effects of turbulence-chemistry interactions in …

The Pennsylvania State University

The Graduate School

College of Engineering

EFFECTS OF TURBULENCE-CHEMISTRY INTERACTIONS IN

DIRECT-INJECTION COMPRESSION-IGNITION ENGINES

A Dissertation inMechanical and Nuclear Engineering

byHedan Zhang

c⃝ 2012 Hedan Zhang

Submitted in Partial Fulfillmentof the Requirementsfor the Degree of

Doctor of Philosophy

December 2012

The thesis of Hedan Zhang was reviewed and approved* by the following:

Daniel C. HaworthProfessor of Mechanical EngineeringDissertation Adviser, Chair of Committee, Graduate Program Chair

Stephen R. TurnsProfessor of Mechanical Engineering

James G. BrasseurProfessor of Mechanical Engineering, Bioengineering, and Mathematics

Andre L. BoehmanProfessor of Fuel Science and Mechanical Engineering

Karen A. TholeProfessor of Mechanical EngineeringHead of the Department of Mechanical and Nuclear Engineering

*Signatures are on file in the Graduate School.

Abstract

Advanced combustion strategies are emphasized in modern compression-ignition engine sys-

tems, aiming at improving diesel engine efficiency and reducing pollutant emissions, espe-

cially soot and NOx, together with strategies to accommodate unconventional fuels. Recent

studies have shown the importance of turbulence and turbulence-chemistry interactions on

emissions from laboratory flames and compression-ignition engines.

Constant-volume, high-pressure spray combustion is an important intermediate step for

model validation and scientific understanding of combustion in direct-injection compression-

ignition engines. The Engine Combustion Network (ECN) provides a series of well-

documented experimental data for spray combustion under typical diesel-engine conditions,

and this serves as a good resource for simulation and validation purposes. Here simulations

for the ECN constant-volume, n-heptane spray configuration have been performed using

OpenFOAM, an object-oriented C++ based code. The effects of exhaust-gas recirculation

(EGR), ambient temperature and density on combustion were investigated computationally.

The simulations demonstrate that the CFD model is capable of predicting sprays, mixing,

ignition and combustion, quantitatively, for engine-relevant conditions reasonably well. The

numerical results show that the ignition delay and lift-off lengths are strongly influenced by

EGR, ambient gas temperature and ambient gas density, in agreement with measurements.

Results from a model using a transported probability density function (PDF) method that

explicitly accounts for turbulence-chemistry interactions have been compared to those from a

model that simplistically accounts for turbulence-chemistry interactions, including mixture

fraction profiles, ignition delays, lift-off lengths and flame structures under various ambient

conditions. Significant differences between these two models have been observed, which

iii

shows the importance of turbulence-chemistry interactions. The turbulent flame structure

predicted by the PDF method is more realistic than that obtained from a simplistic model

to account for turbulence-chemistry interactions. The choice of chemical mechanism also

plays a strong role.

Next, the high-fidelity CFD-based models have been used to simulate fuel effects and

complex interactions between turbulence and gas-phase chemistry on emissions for biodiesel

combustion and hydrogen-assisted diesel combustion in common-rail diesel engines. The

sensitivity of predicted NOx emissions to variations in the physical properties of the fuel

(density and viscosity) has been explored to determine the origins of the so-called biodiesel-

NOx effect: the increase in NOx emissions that has been observed when petroleum-based

diesel fuel is replaced with biodiesel fuel. Interactions between turbulence and gas-phase

chemistry have been found to be important in the fuel density effect on NOx emissions.

CFD also has been used to explore the changes in NOx emissions with hydrogen substitu-

tion that have been observed experimentally in hydrogen-enriched diesel combustion over a

range of operating conditions. In spite of the significant simplifications and approximations,

the model is able to reproduce the experimentally observed trends for some operating con-

ditions. A model using a transported PDF method that explicitly accounts for turbulence-

chemistry interactions does somewhat better than a model using well-stirred reactor model

which ignores turbulence-chemistry interactions, in low-speed conventional diesel combus-

tion cases. The CFD results are consistent with the hypothesis that in-cylinder HO2 levels

increase with increasing H2, which enhances the conversion of NO to NO2.

In close collaboration with engine experiments, this research shows that fuel physical

properties and complex interactions between turbulence and chemistry have important ef-

fects on emissions. It has provided new physical insight into in-cylinder processes, which in

turn allows better understanding for advanced engine development.

iv

Contents

List of Figures viii

List of Tables xv

List of Acronyms xvi

1 Introduction 1

1.1 Background and Motivation . . . . . . . . . . . . . . . . . . . . . . . . . . . 1

1.1.1 Alternative Fuels for IC Engines in Transportation . . . . . . . . . . 4

1.1.2 Turbulence-Chemistry Interactions in Chemically Reacting Flows . . 6

1.2 Hypothese, Objectives and Approaches . . . . . . . . . . . . . . . . . . . . . 10

1.3 Organization of Thesis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11

2 Turbulent Combustion in Direct-Injection Compression-Ignition Engines 13

2.1 The Diesel Combustion Process . . . . . . . . . . . . . . . . . . . . . . . . . 14

2.2 Advanced Diesel Combustion . . . . . . . . . . . . . . . . . . . . . . . . . . 17

2.3 Fuels . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21

2.4 Constant-Volume Turbulent Spray Combustion . . . . . . . . . . . . . . . . 22

3 Mathematical Formulation, Physical Models, and Numerical Methods 27

3.1 Gas-Phase Mean Equations . . . . . . . . . . . . . . . . . . . . . . . . . . . 28

3.1.1 Reynolds-Averaged Equations . . . . . . . . . . . . . . . . . . . . . . 28

3.1.2 Turbulence Models . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30

3.1.3 Turbulence Wall Function . . . . . . . . . . . . . . . . . . . . . . . . 31

v

3.2 Transported Composition PDF method . . . . . . . . . . . . . . . . . . . . 32

3.2.1 Transported Composition PDF Equation . . . . . . . . . . . . . . . 34

3.2.2 Particle Equations . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35

3.2.3 Physical Models for the PDF Method . . . . . . . . . . . . . . . . . 36

3.3 Gas-Phase Chemistry . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39

3.4 Numerical Method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40

3.4.1 Finite-Volume Codes . . . . . . . . . . . . . . . . . . . . . . . . . . . 40

3.4.2 Consistent Hybrid Lagrangian Particle/Finite Volume PDF Method 41

3.4.3 Parallelization and In Situ Adaptive Tabulation . . . . . . . . . . . . 42

3.5 Fuel Injector and Spray Models . . . . . . . . . . . . . . . . . . . . . . . . . 42

3.5.1 The Liquid Phase . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43

3.5.2 Physical Models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45

3.5.3 Coupling of Spray Model with PDF Method . . . . . . . . . . . . . . 47

4 Analysis of Spray and Spray Combustion in a Constant-Volume Chamber 49

4.1 Engine Combustion Network (ECN) N-Heptane Cases . . . . . . . . . . . . 50

4.2 Nonreacting N-Heptane Sprays . . . . . . . . . . . . . . . . . . . . . . . . . 52

4.2.1 Model vs Experiment Comparisons for the Baseline Model . . . . . . 54

4.2.2 Parametric Studies . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57

4.2.3 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 66

4.3 Reacting n-Heptane Sprays: Autoignition and Combustion . . . . . . . . . . 67

4.3.1 With versus Without In Situ Adaptive Tabulation . . . . . . . . . . 68

4.3.2 Model vs Experiment Comparisons . . . . . . . . . . . . . . . . . . . 70

4.4 Summary and Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81

5 Analysis of Biodiesel and Hydrogen Effects on NOx Emissions in Direct-

Injection Compression-Ignition Engines 85

5.1 The Biodiesel NOx Effect in Common-Rail Diesel Engines . . . . . . . . . . 86

5.2 Hydrogen-Assisted Diesel Combustion . . . . . . . . . . . . . . . . . . . . . 90

5.2.1 Computational Configuration and Model Setup . . . . . . . . . . . . 92

vi

5.2.2 Computed vs Measured NOx without Hydrogen Enrichment . . . . . 95

5.2.3 Well-mixed Model with Hydrogen Enrichment . . . . . . . . . . . . . 96

5.2.4 PDF Model with Hydrogen Enrichment . . . . . . . . . . . . . . . . 100

5.2.5 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 100

5.2.6 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 104

6 Conclusions 107

6.1 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 107

6.2 Proposed Future Work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 109

6.2.1 Configurations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 109

6.2.2 Physical Modeling . . . . . . . . . . . . . . . . . . . . . . . . . . . . 110

6.2.3 Numerical Algorithms . . . . . . . . . . . . . . . . . . . . . . . . . . 111

Bibliography 112

Appendix A. Chemical Mechanisms 133

A.1 N-heptane 5-Species Mechanism . . . . . . . . . . . . . . . . . . . . . . . . . 133

A.2 N-heptane 29-Species Mechanism . . . . . . . . . . . . . . . . . . . . . . . . 134



vii

List of Figures

1.1 Transportation Petroleum Use by Mode and the U.S. Production of

Petroleum, 1970-2035. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2

1.2 An overview of internal combustion engine technologies, 2010-2050. . . . . . 4

1.3 Average emission impacts of biodiesel for heavy-duty highway engines. . . . 7

2.1 Summary of the quasi-steady diesel burning processes. . . . . . . . . . . . . 15

2.2 An example of a NOx-soot trade-off curve. . . . . . . . . . . . . . . . . . . . 17

2.3 Φ-T regions with the highest NO and OH concentrations coincide. . . . . . 18

2.4 LTC, PCCI and HCCI concepts on a Φ-T map. . . . . . . . . . . . . . . . . 18

2.5 Relative amounts of various chemical classes in diesel fuel. . . . . . . . . . . 22

2.6 Constant-volume chamber in the experiment. . . . . . . . . . . . . . . . . . 23

2.7 Measured mean soot volume fraction contours. . . . . . . . . . . . . . . . . 24

4.1 Computational axisymmetric mesh for a constant-volume combustion chamber. 52

4.2 Computed (using a simplistic turbulence-chemistry interactions model) and

measured penetration lengths versus time for a non-reacting n-heptane spray.

(a) Liquid penetration length. (b) Vapor penetration length. . . . . . . . . 54

4.3 Computed and measured profiles of mean mixture fraction for a non-reacting

n-heptane spray at 0.49 ms after the start of injection and an axial location

of 17 mm. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55

4.4 Computed and measured profiles of mean mixture fraction for a non-reacting

n-heptane spray at 6 ms after the start of injection and axial locations of 20

mm and 40 mm. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55

viii

4.5 Computed (with versus without PDF method) and measured mean profiles

of mixture fraction for a non-reacting n-heptane spray at 6 ms after the start

of injection and an axial location of 20 mm. . . . . . . . . . . . . . . . . . . 56

4.6 Computed (with versus without PDF method) and measured mean profiles

of mixture fraction for a non-reacting n-heptane spray at 6 ms after the start

of injection and an axial location of 40 mm. . . . . . . . . . . . . . . . . . . 57

4.7 Computed (with PDF method) and measured profiles of mixture fraction

variance for a non-reacting n-heptane spray at 6 ms after the start of injection

and an axial location of 20 mm. . . . . . . . . . . . . . . . . . . . . . . . . . 57

4.8 Computed (with versus without PDF method and with variations in the

PDF mixing model) and measured mean profiles of mixture fraction for a

non-reacting n-heptane spray at 6 ms after the start of injection and an axial

location of 20 mm. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58

4.9 Computed (with versus without PDF method and with variations in the

PDF mixing model) and measured mean profiles of mixture fraction for a

non-reacting n-heptane spray at 6 ms after the start of injection and an axial

location of 40 mm. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58

4.10 Computed (with versus without PDF method and with variations in the PDF

mixing model) and measured profiles of mixture fraction variance for a non-

reacting n-heptane spray at 6 ms after the start of injection and an axial

location of 20 mm. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59

4.11 Computed liquid and vapor penetration lengths with variations in turbulence

model for a non-reacting n-heptane spray. . . . . . . . . . . . . . . . . . . 61

4.12 Computed liquid and vapor penetration lengths with variations in breakup


4.13 Computed liquid and vapor penetration lengths with variations in atomiza-

tion model for a non-reacting n-heptane spray. . . . . . . . . . . . . . . . . 62

4.14 Computed liquid and vapor penetration lengths with variations in dispersion


ix

4.15 Computed liquid and vapor penetration lengths with variations in collision


4.16 Computed liquid and vapor penetration lengths with variations in spray

model coefficient B1 for a non-reacting n-heptane spray. . . . . . . . . . . . 63

4.17 Computed liquid and vapor penetration lengths with variations in turbulence

model coefficient Cϵ1 for a non-reacting n-heptane spray. . . . . . . . . . . 64

4.18 Computed liquid and vapor penetration with variations in the injector model

for a non-reacting n-heptane spray. . . . . . . . . . . . . . . . . . . . . . . 64

4.19 Computational 3D quarter mesh for a constant-volume combustion chamber. 65

4.20 Computed liquid and vapor penetration lengths with variations in computa-

tional mesh for a non-reacting n-heptane spray. . . . . . . . . . . . . . . . 65

4.21 Computed liquid and vapor penetration lengths with variations in computa-

tional time step for a non-reacting n-heptane spray. . . . . . . . . . . . . . 66

4.22 Computed liquid and vapor penetration lengths with variations in the initial

ϵ for a non-reacting n-heptane spray. . . . . . . . . . . . . . . . . . . . . . 66

4.23 Computed liquid and vapor penetration lengths with variations in the criteria

used to define liquid and vapor penetration lengths for a non-reacting n-

heptane spray. (a) Liquid penetration definitions. (b) Vapor penetration

definitions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67

4.24 2D computed mean temperature contours for a reacting n-heptane spray at

baseline conditions of ambient temperature (1000 K), ambient density (14.8

kg/m3) and O2 level (21%), with versus without ISAT, for the 29-species

mechanism. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69

4.25 2D computed mean temperature contours for a reacting n-heptane spray at

less robust combustion conditions of ambient temperature (1000 K), ambient

density (14.8 kg/m3) and O2 level (8%), with versus without ISAT, for the

29-species mechanism. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71

x

4.26 2D computed temperature contours for a reacting n-heptane spray at condi-

tions of ambient temperature (800 K), ambient density (14.8 kg/m3) and O2

level (21%), with versus without ISAT, for the 40-species mechanism. . . . 72

4.27 Computed (with and without PDF) and measured ignition delay versus O2

percentage for a reacting n-heptane spray with ambient temperature 1000 K

and ambient density 14.8 kg/m3. . . . . . . . . . . . . . . . . . . . . . . . . 72

4.28 Computed (with and without PDF) and measured lift-off length versus O2


and ambient density 14.8 kg/m3. . . . . . . . . . . . . . . . . . . . . . . . . 73

4.29 Computed (with and without PDF) and measured ignition delay versus am-

bient temperature for a reacting n-heptane spray with 21% O2 level and

ambient density 14.8 kg/m3. . . . . . . . . . . . . . . . . . . . . . . . . . . . 74

4.30 Computed (with and without PDF) and measured lift-off length versus am-

bient temperature for a reacting n-heptane spray with 21% O2 level and

ambient density 14.8 kg/m3. . . . . . . . . . . . . . . . . . . . . . . . . . . . 74

4.31 Computed (with and without PDF) and measured ignition delay versus O2


and ambient density 30 kg/m3. . . . . . . . . . . . . . . . . . . . . . . . . . 75

4.32 Computed (with and without PDF) and measured lift-off length versus O2


and ambient density 30 kg/m3. . . . . . . . . . . . . . . . . . . . . . . . . . 76

4.33 Computed (without PDF) mean temperature distributions for a reacting n-

heptane spray with ambient temperature 1000 K and ambient density 30

kg/m3 at five different ambient oxygen concentrations at 6 ms. . . . . . . . 77

4.34 Computed (with PDF) mean temperature distributions for a reacting n-


kg/m3 at five different ambient oxygen concentrations at 6 ms. . . . . . . . 78

xi


heptane spray with 21% O2 level and ambient density 14.8 kg/m3 at different

ambient temperatures at 6 ms. . . . . . . . . . . . . . . . . . . . . . . . . . 79


heptane spray with 21% O2 level and ambient density 14.8 kg/m3 at different

ambient temperatures at 6 ms. . . . . . . . . . . . . . . . . . . . . . . . . . 80



kg/m3 at 6 ms. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81



kg/m3 at 6 ms. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82

4.39 Scatter plots of temperature versus equivalence ratio for a reacting n-heptane

spray at baseline conditions of ambient temperature 1000 K, ambient density

14.8 kg/m3 and 21% O2 level through the ignition period. . . . . . . . . . . 83

4.40 Scatter plots of temperature versus equivalence ratio for a reacting n-heptane

spray at baseline conditions of ambient temperature 1000 K, ambient density

14.8 kg/m3 and 21% O2 level at quasi-steady state. . . . . . . . . . . . . . . 84

5.1 Constant-volume combustion bomb mesh. . . . . . . . . . . . . . . . . . . . 88

5.2 Computed pressure versus time with variations in fuel density and viscosity.

The reference case (ref) corresponds to conventional diesel fuel, “den” corre-

sponds to a fuel mass density 1.16 times that of conventional diesel fuel, and

“vis” corresponds to a fuel dynamic viscosity 1.90 times that of conventional

diesel fuel, with all other fuel properties held fixed. Cases labeled “fv” cor-

respond to calculations without the PDF method (ignoring the influence of

turbulent fluctuations in composition and temperatures). . . . . . . . . . . 90

xii

5.3 Computed NO mass versus time with variations in fuel density and viscosity.

The reference case (ref) corresponds to conventional diesel fuel, “den” corre-

sponds to a fuel mass density 1.16 times that of conventional diesel fuel, and

“vis” corresponds to a fuel dynamic viscosity 1.90 times that of conventional

diesel fuel, with all other fuel properties held fixed. Cases labeled “fv” cor-

respond to calculations without the PDF method (ignoring the influence of

turbulent fluctuations in composition and temperatures). . . . . . . . . . . 91

5.4 Computed NO2 mass versus time with variations in fuel density and viscos-

ity. The reference case (ref) corresponds to conventional diesel fuel, “den”

corresponds to a fuel mass density 1.16 times that of conventional diesel fuel,

and “vis” corresponds to a fuel dynamic viscosity 1.90 times that of conven-

tional diesel fuel, with all other fuel properties held fixed. Cases labeled “fv”

correspond to calculations without the PDF method (ignoring the influence

of turbulent fluctuations in composition and temperatures). . . . . . . . . . 92

5.5 Outer surface of the computational mesh, and computed contours of fuel

vapor mass fraction at one instant. . . . . . . . . . . . . . . . . . . . . . . . 93

5.6 Computed and measured pressure traces versus time for six combustion modes. 94

5.7 Computed and measured NO for 0% H2 for six modes. . . . . . . . . . . . . 95

5.8 Computed and measured NO2 for 0% H2 for six modes. . . . . . . . . . . . 96

5.9 Computed and measured NOx for 0% H2 for six modes. . . . . . . . . . . . 97

5.10 Computed (well-mixed model) and measured % changes (wrt/0% H2) in NO

and NO2 w/H2 addition for CD/1800 rpm/25% max load (Mode 1). . . . . 97







xiii


and NO2 w/H2 addition for LTC/1800 rpm/25% max load (Mode 5). . . . . 99


and NO2 w/H2 addition for HECC/1800 rpm/25% max load (Mode 6). . . 100

5.16 Computed (PDF model) and measured % changes (wrt/0% H2) in NO and

NO2 w/H2 addition for CD/1800 rpm/25% max load (Mode 1). . . . . . . . 101








NO2 w/H2 addition for LTC/1800 rpm/25% max load (Mode 5). . . . . . . 103


NO2 w/H2 addition for HECC/1800 rpm/25% max load (Mode 6). . . . . . 103

5.22 Computed (well-mixed model) maximum, minimum, and volume-averaged

in-cylinder temperature versus crankangle for Mode 1 (CD/1800 rpm/25%

max load) with 0% and 15% H2 substitution. . . . . . . . . . . . . . . . . . 105

5.23 Computed (well-mixed model) mass fraction of in-cylinder mixture having a

temperature greater than 1700 K for Mode 1 (CD/1800 rpm/25% max load)

with 0% and 15% H2 substitution. . . . . . . . . . . . . . . . . . . . . . . . 105

5.24 Computed (well-mixed model) global in-cylinder HO2 level versus crankan-

gle for Mode 1 (CD/1800 rpm/25% max load) with 0%, 7.5% and 15% H2

substitution. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 106

xiv

List of Tables

2.1 Advanced modes of combustion in compression-ignition engines. . . . . . . . 19

2.2 Earlier modeling work for the ECN n-heptane spray cases. . . . . . . . . . . 26

3.1 Turbulence models and coefficients. . . . . . . . . . . . . . . . . . . . . . . . 32

3.2 Standard k − ϵ turbulence model and wall function constants. . . . . . . . . 32

3.3 Spray models and coefficients. . . . . . . . . . . . . . . . . . . . . . . . . . . 47

4.1 Baseline n-heptane nonreacting spray case conditions. . . . . . . . . . . . . 51

4.2 Variations in ambient conditions for n-heptane reacting cases. . . . . . . . . 51

4.3 Physical and numerical models for baseline n-heptane nonreacting spray. . . 60

4.4 Computational wall time comparison with versus without ISAT for a baseline

n-heptane case with the PDF method . . . . . . . . . . . . . . . . . . . . . 69

4.5 Comparison of computed ignition delays using different chemical mechanism. 80

5.1 Global parameters for six combustion modes with 0% H2. . . . . . . . . . . 91

5.2 Global engine geometric parameters. . . . . . . . . . . . . . . . . . . . . . . 93

xv

List of Abbreviations

ANL Argonne National Laboratory

Cambridge Cambridge University

CFD Computational fluid dynamics

CMT CMT-Motores Termicos (Valencia)

DDM Discrete droplet method

ECN Engine combustion network

EGR Exhaust-gas recirculation

EMST Euclidean minimum spanning tree

ERC − UW ERC-University of Wisconsin

HCCI Homogeneous-charge compression-ignition

HECC High efficiency clean combustion

IC Internal combustion

IEM Interaction by exchange with the mean

ISAT In situ adaptive tabulation

KH −RT Kelvin-Helmholtz/Rayleigh-Taylor

LES Large-eddy simulation

LISA Linearized instability sheet atomization

LLNL Lawrence Livermore National Laboratory

LTC Low temperature combustion

PaSR Partially stirred reactor

PCCI Premixed-charge compression-ignition

xvi

Penn.State Pennsylvania State University

PDF Probability Density Function

PISO Pressure implicit with splitting of operators

POLIMI Politecnico di Milano

ppm parts per million

Purdue Purdue University

RANS Raynolds-averaged Navier-Stokes

RCCI Reactivity controlled compression ignition

rms Root-mean square

RNG Renormalized Group

SIDI Spark-ignition direct-injection

SIMPLE Semi-implicit method for pressure-linked equations

TAB Taylor analogy breakup

TNF Turbulent Nonpremixed Flames

UNSW University of New South Wales

URANS Unsteady Reynolds-averaged Navier-Stokes

xvii

Chapter 1

Introduction

Piston engines have been widely used in transportation applications for decades, and con-

tinue to dominate in the transportation market. Complex interactions between turbulence

and combustion present challenges to understanding and controlling the turbulent combus-

tion process in piston engines. The application of detailed, high-end CFD-based turbulent

combustion models is crucial for the development of next-generation clean and efficient

combustion systems in engines.

1.1 Background and Motivation

In 2010, the transportation sector used 27.4 quadrillion Btu of energy, accounting for 28%

of total U.S. energy consumption [1]. Ninety-four percent of the energy consumed in this

sector is from petroleum with small amounts of renewable fuels (4%) and natural gas (3%).

Of the total petroleum consumption, 44% is gasoline, 14% is diesel, and 8% is aviation fuel.

Conventional fuels for transportation are produced by refining petroleum-based sweet crude

oil. However, petroleum consumption in the transportation sector surpassed U.S. petroleum

production for the first time in 1989, and by the year 2035, transportation petroleum con-

sumption is expected to grow to almost 17 million barrels per day, creating a gap of almost

7 million barrels per day if using only conventional sources of petroleum fuel, as shown in

Fig. 1.1. The vast majority of motor vehicles in transportation rely on four-stroke internal

1

2

Figure 1.1: Transportation Petroleum Use by Mode and the U.S. Production of Petroleum,1970-2035 [2, 3]. Note: The U.S. production has two lines after 2005. The solid line isconventional sources of petroleum, including crude oil, natural gas plant liquids, and refinerygains. The dashed line adds in other non-petroleum sources, including ethanol, biomass,liquids from coal, other blending components, other hydrocarbons, and ethers. The sharpincrease in values between 2009 and 2010 is caused by the data change from historical toprojected values. The sharp increase in the value for heavy trucks between 2006 and 2007is the result of a methodology change in the Federal Highway Administration data.

combustion engines. These engines usually contain a reciprocating piston within a cylinder,

two or more valves (intake and exhaust), and a spark plug in the case of a spark-ignition (SI)

engine, which is typically fueled by gasoline or natural gas. Compression ignition engines

do not have a spark plug and rely on autoignition of the fuel instead, typically diesel oil.

The majority of the U.S. light-duty vehicle fleet is powered by SI gasoline engines. Sub-

stantial progress in gasoline engine efficiency in recent years has been the result of advances

in engine technologies, including direct in-cylinder fuel injection, flexible valve systems, im-

proved combustion-chamber design, and reduced mechanical friction. While all gasoline

engines sold in the U.S. currently operate with stoichiometric combustion, other areas in

the world are seeing the introduction of lean-burn gasoline engines [4]. Advances in lean-

gasoline emission controls are critical for meeting emerging U.S. regulations, and ultimately

it is expected that this technology will be introduced in the U.S. market [4]. Diesel engines

are also well-suited for light-duty vehicle applications, with their considerably higher fuel

3

economy than comparable SI engines. However, light-duty diesel vehicles have limited mar-

ket penetration in the U.S., accounting for only 1.7 percent of all U.S. sales of new light-duty

vehicles in 2007 [4]; the majority of those are light trucks. Reducing the cost of emissions

compliance continues to be addressed. The heavy-duty diesel is the primary engine for com-

mercial vehicles because of its high efficiency and outstanding durability. More stringent

federal and state standards for vehicle emissions have been proposed over the last decade.

U.S. diesel engine emission standards in 2010 are 0.2 grams per horsepower-hour (g/HP-hr)

for nitrogen oxides and 0.01 g/HP-hr for particulate matter [1]. The implementation of

increasingly stringent heavy-duty engine emissions standards has held efficiency gains to a

modest level. Current heavy-duty diesel engines have efficiencies in the range of 42-43%.

Diesel comprised 73% of the class 3-8 trucks sold in 2010, down from 84% in 2006 [1].

An overview of the various development paths that internal combustion (IC) engines

might take over the next 40 years is illustrated in Fig. 1.2. This shows the actual and

proposed technologies for internal combustion engines in both light-duty and heavy-duty

applications. The projections to 2020 are robust, due to the fact that eight-to-ten years

are typically required for a new engine concept to fully penetrate the marketplace. The

projections for 2020-2050 are more speculative, and are based on predictions of technological

maturity as well as evolution of the internal combustion engine marketplace.

Compared to current engines, likely directions for next-generation clean and efficient

combustion systems include higher pressures, lower temperatures, extremely lean and/or

dilute mixtures, and different fuels including reactant mixtures with high levels of H2, O2,

syngas (CO and H2), and/or exhaust-gas recirculation (EGR). The combustion processes in

these advanced combustion systems remain of research interest. Efforts to understand and

control these processes are being aided by exploring the fundamentals of flow structure and

combustion behavior through experiment and modeling ranging from homogeneous-charge

compression-ignition (HCCI) to advanced direct-injection spark-ignition (SIDI) operation.

These novel combustion strategies offer the potential for enabling engine systems with signif-

icantly increased fuel efficiency and dramatically reduced pollutant emissions. Fuel efficiency

improvements are possible in the next 10 to 15 years [5], enabled by advanced combustion

4

Figure 1.2: An overview of internal combustion engine technologies, 2010-2050. Actualand proposed technologies for internal combustion (IC) engines in both light-duty andheavy-duty applications. Information from Dennis Siebers, Sandia National Laboratories,Livermore, CA.

technologies, of 50% or more for automotive engines relative to the spark-ignition engines

dominating the road today in the U.S., and of 25% or more for heavy-duty truck engines

relative to today’s diesel truck engines.

1.1.1 Alternative Fuels for IC Engines in Transportation

At the same time that efforts are underway to increase the fuel efficiency and decrease the

environmental impact of engines for transportation, a new, diversified fuel source future is

emerging in the marketplace. Currently light- and heavy-duty powertrains, composed of

engines, fuels, and after-treatment devices, are highly optimized systems, and therefore less

tolerant of variations in fuel composition. However, there is increasing pressure driven by

government policy and high oil prices to accommodate a wider variety of replacement can-

5

didate fuels and/or fuel blends (non-petroleum-derived). These new fuels will be produced

from oil sands, oil shale, and coal, as well as from variety of bio-materials. None of these

future fuels are yet in wide use, but relatively small-scale efforts are underway to the extent

that they can simply be combined with current fuels and used in conventional engines [5].

Bio-derived fuels are already being blended with gasoline and diesel fuel for automotive and

heavy-duty ground transportation. Ethanol currently accounts for approximately 3% of the

automotive fuel use in the U.S., and its usage is expected to rise significantly. Likewise,

biodiesel use in the U.S., though very small, has undergone a 300-fold increase in six years.

Diesel-fueled vehicles generally are more fuel-efficient than comparable gasoline-fueled

vehicles. In fuel economy (miles per gallon) ratings published by the U.S. Environmental

Protection Agency (EPA), diesel vehicles show a fuel economy advantage of 20 to 40 percent

over gasoline vehicles, depending on the size and duty requirement of the vehicles. Pen-

etration of even current-technology diesel engines into the light-duty truck market would

reduce fuel use by 25-30% per gasoline vehicle replaced [6]. Diesel vehicles are inherently

more fuel efficient in comparison with conventional gasoline vehicles for several reasons:

1. Diesel engines operate at higher compression ratios than do spark-ignited gasoline

engines, creating higher in-cylinder temperatures before ignition, more complete com-

bustion, and higher thermal efficiency.

2. The energy content of diesel fuel per gallon is 11 percent greater than the energy

content of gasoline.

3. Diesel engines operate with fuel-lean equivalence ratios, while current SI engines in

the U.S. require an equivalence ratio close to one.

4. In a diesel engine, the load is controlled by changing the amount of fuel that is

injected. In contrast, in homogeneous stoichiometric engines, the load is controlled

by throttling.

Products that can be blended with diesel include: aviation fuel, bio-diesel, waste oils, used

motor oil, alcohol, and alkylates [7].

6

The effects of fuel composition variations on autoignition, combustion and emissions can

be subtle. For example, hydrogen has been used in conjunction with diesel fuel to power IC

engines. This dual-fuel combustion is sometimes called diesel pilot-ignited hydrogen com-

bustion. Diesel pilot-ignited hydrogen combustion at low quantities of hydrogen is beneficial

since the diesel fuel is being replaced by hydrogen, which may stretch the supply of hydro-

carbon fuels [8–15]. It has been suggested that hydrogen substitution may be a promising

method to reduce undesired exhaust emissions, especially at high rates of hydrogen substi-

tution. This will be discussed further in Chapter 5. A second example of the effects of fuel

composition variations on emissions is the impact of biodiesel fuel on exhaust emissions.

Biodiesel is a renewable oxygenated diesel fuel derived from vegetable oils or animal fats via

transesterification. Since biodiesel can help to reduce the dependence on petroleum-based

diesel fuels and can provide significant environmental benefits, it has become a promising

alternative to conventional diesel fuels. Biodiesel can be used in its pure form (B100) or

blended with petroleum diesel. Common blends include B2 (2% biodiesel), B5, and B20.

It has been well documented that biodiesel can provide substantial reductions in unburned

hydrocarbons, carbon monoxide, and particulate matter emissions. Biodiesel also has excel-

lent lubricity and can reduce life-cycle CO2 emissions. However, researchers have reported

that there is generally an increase in NOx emissions when using biodiesel [16]. According

to the comprehensive analysis of biodiesel impacts on exhaust emissions performed by the

EPA, the concentration of biodiesel in conventional diesel fuel has been correlated with the

changes in regulated and unregulated pollutants as shown in Fig. 1.3. On average, there is

2% NOx increase for soybean-based biodiesel B20 (i.e., a blend of 20 vol. % biodiesel in the

baseline diesel fuel) and 10% NOx increase for neat biodiesel (B100) in heavy-duty highway

diesel engines [17].

1.1.2 Turbulence-Chemistry Interactions in Chemically Reacting Flows

Turbulence-chemistry interactions and other nonlinear interactions such as turbulence-

radiation interactions are known to strongly influence the local and global behavior of

laboratory turbulent flames. Turbulence and combustion are intimately coupled. The effect

7

Figure 1.3: Average emission impacts of biodiesel for heavy-duty highway engines [17].

of turbulence on chemical reactions takes place through large-scale motions of the turbulent

flow field. This enhanced transport effectively enhances the transport rates of chemical

species and heat. Turbulent fluctuations in temperature and composition substantially in-

fluence the mean chemical reaction rates, which occur at molecular scales. The effect of

chemical reactions on turbulence takes place through large density changes brought about

by the heat release due to combustion.

Turbulence-chemistry interactions and turbulence-radiation interactions that result from

averaging highly nonlinear functions are briefly explained here.

The principal focus of turbulent combustion modeling is the chemical source term in

the mean (Reynolds averaged) species equations. The essence of the averaging problem is

the strong nonlinearity of the chemical source term S = S(ϕ), where ϕ denotes the vector

of physical quantities that is required to determine S (e.g., species mass fractions, pressure

and temperature). While S = S(ϕ)is known (in principle) for a specified thermochemical

system, the mean chemical source term S in general cannot be closed in terms of any

finite number of moments of ϕ [18, 19]. The differences between S(ϕ)and S

(ϕ)

are

manifestations of turbulence-chemistry interactions, and these differences are usually large

in practical combustion systems.

8

A variety of modeling approaches has been used to treat closure problem of species chem-

ical source terms. The simpler ones are based on so-called characteristic time scales [20]

and require additional modeling to treat the ignition process [21, 22]. Despite strong sim-

plifications, these models can be effectively employed to obtain engineering quantities for a

broad range of engine sizes [23] given careful consideration of model constants.

Recently, more advanced models have been applied to treat the turbulence-chemistry

interactions and allow inclusion of complex chemistry. Flamelet models [24, 25], originally

based on precalculated lookup tables, have been successfully applied to study spray diffu-

sion flames [26] and extended to engines [27]. The representative interactive flamelet (RIF)

model, which uses two-way coupling between the flow-field solver and the transient flamelet

integration, has been successful for autoignition of fuel sprays in combustion chambers [28]

as well as in engines [29–31]. However, using one flamelet to represent the entire domain

was found to be insufficient to accurately predict the premixed stage of the combustion and,

in particular, heat-release rates, which poses problems in pollutant formation computation.

Newer developments based on the Eulerian particle flamelet model (EPFM) [32, 33] there-

fore employ multiple RIFs and additionally solve an Eulerian transport equation to obtain

the probability of finding the corresponding flamelet in each cell. More complex situations

such as those with pilot injection have also been treated successfully with a flamelet for-

mulation with two mixture fractions [34]. Alternative developments employing presumed

PDFs and finite-rate chemistry have been proposed in [35, 36]. Alternative modeling based

on conditional moment closure has been proposed [37, 38]. Successful use of conditional mo-

ment closure (CMC) for autoignition problems in simplified flow fields with both first- [39]

and second-order [40] closure of the chemical source term has been reported, and its appli-

cability to spray autoignition with first-order CMC closure has also been shown [41, 42].

In principle, a proper accounting of turbulence-chemistry interactions throughout the au-

toignition phase needs to include fluctuations of the scalar dissipation rate [43, 44], as in

second-order CMC [40]. In practice, however, the computationally simpler first-order clo-

sure must be explored for engine calculations before the added complexity and cost of the

second-order approach are justified. Other approaches for autoignition in the presence of

9

turbulence include models based on transport equations for flame surface density [45–47]

and transported probability density function (PDF) methods [48, 49], both of which give

overall good predictions.

Transported PDF methods are particularly effective at capturing turbulence-chemistry

interactions. A recent review of transported PDF methods in reactive turbulent flows can

be found in [50]. Systematic investigations of turbulence-chemistry interactions have been

carried out targeting configurations from the International Workshop on Measurement and

Computation of Turbulent Non-premixed Flames (TNFs) [51–55], for example. Further

information and data for the TNF workshop flames can be found at their website [56].

In addition, the importance of interactions between turbulence and thermal radiation has

long been recognized [57–61]. Turbulence-radiation interactions arise from highly nonlin-

ear coupling between temperature and composition fluctuations in both non-reacting and

reacting turbulent flows. In this respect, turbulence-radiation interactions are akin to the

turbulence-chemistry interactions that have been the subject of intense research for many

years [62, 63]. The state-of-the-art in physical understanding and modeling of turbulence-

radiation interactions in reacting turbulent flows has been reviewed by Modest [64] and

by Coelho [65]. Complex interactions among turbulence, gas-phase chemistry, soot, and

radiation have been shown to be important even in atmospheric-pressure, laboratory-scale

flames [66–69]. Preliminary work in simulations accounting for turbulence-chemistry inter-

actions in spark-ignition engines has been reported in [70, 71].

Turbulence-chemistry interactions have been shown to have strong influences on emis-

sions and, in some cases, on ignition and heat release, in compression-ignition engines [72–

80]. Numerical simulations that neglect these interactions, or treat them in a simplistic

fashion, can fail to capture local and global flame ignition/extinction [52], and yield inac-

curate predictions of temperature (by as much as several hundred Kelvin) and pollutant

emissions [73]. The degree to which turbulence-chemistry interactions influence autoignition

and emissions is expected to vary with the combustion system and operating conditions.

Turbulent combustion in compression-ignition engines will be discussed further in Chapter

2.

10

The importance of finite-rate chemistry and turbulence-chemistry interactions, and of

participating-medium radiation and turbulence-radiation interactions, is expected to be

greater in next-generation combustion systems compared to current lean-to-stoichiometric

hydrocarbon/air combustion systems. Computational fluid dynamics (CFD) simulations

that account for these complex interactions will be necessary to develop next-generation,

clean, and efficient propulsion systems. A principal requirement identified in a recent DOE

workshop [5] is: “To develop a validated, predictive, multiscale, combustion modeling ca-

pability to optimize the design and operation of evolving fuels in advanced engines for

transportation applications.” To meet this requirement, CFD modeling of fuel effects and

turbulence-chemistry interactions will be addressed in this research.

1.2 Hypothese, Objectives and Approaches

This thesis addresses the following hypotheses:

1. An accurate description of the effects of turbulence-chemistry interactions is impor-

tant in numerial predictions of ignition characteristics, combustion and emissions in

environments that are representative of those in advanced compression-ignition en-

gines.

2. By explicitly accounting for turbulence-chemistry interactions, subtle fuel composi-

tion effects on emissions can be captured in CFD-based simulation with turbulent

combustion modeling.

Multi-dimensional, time-dependent CFD can complement experimental engine measure-

ments. In contrast to engine experiments, detailed spatially- and temporally-resolved infor-

mation on multiple physical quantities is readily extracted from a CFD simulation. On the

other hand, significant simplifications and approximations are inherent in a CFD simulation.

These include (i) simplifications in the geometric configuration, (ii) physical models that

must be introduced for phenomena including liquid fuel sprays, hydrodynamic turbulence,

and combustion, and (iii) inaccuracies that are associated with the numerical algorithms

and discretization. A judicious blend of experiment and CFD simulations can yield deeper

11

insight than either tool used in isolation. Moreover, CFD modeling can provide a much

easier way to isolate and vary one parameter at a time, which would be difficult to realize

experimentally, especially for varying physical properties.

Constant-volume, high-pressure spray combustion is an important intermediate step for

model validation and scientific understanding of combustion in direct-injection compression-

ignition engines. The operating conditions explored in the Engine Combustion Network

(ECN) workshop [81] are typical of diesel combustion, spanning or exceeding those typically

experienced in a modern diesel engine. Also, constant-volume spray combustion allows

the effect of each variable to be assessed independently, which helps to establish scientific

understanding of combustion at conditions specific to engines.

The objective of this thesis is to establish to what extent turbulence-chemistry interac-

tions will influence ignition, combustion and emissions by comparing results from a model

where turbulence-chemistry interactions are considered using a transported PDF method

with results from a model where turbulence-chemistry interactions are either considered

using a simplistic model or ignored altogether. Results will be shown for constant-volume

turbulent spray combustion chambers under diesel-engine-like conditions, and for idealized

and realistic compression-ignition engines. Quantitative comparisons will be made between

model results and experimental measurements, where available.

1.3 Organization of Thesis

1. Chapter 2 reviews turbulent combustion in direct-injection compression-ignition en-

gines. Advanced combustion systems in compression-ignition engines are reviewed,

followed by discussions of diesel and surrogate fuels including n-heptane, and the

constant-volume turbulent spray combustion configuration from the Engine Combus-

tion Network.

2. Chapter 3 describes the governing equations, physical models and numerical meth-

ods that will be used in the CFD simulations. The emphasis is on the transported

composition PDF method.

12

3. Chapter 4 shows quantitative comparisons of computed results with experiment for

constant-volume turbulent spray combustion under conditions that are representative

of those in modern compression-ignition engines. Systematic studies are performed

for non-reacting n-heptane sprays and reacting n-heptane spray flames, and unsteady

Reynolds-averaged (URANS) simulation results with and without PDF method are

compared with experimental measurements.

4. In Chapter 5, the application of PDF models in URANS to idealized and realistic

compression-ignition engines, and the capability to capture subtle differences in NOx

emissions with variations in fuel composition, are explored for two cases: the biodiesel

NOx effect in common-rail diesel engines, and hydrogen-assisted diesel combustion.

5. Chapter 6 concludes the thesis by summarizing the importance of turbulence-

chemistry interactions in the above configurations and key issues that remain un-

resolved. Future work is proposed.

Chapter 2

Turbulent Combustion in

Direct-Injection

Compression-Ignition Engines

Compression-ignition engines have significantly higher efficiency compared to spark-ignition

engines. However, NOx and soot emissions are a concern, and that concern is increasing

as emission standards are tightened. Recently more advanced combustion strategies have

been emphasized in efforts to realize further gains in efficiency and reductions in emissions.

A series of computational studies and experimental tests has been carried out to explore

advanced combustion systems for compression-ignition engines. Turbulence-chemistry in-

teractions have been shown to have strong influence in local and global behavior of labora-

tory turbulent flames, and there is some evidence that they may be important for ignition,

combustion and emissions characteristics in environments representative of those in ad-

vanced compression-ignition engines. In this work, we seek to quantify the extent to which

turbulence-chemistry interactions influence autoignition and emissions for conditions that

are representative of those in current and proposed compression-ignition engines.

13

14

2.1 The Diesel Combustion Process

Diesel engines are of interest due to their higher efficiency in comparison to spark-ignited

engines. In direct-injection diesel engines, fuel is injected directly into the combustion

chamber at a pressure of 30-150 MPa through a multi-hole nozzle which has several orifices

with a diameter of 0.15-0.35 mm. The temperature and pressure at compression top dead

center are normally in the range of 1000-1200 K and 4-12 MPa, respectively [82].

The diesel combustion process can be broken up into four different phases: ignition

delay period, premixed combustion phase, mixing-controlled combustion phase, and the late

combustion phase [8]. The ignition delay period begins at the start of injection. During the

ignition delay period, the rate of heat release drops below zero due to the fuel absorbing

heat while vaporizing [83]. Next is the premixed combustion phase where a rapid rate of

heat release occurs. The portion of the fuel which has mixed with air forms a combustible

mixture and ignites. After all of the premixed air-fuel charge is consumed, the mixing-

controlled combustion phase begins. Here the combustion transitions from a premixed

flame to a diffusion flame. The rate of combustion is controlled by the fuel vaporization

and mixing, in contrast to the fast burn of the kinetics-driven premixed flame. During the

mixing-controlled combustion phase, the end of injection occurs. In the late combustion

phase, unburned fuel seeks oxygen as it is turbulently mixing throughout the cylinder [84].

Dec [86] and Flynn et al. [85] have compiled the results of many studies into a complete

picture of the structure of the diesel spray. A review of the conceptual model introduced

by Dec [86] is given below. The conceptual model describes how the spray develops and

combustion begins, and also the quasi-steady portion of the combustion.

As liquid fuel is injected into the cylinder, high-temperature air is entrained into the

fuel forming a cone-shaped spray. This high-temperature air vaporates and mixes with the

fuel. There is a maximum penetration distance for the liquid fuel after which all the fuel has

vaporized, called the liquid length. This varies with fuel properties, combustion chamber

conditions, and injector geometry, but is basically the result of the energy balance between

the energy of the air entrained and the energy required to vaporize the fuel. Higher air

density and temperature in the cylinder cause more air to be entrained and thus reduce the

15

Figure 2.1: Summary of the quasi-steady diesel burning processes [85].

liquid length.

Beyond the liquid length, the fuel vapor and air continue to mix and penetrate into the

combustion chamber. With the high temperatures in the cylinder, autoignition begins when

the fuel-air ratio and the temperature in the spray reach combustible limits. Combustion of

this premixed, vaporized-fuel and air mixture occurs volumetrically in a premixed reaction.

At the end of the initial premixed burn, a diffusion flame forms where the equivalence

ratio of the mixture is close to one, surrounding the fuel-rich products of the premixed

reaction. Because the liquid length and premixed burn location remain fixed until the end

of combustion while the leading edge continues to move forward and expand radially, this

portion of the combustion process is termed quasi-steady. A schematic diagram of a quasi-

steady diesel combustion flame jet is shown in Fig. 2.1, which includes a fuel-rich premixed

core surrounded by a diffusion flame between the products of fuel-rich combustion and the

surrounding air.

During the quasi-steady phase, the liquid length shortens a small amount due to com-

bustion that increases the energy of the air entrained into the jet. Beyond the liquid length,

the mixture of vapor-phase fuel and hot entrained air increases in temperature until react-

ing in the fuel-rich premixed combustion zone, where the equivalence ratio is between 2

16

and 4 [86] under normal diesel operation. The fuel-rich premixed burn produces interme-

diate temperatures (1600-1900 K), leaving unoxidized products such as CO and unburned

hydrocarbons (HC) due to a lack of oxygen.

A diffusion flame forms an envelope around the rich premixed zone and the liquid spray,

forming a lifted diffusion flame. The distance from the nozzle to the edge of the diffusion

flame is called the lift-off length, which is an extremely important characteristic of the

flame, as it shows how much air is entrained into the rich premixed reaction zone where

soot is initially formed. The lift-off length is typically shorter than the liquid length for

the operating conditions of most modern diesel engines. Longer lift-off lengths allow more

air entrainment, increasing oxygen in the rich premixed reaction zone and thereby reducing

soot formation. The temperature of the diffusion flame sheath is near the stoichiometric

adiabatic flame temperature.

At the end of injection, the spray slows and stops, allowing the flame to move closer to

the nozzle, shortening the lift-off length. The diffusion flame encircles the entire jet. At

this point, a significant portion of the fuel energy remains unreacted, but the conceptual

model is no longer well understood. The rich products within the jet appear to be carried

toward the wall following the quasi-steady phase, splitting and forming large-scale turbulent

structures that entrain air and continue to burn as a diffusion flame.

Although diesel engines have the advantage of high efficiency, a limiting issue is criteria

pollutant emissions: especially soot and NOx. A key diesel emissions issue is the soot/NOx

tradeoff: in general, strategies that reduce emission levels for one of these pollutants tend to

increase the other [87]. An example is shown in Fig. 2.2. An equivalence ratio-temperature

(Φ-T ) map is commonly used to describe how different combustion concepts affect pol-

lutant formation. The typical regions in terms of temperature and equivalence ratio for

NO formation and soot or particulate matter (PM) formation/oxidation are shown in the

map. In Fig. 2.3, the highest NO concentrations coincide with the region of the highest

OH concentrations, illustrating the “soot-NO dilemma”: i.e., in the region with the high

NO concentrations, plentiful OH radicals are available to oxidize the soot previously formed

in the locally rich regions. However, outside this high temperature region, NO will not be

17

formed but soot may be, and only small amounts of OH radicals are available to oxidize it

later.

Fortunately, the tradeoff relationship between NOx and soot is only fixed for a specific

engine. The soot/NOx tradeoff can be broken by strategies that include variations in

fuel composition (oxygenates) and fuel-injection scheduling. Advanced diesel combustion

concepts (discussed in the following subsection) can break the tradeoff by altering the mixing

and ignition parts of the combustion process. The use of exhaust gas recirculation (EGR)

decreases the combustion temperature, and thereby the NOx formation. Recent combustion

models accommodate both premixed and non-premixed burning and formation/destruction

of the key pollutants, NOx and soot.

Figure 2.2: An example of a NOx-soot trade-off curve [84].

2.2 Advanced Diesel Combustion

Advanced combustion strategies are of current interest to maintain or reduce fuel con-

sumption while significantly reducing engine-out soot and/or NOx compared to conven-

18

Figure 2.3: Φ-T regions with the highest NO and OH concentrations coincide [88].

tional diesel combustion. These include homogeneous-charge compression-ignition (HCCI),

premixed-charge compression-ignition (PCCI), low-temperature combustion (LTC), high ef-

ficiency clean combustion (HECC) and reactivity controlled compression ignition (RCCI).

Figure 2.4 [89] shows soot and NOx formation zones and some advanced combustion modes

on a Φ-T map. More advanced strategies are listed in Table 2.1.

Figure 2.4: LTC, PCCI and HCCI concepts on a Φ-T map [89].

In a homogeneous-charge compression-ignition (HCCI) combustion system [137], a

highly lean and/or dilute fuel/air/residual mixture is compression ignited. This results

19

Table 2.1: Advanced modes of combustion in compression-ignition engines.

Advanced com-bustion concept

Primary focus Work and reference

HCCI(homogeneous-chargecompression-ignition)

reduced soot andNOx emissions

Early-DI HCCI: PREDIC (premixed lean diesel com-bustion) by Takeda et al. and Nakagome et al. [90, 91]with subsequent studies [92–96]; UNIBUS (UniformBalky Combustion System) by Yanagihara et al. [97]with further studies [98]; MULINBUMP (multiplestage diesel combustion) by Su et al. [99–101]; NADI(narrow angle diesel injection) [102–106].Late-DI HCCI: MK (modulated kinetics) developedby Nissan [107, 108].Premixed/direct-injected HCCI [109–116]

SRDC (smokelesslocally rich dieselcombustion)


developed by Toyota [117, 118]

LTC (low tem-perature combus-tion)


Natti [119], Henein et al. [120] and Choi et al. [121],Aoyagi et al. [122], Colban et al. [123]. Genzale etal. [124]. Kook et al. [125], Opat et al. [126], Kumarand Zheng [127]

PCCI (partially-premixed chargecompression igni-tion)

lower soot emis-sions

Neely and coworkers [89], Kanda [128] and Araki [129],Sluder and coworkers [130], Lilik [8], Kook andBae [125] and Aronsson et al. [131]

PPC (partiallypremixed com-bustion)


Johansson [132], Hanson et al. [133]

PCI (premixedcompressionignition)

lower soot andNOx emissions

Okude et al. [134]

RCCI (reactivity-controlled com-pression ignition)

high efficiency developed by Splitter, Reitz and Hanson [135]

SCCI (stratifica-tion charge com-pression ignition)

fuel consumptionreduction

Berntsson and Denbratt [88], Arronsrisopon etal. [115]

HECC (high effi-ciency clean com-bustion

efficiency im-provements

developed by ORNL: Sluder et al. [136]

20

in low combustion temperatures and low engine-out NOx. There are no locally fuel-rich

zones, hence little soot formed. Therefore, the system has the potential for diesel-like ther-

mal efficiency with near-zero NOx and particulate-matter emissions. Technical issues with

classical HCCI include a limited load-speed range over which an engine can operate in this

mode, low efficiency at light loads, difficulty in controlling combustion phasing, high levels

of engine-out unburned hydrocarbons (UHC) and carbon monoxide (CO), and noise.

Premixed-charge compression-ignition (PCCI) can be seen as an intermediate step be-

tween conventional diesel combustion and HCCI. The charge in PCCI is not mixed as

thoroughly as in HCCI, so that there will be some hot spots. Also, since in PCCI, the

fuel is injected via the diesel fuel injector, the long ignition delay may result in diesel fuel

penetration to the cylinder walls, resulting in incomplete combustion.

HCCI and PCCI modes induce the engine to burn the fuel in the premixed phase,

resulting in a globally fuel-lean charge and lowered combustion temperature, thus resulting

in engine operation away from zones of NOx and soot formation. The difference is that the

air-fuel charge in HCCI is homogeneous when it enters the cylinder. In PCCI, advanced

in-cylinder injection of fuel leads to an extended premixed combustion phase.

Low-temperature combustion (LTC) has been heavily explored in response to increas-

ingly strict diesel emissions regulations. LTC is a generic term that refers to engine operat-

ing conditions that are below the temperatures that are required for the formation of NOx

(Φ <2.5, T >2000 K) and/or soot (Φ ∼2.5, 1700 K< T <2400 K) [118]. The combustion

temperature can be lowered by introducing EGR or by altering the combustion process to

be locally fuel lean. EGR is introduced into the cylinder by displacing the intake air. With

EGR, O2 is reduced, which successfully reduces NOx. However, soot emissions increase

due to the reduction in oxygen and the resulting inhibition of soot oxidation. HCCI-like

conditions can be coupled with EGR to reduce soot emissions. In that case, a well mixed

air-fuel charge is locally fuel lean. A fuel-lean charge will produce less heat and have more

O2 locally available to oxidize soot or prevent formation of soot.

High efficiency clean combustion (HECC), formally known as efficient-LTC, is accom-

plished by a combination of a single-pulse injection, EGR (∼50%), early injection timing,

21

and increased injection pressure. The HECC mode provides a decrease in NOx emissions

and soot emissions while maintaining or even increasing fuel efficiency. However, the HECC

mode results in increased HC and CO emissions, which is common with HCCI-like combus-

tion modes [130].

Reactivity-controlled compression ignition (RCCI) is a dual-fuel engine combustion

technology developed at the University of Wisconsin-Madison Engine Research Center

(ERC) [135]. RCCI is a variant of HCCI that provides more control over the combus-

tion process and has the potential to dramatically lower fuel use and emissions. RCCI

uses in-cylinder fuel blending with at least two fuels of different reactivities and multiple

injections to control in-cylinder fuel reactivity to optimize combustion phasing, duration

and magnitude. The process involves introduction of a low-reactivity fuel into the cylinder

to create a well-mixed charge of low-reactivity fuel, air and recirculated exhaust gases. The

high-reactivity fuel is injected before ignition of the premixed fuel occurs using single or

multiple injections directly into the combustion chamber. Examples of fuel pairings for

RCCI are gasoline and diesel, ethanol and diesel, and gasoline and gasoline with small addi-

tions of a cetane-number booster. In comparison to conventional diesel combustion, RCCI

combustion exhibits significantly higher peak cylinder pressures and pressure-rise rates.

2.3 Fuels

Gasoline and diesel fuels are composed of hundreds-to-thousands of individual compounds.

Fundamental physical and chemical data are not available for all the components of interest,

and even if they were available, simulations that account for that level of detail would be

beyond the capability of current computational resources. The primary chemical classes

of the components in diesel fuel are n-alkanes, iso-alkanes, cycloalkanes, and aromatics as

shown in Fig. 2.5. Although the composition of diesel fuel is highly variable, there are some

trends [138]: for example, the carbon numbers of the components range from approximately

C10 to C22, with an average of 14 to 15. Considerable interest has been shown in “surrogate

fuels.” A surrogate fuel is “a fuel composed of a small number of pure compounds whose

behavior matches certain characteristics of a target fuel that contains many compounds.”

22

[139] The surrogate fuel should represent both the physical and chemical characteristics of

the target fuel. Key physical properties include density, volatility, viscosity, surface tension

and diffusion coefficients; key chemical properties include C/H/O content, ignition behavior,

adiabatic flame temperature and sooting propensity. N-heptane is a primary reference fuel

Figure 2.5: Relative amounts of various chemical classes in diesel fuel [138].

for octane rating in IC engines, and is often used as a single-component surrogate for

diesel fuels. It has a cetane number of approximately 56, which is close to that of typical

diesel fuels. Another characteristics of n-heptane is its two-stage ignition process, which is

representative of diesel-like fuels. This is related to the “cool flame” phenomenon and the

negative-temperature-coefficient behavior that are important in HCCI and LTC. Hence,

extensive research has been published on measuring ignition delays and other quantities

from experiments that employed n-heptane in engines [140, 141], as well as on developing

chemical mechanisms for n-heptane [142–152]. Most current chemical mechanisms have been

derived from either the “Chalmers” mechanism [153] or a detailed n-heptane mechanism

from Lawrence Livermore National Laboratory (LLNL) [154]. In this thesis, n-heptane

gas-phase chemical mechanisms are used for multidimensional CFD simulations.

2.4 Constant-Volume Turbulent Spray Combustion

Constant-volume turbulent spray combustion is an important intermediate step between

laboratory flames and practical engines. Exploration of laboratory flames such as the TNF

23

Workshop flames emphasizes fundamental issues of turbulence-chemistry interactions in

gaseous flames to establish basic scientific understanding of turbulent combustion. The

liquid-fuel spray atomization and evaporation and fuel-air mixing processes are of great im-

portance in many industrial applications, including internal-combustion engines [155, 156].

Detailed investigations of the main physical and chemical processes governing combustion

in diesel engines, such as fuel-air mixing, auto-ignition, flame development [157, 158] and

in-cylinder charge motions [124], are typically performed in simplified configurations such

as constant-volume vessels.

A key resource is an internet library of well-documented experiments, called the Engine

Combustion Network (ECN http://www.sandia.gov/ECN/). This includes data obtained

in a constant-volume chamber (Fig. 2.6) at typical conditions of diesel combustion. The

goal of ECN is to facilitate validation of computational models at conditions appropri-

ate for engines. The database includes key experimental data that have been acquired at

well-defined boundary conditions over the past ten years, including spray liquid and vapor

penetration, liquid length, lift-off length, ignition delay, pressure-rise rate, soot volume frac-

tion, high-speed movies of chemiluminescence, effects of fuel type, and others. Much of the

data have been obtained at the same conditions, making it suitable for model validation.

A data searching utility provides experimental conditions such as fuel type, ambient con-

Figure 2.6: Constant-volume chamber in the experiment [81].

24

ditions, injection pressure, injection mass and profile, nozzle size and other relevant data.

The following ambient conditions at the time of fuel injection can be controlled, allowing

the effect of each variable to be assessed:

• Ambient gas temperatures from 450 K to 1300 K

• Ambient gas densities from 3 to 60 kg/m3

• Ambient gas oxygen concentrations from 0% to 21%

Figure 2.7: Soot volume fraction contours [81]. Ambient conditions: Ta=1000 K, ρa=14.8kg/m3, 21%O2. Injector conditions: 1500 bar above ambient, 0.1 mm nozzle, n-heptane.

Fuel is injected using modern common-rail fuel injectors with the following parameter

ranges:

• Injection pressures above ambient from 40 to 200 MPa

• Nozzle diameters from 0.05 to 0.5 mm

• No. 2 diesel, single-component reference fuels (n-heptane, n-dodecane), and oxy-

genated fuels

N-heptane sprays under different ambient conditions are of particular interest within the

context of this thesis. For n-heptane sprays, different ambient compositions ranging from

0 to 21% O2 represent various EGR levels that are relevant in many advanced combus-

tion modes. Ambient temperatures from 750 K to 1300 K span conventional diesel engine

25

thermodynamic conditions and advanced combustion conditions including LTC. Two dif-

ferent ambient density conditions are included: 14.8 and 30 kg/m3. Available data include

liquid/jet penetration lengths, mixture fraction, lift-off length, ignition delay, and soot.

Figure 2.7 is an example of experimental data of soot volume fraction for n-heptane.

Earlier published computational modeling work for non-reacting and/or reacting n-

heptane sprays in the Sandia constant-volume chamber are summarized in Table 2.2. Some

have chosen a well-mixed model, which neglects turbulence-chemistry interactions. Excep-

tions include a conditional moment closure (CMC) model, an unsteady flamelet progress-

variable (UFPV) model, a PDF model, a partially stirred reactor (PaSR) model and a

3-Zone Extended Coherent Flame Model (ECFM3Z). The PaSR model was developed at

Chalmers Gothenburg [159], accounting for the unmixedness effect on chemical reaction

rates. In this model, the chemical source term is described by τchemτmix+τchem

ωi, where ωi is the

chemical reaction rate of reaction i, τchem is the chemical time and τmix is the mixing time.

The mixing time τmix is calculated according to,

τmix = Cmix

√µeffρϵ

, (2.1)

where Cmix is a constant set to 0.03, µeff is the effective viscosity, ρ is density and ϵ is the

rate of dissipation of turbulent kinetic energy. PDF and PaSR models have been applied

for constant-volume n-heptane spray flames in this work.

26

Table 2.2: Earlier modeling work for the ECN n-heptane spray cases.

Institution and reference Turbulence-chemistry interaction

Argonne National Laboratory(ANL) [160, 161]

Well-mixed (no model)

Cambridge University [162] Conditional moment closure (CMC)

CMT-Motores Termicos(CMT) [163]

Partially stirred reactor (PaSR)

T.U. Eindhoven (Eind-hoven) [164]


ERC-University of Wisconsin(ERC-UW) [143, 145, 165]

N/A

Pennsylvania State University(Penn. State) [166, 167]

PaSR, PDF

Politecnico di Milano(POLIMI) [168–172]


Purdue University [173–177] Unsteady-flamelet progress variable (UFPV)

University of New SouthWales (UNSW) [178]


Okayama University [179] 3-Zones Extended Coherent Flame Model (ECFM3Z)

Imperial College [180] ECFM3Z

Chalmers University of Tech-nology [181]

PaSR

Chapter 3

Mathematical Formulation,

Physical Models, and Numerical

Methods

Current computational simulations for engines range from zero- to three-dimensional to

complement experimental studies by utilizing a variety of models for sprays, turbulence,

chemical kinetics and combustion. Modeling these phenomena is critical to simulate modern

engines and engine-like conditions. For example, spray characterizations are sensitive to

spray models and parameters, and affect in-cylinder fuel distribution in direct-injection

engines. Turbulence can significantly affect the species and enthalpy distributions, and

thus heat release and emissions.

Two three-dimensional CFD codes have been used here: OpenFOAM [182] and AC-

Flux [183]. Reynolds-averaged forms of the governing equations are solved for ensemble-

averaged mean quantities, which requires modeling the effects of turbulent fluctuations

about local mean values. Simple models for turbulence-chemistry interactions may be suf-

ficient for conditions where the effects of flow dynamics and spatial inhomogeneities are

relatively small. However, under conditions with strong inhomogeneity, a sophisticated

model is needed to deal with the turbulence-chemistry interactions.

In this work, the transported composition PDF method is used to model turbulent com-

27

28

bustion. PDF methods have shown promise in canonical engine configurations and idealized

engine-like geometries. The strength of the model lies in its capability to treat exactly the

effects of turbulent fluctuations on mean chemical source terms. In this chapter, the numer-

ical formulations and physical models of Reynolds-averaged conservation equations with a

composition PDF method will be outlined and discussed.

3.1 Gas-Phase Mean Equations

3.1.1 Reynolds-Averaged Equations

A compressible, multiphase, chemically reacting turbulent flow is considered using a

Reynolds-averaged formulation. Here angled brackets (<>) denote conventionally averaged

mean quantities and tildes (∼) denote density weighted or Favre-averaged mean quantities.

In the IC engine community, RANS refers to unsteady RANS, also known as URANS. In the

context of piston engines, a simulation through a single engine cycle represents the ensemble

average. Computed dependent variables represent ensemble- (phase-) averaged values at a

given piston position. Simulations through multiple engine cycles should give same result

on every cycle (after reaching statistically periodic state), which makes it appropriate to

compare with experiment results that are likewise phase-averaged over many cycles. All

fluctuations about the ensemble average are represented by the turbulence model.

The principal mean partial differential equations for the gas phase (a multicomponent

ideal-gas mixture) can be written using Cartesian tensor notation as follows. Here the

liquid-phase source terms have been omitted for clarity. The detailed derivation for these

29

equations can be found in previous reviews of turbulent combustion modeling [18, 87].

∂2 ⟨p⟩∂xixi

=∂2 ⟨ρ⟩∂t2

− ∂2 ⟨ρ⟩ uiuj∂xi∂xj

+∂2 (⟨τij⟩+ τT,ij)

∂xi∂xj+ gi

∂ ⟨ρ⟩∂xj

(3.1)

∂ ⟨ρ⟩ uj∂t

+∂ ⟨p⟩ uj ui∂xi

=∂ (⟨τij⟩+ τT,ij)

∂xi− ∂ ⟨p⟩

∂xj+ ⟨ρ⟩ gj (3.2)

∂ ⟨ρ⟩ h∂t

+∂ ⟨ρ⟩ hui∂xi

=∂

∂xi

[(λ

Cp+

µTPrT

)∂h

∂xi

]+∂ ⟨p⟩∂t

+ ui∂ ⟨p⟩∂xi

+Φ+⟨Qrad

⟩(3.3)

∂ ⟨ρ⟩ Yα∂t

+∂ ⟨ρ⟩ Yαui

∂xi=

∂

∂xi

[(µ

Scα+

µTScT,α

)∂Yα∂xi

]+ ⟨ρ⟩ Sα (3.4)

Here ui is a velocity component, p is pressure, ρ is density, g is a constant body force per

unit mass, h is enthalpy, Y is mass fraction, subscript α denotes a chemical species, and µ

and µT are molecular viscosity and apparent turbulent viscosity, respectively. The viscous

dissipation rate of kinetic energy to heat Φ is given by Φ = ⟨τij⟩ ∂ui∂xj

+⟨ρ⟩ ϵ. S is a mass-based

chemical source term, and Cp is the constant-pressure specific-heat capacity. The viscous

shear stress is τij ; τT,ij is an apparent turbulent stress. Scα is the molecular Schmidt number

of species α, and PrT and ScT,α are apparent turbulent Prandtl and Schmidt numbers,

respectively. The mean density ⟨ρ⟩ is obtained using an ideal-gas equation of state. Note

that the latter two equations (Eqs. 3.3 and 3.4) will be superseded by the transported PDF

equations, for cases where the transported PDF method is used.

The thermal equation of state and the caloric equation of state provide the density and

temperature, respectively [87, 184]. The unaveraged forms of the equations of state are:

ρ = ρ(p, h, Y ), (3.5)

T = T (p, h, Y ). (3.6)

Ideal-gas mixture properties are typically assumed. The state equations then are given by

p = ρRT (R =RU

W), (3.7)

30

and

h =

NS∑α=1

Yα

(∆h0f,α +

∫ T

T 0

Cp,α(T′)dT ′

), (3.8)

where RU is the universal gas constant, W is the mixture molecular weight, ∆h0f,α is the

formation enthalpy for species α at T 0, the reference temperature, and Cp,α is the constant

pressure specific heat for species α. The averaged forms of the equations of state are

discussed below after the composition PDF is introduced. Fluid properties that are required

include transport properties (fluid viscosity, species diffusivities, thermal conductivities) and

specific heats (constant-pressure). These are standard equations of state [87].

Standard formulations are adopted for molecular transport terms [185]. Thermal diffu-

sion is typically neglected. Species transport is modeled using a multicomponent form of

Fick’s law, and heat conduction is modeled with a multicomponent form of Fourier’s law.

The viscous stress τij is written in a form that is appropriate for a Newtonian fluid,

τij = µ(∂ui∂xj

+∂uj∂xi

)− 2

3µ∂ul∂ul

δij , (3.9)

where µ is a multicomponent mixture viscosity.

3.1.2 Turbulence Models

In AC-Flux, a standard k−ϵ turbulence model with wall functions is used to model turbulent

transport in the mean equations. A renormalization group (RNG) k − ϵ turbulence model

is used in OpenFOAM, which is similar to the standard k − ϵ, but with a modified form of

the ϵ equation developed by Yakhot et al. [186] which attempts to account for the different

scales of motion through changes to the production term. Other turbulence models explored

include the Launder-Sharma k−ϵ model [187] and a realizable k−ϵ model [188]. Turbulence

models and coefficients used in OpenFOAM are listed in Table 3.1. The standard k − ϵ

31

equations are,

∂ ⟨ρ⟩ k∂t

+∂ ⟨ρ⟩ kuj∂xj

=∂

∂xj

[(µ+

µTσk

)∂k

∂xj

]+ τT,ij

∂uj∂xi

− ⟨ρ⟩ ϵ (3.10)

∂ ⟨ρ⟩ ϵ∂t

+∂ ⟨ρ⟩ ϵuj∂xj

=∂

∂xj

[(µ+

µTσϵ

)∂ϵ

∂xj

]− Cϵ2 ⟨ρ⟩

ϵ2

k+ Cϵ3 ⟨ρ⟩

∂uj∂xj

+Cϵ1ϵ

kτT,ij

∂ui∂xj

(3.11)

where k is the turbulence kinetic energy and ϵ is the viscous dissipation rate of turbulence

kinetic energy. Here σk and σϵ are the turbulent Schmidt numbers, and Cϵ1, Cϵ2 and Cϵ3

are model constants (Table 3.2). The apparent turbulent stress is given by

τT,ij = µT

(∂ui∂xj

+∂uj∂xi

)− 2

3µT

∂ul∂xl

δji −2

3⟨ρ⟩ kδji. (3.12)

Here µT is an apparent turbulence viscosity that is given by µT = Cµ ⟨ρ⟩ k2/ϵ.

3.1.3 Turbulence Wall Function

For RANS modeling, wall functions are usually adopted to deal with near-wall turbulence

and to enforce the no-slip condition for the mean velocity. Standard wall functions using a

logarithmic correlation [189] are used in AC-FLux at solid wall boundaries:

⟨U⟩ = uz

(1

kln y+ +B

)(3.13)

ϵ =u3zκy

(3.14)

−⟨uv⟩ = u2z = C1/2µ k. (3.15)

Here ⟨U⟩ is the mean velocity component parallel to the wall, uz is the wall shear velocity,

B is a constant given by B = lnE/κ where κ and E are log-law constants (see Table 3.2),

y+ is the distance y from the wall over the viscous length scale, u and v are the wall-parallel

and wall-normal fluctuating velocity components, respectively, and Cµ is a model constant.

The values for the standard k−ϵ turbulence model and wall functions constants in AC-FLux

are summarized in Table 3.2.

32

Table 3.1: Turbulence models and coefficients.

Standard k − ϵ model

Cµ Cϵ1 Cϵ2 Cϵ3 σk σϵ0.09 1.44 1.92 -0.33 1.0 1.3

RNG k − ϵ model

Cµ Cϵ1 Cϵ2 Cϵ3 σk σϵ η β

0.0845 1.53 1.68 -0.33 0.72 0.72 4.38 0.012

Launder-Sharma k − ϵ

Cµ Cϵ1 Cϵ2 Cϵ3 σk σϵ0.09 1.44 1.93 -0.34 0.7 0.7

Realizable k − ϵ

Cµ C2 A0 σk σϵ0.09 1.9 4.0 1.0 1.2

Table 3.2: Standard k − ϵ turbulence model and wall function constants.

Cϵ1 1.44

Cϵ2 1.93

Cϵ3 -0.34

Cµ 0.09

σk 0.7

σϵ 0.7

κ 0.4187

E 9.793

RANS wall functions have been used here to determine the turbulent scales for the near-

wall PDF particles as in Kung’s work [73]. Dreeben and Pope applied a more sophisticated

wall modeling approach for PDF particles in the velocity-frequency joint-PDF method [190].

3.2 Transported Composition PDF method

In the review by Veynante and Vervisch [18], various turbulent combustion models have

been discussed. PDF methods offer the compelling advantage that the mean chemical

33

source term is closed in terms of the composition PDF:

Sα =

∫Sα(ψ)fϕ(ψ;x, t)dψ, (3.16)

where ψ is the sample-space vector corresponding to the composition variables ϕ. In a

composition PDF method, an appropriate set of variables (here NS species mass fractions

Y and the mixture specific enthalpy h) is treated as a vector denoted by ϕ of dimension

Nϕ = NS + 1. The corresponding composition joint PDF represents the probability of ϕ

taking on a particular value at spatial location x and time t, denoted by fϕ. Thus,

fϕ(ψ;x, t)dψ = Probψ ≤ ϕ < ψ + dψ. (3.17)

Mean values of any function of the composition variables, Q = Q(ϕ), can be expressed

in terms of PDF:

⟨Q⟩ = ⟨Q(x, t)⟩ =∫Q(ψ)fϕdψ, (3.18)

Q = Q(x, t) = ⟨ρQ⟩/ ⟨ρ⟩ = ⟨ρ⟩−1∫ρ(ψ)Q(ψ)fϕdψ =

∫Q(ψ)fϕdψ, (3.19)

where the Favre PDF fϕ = ρ(ψ)fϕ/ ⟨ρ⟩ has been introduced, and the integration is over the

entire composition sample space. The mean value of Q conditioned on the composition ϕ

at location x and time t having the particular value ψ is denoted by ⟨Q(x, t)|ϕ(x, t) = ψ⟩ =

⟨Q(x, t)|ψ⟩.

For nonpremixed flames, the PDF of mixture fraction sometimes is presumed to be a

beta distribution using an infinitely fast chemistry model. Other available models are the

steady laminar flamelet model or conditional moment closure.

The objective of transported PDF modeling is to relax as many assumptions as possible

concerning the shape of the PDFs and other assumptions that are required in simpler

turbulent combustion closures. The main advantage of a transported PDF method lies in

the possibility of treating complex chemical sources directly.

The PDF method has been derived using different sets of independent variables (e.g.,

34

velocity, composition and frequency) to form the probability density function. Several PDF

methods with different choices of independent variables have been reviewed by Haworth [50,

191] and Kung [73], including a joint PDF of velocity, composition, and frequency, a velocity-

composition PDF and a composition PDF.

A transported composition PDF method is used here to explicitly model the effects of

turbulent fluctuations in species composition and enthalpy (hence temperature) relative to

the local mean values. PDF methods can be implemented in both Eulerian [192–194] and

Lagrangian [195] contexts. A stochastic Eulerian field method and a deterministic Eulerian

field method with a direct-quadrature-method-of-moments closure have been implemented

in [193, 194] targeting a series of flames that exhibit different levels of local extinction. Eu-

lerian PDF methods have not been applied to engine configurations, to date. A Lagrangian

method distributes notional particles with scalar properties within the physical domain,

and particles are associated with cells according to their physical positions. In this thesis,

a Lagrangian framework is adopted following the implementation from Subramaniam and

Haworth’s work [195].

3.2.1 Transported Composition PDF Equation

The transport equation for the Favre-averaged composition PDF is:

∂ ⟨ρ⟩ fϕ∂t

+∂ ⟨ρ⟩ uifϕ

∂xi+∂ ⟨ρ⟩Sαfϕ∂ψα

= − ∂

∂xi

[⟨u

′′i |ψ

⟩⟨ρ⟩ fϕ

]+

∂

∂ψα

[⟨ρ−1∂J

αi

∂xi|ψ⟩⟨ρ⟩ fϕ

]. (3.20)

Here summation is implied over indices i or α within a term, and ⟨⟩ denotes the probabilistic

mean. Jα is the molecular diffusive flux of composition variable ϕα, and Sα is the source

term of composition variable ϕα. u is the Favre-averaged mean velocity and u′′ is the

velocity fluctuation about u. On the left-hand side, the first term represents the temporal

variation of the PDF, the second term is the advection of the PDF by mean velocity and

the third term is the chemical source term. On the right-hand side are the transport term

due to turbulent velocity fluctuations (“turbulent diffusion”) and the molecular transport

35

(“mixing”) term, which need closure models.

3.2.2 Particle Equations

Here a Lagrangian particle Monte Carlo method is used to solve the modeled PDF equa-

tion [195]. In this approach, the Eulerian PDE (Eq. 3.20) can be recast in Lagrangian form.

A system of “notional” particles is devised to represent a chemically reacting turbulent

flow, whose one-point, one-time Eulerian joint PDF evolves according to the modeled PDF

transport equation. The total number of notional particles is NP . The ith particle is as-

signed a mass m(i) with position coordinates xi(t) and Nϕ scalar variables ϕ(i)(t). Formally,

a discrete mass density function F∗ is introduced,

F∗ϕx

(ψ, y; t

)≡

NP∑i=1

m(i)δ(ψ − ϕ(i)(t))δ(y − x(i)(t)), (3.21)⟨F∗ϕx

(ψ, y; t

)⟩= F∗

ϕ

(ψ, x; t

)= ⟨ρ(x, t)⟩ fϕ = ρ(ψ)fϕ(ψ;x, t), (3.22)

where δ(y − x(i)(t)) is a three dimensional delta function at the particle location, and

similarly for δ(ψ − ϕ(i)(t)).

In an infinitesimal time increment dt, the position and composition of each notional

particle evolve according to,

dx∗i = u∗i dt+ dx∗i,turb (i = 1, 2, 3),

dϕ∗α = Sα(ϕ∗)dt+ θ∗α,mixdt (α = 1, 2, ..., Nϕ), (3.23)

The superscript ∗ refers to any particle, and dx∗i,turb is the increment in particle position

resulting from turbulent velocity fluctuations about the local mean velocity u∗i , which usu-

ally is modeled by a gradient transport approximation. θ∗α,mixdt is the increment in particle

composition due to mixing. The transport equation of the one-point, one-time Eulerian

36

composition PDF gϕ corresponding to Eq (3.23) is,

∂ρgϕ∂t

+∂ρuigϕ∂xi

+∂ρSαgϕ∂ψα

= − ∂

∂xi

[⟨u

′′i |ψ

⟩ρgϕ

]− ∂

∂ψα

[⟨θ∗α,mix|ψ

⟩ρ(ψ)gϕ

].

(3.24)

To solve the PDF transport equation, an operator-splitting strategy is used, where each

physical process (corresponding to each term in Eq. 3.23) is implemented sequentially.

Local mean quantities are estimated as mass-weighted averages over nearby particle

values. For example, the Favre-averaged value of a quantity of interest, Q = Q(ϕ), at the

centroid of finite-volume cell c is,

Qc,p ≈∑

p∈cm(p)Q(p)∑

p∈cm(p)

, (3.25)

where the summation is taken over all particles p in cell c. Herem(p) is the mass of particle p,

and Q(p) = Q(ϕ(p)) is the physical quantity carried by particle p. More elaborate algorithms

can be found in [195]; however, those are expected to provide little benefit for the systems

of interest here.

3.2.3 Physical Models for the PDF Method

The effects of turbulent velocity fluctuations must be modeled in a composition PDF

method. In this study, the gradient transport approximation is used [73, 196, 197]. This

model simply takes the rate of transport to be proportional to the local gradient in the

mean; this corresponds to a random walk in space at the particle level. The gradient

diffusion model gives:

− ∂

∂xi

[⟨u

′′i |ψ

⟩⟨ρ⟩ fϕ

]=

∂

∂xi

[Γt∂(ρfϕ/ ⟨ρ⟩)

∂xi

], (3.26)

where Γt is the turbulent diffusivity, given by

Γt = µt/σt, µt = Cµ ⟨ρ⟩ k2/ϵ. (3.27)

37

Here σt is the turbulent Schmidt number, usually taken to be 0.7, and Cµ is a turbulence

model constant (Table 3.1). A two-equation turbulence model is used to solve for k and ϵ,

as discussed earlier (e.g., Eqs. 3.10 and 3.11).

The scalar dissipation rate is a key quantity in tubulent combustion systems from the

view of fundamental properties of the flame and of turbulent combustion modeling. One

crucial aspect of PDF modeling is the choice of the mixing model, as it implicitly models

the effects of scalar dissipation. Fox [198] states three constraints for evaluating the validity

of a mixing model:

1. The scalar mean must remain unchanged.

2. The scalar dissipation rate evolves consistent with experimental observations for

constant-density homogeneous flows, where the rate of change is equivalent to a mixing

constant, Cϕ, over the turbulence time-scale, τ = k/ϵ.

3. There must be no correlation with velocity at high Reynolds number.

The interaction by exchange with the mean (IEM) model, also known as the Linear Mean

Square Estimation (LMSE) model, was first proposed in the PDF context by Dopazo and

O’Brien [199]. IEM relaxes scalar values by interaction of each particle to the mean on

a timescale computed by 1Cϕ

kϵ , where Cϕ is a model constant, whose standard value is

2.0. It has been reported that IEM does not capture the time evolution of the PDF in

homogeneous mixing problems [200–203]. Although it does not meet all of the mixing

model requirements, IEM is a very simple and practical model for use in PDF calculations.

Curl’s model, or the coalescence-dispersion (CD) mixing model [204], is a stochastic mixing

model. Two particles, randomly selected from particles in a finite-volume cell, mix with a

given probability. The probability of a pair of particles interacting in a time interval dt is

CϕNωdt. Here Cϕ is a mixing model constant, N is the total number of particles, and ω

is the turbulence frequency ω = ϵ/k = 1/τ . Scalar values of the initial particles are mass-

weighted to form the “mixed” values. In contrast to IEM, Curl’s model does not preserve

the shape of the scalar PDF, although it does not relax toward a Gaussian distribution.

Janika et al. [205] modified the CD model so that the degree of mixing is distributed as a

38

uniform random variable, to solve a key problem: namely, that it does not yield a continuous

PDF, and to help reproduce the correct scalar dissipation rate. Pope [206] attempted to

improve the shape of the PDF from the CD model by proposing a modified Curl’s mixing

model that more accurately captures the flatness of the PDF and the evolution towards a

Gaussian PDF. Other improvements include introducing model parameters involving the

element age to match the experimentally observed decaying fluctuations for passive scalars in

homogeneous turbulence [207]. The Euclidean Minimum Spanning Trees (EMST) mixing

model [208] attempts to remedy the issue of non-localness in reactive scalar space that

the IEM and CD models have, although at increased computational cost. A series of

comparisons of these mixing models has been performed for canonical flames [194, 209–

212]. However, these results do not show that any one model is best for all combustion

situations.

Two mixing models, IEM and EMST, have been used in the PDF method in the present

study. IEM is very simple and computationally fast, whereas EMST seeks locality in com-

position space, which is more physically realistic but is computationally expensive.

With appropriate closures of the two terms on the right-hand side of Eq. (3.20), a

modeled composition PDF transport equation can be written. For the gradient transport

and IEM mixing models:

∂ ⟨ρ⟩ fϕ∂t

+∂ ⟨ρ⟩ uifϕ

∂xi+∂ ⟨ρ⟩Sαfϕ∂ψα

=∂

∂xi

[Γt∂(ρfϕ/ ⟨ρ⟩)

∂xi

]+

1

2

∂

∂ψα

[Cϕϵ

k(ψα − ϕα)ρfϕ

]. (3.28)

The first term on the right-hand side corresponds to the gradient transport model for

the turbulent velocity fluctuations, and the second term corresponds to the IEM mixing

model for molecular transport.

The particle equations corresponding to Eq. 3.28 are,

dx∗i = u∗i dt+ (⟨ρ⟩−1 ∂Γt

∂xi)∗dt+ (2 ⟨ρ⟩−1 Γt)

∗1/2dWi (i = 1, 2, 3),

dϕ∗α = Sα(ϕ∗)dt− 1

2Cϕ(ψα − ϕα)ωdt (α = 1, 2, ..., Nϕ), (3.29)

39

where the superscript * refers to any notional particle. Here W is a vector of independent

isotropic Wiener processes. Properties of Wiener processes and related quantities are re-

viewed in Appendix J of [189]. In a numerical implementation, dWi normally is discretized

as ∆Wi =Wi(t+∆t)−Wi(t) = ηi∆t1/2, where η is a vector of three independent standard-

ized Gaussian random variables and ∆t is the computational time step. Thus turbulent

transport is represented as a random walk of particles in physical space.

3.3 Gas-Phase Chemistry

Various chemical mechanisms have been used in this work, depending on the configuration,

research focus, and the computational effort. For the constant-volume spray combustion

bomb (Chapter 4), three different n-heptane mechanisms have been used: a simple five-

species one-reaction n-heptane mechanism provided in OpenFOAM [182], a 29-species 52-

reaction n-heptane mechanism from the University of Wisconsin [142], which has been tuned

for diesel engine conditions; and a 40-species n-heptane mechanism from Chalmers [153].

The need for detailed chemical mechanisms to accurately predict NOx formation over ranges

of conditions that occur in advanced engines has been emphasized in recent work by Kung

et al. [78]. For that purpose, a 71-species n-heptane/NOx mechanism has been applied

in recent work [73, 78, 79], which is based on a 40-species skeletal n-heptane mechanism

from Chalmers [153], together with NOx chemistry from Glarborg et al. [213]. The mech-

anism includes multiple NOx formation pathways: the thermal NO mechanism, the N2O-

intermediate mechanism and the prompt (Fenimore) NO mechanism. Engine-out NO usu-

ally is much higher than engine-out NO2 for normal diesel combustion, and thermal NO

usually dominates. However, for low-temperature homogeneous-charge compression igni-

tion (HCCI)-like combustion modes, engine-out NO2 can be higher than engine-out NO,

and the NO2 pathway can be important [78]. This is discussed further in Chapter 5.

40

3.4 Numerical Method

The finite-volume method is well suited and well developed for engine applications and

other complex configurations. Features include robust schemes for dealing with arbitrary

geometries using either structured or unstructured meshes, and guaranteed enforcement

and local conservation of numerical fluxes. The Lagrangian PDF method is implemented

using a consistent hybrid particle/finite-volume mesh algorithm. Details of these numerical

algorithms follow.

3.4.1 Finite-Volume Codes

A finite-volume solver has been used to solve the coupled partial differential equations for

mean quantities which include mean continuity, momentum, scalar and enthalpy transport

equations and also the equations for k and ϵ. Two different codes have been used. One

is OpenFOAM [182], an open-source, object-oriented C++ code. The other CFD code,

AC-Flux, uses an unstructured, deforming mesh and a finite-volume discretization [214–

216]. They are both capable of simulating turbulent spray combustion in engines and/or

under engine-like conditions. For each code, the discretization is implicit and first-order in

time and up to second-order in space (central differencing). A deferred correction approach

is used to achieve second-order spatial accuracy. An iteratively implicit, pressure-based,

sequential (segregated) solution procedure is used to solve the coupled system of governing

equations; the pressure algorithm is patterned after SIMPLE (Semi-Implicit Method for

Pressure-Linked Equations) [217] and PISO (Pressure-Implicit Split Operator) [218, 219].

Additional Lagrangian particle algorithms and particle/mesh coupling strategies are

used in both codes to solve the modeled composition PDF transport equation, in cases

where the transported PDF method has been used [74, 183, 191, 195].

The basic differences between the codes are briefly discussed here. The programming

language used in OpenFoam is C++, although the coupled Lagrangian PDF code uses

Fortran. AC-Flux is a Fortran code. OpenFoam has advanced parallelization and syntax

features compared to AC-Flux. However, the current OpenFOAM implementation does

not allow for deforming meshes, as are required for piston engines. Regarding the PDF

41

implementations in these codes, there are differences in the details of the coupling between

the finite-volume solver and the Lagrangian PDF solvers, and in the coupling between the

PDF method and the dispersed-phase liquid spray. These are discussed in the following.

3.4.2 Consistent Hybrid Lagrangian Particle/Finite Volume PDF

Method

In a hybrid Lagrangian particle/finite-volume method, the finite-volume solver is used to

solve the coupled partial differential equations for mean quantities. The principal coupling

with the particle PDF method is through the mean density. This coupling is accomplished

in different ways in the two codes. In AC-Flux, the mean density ⟨ρ⟩ is given by,

⟨ρ⟩ =⟨ p

RT

⟩= R−1

u

⟨pW

T

⟩≈ R−1

u ⟨p⟩⟨W

T

⟩(3.30)

where Ru is the universal gas constant and W is the mixture molecular weight; the quan-

tity⟨WT

⟩can be estimated from particle values according to Eq. (3.25). This approach

may result in instabilities from statistical noise that is inherent in the particle values. An

alternative approach called “equivalent enthalpy” has been used in OpenFOAM. There an

equivalent enthalpy source term derived from particle data is passed to a PDE on the finite-

volume side to filter the noise generated from the particle data. The equivalent enthalpy is

defined as,

heq =γ

γ − 1RuT

NS∑α=1

YαWα

=γ

γ − 1

p

⟨ρ⟩, (3.31)

where γ = 1.4, Ru is the universal gas constant, and Yα and Wα are the mass fraction

and molecular weight of species α. The source term accounts for the changes of equivalent

enthalpy due to mixing, chemical reaction, and thermal radiation (where considered).

Algorithms for mass, velocity, and energy consistency have been developed [72, 74, 183]

to address coupling and consistency issues between finite-volume and Lagrangian particle

sides for composition PDF methods. A variety of configurations has been tested for this

method [74].

42

3.4.3 Parallelization and In Situ Adaptive Tabulation

The simulations have been parallelized using a simple domain decomposition method to

reduce computational cost. Computational effort is generally dominated by the chemical

source term calculation, especially for the PDF method. Parallel processing has also been

adopted to speed up the chemical reaction calculation on the particle side. The paralleliza-

tion strategy used primarily for the work here is a load-balancing algorithm established

based on equally dividing the cells or particles that must be computed in composition

space. In this way, the number of cells or particles assigned to each processor is approxi-

mately the same, and the compositions are randomized to achieve approximately uniform

load balancing.

In situ adaptive tabulation (ISAT) is an example of a storage/retrieval strategy for

chemistry acceleration. This approach has been applied primarily in the context of PDF

methods for turbulent reacting flows, and has proven to be effective for reducing the com-

putational cost by accelerating the computation of the chemical source terms. An improved

ISAT algorithm [220] has been used here. A key parameter for ISAT is the global error

tolerance ϵ; computational accuracy and computational cost vary with ϵ. Here ISAT has

been implemented in OpenFOAM for the PDF method.

3.5 Fuel Injector and Spray Models

The gas phase is solved in a hybrid Lagrangian/Eulerian framework, while the liquid

spray is treated by a second Lagrangian approach, the standard discrete droplet method

(DDM) [221]. In this approach, the spray droplets are described by stochastic particles, or

parcels. Each parcel represents a class of identical, non-interacting droplets, and they are

tracked though the physical domain in a Lagrangian manner according to the exchange of

mass, momentum and energy with the gas phase. The mean conservation equations to solve

for the continuous gas phase are the same as those given earlier in Chapter 3, except there

is an additional source term for each equation due to spray interaction for mass, momentum

and energy, respectively.

43

3.5.1 The Liquid Phase

For a single evaporating droplet, the mass equation for the liquid is given by the expression

dmd

dt= −πDDρvSh ln

p− pv,∞p− pv,s

= −πDDρvSh ln(1 +Xv,s −Xv,∞1−Xv,s

),

(3.32)

where p, pv,∞ and pv,s are the gas pressure and the partial pressure of vapor in the droplet

surroundings and at its surface, respectively, and X, Xv,∞ and Xv,s are the corresponding

mole fractions of the fuel vapor. Here the surface vapor pressure is assumed to be equal

to the saturation pressure at the droplet temperature. D is the droplet diameter, D is the

vapor diffusivity, and ρv is the density of the fuel vapor close the surface of the droplet,

estimated using the ideal gas law:

ρv =p

RvTm, (3.33)

where p is the gas pressure, which is assumed to be equal to the fuel vapor pressure close to

the droplet surface, and Tm is the mean (film) temperature given by Tm = Td+(T∞−Td)/3.

Rv is the mixture gas constant. Sh is the Sherwood number, which is dependent on Schmidt

number Sc and Reynolds number Re, using the Ranz-Marshall correlation [222] for a single

sphere in an undisturbed gas flow,

Sh = 2.0 + 0.6Re1/2Sc1/3, 0 ≤ Re < 200, 0 ≤ Sc < 250. (3.34)

As Saffman, pressure and buoyancy forces are often neglected, the equation of motion

for a discrete particle with mass md is then,

mdduddt

= −πD2

8ρCD|ud − u|(ud − u) +mdg. (3.35)

The first term on the right-hand side is the drag force acting upon a particle surrounded by

gas of density ρ and velocity u. The second term on the right-hand side of the equation is

the gravitational body force. CD is the drag coefficient, an empirically determined param-

44

eter, depending on the geometrical shape of the particle as well as flow conditions and gas

properties using the following expression:

CD =

24Red

(1 + 16Re

2/3d ) forRe < 1000

0.424 forRe > 1000,(3.36)

where the Reynolds number is given by

Red =ρ|ud − u|D

µ. (3.37)

The droplet energy equation is,

dTddt

=T − Tdτh

f − 1

cl,d

hv(Td)

τe(3.38)

where cl,d is the specific heat for the liquid. τh is a characteristic heat transfer relaxation

time, defined as

τh =mdcl,dπDκNu

, (3.39)

τe is an evaporation relaxation time, defined as:

τe =md

πDDρvShln(1 +B), (3.40)

where B is the Spalding mass transfer number given by,

B =Xv,s −Xv,∞1−Xv, s

, (3.41)

and f is a factor that corrects the rate of heat exchange due to the presence of mass transfer:

f =z

ez − 1, (3.42)

z = − cp,vmd

πDkNu. (3.43)

The Nusselt number Nu is specified using a Ranz-Marshall correlation for a single sphere

45

in an undisturbed gas flow [222] here, with all the properties evaluated at the mean film

temperature. Pr is the Prandtl number, and cp and k are the specific heat and thermal

conductivity of the gas, respectively:

Nu = 2.0 + 0.6Re1/2Pr1/3, 0 ≤ Re < 200, 0 ≤ Pr < 250, (3.44)

Pr = µcpk. (3.45)

When using a DDM approach, spray sub-models to describe atomization, breakup and

dispersion are necessary. In the atomization process, the liquid core breaks up into tiny

droplets at the nozzle exit; this is also referred to as primary breakup. The initial conditions

of the spray parcels can either be given by an atomization model, or specified by a constant

spray angle and a constant droplet size serving as a very simple atomization model; the

latter approach is adopted in current work. Later on, the relatively large droplets can

be further distorted and subsequently broken up into smaller secondary droplets. This is

termed secondary breakup, which typically takes place further downstream of the nozzle.

3.5.2 Physical Models

The physical models for the constant-volume spray combustion are described here. The

initial spray angle and initial droplet size distribution from the nozzle are specified as

constants with respect to time. The Ranz-Marshall correlation, which is obtained from

experiment [222], was applied for the heat transfer model. A stochastic dispersion model

accounts for random velocity perturbations. A standard drag model was used. The Ranz-

Marshall model was also selected for droplet evaporation. Droplet collisions were neglected,

due to their weak effect for the sprays of interest. The RNG k − ϵ model [223, 224] with

constant C1 equal to 1.45 was adopted for turbulence. The Chalmers Partially Stirred

Reactor (PaSR) model [159] is hard-coded in OpenFOAM for the non-PDF simulations.

The secondary breakup model uses the Kelvin-Helmholtz/Rayleigh-Taylor (KH-RT) hybrid

model [225, 226]. Two fundamental mechanisms, the Kelvin-Helmholtz and Rayleigh-Taylor

instabilities, govern the spray breakup process in this model. In the KH mode, new child

parcels with size rc are stripped from the parent parcel. The rate of change of the radius

46

of the parent parcel is expressed as:

dr

dt= −r − rc

τKH, (3.46)

where τKH is the breakup time defined by,

τKH =3.788B1D

ΩKHΛKH. (3.47)

Here B1 is a model constant, and Ω and Λ are the frequency of the fastest growing wave

and its corresponding wavelength, respectively. In the RT mode, if the wavelength ΛRT of

the faster growing wave is smaller than the droplet radius, the RT waves start to grow on

the surface of the droplets and the life time of the growing RT waves is tracked from then

on. When the life time exceeds the characteristic breakup time τRT , a catastrophic breakup

occurs, immediately creating much smaller droplets with radii given by:

rc =πCRT

KRT, (3.48)

τRT =Cτ

ΩRT, (3.49)

where ΩRT is the frequency of the fastest growing wave, KRT is the wave number, and Cτ

and CRT are model constants.

Several spray models variants are explored in Chapter 4, include the breakup model,

the injector model, the collision model and the dispersion model. The hollow-cone injector

model adopts a Rosin-Rammler [227] PDF distribution for initial droplet size with scale

parameter d and shape parameter n set to be 9.27·10−5 m and 2, respectively. Minimum and

maximum values are 1.00·10−6 m and 9.27·10−5 m, respectively. The Linearized Instability

Sheet Atomization (LISA) [228] model use an empirical sheet constant value of 12. Other

model coefficients used are summarized in Table 3.3. These models are all available in

OpenFOAM.

For the engine simulations in this thesis, the physical models used in AC-Flux are given

as follows. A stochastic Lagrangian formulation again is used for liquid fuel sprays [230, 231].

47

Table 3.3: Spray models and coefficients.

Blob model [229]

B angle

3.0 7.0 degree

Taylor Analogy Breakup (TAB) model

y0 y0 Cµ Cω Wecrit0 0 10.0 8.0 12

Enhanced Taylor Analogy Breakup (ETAB) model

Cµ Cω Wecrit K1 K2 Wetransition10.0 8.0 12 0.2 0.2 100.0

Reitz-Diwakar (RD) model

Cbag Cb Cstrip Cs

6 0.785 0.5 10

Trajectory model

cspace ctime

1 0.3

The principal models that are available in AC-Flux include droplet deformation, breakup,

drag, turbulent dispersion, collision and coalescence, vaporization and spray-wall impinge-

ment. Here the deformation, drag, turbulent dispersion, vaporization and spray-wall im-

pingement models were enabled, while the breakup, collision and coalescence models were

disabled. In this study, the Taylor Analogy Breakup (TAB) [232] deformation model was

used with the drag model of [79]. The spray model parameters and fuel-injector charac-

terization were taken from Kung [73, 79]; these are representative of those for a modern

light-duty direct-injection diesel engine.

3.5.3 Coupling of Spray Model with PDF Method

The spray model is coupled with the PDF method in URANS through droplet vaporization.

For a reacting multiphase flow, mass and energy source terms due to evaporation need to be

considered in the context of the PDF method. In a hybrid Lagrangian particle/finite-volume

method, the cell mean mass and enthalpy source terms due to evaporation are taken from

the spray model on the finite-volume side, and then passed to the PDF side. To distribute

these cell-level mean source terms among Lagrangian PDF particles in each cell, a simple

48

approach is to take an average of the source term over the number of particles in cell and

to add this particle average mass/enthalpy source term to each particle in cell. Instead

of simple averaging, the mass/enthalpy source term can be distributed proportional to the

mass of the particle, which has been done in this work. The set of composition/enthalpy

variables of the particles are then updated accordingly. Additionally, in the equivalent

enthalpy approach [233, 234], the equivalent enthalpy source derived from the particle data

must also account for changes due to spray evaporation.

Chapter 4

Analysis of Spray and Spray

Combustion in a Constant-Volume

Chamber

In-cylinder combustion process in modern diesel engines are complex. Driven by the need for

reductions in fuel consumption and engine-out emissions while accommodating alternative

fuels, next-generation clean and efficient combustion systems are likely to feature higher

pressures, lower temperatures, extremely lean and/or dilute mixtures, and different fuels.

Combustion characteristics in such advanced engine conditions are still largely unknown

and are challenging to model. Experimental and computational efforts have been initiated

to understand the fundamentals of these advanced combustion systems, such as the ECN

workshop [81]. In this chapter, the transported PDF method is applied in URANS to

explore the effects of turbulence-chemistry interactions on autoignition and combustion

under modern diesel-engine-like conditions. The targeted configuration is a constant-volume

combustion chamber, without the complications of moving pistons and/or valves, where

measurements are available for a wide range of thermochemical conditions representative

of modern diesel engines [81]. A surrogate of diesel fuel, n-heptane, is the focus in this

work. Systematic parametric studies have been performed to explore the importance or

lack thereof of turbulence-chemistry interactions under engine-relevant conditions.

49

50

4.1 Engine Combustion Network (ECN) N-Heptane Cases

The Engine Combustion Network (ECN) [81] provides a platform for collaboration among

experimentalists and computational researchers in engine combustion with measurements

available for multiple fuels and operating conditions. The ECN non-reacting n-heptane

baseline case and reacting n-heptane cases in a constant-volume chamber under various

ambient environments are targeted in this work.

For non-reacting n-heptane sprays, validation is done for liquid and vapor penetra-

tion, and for mean mixture fraction profiles. For reacting n-heptane sprays, computed and

measured ignition delays, lift-off lengths and flame structures are compared. The baseline

n-heptane nonreacting spray case (Table 4.1) has an initial ambient gas temperature of 1000

K, initial density of 14.8 kg/m3, initial pressure of 4.21 MPa and inert ambient (0% O2 in

the initial ambient gas composition). Liquid n-heptane fuel is injected at a temperature

of 373 K with a square-shaped injection-rate profile (constant injection rate over specified

duration). Table 4.2 shows various ambient conditions that have been studied for reacting

cases, including O2 percentage ranging from 0% to 21%, initial ambient gas temperature

ranging from 750 K to 1300 K, and initial density of 30 kg/m3. Measured data available

include liquid and jet penetration lengths, pressure versus time, mixing images, soot volume

fraction and various high-speed movies.

The combustion vessel for the experiment is a cubic chamber with a characteristic length

of 108 mm. Liquid fuel is injected from the top center of the vessel. For computational

expediency, this is modeled as a one-degree axisymmetric wedge with a single layer of cells

in the azimuthal direction (shown in Fig. 4.1). The total number of cells for the nonuniform

axisymmetric mesh is 6372, with approximately 0.56 mm minimum cell size in the axial

direction. The axial direction length of the computational domain is 108 mm and the radial

dimension has been adjusted to ensure the same total volume as that of the experimental

chamber.

A set of model parameters has been selected to match the global spray characteristics

for the nonreacting case. The sensitivity of results to variations in model parameters is

discussed in Section 4.2.2 below. For the baseline model, the initial spray angle was specified

51

Table 4.1: Baseline n-heptane nonreacting spray case conditions.

Fuel n-heptane

Nozzle diameter 0.100 mm

Fuel injection temperature 373 K

Fuel injection pressure 150 MPa

Total fuel mass injected 17.8 mg

Injection duration 6.8 ms

Ambient gas pressure 4.33 MPa

Ambient gas temperature 1000 K

Ambient gas density 14.8 kg/m3

Ambient gas composition 0% O2,(mole fraction) 89.71% N2,

6.52% CO2,3.77% H2O

Table 4.2: Variations in ambient conditions for n-heptane reacting cases.

Ambient O2 Ambient temperature Ambient density(%) (K) (kg/m3)

21 1300 14.815 1200 3012 110010 10008 950

900850800750

as a constant 12.6 degrees and the initial droplet diameter was 0.927 mm; the latter was

derived from the injector diameter and given area contraction coefficient [225]. The spray

breakup was described with the KH-RT model by Reitz (see Section 3.5.2) with B1 equal to

6.4. The Ranz-Marshall correlation was applied for the heat transfer model. A stochastic

dispersion model accounts for turbulent velocity fluctuations and a standard drag model

was used. The Ranz-Marshall model was selected for droplet evaporation. Droplet collisions

were neglected as their effects are weak for these sprays. A renormalization group (RNG)

52

Figure 4.1: Computational axisymmetric mesh for a constant-volume combustion chamber.

k− ϵ turbulence model [223, 224] was used, with the model constant C1 equal to 1.45, with

initial values of k and ϵ estimated as 0.735 m2/s2 and 3.5 m2/s3, respectively. Here, the

radius of the domain was used to characterize the initial turbulence length scale l, and the

initial value of ϵ was calculated as ϵ = C0.75µ k1.5/l. The initial value of k was estimated

from k = 1.5u2rms where urms is approximately 0.7 m/s according to the description of the

experimental data. The computational time step is 2.0·10−7s for this axisymmetric mesh

(shown in Fig. 4.1). A constant wall temperature boundary condition of 850 K is used

to match the measured pressure trace. Other initial conditions are specified according to

Tables 4.1 and 4.2 and the experimental conditions listed at the ECN website [81].

4.2 Nonreacting N-Heptane Sprays

The first step in the constant-volume chamber study was to establish a baseline set of

physical and numerical parameters to match the experimentally measured global spray

characteristics for a nonreacting, vaporizing n-heptane spray (Table 4.1). Key spray char-

acteristics are computed and compared with the experimental data, including liquid and

53

vapor penetration lengths and mixture fraction profiles [166, 167]. Computed mean mixture

fraction and its variance (the latter for cases where turbulence-chemistry interactions are

considered using the PDF method) are compared with experiment. The criteria for defin-

ing liquid and vapor penetration lengths follow the recommendations given on the ECN

website [81]:

• Liquid length: The distance from the injector exit along the injection axis to the

location where the local liquid volume fraction has fallen to a value of 0.15%.

• Vapor penetration: The distance from the injector exit along the injection axis to the

location where the fuel vapor mixture fraction has fallen to 0.001.

• Mixture fraction: For the nonreacting n-heptane spray, mixture fraction is equal to

the fuel mass fraction of n-heptane (C7H16); for reacting n-heptane sprays, mixture

fraction z is defined as:

z =YCH − YCH,O

YCH,F − YCH,O, (4.1)

where YCH is the total elemental mass fraction of C and H; subscripts F and O denote

fuel stream and oxidizer stream, respectively. A fuel-based local equivalence ratio Φ

is defined as:

Φ =z

1− z

1− zstzst

, (4.2)

where subscript st denotes stoichiometric reactants.

A systematic parametric study has been performed to establish sensitivities of the com-

puted liquid and vapor penetration lengths to variations in physical models, numerical

parameters, initial conditions and criteria for definition of penetration lengths. These

parametric studies were conducted using a simplistic model for turbulence-chemistry in-

teractions. In the following, results obtained from a simple model for turbulence-chemistry

interactions are labeled FV (“finite-volume”, to indicate that chemistry is computed using

cell-level mean values of composition and temperature).

54

4.2.1 Model vs Experiment Comparisons for the Baseline Model

(a) (b)

Figure 4.2: Computed (using a simplistic turbulence-chemistry interactions model) andmeasured penetration lengths versus time for a non-reacting n-heptane spray. (a) Liquidpenetration length. (b) Vapor penetration length.

Results of liquid and vapor penetration are shown in Fig. 4.2. As can be seen, the

computed liquid penetration matches the measured data reasonably well during the quasi-

steady period, while over-predicting during the early developing period. The computed

vapor penetration generally follows the experimental curve with slight over-prediction at 1

ms, but under-predicting after 2 ms.

Computed and measured mean mixture fraction profiles are compared in Figs. 4.3

and 4.4. Good agreement of mean mixture fraction profiles was found at 0.49 ms after

injection at the 17 mm axial location, and at 6 ms after injection at the 40 mm axial lo-

cation, where measured data are available. The mean computed mixture fraction profile is

also acceptable at 6 ms after injection at the 20 mm axial location, although it is slightly

over-estimated along the injection axis.

The influence of turbulence-chemistry interactions for nonreacting sprays is explored by

comparing results using a simplistic turbulence-chemistry interactions model versus those

55

Figure 4.3: Computed and measured profiles of mean mixture fraction for a non-reactingn-heptane spray at 0.49 ms after the start of injection and an axial location of 17 mm.

Figure 4.4: Computed and measured profiles of mean mixture fraction for a non-reactingn-heptane spray at 6 ms after the start of injection and axial locations of 20 mm and 40mm.

using the PDF method. The influence on computed mean mixture fraction profiles is shown

in Figs. 4.5 and 4.6. Large differences can be seen with the PDF method versus without

the PDF method, with the PDF method giving higher on-axis values: 20% higher at 20

56

mm, and 50% higher at 40 mm. The reported measured mixture fraction variance profiles

(Fig. 4.7) were based on 40 samples, and are not expected to be quantitatively accurate.

The general shape of the mixture fraction variance profile is captured by the model, but

quantitative accuracy cannot be assessed until more complete data are available.

Figure 4.5: Computed (with versus without PDF method) and measured mean profiles ofmixture fraction for a non-reacting n-heptane spray at 6 ms after the start of injection andan axial location of 20 mm.

The influence of the mixing model and the value of the mixing model coefficient have

been explored in the PDF method. Comparisons of the computed mixture fraction profiles

with variations in the mixing model are shown in Figs. 4.8-4.10. These include results with

two different mixing models (IEM and EMST) and with different values of Cϕ. In general,

mixing model constants have relatively small effect on the mean mixture fraction profiles.

The computed mixing fraction variance decreases with increasing Cϕ as expected, and for

a given value of Cϕ, is lower for EMST compared to IEM.

Here the computed mean mixture fraction profiles are closer to experiment with a simple

model for turbulence-chemistry interactions. It is emphasized that this is because the model

calibration exercise to arrive at the base model was done without the PDF method, for

computational expediency. As will be shown in following subsection, results are highly

sensitive to the spray and turbulence models, in particular.

57

Figure 4.6: Computed (with versus without PDF method) and measured mean profiles ofmixture fraction for a non-reacting n-heptane spray at 6 ms after the start of injection andan axial location of 40 mm.

Figure 4.7: Computed (with PDF method) and measured profiles of mixture fraction vari-ance for a non-reacting n-heptane spray at 6 ms after the start of injection and an axiallocation of 20 mm.

4.2.2 Parametric Studies

Physical models and numerical parameters for the baseline n-heptane case are selected to

match the measured data through tuning process. Sensitivities of model results to variations

58

Figure 4.8: Computed (with versus without PDF method and with variations in the PDFmixing model) and measured mean profiles of mixture fraction for a non-reacting n-heptanespray at 6 ms after the start of injection and an axial location of 20 mm.

Figure 4.9: Computed (with versus without PDF method and with variations in the PDFmixing model) and measured mean profiles of mixture fraction for a non-reacting n-heptanespray at 6 ms after the start of injection and an axial location of 40 mm.

in physical models and numerical parameters are explored by varying one parameter at a

time, to isolate its effect (Table 4.3).

59

Figure 4.10: Computed (with versus without PDF method and with variations in the PDFmixing model) and measured profiles of mixture fraction variance for a non-reacting n-heptane spray at 6 ms after the start of injection and an axial location of 20 mm.

Influence of physical models

Figure 4.11 shows that computed liquid and vapor penetration lengths are both quite sen-

sitive to the choice of turbulence model. All other turbulence models generate lower liquid

penetration lengths compared to the RNG k − ϵ model. For the Launder-Sharma k − ϵ

(LSKE) model, vapor penetration length is extremely high, while liquid penetration is sig-

nificantly low. The other two models (standard k − ϵ model and realizable k − ϵ model),

give relatively low vapor penetration lengths. Significant differences in computed liquid

penetration lengths can be observed in Fig. 4.12 for different breakup models. The liquid

penetration length is much higher for the Reitz-Diwakar model and is lower for the other

models. Relatively minor differences in computed vapor penetration lengths are seen for the

different breakup models. The LISA atomization model gives low liquid penetration length

(Fig. 4.13), while results for the other atomization models are similar. The dispersion and

collision models have relatively small influences on computed liquid and vapor penetration

lengths (Figs. 4.14 and 4.15). In Figs. 4.16 and 4.17, it can be seen that the computed liq-

uid penetration length increases with increasing B1 and vapor penetration length increases

with increasing Cϵ1. Thus B1 and Cϵ1 are key parameters that affect liquid and vapor pen-

60

Table 4.3: Physical and numerical models for baseline n-heptane nonreacting spray.

Model and parameters Baseline model (FV-PDF) Variations performed (FV)

atomization none Linearized Instability SheetAtomization (LISA) model,Blob model

collision none O’Rourke (OR), trajectory

dispersion stochastic gradient, none

breakup KH-RT Reitz-Diwakar (RD),Taylor Analogy Breakup(TAB),Enhanced Taylor AnalogyBreakup (ETAB)

turbulence RNG k − ϵ standard k − ϵ,Launder-Sharma k − ϵ(LSKE),realizable k−ϵ (realizable KE)

injector model constant hollow cone

mesh axisymmetric quarter

time step [s] 1·10−6 1.2·10−6, 8.0·10−7

initial ϵ [m2/s3] 3.5 2.5, 4.5

B1 in KH-RT model 3.3 2.3, 4.3

Cϵ1 in RNG k − ϵ model 1.53 1.43, 1.63

liquid penetration definition liquid fuel mass percent=0.96 0.95, 0.97

vapor penetration definition fuel vapor mass percent=0.99 0.98, 0.97

etration lengths, respectively. The computed liquid penetration length does not vary much

with injector models, while the hollow-cone model gives slightly higher vapor penetration

lengh than the Blob model (Fig. 4.18).

Influence of numerical parameters

A three-dimensional quarter mesh in Fig. 4.19 with comparable mesh size to that used in

the axisymmetric mesh has been implemented for comparison as shown in Fig. 4.20. The

computed liquid penetration length is approximately 2 mm lower for 3D mesh than for the

2D axisymmetric mesh, while the computed vapor penetration length is essentially the same.

Figure 4.21 shows that an overly large computational time step size can cause instability

61

(a) Liquid penetration length (b) Vapor penetration length

Figure 4.11: Computed liquid and vapor penetration lengths with variations in turbulencemodel for a non-reacting n-heptane spray.


Figure 4.12: Computed liquid and vapor penetration lengths with variations in breakupmodel for a non-reacting n-heptane spray.

to the computed liquid penetration length, and can lead to extreme vapor penetration to

the wall of the chamber. Further refinement of the timestep decreases the computed liquid

62


Figure 4.13: Computed liquid and vapor penetration lengths with variations in atomizationmodel for a non-reacting n-heptane spray.


Figure 4.14: Computed liquid and vapor penetration lengths with variations in dispersionmodel for a non-reacting n-heptane spray.

penetration length slightly, and results in little change in the computed vapor penetration

length.

63


Figure 4.15: Computed liquid and vapor penetration lengths with variations in collisionmodel for a non-reacting n-heptane spray.


Figure 4.16: Computed liquid and vapor penetration lengths with variations in spray modelcoefficient B1 for a non-reacting n-heptane spray.

Influence of initial conditions

The assumed initial turbulence level does not have a strong influence on the computed

liquid or vapor penetration lengths, as shown in Fig. 4.22.

64


Figure 4.17: Computed liquid and vapor penetration lengths with variations in turbulencemodel coefficient Cϵ1 for a non-reacting n-heptane spray.


Figure 4.18: Computed liquid and vapor penetration with variations in the injector modelfor a non-reacting n-heptane spray.

Influence of thresholds used to define penetration lengths

In Fig. 4.23, it can be seen that slight variations in the threshold volume fraction values used

to define the computed liquid and vapor penetration result in little change in the computed

65

Figure 4.19: Computational 3D quarter mesh for a constant-volume combustion chamber.


Figure 4.20: Computed liquid and vapor penetration lengths with variations in computa-tional mesh for a non-reacting n-heptane spray.

values. However, computed results defined by 98% of liquid fuel mass and 99% of fuel vapor

mass are relatively lower compared to those defined by fuel volume fraction and mixture

fraction thresholds of 0.001.

66


Figure 4.21: Computed liquid and vapor penetration lengths with variations in computa-tional time step for a non-reacting n-heptane spray.


Figure 4.22: Computed liquid and vapor penetration lengths with variations in the initial ϵfor a non-reacting n-heptane spray.

4.2.3 Discussion

The ECN website [81] provides a good summary of ongoing computational work for the

constant-volume n-heptane spray. Several other groups have shown as good agreement

67


Figure 4.23: Computed liquid and vapor penetration lengths with variations in the criteriaused to define liquid and vapor penetration lengths for a non-reacting n-heptane spray. (a)Liquid penetration definitions. (b) Vapor penetration definitions.

with experiment as we have found here, except that many models tend to under-predict at

later times for vapor penetration lengths. The level of success in agreement with experiment

is most likely due to adjustment of model constants and/or other factors. Most groups show

reasonable agreement of mean mixture fraction profiles with experimental data, and some

noticeable issues with grid convergence and/or statistical convergence have been mentioned

at the 20 mm axial location at 6 ms. Since most of the groups do not account for the

influence of turbulent fluctuations on chemistry, only one group (POLIMI) has shown re-

sults of mixture fraction variance, which are reasonably well predicted with sufficient grid

refinement.

4.3 Reacting n-Heptane Sprays: Autoignition and Combus-

tion

In this section, reacting n-heptane sprays are simulated over a wide range of initial O2

levels (8%, 10%, 12% and 21%), ambient temperatures (750 K, 800 K, 850 K, 900 K, 950

68

K, 1000 K, 1100 K, 1200 K and 1300 K), and ambient gas densities (14.8 kg/m3 and 30

kg/m3). The spray and turbulence models were kept the same as the baseline model from

the nonreacting n-heptane spray simulations of the preceding subsection.

As summarized in ECN proceedings, a variety of chemical mechanisms have been ap-

plied for this configuration, ranging from 23 species to 159 species, and involving skeletal

and reduced mechanisms. These include the Engine Research Center (ERC) 29-species

skeletal mechanism (Appendix A.2) used by three groups (CMT, POLIMI and UNSW),

Golovitchev’s 42-species skeletal mechanism [153], Lu’s 63- and 52-species reduced mecha-

nisms [235], Pitsch’s 23-species reduced mechanism [236], Zeuch’s 110-species skeletal mech-

anism [237], the ERC-PRF 41-species skeletal mechanism [238], Seiser’s 159-species skeletal

mechanism [141], Peters’ 37-species skeletal mechanism and a 42-species skeletal mecha-

nism [239]. In this section, the ERC 29-species, 52-reactions n-heptane mechanism (Ap-

pendix A.2) was the main chemical mechanism used for reacting n-heptane spray cases,

except that some cases with less robust combustion were simulated using a 40-species n-

heptane mechanism (Appendix A.3) to explore the influence of the chemical mechanism.

The primary global quantities of interest for comparison with experiment are the ignition

delays and lift-off lengths. Results of simulations with the PDF method and without the

PDF method are compared to determine the extent to which turbulence-chemistry interac-

tions influence the results.

4.3.1 With versus Without In Situ Adaptive Tabulation

The reacting cases used ISAT to accelerate the chemistry calculations. The ISAT global

error tolerance ϵ was set to 1·10−4, as an acceptable compromise between accuracy and

efficiency. Here the influence of ISAT is shown, to justify this choice. For the 21% O2,

1000 K and 14.8 kg/m3 ambient condition case, the computed ignition delay with the PDF

method is 0.542 ms with ISAT and 0.568 ms without ISAT. In Fig. 4.24, the computed

mean temperature fields at early times show some differences with versus without ISAT.

However, the quasi-steady-state mean temperature fields with ISAT versus without ISAT

are quite similar to each other. The computational wall time for a single-processor run to

69

Table 4.4: Computational wall time comparison with versus without ISAT for a baselinen-heptane case with the PDF method

Single-processor wall time with ISAT Six-processor wall time without ISAT

133,402 s 306,407 s

3 ms with ISAT is less than half that for a 6-processor run without ISAT (Table 4.4). The

wall time for a single-processor run using ISAT is less than that of a parallel computation

without ISAT.

(a) t=1 ms without ISAT (b) t=2 ms without ISAT (c) t=3 ms without ISAT

(d) t=1 ms with ISAT (e) t=2 ms with ISAT (f) t=3 ms with ISAT

Figure 4.24: 2D computed mean temperature contours for a reacting n-heptane spray atbaseline conditions of ambient temperature (1000 K), ambient density (14.8 kg/m3) and O2

level (21%), with versus without ISAT, for the 29-species mechanism.

Results for a less robust combustion case are shown in Fig. 4.25 (8% O2, 1000 K and 14.8

kg/m3). There the computed ignition delay with ISAT is 3.742 ms versus 4.033 ms without

ISAT. Compared to the result without ISAT, the mean temperature contours with ISAT

have a higher maximum temperature by approximately 77 K at 4 ms and 15 K at 5 ms,

70

respectively. For low ambient temperature, the 29-species n-heptane mechanism does not

perform well. Results with versus without ISAT for the 40-species n-heptane mechanism at

800 K ambient temperature are shown in Fig. 4.26. There the computed ignition delay is

1.722 ms with ISAT compared to 1.639 ms without ISAT.

These results suggest that while there are some quantitative differences between results

obtained with versus without ISAT, the differences are not large, even for non-robust com-

bustion conditions, and the results obtained with ISAT will be sufficient if an appropriate

chemical mechanism is chosen. All subsequent PDF results shown in this chapter were

obtained using the same chemical mechanism - the 29-species n-heptane mechanism - so

ISAT has not been used here.

4.3.2 Model vs Experiment Comparisons

According to the description of the experiment on the ECN website, ignition delay is defined

as the time from the start of injection until the high-temperature ignition and combustion

(the premixed burn). Specifically, a documented constant or manually chosen noise thresh-

old on the smoothed pressure-rise-versus-time trace defines the ignition-delay time. The

lift-off length is defined as the axial distance from the injector to the location of the high-

temperature reaction zone in the quasi-steady flame. This is defined quantitatively by

taking the average of two axial distances: the distance between the injector and the axial

location where chemiluminescence from excited-state OH (OH∗) reaches a leveling-off value,

and the distance between the injector and the spray centerline with an intensity greater than

approximately 50% of the leveling-off value. Among computational researchers, definitions

of ignition time vary widely, with most being temperature-based. The lift-off length is also

defined differently in computations, with some using temperature-based and some using OH

mass-fraction-based definitions. Here the ignition delay and lift-off length definitions are

taken as follows:

• Lift-off length: The axial distance from the injector to the nearest location where a

cell-centered mean OH mass fraction value of 0.00025 has been reached.

• Ignition delay: The time after injection when the local temperature rises by 400 K

71

(a) t=4 ms without ISAT (b) t=5 ms without ISAT

(c) t=4 ms with ISAT (d) t=5 ms with ISAT

Figure 4.25: 2D computed mean temperature contours for a reacting n-heptane spray atless robust combustion conditions of ambient temperature (1000 K), ambient density (14.8kg/m3) and O2 level (8%), with versus without ISAT, for the 29-species mechanism.

from the initial ambient temperature of the domain.

Quantitative comparisons of two sets of computational results with experimental data

are provided below: one set that uses a simple model for turbulence-chemistry interactions

(denoted by “FV”) and one that takes turbulence-chemistry interactions into account by

using a Lagrangian particle/Eulerian finite-volume PDF method (denoted by “PDF”).

Figure 4.27 shows that both models follow the experimental trend with variations in O2

level qualitatively, with better predictions at higher O2 levels. However, there are significant

quantitative differences between PDF and non-PDF results. With the PDF method, ignition

72

(a) t=3 ms without ISAT (b) t=3 ms with ISAT

Figure 4.26: 2D computed temperature contours for a reacting n-heptane spray at conditionsof ambient temperature (800 K), ambient density (14.8 kg/m3) and O2 level (21%), withversus without ISAT, for the 40-species mechanism.

is delayed at lower O2 levels by about 1 ms for 10% O2 and 1.8 ms for 8% O2, respectively.

Computed lift-off lengths with the PDF method are generally higher compared to the non-

PDF model, although the trends still follow the measured data qualitatively (Fig. 4.28).

Figure 4.27: Computed (with and without PDF) and measured ignition delay versus O2

percentage for a reacting n-heptane spray with ambient temperature 1000 K and ambientdensity 14.8 kg/m3.

73

Figure 4.28: Computed (with and without PDF) and measured lift-off length versus O2

percentage for a reacting n-heptane spray with ambient temperature 1000 K and ambientdensity 14.8 kg/m3.

With variations in ambient temperature, the computed ignition delays for both models

follow the general experimental trend well, except for extremely low ambient temperatures

(Fig. 4.29). Longer ignition delays are observed for low-ambient-temperature conditions.

For an ambient temperature of 800 K, the ignition delay is over-predicted by 2 ms for the

non-PDF model and by 2.6 ms for the PDF model, respectively. For lower temperatures

(750 K), the 400 K temperature rise criterion is not reached computationally. For ambient

temperatures of 900 K and above, the models match the measured ignition delays quite

well. In Fig. 4.30, the computed lift-off lengths for both models follow the measured data.

Computed lift-off lengths for the non-PDF model are under-estimated by approximately

6 mm at ambient temperatures above 1000 K, but match the measured data well below

1000 K, except for the lowest temperature of 750 K. The PDF lift-off length curve follows

the general trend of the measured data, but over-estimates by 8-15 mm across the full

temperature range.

At the higher ambient density of 30 kg/m3, the computed ignition delay rises slightly

with decreasing ambient O2 percentage for the non-PDF model. For the PDF method, the

computed ignition delays with 12% and 15% initial ambient O2 match the experimental

74

Figure 4.29: Computed (with and without PDF) and measured ignition delay versus am-bient temperature for a reacting n-heptane spray with 21% O2 level and ambient density14.8 kg/m3.

Figure 4.30: Computed (with and without PDF) and measured lift-off length versus ambienttemperature for a reacting n-heptane spray with 21% O2 level and ambient density 14.8kg/m3.

results closely. However, at low ambient O2 levels of 10% and 8%, the PDF results show

significantly longer ignition delay compared to the non-PDF model and experiment, with a

200% over-prediction at 8% O2. The lift-off lengths, as in Fig. 4.32, are not well as predicted

75

as the ignition delays. The computed lift-off lengths for the non-PDF model are consistently

under-predicted, although they follow the experimental trend of decreasing lift-off length

with increasing ambient density for the same ambient O2 level (compared to Fig. 4.28). In

Fig. 4.28, only the non-PDF model results are shown for 10% and higher O2. The reason

is that for 8% O2 in the non-PDF model, and for all cases with the PDF method, the

computed OH mass fraction does not reach 0.00025, and a different criterion needs to be

used.

Figure 4.31: Computed (with and without PDF) and measured ignition delay versus O2

percentage for a reacting n-heptane spray with ambient temperature 1000 K and ambientdensity 30 kg/m3.

There is limited experimental data on the turbulent flame structures, such as high-speed

movies of chemiluminescence imaging. Simulations were performed under various ambient

conditions. Here the computed flame structures are illustrated for different ambient oxygen

percentages, ambient densities and ambient temperatures. Mean temperature contours are

compared at quasi-steady state with and without the PDF method in Figs. 4.33-4.38.

As seen in Figs. 4.33 and 4.34, computed mean temperatures distributions for different

ambient oxygen levels (8%, 10%, 12%, 15% and 21%) show clear differences between PDF

and non-PDF results. With increasing ambient oxygen concentration, the computed peak

temperature rises. In general, the non-PDF model shows higher temperatures in the high-

76

Figure 4.32: Computed (with and without PDF) and measured lift-off length versus O2

percentage for a reacting n-heptane spray with ambient temperature 1000 K and ambientdensity 30 kg/m3.

temperature region than the PDF method. The computed flame structure for the non-PDF

model is thinner than that of PDF method. The PDF model results are more consistent

with the broadened turbulent flame brush that is expected for these highly turbulent flames.

Figures 4.35 and 4.36 show the computed mean temperature distributions for different

ambient temperatures: 750 K, 800 K, 850 K, 900 K, 950 K, 1100 K, 1200 K and 1300 K.

With increasing ambient temperature, the flame becomes thinner and longer, and the peak

flame temperature rises. Results with and without the PDF method are again quite different

from each other, with the flame structures of the PDF method being much wider and usually

located further downstream compared to that of the non-PDF model. Temperatures in the

flame are relatively low for the PDF method. For the lowest ambient temperature (750 K),

the fuel does not ignite (temperature rise of 400 K is not reached).

At the high ambient density of 30 kg/m3, for ambient oxygen levels ranging from 8%

to 15%, the flame structures look quite different compared to those for the same ambient

oxygen percentage at the low ambient density of 14.8 kg/m3. In general, the flames are

shorter for the high-density ambient conditions. The computed flame shapes and lift-off

locations do not vary as much as those for the lower ambient density with variations in

77

(a) O2=8% (b) O2=10% (c) O2=12%

(d) O2=15% (e) O2=21%

Figure 4.33: Computed (without PDF) mean temperature distributions for a reacting n-heptane spray with ambient temperature 1000 K and ambient density 30 kg/m3 at fivedifferent ambient oxygen concentrations at 6 ms.

ambient oxygen level. The computed peak temperatures are also reduced by up to 200

K for the higher ambient density. The PDF method produces shorter and wider flames,

compared to those of the non-PDF model for the same ambient oxygen percentage.

Results from other groups in the ECN proceedings also showed poor agreement at the less

robust combustion conditions, especially for the lower O2 percentages. In general, a common

trend of over-predicted ignition delay has been shown among most modeling groups under

varying ambient O2 conditions. This may in part be due to the lack of appropriate definitions

for low ambient O2. Both the computed lift-off length and ignition delay from one group

(ANL) were well predicted using a different chemical mechanism (Golovitchev mechanism).

In some cases, results for either ignition delay or lift-off length were relatively good, while

those for the other were not as good. Significant qualitative structural differences were

78

(a) O2=10% (b) O2=12%

(c) O2=15% (d) O2=21%

Figure 4.34: Computed (with PDF) mean temperature distributions for a reacting n-heptane spray with ambient temperature 1000 K and ambient density 30 kg/m3 at fivedifferent ambient oxygen concentrations at 6 ms.

reported between models that neglect turbulence-chemistry interactions and those that

consider turbulence-chemistry interactions. In particular, well-mixed models tend to give

unrealistically thin laminar-like flame structures.

Here significant differences have been found between results from the PDF method and a

non-PDF model. The computed turbulent flame structures with the PDF are more realistic,

while quantitative comparisons in lift-off length and ignition delay are generally better for

the non-PDF method at low O2 and low T .

One reason for this poor performance of the PDF method at low ambient O2 and/or low

ambient T may be the chemical mechanism. The 29-species chemical mechanism that has

been used here has been tuned by the Wisconsin-ERC to match the global engine data in a

model that neglects turbulence-chemistry interactions. Therefore, it may not be surprising

79

(a) T=750 K (b) T=800 K (c) T=850 K

(d) T=900 K (e) T=950 K (f) T=1100 K

(g) T=1200 K (h) T=1300 K

Figure 4.35: Computed (without PDF) mean temperature distributions for a reacting n-heptane spray with 21% O2 level and ambient density 14.8 kg/m3 at different ambienttemperatures at 6 ms.

that it performs better with a non-PDF model.

To explore sensitivity of computed results to the chemical mechanism, a 40-species n-

heptane mechanism was used for some cases: a low-ambient-temperature (800 K) case, and

a low-ambient-O2(8%) case, where ignition delay predictions are less robust. Results are

80

(a) T=900 K (b) T=1100 K (c) T=1200 K

(d) T=1300 K

Figure 4.36: Computed (with PDF) mean temperature distributions for a reacting n-heptane spray with 21% O2 level and ambient density 14.8 kg/m3 at different ambienttemperatures at 6 ms.

Table 4.5: Comparison of computed ignition delays using different chemical mechanism.

Case Experiment PDF with 29-species mech PDF with 40-species mech

8% O2 case 1.52 ms 4.033 ms 2.571 ms

800 K case 1.65 ms 4.315 ms 1.639 ms

shown in Table 4.5. The computed ignition delays are improved dramatically with the

40-species mechanism, especially for the low-temperature case.

Scatter plots of temperature versus equivalence ratio can provide insight into the flame

structure in composition space and are useful to explore local conditions in the combustion

chamber, although corresponding experimental data are not available. Computed scatter

plots are shown for the baseline n-heptane case without PDF method in Figs. 4.39 (through

the ignition event) and 4.40 (in the quasi-steady flame). Here Φ is defined in Eq. 4.2.

81

(a) O2=8% (b) O2=10% (c) O2=12%

(d) O2=15%

Figure 4.37: Computed (without PDF) mean temperature distributions for a reacting n-heptane spray with ambient temperature 1000 K and ambient density 30 kg/m3 at 6 ms.

The high-temperature ignition occurs in fuel-rich regions where the equivalence ratio is

approximately 2 (Fig. 4.39). When quasi-steady state is reached, the Φ-T map varies little

further with time. In that case, the peak temperature is found at Φ ≈ 1 (Fig. 4.40), as

expected.

4.4 Summary and Conclusions

Numerical simulations have been performed for a constant-volume high-pressure spray

chamber. For validation purposes, experimental conditions from the Sandia ECN website

were applied. The model was calibrated to match measured liquid and vapor penetration

length for a nonreacting n-heptane spray. The influences of physical and numerical param-

eters on computed liquid and vapor penetration lengths were studied. Then simulations for

82

(a) O2=8% (b) O2=10% (c) O2=12%

(d) O2=15%

Figure 4.38: Computed (with PDF) mean temperature distributions for a reacting n-heptane spray with ambient temperature 1000 K and ambient density 30 kg/m3 at 6 ms.

reacting sprays were performed. Simulation results for reacting n-heptane sprays follow the

measured trends of lift-off length and ignition delay with variations in ambient conditions

(oxygen, temperature and density). The turbulent flame structures were also explored, and

Φ-T maps through the ignition period and in the quasi-steady state were studied.

Results from a PDF method were compared with results from a non-PDF model to

study the effect of turbulence-chemistry interactions under engine-relevant conditions. In

general, both models reproduce the measured trends of lift-off length and ignition delay.

The PDF results show larger differences compared with experiment, especially under low

ambient oxygen and temperature conditions. This may be because of the choice of chemical

mechanism. In any case, the main conclusion is that turbulence-chemistry interactions

effects are important, and a PDF model that accounts for turbulence-chemistry interactions

gives more realistic turbulent flame structure. Quantitative agreement with measured data

83

(a) t=0.6492 ms (b) t=0.6532 ms (c) t=0.6572 ms

(d) t=0.6612 ms (e) t=0.6652 ms (f) t=0.6692 ms

Figure 4.39: Scatter plots of temperature versus equivalence ratio for a reacting n-heptanespray at baseline conditions of ambient temperature 1000 K, ambient density 14.8 kg/m3

and 21% O2 level through the ignition period.

could be improved by further tuning physical and numerical parameters and adopting better

gas-phase chemistry mechanisms, which are subjects of ongoing research.

84

Figure 4.40: Scatter plots of temperature versus equivalence ratio for a reacting n-heptanespray at baseline conditions of ambient temperature 1000 K, ambient density 14.8 kg/m3

and 21% O2 level at quasi-steady state.

Chapter 5

Analysis of Biodiesel and

Hydrogen Effects on NOx

Emissions in Direct-Injection

Compression-Ignition Engines

Alternative fuels are of interest, in addition to advanced combustion strategies, to increase

fuel efficiency and decrease the environmental impact of IC engines [5]. Variations in fuel

composition can have subtle effects on NOx emissions, in particular. In this chapter, the

CFD models are applied to idealized and realistic compression-ignition engines. Numerical

results from two sets of simulations are reported. In the first set, the effects of turbulent

fluctuations in composition and temperature about their local mean values are ignored.

In that case, the 71-species chemical mechanism from Appendix A.4 is used directly to

compute the mean chemical source term in the mean species mass fraction equations us-

ing finite-volume cell-level mean quantities. In the second set, a transported PDF method

has been used [50], with standard models for turbulent transport (gradient diffusion) and

mixing (pair-exchange models). In that case, the composition PDF fϕ is computed using

a consistent hybrid Lagrangian particle/Eulerian mesh (LPEM) method. Comparisons be-

85

86

tween results obtained with versus without the PDF method provide an indication of the

extent to which turbulence-chemistry interactions are important. Comparisons with exper-

iment provide an indication of the extent to which subtle effects of fuel composition NOx

emissions can be captured by the model.

5.1 The Biodiesel NOx Effect in Common-Rail Diesel En-

gines

It has been reported that substantial reductions in CO, UHC and soot can be achieved by

increasing the percentage of biodiesel in biodiesel/petroleum diesel fuel blends. In general,

NOx increases with increasing bio-content of the fuel in an approximately linear relation-

ship [17]. A 1% increase in NOx was observed per 10% biodiesel addition to the base diesel

fuel in [240]. This effect is more prominent for engines operated at low speeds. This increase

in NOx is leading some U.S. regulatory agencies to consider banning the use of biodiesel.

Therefore, the issue of NOx emissions is potentially a significant barrier for expanding the

use of biodiesel fuels in diesel engines. However, research papers presenting results of diesel

engine emissions with biodiesel often ignore some of the basic properties of the biodiesel fuel

that was used, which poses difficulties in interpreting the results and determining whether

fuel quality has a significant effect or not, as pointed out in the review of Lapuerta [241].

As pointed by Cardone et al. [242], the NOx increase is well understood in older pump-

line-nozzle fuel systems where the higher bulk modulus of compressibility of the biodiesel

fuel leads to an advanced injection timing, which in turn leads to an earlier maximum

cylinder temperature, and thereby higher levels of formation of thermal NOx. However,

the cause of the NOx increase is still not clear in modern high-pressure common-rail fuel

systems. Biodiesel fuels do not always lead to injection advances, as indicated by Boehman

et al. [243]. In some cases, injection delays with biodiesel were reported to be longer

compared to a very-low-sulfur-content petroleum diesel fuel. Some recent experiments have

shown increased NOx emissions with biodiesel for fixed injection timing. Several hypotheses

have been proposed to explain this effect. These include physical effects, chemical effects

87

and combinations of different effects. Some of the more prominent hypotheses that have

been proposed are summarized in the following [244].

1. Combustion phasing: The somewhat higher cetane number of biodiesel causes igni-

tion to occur earlier in the cycle. This allows the combustion products to have a

longer residence time at high temperatures, which increases NOx emissions [245, 246].

However, it also has been argued that higher cetane numbers may cause a decrease

in the premixed combustion phase, which may lead to milder temporal variations in

pressure and temperature and thus to lower NO formation [16, 247–249].

2. Premixed-burn fraction: A larger fraction of the heat release for biodiesel occurs

during the premixed-burn phase of combustion at ignition. The difference in NOx

produced during the premixed burn is responsible for the biodiesel NOx increase.

3. Kinetics: There are differences in the chemical-kinetic pathways that form NOx when

biodiesel is used, and these are responsible for the biodiesel NOx increase.

4. Adiabatic flame temperature: Biodiesel has a higher adiabatic flame temperature than

conventional diesel, so thermal NOx production is higher (e.g. [250]). No consensus

is evident in the literature, as some sources state that biodiesel has slightly higher

adiabatic flame temperature than conventional diesel [250–252], while others maintain

the opposite [253, 254].

5. Radiative heat transfer: Biodiesel produces less soot because it is an oxygenated fuel.

Because soot radiation is an important means of heat loss from an in-cylinder flame,

radiative heat losses are lower for biodiesel flames, which produce higher actual flame

temperatures and therefore more thermal NOx (e.g. [240]).

Here we focus on the effects of variations in the physical properties of the fuel (liquid

density and viscosity) on NOx emissions in direct-injection common-rail engines. Sun et

al. [255] summarized the effects of the difference in properties between biodiesel or its blends

and petroleum diesel on engine parameters as follows. Higher liquid density may advance

injection timing and pressure, increase ignition delay and decrease fuel spray penetration

88

and/or angle, while higher liquid viscosity may advance injection timing and ignition delay

and decrease fuel spray angle and spray atomization. Here the simulation strategy is to

assess the extent to which variations in physical fuel properties may be responsible for the

biodiesel NOx effect by perturbing two key physical properties of the fuel: liquid density

and viscosity. However, it is difficult to isolate individual effects of these fuel properties in

the spray models, in particular. For example, the total liquid fuel energy is a function of

the liquid fuel density, so in order to change density without changing anything else, the

effect of the fuel density change on fuel energy content needs to be removed so that the

total liquid fuel energy remains the same.

To better understand the effects of physical properties of biodiesel fuel on NOx emis-

sions from the fundamental point of view, simulations have been performed for an idealized

constant-volume configuration (Fig. 5.1). Initial conditions (temperature, pressure, and

composition) were assigned to correspond to diesel-engine operating conditions where ex-

perimental measurements [240] have been taken: 907 K, 60.6 bar, and air without EGR.

Liquid fuel (0.41 mg at 360.15 K) is injected, with the fuel-spray model parameters corre-

sponding to those for a modern small-bore, light-duty automotive diesel engine [73].

X Y

Z

Figure 5.1: Constant-volume combustion bomb mesh.

The fuel properties that were explored were the mass density, ρ, and the viscosity,

89

µ. Compared to conventional petroleum-derived diesel fuel, the liquid fuel density and

viscosity for biodiesel fuel are generally higher. The ranges of the specific biodiesel fuels

used in the reviews of Lapuerta [241] are 870-895 kg/m3 for density and 3.5-5.5 cSt for

viscosity, whereas conventional petroleum diesel ranges from 810-860 kg/m3 in density and

2-3.5 cSt in viscosity. In this thesis, the properties of biodiesel fuels and conventional diesel

are taken from [256]: a density of 884 kg/m3 for biodiesel, and 837 kg/m3 for ultra-low-sulfur

diesel; and a kinematic viscosity of 4.06 cSt for biodiesel, and 2.48 cSt for ultra-low-sulfur

diesel. These properties correspond to biodiesel having a density that is 1.11 times that of

conventional diesel, and a dynamic viscosity that is a factor of 1.73 higher. To make the

effects of property changes more apparent in the simulations, an additional factor of 1.1

has been added to each property, such that the simulated “biodiesel” fuel is a factor of 1.16

and a factor of 1.90 higher in density and viscosity, respectively, compared to conventional

diesel. Care was taken to change only one fuel property at a time, while leaving other key

parameters (e.g., fuel energy per mass) the same.

Computed pressure, NO, and NO2 versus time for two different fuel densities and viscosi-

ties are shown in Figs. 5.2-5.4. In all cases, the total energy release is the same. However,

the burn rate (rate of pressure rise) is considerably slower with the PDF methods. The burn

rate is insensitive to variations in the fuel properties without the PDF, while a difference is

seen with the PDF method when ρ is varied. These effects are amplified in the NOx levels.

As seen in Figs. 5.3 and 5.4, with the increase in fuel density, the non-PDF case shows

slightly reduced levels of NO and NO2, while with the PDF method the computed mass

of NO and NO2 increase by 62% and 17%, respectively, when the fuel density is increased.

Variations in fuel viscosity had negligible effect on computed NO and the computed NO2 in

all cases. In the spray models, both the liquid fuel density and the viscosity influence the

spray breakup, drag, collision, vaporization, and the wall interaction sub-models. These re-

sults suggest that the difference in density between petroleum-derived and bio-derived diesel

fuel may contribute to the increase in NOx with bio-derived diesel fuel. They also show

that turbulence-chemistry interactions are important, and that these interactions amplify

the effects of the increase in fuel properties on computed NOx levels.

90

Figure 5.2: Computed pressure versus time with variations in fuel density and viscosity.The reference case (ref) corresponds to conventional diesel fuel, “den” corresponds to a fuelmass density 1.16 times that of conventional diesel fuel, and “vis” corresponds to a fueldynamic viscosity 1.90 times that of conventional diesel fuel, with all other fuel propertiesheld fixed. Cases labeled “fv” correspond to calculations without the PDF method (ignoringthe influence of turbulent fluctuations in composition and temperatures).

5.2 Hydrogen-Assisted Diesel Combustion

Next, a series of simulations were performed for a dual-fuel (hydrogen-diesel) engine where

experimental results are available. In the experiment, measurements were made in a

DDC/VM Motori 2.5L, four-cylinder, turbocharged common-rail, direct-injection diesel en-

gine [8] operating in conventional (conventional diesel - CD) and advanced combustion

modes (high-efficiency clean combustion-HECC, and low-temperature combustion-LTC);

see Table 5.1. Conventional modes include four combinations of speed and load (modes

1-4). For each mode, varying amounts of hydrogen were substituted for diesel fuel on a

percent energy basis from 0% to 15%. The hydrogen was premixed in the incoming air and

EGR mixture. As the hydrogen was added, the pilot and main injection timings were locked

and the speed and load were held constant. Hydrogen substitution caused small changes

to EGR percentage, intake-manifold gas temperature and the exhaust-gas temperature in

91

Figure 5.3: Computed NO mass versus time with variations in fuel density and viscosity.The reference case (ref) corresponds to conventional diesel fuel, “den” corresponds to a fuelmass density 1.16 times that of conventional diesel fuel, and “vis” corresponds to a fueldynamic viscosity 1.90 times that of conventional diesel fuel, with all other fuel propertiesheld fixed. Cases labeled “fv” correspond to calculations without the PDF method (ignoringthe influence of turbulent fluctuations in composition and temperatures).

Table 5.1: Global parameters for six combustion modes with 0% H2.

Mode Combustion Load(%max/kW)

Speed(r/min)

TotalEGR

Boost(bar)

InitialT(K)

Pilotinj(CA)

Maininj(CA)

1 CD 25/15.7 1800 11.0% 0.17 332.15 342.6 362.9

2 CD 75/46.5 1800 0.7% 0.7 315.15 321.7 353.8

3 CD 25/26.1 3600 1.4% 0.9 343.45 303.2 347.7

4 CD 75/78.2 3600 1.0% 1.1 349.65 301.9 346.4

5 LTC 25/15.7 1800 48.0% 0.14 343.15 342.6 362.9

6 HECC 25/15.7 1800 50.0% 0.18 348.15 N/A 356

the experiment; these were ignored in the simulations. As hydrogen substitution increases,

the amount of diesel fuel decreases in both the pilot and the main injections to maintain

the desired fixed load. In the experiment, total EGR in Table 5.1 is the sum of actual and

simulated EGR. Simulated EGR used bone-dry CO2 with a purity of 99.8%, and actual

EGR is accomplished by looping exhaust gas back into the intake manifold.

92

Figure 5.4: Computed NO2 mass versus time with variations in fuel density and viscosity.The reference case (ref) corresponds to conventional diesel fuel, “den” corresponds to a fuelmass density 1.16 times that of conventional diesel fuel, and “vis” corresponds to a fueldynamic viscosity 1.90 times that of conventional diesel fuel, with all other fuel propertiesheld fixed. Cases labeled “fv” correspond to calculations without the PDF method (ignoringthe influence of turbulent fluctuations in composition and temperatures).

5.2.1 Computational Configuration and Model Setup

Detailed dimensioned drawings and/or CAD data for the actual engine geometry were

not available for mesh generation. A fuel-injector characterization also was not available.

Therefore, a highly idealized geometric representation was used for the CFD study, together

with a fuel-injector specification that was adapted from a recent modeling study of a different

modern light-duty direct-injection diesel engine [73, 79]. For these reasons, quantitatively

accurate agreement between the CFD model and the experimental measurements is not

expected. Rather, the focus will be on the ability of the model to capture the trends in NOx

emissions with different levels of hydrogen enrichment that were observed experimentally,

and on the importance or lack thereof of turbulence-chemistry interactions. A 45-degree

sector mesh of 5040 cells was used to represent a generic bowl-in-piston configuration that is

representative of a modern small-bore automotive diesel engine (Fig. 5.5). A piston top-ring-

93

land crevice has been included, as this has been shown to be important for emissions [74,

257, 258]. The computational engine geometric parameters have been adjusted as shown in

Table 5.2 so that the global pressure traces for the six combustion modes match reasonably

well with the measured data from the experiment (Fig. 5.6).

Figure 5.5: Outer surface of the computational mesh, and computed contours of fuel vapormass fraction at one instant.

Table 5.2: Global engine geometric parameters.

Bore 86 mm

Stroke 90 mm

Compression Ratio 14.53

Clearance 3.5 mm

Connecting Rod Length 180 mm

The simulations begin post-intake-valve closure (138 crank angle degrees before top-

dead-center - TDC) and are carried through bottom-dead-center (BDC) of expansion to

pre-exhaust valve opening. The initial in-cylinder pressure and temperature are obtained

from the experiments, and the initial composition is specified to correspond to the desired

amount of premixed hydrogen, air, and EGR. Here EGR is simulated using N2, O2, CO2

and H2O. All wall temperatures are set to 450 K.

94

(a) Mode 1 (b) Mode 2

(c) Mode 3 (d) Mode 4

(e) Mode 5 (f) Mode 6

Figure 5.6: Computed and measured pressure traces versus time for six combustion modes.

95

5.2.2 Computed vs Measured NOx without Hydrogen Enrichment

In this subsection, measured engine-out NOx emissions are compared with computed in-

cylinder values at BDC. This comparison implicitly neglects the influence of reactions that

occur post-exhaust-valve opening. In the engine experiments, NOx and NO were measured

using an EcoPhysics chemiluminescence analyzer from the sampled hot exhaust gases, and

NO2 was assumed to be the difference of the measured NOx and NO values [8].N

O[p

pm

]

mode1 mode2 mode3 mode4 mode5 mode60

200

400

600

800

1000

1200

NO_expNO_fvNO_pdf

Figure 5.7: Computed and measured NO for 0% H2 for six modes.

Computed and measured NO, NO2, and NOx are compared for each of the six com-

bustion modes (Section 5.2) and 0% H2 in Figs. 5.7, 5.8 and 5.9. Results from two sets of

simulations are shown: one where the influence of turbulent fluctuations on mean chemical

rates has been ignored (“FV”), and one where the influence of turbulent fluctuations has

been included (“PDF”). The computed NO values are lower than the measured NO values

for all six modes; the quantitative agreement is best for the conventional diesel (CD) light-

load cases (Mode 1 and Mode 3), and the differences between results from well-mixed and

PDF models are relatively small (20-30%). Computed NO2 values (Figs. 5.8) are higher

than the measured NO2 values for all cases except Mode 3 (CD/3600 rpm/25% max load)

and Mode 6 (HECC/1800 rpm/25% max load); NO2 values from the PDF model are con-

96

NO

2[p

pm]

mode1 mode2 mode3 mode4 mode5 mode60

20

40

60

80

100

120

NO2_expNO2_fvNO2_pdf

Figure 5.8: Computed and measured NO2 for 0% H2 for six modes.

sistently lower than those from the well-mixed model. NO dominates for the conventional

diesel cases, but the NO/NO2 ratio is smaller for the low-temperature combustion (LTC)

and high efficiency clean combustion (HECC) combustion modes. The quantitative agree-

ment between model and measurement is far from perfect, and this is to be expected, given

the significant simplifications in the geometric configuration, injector characterization, and

chemistry models. Overall, the best agreement is for the light-load conventional diesel cases

(Modes 1 and 3) with the PDF-based model.

5.2.3 Well-mixed Model with Hydrogen Enrichment

We next explore the ability of the model to capture the experimentally observed trends in

NO and NO2 with up to 15% hydrogen enrichment. Figures 5.10- 5.15 show the computed

and measured percentage changes (relative to 0% H2) in NO and NO2 with H2 substitution

levels of 2.5%, 5%, 7.5%, 10% and 15% without consideration of turbulence-chemistry in-

teractions. The model follows the experimental trends fairly well for the two conventional

diesel, light-load cases (Modes 1 and 3). Results for the higher load and for the uncon-

ventional combustion modes are not as good. In particular, the model fails to capture the

significant increases in NO2 with hydrogen enrichment that are observed experimentally.

97

NO

x[p

pm

]

Mode1 Mode2 Mode3 Mode4 Mode5 Mode60

200

400

600

800

1000

1200

NOx_expNOx_fvNOx_pdf

Figure 5.9: Computed and measured NOx for 0% H2 for six modes.

H2 level [%]

Per

cen

tag

eC

han

ge[%

]

0 5 10 15-50

0

50

100

150

200

NO_expNO_simNO2_expNO2_sim

Figure 5.10: Computed (well-mixed model) and measured % changes (wrt/0% H2) in NOand NO2 w/H2 addition for CD/1800 rpm/25% max load (Mode 1).

98

H2 level [%]

Per

cen

tag

eC

han

ge[%

]

0 5 10 15-50

0

50

100

150

200



H2 level [%]

Per

cen

tag

eC

han

ge[%

]

0 5 10 15-50

0

50

100

150

200



99

H2 level [%]

Per

cen

tag

eC

han

ge[%

]

0 5 10 15

0

100

200

300

400

500



H2 level [%]

Per

cen

tag

eC

han

ge[%

]

0 5 10 15-50

0

50

100

150

200


Figure 5.14: Computed (well-mixed model) and measured % changes (wrt/0% H2) in NOand NO2 w/H2 addition for LTC/1800 rpm/25% max load (Mode 5).

100

H2 level [%]

Per

cen

tag

eC

han

ge[%

]

0 5 10 15-50

0

50

100

150

200


Figure 5.15: Computed (well-mixed model) and measured % changes (wrt/0% H2) in NOand NO2 w/H2 addition for HECC/1800 rpm/25% max load (Mode 6).

Sensitivity of computed results to variations in clearance height, initial temperature,

and initial pressure was explored (not shown). There was a modest improvement in the

computed NO2 versus H2 trend with a 0.5 mm increase in clearance height (not shown).

5.2.4 PDF Model with Hydrogen Enrichment

Results from the PDF model are shown in Figs. 5.16- 5.21. Some improvement with respect

to the well-mixed model can be seen for Mode 2 (CD/1800 rpm/75% max load), and perhaps

smaller improvements in NO for the two advanced combustion modes (Modes 5 and 6).

In general, however, the level of improvement with consideration of turbulence-chemistry

interactions is not as significant as has been reported in other recent studies [73, 74, 79].

5.2.5 Discussion

Hypotheses that were raised in [8] with respect to the decreasing NO/NO2 ratio with in-

creasing H2 enrichment can now be assessed using the CFD model results. Because the

greatest consistency between model behavior and experimental results was found for the

101

H2 level [%]

Per

cen

tag

eC

han

ge[%

]

0 5 10 15-50

0

50

100

150

200


Figure 5.16: Computed (PDF model) and measured % changes (wrt/0% H2) in NO andNO2 w/H2 addition for CD/1800 rpm/25% max load (Mode 1).

H2 level [%]

Per

cen

tag

eC

han

ge[%

]

0 5 10 15-50

0

50

100

150

200



102

H2 level [%]

Per

cen

tag

eC

han

ge[%

]

0 5 10 15-50

0

50

100

150

200



H2 level [%]

Per

cen

tag

eC

han

ge[%

]

0 5 10 15

0

100

200

300

400

500



103

H2 level [%]

Per

cen

tag

eC

han

ge[%

]

0 5 10 15-50

0

50

100

150

200


Figure 5.20: Computed (PDF model) and measured % changes (wrt/0% H2) in NO andNO2 w/H2 addition for LTC/1800 rpm/25% max load (Mode 5).

H2 level [%]

Per

cent

age

Ch

ange

[%]

0 5 10 15-50

0

50

100

150

200


Figure 5.21: Computed (PDF model) and measured % changes (wrt/0% H2) in NO andNO2 w/H2 addition for HECC/1800 rpm/25% max load (Mode 6).

104

light-load conventional diesel cases, we focus our attention on the CD/1800 rpm/25% max

load case (Mode 1).

While a global mean in-cylinder temperature can be deduced using pressure-based com-

bustion diagnostics, no information on spatial temperature distributions are available from

the experiments. Such information is readily extracted from the CFD model, and is shown

in Figs. 5.22 and 5.23. The bulk mean temperature, maximum temperature, and amount of

mixture having a temperature greater than 1700 K (an approximate threshold temperature

above which thermal NO formation becomes important) vary little with hydrogen enrich-

ment. This suggests that the observed changes in NOx with H2 addition are not the result

of changes in thermal NO.

The computed global in-cylinder HO2 level is plotted versus crank angle degrees of

rotation in Fig. 5.24 for different levels of H2 addition. There it can be seen that following

ignition, in-cylinder HO2 levels increase with increasing H2. This lends credence to the

hypothesis [8] that the conversion of NO to NO2 is enhanced with increasing hydrogen

enrichment by the path,

HO2 +NO ↔ NO2 +OH (5.1)

5.2.6 Summary

Two sets of CFD simulations have been used to explore the changes in NOx emissions with

hydrogen substitution that have been observed experimentally in hydrogen-enriched diesel

combustion over a range of engine operating conditions. In the first set, the effects of turbu-

lent fluctuations in composition and temperature about their local mean values are ignored.

In the second set, a transported PDF method has been used [50], with standard models

for turbulent transport (gradient diffusion) and mixing (pair-exchange models). Significant

simplifications were invoked in the CFD model compared to the real engine. These include

an idealized geometric configuration, assumed fuel-injector characteristics, and simplified

chemical kinetics and other physical models. In spite of these approximations, the model is

able to reproduce the experimentally observed trend of decreasing NO and increasing NO2

105

CAD

T[K

]

300 350 400 450 500

500

1000

1500

2000

2500

Tmax_0%H2Tmax_15%H2Tavr_0%H2Tavr_15%H2Tmin_0%H2Tmin_15%H2

Figure 5.22: Computed (well-mixed model) maximum, minimum, and volume-averaged in-cylinder temperature versus crankangle for Mode 1 (CD/1800 rpm/25% max load) with 0%and 15% H2 substitution.

CAD

Mas

sF

ract

ion

ofT

>17

00K

300 330 360 390 420 450 480 510 540-0.1

0

0.1

0.2

0.3

0.4

0.5

baseline_0%H2baseline_15%H2

Figure 5.23: Computed (well-mixed model) mass fraction of in-cylinder mixture having atemperature greater than 1700 K for Mode 1 (CD/1800 rpm/25% max load) with 0% and15% H2 substitution.

106

CAD

HO

2[p

pm

]

300 350 400 450 500

0

5

10

15

20

25

0%H27.5%15%H2

Figure 5.24: Computed (well-mixed model) global in-cylinder HO2 level versus crankanglefor Mode 1 (CD/1800 rpm/25% max load) with 0%, 7.5% and 15% H2 substitution.

with increasing H2 levels for some operating conditions. A model that explicitly accounts for

turbulence-chemistry interactions using a transported PDF method does somewhat better

than a model that ignores the influence of turbulent fluctuations on mean chemical produc-

tion rates, although the importance of fluctuations is not as strong as has been reported in

some other recent modeling studies [73, 74, 79]. The CFD results confirm that temperature

variations alone are not sufficient to explain the observed reductions in NO and increases in

NO2 with increasing H2. They are consistent with the hypothesis [8] that in-cylinder HO2

levels increase with increasing H2, and that the increase in HO2 enhances the conversion of

NO to NO2.

Chapter 6

Conclusions

Although the role of turbulence-chemistry interactions in simulating diesel engines has been

explored and emphasized in some previous research work [67, 73, 74, 194], their influence

on combustion and emissions for advanced combustion systems with nontraditional fuels

are still largely unknown and in need of more extensive research work. This thesis has

shown that simulations that account for turbulence-chemistry effects can significantly alter

computed predictions of combustion compared to those when turbulence-chemistry inter-

actions are ignored, as demonstrated by the differences in computed ignition timing, flame

structure, lift-off length and emissions. However, there are issues in accuracy and model

robustness that need to addressed. In this chapter, the major findings of the thesis are

reviewed and summarized, and future research directions are proposed.

6.1 Summary

Constant-volume turbulent spray combustion is an important intermediate step between

laboratory flames and practical engines. Modeling and simulating constant-volume turbu-

lent spray combustion is an appropriate validation step toward diesel combustion in real

IC engines. A consistent hybrid Lagrangian particle/finite-volume PDF method has been

implemented in an open-source CFD code, OpenFoam, and has been applied to simulate

turbulent spray combustion in a constant-volume chamber over a range of diesel-engine-

107

108

relevant conditions. Sensitivities of computed liquid and vapor penetration lengths and

mixture fraction distributions to varieties in physical and numerical parameters have been

studied. From these results, baseline model parameters were selected for subsequent simula-

tions of reacting n-heptane sprays. These simulations were performed with varying ambient

conditions: oxygen composition, temperature and density. Computed and measured lift-off

lengths and ignition delays were compared for different ambient conditions. The use of

ISAT was tested for several combustion conditions. Flame structures in physical space and

composition space were also examined, and the influence of turbulence-chemistry interac-

tions was explored by comparing results from a PDF method with those from a non-PDF

model. In general, both models reproduce the measured trends of lift-off length and igni-

tion delay. The PDF results show larger differences compared with experiment, especially

under low ambient oxygen and temperature conditions. This may be because of the choice

of chemical mechanism. In any case, the main conclusion is that turbulence-chemistry in-

teractions effects are important, and a PDF model that accounts for turbulence-chemistry

interactions gives more realistic turbulent flame structure. Quantitative agreement with

measured data could be improved by further tuning physical and numerical parameters and

adopting better gas-phase chemistry mechanisms, which are subjects of ongoing research.

To explore the effects of variations in fuel properties on NOx emissions for biodiesel fuel

in common-rail diesel engines, simulations were performed for a constant-volume combustion

bomb mesh under conditions representative of those in a modern, small-bore, light-duty

diesel engine. Results suggest that the difference in density between petroleum-derived and

bio-derived diesel fuel may contribute to the increase in NOx that has been observed with

bio-derived diesel fuel. A model that accounts for turbulence-chemistry interactions shows

NOx with more sensitivity to variations in fuel properties compared to a model that neglects

turbulence-chemistry interactions.

Finally, three-dimensional CFD simulations were used to explore variations in NOx

emissions with variations in the amount of hydrogen used in hydrogen-enriched diesel com-

bustion. Significant simplifications were invoked in the CFD model compared to the en-

gine in the experiment. Results obtained using a transported PDF method to account

109

for turbulence-chemistry interactions were compared to those obtained using a model that

neglects turbulence-chemistry interactions and to experiment over a range of operation con-

ditions including four conventional diesel combustion modes and two advanced combustion

modes, with hydrogen substitution from 0% to 15% on an energy basis for each operating

condition. Hypotheses made in the experimental analysis regarding to the conversion of

NO and NO2 were discussed. The model is able to reproduce the experimentally observed

trend of decreasing NO and increasing NO2 with increasing H2 levels for some operating

conditions. A model that explicitly accounts for turbulence-chemistry interactions using

a transported PDF method does somewhat better than a model that ignores the influ-

ence of turbulent fluctuations on mean chemical production rates, although the importance

of fluctuations is not as strong as has been reported in some other recent modeling stud-

ies [73, 74, 79]. The CFD results confirm that temperature variations alone are not sufficient

to explain the observed reductions in NO and increases in NO2 with increasing H2. They

are consistent with the hypothesis [8] that in-cylinder HO2 levels increase with increasing

H2, and that the increase in HO2 enhances the conversion of NO to NO2.

6.2 Proposed Future Work

Quantitative agreement between model and experiment remains far from perfect. In the

constant-volume device, computed ignition delays and lift-off lengths are far from measured

data at low temperature or oxygen levels. Better chemical mechanisms are needed to resolve

this issue. Other biodiesel fuel properties, including the latent heat of vaporization, may be

relevant for the biodiesel-NOx effect in engines. The following lines of research are proposed

for the future.

6.2.1 Configurations

• Further ECN n-heptane simulations should be performed. Better chemical mech-

anisms are needed to improve lift-off length results, and to include soot and NOx

chemistry. A 52-species mechanism from Lu [259] and a 159-species mechanism from

LLNL [141] would be appropriate ones to consider.

110

• Comparisons with alternative PDF methods should be made. It would be interesting

to systematically compare the results obtained using the stochastic Eulerian field PDF

method [194] with those obtained here using a particle PDF method.

• Other ECN constant-volume configurations should be simulated. “Spray A” (n-

dodecane fuel) would be the appropriate next target.

• Simulations should be extended from the somewhat idealized compression-ignition

piston engines studied here to more realistic engines.

6.2.2 Physical Modeling

The focus of the current work has been on turbulence-chemistry interactions, by comparing

results obtained using a PDF method with results from a model that neglects or simplis-

tically accounts for turbulence-chemistry interactions. More advanced physical models for

key physical subprocesses should be considered.

• Sprays

Spray models are important to model atomization and vaporization processes, which

in turn influence downstream processes such as mixing, ignition and combustion. The

spray model that has been used here must be calibrated to match experimental data.

More predictive models would reduce uncertainties.

• Soot

No soot model has been used here. To compare computed soot distributions with mea-

sured data for the ECN configuration, two-equation semi-empirical soot models [260]

or detailed models using a method of moments [261] can be implemented in a trans-

ported PDF method to account for complex turbulence/chemistry/soot interactions.

• Radiation

The effects of radiation have not been considered here. The sophisticated PDF based

radiation models that have been developed recently [66] should be applied to explore

radiation and turbulence/chemistry/soot/radiation interactions in engines.

111

• Extension to LES/FDF

Here a standard k − ϵ or RNG k − ϵ two-equation model has been used to model

the effects of turbulent velocity fluctuations in a URANS context. With growing

computing power, large-eddy simulation (LES) is becoming more feasible for complex

configurations. Recent LES/PDF simulations have shown promise for atmospheric-

pressure jet flames [262], and those methods could be extended to engine environment.

6.2.3 Numerical Algorithms

An important practical concern with PDF methods is their high computational cost. ISAT

is promising for chemistry acceleration within the context of PDF methods. In the present

work, either ISAT or parallelization has been used, but not both. More effective use of

ISAT in parallel simulations would be an appropriate direction.

ISAT could also be extended to tabulate spectral radiation properties, in addition to

chemical source terms.

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Appendix A

Chemical Mechanisms

CHEMKIN-formatted input files for four chemical mechanisms follow. Three coefficients

are provided for each elementary reaction: preexponential factor, temperature exponent

and activation energy, using cgs units.

A.1 N-heptane 5-Species Mechanism

The following 5-species global n-heptane mechanism was provided with OpenFOAM [182]

v1.5.

ELEMENTS

H O C N AR

END

SPECIE

C7H16 O2 N2 CO2 H2O

END

REACTIONS

C7H16 + 11O2 => 7CO2 + 8H2O 5.00E+8 0.0 15780.0! 1

FORD / C7H16 0.25 /

FORD / O2 1.5 /

END

133

134


The following 29-species, 52-reaction n-heptane mechanism was developed by the University

of Wisconsin Engine Research Center [142].

ELEMENTS

H C O N

END

SPECIE

C7H16 O2 N2 CO2 H2O CO H2

OH H2O2 HO2 H O

CH3O CH2O HCO CH2 CH3 CH4

C2H3 C2H4 C2H5 C3H4 C3H5 C3H6 C3H7

C7H15-2 C7H15O2 C7KET12 C5H11CO

END

REACTIONS

C7H16 + H = C7H15-2 + H2 4.380E+07 2.0 4760.0!4760.0 2.0 4.380E7

C7H16 + OH = C7H15-2 + H2O 9.700E+09 1.3 1690.0!ORIGINAL 1690.5 1.30 4.5E9

C7H16 + HO2 = C7H15-2 + H2O2 1.650E+13 0.0 16950.0!ORIGINAL 16950.0 E13

C7H16 + O2 = C7H15-2 + HO2 2.000E+15 0.0 47380.0!ORIGINAL 47380 2E14

C7H15-2 + O2 = C7H15O2 1.560E+12 0.0 0.0!ORIGINAL 0.0 2E12

C7H15O2 + O2 = C7KET12 + OH 4.500E+14 0.0 18232.712!GA OPTIMIZED #1

! C7H15O2 = C7H14O2H 7.090E+10 0.0 20380.0!20380.0! ORI=6E11INCREASED BY E13 GOOD

! C7H14O2H + O2 = C7H14O2HO2 1.280E+12 0.0 0.0!4.6E+11 AND 0.0

! C7H14O2HO2 = C7KET12 + OH 3.100E+09 0.0 7480.0!ORIGINAL 7480, E9

C7KET12 = C5H11CO + CH2O + OH 9.530E+14 0.0 4.110E+4!ORIGINAL 1.05E15 4.11E4 YRA SUGGESTION

! ELIMINATED C5H11 C5H11CO = C5H11 + CO 1.000E+11 0.0 9.600E+3!9.6E3 AND 1E11

! ELIMINATED C5H11 C5H11 = C2H4 + C3H7 3.200E+13 0.0 28300.0!

C5H11CO = C2H4 + C3H7 + CO 9.84E+15 0.0 4.02E+04 !GA OPTIMIZED #3

! ELIMINATED C4H9 C7H15-2 = C4H9 + C3H6 2.200E+13 0.0 28100.0!

! ELIMINATED C4H9 C4H9 = C2H5 + C2H4 2.500E+13 0.0 28810.0!

135

C7H15-2 = C2H5 + C2H4 + C3H6 7.045E+14 0.0 3.46E+04!GA OPTIMIZED #2

C3H7 = C2H4 + CH3 9.600E+13 0.0 30950.0!

C3H7 = C3H6 + H 1.250E+14 0.0 36900.0!

C3H6 + CH3 = C3H5 + CH4 9.000E+12 0.0 8480.0!

C3H5 + O2 = C3H4 + HO2 6.000E+11 0.0 10000.0!E+11 10000.

C3H4 + OH = C2H3 + CH2O 1.000E+12 0.0 0.0!ADDED AFTER 2ND YRA DIS******

C3H4 + OH = C2H4 + HCO 1.000E+12 0.0 0.0!ADDED AFTER 2ND YRA DIS******

CH3 + HO2 = CH3O + OH 5.000E+13 0.00 0. !ORIGINAL 0. E13

CH3 + OH = CH2 + H2O 7.500E+06 2.00 5000. !CGS 37

CH2 + OH = CH2O + H 2.500E+13 0.00 0. !ADDED AFTER 2ND YRA MEETING******

CH2 + O2 = HCO + OH 4.300E+10 0.00 -500. !ADDED AFTER 2ND YRA MEETING******

CH2 + O2 = CO2 + H2 6.900E+11 0.00 500. !ADDED AFTER 2ND YRA MEETING******

CH2 + O2 = CO + H2O 2.000E+10 0.00 -1000. !ADDED AFTER 2ND YRA MEETING******

CH2 + O2 = CH2O + O 5.000E+13 0.00 9000. !ADDED AFTER 2ND YRA MEETING******

CH2 + O2 = CO2 + H + H 1.600E+12 0.00 1000. !ADDED AFTER 2ND YRA MEETING******

CH2 + O2 = CO + OH + H 8.600E+10 0.00 -500. !ADDED AFTER 2ND YRA MEETING******

CH3O + CO = CH3 + CO2 1.570E+14 0.00 11800. !ADDED AFTER YRA MEETING 1.570E+14 & 11800.

CO + OH = CO2 + H 8.987E+07 1.38 5232.877!5.880E+06 1.30 -4.34E+01!GA OPTIMIZED #4 3.510E+07 1.30 -758.0!

O + OH = O2 + H 4.000E+14 -0.50 0. !ORIGINAL 0.0 E14

H + HO2 = OH + OH 1.700E+14 0.0 875. !GA #7 BUT DID NOT IMPROVE SO SAME AS B4

OH + OH = O + H2O 6.000E+08 1.30 0. !

H + O2 + M = HO2 + M 3.600E+17 -0.72 0. !ORIGINAL 0. E17

H2O/21./ CO2/5.0/ H2/3.3/ CO/2.0/ !HO2-21,CO2-5,H2-3.3,CO-2.0

H2O2 + M = OH + OH + M 1.000E+16 0.00 45500. !ADDED AFTER YRA 0.0 4.3E16 AND 45500.0

H2O/21./ CO2/5.0/ H2/3.3/ CO/2.0/

H2 + OH = H2O + H 1.170E+09 1.30 3626. !ADDED AFTER YRA 1.170E+09 3626.

HO2 + HO2 = H2O2 + O2 3.000E+12 0.00 0. !ORIGINAL 0. E12 DONT TOUCH THIS AMAR

CH2O + OH = HCO + H2O 5.563E+10 1.095 -76.517!GA OPTIMIZED #5 ORIGINAL 2.430E+10 1.20 -447.

CH2O + HO2 = HCO + H2O2 3.000E+12 0.00 8000. !CGS 12

136

HCO + O2 = HO2 + CO 3.300E+13 -0.40 0. !CGS E13

HCO + M = H + CO + M 1.591E+18 0.95 56712.329 !GA OPTIMIZED #6 1.870E+17 -1.00 17000.

CH3 + CH3O = CH4 + CH2O 4.300E+14 0.00 0. !CGS 106 3.3

C2H4 + OH = CH2O + CH3 6.000E+13 0.0 960. !CGS 121 ! 13

C2H4 + OH = C2H3 + H2O 8.020E+13 0.00 5955. !ORIGINAL 5955 E13

C2H3 + O2 = CH2O + HCO 4.000E+12 0.00 -250. !ADDED AFTER 2ND YRA MEETING******

C2H3 + HCO = C2H4 + CO 6.034E+13 0.0 0. !ADDED AFTER 2ND YRA MEETING******

C2H5 + O2 = C2H4 + HO2 2.000E+10 0.0 -2200. !CGS 128

CH4 + O2 = CH3 + HO2 7.900E+13 0.00 56000. !ADDED ON 04/23/03 @ 1:12 PM

OH + HO2 = H2O + O2 7.50E+12 0.0 0. !7.5E12 0 0 ADDED ON 04/28/03 @ 5:19 PM

CH3 + O2 = CH2O + OH 3.80E+11 0.0 9000. !3.8E11 0 9000 ADDED ON 04/28/03 @ 5:22 PM

!CH4 WASNT BEING USED SO AMAR ADDED 5 CH4 DECOMPOSING REACTIONS AS FOLLOWS

CH4 + H = CH3 + H2 6.600E+08 1.60 10840. !ADDED ON 05/07/03 @12:13 PM

CH4 + OH = CH3 + H2O 1.600E+06 2.10 2460. !ADDED ON 05/07/03 @12:13 PM

CH4 + O = CH3 + OH 1.020E+09 1.50 8604. !1.02E9 1.5 8604 ADDED ON 05/07/03 @12:13 PM

CH4 + HO2 = CH3 + H2O2 9.000E+11 0.00 18700. !1E13 0.0 18700 ADDED ON 05/07/03 @12:13 PM

CH4 + CH2 = CH3 + CH3 4.000E+12 0.00 -570. !4E12 0.0 -570. ADDED ON 05/07/03 @12:13 PM

!C3H6 OXIDIZER ADDED ALSO 2 RXN FROM THIS POINT ADDED ON 05/08

! C3H6 + H = C3H5 + H2 5.000E+12 0.0 1500.0!

C3H6 = C2H3 + CH3 3.150E+15 0.0 85500.0!

END


The following 40-species, 165-reaction n-heptane mechanism was developed by

Golovitchev [153].

ELEMENTS

H C O N

END

137

SPECIES

C7H16 O2 N2 CO2 H2O

CO H2 CH4 C2H2 C2H4

H2O2 HO2 OH

H O

CH3 CH3O

CH2 CH2O CH3O2 CH4O2 HCO

C7H15-1 C7H15-2 C7H15O2 C7H14O2H C7H14O2HO2 C7KET12

C6H12 C5H11CHO C5H11CO C5H11 C4H9

C3H7 C3H6 C3H5 C3H4

C2H3 C2H5 C2H6

!CH3HCO CH3CO HCOOCH3 COOCH3

!N2O NO N

END

REACTIONS

C7H16 + H = C7H15-1 + H2 5.600E+07 2.0 7667.0!

C7H16 + H = C7H15-2 + H2 4.380E+07 2.0 4750.0!

C7H16 + OH = C7H15-1 + H2O 8.610E+09 1.10 1815.0!

C7H16 + OH = C7H15-2 + H2O 4.500E+09 1.30 690.5!

C7H16 + HO2 = C7H15-1 + H2O2 1.120E+13 0.0 19300.0!

C7H16 + HO2 = C7H15-2 + H2O2 1.650E+13 0.0 16950.0!

C7H16 + O2 = C7H15-1 + HO2 2.500E+13 0.0 48810.0!

C7H16 + O2 = C7H15-2 + HO2 2.000E+14 0.0 47380.0!

C7H15-1 + O2 = C7H15O2 2.000E+12 0.0 0.0!

C7H15-2 + O2 = C7H15O2 2.000E+12 0.0 0.0!

C7H15O2 = C7H14O2H 6.000E+11 0.0 20380.0!

C7H14O2H + O2 = C7H14O2HO2 4.600E+11 0.0 0.0!

C7H14O2HO2 = C7KET12 + OH 1.000E+09 0.0 7480.0!

138

C7KET12 = C5H11CHO + CH2O + O 1.050E+16 0.0 4.110E+4! 16

C5H11CHO + O2 = C5H11CO + HO2 2.000E+13 0.5 4.220E+4!

C5H11CHO + OH = C5H11CO + H2O 1.000E+13 0.0 0.000E+0!

C5H11CHO + H = C5H11CO + H2 4.000E+13 0.0 4.200E+3!

C5H11CHO + O = C5H11CO + OH 5.000E+12 0.0 1.790E+3!

C5H11CHO + HO2 = C5H11CO + H2O2 2.800E+12 0.0 1.360E+4!

C5H11CHO + CH3 = C5H11CO + CH4 1.700E+12 0.0 8.440E+3!

C5H11CHO + CH3O2 = C5H11CO + CH4O2 1.000E+12 0.0 9.500E+3!

C5H11CO = C5H11 + CO 1.000E+11 0.0 9.600E+3!

C5H11 = C2H4 + C3H7 3.200E+13 0.0 28300.0!

C7H15-1 = C2H4 + C5H11 2.500E+13 0.0 28810.0!

C7H15-2 = C4H9 + C3H6 2.200E+13 0.0 28100.0!

C7H15-1 = C7H15-2 3.600E+16 0.0 80700.0!

C4H9 = C2H5 + C2H4 2.500E+13 0.0 28810.0!

C3H7 = C2H4 + CH3 9.600E+13 0.0 30950.0!

C3H7 = C3H6 + H 1.250E+14 0.0 36900.0!

C3H7 + O2 = C3H6 + HO2 1.000E+12 0.0 4980.0!

C3H6 = C2H3 + CH3 3.150E+15 0.0 85500.0!

C3H6 + H = C3H5 + H2 5.000E+12 0.0 1500.0!

C3H6 + CH3 = C3H5 + CH4 9.000E+12 0.0 8480.0!

C3H5 = C3H4 + H 4.000E+13 0.0 69760.0!

C3H5 + H = C3H4 + H2 1.000E+13 0.0 0.0!

C3H5 + O2 = C3H4 + HO2 6.000E+11 0.0 10000.0!

C3H4 + OH = C2H3 + CH2O 1.000E+12 0.0 0.0!

C3H4 + OH = C2H4 + HCO 1.000E+12 0.0 0.0!

!

!C2H5 + O = CH3HCO + H 5.300E+13 0.0 0.0! 23

!C2H4 + HO2 = HCOOCH3 + H 4.040E+09 0.0 -840. ! 24

!C2H4 + HO2 = CH3HCO + OH 2.200E+13 0.0 17200.0! 25

139

!C2H4 + CH3O = CH3HCO + CH3 3.000E+13 0.0 14500.0 ! 26

!C2H4 + CH3O2 = CH3HCO + CH3O 7.000E+13 0.0 14500.0 ! 27

!C2H3 + OH = CH3HCO 3.000E+13 0.0 0.0! 28

!

!CH3HCO = CH3 + HCO 7.080E+15 0.00 81760. ! 28

!CH3HCO = CH3CO + H 5.000E+14 0.00 87860. ! 29

!CH3HCO + O2 = CH3CO + HO2 2.000E+13 0.50 42200. ! 30

!CH3HCO + H = CH3CO + H2 4.100E+13 0.00 4200. ! 31

!CH3HCO + OH = CH3CO + H2O 1.000E+13 0.00 0. ! 32

!CH3HCO + O = CH3CO + OH 5.800E+12 0.00 1790. ! 33

!CH3HCO + CH3 = CH3CO + CH4 1.700E+12 0.0 8440.0! 34

!CH3HCO + CH2 = CH3CO + CH3 1.660E+12 0.0 3510. ! 35

!CH3HCO + HO2 = CH3CO + H2O2 1.700E+12 0.00 10700. ! 36

!CH3HCO + CH3O2 = CH3CO + CH4O2 1.150E+11 0.0 10000.0! 37

!CH3CO + O = CH3 + CO2 1.000E+13 0.00 0. ! 38

!CH3CO + H = CH3 + HCO 1.000E+14 0.0 0. ! 39

!CH3CO + OH = CH3 + CO + OH 3.000E+13 0.0 0. ! 40

!CH3CO + HO2 = CH3 + CO2 + OH 3.000E+13 0.0 0. ! 42

!CH3CO + CH3 = C2H6 + CO 5.000E+13 0.00 0. ! 43

!

!HCOOCH3 = HCO + CH3O 3.200E+09 1.60 51800. ! 44

!HCOOCH3 = CO2 + CH4 2.950E+09 0.00 24500. ! 45

!HCOOCH3 + O = COOCH3 + OH 5.300E+11 0.60 1470. ! 46

!HCOOCH3 + H = COOCH3 + H2 1.600E+08 1.60 1000. ! 47

!HCOOCH3 + OH = COOCH3 + H2O 1.200E+09 1.30 -150. ! 48

!HCOOCH3 + HO2 = COOCH3 + H2O2 4.000E+12 0.00 6100. ! 49

!HCOOCH3 + CH3 = COOCH3 + CH4 1.000E-02 4.50 1800. ! 50

!COOCH3 = CH3 + CO2 8.730E+42 -8.62 22400. ! 51

!

140

CH3O + CO = CH3 + CO2 1.570E+14 0.00 11800. !CGS 52

CH3O + M = CH2O + H + M 1.000E+14 0.00 25000. !CGS 53

CH3O + H = CH2O + H2 2.000E+13 0.00 0. !CGS 54

CH3O + OH = CH2O + H2O 1.000E+13 0.00 0. !CGS 55

CH3O + O = CH2O + OH 1.000E+13 0.00 0. !CGS 56

CH3O + O2 = CH2O + HO2 1.200E+11 0.00 2600. !CGS 57 10

CH3 + HO2 = CH3O + OH 5.000E+13 0.00 0. !CGS 58

CH3 + O2 = CH3O + O 4.670E+13 0.00 30000. !CGS 59

CH3 + O2 = CH2O + OH 3.800E+11 0.00 9000. !CGS 60 4.8 9000

CH3 + O2 = CH3O2 3.020E+59 -15.0 17204. !CGS 61 3.02

CH3O2 + HO2 = CH4O2 + O2 4.630E+11 0.0 -2583. !CGS 24

CH3O2 + CH4 = CH4O2 + CH3 1.810E+11 0.0 18480. !CGS 25

CH3O2 + CH3 = CH3O + CH3O 2.410E+13 0.0 0. !CGS 26 2.410E+13

CH3O2 + O = CH3O + O2 3.610E+13 0.0 0. !CGS 27

CH3O2 + H = CH3O + OH 9.640E+13 0.0 0. !CGS 28

CH3O2 + CH2O = CH4O2 + HCO 1.000E+12 0.0 11665. !CGS 29

CH3O2 + C2H6 = CH4O2 + C2H5 2.950E+11 0.0 14944. !CGS 30

CH3O2 + CH3O2 = CH3O + CH3O + O2 2.800E+11 0.0 -780. !CGS 31 11

CH3O2 + H2O2 = CH4O2 + HO2 2.400E+12 0.0 10000. !CGS 32

CH4O2 = CH3O + OH 3.000E+16 0.0 42920. !CGS 33 6.000E+16

CH3O2 + C2H4 = C2H3 + CH4O2 7.100E+11 0.0 17110. !CGS 34

CH4O2 + OH = CH3O2 + H2O 1.000E+13 0.0 -258. !CGS 35 ! 8.2

CH4O2 + O = CH3O2 + OH 2.000E+13 0.0 4750. !

CH3 + O = CH2O + H 8.000E+13 0.00 0. !CGS 36

CH3 + OH = CH2 + H2O 7.500E+06 2.00 5000. !CGS 37

CH3 + OH = CH2O + H2 4.000E+12 0.00 0. !CGS 38

CH3O + H = CH3 + OH 1.000E+14 0.00 0. !CGS 39

CO + O + M = CO2 + M 6.170E+14 0.00 3000. !CGS 40

CO + OH = CO2 + H 3.510E+07 1.30 -758. !CGS 41

141

CO + O2 = CO2 + O 1.600E+13 0.00 41000. !CGS 42

HO2 + CO = CO2 + OH 5.800E+13 0.00 22930. !CGS 43

!

H2 + O2 = OH + OH 1.700E+13 0.00 47780. !CGS 44

H2 + OH = H2O + H 1.170E+09 1.30 3626. !CGS 45

O + OH = O2 + H 4.000E+14 -0.50 0. !CGS 46

O + H2 = OH + H 5.060E+04 2.67 6290. !CGS 47

H + HO2 = O + H2O 3.100E+10 0.00 3590. !CGS 48

O + OH + M = HO2 + M 1.000E+16 0.00 0. !CGS 49

H2O/21./ CO2/5.0/ H2/3.3/ CO/2.0/

H + O2 + M = HO2 + M 3.600E+17 -0.72 0. !CGS 50

H2O/21./ CO2/5.0/ H2/3.3/ CO/2.0/

OH + HO2 = H2O + O2 7.500E+12 0.00 0. !CGS 51

H + HO2 = OH + OH 1.700E+14 0.0 875. !CGS 52

O + HO2 = O2 + OH 1.400E+13 0.00 1073. !CGS 53

OH + OH = O + H2O 6.000E+08 1.30 0. !CGS 54

H + H + M = H2 + M 1.000E+18 -1.00 0. !CGS 55

H2/0./ H2O/0./ CO2/0./

H + H + H2 = H2 + H2 9.200E+16 -0.60 0. !CGS 56

H + H + H2O = H2 + H2O 6.000E+19 -1.25 0. !CGS 57

H + H + CO2 = H2 + CO2 5.490E+20 -2.00 0. !CGS 58

H + OH + M = H2O + M 1.600E+22 -2.00 0. !CGS 59

H + O + M = OH + M 6.200E+16 -0.60 0. !CGS 60

O + O + M = O2 + M 1.890E+13 0.00 -1788. !CGS 61

H + HO2 = H2 + O2 1.250E+13 0.00 0. !CGS 62

HO2 + HO2 = H2O2 + O2 2.000E+12 0.00 0. !CGS 63

H2O2 + M = OH + OH + M 4.300E+16 0.00 45500. !CGS 64

H2O/21./ CO2/5.0/ H2/3.3/ CO/2.0/

H2O2 + H = HO2 + H2 1.600E+12 0.00 3800. !CGS 65

142

H2O2 + OH = H2O + HO2 1.000E+13 0.00 1800. !CGS 66

H2O2 + H = H2O + OH 1.000E+13 0.00 3590. !CGS

H2O2 + O = H2O + O2 8.400E+11 0.00 4260. !CGS

H2O2 + O = OH + HO2 2.000E+13 0.00 5900. !CGS

H2 + HO2 = H2O + OH 6.500E+11 0.00 18800. !CGS

!

!CO2 + N = NO + CO 1.900E+11 0.00 3400. !CGS 67

!N2O + O = N2 + O2 1.400E+12 0.00 10810. !CGS 68

!N2O + O = NO + NO 2.900E+13 0.00 23150. !CGS 69

!N2O + H = N2 + OH 4.400E+14 0.00 18880. !CGS 70

!N2O + OH = N2 + HO2 2.000E+12 0.00 21060. !CGS

!N2O + M = N2 + O + M 1.300E+11 0.00 59620. !CGS

!N + NO = N2 + O 3.270E+12 0.30 0. !CGS

!N + O2 = NO + O 6.400E+09 1.00 6280. !CGS

!N + OH = NO + H 7.333E+13 0.00 1120. !CGS

!

CH2O + O2 = HCO + HO2 6.200E+13 0.00 39000. !CGS

CH2O + O = HCO + OH 1.800E+13 0.00 3080. !CGS

CH2O + H = HCO + H2 2.190E+08 1.80 3000. !CGS

CH2O + OH = HCO + H2O 2.430E+10 1.20 -447. !CGS 09

CH2O + HO2 = HCO + H2O2 3.000E+12 0.00 8000. !CGS 12

CH2O + M = CO + H2 + M 6.250E+15 0.00 69540. !CGS

CH2O + M = HCO + H + M 4.000E+23 -1.66 91120. !CGS

!H2 + CO = CH2O 4.300E+07 1.50 79600. !CGS

HCO + HCO = CH2O + CO 3.010E+13 0.00 0. !CGS

HCO + OH = H2O + CO 1.000E+14 0.00 0. !CGS

HCO + H = H2 + CO 1.190E+13 0.30 0. !CGS

HCO + O = OH + CO 3.000E+13 0.00 0. !CGS

HCO + O = H + CO2 3.000E+13 0.00 0. !CGS

143

HCO + O2 = HO2 + CO 3.300E+13 -0.40 0. !CGS

HCO + M = H + CO + M 1.870E+17 -1.00 17000. !CGS

!HCO + H + M = CH2O + M 1.000E+12 0.48 -260. !CGS

HCO + HO2 = CO2 + OH + H 3.000E+13 0.00 0. !CGS

CH4 + O2 = CH3 + HO2 7.900E+13 0.00 56000. !CGS

!CH3 + HO2 = CH4 + O2 1.000E+12 0.00 0. !CGS

CH4 + H = CH3 + H2 6.600E+08 1.60 10840. !CGS

CH4 + OH = CH3 + H2O 1.600E+06 2.10 2460. !CGS

CH4 + O = CH3 + OH 1.020E+09 1.50 8604. !CGS 99

CH4 + HO2 = CH3 + H2O2 1.000E+13 0.00 18700. !CGS 100

CH4 + CH2 = CH3 + CH3 4.000E+12 0.00 -570. !CGS 101

CH3 + CH2O = CH4 + HCO 5.500E+03 2.80 6000. !CGS 102

CH3 + HCO = CH4 + CO 1.200E+14 0.00 0. !CGS 103

CH3 + H = CH4 1.900E+36 -7.00 9050. !CGS 104

CH3 + H = CH2 + H2 9.000E+13 0.00 15100. !CGS 105

CH3 + CH3O = CH4 + CH2O 4.300E+14 0.00 0. !CGS 106 3.3

CH3 + CH3 = C2H6 2.700D+53 -12.0 19400. !CGS

CH3 + CH3 = C2H5 + H 4.990E+12 .100 10600. !CGS

!CH2 + H2 = CH3 + H 5.000E+05 2.00 7230. !CGS

CH2 + OH = CH2O + H 2.500E+13 0.00 0. !CGS 107

CH2 + O2 = HCO + OH 4.300E+10 0.00 -500. !CGS 108

CH2 + O2 = CO2 + H2 6.900E+11 0.00 500. !CGS 109

CH2 + O2 = CO + H2O 2.000E+10 0.00 -1000. !CGS 110

CH2 + O2 = CH2O + O 5.000E+13 0.00 9000. !CGS 111

CH2 + O2 = CO2 + H + H 1.600E+12 0.00 1000. !CGS

CH2 + O2 = CO + OH + H 8.600E+10 0.00 -500. !

CH2 + CH2 = C2H2 + H2 1.200E+13 0.0 800. !

CH2 + CH2 = C2H2 + H + H 1.200E+14 0.0 800. !

CH2 + CO2 = CH2O + CO 1.000E+11 0.00 1000. !CGS 112

144

CH3 + HCO = CH2O + CH2 3.000E+13 0.00 0. !CGS 113

CH3 + C2H4 = CH4 + C2H3 6.620E+00 3.70 9482. !CGS 114

CH3 + CH3 = C2H4 + H2 1.000E+15 0.00 31000. !CGS 115

CH3 + CH2 = C2H4 + H 3.000E+13 0.00 -570. !CGS 116

C2H4 + H = C2H3 + H2 1.100E+14 0.00 8500. !CGS 117

C2H4 + O = CH3 + HCO 1.600E+09 1.20 746. !CGS 118

C2H4 + O = CH2O + CH2 3.000E+04 1.88 180. !CGS 119

C2H4 + O = C2H3 + OH 1.510E+07 1.91 3790. !CGS 120

C2H4 + OH = CH2O + CH3 6.000E+13 0.0 960. !CGS 121 ! 13

C2H4 + HO2 = C2H3 + H2O2 7.100E+11 0.0 17110. !CGS 122

C2H4 + OH = C2H3 + H2O 8.020E+13 0.00 5955. !CGS 123 ! 6.02 5955

C2H4 + M = C2H2 + H2 + M 1.500E+15 0.00 55800. !CGS 124

C2H4 + M = C2H3 + H + M 2.600E+17 0.0 96570. !CGS 125

C2H4 + H = C2H5 2.600E+43 -9.25 52580. !CGS 126

C2H6 + O2 = C2H5 + HO2 1.000E+13 0.00 48960. !CGS 127

C2H5 + O2 = C2H4 + HO2 2.000E+10 0.0 -2200. !CGS 128

C2H4 + O2 = C2H3 + HO2 4.200E+14 0.00 57590. !CGS 128 ! 14

C2H4 + C2H4 = C2H5 + C2H3 5.000E+14 0.0 64700. !CGS 129 ! 14

C2H5 + HO2 = C2H4 + H2O2 3.000E+11 0.00 0. !CGS 130

C2H2 + O2 = HCO + HCO 4.000E+12 0.00 28000. !CGS 2.0

C2H2 + O = CH2 + CO 1.020E+07 2.00 1900. !CGS 131

C2H2 + H + M = C2H3 + M 5.540E+12 0.00 2410. !CGS 132

C2H3 + H = C2H2 + H2 4.000E+13 0.00 0. !CGS 133

C2H3 + O2 = CH2O + HCO 4.000E+12 0.00 -250. !CGS 134

C2H3 + OH = C2H2 + H2O 3.000E+13 0.00 0. !CGS 135

C2H3 + CH2 = C2H2 + CH3 3.000E+13 0.00 0. !CGS 136

C2H3 + HCO = C2H4 + CO 6.034E+13 0.0 0. !CGS 137

C2H3 + C2H3 = C2H2 + C2H4 1.450E+13 0.0 0.0

C2H3 + O = C2H2 + OH 1.000E+13 0.0 0.0

145

C2H2 + OH = CH3 + CO 4.830E-04 4.00 -2000. !CGS 138

C2H3 = C2H2 + H 4.600E+40 -8.80 46200.

END


The following 71-species, 375-reaction n-heptane mechanism combines a core n-heptane

mechanism by Golovitchev [153] (first 165 reactions) and a comprehensive NOx mechanism

from Glarborg [213] (remaining 210 reactions).

! N-HEPTANE MECHANISM

ELEMENTS

H C O N

END

SPECIES

C7H16 O2 N2 CO2 H2O CO H2 CH4 C2H2 C2H4 H2O2 HO2 OH H

O C CH3 CH3O CH2 CH2O CH3O2 CH4O2 HCO C7H15-1 C7H15-2

C7H15O2 C7H14O2H C7H14O2HO2 C7KET12 C6H12 C5H11CHO C2N2

C5H11CO C5H11 C4H9 C3H7 C3H6 C3H5 C3H4 C2H3 C2H5 C2H6 NCN

CH CH2 CH2(S) NO CN N N2O NO2 HCN NCO HCN HCNO NH H2CN

CH3CN HNCO CH2CN HOCN NH2 HNO NO3 HONO NH3 H2NO NNH N2H2

HCCO C2H CH2CO CH2OH

END

REACTIONS

C7H16 + H = C7H15-1 + H2 5.600E+07 2.0 7667.0!

C7H16 + H = C7H15-2 + H2 4.380E+07 2.0 4750.0!

C7H16 + OH = C7H15-1 + H2O 8.610E+09 1.10 1815.0!

C7H16 + OH = C7H15-2 + H2O 4.500E+09 1.30 690.5!

146

C7H16 + HO2 = C7H15-1 + H2O2 1.120E+13 0.0 19300.0!

C7H16 + HO2 = C7H15-2 + H2O2 1.650E+13 0.0 16950.0!

C7H16 + O2 = C7H15-1 + HO2 2.500E+13 0.0 48810.0!

C7H16 + O2 = C7H15-2 + HO2 2.000E+14 0.0 47380.0!

C7H15-1 + O2 = C7H15O2 2.000E+12 0.0 0.0!

C7H15-2 + O2 = C7H15O2 2.000E+12 0.0 0.0!

C7H15O2 = C7H14O2H 6.000E+11 0.0 20380.0!

C7H14O2H + O2 = C7H14O2HO2 4.600E+11 0.0 0.0!

C7H14O2HO2 = C7KET12 + OH 1.000E+09 0.0 7480.0!

C7KET12 = C5H11CHO + CH2O + O 1.050E+16 0.0 4.110E+4! 16

C5H11CHO + O2 = C5H11CO + HO2 2.000E+13 0.5 4.220E+4!

C5H11CHO + OH = C5H11CO + H2O 1.000E+13 0.0 0.000E+0!

C5H11CHO + H = C5H11CO + H2 4.000E+13 0.0 4.200E+3!

C5H11CHO + O = C5H11CO + OH 5.000E+12 0.0 1.790E+3!

C5H11CHO + HO2 = C5H11CO + H2O2 2.800E+12 0.0 1.360E+4!

C5H11CHO + CH3 = C5H11CO + CH4 1.700E+12 0.0 8.440E+3!

C5H11CHO + CH3O2 = C5H11CO + CH4O2 1.000E+12 0.0 9.500E+3!

C5H11CO = C5H11 + CO 1.000E+11 0.0 9.600E+3!

C5H11 = C2H4 + C3H7 3.200E+13 0.0 28300.0!

C7H15-1 = C2H4 + C5H11 2.500E+13 0.0 28810.0!

C7H15-2 = C4H9 + C3H6 2.200E+13 0.0 28100.0!

C7H15-1 = C7H15-2 3.600E+16 0.0 80700.0!

C4H9 = C2H5 + C2H4 2.500E+13 0.0 28810.0!

C3H7 = C2H4 + CH3 9.600E+13 0.0 30950.0!

C3H7 = C3H6 + H 1.250E+14 0.0 36900.0!

C3H7 + O2 = C3H6 + HO2 1.000E+12 0.0 4980.0!

C3H6 = C2H3 + CH3 3.150E+15 0.0 85500.0!

C3H6 + H = C3H5 + H2 5.000E+12 0.0 1500.0!

C3H6 + CH3 = C3H5 + CH4 9.000E+12 0.0 8480.0!

147

C3H5 = C3H4 + H 4.000E+13 0.0 69760.0!

C3H5 + H = C3H4 + H2 1.000E+13 0.0 0.0!

C3H5 + O2 = C3H4 + HO2 6.000E+11 0.0 10000.0!

C3H4 + OH = C2H3 + CH2O 1.000E+12 0.0 0.0!

C3H4 + OH = C2H4 + HCO 1.000E+12 0.0 0.0!

!

!C2H5 + O = CH3HCO + H 5.300E+13 0.0 0.0! 23

!C2H4 + HO2 = HCOOCH3 + H 4.040E+09 0.0 -840. ! 24

!C2H4 + HO2 = CH3HCO + OH 2.200E+13 0.0 17200.0! 25

!C2H4 + CH3O = CH3HCO + CH3 3.000E+13 0.0 14500.0 ! 26

!C2H4 + CH3O2 = CH3HCO + CH3O 7.000E+13 0.0 14500.0 ! 27

!C2H3 + OH = CH3HCO 3.000E+13 0.0 0.0! 28

!

!CH3HCO = CH3 + HCO 7.080E+15 0.00 81760. ! 28

!CH3HCO = CH3CO + H 5.000E+14 0.00 87860. ! 29

!CH3HCO + O2 = CH3CO + HO2 2.000E+13 0.50 42200. ! 30

!CH3HCO + H = CH3CO + H2 4.100E+13 0.00 4200. ! 31

!CH3HCO + OH = CH3CO + H2O 1.000E+13 0.00 0. ! 32

!CH3HCO + O = CH3CO + OH 5.800E+12 0.00 1790. ! 33

!CH3HCO + CH3 = CH3CO + CH4 1.700E+12 0.0 8440.0! 34

!CH3HCO + CH2 = CH3CO + CH3 1.660E+12 0.0 3510. ! 35

!CH3HCO + HO2 = CH3CO + H2O2 1.700E+12 0.00 10700. ! 36

!CH3HCO + CH3O2 = CH3CO + CH4O2 1.150E+11 0.0 10000.0! 37

!CH3CO + O = CH3 + CO2 1.000E+13 0.00 0. ! 38

!CH3CO + H = CH3 + HCO 1.000E+14 0.0 0. ! 39

!CH3CO + OH = CH3 + CO + OH 3.000E+13 0.0 0. ! 40

!CH3CO + HO2 = CH3 + CO2 + OH 3.000E+13 0.0 0. ! 42

!CH3CO + CH3 = C2H6 + CO 5.000E+13 0.00 0. ! 43

!

148

!HCOOCH3 = HCO + CH3O 3.200E+09 1.60 51800. ! 44

!HCOOCH3 = CO2 + CH4 2.950E+09 0.00 24500. ! 45

!HCOOCH3 + O = COOCH3 + OH 5.300E+11 0.60 1470. ! 46

!HCOOCH3 + H = COOCH3 + H2 1.600E+08 1.60 1000. ! 47

!HCOOCH3 + OH = COOCH3 + H2O 1.200E+09 1.30 -150. ! 48

!HCOOCH3 + HO2 = COOCH3 + H2O2 4.000E+12 0.00 6100. ! 49

!HCOOCH3 + CH3 = COOCH3 + CH4 1.000E-02 4.50 1800. ! 50

!COOCH3 = CH3 + CO2 8.730E+42 -8.62 22400. ! 51

!

CH3O + CO = CH3 + CO2 1.570E+14 0.00 11800. !CGS 52

CH3O + M = CH2O + H + M 1.000E+14 0.00 25000. !CGS 53

CH3O + H = CH2O + H2 2.000E+13 0.00 0. !CGS 54

CH3O + OH = CH2O + H2O 1.000E+13 0.00 0. !CGS 55

CH3O + O = CH2O + OH 1.000E+13 0.00 0. !CGS 56

CH3O + O2 = CH2O + HO2 1.200E+11 0.00 2600. !CGS 57 10

CH3 + HO2 = CH3O + OH 5.000E+13 0.00 0. !CGS 58

CH3 + O2 = CH3O + O 4.670E+13 0.00 30000. !CGS 59

CH3 + O2 = CH2O + OH 3.800E+11 0.00 9000. !CGS 60 4.8 9000

CH3 + O2 = CH3O2 3.020E+59 -15.0 17204. !CGS 61 3.02

CH3O2 + HO2 = CH4O2 + O2 4.630E+11 0.0 -2583. !CGS 24

CH3O2 + CH4 = CH4O2 + CH3 1.810E+11 0.0 18480. !CGS 25

CH3O2 + CH3 = CH3O + CH3O 2.410E+13 0.0 0. !CGS 26 2.410E+13

CH3O2 + O = CH3O + O2 3.610E+13 0.0 0. !CGS 27

CH3O2 + H = CH3O + OH 9.640E+13 0.0 0. !CGS 28

CH3O2 + CH2O = CH4O2 + HCO 1.000E+12 0.0 11665. !CGS 29

CH3O2 + C2H6 = CH4O2 + C2H5 2.950E+11 0.0 14944. !CGS 30

CH3O2 + CH3O2 = CH3O + CH3O + O2 2.800E+11 0.0 -780. !CGS 31 11

CH3O2 + H2O2 = CH4O2 + HO2 2.400E+12 0.0 10000. !CGS 32

CH4O2 = CH3O + OH 3.000E+16 0.0 42920. !CGS 33 6.000E+16

149

CH3O2 + C2H4 = C2H3 + CH4O2 7.100E+11 0.0 17110. !CGS 34

CH4O2 + OH = CH3O2 + H2O 1.000E+13 0.0 -258. !CGS 35 ! 8.2

CH4O2 + O = CH3O2 + OH 2.000E+13 0.0 4750. !

CH3 + O = CH2O + H 8.000E+13 0.00 0. !CGS 36

CH3 + OH = CH2 + H2O 7.500E+06 2.00 5000. !CGS 37

CH3 + OH = CH2O + H2 4.000E+12 0.00 0. !CGS 38

CH3O + H = CH3 + OH 1.000E+14 0.00 0. !CGS 39

CO + O + M = CO2 + M 6.170E+14 0.00 3000. !CGS 40

CO + OH = CO2 + H 3.510E+07 1.30 -758. !CGS 41

CO + O2 = CO2 + O 1.600E+13 0.00 41000. !CGS 42

HO2 + CO = CO2 + OH 5.800E+13 0.00 22930. !CGS 43

!

H2 + O2 = OH + OH 1.700E+13 0.00 47780. !CGS 44

H2 + OH = H2O + H 1.170E+09 1.30 3626. !CGS 45

O + OH = O2 + H 4.000E+14 -0.50 0. !CGS 46

O + H2 = OH + H 5.060E+04 2.67 6290. !CGS 47

H + HO2 = O + H2O 3.100E+10 0.00 3590. !CGS 48

O + OH + M = HO2 + M 1.000E+16 0.00 0. !CGS 49

H2O/21./ CO2/5.0/ H2/3.3/ CO/2.0/

H + O2 + M = HO2 + M 3.600E+17 -0.72 0. !CGS 50

H2O/21./ CO2/5.0/ H2/3.3/ CO/2.0/

OH + HO2 = H2O + O2 7.500E+12 0.00 0. !CGS 51

H + HO2 = OH + OH 1.700E+14 0.0 875. !CGS 52

O + HO2 = O2 + OH 1.400E+13 0.00 1073. !CGS 53

OH + OH = O + H2O 6.000E+08 1.30 0. !CGS 54

H + H + M = H2 + M 1.000E+18 -1.00 0. !CGS 55

H2/0./ H2O/0./ CO2/0./

H + H + H2 = H2 + H2 9.200E+16 -0.60 0. !CGS 56

H + H + H2O = H2 + H2O 6.000E+19 -1.25 0. !CGS 57

150

H + H + CO2 = H2 + CO2 5.490E+20 -2.00 0. !CGS 58

H + OH + M = H2O + M 1.600E+22 -2.00 0. !CGS 59

H + O + M = OH + M 6.200E+16 -0.60 0. !CGS 60

O + O + M = O2 + M 1.890E+13 0.00 -1788. !CGS 61

H + HO2 = H2 + O2 1.250E+13 0.00 0. !CGS 62

HO2 + HO2 = H2O2 + O2 2.000E+12 0.00 0. !CGS 63

H2O2 + M = OH + OH + M 4.300E+16 0.00 45500. !CGS 64

H2O/21./ CO2/5.0/ H2/3.3/ CO/2.0/

H2O2 + H = HO2 + H2 1.600E+12 0.00 3800. !CGS 65

H2O2 + OH = H2O + HO2 1.000E+13 0.00 1800. !CGS 66

H2O2 + H = H2O + OH 1.000E+13 0.00 3590. !CGS

H2O2 + O = H2O + O2 8.400E+11 0.00 4260. !CGS

H2O2 + O = OH + HO2 2.000E+13 0.00 5900. !CGS

H2 + HO2 = H2O + OH 6.500E+11 0.00 18800. !CGS

!

!CO2 + N = NO + CO 1.900E+11 0.00 3400. !CGS 67

!N2O + O = N2 + O2 1.400E+12 0.00 10810. !CGS 68

!N2O + O = NO + NO 2.900E+13 0.00 23150. !CGS 69

!N2O + H = N2 + OH 4.400E+14 0.00 18880. !CGS 70

!N2O + OH = N2 + HO2 2.000E+12 0.00 21060. !CGS

!N2O + M = N2 + O + M 1.300E+11 0.00 59620. !CGS

!N + NO = N2 + O 3.270E+12 0.30 0. !CGS

!N + O2 = NO + O 6.400E+09 1.00 6280. !CGS

!N + OH = NO + H 7.333E+13 0.00 1120. !CGS

!

CH2O + O2 = HCO + HO2 6.200E+13 0.00 39000. !CGS

CH2O + O = HCO + OH 1.800E+13 0.00 3080. !CGS

CH2O + H = HCO + H2 2.190E+08 1.80 3000. !CGS

CH2O + OH = HCO + H2O 2.430E+10 1.20 -447. !CGS 09

151

CH2O + HO2 = HCO + H2O2 3.000E+12 0.00 8000. !CGS 12

CH2O + M = CO + H2 + M 6.250E+15 0.00 69540. !CGS

CH2O + M = HCO + H + M 4.000E+23 -1.66 91120. !CGS

!H2 + CO = CH2O 4.300E+07 1.50 79600. !CGS

HCO + HCO = CH2O + CO 3.010E+13 0.00 0. !CGS

HCO + OH = H2O + CO 1.000E+14 0.00 0. !CGS

HCO + H = H2 + CO 1.190E+13 0.30 0. !CGS

HCO + O = OH + CO 3.000E+13 0.00 0. !CGS

HCO + O = H + CO2 3.000E+13 0.00 0. !CGS

HCO + O2 = HO2 + CO 3.300E+13 -0.40 0. !CGS

HCO + M = H + CO + M 1.870E+17 -1.00 17000. !CGS

!HCO + H + M = CH2O + M 1.000E+12 0.48 -260. !CGS

HCO + HO2 = CO2 + OH + H 3.000E+13 0.00 0. !CGS

CH4 + O2 = CH3 + HO2 7.900E+13 0.00 56000. !CGS

!CH3 + HO2 = CH4 + O2 1.000E+12 0.00 0. !CGS

CH4 + H = CH3 + H2 6.600E+08 1.60 10840. !CGS

CH4 + OH = CH3 + H2O 1.600E+06 2.10 2460. !CGS

CH4 + O = CH3 + OH 1.020E+09 1.50 8604. !CGS 99

CH4 + HO2 = CH3 + H2O2 1.000E+13 0.00 18700. !CGS 100

CH4 + CH2 = CH3 + CH3 4.000E+12 0.00 -570. !CGS 101

CH3 + CH2O = CH4 + HCO 5.500E+03 2.80 6000. !CGS 102

CH3 + HCO = CH4 + CO 1.200E+14 0.00 0. !CGS 103

CH3 + H = CH4 1.900E+36 -7.00 9050. !CGS 104

CH3 + H = CH2 + H2 9.000E+13 0.00 15100. !CGS 105

CH3 + CH3O = CH4 + CH2O 4.300E+14 0.00 0. !CGS 106 3.3

CH3 + CH3 = C2H6 2.700D+53 -12.0 19400. !CGS

CH3 + CH3 = C2H5 + H 4.990E+12 .100 10600. !CGS

!CH2 + H2 = CH3 + H 5.000E+05 2.00 7230. !CGS

CH2 + OH = CH2O + H 2.500E+13 0.00 0. !CGS 107

152

CH2 + O2 = HCO + OH 4.300E+10 0.00 -500. !CGS 108

CH2 + O2 = CO2 + H2 6.900E+11 0.00 500. !CGS 109

CH2 + O2 = CO + H2O 2.000E+10 0.00 -1000. !CGS 110

CH2 + O2 = CH2O + O 5.000E+13 0.00 9000. !CGS 111

CH2 + O2 = CO2 + H + H 1.600E+12 0.00 1000. !CGS

CH2 + O2 = CO + OH + H 8.600E+10 0.00 -500. !

CH2 + CH2 = C2H2 + H2 1.200E+13 0.0 800. !

CH2 + CH2 = C2H2 + H + H 1.200E+14 0.0 800. !

CH2 + CO2 = CH2O + CO 1.000E+11 0.00 1000. !CGS 112

CH3 + HCO = CH2O + CH2 3.000E+13 0.00 0. !CGS 113

CH3 + C2H4 = CH4 + C2H3 6.620E+00 3.70 9482. !CGS 114

CH3 + CH3 = C2H4 + H2 1.000E+15 0.00 31000. !CGS 115

CH3 + CH2 = C2H4 + H 3.000E+13 0.00 -570. !CGS 116

C2H4 + H = C2H3 + H2 1.100E+14 0.00 8500. !CGS 117

C2H4 + O = CH3 + HCO 1.600E+09 1.20 746. !CGS 118

C2H4 + O = CH2O + CH2 3.000E+04 1.88 180. !CGS 119

C2H4 + O = C2H3 + OH 1.510E+07 1.91 3790. !CGS 120

C2H4 + OH = CH2O + CH3 6.000E+13 0.0 960. !CGS 121 ! 13

C2H4 + HO2 = C2H3 + H2O2 7.100E+11 0.0 17110. !CGS 122

C2H4 + OH = C2H3 + H2O 8.020E+13 0.00 5955. !CGS 123 ! 6.02 5955

C2H4 + M = C2H2 + H2 + M 1.500E+15 0.00 55800. !CGS 124

C2H4 + M = C2H3 + H + M 2.600E+17 0.0 96570. !CGS 125

C2H4 + H = C2H5 2.600E+43 -9.25 52580. !CGS 126

C2H6 + O2 = C2H5 + HO2 1.000E+13 0.00 48960. !CGS 127

C2H5 + O2 = C2H4 + HO2 2.000E+10 0.0 -2200. !CGS 128

C2H4 + O2 = C2H3 + HO2 4.200E+14 0.00 57590. !CGS 128 ! 14

C2H4 + C2H4 = C2H5 + C2H3 5.000E+14 0.0 64700. !CGS 129 ! 14

C2H5 + HO2 = C2H4 + H2O2 3.000E+11 0.00 0. !CGS 130

C2H2 + O2 = HCO + HCO 4.000E+12 0.00 28000. !CGS 2.0

153

C2H2 + O = CH2 + CO 1.020E+07 2.00 1900. !CGS 131

C2H2 + H + M = C2H3 + M 5.540E+12 0.00 2410. !CGS 132

C2H3 + H = C2H2 + H2 4.000E+13 0.00 0. !CGS 133

C2H3 + O2 = CH2O + HCO 4.000E+12 0.00 -250. !CGS 134

C2H3 + OH = C2H2 + H2O 3.000E+13 0.00 0. !CGS 135

C2H3 + CH2 = C2H2 + CH3 3.000E+13 0.00 0. !CGS 136

C2H3 + HCO = C2H4 + CO 6.034E+13 0.0 0. !CGS 137

C2H3 + C2H3 = C2H2 + C2H4 1.450E+13 0.0 0.0

C2H3 + O = C2H2 + OH 1.000E+13 0.0 0.0

C2H2 + OH = CH3 + CO 4.830E-04 4.00 -2000. !CGS 138

C2H3 = C2H2 + H 4.600E+40 -8.80 46200.

!------------REACTIONS ADDED FOR INCLUDING NOX CHEMISTRY FROM GLARBORG----------

C+NO=CN+O 2.0E13 0. 0

C+NO=CO+N 2.8E13 0. 0

C+N2=CN+N 6.3E13 0. 46019

C+N2O=CN+NO 5.1E12 0. 0

CH+NO2=HCO+NO 1.0E14 0. 0

CH+NO = HCN+O 4.8E13 0.00 0

CH+NO = HCO+N 3.4E13 0.00 0

CH+NO = NCO+H 1.9E13 0.00 0

CH+N=CN+H 1.3E13 0. 0

CH+N2=HCN+N 3.7E07 1.42 20723

CH+N2O=HCN+NO 1.9E13 0. -511

CH2+NO=HCN+OH 2.2E12 0. -378

CH2+NO=HCNO+H 1.3E12 0. -378

CH2+NO2=CH2O+NO 5.9E13 0. 0

CH2+N=HCN+H 5.0E13 0. 0

CH2+N2=HCN+NH 1.0E13 0. 74000

H2CN+N=N2+CH2 2.0E13 0. 0

154

CH2(S)+NO=HCN+OH 2.0E13 0. 0

CH2(S)+NO=CH2+NO 1.0E14 0. 0

CH2(S)+HCN=CH3+CN 5.0E13 0. 0

C2H3+N=HCN+CH2 2.0E13 0. 0

H+CH3CN=HCN+CH3 4.0E7 2. 2000

O+CH3CN=NCO+CH3 1.5E4 2.64 4980

CH4+CN=CH3+HCN 6.2E04 2.64 -437

NCO+CH4 = CH3+HNCO 9.8E12 0.00 8120

CH3+NO=HCN+H2O 1.5E-1 3.523 3950

CH3+NO=H2CN+OH 1.5E-1 3.523 3950

CH3+NO2=CH3O+NO 1.4E13 0. 0

CH3+N=H2CN+H 7.1E13 0. 0

CH3+CN=CH2CN+H 1.0E14 0. 0

CH3+HOCN=CH3CN+OH 5.0E12 0. 2000

N2O+M=N2+O+M 4.0E14 0. 56100

N2/1.7/ O2/1.4/ H2O/12/ CO/1.5/ CO2/3/

HCN+O=NH+CO 3.5E03 2.64 4980

HCN+OH=NH2+CO 7.8E-4 4. 4000

CN+O=CO+N 7.7E13 0. 0

CN+CO2=NCO+CO 3.7E06 2.16 26884

H+NO+M=HNO+M 2.7E15 0.0 -600

H2O/10/ O2/1.5/ H2/2/ CO2/3/ N2/0.0/

H+NO+N2=HNO+N2 7.0E19 -1.50 0

NO+O+M=NO2+M 7.5E19 -1.41 0

N2/1.7/ O2/1.5/ H2O/10/

OH+NO+M=HONO+M 5.1E23 -2.51 -68

H2O/5/

HO2+NO=NO2+OH 2.1E12 0.00 -479

NO2+H=NO+OH 8.4E13 0.0 0

155

NO2+O=NO+O2 3.9E12 0.0 -238

NO2+O(+M)=NO3(+M) 1.3E13 0.0 0

LOW/1.0E28 -4.08 2470./

N2/1.5/ O2/1.5/ H2O/18.6/

NO2+NO2=NO+NO+O2 1.6E12 0.0 26123

NO2+NO2=NO3+NO 9.6E09 0.73 20900

NO3+H=NO2+OH 6.0E13 0.0 0

NO3+O=NO2+O2 1.0E13 0.0 0

NO3+OH=NO2+HO2 1.4E13 0.0 0

NO3+HO2=NO2+O2+OH 1.5E12 0.0 0

NO3+NO2=NO+NO2+O2 5.0E10 0.0 2940

HNO+H=H2+NO 4.5E11 0.72 655

HNO+O=NO+OH 1.0E13 0.0 0

HNO+OH=NO+H2O 3.6E13 0.0 0

HNO+O2=HO2+NO 1.0E13 0.0 25000

HNO+NO2=HONO+NO 6.0E11 0.0 2000

HNO+HNO=N2O+H2O 9.0E08 0.0 3100

HNO+NH2=NH3+NO 3.63E6 1.63 -1252

H2NO+M=HNO+H+M 2.5E15 0.0 50000

H2O/5/ N2/2/

H2NO+H=HNO+H2 3.0E7 2.0 2000

H2NO+H=NH2+OH 5.0E13 0.0 0

H2NO+O=HNO+OH 3.0E7 2.0 2000

H2NO+O = NH2+O2 2.0E14 0 0

H2NO+OH=HNO+H2O 2.0E7 2.0 1000

H2NO+NO=HNO+HNO 2.0E04 2.0 13000

H2NO+NO2=HNO+HONO 6.0E11 0.0 2000

HONO+H=H2+NO2 1.2E13 0.0 7352

HONO+O=OH+NO2 1.2E13 0.0 5961

156

HONO+OH=H2O+NO2 4.0E12 0.0 0

NH3+M = NH2+H+M 2.2E16 0 93470

NH3+H=NH2+H2 6.4E05 2.39 10171

NH3+O=NH2+OH 9.4E06 1.94 6460

NH3+OH=NH2+H2O 2.0E06 2.04 566

NH3+HO2=NH2+H2O2 3.0E11 0.0 22000

NH2+H=NH+H2 4.0E13 0.00 3650

NH2+O=HNO+H 6.6E14 -0.50 0

NH2+O=NH+OH 6.8E12 0. 0

NH2+OH=NH+H2O 4.0E06 2. 1000

NH2+HO2=H2NO+OH 5.0E13 0.0 0

NH2+HO2=NH3+O2 1.0E13 0.0 0

NH2+NO=NNH+OH 8.9E12 -0.35 0

NH2+NO=N2+H2O 1.3E16 -1.25 0

DUP

NH2+NO=N2+H2O -8.9E12 -0.35 0

DUP

NH2+NO2=N2O+H2O 3.2E18 -2.2 0

NH2+NO2=H2NO+NO 3.5E12 0. 0

NH2+H2NO=NH3+HNO 3.0E12 0.0 1000

HONO+NH2=NO2+NH3 71.1 3.02 -4941

NH2+NH2=N2H2+H2 8.5E11 0. 0

NH2+NH=N2H2+H 5.0E13 0. 0

NH2+N=N2+H+H 7.2E13 0. 0

NH+H=N+H2 3.0E13 0. 0

NH+O=NO+H 9.2E13 0. 0

NH+OH=HNO+H 2.0E13 0. 0

NH+OH=N+H2O 5.0E11 0.50 2000

NH+O2=HNO+O 4.6E05 2. 6500

157

NH+O2=NO+OH 1.3E06 1.5 100

NH+NO=N2O+H 2.9E14 -0.4 0

DUP

NH+NO=N2O+H -2.2E13 -0.23 0

DUP

NH+NO=N2+OH 2.2E13 -0.23 0

NH+NO2=N2O+OH 1.0E13 0. 0

NH+NH=N2+H+H 2.5E13 0. 0

NH+N=N2+H 3.0E13 0. 0

N+OH=NO+H 3.8E13 0. 0

N+O2=NO+O 6.4E09 1. 6280

N+NO=N2+O 3.3E12 0.30 0

N2H2+M=NNH+H+M 5.0E16 0. 50000

H2O/15/ O2/2/ N2/2/ H2/2/

N2H2+H=NNH+H2 5.0E13 0. 1000

N2H2+O=NH2+NO 1.0E13 0. 0

N2H2+O=NNH+OH 2.0E13 0. 1000

N2H2+OH=NNH+H2O 1.0E13 0. 1000

N2H2+NO=N2O+NH2 3.0E12 0. 0

N2H2+NH2=NH3+NNH 1.0E13 0. 1000

N2H2+NH=NNH+NH2 1.0E13 0. 1000

NNH=N2+H 1.0E7 0. 0

NNH+H=N2+H2 1.0E14 0. 0

NNH+O=N2+OH 8.0E13 0. 0

NNH+O=N2O+H 1.0E14 0. 0

NNH+O=NH+NO 5.0E13 0. 0

NNH+OH=N2+H2O 5.0E13 0. 0

NNH+O2=N2+HO2 2.0E14 0. 0

NNH+O2=N2+O2+H 5.0E13 0. 0

158

NNH+NO=N2+HNO 5.0E13 0. 0

NNH+NH2=N2+NH3 5.0E13 0. 0

NNH+NH=N2+NH2 5.0E13 0. 0

N2O+H=N2+OH 3.3E10 0. 4729

DUP

N2O+H=N2+OH 4.4E14 0. 19254

DUP

N2O+O=NO+NO 6.6E13 0. 26630

N2O+O=N2+O2 1.0E14 0. 28000

N2O+OH=N2+HO2 1.3E-2 4.72 36561

N2O+OH=HNO+NO 1.2E-4 4.33 25081

N2O+NO=NO2+N2 5.3E05 2.23 46281

CN+H2=HCN+H 3.0E05 2.45 2237

HCN+O=NCO+H 1.4E04 2.64 4980

HCN+O=CN+OH 2.7E09 1.58 29200

HCN+OH = CN+H2O 3.9E06 1.83 10300

HCN+OH=HOCN+H 5.9E04 2.40 12500

HCN+OH=HNCO+H 2.0E-3 4. 1000

HCN+CN=C2N2+H 1.5E07 1.71 1530

CN+OH=NCO+H 4.0E13 0. 0

CN+O2=NCO+O 7.5E12 0. -389

CN+NO2=NCO+NO 5.3E15 -0.752 344

CN+NO2=CO+N2O 4.9E14 -0.752 344

CN+NO2=N2+CO2 3.7E14 -0.752 344

CN+HNO=HCN+NO 1.8E13 0.00 0

CN+HONO=HCN+NO2 1.2E13 0.00 0

CN+N2O=NCN+NO 3.9E03 2.6 3696

CN+HNCO=HCN+NCO 1.5E13 0. 0

CN+NCO=NCN+CO 1.8E13 0. 0

159

HNCO+M=NH+CO+M 1.1E16 0. 86000

HNCO+H=NH2+CO 2.2E07 1.7 3800

HNCO+O=HNO+CO 1.5E08 1.57 44012

HNCO+O=NH+CO2 9.8E7 1.41 8524

HNCO+O=NCO+OH 2.2E6 2.11 11425

HNCO+OH=NCO+H2O 6.4E05 2. 2563

HNCO+HO2=NCO+H2O2 3.0E11 0. 22000

HNCO+O2=HNO+CO2 1.0E12 0. 35000

HNCO+NH2=NH3+NCO 5.0E12 0. 6200

HNCO+NH=NH2+NCO 3.0E13 0. 23700

HOCN+H=NCO+H2 2.0E07 2. 2000

HOCN+O=NCO+OH 1.5E04 2.64 4000

HOCN+OH=NCO+H2O 6.4E05 2. 2563

HCNO+H=HCN+OH 1.0E14 0 12000

HCNO+O=HCO+NO 2.0E14 0. 0

HCNO+OH=CH2O+NO 4.0E13 0. 0

NCO+M=N+CO+M 3.1E16 -0.50 48000

NCO+H=NH+CO 5.0E13 0. 0

NCO+O=NO+CO 4.7E13 0. 0

NCO+OH=NO+HCO 5.0E12 0. 15000

NCO+O2=NO+CO2 2.0E12 0. 20000

NCO+H2=HNCO+H 7.6E02 3. 4000

NCO+HCO=HNCO+CO 3.6E13 0. 0

NCO+NO=N2O+CO 6.2E17 -1.73 763

NCO+NO=N2+CO2 7.8E17 -1.73 763

NCO+NO2=CO+NO+NO 2.5E11 0. -707

NCO+NO2=CO2+N2O 3.0E12 0. -707

NCO+HNO=HNCO+NO 1.8E13 0. 0

NCO+HONO=HNCO+NO2 3.6E12 0. 0

160

NCO+N=N2+CO 2.0E13 0. 0

NCO+NCO=N2+CO+CO 1.8E13 0. 0

C2N2+O=NCO+CN 4.6E12 0. 8880

C2N2+OH=HOCN+CN 1.9E11 0. 2900

NCN+O=CN+NO 1.0E14 0. 0

NCN+OH=HCN+NO 5.0E13 0. 0

NCN+H=HCN+N 1.0E14 0. 0

NCN+O2=NO+NCO 1.0E13 0. 0

H+CH3CN=CH2CN+H2 3.0E7 2. 1000

OH+CH3CN=CH2CN+H2O 2.0E7 2. 2000

CH2CN+O=CH2O+CN 1.0E14 0. 0.

CN+CH2OH=CH2CN+OH 5.0E13 0. 0

H2CN+M=HCN+H+M 3.0E14 0. 22000

CO+NO2 = CO2+NO 9.0E13 0. 33779

CO+N2O=N2+CO2 3.2E11 0. 20237

CO2+N=NO+CO 1.9E11 0. 3400

CH2O+NCO=HNCO+HCO 6.0E12 0. 0

CH2O+NO2 = HCO+HONO 8.0E02 2.77 13730

HCO+NO=HNO+CO 7.2E12 0. 0

HCO+NO2 = CO+HONO 1.2E23 -3.29 2355

HCO+NO2 = H+CO2+NO 8.4E15 -0.75 1930

HCO+HNO=CH2O+NO 6.0E11 0. 2000

C2H6+CN=C2H5+HCN 1.2E05 2.77 -1788

C2H6+NCO = C2H5+HNCO 1.5E-9 6.89 -2910

C2H4+CN = C2H3+HCN 5.9E14 -0.24 0

C2H3+NO=C2H2+HNO 1.0E12 0. 1000

C2H2+NCO = HCCO+HCN 1.4E12 0.00 1815

C2H+NO=CN+HCO 2.1E13 0. 0

CH2CO+CN=HCCO+HCN 2.0E13 0. 0

161

HCCO+NO=HCNO+CO 7.2E12 0. 0

HCCO+NO=HCN+CO2 1.6E13 0. 0

HCCO+NO2=HCNO+CO2 1.6E13 0. 0

HCCO+N=HCN+CO 5.0E13 0. 0

END

Vita

Hedan Zhang

The Pennsylvania State University- 2006-2012. Doctor of Philosophy in Mechanical

Engineering. Graduate Research Assistant under Dr. Daniel C. Haworth working in the

field of turbulent combustion using PDF Methods in internal combustion engines.

Tsinghua University- 2004-2006. Master of Science in Engineering: Thermal Engineering

and Power Engineering

Tsinghua University- 2000-2004. Bachelor of Science in Engineering: Power Engineering

and Engineering Thermophysics

effects of turbulence-chemistry interactions in …

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