1969-7Q
12.
Patterson, D. J., et a1.,
tibles in Exhaust Systems
No.2 to CRC, 1970-71.
"Kinetics of Oxidation and Quenching of Combus-
of Gasoline Engines," Annual Progress Report
"Kinetics of Oxidation and Quenching of Combus-.
of Gasoline Engines," Annual Progress Report
13.
Levenspiel, 0., Chemical Reactor Engineering, Wiley & Sons, New York,
1962.
64
,,~A ~
.,T
I""
-------
C.
REFERENCES FOR PHASE I (Concluded)
14.
Schwing, R. C., "An Analytical Framework for the Study of Exhaust Mani-
fold Reactor Oxidation, II SAE Preprint 700109, January 1970.
15.
Glass, W., et al., "Synchrothermal Reactor System for Control of Automo-
ti ve Exhaust Emissions, II SAE paper 7001~7, 1970.
6)
.n
-------
DETAILED PROGRESS - PHASE II
COMPUTER MODEL DEVELOPMENT
67
-------
1-
FOREWORD
Contents of This Chapter
A theoretical framework for the design of thermal reactors has been syn-
thesized taking into account both the full extent of chemical reactor design
theory and the high frequency cyclic operating characteristics of automotive
exhaust reactors. An array of analytical design tools in the form of highly
adaptive computer simulation programs has been developed tO,aid design efforts
on exhaust reactors where thermal quenching and turbulent mixing are determin-
ing factors.
After a general introduction to the thermal reactor problem, the discus-
sion in this phase is divided into ten subsections. Parts I and II describe
the theory and development of the generalized patterns of flow reactor simula-
tion used for predicting performance of partially mixed reactors under warmed-
up steady state conditions. Part III discusses a method for estimating the
coalescence parameter in a new design. This parameter'is a measure of the
micromixing intensity within the various sections of the reactor. Part IV
describes calculated results which' verify that the performance of the single
cylinder engine experimental kinetics test reactor discussed in Phase I-B was
not mixing limited.
An understanding of Parts I, II, III, and IV is not essential for inter-
preting the comparisons between warmed-up steady state experimental and com-
puted performance of the multicylinder engine DuPont Model V reactor. These
comparisons are included in Part V.
Part VI describes the development of the computer model for unsteady
state warm-up of an initially cold reactor. An understanding of this section
is not essential for interpreting the comparisons between experimental and
compltted warm-up performance for the DuPont Model V reactor which are included
in Pflrt VII or the warm-up computer projections in Part VIII. These projec-
Lions include the effects of specific reactor configurl!\tions, inlet combusti-,
ble {~oncentrations, and ignition sources on time to lightoff. Finally, Parts
[X and, X discuss conclusions and use of the results.
As an aid to the reader, a detailed overview of the modeling efforts
follows.
69
-------
Overview of Modeling Efforts
Previous work on flow patterns and micromixing in chemical reactor desig~
are critically reviewed herein. Cell-wise mixing models and Monte Carlo type
solutions were selected as the best means to treat the coupled mixing and mul-
tiple reactions of separate streams of air and exhaust entering in cyclic
flows and ivi th cyclic temperature and composition. In the most p;eneral model,
different reactoT configurations are simulated by a forward. flow of cells
through a user-designated network of parallel and series modules. 'l'hese are
either cell-wise mixed stirred tanks or cell-wise mixed plug flow reactors.
"Micromixing" is simulated by coalescence and redispersal of cells. Subordi-
nate models wherein particular assumptions are relaxed were investigated, with.
particular attention given to mixing with instantaneous reaction.
An experimental single cylinder stirred tank reactor was described in .
Phase I. It was built to obtain mixing-independent kinetics required for mod-
eling. This reactor was designed to operate under conditions of intense tur-
bulent mixing generated by high velocity entrance jets; both theoretical and
eA~erimental results indicated no significant limitation due to segregation
of air and exhaust. A near-zero reaction order for oxidation of carbon monox-
ide was established.
An unsteady state thermal model was developed to simulate warm-up of an .
arbitrary number of metal surfaces or insulating components in a reactor, sub-
jectto user-specified heat exchange by radiation, convection, and/or conduc-
tion. The computed temperatures of designated surfaces and the computed val-
ues of heat transfer coefficients for exhaust s~de convection were used to
establish heat losses for an ideal backmix simulation of all or part of the
reactor volume. Exhaust temperature and conversions of several species are
obtained using a search strategy. Computations make use of the difference in
time. scale for changes in metal temperatures (minutes) and adjustments in gas
temperature relative to given values of heat generation and heat loss terms
(tenths of a second). Good correspondence was established with experimental
results for unchoked engine start up. Sensitivity of reactor ignition to se-
lected parameters was investigated.
It is concluded for modeling, based on mixing independent kinetics, that
the high temperature conversions substantially below 100% that are observed
in reactors are mixing limited rather than temperature-kinetics limited. The
work of Corrsin on idealized turbulent mixers was found to predict reasonable
mixing intensities from flow and geometry. Mixing intensity is discussed in
relation to entrance geometry and air inlet timing, with the conclusion that
the intensity could perhaps be doubled by changing the timing and location of
air injection. . .
70
-------
INTRODUCTION TO THE THERMAL REACTOR PROBLEM
I'
In recent years groups within the petroleum and automotive industries
have expended considerable efforts to develop effective spark-ignition engine
exhaust treatment systems. Such systems have included catalytic or noncata-
lytic thermal reactors or combinations of the two. Brownson (4), Chandler
(7), Cantwell (5,6), and Schwing (29), have reported on the success with which
noncatalytic thermal reactors oxidize the exhaust carbon monoxide and hydro-
carbon constituents.
The goals of thermal reactor design are. clear: to complete the combus-
tion of unburned and partially burned exhaust components. The operation of
thermal reactors is at first view qualitatively simple: Air and exhaust mix,
oxidation proceeds, and heat is liberated. Carbon monoxide, hydrogen, and.
hydrocarbons are thereby raduced, but nitrogen oxides are not significAntly
altered.
When air is injected into combustible rich exhaust gases in a convention-
al exhaust system, some reaction will occur in the manifold, exhaust pipe,
and muffler without the use of a'specially designed reactor. As a means to
achieve' higher conversions, thermal reactors are designed to extend the resi-
dence time of the exhaust gases in a high temperature zone to provide greater
opportunity for mixing and reaction before reactions are quenched by cooling.
Typical flow through a thermal reactor exhaust system is shown in Figure 1.
Exhaust proceeds through the reactor in three passes so that hot reacted gases
in the outer annu'lus tends to thermally isolate the inner core.
The simulations run in this study have been limited to the thermal reac-
tor itself and the engine exhaust ports which lead to it; no attempt has been
made to model the exhaust pipe and muffler. The methods of analysis developed
would however apply, if sufficient information were available on this high
~uench region to form a valid basis for simulation.
Operation of [l thermal reaction from'a cold start has been characterized
in ThE' Uni ver~;it.Y of Michigan CRC study and others by a latent period of
~lip,ht conversion during which oxidation of combustibles is partially quenched
due to heat loss, followed by an approach to a steady-state mode Ivhere con-
vcr:;ion~~ :'1re high but llo not reach 100% except for hydrogen (approximately 75
to '7J.I(~ 1'01'. carbon monoxide and 93 to 98% for hydrocarbon for lmv pressure air
injection and high temperature operation).
The various rate processes associated with an analysis of thermal reactor
d.esign can be readi)_y identified as heat transfer, mixing, chemical reaction,
and flow. Design information required thus consists of he~t transfer coeffi-
cients, heat capacities, and heats of reaction; mixing parameters, reaction
71
. ,I-"
-------
-J
[\)
Reactor
--
"-- --- -- ---
-- ------ \
.:'
. 'L~
-:: ~--~--
~
~
Muffler
Figure 1.
Schematic of exhaust flow from on~ cylinder through a thermal reactor exhaust system.
-------
J'al." ,:un::I.13.nl.::, and. n:;::o(:iat(-,,j rate law:-:; linel ::-L()'lchiomC'try. rksjr~n con-
sLr'aint:: l'xi::t ['Or Lhe ::ize 01' the reactor, operRting temperature, the t>nergy
available :('01' mixing, the heat losses from the reactor, and the time-
distributed composition, temperature, and flowrate entering the reactor.
The goal of reactor modeling has been to develop basic tools in the form
of highly flexible computer simulations to obtain insights concerning these
interactive processes. Our goal is to divorce our approach from any specific
reactor geometry so as to provide a general design basis that is widely appli-
cable. Given the constraints on thermal exhaust reactors, we wish to predict
the performance of given reactor designs, including correspondence with exper-
imental results for the DuPont Model V reactor and the kinetics test reactor
employed in the CRC study. From these fixed points, it is our intent to in-
terpolate in an approximate manner to judge the limits of performance for
practical exhaust reactors as a class.
Modeling effort has been divided between the problems of warm-up and
conversion at stationA.J'Y state. The a priori assumption made to establish
this division was that warm-up to the point of lit-off operation depended
primarily on change in heat loss and reactor gas temperature occurrinr, on a
time scale of minutes and only negligibly on extent of incomplete mixing. On
the other hand, incomplete conversion during "steady state" operation at ele-
vated temperature was assumed to depend on a coupling of mixing with kinetic
and thermal effects.
Constraints on Design and Operation
Residence times in existing devices are dictated by exhaust flows in the
range of 100 to 300 lb/hr through a reactor volume of approximately 200 cu in.
Corresponding mean residence times are. 084 to .028 see at 1500°F. We Ivill
assume that a doubling of reactor volume is permissible, so that residence
times are restricted to approximately O. 15 sec. Optimum volume is notneces-
r;aril:v the largest possible, since a slower warm-up tends to offset the advan-
tap;e oJ' a longer residence time.
Ii'or the DuPont Model V reactor, the maximum recommended core temperature
if; 1'(')0° [I', Since conversion of carbon monoxide as the specie most resistant
to o:..;id.lltion is obse.1;'vcd to approach its limiting upper value at approximately'
l')()() ° [.', this is not a serious constraint on conversion. It is of. course an
important consideration in determining reactor durability (7).
LO\v exhaust tempCt'Rture resulting from heat loss is a serious limitation
durinr:; \varm-up when temperature primarily governs conversion. Cold-start
tests run in the CRC studies \vere particularly affected because of a necessity
73
-------
to run at a predetermined air/fuel
a high level of combustible .in the.
tice to greatly reduce the time to
ratio from
exhaust at
lightoff.
time zero. Choking to produce
start-up has been used in prac-
Limits on mixing are posed by the energy available and the dimensions
of the inlets to the reactor. A verY large amount of energy is available at
the time of exhaust blowdown through the exhaust valve, however this may not
. be effectively utilized. Pressure drops that are tolerable in a reactor are
comparatively low, perhaps 1 or 2 psi. This important class of constraints
will be discussed later in detail.
Inlet Flow, Composition, and Temperature
Inlet properties represent a special class of constraint on .reactor de-
sign because of their. cyclic character. . The implications of periodic flow
and temperature variation are readily visualized by considering the advers.e
. effect .of a high flow of exhaust entering coincidentally with a low flow of
air or the persistence of a low-temperature fraction within a reactor lacking
a sufficient backmixing effect.
Instantaneous exhaust velocities were measured by Yun and Mirsky on a
one-cylinder engine by a laser-schlieren technique in Phase III. The measured
velocities have been corrected for an assumed temperature span of 800° between
peak blowdown temperature and a l200°F tailing flow to produce the piecewise
linear mass flow curve shown in Figure 2. This TlnormalizedTl curve was used
for all simulations that involve periodic flow. Neither the measurements as
applied to multicylinder engines nor the models are felt to possess an exact-
ness warranting refinement for various operating conditions.
Periodicity in .exhaust flow is also influenced by the timing of cylinder
firings into the reactor. Simulations are run for cylinders 1, 3, 5, and 7
of a v-8 engine discharging at 474°, 24°, 204°, and 294° on a 720° engine
cycle. The span of flow for each cylinder is 278°, corresponding to the dura-
tion of exhaust value opening. Cyl:inders 1 and 3 tend to fire individually.
with a minor amount of overlap, but cylinders 5 and 7 overlap appreciably.
Total TlnormalizedTl exhaust flow for the four combined cylinders is shown in
Figure 3.
The normalized air flow shown in Figure 4 is based on hotwire velocity
. measurements. Flow to each cylinder port is reasonably constant except for
dips coinciding with exhaust pulses occurring during blowdown and again at
the time of maximum piston velocity. The other fluctuations in measured air
flow, which coincide with pulses from the other three cylinders attached to
the reactor, amount to only about ~10% of average flow and are neglected in
the present simulations.
74
-------
z
«
0-
VI 1. 0
~
o
Li O. 8
VI
VI
.~ 0.6
VI
~ 0.4
z
o
V; O. 2
z
L.LJ
:E
c
r\
I \
~ I \
/ \J \ ..
/ ~ Experimental Velocity
I I
I
I
Area Under Normalized
Curve = 0.5155
\
\
\
\
\
QIQ2 Q3 U4 Q5 Q6 Q7 Q8 Q9
FRACT ION OF EXHAUST STROKE
I Normalize
/ Mass Flow
I
I
I
o I
. I
o
1",
I ,
I
\..1 \_r",........
200
50
o
. I
I
I
I
J -50
1.0 1."1
Figure 2. Characteristic variation in cyclic exhaust flow from a
single cylinder spark ignition engine. Velocities measured by laser-
schlieren methods, Yun and Mirsky, CRC program.
75
150
u
Q)
VI
-
-
100 u..
>-
I-
U
g
L.LJ
>
l-
V)
:::>
«
:r:
X
L.LJ
-------
~
o
.....J
w...
V') 1
V')
«
~
2
Ave rage = 1
00
CYL5
CYL 7
200 300 400 .
CRANK ANGLE, degrees
500
Figure 3. Com~ined normalized flow for cylinders 1,3,5, and 7 of a
V -8 engine. .
76
"
-------
.~ 0.9
a..
V')
3: 00 8
9
L..L..
z
~ 0.6
t-
« Ou 5
a:::
«
>
V') 00 4
V')
~
~ Ou 3
V')
~ 0.2
~
c 001
100
~
I
I
I
I
I I
--Hot Wire Anemometer.
Measurements from Phase I
Normalized Mass Air Flow
Used I n Simulations
I
I
I
I I
I J
. 0
o
1.0
O. 1 O. 2 00 3 O. 4 00 5 O. 6 O. 7 00 8 O. 9
. .
FRACT ION OF 720-DEGREE ENG INE CYClf
Firure 4. Characteristic variation in cyclic mass flow through air
in.p.ction tube during a 720° engine cycle. Fraction zero coincides
with opening of the exhaust valve. Area under the normalized curve =
.874. .
77
L..
.J::
-
2
E
..c
~'
o
--I
L..L..
a:::
«
V')
V1
1.
-------
In the absence of experimental dat.a on variation in exhaust temperature,
it was as,sumed that peak temperature occurred coincidentally with peak exhaust
flow, as shown by the solid curve in Figure 5. .All simulations involving
periodic temperature variation were performed on .this temperature pattern
shown by the dotted curve in Figure 5. This curve has been placed in a posi-
tion \vhich averages out the tailing temperature drop, which is felt to be par-
.tially due to greater heat loss specific to exhaust flow as flow drops to
zero. Temperature span for these data as plotted, between 0 and. 1 on the di-
mensionless scale, is approximately 900°F.
In Tabaczynski's (35) study, engine speed between 1300 and 1800 rpm was
shO\vn to have little affect on temperature span. However, departures in air
fuel ratio from stoichiometric did lower the span by up to 200°F.
Since the temperature drop during blowdown is associated with expansion
oJ:' the exhaust gas within the cylinder, we can estim~te temperature span
solely by the change in pressure within the cylinder. Pressure at the time
the exhaust valve opens is approximately 75 psia at ftill load and 20 psia at
no load, based on unpublished engine test data, Automotive Laboratory, The
University of Michigan. If we assume that the gas within the cylinder expands
i:sentropically and that the discharge through the valve is a constant tempera-
ture throttling process, we can then estimate temperature span from the expan-
sion properties of an ideal gas.
i. e. ,
~high.. [:highl
low lOW]
l-y
_C
yc
y .. 1.3
c
Applied to an expansion from 75 to 15 psia for Tlow = 1200°F (16000R), we
obtain a temperature span of 92SoF. At 20 psia, the span is 114°F. This
calculation indicates that the span of temperature variation may change
greatly depending on engine load.
The time variation in concentration of total hydrocarbon shown in Figure
6 was obtained by summing species concentrations published by W. A. Daniels
(12). Carbon monoxide and hydrogen were assumed to be uniformly distributed
in the exhaust. .
'(I;
--- .._-+ .-.,,,-
-------
z
«
a..
V"I
L.LJ
a:::
::::>
I-
«
a:::
L.LJ
a..
~
. L.LJ
I-
Z
Z
o
1.0
0.6
I-
«
a:::
«
>
V"I
V"I
~
Z
o
o. 1 ,
,
,
V"I
Z
L.LJ
~
Q
I \
I \
I \
. \
I \
, \
I \
, \
I
, /',
I Optical. \
measurement. \
Tabaczynski, R. J. \
Assumed variation
in exhaust temperature
used in simulations.
,......
I \
/ \
/ \
-' \
\
\
\
\
,
,
,
O. 1
O. 9 1. 0
O. 2 O. 3 O. 4 O. 5 O. 6 O. 7 O. 8
FRACT ION OF EXHA UST STROKE'
Figure 5. Assumed variation in cyclic exhaust temperature based on
coincidence with measured peak flow, compared with optical'measure~
menta by Tabaczynski (35). . .
79
.
-------
700
"\ --- Approximate Total
I \ Hydrocarbon, W. A Daniel f\
/ , 600
1.0 Normalized Hydrocarbon
0.9 I
500
z I
<1:: 0.8
a.. I E
(/) c::I..
c::I..
~ 0.7 z
co 400 0
a::: co
(5 0.6 a:::
<1::
o u
a::: 0
~ 0.5 a:::
c
::I: .300. .>-
~ 0.4 ::I:
c
~
. z: u..
~ 0.3 ....J
<1::
(/) J-
z: 200 0
I.J.J 0.2 J-
:2:
c \
O. 1 \
" 100
0
----
o
O. 1
O. 2 O. 3 O. 4 O. 5 .. 0.6 . O. 7 0.8
FRACTION OF EXHAUST STROKE
o
O. 9 1. 0
Figure 6. Characteristic variation in cyclic hydrocarbon concentra-
tion. Area under normalized curve = .3954.
80
-------
MODEL BUILDING AND PARAMETER EVALUATION FOR STATIONARY STATE OPERATION
1.
Mixing Coupled with Reaction
Failure to reach complete conversion of combustibles at high exhaust tem-
peratures is a strong indication that conversions are mixing limited. Only a
high-order rate dependence on one of the. vanishing species could otherwise .ac-
count for this failure, and this is not consistent with the kinetics and their
use in the analysis which follows later. Therefore, the simulations under-
taken for steady state reactor operation have been designed to permit a very
general treatment of coupled mixing and reaction. It seems evident that many
problems associated with combustion and pollution control should benefit from
application of the resulting simulation programs.
By virtue of a number of the features of the exhaust problem already
given, it is easy to visualize reasons why a portion of the. exhaust combusti-
bles might escape from the reactor unmixed with air and therefore unreacted.
To enumerate: input of separate streams of air and exhaust into a reactor im-
mediately implies that some nonzero fraction of the reactor volume must con-
tain partially segregated air and exhaust; a very "short" residence time tends
to insure that some appreciable segregation persists throughout the reactor;
the virtual exclusion of air flow during peak input of exhaust (low pressure
air injection) further promotes this segregation; the wide distribution of
inlet temperatures related both to temperature difference between air and ex-
haust and distribution within exhaust potentially allows reaction to be
quenched in a low-temperature fraction of flow in spite of adequate local mix-
ing; and finally the restriction of hydrocarbon combustible primarily to a
small fraction of entering exhaust volume reduces the probability that a sto-
ichiometrically sufficient amount of air will mix with it.
Quantitative treatment of these phenomena is guided by the classical con-
cepts of chemical reactor design, starting with the elementary design equa-
tions for stirred tank and plug flow reactors and extending to constructs for
treatin~ locally segregated reactants. While no ready-made method of solution
ex.isted which would treat the full gambit of features characterizing t.his
problem, the basic concepts needed had been established. Thus, model building
became the task of fitting the concepts into a suitable computat.ional frame-
work. To establish the mot.ivation that guided the development. of simulations,
key literature concepts will be reviewed.
81
-------
A.
REVIEW ON MIXING IN CHEMICAL REACTOR DESIGN
A frequent problem in reactor design is the computation of conversions
for "nonideal" mixing from kinetic data obtained for."ideal" mixing, as for
instance in applying the data obtained from the single cylinder reactor sys-
tem to predicting the performance of the DuPont Model V reactor. If we wer~
only interested in a single device, we could lump all mixing effects with an
empirical correlation of "ki!1etics" and the problem would be at an end. How-
ever, to perform a nontrivial service to design it is necessary to start with
kinetics which are essentially nonmixing limited and to apply these kinetics
in a ivell motivated manner to a range of mixing conditions. Mixing must
therefore be considered both in obtaining kinetic data and in subsequently
applying these data to design.
It is useful to reflect on mixing in descriptive terms before we attempt
a more precise treatment with the aid of literature design concepts. First,
"mixing" involves several distinct, though not mutually exclusive, physical
circumstances: mixing is the blending of two or more separate streams; the
backmixing of flow within a stirred tank as opposed to "segregation" in a nar-
row pipe; the exchange of material between separate droplets in a dispersed
phase or between separate eddies in the structure of a turbulent flow. In
turbulent mixing of miscible fluids having different properties, mixing can
be thought of as. a continual reduction in the length scale of property varia-
tion until the property gradients are eliminated by thermal conduction or
molecular diffusion. Mixing must proceed down to this point of intimate mo-
lecular interspersal before chemical reaction can occur. However, mixing may
be partially restricted on a length scale far larger than this, depending on
the pattern of flow. Consideration of a specific length scale is conveniently
avoided in most of the literature on reactor design. .
The most elementary aspect of mixing in reactors is concerned with pat-
tern of flow on a length scale determined by overall reactor dimensions, which
uses as its starting point the difference in performance between ideal plug
flow and ideal stirred tank reactors. Design equations for these, which are
availabl~ in several texts, e.g., Levenspiel (22), indicate lower conversions
in a stirred tank for all reaction orders greater than zero.but no difference
for zero order (Deglecting thermal effects).. The disadvantage of stirred tank
flmv is that entering material is immediately dispersed equally throughout the
reactor and is therefore subject to early departure; indeed the distribution
of residence times, represented by an exponential decay curve, indicates that
a larger fraction of material departs in the time interval immediately follow-
ing entry than in any similar time interval thereafter.
The first step beyond the treatment of the idealized flow extremes is the
building of models for intermediate flow patterns.. In this area there has
been collected a very large body of literature dealing with numerous models
and their mathematical descriptions; much of this work has been summarized by
t)2
.'
-------
Levenspiel and Bischoff (23) and Lev-enspiel (2:-~).
categorize this work: dispersion models, recycle
in series models.
Three model types serve to
models, and stirred tanks'
The axial dispersion model treats axial mixing for flow through an empty
tube as a diffusional process, wherein all mixing effects of molecular and
turbulent diffusion, and holdback due to velocity profile are lumped together
into an apparent diffusivity in a partial differential equation of the stan-
dard diffusion type.
c~
u -+-
~aU/a'1~
L
~
~ Z
..
......
d2c dc L2
- - Pe - + -c = O.
dy2 dy DL '
y = z/L
Pe = Lu/DL
(I-I)
c + = c + L de I
o 0 Pe dy 0+
(1-2)
de I
dy L-
Q e
(1-3)
The axial dispersion model approximl3.tes behavior ranging from ideal plug t;low
to ideal stirred tank as the axial diffusivity DL ranges from 0 to 00 for L r
0, as length L ranges from 00 to 0 for Dl r 0, or more generally as the Peclet
number, Pe, representing the ratio of bulk transport to dispersion ranges from
00 to O. The model has been extended to cover radial dispersion also (14).
The recycle model (17,28) consists of a plug flow reactor with recycle
from the exit back to the inlet.
~
<
r~
~c
8)
-------
Design equation:
T = (1 + y) c
o
Jx (T ) ,
-r~X)
l~yK(T)
dX
(1-4)
The, recycle model represents ideal plug flow for a recycle ratio r equal to
zero and a.pproaches an ideal stirred tank as r + 00.
The ideal stirred tanks in series model represents degrees of backmix by
means of a series of perfectly mixed tanks, wherein feed to each tank is im.,..
1nediately dispersed uniformly throughout that tank. The condition within one'
tank becomes the inlet condition to the next.
Co
2
C3 ~ .c.j., m Cj . r.bcn
...~...~
j..i . j n.
1
3
Conversion in a one-dimensional array of n equal size tanks for a one step
reaction of order 1'), n r 0, or 1, is shown from the material balance on the
jth tank to be the solution to the set of equations:
k . C 1\-1 1\
T T '0 ( .:.t)
n Co
+:..1 -
Co
Cj-l ::: 0
Co
(1-5)
j == 1,2, ..., n.
For a first order reaction, this reduces to an explicit expression:
c
n
-=
c
o
1
n
(l + kTT)
n
(1-6 )
n4
-------
and for zero-order reaction, the conversion becomes independent of number of
tanks n:
c
n
-=
c
o
1 - kT
T
(I-7)
c
o
;
kTT < Co .
The model is precisely an ideal stirred tank for n = 1 and approaches plug
flow as n ->- 00. For large n, n has been shown to be directly proportional to
the Peclet number Pe in the axial dispersion model (22). At low values of n, .
the ideal tanks in series models represent degree of backmixing in a very dis-
cretized fashion, as they progress from a single CSTR to 2,3,4 ... tanks.
This can be offset by using tanks of different sizes; however, this destroys
the simplicity and computational convenience of the model. Besides different
size tanks, the model has been v~riously generalized to include nonuniform
flow rates between tanks, backflow, and multiple dimensioned arrays of tanks
( 1, 13, 30, 34, 36) .
Having established certain models to represent pattern of flow, it is of
course permissible to combine them to suit specific purposes. A simple exam-
ple is a combination of one or more stirred tanks with a plug flow reactor.
Combinations of this type will be discussed in the next section.
Further details of theory are presented in the Appendices.
B.
THE PATTERN OF FLOW MICROMIXING SIMULATION
A general quasi steady-state (cyclic) simulation program, denoted as
"MICROMIX PATTERN OF FLOW" (MMPOF), was written to investigate the coupled
effects of mixing with reaction and heat loss by providing for forward move-
ment of a train of cells through a user-specified network of (nonideal) reac-
tor modules. This program and subordinate programs which perform more re-
stricted calculations are described here with reference to the assumptions
thRt r;uirle the calculations. More detailed descriptions of the structure and
use' of simulations are given in the computer programs that are on file ,vi th
sponsoring agencies and enclosed on microfiche (see Reference 32).
Solutions
unsteRdy-state
type methods.
for the cyclic stationary state are obtained by performing an
approach from a specified initial condition using Monte Carlo
Flow leaving an engine or an air jet is assumed to be divided into equal
sized cells, each 'containing the same number of moles. Cell input is
85
-------
distributed with respect to time to reflect cyclic variations in flow associa-
ted with the firing of individual cylinders and flow variation therein. Mix-
ing between the segregated inlet streams of air and exhaust is accomplished
by coalescences and redispersals of pairs of cells. The pattern of flow for
cells passing through the reactor system is determined by the design of the
module netw.ork. and the inter-module flow streams. By changing the arrangem~~nt
and type of modules, a large variety of cell residence time distributions can
be simulated. Each module and flow stream arrangement also fixes the availa-
bility of cells to collide \vith other cells present in the reactor system.
Modules within the reactor system can be designated to have either a
nonideal stirred-tank or a nonideal plug-flow pattern of cell flow. In a
stirred tank module, cells are chosen at random to either coalesce or depart
from the module. In a plug flow module, cells proceed through the reactor in
the same order in which they entered; the cells are grouped into sets, called
"slugs," and only cells within the same slug are allowed to experience coal-
escence. By considering a large number of slugs, each containing a number of
cells, it is possible to approach the condition of mixing and reacting only
those materials which enter at the same time. Some longitudinal dispersion
is, however, inevitable.
Reactions within individual cells proceed as though each cell were a sep-
arate batch reactor. The changing temperature and composition of a cell is
. .
updated for reaction and heat loss each time that that cell is chosen to ex-
perience coalescence or to leave the reactor module. The updating procedure
. .
is based on a one-step integration followed by an optional corrector step at
a mean temperature and composition.
Operation of a simulation is conducted for one module at a time, where
this is permitted by the assumption that cells are allowed only forward move-
ment to modules occupying a more advanced serial position. All parameters
for the module: volume, pressure, heat loss, flow, and mixing are supplied
independently for each module. The output from a particular module can be
saved in one of several parallel property rosters for as long as .it is re-
quired as input to a subsequent module in the networl\:. Several output streams
can be combined. to represent a convergence of internal flow streams; or flow
can be divided to proceed from one module to two or more forward positioned
modules.
Inlet cell trains can be generated within the simulation, or a roster of
cell properties can be read as data. All parameters that are necessary for
trial operation of the simulation have been given default values which can be
overridden by reading data.
Simulation output consists of a listing of all input parameters, averaged
outputs for individual modules, and average final outputs. No variances are
computed in "MMPOF," however, if desired, the complete roster of outlet cell
86
-------
properties can be J?rintecl binary form for any or all of the reactor modules.
Variances can be computed for these dumped properties, and in addition auxil-
lary pro~rams have beon written to compute and graph histograms for all dis-
tributed properties. All printing is under control of logical variables with-
in the program, and can be suppressed if desired.
Data for simulations are categorized as follows:
Chemical properties - .
species
. thermodynamic constants
chemical reactions and stoichiometry
chemical rate equations
activation enerRies
reaction orders
Inlet conditions -
number
cyclic
cyclic
cyclic
of' inlet streams
flow rates
temperatures
concentrations
Reactor configuration
(macromixing) -
module network
module types, nonideal stirred tank or
nonideal plug flow
internal flow fractions
replicate flow streams and their phasing
module volumes
Micromixing
parameters -
number of cells per inlet cycle
number of cells per plug-flow slug
the "mixing parameter," I for each
m
module
Heat losses -
a constant value of module heat
a heat transfer coefficient for
heat loss among cells
loss
distributing
'l'iminl~ parameters -
Printing control -
length of simulation
cycles discarded for washout
cycle timing, engine rpm
input parameters
averaged results
cell properties
1)7
-------
All cyclic input flows, temperatures, and compositions are computed in
FORTRAN FUNCTION SUBPROGRAMS, named FNF, FNT, and FNX~ respectively. These
functions are written to allow the user to specify completely arbi t,rary ampli-
tudes for cyclic property variations during the active period of a particular
input stream. Both the amplitude and the active time span are normalized to
a range of 0 to 1. Scaling for the normalized amplitude is supplied by inpnt
data, and the scaled variations are then added to a data-specified low value
for the property concerned to obtain the correct instantaneous value.
1.
Organization of Modules and Flows
In Figure 7, the organization of the pattern of flow simulation is illus-
trated by means of a hypothetical network of modules and internal flow streams.
Inlets, outlets, and reactor modules are positioned on a grid given by the
intersections of "module streams" and "serial positions." The number of
module streams is chosen to equal the largest number of cell property rosters.
that are to be saved at anyone given time. If a property roster is no longer
needed either to supply inlet properties to another module or to contribute
to the final outputs, another module can be positioned ahead of it on the same
stream causing output from the new module to replace the old.
The first and last serial positions in a simulation are reserved for the
inlets and outlets, respectively.' A simulation may have both multiple inlets
and outlets if desired. The intermediate serial positions are occupied by
either nonideal stirred tank or plug flow modules, with the possibility of two
or more occupying parallel positions at a given serial position.
Internal flow streams must proceed from the. last module on a. stream to a
serial position that is further advanced by one or more positions. Calcula-
tions are done in order of serial position, which in the absence of backflow
bet\,rcen modules guarantees that calculations can be performed consecutively.
The L'lOl'i' net\wrk may include both division and confluence of flows. In either
case, the cell size in moles can be adjusted by integer cell division. Non-
integer (li visions are disallowed because of the mixing that is implied by the
. consolidation of cell fragments.
Flow strernns can be replicated to represent parallel streams which con-
tain similar flows except for a shift in phase or position within an engine
cycle. In Figure 7, an original flow stream plus three replicates are shown
between modules [NS,NPJ = [2,2,J and [3,2J to represent flow out of four ex-
haust ports into a single reactor core. Flow from each port can be phased
independently to reflect the timing of cylinder firings. This phasing feature
eliminates the need to perform separate simulations on all four ports.
The ' illustrative simulation network represented in Figure 7 includes the
following features:
88
~~ ~
(
)'
-------
MODULE
"STREAMS"
NP
'=
.L-~
-1-
-2~.
ex,
\0 :
-3-
-4-
I
1
I
EXHAUST
.
.SERIALPOSITI.ON, NS
I . 1 . 1
2 3 4
I I 1
..
EXHA UST --.
---.
AIR
.. .
AIR
..
I NLETS REACTOR MOD ULES
~ . INTERNAL FLOW STREAMS
- ...-.- -.. REPLICATE FLOW STREAMS
1
5
I.
I
6
.1
o UfLET(S)
Figure 7. . Illustrative module network for simulation "MMPOF".
-------
Separate streams of air and exhaust are directed into a stirred tank
port, [NS,NPJ = [2,2J, where they mix and partially react. Outlet prop-
erties from the single port simulatuion are replicated three times and
phased to represent four ports firing into a stirred tank reactor core
[3,2J. An auxilliary flow of air is directed into the core. Ou.tput from
the core is divided between a plug flow module [4,2J representing an ex-
isting annulus, which also receives a bypassed fraction of exhaust, and
a sequence of a stirred tank and a plug flow module. A.single outlet
recei ves flow from two plug flow annuli and from both bypassed Fli r FInd.
exhaust. This particular simulation has never been run and if: used onl.v.
as an illustration. .
2.
Inputs to Simulation Modules
The first set of inputs in serial position NS = 1 can be specified either
by reading rosters of cell properties, which may have been generated by a pre-
vious simulation, or by invoking a property generating subprogram, "ENGINE,"
which supplies cell properties based on the flow and property distributions
described previously (Figures 2 through 6). All simulation parameters con-
trolling input are defined in the computer program documentation (32); input
parameters can be separately identified from the FORTRAN NAMELIST and DATA
declarations, where the latter are used to preassign default values to all
input variables.
'l'he division of integrated flow from subprogram "ENGINE" to generate
cells containing equal moles and the assignment of corresponding temperatures
and mole fractions is shown schematically in Figure 8. The cell roster in-
cludes storage for values of inlet time, temperature, mole fractions, and age
for one engine cycle comprising four cylinder firings. Compilation of rosters
from internal flow streams proceeds similarly. In general, separate rosters
are maintained for outputs from several modules, assuming that their values
will be needed subsequently; only one inlet roster is needed since module
simulations are performed sequentially. Rosters will in general include in-
put or output for several engine cycles to reduce the effect of random error.
Outlet times from one module generally become inlet times
except Hhen they are adjusted for cycles that are discarded to
\Vashout of initial cells in a stirred tank module. Phasing of
may also change inlet times.
for the next,
accomplish
replicate flows
"Age"
traversed;
dence time
is the accumulated time spent in as many reactors as a cell has
these are never adjusted. Their values are used to determine resi-
distribution, both at the terminal exit and at intermediate points.
90
-------
ENG I NE CYCLE
CYLINDER CYCLE CELL ROSTER
EXHA UST
~ CYLI NDER
1 3 5 7
0
- 0
4»
~ ~
EXHAUST
0
~ b .
0 -
. 0
~ -i 8 8 Time, t
HYDROCARBON ~ 9 ~ a Temperature, T
,." o~ Mole fraction, Cj
Ull/
0
o 0 Age, a
. . ~ 0
o -
AIRFLOW. / 0 0
~ .
0
-
0
[ill1l I I o . .
.
Figure 8.
Schematic on the compiling of the inlet cell roster.
91
-------
3.
Flow and Mixing in "POF"
Macromixing in the sense of cell flow pattern is determined entirely by
the module network and the internal flow streams.
a.
Stirred Tank Modules
Micromixing within a stirred tank module is governed by assumptions
stated in Figure 9. Three rosters are required: inlet, reactor, and outlet.
The reactor roster is initialized with unreached but mixed feed, averaged
over one cycle, ,vi th the temperature adjusted by adding T~ to lower or raise
the starting temperature for the purpose of studying ignition. . Cells are
entered sequentially from the input roster and displaced randomly selected
cells out of the reactor into the outlet roster. The simulation is first
operated for a specified number of cycles without saving output to wash out
the initial cells. Total duration of each stirred tank simulation is speci-
fied as a maximum number of engine cycles. If operation proceeds past the
end of the inlet roster, input is resumed from the start.
Mole compression is neglected in cell calculations causing intermediate
mole fractions to be in error by up to approximately .)% of their correct value
. .
for normal exhaust concentrations. Mole fractions are corrected to a sum of
"1" at the end of the simulation. This error would be more serious in other
applications of the simulation if reactants in unequal molar reactions were
less dilute. The error does not affect the mass balance for individual spe-
cies within cells, the low mole fractions times the entering number of moles
give the correct specie mole content. However, use of the uncorrected total
moles per cell causes both individual cell and aggregate cell volumes to pe.
high, producing small errors in cell population and in specie conversion
rates, ri . Vc' . Error in mole fraction changes relating to reaction rates
results only from the contribution of partial pressures appearing in the rate
equations, since the contribution of high cell volume is cancelled out when
the rate is divided by the uncorrected high mole content. The reason for neg-
lecting mole compression was to reduce the running time of the simQlation.
I
Adjustment of the cell population in a stirred tank takes place at the
start of each cycle, to fit the total number of moles in the reactor to the
module volume, using the perfect gas law and the average temperature for cells
exited during the previous cycle. This allows a change in cell population to
correct for the unsteady approach of average cell temperature to the limiting
value experienced at stationary state cyclic operation, but it ignores changes
in aggregate cell volume due to fluctuations in average temperature within a
cycle. For stirred tank simulations performed on an entire. reactor volume
containing most of one cycle of flow, preliminary work with an ideal stirrerl
tank simula.tion indicated fluctuations of npproximal,ely ~.I(fo in reactor mole
contents. When the simulation is used for r:mllll volumes [~uch ns the exhaust
ports, the within cycle temperature fluctuntion will be much higher , with
92
-------
Figure 9.
Flow and mixing in non-ideal stirred tank modules within
"MICROMIX PATTERN OF FLOW"
STIRRED TANK MODULE
Reactor Roster
o
.
o 0
o .
o
Outlet Roster
Inlet Roster.
o
o
Major Assumptions:
1.
Cells contain equal moles.
2.
The slight effect of mole compression due to reaction
of dilute species is neglected until the end of the
simulation, when mole fractions are corrected.
3.
Cell population is adjusted once each cycle to
compensate for the solution's approach to an average
temperature.
4.
CoalescenceSof cells are random independent.
5.
The micromixing parameter "I ", representing
coalescences pet cell entry,mis constant so that
coalescence frequency wi varies in proportion to
cyclic changes in input frequency w .
r
Two cells mix perfectly at coal.escence.
6.
7.
Redispersal is immediate.
8.
Cells departing from the reactor are chosen randomly.
9.
Cells between events are treated as homogeneous batch
reactors.
10.
Heat losses are distributed according to cell tempera-
ture.
93
-------
. .
fluctuation on reactor mole contents being perhaps !15%. However, this is
partially offset by also neglecting fluctuations of approximately !5% in port
pressure, where peak pressure coincides with peak exhaust ~low and peak ex-
haust temperature. Considering the low c~nversions that are'indicated for
the ports, there is little practical reason to change the simulation in favor
of more frequent updates of cell population; however an option has been de-
veloped for checking cell population as often as cells are entered.
b.
Plug Flow Modules
For a plug flow module, operation is simplified by the fact that chRng~s
in cell properties can be computed in place on the inlet roster. 'Iwo indices
shown by the vertical arrows in Figure 10 indicate the first and last cells
present in the reactor. Tee cell population is adjusted by controlling exits
to fit an average temperature for cells in the reactor at the time of exit of
each slug from the reactor. Working with 16 to 44 slugs per cycle, the tem-
perature variation between slug exits was' small.
The important features of the plug flow simulation are that cells enter
and leave in unchanged order and that coalescences occur only between cells
in the same slug. Since slugs need not represent negligible time slices, the
size of a slug is a parameter which can be used to introduce more or less
axial dispersion in the nominally plug flow reactor.
4.
Heat Loss
Heat loss from the reactor is specified both as a total rate of heat
loss, Q Btu/hr, and as a heat transfer coefficient HAc Btu/hroF. These two
parameters are used to distribute heat loss among cells in relation to their
temperature as follows:
Assuming that each cell sees a fraction of wall represented by llNc,
where N~ is the number of cells,
~ell = L HA (T T)
N c cell - wall
c
( I-8)
Q = HA
c
(T avg - Twall)
( I-9)
_L
or Twall = Tavg HA
c
( I-10)
HA
Q - .Q.... + ~c (T - T )
cell - NN cell avg
c c
( I-ll)
;)4
-------
Figure lO~
PLUG FLOW MODULE
Flow and mixing in non-ideal plug flow modules within
''MICROMIX PATTERN OF FLOW"
Inlet Roster
" I I I I I I I
1... C~~ls---t
Reactor ..
Slugs
Major assumptions:
1.
Cells contain equal moles.
2.
The slight effect of mole compression due to
reaction of dilute species is neglected until
the end of the simulation, when mole fractions
are corrected.
3.
Cell population in the reactor is adjusted after
each slug exit.
4.
Coalescences occur only within slugs.
s.
The first cell in a coalescence is chosen
randomly from among all cells in the reactor.
The second is chosen randomly from the same
slug as the first.
6.
The micromixing parameter, I , is constant.
m
7.
Two cells mix perfectly at coalescence.
8.
Redispersal is immediate.
9.
Cells leave in the order they entered.
10.
Cells between events are treated as homogeneous
batch reactors.
11.
Heat losses are distributed according to cell
temperature.
95
-------
)~--
I
5.
Kinetics, Material and Energy Balances
Cell properties, temperature and mole fractions, are updated for batch
reaction before each coalescence or departure from the reactor. All computa-
tions concerned with updating (reaction rates, material and energy balances)
are assigned to a FORTRAN SUBROUTINE, "UPDATE:. " .
The metho,i of updating compu.t.es 'a rate of cell heat loss and rates at'
reRction for "q" l'ombllstible species at the beginning of the update, and per-
forms one-step integrations of temperature and reactant mole frl-lctions based
on these initial rates. An option is provided for a corrector step based on
midvalue mole fractions and temperature.
Reaction stoichiometry' for reaction "k" and species i'i," given by vi, k'
is written for one mole of the combustible specie. A total of "m" species
. are assumed to be ordered with "q" combustibles appearing first,. followed by
oxygen, then products, and finally inerts:
e. g. ,. if CO is the first combustible:
v
. 1,1
CO + v
q+l, k
o + V CO
2 q +2 , 1 2
( 1-12 )
\,ith
v
1,1
=
-1 v
. ' '1+1,1
-l/;~, V ') 1
q+, ,
=
1
l~eaction rrltes are eX"press~d in Arrhenius form:
rk
A e -Ek/RT W (pc. .) TJi, k
k i=l J,l
. (1-13)
A complication .in update calculations is the necessity for checking for
specie disappearance during the update period between the time of the last
updatetl and current simulation time t. If a combustible is depleted, as
shown in Figure 11, its mole fraction becomes zero and its contributions to
the rate of oxygen depletion and to the energy balance are ended. Oxygen mole
. r)'~h~t.ion C j.. '1+1 must be updated in a piecewise fashion where combustible de-
ph'Lions occur. If oxygen itself is depleted, all reaction ceases and only
heaL 1088 is continued to time t.
/
96
-------
. ...
..
u""
r-
%
o
-
t-
u
«
~
~
u.J
. -oJ
o
~
tl
TIM E
t
Figure 11.
Mole fraction integration showing disappearance of species.
Material and energy balance equations for linear updating of mole frac-
tions Cj,i and temperature Tj are as follows:
c. . (t)
J,l
=
c. . (tl)
J,l .
r. (t*) . lIt*. V (t*)
.1. C
+
Mc
, i = l,...,q + 1;
(1-14)
F l( oxygen) is corrected whenever a combustible species d.is~lppears.
q+ .
r.(t-*)
1.
=
q
L,
k=l
Vi,k rk (t*)
i = 1,2,...,q + 1
(1-15)
V. = l' v = O. i = l,...,q; i r k
l,i ' i,k '
V (t*) = M' HT(t-x-)/p (1-16)
c c
97
-------
6t*
i
(disappearance time Mdi' if species disnppen.l'S)
It-tl if species does not disappear
=
T . (t)
J
[ q
Tj(tl) + k:l
v (t*) 6H (t)
cr 1
k
M C (tl)
c p
-
-------
C.
SIMPLIFIED MIXING SIMULATIONS
A number of simplified computer programs were developed to perform
ticular simulations more efficiently on the computer than they could be
formed using "MMPOF." In order of decreasing complexity, these are:
'5.
1.
"MICROMIX I" - stirred tank RTD only;
par-
per-
All of the foregoing except "EXHAUST" are cell coalescence models which
are essentially similar to "MMPOF" in those calculations which they are de-
signed to perform. Descriptions which follow will be limited to the distin-
guishing features.
2.
"MICROMIX n" - stirred tank RTD only.
3.
"MICROMIX PF" - plug flow RTD only;
4.
"EXHAUST" - ideal stirred tank at 1m = 00
but with provision for cyclic input.
"MIXONLY" - cell mixing with instantaneous reaction
for single stirred tank or plug flow modules;
6.
"MIXONLY POF" - cell mixing with instantaneous
reaction for series combinations of stirred tanks
and plug flow modules.
1.
"MICROMIX I"
"MICROMIX I" computes a Monte Carlo solution for the stirred tank cell
mixing model only, based on assumptions that differ from provisions found in
"MMPOF" in the following respects:
( 1)
Cell population is constant.
( ;! )
'l'hc cell inlet frequency (J)r is assumed to be constant.
ties are hOlvever allowed. to fluctuate cyclically.
Cl'll proper-
( :J)
Heat losses from cells are computed. by \vall collisions, asswning
that a cell assumes the ,wall temperature at the time of collision.
The wall collision frequency is computed from a heat transfer coef-
ficient IrA .
c
Q = HA (T - T )
c avg wall
w
w
~ E M C (T -T )
i=l c P celli wall
99
,( 1-22)
-------
If ~~ and Cp are constant,
w
w
&: HA 1M Cpo
c c
(1-;'":\)
( ) I )
IJpd.atinl~ of cell temperature and composition is performed by the
modified Euler method (;~ function evaluations on the first step and
1 evaluation per step thereafter). Step size is computed to limit
conversions for all species to less than a specified fraction during
one time step.
(5)
Reaction stoichiometry is unrestricted and the kth reaction may in-
clude any of."m" species as reactants or products:
m
E
1=1
A - 0
1
([-;-'~) .
V1 k
,
v is positive for products and negative for reactants.
(6 )
Variances are computed for distributed properties.
2.
"MICROMIX II"
"MICROMIX II" is similar to "MICROMIX I" except for the following:
( 1)
Heat loss from individual cells is a constant;
l:.ributed in relation to temperature.
i. e. ,
it is not dis-
( : ~ )
stoj chiometr,V is re8tricted to oxidation:: writtE'n for one mole' of
:1. (~()mbllstiblc, as in "MICROMJX I\W."
(j)
Kinetic inte[1;ration proceeds in a sinr1;le step with a corrector stf:p
option, as in "MICROMIX POF."
3.
"MICROMIX PF"
"MICROMIX PF" computes a Monte Carlo solution for the plug flow cell
model only, based on assumptions that differ from "MMPOF" as follows:
100
-------
( 1)
is filled with a
inlet stream. All
the volume enter-
A slug of cells enters the reactor at the time it
specified number of cells from the integration of
cells in the slug leave together at the time that
ing behind it equals the volume of the reactor.
(2)
Coalescence frequency is specified as Wi/2.
(3)
T = m'/~r is calculated
lTl l .
sired, the time of flight
a specified value of 1m'
when a slug leaves the reactor. If de-
for the slug can be continued to satisfy
( 4 )
Heat losses are treated as cell wall collisions (see MICROMIX I),
with provision for makine; the local wall temperature and the con-
vective coefficient functions of position in the reactor.
(5)
A freCluency can be specified for updating properties Yor all celIe;
in the reactor and computinr: slur: averAgE' propf'l'tie~~.
(C)
The simulation is de~;ir:ned to perform an integer munbel' 0.1' co,~lE's-
cences between the times that all cells are updated. Furthermore,
integration of inlet flows proceeds on a time step which is an
integer fraction of coalescence period or vise versa.
4.
"EXHAUST"
"EXHAUST" is an ideal stirred tank simulation (1m = 00) which utilizes. the
cyclic inlet flows and properties that have been described for "MMPOF." No
cells are involved, since input is assumed to be perfectly mixed with reactor
contents at the time of entry.
"EXHAUST" computes an unsteady state approach to repeated cyclic opera-
tion by integrating rates of change in enthalpy and moles of individual spe-
cies within the reactor obtained from material and energy balances. Integra-
tion is by means of a fourth order Runge-Kutta method. The integration of
change in enthalpy leaves temperature to be computed by a half-interval root
J'indinr,; method.
i"low out oJ' the reactor is computed from gage pressure in the reactor;
ab:wlute pressure in the reactor is computed by the perfect gas law. .
').
"M1XONLY"
The most hi,o;hl,V simplified version of the cell coalescence models con-
siders onl,V instantaneous renctions for two. steady reactant streams entering
n single stirred t"n], or plug flow reactor. Chemical kinetics are not
I
~
101
-------
considered. This program allows two reactants to enter the reactor in R trHin
of cells, some of which contain reactant "A," and the remainder containinp;
reactant "B." The average entering concentrations, stoichiometry, and. propor'-
tion of the entering cells containing "A" are variable. The reactor contains
a pl'eset. nwnber of' cells, and coalescences occur at a specified :t'refluency of
1m per cell inpuL. .
During coalescence, the limiting reactant
reaction), and the cells redisperse containing
tant (equal in each cell). Mixing only occurs
ent. .
is annihilated (instantaneous
products and one excess reac-
if both reactants 'are not pres-
The variables of interest are as follows:
A + vBB -+VCC
( 1)
Stoichiometric coefficients for the reactions, vB' vC~
(2)
The concentrations of reactants in input cells (CAO' CBO)'
(3)
The feed stoichiometric ratio of A:B,
flSR. fI
(4). The dilution ratio, flDRfI = no. of flSfl cells/no. ,of flAfI cells enter-
ing..
(5)
Number of cells in the reactor (Nc)'
( 6)
Number of coalescences per input cell, 1m'
(7 )
Average fractions of A and B converted (during several cycles of
. feed).
Mean residence time is not a parameter of MIXONLY because of the assl.UTlption
that reaction occurs instantaneously upon mixing.
For the plug flow option in flMIXONIJY, fI conversion is determined by ini t-
ializing the contents of a batch of cells with a desired segregated feed and
following the average conversion as a function of cumulative coalescences for
the batch. Conversions are averaged over several batches for the purpose of
eliminating random error.
a.
flMIXONLyfI Reproducibility and Cell-Population Bias
102
-------
For Nc = 100 ceJ,ls in a stirred tank reactor, "MIXONLY" checks the re-
sults of Spielman and Levenspiel (33) for Nc = 500 as shown in Figure 12.
A check on the reproducibility of "MIXONLY" stirred tank simulations
yielded the a limits for IT and 9T (N = 110 cells) shown by the shaded 'areas
c
in Figures 13 and 14. For given values of dilution ratio DR and stoichio-
metric ratio SR, reproducibility is governed by the .number of cells passing
through the reactor rather than by cell population. However, a bias is intro-
duced as the cell population is reduced. With regard to reproducibility.
alone, the YT limits which decline from approximatel,V .02 t.o less than. 01 as
convc'r[~ions increase t'rom .10 t.o . yo are representative of subsC'quent MfXONLY
[;imulatlons that are reported.
tank
To obtain an estimate of' low-population bias, simulations for a stirred
were run at Nc = 2, 5, 10, and, 110 cells in the reactor. The reference
of 110 cells was run for 25T; tests at lower cell counts were run for 9T.
case
The results of Figure 13 for an air dilution ratio DR of O. 1 and a stoich-
iometric ratio SR of 1.5 indicates that the biases introduced by 10 and even
5 cell populations are less than the one a statistical uncertainty for one
mean residence time at Nc = 110 and for mixing parameter 1m out to 3. Beyond
1m = 3, 5 cells produce conversions which are decidedly low. .
In Figure 14, results for DR = 0.5 and SR = 1.5 indicate
for both the 5 and 10 cell populations; however, even here Nc
fall close to the one a limits for 1 T at Nc = 111 cells. .
greater bias
:::: 10 results
In Figures 13 and 14, the extreme condition of having only 2 cells in a
reactor is presented to help visualize the sources of error due to a low cell
population. First, any increase in 1m above the value of 1 has no effect on
conversion since coalescing the same two cells more than one time produces no
additional mixing. The large number of unproductive coalescences that are
thus produced tends to limit conversions to values lower than would be exper-
ienced if a large number of cells were present. Conversely, at lower levels
of mixing and conversion, products are lost in greater proportion than their
mole fraction would warrant. Their rep1,acement by fresh reactant tends to
make coalescences erroneously productive. As cell population increases above
;~, Lhese eff'ects are reduced but are not entirely eliminated for any finite
population.
Comparison of ~onversions in Figures 13 and 14 at Nc = 5 illustrates the
influence that dilution ratio, DR, has on population bias. Where exhaust
cells predominate by 10 to 1 (DR:::: 0.1), the tendency toward unproductive co-
alescences between exhaust and exhaust controls and conversions are low out to
lm= 10. However at DH = .5, coalescences are more effective than they should
be due to excess replenishment of r~actant.
103
-------
I
0.001
Stoichiometric Feed Rotio = 1.0
Dilution = 100%
. Cells in Reactor = 100
o = This Work
0= Spielman a Levenspiel
(Nc=500)
1000
f5100
t-
LaJ
~
-------
Nc =j.- - - -0-
- 6
~C=I N =11
/"" 6~ C
r - "'1(- 7'~ - - -i(- - - - - - -. - - -:- - - ~-
, 0" 6 N c = 2
1//
_«.6 I
I I
z .5 ,0
o
t) .4 1,
« b
a:: I
u.. .3 ,
d I
~ .2,
.
IX .1
- .15
II
o
z .10
o
I- 05
w'
>
~ 0
.-J
~-.05
gs -.I 0
a:::
a::
w-.I5
1.0
o .9
w
.....
a:: .8
w
>
~ .7
u
r--,
I \
I \
x . \
\
\ .
\
\
\ .
.0- \ N _5
" -y------o. -- c-
/ x.. ---
o .', Nc=IO ---0--
- -t1-
- - .... - \\-
..\\........\::.::'.\.:'~ Nc=ll
'- :tU(~)9T
:!:U(X)'T
....
""',
',~~=2
'.....
...........
'x-
A, stream I-"'~ -
B, stream 2...~
A+ 1/2B---'C
DR= stream 2/stream 1=0.5
SR= 2 B/A = 1.5
o
o
5 6 7 8
PARAMETER, I m
9
10
II
12
Figure 13. The effect of a small number of cells in the reactor, N ,
on conversion for a .stirred-tank simulation of mixing with c
instantaneous reaction, A + 1/2 B ~ C. Dilution ratio, DR = 0.5;
stoichiometric ratio, SR = 1.5.
105
-------
en .20
.../.
.../
~ .15
o ./0
II
(.)
z .05
o
t-
W
.>
~ -'.05
.../
~ -.I 0
~ -.I 5
0::
0::
w -.20
.10
o .9
w
t-
0:: .8
w
>
z .7
o
u
:
-------
c.
"MIXONLY POF"
The "M lXONLY .POI"" simulntion extends calculA.t:i.on~~ for cell-Ivi ~;l' mi xinl':
with instant reaction toserief3 combinations of stirred tanks nnd/or plug :1:'10\'1
reactors. No parallel combinations are allowed. As before, calculations are
for two steady reactant streams containing separate reactants.
An optional calculation of "MIXONLY POF" determines the internal distri-
butions of both the cell ages and the Danckwerts' (11) pbirit ages for cell-
wise mixed stirred tanks in series. Cell ages, which are determined by accum-
ulating the time spent in all tanks to any given point without averaging at
times of coalescence, have the same distribution as molecular ages and 'can be
used for estimating the molecular age distribution, ~(a). If accumulated ages
are averaged at time of coalescences, the values obtained are the average ages
of material within cells, which from Danckwerts' (11) definition are point
ages, up. Distributions within any tank can be obtained at the exit, since
the exiting cells are a random sampling of the tank contents. The distribu-
tion over the system is obtained by combining separate distributions for all
t'anks, System variances are computed, so that Dancl<:\verts' "J" = var(O''P)/
var(o:) can be evaluated for various numbers of tanks, n, and values of mixing
parameter, Im'
107
-------
II.
General Parameter Evaluation. .
A.
SIMULATIONS RUN ON MIXING WITH INSTANTANEOUS REACTION
The sensitivities of the "MIXONLY" simulations to the parameter for
Inixing, 1m' for stoichiometry, 3R, and for stream dilution, DR, were mapped
over ranges to be employed later for mixing coupled with kinetics using
"MICROMIX. II." The base case is SR = L "5, DR = 2"5. Conversions of. "A". apply
to CO in general, but could apply to HC or H2 as well.
1.
stirred Tank Simulations
The effect of increasing the coalescence parameter, 1m' in a stirred tank
simulation (Figures 1"5 and 16~ is first to reduce the fraction of "A" uncon-
verted sharply after which further decline proceeds more gradualiy so. that
curves (stoichiometric ration, SR, being greater than 1) become asytnptotic
to zero unreacted only as 1m -+ 00. To achieve 99% conversion requires 1m ~ "5"5
for the base case. .
Sensitivity to stoichiometric ratio "SR" and dilution ratio "DR" (Figures
17 and 18) is a lower stoichiometric ratio and dilution ratio (SR < 1.5 and
DR < .25), but much less change results at higher values. The region of high
sensitivity thus corresponds to the customary operating conditions for exhaust
.reactors; hence these two parameters must be considered important. Their
importance is reduced as 1m becomes large, and would disappear as 1m -+ 00,
except for values of SR less than 1. .
2.
Plug Flow Simulations
For plug flow (Figures 19, 20, and 21), the fraction of "A" unconverted
drops more sharply with increases in 1m due to the elimination of the early
cell departures which can occur in a stirred tank. At the base case (DR =
.2'5,. SR ~ 1.'5) ,conversion goes to completion between Im = 5 and 6 for Wc =
100.
To obtain an estimate of repeatability for the plug-flow MIXONLY simula-
tion, two series of five 100-cell batches were run (Figure 19). The vertical
lines at each point represent the maximum spread in conversion for all 10
batches. The difference betweenaver~ges for the two five-batch series was
approximately .01 fraction conversion.
statistical variance (Figure 19~ in the concentration of the limiting
reactant "A" during plug flow mixing first increases due to reaction and then
108
;
i-'~
.._-~
-------
.9
CI
u..J
1-. 8
0::0
u..J .
>
z
_0 7
u . 0
z
::>
=. .6
~
~
o
\0
~ .5
I-
U
<: . 4
0::
u..
x- .3
.-I
Feed stoichiometric Ratio, of "8" to "A"
.,5 ---x-
l. ~
1.5 0
2, c
5. ~
15, --0-
Cells in reactor ~ 100
Com puter poi nts represe nt
averages over 10 mean
residence times.
Dilution ratio = stream
2/stream 1 = . 25
,2 stream 1, A~O
o 0.. ',I'
,1 strea m 2, 8 0 6 ~ .
Stirred - tank flow pattern
?1
.5
1
2 5 10
MIXING PARAMETER, 1m
02
Figure 15. Stirred-tank mixing with instantaneous reaction, A + 1/2 B + C.
All "A" .enters in stream 1 and all "B" enters in stream 2. Various'
curves represent different values of the feed stoichiometric ratio, SR.
50
100
-------
1.0
.9
0
u..J
J-
~ .8
u..J
>
Z
0 0 7
u
z
. :::::>
- .6
-------
1..0
0
LLJ
J-
a::::
LLJ
> 1m = .5
z x
o.
u . 7
z
=>
-
~ .6
-
z
0 1m = 1
J- .5 *'
u ~...-.
f-' «
f-' a::::
f-' u.
X
I .3
...... 1m = 2
.2
."1 1m = 5
I = 20
00 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16
STOI CH IOMETR I C RATIO, SR (B:A)
Figure 17. Effect of feed stoichiometric ratio, SR, on stirred-tank
cell mixing with instantaneous reaction, A + 1/2 B -+ C. All "A". enters
in stream 1 and all "B" enters in stream 2.
-------
1.0
. 9
£::)
L.U
~ .8
e:::
L.U
>
z. . 7
o
u
z
=>
- . 6
~
.-
z . 5
o
~
u . 4
«
e:::
W-
X . 3
.......t
. 2
. 1
00
1m = . 1
1m
1
1m - 2
1m = 5
1m = 20
.2 .3.4 .6.7.8.9
D I LUT ION RAT 10, STREAM 2/ STREAM 1
1.0
Figure 18. Effect of dilution ratio (stream 2/streaml) on s.tirred-
tank cell mixing with instantaneous reaction, A + 1/2B + C. All
"A" enters in stream 1 and all "B" enters in stream 2.
112
-------
1. 1 x 10-3
X~Xc 1. x 10-3
.9 \ . 9 x 10-3
c x \
UJ
t- \ .8x 10-3
~.8 ~
>
z z
o . 7 X 10-3 0
u .7 \
z t-
:::> \ u
.6XlO-3 «
~ .6 a:::
u...
x ~
z \ .5 x 10-3
0.5 \ 0
2
I-' t- Z
u -3
I-' ~ .4
~ \ Computer points ~ averaged for . 4 x 10. UJ
u... u
10 slugs. Vertical lines show z
>:' .3 .3x 10-3 <
...... \ range of conversions for a:::
«
. 2 ~ifferent slugs. .2 x'1O-3 >
" . 1 x 10-3
. 1 ~
....
~ 1 2 3 4 5, 60
M IX I NG PARAMETER, 1m
Figure 19. Plug-flow cell mixing with instantaneous reaction, A + 1/2 B ~ C.
All "A" enters in stream 1 and all "B" enters in stream 2. Feed.
stoichiometric ratio SR = 1.5; dilution ratio, DR = .25. Number of cells
per slug, Ncs = 100. CA in stream 1 = .07; CB in stream 2 = .21.
-------
1.0
,9
0
w.J . 8
I-
a::
w.J
>
Z . 7
a
u
z
=> .6
-
«
-
z . 5
a
I-
u .4
I-' «
I-' a::
+- u....
X .3
I
-
. 2
. 1
00 1
o
2
3
Di lution ratio, DR = stream 2/stream 1 = . 25
1m = . 5
o
I = 1
m
I = 2
m
I = 3
m
4 5 6 7 ,8 9 10 11
FEED STOICHIOMETRIC RATIO, SR (B:A)
12
Figure 20. Effect of feed stoichiometric ratio on'plug flow cell
mixing with instantaneous reaction, A + 1/2 B -t- C. All "A" enters'
in stream 1 and all "B" enters in stream 2.
13
o
14
15
-------
8 .8
I-
a::::
LLJ
> .7
z
o .
u
~ .6
-
~ .5
z
o
X
I
..... . 2
1.0
. 9
Feed Stoich iometric ratio, (B:A), S R = 1. 5
. 1
00
1=1
m
I = 2
m
I
=3
.9
1.0
Figure 21. Effect of dilution ratio, DR, on plug-flow mixing with
instantaneous reaction, A + 1/2 B -+ C. All "A" enters in stream 1
and all "B" enters in stream 2.
.2 .3 .4 .5 .6 .7 .8
DILlIflON RATIO, stream 2/ stream 1
. 1
115
-------
decays as mixing removes variance faster than it is produced by reaction. As
has been shown, variance in batch mixing without reaction decays exponentially
with time, or with cumulative coalescences in the case of the "MIXOm~Y" model.
3.
Tanks in Series Simulations
The effects of dilution ratio "DR" and stoichiometric ratio "SR" for
plug flow mixing, (Figures 20 and 211 once more depend on the value of the
mixing parameters; and, values of either parameter less than the base values
(DR = .25, SR = 1.5) again represent the region of high sensitivity.
In order to bridge the difference in response to 1m indicated for stirred
tank and plug flow cases, a series of runs were performed an a "MIXONLY POF"
tanks-in-series model for 2, 5, and 10 equal size tanks. The equal size is
of importance only as a basis for assuming an equal distribution of coalescences
among tanks, since residence time per se is not important in the case of
instant reaction. Results, shown in Table I, indicate as expected that at
high values of 1m, conversion increases with an increase in number of tanks--
the largest difference being between 1 and 2 tanks. What was not expected.
but is indicated is that conversions are slightly higher for the stirred tank
at very low values of 1m (see Figure 22 and Table II. This effect can reason-
ably be attributed to the fact that a stirred tank allows early departure of
products as well as reactants and that the removal of more product reduces the
incidence of unproductive duplicate coalescences.
Using the provision for computing internal distributions of molecular and
point ages described earlier, values of Danckwerts' (111 "J" factor were
computed as a function of the number of tanks "n" and the mixing parameter
"1m" (Figure 23). The bound at 1m = 00 was computed from the following formula,
which is developed in Appendix c.
n
z::
i=l
. Z i2 - ~ r Z 12
1:=1 ~
(n-i+2)(n-i+l) -; [i~l (n-i+l)]2
( II-l)
J
:::
To illustrate the effect of ''cr'' on conversion, the base case conversion
(DR =:: .25, SR = 1.5) \~ere plotted versus "J" with "n" and 1m as parameters
(Figure 24). Since a change in "J" at fixed 1m is determined by the number
of tanks in series,. results are similar to those already shown for "n".as the
independent variable; that is, conversion increases as either fIn' or "J"
increases for large 1m and decreases slightly for small 1m. This figureindi-
cates an overwhelming dependence of conversion of the mixing parameter 1m as
compared to "mixedness" defined by "J."
/..
116
-------
TABLE I
CONVERSIONS OF "A" FOR MixING HITH INSTANTANEOUS REACTION OF SEPARATE REACTANT
STREAMS IN "n" EQUAL SIZE CELL-WISE STIRRED TANKS IN SERIES
Reaction: 1
A + -B-+C
2
Stoichiometric ratio, SR, is for "B" in stream 2 to "A" in stream 1.
Dilution ratio, DR = stream 2/stream 1.
DILUTION RATIO, DR
0~10 0.25 1.00
Stoich- n n n
. iometric I 1 2 5 1 2 5 5
Ratio, (X) 10 (X) 1 2 (X)
SR m
f-' .2 .059 .046 .039 .039 .092 .093 .065 .104 .154 .174 .129 .175
f-'
---J 1.0 1. .267 .267 .291 .288 .344 .351 .359 .386 .383 .430 .502 .494
5. .610 .771 .798 .903 .684 .766 .860 .925 .699 .784 .863 .941
.1 .050 .056 .029 .044 .039
.2 .063 .047 .039 .030 .095 .081 .077 .073 .078 .166 .189 .136 .173
1.5 1. .294 .307 .338 .337 .398 .409 .446 .447 .434 .450 .505 .578 .577
5. .802 .884 .932 .988 .815. .921 .961 .983 .995 .828 .906 .961 .997
10. .906 .968 .9968 1. 000 .917 .977 .9974.9997 1.000
.2 .060 .050 .039 .043 .102 .103 .066 .091 .163 .217 .150 .197
5.0 1. .412 .396 .412 .359 .510 .507 .538< .545 .570 <.620 .732 .734
5. .902 .958 .985 .9982 .903 .956 <.987 1.000 .909 .975 .989 1.000
-------
A + 1/2 B C
A in Stream 1 ~
B in Stream 2 . . .
1 2 3 . . . n-l n
o
I..L.J
I-
a:::
uJ
>
Z
o
u
1.0
I = 1 0
. 9
.8
. 7
.6
118
.9
1.0
Figure 22. Mixing with instantaneous reaction for "n" equal size cell-
wise stirred tanks. The mixing parameter, I , is equally distributed
m
among the tanks; stoichiometric ratio (B:A), SR B 1.5; dilution ratio,
stream 2/stream 1 "" 0.25. .
-
~
Z
o
1=1
m .
I-
U
c:::(
a:::
L..i...
.3
. 2
.. 1
1m = . 2
o
o
. 1 . 2 .3 .. 4.. 5 .6. 7 . 8
REC I PROCAL OF NUMBER OF TANKS, lIn
-------
1.0
.9
.8
. 7
-
-
=-'
V1 .6
..-
e::::
~ . 5
~
u
z .4
«
0
.3
. 2
. 1 Analytical
00 . 1
.2 .3 .4 .5 .6 .7 .8
REC I PROCAL OF NUMBER OF TANKS; lIn .
.9
1.0
Figure 23. Danckwerts' (11) liJ" factor for cell-wise mixed stirred
tanks in series. Curves for I =.1 to 10 are computer derived.
. ~
The curve for I = 00 is ana1yt1ca1.
m .. .
119
-------
100
. 9 \
" \ \
\
\ \
.8 \
\ \
\
c .7 \ \ n = ro
I..LJ 1,\
...- 2\ 5\
a:::
I..LJ .6 \
> \ \
z
0 \
u \
- 05
~
-
z .4 \
0 I = 1 \ \
I- m
u " \ \\
« .3
e:::: " . \ \\
u..
.2 A ~ ,,~ ,\
. 1 B '.tm -. 2, \
1m = . 1
0
0 . 1 .2 .3 .4 .5 .6 . 7 .8 . 9 1.0
DANCKWERTS "J"
Fig\1re 24. Influence of Danckwerts' "J" on fraction "A" converted for
instantaneous reaction of "A".in cell-wise mixed tanks in series.
A + 1/2 B ~ C; Feed stoichiometric ratio (B:A), SR = 1.5; stream
dilution ratio (stream B: stream A), DR = 0.25.
120
-------
B.
rOUPLF.D MIXING AND KINETICS AT STEADY
FLOW: PARAMETER STUDY ON "MICROMIX II"
In order to obtain an overview of sensitivities to important parameters,
including kinetics, a large number of steady flow simulations were run on the
stirred tank cell mixing program MICROMIX II. The parameters added to 1m; DR,
and SR (which were investigated already in MIXONLY) were cell temperature
"Tj'" mean residence time "T," reaction orders "T)i.k" and activation energy
"F.k." Simulations were again conducted about a base condition (Table In,
which here included the assumption that air was preheated t,,) enter at the
same temperature as the exhaust. Cold air was tested as a variation on the
base case.
Simulations were run for approximatel;)T 30 cells in the reactor (depending
on dilution ratio and temperature) and 10 mean residence times, resulting in
a statistical uncertainty of about 0 = 0.035 or less depending on conversion
level. The statistical limits for the high temperature asymptotes fr'::Jm
"MIXONI,Y" are II = 0.02 or less.
The reaction treated in these simulations is intended to represent oxi-
dation of carbon monoxide. Base case reaction kinetics are zero order and
represent a rounding of constants in the rate equation determined for carbon
monoxide in the CRC study.
1
CO + '2 02 .... C02
"CRC" Rate equation:
rCO = .0721 e-28,200/RTpgo269
(II-2)
Corresponding zero order rate equation:
= 1035 -30,000/RT
rCO' e
( II- 3)
The lead:i.ng coefficient in the zera-order equation was chosen so that conver-
sion f',)r the two equations would match at l420"p and '5C'P!o conversion for a feed
of 217<, CO, f' = 15 psia, and T = .05 see mean residence time at 1500"F (Figure
2'5) .
1.
;,tream Dilution Ratio
Figures 26,2'"(,28, and 29 are for dilution ratios, DR, of .1, .2'5, .50,
and 1. These tests were run at a constant stoichiometric ratio, SR, by
121
-------
TABLE II
CONDITIONS FOR TESTING PARAMETERS OF MICROMIX II
stream 1, A
stream 2, B
o
o
o 0
-II
O*0~
.E/RTpYtA pYla
r A . ke A . &
A + III 8 .... C
Test simulations were run for a base condition representative of oxida-
tion of carbon monoxide in a thermal exhaust reactor and for departures
from the base condition for each of the designated parameters. The
particular inlet concentrations and rate equations are given with the
results in Figures 26 to 39.
Parameter
Dilution ratio,
DR = stream2/stream 1
Feed stoichiometric
ratio, SR = 2B/A
Mixing parameter, I
m
Activation energy,
E, callg mole.
Reaction order in "A" T)
, A
Reaction order in liB" T)
. , B
Heat loss
Mean residence time.
at 1500°F, 1:
Temperature of stream 2
Base Condition
(Figure 27)
.25
1.5
1,2,5,20
30,000
o
o
None
.050 see
same temp.
as stream 1
122
Alternate Parameter Values
.1 (Fig.26), .5 (Fig. 28)
1 (Fig. 29)
1 (Fig. 30), 2 (Fig. 31),
5 (Fig. 32), 15 (Fig. 33)
None
10,000 (Fig. 34),
50~000 (Fig. 35)
1 (Fig. 36)
1 along w1th T)A = l(Fig. 37)
None
.002 sec (Fig. 38),
.150 see (F1g.39)
100°F, cold air
-------
b
UJ
I-
0:::
UJ
>
Z
o
U
o
U
Z
o
I-
U
.«
a::::
u...
100
. 1
o
1000
r co = .1035e -30, OOO/RT
r co = 0 0721e -28, 198/RT P co. 269.
1200 1400 1600
REACTOR GAS TEMPERATURE, of
1800
2000
Figure 25.. Comparison of stirred-tank conversion for zero order and
.269 order CO kinetics at I = 00. cOi = 2%, P 1 = 15 psia, T = .05
. id m15000 n tota
sec mean res ence time at F. .
123
-------
1.0
T=. 050 see @15000
.9 r=J035e -30,OOO/RT
.8 DR = 0 1
o SR = 1. 5
w
J- 07
a:::
w
>
Z .6
0
u A+ 0 5S-.C
o B2 = 0 21
u . 5
z Al =. 028
o
I-' J- Bo = . 019091
~ u Ao = . 025454
«
a:::
L.L.. . 3
. 2
0 1
o
1200
1400
I
I
/
I
1600 1800 2000
REACTOR GA S TEM.PE RAT URE, of
I
1m = 20
0..-
1m = 5
1:1
~
1m = 2
o
I = 1
m
. MIXONLY values
Computer Poi nts
2200
2400
Figure 26. Material and energy balance. curves for coupled reaction
and mixing, I = I to ~, in a cell-wise mixed stirred tank at
dilution rati~, DR = .1.
-------
1.0
T = . 050 see @ 15000F
. 9 r = . 1035e-30, OOO/RT
DR = 0 25
. 8 SR = 1. 5
£::\
w . 7
I-
a:::
w
> A +. 5B-.C
z .6
o
u B2 = . 21
o . 5 Al =. 07
u
z Bo = . 042
o
I- . 4 Ao = . 056
u
-------
f--'
I\)
0'\
LO
T = . 050 see @ 15000F
. 9 r = . 1035e-30, OOO/RT
DR = . 50
SR = 1. 5
.8
o
UJ
I-
c:::
UJ
>
Z
o
u
o
u
z
o
I-
u
«
c:::
u....
. 7
. 6 A +. 5 8~C
82 = . 21
.5 Al = 014
8 = 07
° .
.4 A =.0933
°
. 3
.2
. 1
o.
1200
1400
/
~/
\,~~ ",
/
/
/
)Y
~
~~ /
~
6~/
;,
c
1m = 20
/~
7
t».
1m - 2
1m = 1
--. MIXONLY values
Computer Points
1600
1800 . 2000 2200 .. 2400
REACTOR TEMPERATURE, of
2600
.2800 .
Figure 28. Material and energy balance curves for coupled reaction
and mixing, I = 1 to co, in a cell-wise mixed stirred tank at. .
dilution rati~, DR =.50. . . .
-------
10 T = . 050 see @) 15000F
.9 r = .. 1035e-30, OOO/RT
DR = 1
.8 SR = 1. 5
C)
u..J .7
I-
0::::
u..J
> A+. 5B---C
z .6
a B2 = . 21
u
a .5 Al =. 28
u
z Bo = ,105
a
- .4 Ao = . 140
I-
u
f--' 1m= 20
/
c
1m = 5./
"
/
A/ 1m = 2
/
Q " ~
\~V. 1m = 1
~ 0
. MIXONLY values
Computer Points
2000 2200 2400 2600
REACTOR GAS TEMPERATURE, of
2800
3000
3200
Figure 29. Material and energy balance curves for coupled reaction
and mixing, I = I to 00, in a cell-wise mixed stirred tank at dilution
ratio, DR = l~
-------
maintaining the incoming concentration of flBfI or air at 21% and increasing the
concentration of "Afl or carbon monoxide. The solid curves represent the
material balances for different values of the mixing papameter Inp and the
dashed curves are energy balance lines for zero heat loss. . .
As the inlet CO concentration is increased, the slopes of the energy
balance lines as drawn are reduced since given fractions of conversion produce
a larger temperature increase. At the higher levels of carbon monoxide, low
temperature energy balance curves intersect the material balance curves once
at very low' temperature and conversion off the left side of the graphs and
again at high temperature and conversion appearing on the graphs. Reaching
the high temperature solutions depends in these cases on specifying a high
initial temperature for cells in the reactor at time zero. A low initial
temperature results in virtually no reaction for these cases. Thus, a cell-
wise mixed stirred tank is observed to exhibit an ignition phenomenon similar
to that of an ideal stirred tank.
The behavior of all the material balance curves shown is similar, in. that
the ideal backmix result for 1m = 00 represents a low-temperature bound from
which curves depart and progress toward the flM1XONLyfI asymptotes. The affect
of increasing dilution ratio, DR, is to shift these asymptotes slightly toward
higher conversion. The shift is greater at lower values of 1m' causing the
spread in high temperature conversions associated with an increase in 1m to be
smaller for a higher dilution ratio up to DR = 1. . .
2.
stoichiometric Ratio
. .
. In Figures 30, 31, 32! and 33, an increase in stoichiometric ratio for
flBfI ( oxygen) to flA" (carbon monoxide) is accomplished by holding the dilution
ratio DR at .25 and the inlet oxygen concentration at 21% while reducing the
inlet carbon monoxide concentrations. This can be interpreted to represent
either a change in total exhaust combustible or the earlier and later conver-
sions of different exhaust species at effectively higher or lower stoichiometric
ratios. An example of the latter is the effectively higher stoichiometric
ratio associated with the early conversion of hydrocarbon compared to the.
effectively lower ratio for later conversion of carbon monoxide.
The shift in high temperature conversion between SR = 1 and SR = 15 is
approximately 87% to 99% at 1m = 20 and 30% to 55% at 1m = 1. At the low
value SR = 1, representing the high inlet flAfI concentration, achieving high
conversion at the 1000°F inlet temperature depends again on specifying a high
initial temperature.
128
-------
f-'
.1\)
\0
c
UJ
~ .7
UJ
>
~ .6
u
8 .5
z...
o
S .4
,/
A
'" 0.
~/
~~
6
1m = 5
A+ .5B-.C
B? = . 21
L-
A 1 =. 105
Bo = . 042
Ao = . 084
I = 2
m
I m= 1
1400
1600 1800 2000 2200
REACTOR GAS TEMPERATURE of
. ,
2400
2600
Figure 30. Material and energy balance curves for coupled reaction
and mixing, ~ = 1 .to 00, in a cell-wise mixed stirre1 tank at a feed
stoichiometric ratio (B:A), SR = 1.
-------
1.0
T = . 050 see @ 15000
o 9 r =. 1035e-30,OOO/RT
DR = . 25
.8 S R = 2.
a
L.U . 7
I-
Q::
L.U
>
Z .6 A+ . 58-'C
o
u 82 = . 21
o
u .5 A 1 = . 0525
z
0 80 = . 042
I- .4
u Ao = . 042
~
Q::
u... .3
.2
. 1
o
1200
1m = 2Y
I I = 5
/ m
I m = 2
I m= 1
.MIXONLY
values
Computer Points
2200
2400
~/'
~I
"'Y
I
7
I
/
I
1400
1600 1800 2000
REACTOR GAS TEMPERATURE, of
Figure 31. . Material and energy balance curves for coupled reaction
and mixing, I = 1 to 00, in a cell-wise mixed stirred tank at a feed
stoichiometri~ ratio (B:A), SR = 2.
130
-------
I
I~----
CI
L&.J
~ .7
L&.J
>
~ .6
u
o
u .5
:z
o
I- .4
u
-------
1.0
y= .050 see @)
o 9 15000
r =.l035e -30,0001 RT
. 8
Q
~ .7
e::::
I.J..J
>
6 .6
u
3 .5
:z
o .4
t-
u
.q::
8: .3
DR = . 25
SR = 1. 5
A+.58---.c.
82 = . 21
Al =.007
80 = . 042
Ao = . 0056
02
. I
o
1000
I
I
I
1200
1400 1600 1800
REACTOR GAS TEMPERATURE, of
,
I
1m~
1m = 5
~
J
,
1m = 2
1m = I
I
,
!---.MIXONLY
values
, Computer Poi nts
2000
2200
Figure 33. Material and energy balance curves for coupled reaction
and mixing, I = 1 to 00, in a cell-wise mixed stirred tank at a feed
stoichiometri~ ratio (B:A), SR = 15.
132
-------
3.
Reaction Kinetics - Activation Energy and Order
Figures 34 and 35 demonstrate the change in the material balance curves
when activation energy E is increased from 10,000 cal/g mole to 50,000 cal!g
mole. A change was also made in the leading coefficient of the rate equation
so that conversions match at 1615°F and 50% conversion. The change in slope
is most evident in the material balance bound at 1m = 00; however, at the lower
activation energy, the approaches to the "MIXONLY" asymptotes for 1m < 00 are
also more gradual. . .
First order and second order kinetics (Figures 36 and 3(7) shift high
conversions toward higher temperatures. When a high conversion must be obtained
subject to an upper limit on temperature; reaction order vies with mixing as
a fundamental factor limiting conversion. Since mixing can be improved whereas
kinetics are constant, it is a matter of the highest concern in reactor design
to establish which of these effects govern. Further discussion of this matter
will be offered later in reference to determination of exhaust reactor kinetics.
4.
Mean Residence Time
Mean residence time (Figures 38 and 39) was changed from the base value
of .50 sec to .002 and .150 see, respectively, to indicate the relative conver-
sions that would be obtained in an exhaust port volume and in a volume nominally
twice that of the DuPont Model V reactor assuming operation as partially mixed
stirred tanks.
At the .002-sec residence time, an appreciable level of conversion for
CO is attainable only at high temperatures such as might be found in the hot
fraction of a temperature distribution and not at an averaged exhaust temper-
ature. The threefold increase in mean residence time to .150 sec has the
effect of lowering the 1m = 00 bound by approximately 150°F and moving it
slightly more toward the vertical. For a zero-order reaction, as is being
considered, the shift in temperature T2 - Tl is given by R . ln (T2/Tl) .
T1T2/P., which for "small" changes in reactor volume makes the shift approximate
propartional to the natural logarithm of the volume ratio.
,-
).
Mixing Hot and Cold streams
f\ simulation run at the base condition in all respects except for sub-
stitution of cold air for hot essentially reproduced the base case result shown
previously in Figure 2.'7. The only difference observed (which was not graphed)
was a sn~ll upward shift in conversions at low temperatures, to place conver-
sions for 1m ::: 1 and 2 about two percentage points above the 1m = 00 curve
rather than just below. It is important to recognize that these conversions
1\'ere enhanced in reference to average reactor gas temperature, where entrance
of c'~~ld air Rutomatically implies a hotter exhaust to attain the same average.
133
-------
1.0
. 9
.8
CI
w.J .7
~
e::::
I..LJ
>
Z .6
o
u
0 . 5
u
z
0
I-' t- . 4
'vi U
+:- «
e:::: .3
u..
. 2
. 1
o
1000
T = . 050 see (ID 15000F
r = 1. 796XlO~3 e-lO, OOO/RT
DR = . 25
SR = 1. 5
A+ . 58--.C
82 = . 21
Al =. 07
B ° = . 042
Ao = . 056
1400
/
/
1600 1800 2000
REACTOR GAS TEMPERATURE, of
~
~
/
~
1m = 20
or
/ 1m = 5
~/
~
J
2200.
Figure 34. Material and energy balance curves for coupled reaction
and mixing,! =1 to 00, in a ce11-wisemixed stirred tank at activa-
tion energy, ~ = 10,000 cal/g mole.
c.
~
1m=2
I = 1
m
.MIXONLY values
Computer Points
2400
2600
1200
-------
t-'.
'vJ
\Jl
/:!A Y.~ /Im=2.
~
'\)
~
1m = 1
LO ,
T = .050 se(:@ . Im;(1)
.9 15000 ~ '
r=602e -50,000/RT~
,8
o
L..U
~ .7
L..U
>
Z
a ,6
u
a
u .5
z
a
~
u
«
a:::
u..
c
c
/
A + . 5 B.....c
B2 = . 21
Al =. 07
.4 Bo = 0042
Ao = . 056
. 3
/
. 2
/
Im=20.
/
1m = ~
/
----M IXONLY values
Computer Points
. 1
o
1400
1600
1800 2000 2200 2400
REACTOR GAS TEMPERATURE, of
2600
2800
Figure 35. Material and energy balance curves for coupled reaction
and mixing, I = I to 00, in a cell-wise mixed stirred tank at activa-
tion energy, ~ = 50,000 cal/g mole.
-------
1.0
T = 0 050 see ~ 15000F
.9 r = . 245e-30, 0 OIRT PAL 0
.8 DR = . 25
c SR = 1. 5
w.
I- . 7
a::::
w
>.
Z .6
0 A+.5B~
u
0 B2 = . 21
u . 5 Al = .07
z
0 B 0 = . 042
- .4
I-
u
I--'
-------
1.0
. 9
. 8
c
UJ . 7
I-
0::::
UJ
>
z: .6.
a
u.
a .5
u
z:
a
f-' 1- .4
\.)j
-..:J U
«
. 0:::: . 3
L.L.
o
T = . 050 see @) 15000F
r =. 574e-30, OOOlRTPAl. PBI.
DR = . 25
SR = 1. 5
A+.5B---'C
B2 = . 21
Al = .07
Bo = . 042
Ao = . 056
o
1200
1400
1800 2000 2200 . 2400
REACTOR GAS TEMPERATURE, of
/
/
/
/
7 I m = 20
99%
c+-
/ 1m = 5
/
I = 2
m
()ooC>
1=1
m
~ MIXONLY values
Computer Poi nts
2600
2800
3000
1600
Figure 37. Material and energy balance curves for coupled reaction
and mixing, I = 1 to 00, in a cell-wise mixed stirred tank for second
order reactio¥L Points (), C, A ,0 are from simulation "MICROMIX II".
Paint /j( is experimental.
-------
1.0
.9
. 8
Q
I.I.J . 7
l-
e::::
I.I.J
>
:z .6
a
u
a . 5
u
:z
a
I-' .4
VI I-
OJ U
-------
1,0
. 9
Q
l.J.J
~ .7
l.J.J
>
Z
a ,6
.u
a
U ,5
z
a
f-'
\..N
\0
.8
P. 150 see @ 1500° ~
r = . 1035e-30, OOO/RT 1m= (1) <>
DR= . 25 ~<>
SR = 1. 5
/
,
/ 1m = 20
~
A+c5B-'C
82 = . 21
Ai = .07
80 = . 042
Ao = .056
1=5
~/
~~
1m = 2
o
I = 1
m
.2
. 1
0
1000 1200
--'MIXONLY values
Computer Poi nts
1400 1600 1800 2000
REACTOR GAS TEMPERATURE, of
2200
2400
Figure 39. Material and energy balance curves for coupled reaction
and mixing, I = I to 00, in a cell-wise mixed stirred tank at a mean
residence tim~~ T = .150 seco at lSOO°F.
-------
SIMULATIONS ON STATIONARY STATE REACTOR OPERATION:
COMPARISON WITH EXPERIMENTAL STUDIES
III.
Estimates of the Caalescence Parameter, I
m
starting with Corrsin's (8,9) correlation for the decay constant for
variance in concentration, we proceed to compute values of 1m correspond ing
. t(, the one-cylinder reactor and the DuPont M'Jdel V reactor.
We assume, as Evangelista (15,16) did
mixing power "Pm". can be computed form the
streams of jets. Initial consideration of
in density for the entering gas.
for a spherical combustor, that
dinetic energy of the entering
the problem will neglect change
For the ratio of mixing power P to mass in the reactor M we write
m
P
m
~ p v. S)( 1/2 l/g )]
~ J J C .
[1/6 n L~ p]
( III-l)
M
where 8 is the total cross sectional area for all entering streams (or jets),
vjis ,jet velocity, and Lr is a sphere equivalent diameter for the reactor.
We proceed by substitution to find 1m as a function of Lr' S and the integral
scale of turbulent fluctuation L. Evangelista (16) furtner assumed that the
c .
3
'T 1/6 rr L /S v.
r J
G P, 1/3
,.., c m
~ = 1.0'7 2
eM/, 3~/3 GL3J
,.., 3 S Vj
I ~ ~ " 1. 07 Q 3 2 6 srv
m
~~)2/3. Lr Lc
~
I 0.55 -
m . S L
c
( III-2)
(III-3)
( III-4)
( III-'))
integral scale of turbulent fluctuation J.c WaS equal to the sphere equivalent
diameter 1.1" Using the leading coefficient of 1/2 that is olJta.inerl from
140
-------
Corrsin's earlier publication (8) (rather than 1.07 as above) Evangelista
obtained:
L 2 2/3
131 '" 1/4 (-!. )
s
( II1-6)
We first apply this analysis to the single cylinder reactor having a
sphere equivalent diameter of Lr = 4.87 in. for a reactor volume of ~9.~ cu in.
and an inlet cross sectional area S of 0.0779 sq in. for 11 inlet holes of
3/32-in. diameter. Using Evangelista's assumption of Lc = Lr,we obtain 1m =
11.4, which limits covnversions Sco to approximately 92% for a dilution ratio
DR = .25 and stoichiometric ratio SR = 1. 7, based on results from "M1XONLY."
Changing only the leading coefficient to 0.77,changes the prediction to 1m =
27 and Xco ~ .96. Experimental conversions for all combustibles including
carbon monoxide were observed to reach 99% or higher at sufficiently high
temperature, indicationg that a mixing pa,rameter value based on Lc = Lr is
low.
Evangelista's assumption, equating the Gcale of turbulent concentration
fluctuation to the gross dimensions of flow, is quite obviously the most
conservative estimate that can be offered. A calculation based on injection
system dimensions yields a much higher estimate of 1m, which for Lc equal to
the 3/32-in. jet orifices in the single cylinder reactor predicts 1m = 102 for
the leading coefficient of 1/4 or 1m = 22~ for the leading coefficient of .~~.
"M1XONLytI simulations run at high values of 1m indicate that 1m = 100
corresponds to a conversion of 99.6% at DR = .2~, SR = l.~ and of 98.~ at
DR = .1, SR = 1.~. At 1m = 200, the conversion is 99.4% at DR = .1 and SR =
l.~. The dilution ratio for the majority of experimental runs on the single'
cylinder reactor was in the vicinity of DR = .1; at this dilution ratio and
at temperatures above approximately 1400°F hydrocarbons were converted by
99+%. Carbon monoxide which requires a higher exhaust temperatu~e for its
oxidation was converted by 99% only in an experiment conducted at 1687°F and
DR ~ . 3, , SR ~ 2.
Thus, conversions computed from "MIXONLY" for values of 1m obtained by
using a jet orfice diameter for Lc are in approximate agreement with experi-
mental results. In view of uncertainties in the leading multiplier for
Corrsin's equation (an efficiency factor) and in the percision of high experi-
mental conversions, the extent of discrepancy between a simulation based on
entrance dimensions and experiments cannot be judged. We would expect that
values of 1m based on jet orifice diamet~r might be high due to neglect of jet
expansion beyond the inlet.
Application of Corrsin's (8,9) equation to the DuPont Model V reactor is
more difficult due to the complex flow and geometry. Exhaust enters through
141
-------
an exhaust valve of 1. "5-in. diameter which opens to 0.41 in. and closes during
a 2780 interval on a 7200 engine cycle. The peak flow of exhaust occurring
during blowdown produces a high level of turbulence, but little or no air is
added (with a low pressure air injection system) to the port during this
period. Thus exhaust and air tend to enter the 1.36-in. diameter port sequen-
tially and mix only after emptying into the core of the reactor.
If we proceed by neglecting change in density, we again compute 1m =
O. "5"5 (L~/SLo). Far a free volume of approximately 230 cu in. (which excludes
the volume occupied by internal baffles and heat shields), the sphere equivalent
diameter Lr is 7.6 in. 8 and Lc depend on what we assume for the scale af
turbulent fluctuation; the worst assumption being that exhaust and air mix
only after assuming the dimension of the port resulting in values of L =
- c
1.36 in. and 8 = '5.80 sq in. This assumption results in 1m = 8.0, which
corresponds to conversions in the range of 80 to 90% for a stirred tank MIX ONLY
simulation.
If air flow were caincident with
would be the valve opening, Lc = 0.41
This assumption predicts 1m = 14.7.
exhaust flow, a good estimate of Lc
in., with corresponding 8 = 7.7 sq in.
In the case where exhaust blowdown is the effective means of mixing, the
change in density for gas entering from the cylinder is large at the initial
exhaust valve opening but is relatively smaller thereafter. Both the pressure
drop and the orifice size are changing as the valve opens and the piston
moves upward to displace exhaust out af the cylinder. Critical flow will be
experienced during the initial period of blowdown, during which time the
instantaneous valve opening will represent the throat of a critical flow nozzle
beyond which velocity will continue to increase due to expansion of the gas.
The effective entering jet diameter will in this case be the dimension of an
expansion cross section of a nozzle at the downstream pressure rather than
the throat dimension. Hence we are justified in using the constant density
analysis for 1m within the reactor provided that 8 and Lc reflect mixing after.
expansion at the inlet. To illustrate, consider the instantaneous condition
where exhaust is flowing from Pl = 30 psia to P2 = 1'5 psia, which is. just over
critical. For a well designed nozzle, the final velocity would approach that
of an isentropic expansion; it would af course be lower for flow through an
exhaust valve. However, to illustrate the effect in the limit, we compute
final velocity for an isentropic expansion:
u2
7), [ 7c-~
22~.7 Cp Ti ~-(P2/Pl)~
( III-7)
where Cp
] ,:)5\) ftj
c11.ameter
is Btu/lb°ji' and Tl is oR. The va.J \le of \J2 at 1800"1\ (1"11+0°1") is then
sec. For a mass flow rate fm = ~() lb/hr through an exhaust valve of
D, 82 = fm/P2u2 = 0.0278 sq in. and llc = 82/ Tf D = .00'59 in. The
142
-------
corresponding coalescence rate 1m for mixing throughout the entire reactor
volume is very large, 1m ~ 10,000, which illustrates that air injected at the
time of blowdown in immediate proximity to the exhaust valve would likely
experience a very thorough mixing with exhaust as it passes through the reactor.
As the exhaust valve opens and
flow can be treated as flow through
dimension is the effective entering
opening of .410 in., we are brought
previously, 1m = 14.7.
pressure drops, the resulting noncritical
a convergent nozzle where the throat
jet diameter. Thus, for the maximum valve
back to the Inixing parameter value given
To summarize, the opening of an exhaust valve involves a rapid transition
in 1m from a value of several thousand to approximately 15. If air in suffi-
cient quantity is injected near the exhaust valve during blowdown, this range
of mixing intensities should be experienced. If however, air enters primarily
in sequence with exhaust, both air and exhaust take on the dimension of the
port and mixing will proceed with 1m equal to 8.
All foregoing estimates of 1m for the DuPont Model V reactor have assumed
that turbulent mixing initiated at the inlet persists throughout the entire
reactor. A more conservative view would allow for a decay of turbulence, and
therefore a decay in the local value of 1m in relation to volume. If for
example we assume that mixing persists unabated in the core but is samped to
a negligible value thereafter in the annulus, 1m values corresponding to the
core volume alone would be Im= 3.5 for Lc = 1.36 in. (port diameter) and
1m = 6.7 for Lc = 0.41 in. (maximum valve opening).
The preceeding analysis has been based solely on the flow of exhaust
since air injection at low pressure .is a decidedly second-order effect. A
high pressure air jet would, however, exercise a significant mixing effect
depending on pressure drop and jet dimension. Multiple small jets would be
more effective than a single larger jet. Calculation of 1m for particular
designs would follow the course outlined in the foregoing discussion of exhaust
blowdown.
143
-------
IV.
Simulations on the Kinetics Test Reactor
"MICROMIX II" was run on conditions corresponding to the kinetics test
reactor to establish whether or not microsegregation of air and exhaust had
influenced the conversion data from the system.
Simulations were performed for fm :;: ~3 lb/hr, reactor volume V :;:
'59.'5 cu in., and entering exhaust concentrations of .02 mole fraction CO and
.008 mole fraction H2' Inlet temperatures investigated ranged from 1240°F to
1600°F. Hydrocarbons were not included in the simulations.
Simulations were run at values of the mixing parameter, 1m' of 1, '5, 20,
and 100 (Figure 40). The calculations presented based on the mixing theory of
Corrsin (8,9) predict an 1m in the range of 100 to 200 for the experimental
reactor. This is corroborated by the fact that experimental conversion ranged
up to 99%, which is consistent with an 1m equal to 100.
At high temperatures, conversions as already noted approach the limiting
upper bound representing the conversion for an infinitely rapid reaction
limited only by mixing. The limiting values observed in Figure 40 for carbon
monoxide agree well with those determined previously by the mixing simulation
"MIXONLY" f~r a stoichiometric ratio of 1. '5 to 1 for oxygen to combustibles.
In Figures 40, 41, and 42, the solid line represents conversion in a
continuous ideal stirred tank reactor, CSTR, at 1m :;: 00. The departure of the
dashed curves, representing finite levels of micromixing, from the solid curve
is a measure of the error introduced by neglecting micromixing. The departure
of these curves increases as temperature and conversions increase, indicating
as expected that mixing becomes relatively more critical compared to kinetics
at higher temperatures where resistance due to chemical kinetics is small.
The important fact to observe from the simulation is that departure from a
CSTR conversion at 1m '-= 100 is negligible at 9'5% conversion. Since the data
. that were used for determination of kinetic parameters were truncated. at 80%
conversion, we can be sure that the effect of micromixing on these data was
insignificant.
In order to obtain a measure of the correspondence between the simulation
in Figure 40 and the kinetics test data, a subset of this data has been plotted
on the same simulation, in Figure 41. The data points chosen are those for
which the inlet concentration for CO and the flow rate are within +10% of the
simulation condition (2% CO, 30 lb/hr exhaust, 3 lb/hr air). -
. The data points in Figure 41 have been corrected slightly in temperature,
based on an ideal CSTR material balance and the rate equation for oxidation of
carbon monoxide. In the cases of CO, however, we have an order on partial
144
-------
1. 000
.900 1m
1
.800 5
20
100
.700
fJ.
o
~------ -
1m = 100
07 ~-t--~-
("'. / 1m' 20
II ,II
/'1 /1-0 ----
/ I .f.~ 1m = 5
1.~1 /
II I
II' / /
I/) / '
//. /
/1.' /. j /
/1// / _-r-~---
/'/, (' -- -- I 1 1m - 1
~ ~ M" I
1/~//./ ,I
/, I" , /
,i'-ct~LL I x/ I /'
1200 1300 1400 1500
REACTOR GAS TEMPERATURE, of
.
.
'il
Computer Poi nts
Inlet Temperature, of
1240 1280 1320 1360 1400 1500 1600
-'------
fJ.O 0 <> 'il X +
.
.
o
.
<>
'il
.600
1m = CO
-- -- Constant 1m
--- Energy Balance
:z
a
(/)
Q::
~ .500
:z
a
u
a
u .400
.300
.200
.100
o
1000 .
HOO
1600 .
1700
1800
Figure 40. Simulation of CO conversions in the kinetic test reactor.
Departure of cell~wise mixed conversions, I = 1 to 100, from the
m
ideal CSTR, I = 00. Points from simulation "MICROMIX II". Feed: 30
lb. exhaust/h~., CO = 2%, H2 = .8%, air = 31b/hr.
145
-------
1.000
.900
.800
.700
,600
1m = CD
- - - - Constant 1m
z
o
V1
0:: ',500
~ .
z
o
u
8. .400
. Experimental Points
.300
,200
,100
1100
1200
1300 1400 1500
REACTOR GAS TEMPERATURE, of
1600
I = 20
m
1700
1800
Figure 41. Experimental conversions from kinetics test data plotted
on the cell-wise mixing simulation of Figure 40. Data points corrected
to the simulation conditions of Figure 40.
146
-------
1. 000
.900
.800
.700
.600
z
o
II')
0:::
LLJ
~ .500
o
u
N
::r:
.400
.300
.200
.100
qooo
1200 1300 1400
REACTOR TEMPERATURE, of
1100
6.
-
1m=CO "'----':=0=0...: o~
/ 1m = ~......... 1m = 20
/ /
~ /
I. "-8-.-'\7_-
/ /' ./ . 1m = 5
1 /
I /
1/ .
II
II
II
~
r
~
x
. 1m = 1
. B.---'\7- -----+
/'-
/'
x.
+
Computer Points
1500
1600
1700
Figure J.).2. The effect of mixing parameter (1m) on. hydrogen conversion.
Feed: 30 lb. exhaust/hr., CO = 2%, H2 = .8%, air = 3 1b./hr.
147
-------
pressure of carbon monoxide, which makes the correction easier if we correct
temperature rather than conversions.
From the CSTR material balance on CO, with
x ~ (foC - fC )/foC
co 0 co 0
co co
( IV-l)
fo C
o
co
For ~g = .02 mole fraction, we neglect departure of fo/f from 1, and we
define
x
co "
(I-X) 11
co
A
co
" V p11
11-1
(£0) 11
£
-E /RT
co
=
e
( IV - 2 )
*
A
V p11
=
A
co
* *
£ Co
co
( IV- 3)
where f* and r.~ are condition on mole flow and inlet mole fraction to which we
" ~o
wish to correct a set of data. Then, taking the logarithm, we obtain
TI(-
E ~ 1 .
T + - "
R {£nA*-£nX +Tj£n(l-X I)
co co
"1 J
A VpTj
f£n~co 9- 2nX +Tj£n( l-X))
TJ-l co
for. 0
co
( IV - ) t )
The data in Figure )+1 indicate a steeper rise in conversion along with
temperatuie than is indicated by the simulation, even at 1m = 00. This is a
property of the subset of data that are plotted, since correcting all data
produces a scatter diagram about the ideal CSTR line. However, we note that
the exper~rental data most nearly represented by the simulation condition
indicates "less of the trailing off to high temperature (which is indicative of
mixing limitedness, low activation energy. e>r highreactie>n orderi than de>es
the I = 00 bound for the least-squares kinetics.
m
Besides the 22 kinetics data pe>ints in Figure 41 (which are truncated
between 20 and 800/0 conversion), the high temperature test for CO run at r.O =
.0'525, EXHAUST = 30 Ib/hr, AIR = 9 lb/hr, was corrected by the method in~{r;8"terl
from 1687° to 1710°F for 99% conversion. Agreement vJi th the sirnull3.tiofj is
good. Likewise, if we look back to the experimental point )(- in Figure 2'(,
which is the same high temperature run corrected by means of a zero order
rate equation, we again observe quite good agreement. However, if we observe
148
-------
the point plotted on simulations for first or second order (Figures ~6 and
37), we observe a very large discrepancy. Along the 1m = 00 bounds, 99% con-
version is reached at 2770°F for order 1, and ~OOO°F for order 2. This
demonstrates' both the difficulty in attaining high conversions for high order
reactions and the necessity for near zero order to match the experimental
observation for oxidation of carbon monoxide.
Results for hydrogen at single-cylinder reactor conditions (Figure 42)
indicate that bounds on conversion set by the mixing parameters are higher
than those observed for carbon monoxide. The explanation for this is that
hydrogen reacts at lower temperatures, where the excess of oxygen is larger
due to the slight oxidation of carbon monoxide. When compared with results
from "MIXONLY," the limiting conversions for hydrogen lie between those for
a stoichiometric ratio for oxygen to hydrogen alone and for oxygen to hydrogen
plus carbon monoxide.
1~9
-------
V.
Simulations 011 the DuPont Model V Reactor
Simulations were run on "MIXONLY," "MICROMIX II," and "MICROMIX POF" pro-
grams using both steady and cyclic inlet flows for the purpose of identif,yillg
the mixing parameter values (for flow pattern and the mixinG intensity 1m)
which characterize this exhaust reactor. By bracketing the mixillg perfOrmaJ1Ce
of exhaust reactors as a class between the optimized mixing of tile Silll~le C,Y L-
inder reactor and that of the Model V, it is possible to il~erpolate with some
degree of confidence to reach conclusions regarding the attainable performarlce
of an improved practical device. .
Two classes of experimental results were available from the Phase I study
.to form the basis for simulations: tests where air dilution fraction was
varied for a constant exhaust feed; and tests where exhaust temperature was
increased to achieve a level of maximum conversion by retarding the engine
spark while holding other inlet properties essentially constant.
Patterns of flow for the Model V simulations are shown in Figure 43, along
with values of the key parameters. Changes in these and other parameters are
discussed in the text. In the patterns numbered 2, 4, and 5, the modules
shown represent four engine exhaust ports, a reactor core, and an exit annulus.
In pattern number 3, the annulus is divided and the parts assigned different
rates of heat loss. .
A.
MAXIMUM CONVERSIONS FOR INSTANTANEOUS REACTION- "MIXONLY POF"
Simulations were run to parallel CRC experiments on the DuPont Model V
reactor using "MIXONLY POF".(Table III).. In these, the experiment which indi-
. cated a limiting high temperature conversion of 8'2?/o was used as a bench mark
to establish values of the mixing parameter, 1m, subject to six conditions
(plug flow, five tanks in series, and one stirred tank at assumptions 1 and 2
of Table III). These values of 1m were then used to predict conversions for
two other sets of experimental conditions, which dictated the stoichiometric
ratio SR and dilution ratio DR parameters used in the simulations.
The two assumptions of Table III differ in the amount of combustible
which is considered. to. depend on mixing for reaction. The uncertainty is in-
troduced because of a. measurement showing 0.6')1/0 oxygen in the entering exhaust,
.which if actually present would have first claim on combustibles because of
its premixed condition. The first calculation assumes that this oxygen mea-
surement was spurious and should be zero, thereby causing all the combustibles
to depend on injected air for oxidation. The conversions compared in this
case are for. the total combustible content. The second calculation assumes
that the measurement is correct and that the combustible corresponding to it
150
-------
Exhaust
1
Air
V cu. in.
Q Btu/hr
h Btu/hr ft2 of
1m
2
V
Q
h
1m
3
V
Q
h
1m
4
V
~
I
5
.V
Q
h
1m
Figure 43.
6400
5 7 or 8
Ii}- - -- .. - ~o
. a-o-~ -~~ 0 0 --.,J
-... 0 0
0--
4 x 6 68
4 x 900 400
16. 2 5. 2
1 2
~ ~
o-l8-=<=i~ 00 : --~o 0 0 o~- ..,aC) 0 0 ~
- 0 .
0----
4 x 6 68 58 80 .
4 x 900 400. 1000. 5000
16. 2. 5.2 7.1 11. 7
.37 1.04 .88 L21
::as--- 0 0
&- -=-* 0
- 0
o 0
~ ~ Y500
10.8
. .42
. ......
138
6000
9.9
2
- --.10 0 0 .....
200
5.2
1. 18
3086
9.9
2.40
....Jg". L'f1--~
c=:::J-..po.:::.,-lo . . 01-- -018 . 0 0"
c:=:::J- .Ji? ."
c::=:::J...-.Jr
4x6
4 x 900
16.2
1
68
400
5.2
2
138
6000
9.9
2
Patterns of flow run to simulate the DuPont Model V reactor.
151
-------
TABLE III
COMPARISON OF HIGH TEMPERATURE EXPERIMENTAL CONVERSION WITH "MIXONLY POF"
SIMULATIONS OF MIXING WITH INSTANTANEOUS REACTION
EXPERIMENTAL INLET CONDITIONS
CO H2 HC 0
% % ~ %2
EXPERIMENTAL
CONVERS IONS, X
Total
Combustible CO
Assumption 1
"SR" I'
, m--
Pattern
of Flow
AIR
"DR"
'-
*** Test 3C8 used to establish mixing parameter values, 1m ' ***
1.91
820.
.097
1.20
.884
0.65
.82
0.52
pf
5st
1st
3.7
4.5
11.4
I-'
\J1
1\)'
*** Simulations of conversions at other test conditions using the same IS. ***
m
"X"
TOTAL
COMB.
2.84
0.83
0.5
770.,
.093
.831
.75 .85
pf .769
5st .718
1st .695
.93 1."55
pf .970 .
5st .950
1st .932
3.08
1.20
79
-------
is removed from dependence on mixing. In this latter case, "MIXONLY POF" con-
versions are compared directly with experimental conversions for carbon monox-
ide, since the amount of hydrogen plus hydrocarbon is nearly equivalent to the.
oxygen measurement on the exhaust. .
The results for either assumption indicate. a proper trend but not a close
agreement.
B.
"cOMPARISON DILUTION RATIO ON CHANGES IN AIR
. The experimental data on .effect of dilution ratio DR, or air injection
fraction, is shown by; the solid lines in Figures 44 and 4.5. Starting at a.
combustible content of nominally 4.')1/0 CO and 320 ppm hydrocarbon, carbon mon-
oxide was reduced by approximately 9~k to l/~ and hydrocarbon by 98+% to be-
low 10 ppm. Maximum conversions were reached. at dilution ratios of .2 to .3,
where the increased probability of mixing and greater mass action from oxygen
content (at least for hydrocarbon, which has a half order rate dependence on
oxygen) produced.their greatest beneficial effect before being counteracted by
temperature drop associated with excess cold air.
. The hysteresis shown by the experimental data in Figures 44 and 4.5 results
from heating of a cold reactor versus cooling of a hot reactor. This behavior
results from changes in heat loss and in the "initial" condition which estab-
lishes which of possibly several operating points will be assumed in relation
. to different combustible species and different regions of the reactor. For.a
single reactant in an ideal backmix reactor (1m = 00), ignition and hysteresis
have been discussed in detail by Schwing (29). Further discussion on ignition
is given in a later section of this report dealing with reactor warm-up. How-
ever, the more cumbersome mixing simulations treated here were not used to in-
vestigate ignition phenomena.
Hydrogen was not measured in the dilution ratio experiments, however it
was included in the simulations because of its coupled thermal contribution.
An inlet concentration of 1. 8% H2 was chosen based on a 4/10 ratio to inlet CO.
This is approximately the average ratio observed. for analyses performed on ex-
he.ust from the single cylinder test engine; it is equivalent to the equilibrium
ratio for the water gas shift reaction at 2160°F assuming equal concentrations
for C02 a.nd H20.
The simulations on the effect of dilution ratio for the Model V were run
both on the stirred ta.nk cell mixing program "MICROMIX II!1 (Figure 44) and on
the pattern-of-flow program "MICROMIX POF" (Figure 4.5) for the module network
number 2 shown in Figure 43. The modules represent four ports of 6 cu in., a
68 CLI in. stirred tank core, and a 138 cu in. plug flow annuI"us. Average ex-
ha.ust flowra.te ma.tched the test rate of 115 Ib/hr. Total reactor heat loss
exclusive of ports, obtained from a typical ''WARM-UP'' simulations on the DuPont
1.53
-------
~. 200
IX)
a::
<.
u.
.0
0::
~ 100
::I:
g- 1800
L.LJ .
~ 1600
I-
< .
ffi 1400
c..
:E .
~ 1200
0::
o
t5 1000
< .
L.LJ
0:: 800
E
0.
0.
. Experimental
MICRO MIX IT Simulations
. . -0- TlOW = 10000F
",,0. -fr. T LOW = 12000F
",
",,"" A[ Inlet Temps. at
?" T LOW .. 12000F
/ TS PAN = 8000F
/ TAIR = lOooF
I /tf
/p ./'
.u'
o
1.0
0.2 0.4 0.6 0.8 1.0
~
L.LJ.
0
-
x 3
0
z
0
:E 2
z
0
IX) 1
0::
<
U
0
0.2 0.4 0.6 0.8 1.0
AIR INJECTION FRACT ION
Figure 44. Stirred-tank simulation of the effect of air irtjection
fraction at a mixing parameter value of I = 8. Experimental values
are from the DuPont Model V reactor opera~ed at 115 lb. exhaust per
hour and at 12.3:1 air fuel ratio. .
154
-------
2.
~ \
z' \ if'
UJ L q
c:.:>
0 '6 /
Q::: "
0 ....~.... 0/
~
:r: 0 "
, MIXING
PARAMETER, 1m
300 , Port Code Annulus
E \ ~}1. 3
c.. 3. 7 0
c.. b
z' 200 '0 1 3 1
o \
a) 0 1 2 2
Q::: 6 .5 1.5 3
<
<->
0 100
Q:::
0
~ TLOW, of
:r:
0 x 00 - 1250
06 - 1200
/S- 1800
,
UJ 1600
Q:::
::J TS PAN = 400°F
.......
~ 1400 TAIR = 6000F
~ 1200
: 1000
Q:::
0 800
u
5
~
UJ'
0
-
x
0
z
0
~
z 1
0
a)
0:: 0 0
< .6 .8 1.0
u
Figure 45. Simulation of the effect of air injection fraction using
the pattern of cell flow shown in Figure 4~, item 2. '
155
-------
Model V, was 6400 Btu/hr. In the POF simulation, heat loss was distributed:
900 Btu/hr for each port; 400 Btu/hr for the core; and 6000 Btu/hr for the
annulus. Inlet properties were cyclically varied in accorda.nce with the char-
acteristic patterns described previously; temperature spans used were TSPAN =
800°F for "MICROMIX II," and TSPAN' = 400°F for "MICROMIX POF. "
Tne mixing parameter was set at 1m = 8 for the stirred tank simulations
and 1m = 5 bverall for the pattern of flow simulations. The mixing parameters
for modules in POF were variously distributed as shown in Figure 45.
Trends in simulated conversions for increased air dilution ratio are ill
general agreement with the experimental results. The apparent lag in experi-
mental conversions at low dilution ratio is, like hysteresis, an ignition phe-
" "
nomena which was not investigated in the simulation. The slope with which the
combustible species disappear as the air fraction (DR) is increased indicates
that blending of exhaust from successive firings of cylinders with air entering
from all cylinder ports is quite complete. "More specifically, under favorable
lightoff conditions conversions tend to follow their stoichiometric limit
leading to complete conversion at an air injection fraction of approximately
.15, although leveling off prior to that point. Thus, even though air injec-
tion is maldistributed in time and in position (during the time that exhaust
flows into the reactor from a given cylinder, air is flowing primarily from
"the three nonactive cylinders), no large amount of air is lost. This suggests
that the core of the reactor, where blending must occur, is quite well mixed
on a macro scale. "
Poorer agreement is indicated between the simulations and experiments for
the reactor gas temperature. This may be caused by a number of factors, all
tied in with the fact that the single "time average" tempetature measurement
at the core center line will bear a different relationship to either simulated
or measured conversions depending on the distribution of tem~eratures and con-
version throughout the reactor. First, the "time average" temperature measured
by the thermocouple at the center line will tend to be low due to inadequate
weighting of the high temperature-high flow exhaust pulses entering at blowdown
and over weighting of air flow at low temperature entering over a longer period
of time. The severity of this effect will depend on t11e placement of the
thermocouple in relation to one of the entering exhaust ports. "" Then, when re-
action begins only part of the resultant temperature rise will be evidenced in
. the port, the part depending on the amount of reaction in the port as opposed
to the amount in the annulus that follows. Finally, at high dilution ra.tio,
the decline in simulated temperature is greater than in the experimental due
to a more rapid decline in conversions. This relates to the distribution of
temperature, with persistence of a high temperature fraction favoring persis-
tence of conversion as air injection increases. For hydrocarbon, persistence
is evidenced in the "MICROMIX POF" simulation where backmixing is reduced below
that of the stirred tank. Running the "POF" simulation at a higher temperature
span for the entering exhaust would further prolong conversions toward higher
air fractions.
1~6
-------
The "POF" simulations were run at a lower temperature span and a lower
average temperature for the entering exhaust. Average inlet exhaust tempera-
ture for "TLOW" == 1200°F is approximately 1600°F for the "MICROMIX II" simula-
tion with TSPAN ==800°F, and is 1400°F for the "POF" simulation with "TSPAN" ==
400°F. The larger temperature rise shown in Figure 45 for "POF" is the result
of 'a low rate of heat loss from the core and use of a higher inlet air tempera- '
ture (air was assumed to be preheated in the injection system to 600°F rather
than entering at 100°F).
In the "POF" simulation shown in Figure 44, points are plotted faT four
different distributions of 1m among the reactor modules. The three points run
at "TLOW" == 1250°F and DR == .3, [x, 0, and 0], represent a sequence from
earlier to later mixing for flow through the reactor. Only the conversion of
carbon monoxide is appreciably affected by this change, and it is found to be
maximum (lowest CO concentration) at the middle distribution. This is a small
indication of counterbalancing effects between an advantageous increase in res-
idence time after mixing versus a disadvantageous coalescing of cells prior to
adequate blending and backmixing of maldistributions. It should be recalled
here that the "plug flow" section of the POF simulation does involve some back-
mixing of material depending on the size of the 'slugs (slugs in this insta.nce
represented 1/16 of an engine flow cycle and roughly 6 slugs were contained in
the plug flow module at a given time). '
The simulations that were run on dilution ratio ,do not attempt either to
optimize the fit with the experimental data or to provide an extensive mapping
of sensitivity to parameters. The two' simulations run illustrate that higher
conversions are obtained at lower dilution ratio and lower average inlet ex-
haust temperature for a POF representation of the Model V than for a "MIXONLY"
representation. Since it is de~irable to optimize such a trend, it would
appear useful to run further simulations in this area. Considering the mal-
distribution of inputs, the principle of a blending volume as represented by
the stirred tank core simulation followed by a "plug flow'~ exit section to
eliminate early departure is a soilnd design feature (which is already incorpo-
rated in the Model V design to, some extent). Simulations could be run on the
relative size of these regions as one means of optimizing a,design.
C.
APPROACH TO A HIGH TEMPERATUHE LIMIT ON CONVERSION OF CARBON MONOXIDE
e.:xperiments in which the temperature of entering exhaust wa.s increased by
retarding the spark of the engine while at the same time holding other inlet
properties essentially fixed, resulted in carbon monoxide conversions which in-
creased from near zero to a maximum value of less than 100 in intervals of a.p-
proxilnately 200°1" 'increase. Conversi~ns remained at an essentially constant
maximum level even though temperature was further increased by as much as 250°F.
I!llet conditions for one such experiment were chosen as the basis for ,a
series of simula.tions conducteQ for different patterns of flow using the'
157
-------
i
IIMICROMIX POF"program. The purpose of these tests was'to determine the effect
that various combinations of mixing parameter 1m and flow pattern had on the
approach'to a high,conversion, and to establish if possible a good correspon-
dence between the experimental data and one particular pattern of flow.
The test chosen (test 3C8) was run for a mass flowrate of 117 lb/hr ex-
haust at L 91% CO, o. ')~ H2, 0.6'Y/o 02' and 820 ppm hydrocarbon; air dilution'
ratio was nominally DR = 0.10. Temperature was again measured at the reactor
core centerline. As mentioned before, this temperature will not reflect the
temperature rise associated with reaction occurring downstream from the core.
In order to portray the important differences between these simulations
clearly without becoming lost in detail, we will first discuss only the high':'
.lights of ea,ch and return l~ter to point out several of the interesting but
less important features.
The five simulations in Figures 46, 47, 48, 49, and 50 were run on the
respective flow patterns given in Figure 43. In Figure 46, results are shown
for a stirred tank simulation (MICROMIX II) performed at values of 1m equal to
'), 7, and 8. The high temperature conversion at 1m = 7 best corresponds to
the experimental conversion of 8~ for carbon monoxide.' A value of 1m = 8 was
obtained based on Corrsin I s equation with Lc equal to the port diameter.'
Experimental conversions for hydrocarbon and hydrogen were 96% and 100%.
,The stirred tank simulation at 1m = 7 and a reactor temperature of 1720°F pre-
dicted 83% conversion for hydrocarbon and 97% for hydrogen (not graphed). The
discrepailcies in these values were felt to relate to allocation of the 0.6')1/0
oxygen that was reported to be contained in the entering exhaust. If this
oxygen were consumed preferentially by hydrogen and then by hydrocarbon, all
hydrogen would be consumed and hydrocarbon would be reduced to 270 ppm.
Accordingly, a series of simulations were run on exhaust input containing
L 910/0 CO as before but at 0.% H2, 0.% 02' and only 270 ppm hydrocarbon. The
high temperature conversion for the smaller amount of hydrocarbon was in this
case 0.87, which amounts to 96% of the total hydrocarbon. The success of this
strategy prompted the IIpreoxidized" inlet condition with 0.% Hc and 0.% 02 to
be used for the remaining simulations. Whether this is justifiable depends
largely on the precision of the 0.65% 02 exhaust measurement (which is in
doubt). This points out the general difficulty that exists in pr~dicting con-
versions for small amounts of reactive combustibles (hydrogen and hydrocarbons)
where a small but uncertain amount of oxygen characteristically enters with
the exhaust, and the distribution of this oxygen is unknown.
The simulation approach to the maximum conversion for CO in the stirred
tank was decidedly more gradual than the experimental (Figure 46).Particu-
larly when cyclic input was used, a considerable conversion persisted at low
average temperature. The augmented conversion for the cyclic input over the,
steady input is due mainly to the persistence of a'high temperature region in
158
-------
Q
L.U
~.o. 7
L.U
>
~ .0.6
u
8 .0.5
z
o.
j:: .0. 4
u
«
e: .0. 3
1..0
-o-DuPont.React~r, Test 3C8 Experimental /'/
.0.9 -,- CSTR SimulatIOn at 1m =co '
MICROMIX II Simulations / ....-..:e==..{J
Computer Points / ':,....or.-
. /" .
Note 2 Note 3 ~' . A
-+- /~i/o
--tl-- - ..~/ ji"
/ ;/1/
. //- 1/
// /'
.0. 2 ...........""'" /'
/'
.0.8
.Im
5
7
8
Note 1
-*--
--.-
18.0.0
0,1
.0
11.0.0
1200
13.0.0 140.0 15.0.0
REACTOR GAS TEMPERATURE, of
Figure 46. . Simulation of the approach to high-temperature mixing-
limited conversion for CO using a stirred tank cell mixing model. .
Input: exhaust - CO = 1.9%, H2 = 0.52%, 02 ~ 0.65%, HC = 820 ppm. Air
dilution ratio, DR = .10 (air/exhaust). .
Note 1: Cy.c1ic inlet properties about the average values
measured.
Note 2: Cyclic inlet properties at average inlet exhaust
mole fractions of 1.91% CO, 0.0% HZ' 0.0% 02' and
270 ppm HC.
Note 3. Steady mass-averaged inlet properties from each
cylinder. Flow pulses due to timing of cylinders
are retained.
. 159
-------
1.0
01000
x x 0 a
"A- :;:::6--
/~
. Exit /
/;P P
/ 0 ~ a
6 / ;/)
/ I
a °
/ /
9-' 0/
/ /
6 xO. 6 R
if /-
oP/ V ~,~o
~O~ O'~ -
~CY - ---~.!----~--Port
1200 1300 1400 1500 1600
REACTOR GAS TEMPERATURE, of
o
. 9
.8
. 2
Exit Conversion
Versus Core Temp.
" .
/~ Core
~
, .
,
/
,
"0
/0
ff
o
Experimental
-Data
I-'
(J\
a
8 .7
I-
0:::
UJ
~ .6
o
u
o .5
u
z
o .4
I-
u
-------
f--'
0'\
f--'
o
. u.J .
I-
0:::
u.J
>
Z
o
u
o
u
z
o
I-
U
Port
Tern
.6
.5
.4
o
1200
1400
1900
2000
1500 1600 1700
REACTOR GAS TEMPERAT URE, of
1800
1300
Figure 48. Simulation of the approach to high-temperature conversion
for CO using the cell pattern of flow shown in Figure 43, item 3.
Input: exhaust - CO = 1.9%, H2 = 0.0%, 02= 0.0%., HC = 270 ppm.
-------
I--'
0'\
r\)
~
1.0
.9
.8
c .7
LLJ
~
a::
~ .6
:z
a
u .
a .5
u
~ .4
~
u
~ .3
u...
.2
. 1
o .
1100
/
/
/
/
/
o
/
/
/
/
o
/.
1200
--
...-- -- -0
~
Experimental
Data
,/'
/""
./ .
~
1m =2
BOO
1400 1500 1600
CORE GAS TEMPERATURE, of
1700
--"
~-- .
1m = 5
---.
,...,..,0
~
Computer Points
1800
1900
Figure 49. Cell mixed plug flow simulation (see Figure 43, itemS).
Air flow ratioed to exhaust.
..-D
--
2CXX>
-------
. 2. 000
. 1. 600
Mean
exit
age = 1 tau
t 0691 sec)
. 1. 200 Variance = O. 127
>-
u
2:
~
0
LLJ
0::
LL.
.800 0
.400
o
o
. 0 400 . 800 1. 200 1. 600 2. 000
DIMENSIONLESS TIME, UNITS OF TAU
2. 400
Figure 50. Residence time distribution for the simulation shown in .
Figure 47 and item 2, Figure 4 ~ . .
163
.,
" .
-------
the cell temperature.distribution. However, even when inlet properties are
steady a difference still exists which must be explained by the relationship
that measured temperature bears to the distribution of reaction in the reactor.
The behavior that we would most desire to explain is the transition in conver-
sionfrom zero to maximum in 200°F; an offset in temperature can be more ea.sily
accepted if we consider the scatter in conversions observed about the least
squares correlation o~ kinetics.
The simulations shown in Figures 46, 47, 48, and 49 represent a progres-
sive shift from stirred tank to plug flow behavior. In Figure 47, the module
network,. the bias of 1m toward early mixing, and the high rate of heat loss
. that is exacted throughout. the plug flow exit section cause approximately half
the total reaction to occur in the stirred tank core. The combination of
these factors causes the conversions for cyclic input to be shifted toward the
experimental curve. Further change toward plug flow is represented in Figure
48, where a smaller heat loss in the leading section of the annulus and prora-
tion of 1m ~3trictly by volume causes more reaction to occur in the plug flow
sections. In this simulation and the one incorporating only plug flow elements
(Figure 49), the increase in conversion with temperature is much more gradual,
representing a distinctly different character than the experiment result.
Hence on an overall view, the rapid increase in experimental conversions with
temperature is best represented by the pattern-of-flow type simulation least
removed from the stirred tank.
I,
The "best" simulation (Figure 47, "POF" number 2 in Figure 43) still rep-
resents some departure from the experimental result; and the source of the
discrepancy remains difficult. to explain because of the larger number of fac-
tors bearing on the problem. The worst departure from the experimental obser-
vation is below 2(jJ!o conversion, which it is interesting to note is a region
that was truncated in developing the kinetics. However, to provide direction
for future work we note that this "best" fit is given by a relatively small.
stirred tank core experiencing only negligible heat loss follows by an annulus
which experiences a high rate of heat loss. In this arrangement, it can be
argued that partial reaction in the core acts as a triggering mechanism to
overconie the heat loss in the annulus. That is: partial conversion in the
'small core guarantees a rise in temperature since heat loss is small; tempera-
ture tends to decline.in the annulus but reaction continues toward completion
to some extent depending on the temperature extent upon entering and the extent
to which heat of reaction forestalls quenching; thereby a partial conversion
a.nd modest temperature rise in. the core may be amplified to a. greater ,or lesser
extent in the annulus depending on the influence that is exerted by the heat
balance. The tendency for reaction in the core to influence CO oxidation in
the annulus also depends on the. amounts of hydrogen a.nd hydrocarbon that are
present to boost the temperature in the core without necessarily reacting the
carbon monoxide, which depends on the operating point attained by the stirred
tank core. A smaller stirred core volume would tend to raise the temperature'
a.t which triggering occurred; and a higher rate of heat loss from the annulus
would increase the important of a triggering effect. Ignition in the stirred
164
-------
core would again depend on initiai condition; this is
section where an entering element of flow experiences
to what entered earlier.
not true of a plug flow
no direct influence due
Balanced against the thermal triggering effect just described, we have
, '
the general tendency in moving from stirred tank plug flow behavior for reac-
tion to be spread over a wider range of average temperature as the variance in
entering temperature is allowed to persist due to lesser backmixing.
The residence time distribution for the "best" simulation is shown in
Figure 50. The double peak is associated with the cyclically fluctuating in-
let flow; specifically the high rate of flow during overlap of exhaust strokes
for cylinders 3 and 5 causes early departure for a fraction of the cells in
the reactor, thereby produc,ing the early peak shown in the RTD. The variance
for the RTD is 0.127, which corresponds to the variance for eight equal sized
tanks in series. This is one measure bf dispersion, which however will be low
in this instance since the RTD for cells as computed ignores the axial disper-
sion, that is implied by coalescence of cells within slugs in the plug flow
module.
The distribution of reaction for carbon monoxide in the ''best'' simulation
(Figure 47) indicates that less than 5% of total conversion occurs in the
ports, something over 50% occurs in the core and the remainder occurs in the
annulus. Hydrocarbons, subject to the assumption that oxygen in entering ex-
haust preferentially oxidizes H2 and He, was converted by approximately 9010 in
the core. High core conversions have been established by experimental measure-
ments (25), which indicate 6010 and higher conversions of CO in the core and
80% and higher conversion of hydrocarbon depending on dilution ratio.
The distribution of temperatures in Figure 47 indicates that the exit
temperature is characteristically 100°F lower than the core temperature. This
agrees with Blenk's (3) measurements for a low inlet CO concentration. At
higher levels of entering CO, the experimental temperature difference increases
to 250°F ,(3,25); which was not indicated by the POF simula.tions. However,
temperature distribution becomes highly sensitive to the distribution of reac-
, .
tion through the reactor as combustible concentrations increase. Insufficient
data were obtained to establish any detailed correspondence with reactor tem-
perature distributions. However, considering that temperature rise may be the
best available indication of local conversions within a reactor, more careful
attention should be given to this facet of reactor studies in future coordina-
tiol1 of POF-type simulations with experimental design. This would contrast
with the prevading philosophy in the current effort, which was to treat con-
versions primarily 0/1 an entrance to exit basis. Some ca.ution should be exer-
cised in heading too f8,r in the other direction (of identifying physical parts
with simulation modules); since the entire approach to modeling represents a
very profound idealization as compared to the complexity of any real reactor.
165,
-------
I .
I
. . Other changes which were made in running the POF' simulation (see Figure
51 and keyed points in Figure 47) involved the exhaust temperature span and
cyclic versus steady input. At low and intermediate temperature a.nd conversion
levels,' conversion was enhanced by increasing the temperature span. . At high
temperature (1460°F entering exhaust), the conversion was slightly lower for
TSPAN = 800°F than for an entirely uniform inlet flow, temperature and concen-
tration. At both 740/0 and 2')1/0 conversion levels, the use of cyclic flow and
concentration versus steady flow and concentration was shown to have a. negli-
gible effect when variance in entering temperature was zero (i.e., TSPAN = 0
and TAIR = TEXHAUST)' .
Distribution of the mixing parameter was changed in the simulations of'
Figure 47 from 1m = (L3,3.7,0)to Im= (1,2,2) for port, core, and arlnulus,
respectively. Pairs of points (0,' and 0,8) that are comparable except for.
this change exist at reactor gas temperatures of~llOO°F and.~1650°F, and in
both cases a high conversion is predicted by the distribution (1,2,2). This
is felt to be true primarily because of the unproductive coalescences which
occur in the port, where the very small size of the module and essentially
sequential entry of air and exhaust prevent any significant blending of air
and exhaust cells. .
. Hydrogen reintroduced into the inlet feed (Figure 46) along with 820 ppm
hydrocarbon and 0.6')1/0 oxygen appears on the basis of two sets of points to
shift the conversion curves to a more horizontal position, contrary to the
behavior desired to match the experimental curve. .
The simulation of a half reactor assuming symmetry (Figure 52) is similar
to the ''best'' simulation, but requires a noticeably greater temperature in-
crease to ra.ise the CO conversion. This is in part due to proration of 1m
strictly according to module volumes, which placE!s a greater emphasis on the
large plug flow exit section than on the stirred core and therefore tends to
reduce the effectiveness of backmixing.
D.
SENSITIVITY TO RESIDENCE TIME DISTRIBUTION AND MICROMIXEDNESS (1m)
Results of "MIXONLY" simulations (Tables I and III) demonstrateQ that
. .
generally higher conversions result from plug flow residence time distributions
due to the avoidance of early cell departures. If we consider sufficientl~
high temperatures, the same conclusion would be reached using the POF simula-
tions. However, at normal operating temperatures this view must be modified.
In Figure 53, the sensitivity of conversions for CO to change in 1m is
considered for the ''best II simulation (Fig0.re 47 and Figure 43, item 2) and for
the all-plug-flow simulation of Figure 49. Two inlet temperature levels a.re
considered: TEXHAUST = 1663°F and 20l3°F. 'rhe first is near the upper limit
. of enterirlg exhaust tempera.tures found iil practice a.nd the second outside the
Tlorrna..L operat:i.lll~ rane;e.
166
-------
1.
.
1460
Average
Inlet.
Temper-
at u re
. 7
c
L.LJ
.....
0::
LLJ
>.
:z
0 .
u
0
.U
Z
0
t- ..
u \260.
<
0::
u..
Computer Points
. 0
.200
400 600
TS PAN, of
800
1000
Figure 51.
conversion.
The effect of inlet exhaust temperature span (cyclic) on
Pattern of flow for simulation shown in Figure 43, item 2.
167
-------
1.0
.9
.8
c . 7
I...L.J
I-
e:::: .6
I...L.J
>
Z
a .5
u
I--' a
(j\ u
0:>
z .4
a
I-
u .3
«
e::::
L..I-
.2
. 1
.00- Exit.
---
-- .
.~
/0 .
../ ./j
//
.,/ /
Exit / /. .
Temp ~ore /
. 1_'// Temp/
~~. .1,...
/ .
/1::.------
--
~~
~ ,?"
//
v/
..- Uniform Inlet
Temperature
and Composition
Q100
Port.
1800
2000
-- --
. ----
. --
. ----n
.--
---
-
-- .
.--
A-- Core
x-
1400 . 1500 1600 1700
REACTOR GAS TEMPERATURE, of
1200
1300
1900
Figure 52. . Simulation of a half reactor assuming symmetry.
1 and 3 firing half the core and half the annulus.
Cylinders
-------
.01
.008
.006
.0
.002
.001
o
Figure 53.
parameter,
(number 2,
Figure 43)
.4
.2
\
.\
\
,
'.
\
\
\
\
\
\
\
\
\
'.
\
\
\
\
--- 0
"-
"""
"""
--
---A_-
Inlet Gas Temperature, of
liT Low" Exhaust Air and
Average Exhaust
Average
1663 1568 0 A 0
2013 1884 .. .
TS PAN = 4000F
Pattern of flow from Figure 52
Number 2
low pressure air - Number 5
- ratioedair - - - Number 5
1450
1800
2
12
10
14
4
6 8
MIXING PARAMETER, 1m
Sensitivity of simulation conversions to the mixing
I . Comparison of the stirred-tank-with-plug-flow
Flfgure 43) and the all plug flow simulation {number 5, . ..
using low pressure and ratioed air. See note 2, Figure 46.
169
-------
In Figure 53, the simulation that we have termed "best" (Figure 43, item
2) e~hibits a rapid decline in the fraction CO unconverted at the lower inlet
temperature to reach a level of 9r::p!o conversion a.t 1m == 8. At this lower tem-
perature, the all-plug-flow simulatiori exhibits a much smaller change in frac-
tion unconverted both in the cast= of iow pressure air and of air ratioed to
exhaust flow. In both cases, therfraction unconverted appears to have nearly
leveled off at 1m :::: 10. For the low pressure air, this is due both to the
maldistribution of air and exhaust and the persistence of low..;tempera.ture re-
gions in the temperature distributioh which are not eliminated by backrnixing.
With ratioed air, the maldistributioh of flow is eliminated, but the tempera-
ture distribution still limits conver~ion.
Raising the inlet exhaust temperature by 350° raises the entire tempera-
ture distribution sufficiently to react any exhaust that mixes with air,
causing the ratioed~air simulation to exhibit a high sensitivity to increased
lUll reaching 9r:P/o conversion at 1m == 6. Unfortunately, this is true' only out-
side the range of acceptable ;operating temperature and a plug-flow, ratioed
air reactor cannot be considered as an improved practical device.
For low pressure air, the plug fiow simulation at the higher temperature
shows only slightly improved conversion, because of the overriding effect of
. flow maldistribution. This simulation does allow blending of air and exhaust
entering the reactor coincidentally from all ports; consequently,the 6010 con-
version at the higher temperature is an indication of the penalty associated
with'time maldistribution alone where backmixing is nearly eliminated (40 slugs
per cycle).
To place the "best" simulation (Figure 43, item 2) into a fa.miliarmacro-
mixing frame of reference, its sensitivity is plotted a.long with those for
cell-wise stirred tanks in series (MIXONLY) in Figure 54. There exists a
close correspondence between the '~est" simulation and five stirred tanks. We
recall that on the basis of the variance in the RTD, correspondence should be
established with eight tanks in series; this difference is due at least in
part to axial dispersion within slugs for the plug flow element of the "best"
simulation (16 slugs per engine cycle).
170
-------
.2 Iin" Tanks in Series
" n = 1
" c
. 1 "~
. 08 ----
-
o .06
~
e:::: n=2
~
0
u
:z
::J
:z
0
I- .02
u
-<
e::::
u..
.01
.008 ~ n = 5
.006 \
. .004 \
\.
\
.002
.001
o
2
46 8
MIXING PARAMETER, I.,;,
14
Figure 54. Comparison of the stirred tank-with-plug-flow simulation
(number 2, Figure 43) with cell-wise stirred tanks in series.
Simulation number 2 is run at an average inlet temperature of l663°.F.
Tanks in series are for instantaneous reaction after mixing. See
note 2, Figure 46.
171
-------
MODELING REACTOR OPERATION DURING WARM-UP
Warm-up of the DuPont Model V reactor during unchoked engine operation
with air injection has been characterized by a nonreactive period of several
minutes during which reactions are largely quenched due to heat loss, followed
by a transition to a lightoff condition that is gradual for hydrocarbon con-
version but more abrupt for carbon monoxide. No experimental conversions have
been determined for hydrogen during warm-up.
For a sufficiently high inlet temperature and/or high entering combusti-
bleconcentration, thelightoff should occur at time zero. However, this was
not observed for the range of conditions run on the Model V reactor.
I
Model building for the warm-up period has had the objective of developing
a rapid computer simulation to predict the warm-up time required to achieve
lightoff for various reactor designs and operating conditions. The computer
program allows the user to d.esignate a wide range of design specifications;
the coupled reaction kinetics are restricted to zero-order oxidations in a
continuous stirred tank reactor. This severe restriction on kinetics can be
relaxed within the general framework of the existing model, but not without
considerably complicating the calculations.
VI.
Model Building for .Unsteady State Operation
A.
KEY FEATURES AND ASSUMPTIONS
All of the stationary state simulations of species conversions described
in the previous sections solved for an ~nsteady state approach to the station-
ary state solutions (or periodic solution) on a reactor tim~ scale measured in
tenth,; 01' :l. second. Changes in surface temperatures occur on a much longer
Lime scale, mca:;urcd in minute:;. To reconcile these time scales .without in-
currinp; t,he hir:h cost of running an unstearly state simuiation of speci~s con-
vE~rsion:; rOT' a ;;imlllation time. of several minutes, the warm-up simulation was
designed to compute steady state conversions and reactor gas temperature. at
intervals of several seconds, and then to extrapolate these gas temperatures
for the purpose of computing more frequent estimates of the unsteady state
heat balance on reactor parts and their rise in temperature.
Reactor gas temperature and chemical conversions are calculated assolu-
tions for an ideal backmix reactor with continuous feed and feed properties.
This assumption ignores all distributions of temperature and composition and
172
-------
causes the transition to a lightoff condition to proceed in'a narrower range
of time and temperature than would occur in practice. The assumption of zero-
order kinetics is discussed in the subsequent section on method of solution.
The unsteady state simulation of surface temperatures integrates tempera-
ture change based on heat balance for as many components in a reactor as the
user wishes to ascribe different average temperatures. All of the defined
parts are assumed to have a uniform internal temperature. If insulation is
present, it must be divided into thin layers.
Any defined part of a reactor'can be. caused to exchange heat with exhaust
gas and/or ambient air by.convection, or with any other part by radiation or
conduction. Many of the possible paths of heat transfer will be redundant in
a particular reactor design, and these. will be excluded from the calculations
by preassigning heat transfer coefficients of zero.
Heat transfer by radiation assumes a view factor that is appropriate to
concentric cylinders or spheres, where each component is uniformly irradiated
by an opposite surface. The contribution of radiation to the heat balance
for a part is treated as an equivalent conductance term which can be lumped
with convection and/or conduction in circumstances of parallel heat transfer
to an infinite surrounding, across a closed gas space, or between connected
parts. Heat transfer by convection is computed using coefficients that are
obtained from steady flow correlations based on the usual Reynolds (Re),
Prandtl (Pr), and Grashof (Gr) numbers. Calculations employ user-designated
parameters describing reactor geometry, mass flow, and the division of mass
.flow into fractions passing each of the designated surfaces. Where specific
data on convective heat transfer coefficients are available, the computed
values can be adjusted.
B.
REACTOR PARTS TEMPERATURE SIMULATION
The operation of the parts temperature simulation will be illustrated by
referring to a thermal network (Figure 55) which corresponds to the DuPont
Model V reactor with two layers of insulation at the outside and a wrapping
on the insulation. The reactor itself is represented as six concentric parts:
the core, two layers of radiation shield, and three layers of outer shell.
Heat losses at the insulated ends are neglected. The insulation is treated'
as a half layer resistance at the inside and outside. The two other entities
which exchange heat are the exhaust gas and ambient air; which brings the
total number of heat exchange "bodies" to eleven.
All heat transfers are computed as a conductance, \vhich \ve designate "HA,"
times a temperature difference. "HA" in the computer program is an array
which reserves storage for conductances between all pairings of bodies in the
thermal network, except that no storage exists for conductance directly.
173
-------
Reactor Center Li ne
Core
Tl
Reactor
Gas, T G
Double
T2 Radi~tion
Shield.
T3
. Triple
HA . T4 Outer
r Wall
HAr TS
HAc T7 T6
HAc Insulation.
HAc .T
8
HAr HAc T9 Wrappi ng
Ambient
Ai r, T
Figure 55. Thermal conductance network for the DuPont Model V
reactor'with external insulation. '
174
-------
between ambient air and exhaust. Where heat transfer between two bodies is
both by radiation and by conduction or convection, there exist parallel con-
ductances.which we refer to as HAr and HAc' respectively. .
There
two part s ,
resistance
is assumed to exist only a single thermal resistance
by virtue of neglecting internal resistan~e in parts
between insulation and other parts.
between any
in contact
For the thermal network shown in Figure 55, the computer program Ivould
reserve (9xll) storage locations for both HAc and HAr. Of the 198 paths for
for heat exchange thus allowed, only 17 are used. . The redundant paths are
exempted from calculations by assigning zero initial values, which signal a
null computation. The redundancy provides flexibility to the user in the
thermal networks which can be represented.
Prior to each time that the part temperatures are integrated, a nelv reac-
tor temperature has been computed from the coupled CSTR simulation. After
two successive gas temperatures have been computed, the value used for comput-
ing heat transfer to reactor parts may be a linearly extrapolated value (op-
tional). Integration of the parts temperatures proceeds over a designated
number of steps before another gas temperature is computed. Step size is
variable to limit the change in parts temperatures within designated bounds.
Conductances may be recomputed for each step in the parts temperature
integration, or optionally may be computed only once after each new calcula-
. tion of reactor gas temperature. The conductance calculations that are pro- .
grammed into the simulation include the following: .
Radiation between bodies i and j (21, p. 227).
HA
r
i,j
~l-Ei
-+
A.E.
1 1
('1'4- '1'4).
o . .
r 1 J
l-E~ .
1 .
- + --.J.. ( T
A A .E. i
J 1
- '1'.)
J
Convection between air or exhaust and any part j.
HA
c .
G,J
=
2 sides
L
s=l
h.
J,s
A
j,s
Where "h" is computed from steady flow correlations.
175
-------
Forced convection in a closed conduit.
Laminar flow, RE < 2000. . (25 ,po 392)
. Nu =
8,57(RePrD/L).27; (RePrD/L) <.3
( VI - 3)
Nu =
10.02(RePrD/L).40; (RePrD/L) <.3
( VI -~ )
Transition flow, 2000 < Re < 10,000 (31, p. sec, 10, p. 14)
h =
418 G Cp (Re2/3 - 125)(1 + (D/L)2/3)
pr2/3 Re .
( VI - 5 )
Fully turbulent flow, RE > 10,000 (26, sec. 10, p. 14)
Nu =
.023. Re' 8 prl/3
( VI-6)
Free convection outside a horizontal cylinder (21, p. 342)
Nu =
1/4
o. 53( GrPr)
(VI-'J)
Gas flOlv normal to the outside of a circular cylinder (21, p. ~ll)
Nu =
0.536(Re)" 496 .
(VI-8 )
.. Convection and conduction across a narrow closed gas space. (21, p. 347)
Nu =
.324
. 0712 Gr ; Gr > 3500
(VI-9)
176
-------
h
=
kf
j); Gr < 3500
(VI-10)
Conduction through insulation
HA
c
=
k A
t
tlL
( VI-ll)
The use of steady flow convective heat transfer correlations was dictated
by an absence of any detailed measurement of hea~ fluxes within an exhaust
reactor. However, all of these correlations are assigned variable leading
coefficients so that the values can be adjusted by the program user. This
was done, as described later, to adjust the change in parts temperatures to
measured values.
When all conductances have been computed, a heat balance is performed on
each reactor part and a temperature change computed for one integration step.
For a part "j" in Figure 55, we sum the heat fluxes from all eleven heat ex-
change bodies. .
=
T
jlast
11
L
i=l
11
HA (T,-T.) + L
c.. ~ J
~,J
i=l
MjC
P.
J
HA (T,-T.)
r. , ~ J
~,J.
tit
T.
J
+
( VI-12)
The simple Euler's method of integration shown is
mate nature of this entire simulation. An option
midpoint. slope method.
consistent with the approxi-
is provided, however, for a
c.
SOLUTIONS FOR MULTIPLE OXIDATIONS IN A "CSTR"
A general method of solution will be outlined, and then assumptions will
be invoked to reduce the complexity of the calculation~
Obtaining solutions for an ideal backmix reactor where more than one re-
action is represented can be approached either as an initial value problem
where an unsteady state approach is computed to the steady state solution (as
in the program "EXHAUST"), or as the simultaneous solution of nonlinear alge-
braic equations derived from the steady state material and energy balances.
177
-------
Efforts made to s~plify and adapt the "unsteady-state-approach" program,
"EXHAUST," to the warm:-up problem did not produce an acceptably rapid version.'
The essential difficulty resulted from the fact that a short time step was re-
quired in the Runge-Kutta integration, which unavoidably 'implied unacceptable
running costs on the computer. The alternative of solving nonlinear algebraic
equations was used.
We wish to determine an exit temperature T and exit conversions Xi for
i == 1, ..., q combustible species which are assumed to be oxidized indepen-
dently (no series reactions). Stoichiometry given by vi k for specie "i" in
,
reaction "k" is .wTitten for one mole of the oxidized species to cause rates
of reaction rk' k == 1, ..., q to equal rates of "appearance" of species "i,"
r i' i == 1, ..., q.
Rates of reaction are assumed to have the following form and to involve
an order dependence on any of the "m" species that are present:.
r.
l
l'
k
==
-Ek/RT m ~. k
-A e . J1l (PC.) l,
k l== l
(VI-13)
From the material balance,
f C
o i
o
+ l' V - fC
i i
o
(VI-14 )
we obtain "q" euations of the form:
q q . q act ~- ~ ~~ -E k/R'r
('), -)(- (l-X.) J,k L v X j,k
F - X - A 11 Jl e
i i i j==l J - - j =q + 1 t:l j,x: £
i
==
k
==
.l,...,q
x-
A
. i
I::,
(f0b m
A V...E.p 11
i - f j==l
f C.
o l
o
~. .
C l,J
jo .
; b
==
m
Z ~. k
. 1 J,
J==
. (VI -15 )
L'W
-------
where
f q "q act
f .1- L. L. v'kC, X,
J, J,o J
o k==l j==l
(VI-16)
The term fjfo isl if all reactions are equilmolar or if mole compression
is small enough to be ignored, If it cannot be ignored, the expression for
fjfomustbe substituted into the functions Fi' .
From the energy balance:
I::.
m
L: C.H.(T)
j==l J,o J 0
p
r
sinks
F
q+l
1
f
o
L:
k::::l
HA (T-Tk)
ck
q
- L: C, (l-X,)H,(T)-
j==l J,o J J
m
L:
j==q act + 1
C, H,(T)
J,o J
q act
L.
j==q+l
~ +
[j,O
q
L:
k==l
v C X 1
j,k k,o kJ
H ,( T) .
J
( VI-17)
A solution is obtained when we find T and Xi' i == 1, '" q, which satisfy
Fi == 0, i == 1, .., , q + 1. Because of the coupling that is introduced by
assuming that the rate of a particular reaction is order dependent on species
which are appearing or disappearing in other reactions, a solution must be
approached by a multivariate search method or by an iteration such as Newton's
method "for vector functions,. In the latter case, an approach to a solution
is obtained from:
X
i
n
==
X
i
n-l
+ I::.X. , i == 1, "', q
l
n==l
T
n
==
T + I::.T
ri.:.l n-l
179
-------
--~
Where ~Xi and ~T are the solution to the system of linear algebraic equations:
( ::~)-l
/:,X .
1
n-l
+.. ... +
GF ) ~F~..
. dXl /:,X. +. dTl /:'T- + F
q . qn-l. -1 n 1 1
=
o
(dF)
2
- .~X
dX, 1
1 -1 n-l
+ ...
+ F
2
=
o
QF0 ..
q+l
dX /:'Xl + ...
n-l n-l
+ F
q+l
=
o
(VI-iS)
Here "n" refers to the step in the iteration. Given the fact that the nonlin-
ear equations will in general possess several possible solutions, the particu-
lar solution that is obtained as well as the question of whether Newton's
method will converge at all will depend heavily on the guess used to start the
. iteration.
. ,
To reduce the difficulty in searching for a solution we are aided by as-
sumptions which red~ce the interdependenc~ between the several conversions Xi.
For example, if order dependence for each reaction is limited to the oxidized
specie and oxygen, we are left with only a two-dimensional search on oxygen
'conversion and temperature; 1. e., the equations for Fi ar.e reduced to
F.
l
-
X
i
- E T]. . 11 +1 '
A*e i/RT (l-X,) l,l (l-X ) q,l
i l. q+l
o
i
=
1,. .. , q
( VI -19)
\vhere if we have search values of Xq+l and T, the equations are solvable for
X.by a root finding method.
.l
If we proceed to an order dependence of zero, we are reduced toea one-
dimensional search on temperature alone, and the calculation of Xi is explicit,
180
-------
X.
1
=
A* .e-E/RT
( VI-20)
This assumption was used in the present work.
To justify this sweeping assumption, it should be noted that the reac-
tion orders for carbon monoxide in the current study were close to zero (.269
~ 20 = .100 for order with respect to CO and -. 032 ~ 20 = .106 for order, ,vith
respect to 02' For hydrogen, no statistically satisfactory rate expression
was obtained by the method qf least-squares, and a rate equation for tempera-
ture dependence alone based on a plot of conversion versus temperature is the
only estimate which can be safely offered. Finally, although hydrocarbon oxi-
dation involves statistically valid orders, its contribution to a change ih
reactor gas temperature is only about 10% of that for total combustibles
(based on a characteristic exhaust 'analysis of 4% co, 1.6% H2, and 500 ppm
hydrocarbon). Hence some imprecision in simulated values of hydrocarbon con~
version can be tolerated.
I
I
I
I
The strategy for finding a solution in the zero-order case depends solely
on finding the exit gas temperature which satisfies both the energy balance
(based on the inlet composition and temperature of exhaust, the air dilution
fraction, and heat loss) and the material balances for the various reactive
species (based on the exit temperature and reaction kinetics). This is ,
equivalent to searching for the value of exiting gas temperature which satis-
fies the energy baiance written
F
q+l
=
m
L
'j=l
C. H.(T)
J,o J 0
1 P sinks
f L
o
k=l
HA (T-Tk)
ck
f
-f
o
m
L
j=l
C.H.(T)
J J
=
o
(VI-21)
with
C.
J
=
fO 'C < - A*e-Ej/RT\
f j,o ~ )
(VI-22 )
181
-------
The method used to find the exiting temperature begins as a one-direction01
search of uniform step size in temperature, using the fact that a positive di-
rection of search is indicated where Fq+l is positive. As the search approaches
a solution, the step size is reduced by application of Newton's method, or in
the event that the solution is overshot, the half interval root-finding method
is invoked.
The familiar possibility that a stirred tank reactor may exhibit more
than one operating point for a given set of inlet conditions, which has been
discussed at length by Schwing (29) for lightoff of a single reactant in 0
stirred thermal reactor, attests to the importance of both the stQrting point
in the search and 31so the step size used. In the case where several reactions
occur simultaneously, there exists in general the possibility of multiple so- .
lutions. Where multiple solutions exist, the solution actually obtained will
depend both on the starting temperature and on the search step size, by virtue
of the possibility of over shooting an entire region associated with some par-
ticular stable solution. .
Because the warm-up computer program as used has no provision for intro-
ducing nonzero-order kinetics, use of the program with rate expressions which
include order dependence requires averaging out this dependence. ' For hydro-
carbon, which is fractional order in HC, 02' NO, and 02 for a total order of
1.'7, the rate equation was corrected by inserting the log mean values of the
order determining species for the 105 data sets used in the least-squares de-
termination.
Least squares equation for hydrocarbon:
l'
HC
=
1.191 e-29,836/RTp0238 p.53'7 p.415 p.512
o NO CO
HC 2 '
(VI-23 )
Rate equation for hydrogen corrected to zero order.
rHC
=
.00325 e-29,836/RT
( VI-24)
For carbon monoxide and hydrogen, zero-order equations are:
Zero-order rate equation for carbon monoxide
RCO
=
6 - 33, 800/RT
. 21 e
(VI-25 )
182
-------
Zero-order rate equation for hydrogen
rH
2
1"2660.
-52,000/RT
e .
( VI-26)
The conversions previously determined (Phase I) corrected on th0 basis of
zero-order kinetics to a flow f* = 1. 99xlO-Lf lb mOles/see and inlet"concentra-
tion C~ = .006 mole fraction, provide a measure of the uncontrolled variation
in conversion for hydrogen under the assumption of zero-order kinetics. Cor-
rections are shown for the data for carbon monoxide (Fi~ure 56; f* = 2.98xlO-~,
C~ = .02) and for hydrocarbon (Figure 57; f* = 1. 99xlO- , C~ = .0004).
183
-------
LO
o
o
0.9
0.8
o
o
a
I..LJ
to- .
ffi O. 7
>
z
.0
u
. ~ 0.6
o
o
x
o
z
o
~ 0.5.
z
o
CC\
a:::
~ 0.4
z
b
t-
U
« o. 3
a:::
w..
o
.0
o
1000
00
000
000
~OO 0
o
OCX>
.CW
000
0.2
o. 1
1200 1300 1400
REACTOR GAS TEMPERATURE, OF
Figure 56. Conversions of carbon monoxide corrected to 30 lb. exhaust!
hr and .02 mole fraction CO entering.
1100
1500
1600
1($4
-------
1.0
0.9
.0.8
8 0.7
~
e::::
u.J
>
z
8 0.6
z
o
co
e::::
5 0.5
o
e::::
o
>-
.~ 0.4
o
~
u
«
e:::: O. 3
u.
0.2
O. 1
o. qooo
o
o
o
ex>
001
.0 0
CXX>
CX>
00
CQ)
o 00
o 0
o
..
.
.
o
o
o
o
o
1500
1600 .
o
o
o
o
o
o
o 0
o
00
o
o
00
db
o 0
o
o
o
~oo
o
1100 .1200 1300 . 1400
REACTOR GAS TEMPERATURE, of
Figure 57. Conversions of hydrocarbon corrected to 20 Ib 'exhaust!hr
and 400 ppm hydrocarbon entering. . .
o
185
-------
VII.
Base Case Warm-Up Simulatians for the DuPont Madel V Reactor
Base case simulations on the DuPont
six concentric cylinders representing--l
ation shield, and 4, 5, and 6--the three
insulation was included.
Model
inner
outer
V reactarwere performed on,
core, 2 and 3--the double radi-
shells (see Figure ~~). No
A. WARM-UP WITHOUT REACTION--THERMAL PARAMETER EVALUATION
The first simulations were run without appreciable reaction on 150 Ib af
exhaust per hour passing through the reactor for the purpose of testing the
sensitivity of the model heat loss at steady state to changes in emissivities
and convective heat transfer coefficients. Results (Figures 58, 59, and 60)
allow approximate comparisons ta be made with selected experimental results;
however, na precise determination of "best" thermal parameters can be claimed
in consideration of the complete mixing assumption made in modeling.
Model heat losses at steady state, expressed as temperature drap, are
presented in Figure 58 far ranges af emissivities, convective coefficients,
and inlet temperatures. Surface emissivities playa large role in determining
heat loss, more so than exhaust-side convective heat transfer coefficients.
The relative insensitivity to exhaust side convectian at steady state is due
to the fact that all inner surfaces are at high temperatures, approaching the
gas temperature, whereas most af the temperature drop ta ambient level is
across the air spaces between the three auter shells (Figure 59).
Temperature measurements reparted for the DuPont reactar by Blenk (3)
indicate a temperature drap between care and autlet varying from, 160° to 215°
for unreacting exhaust in a range of appraximately 1350° to 1750° inlet exhaust
,.temperature. Since these values do not appear carrelatable, no single value
can be selected for comparisan. However, based on the median value of apprax-
imately 190°F, we are directed ta a model emissivity of .5 to .6 to match a
190°F drop at an inlet temperature of 1725°F.
A second group of experimental data that are available for comparison are
the measurements of temperatures of concentric enclosures within the reactor
at steady state. Experimental points (Fi~ure 59) indicate that all of the
surfaces in contact with exhaust exhibit temperatures differing fram the core
exhaust temperature of no more than about 200°F. The profile of parts temper-
atures with reaction (90% conversion of 3% CO) is slightly flatter than with-
aut, 'due to compensation for heat loss by heat of reaction. However, even with
react:LL~n the experimental gas temperature is indicated to drop by approximately
the same 200°F between the core and the exit, according to both the CRC study
and Blenk (3). This occurs even though oxidation of the combustible content
186
-------
u..
o.
.
z
o
t-
u
«
. I..LJ
a:::
~
.0
:r::
t-
~
C-
O
a:::
o
I..LJ
a:::
::::>
t-
«
a:::
~
~
I..LJ
t-
V')
«
e",
250
200
150
1000
200
150
200 .
150
10~400
Emissivities are the same for all surfaces.
Literature values for exhaust side hS.
I nlet temperature = 1725 of
. 1
.3 .4 .5 .6.7
SURFACE EMISS IVITIES
1.0
x
)(
1 1.5 2.
. EXHA UST S I DE HEAT TRANSFER MULTI PLIERS, (h/h lit)
Exhaust side h = 1. 5 x literature values
Em i ss ivity = O. 9 in s.ide
0.5 between shields
O. 3 betwee n
shell
1500
1600 1700
INlET TEMPERATURE, of
1800
1900
Figure 58. Simulated steady-state heat loss measured as drop in
exhaust .temperature. DuPont Model V reactor configuration. Mass f10w'~
150 1b/hr.
187
-------
~ 2.28'~ .
, I
1600
+
+ With reaction
08 Without reaction
LL 1200
o
UJ
0::
i=IOOO
-------
I ' 1400
1300
, 1200
1100
1000
900
LL. 800
o
UJ 700
0::::
=>
I-
-------
(nominally 3% co, 1% H2' and 500 ppm HC ~. releases heat which. would raise the
temperature by. 500°F. This persistent drop in temperature between the core
and the exit during lightoff operation is an indication that a large porti~n
of the reaction occurs in the core. .
Given the experimental fact that gas temperature does drop after leaving
the core , it. is evident that a simulation based on complete mixing. to a uni-
form gas temperature should predict less difference in metal temperatures,
measured from the core outward to the shell, than w~uld be observed experi-
mentally. However, use of plausible emissivities for partially blackened
metal (s= .]0 and .85), applied to all surfaces alike, and on convective
coefficients up to double the steady-flow values (not graphed) caused the
simulation metal temperatures progressing. out from the core to drop more
sharply than the experimental. To counter this behavior, it was assumed that
emissivities in closed gas spaces were lower (mo~e reflective) than those for
surfaces darkened by contact with exhaust. By assuming an emissivity of .5
between the two layers of the heat shield and an even lower .3 between the
three layers of outer sheel (polished stainless has s = .2), the general agree-
ment shown in Figure 59 between the simulations and measurements was obtained.
The convective coefficients used were one and one half times values computed
from steady-flow correlations. Agreement is better for the experimental
points obtained with reaction. At the very outside surface of the reactor.
the simulation temperature is high (due in part to neglect of the metal.
supports) .
. Values of the convective coefficients and equivalent radiative coefficients,
HAr/A, computed by the simulation are given in Figure 59. The convective
coefficients on the exhaust side change negligibly during warm-up; convection
at the outside surface based on an external air velocity of 8 ft/sec approx-
imately doubles; and the radiative coefficients r1se sharply from zero to
their given values in proportion to (Tf - T~) /( Tl - T2). . .
Figure 60 shows the unsteady-state approach to the metal temperature
profile of Figure 59 (without reaction). Good agreement was obtained between
the simulation and the experimental observations. That the simulation curves
exhibit values that are higher than the observed values at 1 min can be attrib-
uted in part to the fact that the simulation treats hot exhaust entering a
cold reactor whereas the experimental values represent start up of a cold
engine and reactor. A good fit for the temperature transients, as shown, is
very important to achieving useful estimates of time to lightoff. Furthermore,
accuracy in the time constant for warm-up implies that the heat transfer pa- .
rameters used are approximately correct;
The emissivities and convective coefficients shown in Figure 59 are
representative of those used in subsequent simulations involving reaction,
since the same heat transfer parameters are used. That these parameters taken
together are plausible representation of the heat transfer re/!,ime is supported
199
-------
by three aspects of the simulations without reaction just .cited: (1) The total
heat loss for gas passing through the reactor (Figure 58) checks experimentally
observed values (approximately); (2) the temperatures of concentric shells in
the reactor (Figure 59) check experimental profiles (approximately); and ())
the unsteady state warm-up traces (Figure 60) check experimental data very
welL The 0.3 values of emissivity are the most difficult parameter values
to accept; however, in the absence of insulation between the outer shells,
. .
emissivities must necessarily be low to preserve a large temperature drop.
The other possibility is that the small closed spaces between these outer
shells may have filled with insulating scale particles; which would produce
an effect similar to a low emissivity, althought not changing with temperature.
in the same way.
Future work to obtain better values of heat transfer parameters could
proceed by taking more data of the type shown and attempting to optimize by
formally minimizing deviations indicated by the simulations; or more satis-
factorily a detailed experimental study could be undertaken of the heat fluxes
. at surfaces throughout the reactor. Any optimization beyond the informal
search that was conducted to establish the agreement cited is counter recom-
mended by the severity of the assumptions in the existing simulation (especially
a uniform gas temperature). If a detailed heat flux study were to be under-
taken, consideration should be given to studying time variations in convective
coefficients linked to the cyclic flow.
B.
WARM-UP WITH LIGHTOFF
Base case warm-up simulations with reaction were performed for 150 lb of
exhaust.per hour at 4% co, 1.6% H2' and 500 ppm hydrocarbon. The experimental
data on warm-up was obtained by presetting the test engine ~t a particular.
air/fuel ratio, typically 12.5/1, and running at that fixed ratio from time
zero forward. This mode of operation is not characteristic of choked operating
modes used in practice to acceleration reactor lightoff and warm-up.
A typical comparison of simulated and experimental results is shown in
Figure 61 for an entering exhaust temperature of 1600°F and air dilution ratio
. .
of DR = .25. Time to lightoff and the temperature of approximately l200°F at
the threshold to ignition are in agreement with experimental results. The
lesser amount of tailing in simulatians for hydracarbon and CO cancentrations
(H2 was not measured experimentally and is not platted) have already been
mentioned in relation to reaction order and mixing. The other difference is
the greater temperature rise after ignition in the silnulation, which is ex-
plained by the conversion which takes place beyond the core, where temperature
was measured, in the actual reactor. In the simulation, the ideal backmix
assumption causes the entire temperature rise .associated with reaction to be
evidenced throughout the reactor.
191
:\ .~
.,
-------
5
2000
.1000
4 1600 800 '-
ca
><
CJ.)
:J:
L.L. .E
o 0 0-
U 3 1200 ~ 600 0-
I-- L.LJ ~
Z a:: z
L.LJ :=) 0
U I- co
a::: ---- « a:::
~ 2 a:: «
.~ 800 ~ 400
//"Shell temp. u
.~ .~ 0
a::
z "".. L.LJ 0
I- ",;'. I-
.e;s 1 /. :t:
400 200 0
L.L.
10 15
TIME, Mi nutes
20
250
o
o
. Figure 61. Comparison of experimental and typical simulated warmup
for the DuPont Model V reactor.
192
-------
By running simulations similar to the one in Figure 61 but different
inlet temperatures and air dilution ratios, a map of time to ignition vs.
inlet temperature and dilution ratio (Figure 62) was obtained. All of these
simulations were conducted for an initial temperature of l200°F in the CS1~,
which caused the search to tend toward a low-coversion operating point at
time zero. The dilution ratio of 0.148 represents the air fraction needed to
stoichiometrically burn all combustible species. The lightoff curve for zero
dilution ratio (no air) is a hypothetical curve representing the time required
to bring the reactor gas temperature to 1300°F, which was approximately the.
temperature at which lightoff occurred when air was injected. This represents
a limiting warm-up time which could perhaps be approached by shutting off air
injection until a 1300°F reactor gas temperature was ~chieved 'and then slowly
bleeding in air until ignition was established.
The base case simulations did not produce any immediate lightoff for the
exhaust inlet temperatures (before air dilution) shown in Figure 61.
193
-------
36
34
32
30
28
26
24
VI
LU
~ 22
z
- 20
~
u.: 18
u..
0
t-
~ 16.
(..:>
....J
0 14
t-
LU 12
~
t- 10
8
6
4
2
1200 1300
. Figure 62.
Base case:
Air Dilution Ratio.
o O. 148
!
0.25
!
0.4
Computer Points
1400
1500 1600 1700
INLET TEMPERATURE, of
2000
1800
. 1900
Simulation of light off for the DuPont Model V reactor.
4% CO, 1.6% H2' 500 ppm HC. ..
194
-------
VIII.
Variations on the Base Case Warm-up Simulation
A.
DESIGN AND OPERATION
A series of runs were made based on changes in design and combustible
concentrations with air dilution ratios maintained the same as for base case.
" "
The variations made in the base case and results are given in Table IV and
Figure 63. The discussion that follows relates to Figure" 63, which represents
simulation run at dilution ratio, DR = .25. Again, the initial temperature
in the CSTR was set at l200°F, tending to cause the search to approach at low
conversion operating point at time zero. "
A decrease in reactor diameter to 1/2 the base value while maintaining
the same reactor length (points 1, Figure 63) caused the inlet exhaust temper-
ature required to attain lightoff to increase by approximately 100°F. A"
fourfold decrease in reactor volume was here the controlling factor; the two-
fold reduction in heat transfer areas tended to counteract the volume change
but was a smaller effect in the temperature range studied. Lightoffs at
higher temperatures and earlier times were less affected due to the greater
importance of heat loss in this region.
Doubling the reactor "diameter (points 2, Figure 63) was actually detrimen-
tal at high inlet temperatures because of a controlling effect due to increased
heat transfer area. However, at lower inlet temperatures and later times past
start up, ignition was promoted by the longer residence time.
Reducing the combustible content (points 3, Figure 63) to 210 CO and "0.810
H2 increased the inlet temperature for lightoff by approximately 50°F. In
the context of the zero-order rate assumption and a low starting temperature
in the search for an operating point, increasing the inlet reactant concentra-
tions affects the lightoff of CO favorably only because of the larger tempera-
ture boost provided by reacting more of the readily oxidized hydrogen. HYdro-
carbon, which was not changed in this simulation, would have a similar effect.
Increasing the combustible content from 410 co, 1. 610 H2' to 810 CO, "3.210
H2 (points 4, Figure 63) produced no appreciable effect. Interpretation of
this result must again be tempered by realizing the obvious implications of
the zero-order rate assumption. However, subject to this assumption, the
greater hydrogen content has no effect simply because the primer effect of the
lesser amount (1. 610 ~) was already sufficient to "ignite" the carbon monoxide.
Increasing hydrogen content alone from 1.610 to 410 (points 5, Figure 63) had no
effect for the same reason. "
The existence of a triggering effect for hydrogen and hydrocarbon on the
oxidation of carbon monoxide is very clearly evidenced in both simulations and
195
-------
TABLE IV
TIME TO LIGHTOFF FOR VARIATIONS TO THE DUPONT MODEL V BASE CASE
(4% CO, 1.6% HZ' 500 ppm HC, 150 lb. exhaust per hour)
AIR DILUTION RATIO
0.1 O~148 0.25 0~4
2 Exhaust Time to ExhaUst Time to Exhaust Time to Exhaust Time to
Variation on inlet lightoff, inlet lightoff, inlet lightoff, inlet lightoff,
base case, No. temp~, of minutes temp.,oF . minutes temp.,oF minutes temp. t of minutes
1 1350 >25 1500 >25 1700 >25 1900 >25
1400 9 1/2 1600. 14 1725 15 1925 5
1450 4 1650 4 1/2 1750 9 1950 4 1/2
1600 1 1700 3 1/2 1800 4 1/2 2000 3
1700 1 1800 2 1850 3
f-' 1900 2 1/2
\{)
0'\
2 1350 >25 . 1450 >25 1450 >25 1600 >25
1400 15 1/2 1475 16 1/2 1500 15 1/2 1650 13 1/2
1450 9 1/2 1500 12 1550 9 1/2 1700 . 8 1/2
1500.. 7 1/2 1600 6 1/2 1600 7 1/2 1750 6 1/2
I. 1600 4 1/2 1700 5 1700 4 1/2 1800 5 1/2
1700 4 1800 4 1850 4 1/2
2000 2 1/2
3 1425 15 1500 17 1/2 1600 23 1/2 1750 22- 1/2
1450 7 1/2 1550 8 1/2 1650 9 1/2 1800 9 1/2
1550 5 1600 6 1700 5 1/2 1850 4 1/2
1600 3 1700 4 1800 2 1/2 1950 3
4 1425 14 1500 12 1/2 1600 9 1/2 1750 11 1/2
1450 9 1/2 1550 6 1/2 1650 4 1/2 1800 5 1/2
1600 3 1700 2 1700 3 1/2 1900 3 1/2
-------
TABLE IV (Contd.)
1
2 o. 0.148 0.25 ' 0.40
Exhaust Time to Exhaust Time to "Exhaust Time to Exhaust Time to
Variation. on inlet lightoff, inlet lightoff, inlet lightoff, inlet lightoff,
base case. No. temp.. 0p minutes temp..op Iilimites temp. . ° p minutes temp..op minutes
5 1425 13 1/2 1475 19 1/2 1575 21 1/2 1725 16 1/2
1450 7 '1/2 1550 5 1/2 1650 4 1/2 1800 4 1/2
1550 '4 1750 2 1/2 1900 2 1/2
6 1350' >25 1425 19 1/2 1525 >25 1675 21 1/2
, 1375 12 1450 11 1/2 1550 12 1/2 1700 ,10 1/2
1400 7 1475 9 1/2 1575 9 1/2 1725 8 1/2
1450 5 1/2 1525 6 1625 6 1775 5 1/2
1550 4 1625 3 1/2 1725 3 1/2 1875 3 1/2
I-' 7. 1500 10 1500 >25 1650 8 1/2' 1800 10 1/2
\() 1550 6 1575 5 1/2 1725 4 1875 5 1/2
-..:]
1650 3 1/2 1650 3 1800 2 1950 3 1/2
1750 1 1/2 1800 1 1950 1 2100 1
8 ,1400 11 1/2 1400 >25 1550 ' 13 1/2 1700 16 1/2
1450 5 1/2 1425 17 1/2 1600 7 1/2 1750 9 1/2
1500 1 1/2 1450 12 1/2 1650 3 1/2 1775 2 1/2
1550' 0 1525 4 1/2 1675 2 1/2 1800 1/2
1600 0 1750 0
-------
NOTES TO TABLE IV
1 .
Times to 1ightoff for an air dilution ratio of zero
required to reach a gas temperature of 1300°F within
was the temperature which characterized 1ightoff for
indicate the time
the reactor, which
the base case.
2
Variations to the DuPont Model V base case.
1 - reactor diameter 1/2xbase (1/4xvo1ume) with geometric similarity.
2 - reactor diameter 2xbase (4xvo1ume) with geometric similarity.
3. - low combustible entering; 2% CO, 0.8% H2' 500 ppm HC.
4 - high combustible entering; 8% CO, 3.2% H2' 500 ppm HC.
5 - high H2/CO ratio; H2/CO = 4%/4%.
6 - 1/2" asbestos insulation on outside of DuPont base case reactor.
7 - ceramic reactor - 1/16" thick core and shield, 1/8" thick shell.
8 - empty can with 1/2" asbestos insulation; no baffles.
198
-------
36
34
32
30
28
26
~ 24.
~ 22
-
:E 20
u...-
~ 18
I-
:J: ,
~ 16
-J '
~ 14
~ 12
I-
10
8
6
4
,2
01300
Curve represents DuPont Model V base case (4%, CO,!. 6% H2)
Air dilution ratio = 0.25 ' '
~'
4
5
2
8
6
.
1
VARIATIONS ON BASE CASE
1 reactor diameter = 1/2 std
2 reactor diameter = 2 std
3 low CO & H2 (2%, O. 8%)
4 high CO & H2 (8%, 3.2%)
5 high H2' CO rat io (4%, 4%)
6 insulated 0/2") DuPont
reactor
7 ceram ic reactor
8 insulated (1/2") empty can
1
2 6 3 4
~7 1
. \~)4~ I
, 8~4,1
7-
199
1
2100
Figure 63. Deviations in time'to lightoff for variations to the
DuPont Model V base case. '
-------
in practice by the fact that at low entering combustible concentrations, these
three major species may disappear one at a time with a rather long time lapse
(minutes) between th~ successive events (this was particularly evident in the
kinetics test reactor). At higher concentration, any time interval between
events is bridged by the temperature rise due to the first specie oxidized,
and all species disappear together in an avalanche ignition.
Returning to Figure 63 (points 6), placing 1/2 in. of asbestos insulation
on the outside of the DuPont reactor retarded lightoff slightly at high inlet
temperature in the period just following start up due to an added heat sink
effect, it aided lightoff at lower temperatures due to the l~sser heat loss
wi th approach to steady state. .
. Simulations on a three-component ceramic reactor (Figure 63, points 7)
having a 1/16 in. wall thickness for core and shield and a 1/8 in. shell
indicated a slight deterioration in performance due to greater heat loss at
the longer light off times approaching steady state.. This may not represent a
feasible design, and no general significance should be attributed to the result.
It does, however, demonstrate that different materials of construction can be
tested in the simulation.
The last design variation tested was a simulation of an empty insulated
can (points 8, Figure 63), with no internal baffles to increase the mass and
area for transient heat loss. In the region of short time to lightoff, this
design was superior to all others and reached lightoff at time zero for an
inlet exhaust temperature of 1750°F.
B.
LIGHTOFF AT TIME ZERO
The simulation results shown in Figure 64 were run on the. DuPont reactor
configuration with a starting temperature of 3000°F to insure that a high.
temperature-high conversion solution would be the one approached provided it
existed'. At81oco, 3.210 H2' and 1000 ppm HC (stoichiometric air rate), the
approach to immediate lightoff is gradual, indicating that the role of change
in heat loss after start-up remains important. . That is, for the points along
this approach, there existed no high-conversion sol~tion at time zero, however,
the low temperature solution is high enough to permit ignition as the heat loss
declines after time zero.
At higher combustible contents, 1210 and 16% CO, the existence of a high-
conversion solution at time zero was evidenced at much lower inlet temperatures.
However, if stable ignition did not occur at time zero as a result of the high
initial temperature specified, the subsequent decline in heat loss was not
sufficient to produce a transition to high conversion at a later time from the
low temperature .direction. Consequently, we obtain the sharp light-no light
condition indicated in Figure 64.
200
-------
2. 0 .
L5
VI
5'
z
:E 1
u..-
u..
0
I-
::J:
<.=>
~
0
I-
~
:E
I-
.5
01000
x -Stable Ignition
Carbon monoxide, percent
16.
12.
8.
Model"'[ . .
Reactor Configuration
Stoichiometric air rate
H2/CO ratio = 0.4
HC/HO ratio = 0.0125
1200
1400 1600 1800 2000 2200
INlET EXHAuST TEMPERATURE, of
2400
2600
2800
Figure 64. Approach to immediate lightoff.
201
-------
Ignition at time zero in relation to inlet combustible concentrations is
. .
greatly influenced by the amount of heat loss occurring at start up. For a
lower heat loss, the energy balance curve for.a given feed concentration slopes
more toward higher temperature (see Figure 61), causing a stable ignition to
be achieved with less combustible. Returning to the simple insulated can,
ignition from the high temperature side (an initial reactor temperature of
3000°F) was simulated and compared with previous results for a low temperature
approach (Figure 64). Ignition at time zero for 4% co was established at
1475°Ffrom the high temperature side compared to 1150°F from the low. Again,
use of the high temperature initial condition resulted in a sharp light-no
light behavior. Since this is directly due to searching from the high temper-
ature side only at time zero (the initial condition), the abruptness can be
eliminated by searching from the high temperature side beyond time zero (Figure
65, "continuous ignition source"). Physically, this represents any continuing
source of ignition, including hot regions in the temperature distribution of
entering exhaust. .
The "continuous-ignition-source" curve in Figure 65 was shown by a few
.isolated simulations to be highly sensitive to changes in feed concentrations.
By changing the concentration from 4% co to 3% and 5%, the time to lightoff
at an entering exhaust temperature of 1350°F was observed to be changed to a
time greater than 25 min and to zero (immediate lightoff), respectively. This
contrasts very markedly with the low sensitivity to change in feed concentration
observed for ignition approached from the low temperature side (Figure 63);
To better illustrate the simulation conditions which produced immediate
lightoff, Figure 66 shows combinations of inlet exhaust temperature and feed
CO concentration which produced complete reaction at time zero. All points
. were obtained by a high. temperature approach to solutions. Because of higher
heat loss, the DuPont reactor is indicated to require much higher inlet temper-
atures and/or inlet CO concentrations to achieve immediate lightoff than does
the insulated can. Augmenting the hydrocarbon fraction, which was not sim-
ulated, would be expected to produce instant lightoff at lower concentration
levels due to a much higher heat of reaction. This is an approach which could
be taken to simulate warm-up on exhaust from a choked engine.
C.
SUMMARY ON IGNITION EFFECTS
. .
If we plot the amount of total combustible oxidized versus temperature
for multiple oxidations in a CSTR, we obtain a material balance curve for
which the amount converted tends to increase along with temperature in stages
as shown in Figure 61. The zero-order assumption causes all segments of the
curve to be concave upward. By increasing the amounts of the combustible
types that are oxidized at lower temperatures, it is possible to cause the
energy balance to shift past the right side of the material balance curve so
that a high total conversion intercept is established in a low temperature
202
-------
I
I
!
28
26
24
22
V') 20
UJ
5 18
z
.:E 16
u..-
u.. 14
o
t-
:J:
c..=> 12
.~
0 10
t-
UJ
:E 8
t-
6
4
2
o
1200
~
High I nitial Tem.perature
Continuous
Ignition
Source
\ Low Initial Temper-
at u re
\ .
\
\
\
x
\
\
~.
"
1300 1400 1500 1600 1700
INLET EXHAUST TEMPERATURE
1800
Figure 65. Simulated lightoff for insulated empty can.
X-T(time zero) = l200°F;8 -T(O) = 2400°F;
()-continuouB source of ignition;
. fm = 150 lb. exhaust/hr.; DR = .25;
. V = 220~u.in.;
Inlet mole fractions: CO = 4%, H2 = 1.6%, HC = 500 ppin.
203
-------
3000
2800
. 2600
2400
L&..
o
LAJ 2200
e:::: .
=>
I-
!C(
e::::
. ~2000
:E
LAJ
l-
I-
V)
~ 1800
:I:
x
LAJ
I-
~1600
1400
1200
1000
2
DuPont -ModelY
Reactor Configuration.
Insulated Can
Without Internal
Baffles
4
6
18
8 10 12 14
CARBON MONOX IDE,. PERCENT
16
Fig~re 66. Warmup simulation of inlet properties required to achieve
immediate ignition with stoichiometric air at 100°F. H2/CO ratio-
0.4; HC/CO ratio = 0.012. '.
204
-------
V)
~
o
::E
.
o
LU
N
o
-
X
.0
~
CO
t-
V)
::::>
CO
:!:
o
u
u.
o
t-
Z
::::>
o
~
-------
approach to a solution. Such a change in H~ or HC
but can. be visualized. This is the type of effect
combustible cQncentration in Figure 63.
is not shown in Figure .6'7,
evidenced by changes in
. .
Referring to the energy balance lines in Figure 67, lines starting at
the same inlet temperature (Tl' T2' or T3) but proceeding upward at different
slopes are used to represent the shift in the energy balance with the progress
of time past start up (to' tl' ...) as heat losses are reduced. For the inlet
temperature Tl. in Figure 67, no high conversion solution exists at time zero.
If we increase inlet temperature slightly to T2 and impose a high initial
tempera ture, we do obtain a high conversion solution. If., however, the high
temperature approach to a solution is invoked only at time zero, to' all subse-
quent solutions approached from low temperature at times tl' t2' ... , will
exhibit low conversion. It is in this manner taht we obtain the light-no
light ignition behavior shown in Figures 64 and 65. If, however, the approach
to a solution continues to be from the high temperature side, the energy
balance for Tl at time tl does establish a high temperature solution and we
obtain a "continuous-ignition source" result as is shown in Figure 65.
As the amount of total combustible is reduced, higher inlet temperatures
are required to achieve lightoff (Figure 6'7, inlet temperature T~). If the
energy balance slopes are as shown at to' tl' and t2' it is poss~ble to achieve
three types of ignition for the same inlet temperature, T3: (1) low conversion
only at time to; (2) high conversion for a continuous-ignition-source approach
at time tl; and (3) a high temperature conversion from a low temperature
approach at time t2"
206
~
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CONCLUSIONS AND USE OF RESULTS
IX.
Summary and Conclusions
Reaction kinetics in the CRC study were determined at an experimentally
verified stirred tank RTD; at a nonlimiting intensity of micromixing (based on
simulations and high experimental conversions); and in contact with Hastelloy
X and copper wall surfaces, without significant change in conversion. Tests
were distributed reasonably evenly'over the range of parameters. Results in a
conversion range of 20 to 80% were linearly regressed to obtain least-squares
values 'of the constants in an Arrhenius-type rate equation. A near-zero-order
rate equation was determined for oxidation of carbon monoxide, which corrobo-
rated a test result of 99% conversion at 1687°F. Since. simulations for first~
or second-order'reactions predict 99% conversion Only at temperatures more
than 1000°F higher than this, we are led to a strong conclusion that the near-
zero-order kinetics are valid and that failure to achieve a close approach to
complete conversion for CO in the buPontreactor is due to incomplete mixing
rather than order dependence.
Considering the blending of multiple cyclic inputs which characterizes
the exhaust reactor problem, failure to approach complete conversion at a high
temperature stationary state depends strongly on both the pattern of flow and
the turbulent mixing intensi~y. Without a direct measurement of one or the
other in a particular device, we. cannot differentiate absolutely between the
effect of a low backmix flow pattern which prevents maldistributed reactants
from coming into proximity and a low mixing intensity which limits mixing
after reactants are in proximity. IIProximity" implies a mixing scale, which
for a one-phase system is a continuum of scales from molecular diameter to the
system diameter, but which under the idealization of Danckwerts' (11) is con-
sidered to consist of distinct macro- and micros cales of mixing.
Taken together the simulations run indicate three basic limitations on
conversion due to. mixing: departure of reactants from the reactor prior to
cell-wise mixing due to insufficient micromixing intensity relative to a given
flow pattern; lack of sufficient backmixing to blend mal-timed input of air
and exhaust; and lack of sufficient backmixing to bring a low-temperature
fraction of exhaust up to reaction temperature irrespective of timing of air
injection. In all simulations, an improved conversion is indicated for an in-
crease in the mixing intensity, 1m. An optimum flow pattern lies between the
nonidea,l stirred tank and the nonideal plug flow reactor, since the first ac-
centuates early departure and the second a persistence of maldistributions
originating with input. Best simulated operation is indicated for a stirred
tank core for backmixing followed by a plug flow exit section for preventing
early departure. .
207
!~
',-
-------
The work of Corrsin (8) on turbulent reactor.s permits calculations of
mixing intensity that are consistent with the geometry and performance of
existing thermal exhaust reactors. Thus, this body of theory lea.ds to esti-
mates of the improvement which can be obtained. .
Use of Corrsin's (8) theory requires that a length scale for turbulent
variation in fluid properties be chosen in reference to the geometry of the
reactor. Evangelista's (15,16) assumption that this length scale should be
the sphere equivalent diameter of the reactor predicts conversions that are
lower than the currently obtained experimental values. Use of the dimension
of the inlet was found to give good agreement with experimental conversions.
In the kinetics test reactor having stirred tank flow, the calculation of
mixing intensity from Corrsin's (8) theory based on the entire reactor volume
predicts conversions that agree reasonably with experimental results. In the
DuPont Model V reactor. with a more dispersed flow, better agreement is obtained
if an attenuation of mixing intensity through the reactor is assUmed.
Experiments on the kinetics test reactor indicate that the early departure
characteristic of a nonideal stirred tank are overcome sufficiently to yield
99~ CO conversion for surge-tank stabilized input for inlet dimensions which
result in a pressure drop of 10 in. Hg. However, the large surge tank and the
10 in. Hg pressure drop are impractical in an engine mounted device.
Failure to reach essentially complete conversion in the DuPont Model V
.reactor is due to inadequate mixing rather than to a high order dependence on
disappearing species. Cell simulations paralleling the operation of the DuPont
reactor indicate that sufficient backmix blending can be accomplished in a .
network consisting of a nonideal stirred tank representing approximately one
third the total reactor volume followed by a plug flow module so that simula-
tion CO conversion for cyclic inputs c~n be increased to 99% or higher by suf-
ficiently increasing mixing intensity.. In an all plug flow simulation, con-
versions are kept below 50% for low pressure air and below 90% for ratioed air
irrespective of mixing intensity due to ~ersistence of maldistributions of
reactant concentrations and temperature.
The actual flow pattern in the DuPont Model V reactor is not known.How-
ever, based on the best. general correspondence between experimental and simu-
lated conversions over a range of a,ir injection fractions and reactor gas tem-
peratures, a degree of backmixing which is consistent with 99% conversion for
CO is inferred for high mixing intensities. Experimentally, it is indicated
that no gross fraction of air leaves the reactor without coming into proximity
with exhaust since a maximum conversion is approached with stoichiometrically
equivalent air under favorable light off conditions.
The air dilution ratios and stoichiometric ratios that characterize opera-
tion of exhaust reactors fall in a range where mixing dependent conversions
a,re importantly a.ffected by them. .
208
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Simulated conve~sions for the DuPont reactor are very sensitive to an in-
crease in the mixing parameter, 1m. The energy available in the exhaust blow-
down occurring just after the exhaust valve opens is potentially capable of
producing high mixing intensities and high conversions, based on an analysis
using Corrsin's (8) theory of turbulent reactors. It has been tentatively
concluded that failure to realize this potential "is due to the essentially se-
quential input of air and exhaust which occurs with low pressure air injection.
Sequential input of air and exhaust causes reactants to assume the dimension
of the inlet port before they mix. The CO conversions obtained in the DuPont
reactor are consistent with a mixing intensity 1m computed from this dimension
and Corrsin's theory. Ratioed injection of air in close proximity to the ex-
haust valve would promote mixing based on the dimensions of the exhaust valve
opening and the air jet. Mixing based on the maximum valve opening rather
than the port diameter predicts an approximate doubling of the mixing inten-
sity, Im, and an increase in conversion from approximately 80 to 9910, based on
simulation results only.
The use of ratioed air without "sufficient ba.ckmixing would not have a
beneficial effect because, in the absence of backrnixing, a considera.ble propor-
tion of the exhaust would remain at too low a temperature to react, despite
adequate air.
Experimental results indicating 6010
the DuPont reactor were matched by "POF"
parameter 1m was distributed in a manner
for flow passing through the reactor.
and higher conversions in the core of
simulations only when the mixing
that represented a decay of turbulence
Reaction in the ports entering a reactor contribute only negligibly to
the overall combustible conversion obtained. This is true for low pressure
air injection because ports tend to be full of either air or exhaust alone due
to zero air flow during peak exhaust flow. With ratioed air, significant reac-
tion in the ports would occur in the high temperature peaks in the inlet flow.
The transition of conversions from a quenched low at start up to a high
lightoff level occurs in practice after times ranging from a minute or less to
an indefinite period. Modeling of warm-up is used to characterize the affects
of design and operation on this time lapse to ligl1toff.
Lightoff involving a rapid transition at a time after start up occurs as
the result of declining heat loss in a reactor which must be at least partially
backmixed. For plug flow, exit conversion would be uniquely determined by in-
Let conditions and heat loss. However, with backmixing there exit multiple
operating states and transitions between them; and the initial reactor temper-
a.ture and perturbations in temperature are introduced as additional determining
fa.ctors. In an ideal stirred tank, this ignition phenomenon is amenable to
rela.tively simple analysis based on simultaneous solutions to material and
energy balances on reactor contents.
209
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Modeling warm-up to predict time to ignitibn is prohibitively expensive
(on the computer) if numerical integration of unsteady state gas properties is
performed continuously over a simulation of several minutes. Therefore, only
changes in wall temperatures are integrated over the entire period, whereas
gas temperature is updated periodically at intervals of several seconds ~ld
either extrapolated or treated by means of step increases.
Neglecting cyclic input, solutions for gas temperature ~,nd species con-
versions for multiple reactions are obtainable either by integrating from a
last condition to a new quasi steady state (negligible change in wall tempera-
ture occurs during the time span of integration) or by solving simultaneous
nonlinear algebraic equations representing the steady state. Since there
exist. in general several steady states, a well behaved method of solution must
be sought taking into consideration the initial condition, perturbation condi-
tions, and step size.
. Integrations performed on properties of reactor contents are unstable
unless a very short time step is used, since property changes occur on a time
scale determined by residence time in the reactor. Therefore, the cost of
even periodic computations remains prohibitively high.
Simultaneous solution of the algebraic equations is a one-dimensional
search problem involving only explicit functions in the case of zero-order
reactions. Oxidation of CO is indicated to be essentially zero order in this
study; oxidation of H2 is assumed to be zero order; and HC normally affects
the energy balance only slightly. Thus, for these reactions a simple search
strategy is a workable and useful method of solution. To investigate reaction
order effects on warm-up, the computer simulation developed must be generalized
by using a multivariate search strategy or Newton's method for vector valued
functions. . .
Convective heat transfer coefficients and emissivities used in warm-up
simlilations all the DuPont reactor satisfy measured warm-up curves and steady
s tate metal temperature profiles. Chan.ge in exhaust side coefficients from
steady flow values obtained for literature correlations to twice these values
has little a.ffect on steady state heat loss, but does affect rate of metal
warm-up. Change in emissivities between £ = .1 and .9 has an important effect
at steady state, indicating sensitivity to the effectiveness of heat shielding.
Simulated ignition proceeds more abruptly than observed ignition, which
can be attributed to either 'the assumption of CSiI'R flow, or zero-order reac-
tions, or both. For most simulation conditions, H2, HC, and CO disappear.
nearly simultaneously; however, at low inlet concentrations they disappear
consecutively with a time lapse between, which agrees with tests on the kinet-
ics test reactor.
The ignition behavior of a particular reactor design operating on a given
inlet exhaust composition is characterized by running simulations of time to
210
-------
L
lightoff versus inlet temperature and air injection fraction. Such simulations
can also be run for a low initial temperature for reactor contents) a high ini-
tial temper~ture) or a continuing high perturbation temperature (indicating a
continuing source of ignition such as hot particulate matter or a hot segre-
gated gas fraction).
Simulations for variations in design and operation using the DuPont reac-
tor as a base case and starting at a low initial temperature indicated the
following: changes in reactor diameter may either increase or decrease time
to lightoff depending on the relative importance of change in area compared to
change in reactor volume; under the prevailing assumptions including low ini-
tial temperature) a change in the inlet concentration of combustible affects
time to ignition only to the extent that H2 and CH as the more readily
oxidizable species boost the temperature to promote oxidation of CO; insula-
tion at the outside of the reactor slightly increases time to an ignition
occurring immediately after start up but reduces it thereafter; removal of
'baffles produces an important reduction in time to lightoff.
Immediate lightoff at start up is predicted by simulations run at a high
initial temperature) provided that inlet combustible concentration is high.
The combustible concentration required is far lower in the absence of internal
baffles than it is for .the DuPont Model V design.
If a simulation approaches a solution from a high temperature only at
time zero, there exists a critical inlet exhaust temperature which sharply
separates immediate lightoff from indefinite unlit operation. However) if a
simulation approaches a solution from a high temperature each time a new gas
temperature is computed) to represent a continuing source of ignition, light-
off occurs below this critical temperature beyond time zero and an increase in
inlet combustible concentration shifts lightoff sharply toward shorter times
and lower temperatures. Since there exists a high temperature spike in the
temperature distribution of the incoming exhaust) the simulations based on
continuous ignition represent the most likely operating mode for. a reactor.
211
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X.
Use of Results
It is established that stationary state conversions are limited by poor
mixing which can be improved, rather than by an order dependence on disa.p-
pearing species which could not be altered. Thus, justifica.tion exists for
further simulations coordinated with experimental work to optimize the design
and operating cycle of exhaust reactors at their stationary state.
Optimization for the high temperature stationary state is concerned with
finding the reactor configuration which establishes the best pattern of flow
together with the air injection location, timing, and pressure which best uti-
lizes exhaust blowdown turbulence to accomplish mixing.
The work of Corrsin (8) provides a basis for correlating mixing intensi-
ties with. reactor size and inlet geometry. However, the efficiency factor in
the correlation is not known precisely, and should be determined more exactly
for geometries that apply to exhaust reactors. For a known RTD, a "MIXONLY"
type simulation could be fit to conversions for a very rapid reaction (possibly
an oxidation at high temperature) to establish the effective mixing intensity
for various inlet jet sizes and jet locations. By determining mixing efficien-
cies first for various simple geometries and then their combina~ions, a firm
basis would be estaQlished for relating overall mixing effectiveness with com-
plex geometries.
An 'extension of work on mixing efficiencies would be the determination of
the distribution of mixing intensities where the intensity is decaying due to
dissipation of turbulence or incr~asing due to generation of turbulence. An
experimellt might determine the distribution of conversions for a rapid exo-
thermic ~'ea.ctioll by measuring t.emperature distribution b,y optical methods. A
PJ\'L'TI':I{N OF FLOW type cell mixing simulation could be used to fit the measured
tetllpel'ature Or' converSiOtl distribution, amJ thereby infer a pattern of mixing
intensiL,y. Ka.ttan and Adler (20) did essentially this for a rapid reaction in
a plug flow rea.ctor. Development 01' characteristic patterns of decay or growth
of mixing intensity for flow through various geometries would provide a greatly
improved basis for design in relation to geometry.
Further global-type simulations, of complex reactors, similar to current
simulations paralleling experimental work on the DuPont Model V reactor, should
be carried forward to better determine the interrelation between cyclic input,
extent and location of backmixing, and intensity and distribution of cell
micromixing in determining reactant conversions. The optimal relative size of
a. nonideal stirred ta.nk module and plug flow module in series should be inves-
tigated. A plug flow leading element should be added and air input ratioed to
determine the advantage, if any, of reacting the combustibles in the inlet
temperature spike prior to backmixing.
212
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Distribution of heat losses should be further investigated from the view-
point that reactions are accelerated by temperature rise in a reactor core
where heat loss is low whereas they are decelerated by temperature drop in an
outer annulus due to a high rate of heat loss. The amount of mixing that is
accomplished in the core is coupled with heat loss and kinetics in determining
the amount of temperature rise that will occur in the core to extend reaction
into the annulus.
The warm-up simulation program can be used in present form to investigate
further the effect of insulation and surface emissivities on the distribution
of heat losses at stationary state. These heat losses can then be used as
motivated estimates for mixing simulations.
A second tie in between warm-up and stationary state which should be simu-
lated is the trade off that would be indicated for elimination of baffles to
. achieve earliest lightoff but also to surrender control of mixing geometry.
The detailed effects of geometry on mixing limited conversion would have to be
resolved before this trade off could be evaluated.
I
I
I
I.
The ignition phenomenon of exhaust reactors should be further simulated
using inlet combustible concentrations that are characteristic of choked engine
operation. Simulations should be run, in a pattern which would establish both
the inlet combustible concentration and air injection fraction versus time
which yield the lowest integrated emission during warm-up.
Cell mixing simulations can be used to check for bias introduced into the
determination of activation energies and reaction orders provided that the
experimental conditions and the distribution of data points in relation to
conversion level are known.
Further simulations in the areas mentioned would be more profitable if
certain extensions were made in existing simulation programs~ These include:
The MICROMIX PATTERN OF FLOW simulation should be modified by a.ddition of
an executive iteration loop to handle backflow.
MIXONLY PATTERN OF FLOW should include both parallel modules a.nd backflow.
All energy balance feature for determining temperature distribution would also
be lIsefuL '
WM{M-UP should be extended to handle nonzero-order reactions.
The facility of WARM-UP to treat subvolumes should be extended to an ideal
stirred tanks in series representation of gas temperature(s) and species'con-
versions. Further coupling with "MICROMIX POF" should be considered.
213
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APPENDIX A
MIXING AND REACTOR THEORY
1.
MIXING IN REACTOR DESIGN
This appendix contains further information on the present state of mixing
theory, in conjunction with chemical reactors.
A great-. deal of information about the state of mixing for the models de-
:~cribed in Chapter I and for reactors in general can be obtained from the ex-
ternal, or exit residence time distribution. For simple models such as recycle
or tanks in series, such residence time distributions can be expressed in a
simple algebraic formulae:
Residence time distribution for a recycle model:
00 yj * .
f(t) = L (1 +y)j 6 (t - jT );
j=l
( A-I)
*
T
v
- (1 +y)v
o
( A-2)
Residence time distribution for n ideal tanks stirred in series:
n
f(t) = (-E.)
TT
n-I
t
(n-I)!
-nt/T
e
( A- 3)
These formulae are obtainable from the
with the aid of LaPlace transforms, as
(23) for the case of tanks in series.
unsteady differential material balance
outlined by Levenspiel and Bischoff
Conversions cannot be obtained unambiguously from kinetics and the HTD
except in the very special case of a first-order reaction occurring without
thermal effects on a single steady inlet flow of uniform composition. Leven-
spiel (22) points out that an average exiting composition computed from
214
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c =
t=oo
f t=oc(t)
f(t) dt.
will
be the correct exiting composition for
an upper bound for orders greater than
a lower bound for orders less .than 1;
order 1,
1,
subject to the qualifications in input given above. The
single inlet is of obvious necessity if we consider that
. this point have had nothing to say concerning the extent
separate entering streams.
stipulation of a
the arguments up to
of blending between
To understand first the cau~e of ambiguity where there exists a single
uniform input but order differs from 1, \'le turn to the concept of local mixed-
nes:s introduced by Danc.kwerts (11). Working with a stirred tank residence
time distribution, he assumed the following two limiting circumst.:=mces:
( 1)
Inflowing material is dispersed on
less than T, a condition described
condition has been implied for all
up to this point.
a molecular scale in a time much
as complete micromixing. This
discussion on ideal stirred tanks
( 2)
Inflowing material is broken into cells which are far smaller than
the tank and are uniformly dispersed through it, but which contain
nevertheless a very large number of molecules which remain together
for their entire stay in the reactor. This condition he described
by saying that the fluid was completely "segregated." The length
scale of segregatedness is not specified, and it is not directly
important so long as there are a sufficiently large number of cells
to be representative of the segregated property distributions that
are now possible within the reactor.
Extents of conversion calculated for the above two cases ATe indicated
by Zwietering (39) to show greater conversion for the completely segregated
case when reaction order is greater than 1 and greater conversion for the com-
pletely micromixed c~se when order is less than 1. This still of course im-
plies a single or premixed feed, since segregated cells of different reactants
would not react at all in the segregated case~
Danckwerts (11) proceeded to define an index of segregatedness based on
the ages of material within the system. He first defined. a point age, ap,
which is the average age of material in one particular cell. If materials
are uniformly distributed down to the molecular level, this average or point
age will be the same for any defined cell containing a large number of mole-
cules, and the distribution of point ages will be a delta function positioned
215
-------
at the mean age, 5(a). However, if material is entirely segregated, point
ages will possess the same distribution as the molecules. '
The index of segregation proposed by Danckwerts (11) was the
statistical variance in point ages to be the statistical variance
ages, both internal to the system.
ratio of
in molecular
b.
J = Var a /Var a.
p
( A-"5)
For a completely micromixed stirred tank, the variance in point ages is zero;
thus J = O. For a segregated stirred tank, the variance in point ages equals
the variance in molecular ages, and J = 1.
To obtain a better perspective on the significance of segregatedness,
consider again conversion for a zero-order reaction in n ideal stirred tanks
in series. Recall that conversion was indicated to be independent of n, and
therefore apparently unaffected by flow pattern per se. In consideration of
the early-departure property of a single ideal stirred tank, we can visualize
this lack of dependence on, pattern of flow only by considering the- immediate
dispersal on a molecular scale as in effect hiding low inlet concentrations
to prevent immediate departure of all but a very small, second-order amount
of reac'tant. However, if a reactant enters and remains segregated in one
cell, early departure of that cell removes a not insignificant amount of reac-
tant, and conversion is lowered. This intuititive reasoning is lent rigor by
the fact that it is confirmed by calculations. Furthermore, we observe in
this example evidence of the fact that kinetics and residence time distribu-
tion do not alone determine conversion.
If \ve apply the definition of Danckwerts' I1JI1 to an ideal plug flow reac-
tor, we 'see that all molecules at a "point" must possess the same age since
all entered at essentially the same time. Consequently, point age and molecu-
lar 8.p;e :lre synonomous, and J == 1. This argues that an ideal plug flow reac-
tor is all-rays completely segregated.
It is demonstrated that J may assume values from 0 to 1 for an ideal
~-,til'red tRnl, but must be precisely 1 for an ideal plug flow reactor. In
general, J can approach a limit of 1 for any residence time distribution
since complete segregation as defined is always possible. However, complete
micromixing to produce point ages that are everYwhere the same depends directly
on the random mixing occurring throughout a stirred tank. Therefore a value
of J = 0 can be approached only for a CSTR residence time distribution; for
an at'bitrat',Y 1\'1'1), the value of J will approach some lower bound betvreen 0 and
1.
216
-------
(mc: 1'1] rthcr word concerning zero-order reactions; incle'penctence between
r;(Jnv(;r:.;ion and the number of ideal tanks in series indicates that the in-
~~eascrJ tendency for early departure in going from plug flow to stirred tank
f10',[ must be cancelled out by a greater allowable extent of micromixing.
Since the locus of this effect leads to the J = 0 bound for n = 1, we could
be tempted to assume that the ideal tanks in series models provide a lower
bound on J for all n, however, this has been demonstrated to be untrue based
on the maximum mix~dness concept of Zwietering (39), which is discussed next.
Zwietering (39) considered the bounding affect of residence time distri-
bution on micromixing and devised two very clever models which represent, re-
spectively, the minimum mixedness and maximum mixedness consistent with any
arbitrary RTD
Minimum mixedness model:
v
0(
~
'To
c:o
c
The minimum mixedness model consists of a plug flow reactor with side exits.
Since all molecules at a given point in the plug flo,v reactor are of the same
age, altering the distribution of side flow at points along the lenp;th of the
reactor is a direct means of establishing any desired residence time distribu-
tion. Because of the complete segregation of material remaining within the
reactor, we are assured that variance in point age equals variance j.n molecu-
lar age, and J = 1. A property that is demonstrated to coincide with segre-
p;atednesR in this model is that mixing occurs as late as possible, i.e., at
the reactor exit. Since each increment of material in the reactor acts inde-
pendently, "Je can obtain the average exit concentratioll form:
c =
fCOC(t) f(t) dt
o
(AI-4)
Parametric equations relating side flow q and displaced volume V for a desig-
nated residence time distribution are given by Zwietering (39).
217
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Maximum mixedness model:
. Vo
C
l'
c.
~ V
A ~
Any desired RTD can also be established with side entrance
reactor, as illustrated above. In this case, all material at a
in the reactor will possess the same life expectancy~, and the
equation.for the model is written in terms of ~ as follows:
to a plug flow
given point
differential.
dc
dA
. f ().)
I-F().) ( c - Co) - r(c) = 0
(A-6)
This equation can be solved by integrating from ~ = 00 to ~ = 0 if we have
c(~ = ~) as a boundary condition at the left of the reactor, which is obtain-
able from the differential equation by noting that dc/d~ (~ = 00) = O. If the.
RTD is given by data, we do not know lim f(~)/l-F(~) as ~~, and a starting
value for c must be estimated for some "large" ~ (perhaps 3 or 4 times the mean
resident time). Zwietering (39), by expressing age a as a function of life
expectancy ~ and using the definition J = Var(a )/Var(a), was able to prove
that this model satisfies sufficient conditionsPfor Jmin, and hence that the
model is indeed a maximum mixedness model. The intuitive counterpart of this
proof is that the model mixes feed and reactor contents at the earliest time
possible.
In order to compute conversions for intermediate micromixedness, it is
necessnry to assume.some history for groups of molecules, or cells, as they
pass through the reactor. The issue in question is which molecules should be
given opportunity to mix, and when in the sense for example that molecules in
the minimum mixedness model are allowed to mix only with other molecules of
the same age or with molecules at the exit from the reactor.
There exists in the literature two
models: extensions of Zwietering's min
the two, and cell models wherein mixing
redispersal of cells.
classes of intermediate mixedness
and max models through combination of
is accomplished by coalescence and
218
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Villermaux and loulalian (37) have proposed a parallel combination of
minimum and maximum mixedness models with inlet flow divided between the two.
Intermediate mixedness model:
t.).=oo
teO
v
The state of mixedness is defined by a function of residence time, g(t), such
that
s(t)
e;(t-.)f(t)
m(t)
=
(l-g(t))f(t) and
s(t) + m(t)
f (t).
Complete segregation is indicated where g(t) = O. Outlet conversion is com-
puted by weighting the conversions from the minimum and maximum mixedness
sections, which are obtainable from the differential equations already ~iven
for the min and max modules.
L e.,
x = fOClXs (t) get) f(t)dt + [ fOCI (l-g(t» f(t)dt] X (0)
o 0 m
( A-7)
Weinstein and Adler (38) proposed a similar parallel model with g(t) equal to
the step function U( t">e - t), which is to say that material c<;:>rresponding to
219
-------
the early portion of the residence time distribution from t = 0 to t = t* is
directed through a minimum mixedness model, and that corresponding to t = t~.
to t = 00 through a maximum mixedness model. Villermaux has pointed out. that
Weinstein and Adler made the error of integrating the maximum mixedness con-
version to A = 0, where~s its contribution should vanish for A < t*.
Series combinations of minimum and maximum mixedness models have also
been proposed by Weinstein and Adler (38) and by Ng and Rippin (24). In the
model of Ng and Rippin, it is assumed that material entering a reactor re-
mains for a period of time in a poorly mixed region which is represented by
minimum mixedness and then proceeds to a well mixed region around an impeller
which is represented by maximum mixedness. Material is assumed to be trans-
ferred from the min to the max environment in proportion to the amount re-
maining in the first, and therefore in accordance with diffusional transfer.
While this concept is simple, its execution is exceptionally involved.
The cell model concept of mixing which treats intermediate micromixedness
by averaging properties for selected cells was introduced by Curl (10) to
treat mixing of droplets in a dispersed phase. This model assumes that drop-
lets themselves are uniformly dispersed throughout a well-stirred flow reactor
and that the spread in concentration among drops tends to be averaged out by
coalescences and redispersals for randomly selected drops. The model as de-
veloped further assumed that the drop opulation remains constant, that all
drops are the same size, that departure from the reactor as well as coales-
cence involves rQ.ndomly selected drops (due to stirred tank flow), that per-
fect mixing to a single concentration occurs when two drops coalesce, and that
redispersals occur immediately after coalescences.
I
While the random coalescence cell model is physically motivated by dis-
persed droplets, it is entirely consistent with Danckwerts' original defini-
tion ofmicromixedness and may legitimately be proposed as a mechanism for
describing intermediate mixedness for any system that has a stirred-tank flow
pattern. Even prior to considering the mathematical description of the model,
it is intuitively evident that the transition from complete segregation to .
complete mixedness can be accomplished by defining a rate of coalescence or
"interaction frequency," (Di' that assumes values from 0 to 00.
The very special integro-differential equation derived by Curl (10) for
this model was developed by performing a material balance on a concentration
interval c to c + dc of the concentration distribution p( c). Based on the
parameters (Di defined as the fraction of cells coalescing per second and (Dr
defined as the fraction of cells leaving per second ((Dr = liT), the equation
is as follows:
Rate of
Change
Flow
In
Flow
Out
10ss by +
reaction
Coalescence
into c to c+dc
Coalescence out
of c to c+dc
220
-------
op(c)
ot
. o[rp(c)]
== ru p (c) - ru p( c) - - 0 -
r 0 r t
c
+ 4ru.J p(c')p(2c-c')dc' - ru.p(c)
l 0 l
(A-8 )
No analytical solution is known for this equation, but it can be solved
numerically either by treating the equation directly or by applying the Monte
Carlo method to the original conditions describing the model. . The equation
has been solved numerically at steady state by Curl (10) for zero- and second-
order reactions on a single feed concentration. Evangelista (15) describes a
method of steady state solution based on the moments of the concentration dis-
tribution, which applies for high mixing intensities where the quotient rur/rui
is close to zero and can be used in power expansions of "p" and its moments.
Spielman and Levenspiel (33) solved Curl's model by the Monte Carlo
method to determine conversions for zero- and second-order reactions on a
single inlet stream and for second-order reaction on two inlet streams carry-
ing different reactants. The Monte Carlo method because of its simplicity
is very easy to use fordiscretized systems compared to more cumbersome numer-
ical methods, but it exacts a penalty in running time on a computer if large
number of cells are to be treated.
The mixing intensity parameter used in correlation by Spielman and
Levenspiel (33) was 1/2 == rui/anr, which is the number of coalescences. that
occur during the time interval between entering droplets. To avoid the cum-
bersome quotient notation we will denote this parameter as 1m'
The .cell coalescence principle of. Curl's model was extended by Kattan
and Adler (20) to treat the mixing of separate reactant streams in a plug flow
reactor. Here coalescence occurs only for cells occupying the same axial po-
sition, and the cells are thereby available to coalesce act as a miniature
batch reactor with a reaction time equal to time of flight through the reactor.
Kattan and Adler used this to fit experimental data by allowing the coales-
cence rate to change as a function of axial position.
2.
'l'HEOHY OF AN IDEALIZED TURBULENT MIXER
In order to make use of cell models for treating mixing in reactors, it
is necessary that we have a practical estimate of the mixing parameters rui and
1m based on obtainable system parameters. The work of Corrsin (8,9) on the
scale up of stirred tanks leads to such an estimate, based on an assumption of
homogeneous isotropic turbulence. A summary of this work and its relation to
current mixing parameters follows.
221
-------
'I
I
I
I
I
I
II
1
i
I
-- From the work of Corrsin, the mean square fluctuation in concentration
C2 in a homogeneous turbulent field obeys:
dc2 3 ~
2D L--.£.
dt = - vi=laxi
(A-9)
Under the assumption of a homogeneous isotropic field,
components are equal and have one common value 2C2/1fu,
the microscale of turbulence. Hence
the three mean-square
where this defines £m'
-2
(~)
ax.
1
2
= 6 E-
Jl,m2
( A-10)
and,
2
de
-=
dt
D
v
- 12--
Jl,m2
2
e
(A-ll)
From this equation, it is established that variance in concentration decays
exponentially with a decay constant of 12Dv/£~' which we will define as~. It
remains to express ~ in system parameters, and then to establish a correspon-
dence with ill. and I .
l m
For a Schmidt number Nsc < 1, Corrsin (9) has derived an engineering ex-
pression for ~ as follows:
8 '"
3-N2
Be
2 T)1/3
m
2/3
(~)
5
gePm
(
L 2M
c r
1/3
)
(A-12)
222
-------
where ~m is an efficiency,
Nsc is Schmidt Number,
Lc is the integral scale of concentration fluctuations,
~ is the mass in the reactor, and
Pm is the mixing power applied to the reactor.
Corrsin in an earlier publication (8) indicates that ~ ~ 1/2; and since for
CO and air, Nsc ~ .82 at 1000K (1340°F), we obtain, approximately,
13 '"
g P 1/3
1.07 (~ )
Lc~r
(A-:L3)
Corrsin's earlier publication (8) differs from the latter (9)
tor of 2, and predicts a leading coefficient of approximately
recti on is made for an arithmetic error.
by about a fac-
1/2 after cor-
To establish a correspondence between B and wi' we return to the intego-
differential equation for Curl's random coalescence model. This equation can
be solved for the special case of batch mixing to establish the ielationship.
of wi to the decay of variance in concentration, and therefore its relation-
ship to ~. .
In Appendix B, a general formula is developed for moment equations for
the concentration distribution p(c). For batch mixing without feed (wr =0)
and without reaction (r = kC~), this formula reduces to:
dm
dtk + (1 - 2kl_l) wimk
k-1
= W L:
i . 1
J=
a m m
k,j j k-j
(A-14r
a
l,j
-
0, j
=
1 and 0
a
k,l
k-l
- k
k-l'
2
=
2,3,...
223
-------
a
k,k"';l
1
k-l k
2 '
=
3,4,...
ak .
, J
=
1 .
2 (ak-l,j-l + ak-l,j)' k
4,5,.. .
j
=
2,... ,k-2
For k =.1,
dM
1
dt
=
o or M
1
=
M
1
a
(A-l'5)
This of course only confirms what we already know; that the average concentra-
tion Ml remains constant. However for k = 2,
dm (I)
2 i
-+-m
dt 2 2
=
(l)i 2
-m
2 1
(A-16)
(I),
-.2. t
2 2
K e + m
1,0
m2
=
( A-17)
C2
variance
=
2
o
=
2
m2 - ml
=
2
o
a
(I)
i
--t
2
e
(A-18)
Thus, with reference to (l)i' variance decays exponentially with a decay con-
stant (l)i/2; ~ = (l)i/2, and 1m = (l)iT/2 = ~T.
3.
SELECTION OF A MODEL TYPE FOR EXHAUST REACTOR SIMULATION
With reference to the review on reactor modeling, we recognize that a
simulation of exhaust reactor performance should include provisions for alter-
ing both the pattern of flow and the degree of intermediate micromixing, or
conversely segregatedness. The latter can be roughly viewed as the effective-
ness of "local" mixing, recognizing however that the pattern of flow sets
224
-------
bounds that are related to the selection of the material that is allowed to
mix.
Selection of a model type was guided by the necessity fpr handling the'
mixing of separate streams, where the rates of flow and properties of these
streams vary cyclically. All of the literature models representing combina-
tions of Danckwerts' minimum and maximum mixedness devices have been developed
for steady flow to a single inlet and a single inlet concentration. Extension
to treat the conditions of exhaust reactors, if possible, would 'require a high
degree of mathematical sophistication.
By treating micromixedness in terms, of functions that are single valued
in J and which cause J to vary over a range from 1 to Jmin' the class of
models proposed by Villermaux and Zoulalian (37) and others does not allow
differences in local segregation within a plug flow device, where J = 1. This
is the result of assuming that micromixedness is an effect occurring in only
one dimension. This view is satisfactory for a single or premixed feed en-
tering an ideal plug flow device only because of the one-to-.one correspondence
between concentration and position, z. One-to-one correspondence between po-
sition and concentration is retained in the intermediate mixedness models be-
cause of the assumption that material transferred into Danckwerts' maximum
mixedness model is instantaneously mixed with the material already at that
position.
A more general view of the mixing problem is easily constructed. First,
the ideal plug flow assumption can be relaxed to permit radial segregation,
as in the cell model for progressive mixing of separate streams in a plug flow
reactor proposed by Kattan (20). Beside segregation introduced in the feed,
there exist in any real device internally generated property distributions
which may be radially oriented. For reactors that are not radially symmetric,
we could add a third dimension; and in general we could continue to relax
stated or implied assumptions to treat the distributed mass transfer that we
refer to as "mixing" with respect to an arbitrary set of dimensions: e.g.,
add to the three Euclidean dimensions-time, temperature, velocity, energy, a
length scale on turbulence, state, density, .... This is not a useful ap-
proach (it is a lack of an approach); but to point it out does emphasize that
a model does not represent an entirely general approach to mixing simply
because it allows us to treat any arbitrary residence time distribution and
intermediate values of "J" as a defined measure of "micromixedness. "
What Villermaux and Zoulalian's (37) models (and other similar models)
represent are a very special geometric flow pattern for given functions f(t)
and s(t). That selection of f(t) and a s(t) value corresponding to a given
"J" does not provide an unambiguous description of mixing has been shown by
counter example: i. e., when Rippin (27) applied his model to the RTD for two
ideal backmix reacto:.~s in series (1m = (0) at a mixedness given by the two-
tank value of "J," conversion predicted for second-order reaction differed
225
-------
from that obtained. from the two-tanks-in-series model itself. Since the "hlO-
parametet' approach of specifying f(t) and J does not produce a unique result,
there exists no compelling reason to follow it except where it is computa-
tionally convenient or there exists a particular geometric motivation for such
a model. In view of the apparent difficulties in extending the approach to
exhRLwt reactors, this type of modeling was dropped from consideration.
Cell models fashioned after those of Curl (10) for the stirred tank and
Kattan and Adler (20) for plug flow have no inherent limitation in regard to
number of inlet streams or periodicity of flow and inlet properties. The
periodicity does however necessitate solution of the unsteady approach to a
quasi-steady cyclic performance. In Curl's equation (10), application to
exhaust reactor design involves replacing .
k
WrP (c) by L W P
° j=l rj OJ
(Ci )
,t
( A-19)
for j = 1,2,..., k inlet streams and i = 1,2,..., m chemical species; similarly
making the c' concentration a vector valued function of time; writing a simi-
lardispersion equation for distribution of temperature, including provision
for distributed heat loss; and making reaction rates appropriate functions of
concentrations and temperature. For Curl's model per se, the method of treat-
inp.; moments o:f distributed properties was developed (Appendix B) sufficiently
to show that the resulting differential equations were not a closed set. .
Bvangelista's method. of moments involving expansion in powers of (mr/mi) does
not, apply to low levels of mixing intensi t,y and is unsatisfactory for that
renson. further, any treatment of these moments is still restricted to con-
sideration of a stirred tank residence time distribution only.
In view of the complexity and the restrictions that result from treating
Curl's equation or the corresponding moments, it was decided to pursue a
Monte Carlo method of solution to the cell-wise models. The Monte Carlo ap-
proach applies for both stirred-tank and plug-flow flow patterns; it places
no severe limitation on treatment of multiple inlets, periodicity, numerous
species concentrations, temperature distribution, expressions for reaction
rates, or extent and distribution of heat loss; and,it allows the building of
complex flow patterns by series and parallel combination of nonideal plug flow
and stirred tank modules. Use of the flow pattern modules is also a geomet-
rically motivated approach which readily allows a correspondence to be visual-
ized between a model and the particular reactor which it represents; this is
generally not true when specifying f(t) and ~
226
-------
The Monte Carlo method applied to reaction coupled with cell-wise mixing
in a network of reactor modules accounts for both "axial" dispersion and
"local" segregation without solving a split boundary value problem as in the
axial dispersion model or an integro-differential equation problem as in the
random coalescence cell model. approached from an analytical standpoint.
Reproducibility using the Monte Carlo method is determined by the total
number of cells transiting a simulation module. A bias is introduced by the
number of cells that are used to represent the contents of a module, with the
correct number determined by the module size and the size of actual droplets
or eddies. Viewed as a representative sample, the number of cells used is
not critical so long as bias is satisfactorily small.
Spielman's (33) use of 500 cells to represent an arbitrarily large popu-
lation caused unnecessary expense in running simulations, since current runs
on 100 cells produced very nearly the same results for the case of mixing
with instantaneous reaction. Even for only 10 cells in the reactor, the bias
is comparable to the standard error of estimate for a throughput of 100 cells.
Thus, first estimates can be obtained relatively inexpensively using a few
cells. In the instance of a very small reactor volume or subvolume and a
relatively large eddy size, a small number of cells will provide the best
approximation of the true result.
Convergence to average stationary state conversions occurs in three or
four mean residence times in a cell-wise mixed stirred tank. . However, compu-
tation of variances and values of Danckwerts' (11) "J" necessitates a longer
period of simulation, out to about ten mean residence times, because the
weight given to the tails on the distributions of residence time and cell
properties.
Combinations in series or parallel of Danckwerts' (11) minimum and maxi-
mum mixedness models (min-max models) as proposed in most general form by
Villermaux and Zoulalian (37), were concluded to be inapplicable to treatment
of multiple segregated reactant streams. All models of this type impose a
rule of correspondence between the RTD and degree of micromixing by defining
a function (or parameter) which causes the Danckwerts' "J" to vary from "1"
to a minimum value by apportioning flow. Regardless of the apportionment, an
element of' entering feed is caused, under Danckwerts' original assumptions,
to be immediately mixed with reactor contents at a point or points within the
reactor, with no provision for mixing between points. Thus, for a plug flow
RTD, feed from multiple inlet streams would necessarily be mixed at the inlet
point and would remain segregated from other reactor contents in passing
through the reactor; no progressive mixing as proposed by Kattan and Adler
(20) is allowed.
Adaptation of a min-max type model.to progressive mixing of streams
would .necessitate introducing partial mixing at Danckwerts' (11) points.
227
-------
I!
'I
i
Ii
I
,
I
':
'I
i
,
I!
Partial mixing at a point would necessitate the introduction of cells and
slugs of cells or their equivalent, as in the "POF" simulation, which would
destroy the simplicity of the min-max model class and invalidate our ability
, to solve comparatively simple differential equations by standard numerical
methods. Alternatively, we would be forced back to using the Monte Carlo
method, with the min-max model supplying ,the rules for selecting cells that
coalesce or leave the reactor.
;j
I:
I
If cell coalescence is used, it is deemed more desirable and practical
to use geometry and flow to motivate mixing rules than to use the RTD in the
context of a min-max model. The network flow and coalescence model, as de-
veloped in the MICROMIX PATTERNS OF FLOW simulation program, possesses ability
to treat segregated feed; cyclic operation; multiple reactions; distribution
of temperature under the influence of inlet temperatures, heat of reaction,
and heat loss; the distribution of heat loss among cells and among modules;
and distribution of mixing intensities among modules. The module network ap-
proach contains the,nonideal stirred tank and the nonideal plug flow bounds
as subsets. The solely mixing limited bound (instantaneous reaction) can be
investigated by removing the kinetics and substituting a rule of complete dis-
appearance for the limiting reactant in each coalescence.
Danckwerts' (11) "J" defined ,as the ratio of internal variance for point
ages to that for molecular ages is not a sufficient index of "mixedness" for
a system receiving segregated feed. This is' true simply because "J" reflects
only that segregation which is related to age, whereas segregation entering
in the feed originates independently from age. In the specific instance of
a ,series of nonideal stirred tanks, the value of "J" is related to both the
number of tanks "n" and the cell mixing intensity, 1m' ,For instantaneous
reaction, mixing limited conversion depends overwhelmingly on 1m and only
slightly on changes in "J" that are independent of 1m (i. e., only slightly
on the number of tanks).
An alternative "index," which is sensitive to segregation determined both
by the feed and by internal mixing, is the conversion level that is attained
for an infinitely rapid reaction. Its value for steady inlet flow of segrega-
ted reactant streams goes from 0 to a stoichiometric limit (100% conversion
for the limiting reactant) as 1m goes from 0 to 00, irrespective of flow pat-
tern. For given cyclic inlet flows and concentrations, the solely mixing
limited conversion goes from 0 to a maximum that is determined both by stoichi-
ometry and backmixedness.
The solely mixing limited result provides an upper bound on conversion
as temperature is increased. For a cell-wise-mixed stirred tank receiving
feell 8.t one temperature, the material balance curve (conversion versus temper-
ature) has been observed to characteristically follow the curve for 1m = 00
(ideal CSTR) until the mixing limited maximum is approached and then to asymp-
totically tend toward that maximum as temperature is further increased. This
228
-------
behavior is sufficiently regular to permit good estimates of the material
balance for coupled mixing and kinetics to be obtained solely from the ideal
CSTR curve and the "MIX ONLY" maximum in many cases.
229
-------
APPENDIX B
MOMENTS OF THE CONCENTRATION DISTRIBUTION FOR CURL j S RANDOM
COALESCENCE MODEL APPLIED TO A REACTION VELOCITY OF ORDER ~, r = - kc~
Starting with Curl's (10) equation for the r~ndom coalescence model, we
ap(c) = W p (c) - (wr + Wi)P(c) -
at . r 0
~~p(c) + 4wi fCp(C')P(2C ~. c')dc',
o (B-1) .
substitute -kc~ for r (~ a positive integer or zero) and take the partial
derivative of the reaction term:
a~~(c)= - k [cn ~~~c) + ncn-l p(c)].
( B-2)
We then proceed to take the LaPlace transform of the first equation, focusing
attention first on the integral term.
L [4wi .Jcp(C')P(2C - c')dc'] = 4wi Jooe-CS
o 0
JCp(C')P(2C -c)dc'dc .
0-("'8-=- 3 )
Recognizing that the product p(c')p(2c - c') is symmetric in c' about any
point c, we change the integral JC to 1/2 J~c; and since p(2c -c') is zero for
o 00
all c' > 2c, this is equal to the integral 1/2 fo. Then, substituting 1 =
2c -c' we obtained:
L[
] = 2w
i
fOO,s
e-c '2 p(c')dc'
o
fOO s
e -Y2 p (y)dy,
o
( B-4)
or
L[
2 s
] = wiP (2").
( B-5)
The LaPlace transform of the entire original equation is then:
rr-1
~ - wp - (w + w.)p + k(-l)naT) (sp(s» + kn(-l)~-l a pes) +w ~2(~)
at - r 0 r ~ as 1') as 11-1 i 2
( B- 6 )
230
-------
To obtain moment equations for the transformed equation, we use the property
of the kth moment given by
k ak
~ = (-1) lim T
8-+0 as
( B-7)
Applying this property, we obtain
amI
~ + wrml = wrml
. 0
-km
11'
( B- 8 )
where ml is the first moment of the feed.
a
BY successively taking partial derivatives with respect to s and taking
the limit as s+o, we find
a~ (. ~ 2
~ + wr + '"2 )m2 = wrm2 + 1/2wiml - 2kmT)+1
o
( B-9)
am3
~ + (wr + 3/4wi) m3 = wrm3 + 3/4wimlm2 - 3kmT)+2
o
( B-IO)
am4 2
at + (wr + 7/8wi) m4 ... wrm4. + 1/2wimlm3 + 3/8wim2 - 4kmT)+3
o . (B-ll)
oms
at + (wr + 15/16wi) mS = wrm5 + 5/16wimlm4 + 5/8wim2m3 - SkmT)+4
. 0
( B-12)
am6 2
~ + (wr + 31/32wi) m6 =wrm6 + 3/16wimlmS + lS/32wim2m4+5/16wim3
. 0
-6kmTl+5
( B-1,)
Or in genera.l the kth moment equa.tion is
a~
at + (wr +
k-l
(1 - 2~-1)Wi)~ = wr~o + Wij:tk~mj~_j - kmT1+j-l
( B-14 )
231
-------
wr:ere "':Ie define
a1 0 =
,
o
k-1
a = ---- , k = 1,2,...
k,1 2k-l
1
ak,k-l'= 2k-l, k = 3,4,...
ak-l,j-l + ~-l,j
ak,j = 2
k = 4,5,...
, j ::: 2,...,k-2
For a zero-order reaction (~ = 0) at steady state,
wrml = wrml
o
- km ;
o
( B-15)
and if we set mo = 1, we obtain for c = ml and Co = mlo
c
k . 0
c = Co - W = Co - kT, T~ k
r
( B-16)
This suggests that
which is not true.
singularity in the
sents the fraction
for a given T, c is independent of mixing frequency, ~,
This discrepancy results from ignoring the delta function
solution at c = 0, which as pointed out by Curl (10) repre-
of cells in which reactant has been completely consumed.
For first-order reaction (~ = 1) at steady state,
wrffil = wrml
o
-km.
l'
( B-17)
and for ml = C , C = c 1/1 + kT. Since for a first-order reaction the reac-
t~nt conce%trat10n of aOcell reaches zero only as time goes to infinity, we
are not concerned with a singularity at c = 0; and the last result confirms
that the average conversion for ~ = 1 is independent of U1. This conclusion
is invalid for feed comprised to two or more different streams, where cells
enter at different concentration.
For
1,2,...,
being of
integer values of ~ greater than 1, the moments equations for j =
k are not a closed set since the reaction term in the kth equation,
the form km . , will always introduce the (k+l)th or higher moment
, ~+J-l
232
-------
for ~ = 2,3,.... Thus regardless how far we extend the sequence of equations,
there will always be one more unknown (moment) than there are equations. We
can by scaling concentration so that c < 1 cause higher moments to become
small and essentially zero for some sufficiently large k. This would close
the set. There remain however many additional mathematical complexities in
dealing with multiple inlet streams, temperature dependence and.heat loss,
competing reactions, and the extension of cell-wise mixing to nonstirred .
residence time distributions.
233
-------
APPENDIX C
DANCKWERTS' "J" FACTOR FOR STIRRED TANKS IN SERIES AT 1m = 00
In order to evaluate "JI.f from the definition given by Danckwerts (11),
J = Var(a )/Var(a),
p
(C-l)
we must find the internal age distributions ~(ap).
obtain from
The first of these we
I
$(a) = l [1 - F(a)];
T
(C-2)
the second is calculated directly
ith tank will have the same value
(api == TT . i/n). .
based on the fact that all point ages in the
as the mean age in the ith tank
( C- 3)
To find ~(a), we start with the material balance on a tracer concentration
in the ith tank of "n" equal size tank:
'" 1'T dC!
Ci-l - Ci n dt
(C-4)
By taking the LaPlace transform of this equation, i.t can be shown that the
exit residence time distribution for n tanks in series is:
n n-l
n t e-nt/TT
fn (t) =
-------
n-l
F (t) CI 1- r ( E.....-)
n or
T
1 n-l -nt/T
Tn-1)! t e T
( c-'()
+ ( .!!.-)n-2
'T
1 0 n-2 -nth,],
-(u-2): t e .
+ ...
1
+ (E-.) 4 tl e-nt/'T
'T 1.
+ e-nt/TT] .
1
And, by substitution of a for t into ~(a) = ~[l - F(a)],
1 n-l
cp(a) :: - [(E-)
o 'T TT
1
(n-i)!
n-l -naIL
a e T
( c-8)
n-2
+ ( E-)
'T
1 n-2 -na/,
(n-2)! a e T
+ ...
+ 11 -n aI, 0
- ae T
TT
+ e -n al 1T] .
Variance, the second moment about the mean cr2, is computed from the first
and second moments about the origin ml and ~. 0
ml (a) == j"> acp(a)do(
o
(C-9)
Integration of a~(af is simplified by noting that only those terms involving
the factor aOe-nalT will contribute to the integral, all others being zero.
m (a) :: T 0 [ E- +.£:! + E.:1. + 1 Ton
1 T 2 2 2 ... +2"]'" 2i~l.(n-i+1)
n n n n n
(C-IO)
Similarly, m2( a) is evaluated from J:a2( a)da,
235
-------
And,
,2 n
T
. m2 (a) := 3 i~1 [(n - 1+ 1) (n - 1 + 2)]
n
1 . 2
Var(a) = 0 = m2(a) - [ml(a)]
2 nl 2
Var(a) = T 3 {i~1 (n - 1 +1) (n.- 1 + 2) - Ii [ L (n-1+1)] }
n
Fo~ point ages in the ith tank,
so that
- i
. api - nTT
1
~(ap)i = ~(a - a );
n p P1.
n 1 )
m~ (ap) =i~l ( ~T
1 'T n
(-) =- I: i
n 2 1=1
n
'1"2
(1) = 2.... ¥ i2
n 3 i=l
n .
n i 2
m2 (ap) = i~1 (n 1)
2.
Var(a ) = 'T3 {i£l i2 - l [¥ i]2}.
P n n i=1
And finally,
J - Var(a )/Var(a)
p
~ i2- l [ ~ i]2
n
J := 1=1 i=1
n 1 n 2
i~1(n-i+1) (n-i+2) - - [ r (n-i+U]
n i-I
236
.(c-n)
(C-12)
(C-13)
( C-14)
(C-15)
(c-16)
( C-17)
(c-18)
(C-19)
( C-20)
-------
REFERENCES FOR PHASE II .
1.
Bell, R.L. and Babl, A. L., "On the Extension of the Method of Moments
to a Cascade of Well Mixed Discrete Stages with Backflow Between Stages,"
Chemical Engineering Science, 20, Dec. 1965, pp. 1001-1006.
2.
Bird, R. B., Stewart, W. E., and Lightfoot, E. N., Transport Phenomena,
Wiley, 1960, 24. .
3.
Blenk, M. H., and Franks, R.G.E., "Math Madeling
SAE, Paper No. 710607, Mid-Year Meeting, January
Quebec, Canada.
of an Exhaust Reactor,"
7-11, 1971, Montreal,
4.
Brownson, D. A., and Stebar, R. F., "Factors Influencing the Effectiveness
of Air Injection in Reducing Exhaust Emissions," SAE Transactions, 1966,
74.
5.
Cantwell, E. N., and Pahnke, A. J. (DuPont), "Design Factors Affecting
the Performance of Exhaust Manifold Reactors," SAE Transactions, 1966,
74." "
6.
Cantwell, E. N., Rosenlund, I. T., Barth, W. J., Kinnear, F. L., and
Ross, S. W., "A Progress Report on the Development of Exhaust Manifold
Reactors," SAE, Paper No. 690139, International Automotive Engineering
Congress, Detroit, Michigan, January 13-17, 1969.
7.
Chandler, J. M., Smith, A. M., and Struck, H. J., t~evelopment of the
Concept of Non-flame Exhaust Gas Reactors," SAE, Paper No. 486 M, National
Automobile Week, March 1962. ---
8.
Corrsin, S., "Simple Theory of an Idealized Turbulent Mixer," AIChE
-
Journal, 3,. No.3, Sept. 1957, pp. 329-330.
9.
Corrsin, S., "The Isotropic Turbulent Mixer: Part II, Arbitrary Schmidt
Number," AIChE Journal, 10, No.6, Nov. 1964, pp. 870-877.
10.
Curl, R. 1., "Dispersed Phase Mixing: 1. Theory and Effects in Simple
Reactors,: AIChE Journal, 9, NO.2, March 1963, pp. 175-181.
11.
Danckwerts, P. V., "The Effect of Incomplete Mixing on Homogene ous
Reactions," Chemical Reaction Engineering, 12th Meeting. Europ. Fed.
Engrg., Amsterdam, 1957.
Chern.
237
-------
I.
21.
'REFERENCES FOR PHASE II (C ontinued)
12.
Daniels, W.A. (General Motors), "Engine Variable Effects on Exhaust
Hydrocarbon Composition (A Single-Cylinder Engine Study with Propane as .
. the Fuel)," SAE, Paper No. 670124, Automotive Engineering Congress,
Detroit, Michigan, January 9-13, 1967.
13.
Deans, H. A., and Lapidus, L., "Effects of Non-Ideal Flow Represented by
a Tanks-In-Series Model," AIChE Journal, 6, '1960, pp. 656-663.
14.
. Dryer, P., Naegeli, D., and Glassman, 1., "High-Temperature Oxidation
Reactions of Carbon Monoxide," Western states Section Combustion Institute
Preprint No. 71-26, 1971. .
15.
Evangelista, J. J., Katz, S., and Shinnar, R., "Scale-up Criteria for
Stirred Tank Reactors," AIChE Journal, 15, No.6, pp. 843-853.
16.
Evangelista, J. J., Shinnar, R., and Katz, S., "The Effect of Imperfect
Mixing on Stirred Combustion Reactors,". Twelfth Symposium (International)
on Combustion. Poitiers, France, July 1968.
17.
Gillespie, B., and Carberry, J. J., I. and E. C. Fund., 5, 1966, 164.
18.
Kim, D. S., and Kraus, E. J. (Esso), "Synchrothermal
Control of Automotive Exhaust Emissions," SAE, Paper
Eng. Contress, Detroit, Michigan, Jan. 12-14, 1970.
Reactor
No. 700147,
Glass, W.,
System for
Automotive
19.
Horn, F~J.M., and Parish, T. D., "The Influence of Mixing on Tubular
Reactor Performance," Chern. Eng. ScL 22, Dec. 1967, pp. 1549-1560.
20.
Kattan, A., and Adler, R. J., "A Stochastic Mixing Model for Homogeneous,
Turbulent, Tubular Reactors," AIChE Journal, 18, 8, 1967, 585. .
Kreith, F., Principles of Heat Transfer, International Textbook Company,
1965. .
22.
Levenspiel, 0., Chemical Reactor Engineering, John Wiley and Sons, Inc.,
1962 .
23.
Levenspiel, 0., and Bischoff, K. B., "Patterns of Flow in Chemical Process
Vessels," Advances in Chemical Engineering, 4, 1963, pp. 95-108.
24.
Ng, D.Y.C., and Rippin, D.W.T., "The Effect of Incomplete Mixing on
Conversion in Homogeneous Reactions," Third European Symposium on Chemical
Reaction Engineering, Amsterdam, Sept. 1964; p. 161. Pergamon Press,
Oxford, 1965.
238
-------
REFERENCES FOR PHASE II (Continued)
25.
"Kinetics of Oxidation and Quenching of Combus-
of Gasoline Engines," Annual Progress Report
Patterson, D. J., et al.,
tibles in Exhaust Systems
No.2 to CRC, 1970-71.
26.
Perry, R. H., Chilton, C. H., and Kirkpatrick, S. D., Chemical Engineers'
Handbook, McGraw-Hill Book Company, 1963.
27.
Rippin, D.W.T., "Segregation in a Two-Environment Model of a Partially
Mixed Chemical Reactor," Chem. Eng. ScL, 22, 1967, pp. 247-251.
28.
Rippin, S.W.T., 1. and E. C. Fund., 6, 1967, 488.
29.
Schwing, R. C.( General Motors), "An Analytical Framework for the Study
of Exhaust Manifold Reactor Oxidation," SAE preprint 700109, Jan. 1970.
30.
Shinnar, R., and Naor, P., "Residence Time Distribution .in Systems with
Internal Reflux," Chem. Eng. ScL, 22, Oct. 1967, pp. 1369-1381.
31.
Sigworth, H. W.; Jr., Myers, P. S., and Uyehara, O. A., "The Disappearance
of Ethylene, Propylene, n-Butane, and l-Butane in Spark-Ignition Engine
Exhaust," SAE, Paper No. 700472, Mid-Year Meeting, Detroit, Michigan,.
May 18-22, 1970. . . .
32.
Sondreal, E. A., Kadlec, R. H., and Carnahan, B., "Computer Programs for
Reactor Design," Coordinating Research Council, APRAC-CAPE 8-68, New York,
New York. (Unpublished computer listings with documentation on file.)
33.
Speilman, L. A., Levenspiel, 0., "A Monte Carlo Treatment
and Coalescing Dispersed Phase Systems," Chem. Eng. ScL,
247-254. .
for Reacting
20, 1965, pp.
34.
Stainthrop, F. P., and Sudall, N., "Backmixing in a Rotating Disc Contrac-
tor," Trans. Inst. of Chem. Eng., 42, 1964, pp. T193-T208.
35.
Tabaczynski, R. J., Heywood, J. B., and Keck, J. C., "Time-Resolved
Measurements of Hydrocarbon Mass Flow-R8te in the Exhaust of a Spark-
Ignition Engine," SAE, Paper No. 720112, Automotive Engineering Congress,
Detroit, Michigan~ Jan. 10-14, 1972.
36.
Terukatsu, M., and Vermeulen, T., "Diffusion and
Two-Phase Axial Dispersion," 1. and E. C. Fund.,
320.
Back-Flow Models for.
2, Nov. 1963, pp. 304-
239
-------
REFERENCES FOR PHASE II (Concluded)
37.
Villermaux, J., and Zoulalian, A., "State of Mixedness of Fluid in a
Continuous Reactor-With Respect to a Model of Weinstein and Adler,"
Chern. Eng. Sci., 24, 1969, pp. 1513-17.
38.
Weinstein, H., and Adler, J., "Micromixing Effects in Continuous Chemical
Reactors," Chern. Eng. Scl., 22, 1967, pp. 65-75.
39.
Zwietering, T. N., "The Degree of Mixing in Continuous Flow Systems,"
Chern. Eng. Sci., 11; No.1, 1959, p. 1.
240
~
't
'i
-------
t.~.
NOMENCLATURE FOR PHASE II
Quantity
:Let ter Symbols
a coefficj.8nt 1n the kth moment equation
for the property distribution p(c) belong-
ing to the product ak,j . mj . ~-j.
ai,bi,ci' and di constants in specific heat equations
Symbol
ak,j
A
area, sq. ft.
Ak
the preexponential term in the rate equation
for a reac.tion "k".
c
concentration, lb moles/cu. in.
Gj ,i
Ci
C
P
mole fraction of specie "i" in cell "j".
mole fraction of specie "i".
specific heat (at constant pressure), Btu/lb mass of
or Btu/lb mole of.
D
diameter, ft.
axial dispersion coefficient, ft2/sec.
DL
D
v
2
molecular diffusivity, ft /sec.
DR
dilution ratio for exhaust with air; volumetric
air flow (stream 2)/vo1umetric exhaust flow
(stream 1).
~
activation energy for reaction "k", ca1/gmo1e.
f
m
mass flow rate, lb mass/hr.
f (t)
F(t)
eX:!..t Age distribution function, dimensionless.
dimensionless tracer
F(t) = it f(t)dt.
o
response to a step input;
Fi
functions defined by the material and energy
balance, which are to be minimized (to zero)
to solve for operating temperature and conver~
sions in a CSTR. .
get)
a function of time having value less than or
equal to 1 used in Vi11ermaux and Zou1a1ian's
(:'6) inixedness model. g (t) :: 1. implies complete
segregation and get) = 0 complete segregation.
(f'
",;'
241
hI;
-------
NOMENCLATURE FOR PHASE II (Continued)
Symbol
G
mass velocity or flow rate per unit area,
lb /hr. sq. ft.
m
Gr
h f b g L3 A T P2/112
Grass 0 nurn er = ST U ~
gas phase heat transfer coefficient, Btu/hr.sq.ft.oF.
h
Hi
~H
rk
the enthalpy of a pure specie, "i", Btu/1b mole
heat of reaction for a reaction k represented by
stoichiometry vi k' Btu, for the reaction a8
written. . ,
HA
c
thermal conductance by conduction or convection,
Btujhr of.
HA
r
thermal conductance, Btu/hr.oF.
I
m
the number of coa1escences occurring per unit of
residence frequency, 1 = mi/2w
m r
J
Danckwerts' (12) index of segregation:
(a ) , internal ages.
p
J ::0 var (a)/
k
1-n
reaction rate constant, (cu.in/lb mole) /sec.
kf
thermal conductivity of a fluid ~t the mean film
temperature, Btu/hr.ft.oF.
k
t
thermal conductivity, Btu/hr.ft.oF.
L
length, ft.
L
c
the "integral Bcale of turbulence", ft.
L
r
sphere equivalent reactor diameter, ft.
m
the total number of chemical species in a simulation.
m(t)
= (1-g (t»f (t).
th
the k moment of
~ ~ f~ p(c) ck dc
o
mass, 1b mass.
a property distribution;
~
M
242
-------
NOMENCLATURE FOR PHASE II (Continued)
Symbol
M
c
mole contents of a cell, lb moles.
M
r
mass in the reactor, lb.
m
M
w
i
molecular weight of a species "i".
n
number of tanks in a tanks in series model.
N
c
the number of cellsin a cell-wise mixed reactor
module.
p(c)
the normalized distribution function for concentration,
( foo p(c)dc = 1).
o
the number of parts in the thermal simulation of a
reactor.
P
r
P
pressure, psia. .
Pi
P
m
partial pressure of specie "i", psia.
q
mixing power in Corrsin's (9,10) engineering
correlation for B, ft lbf/sec.
the number of oxidizable chemical species, or the
number of reactions.
qact
the number of active species, which appear as
reactants or products in any reaction, as opposed
to inert species.
Q
heat loss from a reactor or reactor module, Btu/hr.
-
ri
the rate of "appearance" of a specie "i", lb molesl
sec. cu.in.
rk
R
the rate of a reaction "k", lb moles/sec.cu.in.
gas law constant, 1.987 cal/gmole oK or l8540.psi
cu. in. lIb mole oR.
s
the LaPlace transform variable
L[(f(t)] a foo e-ts f(t)d t .
. 0
defined by
243
-------
NOMENCLATURE FOR PHASE II (Continued)
Symbol
s (t)
a fraction of the residence time distribu-
tion function defined by s(t) = g(t) f(t),
used in Villemaux and Zoulalian's (46) mixed-
ness model.
SR
the stoichiometric ratio of oxygen to the oxidized
specie (s).
t
time, seconds or hours.
T
temperature, degrees F, except oR for radiant
heat transfer and oK in Arrhenius term.
TLOW
a computer variable for the low temperature assumed
during cycling of temperature, of.
TSPAN
the span of temperature change for cycling exhaust
temperature, of.
u
velocity, ft/sec.
*
U (t -t)
*
the unit step function at.t = t .
. 3
volumetric flow rate, ft Isec.
v
v
m
molar flow rate, lb moles/sec.
'V
reactor volume, cu.in.
v
c
volume of a single cell, cu.in.
Xi
chemical conversion of specie "i"; fraction
converted into product.
X
m
conversion in a maximum mixedness reactor.
x
s
conversion in a segregated reactor.
y
fractional length through a reactor, z/L.
z
length
244
-------
Symbol
CI.
CI.
P
s
8T
y
Yc
<5 (t)
E:
11 or 11i k
,
11m
A
lli
'\ k
,
p
T
TT
a
.a
.r
I
I
NOMENCLATURE FOR PHASE II (Continued)
Greek Letter Symbols
. age, sec.
average age at a point, as defined by
Danckwerts (12), sec.
a constant for the decay of turbulence defin~d
dc2 2
by ~ = - 8 C .
temperature coefficient of volume expansion, l/oR.
recycle ratio.
ratio of specific heats, C Ic .
p v
Dirac delta function, representing an idealized
pulse occurring at time zero.
emissivity for radiation.
reaction order (0£ a specie "i" in a reaction "k".)
mixing efficiency.
life expectance, sec.
viscosity of a pure specie, "i", lb I£t.sec.
m
a stoichiometric coefficient for a specie "i"
in a reaction "k"; negative value indicates a
reactant and positive value a product.
3
density, 1b 1ft.
m
mean residence time, sec.
mean residence for a system, as for example all
tanks in a tanks in series model, sec.
o~e unit of standard deviation for a normally
distributed statistic.
Stefan-Boltzman constant, Btu/hr.sq.ft.oR4.
245
-------
NOMENCLATURE FOR PHASE II (Concluded)
Symbol
2
o
variance, or the second moment about ~he mean,
for the propeity distribution p(c); 0 =
fro
o
- 2
p(c) (c-c) dc.
-------
DETAILED PROGRESS - PHASE III
SPECIAL INSTRUMENTATION DEVELOPMENT AND MEASUREMENTS
247
-------
A.
SUBTRACTIVE COLUMN HYDROCARBON ANALYSIS
1.
Purpose
For assessing thermal reactor performance or for that matter performance
of any emission control device, it is desirable to determine not only the re-
duction possible in total hydrocarbon emission but also the reduction in reac-
tive constituents. In our study the subtractive column technique of Sigsbyl
was selected for a measure of reactivity change since our laboratory did not
possess adequate gas chromatographic capability and because this technique
allowed relatively rapid determinations to be made. Thus data could be ob-
tained for a variety of operating points. Olefinic exhaust content was used
as the reactivity measure. Experimental results were reported in a number of
curves in both the First and Second Annual Progress Reports.
2.
Equipment
According to Sigsby, the subtractive column subdivides the hydrocarbons
into three subgroups, olefins plus acetylenes, aromatics, and paraffins. Two
scrubbers are used. Olefins and acetylenes are removed by a mercuric sulfate-
sulfuric acid scrubber and aromatics are removed by a palladium sulfate-
sulfuric acid scrubber. A flame ionization detector (FID) is used as the hy-
drocarbon detector.
Figure 1 shows a flow schematic of The University of Michigan system.
The unit has three parallel paths. The exhaust sample is directed either
through path Sl (total hydrocarbons), S2 (total minus ole fins and acetylenes),
or S3 (total minus olefins, acetylenes, and aromatics). Provisions were made
for zeroing the FID and for backflushing with dry nitrogen. A master timer
selects the flow path and controls sampling and backflushing. Details of
construction are included in Ref. 1 and are not repeated here.
lKlosterman, D. L., and J. E. Sigsby, "Application of Subtractive Techniques
to the Analysis of Automotive Exhaust," Environmental Science and Technology,
1., No.4, April 1967, p. 309. .
249
-------
'.
HYDROCARBON
CALIBRA nON GASES
FIL TER
V2
S2
FILTER
ICE
BATH
Flame
Ioniza-
tion.
etector
ROTO-
METER
w / needle
valve
N
I\)
V1
o
N2
BACK FLUSH
V7
N - Needle Valve
Posi-
tion
1
2
Sample Seen Flow
by FID Path
Back flush S2S3
Paraffins and S3
benzene
Total olefins 52
T.otal cr zero 51
Scrubber
All
HgSO 4
and Pd
HgS04
None
Operation of Valves
V7,aVl V2.5 V3.6 V4
On Off Off Off On
Off On Off On Off
3
4
Off On On
Off On Off
Off
Off
Off
On
?ig'J.re 1. Flow schematic 0:':' University c:' !/'ichigan subtractive column-flame ionization hydrocarbon analysis
sys:em. The subtractive analyzer is patte:>:nec. after that of Sigsby, Ref. 1.
-------
3.
Experimental Verification
A.
GAS CHROMATOGRAPHIC COMPARISON
Results from a detailed G.C. analysis were compared to subtractive col-
umn results to determine the performance of The University of Michigan unit on
exhaust gas. Since our laboratory lacked the necessary ~C. capability, ar-
. rangements were made to check our unit against a Beckman GC-4 at the Ford
Motor Company Engineering Staff. Tests were run using exhaust from an ,idling
2000 cc Pinto. Three series of tests were run.
In the first test, exhaust
tractor columns and then to the
( ppmc): .
was passed through the olefin + aromatic sub-
~C. The following results were obtained
Paraffins
Olefins & Acetylenes
Aromatics
1087
19
44
Our analyzer would report 1150 ppmc as paraffins rather than
Thus the error in reporting paraffins was +63/1087 or +5.8%.
overestimated the paraffin content of the exhaust by 5.8%.
Total
1150
the correct 1087.
Our analyzer
In the second test exhaust gas was passed through the olefin subtractor
only. The results were:
Paraffins.
Olefins & Acetylenes
Aromatics
1344
27
1130
Total
2:501
Our analyzer would report 2501 ppmc as paraffins and aromatics rather than the
correct 2474. Thus the error in reporting paraffins plus aromatics was +27/
2~7~ or +1.1%. The error in reporting aromatics alone must be estimated since
the emission base line shifted between tests. If we assume that the subtrac-
tive column would report paraffins 5.8% too high, then an estimated value.
would be: 1344 x 1.058 = 1420 ppmc. By differencing, we find 2501 - 1420 =
1081 to be .the aromatic content that would be reported by the subtractive col-
umn. The error is 1130 - 1081 or 49 ppmc. Thus the subtractive column under-
estimated aromatics by 49 ppmc or -49/1130 = -4.3%..
I'
I
251
-------
In the final test J exhaust was passed. directly into the G. C.
sults were:
The re-
Paraffins
Olefins & Acetylenes
Aromatics
Total
1364
1905
1435
4722
In the above test paraffins plus aromatics were 2817 ppmc. From Test 2, this
may be assumed to be 1.1% lower than the subtractive column would yield. The
subtractive column value would be 2817 x 1.011 = 2848 ppmc. The subtractive
column prediction of olefins plus acetylenes would then be 4722 - 2848 = 1874.
This is too low by 1905 - 1874 = 31 ppmc or -31/1905 = -1.6%.
Based on G.C. results one can conclude that the subtractive column class
results differed from ~C. class results as below in Table I:
TABLE I
SUBTRACTIVE COLUMN-G. C. COMPARISONS
Class
Percent Error
Acetylenes + Olefins
Aromatics
Paraffins
-1.6
-4. 3
+5.8
Since acetylenes were about 7.5% of the total in these tests, interpreting the
subtractive column results to be olefins rather than olefins plus acetylenes
would overestimate olefin content by 5.8%.
Considering thenonparaffin constituents which broke through in Test 1,
14 were olefins and 6 aromatics. Of the 14 olefins, 7 were either 2 or 3 ppm~
the rest were less. Of the 6 aromatics, the ppmc contributions were:
Constituent
ppmc After Sub.
Benzene
Toluene
Ethyl benzene
Xylenes
Mono substituted ethyl benzenes
Di substituted ethyl benzene
Total
3
17
5
6
8
.2
44
252
-------
Only 1 or 2% of the smaller aromatics broke through but virtually all of the
large aromatics did. This result is different from that of Sigsby. In his
tests virtually no larger aromatics broke through but a large percentage
(>80%) of benzene did. Fortunately the concentration of the larger aromatics
was small.
B.
CALIBRATION GAS COMPARISON
Additional evaluations, reported
page 27, were made with the following
manufacturer) .
in the First Annual Progress Report,
calibration gases (as analyzed by the
paraffinic:
aromatic:
olefinic:
4620 ppmc propane in nitrogen
315 ppmc toluene plus 282 ppmc benzene in nitrogen--597 ppmc
100 ppmc acetylene, 150 ppmc propylene, 101 ppmc ethylene,
and 205 ppmc l--butene in nitrogen--tota1556 ppmc
These gases were used to check the day to day operation of the unit.
Results were:
a.
With propane the analyzer worked perfectly (no olefins or aromatics
reported) .
b.
With the aromatic calibration gas about 60% of the benzene broke
through to be reported as paraffins (no olefins reported). It was
found that flowing dry nitrogen through the aromatic subtract or im-
proved benzene retention. However, benzene scrubbing efficiency was
variable.
c.
All the acetylene in the olefinic calibration gas was reported as an
olefin (no paraffins or aromatics reported).
4.
Conclusions
In conclusion, within the limitations of the vehicle tests with shifting
baseline exhaust emission levels, the subtractive columns were very accurate
(better than 6%) in reporting the classes. The major drawback was that acet-
ylene was reported as an olefin. Results with the calibration gases confirmed
the acetylene reporting problem and in addition demonstrated variability in .
benzene retention. Thus the subtractive column is somewhat limited in accu-
racy by these problems but was concluded to give a reasonable indication of
.exhaust reactivity changes particularly if a fuel with fixed aromatic content
253
-------
is used. Some improvement in accuracy can be made by estimating the acetylene
content of the ~xhaust and correcting the olefinic results accordingly. Esti-
mation of acetylene content in exhaust gas is discussed in the following sec-
tion.
254
-------
B.
GAS CHROMATOGRAPHIC STUDIES OF EXHAUST ACETYLENE
1.
Purpose
Gas chromatographic analysis for acetylene was performed on R number of
exhaust samples at various engine air-fuel ratios, air injection fractions,
and with and without exhaust reaction suppression. The objective was to es-
timate acetylene content both in engine exhaust and reactor exhaust. For
these tests the engine was run at 1200 rpm, 30 BHP and MBT spark. Manifold
vacuum was 11-13 in. Hg.
2.
Sampling Technique
A total of 12 samples of exhaust gas from the 350 CID Chevrolet engine
were taken at a point downstream from the duPont thermal reactor. In all
cases the samples were passed through an ice bath and then collected in 500 cc
stainless steel cylinders maintained at 110°-120°C. Usually, several days
passed before the contents of the cylinders were withdrawn for ~C. analysis.
However, immediately before and after each sample collection the exhaust gas
was measured on-line with an FID and a subtractive column analyzer to deter-
mine total hydrocarbons, paraffins, olefins, and aromatics. In some. cases
quench coils at the engine exhaust ports just ahead of the reactor were turned
off and the reactor was simply acting as an exhaust manifold. The conditions
of sampling for each run are given in the right-hand column of Table II. Also
. presented are the air-fuel ratio in the feed to the engine and the concentra-
tions determined by the FID. The air fraction added, as given under Samplin~
Conditions, refers to the air pumped directly into the reactor to oxidize the
. incompletely burned fuel in the exhaust issuing from the engine.
3.
Gas Chromatograph Operation
Dual columns were employed in the heated oven section of a Perkin-Elmer
800 gas chromatograph. The columns were 1/8 in. O.D. by 4 ft long, wo~nd in
spirals, and packed with Poropak-N. This packing gave an excellent separation
of the light hydrocarbons. In order to obtain sharp peaks for the components
. in a reasonable time temperature programming was employed. Beginning with an
ini tial temperature of 60°C, the oven was raised 10°C/min. . This caused. some
255
-------
TABLE II
FID AND SUBTRACTIVE COLUMN .t.NALYSES
.t.ir/Fuel Total Hydrocarbon Paraffin f..roffia tic Olefin *Sampling Conditions
Sample ?.s:.tio ( ppm) (ppm) (PPm) (ppm)
10.5 1290 640 340 310 Q,uench coils on, no
A air added to reactor
B 13.2 800 318 232 250 "
C 14.65 630 200 1!30 250 "
D 16.45 510 162 133 215 "
17.45 200 160 170 Quench coils off, no
E 530 air added to reactor
F 12.05 940 435 260 245
G 13.38 326 84 67 175 Quench coils off,
I\) added air fraction
\J1 .167
0'\
H 13.38 38.5 4 10 24.5
.359
I 11. 73 152 52 27 73 "
.131
J 11. 73 950 402 209 339 "
Did not .123
ignite
K 13.42 418 92 99 227 "
.535
L 17.33 560 205 172 183 Quench coils on, no
air added to reactor
*Exhaust cooling coils .'"ere used to quench after-reactions in the exhaust ports of the engine. Thus,
results' reflecting either a high or low degree of after-reaction were obtained.
-------
baseline drift after the propane-propylene peak. Consequently, no attempt was
made to analyze for the concentration of the higher molecular weight species.
An Infotronics electronic integrator, Model CRS-10H, was used in conjunc-
tion with the G. C. to determine the peak areas.
4.
Data Analysis
The light hydrocarbon content of the samples was calculated from ~C. re-
sults by comparing the ratio of the peak area to the sample pressure (P.A./Pr),
of each of the light end components in the sample with the same ratio for an
olefinic standard.* The olefinic standard was reported to contain ethylene
(50.7 ppm), acetylene (49.9 ppm), propylene (50.7 ppm), and l-butene (51.;?
ppm). Since the st~ndard did not contain known amounts of methane and ethane
(two important components of the actual exhaust samples analyzed), their con-
tent in the samples was estimated from the following relations:
ppm methane
= (p ~j methane
in sample
r: 2 ~ 50. 7
x \1. oy (P~.7
ethylene
standard
in
ppm ethane
=
(P. A:\
\ Pr 7 ethane
sample
in
~ 1 -, 50.7 .
x ~. 05) (P ~~~
) ethylene
standard
in
In the first equation the
difference between methane and
mate of the correction for the
the FID detector.
factor of
ethylene;
different
2 corrects for the carbon atom/mole
while the factor 1/1.05 is an esti-
responses of paraffins and olefins in
DuplicRte rLlns were made Ivith the standard and the samples. The results
of the analyses are reported in Table III, as ppm of each component converted
to its hexane equivalent. This conversion was accomplished by multiplying the
actual ppm of each component by the carbon ratio; i.e., the carbon atoms of a
given species divided by 6,which is the number of carbons in hexane.
*Standard prepared by Scott Research Laboratories, Inc.
be accurate to :1:.2% or better.
Composition stated to
257
-------
!
TABLE III
, HEXANE EQUIVALENT OF COMPONENTS DETERMINED BY GC ANALYSIS
i
I
. Sample Component ppm Hexane
CH4 C2H6 C2H4 C2H2 C3H6 + C3H8
A 81.0 4.4 63.7 53.4 33.9
B 24.5 7.4 28.7 22.0 9.4
C 12.8 6.5 26.1 15.9 5.9
D 5.7 3.6 23.6 10.8 3.4
E 3.3 2.0 6.0 5.6 0.32
F 45.5 5.6 55.7 40.0 37.8
.G 28.3 2.4 71.5 18.5 11.0
H 1.5' 0.04 3.9 .1.9 0.34
I 30.8 0.95 25.9 9.9 8.0
J 68.8 6.2 79.1 42.6 55.8
K 22.1 2.9 7.8 16.0 0.38
L 3.3 2.5 3.7 0.27
258
-------
The olefin content, Listed in 'l'able II, includes acet.vlenic (tdplf' band)
components. The "true" olefin content has been estimated by deducting the
acetylene content given by G.C. analysis from the olefin content given by FID
and subtractive column analysis. The "true" olefin content is given in Table.
IV as ppm hexane and also as a percentage of the total hydrocarbons, while the
acetylene content is given as a percentage of both true olefins and of total
hydrocarbons.
. As indicated in Table II, samples A-D and L were taken with the quench
coils on, samples E and F had the quench coils off but no air added to the
exhaust, and samples G-K had the quench coils off and air added to the reactor
to effect after-reaction. It was observed, however, that for sample J there
was no rise in the temperature of the reactor indicating that the air-exhaust
mixture did not ignite.
Figure 2 shows total hydrocarbons, % "true" olefins, and % acetylene for
samples A-F, J, and L as a function of the air-fuel ratio, A/F~ Figure 3
shows the same results for samples at A/F >?!:. 13. 3 and 11.73 as a function of
volume fraction added air in the reactor. Figures 4 and 5 show the percentage
of acetylene in the olefins determined by the FID and subtractive column ana-
lyzer for the sample sets corresponding to Figures 2 and 3, respectively.
. Although the methane, ethane, ethylene, acetylene, and propane-propylene
combination contents of the exhaust were determined, the principal interest
here i~ in the acetylene content for correction of the FID-subtractive column
olefin results. From Figures 2 and 4 (no after-reaction), it is seen that the
correction to the FID olefin is a function of the A/F ratio; although there
was some scatter in the results. Figure 4 shows that acetylene as a percent
of total ole fins decreased nearly linearly from 16% at 11:1 A/F to 2% at 18:1
A/F. Likewise, acetylene varied from 4 to 2% of the total HC content (Figure
2). After-reaction (in the reactor) had little effect on acetylene as a per-
cent of remaining olefins (Figure 5) but did affect acetylene as a percent of
total HC (Figure 3).
,-
).
Conclusion
Our conclusion, based upon these limited tests, with a single Indolene
fuel is l.hat the FI.O-subtractive column olefin results can be corrected for
acet.vlene content through the A/F ratio variations according to Figure 4 with
no Il.dditional correction needed for air injection. Thus, for estimating ole- >
fin content from subtractive column analysis, "true olefin %" equals value ob-
served from subtractive column analysisdi vided by .
fr + % in Figure 4)
\J. 100
259
-------
- -----------
.--~~-------_.-_.-
TABLE IV
CORRECTED OLEFIN CONTENT OF SAMPLES
Total Hydrocarbon "True" Olefin "True" Olefin Acetylene % Total Olefin*
Sample ppm Hexane ppm Hexane % Total Hydrocarbon % Total HC
A 1290 257 19.9 4.14 17.2
B 800 228 284 2.75 8.79
C 630 234 37.2 2.52 6.35
D 510 204 40.2 2.04 5.02
E 530 164 31.0 1.06 3.30
!\)
0'\ F 940 205 21.8 4.25 16.4
a
G 326 157 47.9 5.68 10.6
H 38.5 22.6 58.9 4.93 7.75
I 152 63 41.7 6.51 13.6
J 950 296 31.2 4.49 12.6
K 418 211 50.5 3.83 7.04
L 560 179 31.9 0.66 2.02
*Total olefin includes acetylene.
-------
1400
1200
. Total Hydrocarbon
60
70
1000 50 z
&.J 0
~
z e:::
« "True" Olefin .. «
>< u
&.J 0
:J: e:::
E 800 40 c
0.. . ',f' >-
0.. :c
, -J
Z «
o I-
co 0
e::: A I-
« 600 30 I.J..
U 0
o
e::: l-
e z
>- &.J
U
:J: e:::
-J &.J
« 400 20 a..
b
I-
200
,.
, e
Acetylene
o
10
12
14
Figure 2.
16
18
A/F
Results for samples without after-reaction.
261
10
.
o
20
-------
60
50
LJ..J Z'
Olefi n 0
z ~ ex)
« a::::
X A/F Symbol «
LJ..J
:r:. 80 40 g
E a::::
c. 11. 73 Closed Q
c. >-
::J:
~ 13. 30 Open
z -I
g 60 «
30 b
a::::
« Hydrocarbon t-
u u..
o 0
a::::
Q t-
~ 400 z
20 ~
-I. a::::
« LJ..J
I-'- Ct..
o
t-
10
0..1
Acetylene
O. 2 O. 3
FRACTION AIR ADDED
0.4
0.5
Figure 3.
Results for samples with a.fter-rea.ction.
A/F ~ 13.3 and 11.73.
262
o
-------
I -
20
z 16 0
u..
L.J.J
--.J
0
C
u.. 12
I--
z
L.J.J'
u
c::=
L.J.J
a..
- 8
L.J.J
Z
L.J.J
--.J
>-
~
u 4
«
Stochiometric
o
10
. 14
A/F
16
18
12
Figure 4.
Results for samples without after-reaction.
263
. 20
-------
-- --~-~"--
i I
I
I
! I
I
20
I ~--
A/F SYM BOL
d 11. 73 ~
I- 16
I 13. 30 0
z
L&..
I-
Z
I..I.J
U
0:::
I..I.J
0-
Ii ..
I..I.J
Z
~
>- 4
I-
,! L&.J
I U
«
o
00 1
O. 2 O. 3
FRACTION A IR ADDED -
0.4
0.5
Figure 5.
Results for samples with after-reaction.
A/F ~ 13.3 and 11.73.
264
-------
C.
MEASUREMENT OF INSTANTANEOUS ENGINE EXHAUST VELOCITY AND TEMPERATURE
The studies in Phase II of this project brought out the fact that the
reactor model was quite sensitive to the exhaust enthalpy input to the reactor.
Since an accurate experimental determination of the enthalpy input requires
good measurements of both instantaneous engine exhaust velocity and tempera-
ture, and since no known conventional techniques were available for getting
these measurements, developmental work was undertaken on a new technique which
appeared promising for both the velocity and temperature measurements.
The method used laser-schlieren photography with a rotating-mirror slit-
streak camera. The laser-schlieren system was used to detect turbulent eddies
in the exhaust as they moved with the exhaust stream. The average eddy-
spatial-velocity was assumed to be equal to the exhaust stream velocity. By
projecting the eddy schlieren image through a narrow slit and moving the slit
image. at a fixed rate across a sheet of Polaroid film, Figure 6, a photograph
was obtained which gave continuous records of both eddy position and time,
over a short-time interval. The slope of the resulting image at any point
gave instantaneous velocity. Figure 7 is an example of such a photograph.
. Unsuccessful measurements of instantaneous gas temperature were also
attempted using the same technique for measuring the speed of a spark-induced
low amplitude shock wave in the gas stream. Since sound velocity is propor-
tional to Tl/2, the gas stream temperature can, in theory, be estimated from
the measured sound velocity. Good results were obtained in open air and in a
motored engine, but the interference generated by the hot exhaust re~ulted in
too low a signal-to-noise ratio for reliable measurements.
1.
The Measurement of Engine Exhaust Velocity
The laser-schlieren optical system and associated timing and synchroniza-
tion circuits are shown in Figures e and 9. Exhaust gas velocity as a fUllc-
tion of crankangle was obtained from photographs snch as shown in Figure 10,
and Ule result from an early run is shown plotted in Figure 11. Specifications
of the engine used in this work are summarized in Table V.
The photographic procedure required that the camera mirror be properly
phased with the engine rotation so that any preselected portion of the engine
cycle can be photographed. This phasing was accomplished with the circuit
sllownin Figure 9, and required that both engine and mirror be in their proper
positions for the recording of an event. The mirror had to be at the position
where the slit image was at the start of its sweep across the photographic
265
1- .
-------
I-
I
SM
T
SR
K
SLIT
IMAGE
F
~
sLir IMAGE
MO VEME NT
SR - LIGHT SOURCE
T - TEST SECTION
SM - SCHLIEREN MIRROR
K- KNIFE EDGE
S - SLIT
RM - ROTATING MIRROR
F - FI LM PLANE
T
SR
--
--
--
---
. Figure 6. Schematic diagram of laser-schlieren optical system.
266
-------
f\)
0\
--::J
Ole
TIME
"
r
0.5 msec
5200 C.A.
t
Figure 7. streak schlieren photograph showing the start of the exhaust process.
Engine speed is 600 rpm. Exhaust valve opens at 500° C.A.
-------
'-
#2
. #/
. SPHERICA" .
MIRROR .-.-.
'".
"
"
"
'~KNIFE EDGE
"
"
"
"
SHUTTER # /--""
FL YWHEEL
WINDOWS (2)
. - . -E:::::=l LASER I
EXHAUST PIPE
FILM CARRIER
CAMERA SLIT
Figure 8. Exhaust velocity measurement system.
Mechanical and optical schematic.
268
SHUTTER #: 2
FLASH #2
-------
SCR
I
t
I.
1.5 vi
. D.C.
100.0.
VV\,
I\)
(j\
\0
To Scope
Trigger.
A (~f;8
I
. I
I
I
I
I
I
I
I
I
. I S2
1.5v ro
D.C.
Sl: Camera eam switch
S2: Switch operated by relay #3
S3: Manual DPDr switch
s4: Manual ON -OFF switch.
Dl: Engine distributor #1
D2: Engine distributor #2
1.5K
Figure 9.
Electrical schematic.
#2 Shutter
Relays
a"T-t-o To G.R.
Strobe
S'ave
-------
180
160
140
120
100
f\)
-.J
o
o 80
w
~ 60
l-
lL.
>- 40
I-
U 20
o
~ 0
>
-20
-40
-60
-80
Exh. Valve Opens (500°)
-100
500 540
580
620
660
.1elocity Estimated
/ " .....-....
I \ /,
. /,
, ~ x,
,,// , ./
'-..... ',,,,,
'1(''''''
Exh. Valve Closes (15°)
700
20
60
100
140
180
Fi~~re 10. Velocity as a function of crankangle.
Engine speed == 600 rpn.
-------
220
200
180
160
140 .
120
u
I.LJ 100
V)
-
~
u..
>- 80
~
f\)
-.:J U
~ 0 60
--'
I.LJ
>
40
Exh. valve opens (5000)
540 580
-40
-60
EXHAUST GAS VELOC ITY
Single cylinder 4 stroke CFR engine
Speed 1000 :t 35 R PM
Spark adv. 130
Dynamometer load 12. 7 Ibs.
Compression ratio 6. 17
Th rott led
I ntake manifold vac. 0.9 in. Hg
140
620
100
Fig1JTe 11. Exhaust gas velocity vs. crankangle. Eugine speed = 1000 rpm.
-------
TABLE V
ENGINE SPECIFICATIONS
(ASTM-CFR Single Cylinder 4-Stroke Spark-Ignition Engine)
Valve Timing
Compression ratio
Bore.
Stroke
Displacement
Speed
Spark advance
4 to 10
3.25 in.
4.50 in.
37.33 in.3
600 :t 6 rpm
13° btdc
LV. O.
LV.C.
10 atdc
34 abdc
40 bbdc
15 atdc
E.V.O.
E.V.C.
plate, witl~ the engine at the selected crankangle position. At the proper
times, the phasing cam on the mirror shaft closed Sl (see Figure 9) for a few
degrees of rotation, while an auxiliary distributor on the engine performed a
similar phasing function by closing Dl. Only when the mirror and engine were
in proper phase would both Sl and Dl be closed simultaneously to trigger the
SCR. In turn, the SCR opened shutter #1 to admit the schlieren image, shutter
#2 to admit the repetitive timing mark signal and closed S2. A short time
later distributor cam D2, which was phased to lag Dl, closed D2 and fired the
strobe light to record the bright single timing mark on the photograph (see
Figure 7). The same strobe, but with S3 in position A, was used to illuminate
the flywheel to get an exact crankangle reading at the time of this strobe
flash.
Figure 7 is a typical photographic result and shows the initial movement
of the exhaust gas as the exhaust valve starts to open. The repetitive timing
marks at the top of the photograph give time intervals of 1/2 msec and the
bright single mark indicates an engine crankangle position of 520°. The total
vertical dimension of the schlieren image corresponds to slightly over 1/2 in.
at the exhaust pipe. The slope of the image at any position gives (6x/6t) or
velocity and the measured result for this photograph shows that the instanta-
neous velocity at 520° crankangle is 59 ft/sec. Similar results over the en-
tire portion of the exhaust cycle were made and the results are shown plotted
in Figure 10.
Figure 11 shows similar results obtained at an engine speed of 1000 rpm.
A peak velocity of approximately 200 ft/sec was observed compared with 160
ft/sec for the engine speed of 600 rpm. This increase of velocity was expected
since mass flowrate increases as engine speed increases. However, the first
flow reversal shown in the curve for 600 rpm was not observed in the latter
test. It is believed that the first flow reversal was due to a pipe elbow
located upstream of the test section and later removed for the test at 1000
rpm. The occurrence of the flow reversal just before the closing of the ex-
Ilrtl11;t vul.v.e was about the ~~a.rne ill both c(j,ses.
2'72
-------
These results show excellent agreement with respect to the opening and
closing of the exhaust valve, give reasonable values for the exhaust velocity,
and show an expected oscillation of the gas flow after the exhaust valve
closes.
.An attempt was made to .obtain an instantaneous schlieren picture of the
exhaust gas flow using a short-duration, high-intensity spark as a light source
replacement for the laser. The objective was to investigate the possible ef-
fects of the secondary flows, created by a pipe elbow just upstream of the test
section, on the flow reversal shown in Figure 10. The effort was not success-
ful due to erratic operation of the spark light source. Later the elbow was
removed with a consequent optical system rearrangement.
2.
The Attempted Measurement of Instantaneous Exhaust Temperature
Having obtained preliminary data on exhaust velocity measurement, studies
were started to consider the system changes required for measuring exhaust gas
temperature. As proposed, exhaust temperatures were to be obtained indirectly
by measuring the speed of spark-induced pressure waves. The speed of sound at
a typical exhaust temperature is of the order of 2000 ft/sec. To obtain rea-
sonable time scales on the schlieren-streak photographs, the required rotating
mirror speeds turn out to be several thousand revolutions per minute. An addi-
tional requirement was that the camera shutter open very quickly so as not to
miss the event. It was also found that when the camera was operated at high
mirror speeds of about 1000 rpm, the camera unit vibrated due to a slight un-.
balance of the rotating mirror and mount. .
To avoid these difficulties, a new method was investigated for detecting
the schlieren image utilizing photbdiodesas light detectors. Instead of the
streak photograph technique, several photodiodes were mounted at the film plane
along the axis of the exhaust pipe image to detect the passage of the schlieren
image of the spark-induced pressure wave. As the pressure wave moves down the
exhaust pipe, its image passes over each of the photodiodes in turn, generathlg
pulses which are displayed on the single sweep of an o~cilloscope. The dis-
tance betweell successive pulses gives the time for passage of the wave over a
Imowll distance and thus gives velocity from (t:.x/t:.t).
The photodiode used in this work was the Hewlett-Packard Pin Photodiode
:;0(32-420) with a response time of less than 1 nsec. The detection circuit and
the dimensions of the photodiode are shown in Figures 12 and 13. This one-
channel amplifier was built to test the feasibility of the new method. The
perliminary test results indicated adequate sensitivity and excellent time re-
sponse. However, the system was found to be extremely sensitive to slight
building vibrations. Efforts to vibration-isolate the system were reasonably
successful, even though some vibration "noise" still appeared on the oscillo-
scope. .
273
-------
PHOTO
D lODE
10M
.200K
10M
lOOK
o LIT
10M
N3251
470K
Figure 12. Photodiode amplifier circuit.
-+
.030.
T
.067
L
.088
fE91
Figure 13. Dimensions. of Hewlett.;.Packard
pin photodiode 5082-4205.
274
\'::.[
c'J
..11..-
+
E9V
+
.::- 9 V
-
-------
Following these initial tests, two more CIW,llIleU; wet'e added I-,l> Lilt,
photodiode-amplifier unit, with the detector photodiodes spaced lilt in. apa,rL.
Time response of each channel was checked using a high frequency strobotac.
The result was excellent, far exceeding the requirements~
The spark electrodes and triggering -circuit for the sound wave generator
are shown in Figure 14.
110 VAC
0-30 KVDC
POWER SUPPLY
VARIAC
20 x 106.0.
0.01 p.f
20KV
SOUND SPARK
TICKLER
SPARK
~
(TO TRIGGER
, SOUND SPARK)
TICKLER
SPARK
GENERATOR
W!DELAY
CIRCUIT
TRIGGERING SIGNAL
FROM ENGINE
Figure 14.
Spark circuit.
Tests on the spark wave form showed good rep~atability in both timing and
wave amplitude. Measurements of the speed of sound in free air at room tem-
peratures were carefully performed in order to determine the radius of the
spark wave at which the speed of the wave approached that of the sound wave.
It was found that the speed of the spark wave becomes identical to the speed
of sound at a distance as close as 3/1:3 in. from the spark electrodes. '
'r,Vpically the exhaust gas temperature ranges from 16000R to 2500oR, and
the pressure is nearly atmospheric except during the blowdown period, so that
, the ideal gas assumption holds with reasonable accuracy. The equation for the
speed of sound for an id eal gas, a = , .J kgRT, was used to convert the meas ured
speed of sound to gas temperature. The specific heat ratio, k, and the gas
constant, R, were obtained from Hottel's combustion chart as functions of the
fuel-air ratio., Figure 15 shows the variation of the speed of sound vs. fuel-
air ratio. ' '
Figure 16 and 17 show the signal of the spark wave. recorded on the scope
while the test section was open to the air at 72°F. The time delay between
two signals was measured to be 9.6 ~sec. The equivalent distance between two
275
.-
"4
~(L
-------
2500
Pure air
4>=0
-
o.
Q)
en
.......
-
~
-
f\)
-.;J
()\
Q
Z
::>
o
en
g, 2000
Q
W
W
Cl.
en
cI> = 0.8
4>=1.0
cI> = 1.2
cI> = 1.4
~ =1.6
1400
1000
1500
2000
TEMPERATURE. OR
2500
3000
Figure 15. Speed of sound in exhaust gas as a function of temperature and equivalence ratio. .
-------
Figure 16. Photodiode signals from velocity of sound
measurements in room air at 72°F.
. '--i
,
- -. r'-'T---r-r--r-'-'----'---
~ . i ! ' i;
.. i ... 'i~:~.i~J'1
~t --111 -h--t.. . ... .~~... ... .1' ~. . +~:=i~~r
-to.. r-~ - iA~--~.-r-.. :. ~..:
.\ --.1-- (-,~~..t' ..L. L_. : . j
".:.._.....t.!'/l'lt.....;._.~.:'.: :f
t tj/" I; : ... - - - , ..
;.1 . , 1 I .
! ~-"'~.1' ..q, .....;--- : .
. :
: ..__LJ___J..-
L-..
Figure 17. Photodiode signals with expanded time scale.
Figure 18. Photodiode signals showing repeatability.
277
-------
~----
photodiodes at the test section was 0.132 in., taking into
magnification factor. The calculated velocity of the a,ir
ft/sec and the measured velocity was 1145 ft/sec.
account the optical.
at 72°F was 1130
,
.,
Figure 18 shows the repeatability of the spark wave. Even though slight
variations in the magnitude of the signal are evident, the main interest in
our measurement was the time delay between the two signals. This difference
was repeatable. .
The spark electrodes were next mounted in the exhaust pipe to determine
the effects of the exhaust gas flow on the spark characteristics. The elec-
trodes were sealed into Norton's alundum thermocouple tubes with Sauereisen
Eiectrotemp Cement Powder No.8. This cement was particularly suitable for
the electric insulation at high voltages and temperatures.
It was found that due to the water vapor in the exhaust gas, the spark
breakdown voltage in the hot exhaust dropped to approximately one third of
that in atmospheric air. As a result, triggering of the spark system became
irregular and the spark intensity was too weak to generate a reasonably sharp
signal.
After several attempts with minimum system changes the problem was solved
by employing a double spark method. In this system, two spark gaps are con-
nected in series by a floating electrode. The spark gap at the high voltage
side, called the '~riggering spark gap," is triggered by a tickler spark lo-
cated outside of the ~xhaust pipe. The second spark gap, the "sound spark
gap," is located in the test section. The sound spark is discharged instantly
when the triggering spark gap 1S ionized by the tickler spark. Good control
of the spark system was possible with this arrangement.
. Subse~uent attempts to measure the sound-wave signal in the
flow were unsuccessful due to the low signal-to-noise ratio, the
from the exhaust eddies, and the building vibrations.
exhaust gas
noise coming
At first, it was thought that the position of t0e test section was af-
fected by the "thermal expansion of the exhaust pipe due to the hot exhaust gas.
This would alter not only the shape of the signal but the sensitivity of the
system. A plain glass window with an adjustable angular position was installed
to allow quick adjustments of the beam direction. Following these adjustments,
it was still not possible to detect useful signals.
Further tests were ma.de by motoring the engine while the engine remained
hot to examine whether or not the exhaust gas itself was the main factor that
caused the difficulty. With the engine motoring, the shape and intensity of
the sound signal appeared to be as good as that obtained in atmospheric air.
Despite.considerable effort to solve the" "noise" problem, the measurement
of exhaust gas temperature using the speed-of-sound method was not successful.
278 "
", ~ .,
-------
Tile sound wave signal could not be detected in the presence of the hot exhaust
'gases. It was concluded that the sound wave signal was obscured by the back-
ground noises which were generated by the density eddies of the exhaust gas
itself. Several checks were made before reaching this conclusion~ Various
optical effects such as the position shift of the test section due to the
thermal expansion' of the pipe, the orientation of the photodiode plate rela-
tive to the location of the spark electrodes, and the position of the knife-
edge, were examined carefully without any success. A high-pass filter circuit
was constructed and used to eliminate the low-frequency signals from the ex-
haust gas.
Since no problems were encountered in detecting the sound wave in still
air or a motored engine, the problem appears to be caused by the exhaust gas
eddies. When the exhaust gas is introduced into the test sectioll, the light
is deflected not only by the sound wave but by the density fronts of the gas
itself.' The magnitudes of these deflections were observed to be approximately
of the same order. Since these two effects are independent of each other, the
net output signal from the combined schlieren effect would be completely
random. Since this is a basic difficulty associated with the measuring tech-
nique itself, further continuation of the work was not pursued.
279
. .
- -. :','j' .~' ~~+~'__i_, ~~~:- :-:..,.-."
-------
DISTRIBUTION LIST
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Copies
Mr. Alan E. Zengel
Assistant Project Manager
Coordinating Research Council, Inc.
30 Rockefeller Plaza
New York, New York 10020
[100
Dr. P. R. Ryason
Chevron Research Company
576 Standard Avenue
Richmond, California 94802
2
Mr. R. J. Corbeels
Research and Technical
Texaco, Inc.
P.O. Box 509
Beacon, New York 12508
1
Department
Dr. E. N. Cantwell
Automotive Emissioni Division
Petroleum Laboratory
E. I. DuPont de Nemours and Company, Inc.
Wilmington, Delaware 19898
1
. Dr. J. B. Edwards'
418-18-22
Chrysler Corporation
12800 Oakland Avenue
Detroit, Michigan 48203
1
Dr. Joseph Somers
Environmental Protection Agency
2565 Plymouth Road
Ann Arbor, Michigan 48105
5
Dr. C. LaPoint
Scientific Laboratory
Ford MotOl' Company
P.O. Box 2053
Dea.rborn, Michiga.n 48121
2
280
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DISTRIBUTION LIST (Concluded)
Contract Distribution
Mr. R. C. Schwing
Research Center Laboratories
Fuels and Lubricants Department
General Motors Corporation
General Motors Technical Center
12 Mile and Mound Roads
Warren, Michigan 48090
Mrs. Mary Englehart
Department of Health, Education, and Welfare
National Air Pollution Control Administration
411 W. Chapel Hill Street
Durham, North Carolina 27701
Internal Distribution
Professor J~ A. Bolt, Dept. of Mech. Eng., Auto. Lab., N.C.
Professor B. carnahan, Dept. of Chern. Eng., East Eng. Bldg.
Professor J. A. Clark, Dept. of Mech. Eng., West Eng. Bldg.
Professor D. E. Cole, Dept. of Mech. Eng., Auto. Lab., N.C.
Professor R. Kadlec, Dept. of Chern. Eng., East Eng. Bldg.
Professor H. Lord, Dept. of Mech. Eng., Auto. Lab., N.C.
Professor J. J. Martin, Dept. of Chern. Eng., East Eng. Bldg.
Professor W. Mirsky, Dept. of Mech. Eng., Auto. Lab., N.C.
Mr. E. Sondreal, Dept. of Chern. Eng., East Eng. Bldg.
Professor D. J. Patterson, Dept. of Mech. Eng., Auto. Lab., N.C.
Project File
Total
281
, ~ ,
No. of
Copies
12
1
1
1
1
1
10
1
1
1
1
2
54
500
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