Contents

• Using This Manual
  • The Contents of This Manual
  • The Contents of the Other Manuals
  • Typographical Conventions
  • Mathematical Conventions
  • Technical Support
    • Contacting Technical Support
• 1. Basic Fluid Flow
  • 1.1 Overview of Physical Models in ANSYS FLUENT
  • 1.2 Continuity and Momentum Equations
  • 1.3 User-Defined Scalar (UDS) Transport Equations
    • 1.3.1 Single Phase Flow
    • 1.3.2 Multiphase Flow
  • 1.4 Periodic Flows
    • 1.4.1 Overview
    • 1.4.2 Limitations
    • 1.4.3 Physics of Periodic Flows
  • 1.5 Swirling and Rotating Flows
    • 1.5.1 Overview of Swirling and Rotating Flows
    • 1.5.2 Physics of Swirling and Rotating Flows
  • 1.6 Compressible Flows
    • 1.6.1 When to Use the Compressible Flow Model
    • 1.6.2 Physics of Compressible Flows
  • 1.7 Inviscid Flows
    • 1.7.1 Euler Equations
• 2. Flows with Rotating Reference Frames
  • 2.1 Introduction
  • 2.2 Flow in a Rotating Reference Frame
    • 2.2.1 Equations for a Rotating Reference Frame
    • 2.2.2 Single Rotating Reference Frame (SRF) Modeling
  • 2.3 Flow in Multiple Rotating Reference Frames
    • 2.3.1 The Multiple Reference Frame Model
    • 2.3.2 The Mixing Plane Model
• 3. Flows Using Sliding and Deforming Meshes
  • 3.1 Introduction
  • 3.2 Sliding Mesh Theory
    • 3.2.1 The Sliding Mesh Concept
  • 3.3 Dynamic Mesh Theory
    • 3.3.1 Dynamic Mesh Update Methods
    • 3.3.2 Six DOF (6DOF) Solver Theory
• 4. Turbulence
  • 4.1 Introduction
  • 4.2 Choosing a Turbulence Model
    • 4.2.1 Reynolds-Averaged Approach vs. LES
    • 4.2.2 Reynolds (Ensemble) Averaging
    • 4.2.3 Boussinesq Approach vs. Reynolds Stress Transport Models
  • 4.3 Spalart-Allmaras Model
    • 4.3.1 Overview
    • 4.3.2 Transport Equation for the Spalart-Allmaras Model
    • 4.3.3 Modeling the Turbulent Viscosity
    • 4.3.4 Modeling the Turbulent Production
    • 4.3.5 Modeling the Turbulent Destruction
    • 4.3.6 Model Constants
    • 4.3.7 Wall Boundary Conditions
    • 4.3.8 Convective Heat and Mass Transfer Modeling
  • 4.4 Standard, RNG, and Realizable $k$- $\epsilon$ Models
    • 4.4.1 Standard $k$- $\epsilon$ Model
    • 4.4.2 RNG $k$- $\epsilon$ Model
    • 4.4.3 Realizable $k$- $\epsilon$ Model
    • 4.4.4 Modeling Turbulent Production in the $k$- $\epsilon$ Models
    • 4.4.5 Effects of Buoyancy on Turbulence in the $k$- $\epsilon$ Models
    • 4.4.6 Effects of Compressibility on Turbulence in the $k$- $\epsilon$ Models
    • 4.4.7 Convective Heat and Mass Transfer Modeling in the $k$- $\epsilon$ Models
  • 4.5 Standard and SST $k$- $\omega$ Models
    • 4.5.1 Standard $k$- $\omega$ Model
    • 4.5.2 Shear-Stress Transport (SST) $k$- $\omega$ Model
    • 4.5.3 Wall Boundary Conditions
  • 4.6 $k$- $kl$- $\omega$ Transition Model
    • 4.6.1 Overview
    • 4.6.2 Transport Equations for the $k$- $kl$- $\omega$ Model
  • 4.7 Transition SST Model
    • 4.7.1 Overview
    • 4.7.2 Transport Equations for the Transition SST Model
    • 4.7.3 Specifying Inlet Turbulence Levels
  • 4.8 The $v^2$- $f$ Model
  • 4.9 Reynolds Stress Model (RSM)
    • 4.9.1 Overview
    • 4.9.2 Reynolds Stress Transport Equations
    • 4.9.3 Modeling Turbulent Diffusive Transport
    • 4.9.4 Modeling the Pressure-Strain Term
    • 4.9.5 Effects of Buoyancy on Turbulence
    • 4.9.6 Modeling the Turbulence Kinetic Energy
    • 4.9.7 Modeling the Dissipation Rate
    • 4.9.8 Modeling the Turbulent Viscosity
    • 4.9.9 Wall Boundary Conditions
    • 4.9.10 Convective Heat and Mass Transfer Modeling
  • 4.10 Detached Eddy Simulation (DES)
    • 4.10.1 Spalart-Allmaras Based DES Model
    • 4.10.2 Realizable $k$- $\epsilon$ Based DES Model
    • 4.10.3 SST $k$- $\omega$ Based DES Model
  • 4.11 Large Eddy Simulation (LES) Model
    • 4.11.1 Overview
    • 4.11.2 Filtered Navier-Stokes Equations
    • 4.11.3 Subgrid-Scale Models
    • 4.11.4 Inlet Boundary Conditions for the LES Model
  • 4.12 Near-Wall Treatments for Wall-Bounded Turbulent Flows
    • 4.12.1 Overview
    • 4.12.2 Standard Wall Functions
    • 4.12.3 Non-Equilibrium Wall Functions
    • 4.12.4 Enhanced Wall Treatment
    • 4.12.5 User-Defined Wall Functions
    • 4.12.6 LES Near-Wall Treatment
• 5. Heat Transfer
  • 5.1 Introduction
  • 5.2 Modeling Conductive and Convective Heat Transfer
    • 5.2.1 Heat Transfer Theory
    • 5.2.2 Natural Convection and Buoyancy-Driven Flows Theory
  • 5.3 Modeling Radiation
    • 5.3.1 Overview and Limitations
    • 5.3.2 Radiative Transfer Equation
    • 5.3.3 P-1 Radiation Model Theory
    • 5.3.4 Rosseland Radiation Model Theory
    • 5.3.5 Discrete Transfer Radiation Model (DTRM) Theory
    • 5.3.6 Discrete Ordinates (DO) Radiation Model Theory
    • 5.3.7 Surface-to-Surface (S2S) Radiation Model Theory
    • 5.3.8 Radiation in Combusting Flows
    • 5.3.9 Choosing a Radiation Model
• 6. Heat Exchangers
  • 6.1 The Macro Heat Exchanger Models
    • 6.1.1 Overview and Restrictions of the Macro Heat Exchanger Models
    • 6.1.2 Macro Heat Exchanger Model Theory
  • 6.2 The Dual Cell Model
    • 6.2.1 Overview and Restrictions of the Dual Cell Model
    • 6.2.2 Dual Cell Model Theory
• 7. Species Transport and Finite-Rate Chemistry
  • 7.1 Volumetric Reactions
    • 7.1.1 Species Transport Equations
    • 7.1.2 The Generalized Finite-Rate Formulation for Reaction Modeling
  • 7.2 Wall Surface Reactions and Chemical Vapor Deposition
    • 7.2.1 Surface Coverage Reaction Rate Modification
    • 7.2.2 Reaction-Diffusion Balance for Surface Chemistry
    • 7.2.3 Slip Boundary Formulation for Low-Pressure Gas Systems
  • 7.3 Particle Surface Reactions
    • 7.3.1 General Description
    • 7.3.2 ANSYS FLUENT Model Formulation
    • 7.3.3 Extension for Stoichiometries with Multiple Gas Phase Reactants
    • 7.3.4 Solid-Solid Reactions
    • 7.3.5 Solid Decomposition Reactions
    • 7.3.6 Solid Deposition Reactions
    • 7.3.7 Gaseous Solid Catalyzed Reactions on the Particle Surface
• 8. Non-Premixed Combustion
  • 8.1 Introduction
  • 8.2 Non-Premixed Combustion and Mixture Fraction Theory
    • 8.2.1 Mixture Fraction Theory
    • 8.2.2 Modeling of Turbulence-Chemistry Interaction
    • 8.2.3 Non-Adiabatic Extensions of the Non-Premixed Model
    • 8.2.4 Chemistry Tabulation
  • 8.3 Restrictions and Special Cases for Using the Non-Premixed Model
    • 8.3.1 Restrictions on the Mixture Fraction Approach
    • 8.3.2 Using the Non-Premixed Model for Liquid Fuel or Coal Combustion
    • 8.3.3 Using the Non-Premixed Model with Flue Gas Recycle
    • 8.3.4 Using the Non-Premixed Model with the Inert Model
  • 8.4 The Laminar Flamelet Models Theory
    • 8.4.1 Restrictions and Assumptions
    • 8.4.2 The Flamelet Concept
    • 8.4.3 Flamelet Generation
    • 8.4.4 Flamelet Import
  • 8.5 The Steady Laminar Flamelet Model Theory
    • 8.5.1 Overview
    • 8.5.2 Multiple Steady Flamelet Libraries
    • 8.5.3 Steady Laminar Flamelet Automated Grid Refinement
    • 8.5.4 Non-Adiabatic Steady Laminar Flamelets
  • 8.6 The Unsteady Laminar Flamelet Model Theory
    • 8.6.1 The Eulerian Unsteady Laminar Flamelet Model
    • 8.6.2 The Diesel Unsteady Laminar Flamelet Model
• 9. Premixed Combustion
  • 9.1 Overview and Limitations
    • 9.1.1 Overview
    • 9.1.2 Limitations
  • 9.2 Zimont Turbulent Flame Closure Theory
    • 9.2.1 Propagation of the Flame Front
    • 9.2.2 Turbulent Flame Speed
  • 9.3 Extended Coherent Flamelet Model Theory
    • 9.3.1 Closure for ECFM Source Terms
    • 9.3.2 Turbulent Flame Speed in ECFM
  • 9.4 Calculation of Temperature
    • 9.4.1 Adiabatic Temperature Calculation
    • 9.4.2 Non-Adiabatic Temperature Calculation
  • 9.5 Calculation of Density
• 10. Partially Premixed Combustion
  • 10.1 Overview and Limitations
    • 10.1.1 Overview
    • 10.1.2 Limitations
  • 10.2 Partially Premixed Combustion Theory
    • 10.2.1 Calculation of Scalar Quantities
    • 10.2.2 Laminar Flame Speed
• 11. Composition PDF Transport
  • 11.1 Overview and Limitations
  • 11.2 Composition PDF Transport Theory
  • 11.3 The Lagrangian Solution Method
    • 11.3.1 Particle Convection
    • 11.3.2 Particle Mixing
    • 11.3.3 Particle Reaction
    • 11.3.4 The ISAT Algorithm
  • 11.4 The Eulerian Solution Method
• 12. Engine Ignition
  • 12.1 Spark Model
    • 12.1.1 Overview and Limitations
    • 12.1.2 Spark Model Theory
  • 12.2 Autoignition Models
    • 12.2.1 Overview and Limitations
    • 12.2.2 Ignition Model Theory
  • 12.3 Crevice Model
    • 12.3.1 Overview
    • 12.3.2 Limitations
    • 12.3.3 Crevice Model Theory
• 13. Pollutant Formation
  • 13.1 NOx Formation
    • 13.1.1 Overview
    • 13.1.2 Governing Equations for NOx Transport
    • 13.1.3 Thermal NOx Formation
    • 13.1.4 Prompt NOx Formation
    • 13.1.5 Fuel NOx Formation
    • 13.1.6 NOx Formation from Intermediate N $_2$O
    • 13.1.7 NOx Reduction by Reburning
    • 13.1.8 NOx Reduction by SNCR
    • 13.1.9 NOx Formation in Turbulent Flows
  • 13.2 SOx Formation
    • 13.2.1 Overview
    • 13.2.2 Governing Equations for SOx Transport
    • 13.2.3 Reaction Mechanisms for Sulfur Oxidation
    • 13.2.4 $SO_2$ and $H{_2}S$ Production in a Gaseous Fuel
    • 13.2.5 $SO_2$ and $H{_2}S$ Production in a Liquid Fuel
    • 13.2.6 $SO_2$ and $H{_2}S$ Production from Coal
    • 13.2.7 SOx Formation in Turbulent Flows
  • 13.3 Soot Formation
    • 13.3.1 Overview and Limitations
    • 13.3.2 Soot Model Theory
• 14. Aerodynamically Generated Noise
  • 14.1 Overview
    • 14.1.1 Direct Method
    • 14.1.2 Integral Method Based on Acoustic Analogy
    • 14.1.3 Broadband Noise Source Models
  • 14.2 Acoustics Model Theory
    • 14.2.1 The Ffowcs Williams and Hawkings Model
    • 14.2.2 Broadband Noise Source Models
• 15. Discrete Phase
  • 15.1 Introduction
  • 15.2 Particle Motion Theory
    • 15.2.1 Equations of Motion for Particles
    • 15.2.2 Turbulent Dispersion of Particles
    • 15.2.3 Integration of Particle Equation of Motion
  • 15.3 Laws for Drag Coefficients
    • 15.3.1 Spherical Drag Law
    • 15.3.2 Non-spherical Drag Law
    • 15.3.3 Stokes-Cunningham Drag Law
    • 15.3.4 High-Mach-Number Drag Law
    • 15.3.5 Dynamic Drag Model Theory
    • 15.3.6 Dense Discrete Phase Model Drag Laws
  • 15.4 Laws for Heat and Mass Exchange
    • 15.4.1 Inert Heating or Cooling (Law 1/Law 6)
    • 15.4.2 Droplet Vaporization (Law 2)
    • 15.4.3 Droplet Boiling (Law 3)
    • 15.4.4 Devolatilization (Law 4)
    • 15.4.5 Surface Combustion (Law 5)
    • 15.4.6 Multicomponent Particle Definition (Law 7)
  • 15.5 Vapor Liquid Equilibrium Theory
  • 15.6 Wall-Jet Model Theory
  • 15.7 Wall-Film Model Theory
    • 15.7.1 Introduction
    • 15.7.2 Interaction During Impact with a Boundary
    • 15.7.3 Splashing
    • 15.7.4 Separation Criteria
    • 15.7.5 Conservation Equations for Wall-Film Particles
  • 15.8 Particle Erosion and Accretion Theory
  • 15.9 Atomizer Model Theory
    • 15.9.1 The Plain-Orifice Atomizer Model
    • 15.9.2 The Pressure-Swirl Atomizer Model
    • 15.9.3 The Air-Blast/Air-Assist Atomizer Model
    • 15.9.4 The Flat-Fan Atomizer Model
    • 15.9.5 The Effervescent Atomizer Model
  • 15.10 Secondary Breakup Model Theory
    • 15.10.1 Taylor Analogy Breakup (TAB) Model
    • 15.10.2 Wave Breakup Model
  • 15.11 Droplet Collision and Coalescence Model Theory
    • 15.11.1 Introduction
    • 15.11.2 Use and Limitations
    • 15.11.3 Theory
  • 15.12 One-Way and Two-Way Coupling
    • 15.12.1 Coupling Between the Discrete and Continuous Phases
    • 15.12.2 Momentum Exchange
    • 15.12.3 Heat Exchange
    • 15.12.4 Mass Exchange
    • 15.12.5 Under-Relaxation of the Interphase Exchange Terms
    • 15.12.6 Interphase Exchange During Stochastic Tracking
    • 15.12.7 Interphase Exchange During Cloud Tracking
• 16. Multiphase Flows
  • 16.1 Introduction
    • 16.1.1 Multiphase Flow Regimes
    • 16.1.2 Examples of Multiphase Systems
  • 16.2 Choosing a General Multiphase Model
    • 16.2.1 Approaches to Multiphase Modeling
    • 16.2.2 Model Comparisons
    • 16.2.3 Time Schemes in Multiphase Flow
    • 16.2.4 Stability and Convergence
  • 16.3 Volume of Fluid (VOF) Model Theory
    • 16.3.1 Overview and Limitations of the VOF Model
    • 16.3.2 Volume Fraction Equation
    • 16.3.3 Material Properties
    • 16.3.4 Momentum Equation
    • 16.3.5 Energy Equation
    • 16.3.6 Additional Scalar Equations
    • 16.3.7 Time Dependence
    • 16.3.8 Surface Tension and Wall Adhesion
    • 16.3.9 Open Channel Flow
    • 16.3.10 Open Channel Wave Boundary Conditions
  • 16.4 Mixture Model Theory
    • 16.4.1 Overview and Limitations of the Mixture Model
    • 16.4.2 Continuity Equation
    • 16.4.3 Momentum Equation
    • 16.4.4 Energy Equation
    • 16.4.5 Relative (Slip) Velocity and the Drift Velocity
    • 16.4.6 Volume Fraction Equation for the Secondary Phases
    • 16.4.7 Granular Properties
    • 16.4.8 Granular Temperature
    • 16.4.9 Interfacial Area Concentration
    • 16.4.10 Solids Pressure
  • 16.5 Eulerian Model Theory
    • 16.5.1 Overview and Limitations of the Eulerian Model
    • 16.5.2 Volume Fraction Equation
    • 16.5.3 Conservation Equations
    • 16.5.4 Interphase Exchange Coefficients
    • 16.5.5 Solids Pressure
    • 16.5.6 Maximum Packing Limit in Binary Mixtures
    • 16.5.7 Solids Shear Stresses
    • 16.5.8 Granular Temperature
    • 16.5.9 Interfacial Area Concentration
    • 16.5.10 Description of Heat Transfer
    • 16.5.11 Turbulence Models
    • 16.5.12 Solution Method in ANSYS FLUENT
    • 16.5.13 Dense Discrete Phase Model
    • 16.5.14 Immiscible Fluid Model
  • 16.6 Wet Steam Model Theory
    • 16.6.1 Overview and Limitations of the Wet Steam Model
    • 16.6.2 Wet Steam Flow Equations
    • 16.6.3 Phase Change Model
    • 16.6.4 Built-in Thermodynamic Wet Steam Properties
  • 16.7 Modeling Mass Transfer in Multiphase Flows
    • 16.7.1 Source Terms due to Mass Transfer
    • 16.7.2 Unidirectional Constant Rate Mass Transfer
    • 16.7.3 UDF-Prescribed Mass Transfer
    • 16.7.4 Cavitation Models
    • 16.7.5 Evaporation-Condensation Model
  • 16.8 Modeling Species Transport in Multiphase Flows
    • 16.8.1 Limitations
    • 16.8.2 Mass and Momentum Transfer with Multiphase Species Transport
    • 16.8.3 The Stiff Chemistry Solver
• 17. Solidification and Melting
  • 17.1 Overview
  • 17.2 Limitations
  • 17.3 Introduction
  • 17.4 Energy Equation
  • 17.5 Momentum Equations
  • 17.6 Turbulence Equations
  • 17.7 Species Equations
  • 17.8 Pull Velocity for Continuous Casting
  • 17.9 Contact Resistance at Walls
• 18. Solver Theory
  • 18.1 Overview of Flow Solvers
    • 18.1.1 Pressure-Based Solver
    • 18.1.2 Density-Based Solver
  • 18.2 General Scalar Transport Equation: Discretization and Solution
    • 18.2.1 Solving the Linear System
  • 18.3 Discretization
    • 18.3.1 Spatial Discretization
    • 18.3.2 Temporal Discretization
    • 18.3.3 Evaluation of Gradients and Derivatives
    • 18.3.4 Gradient Limiters
  • 18.4 Pressure-Based Solver
    • 18.4.1 Discretization of the Momentum Equation
    • 18.4.2 Discretization of the Continuity Equation
    • 18.4.3 Pressure-Velocity Coupling
    • 18.4.4 Steady-State Iterative Algorithm
    • 18.4.5 Time-Advancement Algorithm
  • 18.5 Density-Based Solver
    • 18.5.1 Governing Equations in Vector Form
    • 18.5.2 Preconditioning
    • 18.5.3 Convective Fluxes
    • 18.5.4 Steady-State Flow Solution Methods
    • 18.5.5 Unsteady Flows Solution Methods
  • 18.6 Multigrid Method
    • 18.6.1 Approach
    • 18.6.2 Multigrid Cycles
    • 18.6.3 Algebraic Multigrid (AMG)
    • 18.6.4 Full-Approximation Storage (FAS) Multigrid
  • 18.7 Full Multigrid (FMG) Initialization
    • 18.7.1 Overview of FMG Initialization
    • 18.7.2 Limitations of FMG Initialization
• 19. Adapting the Mesh
  • 19.1 Static Adaption Process
    • 19.1.1 Hanging Node Adaption
  • 19.2 Boundary Adaption
  • 19.3 Gradient Adaption
    • 19.3.1 Gradient Adaption Approach
    • 19.3.2 Example of Steady Gradient Adaption
  • 19.4 Dynamic Gradient Adaption
  • 19.5 Isovalue Adaption
  • 19.6 Region Adaption
    • 19.6.1 Defining a Region
    • 19.6.2 Region Adaption Example
  • 19.7 Volume Adaption
    • 19.7.1 Volume Adaption Approach
    • 19.7.2 Volume Adaption Example
  • 19.8 Yplus/Ystar Adaption
    • 19.8.1 Yplus/Ystar Adaption Approach
  • 19.9 Anisotropic Adaption
  • 19.10 Geometry-Based Adaption
    • 19.10.1 Geometry-Based Adaption Approach
  • 19.11 Registers
• 20. Reporting Alphanumeric Data
  • 20.1 Fluxes Through Boundaries
  • 20.2 Forces on Boundaries
    • 20.2.1 Computing Forces, Moments, and the Center of Pressure
  • 20.3 Surface Integration
    • 20.3.1 Computing Surface Integrals
  • 20.4 Volume Integration
    • 20.4.1 Computing Volume Integrals
• Nomenclature
• Bibliography
• Index