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Acknowledgments
1. Introduction
1.1. Chemistry—Species and Phases
1.2. Species Indexing Conventions
1.3. Footnote Notation
2. Thermodynamic Expressions
2.1. State Variables
2.1.1. Gas-phase State Variables
2.1.2. Surface State Variables
2.2. Gas Equation of State and Conversion Formulas
2.2.1. Mass Fraction to Mole Fraction
2.2.2. Mass Fraction to Molar Concentration
2.2.3. Mole Fraction to Mass Fraction
2.2.4. Mole Fraction to Molar Concentration
2.2.5. Molar Concentration to Mass Fraction
2.2.6. Molar Concentration to Mole Fraction
2.3. Standard-state Thermodynamic Properties
2.3.1. Specific Heat Capacity at Constant Pressure
2.3.2. Species Molar Enthalpy
2.3.2.1. Surface-coverage Dependent Enthalpy for Surface Species
2.3.3. Species Molar Entropy
2.3.4. Standard Form of Polynomial Fits
2.3.5. Other Species Molar Properties
2.3.6. Specific (Mass-based) Species Properties
2.3.7. Molar and Specific Properties of Gas Mixtures
2.3.8. Properties of Surface or Bulk Mixtures
2.4. Real Gas Model
2.4.1. Introduction to Real Gas Model
2.4.1.1. Cubic Equation of State for Pure Substance
2.4.2. The P-V-T Behavior of a Real-Gas Mixture
2.4.2.1. Single-Fluid Approach
2.4.2.1.1. The Pseudocritical Method
2.4.2.1.2. The van der Waals Mixing Rule (for the cubic equation of state)
2.4.3. Departure Function of Thermodynamic Property
2.4.3.1. Departure Function of Thermodynamic Property for Real Gas Species
2.4.3.2. Departure Function of Real Gas Mixture
2.4.4. Fugacity Ratio
2.4.4.1. Fugacity of Real Gas Species
2.4.4.2. Equilibrium Constant
2.5. Liquid Species
2.5.1. Liquid Phase State Variables
2.5.2. Liquid Density and Conversion Formulas
2.5.2.1. Liquid Species Density Models
2.5.2.1.1. Curve-Fitting Density Equations
2.5.2.1.2. Rackett Density Model
2.5.2.1.3. Density of Liquid Mixture
2.5.2.1.4. Tait Equation for Pressure-dependency
2.5.2.2. Mass Fraction and Mole Fraction
2.5.2.2.1. Liquid Mass Fraction
2.5.2.2.2. Mass to Molar Concentration
2.5.2.2.3. Mole to Molar Concentration
2.5.2.2.4. Molar Concentration to Mass
2.5.3. Standard-State Liquid Properties
2.5.3.1. Critical Properties
2.5.3.2. Liquid Standard-State Enthalpy
2.5.3.3. Liquid Standard-State Entropy
2.5.3.4. Heat of Vaporization
2.5.3.5. Vapor Pressure
2.5.4. Liquid Species Thermodynamic Properties
2.5.4.1. Heat Capacity at Constant Pressure Cp
2.5.4.2. Liquid Species Enthalpy H
2.5.4.3. Liquid Species Entropy S
2.5.4.4. Thermodynamic Properties of Liquid Mixture
2.5.5. Other Liquid Species Properties
2.5.5.1. Viscosity
2.5.5.2. Thermal Conductivity
2.5.5.3. Surface Tension
3. Gas-phase Chemical Rate Expressions
3.1. Basic Rate Expressions
3.2. Non-integer Stoichiometric Coefficients
3.3. Reactions with Arbitrary Reaction Order
3.4. Three-body Reactions
3.5. Collision Frequency Efficiency Expression
3.6. Pressure-dependent Reactions
3.6.1. Unimolecular/Recombination Fall-off Reactions
3.6.2. Chemically Activated Bimolecular Reactions
3.6.3. General Pressure Dependence Using Logarithmic Interpolation
3.6.4. Usage of Multiple Bath-gas Species
3.6.5. Multiple-well Multiple-channel Reactions Using Chebyshev Polynomials
3.7. Landau-Teller Formulation of the Rate Expressions
3.8. Other Allowable Rate Constant Fitting Options
3.9. Rates of Creation and Destruction of Species
3.10. Separating Temperature from Composition Dependence
4. Surface Chemical Rate Expressions
4.1. Atomic vs. Open Site Reaction Formalism
4.2. Basic Surface Reaction Rate Expressions
4.3. Equilibrium Constants for Reactions Involving Surface Species
4.4. Non-integer Stoichiometric Coefficients and Arbitrary Reaction Orders
4.5. Surface-coverage Modification of Rate Expression
4.6. Sticking Coefficients
4.7. Langmuir-Hinshelwood and Eley-Rideal Reactions
4.8. Plasma-surface Interactions
4.8.1. Bohm Rate Expression for Ionic Reactions
4.8.2. General Ion-energy-dependent Rate Expression
4.8.3. Ion-enhanced Reaction Yield Expression
4.9. Manipulation of Chemical Rate Sensitivity Coefficients
4.10. Flux-matching Conditions at a Gas-surface Interface
4.11. Surface Site Non-conservation
4.12. Given K-Product for Ion Dissociation Reactions in the Liquid Phase
5. Gas-phase Species Transport Properties
5.1. Pure Species Viscosity and Binary Diffusion Coefficients
5.2. Pure Species Thermal Conductivities
5.3. The Pure Species Fitting Procedure
5.4. The Mass, Momentum, and Energy Fluxes
5.5. The Mixture-averaged Properties
5.6. Thermal Diffusion Ratios
5.7. The Multicomponent Properties
5.8. Species Conservation
6. Determining Chemical Equilibria
6.1. Minimization of Gibb’s Free Energy
7. Normal Shock Equations
7.1. Shock Tube Experiments
7.2. Rankine-Hugoniot Relations for Normal Shocks
7.2.1. Shock Tube Laboratory Time and Gas-particle Time
7.2.2. Incident Shock Initial Conditions
7.2.3. Reflected Shock Initial Conditions
7.3. Downstream Model Equations
7.3.1. Shock Tube Boundary-layer Effects
7.3.2. Thermicity
8. Homogeneous 0-D Reactor Models
8.1. Reactor Clusters—Special Case of Reactor Networks
8.2. Assumptions and Limitations
8.3. General Equations
8.3.1. Mass Conservation and Gas-phase Species Equations
8.3.2. Surface Species Equations
8.3.3. Bulk Species Equations During Deposition
8.3.4. Bulk Species Equations During Etch
8.3.5. Non-constant Surface Phase Site Densities
8.3.6. Gas Energy Equation
8.3.7. Heat Exchange Between Reactors in Reactor Clusters
8.3.8. Optional Wall Energy Balance and Heat Capacity Effects
8.3.9. Treatment of Activities for Bulk Species
8.4. Internal Combustion Engine Model
8.4.1. Piston Offsets
8.4.2. Special Piston Motions
8.4.2.1. Conventional Opposed-Piston Movement
8.4.2.2. Opposed-Piston Opposed-Cylinder Movement
8.4.2.3. Piecewise-Linear Crank Angle-Volume Profile
8.4.3. Empirical Heat-transfer Options for the IC Engine Models
8.4.3.1. Woschni Correlation for Gas Velocity IC Engine Cylinder
8.4.3.2. Huber-Woschni Correlation for Gas Velocity in IC Engine Cylinder
8.4.3.3. Wall-Function IC Engine Heat Transfer Model
8.4.4. Multi-zone HCCI Model
8.4.4.1. Model Description
8.4.4.2. Governing Equations
8.4.4.2.1. Species
8.4.4.2.2. Internal Energy/Temperature
8.4.4.2.3. Volume/Accumulated Volume
8.4.4.2.4. Cylinder pressure
8.4.5. SI Engine Zonal Simulator
8.4.5.1. Fuel Burn Rate: Mass Exchange Rate Between the Zones
8.4.5.2. Governing Equations for the Combustion Stage
8.4.5.2.1. Mass Conservation of Zones
8.4.5.2.2. Conservation of Species Mass
8.4.5.2.3. Conservation of Energy
8.4.5.2.4. Zone Volume
8.4.5.2.5. Cylinder Pressure
8.4.6. Direct-Injection Diesel Engine Simulator
8.4.6.1. Liquid Properties
8.4.6.2. Discretization of the Injection
8.4.6.3. Liquid Injection Sub-Models
8.4.6.3.1. Injector Nozzle Flow
8.4.6.3.2. Liquid Jet Break-Up Time
8.4.6.3.3. Initial Droplet Size
8.4.6.3.4. Spray-Tip Penetration
8.4.6.4. Air Entrainment Model
8.4.6.5. Spray Parcel Mixing Model
8.4.6.6. Vaporization Model
8.4.6.6.1. Vapor Mass Production Rates
8.4.6.6.2. Energy Balance at the Droplet Surface
8.4.6.7. Governing Equations of the Droplet Variables
8.4.6.7.1. Conservation of Liquid Mass
8.4.6.7.2. Conservation of Droplet Energy
8.4.6.7.3. Droplet Diameter
8.5. Plasma Systems
8.5.1. Electron Energy Equation for Plasma Systems
8.5.2. Gas Energy Equation Adjusted for Plasma Systems
8.5.3. Application of the Bohm Condition for Ion Fluxes to Surfaces
8.5.4. Summary of Solution Variables for Homogeneous Systems
9. Multiphase Reactor Model
9.1. Governing Equations
9.1.1. Mass Conservation
9.1.2. Energy Conservation
9.1.3. Species Equations
9.1.4. Phase/Mixture Density
9.1.5. Global Constraints
9.2. Phase Transfer Models
9.2.1. Vapor Liquid Equilibrium Model for Phase Change
9.2.2. Mass Transfer
9.2.3. Heat Transfer
9.3. Supported Reaction Types and Capabilities
9.4. Limitations in the Current Release
10. Partially Stirred Reactor (PaSR) Model
10.1. The Joint PDF Transport Equation
10.2. Molecular Mixing Models
10.3. Reactor Equations
10.4. Stochastic Simulation
10.4.1. Through-flow (Convection)
10.4.2. Molecular Mixing
10.4.3. Chemical Reaction
11. Plug-flow Assumptions and Equations
11.1. Honeycomb Monolith Reactor Calculations
11.2. Plasma Plug-flow Extensions
12. Boundary-layer Channel Flow
12.1. Boundary-layer Equations
12.2. Boundary Conditions
12.3. Initial Conditions on Species Concentrations at Boundaries
12.4. Implementation of Multicomponent Transport
12.5. Thermal Diffusion
12.6. Finite Difference Approximations
12.7. Non-Uniform Grid
13. 1-D Premixed Laminar Flames
13.1. 1-D Flame Equations
13.2. Mixture-averaged Transport Properties
13.3. Multicomponent Transport Properties
13.4. Gas and Particulate Thermal Radiation Model for Flames
13.4.1. Particulate Absorption Coefficient
13.5. Boundary Conditions
13.5.1. Boundary Condition Details
13.6. Finite Difference Approximations
13.7. Transient Forms of the Equations
13.8. Options for Generating Flame Speed Tables for Autoigniting and Failed Cases
13.8.1. Flame Speeds Under Autoigniting Conditions
13.8.2. Flame Speeds for Failed Cases
14. Opposed-flow and Stagnation Flames
14.1. Axisymmetric and Planar Diffusion
14.2. Pre-mixed Burner-stabilized Stagnation Flame
14.3. Emission Indices
14.4. Finite-difference Approximations
14.5. Regrid Operation
14.6. Simulation of Flame Extinction
14.6.1. One-point Control
14.6.2. Two-point Control
14.6.3. Extinction Strain Rate
14.7. Flamelet Calculation
14.7.1. Flamelet Generation with Opposed-flow Flame Model
14.7.2. Diffusion Flamelet Generation Based on Stoichiometric Scalar Dissipation Rate
15. Stagnation-Flow and Rotating-Disk CVD
15.1. Impinging-flow Conservation Equations
15.2. Finite Difference Approximations
16. Numerical Solution Methods
16.1. Steady-state Solver for Homogeneous Systems
16.1.1. Starting Estimates
16.1.2. Modified Damped Newton’s Method for 0-D Reactors
16.1.3. Jacobian Matrix
16.1.4. Pseudo Time-Stepping Procedure
16.2. Steady-state 1-D Solution Methods
16.2.1. Starting Estimates
16.2.2. Continuation Start-up Procedure and User-Specified Temperature Profile
16.2.3. Modified Damped Newton’s Method
16.2.4. Adaptation
16.3. Transient Solution Method
17. Sensitivity Analysis
17.1. Sensitivity Analysis for Steady-state Solutions
17.2. Sensitivity Analysis For Transient Solutions
17.3. Normalization of Sensitivity Coefficients
17.4. Sensitivity of Bulk Growth or Etch Rates
18. Rate-of-production Analysis
18.1. 0-D Homogeneous and Plug-flow Systems
19. Particle Size-Distribution Tracking
19.1. Description and Properties of a Particle Population
19.1.1. Moments of Particle-Size Distribution Functions
19.1.2. Total Particle Number of a Particle Population
19.1.3. Total and Average Particle Mass
19.1.4. Total and Average Geometric Properties of a Particle Population
19.2. Sectional Model for Tracking Particle-Size Distribution
19.2.1. Sectional Model Details
19.2.2. Creation/Selection of Sections
19.2.2.1. Validation of the Sectional Model in the Particle Tracking Facility
19.2.2.2. Sample Results
19.3. Particle Inception
19.3.1. Nucleation Reaction Description
19.3.2. Nucleation Reaction Data
19.3.3. Site Density and Surface Species on Nuclei
19.3.4. Determination of Stoichiometric Coefficients
19.3.5. Native Surface Sites
19.3.6. Nucleation Rates
19.3.6.1. Implementation for Method of Moments
19.3.6.2. Implementation for Section Method
19.3.6.3. AGeneral Guideline for the Nucleation Rate Parameters
19.4. Particle Coagulation
19.4.1. Collision Efficiency
19.4.2. Implementation for Method of Moments
19.4.3. Sectional Method
19.4.3.1. Particle-Size-Dependent Collision Efficiency
19.4.4. Validation of Coagulation Model
19.5. Chemical Processes on Particle Surfaces
19.5.1. Surface Reaction and Particle Size Distribution Function
19.5.2. Rates of Gas-Particle Reactions
19.5.2.1. Implementation for Method of Moment
19.5.2.2. Implementation for Sectional Method
19.5.3. Collision Diameter Data for Gas Species
19.5.4. Reaction Rate Between Surface Species on Particles
19.5.4.1. Implementation for Method of Moments
19.5.4.2. Implementation for Sectional Method
19.6. Particle Depletion
19.6.1. Particle-Depletion Model Details
19.6.2. Soot Burnout Example
19.7. Particle Transport Equations
19.7.1. Transport Equations for Size Moments
19.7.2. Transport Equations for Particle Surface Species
19.7.2.1. Implementation for Method of Moments
19.7.3. Implementation Considerations for Different Reactor Models
19.7.4. 0-D Closed and Open Reactors
19.7.5. Plug-Flow Reactor
19.7.6. Flame Simulators
19.8. Particle Aggregation Model
19.8.1. Driving Force for Fusion/Sintering
19.8.2. Aggregate Geometry and Collisions
19.8.3. Aggregation Model for the Moment Method
19.8.3.1. Aggregate Properties
19.8.3.2. Collision Frequency of Aggregates in the Moments Method
19.8.4. Aggregation Model for the Sectional Method
19.8.4.1. Sintering
19.8.4.2. Simple Aggregation Model
19.9. Solution Technique
19.9.1. Keeping the Numbers Well-behaved
19.9.2. Computational Efficiency
19.10. Summary of Particle Tracking Capabilities
20. Uncertainty Analysis
20.1. Reducing the Dimensionality of the System through Polynomial Chaos Expansion
20.2. Solving for the Coefficients of the Expansions
20.2.1. Polynomial Chaos Expansion for Uncertain (Variant) Input Parameters
20.2.2. Polynomial Chaos Expansion for the Model Outputs
20.2.3. Selecting the Points for Model Evaluation
20.2.4. Solving for the Expansion Coefficients for the Model Outputs
20.2.5. Determining the Error of the Approximation
20.2.6. Variance Analysis
21. Tear-stream Algorithm
21.1. An Overview of Tearing
21.2. Mathematical Description
21.3. Tearing algorithm
22. Nomenclature
22.1. Latin Equation Symbols
22.2. Greek Equation Symbols
22.3. Subscript Equation Symbols
Bibliography