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1. Basic Solver Capability Theory
1.1. Documentation Conventions
1.1.1. Dimensions
1.1.2. List of Symbols
1.1.2.1. Subscripts
1.1.3. Variable Definitions
1.1.3.1. Isothermal Compressibility
1.1.3.2. Isentropic Compressibility
1.1.3.3. Reference Pressure
1.1.3.4. Static Pressure
1.1.3.5. Modified Pressure
1.1.3.6. Static Enthalpy
1.1.3.6.1. Material with Variable Density and Specific Heat
1.1.3.7. Total Enthalpy
1.1.3.8. Domain Temperature
1.1.3.9. Static Temperature
1.1.3.9.1. Material with Constant Density and Specific Heat
1.1.3.9.2. Ideal Gas or Solid with cp=f(T)
1.1.3.9.3. Material with Variable Density and Specific Heat
1.1.3.10. Total Temperature
1.1.3.10.1. Material with Constant Density and Specific Heat
1.1.3.10.2. Ideal Gas with constant cp
1.1.3.10.3. Ideal Gas with cp = f(T)
1.1.3.10.4. Material with Variable Density and Specific Heat
1.1.3.11. Entropy
1.1.3.11.1. Material with Constant Density and Specific Heat
1.1.3.11.2. Ideal Gas with constant cp or cp = f(T)
1.1.3.11.3. Material with Variable Density and Specific Heat
1.1.3.12. Total Pressure
1.1.3.12.1. Incompressible Fluids
1.1.3.12.2. Ideal Gases
1.1.3.12.3. Material with Variable Density and Specific Heat
1.1.3.13. Shear Strain Rate
1.1.3.14. Rotating Frame Quantities
1.1.3.14.1. Incompressible Fluids
1.1.3.14.2. Ideal Gases
1.1.3.14.3. Material with Variable Density and Specific Heat
1.1.3.15. Courant Number
1.1.4. Mathematical Notation
1.1.4.1. The Vector Operators
1.1.4.1.1. Gradient Operator
1.1.4.1.2. Divergence Operator
1.1.4.1.3. Dyadic Operator
1.1.4.2. Matrix Transposition
1.1.4.3. The Identity Matrix (Kronecker Delta function)
1.1.4.4. Index Notation
1.2. Governing Equations
1.2.1. Transport Equations
1.2.1.1. The Continuity Equation
1.2.1.2. The Momentum Equations
1.2.1.3. The Total Energy Equation
1.2.1.4. The Thermal Energy Equation
1.2.1.5. Turbulent Flux Closure for Heat Transfer
1.2.2. Equations of State
1.2.2.1. Incompressible Equation of State
1.2.2.2. Ideal Gas Equation of State
1.2.2.3. Real Gas and Liquid Equations of State
1.2.2.3.1. Real Gas Properties
1.2.2.3.1.1. Redlich Kwong Models
1.2.2.3.1.1.1. The Standard Redlich Kwong Model
1.2.2.3.1.1.2. The Aungier Redlich Kwong Model
1.2.2.3.1.1.3. The Soave Redlich Kwong Model
1.2.2.3.1.2. Peng Robinson Model
1.2.2.3.1.3. Real Gas Constitutive Relations
1.2.2.3.2. Real Gas Saturated Vapor Properties
1.2.2.3.3. Real Gas Liquid Properties
1.2.2.3.4. IAPWS Equation of State
1.2.2.3.5. Metastable Superheated Liquid/Supercooled Vapor States
1.2.2.3.6. Numerical Testing to Delineate Metastable Regions
1.2.2.3.7. The Acentric Factor
1.2.2.4. General Equation of State
1.2.3. Conjugate Heat Transfer
1.3. Buoyancy
1.3.1. Full Buoyancy Model
1.3.2. Boussinesq Model
1.4. Immersed Solids
1.4.1. Momentum Sources
1.4.2. Near-Wall Treatment for Immersed Solid Boundary
1.4.2.1. Notation
1.4.2.2. Laminar Flow Treatment
1.4.2.3. Turbulent Flow Treatment
1.4.2.3.1. Wall Distance
1.4.2.3.2. SST Model
1.4.2.3.3. Scalable Wall Function
1.5. Multicomponent Flow
1.5.1. Multicomponent Notation
1.5.2. Scalar Transport Equation
1.5.3. Algebraic Equation for Components
1.5.4. Constraint Equation for Components
1.5.5. Multicomponent Fluid Properties
1.5.6. Energy Equation
1.5.7. Multicomponent Energy Diffusion
1.6. Additional Variables
1.6.1. Transport Equations for Additional Variables
1.6.2. Diffusive Transport Equations for Additional Variables
1.6.3. Poisson Equations for Additional Variables
1.6.4. Algebraic Equations for Additional Variables
1.7. Rotational Forces
1.7.1. Alternate Rotation Model
1.8. Sources
1.8.1. Momentum Sources
1.8.1.1. Isotropic Loss Model
1.8.1.2. Directional Loss Model
1.8.1.3. General Momentum Sources
1.8.1.4. Immersed Solid Sources
1.8.2. General Sources
1.8.3. Mass (Continuity) Sources
1.8.4. Bulk Sources
1.8.5. Radiation Sources
1.8.6. Boundary Sources
1.9. Boundary Conditions
1.9.1. Inlet (Subsonic)
1.9.1.1. Mass and Momentum
1.9.1.1.1. Normal Speed in
1.9.1.1.2. Cartesian Velocity Components
1.9.1.1.3. Cylindrical Velocity Components
1.9.1.1.4. Total Pressure
1.9.1.1.5. Mass Flow Rate
1.9.1.2. Turbulence
1.9.1.2.1. Default Intensity and Autocompute Length Scale
1.9.1.2.2. Intensity and Autocompute Length Scale
1.9.1.2.3. Intensity and Length Scale
1.9.1.2.4. k and Epsilon
1.9.1.3. Heat Transfer
1.9.1.3.1. Static Temperature
1.9.1.3.2. Total Temperature
1.9.1.4. Additional Variables
1.9.2. Inlet (Supersonic)
1.9.2.1. Heat Transfer
1.9.2.1.1. Static Temperature
1.9.2.1.2. Total Temperature
1.9.3. Outlet (Subsonic)
1.9.3.1. Mass and Momentum
1.9.3.1.1. Static Pressure (Uniform)
1.9.3.1.2. Normal Speed
1.9.3.1.3. Cartesian Velocity Components
1.9.3.1.4. Cylindrical Velocity Components
1.9.3.1.5. Average Static Pressure: Over Whole Outlet
1.9.3.1.6. Average Static Pressure: Above or Below Specified Radius
1.9.3.1.7. Average Static Pressure: Circumferential
1.9.3.1.8. Mass Flow Rate: Scale Mass Flows
1.9.3.1.9. Mass Flow Rate: Shift Pressure with or without Pressure Profile
1.9.3.1.10. Mass Flow Rate: Shift Pressure with Circumferential Pressure Averaging
1.9.3.1.11. Exit Corrected Mass Flow Rate
1.9.3.1.12. Radial Equilibrium
1.9.3.2. Turbulence, Heat Transfer, Convected Additional Variables, and Other Scalars
1.9.4. Outlet (Supersonic)
1.9.5. Opening
1.9.5.1. Mass and Momentum
1.9.5.1.1. Cartesian Velocity Components
1.9.5.1.2. Cylindrical Velocity Components
1.9.5.1.3. Pressure and Direction
1.9.5.1.3.1. Loss Coefficient
1.9.5.2. Heat Transfer
1.9.5.2.1. Static Temperature
1.9.5.3. Additional Variables
1.9.6. Wall
1.9.6.1. Mass and Momentum
1.9.6.1.1. No Slip (Not Moving, No Wall Velocity)
1.9.6.1.2. Free Slip
1.9.6.1.3. Finite Slip
1.9.6.1.4. Specified Shear
1.9.6.1.5. No Slip (Moving, with Wall Velocity)
1.9.6.2. Turbulence
1.9.6.3. Heat Transfer
1.9.6.3.1. Adiabatic
1.9.6.3.2. Fixed Temperature
1.9.6.3.3. Heat Flux
1.9.6.3.4. Heat Transfer Coefficient
1.9.6.4. Additional Variables
1.9.7. Symmetry Plane
1.10. Automatic Time Scale Calculation
1.10.1. Fluid Time Scale Estimate
1.10.2. Solid Time Scale Estimate
1.11. Mesh Adaption
1.11.1. Adaption Criteria
1.11.2. Mesh Refinement Implementation in Ansys CFX
1.11.2.1. Adaption in Inflated Regions of the Mesh
1.11.2.2. Adaption to the Original Geometry
1.11.3. Mesh Adaption Limitations
1.11.3.1. Mesh Adaption Tips
1.12. Flow in Porous Media
1.12.1. Full Porous Model
1.12.1.1. Heat Transfer Through the Fluid Only
1.12.1.2. Additional Variable Transfer Through the Fluid Only
1.12.1.3. Heat Transfer Through the Fluid and Solid
1.12.1.4. Additional Variable Transfer Through the Fluid and Solid
1.12.1.5. Time-varying Porosity
1.12.2. Porous Momentum Loss Models
1.13. Wall and Boundary Distance Formulation
1.13.1. 1D Illustration of Concept
1.13.2. Concept Generalized to 3D
1.14. Wall Condensation Theory
1.14.1. Wall Condensation Model
1.14.1.1. Laminar Boundary Layer Model
1.14.1.2. Turbulent Boundary Layer Model
1.14.2. Condensation Heat Transfer (CHT)
1.14.3. Specification of Secondary Fluxes
2. Turbulence and Wall Function Theory
2.1. Turbulence Models
2.1.1. Statistical Turbulence Models and the Closure Problem
2.1.1.1. Reynolds Averaged Navier-Stokes (RANS) Equations
2.2. Eddy Viscosity Turbulence Models
2.2.1. The Zero Equation Model in Ansys CFX
2.2.2. Two Equation Turbulence Models
2.2.2.1. The k-epsilon Model in Ansys CFX
2.2.2.2. Buoyancy Turbulence
2.2.2.3. The RNG k-epsilon Model in Ansys CFX
2.2.2.4. The k-omega Models in Ansys CFX
2.2.2.4.1. The Wilcox k-omega Model
2.2.2.4.2. The Baseline (BSL) k-omega Model
2.2.2.4.3. The Shear Stress Transport (SST) Model
2.2.2.4.3.1. Blending Functions
2.2.2.4.3.2. The Wall Scale Equation
2.2.2.4.3.3. Modifications to SST for High Lift Devices
2.2.2.4.4. The Reattachment Modification (RM) Model
2.2.2.4.5. The GEKO Model
2.2.2.5. Production Limiters
2.2.2.6. Curvature Correction for Two-Equation Models
2.2.3. The Eddy Viscosity Transport Model
2.2.3.1. Low Reynolds Number Formulation
2.3. Reynolds Stress Turbulence Models
2.3.1. The Reynolds Stress Model
2.3.1.1. Pressure-Strain Terms
2.3.2. Omega-Based Reynolds Stress Models
2.3.2.1. The Omega Reynolds Stress Model
2.3.2.2. The BSL Reynolds Stress Model
2.3.2.3. Pressure-Strain Correlation
2.3.2.4. Wall Boundary Condition
2.3.3. Rotating Frame of Reference for Reynolds Stress Models
2.3.4. Explicit Algebraic Reynolds Stress Model
2.3.4.1. Streamline Curvature and System Rotation
2.4. Ansys CFX Laminar-Turbulent Transition Models
2.4.1. Two Equation Gamma Theta Transition Model
2.4.1.1. Overview
2.4.1.2. Transport Equations for the Gamma Theta Transition Model
2.4.1.3. Separation-induced Transition Correction
2.4.1.4. Coupling to the SST Model
2.4.1.5. Gamma Theta Transition Model and Rough Walls
2.4.2. One Equation Intermittency Transition Model
2.4.2.1. Overview
2.4.2.2. Transport Equation for the Intermittency Transition Model
2.4.2.3. Coupling to SST Model
2.4.2.4. Intermittency Transition Model and Rough Walls
2.5. Large Eddy Simulation Theory
2.5.1. Subgrid-Scale Models
2.5.1.1. Smagorinsky Model
2.5.1.1.1. Wall Damping
2.5.1.2. WALE Model
2.5.1.3. Dynamic Smagorinsky-Lilly Model
2.6. Detached Eddy Simulation Theory
2.6.1. SST-DES Formulation Strelets et al.
2.6.2. Delayed and Shielded DES-SST Model Formulation
2.6.3. Stress-Blended Eddy Simulation (SBES)
2.6.3.1. General Concept
2.6.3.2. Example
2.6.4. Discretization of the Advection Terms
2.6.5. Boundary Conditions
2.7. Scale-Adaptive Simulation Theory
2.7.1. Discretization of the Advection Terms
2.8. Modeling Flow Near the Wall
2.8.1. Mathematical Formulation
2.8.1.1. Scalable Wall Functions
2.8.1.2. Solver Yplus and Yplus
2.8.1.3. Automatic Near-Wall Treatment for Omega-Based Models
2.8.1.4. Treatment of Rough Walls
2.8.1.4.1. Rough Wall Treatment for Turbulence Models Based on the Dissipation Equation
2.8.1.4.2. Automatic Rough Wall Treatment for Turbulence Models Based on the Omega Equation
2.8.1.4.3. Transition and Rough Walls
2.8.1.4.4. Wall Function Approach for Omega-Based Turbulence Models
2.8.1.4.5. Treatment of the SST Model for Icing Simulations
2.8.1.5. Heat Flux in the Near-Wall Region
2.8.1.5.1. Scalable Wall Functions
2.8.1.5.2. Automatic Wall Treatment
2.8.1.5.3. Effect of Rough Walls
2.8.1.5.4. Treatment of Compressibility Effects
2.8.1.6. Additional Variables in the Near Wall Region
3. GGI and MFR Theory
3.1. Interface Characteristics
3.2. Numerics
4. Transient Blade Row Modeling Theory
4.1. Profile Transformation
4.2. Time Transformation
4.3. Fourier Transformation
4.4. Harmonic Analysis
4.4.1. Harmonic Balance Control
5. Multiphase Flow Theory
5.1. Multiphase Notation
5.1.1. Multiphase Total Pressure
5.2. The Homogeneous and Inhomogeneous Models
5.2.1. The Inhomogeneous Model
5.2.1.1. Interfacial Area Density
5.2.1.1.1. The Particle Model
5.2.1.1.2. The Mixture Model
5.2.1.1.3. The Free Surface Model
5.2.2. The Homogeneous Model
5.3. Hydrodynamic Equations
5.3.1. Inhomogeneous Hydrodynamic Equations
5.3.1.1. Momentum Equations
5.3.1.2. Continuity Equations
5.3.1.3. Volume Conservation Equation
5.3.1.4. Pressure Constraint
5.3.2. Homogeneous Hydrodynamic Equations
5.3.2.1. Momentum Equations
5.3.2.2. Continuity Equations
5.3.2.3. Volume Conservation Equations
5.3.2.4. Pressure Constraint
5.4. Multicomponent Multiphase Flow
5.5. Interphase Momentum Transfer Models
5.5.1. Interphase Drag
5.5.2. Interphase Drag for the Particle Model
5.5.2.1. Sparsely Distributed Solid Particles
5.5.2.1.1. Schiller Naumann Drag Model
5.5.2.2. Densely Distributed Solid Particles
5.5.2.2.1. Densely Distributed Solid Particles: Wen Yu Drag Model
5.5.2.2.2. Densely Distributed Solid Particles: Gidaspow Drag Model
5.5.2.3. Sparsely Distributed Fluid Particles (Drops and Bubbles)
5.5.2.3.1. Sparsely Distributed Fluid Particles: Ishii-Zuber Drag Model
5.5.2.3.2. Sparsely Distributed Fluid Particles: Grace Drag Model
5.5.2.4. Densely Distributed Fluid Particles
5.5.2.4.1. Densely Distributed Fluid Particles: Ishii-Zuber Drag Model
5.5.2.4.2. Densely Distributed Fluid Particles: Dense Spherical Particle Regime (Ishii Zuber)
5.5.2.4.3. Densely Distributed Fluid Particles: Dense Distorted Particle Regime (Ishii Zuber)
5.5.2.4.4. Densely Distributed Fluid Particles: Dense Spherical Cap Regime (Ishii Zuber)
5.5.2.4.5. Densely Distributed Fluid Particles: Automatic Regime Selection (Ishii Zuber)
5.5.2.4.6. Densely Distributed Fluid Particles: Grace Drag Model
5.5.3. Interphase Drag for the Mixture Model
5.5.4. Interphase Drag for the Free Surface Model
5.5.5. Lift Force
5.5.5.1. The Saffman Mei Lift Force Model
5.5.5.2. The Legendre and Magnaudet Lift Force Model
5.5.5.3. The Tomiyama Lift Force Model
5.5.6. Virtual Mass Force
5.5.7. Wall Lubrication Force
5.5.7.1. The Antal Wall Lubrication Force Model
5.5.7.2. The Tomiyama Wall Lubrication Force Model
5.5.7.3. The Frank Wall Lubrication Force Model
5.5.8. Interphase Turbulent Dispersion Force
5.5.8.1. Favre Averaged Drag Model
5.5.8.2. Lopez de Bertodano Model
5.6. Solid Particle Collision Models
5.6.1. Solids Stress Tensor
5.6.1.1. Empirical Constitutive Equations
5.6.1.2. Kinetic Theory Models for the Solids Stress Tensor
5.6.2. Solids Pressure
5.6.2.1. Empirical Constitutive Equations
5.6.2.2. Kinetic Theory Models for Solids Pressure
5.6.3. Solids Shear Viscosity
5.6.3.1. Constitutive Equation Models
5.6.3.2. Kinetic Theory Models for Solids Shear Viscosity
5.6.4. Solids Bulk Viscosity
5.6.4.1. Constitutive Equation Models
5.6.4.2. Kinetic Theory Models for Solids Bulk Viscosity
5.6.5. Granular Temperature
5.6.5.1. Algebraic Equilibrium Model
5.6.5.2. Zero Equation Model
5.7. Interphase Heat Transfer
5.7.1. Phasic Equations
5.7.2. Inhomogeneous Interphase Heat Transfer Models
5.7.2.1. Overall Heat Transfer Coefficients
5.7.2.2. Particle Model Correlations
5.7.2.3. Mixture Model Correlations
5.7.2.4. The Two Resistance Model
5.7.3. Homogeneous Heat Transfer in Multiphase Flow
5.8. Multiple Size Group (MUSIG) Model
5.8.1. Model Derivation
5.8.1.1. Population Balance Equation
5.8.1.2. Size Fraction Equations
5.8.1.3. Source Terms
5.8.2. Size Group Discretization
5.8.2.1. Equal Mass Discretization
5.8.2.2. Equal Diameter Discretization
5.8.2.3. Geometric Mass Discretization
5.8.2.4. Comparison
5.8.2.5. Size Group Boundaries
5.8.3. Breakup Models
5.8.3.1. Luo and Svendsen Model
5.8.3.2. User-Defined Models
5.8.4. Coalescence Models
5.8.4.1. Prince and Blanch Model
5.8.4.2. User-Defined Models
5.9. The Algebraic Slip Model
5.9.1. Phasic Equations
5.9.2. Bulk Equations
5.9.3. Drift and Slip Relations
5.9.4. Derivation of the Algebraic Slip Equation
5.9.5. Turbulence Effects
5.9.6. Energy Equation
5.9.7. Wall Deposition
5.10. Turbulence Modeling in Multiphase Flow
5.10.1. Phase-Dependent Turbulence Models
5.10.1.1. The Eddy Viscosity Hypothesis
5.10.1.2. Algebraic Models
5.10.1.2.1. Zero Equation Model
5.10.1.2.2. Dispersed Phase Zero Equation Model
5.10.1.3. Two-Equation Models
5.10.1.4. Reynolds Stress Models
5.10.2. Enhanced Turbulence Production Models
5.10.2.1. Sato Enhanced Eddy Viscosity
5.10.2.2. Turbulence Source Terms
5.10.3. Homogeneous Turbulence for Multiphase Flow
5.11. Additional Variables in Multiphase Flow
5.11.1. Additional Variable Interphase Transfer Models
5.11.1.1. Particle Model Correlations
5.11.1.2. Mixture Model Correlations
5.11.2. Homogeneous Additional Variables in Multiphase Flow
5.12. Sources in Multiphase Flow
5.12.1. Fluid-specific Sources
5.12.2. Bulk Sources
5.13. Interphase Mass Transfer
5.13.1. Secondary Fluxes
5.13.2. User Defined Interphase Mass Transfer
5.13.3. General Species Mass Transfer
5.13.3.1. Equilibrium Models
5.13.3.1.1. Raoult’s Law
5.13.3.1.2. Henry’s Law
5.13.3.2. Two Resistance Model with Negligible Mass Transfer
5.13.4. The Thermal Phase Change Model
5.13.4.1. Wall Boiling Model
5.13.4.1.1. Partitioning of the Wall Heat Flux
5.13.4.1.2. Sub-models for the Wall Boiling Model
5.13.4.1.2.1. Wall Nucleation Site Density
5.13.4.1.2.2. Bubble Departure Diameter
5.13.4.1.2.3. Bubble Detachment Frequency
5.13.4.1.2.4. Bubble Waiting Time
5.13.4.1.2.5. Area Influence Factors
5.13.4.1.2.6. Convective Heat Transfer
5.13.4.1.2.7. Quenching Heat Transfer
5.13.4.1.2.8. Evaporation Rate
5.13.4.1.3. Determination of the Wall Heat Flux Partition
5.13.5. Cavitation Model
5.13.5.1. The Rayleigh Plesset Model
5.13.5.2. User Defined Cavitation Models
5.13.6. The Droplet Condensation Model
5.14. Free Surface Flow
5.14.1. Implementation
5.14.2. Surface Tension
6. Particle Transport Theory
6.1. Lagrangian Tracking Implementation
6.1.1. Calculation of Particle Variables
6.1.2. Interphase Transfer Through Source Terms
6.2. Momentum Transfer
6.2.1. Drag Force on Particles
6.2.2. Buoyancy Force on Particles
6.2.3. Rotation Force
6.2.4. Virtual or Added Mass Force
6.2.5. Pressure Gradient Force
6.2.6. Turbulence in Particle Tracking
6.2.7. Turbulent Dispersion
6.3. Heat and Mass Transfer
6.3.1. Heat Transfer
6.3.2. Simple Mass Transfer
6.3.3. Liquid Evaporation Model
6.3.3.1. Extension of the Liquid Evaporation Model
6.3.3.1.1. Examples of ideal mixtures
6.3.3.2. Determination of the Total Vapor Pressure of an Ideal Mixture
6.3.3.3. Diffusion Regime (Non-Boiling Particles)
6.3.3.4. Boiling Particles
6.3.4. Oil Evaporation/Combustion
6.3.4.1. Light Oil Modification
6.3.5. Reactions
6.3.5.1. Arrhenius Reactions
6.3.5.2. Heat Release
6.3.5.3. Char Oxidation
6.3.5.3.1. Field
6.3.5.3.2. Gibb
6.3.5.4. Radiative Preheating
6.3.5.5. Coal Combustion
6.3.5.5.1. Coal Combustion - Gas Phase
6.3.5.5.2. Coal Decomposition
6.3.5.5.3. Devolatilization
6.3.6. Hydrocarbon Fuel Analysis Model
6.4. Basic Erosion Models
6.4.1. Model of Finnie
6.4.1.1. Implementation in CFX
6.4.2. Model of Tabakoff and Grant
6.4.2.1. Implementation in CFX
6.4.2.1.1. Mapping of CFX to Original Tabakoff Constants
6.4.2.1.2. Constants
6.4.3. Overall Erosion Rate and Erosion Output
6.5. Spray Breakup Models
6.5.1. Primary Breakup/Atomization Models
6.5.1.1. Blob Method
6.5.1.2. Enhanced Blob Method
6.5.1.2.1. Input Parameters for the Enhanced Blob Method
6.5.1.3. LISA Model
6.5.1.3.1. Film Formation
6.5.1.3.2. Sheet Breakup and Atomization
6.5.1.3.3. User Input Data for the LISA Model
6.5.1.4. Turbulence Induced Atomization
6.5.1.4.1. User Input Data for Turbulence Induced Atomization
6.5.1.5. Usage and Restrictions for Primary Breakup Models
6.5.2. Secondary Breakup Models
6.5.2.1. Breakup Regimes
6.5.2.2. Numerical Approach to Breakup Modeling
6.5.2.3. Reitz and Diwakar Breakup Model
6.5.2.3.1. Bag Breakup
6.5.2.3.2. Stripping Breakup
6.5.2.4. Schmehl Breakup Model []
6.5.2.4.1. Breakup Process for Schmehl Breakup Model
6.5.2.5. Taylor Analogy Breakup (TAB) Model []
6.5.2.6. ETAB []
6.5.2.7. Cascade Atomization and Breakup Model (CAB)
6.5.3. Dynamic Drag Models
6.5.3.1. Liu []
6.5.3.2. Schmehl []
6.6. Particle Collision Model
6.6.1. Introduction to the Particle Collision Model
6.6.1.1. Background Information
6.6.2. Implementation of a Stochastic Particle-Particle Collision Model in Ansys CFX
6.6.2.1. Implementation Theory
6.6.2.1.1. Particle Collision Coefficients Used for Particle-Particle Collision Model
6.6.2.1.2. Particle Variables Used for Particle-Particle Collision Model
6.6.2.1.2.1. Particle Number Density
6.6.2.1.2.2. Turbulent Stokes Number
6.6.2.1.2.3. Standard Deviation of Particle Quantities
6.6.2.1.2.4. Integration Time Step Size (User Fortran Only)
6.6.3. Range of Applicability of Particle-Particle Collision Model
6.6.4. Limitations of Particle-Particle Collision Model in Ansys CFX
6.7. Particle-Wall Interaction
6.7.1. Introduction to Particle-Wall Interaction
6.7.1.1. Background Information
6.7.2. The Elsaesser Particle-Wall Interaction Model
6.7.2.1. Classification of Impact Regimes
6.7.2.1.1. Cold Wall with Wall Film (TWall < TPA)
6.7.2.1.2. Hot Wall with Wall Film (TPA < TWall < TRA)
6.7.2.1.3. Hot Wall Without Wall Film (TWall > TRa)
6.7.2.2. Wall Roughness
6.7.2.3. Range of Applicability, Input Data and Restrictions
6.7.3. Stick-to-Wall Model
6.7.4. The Sommerfeld-Frank Rough Wall Model (Particle Rough Wall Model)
6.8. Quasi Static Wall Film Model
6.8.1. Assumptions
6.8.2. Determination of Flooded Regime
6.8.3. Energy Transfer to and from the Wall Film
6.8.3.1. Conductive Heat Transfer
6.8.3.1.1. Non-flooded Regime
6.8.3.1.2. Flooded Regime
6.8.3.2. Convective Heat Transfer
6.8.3.2.1. Non-flooded Regime
6.8.3.2.2. Flooded Regime
6.8.3.3. Calculation of the Average Wall Film Temperature
6.8.3.4. Evaporation from Film
6.8.3.4.1. Non-flooded Regime (Non-boiling)
6.8.3.4.2. Flooded Regime (Non-boiling)
6.8.3.4.3. Flooded and Non-flooded Regime (Boiling Particles)
6.8.4. Mass Transfer to and from the Wall Film
6.8.5. Wall Film Thickness
6.8.6. Wall Film in Moving Mesh Applications
6.8.6.1. Wall Film Moving with Mesh
6.8.6.2. Wall Film Moving Relative to Underlying Mesh
6.8.7. User Control for Heat and Mass Transfer Terms of Wall Particles
7. Combustion Theory
7.1. Transport Equations
7.2. Chemical Reaction Rate
7.3. Fluid Time Scale for Extinction Model
7.4. The Eddy Dissipation Model
7.4.1. Reactants Limiter
7.4.2. Products Limiter
7.4.3. Maximum Flame Temperature Limiter
7.5. The Finite Rate Chemistry Model
7.5.1. Third Body Terms
7.6. The Combined Eddy Dissipation/Finite Rate Chemistry Model
7.7. Combustion Source Term Linearization
7.8. The Flamelet Model
7.8.1. Laminar Flamelet Model for Non Premixed Combustion
7.8.2. Coupling of Laminar Flamelet with the Turbulent Flow Field
7.8.3. Flamelet Libraries
7.9. Burning Velocity Model (Premixed or Partially Premixed)
7.9.1. Reaction Progress
7.9.2. Weighted Reaction Progress
7.10. Burning Velocity Model (BVM)
7.10.1. Equivalence Ratio, Stoichiometric Mixture Fraction
7.11. Laminar Burning Velocity
7.11.1. Value
7.11.2. Equivalence Ratio Correlation
7.11.2.1. Fifth Order Polynomial
7.11.2.2. Quadratic Decay
7.11.2.3. Beta Function
7.11.2.4. Residual Material Dependency
7.11.2.5. Metghalchi and Keck
7.12. Turbulent Burning Velocity
7.12.1. Value
7.12.2. Zimont Correlation
7.12.3. Peters Correlation
7.12.4. Mueller Correlation
7.13. Extended Coherent Flame Model (ECFM)
7.13.1. Turbulent Flame Stretch
7.13.2. Laminar Flame Thickness
7.13.3. Wall Quenching Model
7.14. Residual Material Model
7.14.1. Exhaust Gas Recirculation
7.14.2. Principal Variables and Transport Equation
7.14.3. Mixture Composition
7.14.4. Reinitialization for Subsequent Engine Cycles
7.14.5. Equivalence Ratio and Conditional Fresh/Residual Mixtures
7.15. Spark Ignition Model
7.16. Autoignition Model
7.16.1. Ignition Delay Model
7.16.2. Knock Model
7.16.3. Ignition Delay Time
7.16.3.1. Douaud and Eyzat
7.16.3.2. Hardenberg and Hase
7.17. Phasic Combustion
7.18. NO Formation Model
7.18.1. Formation Mechanisms
7.18.1.1. Thermal NO
7.18.1.2. Prompt NO
7.18.1.3. Fuel Nitrogen
7.18.1.4. NO Reburn
7.18.1.5. Turbulence Effects
7.18.1.6. Temperature Variance Equation
7.18.1.7. Model Control
7.18.1.7.1. Adjusting Model Coefficients
7.18.1.7.2. User Defined NO Formation Mechanisms
7.19. Chemistry Postprocessing
7.20. Soot Model
7.20.1. Soot Formation
7.20.2. Soot Combustion
7.20.3. Turbulence Effects
8. Radiation Theory
8.1. Radiation Transport
8.1.1. Blackbody Emission
8.1.2. Particulate Effects to Radiation Transport
8.1.3. Quantities of Interest
8.1.3.1. Optical Thickness
8.1.4. Radiation Through Domain Interfaces
8.2. Rosseland Model
8.2.1. Wall Treatment
8.3. The P1 Model
8.3.1. Wall Treatment
8.4. Discrete Transfer Model
8.5. Monte Carlo Model
8.5.1. Monte Carlo Statistics
8.6. Spectral Models
8.6.1. Gray
8.6.2. Multiband Model
8.6.3. Weighted Sum of Gray Gases
8.6.3.1. Weighted Sum of Gray Gases Model Parameters
9. Electromagnetic Hydrodynamic Theory
9.1. Electromagnetic Models
9.1.1. Constitutive Relationships
9.1.2. Magnetohydrodynamics (MHD)
9.1.3. Electrohydrodynamics (EHD)
9.1.4. Ferrohydrodynamics (FHD)
9.1.5. Electromagnetic Basics: Potential Formulation in Ansys CFX
9.1.6. Boundary Conditions
9.1.7. Transformed Equations
9.1.8. Conductive Media Approximation
9.2. Fluid Dynamics Model
10. Rigid Body Theory
10.1. Equations of Motion of Rigid Body
10.2. Rigid Body Solution Algorithms
10.2.1. Translational Equations of Motion
10.2.1.1. Newmark Integration
10.2.2. Rotational Equations of Motion
10.2.2.1. First Order Backward Euler
10.2.2.2. Simo Wong Algorithm
11. Discretization and Solution Theory
11.1. Numerical Discretization
11.1.1. Discretization of the Governing Equations
11.1.1.1. Order Accuracy
11.1.1.2. Shape Functions
11.1.1.2.1. Hexahedral Element
11.1.1.2.2. Tetrahedral Element
11.1.1.2.3. Wedge Element
11.1.1.2.4. Pyramid Element
11.1.1.3. Control Volume Gradients
11.1.1.4. Advection Term
11.1.1.4.1. 1st Order Upwind Differencing Scheme
11.1.1.4.2. Specified Blend Factor
11.1.1.4.3. Central Difference Scheme
11.1.1.4.4. Bounded Central Difference Scheme
11.1.1.4.5. High Resolution Scheme
11.1.1.5. Diffusion Terms
11.1.1.6. Pressure Gradient Term
11.1.1.7. Mass Flows
11.1.1.7.1. Pressure-Velocity Coupling
11.1.1.7.2. Compressibility
11.1.1.8. Transient Term
11.1.1.9. Mesh Deformation
11.1.2. The Coupled System of Equations
11.2. Solution Strategy - The Coupled Solver
11.2.1. General Solution
11.2.2. Linear Equation Solution
11.2.2.1. Algebraic Multigrid
11.2.3. Residual Normalization Procedure
11.3. Discretization Errors
11.3.1. Controlling Error Sources
11.3.2. Controlling Error Propagation