nitric oxide formation and thermodynamic modeling in spark
TRANSCRIPT
Nitric Oxide Formation and Thermodynamic Modeling inSpark Ignition Engines
by
Matthew J. Rublewski
B.S.M.E., Pennsylvania State University(1998)
Submitted to the Department of Mechanical Engineeringin Partial Fulfillment of the Requirements for the Degree of
Master of Science in Mechanical Engineering
at the
Massachusetts Institute of Technology
February 2000
@ 2000 Massachusetts Institute of TechnologyAll rights reserved
MASSACHUSETTS INSTITUTEOF TECHNOLOGY
SEP 2 0 2000
LIBRARIES
Signature of A uthor ....... .. .......... . . .... . .......................Department of Mechanical Engineering
February 3, 2000
Certified by ............................................................. ........John B.Heywood
Sun Jae Professor of Mechanical EngineeringThesis Supervisor
Accepted by ............................ .......Ame A. Sonin
Chairman, Department Committee on Graduate Students
Nitric Oxide Formation and Thermodynamic Modeling inSpark Ignition Engines
by
Matthew J. Rublewski
Submitted to the Department of Mechanical EngineeringFebruary 4, 2000 in Partial Fulfillment of the Requirements
for the Degree of Master of Science in Mechanical Engineering
ABSTRACT
An assessment of a thermodynamic based cycle simulation's ability to predict steady state engineout NO concentration over a wide range of operating conditions has been conducted. Anexperimental data base, which included measurements of NO concentration, cylinder pressure,and residual gas fraction, was obtained from a 2.0 liter Nissan engine while firing on propane.Using experimentally derived bum rate information, ensuring that the correct total mass andmixture composition is considered, modeling combustion inefficiency effects, and increasing theamount of heat transfer during combustion were all concluded to be necessary for makingaccurate predictions of in-cylinder pressure. Based on experimental data, accounting fortemperature stratification during combustion with a layered adiabatic core routine improved theslope of model predictions in comparison to a fully mixed adiabatic core. With a layered model,the three reaction extended Zeldovich mechanism, alone, was capable of predicting NOconcentration as a function of equivalence ratio, spark timing, and intake manifold pressure towithin 15% accuracy. This was achieved by using a forward reaction rate of 1.66E+12T'.3 forthe first reaction of the Zeldovich mechanism. A sensitivity analysis was performed whichshowed NO predictions to be fairly insensitive to the heat transfer amount and size of the creviceused to model combustion inefficiency. This analysis also confirmed that residual fraction andbum rate are the most critical engine variables for making NO predictions, and indicated thatperforming a kinetic calculation instead of assuming an equilibrium radical pool may furtherimprove model accuracy.
A fast response NO meter was then placed in the exhaust port of the Nissan engine to investigatethe amount of cyclic variation during steady state operation. Cycle resolved values of NO weredetermined by mass weighting the fast NO signal over the shifted exhaust valve open period.Under light loads, lean conditions, and EGR operation, NO concentration was shown to correlatealmost linearly with peak pressure. However, NO variation increased with engine load. Thelarge amount of observed high load scatter was attributed to mixture non-uniformity effects anderror introduced by the single point measurement. By using bum rate, alone, as an input variable,the previously calibrated cycle simulation was capable of following general trends in the cycle bycycle NO data.
Thesis Advisor: Professor John B. HeywoodTitle: Sun Jae Professor of Mechanical Engineering
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Acknowledgments
Its over, and I want to sincerely thank many people.
It has been a pleasure to have Professor John Heywood as a supervisor. I would like tothank him for picking up a student and project in progress, and for providing expert adviceand guidance during all of our meetings. I would also like to thank Professor SimoneHochgreb for giving me the opportunity to come to MIT and for providing good directionin the early stages of this thesis. Professor Wai Cheng also provided many helpfulsuggestions.
I thank God for my office mate Jim Cowart, without him I would not have had a prayer offinishing this work. He is a gifted person who truly cares about others; I hope to becomemore like him. Thanks to Brian Corkum for being an outstanding technician who taughtme a great deal about engineering and provided many a good lunch; the lab has not beenthe same since he left. Special thanks to Mark Dawson, Gary Landsberg, and ChrisO'Brien for their direct help with my project, and to John Baron for his support of mycycling career. I would also like to say thank you to all the members of the Sloan Lab whoserved with me for their friendship and help in various ways.
I would like to thank the members of the MIT Engine and Fuels Consortium for theirfinancial support of my two years of work at MIT.
Finally, I would like to thank the following very important people: My parents for theircontinued love and support. Chet and Mona for their steady advice and for alwayswelcoming me at their home away from MIT. Kate for being there for me in the beginning.
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TABLE OF CONTENTS
L IST O F T A B L E S ............................................................................................ 7
L IST O F FIG U R E S ......................................................................................... 8
CHAPTER 1 INTRODUCTION........................................................................... 111.1 Role of Oxides of Nitrogen, NOx, in Air Pollution ...................................... 111.2 Role of Automotive Industry in Overall NO Emission and Control.................... 121.3 Background on NO Formation and Modeling ............................................. 121.4 P revious W ork ................................................................................. 141.5 Structure of T hesis ............................................................................ 161.6 Steady State Modeling - Objectives ......................................................... 161.7 Cycle by Cycle NO Variation - Objectives ................................................ 17
CHAPTER 2 EXPERIMENTAL METHOD ............................................................. 212.1 Experimental Test Matrix ................................................................... 212 .2 T est E ngine .................................................................................. . . 222.3 M ixture Preparation .......................................................................... 232.4 Cylinder Pressure Measurement ............................................................ 242.5 C ylinder Pressure A nalysis .................................................................... 262.6 Residual Fraction Predictions ................................................................. 27
2.6.1 Residual Measurement with Atmospheric CP Chamber ..................... 282.6.2 Residual Measurement with CP Chamber Under Vacuum .................. 292.6.3 Verification and Extension of Limited Experimental Data .................. 30
2.7 N O M easurem ent ............................................................................... 32
CHAPTER 3 MODELING METHOD ................................................................... 453.1 Modeling Approach .......................................................................... 453.2 Cycle Simulation General Description ..................................................... 463.3 Valve Flow Sub-Model ........................................................................ 473.4 Combustion Sub-Model ..................................................................... 483.5 Heat Transfer Sub-Model ................................................................... 483.6 Combustion Inefficiency Sub-Model ....................................................... 493.7 NO Formation Sub-Model ................................................................... 513.8 Temperature Profiles within NO Sub-Model ............................................. 52
3.8.1 Fully Mixed Temperature Profiles .............................................. 533.8.2 Unmixed / Layered Temperature Profiles ...................................... 55
CHAPTER 4 STEADY STATE MODELING RESULTS & DISCUSSION ...................... 654.1 Model Calibration Approach................................................................ 654.2 V alve Flow C alibration ........................................................................ 664.3 Heat Transfer and Crevice Calibration ..................................................... 68
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4.4 Calibration of Kinetic Routine ............................................................. 704.5 Load Sweep Modeling Results ............................................................. 724.6 Equivalence Ratio Sweep Modeling Results .............................................. 734.7 Exhaust Gas Recirculation Sweep Modeling Results ..................................... 754.8 Spark Timing Sweep Modeling Results ................................................... 76
CHAPTER 5 SENSITIVITY ANALYSIS ............................................................... 875.1 Effect of Adding N20 Mechanism ........................................................ 875.2 Effect of Considering the Residual NO Concentration .................................. 895.3 Upgrade to Full Equilibrium Calculation ................................................... 905.4 Kinetically Controlled Radical Pool Investigation ....................................... 925.5 General Sensitivity Analysis ................................................................. 95
5.5.1 Variables of Uncertainty - Residual, Heat Transfer, Crevice Size ............ 955.5.2 Input Parameter Perturbation ...................................................... 985.5.3 NO Sub-Model Variables ........................................................ 1005.5.4 Fully M ixed Sensitivity .......................................................... 100
5.6 Summary and Conclusions - Steady State Modeling .................................... 101
CHAPTER 6 CYCLE BY CYCLE NO VARIATION - STEADY STATE OPERATION..... 1136.1 F ast N O M eter N otes ........................................................................ 1136.2 Signal Characteristics During Lean Operation - PHI=0.914 ........................... 1146.3 Processing the Fast NO Exhaust Data ..................................................... 115
6.3.1 Signal Characteristics as a Function of Load .................................. 1156.3.2 Plug Flow Modeling of the Exhaust Event .................................... 116
6.4 Three Different Methods of Determining a Cycle Resolved NO Value ............... 1176.4.1 Analysis of Three Methods for MAP = 0.5 bar , PHI=0.91 .................. 1186.4.2 Analysis of Three Methods for MAP = 0.8 bar, Stoichiometric ............ 1196.4.3 Analysis of Three Methods for MAP = 0.5 bar, Stoichiometric ............ 120
6.5 Load Sweep Cycle by Cycle Variations ................................................... 1206.6 Cycle by Cycle NO Variation - EGR, Equivalence Ratio, and Spark Sweeps ....... 122
6.6.1 E G R Sw eep ........................................................................ 1226.6.2 L ean O peration ..................................................................... 1246.6.3 Rich Operation and Spark Sweep ............................................... 124
6.7 Cycle by Cycle Bum Rate Modeling ...................................................... 1256.7.1 Load Sweep CBC Modeling ..................................................... 1256.7.2 Lean and EGR Points - CBC Modeling ........................................ 127
6.8 Observations and Recommendations ...................................................... 127
B IB L IO G R A PH Y .......................................................................................... 139
A P PE N D IC E S ............................................................................................. 143
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LIST OF TABLES
Table 2.1: Experimental Operating Conditions ....................................................... 21Table 2.2: Nissan SR20DE Specifications ............................................................ 22Table 2.3: Experimentally Measured Residual Fraction with Atmospheric Sampling ........... 29Table 2.4: Experimentally Measured Residual Fraction with CP Chamber held at 0.46 bar .... 30Table 2.5: Assumed Residual Mass Fraction Values - Load Sweep ............................... 32Table 2.6: Assumed Residual Mass Fraction Values - PHI, EGR, and Spark Sweep ............ 32
Table 3.1: Cycle Simulation Input Variables ........................................................... 58
Table 4.1: Model and Experimental Comparison of IMEP -1500 rpm , $ = 1.0, Load Sweep ............................................................ 65
Table 4.2: Model and Experimental Comparison of Air and Residual Fraction1500 rpm, $ = 1.0, Load Sweep........................................................... 66
Table 4.3: Comparison of Recommended Rate Constants for Reaction 1,N + N O = N 2 + O ........................................................................... 71
Table 5.1: Percent Difference between SENKIN and Simulation Predicted-L ayer N O P rofiles .............................................................................. 94
Table 5.2: Input Parameter Sensitivity Analysis - Load Points .................................... 96Table 5.3: Input Parameter Sensitivity Analysis - Lean and EGR Points ........................ 97
Table 6.1: Comparison of Different Methods for Calculating a Cycle Resolved NO Value -0 .5 b ar - L ean ................................................................................. 1 18
Table 6.2: Comparison of Different Methods for Calculating a Cycle Resolved NO Value -0.8bar - Stoichiom etric ..................................................................... 120
Table 6.3: Linear Correlation Analysis Results for Cyclic NO Concentration -P eak P ressu re ................................................................................. 123
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LIST OF FIGURES
FigureFigureFigure
FigureFigureFigureFigureFigureFigureFigureFigureFigureFigureFigureFigureFigureFigureFigureFigure
1.11.21.3
2.12.22.32.42.52.62.72.82.92.102.112.122.132.142.152.16
Figure 2.17
FigureFigureFigureFigureFigureFigureFigureFigureFigure
3.13.23.33.43.53.63.73.83.9
- Photochemical Smog Formation Time Scales and NOx Ozone Cycle .............. 18- Major Sources of Smog Formation Pollutants ....................................... 18- In-cylinder Strategies for Reducing Engine Out NO Emissions .................... 19
- Pressure Transducer Experimental Location - Side View ............................ 35- Pressure Transducer Experimental Location - Top View............................ 35- Motoring Log P - Log V Correct Phasing with Respect to Volume ............... 36
- Motoring Log P - Log V 1' Off in Phasing with Respect to Volume .............. 36- Investigation of Cylinder Pressure Accuracy ......................................... 37- Experimentally Derived Burn Rate with Wiebe Function ........................... 37- Fast Flame Ionization Detector Experimental Set-up ................................. 38- Residual Fraction Measurements with Atmospheric CP Chamber .................. 38- Residual Fraction Measurements with CP Chamber Held Under Vacuum ........ 39- Cyclic V ariability of Residual Signals .................................................. 39- Experimentally Measured Valve Lift for Nissan Engine ........................... 40- N issan V alve O verlap Period .......................................................... 40- Comparison of Experimental Residual Data Sets and Correlation ................ 41- SAE 982046 Ford Residual Data Sets for Equivalence Ratio and EGR ........... 41- Schematic of Cambustion Fast NO Meter Sampling System ...................... 42- Steady State Experimental Engine Out NO -
Load and Equivalence Ratio Sweeps ................................................. 43- Steady State Experimental Engine Out NO -
EGR and Spark Tim ing Sweeps ......................................................... 43
- Modeling Approach Flow Chart .........................................................- Thermodynamic Representation of Cylinder Contents ...............................- Cycle Simulation Valve Flow Discharge Coefficient Map ...........................- NO Sub-model Temperature Profile Options ..........................................- Fully Mixed Temperature and Boundary Layer Profiles ..............................- Fully Mixed NO Concentration Profiles ................................................- Unmixed / Layered Temperature Profiles ..............................................- Unmixed / Layered NO Concentration Profiles .......................................- Comparison of Layered and Fully Mixed Temperature Profiles ....................
575960606161626263
Figure 4.1 - Uncalibrated Model NO Predictions - Load Sweep .................................. 77Figure 4.2 - Uncalibrated Model IMEP Predictions - Load Sweep ................................ 77Figure 4.3 - Baseline Operating Condition Pressure Trace Analysis -
Uncalibrated Model Comparison ...................................................... 78Figure 4.4 - Uncalibrated Model Air and Residual Fraction Predictions - Load Sweep ........ 78Figure 4.5 - Baseline Operating Condition Pressure Trace Analysis-
Correct Charge Mass and Composition ............................................... 79Figure 4.6 - Baseline Operating Condition Pressure Trace Analysis-
Heat Transfer and Crevice Effects ..................................................... 79
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Figure 4.7 - Baseline Operating Condition Pressure Trace Analysis-Fully Calibrated Model Comparison ................................................... 80
FigureFigure
Figure
Figure
Figure
Figure
Figure
Figure
Figure
FigureFigure
Figure
4.8 - Calibrated Model Heat Transfer Predictions - Load Sweep ........................ 804.9 - Calibrated Model IMEP and Peak Pressure Predictions -
L o ad S w eep ............................................................................. .. 8 14.10 - Calibrated Model IMEP and Peak Pressure Predictions -
Equivalence R atio Sw eep .............................................................. 814.11 - Load Sweep Modeling Comparison with k1=3.3E+12T 3 -
1500rpm - P H I = 1.0 ..................................................................... 824.12 - Equivalence Ratio Sweep Modeling Comparison with k1=3.3E+12T'.3 _
1500rpm - M A P = 0.5bar ................................................................ 824.13 - Final Load Sweep Modeling Comparison with k1=1.66E+12T03 -
1500rpm - P FH = 1.0 ..................................................................... 834.14 - Amount of NO Reduction After Factor of 2 Adjustment to ki -
Layered A .C . - Load Sweep ............................................................ 834.15 - Final Equivalence Ratio Sweep Modeling Comparison with k1=1.66E+12T03 -
1500rpm - M A P = 0.5bar ................................................................ 844.16 - Amount of NO Reduction After Factor of 2 Adjustment to kI -
Layered A.C. - Equivalence Ratio Sweep ............................................... 844.17 - Comparison of Layered Model Predictions with Previous Work .................. 854.18 - Final EGR Sweep Modeling Comparison with k1=1.66E+12T0 3 -
1500rpm - PH I = 1.0 ..................................................................... 854.19 - Final Spark Sweep Modeling Comparison with ki=1.66E+12T0.3 _
1500rpm - PH I = 1.0 ..................................................................... 86
Figure 5.1 - Effect of Adding N20 Mechanism - Equivalence Ratio Sweepwith ki=1.66E+12TO3 -1500 rpm - MAP = 0.5bar................................... 104
Figure 5.2 - Effect of Adding N20 Mechanism - Equivalence Ratio Sweepwith k1=1.5E+12T0 3 - 1500 rpm - MAP = 0.5bar.....................................104
Figure 5.3 - Overall Effect of Adding N20 Mechanism - All Sweeps ........................... 105Figure 5.4 - Amount of Residual NO Concentration in Unburned Mixture - Load Sweep.....105Figure 5.5 - Effect of Modeling Residual NO Concentration - Load Sweep .................... 106Figure 5.6 - Overall Effect of Modeling Residual NO Concentration ........................... 106Figure 5.7 - Baseline Operating Condition Thermodynamic Property Analysis -
Burned Zone Temperature Comparison .............................................. 107Figure 5.8 - Baseline Operating Condition Thermodynamic Property Analysis -
Burned Zone Specific Heat and Gamma Comparison .............................. 107Figure 5.9 - Baseline Operating Condition Thermodynamic Property Analysis -
Burned Zone Enthalpy and Density Comparison..................................... 108Figure 5.10 - Layered Model A.C.Temperature Profiles - Baseline Operating Condition ...... 108Figure 5.11 - Constant Enthalpy Combustion Process from Tunburned = 850K -
1500rpm - Stoichiometric - M AP =0.5bar..............................................Figure 5.12 - Cycle Simulation and SENKIN NO Profiles for Selected Layers - 0.5 bar ......Figure 5.13 - Cycle Simulation and SENKIN NO Profiles for Selected Layers - 0.3 bar ......Figure 5.14 - Cycle Simulation and SENKIN NO Profiles for Selected Layers - 0.8 bar ......
109109110110
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5.15 - Cycle Simulation and SENKIN NO Profiles for Selected Layers - Lean ......... 1115.16 - Cycle Simulation and SENKIN NO Profiles for Selected Layers - EGR ......... 111
FigureFigure
FigureFigureFigureFigureFigureFigureFigureFigureFigure
FigureFigure
Figure
Figure
Figure
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FigureFigureFigure
6.1 - Fast NO Meter Sampling System Specifications .....................................6.2 - Fast NO Detector Output for Five Consecutive Cycles - 0.5 bar - Lean ..........6.3 - Cycle by Cycle Modeling Comparison - Layered A.C. - 0.5 bar - Lean ..........6.4 - Exhaust Port NO Signal Variation with MAP ...........................6.5 - Cycle Simulation Calculated Exhaust Mass Flowrate Profiles ....................6.6 - Exhaust Port NO Profiles for Five Consecutive Cycles - 0.5 bar - Lean .........6.7 - Exhaust Port NO Profiles for Five Consecutive Cycles - 0.8 bar ..................6.8 - Exhaust Port NO Profiles for Five Consecutive Cycles - 0.3 bar ..................6.9 - Cycle by Cycle Variation of Exhaust Port NO with Peak Pressure -
L o ad S w eep ..............................................................................6.10 - Different Techniques for Determining Cycle Resolved NO Value ...............6.11 - Cycle by Cycle Variation of Exhaust Port NO with Peak Pressure -
E G R S w eep ..............................................................................6.12 - Cycle by Cycle Variation of Exhaust Port NO with Peak Pressure -
L ean O peration ...........................................................................6.13 - Cycle by Cycle Variation of Exhaust Port NO with Peak Pressure -
L ean O peration cont. ....................................................................6.14 - Cycle by Cycle Variation of Exhaust Port NO with Peak Pressure -
R ich O p eration ...........................................................................6.15 - Cycle by Cycle Variation of Exhaust Port NO with Peak Pressure -
S p ark S w eep ..............................................................................6.16 - Individual Cycles Selected for Modeling Comparison - Load Sweep .............6.17 - Cycle by Cycle Modeling Comparison - Layered A.C. - Load Sweep ............6.18 - Cycle by Cycle Modeling Comparison - Layered A.C. - Lean - EGR ............
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CHAPTER 1
INTRODUCTION
1.1 Role of Oxides of Nitrogen, NOx, in Air Pollution
Nitric oxide and nitrogen dioxide, has been studied and regulated extensively since
the 1950s and for good reason. Two harmful components of spark ignition engine exhaust,
unburned hydrocarbons (HG) and nitric oxide (NO), are responsible for the formation of
low level ozone which is also known as photochemical smog. Figure 1.1 gives a good
general description of the time scales involved with smog formation. During summer
months, the morning rush hour traffic can lead to high concentrations of NO and HC in the
lower atmosphere. When the midday sun provides the necessary ultraviolet light, NO is
quickly oxidized to NO 2 with the aid of available HC. Finally, NO 2 leads to the formation
of low level ozone according to the reaction mechanism next to figure 1.1. One last
requirement for smog formation is an extended period of stagnant air conditions which
allows the necessary reactions to take place before the pollutants are dispersed. Weather
patterns can also dictate where the low-level ozone will end up, since smog formed in
highly populated areas can be carried hundreds of miles down wind.
Low-level ozone, PAN, and other oxidizing species can be harmful to architecture,
are responsible for millions of dollars of crop damage yearly, and have devastated large
forest areas in the past. For people, smog can irritate the eyes and extended exposure can
lead respiratory problems. Therefore the risk groups include anyone who spends a
significant amount of time outdoors in problem areas during summer months, such as
young children, outdoor workers, joggers, and cyclists. The environmental protection
agency has defined unhealthy levels of ozone as greater than 0. lppm and, in recent years,
has developed online monitoring services to check air quality during summer months
everywhere in the country. [1]
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1.2 Role of Automotive Industry in Overall NO Emission and Control
Figure 1.2 details the major sources for the two smog formation pollutants. The
automotive industry is responsible for approximately half of the total NO emitted into the
environment. In most major cities, the NO contribution from motor vehicles easily
exceeds 50%, and the vast majority of those vehicles are powered by spark ignition
engines. This does not mean that automobiles today are not extremely clean; it is more a
volume issue now because of the shear number of vehicles in operation, over 150 million
in the United States alone. Consider that a vehicle is producing over 4g/mile of engine out
NOx prior to catalyst after treatment. In 1973, the first regulations of NOx were set at
3g/mile. In California today an Ultra Low Emission Vehicle is required to emit less than
0.2g/mile over its lifetime. Tier II regulations set to take affect for all vehicle
manufactured after 2004, would require vehicles in California to emit less than 0.05g/mile
of NO over the first 50,000 miles of operation. Two orders of magnitude reduction is quite
an engineering task.
In reaction to the first wave of regulation, the automotive community was doing
extensive research in the early 1970s to understand and control NO formation at the source,
in the cylinder. The amount of research on NO related topics, in recent years, has been on
a slight decline, mainly due to the effectiveness of three way catalyst after treatment
advances. On a modern vehicle, a cold catalyst can convert over 95% of the engine out
NOx. Once the catalyst has warmed up after a few minutes of operation, over 99% of the
NOx is successfully converted along with converting HC and CO at the same time.
However, the catalytic converter does require engine operation that cycles around the
stoichiometric amount of fuel, and this limits overall engine fuel economy.
1.3 Background on NO formation and Modeling
Although the catalyst is very effective at meeting the regulations of today,
controlling NO production in the cylinder will continue to be a concern as design strategies
aim at tier II levels. Whenever, a fuel is burned and flame temperatures exceed 1800K a
significant amount of the nitrogen present in atmospheric air will start to become oxidized.
Zeldovich [2] was the first to recognize and model the NO formation process in 1946, and
12
research done at MIT in the early 1970s by Lavoie, Keck, and Heywood [3] completed the
reaction scheme known as the extended Zeldovich mechanism shown below.
N+NO * >N2+O
N+02 >NO+O
N+OH 3 >NO+H
By making a few assumptions, which will be discussed in detail later, about the state of the
cylinder gases after the flame has passed, NO concentration levels can be calculated from a
single in-cylinder temperature profile. The level of NO concentration will be a function of
the cylinder temperatures and the amount of available oxygen. The only way to limit the
amount of oxygen in the cylinder would be to run under fuel rich conditions. Though, this
is not an option since HC concentration would grow substantially.
Therefore, controlling NO formation in the cylinder, becomes as simple as limiting
the temperature of the burned gases during combustion and expansion, without running
rich. The most dramatic effect can be seen when the engine is forced to operate under lean
conditions. As the engine goes slightly lean, NO concentration reaches a maximum since
temperatures are still high and more oxygen is now available. However, if the mixture can
be reduced to fuel air equivalence ratios of approximately 0.7, flame temperature drops
substantially and NO concentration can be reduced by an order of magnitude. Lean
operation today is limited by an available catalyst that can operate while being fed steady
lean exhaust products. Based on the current conversion efficiency, it would not be helpful
to reduce NO concentration by one order of magnitude without a catalyst, if three way
catalysts can reduce stoichiometric NO concentration by two orders of magnitude.
Another method of limiting NO concentration is by increasing the amount of
burned gases present in the intake mixture by recirculating a fraction of the exhaust back
into the intake manifold; this control strategy is known as exhaust gas recirculation, EGR.
Burned gas present during combustion increases the thermal capacity of the burnable
mixture, thus reducing overall flame temperatures. If the level of EGR is increased to
approximately 20% of the incoming fresh mixture, NO reduction can again approach an
order of magnitude. In addition, this strategy allows the three way catalyst to be used,
since it does not significantly change the stoichiometry of the exhaust gases. The effect of
13
lean and EGR operation on NO concentration was illustrated nicely by Blumberg and
Kummer [4] in an early fundamental work. Even without EGR, the unburned mixture
always has some burned gas present due to residual gases from the previous cycle. This
natural EGR is mainly a function of engine load and will be discussed extensively in this
study. One final strategy commonly used to reduce NO concentration while not affecting
the catalyst operation is to retard the spark timing from its maximum brake torque (MBT)
point. This will effectively move the fuel heat release process out of phase with the piston
compression process, reducing peak pressures and corresponding temperatures. However,
all of the above mentioned strategies come at the sacrifice of combustion stability and
engine performance, so the challenge of controlling NO is not at all simple. Figure 1.3
presents a preview of experimental data that illustrate the changes in NO concentration
seen with the above mentioned parameters.
Since emission regulations will force NO concentration to always be one of the
most critical design parameters to meet, effective computer models must be available to the
automotive industry. By using a model to predict NO concentration and performance
accurately as a function of operating conditions instead of doing extensive dynamometer
testing, new engine design and control methods can be explored much faster and at a
fraction of the cost. The availability of accurate computer simulations is also a valuable
tool to the large number of researchers working in the area of exhaust after treatment.
1.4 Previous Work
NO formation and modeling in spark ignition engines has being studied in detail for
the past four decades, and the amount of published work is immense. Therefore only a
brief discussion of the previous work that has shaped this thesis directly will be discussed
now. Two investigations at MIT by Poulos and Heywood [5] and McGrath [6] laid the
foundation for the modeling predictions shown later in this thesis. Poulos originally
developed the quasi-dimensional MIT cycle simulation for the purpose of investigating the
effects of combustion chamber geometry on bum rate, but the main structure of the model
still remains although several minor changes have occurred over time. McGraths main
focus was to investigate the effect of engine crevices on NO predictions. This work also
14
developed a representation of the burned gases that combined both a thermal boundary
layer and a model for temperature stratification. However, the McGrath study was limited
by not having a detailed enough experimental data set to validate the model with. In
addition, several minor errors in handling the mass balance of the crevice routine and
calculating the temperature profiles of the stratification model clouded the conclusions of
the study. Regardless, the work of McGrath marked an excellent starting point for this
investigation.
Ford Motor Company has published two recent papers [7,8] that deal with accuracy
of NO predictions from thermodynamic based cycle simulations such as the one used at
MIT. Both of these papers were published during the course of this thesis and three main
conclusions were drawn. First, Fords cycle simulation was predicting NO concentration
nearly 25% lower than experimental data under lean operating conditions. Therefore, the
NO chemistry considered was extended from the three reaction Zeldovich mechanism to
over seventy reactions in order to improve lean operation accuracy. Secondly, the reaction
rate used for the first reaction of the Zeldovich mechanism had to be adjusted by a factor of
five over the load range in order to obtain good agreement with experimental data. Finally,
an investigation of modeling predictions of residual gas fraction was performed and
correcting cylinder charging errors improved the NO concentration predictions as well. It
was unclear if a model for temperature stratification was used in these studies, and the
effect of engine crevices was neglected.
Two papers, both with collaboration by Stone, were also consulted extensively
during the course of this thesis. First, in 1995, Raine and Stone [9] demonstrated that
using a layered representation of the cylinder gases during combustion improved the NO
predictions from a relatively simple engine simulation. Recently in 1999, Ball, Stone, and
Collings [10] used a similar model to make predictions of cycle by cycle NO concentration
measured with a fast response NO detector. This worked attempted to model combustion
inefficiency based on the estimated mass fraction burned calculated from a pressure trace
heat release analysis code. However, both of these studies gave few details concerning
model calibration techniques and considered a limited range of engine operating
conditions.
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1.5 Structure of Thesis
Discussion will begin with a presentation of the specific objectives of this project.
From there, the work will be presented in five additional chapters. Chapter 2 gives an
overview of the experimental test matrix. Chapter 3 presents the important features of and
assumptions made by the cycle simulation used to generate the modeling results in this
thesis. Chapter 4 details the steady state model calibration methodology used to accurately
represent of the thermodynamic state of the gases. This chapter will then explore the
reaction rate constants used with the extended Zeldovich mechanism, and a comparison of
modeling results and experimental data will be presented and discussed. Chapter 5 will
conclude the steady state modeling section after a detailed sensitivity analysis is performed.
Finally, Chapter 6 will present an initial investigation of NO cyclic variability while
operating under steady state conditions. This chapter will attempt to explain the cycle by
cycle trends observed in fast NO meter data by applying the earlier modeling results. Then,
the thesis will end with some brief conclusions and recommendations for future work in
the area of cyclic variability.
The main focus of this thesis throughout will be to investigate the ability of
thermodynamic cycle simulations to predict, both average and cycle by cycle, engine out
NO concentration over a wide range of operating conditions. The specific objectives of
this thesis can be summarized as follows:
1.6 Steady State Modeling - Objectives
" develop an experimental data base that effectively covers the entire operating range ofthe spark ignition engine and includes accurate measurements of cylinder pressure andmixture composition
* develop a model calibration methodology to determine whether the challenge ofpredicting NO concentration is primarily a thermodynamic or chemistry problem. Thenan assessment of the completeness of the extended Zeldovich mechanism alone will bemade after confidence in model predictions of cylinder pressure and temperature isgained
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* complete a sensitivity analysis that will explore the limitations of the current MIT cyclesimulation, identify which model components are potential sources of error, andidentify which engine variables are most critical for predicting NO concentration
1.7 Cycle by Cycle NO Variation - Objectives
* demonstrate the amount of NO cycle by cycle variation over the complete range ofoperating conditions considered in the steady state modeling discussion
* develop an appropriate data analysis method to be used for determining a cycleresolved value of NO concentration based on the output signal of the fast NO meterplaced in the exhaust port
* apply what was learned from the modeling results and sensitivity analysis to explain theobserved trends in cyclic NO data
17
NOx - Ozone Cycle
N02+hv ->NO+O
0+02+M -03+M
03+ NO--N02+02
hv- - N02 -- > 03, PANoxidizing species
Figure 1.1: Photochemical Smog Formation Time Scales and NOx Ozone Cycle
Sources of NOxSources of VOC - HC
Consumer Solvents5%
Figure 1.2: Major Sources of Smog Formation Pollutants
18
NOHC
hv
(a) Lean Operation
E%%0,
0z
0()C
0).C
2000-
1500 "
1000_-
500
0
MHigher Dilution
2000E
CL 15000z3 100000
500
0
0.6 0.8 1.0 1.2 1.4 0 5 10 15 20
Equivalence Ratio %EGR
Figure 1.3: In-Cylinder Strategies for Reducing Engine Out NO Emissions
19
M aM
- Lean
M
U
N
N
.
wM
w U
I I
(b) EGR Operation
-
20
CHAPTER 2
EXPERIMENTAL METHOD
2.1 Experimental Test Matrix
Because NO formation is highly dependent on in-cylinder temperatures and
pressures, an experimental test matrix had to be developed that would cover most of the
parameters affecting burned gas temperature. The review of previous work done in the
area indicated that equivalence ratio, spark timing, and burned gas fraction are the key
parameters affecting in-cylinder temperatures. The last of these can be considered in two
different ways, either residual fraction alone or residual plus exhaust gas recirculation
(EGR). The main parameter affecting residual fraction is engine load or intake manifold
absolute pressure (MAP) because of backflow effects, which will be discussed later.
The baseline operating condition was chosen to be 1500 rpm with MAP equal to
0.5 bar, because this is close to what the auto-industry considers to be a typical part load
operating point. Speed was not considered in this study because it should have only minor
effects on temperature through time available for heat transfer, and the single cylinder
setup of the test engine gave a limited speed range. This leaves four independent sweeps of
equivalence ratio, MAP, EGR, and spark timing which all revolve around the baseline
operating point: 1500 rpm, stoichiometric, MAP = 0.5 bar. Table 2.1 shown below
characterizes all of the experimental test points in more detail. It should be noted that the
engine was fully warmed up and fired on propane for all test points. Aside from the spark
sweep, the timing was optimized for maximum brake torque (MBT). MBT was defined as
the timing which yielded maximum IMEP. This corresponds well with peak pressure
location between 13' and 15' ATDC, and maximum heat release rate location near
70 ATDC.
Table 2.1 Experimental Operating Conditions
Engine Speed 1500 rpmSpark Timing Optimized for MBT
FuelType PropaneCoolant Temperature 75 - 800 C
21
2.2 Test Engine
All experiments were performed on a Nissan SR20DE production four cylinder
spark ignition engine. The engine was designed with a pentroof combustion chamber, four
valves per cylinder, and a centrally located spark plug. Complete technical specifications
are listed below in Table 2.2.
Table 2.2 Nissan SR20DE SpecificationsEngine Type 4 valve/cylinder DOHC
Aluminum Head/BlockDisplacement / Cylinder (cm3) 500
Clearance Volume (cm3) 58.77Bore x Stroke 8.6 x 8.6
Compression Ratio 9.5Intake Valves Open 130 BTDC
(34 mm Diameter/ 10.2 mm Max Lift) Close 235' ATDCExhaust Valves Open 4830 ATDC
(30 mm Diameter / 9.4 mm Max Lift) Close 7230 ATDCValve Overlap Period 160
The engine was modified to fire on a single cylinder, prior to this study, to make
mixture preparation and exhaust gas analysis easier to interpret. To accomplish this, the
intake manifold has been modified so that three of the intake runners are sealed off from
the plenum and vented to the atmosphere. This allows fuel and air from the throttle to only
enter the first cylinder for combustion. The exhaust manifold runner for the firing cylinder
has also been isolated from the other three and attached to a ten gallon damping tank before
reaching a trench. The fuel/air ratio was monitored at all times with a Horiba, Model
22
Load 0.33, 0.4, 0.5, 0.6, 0.9 bar
($= 1.0)Equivalence Ratio, $ Rich 1.25, 1.12, 1.06, 1.00
(MAP = 0.5 bar) Lean 0.96, 0.91, 0.84, 0.77, 0.71Spark Timing Retarded 50, 100
(MAP=0.5 bar, $ = 1.0) Advanced 50, 100, 150, 200EGR 4%, 8%,12%,16%
(MA P=0.5 bar, $ = 1.0)
MEXA-I10 ,universal exhaust gas oxygen sensor, which was mounted approximately 10
cm downstream of the exhaust port. Engine coolant flow and temperature are controlled by
an external pump, water heater, and heat exchanger unit. This gave precise control of the
engine block temperature and allowed preheating to take place prior to experimental runs.
An external oil cooling circuit was also used to maintain the oil sump temperature at
approximately 750 C for all experiments.
The Nissan engine is coupled to a 100HP Dynamatic dynamometer which is
capable of motoring the engine or absorbing the output while firing. Because of the intake
manifold design, three of the four cylinders are motoring at all times. Therefore, even
while firing on one cylinder, the engine load must increase to approximately 70% of
maximum to overcome the friction of the other three and switch to absorption on the dyno.
Regardless of load however, the engine speed was maintained with a Digalog controller.
The distributor has also been modified, and a separate custom ignition system was used for
the active cylinder.
2.3 Mixture Preparation
The engine air supply was monitored with a Kurz, model 505-9A, air mass flow
meter and is displayed in units of grams per second. Since the instrument had not been
calibrated since its installation, verification experiments were performed using a Meriam
laminar flow element connected in series with the Kurz meter. The two methods showed
agreement to within 3% over the range of engine operation studied. The engine test cell
environment was not controlled, therefore intake air temperature and humidity level varied
day to day in the laboratory. For all of the experimental data sets shown later, the intake air
temperature, measured just after the throttle body, ranged from 23' to 28' C and relative
humidity levels, measured in the test cell, ranged from 25% to 40%. A discussion of
humidity and intake air temperature effects on NO emissions will be held until Chapter 4.
To avoid liquid fuel effects and limit mixture non-uniformity, the engine was fired
with propane as the fuel for all experiments. The port fuel injectors were removed from
the manifold and properly sealed. A continuous flow of propane was introduced to the
back of the intake runner, approximately 30 cm upstream of the intake valves. The amount
23
of fuel supplied was determined with the aid of a critical flow orifice. As long as the ratio
of the manifold pressure to supply pressure was larger than 0.522, the flow of propane
through the orifice has reached sonic velocities, and mass flow is only a function of the
upstream supply pressure. The calculation of propane mass flow in grams per second is
shown in the equation 2.1 below:
d mprpndm r n = Psupply VyR TA eff (Eq. 2.1)
This flow rate was also verified off the engine using a soap film bubble test setup. The
final test of whether the fuel and air flow rates were accurate was based on a comparison
with the average air fuel ratio readout from the oxygen sensor.
Finally, for several test points, EGR was simulated with a mixture of 83% N2 and
17% C02, by volume, and introduced continuously into the intake manifold after the
throttle body, at the entrance to the plenum. This mixture composition was chosen based
on a method detailed by Hinze [11], because it has approximately the same molar heat
capacity as natural exhaust gas, only without water vapor. EGR mass flow rates are
typically described as percent of ingested mass according to equation 2.2 below:
M EGR% E GR = MEGR + Mpropane + Mair (Eq. 2.2)
Again the flow was regulated with critical flow orifices and ranged from 4% to 16% of the
total ingested mass. The artificial EGR was left at room temperature for ease while
performing the experiments. Since the upcoming modeling analysis takes EGR
temperature as an input, this will not lead to any modeling discrepancies.
2.4 Cylinder Pressure Measurement
Cylinder pressure was measured with a side-mounted Kistler 605 1B piezoelectric
pressure transducer located in the engine head approximately 1 cm above the travel of the
piston. The transducer sensor sits in a cylindrical crevice with an approximate depth of
6mm and a diameter of 3mm. Figures 2.1 and 2.2, illustrate the location of the transducer
from a top and side view. An output signal from the transducer was sent to a Kistler model
5010A dual mode charge amplifier and then sampled by a pc based data acquisition
24
system. Pressure data was recorded at 1 degree intervals using the output from a 360'
degree per revolution optical shaft encoder as an external trigger. An additional reference
flag at BDCC was also recorded from a combination of the shaft encoder pulse and cam
shaft position sensor.
In order to get an absolute pressure measurement from a piezoelectric transducer,
the pressure signal must be pegged to the manifold pressure at some point in the cycle. For
all experiments, the voltage at BDCC was set equal to the average intake manifold pressure
obtained from a Data Instruments, model SA, absolute pressure sensor. This is the
recommended procedure used by Ford Motor Company for low speed operation [12].
Before and after gathering all experimental data sets, the pressure transducer was calibrated
with a dead weight tester to verify linearity and sensitivity, in bar per volt, over the
pressure range of 0 to 40 bar.
Several authors have also addressed the subject of cylinder pressure data integrity,
in particular peak pressure and phasing with respect to volume. Both Kenney et al. [12]
and Lancaster et al. [13] recommend plotting motored log P vs. log V to verify that the
compression and expansion strokes are linear and have polytropic exponents between
(1.30 - 1.42) and (1.33 - 1.45) respectively. Figure 2.3 shows a plot of volume vs. pressure
on a logarithmic scale generated from the ensemble average pressure trace while motoring
the engine at 1500 RPM with intake pressure of 0.5 bar. The polytropic exponents were
1.34 for compression and 1.42 for expansion which is within the expected range, and the
sharpness of the point at which they meet is indicative of correct phasing with respect to
volume. Figure 2.4 illustrates the effect of even a one degree shift in the phasing. These
plots further confirm the accuracy of the test set-up because a crossover is seen near TDC
when advanced, and the sharpness of the point is lost when retarded. A final verification
of proper phasing is to check that the maximum pressure while motoring the engine occurs
approximately 1 degree BTDC. For the test point discussed above, the average peak
pressure location for 150 cycles was 179.3' ABDC.
In addition to phasing errors, Ford motor company also recommends periodically
checking the transducer for thermal shock effects while firing. In a paper by Stein et al.
[14], thermal shock or strain was defined as a reduction of measured peak pressure and
25
IMEP due to cyclical exposure of piezoelectric transducers to high temperature combustion
gases. This thermal strain was shown to cause a reduction in peak pressure of 1.5% at
1500rpm, WOT, while the effect was much smaller at part load.
To verify measured peak pressure, tests were performed at 0.5 bar and 0.8 bar using
a fiber optic, Optrand Model C81255-SP, spark plug mounted transducer at the same time
as the side mounted Kister 6051. Figure 2.5 shows a comparison of the two pressure traces
for three consecutive cycles at 1500 rpm, 0.5 bar MAP. Excellent peak pressure
agreement, less than 1% difference, was observed at both 0.5 bar and 0.8 bar. However,
the accuracy of the Optrand spark plug transducer was poor during the intake and exhaust
stroke, which prevented its use alone. It should also be reiterated that the highest load
point observed in this study was 0.8 bar MAP, and a majority of the experimental points
were taken at 0.5 bar MAP, where the effects of thermal strain should be small. The
pressure transducer used was also recessed slightly from the head, as shown previously in
figure 2.1. This should allow it to operate at cooler temperatures than a flush mounted
transducer.
2.5 Cylinder Pressure Analysis
For each individual test point, two data files were collected containing 150 cycles
of cylinder pressure each. These data files were processed using the MIT Burn Rate
Analysis code, which is based on a general heat release program originally developed by
Gatowski et al. [15] and Chun et al. [16] and later modified by Chueng and Heywood [17].
This program uses a simple one zone energy model which includes the effects of engine
crevices and heat transfer to the cylinder walls. Gamma values for propane are fitted by
linear functions of charge temperature during compression and expansion but are assumed
to be constant during combustion, as set by Chueng. With these approximate gamma
values, the rate of chemical energy release can be determined from the measured in-
cylinder pressure with equation 2.3 shown below:
dQchem _ y -1 dV 1 dp dQcrev dQht= p + V + + E 23)dO y ~dO y - dO dO dO (Eq2.3
26
Output of the bum analysis program includes peak pressure with location, IMEP,
and total mass fraction burned for each individual cycle, as well as, summary statistics,
ensemble pressure trace information, and mean polytropic exponents. For all the
experimental operating conditions, the polytropic exponents, while firing, ranged from
(1.26-1.32) for compression and (1.30- 1.32) for expansion. This further confirmed the
integrity of the pressure data according to Kenney et al. [12].
In addition to these parameters, equation 2.3 can be used to calculate the amount of
fuel that must be burned at each crank angle to match the heat released. These values can
then be normalized to the total mass fraction burned to give the following bum angles: 0-
2%, 0-10%, 0-50%, and 10-90%. Since the modeling analysis requires bum rate as an
input, the parameters of the burn profile wiebe function are specified for a good match with
the experimental bum angles. A sample plot of the bum angles from the baseline operating
condition, and the corresponding wiebe function equation are shown in figure 2.6. A more
detailed discussion of the Wiebe function will be held until the MIT cycle simulation is
discussed next chapter.
2.6 Residual Fraction Predictions
Quader [18] and Aiman [19] both showed the dramatic effect of charge dilution on
NO formation in spark ignition engines. However, because sampling in-cylinder gases
prior to the flame arrival is a difficult experiment, little data exists on residual fraction as a
function of operating conditions. When this project was started, there was no published
experimentally measured residual fraction data for a modem dual overhead cam four valve
engine. However, one of the major works done on a two-valve engine was performed at
MIT by Galliot et al. [20], and later Fox et al. [21] developed a theoretical model for
predicting residual fraction as a function of operating conditions. Since a four valve engine
had never been studied, experiments were conducted following the method demonstrated
by Galliot in 1990.
Galliot's method involves using a Cambustion fast flame ionization detector (FFID)
to measure in-cylinder hydrocarbon concentration just prior to spark discharge. A relative
comparison to the HC concentration while motoring the engine is then made to determine
27
the residual fraction. Since this technique has been documented before in many papers
[20,22], only a brief description of the sampling method will be given here.
2.6.1 Residual Measurement with Atmospheric CP Chamber
Figure 2.7 shows a schematic of the sampling system used along with a table of
sampling specifications. The FFID acts as a carbon atom counter that produces a voltage
that depends upon both hydrocarbon concentration and the mass flow rate of the sampled
gas. A continuous stream of gas was pulled from the cylinder using a small sampling
probe, which was design to go through a Kister 6051 pressure transducer blank. This was
done to avoid drilling an extra hole in the engine head. Since the cylinder pressure is
fluctuating greatly throughout the cycle, the sample must be sent to an expansion tube,
which is contained within a constant pressure (CP) chamber that is vented to the
atmosphere. A fraction of the flow exiting the expansion tube is then pulled through a tee-
piece into the hydrogen-air flame (see figure 2.7 again). The pressure difference across the
tee-piece is fixed at 0.14 bar. Therefore, the mass flow rate into the flame is held constant
regardless of the driving pressure in the cylinder, and the output voltage is only
proportional to the sample HC concentration.
An illustration of the three typical FFID signals needed for the residual fraction
measurement along with corresponding pressure traces are shown in figure 2.8, and a
discussion of each trace will now begin. Looking at the firing trace, it can be seen that
once the cylinder pressure rises above CP chamber atmospheric pressure, the hydrocarbon
concentration rises as fresh mixture is brought into the cylinder and mixes with the left
over residual gases. The trace attempts to reach a plateau level before the flame reaches
the tip of the sampling probe, causing the voltage to drop sharply back to zero. Because of
the short plateau level, it was necessary to skip fire the engine or disable the spark once
every 15 cycles to obtain a longer plateau level. Looking at the skip fired trace, it is seen
that without the arrival of the flame, a longer plateau is observed until the cylinder pressure
drops back below atmospheric pressure resulting in a back flow in the sampling line. This
skip fired plateau level now represents the HC concentration of the cylinder gases with
residual present.
28
The final piece needed for a residual fraction measurement is a calibration voltage
level corresponding to the HC concentration of the cylinder gases with no residual fraction
present. This is accomplished by motoring the engine for several minutes to allow all of
the residual gas to be purged from the cylinder, leaving only a fresh mixture of propane and
air. The calibration trace appears very similar to a skip fired trace. However, it now
reaches a higher plateau since no residual gas is present. Finally, the molar residual
fraction can be determined from the voltage difference between the calibration trace and
the skip fired trace, according to equation 2.4 shown below. Galliot showed that this molar
residual fraction is approximately equal to the residual mass fraction to within 4%.
Vmotored - VskipfiredXresidual 1 - Vmotored (Eq. 2.4)
Using the method described above, experiments were performed while varying the
intake manifold pressure, since MAP is the major parameter affecting residual fraction
level. Four of the five load points were observed between 0.33 and 0.6 bar MAP, but the
highest load point could not be taken because the single cylinder setup did not allow skip
firing to occur above 0.6 bar. At each load point, 100 cycles of motoring data were
recorded, and 300 cycles of skip firing data were collected. The experimental residual
value was then determined from the average motoring plateau level and the average of the
20 skip fired cycles, according to equation 2.4. Table 2.3, shown below, summarizes the
limited data set recorded under these sampling conditions. It should also be noted that day
to day variation or repeatability of this data set was approximately +/- 15%.
Table 2.3: Experimentally Measured Residual Fraction with Atmospheric Sampling
MAP (bar) 0.33 0.40 0.50 0.60Residual Fraction % 19.6 15.5 13.4 11.1
2.6.2 Residual Measurement with CP Chamber Held Under Vacuum
Earlier attempts at measuring residual fraction were performed with a different
sampling system. For this data set, the CP chamber was held under vacuum at 0.46 bar and
the volume of the CP chamber was increased by 1 liter to dampen out pressure fluctuations.
By keeping the CP chamber under vacuum, there will be forward flow from the cylinder
29
for a much longer portion of the cycle. This results in a longer plateau and skip firing was
not deemed to be necessary at the time. The motoring calibration technique was kept the
same.
Figure 2.9 shows the two typical FFID signals needed for the residual fraction
measurement, without skip firing, along with corresponding pressure traces. Figure 2.10
shows the typical cycle by cycle variation observed with this technique for five consecutive
cycles. From these two figures, it can be seen that the signals have the same general
characteristics that the atmospheric sampling system produced for the firing case.
However the motored trace appears different because there is always a forward flow of gas
from the cylinder. It should also be noted that since skip firing was not as necessary with
this technique, a high load point could be obtained in addition to the four low points
already observed above. Equation 2.4 can again be used to calculate residual using the
average of all 300 fired cycles instead of the skip fired traces as before. Table 2.5 shown
below lists the data set collected in this earlier attempt. The residual data had repeatability
to within 15% with this technique also.
Table 2.4: Experimentally Measured Residual Fraction with CP Chamber held at 0.46 bar
MAP (bar) 0.33 0.40 0.50 0.6 0.9Residual Fraction % 17.5 15.8 14.1 11.8 10.2
2.6.3 Verification and Extension of Limited Experimental Data
To verify the limited experimental data shown above for the load sweep, and to
extend the data set for the equivalence ratio, EGR, and spark timing sweeps, a review of
other papers containing measurements of residual fraction was performed. The load sweep
will be discussed first.
One major work done to measure residual fraction as a function of load on a
modem four valve engine was done by Miller et al. [8] at Ford Motor Company in 1999.
Miller took experimental measurements of residual fraction as a function of MAP,
equivalence ratio, EGR, and spark timing using a fast sampling valve technique. The
engine used in the study was a four cylinder two liter engine with a pentroof chamber, dual
30
overhead cams, and a 200 overlap period. Referring back to table 2.2, this is almost
identical to the Nissan engine used in this study, so the results should be directly
comparable. The Fox correlation based on the Galliot data set was adjusted to match the
Nissan four valve geometry and was also used for a comparison over the load sweep.
Equation 2.5 shown below summarizes the Fox correlation:
___.87 0.3-0.74- O F pi - .7rT:-i+0.6 32 pi-07
Xr = 1.266 N ( i + ( e) (Eq. 2.5)
By calculating the overlap factor for the Nissan engine, equation 2.5 can be used to predict
residual fraction as a function of intake pressure.
Fox defined overlap factor according to equation 2.6 shown below:
D A + D AeOF = V (Eq. 2.6)disp
IV=EV EVC
with Ai- = Lj-dO and Ae= fLe -dOIVO IV=EV
Since the displacement volume and the diameter of the valves is known, the only
measurement needed was valve lift as a function of crank angle. A static measurement on
the Nissan engine was performed for both the intake and the exhaust valves, and the results
are shown in figure 2.11. Figure 2.12 is a zoom in on the overlap period to show explicitly
how the two valve areas are calculated. For the Nissan engine the overlap factor was then
calculated to be 0.22 '/m.
A comparison of the Ford data set, the fox correlation, and the two different
experimental data sets measured on the Nissan engine is shown in Figure 2.13. Reasonable
agreement was observed between experimental data sets and the Fox correlation. The one
high load point observed begins to deviate from the expected trend, possibly due to
experimental error or back pressure effects. For ease during the upcoming modeling
analysis, whole number residual estimates were made for the five load points based on
Figure 2.13, and the final values are summarized below in table 2.5.
31
Table 2.5: Assumed Residual Mass Fraction Values - Load Sweep
MAP (bar) 0.33 0.40 0.50 0.6 0.8Residual Fraction % 19 16 14 12 10
EGR, equivalence ratio, and spark timing have all been shown to have only modest
effects on residual gas fraction [23,8]. Since, Miller is the only author who studied a four
valve engine, extrapolation of the residual fraction value at 0.5 bar MAP were based off of
his data sets (see Figure 2.14). The residual values assumed for the remainder of the
experimental matrix is summarized below in table 2.6 below. A sensitivity analysis will be
performed in Chapter 5 to explore how residual fraction errors will affect NO predictions.
Table 2.6: Assumed Residual Mass Fraction Values - PHI, EGR, and Spark Sweep
Equivalence Ratio 1.252 1.12 1.06-0.914 0.838 0.77-0.71Residual Fraction % 15 14.5 14 13.5 13
E.G.R. 0 4 8 12 16Residual Fraction % 14 17.5 21 24 27
Spark Timing + 10 +5 MBT -5 -15 -20Residual Fraction % 13.5 13.5 14 14.5 14.5
2.7 NO Measurements
NOx emissions include both nitric oxide (NO) and nitrogen dioxide (NO 2).
However in spark ignition engines, the ratio of N0 2/NO is very small, and NO2 is assumed
to be negligible in comparison. Therefore, experimental measurements of NO
concentration are only considered and modeled in this study. The most well established
technique used for measuring NO concentration in exhaust gases is chemiluminescence.
With this technique, dried exhaust gas is mixed with a controlled flow of ozone which
reacts with the NO in the sample to form NO2. The chemical reaction between NO and
ozone then produces energy in the form of light proportional to the NO concentration,
which can be amplified and measured with a photomultiplier.
Until recent years chemiluminescence could only be used for steady state
measurements with a resolution time of several seconds. Cambustion has now developed a
sampling system (Fast NOx meter, FNO) based on the FFID that can measure changes in
32
NO concentration with a response time of approximately 4 ms [24,25]. The Fast NO meter
allows cycle by cycle measurements to be made during each exhaust event which lasts 27
ms at 1500 rpm. Figure 2.15 shows a schematic of the FNO meter sampling system, and
the similarities to the FFID, shown previously in figure 2.9, are obvious. A sampling probe
is attached to an expansion tube that is contained in a constant pressure chamber held under
vacuum at 0.46 bar. A tee piece is then connected to the end of the expansion tube for
taking a small fraction of the exhaust gases up into the reaction chamber. In the reaction
chamber, the exhaust gases are mixed with a flow of ozone, and a fiber optic cable then
picks up the light emission from the reaction and carries it to a remote photomultiplier.
For this experimental work, two different measurements were required, steady state
average engine out NO concentration, and cycle by cycle exhaust port NO concentration.
The steady state measurement will be used to validate MIT's cycle simulation over the
range of engine operation, and the exhaust port NO values will be used to investigate and
understand the amount of NO cyclic variation. To remain consistent, the Fast NO meter
was used for both of these measurements even though the extra speed is not a requirement
for measuring steady state NO. The steady state measurements were taken from a 10
gallon damping taken located downstream of the exhaust port. The details of the exhaust
port measurement technique and signal analysis will be saved for chapter 6, after the steady
state results are discussed.
The same sampling probe was used for both measurement types. The probe had an
overall length of 250 mm and an inside diameter of 0.6mm. A resistive heating unit was
also used to keep the probe temperature at approximately 120 'C and to avoid water
condensation. It should be noted that no sample drier is used in the Fast NO sampling
system. Since water vapor adversely interferes with the NO and ozone chemical reaction
light emission, Cambustion recommends a 0.5% increase in NO concentration for every
1% of water vapor present in the exhaust sample [26]. To estimate water vapor
concentration as a function of operating conditions, a correlation from Heywoods text was
employed [23]. Finally, a calibration of the Fast NO meter was performed outside the
engine before and after gathering each data set, by introducing a 1000 ppm and then a 5000
ppm mixture of NO and nitrogen, to the front of the sampling probe. The instrument was
33
zeroed with a pure mixture of nitrogen. Negligible drift in the calibration and zero values
was observed during all experiments.
Figures 2.16 and 2.17 show the four steady state NO sweeps of MAP, equivalence
ratio, EGR, and spark timing. It should be re-emphasized that the baseline operating
condition, 1500 rpm - 0.5 bar MAP - Stoichiometric - MBT, appears in all of the
experimental sweeps. A discussion of each sweep will occur along with model
comparisons in Chapter 4. Appendix A contains a more detailed listing of experimental
results in spreadsheet form.
34
mM
Piston #4@ TDC
Recession = 6 mm +---+
Figure 2.1: Pressure Transducer Experimental Location - Side View
~ -
pressure transducer or FFID
Figure 2.2: Pressure Transducer Experimental Location - Top View
35
X
e Kitler6051 3
101
0-)
CL LO
10.E10
Figure 2.3: Motoring
1' Advanced Phasing101
03na):3
a)
0~a)
~ 10~U
102Cylinder Volume (cc)
10 3
Log P - Log V Correct Volume Phasing1500rpm - 0.5bar
1 Retarded Phasing
101
(D
0,
U
102Cylinder Volume (cc)
102Cylinder Volume (cc)
Figure 2.4: Motoring Log P - Log V 10 Error in Volume Phasing1500rpm - 0.5bar
36
N
I IV
10 3 10
L.(U.0a)I..
(0(0a)L.0.I...a)VC
0
25-
20-
15-
10-
5-
0Li0
- Kistler 6051 - Side MountedFiber Ontic - Spark Mounted
U500
I1000
'I
1500 2000
Crank Angle Acquired
Figure 2.5: Investigation of Cylinder Pressure Accuracy
100-
90-80-70-
60-50-40-
30-20-
10-
0
n Experimental Burn Angles
- Fitted Wiebe Function
I
500
Vb = 1- exp[-9.2 0 j50)
100 150 200
Oasp - Crank Angle after Spark (deg)
Figure 2.6: Experimentally Derived Burn Rate with Wiebe Function
37
.0
*0
U)
(UM.
MI
I
IaI
FID Flame Chamber
Ion Collector-
FID Bleed
Vacuum
CP Bleed
r Sample Tube I.D. 0.254 mmTee Piece I.D. 0.200 mm
Sample Tube Length 122 mm
Fampling'robe
Pisto@ T
CP Chamber
n #4DC
Figure 2.7: Fast Flame Ionization Detector Experimental Setup
8--
7-
6--
5-
4-
3 -
2-
12
24
I
Ia Low LoadI. Motoring Calibration
-- -
Molar Residual S- Fraction .' 'Skip Fired
Trace
- Firing Trace
290 340 390 440 490
-25
-. 20
- 15
a--10
k 5
0
540
Crank Angle Acquired
Figure 2.8: Residual Fraction Measurements with Atmospheric CP Chamber
38
0)
CD
L
I
0
Mi
7 --- 20
66
5 15>(
4
cc 10
2 -- 51 0
240 340 440 540
Crank Angle
Figure 2.9: Residual Measurements with CP Chamber Held Under Vacuum
8 -- 30
-- 25'
202
4-- 15
9 3 -- -10 C
u2 - 111- 2 -5
240 340 440 540
Crank Angle
Figure 2.10: Cyclic Variability of Residual Signals
39
a - 25
.** 0
C'.* U
* U
0
*
e
Exhaust Valv
U
U
U
U
Intake Valvee
0
00
r" i I I M
580 680 780 880
Crank Angle
Figure 2.11: Experimentally Measured Valve Lift for Nissan Test Engine
0.30 -
0.25 -
0.20 -
0.15 -
0.10 -
0.05 -
0.00
Ivc
Ai Ae
EVC
700 705 710 715 720 725 730
Crank Angle - TDC = 720
Figure 2.12: Nissan Valve Overlap Period
40
12 -
10 -
E
-
8
6-
4-
0*0
*
U
U
U
U
S
S
00
0
2
0
U
UU
U
480
N
980
E.
EI
0.25 --
0.20-
0.15 --
0.10--
0.05 -
0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
Intake Manifold Pressure - MAP (bar)
Figure 2.13: Comparison of Experimental Residual Data Sets and Correlation
251
201+
. I I I
.8 1 1.2
PHI
1.4 (0
0
35
30
25
20
15
10
5
0
-i
-I I I I0 5 10 15 20 25
% EGR
5
00 10 20 30 40 50
Spark Advance (deg)
Figure 2.14 SAE 982046 Ford Residual Data Sets for Equiv. Ratio and EGR
41
Fox Correlation- -- - - Ford Data Set - SAE 982562
. CP Chamber - ATM PressureA CP Chamber under Vacuum
SI I I I
a0
0L.U-
0.00
15(0
0
0 0
10 +
5
00.6 0
25
20 -
:2(00
6
0
0
0
a
15
10
* *
Reaction chamber
Sam SeIn
CP chambr CLSamT
Ozone in
Optic-fibre Gas in'putS
CP VAC
D Remotepling Head
Figure 2.15: Schematic of Cambustion Fast NO Meter Sampling System
42
,2000 -E0-
- 1500 -0z3 1000 -
0
. 500-CwU
U
No
U
0.E.
0z
0
C0)Cw
0
0
0
3000--
2500--
2000--
1500--
1000--
U
0.6 0.8 1.0 1.2 1.4
Equivalence Ratio
Figure 2.16: Steady State Exp. Engine Out NO - Load and PHI Sweeps
0z
0(DC
U 0)m EC
' ' ' ' wmI I I I
3000
2500
2000
1500
1000
500
00 5 10 15 20
% EGR
UE
0E
"0
-
10 15 20 25 30 35 40 45
Spark Timing
Figure 2.17: Steady State Exp. Engine Out NO - EGR and Spark Sweeps
43
0
N
E
500 -
04-0.2
00
0
N
0.4 0.6 0.8
MAP (bar)
2000
1500Ea0z
0t:;O
)
C
N1000 -
500 -
0- -
44
CHAPTER 3
MODELING METHOD
3.1 Modeling Approach
In order to gain useful information from a comparison of experimental data and
model output, it is necessary to describe in detail how the modeling results were generated.
One of the specific objectives of this study was to understand whether the primary
difficulty in predicting engine out NO concentration is a thermodynamic problem or a
chemistry problem. Therefore, a modeling approach was designed to investigate each of
these independently. In particular, a great deal of effort was put into making accurate
predictions of in-cylinder pressure and temperature before predictions of NO concentration
were considered. Figure 3.1 visually describes the modeling approach used to generate
comparisons of experimentally measured NO and model output.
Following the top half of the flow chart, the first box represents the variables that
can easily be measured on the Nissan test engine. Through data analysis, an accurate
picture of the thermodynamic state of the cylinder gases throughout the engine cycle can be
gained and is represented by the variables shown in the second box. Following the bottom
half of the flow chart, the first box represents the main inputs that are typically feed to an
engine cycle simulation. Prior to making a meaningful prediction of NO concentration,
one must compare how well the cycle simulation has done in modeling the thermodynamic
state of the gases. In particular crevice, heat transfer, and valve flow sub-models must be
properly calibrated to ensure that the correct composition and amount of mass is being
considered and that the gases are being subjected to the correct pressure history. Finally,
once the thermodynamic modeling is accurate, a meaningful prediction of NO can be
made, and an analysis of the chemical kinetics can follow.
The modeling study performed here was done with a modified version of the MIT
Quasi-Dimensional Cycle Simulation that was originally developed and documented by
Poulos and Heywood in 1982 [5]. Because a significant number of changes have been
made over time, a brief description of the simulation's current status and sub-models will
now follow to aid the reader in understanding the modeling predictions shown later.
45
3.2 Cycle Simulation General Description
The MIT cycle simulation is a zero dimensional, two zone thermodynamic model
that solves a set of twenty differential equations derived mainly from the conservation of
mass, energy, and the ideal gas law for each of the four main engine processes: intake,
compression, combustion/expansion, and exhaust. Chapter 14 of Heywoods text [23] gives
a good general description of this type of spark ignition engine model. Figure 3.2 gives a
visual description of how the cycle simulation is set up including a crevice volume. The
simulation gets the name quasi- because it utilizes a geometry routine that can calculate the
position of the flame front with respect to the combustion chamber, by assuming the flame
develops as a sphere anchored at the spark plug electrode.
At each crank angle of the 720 degree cycle, the in-cylinder pressure, unburned gas
temperature, and burned gas temperature are calculated and assumed to be spatially
uniform. The unburned gases are assumed to be a uniform mixture of fuel, air, and
residual, and their thermodynamic properties are calculated from polynomial curve fits to
the JANAF tables. During combustion, the burned gas thermodynamic properties are
determined using a method developed by Martin and Heywood [27]. This method,
developed for saving numerical time, uses an approximation to equilibrium properties, and
all of the modeling results shown in Chapter 4 were calculated using the Martin routine.
The effect of using Sandia's full equilibrium code, STANJAN, instead of this
approximation will be discussed in Chapter 5. Finally, during the exhaust process, when
the temperature drops below 1800K and dissociation is no longer important, the burned
gases are again assumed to be a uniform mixture and thermodynamic properties are
obtained from JANAF table curve fits.
Table 3.1 shown at the end of the chapter contains a list of the input variables
required by the cycle simulation. It should be noted that the pressure and temperature at
IVO must be specified to start the routine. The simulation then goes through the entire
cycle and compares the state of the gases at the end of the cycle with the initial guess made.
If the values are not in agreement, the end state is used for a second iteration and so on
until the cycle simulation converges on a steady state solution.
46
3.3 Valve Flow Sub-Model
Flow through the intake and exhaust valves is modeled as a one dimensional
compressible flow according to equation 3.1 and 3.2, for choked flow, shown below.
- - 1/2S C DA ,efP o P T 1/y 2 y PTr( -
m - J 1 ri- --- )0 (Eq. 3.1)
* C DA rejP0 K 2 N ('~2 (l _____(R= ) 1 1 y C + with Aref -- (Eq. 3.2)M (R To) 1/ + 14
The mass flow is a function of the pressure ratio across the valve and the effective (CD)
discharge coefficient. Since the reference area used by the cycle simulation is a constant,
based on the inner seat diameter of the valves, the discharge coefficient must be a function
of crank angle. Figure 3.3 shows the assumed value of the discharge coefficient map as a
function of crank angle used by the cycle simulation. This map was experimentally
determined for a Ford engine, but it had to be used for this study because no discharge
coefficient information was available from Nissan. This is one possible source of error in
the cylinder charging process routine.
Also, since the pressure in the cylinder at IVO is approximately equal to the exhaust
port pressure (-1.01bar), there is a large amount of blowback when the engine is throttled.
This means that residual gases will flow from the cylinder up into the intake manifold until
the pressure in the cylinder drops below the intake manifold pressure. During this period,
the model assumes that the residual gases are in a plug flow, and that no heat transfer or
mixing takes place in the intake manifold. Therefore, all of the residual gases that flow
into the intake manifold return to the cylinder at the same temperature, before any fresh
mixture can enter. In reality, under highly throttled conditions, the blowback process
would be a vigorous flow with a significant amount of mixing and heat transfer taking
place. Those assumptions add another source of modeling error.
However, the focus of this thesis was not to improve the valve flow sub-model of
the cycle simulation. So, rather than attempting to model the blowback process and
calibrate the discharge coefficient map, it was decided to force the model to ingest the
47
correct amount of fuel, air, and residual. This procedure will be explained in detail
when the model calibration procedure is discussed next chapter.
3.4 Combustion Sub-Model
Once the cylinder has been charged and compressed, the combustion process is
started at the specified spark timing. At this time, the gases are divided into an unburned
zone and a burned zone, with a fixed combined mass. The flame is assumed to propagate
through the unburned gases as an infinitely thin sheet which leaves behind burned gases in
chemical equilibrium. The transfer of mass from the unburned to the burned zone is
controlled by the Wiebe function which is shown below in equation 3.3.
F (-Ospark N +Xb = 1-exp - ay A sur ) j (Eq. 3.3)(A Burn)
The constant, a, exponent, m, and the burn duration are determined from the heat release
analysis burn angles as was described in Chapter 2. By using the Wiebe function, burn rate
is eliminated as a variable and possible source of modeling error.
3.5 Heat Transfer Sub-Model
During the entire cycle, convective heat transfer takes place between the cylinder
gases and the combustion chamber component surfaces. As was shown in Table 3.1, the
component temperatures are taken as inputs to the model and assumed to be fixed
throughout the cycle. The final variable needed to model heat transfer is a heat transfer
coefficient between the cylinder gases and the surfaces. Heat transfer coefficients were
calculated from the well accepted Woshni Correlation, which does not require any
turbulence model. The Woshni heat transfer coefficient is a function of the mean piston
speed and the state of the cylinder gases according to equation 3.4 shown below.
hc(w / m2K) = Ci(3.26)Bore(m) 0 2 P,, (kpa)0" T(K)~05 3 W(m / s)0. (Eq. 3.4)
W(m / s) = f ( MeanPistonSpeed , DisplacementVolume, Pvc, Tvc,Vic)
48
00MII-
head = 380 K
Burned gases
Unburned gases
Tpion =420 K
During intake, compression, and
assumed to be at a uniform temperature.
calculated for each different component.
zones, each at a uniform temperature, as
The variable named C1 is a calibration constant
which will be used next chapter for making
accurate predictions of in-cylinder pressure.
With the heat transfer coefficient known, the
amount of heat lost to the component surfaces
can easily be calculated according to equation
3.4 shown below:
Q=hAon,(Tzone- Tcom) (Eq. 3.4)
exhaust all of the gases are in one zone and
Therefore three components of heat loss are
During the combustion process, there are two
is illustrated in the figure shown above. Since the
flame is assumed to be a sphere anchored at the spark, the geometry routine is able to
calculate the contact area between the two zones and the three components. Then, six
components of heat loss are calculated. It should be noted that no heat is exchanged
between the unburned and burned gases during combustion, and radiative effects are
neglected.
3.6 Combustion Inefficiency Sub-Model
In a firing spark ignition engine, a small percentage of the mass trapped inside the
cylinder will escape the normal combustion process either due to blowby (leakage past the
piston and valves), flame quenching at the wall, or by being trapped in crevices. This
absence of burnable mixture will cause a reduction in peak pressure and corresponding
temperatures. Therefore, this combustion inefficiency must be modeled to make accurate
predictions of engine out NO concentration.
Blowby in well designed modern engines is usually less than one percent of the
inducted mixture, so crevices have a larger effect on in-cylinder pressure. Crevices are
small volumes in the combustion chamber which the flame can not propagate into, such as
the piston top land, head gasket area, and pressure transducer tap. The flow of cylinder
49
gases into and out of these crevice regions is a function of the cylinder pressure, as shown
in equation 3.5 below:
-c e(Eq. 3.5)( V )
As the cylinder pressure increases, mass is packed into the crevice. After peak pressure,
gas flows from the crevices back into the combustion chamber.
The total volume of all the known engine crevices is generally assumed to be a few
percent of the clearance volume. However, since this trapped gas is in direct contact with
the combustion chamber surfaces, crevice gas temperature is much lower than the average
cylinder temperature during combustion. This means that a small crevice volume can hold
as much as 6-8% of the in-cylinder mass at the time of peak pressure due to the density
effect. In reality, the composition of the gas in the crevices is a mixture of both unburned
and burned gas, with the relative percentage of each depending on in-cylinder motion and
the location of the spark plug.
The model used for combustion inefficiency in this study was based on a crevice
model initially developed by McGrath [6]. The McGrath thesis gives a complete
derivation of the cycle simulation equations needed when using the crevice model.
However, mass initialization and accounting errors during combustion clouded the
conclusions reached in that study. At this time, only the major assumptions of this sub-
model will be discussed. The size of the total crevice volume was set equal to 2.2% of the
cylinder clearance volume (see model calibration section in Chapter 4) and was assumed to
remain fixed for all operating conditions. The location of this crevice volume is assumed
to be entirely around the piston top land. This will allow the geometry routine to easily
determine where the flame is in relation to the crevice. The pressure in the crevice is the
same as the cylinder pressure, and the temperature was assumed to remain constant
regardless of the operating conditions as defined by equation 3.6 shown below.
Trevice 2 Twaii (Eq. 3.6)
Several things about this simple model will lead to a large deviation from what
actually occurs with real engine crevices. First, since the flame propagates as a perfect
sphere and all of the volume is located at the piston top land, no burned mixture reaches
50
the crevice before peak pressure with a centrally located spark plug. After peak pressure,
the flow will only be out of the crevice. Therefore, all of the gas in the crevice will remain
unburned regardless of operating condition. Also the temperature of the crevice and thus
the effective size, would fluctuate with operating conditions (e.g. higher loads with slightly
higher component temperatures). Thus, it should be noted that this is not intended to be a
crevice model but rather an overall combustion inefficiency model which accounts for the
all of the effects (blowby, crevices, and flame quenching) that reduce cylinder pressure.
Also, the effect of varying the size of the crevice will be studied in the final sensitivity
analysis presented in Chapter 5.
3.7 NO Formation Sub-model
There are essentially four formation mechanisms for NO in combustion processes:
thermal, N20, prompt, and fuel bound. Since propane was used for all experiments in this
study, there is no nitrogen in the fuel and fuel bound NO can be eliminated immediately.
Prompt NO refers to the formation of NO in the flame zone. However, in spark ignition
engines, the combustion process occurs at high pressure, and the flame can be assumed to
be thin. Therefore residence times within the flame zone will be short, and the contribution
from the prompt mechanism can be assumed to be small in comparison to NO formed in
the post flame gases. This leaves the thermal (extended Zeldovich) mechanism and the
N20 mechanism. One of the main objectives of this study was to determine whether the
challenge of predicting NO was primarily a thermodynamic or chemistry problem. In light
of the recent modeling work done by Ford [7,8], a more specific objective along these lines
was to verify whether the extended Zeldovich mechanism alone was accurate enough to
predict NO formation, once the thermodynamic routines were calibrated. For this reason
only the thermal mechanism will be used in the modeling study, and a discussion of the
N20 mechanism will be held until the sensitivity analysis section in Chapter 5.
It is well established that the main pathway to NO formation in high temperature
fuel-air combustion applications is by oxidation of atmospheric nitrogen in the post flame
gases. Zeldovich was the first to study this process [2], which is commonly referred to as
the thermal mechanism, and he proposed equations 3.6 and 3.7 as the principal reactions.
51
This reaction set was later extended by Lavoie, Keck, and Heywood with equation 3.8 [3]
to give the complete extended Zeldovich mechanism shown below.
N+NO - >N2+O (Eq. 3.6)
N+0 2 2 >NO+O (Eq 3.7)
N+OH 3 >NO+H (Eq. 3.8)
The forward rate constants for each of these reactions have been measured
experimentally, however the accuracy of the measurement is only known to within a factor
of 2. The reaction rates used for the initial model assessment were taken from a recent
study done by Miller and Bowman [28] and are listed below:
ki = 3.3E+12 T'2 k2 = 6.4 E+9 T e-3 160/T k3= 3.8 E+13
From equations 3.6 through 3.8, expressions for the rate of change of NO and N can be
made after calculating reverse reaction rates as well, and the complete derivation was
shown in other works [6,23]. By making the assumption that N atom formation has
reached steady state and assuming the radical pool in the post flame gases has reached
chemical equilibrium, a single differential equation that describes the formation of NO by
the thermal mechanism can be written as in equation 3.9 shown below.
d[NO] 2R1{1 - ([NO] / [NO]e) 2 }dt 1 + ([NO] / [NO]e)Ri / (R2+ R3) (Eq. 3.9)
with Ri ki[ NO]e[ N]e R2 = k2[02]e[N]e R3 = k3[OH]e[N]e
In the above expressions [] denotes the concentration of the species in moles per cubic
centimeter, and the subscript e denotes the equilibrium concentration. Therefore the only
thing needed for calculating NO formation with the Zeldovich mechanism is a temperature
profile and equilibrium concentrations for the post flame gases.
3.8 Temperature Profiles within the NO Sub-model
There are three different ways in which the temperature profile to be used for
equation 3.9 can be generated with MIT's cycle simulation. The first is that the burned
zone temperature calculated from the energy equation during combustion can be used
52
directly without any adjustment. The second is to assume that the burned zone is adiabatic
and surrounded by a thermal boundary layer whose thickness if a function of the calculated
heat transfer. With this method, there are three zones set up within the cylinder, each at a
uniform temperature and composition. The third possible method of calculating NO is to
again assume there is a thermal boundary layer, but now the adiabatic core is layered to
model the temperature stratification that has been shown to exist in the cylinder during
combustion [3,9]. With this method, a new layer is formed at each crank angle, and it is
assumed that no mixing or heat transfer takes place between subsequent layers. Figure 3.4a
shows the concept of a fully mixed adiabatic core with a mean temperature, and figure 3.4b
shows an unmixed adiabatic core which has many different layers that each have a unique
temperature profile.
It is worth emphasizing that the choice of NO routine has no effect on the
calculated pressure trace of the cycle simulation. The NO sub-model is called only during
the combustion/expansion process and only after the pressure, heat transfer amount, and
temperature of the unburned and burned zones are already calculated. Therefore, the
temperature profile used for the NO routine results from a secondary calculation and has no
effect on any of the performance calculations of the cycle simulation.
A more detailed discussion of how the different temperature profiles are generated
will now follow. It is well established that during combustion, a thermal boundary layer is
set up everywhere the burned gases come in contact with the combustion chamber surfaces.
So, for the purposes of this modeling study, a thermal boundary layer routine was always
used and only the choice of whether the adiabatic core was fully mixed or layered remains.
3.8.1 Fully Mixed Temperature Profiles
The fully mixed model of the adiabatic core works as follows. At each crank angle
during the combustion process, the new mass fraction burned, temperature of the burned
and unburned gases, cylinder pressure, and heat loss from the burned zone is passed to the
NO routine. Using this information, the temperature characteristics of thermal boundary
layer can be assumed by using equations 3.10 and 3.11 shown below:
53
Tburned + TwauTb.!. 2 (Eq. 3.10) Tburned (Eq. 3.11)
Thermodynamic properties of this boundary layer can be easily calculated using curve fits
to JANAF tables, since the temperature is below 1800K and the composition is assumed to
be frozen. The mass fraction of the boundary layer can now be calculated based on these
properties and the total heat lost to the three cylinder components with equation 3.12
shown below:
X urned B dpb.1. dpb.1. Q burned
Xb.A [b!- Apb.l. dTb.I. T dpb.1. mass
X b.. (hburned - hb.i.)
(w/ A&B thermodynamic variables of the boundary layer) (Eq. 3.12)
Once the boundary layer size is known, the mass and enthalpy of the adiabatic core
can easily be calculated by using equation 3.13 and the simple energy balance shown in
equation 3.14. This enthalpy and the cylinder pressure then completely define the state of
the adiabatic core and the temperature can be iterated for with the thermodynamic property
routines.
ma.c. =Xbumed(mass) - Xbl (mass) (Eq. 3.13)
h- mburned (hurned ) -m (hbi )hc =a (Eq. 3.14)
The boundary layer mass fraction and adiabatic core temperature profiles generated by
using equations 3.12 and 3.14 are illustrated in figure 3.5 for the baseline operating
condition. To aid in understanding the figure, the burned gas temperature and burned mass
fraction, from the main simulation, are also shown. As the burned mass fraction increases,
the size of the boundary layer grows, and this drives the temperature of the adiabatic core
above the burned zone temperature for the remainder of the combustion process. Equation
3.9 can now be used to calculate the amount of NO in the adiabatic core gases at each
crank angle. Because of its much lower temperatures, NO is not formed in the boundary
layer, but NO is transferred in as it grows according to equation 3.15 shown below.
54
d[iNO]b.l. (Xbl [NO]ac )+(XbH [NOL) (Eq. 3.15)dt Xb,
With the NO concentration in the adiabatic core and boundary layer now known, the
overall cylinder NO concentration can be calculated by mass weighting the zones as in
equation 3.16. The NO profiles for the two different zones and the overall cylinder NO
concentration are illustrated in Figure 3.6 for the baseline operating condition.
[NO]cyl =NOIL.c. a.c. +INObLMbl (Eq. 3.16)mac + mb.1. + m
3.8.2 Unmixed/ Layered Temperature Profiles
When using the layered or unmixed model NO routine, the boundary layer analysis
stays the same, but now the temperature in the adiabatic core is calculated as follows. For
each crank angle during the combustion process, a new layer of the adiabatic core will be
formed and followed through the expansion process. The initial temperature of the layer is
calculated by assuming that the unburned mixture goes through a constant enthalpy
combustion process. The thermodynamic routines are called to iterate for a burned gas
temperature that meets the constraints of equation 3.17. Once the initial temperature is
known, the layer is assumed to follow an isentropic compression and expansion process
until the exhaust valve opens as given by equation 3.18.
T( j,1)= f (j, P~ , hunbuned, Compositionbuned) (Eq. 3.17)
- . ybi-Ilybi
T(i )i j, EVO = T(ji P) L -I+E (Eq. 3.18)
Therefore, a new adiabatic core layer is formed at each crank angle until the burned
fraction reaches 1. For example, at the baseline operating conditions, j = 49 different
layers are formed each with a unique temperature profile. The temperature profile for the
first, tenth, twentieth, thirtieth, and fortieth layers are shown in figure 3.7 to illustrate this
layering routine at the baseline operating condition. Each of these temperature profiles can
be fed to equation 3.9 to calculate the NO concentration of each layer. Figure 3.8
illustrates the resulting NO concentration profiles calculated from the above listed layer
55
temperature profiles. The first layer to burn has a frozen concentration of over 6000 ppm,
while the fortieth layer to burn is below 200 ppm. This emphasizes the large amount of in-
cylinder NO stratification that can exist. The first and tenth layers also show that NO
concentrations are limited by the equilibrium concentration as indicated by the negative
formation rates. To determine the overall adiabatic core NO concentration, the amount of
mass that burned during each crank angle must be used to mass weight the results
according to equation 3.19.
mass,[ NO]j[NO]. = massi (Eq. 3.19)
A comparison of the temperature profiles generated with a fully mixed and a
unmixed layered model is shown in Figure 3.9. It should be noted that almost no mass is
subjected to the first two layered temperature profiles, j=1 and 10, shown in the figure 3.9.
Therefore, even though the NO concentration in these early layers is very high, there
contribution to the overall adiabatic core NO is limited. The same is true for the last
profile, j = 40, which has very little NO. This leaves the third and fourth profiles which
straddle the fully mixed temperature profile. It will be shown later in Chapter 4, that the
layered model can predict, both, higher and lower overall NO concentrations, depending on
operating conditions.
56
Steady StateMeasurements
Model Inputs
Engine GeometrySpark TimingSpeedMAPA/F RatioBurn Rate
COMPARE-- --------
Valve Flow
CYCLE NO (ppm)SIMULATION predicted
Chemical Kinetics
Figure 3.1: Modeling Approach Flow Chart
MAPEquivalence RatioAir FlowResidual FractionCylinder PressureSpeedNO (ppm)
I NO (ppm)experimentalTotal MassMixture CompositionIMEPBurn RateMaximum Pressure
9[H-eatuTran0f7erjj I[CreviceFlow -1
Table 3.1: Cycle Simulation Required Inputs
Variable Definition DescriptionMAXITS = 5 Maximum Number of Iterations Allowed
PSTART = 1.015 Pressure at Intake Valve Open (atm)
TSTART = 900 Temperature at Intake Valve Ogen (K)
RPM = 1500 Engine Speed in Revolutions 1er Minute
FUELTP = 2 Fuel Tvoe Used - 2 for Progane
PHI = 1.004 Fuel Air Equivalence RatioEGR 2.5 Percent Exhaust Gas Recirculation
TEGR = 300 Temperature of Exhaust Gas Recirculation (K)
TATM = 298 Ambient Temperature (K)
TFRESH = 310 Temoerature of the Fuel Air Mixture in Manifold (K)
PIM = 0.467 Intake Manifold Pressure - MAP (ATM)PATM = 1.00 Ambient Pressure (atm)
PEM = 1.00 Exhaust Manifold Pressure (atm)
BORE = 8.6 Piston Bore (cm)
CLVTDC = 58.77 Cylinder Clearance Volume (CC)TIVO = -13 Intake Valve Open (BTDCE)
TIVC = 235 Intake Valve Close (ATDCE)
TEVO = 483 Exhaust Valve Open (ATDCE)
TEVC = 723 Exhaust Valve Close (ATDCE)
TSPARK = 337 Spark Timing (ATDCE)
c1 = 1.63 Calibration Constant for Woshni Correlation
TPSTON = 420 Temperature of Piston (K)
THEAD = 380 Temnerature of Engine Head (K)
TCW 380 Temierature of Cylinder Walls (K)
ILAYER = T/F Trigger between Layered and Mixed Burned Zone
BLAYR = T/F Trigger for Boundary Layer during NO calculation
SPBURN = T/F Trigger for Burn Rate Model
DTBRN = 50 Wiebe Function Burn Duration
CONSPB = 9.2 Wiebe Function Constant
EXSPB = 3.6 Wiebe Function Exoonent
CREVICE = T/F Trigger for Crevice Sub-model
air = T/F Trigger for Specified Charge
resid = T/F Trigger for Specified Charge
aexp = 0.189 Exoerimentally Measured Air Flow (grams/cycle)resexp = 0.14 Experimentally Measured Residual Fraction
imf = T/F Trigger for using Stanian for Thermodynamic Routine
ieg = T/F Trigger for using Stanian for Mole Fraction Routine
o2 = 0.162 Intake Mixture Mole Fraction - Oxvenc3h8 = 0.0325 Intake Mixture Mole Fraction - Prooanen2 = 0.7522 Intake Mixture Mole Fraction - Nitrogen
co2 = 0.0227 Intake Mixture Mole Fraction - Carbon Dioxideco = 0.0002 Intake Mixture Mole Fraction - Carbon Monoxideh2 = 0.0001 Intake Mixture Mole Fraction - Hydrogenno = 0.00017 Intake Mixture Mole Fraction - Nitric Oxide
h2o = 0.0304 Intake Mixture Mole Fraction - Water Vapor
58
0 0
Burned Zone
Unburned Zone
//
I
0
mcrev-I
dEEnergy: d t
Mass:dmdt =
dm '
d t0
m0
- m e
0
W=pV Q= hAAT p = pRT
Figure 3.2: Thermodynamic Representation of Cylinder Contents
59
Me
mcrev
0
- m
0
c rev
00
0w
i
~ - - - --- . - - - -
"WI
IntakeValve
ExhaustValve
I I II I I
-15 85 185 285 385 485 585 685
Crank Angle
Figure 3.3: Cycle Simulation Valve Flow Discharge Coefficient Map
(a) Fully Mixed Adiabatic Corewith Boundary Layer
KAdiabatic Core
(b) Unmixed/ Layered Adiabatic Corewith Boundary Layer
Figure 3.4: NO Sub-model Temperature Profile Options
60
0.6
0 0.5 -
00.4 -
0 0.3 -
0.2-
0.1
Ir0.0
-- Adiabatic Core Temperature
- - - - Burned Zone Temperature
. Burned Mass Fraction - Xb
A Boundary Layer
'S -
- eeeeeeeee eeteeeSe
3000 -
2500 -
2000 -
1500 -
1000 -
50 -
0 -
A AAA AAA AAA AAA A
cc
0-EC)
C0
LL.o*I)
335 360 385 410 435 460 485
Crank Angle (Spark = 335)
Figure 3.5 Fully Mixed Temperature and Boundary Layer Profile
I jV
/ A1 'I,
//
- as
- - Adiabatic Core NO- Cylinder NO- -- Boundary Layer NO
335 360 385 410 435 460 485
Crank Angle (Spark 335)
Figure 3.6: Fully Mixed NO Concentration Profiles
61
1.4
1.2
1
0.8
0.6
0.4
-0.2
0
A0
A AAAA
AA
AA AA A
2000
1600
1200
800
400
E0.
U-0
0z
0 - - --
M.F. - Xb.1.
3000 -
2500 -
2000 -
2 1500 -QE.E 1000 -
500 -
0-
Constant EnthalpyCombustion
Unburned ZoneTemperature
335 360 385 410 435 460 485
Crank Angle (Spark = 337)
Figure 3.7: Unmixed/ Layered Temperature Profiles
10000 -
8000 -
6000 -
4000 -
2000 -
0- r-II-
1st Element
1 Oth Element
20th Element
30th Element
40th Element
337 357 377 397 417 437 457
Crank Angle (Spark = 337)
Figure 3.8: Unmixed/Layered NO Concentration Profiles
62
E0.0.
C
0C
(U
3000 -
2500
2000 -
1500 -
1000
500 -
a)
Lw
E
x Fully Mixed Core Temp. Burned Zone Mass Fraction
.IumI..E* I I I I I
360 385 410 435 460
Crank Angle (Spark = 337)
Figure 3.9: Comparison of Layered and Fully Mixed Temperature Profiles
63
U -X
0
2
- 1.8
- 1.6
- 1.4
- 1.2
-1 C0-0.8 '
- 0.6 L-
- 0.4
- 0.2
-1-0485
E
0
335
64
CHAPTER 4
STEADY STATE MODELING RESULTS & DISCUSSION
4.1 Model Calibration Approach
The easiest way to motivate a discussion of model calibration is to examine the error
between the uncalibrated model and the experimental data. Figure 4.1 shows a comparison
of cycle simulation predictions of NO concentration and experimental data for the
stoichiometric load sweep prior to calibration. Obviously, regardless of the NO
temperature profile routine used (Fully Mixed or Layered), the modeling predictions of NO
concentration are over a factor of two higher than the experimentally measured values.
Referring back to the modeling approach flow chart shown in figure 3.1, these modeling
results were generated by using burn rate, MAP, engine geometry, and timing as inputs.
However, crevice effects were neglected, and no investigation of whether the model was
accurately modeling the thermodynamic state of the cylinder gases was performed yet.
In modeling studies, gross indicated mean effective pressure, IMEP, is often chosen
as an indicator of accurate thermodynamic predictions. Figure 4.2 shows a comparison of
the uncalibrated model predictions of IMEP and the experimentally determined IMEP for
the same load sweep, both calculated using equation 4.1 below. It can be seen that the
modeling predictions of IMEP are higher at all load points, with percent differences shown
below in Table 4.1. Therefore, a model calibration must be performed to correct the
thermodynamic routines before an assessment of the NO predictions can follow.
BDCE
IMEP = I PdV (Eq. 4.1)BDCC
Table 4.1: Comparison of Uncalibrated Model and Experimentally Determined IMEP1500 rpm, = 1.0, Load Sweep
MAP (bar) 0.33 0.4 0.5 0.6 0.8Model IMEP % Higher 19 23 26 30 33
Since all of the experimental points used in this study revolve around the baseline
operating point (1500 rpm, stoichiometric, 0.5bar MAP), the calibration procedure will be
65
performed at this point initially. To further illustrate the large IMEP difference, figure 4.3
shows the uncalibrated model pressure trace, the experimental pressure trace, which is the
ensemble average of 150 cycles of measured pressure, and a unit-less rate of volume
change curve for the baseline operating condition. Two things should be noted from figure
4.3: the large over prediction of peak pressure and the higher pressures during the
expansion stroke. Looking at the rate of change of volume curve, it is clear that IMEP will
be much more sensitive to expansion stroke differences than peak pressure differences.
However, high peak pressures will lead to high peak temperatures and corresponding NO
concentrations, whereas NO predictions are fairly insensitive to late expansion stroke
errors because production of NO freezes well before EVO. Therefore, IMEP may be an
informative variable for performance calculations, but peak pressure and its location are
more critical variables for modeling NO formation. It is now important to understand what
model deficiencies are causing the pressure trace differences. Inaccurate cylinder charging,
underestimating heat transfer, and neglecting crevice effects are all possible reasons for
higher predicted pressure. Each of these will now be discussed independently.
4.2 Valve Flow Calibration
Figure 4.4 shows a comparison between model predictions of inducted air and residual
gas fraction and the experimentally measured values. Since the amount of fuel scales with
inducted air, the total mass being considered by the cycle simulation is higher than the
experiment for all operating conditions. The overall mixture composition is also off
because the predictions of residual fraction are lower than experiment. The actual percent
difference for amount of air and residual are shown in Table 4.2 below:
Table 4.2: Uncalibrated Model and Experimental Comparison of Air and Residual Fraction1500 rpm, $ = 1.0, Load Sweep
MAP (bar) 0.33 0.4 0.5 0.6 0.8Model Air % Higher 8 11 12 18 22
Model Residual % Lower 24 25 30 28 40
Both of these valve flow modeling errors will lead to a poor prediction of pressure and NO
concentration. By inducting too much air, there will be more burnable mixture in the
66
cylinder to increase heat release and peak pressures. The mixture composition error caused
by lower residual fraction predictions, will have only a minor effect on pressure. However,
lower residual fraction will decrease the heat capacity of the mixture allowing it to attain
higher temperatures and NO when subjected to the same pressure trace.
Because a discharge coefficient map could not be obtained for the Nissan engine, and
modeling heat transfer and mixing during the blowback process was neglected, the residual
and total mass errors are to be expected. However, the purpose of this study was not to
improve valve flow modeling. Thus, in order to eliminate total mass and mixture
composition errors, the experimentally averaged inducted air mass and residual fraction
approximations from Chapter 2 were added as inputs to the cycle simulation. At the end of
each complete cycle calculation, the predicted inducted air and residual fraction were
compared with the experimental inputs. If the two values were in disagreement by more
than 0.5%, the MAP and amount of EGR were adjusted according to equations 4.2 and 4.3
shown below:
MAP =MAP -(AIRdel - AIRxp) (Eq. 4.2)new, oldmoe p
EGRnew EGRoli - (RESIDmodel - RESIDexp) (Eq. 4.3)
Using this iterative method, the cycle simulation is able to converge on the correct total
mass and mixture composition at all of the operating conditions. This allows the valve
flow routine to be eliminated as a source of modeling error.
Appendix A contains a list of the model inputs for MAP and EGR, from equations
4.2 and 4.3 above, that had to be used to obtain the exact cylinder charge for each sweep.
At all operating conditions, the MAP was lowered by approximately ten percent, and the
EGR ranged from 0-3 percent of the total charge. Figure 4.5 shows the pressure trace for
the baseline operating condition before and after the valve flow routine was forced to trap
the correct charge. The peak pressure has been reduced by seven percent and the IMEP has
dropped by nine percent, but a considerable error still exists.
Because the intake manifold pressure was lowered to make the inducted mass
correct, IMEP values should be slightly lower than experiment even if the peak pressure
period is accurate. One other assumption that should be re-emphasized is that the
temperature of the incoming mixture, including the EGR, was assumed to be at 310K,
67
regardless of the operating conditions. This will lead to errors in the overall temperature of
the charge at the time of spark and affect the combustion and expansion temperatures even
if the pressure trace is accurate. The effect of assuming a higher temperature of the
incoming mixture will be explored during the sensitivity analysis chapter later.
4.3 Heat Transfer and Crevice Calibration
Referring back to figure 4.5, the model still over predicts peak and expansion stroke
pressures at the baseline operating condition. Both the heat transfer routine and the lack of
a crevice routine were considered to be possible sources of further pressure differences. In
a first law analysis, as more heat is removed from the cylinder gases, pressure will be
reduced. The effect should be more dramatic during the later stages of combustion and
expansion when a large percent of the cylinder gases have been burned and average
cylinder temperatures rise above 2000 K. The crevice effect represents a reduction of
burnable mixture that reduces the total amount of heat released and corresponding
pressures during combustion. Thus, including a crevice routine should have the same
effect on the baseline pressure trace that the charge correction above did.
Initially, adjustments to each routine were made independent of the other to see if crevice
or heat transfer effects alone could explain the pressure differences that still exist even after
the valve flow calibration. Figure 4.6 shows a pressure trace when the amount of heat
transfer was doubled during combustion and expansion with no crevice volume, and a
pressure trace when a crevice volume equal to 5% of the clearance volume was used with
no heat transfer adjustment. These two sizes are extreme but were selected because the
resulting pressure traces all had approximately the same IMEP. Figure 4.6 now illustrates
that large pressure differences can exist, even though the IMEP is correct. It also shows
that increasing heat transfer has little effect on peak pressure, but a larger effect on the
expansion stroke pressure. Including the large crevice had the opposite effect as heat
transfer, with a larger peak pressure effect but almost no change to expansion pressure
slope.
It becomes clear that combining both a heat transfer increase and a smaller crevice
volume could give a good match to the experimental pressure trace. Figure 4.7 shows an
68
almost exact match of peak pressure and good agreement during the expansion process.
This calibrated pressure trace results from using a crevice volume equal to 2.2 % of the
clearance volume and increasing heat transfer by 70% from the time of spark until the
exhaust valve opens. The calibrated pressure trace has an IMEP equal to 3.85 bar, which is
slightly lower than the 3.9 bar experimental trace. However this is to be expected since the
intake pressure was lowered for the model.
If the crevice volume is meant to model combustion inefficiency in the form of
crevices, blowby, leakage, and flame quenching, then a 2.2% volume is not unreasonable.
The heat transfer increase is justifiable because the spherical flame assumption minimizes
contact area between the burned zone and the walls for a centrally located spark plug, and
radiation effects were neglected. The single cylinder engine set-up also operates with a full
4 cylinder cooling system, thus the engine would tend to operate cooler. Also, the original
valve flow error of not predicting enough residual fraction indicates that more heat should
be removed, since cooler end gas temperatures result in higher residual gas density.
Calibrating the heat transfer routine during other parts of the cycle was not considered,
simply because NO concentration is frozen by the time the exhaust valve opens and the
valve flow routine was forced to trap the correct charge. This leaves only a possible
temperature error at the time of spark as was mentioned before.
Figure 4.8 shows the total amount of heat transferred from the cylinder gases to the
combustion chamber surfaces for the load sweep before and after the 70% increase. The
bar chart is expressed as the percent of the available fuel energy, which is equal to mass of
the fuel times the heating value. The total heat transfer was increased by only 25% with a
70% increase during the combustion and expansion events, since no adjustment to the
Woshni coefficient was made during the intake, compression, or exhaust process. The
overall amount of heat loss after calibration is typically less than 35% of the available fuel
energy. This seems reasonable based on the limited experimental data available on
measured heat loss. The same size crevice volume and the same 70% increase in heat
transfer will be employed for all the operating conditions. To summarize, the valve flow
routine was calibrated at each operating point, and a single calibration of the heat transfer
and crevice routine was done only at 1500 rpm, 0.5bar, Phi=1.0, and assumed to be the
69
same for all the experimental points. Figures 4.9 and 4.10 show how effective the single
point calibration was for the load and equivalence ratio sweep. The predictions of peak
pressure and IMIEP were all within 6 percent of the experimental results. Location of peak
pressure was also in agreement within 1 crank angle, which indicates that the bum rate was
accurate for all test points. The spark and EGR sweeps both showed similar accuracy, with
the details shown in Appendix A.
4.4 Calibration of Kinetic Routine
By guaranteeing that the mixture composition was correct at every operating point and by
calibrating the heat transfer and crevice routines at the baseline point, the thermodynamic
portion of the modeling process has been eliminated as a major source of error. With
confidence in the temperature and pressure profiles, meaningful predictions of NO
concentration can now be made, and the kinetic routine can be investigated. Figure 4.11
shows the steady state load sweep after the thermodynamic calibration; the NO profiles
were generated with both fully mixed and layered adiabatic core temperature profiles.
Referring back to figure 4.1, the thermodynamic calibration has improved NO predictions
considerably. Both of the curves appear to have the correct slope of the experimental data,
with the layered adiabatic core predicting NO concentration approximately 20% lower than
the fully mixed routine at all points. However, even the layered adiabatic core results are
still higher than the experimental data.
Figure 4.12 shows the steady state equivalence ratio sweep with accurate
thermodynamics. Again both routines are predicting NO levels higher than the
experimental values, but the slope of the two curves is not as consistent as the load sweep.
It should be noted that the layered profile is again predicting NO values lower than the
fully mixed routine near stoichiometric points. However, under extreme rich and lean
conditions, the layered profile predicts higher NO values when compared to the fully mixed
routine. This initial comparison of the two routines with the experimental data, indicates
that the layered routine has the slope captured more accurately. Regardless of the slope
difference though, these two initial sweep comparisons merit an investigation of the rate
constants used to describe the Zeldovich mechanism, since the model predictions are
70
always higher than experiment. So, a more detailed discussion of the results will be held
until the rate constants are adjusted.
It is well excepted that rate constants for the Zeldovich mechanism can be in error
by as much as a factor of two. Previous work done by McGrath [6] showed that NO
concentrations are mainly a function of the first reaction rate constant, ki, which was taking
to be 3.3E+12TO.3 . The calibration procedure chosen for the rate constants was simple and
consistent with the thermodynamic routine calibration: a single point calibration of k, was
done only at the baseline point. Miller et al. [7,8] at Ford Motor Company also
recommend this single point calibration of k1 at the world wide map point, which is almost
identical to the baseline point of this study. The layered routine will be used to set k, for
an exact match with the experimentally measured NO concentration. At 1500 rpm,
stoichiometric, 0.5 bar MAP, the measured NO level was 1579ppm, while the layered
routine with k, equal to 3.3E+12T0 3 predicts 2035ppm. The k, value had to be adjusted
down to 1.66E+12 T0 3 until the layered routine predicts 1577ppm. This corresponds to
nearly a factor of two decrease in k, which is typically considered to be the accuracy with
which rate constants can be determined. It should also be noted that experimentally
determined rate constants are studied at atmospheric pressure and 1000K. This could lead
to large discrepancies from engine conditions of interest which are typically 2300 K and 20
atm at 0.5 bar MAP. Therefore, it is not unreasonable to adjust the rate constant by this
factor of two. A comparison of the calibrated k, value used in this study with those used
by the authors discussed in the previous work section of this thesis is shown in Table 4.3.
Table 4.3: Comparison of Rate Constants for Reaction 1, N + NO -+ N2 + 0
Authors - Affiliation Year ref. # Rate Constant, ki *
Ball, Stone, Collings - Cambridge 1999 10 1.60E+13University
Miller, et al. - Ford Motor Company 1998 7,8 1.55E+1 2 T-3+/- 30% **
Raine, Stone - University of Auckland 1995 9 1.6E+13 - 3.3E+12TuMiller and Bowman 1989 28 3.3E+12Tu
McGrath - MIT 1996 6Bowman 1976 29 1.60E+13
This Study after Calibration 2000 1.66E+1 2 T0.T 3 is equal to 7.94 @ 1000K, 10.2 @ 2300K
** This applies to peak pressure of 15-20atm, typical of MAP = 0.5 bar
71
The above table indicates that at typical spark ignition engine combustion
temperatures and pressures, the rate constant used in this study for an exact match at the
baseline operating condition is in good agreement with other researchers. Miller and
Bowman's [28] most recent study in 1989 was purely a chemistry review and involved no
engine specific analysis. Ford motor company also used the Miller and Bowman value but
had to employ a factor of five reduction over the load sweep for good agreement with
experiment. The value at half load conditions is shown in table 4.3. With the appropriate
rate constant now being used, a modeling assessment of the four sweeps can be made.
4.5 Load Sweep Modeling Results
Figure 4.13 shows the steady state load sweep with k, = 1.66E+12T0 3 used for both
the fully mixed and layered adiabatic core. The experimental data shows the expected trend
of increasing NO with engine load. As the intake manifold pressure increases, the amount
of burnable fuel air mixture increases, and the corresponding heat release drives the
increase of pressure, temperature, and NO concentration. The amount of residual gas
present is also decreasing with load, and this will lead to higher NO as well. Since the rate
constant was calibrated at 0.5 bar MAP, an exact match is seen at that operating condition.
However, now it becomes clear that the slope of the modeling predictions is not in line
with the experimental data points. With the layered adiabatic core temperature profile, the
model predicts 3% lower than experiment at 0.33 bar MAP and 12 % higher at 0.8bar. A
similar but larger difference trend was also noted by Ford Motor Company [7,8], with a
25% over prediction at wide open throttle after calibrating the rate constant for an exact
match at a mid load point.
It is important to note that the factor of two adjustment to k, used for an exact
match at 0.5 bar, had a varying effect over the entire load sweep. Figure 4.14 illustrates the
percent reduction in NO concentration after dropping k, from 3.3E+12T0 .3 down to
1.66E+12T0 3 . As the engine load decreases, the sensitivity to the rate constant grows.
This is explainable since NO formation is limited by the equilibrium NO concentration as
is shown in equation 4.4 below.
72
d[N - [NO] (Eq. 4.4)dt [NO Ieq
When the rate constant is increased at higher loads, the ratio of NO concentration to the
equilibrium level grows large and formation rates are slowed to limit the effect. Also, if
the level ever exceeds the equilibrium concentration, the rate of NO production becomes
negative and decomposition will drive NO formation back down until freezing occurs.
While at light loads, the NO concentration is held well below equilibrium for all layers,
making rate constant adjustments more pronounced. During the sensitivity analysis
section, this varying rate constant effect should be remembered when determining if any of
the variables actually change the slope of the modeling prediction curve.
When using a fully mixed adiabatic core, the slope of the model predictions is even
steeper. The difference between layered and fully mixed predictions ranges from 9%
higher at 0.33 bar to 18% higher at 0.8 bar. The sensitivity to the factor of two rate
constant adjustment with a fully mixed adiabatic core is very similar to the layered model
shown in figure 4.14. Therefore, if the rate constant was further reduced to get an exact
match with the fully mixed model at 0.5 bar, the deviation at high loads would be
considerably higher than the 12% seen with layering. This may explain why the work
presented by Ford, which did not use a layered adiabatic core, showed a larger error at
higher loads than seen here. A more detailed investigation of the possible causes of this
slope difference will be carried out in the sensitivity analysis section next chapter.
4.6 Equivalence Ratio Sweep Modeling Results
Figure 4.15 shows the steady state equivalence ratio sweep after the single point
rate constant calibration. It is seen that NO concentration reaches a maximum at the
slightly lean condition where temperatures are still high and oxygen is readily available.
As the engine is forced leaner, temperatures continue to fall and NO formation is limited
even with the excess oxygen. Temperatures are highest under slightly rich conditions,
however available oxygen, which is critical to NO formation, is limited as the fuel air ratio
increases. Again, the exact match is seen at the stoichiometric point and only of the slope
of the curves is important.
73
When using the layered adiabatic core temperature profile, the modeling accuracy is
quite good for the entire range of equivalence ratios. The layered model predicts 11 %
higher at the extreme lean condition, 0.713, but predicts 16% lower at the extreme rich
condition of 1.25. The rest of the sweep is within 10% accuracy. It should also be noted
that the two extreme points have experimental concentrations below 200 ppm. Here,
neglecting more detailed chemistry and NO formed in the flame, could have a larger
impact in terms of percent errors. Some of the modeling error could also be attributed to a
lack of experimentally measured residual fraction at the very lean and rich points. From
Chapter 2, less residual than stoichiometric was assumed under lean operation and more
while rich. If residual was allowed to remain fairly constant, modeling accuracy would be
improved. Figure 4.16 again illustrates the percent reduction in NO before and after the
factor of two rate constant adjustment over the equivalence ratio sweep. There is a distinct
increase in rate constant sensitivity as the mixture becomes leaner. This is also explainable
by the ratio of NO concentration to equilibrium levels.
With a fully mixed adiabatic core routine, the slope of the sweep is too steep on
both sides of stoichiometric. If the rate constant was adjusted to match at 0.5 bar MAP, the
last two lean and rich operating conditions would be substantially lower than the
experimental values. This would indicate that a fully mixed model does not accurately
represent the contribution from the early and late burning elements. It is difficult to fully
explain why the ratio of layered to fully mixed routine predictions varies widely with
operating conditions. However, the results observed in this study are consistent with some
of the previous work done with layered models. Figure 4.17 shows an equivalence ratio
sweep comparison of this study and an early work done by Blumberg and Kummer [4]. A
similar slope is seen with slight differences on the rich side. The study by Raine and Stone
[9] also showed an approximately 15% reduction with a layered model compared to fully
mixed routine at stoichiometric conditions. However, neither of these two studies used a
boundary layer analysis, combustion inefficiency routine, or experimentally determined
bum rates.
74
4.7 Exhaust Gas Recirculation Sweep Modeling Results
Figure 4.18 shows the steady state EGR sweep after the model has been calibrated.
The experimental data shows that NO concentration is reduced as the incoming mixture
becomes more diluted. This is explained by the fact that EGR increases the heat capacity
of the cylinder contents, keeping cylinder temperatures down during combustion. An exact
match with experiment is seen again at the baseline operating condition, but now the slope
of the layered model predictions departs more significantly from the experimental data. At
8% EGR the error has reached 12%, and with 16% EGR the model is predicting
concentrations 29% lower than experiment. Again, it should be noted that a fully mixed
model has an even steeper slope than the layered routine. If calibrated at the 0% EGR
point, the fully mixed error would be much larger at the high dilution points.
Several possible reasons could be given for why the error is larger as dilution
increases. First, experimental error could have occurred while metering the flow of EGR
into the cylinder with the critical flow set up. The orifices could only be calibrated with a
bubble flow meter outside the engine, so as to avoid the fluctuating manifold conditions
which are under vacuum. The EGR was also simulated with a mixture of nitrogen and
carbon dioxide, which merely had the same heat capacity as natural EGR. Therefore, not
as much water vapor was present in the cylinder as would be with natural EGR. This
would be similar to lowering the humidity ratio of the incoming mixture which has been
shown to decrease NO concentrations [4]. Since the thermodynamic and equilibrium
concentration routines both assume natural EGR composition, modeling error could be
introduced. These problems will be briefly explored in the sensitivity analysis section.
One final note is that the Zeldovich mechanism can only model post flame production, not
flame NO, with a limited amount of chemistry considered. Thus as post flame production
drops, say below 500 ppm, using the Zeldovich mechanism alone could be a poor
assumption.
75
4.8 Spark Timing Sweep Modeling Results
Figure 4.19 shows the steady state spark timing sweep in comparison with the
calibrated model. The experimental data represents the effect of maximum heat release
location. As spark timing is retarded, a large portion of the heat release occurs later in the
expansion stroke and peak pressure, temperature, and NO concentration all decrease
sharply. When the timing is advanced, the heat release process is taking place in
conjunction with the compression stroke. This will lead to higher observed pressures and
corresponding NO concentrations.
With the exact match at MBT timing guaranteed, the layered model gives an
exceptional match with experimental data over the range of timings. The error for all data
points is less than 6%. Unlike the other sweeps, the fully mixed model appears to also
have the correct slope. If the rate constant was further reduced at MBT, the fully mixed
model could be used to accurately predict NO concentration as a function of spark timing.
This accuracy with spark timing is expected, since little changes in terms of the radical
pool, cylinder charging process, and mixture composition when only the ignition point is
varied.
76
4000 -
3000 -
2000
1000 -
Fully Mixed Routine- - - Layered Routine
n Experimental Data
-0
,-U
WN
v
9
0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9
Intake Manifold Pressure (bar)
Figure 4.1: Uncalibrated Model NO Predictions - Load Sweep
10 -
8-
6 -
- - -Uncalibrated Model
* Experimental Data
0
E
4+ U
2 --
0
0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9
Intake Manifold Pressure (bar)
Figure 4.2: Uncalibrated Model IMEP Predictions - Load Sweep
77
5000
E
0z
0
U)0)
C.w
CU
.0
0
(0
i i i
- - - - Uncalibrated Model30
25
20
15
10-
I I i I
280 305 330 355 380 405 430 455 480
Crank Angle (Spark = 337)
Figure 4.3: Baseline Operating Condition Pressure Trace AnalysisUncalibrated Model Comparison
U
UU
UU
I I
C0
..
-
25 -
20 -
15 -
10 -
5 -
0
U
UU
UU
I I I0.2 0.3 0.4 0.5 0.6 0.7 0.8
MAP (bar)0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9
MAP (bar)
Figure 4.4: Uncalibrated Model Air and Residual Predictions - Load Sweep
78
m Experimental Data
IM U
rE U
dV/dO*
CL
(I)
0.4 -
Z 0.3 -
0
0.1 -
0
Ii-
5
v
0.9
IMEP = 4.88 -\ . - - Uncalibrated
IMEP =4.46 ,Correct Charge20 \ A Experimental Data
A A
A AS15 AA\
A Exp.=3.910
5 -- A,
0
280 305 330 355 380 405 430 455 480
Crank Angle (Spark = 337)
Figure 4.5: Baseline Operating Condition Pressure Trace AnalysisCorrect Charge Mass and Composition
25 -
20 -
15 -
10 -
5 -b
0
IMEP = 4.46 2x Heat Transfer\ A Experimental Data
AAA A Correct Charge
---- 5% Crevice
HT & Crevice p 3IME = .9 Exp.= 3.9 barIMEP 3.94
AA
/A
350 380 410 440320
Crank Angle (Spark = 337)
Figure 4.6: Baseline Operating Condition Pressure Trace AnalysisHeat Transfer and Crevice Effects
79
30 -
25 -
L.
.0
a)L..
U,(00)a-L..0)
C
0
r
25 -
20 -
15 -
10 -
5 -
-t I I I I I I I
280 305 330 355 380 405 430 455 480
Crank Angle (Spark = 337)
Figure 4.7: Ba
4C
0E
a(0
I4-'i
0
CIi*
35
30
25
20
15
10
5-
0-0.33
seline Operating Condition Pressure Trace AnalysisFully Calibrated Model Comparison
-r * Calibrated
0 Uncalibrated
I - I - I
0.4 0.5 0.6+ -I
0.8
Intake Manifold Pressure (bar)
Figure 4.8: Calibrated Model Heat Transfer Predictions - Load Sweep
80
Final Calibration
A Experimental Data
-
cc
Cu
.U)
CL
A
0
U
40 -
cc
630-
u 20-0.Q~
Cu0)0~
0.6
MAP (bar)
0.8
10-
0
0.2
I I
0.4 0.6 0.8
MAP (bar)
Figure 4.9: Calibrated Model IMEP & Peak Pressure PredictionsLoad Sweep
Eu U
U
U
I I I I
"25-
20-.0
L- 15-a-
)1 0 .a.
0.6 0.8 1.0 1.2 1.4 0.6 0.8 1.0 1.2 1.4
Equivalence Ratio Equivalence Ratio
Figure 4.10: Calibrated Model IMEP & Peak Pressure PredictionsEquivalence Ratio Sweep
81
8-
c 6-
N 4-
Cl2202-
0 1-
0.2 0.4
5-
.
3-0
2-
' - -' ' '
I I
Fully Mixed A.C.- - -Layered A.C.
* Experimental Data
4-
=U
-I *0
oo
0.4 0.6
MAP (bar)
Figure 4.11: Load Sweep Modeling Comparisonw/ kl=3.3E+12T. 3 - 1500rpm - PHI=1.0
3500
0.
0z
00)
0
C--w
3000 -
2500 -
2000 -
1500 -
1000 -
500 -
00.6
Fully Mixed A.C.Lavered A.C.
* E xperime
r-~N
/ U..\
=U
0.8 1.0 1.2
ntal Data
1.4
Equivalence Ratio
Figure 4.12: Equivalence Ratio Sweep Modeling Comparisonw/ kl=3.3E+12T0 .3 - 1500rpm - MAP=0.5bar
82
4000
3500
3000
2500
2000
1500
1000
500
0E
O0z
Cw
U
E
0 I
0.2 0.8
3500 -
3000 -
2500 -
2000 -
1500 -
1000 -
500
00.2
-Fully Mixed A.C.- - - Layered A.C.
N Experimental Data
0.
0.4 0.6 0.8
MAP (bar)
Figure 4.13: Final Load Sweep Modeling Comparisonw/ kl=1.66E+12T 3 - 1500rpm - PHI=1.0
40 -
30 -
20 +
10 -
0 - i0.33
i
0.4
-H--0.5 0.6
-- i0.8
MAP (bar)
Figure 4.14: Amount of NO Reduction After Factor of 2 Adjustment to k1Layered A.C.
83
EC-
C-0z
0
C
0z
1-0
C~'I
'
2500 TF
2000 _
0 1000 -
1500 -
00.6
-Fully Mixed A.C.- - -Layered A.C.
. Experimental Data
0.8 1.0 1.2 1.4
Equivalence Ratio
Figure 4.15: Final Equivalence Ratio Sweep Modeling Comparisonw/ kl=1.66E+12T0.3 - 1500rpm - MAP=0.5bar
0z
010*
45
30
15
U ~1~~~~' I I ' 111I I I I I I I I
0.72 0.77 0.84 0.91 0.96 1.01 1.06 1.12 1.25
Equivalence Ratio
Figure 4.16: Amount of NO Reduction After Factor of 2 Adjustment in k1Layered A.C.
84
-
-
-
(A) Blumberg and Kummer [4]
.7.9 1.0 1-1 .2 1,3
FUEL-AIR EQUIVALENCE RATIO
1.3-
1.2
1.1
6z0.9-
1500 rpm, 0.66 bar MAP
- I -
0.7 0.8 0.9 1.0 1.1 1.2 1.3
Equivalence Ratio
Figure 4.17: Comparison of Layered Model Predictions with Previous Work
-Fully Mixed A.C.- - -Layered A.C.
. Experimental Data
-
10 15
% EGR
Figure 4.18: Final Exhaust Gasw/ kl=1.66E+12T03 -
Recirculation Sweep Modeling Comparison1500rpm - PHI=1.0 - MAP=0.5bar
85
1500 rpm, 0.5 bar MAP
NOmixed 1
NOunmixed
to0
.9
0.8
2000 -
1800 -
1600 I
0.0.
0z
0
G)C
1400 -
1200 -
1000 -
800 -
600-
400
200 -
0
C 5
(B) This Study
1.2
I
3500 .
3000-E0- 2500 -
0z 2000
o 1500
5> 1000 -C
500 -
Fully Mixed A.C.- - -Layered A.C.
* Experimental Data
000',....0- --
F
+
0 I i i
10 20 30
Spark Timing (0BTC)
Figure 4.19: Final Spark Timing Sweep Modeling Comparisonw/ kl=1.66E+12T' 3 - 1500rpm - PHI=1.0 - MAP=0.5bar
86
40
CHAPTER 5
SENSITIVITY ANALYSIS
Whenever model results are presented in comparison to experimental data, it is
important to explore the limitations of the model and identify how key parameters can
change model predictions. This section will attempt to investigate the impact of model
assumptions on NO predictions (i.e. the completeness of the Zeldovich mechanism,
replacing Martin's simplified thermodynamic routine with a full equilibrium code, NO
formation starting from a non-zero level, and using a kinetically controlled radical pool).
In addition, a more general sensitivity analysis will be performed in which selected
parameters are perturbed, and the corresponding change in NO predictions are tabulated.
Other than the N20 mechanism and residual NO concentration sections, five operating
conditions were chosen for this sensitivity analysis: 0.3 bar, 0.5 bar, 0.8 bar, PHI = 0.912,
and 8% EGR. The points were chosen to give a wide variety of different in-cylinder
temperature and pressure histories. Once the sensitivity analysis is complete, conclusions
on the steady state modeling results can then be made.
5.1 Effect of Adding N20 Mechanism
In all of the modeling results shown so far, only the three reaction Zeldovich
mechanism was used to describe the NO formation process. This was done to determine
its accuracy alone over the operating range. However, under highly dilute conditions with
excess air or exhaust gas recirculation, other researchers [3,6,7] have suggested that
another chemical pathway to NO, called the N20 mechanism, can become important. The
set of equations below show the mechanism used to describe the formation of N20 and
additional NO in the post flame gases.
87
N 20+H >N 2 + OH.......k 4 = 3.OE +13exp(-5350 / T)
N 2 0+0->N 2 I +02.........k 5 = 3.2E + 12 exp(-18900 /T)
N 20+0 -N0N NO...k6 = 3.2E + 12 exp(-18900 T)
N 20+N 2 7 >2N 2 +0......k 7 = 1.E +15exp(-30500 / T)
By employing a steady state assumption for N20, as was done with the N atom in the
extended Zeldovich mechanism, a single equation can still be used to describe the rate of
NO formation in each layer of or the fully mixed adiabatic core as in equation 5.1 below.
The radical pool is again assumed to be in equilibrium.
d[NO] _ d[N NO]] 2R 6 {1 -([NO] / [NO]e )2
dt L dt +ldh I?6 /' (R 4 + R5 + R,) (
R4 = k4[ N 2O]e[H]e R5 R6 = k5 [N 2 0]ie[O]e R 7 = k,[N20]e[N2 ]e
The same temperature profiles that were used to generate the results presented last
chapter can now be used with equation 5.1 to evaluate the amount of additional NO formed
through the N20 mechanism. Figure 5.1 shows the steady state equivalence ratio sweep
with the predictions from the Zeldovich mechanism shown last chapter and the new curve
after adding the N20 effect. On the rich side of the sweep, the predictions seem to be
relatively unaffected. However, near stoichiometric and leaner, the predictions are
noticeably increased by the N20 mechanism as was expected. To make a fair estimate of
what actual increase has occurred, the same rate constant calibration procedure must be
applied at the baseline operating condition. At 0.5bar, the NO prediction was increased
from 1577 ppm up to 1622 ppm. Thus, k1 will now have to be reduced to maintain the
exact match. Recalling figure 4.15 , the lean side was shown to be more sensitive to rate
constant adjustments than stoichiometric. Therefore, the N20 mechanism effect may not
be as large as it appears in figure 5.1.
Figure 5.2 shows the readjusted N20 curve with k1 now equal to 1.5E+12TO. 3 for an
exact match at the baseline point. The rich side still remains unaffected, but now the lean
side is showing only modest increases. Figure 5.3 shows the percent increase seen by
adding the N20 mechanism for all the sweeps after the re-calibration of k1. The maximum
88
increase is 14% at the extreme lean condition. The EGR and load sweep both showed a
negligible amount of change after re-calibration of k1.
With the Zeldovich mechanism alone, the lean side was already over predicting NO
concentration. Now the predictions will be even higher. In addition to a possible residual
error that was mentioned earlier, it now becomes clear that a combination of the fully
mixed and layered routines may be a better solution. Recalling the Chapter 4 analysis that
showed a fully mixed model would under predict lean operation, if the number of layers
were cut down to allow some mixing, a more accurate prediction may result.
5.2 Effect of Considering the Residual NO Concentration
When modeling the NO formation process, the amount of NO present in the
cylinder due to residual gases is neglected, and the NO concentration starts from zero when
using equation 3.5 or 5.1. Because residual fraction varied in this study from 10 to 19 %,
there will always be a small amount of NO in the cylinder before the spark, depending
upon the previous cycles NO level. As was discussed earlier, residual fraction is mainly a
function of MAP, with fixed valve timing, and figure 5.4 shows the experimentally
determined residual fraction and average exhausted NO concentration. By assuming the
residual gases have an average level of NO present, a multiplication of the two experiment
curves will give an estimate of the amount of NO present in the cylinder prior to spark
discharge. With the temperature and NO stratification effect already demonstrated with the
layered model, it is probably not a fair assumption to assume the residual gases have the
average NO level. However, the solid line in figure 5.4 describes the relative NO
concentration in the unburned mixture with this assumption.
By adding the unburned mixture NO concentration to the input of the cycle
simulation, a new model prediction curve can be generated for the load sweep. Figure 5.5
shows the percent increase observed at each operating conditions. At 0.33bar, where
residual fraction levels were 19%, almost all of the residual NO concentration shows up in
the exhaust. However at 0.8 bar, where residual was 10%, less than one third was still
present in the exhaust. This is again explainable by the level of NO being formed in the
cylinder in relationship to the equilibrium concentrations. At light load the ratio of
89
NO/NOeq at time of peak pressures and temperatures with a fully mixed analysis is quite
small, ~ 0.1, while the ratio at 0.8bar is near 0.6. Therefore forward rates at low loads will
not be affected by the equilibrium level and most of the residual gas NO is merely added
the amount formed during combustion. As NO concentrations near equilibrium at high
loads, the forward rate is limited, making the starting level less important.
Looking at the load sweep predictions presented from last chapter in figure 5.6a, the
residual NO effect looks encouraging. However, remembering the rate constant sensitivity
curve, figure 5.6b, it is seen that a ki reduction to remove the rise of 8% at 0.5 bar will not
drop the NO level at 0.8bar by the same 8% which would help correct the slope. Rather,
the decrease would only be around 4%. Similarly, the 0.33 bar level would be decreased
by over 12% with an 8% adjustment at half load. Therefore, the residual NO effect will not
significantly change the slope of the modeling curve, because the sensitivity to rate
constant adjustments and the residual NO level follow the same trend. It is assumed that
the remaining sweeps would also by only slightly changed. However, later in chapter six
when cycle by cycle NO is considered, the amount of left over NO should be remembered.
5.3 Upgrade to Full Equilibrium Calculation
As was discussed in Chapter 3, at each crank angle of the engine cycle, the
simulation calls upon a sub-routine for a complete description of the thermodynamic state
of the cylinder gases (enthalpy, gamma, density, and rates of change of these variables with
respect to pressure and temperature). For unburned mixtures and burned gases below
1800K, it is safe to assume the mixture is frozen. With this assumption and by considering
only major species (no dissociation), the composition of the mixture can be determined
from stoichiometry, and then properties are determined from JANAF tables.
During combustion and expansion, when burned gases are well above 1800K, a
significant amount of dissociation occurs. By assuming the combustion products are in
chemical equilibrium, a standard equilibrium code such as STANJAN can be used to
calculate the thermodynamic properties at any given temperature and pressure. This
calculation can be time consuming, so an approximation developed by Martin and
Heywood [27] is used by the cycle simulation to approximate the effects of dissociation on
90
thermodynamic properties. An analysis was performed at the five sensitivity analysis
points to compare predictions of burned zone temperature and properties from STANJAN
and the Martin routine.
Several things should be noted about this analysis. First, STANJAN did not have a
direct variable for the rate of change of enthalpy with respect to pressure, dh/dP, so a one
sided direct derivative was calculated with an additional call. Rates of change of density,
dp/dT and dp/dP, had to be calculated in the same manor. Also, STANJAN was not used
for the NO sub-routine which generates an adiabatic core temperature profile after the
burned zone temperature is known. Therefore no direct comparison was made for NO
calculations during this initial investigation. Using the full equilibrium code just for
calculating burned zone temperature increased run times by over a factor of ten. Some
evidence of a significant error due to the Martin routine will be needed to merit the use of
STANJAN elsewhere in the cycle simulation.
Figure 5.7 shows the burned zone temperature predictions generated using the two
different property routines. The temperature profile while using STANJAN was
approximately 0.6% higher than the Martin routine up until NO formation would become
frozen. The difference between the two at maximum temperature was 14 K. Cylinder
pressure predictions showed negligible differences with the two different routines. Figures
5.8 and 5.9 show the predictions of specific heat, ratio of specific heats, enthalpy, and
density for the baseline conditions during the entire combustion and expansion process.
Gamma differences were less than one percent, so this confirms the layered routine which
is based on isentropic compression and expansion. Specific heat and enthalpy differences
were small throughout the cycle, and density predictions were essentially identical.
Similar trends were observed at 0.33 bar, 0.8bar, 8% EGR, and lean operating conditions,
with burned zone temperature profiles always within 0.6% agreement. This slight error
could be attributed to the direct derivative calculations. Because STANJAN was in such
good agreement with the cycle simulation, further work to upgrade the NO adiabatic core
temperature routines was deemed unnecessary.
91
5.4 Kinetically Controlled Radical Pool Investigation
As was discussed in Chapter 3, during the thermodynamic and NO formation
routines, the post flame gases are assumed to instantly reach a chemical equilibrium
composition. By making this assumption and a steady state assumption for the N atom, the
calculation of rate limited NO is easily written with a single differential equation. For a
comparison, Sandia's SENKIN [30] chemical kinetics package was employed to calculate
NO formation through the extended Zeldovich with a kinetically controlled radical pool.
This will allow an assessment of the error introduced by the equilibrium radical pool
assumption to be made.
To set up the analysis for SENKIN, a detailed propane oxidation mechanism
proposed by Daguat et al. [31] was used which completely describes 68 species of the C-H-
O system. The three reactions of the Zeldovich mechanism with the calibrated rate
constants from Chapter 4 were added to this mechanism. It should be noted that no
additional nitrogen flame chemistry was considered in the mechanism used. This analysis
was conducted to test the NO formation profile from the extended Zeldovich mechanism
with a kinetically controlled C-H-O species radical pool during and after the flame
oxidation process.
SENKIN requires an input file with the details of the unburned mixture
composition, and the temperature and pressure history as a function of time. A fully mixed
model is not applicable for this type of analysis, since the adiabatic core continually has
unburned mass being added and mixed with the burned gases. However, the layered
routine sets up nicely for a comparison, since each individual layer is treated separately and
has an isentropic pressure and temperature history. Figure 5.10 again shows the baseline
operating condition temperature profiles from the layered adiabatic core routine. Three
representative layers were selected from figures like 5.10 for each of the five sensitivity
analysis points and sent to the SENKIN package along with the corresponding time step
(crank angle) and cylinder pressure. For example, at 0.5 bar, the 2 0 th, 2 5 th and 3 5th layer
temperature profiles where chosen since over 75% of the mass bums in between layers 20
and 35.
92
The last unknown needed for the SENKIN analysis was a temperature profile for
the gases during the first few time steps. This is during the fuel breakdown period when
unburned mixture is converted to burned products. In reality, the unburned mixture would
go through a constant enthalpy fuel oxidation process at near constant pressure. A brief
investigation of the temperature profile that would result from a constant enthalpy reaction
was performed. Figure 5.11 shows that the rise from unburned temperature to burned
temperature, which could represent the flame, occurred over a time step of around two
crank angles and that little NO forms through the Zeldovich mechanism during this
process.
Therefore, for a simple analysis, the unburned gases were assumed to experience a
step change from the unburned mixture temperature up to the initial burned zone
temperature over a two crank angle (0.22ms) time step. For example, looking at figure
5.10 again, the input file for the 2 0 th element would have a specified temperature of 750 K
at time zero and a temperature of 2421 K at 0.22ms. Then, the remainder of the time steps
would follow the circle marked profile. If the unburned mixture was started at 2421 K at
time zero, NO formation rates would have a large initial spike. This would be due to high
radical concentrations combining with the unrealistically high temperatures during the fuel
breakdown period, which would not be correct. By starting at the unburned temperature of
750K, NO formation rates were small until all of the hydrocarbon species were oxidized
which agrees with the constant enthalpy calculation. This allowed a fair comparison with
the cycle simulation NO profiles for the remainder of the process.
Figures 5.12 through 5.16 show the three selected representative layer NO profiles
for each of the five sensitivity analysis points. It can be seen that the SENKIN analysis and
the cycle simulation both predict similar NO formation profiles for all the points. Though,
the amount of error is varying with operating conditions. Table 5.1 summarizes the percent
difference between the two methods for the three layers at each condition.
93
Table 5.1: Percent Difference between SENKIN and Simulation Predicted Layer NO Profiles
Operating Condition first second third fourth0.3 bar - Stoich 4.8% -1.3% 0.4% -
0.5 bar - Stoich 5.9% 2.8% 2.7% -
0.8 bar - Stoich 7.9% 7.3% 9.2% -0.5 bar - Lean - 0.91 17.3% 19.8% 21.7% 23.4%0.5 bar - 12 % EGR 4.4% 1.8% -1.5% -
Several trends should be noted from table 5.1. Since each layer analysis with
SENKIN is quite time consuming, NO predictions could not be made for an entire cycle.
However, if these layers are truly representative, the general trend in what the NO
prediction would be can be inferred. The cycle simulation routine shows its largest over
prediction, 25%, under lean operation. The load sweep showed an increasing amount of
over prediction, but the differences were all under 10%. The EGR point showed a slightly
lower over prediction than the baseline operating condition. (These small errors are
attributed to slight differences in radical concentration, either due to calculation error or
non-equilibrium effects. The varying amount of error with operating conditions my be
explained by the radical error combining with varying temperatures and excess oxygen.)
Nonetheless, all three of these trends were noted during the comparison with experimental
data in chapter 4. Correcting these three trends would move model predictions closer to
experimental data points. This brief analysis is encouraging and merits further work with
kinetic calculations, and this SENKIN analysis method would allow more detailed nitrogen
chemistry to be investigated. It may also be useful to develop a cycle simulation that fully
utilizes both SENKIN and STANJAN to calculate the NO routine temperature profiles and
formation rates for the entire combustion expansion process, if numerical time is not a
concern.
94
Representative Layer
5.5 General Sensitivity Analysis
It is often helpful to see how slight changes, to variables that are expected to be
important and parameters where uncertainty exists, will affect the model NO predictions.
Tables 5.2 and 5.3, shown on the following two pages, detail this type of analysis applied
to the five different sensitivity analysis points. The excess of load points was chosen for
the purpose of exploring the mismatch in the modeling slope and for the upcoming cycle
by cycle analysis section. A spark timing point was neglected because of the absence of
any substantial modeling error for that sweep. The tables represent the amount of forced
change given to a input parameter and a corresponding delta NO value listed in ppm and
percent change. A listing of the models corresponding IMEP prediction was also included
to demonstrate how the parameter adjustment would affect the thermodynamic calibration
from Chapter 4. All of the delta NO values are in reference to the final modeling
comparison figures shown last chapter (figures 4.13, 4.15, 4.18, 4.19) which were after the
calibration of k, = 1.66E+12T0 3 . A large number of the variables were considered with a
layered adiabatic core since that was the main focus of the modeling results section.
However, a few selected variables are also shown while using a fully mixed routine to
generate the adiabatic core temperature profile. The layered model analysis results will be
discussed first.
5.5.1 Variables of Uncertainty - Residual, Heat Transfer, Effective Crevice Size
The discussion of Table 5.2 and 5.3 will begin with the first three variables,
residual fraction, heat transfer increase, and effective crevice volume, which were pivotal
in making accurate predictions of cylinder pressure and temperature during the calibration
of the models thermodynamic routine. For the entire load sweep, it is seen that residual
fraction is the most important of these three. Though, a ten percent change in residual had
a decreasing effect as the manifold pressure increased. This may be simply explained
because the residual changed from 19% at 0.33bar down to 10% at 0.8bar, making the
absolute change greater at low load. Regardless, the sensitivity to residual fraction remains
substantial for all of the operating conditions shown, because of its large effect on the
thermal capacity of the unburned mixture and resulting burned gas temperature. This large
95
Table 5.2: Input Parameter Senstivity Analysis - Load Sweep
Operating ConditionFinal Layered Model
Residual +10%Residual -10%
Heat Transfer Mult. +10%Heat Transfer Mult. -10%
Crevice Volume +10%Crevice Volume -10%
Delta Burn +50Delta Burn -50
Fuel Air Ratio +1%Fuel Air Ratio -1%
Spark Timing ADV 20Spark Timing RET 20
Intake Mixture Temp (+200)Rate Consant 1 +50%Rate Consant 1 -50%
Adiabatic Core Temp +1%Adiabatic Core Temp -1%
Mole Fraction Routine
Final Fully Mixed Model
Delta Burn +50Delta Burn -50
Adiabatic Core Temp +1%
0.3 bar MAP - PHI = 1.0706ppm - 240 IMEP
IMEP Delta NO % Change
0.5 bar MAP - PHI = 1.01577ppm - 385 IMEP
IMEP Delta NO % Change
0.8 bar MAP2649ppm -
- PHI = 1.0628 IMEP
IMEP Delta NO % Change235 -178 -25.21 380 -218 -13.82 622 -194 -7.32244 201 28.47 390 245 15.54 634 178 6.72236 -33 -4.67 378 -79 -5.01 625 -82 -3.10245 71 10.06 393 83 5.26 641 29 1.09240 -4 -0.57 383 -27 -1.71 624 -29 -1.09241 15 2.12 387 40 2.54 631 21 0.79243 -139 -19.69 391 -237 -15.03 644 -285 -10.76235 174 24.65 378 261 16.55 624 263 9.93240 -13 -1.84 385 -70 -4.44 628 -174 -6.57238 25 3.54 384 87 5.52 618 123 4.64237 117 16.57 381 143 9.07 622 153 5.78243 -81 -11.47 389 -139 -8.81 642 -143 -5.40237 77 10.91 382 128 8.12 622 123 4.64241 224 31.73 385 280 17.76 628 229 8.64240 -281 -39.80 385 -513 -32.53 628 -553 -20.88240 198 28.05 386 332 21.05 628 360 13.59240 -165 -23.37 385 -298 -18.90 628 -356 -13.44242 -12 -1.70 385 -30 -1.90 639 -81 -3.06
776ppm - 240 IMEP 1858ppm - 385 IMEP 3259ppm - 628 IMEPIMEP Delta NO % Change IMEP Delta NO % Change IMEP Delta NO % Change243 -80 -10.32 390 -187 -10.06 644 -209 -6.41235 86 11.10 377 159 8.56 625 170 5.22240 259 33.42 386 479 25.78 628 463 14.21
Experimental NO = 734ppm Experimental NO = 158 1ppm Experimental NO = 232 1ppm
Table 5.3: Input Parameter Senstivity Analysis - Lean and EGR Points
Operating ConditionFinal Model Predictions
Residual +10%Residual -10%
Heat Transfer Mult. +10%Heat Transfer Mult. -10%
Crevice Volume +10%Crevice Volume -10%
Delta Burn +50Delta Burn -50
Fuel Air Ratio +1%Fuel Air Ratio -1%
Spark Timing ADV 2*Spark Timing RET 20
Intake Mixture Temp (+200)Rate Consant 1 +50%Rate Consant 1 -50%
Adiabatic Core Temp +1%Adiabatic Core Temp -1%
Mole Fraction Routine
Final Model Predictions
Delta Burn -50Delta Burn +50
Adiabatic Core Temp +1%
0.5 bar MAP -1731ppm -
PHI = 0.914359 IMEP
IMEP Delta NO % Change355 -256 -14.79363 279 16.12346 -103 -5.95366 85 4.91357 -44 -2.54360 8 0.46364 -330 -19.06346 371 19.13355 -68 -3.93361 42 2.43354 214 12.36363 -215 -12.42354 166 9.59359 429 24.78359 -667 -38.53359 376 21.72359 -339 -19.58359 -69 -3.99
1731ppm - 359 IMEPIMEP Delta NO % Change345 216 11.14363 -256 -13.20359 530 27.33
Experimental NO = 1649ppm
0.5 bar MAP700ppm -
- EGR = 8%393 IMEP
IMEP Delta NO % Change384 -98 -14.00397 91 13.00380 -33 -4.71401 43 6.14392 -11 -1.57395 4 0.57399 -156 -22.29379 199 29.14382 -56 -8.00391 32 4.57389 100 14.29398 -99 -14.14387 53 7.57393 184 26.29393 -278 -39.71393 186 26.57393 -158 -22.57392 -21 -3.00
700ppm - 393 IMEPIMEP Delta NO % Change379 -96 -13.71398 109 15.96393 242 35.43
Experimental NO = 803ppm
effect on NO also comes with very little change in predicted IMEP, meaning the pressure
trace was relatively unaffected by the residual perturbation. For the mid load lean and
EGR points a ten percent error in residual fraction could lead to an approximate 15% error
in NO predictions. Since very little experimental data is available for residual fraction, a
10% error in the assumed values used is not unreasonable.
The heat transfer multiplier, used to increase the amount of heat loss to the walls
during the combustion and expansion process, affected NO predictions less than half as
much as residual fraction for the same ten percent change at all operating conditions. A ten
percent change in the size of the crevice used to model combustion inefficiency had a
negligible effect on NO predictions for all cases. This variation in crevice size is assumed
to also verify the insensitivity of NO to the assumed temperature of the crevice volume.
However, neglecting the combustion inefficiency effect altogether would cause large
modeling errors as was demonstrated earlier.
5.5.2 Input Parameter Perturbation
The following section will explore the sensitivity of NO to parameters which were
assumed to be known with certainty and used as model inputs (Burn Rate, Fuel Air
Equivalence Ratio, Spark Timing, and Fresh Mixture Temperature). Burn rate was varied
by changing the delta burn parameter of the Wiebe Function to simulate a 5 degree slower
and faster burning cycle. This will essentially keep the 0-2% bum angle the same while
extending or reducing the 0-50 and 0-90 bum angles. Faster burning cycles will shift the
heat release earlier in the cycle increasing cylinder pressure and temperature, and slow
burns will have the opposite effect. The layered model has a large amount of sensitivity to
these modest changes for all of the operating conditions, with a maximum delta NO change
of over twenty percent at the light load and EGR points. However, these slight changes in
burn rate do have a large effect on the location of peak pressure. So, it is unlikely that any
of the experimentally determined bum rates used to generate the modeling results could
have been in error by +/- five degrees without this being detected easily.
Fuel air ratio changes of one percent had only moderate effects on the predicted NO
values overall. A 1% error though is reasonable and often accepted to be the level of
98
accuracy for the Horiba Meter used. Also, unlike the other parameters investigated thus
far, NO predictions show their largest sensitivity, over 6 %, to the amount of fuel at the
high load point and EGR point. This is interesting mainly because these tables were
generated in hope of identifying why high load points are over predicted and EGR points
are under predicted. Sensitivity to fuel air ratio may also be important when trying to
understand how mixture non-uniformity will affect NO predictions. All model results are
generated under the assumption that the charge composition is uniform throughout the
cylinder.
Spark timing variation was investigated mainly because from cycle to cycle the
initial kernel development often varies, causing an effective degree or two shift in 0-2%
burn rate. The sensitivity results are obvious based on the spark timing sweep discussed
earlier. Also, as with adjusting the burn rate duration parameter, these errors are easily
detected because of the shift in peak pressure location they cause. Regardless, it is
important to show both of these sensitivities to demonstrate that accurate burn rate data is
critical to NO predictions.
Finally, the assumed incoming fresh mixture temperature was increased from 310K
up to 330K. Since intake temperature has a large affect on the amount of trapped mass, the
routine to guarantee accurate cylinder charging was used with this parameter. This was
done to effectively increase the temperature of the unburned mixture prior to spark
discharge with out changing the total mass or composition. The NO sensitivity to this 20
degree increase was less than 10 percent for all operating conditions and had a diminishing
affect at high load. This is an important variable, however, because the thermal
environment of the intake manifold will vary with operating conditions, and the amount of
heat absorbed by the incoming mixture would fluctuate.
Rate constant effects were again explored because the percent change curves shown
earlier were developed while going from 3.3E+12T 3 down to 1.66E+12TO.3. A plus or
minus fifty percent value was employed to the calibrated value of 1.66, and the expected
trend was again observed. Unlike earlier observations, decreasing k, further below the
already calibrated value showed less variation with load than before, since NO levels are
99
now further below equilibrium values at the time of peak pressure and temperature. This
could make effects such as residual NO slightly more of a factor.
5.5.3 NO Sub-model Variables
The final two parameters adjusted relate to the temperature profile generated for the
adiabatic core and the mole fraction routine. Since STANJAN had been implemented to
investigate the thermodynamic routines, it was easy to validate MIT's simplified
equilibrium concentration routine as well. When species concentrations are required for
the Zeldovich reactions, the MIT cycle simulation uses a code which takes pressure and
temperature as inputs and returns burned gas composition, considering only fourteen
chemical species. Therefore, in place of this routine, STANJAN was called. NO showed
very little sensitivity, less than 4 %, to the equilibrium mole fraction routine used for all
conditions. This is interesting for the EGR point since direct mole fractions could be input
to STANJAN that matched the artificial EGR used, instead of the original cycle
simulation's natural EGR with water vapor.
The adiabatic core temperature parameter represents a direct 1% increase to the
temperature of each layer in the adiabatic core during the combustion and expansion
process. This shows the dramatic effect that an approximate 25 degree error in the peak
temperature prediction can have on NO concentrations. A one percent change in adiabatic
core temperature caused predictions to be off by over twenty percent at all points other than
the high load condition. Therefore, it seems unreasonable to expect a model with this level
of sophistication to predict NO concentration with more accuracy an what was
demonstrated earlier. The room for error is just too large. This also makes the STANJAN
section more of a concern, since a 0.6 % temperature error can be so important.
5.5.4 Fully Mixed Sensitivity
Even though the layered routine was chosen to be the focus of this study, the fully
mixed NO sensitivity to burn rate was investigated for the purpose of later discussion. It is
seen that when subjected to the same amount of burn duration variation, +/- five degrees, a
fully mixed routine shows only half the sensitivity as with a layered model. This is too be
100
expected since a fully mixed routine is essentially removing the contribution of early and
late elements, unlike the layered model which will pick up and amplify slight changes in
the bum angle development. This point will be discussed again in the cycle by cycle
analysis section next chapter. The fully mixed model is also shown to be equally sensitive
to even a one percent error in adiabatic core temperature.
5.6 Summary and Conclusions - Steady State Modeling
A modeling calibration methodology was developed to ensure accurate
thermodynamic representation of the cylinder gases throughout the cycle. The first
variable considered was the total mass and mixture composition in the cylinder at the time
the intake valve closes. Since it would not be meaningful to compare NO results from a
model with poor residual and total mass predictions, the MIT cycle simulation was forced
to trapped the correct charge for all experimental points considered. This resulted in
having to drop the intake manifold pressure slightly to reduce total mass and inputting a
small amount of EGR to match the amount of expected residual gas fraction.
However, predicting accurate cylinder pressure required more than just correct
mass. A single point calibration of the heat transfer routine was done at the baseline
operating condition. It was concluded that a 70% increase to the Woshni correlation, from
the time of spark through EVO, gave good pressure agreement during the expansion stroke.
Taking in to account that not all of the inducted mass contributes to the heat release
analysis was also deemed necessary for improving model pressure predictions. To handle
this, a combustion inefficiency sub-model, based on a simple crevice analysis, was
employed to get an accurate match of peak pressures. A comparison of model and
experimental pressure data showed that the single baseline point calibration of heat transfer
and combustion inefficiency was effective over the operating range considered. Finally,
since bum rate was used as an input, peak pressure location agreed well with experiment
and modeling error was reduced.
After the thermodynamic routines were calibrated in the manor described above,
NO predictions were investigated. It was concluded that using a Zeldovich mechanism
reaction one rate constant of 1.66E+12TO.3 gave an exact match with experimental data at
101
the baseline operating condition. Using this same rate constant, the extended Zeldovich
mechanism alone was shown to be able to predict NO concentration as a function of engine
load, fuel air equivalence ratio, and spark timing to within 15% accuracy. It was also
concluded that, for all experimental sweeps, using a layered adiabatic core with a boundary
layer improved the slope of modeling predictions in comparison with a fully mixed model.
A great deal of accuracy would be lost without using a layered routine to model in-cylinder
temperature stratification. An attempt was made at modeling the effects of EGR on NO
concentration by using a simulated mixture of nitrogen and carbon dioxide. The accuracy
of the calibrated model with the Zeldovich mechanism was shown to deviate from
experiment by close to 30%.
A detailed sensitivity analysis was carried out to explore the key factors in NO
formation and limitations of both the cycle simulation itself and the extended Zeldovich
mechanism. Increasing the amount NO chemistry considered, by adding the N20
mechanism, was shown to have a negligible effect on the load, spark, and EGR sweeps and
only modest increases under lean operation. The simplified thermodynamic routine
developed by Martin and Heywood to approximate equilibrium properties was verified by
STANJAN over the operating range studied. The effects of considering the left over
residual NO concentration was concluded to have only a minor effect on the load sweep,
but could be important for cycle by cycle modeling. Using a detailed kinetic calculation
instead of a simple equilibrium radical pool analysis was shown to improve the slope of the
Zeldovich mechanism predictions at the cost of more computational time. Based on the
input/unknown parameter sensitivity analysis tables, model predictions of NO
concentration were demonstrated to be most sensitive to residual gas fraction and bum rate.
NO predictions were also concluded to be only slightly affected by small changes in the
amount of heat transfer and effective size of crevice volume used.
For practical applications, this investigation showed that model areas that require
the most attention to detail are the valve flow routines and the burn rate model. With
confidence in these two areas, a single point calibration of combustion inefficiency effects
and heat transfer was concluded to be adequate for making good predictions of cylinder
pressure and its phasing. The final conclusion reached was that predicting NO
102
concentration is mainly a thermodynamic problem, and the extended Zeldovich mechanism
alone with a layered adiabatic core and boundary layer can be used to make predictions of
NO concentration over a wide variety of operating conditions with reasonable accuracy.
103
20001800
16001400
12001000
800600400
2000
chanismh Mech.
ental Data
I W I I i I
0.8 1.0 1.2 1.4
Equivalence Ratio
Figure 5.1: Effect of Adding N20 Mechanism - Equivalence Ratio Sweepw/ kl=1.66E+12TO. 3 - 1500 rpm - MAP=0.5bar
2000
180016001400
1200
1000800600400
2000
Adjusted N20 Mech.
- - -Zeldovich Mech.
' Experimental Data'
/
I
-I I I
0.8 1.0 1.2 1.40.6
Equivalence Ratio
Figure 5.2: Effect of Adding N20 Mechanism - Equivalence Ratio Sweepw/ kl=1.5E+12T0 .3 - 1500 rpm - MAP=0.5bar
104
N20 Me- - -Zeldovic
/' * ExperirrIm
/
I'
I'
'
I
0.
0.
lo-N0z
0
CW
0.6
0-
0z
0
1.30 -
1.15
1.00
0.85
0.70
AA
A
AA
AA a A
-C)
0
N
0C'Jz
1.000 -
i i i i 1 0.8500.60 0.80 1.00 1.20 1.40
Equivalence Ratio
* Load Sweep
* EGR Sweep
aU
0.33bar0% EGR
£ a
0.8bar16% EGR
Figure 5.3: Overall Effect of Adding N20 Mechanism - All SweepsRatio of N20 over Zeldovich
0 Exp. Engine Out NO
- -- NO in Unburned MixtureA & Exp. Residual
A
n
E
0A
0 A
.
A
I I
0.5 0.7
-20
.16L
14
10
88
-- 60.9
MAP (bar)
Figure 5.4: Amount of Residual NO in Unburned Mixture - Load Sweep
105
0
N)
0
C)4
z
+
00CL
CL0
LM000z
2500 -
2000 -
1500 -
1000 -
500-
0-
0.3
1.150
20 -
15 +
10 +
5 +
0±4-
6
iH
0 C;
MAP (bar)
Figure 5.5: Effect of Modeling Residual NO Concentration - Load Sweep
(a)Steady State Load Sweep
3500-
3000-
2500 --
0 1500-
1000
500
0
--- Layered AC.*Experimental Data
7-dVmeCU/~elwt
0.2 0.4 0.6 0.8
MAP (bar)
(b) Sensitivity to Rate Constant k1
40-
30-0z
10_
0.33 0.4 0.5 0.6 0.8
MAP (bar)
Figure 5.6: Overall Effect of Modeling Residual NO Concentration
106
0z7@10
0
0)
-H -1i
6
m Stanjan Equilibrium Code
Martin Simulation Routine
- ~--
335 350 365 380 395 410 425 440
Crank Angle (Spark = 3350)
Figure 5.7: Equilibrium Property Analysis - Baseline Operating ConditionBurned Zone Temperature Predictions
m Specific Heat Cp - Stanjan
Specific Heat Cp - Martin
MuEE
CU
1.28 -
1.26
1.24
1.22
1.2
1.18
1.16
1.14
_ Gamma - Stanjan-Gamma - Martin
U.
-
-U
-U
-U
2000 2500 1500
Temperature (K)
2000
Temperature (k)
Figure 5.8: Equilibrium Property Analysis - Baseline Operating ConditionBurned Zone Specific Heat and Gamma - (Spark - EVO)
107
3000 -r
0.E
C)
0N
2500 -
2000 -
1500
0D
*1)
CD
0.(0
2.3E+07 _
2.1 E+07 -
1.9E+07 -
1.7E+07 -
1.5E+07 -
1.3E+071500 2500
' ' '
+ Enthalpy - Stanjan
Enthalpy - Martin
(D
0'a
(D
2000 2500
3.OE-03 -
2.5E-03 -
2.OE-03 -
1.5E-03 -
1.OE-03 -
5.OE-04 -
0.OE+00
+ density - STANJAN
- density - Martin
-/-/
-/-~
1500 2000
Temperature (K) Temperature (K)
Figure 5.9: Equilibrium Property Analysis - Baseline Operating ConditionBurned Zone Specific Enthalpy and Density - (Spark - EVO)
3000
2500
2000 -
m 1500-CLE.E 1000 -
500 -
0-
. 20th Element
Constant EnthalpyCombustion
- Unburned ZoneTemperature
335 360 385 410 435 460 485
Crank Angle (Spark = 337)
Figure 5.10: Layered Model A.C. Temperature ProfilesBaseline Operating Condition
108
0.0-
Q
w(I,
VC)
6.OE+094.OE+09
2.OE+090.OE+00
-2.0E+09-4.OE+09
-6.OE+09
-8.OE+09-1.0E+10
1500 2500
'
-
-
11
L
ECD:-
x
3000 --
2500 --
2000 -
1
Temperature
- - - - NO concentration
500 4
1000 -
500 -
01
*1
2 3 4 5
Time (Arbitrary CA @ 1500rpm)
Figure 5.11: Constant Enthalpy Combustion Process from Tunburned = 850K1500 rpm, Stoichiometric
- - - - Layer Temperature
2800 -
2400 -
2000 -
1600 -
1200 -
800 -
400 -
0 !
337
. Senkin -NO,:~:-- Simulation-NO
387
7000E
6000 a-
5000 o
4000 d
3000 C00
2000 0z
1000
0
437
Crank Angle (Spark = 337)
Figure 5.12: Cycle Simulation and SENKIN NO Profiles for Selected Layers1500 rpm, MAP=0.5bar, Stoichiometric
109
E
0
.i
- - - - Layer Temperature
. Senkin -NOSimulation - NO
ME
*u mu u m -
~-
- 3500
- 3000 ECL
00
- 1500 C
0
- 1000 z
- 500
0
330 350 370 390 410 430 450
Crank Angle (Spark = 330)
Figure 5.13: Cycle Simulation and SENKIN NO Profiles for Selected Layers1500 rpm, MAP=0.3bar, Stoichiometric
-- -- Layer Temperature
U Senkin - NO
Simulation - NO
* mesmmmmmummm
I I -
8000E
CL
-7000 C-
- 6000 C
0
.- 5000
- 4000
- 3000 0
-0 -- 20000O
- 1000
0
342 362 382 402 422 442 462
Crank Angle (Spark = 342)
Figure 5.14: Cycle Simulation and SENKIN NO Profiles for Selected Layers
1500 rpm, MAP=0.8bar, Stoichiometric
110
2800
2400
2000
1600
1200
800
400
Q
E(Dc-
0
2800-
2400
.2 2000 -
E. 1600 -E11200-
800-
9 400-
0
-
-
- - - - Layer Temperature 8000. Senkin - NO-: Simulation - NO
e: --- --
- ~.--
2800 -
2400 -
2000 -
1600 -
1200 -
800 -
400 -
(D
E
.
7000
- 60000
- 5000
- 4000
- 3000 00
- 2000 z
- 1000 %
-0
337 357 377 397 417 437 457
Crank Angle (Spark = 337)
Figure 5.15: Cycle Simulation and SENKIN NO Profiles for Selected Layers1500 rpm, MAP=0.5bar, PHI=0.914
- - - - Layer Temperature
. Senkin - NOSimulation - NO
2800 -
2400
2000 -
- - - ----
600 -
200 mU""" ""ME "
800 -
400 --
0328 348 368 388 408 428
- 2000
- 1800
- 1600 ECLC.
- 1400 r0
- 1200C
- 1000
-800 00
- 600 z
400
-200
0448
Crank Angle (Spark = 328)
Figure 5.16: Cycle Simulation and SENKIN NO Profiles for Selected Layers1500 rpm, EGR=12%
111
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Eu....
E.. .
' '
...
.,,
.
0
Q
L
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ca-j0
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1
--
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: q
CHAPTER 6
CYCLE BY CYCLE NO VARIATION - DURING STEADY STATE
OPERATION
Up to this point, all of the NO data shown was from time averaged steady state
operation results. This is very useful for understanding general trends in NO formation,
and modeling this process only requires an estimation of average input parameters, such as
air flow, equivalence ratio, residual fraction, burn rate, and so on. However, even while
operating at a steady state point, it is well established that cycle by cycle variation of the
above listed parameters can be substantial [11]. From chapter 5, it was also clear that
slight variations to these input parameters can cause large changes in model predictions for
engine out NO. Thus, it would be interesting to explore the amount of cycle by cycle
variation that occurs while operating at a steady state point, and see if what was learned
during chapter 4 could be used to explain cyclic trends in NO concentration.
6.1 Fast NO Meter Notes
As was discussed in Chapter 2, Cambustion has developed a fast NO detector
which is capable of measuring NO concentration with a response time of approximately 4
ms. With each exhaust event lasting 27 ms, the device can be used to sample gas from the
exhaust port and analyze engine out NO on a cycle by cycle basis. Figure 6.1 re-illustrates
the fast NO sampling system as well as the sampling location used to gather the upcoming
experimental data. A sample probe with a length of 250 mm and inside diameter of 0.6
mm was placed in the exhaust port of the firing cylinder approximately 10 cm downstream
of the valves, just after the port septum, as marked by the X in figure 6. 1b.
By estimating the volume in the port between the tip of the probe and the valves, a
calculation of the amount of exhaust gas mass lying ahead of the probe can be made using
the ideal gas law. At an assumed exhaust temperature of 1000 K, there is approximately
0.05 g of exhaust ahead of the probe; this will be used in an upcoming illustration. The
reader is referenced back to chapter 2 for how the fast NO meter, shown in figure 6.1a,
operates. For our purposes later, it is also important to note that, it takes approximately 32
CA at 1500 rpm for exhaust gas to travel from the tip of the probe up into the reaction
chamber for analysis. This value was calculated with the flow modeling software provided
by Cambustion [26], SATFLAP 3, based on the size of sampling probes and system
operating pressures.
For the upcoming analysis, 150 cycles of data were processed, containing exhaust
port NO readings, cylinder pressure, and fuel air equivalence ratio, at each of the operating
points in the four sweeps discussed in the steady state modeling chapter.
6.2 Signal Characteristics During Lean Operation - PHI = 0.91
When using a fast response emission analyzer, considerable effort must be made to
understand and interpret the signal as a function of operating conditions. Figure 6.2 shows
the fast NO output signal along with cylinder pressure for five consecutive cycles while
firing the engine under steady state conditions with PHI = 0.914, MAP = 0.5 bar. The
steady state average NO concentration for this operating condition was 1694ppm.
Following the figure from left to right, it can be seen that while the first cycle is in the
compression and combustion process, the fast NO signal remains steady at around
1500ppm, since there is no motion in the exhaust port. At this time, the detector is
sampling the left over exhaust from the previous cycle. Late in the expansion stroke, when
the exhaust valves open, fresh exhaust is released into the port pushing the previous cycle
along, causing the NO concentration to rise sharply. (The first cycle shown is the fastest
burning of the five and has the highest peak pressure, thus the high level of NO is
understandable.) The signal then has an initial spike before leveling off at its new closed
exhaust valve level. The signal is again steady until the exhaust valves open from the
second cycle shown. Now there is a rapid drop in the signal from 2200 ppm back down to
1200ppm, because the second cycle was a very slow bum with a low peak pressure.
The amount of observed variation seen here is quite substantial and illustrates the
importance of accurately modeling the burn rate and peak pressure when making
predictions of NO. In figure 6.2, the NO level seems to scale well with the observed peak
114
pressure of the cycles. Other researchers have looked at making the correlation of NO with
peak pressure for steady state operation [32] and recently for exhaust port readings [10].
Figure 6.2 offers an excellent opportunity to see if the steady state model we have
discussed up to this point can predict the large amount of variation seen on a cycle by cycle
basis. By processing this data set with the MIT heat release analysis program, the 0-2, 0-
10, and 0-90 percent burn angles can be determined for the five cycles shown. The Wiebe
function can again be defined for each cycle and fed to the simulation, while leaving the
remainder of the inputs at the same values used for accurately modeling the steady state
ensemble results. Figure 6.3 shows modeling predictions of cylinder pressure and cyclic
NO level in comparison to experiment. Simply by changing the bum rate alone, the
layered model is able to predict peak cylinder pressure to within 4% and location of peak
pressure to within 1 degree. The wide variation in NO concentration is also captured quite
well. However, displaying the over 3400 cycles of data collected in this manor would not
be practical or informative, a methodology must be developed to tag an EVO period NO
concentration level to each cycle. Then this value can be filed with heat release analysis
information and interpreted in a broader sense.
6.3 Processing the Fast NO Exhaust Data
The first step in generating a cycle resolved value for NO concentration is
understanding the appearance of the signals and how the signal varies with operating
conditions. To accomplish this, many cycles from the five sensitivity analysis points (0.3
bar, 0.8 bar, 0.5 bar, PHI = 0.91, and 10% EGR) were analyzed individually. The first
thing noted was that the three operating conditions that all have MAP = 0.5 bar had signals
with similar characteristics. This is easily explainable since the exhaust flow event is
mainly a function of the engine load. Therefore, the analysis will proceed while
considering only three conditions: 0.3 bar, 0.8 bar, and 0.5 bar lean.
6.3.1 Signal Characteristics as a Function of Load
Figure 6.4 shows one complete representative cycle from each of three load points
along with corresponding pressure traces. This figure will be discussed extensively in the
115
next several pages, and several things should be noted. First, the exhaust valve closed
period (0-303CA) has a stable level for all three operating conditions, since the exhaust in
the port is stagnant and mixed during this time. Secondly, the three traces all take a
different amount of time to peak or bottom out denoted by the dashed line. This response
time delay can be attributed to two areas of the sampling set-up: mixing in the exhaust port
and mixing in the reaction chamber. Since the blowdown event is smaller at 0.5 bar, more
time would be available for mixing in the port and the previous cycle NO concentration
may have a larger impact on the new level than at 0.8 bar, where the old exhaust gases will
be purged quickly during blowdown. Looking at the trace labeled PHI=0.91, one could
speculate that at 360' CA new exhaust is entering the port at a concentration level of
around 1000 ppm. However, due to mixing effects in the port and reaction chamber, the
signal takes over 1600 CA to reach its steady level and no longer be influenced by the 2200
ppm previous cycle exhaust.
One final note from figure 6.4, all three traces have a distinct delay from the time
the exhaust valve opens to the point at which the NO signal starts to change from the
closed valve level to the new cycle NO concentration. This delay is marked by the arrows
and labeled in crank angles after EVO. This signal delay of 65' CA for 0.5/0.8 bar and
180' CA for 0.33 bar has two sources: time for the new exhaust to reach the front of the
probe and time for the new gases to flow through the sampling system, 32' CA. Since the
sampling system pressures are fixed for all operating conditions, the 32' CA shift will
remain constant. However, the time for new exhaust to travel from the cylinder to the tip
of the probe requires a more detailed analysis.
6.3.2 Plug Flow Modeling of the Exhaust Event
Figure 6.5 shows the predicted exhaust mass flow rate and integrated total mass
exhausted, taken from cycle simulation output generated during the steady state analysis.
As the intake manifold pressure increases, the initial blowdown process becomes larger.
This is expected since the ratio of cylinder pressure to exhaust manifold pressure, at EVO,
varies from near 1 at 0.33 bar to approximately 4 at 0.8 bar as was shown in figure 6.4.
The displacement part of the exhaust flow profile remains consistent regardless of load.
116
Because modeling of mixing phenomena in the exhaust port of a firing engine was beyond
the scope of this study, the flow through the port will be modeled as a plug flow.
Therefore, when the exhaust valves open, it is assumed that the new exhaust will push the
previous cycles exhaust gas away with little mixing. With this assumption, the time it
takes the new cycle exhaust to reach the tip of the sampling probe can be calculated. Since
the mass ahead of the probe was estimated at 0.05 g, figure 6.5 marks the added delay due
to this effect. For 0.5 bar and 0.8 bar the port is filled in about 35 CA. While at 0.33 bar
the delay is over 150 CA since mass flow is initially from the exhaust port back into the
cylinder at EVO. By adding this to the 32 CA transit time, the total delay seen in figure 6.4
is closely approximated.
6.4 Three Different Methods of Determining a Cycle Resolved NO Value
With the signal appearance now better understood, three different ways of
calculating the cycle resolved NO concentration from the data in figure 6.4 can be
considered. The simplest method would be to time average the NO level over the exhaust
valve closed period, and attribute this concentration level to the previous cycles pressure
history. At light loads this may be an acceptable assumption since the mass remaining
ahead of the probe will represent a large fraction of the total exhaust. The next method
considered was to assume a constant delay, equal to the transit time through the system and
additional time to fill the port, as described above. Then the signal can be time averaged
over the shifted exhaust valve open period. In figure 6.4, this would be equivalent to
averaging the NO concentration for 0.8 bar, or 0.5 bar lean, from 3700 to 6100 CA. The
final method would be to assume the exhaust is a plug flow with the same constant delay.
Then the exhaust profiles from figure 6.5 can be used to mass weight the NO trace between
370 and 610 CA. To determine which of these methods would be the most accurate, it
is important to consider more than one representative trace, to understand whether the
analysis used above can be applied to all the cycles collected.
117
6.4.1 Analysis of Three Methods for MAP = 0.5 bar, PHI = 0.91
Figure 6.6 now shows five consecutive cycles at the 0.5 bar lean operating
conditions used in figures 6.2 and 6.3. The cycle used in figure 6.4 is the last cycle in this
plot, represented by the square data points. For discussion purposes, the mass flow rate
profile from the cycle simulation is also shown along with the highest and lowest pressure
traces.
The first thing noted is that the 65' CA delay time is consistent for all of the cycles.
The signal remains steady during the exhaust valve closed period and then begins to change
at approximately 370' CA. The fastest burning cycle, 1, has the highest peak pressure and
the highest NO concentration level. Cycle number 5 represents the lowest peak pressure
and NO level. The response time or time it takes each cycle to reach a maximum or
minimum level is similar for each trace. Assuming new exhaust reaches the front of the
probe at 370' CA, it takes between 1200 and 180' CA for each trace to reach a maximum
or minimum. Using the mass flow curve, both time and mass average NO values can be
calculated between 370' and 610' CA. It should be noted that the same cycle simulation
mass flow rate profile was used for all the cycles at any one operating condition. (Cyclic
variation in the cylinder pressure trace will change the mass flow diagram slightly.
However, investigation showed, this effect was negligible.) Table 6.1 shows a comparison
of cycle resolved NO values calculated with the three different approaches.
Table 6.1: Comparison of Different Methods for Calculating a Cycle Resolved NO Value1500 rpm, MAP = 0.5 bar, PHI = 0.914
Cycle # Mass Avg. Time Avg. EVC1 2236 2230 21292 1266 1315 12143 1558 1589 13724 2066 1962 22395 1352 1474 991
For the all the cycles, the mass averaging and time averaging method predict NO
levels within 10% of each other. However, for the last three cycles noticeable differences
exist between the EVC value and the others, with a maximum of 27 % for cycle number 5.
Cycle five shows a gradual drop from 2200 down to 990 ppm over the first 180' CA.
118
During this period, its unclear how much of the signal's appearance is due to mixing with
the previous cycle in the port and reaction chamber and how much is due to NO
stratification effects. If it was a stratification effect, it would be expected to be more
consistent, such as the first gases through the valve are always higher or lower than the
remainder of the cycle. Because it appears to be a mixing effect, the cycle resolved NO
level will be biased by the previous cycle when using the mass and time averaging
methods.
6.4.2 Analysis of Three Methods for MAP = 0.8 bar, Stoichiometric
Figure 6.7 shows five consecutive cycles for the 0.8 bar operating conditions
plotted with the same format. Again, all the cycles begin responding to the fresh exhaust
event at approximately the same location of near 360' CA. The fastest burning cycle is
again producing the most NO, but the slowest burning cycle does not produce the least NO
anymore. The appearance of the traces overall is much different than the 0.5 bar lean
condition shown before. The response time or time to reach a maximum or minimum has
also shortened.
Four of the traces show an initial dip followed by a substantial rebound back up
before the exhaust valve closes, as in cycles 1 and 3. This could be due to a stratification
effect in the exhaust or possibly due to flow disturbance in the sampling system due to the
vigorous blowdown period. If it is truly due to stratification, the importance of mass
weighting the signals now becomes clear. The large mass flow during the blowdown
process corresponds well with the initial dips and most be taken into account when
determining the cycle resolved NO concentration. Table 6.2 again shows the difference in
calculated NO values with the three different approaches. Mass and time averaged values
again agree quite well for all the cycles. For the two cycles that showed the largest initial
dip, the EVC value is significantly higher than the other two methods.
119
Table 6.2: Comparison of Different Methods for Calculating a Cycle1500 rpm, MAP = 0.8 bar, PI = 1.0
Cycle # Mass Avg. Time Avg. EVC1 1718 1806 22852 2158 2116 20763 1684 1772 21584 2061 2112 21815 2606 2639 2673
Resolved NO Value
6.4.3 Analysis of Three Methods for MAP = 0.33 bar, Stoichiometric
For completeness, figure 6.8 shows five consecutive traces for the lowest load
considered in this study, MAP = 0.33 bar. However this operating condition showed
similar characteristics and does not exhibit any features that have not been discussed.
Appendix B of this thesis contains a summary of the bum rate analysis output and the three
different calculated NO values for all the operating conditions considered, and the reader
should review this information now before continuing. The format shows the first and last
cycle details, along with average, standard deviation, and coefficient of variation values for
the 150 cycle data sets. The coefficient of variation, COV, is defined according to
Heywood [23] as the standard deviation of a variable over the mean value. A discussion of
the four different sweeps will now be given.
6.5 Load Sweep Cycle by Cycle Variation
Figure 6.9 shows the amount of cyclic variation observed over the entire
stoichiometric load sweep. The 150 cycles of mass weighted NO data are plotted against
the observed peak pressure of each cycle for the five different load points. Several
interesting trends should be noted. At low loads, the cycle resolved NO value corresponds
almost linearly with peak pressure. It is expected that if the pressure trace is modeled
accurately at low loads, the scatter, at any given peak pressure, could be explained by slight
variations in residual fraction, fuel/air ratio, or overall crevice effect. However, as the load
increases, the amount of scatter in the data appears to be growing and no clear correlation
with peak pressure can be observed. This raises the question: Why, with essential the same
pressure trace, does engine out NO concentration vary greatly at high load? When the NO
cyclic data was plotted against IMEP or representative bum angles, the scatter showed
120
similar trends. Therefore, peak pressure was determined to be the most informative and
will continue to be used. Appendix B, table B.1, shows the average heat release
information and a summary of the three different ways of calculating the cycle resolved NO
value for the five different load points. The information in this table will now be used to
examine the spread in the data at high load.
Figure 6.10 shows the effect of using time averaging and exhaust valve closed
period NO calculations instead of mass weighting. Even though, individual cycles were
shown earlier to be sensitive to the method used, the overall scatter and 150 cycle average
value remained almost unchanged. This is seen in the last three columns of table B.1.
Therefore the high load trend is not attributable to how the cycle resolved NO value is
being determined. Since mass weighting most accurately represents what is physically
happening in the port, all upcoming NO results will be presented with this method.
The scatter at high load expressed in terms of COV of NO about the single point
mean is changing very little. However, along any given line of peak pressure, the amount
of variation is increasing with load. The COV of IMEP and the 10 - 90% burn angles,
from table B.1, both remain small over the entire sweep. Thus, nothing about the
combustion process changes can explain the added scatter. The only variable that shows
increasing variation with load is the fuel/air equivalence ratio. Referring back to table 5.1
and 5.2 from chapter 5, high load operation also showed the least amount of sensitivity to
residual, heat transfer, crevice volume, and burn rate. Thus, the sensitivity analysis does
not explain the added variation. Again, the only variable that showed larger sensitivity at
high loads was fuel/air ratio.
One possible explanation for the larger high load scatter is that the exhaust port NO
value was calculated from a single point measurement. The larger scatter could simply be
due to error introduced by the single measurement location, becoming more significant as
mass flow rates past the probe are increasing. The overshoot and recovery effect
demonstrated in figure 6.7, would support this explanation. If point measurements were
taken from several different locations in the port simultaneously, a better understanding of
NO stratification and mixing would be developed.
121
Another explanation could be that mixture non-uniformity effects are growing with
intake pressure. The mass closest to the spark plug which bums early in the cycle could be
varying from rich to lean on a cyclic basis. If the first few layers to bum were slightly lean,
the NO concentration could be maximized. With the opposite being true, if the first few
layers bum under rich conditions. The question that remains is why would the mixture be
less uniform at high load conditions than light loads. The first thing that would support
this explanation would be the increasing amount of fuel/air ratio variation with load noted
in table B.1. One standard deviation at 0.8 bar was shown to exceed one percent of the
average value. From the sensitivity analysis, table 5.1, a one percent change in fuel air
ratio could cause NO prediction errors of approximately 6%. It could be speculated that
early burning layers could be several percent lean or rich and drive the NO concentration
swings. The second thing that would support this explanation is that the blowback of
residual into the intake during the valve overlap period is decreasing with load. Therefore,
at MAP = 0.8 bar, the amount of mixing in the manifold would be less vigorous than the
low load conditions. The propane was continually fed into the manifold rather than being
injected cyclically, and this would also support the need for blowback mixing.
6.6 Cycle by Cycle NO Variation - EGR, Equivalence Ratio, and Spark Sweeps
Figures 6.11 through 6.14 describe the amount of cyclic variation seen while
operating the engine at 1500 rpm, 0.5 bar, and varying the fuel/air equivalence ratio and the
amount of EGR. Figure 6.12 was used to make the lean side of the sweep clearer and
shows only the first two lean points. Tables B.2 through B.4 contain a summary of NO
values and combustion variables along with statistics for each sweep. Again, the NO
values calculated with the three different approaches showed negligible differences for
average NO value and experimental scatter.
6.6.1 EGR Sweep
Looking at the EGR sweep in figure 6.11 first, each level of dilution appears to
follow a linear correlation with peak pressure, and the fit gets better as the EGR level rises.
This information is detailed in table 6.3 along with the slope of each linear fit and the 150
122
cycle average NO value. The range of peak pressure variation remains fairly consistent
between 17 and 24 bar, and the NO sensitivity to peak pressure appears to decrease with
higher dilution levels. However, when looking at the slope of the linear fit, the average NO
level must be considered. On a percent basis, the NO sensitivity to peak pressure changes
is actually growing with increasing amounts of EGR. From the layered modeling approach
applied earlier, NO concentration should roughly scale with peak pressure and
corresponding temperature as shown in equation 6.1 below. Therefore, as burned gas
gamma increases, the sensitivity to peak pressure should increase slightly. Exhaust gas
recirculation will cause slight increases in burned gas gamma based on output from the
cycle simulation thermodynamic routines so the data follows the expected trend.
(7 Y-1/y
NO~ T max (Eq.6.1)spark
The heat release analysis from appendix B showed that combustion variability, in
terms of 10-90 percent bum angle and IMIEP, remained similar for all the levels of EGR
considered in this study. The increasing COV of NO about the mean value is explained by
the increasing sensitivity to peak pressure fluctuations and the slight increase in range of
peak pressure observed. It can be assumed that, for each operating condition, all the cycles
with same peak pressure would have a similar mean NO formation profile. Then, the
spread about the linear fit would have to be explained by variations in the amount of fuel,
residual, and mixture non-uniformity from cycle to cycle.
Table 6.3: Linear Correlation Analysis Results for Cyclic NO Concentration and Peak Pressure
Map = 0.5 bar Linear Fit Equation Goodness of Fit 150 Cycle Average NOOperating Condition y = mx+b R2 - Value Concentration (ppm)
Stoichiometric NO = 95(P.P.) - 388 0.45 16224% EGR NO = 82(P.P.) - 594 0.51 11618% EGR NO = 66(P.P.) - 580 0.61 805
12% EGR NO = 64(P.P.) - 792 0.73 53016% EGR NO = 42(P.P.) - 527 0.74 340
lean - 0.956 NO =136(P.P.) - 1050 0.71 1709lean - 0.914 NO = 169(P.P.) - 1695 0.8 1741lean - 0.838 NO = 179(P.P.) - 2355 0.74 1154rich - 1.06 NO = 75(P.P.) - 466 0.24 1167rich - 1.12 NO = 44(P.P.) - 331 0.24 644rich - 1.21 NO = 14(P.P.) - 133 0.32 178
123
6.6.2 Lean Operation
Figure 6.12 illustrates that as the mixture becomes slightly lean, the NO
concentration correlates well with the measured peak pressure. Figure 6.13 then shows the
remainder of the lean operation data with only the linear fit lines included from the first
two points. Appendix B, table B.3 again shows the combustion information for the entire
lean sweep.
The first thing noted from these two figures is that a linear fit is considerably better
for the first three lean points than under stoichiometric conditions as detailed above in table
6.1. NO sensitivity to changes in peak pressure is shown to be increasing as the mixture
becomes leaner. The same trend was demonstrated in the Chapter 5 sensitivity analysis.
This can again be explained by using equation 6.1 and noting that burned gas gamma will
increase on both side of stoichiometric. Below PHI of 0.838, the combustion variability
begins to grow substantially, and a linear fit is no longer appropriate. Here, the COV of
NO about the mean is over 35%. This should again demonstrate why expecting steady
state modeling results to be better than about 15% is unrealistic.
6.6.3 Rich Operation and Spark Sweep
Figure 6.14 and table B.4 give the details of the cyclic variation of NO under rich
operating conditions. As the mixture becomes rich, the combustion stability improves
slightly and the peak pressure variation is reduced. The linear fit is no longer as good a
correlation as it was on the lean side. Since burned gas gamma will increase as the mixture
goes rich, sensitivity to bum rate and peak pressure is also expected to increase.
Finally, figure 6.15 shows the cyclic variation of NO with peak pressure over the
stoichiometric, 0.5 bar spark sweep. The main thing to note is that the overall curve
becomes non-linear as the timing is advanced. This can be explained by the fact that NO
formation rates are non-linear with temperature. At retarded timings, the amount of peak
pressure variation is large and the data sets appear similar to those discussed above. As the
timing is advanced, peak pressure location nears TDC and the variation of peak pressure
itself is reduced. On a percent basis, though, the amount of scatter at any given peak
pressure value in the spark sweep is remaining fairly constant.
124
6.7 Cycle by Cycle Burn Rate Modeling
Since the amount of NO cyclic variation has been presented, it would be interesting
to see how well the steady state model used in Chapter 4 captures the slope of NO variation
with peak pressure. Figure 6.3 showed that, for the lean operating condition of PFH=0.914,
MAP = 0.5 bar, the steady state model was capable of following the NO variation by
simply matching the bum rate alone for each cycle. No adjustment to the residual fraction,
fuel air ratio, or temperature at the time of spark was considered. Now, this same burn rate
modeling approach will be applied to fifteen cycles from each of the five sensitivity
analysis points considered earlier, (0.5 bar, 0.33 bar, 0.8 bar stoichiometric and 0.5 bar
10% EGR and PHI = 0.914). Rather than simply taking 15 consecutive cycles at random
from each operating condition, five cycles around the mean bum rate, the five slowest
burning cycles, and the five fastest burning cycles were chosen at each condition. This will
test whether the layered model can capture the slope of the NO variation with peak
pressure. However, there are just too many unknown variables (residual fraction variation,
fuel variation, NO present in the residual variation, temperature at time of spark, and
mixture non-uniformity) to make a realistic, meaningful cycle resolved prediction without
making too many assumptions. For this reason, the slope of modeling predictions will only
be discussed in this section.
6.7.1 Load Sweep CBC Modeling
Figure 6.16 illustrates the 15 cycles chosen at the each load condition. The
modeling curve is not new, rather it is from the steady state modeling section shown earlier
in Chapter 4. It is displayed here for the purpose of illustrating the room for error when
making predictions of average NO concentration at any single operating condition. At
MAP = 0.5 bar and 0.33 bar, the NO concentration level of each peak pressure group
showed less than +/-10 % variation. Therefore, if the slope of the data with peak pressure
could be modeled, it is reasonable to attribute the variation to slight differences in residual,
fuel, or temperature at spark, based on the Chapter 5 sensitivity analysis. However at 0.8
bar, the five slowest burning cycles, with peak pressure of approximately 30 bar, show NO
125
concentrations ranging from 1500 ppm to nearly 3000 ppm. It does not seem reasonable
that this large variation is due simply to residual, or fuel. It is clear that either the model
used is missing some key physics at high load (such as mixture non-uniformity), or
measurement error due to mixing effects is driving the scatter.
Figure 6.17 shows model predictions of peak pressure and NO concentration when
only bum rate is fed to the cycle simulation. All the model points are generated using the
starting temperature, pressure, EGR amount, and MAP that resulted in the assumed steady
state levels of residual fraction and total mass. Thus, the state of the mixture prior to spark
was identical for all fifteen cycles at each operating condition. The Wiebe function
parameters were then defined based on the experimentally derived burn angles of each
cycle, and this was the only thing changed in the input file. For 0.33 bar and 0.5 bar, the
layered model was capable of predicting the changes in peak pressure and its location quite
well simply by changing bum rate. However, the model predicts higher sensitivity to peak
pressure than the experimental data showed based on the slope of the two different data
sets. The largest difference between model and experiment was 25% for both the high
pressure group at 0.33 bar and the low pressure group at 0.5 bar. From Chapter 5, table
5.2, a fully mixed model was shown to be approximately half as sensitive to burn rate
changes as the layered routine. Accounting for mixing between layers, by decreasing the
amount of new layers formed, could improve the slope of the NO predictions with peak
pressure.
Several things should be noted before discussing the high load condition. First,
from the steady state results summarized in table A. 1, the model was already predicting
average concentration 12% higher than experiment. Thus, the model is expected to be
making higher predictions in figure 6.17. The calibrated model was also under predicting
pressure slightly, and this can be seen at all of the peak pressure groups. For the high
pressure group, the bum rate of all five cycles was very similar and only one modeling
point was needed. The slope of the modeling predictions is close to the experimental trend.
However, the extreme variation of NO concentration in the low pressure group is difficult
to explain with anything explored in the sensitivity analysis section.
126
6.7.2 Lean and EGR Points - CBC Modeling
Figure 6.18 shows the last two operating conditions considered in the sensitivity
analysis section. Again the slope of the model predictions is steeper than the experiment
data for both operating conditions. For the lean condition, at high peak pressures, model
predictions of NO are with 5% accuracy even though the peak pressure is slightly low.
This was also seen in the first modeling example, figure 6.2. By again returning to figures
6.4 and 6.6 now, some of this slope difference at the lean condition may be explainable.
The PHI=0.91 trace showed exhaust port NO profiles with slow response times, and the
previous cycles NO concentration may be affecting the cycle resolved value. The number
5 trace in figure 6.6 and table 6.1 illustrates this point by showing that if the exhaust valve
closed level was used, cycle resolve NO would be much lower. Regardless, burn rate
appears to explain most of the cycle by cyclic variation observed for peak pressure and NO
scatter can be explained with the sensitivity analysis, other than at the high load condition.
6.8 Observations and Recommendations
Three different techniques were considered for obtaining a cycle resolved value of
NO concentration. For all of the individual cycles collected, less than 10% difference was
observed between time averaging and mass weighting the fast NO signal during the
exhaust open event. This is in agreement with the conclusion reached by Ball and Stone
[10]. Differences between mass weighting and exhaust valve closed period NO
concentration were as large as 40% for certain cycles. However, overall the three
techniques showed a similar amount of scatter at each operating condition.
A large amount of NO cyclic variation was observed at each operating point. This
re-emphasizes the importance of accurately modeling the experimental burn rate. Cyclic
NO concentration correlates almost linearly with peak pressure for low load, EGR, and
lean engine conditions. A given delta change in peak pressure resulted in a larger percent
difference in NO concentration (larger sensitivity to peak pressure) on both sides of
stoichiometric and with EGR. This trend was attributed to increasing burned gas gamma
under these conditions. The amount of NO variation at any given line of peak pressure was
shown to increase with engine load. The variation at low and mid load could be attributed
127
to slight variations in mixture composition and starting temperature differences according
to the sensitivity analysis results. However, the larger amount of scatter at a given high
load peak pressure was attributed to increasing variation in fuel air equivalence ratio and
possible mixture non-uniformity effects.
The brief burn rate modeling analysis with a layered model showed the cycle
simulation to be overly sensitive to bum rate changes as indicated by a steeper slope of NO
with peak pressure. Since a fully mixed model was demonstrated to be half as sensitive to
burn rate, it was concluded that limiting the number of layers used could improve the slope
of predictions. The large amount of high load scatter merits that future modeling efforts
should investigate the effects of mixture non-uniformity on NO predictions.
Any future work with the fast NO meter must focus on developing a better
understanding of the response time of the instrument and modeling the mixing process in
the port and reaction chamber. Sampling probes should be placed in several different
location of the exhaust port to ensure error is not introduced by a single point
measurement. This could reduce the amount of experimental scatter, by de-coupling the
current cycle of exhaust from the previous NO level.
128
Reactic chamber
Ozone in ....
A t_
Sample e-..MCUn MCUIDOptic-fibre Gaw mput
CP VAC
CP chamber CLD RemoteSampling Head
Transit time for Gas to Travel fromTip of Probe to Reaction Chamber
-32 CA at 1500rpm
X ~t
Estimated Mass in Exhaust PortAhead of Sampling Probe, X
- 0.05g @ 1000K
Figure 6.1: Fast NO Detector Sampling System Specifications
2800
2400
E. 2000
0z 16000
1200
800Lx
400
00 1000 2000 3000 4000
Crank Angle Arbitrary
Figure 6.2: Fast NO Detector Output for Five Consecutive Cycles1500rpm - MAP = 0.5bar - PHI = 0.913
129
25
20
15
10
5
0
--
' II
A Model NO and Pressure Prediction- Experiment NO and Pressure
1000
2400
2000
1600
1200
800
2000
-AA-A
-
--
I ti
25
20
10
5 0
0
3000
Crank Angle
Figure 6.3: Cycle by Cycle Modeling Comparison - Layered A.C.1500rpm - MAP = 0.5bar - PHI = 0.913
EVO
- I
- K
(XXXXXX xxx x
I a a
- MAP = 0.8 bar. PHI= 0.91
- 35
x MAP = 0.33 bar - 30
"xXXXxx :bb CA Dei1ay
1CXXXXXXXXAX180 CA Delay
c-
-25A
20
150--0
10
r 10 .S
-5
-0
0 60 120 180 240 300 360 420 480 540 600 660 720
Crank Angle Acquired
Figure 6.4: Exhaust Port Signal Characteristics - Variation with MAP
130
2800 -
*1
0.%E
.
0z
x-
400
0 10
E
0.%fz-0
0
LU
3500
3000 -
2500 -
2000
1500
1000 -
500
0-
klil ~ ~~ 1 kmm,\0I
flI I I
I
0.007 MAP = 0.8 bar 0.35------- MAP = 0.5 bar
0.006 A MAP = 0.33 bar 0.3
3 0.005 0.25
0.004 0.20
0.003 - 0.15 Wj
2 0.002 'A- 0.1
0.001 A 0.05 @SA 0
A AA A AAAA"AAA Mass Level to Fill Port"A-0.001 -0.05
483 523 563 603 643 683 723
Crank Angle (EVO - EVC)
Figure 6.5: Cycle Simulation Calculated Exhaust Port Mass Flowrate1500rpm - Load Sweep
3000 -- NO-1 - - -NO-2 25x NO-3 A NO-4
1 > NO-52500 A
20.
- 2000 Ao 15
L 1500 -xx x x x x X x x x x x xo 10
3 1000
w 500 Mass Flow - 50
0 0
0 60 120 180 240 300 360 420 480 540 600 660 720
Crank Angle Acquired
Figure 6.6: Exhaust Port NO Profiles for Five Consecutive Cycles1500rpm - MAP = 0.5bar - PHI = 0.914
131
3000 -
E_ 2500CL
0z
200001
(L
=~ 1500XwU
1000
-NO-1x NO-3. NO-5
- - -NO-2A NO-4
3
X L X X
X~ X
EVOass Flow -
40
35
30
25
20 g
15 )
10
5
00 60 120180240300360420480540600660720
Crank Angle Acquired
Figure 6.7: Exhaust Port NO Profiles for Five Consecutive Cycles1500rpm - MAP = 0.8bar - PHI=1.0
1000-
800-
600-
400-
200-
0
kAAAA - NO-1 - - NO-2 X xx NO-3 A NO-4 A hAA NISO So l NO-5 IN AA' AA&
3
'fss Flow
r~f~20V
10 -
12 $
C
8AQ
4
0
0 60 120 180 240 300 360 420 480 540 600 660 720
Crank Angle Acquired
Figure 6.8: Exhaust Port NO Profiles for Five Consecutive Cycles1500rpm - MAP = 0.3bar - PH1=1.0
132
E0.
0z
0-'
-cXw
3500
3000
2500
2000
1500
1000
500 -
0.8 bar
0.33 - 0.41
0 i
10 15
0.5 bar -
-- a
bar
UN-
A AA AA A
A~ AAAL
AA ~ A
AL A
I I I I
20 25 30 35
Measured Peak Pressure (bar)
Figure 6.9: Cycle by Cycle Variation of Exhaust Port NO - Peak Pressure1500rpm - Stoichiometric - Load Sweep - Mass Weighted NO
(a) Time Averaging
U.
A A
A A
AA
A&A
3500 -F
0-.W
0z0M~
4-(0
I i i I i i
3000 -
2500 -
2000-
1500-
1000-
500
0
(b) Exhaust ValveClosed Period Averaging
AA A
A A
Al
Ak
U
AI I I
I I I I
10 15 20 25 30 35 40
Measured Peak Pressure (bar)
10 15 20 25 30 35 40
Measured Peak Pressure (bar)
Figure 6.10: Cycle by Cycle Variation of Exhaust Port NO - Peak Pressure1500rpm - Stoichiometric - Load Sweep
133
E
0z
0
0XW-
A P
LA AA
" AA#4tA AA
40
3500 -
3000 -
2500
2000-
1500-
1000 -
500-
0-
0
(0
xL
w
0.6 ba p
2000 -
1750 -
1500 -
1250 -
1000 -
750 -
500
20 25 30
Measured Peak Pressure (bar)
Figure 6.11: Cycle by Cycle Variation of Exhaust Port NO - Peak Pressure1500rpm - Stoichiometric - EGR Sweep - Mass Weighted NO
(a) PHI = 0.956 (b) PHI = 0.914
2500--
Eo. 2000 --0
z 1500--
0
- 1000--
500--
0-
2500 -
4.1
I I |
Ea. 2000 -0.
0z 1500-0O 1000-
- 500-Xw_ I_
10 12.5 15 17.5 20 22.5 25
Measured Peak Pressure (bar)
U
U
* U
0 1 1 i I i i
10 12.5 15 17.5 20 22.5 25
Measured Peak Pressure (bar)
Figure 6.12: Cycle by Cycle Variation of Exhaust Port NO - Peak Pressure1500rpm - MAP = 0.5 bar - Lean Operation - Mass Weighted NO
134
* 0% EGR
x4% EGR
x A 8% EGRx x
A . 12% EGR
* 16% EGR
0z4-0
0.
4-
250
0-V
10 15
PHI = 0.914
PHI = 0.956
J PHI = 0.838
m a 4 .PHI =0.773
_ vPHI=0.715
_F --
10 12.5 15 17.5 20 22.5
Measured Peak Pressure (bar)
Figure 6.13: Cycle by Cycle Variation of Exhaust Port NO - Peak Pressure1500rpm - MAP = 0.5 bar - Lean Operation cont. - Mass Weighted NO
2000-
1750
1500
1250
1000
750--
500 --
250--
0 --
10 15
PHHI = 1.00
AX3& X PHI = 1.06
x --... PHI = 1.12
AA, PHI = 1.21
20 25 30
Measured Peak Pressure (bar)
Figure 6.14: Cycle by Cycle Variation of Exhaust Port NO - Peak Pressure1500rpm - MAP = 0.5 bar - Rich Operation - Mass Weighted NO
135
2500 T
2000
1500
1000
500
0
I-E
CL
0.0z
0
w
25
0
z
0
II
ADV + 5,10,15,20 deg
MBT
3500
3000
2500
2000
1500
1000
500
WI-- - U
E.
0z0.a-
-
xwL
15 20 25
Measured Peak Pressure (bar)
Figure 6.15: Cycle by Cycle Variation of Exhaust Port NO - Peak Pressure
1500rpm - Stoichiometric - Spark Sweep
4000
3500
------- Steady State Model - Layered A.C.* MAP = 0.8 bar* MAP = 0.5 bar* MAP = 0.33 bar
E
SS
0.'..-0
~i.a:
20
*R
0
S U
U
U
U
30
Peak Pressure (bar)
Figure 6.16: 15 Individual Cycles Selected for Modeling Comparison
1500rpm - Stoichiometric - Load Sweep
136
RET - 5,10 deg
:. 1 -+ 4
0
10 30
3000
2500
2000 -
1500 -
1000
E00.
0zV_0
0MXI
-c
E
500 -
0
0
A&
10 40
rY
-Is
i i
Open Symbols - ModelClosed Symbols - Exp.
0
A
A AIt
AA
AA
Ir
00
0
0
0
0
0
0
A
OFFu
0 i i i
5 10 15 20 25 30 35 40 45
Peak Pressure (bar)
Figure 6.17: Cycle by Cycle Modeling Comparison - Layered A.C.1500rpm - Stoichiometric - Load Sweep
(a) PHI = 0.914 (a) 10% EGR
1500
0 0 N0 o *
U
E0.
0.z0
CL
xwL
011
I i
1250
1000
750
500
250
015 17.5 20 22.5 25
Peak Pressure (bar)
0
U.
U
MJ13
"
i i i i i
15 17.5 20 22.5 25
Peak Pressure (bar)
Figure 6.18: Cycle by Cycle Modeling Comparison - Layered A.C.1500rpm - MAP=0.5bar
137
3500
3000
2500
0.
0zV-0a.
cxwU
2000
1500
1000
500
E0.
0z00
CLu
xw
3000 -
2500 -
2000 -
1500 -
1000 -
500
0-
138
BIBLIOGRAPHY
pi www.epa.gov
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[9] Raine, R.R., Stone, C.R., "Modeling of Nitric Oxide Formation in Spark IgnitionEngines with a Multizone Burned Gas," Combustion and Flame, Vol. 102, pp. 241-255, 1995.
[10] Ball J.K., Stone, C.R., Collings, N., "Cycle-by-cycle modelling of NO formationand comparison with experimental data," Proc Instn Mech Engrs, Vol. 213 Part D,pp. 175-189, 1999.
[11] Hinze P.C., "Cycle to Cycle Combustion Variations in a Spark Ignition EngineOperating at Idle," PhD. Thesis, Massachusetts Institute of Technology, 1997
[12] Kenney T., Fader, H., Fenderson, A., Gardner, T., Keeble, B., Kwapis, J., Meyer,D., Morris, G., Rehagan, L., Shearer, S., Stein, R., Tobis, B., Tuggle, G., Wagner,T., Wernette, B., "Acquisition and Analysis of Cylinder Pressure DataRecommended Procedures" Ford Manual, 1992.
139
[13] Lancaster, D., Krieger, R.B., Lienesch, J.H. "Measurements and Analysis of EnginePressure Data," SAE Paper 750026, 1975.
[14] Stein, R.A., Mencik, D.Z., Warren, C.C., "Effect of Thermal Strain onMeasurement of Cylinder Pressure," SAE Paper 870455, 1975.
[15] Gatowski, J.A., Balles, E.N., Chun, K.M., Nelson, F.E., Ekchian, J.A., Heywood,J.B., "Heat Release Analysis of Engine Pressure Data" SAE Paper 841359, 1984.
[16] Chun, K.M., and Heywood J.B., "Estimating Heat-Release and Mass of MixtureBurned from Spark Ignition Engine Pressure Data," Combustion Science and
Technology, Vol. 54, pp. 133-143, 1987.
[17] Cheung, H.M. and Heywood J.B., "Evaluation of a One-Zone Burn Rate AnalysisProcedure Using Production SI Engine Pressure Data," SAE Paper 932749, 1993.
[18] Quader, A.A., "Why Intake Charge Dilution Decreases Nitric Oxide Emission fromSpark Ignition Engines," SAE Paper 710009, 1971.
[19] Aiman, W.R., "Engine Speed and Load Effects on Charge Dilution and NitricOxide Emission," SAE Paper 720256, 1972.
[20] Galliot, F., Cheng, W., Cheng, C., Sztenderowicz, M., Heywood, J., Collings, N.,"In-cylinder Measurements of Residual Gas Concentration in a Spark IgnitionEngine," SAE Paper 900485, 1990.
[21] Fox, J.W., Cheng, W.K., and Heywood, J.B., "A Model for Predicting ResidualGas Fraction in Spark Ignition Engines," SAE Paper 931025, 1993.
[22] Cheng W.K., Galliot, F., Collings, N., "On the Time Delay in Continuous In-
cylinder Sampling from IC Engines," SAE Paper 890579, 1989.
[23] Heywood, J.B., Internal Combustion Engine Fundamentals, McGraw-Hill BookCo., New York, 1988.
[24] Reavell, K., Collings, N., Peckham, M., Hands, T., "Simultaneous Fast ResponseNO and HC Measurements from a Spark Ignition Engine," SAE Paper 971610,1997.
[25] Peckham, M., Hands, T., Burrell, J., Collings, N., Schurov, S., " Real Time In-
cylinder and Exhaust NO Measurements in a Production SI Engine," SAE Paper
980400, 1998.
140
[26] "fNOx400 High Frequency Response NO Detector User Manual," CambustionLtd., 1992.
[27] Martin, M.K., and Heywood, J.B., "Approximate Relationships for theThermodynamic Properties of Hydrocarbon-Air Combustion Products,"Combustion Science and Technology, Vol.15, pp. 1-9, 1976.
[28] Miller, J.A. and Bowman, C.T., Prog. Ener. Combust. Sci., Vol. 15, pp. 287-338,1989.
[29] Bowman C.T., "Kinetics of Pollutant Formation and Destruction in Combustion,"Prog. Ener. Combust. Sci., Vol.1, pp. 33-45, 1975.
[30] Lutz., A., Kee, R., Miller, J., "SENKIN: A Fortran Program for PredictingHomogeneous Gas Phase Chemical Kinetics with Sensitivity Analysis," SAND87-8248 Sandia National Laboratories Unlimited Release, 1988.
[31] Dagaut, P., Cathonnet, M., and Boettner, J., "Kinetic Modeling of PropaneOxidation and Pyrolysis," International Journal of Chemical Kinetics, Vol. 24, pp.813-837, 1992.
[32] Kalghatgi, G.T., "Effects of Combustion Chamber Deposits, Compression Ratioand Combustion Chamber Design on Power and Emissions in Spark IgnitionEngines," SAE Paper 972886, 1997.
141
142
Table A.1- Steady State Modeling Analysis - Load Sweep
EXPERIMENTAL RESULTSFile MAP Spark Gross Theta Max Average Air in Exhaust NO Coolant Residual Fast NO Fast NO
Name bar 0BTC IMEP Pmax Pressure phi g/cyc Temp C volts Temp Exper. ppm corrected3bar12 0.33 30 2.48 12.90 13.79 1.003 0.1176 498 1.09 75 19 685.5346 733.5224bar12 0. 4 24 3.08 14.67 16.25 1.000 0.1464 510 1.59 75 16 1000 10705barl2 0.5 23 3.91 13.45 21.09 1.003 0.189 548 2.33 75 14 1477.987 1581.4476bar12 0.6 21 4.78 13.93 25.46 1.002 0.2256 566 2.67 75 12 1679.245 1796.7928bar12 0.8 18 6.58 14.10 34.82 0.999 0.3064 586 3.45 75 10 2169.811 2321.698
MODEL RESULTSFile UNCal UNCal UNCal Calibrat Calibrat Calibrat Uncal NO Uncal NO CAL - NO CAL NO FINAL NO FINAL NO
Name Residual Air IMEP IMEP Pmax opmax MIX LAYER MIX LAYER MIX LAYERSbar12 14.50 0.1275 2.96 2.4 13.23 13 2979 2303 1283 1055 776 7064bar12 11.98 0.1631 3.8 2.99 16.01 14 3545 2854 1909 1561 1228 10865bar12 9.80 0.2108 4.92 3.86 21.03 14 3871 3287 2559 2025 1858 15786bar12 8.62 0.2662 6.23 4.62 24.84 14 3996 3554 3094 2465 2466 20188barl2 5.97 0.3724 8.76 6.28 33.83 13 4035 3807 3620 2997 3259 2649
MODEL INPUTSFile Wiebe Constants Calibrat Calibrat
Name CONSPB EXSPB DTBRN EGR MAP3bar12 9 3.6 61 2.55 0.31954bar12 9 3.6 53 2.05 0.375
bar12 9.2 3.6 50 2.76 0.46356bar12 9 3.6 47 2.2 0.5358barl2 9 3.6 42 2.4 0.7
z
Table A.2- Steady State Modeling Analysis - Equivalence Ratio Sweep
EXPERIMENTAL RESULTS
File MAP Spark Gross Theta (atc Max Average Air in Exhaust NO Coolant Residual Fast NO Fast NO
Name bar *BTC IMEP Pmax Pressure PHI g/cyc Temp C volts Temp Exper. ppm corrected
rich56 0.5 22 3.93 12.39 22.33 1.252rich34 0.5 21 3.97 13.01 22.06 1.121
richl2 0.5 22 3.99 13.16 21.95 1.058
st12 0.5 23 3.94 13.56 21.11 1.005lean12 0.5 23 3.79 13.95 20.26 0.956lean34 0.5 25 3.73 13.16 20.35 0.914
lean56 0.5 29 3.52 12.80 19.39 0.838lean78 0.5 33 3.36 12.95 18.26 0.773lean9l0 0.5 37 3.11 13.30 16.12 0.715
0.1890.1890.189
0.1890.1890.1890.1890.189
530 0.94 77 14.5 591.195 632.5786
544 1.68 77 14 1056.604 1130.566
550 2.35 77 14 1477.987 1581.447
544 2.52 77 14 1584.906 1687.925
529 2.53 77 14 1591.195 1694.623
498 1.62 77 13.5 1018.868 1080
475 0.75 77 13.5 471.6981 497.6415
460 0.21 77 13 132.0755 139.3396
MODEL RESULTS
File UNCal UNCal UNCal Calibrat Calibrat Calibrat Uncal NO Uncal NO CAL - NO CAL NO FINAL NO FINAL NO
Name Residual Air IMEP IMEP Pmax opmax MIX LAYER MIX LAYER MIX LAYER
rich56 10.00 0.2129 4.83 3.7 22.1 12 391 348 122 173 69 146
rich34 9.87 0.2137 4.93 3.75 21.62 13 1302 1129 776 683 561 588
richl2 9.75 0.2143 4.98 3.83 21.69 13 2399 2100 1662 1346 1267 1126
st12 9.80 0.2108 4.92 3.86 21.03 14 3871 3287 2559 2025 1858 1578
lean12 9.83 0.2147 4.85 3.75 20.27 14 5088 4135 3069 2393 2077 1758
lean34 10.04 0.2150 4.66 3.59 20.11 13 5622 4453 3044 2460 1939 1731
lean56 10.45 0.2154 4.35 3.31 18.88 13 4524 3592 2106 1838 1197 1193
lean78 10.73 0.2155 4.06 3.16 17.42 14 2228 1977 881 852 462 512
Iean9l0 10.92 0.2163 3.78 2.98 15.6 16 730 713 283 281 145 156
MODEL INPUTS
File Wiebe Constants Calibrat CalibratName CONSPB EXSPB DTBRN EGR MAP
rich56 9 3.4 47 3.4 0.467
rich34 9 3.4 47 2.95 0.468
rich12 9 3.5 48 2.55 0.465
st12 9.2 3.6 50 2.76 0.4635
lean12 9.5 3.6 52 2.56 0.463
lean34 9.5 3.6 54 2.27 0.461
lean56 9 3.6 60 1.35 0.459
lean78 12 3.7 73 1 0.457
lean9l0 16 5 87 0.2 0.45
174&.9686o0.26 77 f 15 113.522501
Table A.3- Steady State Modeling Analysis - Spark Timing Sweep
3.78bar *BTC0.5 130.5 -180.5 530.5 280.5 2:3 -r0.5 30.5 24%
UN~aI UN~aI
24.50 15.04 1.003 0.189 576 1.29 77 13.5 811.32081868.1132
3.88 18.50 18.25 1.000 0.189 563 1.87 77 13.5 1176.101 1258.428
3.91 13.97 20.73 1.003 0.189 549 2.31 77 14 1477.987 1581.447
3.85 8.93 23.43 1.003 0.189 541 2.91 78 14 1830.189 1958.3023.72 5.56 24.83 1.002 0.189 535 3.29 78 14 2069.182 2214.0253.69 3.61 25.68 1.002 0.189 531 3.66 78 14.5 2301.887 2463.019
3.57 1.58 26.45 1.002 0.189 526 3.99 78 14.5 2509.434 2685.094
MODEL RESULTSUNCaI Calibrat Calibrat Calibrat Uncal NO Uncal NO CAL - NO CAL NO FINAL NO FINAL NO
Name Residual Air IMEP IMEP Pmax Opmax MIX LAYER MIX LAYER MIX LAYER
ret12 3.91 16.33 23 1866 1377 1233 918ret34 3.93 18.45 18 2260 1712 1529 1219
mbtl2 9.80 0.2108 492 3.86 21.02 14 3842 3282 2602 2059 1841 1579
adv12 3.75 22.66 9 2895 2358 2264 1938
adB4 3.61 23.92 7 3219 2638 2612 2247
ad%66 3.47 24.61 5 1 1 3364 2795 2831 2454
adv78 3.27 25.43 3 1 _ 3597 3082 3161 2781
MODEL INPUTSFile Wiebe Constants Calibrat Calibrat
Name CONSPB EXSPB DTBRN EGR MAPret12 9 3.6 51 2.86 0.4635ret34 9 3.6 51 2.7 0.4635mbt12 9.2 3.6 50 2.76 0.4635adv12 9 3.6 51 2.5 0.4635ad84 9.6 3.7 53 2.4 0.4635ad66 9.7 3.8 56 2.65 0.4635adv78 9.8 4 57 2.57 0.4635
I-lieNameret12ret34mbt12adv12ad\64ad\66adv78
FileI'
Table A.4- Steady State Modeling Analysis - Exhaust Gas Recirculation Sweep
FileName
MAPbar
Spark*BTC
GrossIMEP Pmax
Max I Average in txnaustI 14 IPressure phi 9/cyc Temp C
NU
ppmUooiani i
Temp I
base12 0.5 23 3.89 13.80 20.67 1.003 0.189 549 2.28 77
512 0.517 27 3.94 12.88 21.21 1.004 0.189 538 1.71 77
1012 0.533 29 3.97 13.08 20.88 1.005 0.189 532 1.19 77
1512 0.55 32 3.99 13.47 20.46 1.001 0.189 520 0.78 77
2012 0.568 35 4.03 12.95 20.73 1.004 0.189 517 0.49 77
MODEL RESULTS
r. ppmj 1477.987
1075.472748.4277
S490.566308.1761
File UNCal UNCal UNCal Calibrat Calibrat Calibrat Uncal NO Uncal NO CAL - NO CAL NO FINAL NO FINAL NO
Name Residual Air IMEP IMEP Pmax opmax MIX LAYER MIX LAYER MIX LAYER
base12 9.80 0.2108 492 3.86 21.02 14 3842 3282 2602 2059 1841 1579
512 1 3.89 21.84 13 1821 1527 1160 1106
1012 3.93 21.88 13 1123 1004 681 700
1512 3.96 21.2 14 621 592 349 384
2012 1 4.01 21.34 13 356 373 194 231
MODEL INPUTSFile Wiebe Constants Calibrat Calibrat
Name CONSPB EXSPB DTBRN EGR MAPbase12 9.2 3.6 50 2.76 0.4635
512 9.8 4 54 6.9 0.482
1012 9.8 4 58 10.6 0.5
1512 9.8 4 65 14.2 0.515
2012 9.8 4 70 17.51 0.532
Fast NOcorrected1581.4471150.755800.8176
[524.9057329.7484
' * '
Table B.1: Summary of Cycle by Cycle Heat Release Analysis Results - Load Sweep
MAP = 0.33 barCycle # P.P. CA P.P. IMEP Lambda 0-2 0-20 0-50 0-90 a10-90 xbmax NO - EVC NO - time NO - mass
1 14.77 190 2.40 1.000 16.6 22.6 30.9 39.2 16.6 0.91 810 801 833150 14.89 192 2.48 0.990 16.3 22.9 32.4 39.9 17.0 0.94 807 813 812
Average 13.80 194 2.48 0.996 16.9 23.7 34.5 43.7 20.0 0.94 735 731 7371 -STD 0.94 2 0.03 0.007 1.6 1.9 2.5 3.2 1.9 0.02 107 100 116C.O.V. 6.82 1 1.38 0.687 9.7 7.9 7.1 7.3 9.6 1.67 14 14 16
MAP = 0.4 barCycle # P.P. CA P.P. IMEP Lambda 0-2 0-20 0-50 0-90 al0-90 xbmax NO - EVC NO - time NO - mass
1 15.65 197 3.09 0.990 14.4 20.5 31.6 40.5 20.0 0.94 976 988 959150 16.71 195 3.05 1.000 12.9 19.5 29.4 37.9 18.4 0.94 1082 1086 1069
Average 16.25 196 3.08 1.000 14.2 20.2 30.4 39.2 18.9 0.94 1067 1060 10591 - STD 0.94 2 0.04 0.007 1.3 1.5 1.9 2.5 1.8 0.02 135 118 129C.O.V. 5.79 1 1.28 0.709 9.4 7.6 6.4 6.4 9.6 1.91 13 11 12
MAP = 0.5 barCycle # P.P. CA P.P. IMEP Lambda 0-2 0-20 0-50 0-90 al 0-90 xbmax NO - EVC NO - time NO - mass
1 20.64 195 3.91 1.000 12.3 17.9 27.7 37.7 19.9 0.91 1728 1806 1850150 20.64 196 3.92 1.010 13.6 19.8 30.3 37.7 17.9 0.92 1595 1618 1669
Average 21.23 194 3.94 0.994 13.2 19.0 28.3 37.1 18.2 0.93 1568 1600 16221 - STD 1.37 2 0.04 0.009 1.5 1.9 2.4 3.0 2.0 0.01 218 191 194C.O.V. 6.47 1 1.14 0.899 11.3 10.0 8.5 8.2 11.1 1.55 14 12 12
MAP = 0.6 barCycle # P.P. CA P.P. IMEP Lambda 0-2 0-20 0-50 0-90 a10-90 xbmax NO - EVC NO - time NO - mass
1 23.79 196 4.74 1.020 12.0 18.4 28.1 37.7 19.3 0.94 1458 1467 1467150 27.00 193 4.80 1.000 10.9 16.3 24.4 32.4 16.1 0.95 1662 1979 2011
Average 25.61 195 4.78 0.999 12.2 17.9 26.7 34.9 17.0 0.95 1758 1811 18211 -STD 1.40 2 0.06 0.011 1.3 1.7 2.0 2.3 1.6 0.01 282 255 256C.O.V. 5.46 1 1.27 1.070 10.3 9.5 7.7 6.7 9.3 1.55 16 14 14
MAP = 0.8 barCycle # P.P. CA P.P. IMEP Lambda 0-2 0-20 0-50 0-90 a10-90 xbmax NO - EVC NO - time NO - mass
1 37.13 192 6.54 1.000 10.0 14.7 21.6 29.6 14.9 1.00 2149 1951 1886150 33.51 197 6.40 0.990 11.8 18.1 26.4 33.9 15.8 0.99 1897 1717 1668
Average 35.12 195 6.60 1.001 10.9 16.7 25.2 32.7 16.0 1.01 2390 2328 23291 - STD 2.05 2 0.10 0.013 1.2 1.7 2.2 2.4 1.4 0.02 1_354 333 347C.O.V. 5.84 1 1.50 1.279 11.1 10.3 8.7 7.5 8.9 1.72 15 14 15
Table B.2: Summary of Cycle by Cycle Heat Release Analysis Results - EGR Sweep
0% EGRCycle # P.P. CA P.P. IMEP Lambda 0-2 0-20 0-50 0-90 a10-90 xbmax NO - EVC NO - time NO - mass
1 20.64 195 3.91 1.000 12.3 17.9 27.7 37.7 19.9 0.91 1728 1806 1850150 20.64 196 3.92 1.010 13.6 19.8 30.3 37.7 17.9 0.92 1595 1618 1669
Average 21.23 194 3.94 0.994 13.2 19.0 28.3 37.1 18.2 0.93 1568 1600 1622STD 1.37 2 0.04 0.009 1.5 1.9 2.4 3.0 2.0 0.01 218 191 194
6.47 1 1.14 0.899 11.3 10.0 8.5 8.2 11.1 1.55 14 12 12
4% EGRCycle # P.P. CA P.P. IMEP Lambda 0-2 0-20 0-50 0-90 a10-90 xbmax NO - EVC NO - time NO - mass
1 22.40 192 3.91 1.000 15.4 21.5 30.4 39.3 17.7 0.92 1177 1216 1195150 18.23 196 3.86 1.000 16.2 22.6 35.5 49.0 26.4 0.93 961 1051 1061
Average 21.16 194 3.91 0.996 15.4 21.7 31.7 42.1 20.4 0.93 1145 1170 11611 - STD 1.45 2 0.05 0.009 1.7 2.0 2.6 3.5 2.5 0.01 189 169 169
6.85 1 1.28 0.943 11.1 9.4 8.3 8.3 12.4 1.46 16 14 15
8% EGRCycle # P.P. CA P.P. IMEP Lambda 0-2 0-20 0-50 0-90 a10-90 xbmax NO - EVC NO - time NO - mass
1 21.41 193 3.97 0.990 18.2 23.9 33.6 44.0 20.0 0.92 988 932 924150 21.85 192 3.97 1.000 17.2 23.0 32.4 44.2 21.2 0.94 603 618 611
Average 20.85 194 3.97 0.994 16.9 23.5 34.2 46.3 22.9 0.94 790 814 8051 - STD 1.61 3 0.05 0.008 2.1 2.5 3.0 3.9 2.8 0.01 157 140 137
7.70 1 1.30 0.774 12.5 10.81 8.8 8.3 12.0 1.47 20 17 17
12% EGRCycle # P.P. CA P.P. IMEP Lambda 0-2 0-20 0-50 0-90 a10-90 xbmax NO - EVC NO - time NO - mass
1 20.66 196 4.01 1.000 19.0 27.0 39.0 49.8 22.8 0.93 522 509 501150 20.90 195 4.01 1.010 19.9 27.4 38.4 50.4 23.0 0.93 575 557 551
Average 20.50 194 3.98 0.998 19.0 26.3 37.8 51.8 25.6 0.93 519 538 5301 - STD 1.64 2 0.06 0.008 1.9 2.3 3.0 4.4 3.3 0.02 131 128 124
8.01 1 1.55 0.793 10.0 8.9 7.8 8.5 12.7 1.67 25 24 23
16% EGRCycle # P.P. CA P.P. IMEP Lambda 0-2 0-20 0-50 0-90 a10-90 xbmax NO - EVC NO - time NO - mass
1 20.31 192 3.91 1.000 18.3 26.1 39.3 58.3 32.2 0.90 239 285 284150 17.86 198 3.98 0.990 20.4 28.6 45.6 60.8 32.2 0.93 240 267 266
Average 20.76 194 4.03 0.995 21.2 28.6 40.6 55.7 27.1 0.93 329 343 3401 - STD 1.79 3 0.06 0.007 2.4 2.7 3.3 4.6 3.4 0.02 89 89 87
8.63 1 1.58 0.725 11.2 9.3 8.2 8.2 12.4 1.65 27 26 26
00
Table B.3: Summary of Cycle by Cycle Heat Release Analysis Results - Lean Operation
PHI = 0.956Cycle # P.P. CA P.P. IMEP Lambda 0-2 0-20 0-50 0-90 a10-90 xbmax NO - EVC NO - time NO - mass
1 21.47 193 3.82 1.040 12.0 17.5 26.3 35.8 18.3 0.93 1938 1934 1973150 17.47 199 3.74 1.050 15.5 22.3 33.4 44.9 22.6 0.93 1447 1420 1427
Average 20.19 195 3.78 1.048 13.5 19.3 29.0 38.4 19.1 0.92 1679 1697 17091 - STD 1.40 2 0.05 0.009 1.6 2.0 2.5 3.3 2.2 0.02 256 221 227
6.92 1 1.44 0.903 12.1 10.2 8.5 8.5 11.7 1.64 15 13 13
PHI = 0.914Cycle # P.P. CA P.P. IMEP Lambda 0-2 0-20 0-50 0-90 a10-90 xbmax NO - EVC NO - time NO - mass
1 22.16 192 3.75 1.100 12.2 17.3 26.6 36.3 18.9 0.95 1919 1909 1932150 20.03 194 3.70 1.100 14.5 20.6 30.4 42.2 21.6 0.94 1390 1559 1492
Average 20.35 194 3.73 1.095 14.5 20.4 30.2 40.2 19.8 0.94 1697 1731 17411 - STD 1.35 2 0.06 0.009 1.7 2.1 2.4 3.1 2.2 0.02 295 246 254
6.62 1 1.56 0.831 12.0 10.3 8.1 7.7 11.3 1.68 17 14 15
PHI = 0.838Cycle # P.P. CA P.P. IMEP Lambda 0-2 0-20 0-50 0-90 al0-90 xbmax NO - EVC NO - time NO - mass
1 19.44 193 3.53 1.200 16.0 22.7 33.2 46.7 24.0 0.96 979 1226 1180150 21.08 190 3.44 1.190 14.4 20.5 29.6 42.2 21.8 0.94 1692 1728 1754
Average 19.62 193 3.52 1.195 16.6 23.1 33.6 44.8 21.8 0.95 1117 1146 11541 -STD 1.32 2 0.05 0.008 1.8 2.1 2.5 3.3 2.4 0.01 314 260 276
1 6.75 1 1.43 0.676 11.1 9.1 7.5 7.3 11.2 1.56 28 23 24
PHI = 0.773Cycle # P.P. CA P.P. IMEP Lambda 0-2 0-20 0-50 0-90 al0-90 xbmax NO - EVC NO - time NO - mass
1 18.85 193 3.39 1.290 19.5 26.6 37.8 51.1 24.4 0.98 541 523 543150 21.45 190 3.41 1.300 18.0 23.9 33.2 44.7 20.9 1.02 830 763 811
Average 18.25 194 3.36 1.294 19.8 26.9 38.5 51.7 24.8 0.97 479 497 5041- STD 1.71 2 0.06 0.009 2.3 2.5 3.3 5.0 3.4 0.02 229 175 191
1 9.37 1 1.83 0.715 11.4 9.3 8.6 9.6 13.9 1.93 48 35 38
PHI = 0.715Cycle # P.P. CA P.P. IMEP Lambda 0-2 0-20 0-50 0-90 al0-90 xbmax NO - EVC NO - time NO - mass
1 16.39 195 3.22 1.390 25.3 33.0 44.9 60.6 27.5 0.99 149 125 140150 20.30 190 3.19 1.390 23.2 29.2 37.5 48.7 19.4 0.98 317 270 337
Average 16.03 195 3.15 1.398 24.0 31.8 45.3 62.2 30.4 0.98 131 143 1491 - STD 2.10 3 0.10 0.012 2.9 3.2 4.6 7.8 5.5 0.02 108 85 97
13.09 1 3.06 0.877 12.0 10.1 10.1 12.6 18.0 2.18 82 60 65
Table B.4: Summary of Cycle by Cycle Heat Release Analysis Results - Rich Operation
PHI = 1.0Cycle # P.P. CA P.P. IMEP Lambda 0-2 0-20 0-50 0-90 a10-90 xbmax NO - EVC NO - time NO - mass
1 20.64 195 3.91 1.000 12.3 17.9 27.7 37.7 19.9 0.91 1728 1806 1850150 20.64 196 3.92 1.010 13.6 19.8 30.3 37.7 17.9 0.92 1595 1618 1669
Average 21.23 194 3.94 0.994 13.2 19.0 28.3 37.1 18.2 0.93 1568 1600 16221 - STD 1.37 2 0.04 0.009 1.5 1.9 2.4 3.0 2.0 0.01 218 191 194
6.47 1 1.14 0.899 11.3 10.0 8.5 8.2 11.1 1.55 14 12 12
PHI = 1.058Cycle # P.P. CA P.P. IMEP Lambda 0-2 0-20 0-50 0-90 a10-90 xbmax NO - EVC NO - time NO - mass
1 22.58 191 3.95 0.930 9.7 14.3 23.5 33.7 19.4 0.92 1128 1128 1145150 21.20 196 4.04 0.940 14.7 20.7 29.7 37.4 16.7 0.96 1003 964 978
Average 21.92 194 3.97 0.945 12.2 17.7 26.7 35.0 17.3 0.93 1128 1146 11671 - STD 1.10 2 0.03 0.007 1.4 1.7 2.0 2.3 1.6 0.01 183 163 167
5.02 1 0.75 0.782 11.7 9.8 7.3 6.6 9.5 1.12 16 14 14
PHI = 1.121Cycle # P.P. CA P.P. IMEP Lambda 0-2 0-20 0-50 0-90 a10-90 xbmax NO - EVC NO - time NO - mass
1 22.97 191 3.97 0.890 10.9 15.7 23.4 32.0 16.4 0.94 729 667 684150 19.04 200 3.96 0.890 13.6 20.3 30.6 39.5 19.2 0.93 395 428 430
Average 22.05 194 3.97 0.892 11.3 16.8 25.8 33.7 16.9 0.93 627 630 6441 - STD 1.13 2 0.03 0.007 1.3 1.7 1.9 2.3 1.5 0.01 122 101 102
5.12 1 0.71 0.754 11.4 9.9 7.6 6.7 8.9 1.17 19 16 16
PHI = 1.252Cycle # P.P. CA P.P. IMEP Lambda 0-2 0-20 0-50 0-90 al0-90 xbmax NO - EVC NO - time NO - mass
1 21.28 194 3.92 0.800 13.1 19.8 28.0 35.6 15.8 0.93 174 164 171150 23.98 190 3.90 0.800 8.9 14.3 22.7 30.0 15.8 0.94 177 193 196
Average 22.32 193 3.93 0.799 11.3 17.0 25.9 33.7 16.7 0.94 171 173 1781 - STD 1.07 2 0.04 0.005 1.4 1.8 1.9 2.1 1.4 0.01 31 25 27
4.80 1 0.96 0.647 12.5 10.5 7.3 6.2 8.5 1.26 18 15 15