Chemkin Theory Manual

17.0

Chemkin Theory Manual

Chemkin? Software

CK-THE-15151-1601-UG-1 January 2016

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Copyright? 2016 Reaction Design. All rights reserved. No part of this book may be reproduced in any form or by any means without express written permission from Reaction Design.

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Literature Citation for CHEMKIN:

ANSYS Chemkin Theory Manual 17.0 (15151) should be cited as: ANSYS Chemkin Theory Manual 17.0 (15151), Reaction Design: San Diego, 2015.

ANSYS CHEMKIN THEORY MANUAL 17.0

Contents

Table of Contents

Acknowledgments .................................................................................................................................................... 15

1 Introduction................................................................................................................................................................17

1.1 Chemistry--Species and Phases..............................................................................................................17 1.2 Species Indexing Conventions ..................................................................................................................19 1.3 Footnote Notation ........................................................................................................................................20

2 Thermodynamic Expressions................................................................................................................................21

2.1 State Variables .............................................................................................................................................22 2.1.1 Gas-phase State Variables .......................................................................................................22 2.1.2 Surface State Variables.............................................................................................................23

2.2 Gas Equation of State and Conversion Formulas ..................................................................................24 2.2.1 Mass Fraction to Mole Fraction ................................................................................................26 2.2.2 Mass Fraction to Molar Concentration ....................................................................................26 2.2.3 Mole Fraction to Mass Fraction ................................................................................................26 2.2.4 Mole Fraction to Molar Concentration .....................................................................................26 2.2.5 Molar Concentration to Mass Fraction ....................................................................................27 2.2.6 Molar Concentration to Mole Fraction .....................................................................................27

2.3 Standard-state Thermodynamic Properties.............................................................................................27 2.3.1 Specific Heat Capacity at Constant Pressure........................................................................27 2.3.2 Species Molar Enthalpy.............................................................................................................29 2.3.3 Species Molar Entropy...............................................................................................................31 2.3.4 Standard Form of Polynomial Fits ...........................................................................................31 2.3.5 Other Species Molar Properties ...............................................................................................32 2.3.6 Specific (Mass-based) Species Properties.............................................................................33 2.3.7 Molar and Specific Properties of Gas Mixtures .....................................................................34 2.3.8 Properties of Surface or Bulk Mixtures ...................................................................................36

3 Gas-phase Chemical Rate Expressions..............................................................................................................37

3.1 Basic Rate Expressions..............................................................................................................................37 3.2 Non-integer Stoichiometric Coefficients ...................................................................................................41 3.3 Reactions with Arbitrary Reaction Order..................................................................................................41 3.4 Three-body Reactions.................................................................................................................................43 3.5 Collision Frequency Efficiency Expression..............................................................................................44 3.6 Pressure-dependent Reactions .................................................................................................................44

3.6.1 Unimolecular/Recombination Fall-off Reactions ...................................................................45 3.6.2 Chemically Activated Bimolecular Reactions.........................................................................49

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Table of Contents

3.6.3 General Pressure Dependence Using Logarithmic Interpolation .......................................51 3.6.4 Multiple-well Multiple-channel Reactions Using Chebyshev Polynomials.........................52 3.7 Landau-Teller Formulation of the Rate Expressions..............................................................................55 3.8 Other Allowable Rate Constant Fitting Options ......................................................................................55 3.9 Rates of Creation and Destruction of Species ........................................................................................56 3.10 Separating Temperature from Composition Dependence ....................................................................58

4 Surface Chemical Rate Expressions ...................................................................................................................59

4.1 Atomic vs. Open Site Reaction Formalism ..............................................................................................59 4.2 Basic Surface Reaction Rate Expressions ..............................................................................................62 4.3 Equilibrium Constants for Reactions Involving Surface Species .........................................................64 4.4 Non-integer Stoichiometric Coefficients and Arbitrary Reaction Orders.............................................64 4.5 Surface-coverage Modification of Rate Expression ...............................................................................65 4.6 Sticking Coefficients ....................................................................................................................................66 4.7 Langmuir-Hinshelwood and Eley-Rideal Reactions ...............................................................................69 4.8 Plasma-surface Interactions.......................................................................................................................74

4.8.1 Bohm Rate Expression for Ionic Reactions............................................................................74 4.8.2 General Ion-energy-dependent Rate Expression..................................................................75 4.8.3 Ion-enhanced Reaction Yield Expression...............................................................................76 4.9 Manipulation of Chemical Rate Sensitivity Coefficients ........................................................................77 4.10 Flux-matching Conditions at a Gas-surface Interface............................................................................79 4.11 Surface Site Non-conservation..................................................................................................................81

5 Gas-phase Species Transport Properties ..........................................................................................................83

5.1 Pure Species Viscosity and Binary Diffusion Coefficients ....................................................................84 5.2 Pure Species Thermal Conductivities ......................................................................................................88 5.3 The Pure Species Fitting Procedure.........................................................................................................91 5.4 The Mass, Momentum, and Energy Fluxes.............................................................................................92 5.5 The Mixture-averaged Properties..............................................................................................................95 5.6 Thermal Diffusion Ratios ............................................................................................................................96 5.7 The Multicomponent Properties ................................................................................................................97 5.8 Species Conservation ...............................................................................................................................102

6 Determining Chemical Equilibria........................................................................................................................105

6.1 Minimization of Gibb's Free Energy........................................................................................................106

7 Normal Shock Equations......................................................................................................................................109

7.1 Shock Tube Experiments .........................................................................................................................109 7.2 Rankine-Hugoniot Relations for Normal Shocks ..................................................................................111

7.2.1 Shock Tube Laboratory Time and Gas-particle Time.........................................................111 7.2.2 Incident Shock Initial Conditions ............................................................................................113 7.2.3 Reflected Shock Initial Conditions .........................................................................................116 7.3 Downstream Model Equations.................................................................................................................121 7.3.1 Shock Tube Boundary-layer Effects......................................................................................123

8 Homogeneous 0-D Reactor Models ...................................................................................................................127

8.1 Reactor Clusters--Special Case of Reactor Networks .......................................................................128 8.2 Assumptions and Limitations ...................................................................................................................128 8.3 General Equations .....................................................................................................................................129

8.3.1 Mass Conservation and Gas-phase Species Equations....................................................131 8.3.2 Surface Species Equations.....................................................................................................133 8.3.3 Bulk Species Equations During Deposition..........................................................................136

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Theory Manual

8.3.4 Bulk Species Equations During Etch.....................................................................................139 8.3.5 Non-constant Surface Phase Site Densities ........................................................................139 8.3.6 Gas Energy Equation...............................................................................................................140 8.3.7 Heat Exchange Between Reactors in Reactor Clusters.....................................................143 8.3.8 Optional Wall Energy Balance and Heat Capacity Effects ................................................145 8.3.9 Treatment of Activities for Bulk Species ...............................................................................148 8.4 Internal Combustion Engine Model.........................................................................................................148 8.4.1 Piston Offsets ............................................................................................................................151 8.4.2 Heat-transfer Options for the IC HCCI Engine Model.........................................................154 8.4.3 Multi-zone HCCI Model ...........................................................................................................156 8.4.4 SI Engine Zonal Simulator ......................................................................................................161 8.5 Plasma Systems ........................................................................................................................................167 8.5.1 Electron Energy Equation for Plasma Systems...................................................................168 8.5.2 Gas Energy Equation Adjusted for Plasma Systems .........................................................172 8.5.3 Application of the Bohm Condition for Ion Fluxes to Surfaces..........................................172 8.5.4 Summary of Solution Variables for Homogeneous Systems.............................................174

9 Partially Stirred Reactor (PaSR) Model .............................................................................................................177

9.1 The Joint PDF Transport Equation .........................................................................................................179 9.2 Molecular Mixing Models ..........................................................................................................................181 9.3 Reactor Equations .....................................................................................................................................183 9.4 Stochastic Simulation................................................................................................................................184

9.4.1 Through-flow (Convection)......................................................................................................184 9.4.2 Molecular Mixing.......................................................................................................................185 9.4.3 Chemical Reaction ...................................................................................................................185

10 Plug-flow Assumptions and Equations.............................................................................................................187

10.1 Honeycomb Monolith Reactor Calculations ..........................................................................................192 10.2 Plasma Plug-flow Extensions...................................................................................................................194

11 Boundary-layer Channel Flow.............................................................................................................................197

11.1 Boundary-layer Equations ........................................................................................................................198 11.2 Boundary Conditions .................................................................................................................................204 11.3 Initial Conditions on Species Concentrations at Boundaries ..............................................................205 11.4 Implementation of Multicomponent Transport.......................................................................................206 11.5 Thermal Diffusion.......................................................................................................................................208 11.6 Finite Difference Approximations ............................................................................................................208 11.7 Non-Uniform Grid.......................................................................................................................................210

12 1-D Premixed Laminar Flames ............................................................................................................................211

12.1 1-D Flame Equations.................................................................................................................................212 12.2 Mixture-averaged Transport Properties .................................................................................................214 12.3 Multicomponent Transport Properties ....................................................................................................215 12.4 Gas and Particulate Thermal Radiation Model for Flames .................................................................216

12.4.1 Particulate Absorption Coefficient..........................................................................................217 12.5 Boundary Conditions .................................................................................................................................219

12.5.1 Boundary Condition Details ....................................................................................................220 12.6 Finite Difference Approximations ............................................................................................................221 12.7 Transient Forms of the Equations ...........................................................................................................223

13 Opposed-flow and Stagnation Flames ..............................................................................................................225

13.1 Axisymmetric and Planar Diffusion .........................................................................................................225

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