<?xml version="1.0" encoding="utf-8"?><toc><title href="cfx_thry.html" title2="CFX-Solver Theory Guide">Theory Guide</title><dl><dt><span class="chapter"><a href="i1297852.html">1. Basic Solver Capability Theory</a></span></dt><dd><dl><dt><span class="section"><a href="i1297935.html">1.1. Documentation Conventions</a></span></dt><dd><dl><dt><span class="section"><a href="BGBJBJBJ.html">1.1.1. Dimensions</a></span></dt><dt><span class="section"><a href="i1396257.html">1.1.2. List of Symbols</a></span></dt><dd><dl><dt><span class="section"><a href="i1396257.html#cfxBasiListSubs">1.1.2.1. Subscripts</a></span></dt></dl></dd><dt><span class="section"><a href="i1298716.html">1.1.3. Variable Definitions</a></span></dt><dd><dl><dt><span class="section"><a href="i1298716.html#cfxBasiVariIsot">1.1.3.1. Isothermal Compressibility</a></span></dt><dt><span class="section"><a href="i1298716.html#cfxBasiVariIsen">1.1.3.2. Isentropic Compressibility</a></span></dt><dt><span class="section"><a href="i1298716.html#i1298719">1.1.3.3. Reference Pressure</a></span></dt><dt><span class="section"><a href="i1298716.html#i1298737">1.1.3.4. Static Pressure</a></span></dt><dt><span class="section"><a href="i1298716.html#i1298760">1.1.3.5. Modified Pressure</a></span></dt><dt><span class="section"><a href="i1298716.html#i1298778">1.1.3.6. Static Enthalpy</a></span></dt><dd><dl><dt><span class="section"><a href="i1298716.html#sect_rho_cp">1.1.3.6.1. Material with Variable Density and Specific Heat</a></span></dt></dl></dd><dt><span class="section"><a href="i1298716.html#i1298862">1.1.3.7. Total Enthalpy</a></span></dt><dt><span class="section"><a href="i1298716.html#i1298876">1.1.3.8. Domain Temperature</a></span></dt><dt><span class="section"><a href="i1298716.html#i1298883">1.1.3.9. Static Temperature</a></span></dt><dd><dl><dt><span class="section"><a href="i1298716.html#cfxBasiStatMate">1.1.3.9.1. Material with Constant Density and Specific Heat</a></span></dt><dt><span class="section"><a href="i1298716.html#cfxBasisubs">1.1.3.9.2. Ideal Gas or Solid with c<sub>p</sub>=f(T)</a></span></dt><dt><span class="section"><a href="i1298716.html#cfxBasiStatMate1">1.1.3.9.3. Material with Variable Density and Specific Heat</a></span></dt></dl></dd><dt><span class="section"><a href="i1298716.html#i1298929">1.1.3.10. Total Temperature</a></span></dt><dd><dl><dt><span class="section"><a href="i1298716.html#cfxBasiTotaMate">1.1.3.10.1. Material with Constant Density and Specific Heat</a></span></dt><dt><span class="section"><a href="i1298716.html#cfxBasisubs1">1.1.3.10.2. Ideal Gas with constant c<sub>p</sub>
</a></span></dt><dt><span class="section"><a href="i1298716.html#cfxBasisubs2">1.1.3.10.3. Ideal Gas with c<sub>p</sub> = f(T)</a></span></dt><dt><span class="section"><a href="i1298716.html#cfxBasiTotaMate1">1.1.3.10.4. Material with Variable Density and Specific Heat</a></span></dt></dl></dd><dt><span class="section"><a href="i1298716.html#i1298997">1.1.3.11. Entropy</a></span></dt><dd><dl><dt><span class="section"><a href="i1298716.html#cfxBasiEntrMate">1.1.3.11.1. Material with Constant Density and Specific Heat</a></span></dt><dt><span class="section"><a href="i1298716.html#cfxBasisubs3">1.1.3.11.2. Ideal Gas with constant c<sub>p</sub> or c<sub>p</sub> = f(T)</a></span></dt><dt><span class="section"><a href="i1298716.html#cfxBasiEntrMate1">1.1.3.11.3. Material with Variable Density and Specific Heat</a></span></dt></dl></dd><dt><span class="section"><a href="i1298716.html#i1299099">1.1.3.12. Total Pressure</a></span></dt><dd><dl><dt><span class="section"><a href="i1298716.html#cfxBasiTotaInco">1.1.3.12.1. Incompressible Fluids</a></span></dt><dt><span class="section"><a href="i1298716.html#cfxBasiTotaIdea">1.1.3.12.2. Ideal Gases</a></span></dt><dt><span class="section"><a href="i1298716.html#cfxBasiTotaMate2">1.1.3.12.3. Material with Variable Density and Specific Heat</a></span></dt></dl></dd><dt><span class="section"><a href="i1298716.html#cfxBasiVariShea">1.1.3.13. Shear Strain Rate</a></span></dt><dt><span class="section"><a href="i1298716.html#i1299209">1.1.3.14. Rotating Frame Quantities</a></span></dt><dd><dl><dt><span class="section"><a href="i1298716.html#cfxBasiRotaInco">1.1.3.14.1. Incompressible Fluids</a></span></dt><dt><span class="section"><a href="i1298716.html#cfxBasiRotaIdea">1.1.3.14.2. Ideal Gases</a></span></dt><dt><span class="section"><a href="i1298716.html#cfxBasiRotaMate">1.1.3.14.3. Material with Variable Density and Specific Heat</a></span></dt></dl></dd><dt><span class="section"><a href="i1298716.html#cfxBasiVariCour">1.1.3.15. Courant Number</a></span></dt></dl></dd><dt><span class="section"><a href="i1299301.html">1.1.4. Mathematical Notation</a></span></dt><dd><dl><dt><span class="section"><a href="i1299301.html#cfxBasiMathVect">1.1.4.1. The Vector Operators</a></span></dt><dd><dl><dt><span class="section"><a href="i1299301.html#cfxBasiVectGrad">1.1.4.1.1. Gradient Operator</a></span></dt><dt><span class="section"><a href="i1299301.html#cfxBasiVectDive">1.1.4.1.2. Divergence Operator</a></span></dt><dt><span class="section"><a href="i1299301.html#cfxBasiVectDyad">1.1.4.1.3. Dyadic Operator</a></span></dt></dl></dd><dt><span class="section"><a href="i1299301.html#cfxBasiMathMatr">1.1.4.2. Matrix Transposition</a></span></dt><dt><span class="section"><a href="i1299301.html#cfxBasiMathIden">1.1.4.3. The Identity Matrix (Kronecker Delta function)</a></span></dt><dt><span class="section"><a href="i1299301.html#cfxBasiMathInde">1.1.4.4. Index Notation</a></span></dt></dl></dd></dl></dd><dt><span class="section"><a href="i1299405.html">1.2. Governing Equations</a></span></dt><dd><dl><dt><span class="section"><a href="i1299421.html">1.2.1. Transport Equations</a></span></dt><dd><dl><dt><span class="section"><a href="i1299421.html#cfxBasiTranCont">1.2.1.1. The Continuity Equation</a></span></dt><dt><span class="section"><a href="i1299421.html#cfxBasiTranMome">1.2.1.2. The Momentum Equations</a></span></dt><dt><span class="section"><a href="i1299421.html#BGBCHDHC">1.2.1.3. The Total Energy Equation</a></span></dt><dt><span class="section"><a href="i1299421.html#BGBGEBIE">1.2.1.4. The Thermal Energy Equation</a></span></dt></dl></dd><dt><span class="section"><a href="i1299475.html">1.2.2. Equations of State</a></span></dt><dd><dl><dt><span class="section"><a href="i1299475.html#a1258tg">1.2.2.1. Incompressible Equation of State</a></span></dt><dt><span class="section"><a href="i1299475.html#i1299497">1.2.2.2. Ideal Gas Equation of State</a></span></dt><dt><span class="section"><a href="i1299475.html#a1259tg">1.2.2.3. Real Gas and Liquid Equations of State</a></span></dt><dd><dl><dt><span class="section"><a href="i1299475.html#i1299514">1.2.2.3.1. Real Gas Properties</a></span></dt><dd><dl><dt><span class="section"><a href="i1299475.html#cfxBasiRealRedl">1.2.2.3.1.1. Redlich Kwong Models</a></span></dt><dd><dl><dt><span class="section"><a href="i1299475.html#cfxBasiRedlStan">1.2.2.3.1.1.1. The Standard Redlich Kwong Model</a></span></dt><dt><span class="section"><a href="i1299475.html#cfxBasiRedlAung">1.2.2.3.1.1.2. The Aungier Redlich Kwong Model</a></span></dt><dt><span class="section"><a href="i1299475.html#cfxBasiRedlSoav">1.2.2.3.1.1.3. The Soave Redlich Kwong Model</a></span></dt></dl></dd><dt><span class="section"><a href="i1299475.html#cfxBasiRealPeng">1.2.2.3.1.2. Peng Robinson Model</a></span></dt><dt><span class="section"><a href="i1299475.html#cfxBasiRealReal">1.2.2.3.1.3. Real Gas Constitutive Relations</a></span></dt></dl></dd><dt><span class="section"><a href="i1299475.html#cfxBasiRealReal1">1.2.2.3.2. Real Gas Saturated Vapor Properties</a></span></dt><dt><span class="section"><a href="i1299475.html#cfxBasiRealReal2">1.2.2.3.3. Real Gas Liquid Properties</a></span></dt><dt><span class="section"><a href="i1299475.html#BGBDDGAI">1.2.2.3.4. IAPWS Equation of State</a></span></dt><dt><span class="section"><a href="i1299475.html#cfxBasiRealMeta">1.2.2.3.5. Metastable Superheated Liquid/Supercooled Vapor States</a></span></dt><dt><span class="section"><a href="i1299475.html#cfxBasiRealNume">1.2.2.3.6. Numerical Testing to Delineate Metastable Regions</a></span></dt><dt><span class="section"><a href="i1299475.html#sect_acentric_fact">1.2.2.3.7. The Acentric Factor</a></span></dt></dl></dd><dt><span class="section"><a href="i1299475.html#a1257tg">1.2.2.4. General Equation of State</a></span></dt></dl></dd><dt><span class="section"><a href="i1299720.html">1.2.3. Conjugate Heat Transfer</a></span></dt></dl></dd><dt><span class="section"><a href="i1299740.html">1.3. Buoyancy</a></span></dt><dd><dl><dt><span class="section"><a href="i1299774.html">1.3.1. Full Buoyancy Model</a></span></dt><dt><span class="section"><a href="i1299782.html">1.3.2. Boussinesq Model</a></span></dt></dl></dd><dt><span class="section"><a href="cfx_th_bascap_immsol.html">1.4. Immersed Solids</a></span></dt><dd><dl><dt><span class="section"><a href="cfx_th_bascap_immsol_mom_source.html">1.4.1. Momentum Sources</a></span></dt><dt><span class="section"><a href="cfx_th_bascap_immsol_nwt_ims_desc.html">1.4.2. Near-Wall Treatment for Immersed Solid Boundary</a></span></dt><dd><dl><dt><span class="section"><a href="cfx_th_bascap_immsol_nwt_ims_desc.html#cfx_th_bascap_immsol_boundarydetails">1.4.2.1. Notation</a></span></dt><dt><span class="section"><a href="cfx_th_bascap_immsol_nwt_ims_desc.html#cfx_th_bascap_immsol_laminar">1.4.2.2. Laminar Flow Treatment</a></span></dt><dt><span class="section"><a href="cfx_th_bascap_immsol_nwt_ims_desc.html#cfx_th_bascap_immsol_turb">1.4.2.3. Turbulent Flow Treatment</a></span></dt><dd><dl><dt><span class="section"><a href="cfx_th_bascap_immsol_nwt_ims_desc.html#cfx_th_bascap_immsol_turb_wallscale">1.4.2.3.1. Wall Distance</a></span></dt><dt><span class="section"><a href="cfx_th_bascap_immsol_nwt_ims_desc.html#cfx_th_bascap_immsol_turb_sst">1.4.2.3.2. SST Model</a></span></dt><dt><span class="section"><a href="cfx_th_bascap_immsol_nwt_ims_desc.html#cfx_th_bascap_immsol_turb_swf">1.4.2.3.3. Scalable Wall Function</a></span></dt></dl></dd></dl></dd></dl></dd><dt><span class="section"><a href="i1299805.html">1.5. Multicomponent Flow</a></span></dt><dd><dl><dt><span class="section"><a href="i1299807.html">1.5.1. Multicomponent Notation</a></span></dt><dt><span class="section"><a href="BGBGEJFE.html">1.5.2. Scalar Transport Equation</a></span></dt><dt><span class="section"><a href="BGBIFAFC.html">1.5.3. Algebraic Equation for Components</a></span></dt><dt><span class="section"><a href="BGBJFJCJ.html">1.5.4. Constraint Equation for Components</a></span></dt><dt><span class="section"><a href="BGBEFEGH.html">1.5.5. Multicomponent Fluid Properties</a></span></dt><dt><span class="section"><a href="BGBJBABA.html">1.5.6. Energy Equation</a></span></dt><dt><span class="section"><a href="BGBHJAGD.html">1.5.7. Multicomponent Energy Diffusion</a></span></dt></dl></dd><dt><span class="section"><a href="i1300000.html">1.6. Additional Variables</a></span></dt><dd><dl><dt><span class="section"><a href="i1413398.html">1.6.1. Transport Equations for Additional Variables</a></span></dt><dt><span class="section"><a href="i1413421.html">1.6.2. Diffusive Transport Equations for Additional Variables</a></span></dt><dt><span class="section"><a href="i1413966.html">1.6.3. Poisson Equations for Additional Variables</a></span></dt><dt><span class="section"><a href="i1413968.html">1.6.4. Algebraic Equations for Additional Variables</a></span></dt></dl></dd><dt><span class="section"><a href="i1300016.html">1.7. Rotational Forces</a></span></dt><dd><dl><dt><span class="section"><a href="i1300039.html">1.7.1. Alternate Rotation Model</a></span></dt></dl></dd><dt><span class="section"><a href="i1300055.html">1.8. Sources</a></span></dt><dd><dl><dt><span class="section"><a href="i1300063.html">1.8.1. Momentum Sources</a></span></dt><dd><dl><dt><span class="section"><a href="i1300063.html#cfx_th_isotropiclossmodel">1.8.1.1. Isotropic Loss Model</a></span></dt><dt><span class="section"><a href="i1300063.html#cfx_th_directionallossmodel">1.8.1.2. Directional Loss Model</a></span></dt><dt><span class="section"><a href="i1300063.html#cfxBasiMomeGene">1.8.1.3. General Momentum Sources</a></span></dt><dt><span class="section"><a href="i1300063.html#cfxBasiMomeImme1">1.8.1.4. Immersed Solid Sources</a></span></dt></dl></dd><dt><span class="section"><a href="i1300159.html">1.8.2. General Sources</a></span></dt><dt><span class="section"><a href="i1300172.html">1.8.3. Mass (Continuity) Sources</a></span></dt><dt><span class="section"><a href="cfxBasiSourBulk.html">1.8.4. Bulk Sources</a></span></dt><dt><span class="section"><a href="cfxBasiSourRadi.html">1.8.5. Radiation Sources</a></span></dt><dt><span class="section"><a href="cfxBasiSourBoun.html">1.8.6. Boundary Sources</a></span></dt></dl></dd><dt><span class="section"><a href="i1300210.html">1.9. Boundary Conditions</a></span></dt><dd><dl><dt><span class="section"><a href="i1300213.html">1.9.1. Inlet (Subsonic)</a></span></dt><dd><dl><dt><span class="section"><a href="i1300213.html#cfxBasiInleMass">1.9.1.1. Mass and Momentum</a></span></dt><dd><dl><dt><span class="section"><a href="i1300213.html#cfxBasiMassNorm">1.9.1.1.1. Normal Speed in</a></span></dt><dt><span class="section"><a href="i1300213.html#cfxBasiMassCart">1.9.1.1.2. Cartesian Velocity Components</a></span></dt><dt><span class="section"><a href="i1300213.html#cfxBasiMassCyli">1.9.1.1.3. Cylindrical Velocity Components</a></span></dt><dt><span class="section"><a href="i1300213.html#cfxBasiMassTota">1.9.1.1.4. Total Pressure</a></span></dt><dt><span class="section"><a href="i1300213.html#cfxBasiMassMass1">1.9.1.1.5. Mass Flow Rate</a></span></dt></dl></dd><dt><span class="section"><a href="i1300213.html#cfxBasiInleTurb">1.9.1.2. Turbulence</a></span></dt><dd><dl><dt><span class="section"><a href="i1300213.html#cfxBasiTurbDefa">1.9.1.2.1. Default Intensity and Autocompute Length Scale</a></span></dt><dt><span class="section"><a href="i1300213.html#cfxBasiTurbInte">1.9.1.2.2. Intensity and Autocompute Length Scale</a></span></dt><dt><span class="section"><a href="i1300213.html#cfxBasiTurbInte1">1.9.1.2.3. Intensity and Length Scale</a></span></dt><dt><span class="section"><a href="i1300213.html#cfxBasiTurbEpsi">1.9.1.2.4. k and Epsilon</a></span></dt></dl></dd><dt><span class="section"><a href="i1300213.html#i1300345">1.9.1.3. Heat Transfer</a></span></dt><dd><dl><dt><span class="section"><a href="i1300213.html#sect_static_temp">1.9.1.3.1. Static Temperature</a></span></dt><dt><span class="section"><a href="i1300213.html#cfxBasiHeatTota1">1.9.1.3.2. Total Temperature</a></span></dt></dl></dd><dt><span class="section"><a href="i1300213.html#cfxBasiInleAddi">1.9.1.4. Additional Variables</a></span></dt></dl></dd><dt><span class="section"><a href="i1300412.html">1.9.2. Inlet (Supersonic)</a></span></dt><dd><dl><dt><span class="section"><a href="i1300412.html#cfxBasiInleHeat">1.9.2.1. Heat Transfer</a></span></dt><dd><dl><dt><span class="section"><a href="i1300412.html#cfxBasiHeatStat">1.9.2.1.1. Static Temperature</a></span></dt><dt><span class="section"><a href="i1300412.html#cfxBasiHeatTota2">1.9.2.1.2. Total Temperature</a></span></dt></dl></dd></dl></dd><dt><span class="section"><a href="i1300438.html">1.9.3. Outlet (Subsonic)</a></span></dt><dd><dl><dt><span class="section"><a href="i1300438.html#i1300438mm">1.9.3.1. Mass and Momentum</a></span></dt><dd><dl><dt><span class="section"><a href="i1300438.html#cfxBasiMassStat">1.9.3.1.1. Static Pressure (Uniform)</a></span></dt><dt><span class="section"><a href="i1300438.html#cfxBasiMassNorm1">1.9.3.1.2. Normal Speed</a></span></dt><dt><span class="section"><a href="i1300438.html#cfxBasiMassCart1">1.9.3.1.3. Cartesian Velocity Components</a></span></dt><dt><span class="section"><a href="i1300438.html#cfxBasiMassCyli1">1.9.3.1.4. Cylindrical Velocity Components</a></span></dt><dt><span class="section"><a href="i1300438.html#cfxBasiMassAver">1.9.3.1.5. Average Static Pressure: Over Whole Outlet</a></span></dt><dt><span class="section"><a href="i1300438.html#cfxBasiMassAver1">1.9.3.1.6. Average Static Pressure: Above or Below Specified Radius</a></span></dt><dt><span class="section"><a href="i1300438.html#cfxBasiMassAver2">1.9.3.1.7. Average Static Pressure: Circumferential</a></span></dt><dt><span class="section"><a href="i1300438.html#i1300438mmsmf">1.9.3.1.8. Mass Flow Rate: Scale Mass Flows</a></span></dt><dt><span class="section"><a href="i1300438.html#i1300438mmsp">1.9.3.1.9. Mass Flow Rate: Shift Pressure with or without Pressure Profile</a></span></dt><dt><span class="section"><a href="i1300438.html#i1300438mmcpa">1.9.3.1.10. Mass Flow Rate: Shift Pressure with Circumferential Pressure
Averaging</a></span></dt><dt><span class="section"><a href="i1300438.html#cfx_thry_abr_ecmf">1.9.3.1.11. Exit Corrected Mass Flow Rate</a></span></dt><dt><span class="section"><a href="i1300438.html#cfxBasiMassRadi">1.9.3.1.12. Radial Equilibrium</a></span></dt></dl></dd><dt><span class="section"><a href="i1300438.html#cfxBasiOutlTurb">1.9.3.2. Turbulence, Heat Transfer, Convected Additional Variables,
and Other Scalars</a></span></dt></dl></dd><dt><span class="section"><a href="i1300563.html">1.9.4. Outlet (Supersonic)</a></span></dt><dt><span class="section"><a href="i1300568.html">1.9.5. Opening</a></span></dt><dd><dl><dt><span class="section"><a href="i1300568.html#cfxBasiOpenMass">1.9.5.1. Mass and Momentum</a></span></dt><dd><dl><dt><span class="section"><a href="i1300568.html#cfxBasiMassCart2">1.9.5.1.1. Cartesian Velocity Components</a></span></dt><dt><span class="section"><a href="i1300568.html#cfxBasiMassCyli2">1.9.5.1.2. Cylindrical Velocity Components</a></span></dt><dt><span class="section"><a href="i1300568.html#i1300585">1.9.5.1.3. Pressure and Direction</a></span></dt><dd><dl><dt><span class="section"><a href="i1300568.html#cfxBasiPresLoss">1.9.5.1.3.1. Loss Coefficient</a></span></dt></dl></dd></dl></dd><dt><span class="section"><a href="i1300568.html#cfxBasiOpenHeat">1.9.5.2. Heat Transfer</a></span></dt><dd><dl><dt><span class="section"><a href="i1300568.html#cfxBasiHeatStat1">1.9.5.2.1. Static Temperature</a></span></dt></dl></dd><dt><span class="section"><a href="i1300568.html#cfxBasiOpenAddi">1.9.5.3. Additional Variables</a></span></dt></dl></dd><dt><span class="section"><a href="i1300632.html">1.9.6. Wall</a></span></dt><dd><dl><dt><span class="section"><a href="i1300632.html#cfxBasiWallMass">1.9.6.1. Mass and Momentum</a></span></dt><dd><dl><dt><span class="section"><a href="i1300632.html#cfxBasiMassSlip">1.9.6.1.1. No Slip (Not Moving, No Wall Velocity)</a></span></dt><dt><span class="section"><a href="i1300632.html#i1300643">1.9.6.1.2. Free Slip</a></span></dt><dt><span class="section"><a href="i1300632.html#cfxBasiMassFini">1.9.6.1.3. Finite Slip</a></span></dt><dt><span class="section"><a href="i1300632.html#cfxBasiMassSpec">1.9.6.1.4. Specified Shear</a></span></dt><dt><span class="section"><a href="i1300632.html#cfxBasiMassSlip1">1.9.6.1.5. No Slip (Moving, with Wall Velocity)</a></span></dt></dl></dd><dt><span class="section"><a href="i1300632.html#cfxBasiWallTurb">1.9.6.2. Turbulence</a></span></dt><dt><span class="section"><a href="i1300632.html#cfxBasiWallHeat">1.9.6.3. Heat Transfer</a></span></dt><dd><dl><dt><span class="section"><a href="i1300632.html#cfxBasiHeatAdia">1.9.6.3.1. Adiabatic</a></span></dt><dt><span class="section"><a href="i1300632.html#cfxBasiHeatFixe">1.9.6.3.2. Fixed Temperature</a></span></dt><dt><span class="section"><a href="i1300632.html#cfxBasiHeatHeat">1.9.6.3.3. Heat Flux</a></span></dt><dt><span class="section"><a href="i1300632.html#cfxBasiHeatHeat1">1.9.6.3.4. Heat Transfer Coefficient</a></span></dt></dl></dd><dt><span class="section"><a href="i1300632.html#cfxBasiWallAddi">1.9.6.4. Additional Variables</a></span></dt></dl></dd><dt><span class="section"><a href="i1300716.html">1.9.7. Symmetry Plane</a></span></dt></dl></dd><dt><span class="section"><a href="i1300731.html">1.10. Automatic Time Scale Calculation</a></span></dt><dd><dl><dt><span class="section"><a href="i1300737.html">1.10.1. Fluid Time Scale Estimate</a></span></dt><dt><span class="section"><a href="i1300794.html">1.10.2. Solid Time Scale Estimate</a></span></dt></dl></dd><dt><span class="section"><a href="i1409829.html">1.11. Mesh Adaption</a></span></dt><dd><dl><dt><span class="section"><a href="cfxBasiMeshAdap.html">1.11.1. Adaption Criteria</a></span></dt><dt><span class="section"><a href="cfxBasiMeshMesh.html">1.11.2. Mesh Refinement Implementation in ANSYS CFX</a></span></dt><dd><dl><dt><span class="section"><a href="cfxBasiMeshMesh.html#cfxBasiMeshAdap1">1.11.2.1. Adaption in Inflated Regions of the Mesh</a></span></dt><dt><span class="section"><a href="cfxBasiMeshMesh.html#cfxBasiMeshAdap2">1.11.2.2. Adaption to the Original Geometry</a></span></dt></dl></dd><dt><span class="section"><a href="cfxBasiMeshMesh1.html">1.11.3. Mesh Adaption Limitations</a></span></dt><dd><dl><dt><span class="section"><a href="cfxBasiMeshMesh1.html#cfxBasiMeshMesh2">1.11.3.1. Mesh Adaption Tips</a></span></dt></dl></dd></dl></dd><dt><span class="section"><a href="LJNHHGKE.html">1.12. Flow in Porous Media</a></span></dt><dd><dl><dt><span class="section"><a href="darcymodel.html">1.12.1. Full Porous Model</a></span></dt><dd><dl><dt><span class="section"><a href="darcymodel.html#cfx_thry_por_heat_fluid">1.12.1.1. Heat Transfer Through the Fluid Only</a></span></dt><dt><span class="section"><a href="darcymodel.html#cfx_thry_por_av_fluid">1.12.1.2. Additional Variable Transfer Through the Fluid Only</a></span></dt><dt><span class="section"><a href="darcymodel.html#cfx_thry_por_heat_flu_sol">1.12.1.3. Heat Transfer Through the Fluid and Solid</a></span></dt><dt><span class="section"><a href="darcymodel.html#cfx_thry_por_av_flu_sol">1.12.1.4. Additional Variable Transfer Through the Fluid and Solid</a></span></dt><dt><span class="section"><a href="darcymodel.html#cfx_thry_por_time_vary">1.12.1.5. Time-varying Porosity</a></span></dt></dl></dd><dt><span class="section"><a href="directionallossmodel.html">1.12.2. Porous Momentum Loss Models</a></span></dt></dl></dd><dt><span class="section"><a href="i1303889.html">1.13. Wall and Boundary Distance Formulation</a></span></dt><dd><dl><dt><span class="section"><a href="sect_wall_dist_form.html">1.13.1. 1D Illustration of Concept</a></span></dt><dt><span class="section"><a href="cfx_thry_3dwallscaleeqn.html">1.13.2. Concept Generalized to 3D</a></span></dt></dl></dd><dt><span class="section"><a href="wall_con_theory.html">1.14. Wall Condensation Theory</a></span></dt><dd><dl><dt><span class="section"><a href="wall_con_mass_trans.html">1.14.1. Wall Condensation Model</a></span></dt><dd><dl><dt><span class="section"><a href="wall_con_mass_trans.html#wall_con_lambound">1.14.1.1. Laminar Boundary Layer Model</a></span></dt><dt><span class="section"><a href="wall_con_mass_trans.html#wall_con_turb_bound">1.14.1.2. Turbulent Boundary Layer Model</a></span></dt></dl></dd><dt><span class="section"><a href="wall_con_cond_heat_trans.html">1.14.2. Condensation Heat Transfer (CHT)</a></span></dt><dt><span class="section"><a href="wall_con_spec_sec_flux.html">1.14.3. Specification of Secondary Fluxes</a></span></dt></dl></dd></dl></dd><dt><span class="chapter"><a href="i1302116.html">2. Turbulence and Wall Function Theory</a></span></dt><dd><dl><dt><span class="section"><a href="i1302147.html">2.1. Turbulence Models</a></span></dt><dd><dl><dt><span class="section"><a href="cfxTurbTurbStat.html">2.1.1. Statistical Turbulence Models and the Closure Problem</a></span></dt><dd><dl><dt><span class="section"><a href="cfxTurbTurbStat.html#i1376347">2.1.1.1. Reynolds Averaged Navier-Stokes (RANS) Equations</a></span></dt></dl></dd></dl></dd><dt><span class="section"><a href="i1302234.html">2.2. Eddy Viscosity Turbulence Models</a></span></dt><dd><dl><dt><span class="section"><a href="KOFHHMFL.html">2.2.1. The Zero Equation Model in ANSYS CFX</a></span></dt><dt><span class="section"><a href="i1302321.html">2.2.2. Two Equation Turbulence Models</a></span></dt><dd><dl><dt><span class="section"><a href="i1302321.html#i1302327">2.2.2.1. The k-epsilon Model in ANSYS CFX</a></span></dt><dt><span class="section"><a href="i1302321.html#i1302408">2.2.2.2. Buoyancy Turbulence</a></span></dt><dt><span class="section"><a href="i1302321.html#i1302452">2.2.2.3. The RNG k-epsilon Model in ANSYS CFX</a></span></dt><dt><span class="section"><a href="i1302321.html#i1302479">2.2.2.4. The k-omega Models in ANSYS CFX</a></span></dt><dd><dl><dt><span class="section"><a href="i1302321.html#PHHFINEJ">2.2.2.4.1. The Wilcox k-omega Model</a></span></dt><dt><span class="section"><a href="i1302321.html#i1302567">2.2.2.4.2. The Baseline (BSL) k-omega Model</a></span></dt><dt><span class="section"><a href="i1302321.html#i1302649">2.2.2.4.3. The Shear Stress Transport (SST) Model</a></span></dt><dd><dl><dt><span class="section"><a href="i1302321.html#cfxTurbSheaBlen">2.2.2.4.3.1. Blending Functions</a></span></dt><dt><span class="section"><a href="i1302321.html#cfxTurbSheaWall">2.2.2.4.3.2. The Wall Scale Equation</a></span></dt><dt><span class="section"><a href="i1302321.html#i116827704359282">2.2.2.4.3.3. Modifications to SST for High Lift Devices</a></span></dt></dl></dd><dt><span class="section"><a href="i1302321.html#i174623347923027">2.2.2.4.4. The Reattachment Modification (RM) Model</a></span></dt></dl></dd><dt><span class="section"><a href="i1302321.html#CIHFECEJ">2.2.2.5. Production Limiters</a></span></dt><dt><span class="section"><a href="i1302321.html#thry_turb_curvcorrection">2.2.2.6. Curvature Correction for Two-Equation Models</a></span></dt></dl></dd><dt><span class="section"><a href="CIHDIIDC.html">2.2.3. The Eddy Viscosity Transport Model</a></span></dt><dd><dl><dt><span class="section"><a href="CIHDIIDC.html#cfxTurbEddyReyn">2.2.3.1. Low Reynolds Number Formulation</a></span></dt></dl></dd></dl></dd><dt><span class="section"><a href="i1302786.html">2.3. Reynolds Stress Turbulence Models</a></span></dt><dd><dl><dt><span class="section"><a href="cfxTurbReynReyn.html">2.3.1. The Reynolds Stress Model</a></span></dt><dd><dl><dt><span class="section"><a href="cfxTurbReynReyn.html#i1302887">2.3.1.1. Pressure-Strain Terms</a></span></dt></dl></dd><dt><span class="section"><a href="i1303039.html">2.3.2. Omega-Based Reynolds Stress Models</a></span></dt><dd><dl><dt><span class="section"><a href="i1303039.html#cfxTurbOmegOmeg">2.3.2.1. The Omega Reynolds Stress Model</a></span></dt><dt><span class="section"><a href="i1303039.html#cfxTurbOmegReyn">2.3.2.2. The BSL Reynolds Stress Model</a></span></dt><dt><span class="section"><a href="i1303039.html#cfxTurbOmegPres">2.3.2.3. Pressure-Strain Correlation</a></span></dt><dt><span class="section"><a href="i1303039.html#cfxTurbOmegWall">2.3.2.4. Wall Boundary Condition</a></span></dt></dl></dd><dt><span class="section"><a href="cfxTurbReynRota.html">2.3.3. Rotating Frame of Reference for Reynolds Stress Models</a></span></dt><dt><span class="section"><a href="thry_turb_earsm.html">2.3.4. Explicit Algebraic Reynolds Stress Model</a></span></dt><dd><dl><dt><span class="section"><a href="thry_turb_earsm.html#cfxTurbExplStre">2.3.4.1. Streamline Curvature and System Rotation</a></span></dt></dl></dd></dl></dd><dt><span class="section"><a href="i1335978.html">2.4. ANSYS CFX Transition Models</a></span></dt><dd><dl><dt><span class="section"><a href="i168504023837015.html">2.4.1. Two Equation Gamma Theta Transition Model</a></span></dt><dd><dl><dt><span class="section"><a href="i168504023837015.html#i202236002473935">2.4.1.1. Overview</a></span></dt><dt><span class="section"><a href="i168504023837015.html#i124641235151426">2.4.1.2. Transport Equations for the Gamma Theta Transition Model</a></span></dt><dt><span class="section"><a href="i168504023837015.html#i141647147338457">2.4.1.3. Separation-induced Transition Correction</a></span></dt><dt><span class="section"><a href="i168504023837015.html#i176114374958801">2.4.1.4. Coupling to the SST Model</a></span></dt><dt><span class="section"><a href="i168504023837015.html#cfxTurbANSYTran">2.4.1.5. Gamma Theta Transition Model and Rough Walls</a></span></dt></dl></dd><dt><span class="section"><a href="i106742654367865.html">2.4.2. One Equation Intermittency Transition Model</a></span></dt><dd><dl><dt><span class="section"><a href="i106742654367865.html#i173696547837983">2.4.2.1. Overview</a></span></dt><dt><span class="section"><a href="i106742654367865.html#i113048259015287">2.4.2.2. Transport Equation for the Intermittency Transition Model</a></span></dt><dt><span class="section"><a href="i106742654367865.html#i128113336331409">2.4.2.3. Coupling to SST Model</a></span></dt><dt><span class="section"><a href="i106742654367865.html#i168003212172760">2.4.2.4. Intermittency Transition Model and Rough Walls</a></span></dt></dl></dd></dl></dd><dt><span class="section"><a href="i1303244.html">2.5. Large Eddy Simulation Theory</a></span></dt><dd><dl><dt><span class="section"><a href="cfxTurbLargSubg.html">2.5.1. Subgrid-Scale Models</a></span></dt><dd><dl><dt><span class="section"><a href="cfxTurbLargSubg.html#cfxTurbSubgSmag">2.5.1.1. Smagorinsky Model</a></span></dt><dd><dl><dt><span class="section"><a href="cfxTurbLargSubg.html#cfxTurbSmagWall">2.5.1.1.1. Wall Damping</a></span></dt></dl></dd><dt><span class="section"><a href="cfxTurbLargSubg.html#cfxTurbSubgWALE">2.5.1.2. WALE Model</a></span></dt><dt><span class="section"><a href="cfxTurbLargSubg.html#cfxTurbSubgDyna">2.5.1.3. Dynamic Smagorinsky-Lilly Model</a></span></dt></dl></dd></dl></dd><dt><span class="section"><a href="i1303383.html">2.6. Detached Eddy Simulation Theory</a></span></dt><dd><dl><dt><span class="section"><a href="i1303409.html">2.6.1. SST-DES Formulation Strelets et al.</a></span></dt><dt><span class="section"><a href="cfxTurbDetaZona.html">2.6.2. Delayed and Shielded DES-SST Model Formulation</a></span></dt><dt><span class="section"><a href="i213009681647479.html">2.6.3. Stress-Blended Eddy Simulation (SBES)</a></span></dt><dd><dl><dt><span class="section"><a href="i213009681647479.html#i129548750824254">2.6.3.1. General Concept</a></span></dt><dt><span class="section"><a href="i213009681647479.html#i180909796885837">2.6.3.2. Example</a></span></dt></dl></dd><dt><span class="section"><a href="CIHEGJAA.html">2.6.4. Discretization of the Advection Terms</a></span></dt><dt><span class="section"><a href="cfxTurbDetaBoun.html">2.6.5. Boundary Conditions</a></span></dt></dl></dd><dt><span class="section"><a href="thry_turb_sas.html">2.7. Scale-Adaptive Simulation Theory</a></span></dt><dd><dl><dt><span class="section"><a href="cfxTurbScalDisc.html">2.7.1. Discretization  of the Advection Terms</a></span></dt></dl></dd><dt><span class="section"><a href="i1303467.html">2.8. Modeling Flow Near the Wall</a></span></dt><dd><dl><dt><span class="section"><a href="cfxTurbModeMath.html">2.8.1. Mathematical Formulation</a></span></dt><dd><dl><dt><span class="section"><a href="cfxTurbModeMath.html#JOKELLGF">2.8.1.1. Scalable Wall Functions</a></span></dt><dt><span class="section"><a href="cfxTurbModeMath.html#i1303553">2.8.1.2. Solver Yplus and Yplus</a></span></dt><dt><span class="section"><a href="cfxTurbModeMath.html#i1303576">2.8.1.3. Automatic Near-Wall Treatment for Omega-Based Models</a></span></dt><dt><span class="section"><a href="cfxTurbModeMath.html#i1303614">2.8.1.4. Treatment of Rough Walls</a></span></dt><dd><dl><dt><span class="section"><a href="cfxTurbModeMath.html#cfxTurbTreaRoug">2.8.1.4.1. Rough Wall Treatment for Turbulence Models Based on the Dissipation
Equation</a></span></dt><dt><span class="section"><a href="cfxTurbModeMath.html#cfxTurbTreaAuto">2.8.1.4.2. Automatic Rough Wall Treatment for Turbulence Models Based
on the Omega Equation</a></span></dt><dt><span class="section"><a href="cfxTurbModeMath.html#cfxTurbTreaTran">2.8.1.4.3. Transition and Rough Walls</a></span></dt><dt><span class="section"><a href="cfxTurbModeMath.html#cfxTurbTreaWall">2.8.1.4.4. Wall Function Approach for Omega-Based Turbulence Models</a></span></dt><dt><span class="section"><a href="cfxTurbModeMath.html#i767634475347675670086">2.8.1.4.5. Treatment of the SST Model for Icing Simulations</a></span></dt></dl></dd><dt><span class="section"><a href="cfxTurbModeMath.html#i1303638">2.8.1.5. Heat Flux in the Near-Wall Region</a></span></dt><dd><dl><dt><span class="section"><a href="cfxTurbModeMath.html#i1435225">2.8.1.5.1. Scalable Wall Functions</a></span></dt><dt><span class="section"><a href="cfxTurbModeMath.html#i1256558">2.8.1.5.2. Automatic Wall Treatment</a></span></dt><dt><span class="section"><a href="cfxTurbModeMath.html#i135626">2.8.1.5.3. Effect of Rough Walls</a></span></dt><dt><span class="section"><a href="cfxTurbModeMath.html#i1354232">2.8.1.5.4. Treatment of Compressibility Effects</a></span></dt></dl></dd><dt><span class="section"><a href="cfxTurbModeMath.html#cfxTurbMathAddi">2.8.1.6. Additional Variables in the Near Wall Region</a></span></dt></dl></dd></dl></dd></dl></dd><dt><span class="chapter"><a href="i1304366.html">3. GGI and MFR Theory</a></span></dt><dd><dl><dt><span class="section"><a href="BGBEBDEG.html">3.1. Interface Characteristics</a></span></dt><dt><span class="section"><a href="BGBCHBEI.html">3.2. Numerics</a></span></dt></dl></dd><dt><span class="chapter"><a href="cfx_thry_abr.html">4. Transient Blade Row Modeling Theory</a></span></dt><dd><dl><dt><span class="section"><a href="i5764405865124665156556.html">4.1. Profile Transformation</a></span></dt><dt><span class="section"><a href="cfx_thry_abr_time.html">4.2. Time Transformation</a></span></dt><dt><span class="section"><a href="cfx_thry_abr_fourier.html">4.3. Fourier Transformation</a></span></dt><dt><span class="section"><a href="i199865067149197.html">4.4. Harmonic Analysis</a></span></dt></dl></dd><dt><span class="chapter"><a href="i1304475.html">5. Multiphase Flow Theory</a></span></dt><dd><dl><dt><span class="section"><a href="i1304552.html">5.1. Multiphase Notation</a></span></dt><dd><dl><dt><span class="section"><a href="i1304578.html">5.1.1. Multiphase Total Pressure</a></span></dt></dl></dd><dt><span class="section"><a href="i1304590.html">5.2. The Homogeneous and Inhomogeneous Models</a></span></dt><dd><dl><dt><span class="section"><a href="cfxMultHomoInho.html">5.2.1. The Inhomogeneous Model</a></span></dt><dd><dl><dt><span class="section"><a href="cfxMultHomoInho.html#i1304594">5.2.1.1. Interfacial Area Density</a></span></dt><dd><dl><dt><span class="section"><a href="cfxMultHomoInho.html#cfxMultIntePart">5.2.1.1.1. The Particle Model</a></span></dt><dt><span class="section"><a href="cfxMultHomoInho.html#i1304620">5.2.1.1.2. The Mixture Model</a></span></dt><dt><span class="section"><a href="cfxMultHomoInho.html#CHDCJDAG">5.2.1.1.3. The Free Surface Model</a></span></dt></dl></dd></dl></dd><dt><span class="section"><a href="i1304667.html">5.2.2. The Homogeneous Model</a></span></dt></dl></dd><dt><span class="section"><a href="i1304694.html">5.3. Hydrodynamic Equations</a></span></dt><dd><dl><dt><span class="section"><a href="cfxMultHydrInho.html">5.3.1. Inhomogeneous Hydrodynamic Equations</a></span></dt><dd><dl><dt><span class="section"><a href="cfxMultHydrInho.html#i1304702">5.3.1.1. Momentum Equations</a></span></dt><dt><span class="section"><a href="cfxMultHydrInho.html#i1304728">5.3.1.2. Continuity Equations</a></span></dt><dt><span class="section"><a href="cfxMultHydrInho.html#the_multi_sect_vol_cons">5.3.1.3. Volume Conservation Equation</a></span></dt><dt><span class="section"><a href="cfxMultHydrInho.html#the_multi_sect_press_cons">5.3.1.4. Pressure Constraint</a></span></dt></dl></dd><dt><span class="section"><a href="i1304782.html">5.3.2. Homogeneous Hydrodynamic Equations</a></span></dt><dd><dl><dt><span class="section"><a href="i1304782.html#cfxMultHomoMome">5.3.2.1. Momentum Equations</a></span></dt><dt><span class="section"><a href="i1304782.html#cfxMultHomoCont">5.3.2.2. Continuity Equations</a></span></dt><dt><span class="section"><a href="i1304782.html#cfxMultHomoVolu">5.3.2.3. Volume Conservation Equations</a></span></dt><dt><span class="section"><a href="i1304782.html#cfxMultHomoPres">5.3.2.4. Pressure Constraint</a></span></dt></dl></dd></dl></dd><dt><span class="section"><a href="i1304819.html">5.4. Multicomponent Multiphase Flow</a></span></dt><dt><span class="section"><a href="i1304834.html">5.5. Interphase Momentum Transfer Models</a></span></dt><dd><dl><dt><span class="section"><a href="i1304881.html">5.5.1. Interphase Drag</a></span></dt><dt><span class="section"><a href="i1304903.html">5.5.2. Interphase Drag for the Particle Model</a></span></dt><dd><dl><dt><span class="section"><a href="i1304903.html#cfxMultInteSpar">5.5.2.1. Sparsely Distributed Solid Particles</a></span></dt><dd><dl><dt><span class="section"><a href="i1304903.html#i1304973">5.5.2.1.1. Schiller Naumann Drag Model</a></span></dt></dl></dd><dt><span class="section"><a href="i1304903.html#i1304988">5.5.2.2. Densely Distributed Solid Particles</a></span></dt><dd><dl><dt><span class="section"><a href="i1304903.html#cfxthry_wenyu">5.5.2.2.1. Densely Distributed Solid Particles: Wen Yu Drag Model</a></span></dt><dt><span class="section"><a href="i1304903.html#cfxthry_gidaspowdragmodel">5.5.2.2.2. Densely Distributed Solid Particles: Gidaspow Drag Model</a></span></dt></dl></dd><dt><span class="section"><a href="i1304903.html#i1305008">5.5.2.3. Sparsely Distributed Fluid Particles (Drops and Bubbles)</a></span></dt><dd><dl><dt><span class="section"><a href="i1304903.html#cfxMultSparSpar">5.5.2.3.1. Sparsely Distributed Fluid Particles: Ishii-Zuber Drag Model</a></span></dt><dt><span class="section"><a href="i1304903.html#i1305054">5.5.2.3.2. Sparsely Distributed Fluid Particles: Grace Drag Model</a></span></dt></dl></dd><dt><span class="section"><a href="i1304903.html#i1305089">5.5.2.4. Densely Distributed Fluid Particles</a></span></dt><dd><dl><dt><span class="section"><a href="i1304903.html#cfxMultDensDens">5.5.2.4.1. Densely Distributed Fluid Particles: Ishii-Zuber Drag Model</a></span></dt><dt><span class="section"><a href="i1304903.html#cfxMultDensDens1">5.5.2.4.2. Densely Distributed Fluid Particles: Dense Spherical Particle
Regime (Ishii Zuber)</a></span></dt><dt><span class="section"><a href="i1304903.html#cfxMultDensDens2">5.5.2.4.3. Densely Distributed Fluid Particles: Dense Distorted Particle
Regime (Ishii Zuber)</a></span></dt><dt><span class="section"><a href="i1304903.html#cfxMultDensDens3">5.5.2.4.4. Densely Distributed Fluid Particles: Dense Spherical Cap Regime
(Ishii Zuber)</a></span></dt><dt><span class="section"><a href="i1304903.html#cfxMultDensDens4">5.5.2.4.5. Densely Distributed Fluid Particles: Automatic Regime Selection
(Ishii Zuber)</a></span></dt><dt><span class="section"><a href="i1304903.html#i1305120">5.5.2.4.6. Densely Distributed Fluid Particles: Grace Drag Model</a></span></dt></dl></dd></dl></dd><dt><span class="section"><a href="CHDFJHJC.html">5.5.3. Interphase Drag for the Mixture Model</a></span></dt><dt><span class="section"><a href="cfxMultInteInte1.html">5.5.4. Interphase Drag for the Free Surface Model</a></span></dt><dt><span class="section"><a href="i1305163.html">5.5.5. Lift Force</a></span></dt><dd><dl><dt><span class="section"><a href="i1305163.html#saffmanmei">5.5.5.1. The Saffman Mei Lift Force Model</a></span></dt><dt><span class="section"><a href="i1305163.html#legendremagnaudet">5.5.5.2. The Legendre and Magnaudet Lift Force Model</a></span></dt><dt><span class="section"><a href="i1305163.html#tomiyama">5.5.5.3. The Tomiyama Lift Force Model</a></span></dt></dl></dd><dt><span class="section"><a href="i1305185.html">5.5.6. Virtual Mass Force</a></span></dt><dt><span class="section"><a href="i1305214.html">5.5.7. Wall Lubrication Force</a></span></dt><dd><dl><dt><span class="section"><a href="i1305214.html#theantalmodel">5.5.7.1. The Antal Wall Lubrication Force Model</a></span></dt><dt><span class="section"><a href="i1305214.html#thetomiyamamodel">5.5.7.2. The Tomiyama Wall Lubrication Force Model</a></span></dt><dt><span class="section"><a href="i1305214.html#thefrankmodel">5.5.7.3. The Frank Wall Lubrication Force Model</a></span></dt></dl></dd><dt><span class="section"><a href="i1305261.html">5.5.8. Interphase Turbulent Dispersion Force</a></span></dt><dd><dl><dt><span class="section"><a href="i1305261.html#i4784g5d">5.5.8.1. Favre Averaged Drag Model</a></span></dt><dt><span class="section"><a href="i1305261.html#i39du5723">5.5.8.2. Lopez de Bertodano Model</a></span></dt></dl></dd></dl></dd><dt><span class="section"><a href="i1305301.html">5.6. Solid Particle Collision Models</a></span></dt><dd><dl><dt><span class="section"><a href="CHDJEAFF.html">5.6.1. Solids Stress Tensor</a></span></dt><dd><dl><dt><span class="section"><a href="CHDJEAFF.html#cfxMultSoliEmpi">5.6.1.1. Empirical Constitutive Equations</a></span></dt><dt><span class="section"><a href="CHDJEAFF.html#cfxMultSoliKine">5.6.1.2. Kinetic Theory Models for the Solids Stress Tensor</a></span></dt></dl></dd><dt><span class="section"><a href="CHDEBCBJ.html">5.6.2. Solids Pressure</a></span></dt><dd><dl><dt><span class="section"><a href="CHDEBCBJ.html#cfxMultSoliEmpi1">5.6.2.1. Empirical Constitutive Equations</a></span></dt><dt><span class="section"><a href="CHDEBCBJ.html#i6fhsh36">5.6.2.2. Kinetic Theory Models for Solids Pressure</a></span></dt></dl></dd><dt><span class="section"><a href="CHDFJDJH.html">5.6.3. Solids Shear Viscosity</a></span></dt><dd><dl><dt><span class="section"><a href="CHDFJDJH.html#cfxMultSoliCons1">5.6.3.1. Constitutive Equation Models</a></span></dt><dt><span class="section"><a href="CHDFJDJH.html#cfxMultSoliKine2">5.6.3.2. Kinetic Theory Models for Solids Shear Viscosity</a></span></dt></dl></dd><dt><span class="section"><a href="CHDHDGIJ.html">5.6.4. Solids Bulk Viscosity</a></span></dt><dd><dl><dt><span class="section"><a href="CHDHDGIJ.html#cfxMultSoliCons">5.6.4.1. Constitutive Equation Models</a></span></dt><dt><span class="section"><a href="CHDHDGIJ.html#cfxMultSoliKine1">5.6.4.2. Kinetic Theory Models for Solids Bulk Viscosity</a></span></dt></dl></dd><dt><span class="section"><a href="CHDDGACH.html">5.6.5. Granular Temperature</a></span></dt><dd><dl><dt><span class="section"><a href="CHDDGACH.html#cfxMultGranAlge">5.6.5.1. Algebraic Equilibrium Model</a></span></dt><dt><span class="section"><a href="CHDDGACH.html#cfxMultGranZero">5.6.5.2. Zero Equation Model</a></span></dt></dl></dd></dl></dd><dt><span class="section"><a href="i1305683.html">5.7. Interphase Heat Transfer</a></span></dt><dd><dl><dt><span class="section"><a href="cfxMultIntePhas.html">5.7.1. Phasic Equations</a></span></dt><dt><span class="section"><a href="i1305719.html">5.7.2. Inhomogeneous Interphase Heat Transfer Models</a></span></dt><dd><dl><dt><span class="section"><a href="i1305719.html#cfxMultInhoOver">5.7.2.1. Overall Heat Transfer Coefficients</a></span></dt><dt><span class="section"><a href="i1305719.html#i1305747">5.7.2.2. Particle Model Correlations</a></span></dt><dt><span class="section"><a href="i1305719.html#cfxMultInhoMixt">5.7.2.3. Mixture Model Correlations</a></span></dt><dt><span class="section"><a href="i1305719.html#i1305806">5.7.2.4. The Two Resistance Model</a></span></dt></dl></dd><dt><span class="section"><a href="cfxMultInteHomo.html">5.7.3. Homogeneous Heat Transfer in Multiphase Flow</a></span></dt></dl></dd><dt><span class="section"><a href="i1305857.html">5.8. Multiple Size Group (MUSIG) Model</a></span></dt><dd><dl><dt><span class="section"><a href="cfxMultMultMode.html">5.8.1. Model Derivation</a></span></dt><dd><dl><dt><span class="section"><a href="cfxMultMultMode.html#cfxMultModePopu">5.8.1.1. Population Balance Equation</a></span></dt><dt><span class="section"><a href="cfxMultMultMode.html#cfxMultModeSize">5.8.1.2. Size Fraction Equations</a></span></dt><dt><span class="section"><a href="cfxMultMultMode.html#cfxMultModeSour">5.8.1.3. Source Terms</a></span></dt></dl></dd><dt><span class="section"><a href="i1404263.html">5.8.2. Size Group Discretization</a></span></dt><dd><dl><dt><span class="section"><a href="i1404263.html#cfxMultSizeEqua">5.8.2.1. Equal Mass Discretization</a></span></dt><dt><span class="section"><a href="i1404263.html#cfxMultSizeEqua1">5.8.2.2. Equal Diameter Discretization</a></span></dt><dt><span class="section"><a href="i1404263.html#cfxMultSizeGeom">5.8.2.3. Geometric Mass Discretization</a></span></dt><dt><span class="section"><a href="i1404263.html#cfxMultSizeComp">5.8.2.4. Comparison</a></span></dt><dt><span class="section"><a href="i1404263.html#cfxMultSizeBound">5.8.2.5. Size Group Boundaries</a></span></dt></dl></dd><dt><span class="section"><a href="i1404264.html">5.8.3. Breakup Models</a></span></dt><dd><dl><dt><span class="section"><a href="i1404264.html#cfxMultBreaSven">5.8.3.1. Luo and Svendsen Model</a></span></dt><dt><span class="section"><a href="i1404264.html#cfxMultBreaUser">5.8.3.2. User-Defined Models</a></span></dt></dl></dd><dt><span class="section"><a href="cfxMultMultCoal.html">5.8.4. Coalescence Models</a></span></dt><dd><dl><dt><span class="section"><a href="cfxMultMultCoal.html#cfxMultCoalPrin">5.8.4.1. Prince and Blanch Model</a></span></dt><dt><span class="section"><a href="cfxMultMultCoal.html#cfxMultCoalUser">5.8.4.2. User-Defined Models</a></span></dt></dl></dd></dl></dd><dt><span class="section"><a href="i1306440.html">5.9. The Algebraic Slip Model</a></span></dt><dd><dl><dt><span class="section"><a href="cfxMultAlgePhas.html">5.9.1. Phasic Equations</a></span></dt><dt><span class="section"><a href="cfxMultAlgeBulk.html">5.9.2. Bulk Equations</a></span></dt><dt><span class="section"><a href="cfxMultAlgeDrif.html">5.9.3. Drift and Slip Relations</a></span></dt><dt><span class="section"><a href="i1306512.html">5.9.4. Derivation of the Algebraic Slip Equation</a></span></dt><dt><span class="section"><a href="cfxMultAlgeTurb.html">5.9.5. Turbulence Effects</a></span></dt><dt><span class="section"><a href="cfxMultAlgeEner.html">5.9.6. Energy Equation</a></span></dt><dt><span class="section"><a href="cfxMultAlgeWall.html">5.9.7. Wall Deposition</a></span></dt></dl></dd><dt><span class="section"><a href="i1306589.html">5.10. Turbulence Modeling in Multiphase Flow</a></span></dt><dd><dl><dt><span class="section"><a href="cfxMultTurbPhas.html">5.10.1. Phase-Dependent Turbulence Models</a></span></dt><dd><dl><dt><span class="section"><a href="cfxMultTurbPhas.html#cfxMultPhasEddy">5.10.1.1. The Eddy Viscosity Hypothesis</a></span></dt><dt><span class="section"><a href="cfxMultTurbPhas.html#cfxMultPhasAlge1">5.10.1.2. Algebraic Models</a></span></dt><dd><dl><dt><span class="section"><a href="cfxMultTurbPhas.html#cfxMultAlgeZero">5.10.1.2.1. Zero Equation Model</a></span></dt><dt><span class="section"><a href="cfxMultTurbPhas.html#cfxMultAlgeDisp">5.10.1.2.2. Dispersed Phase Zero Equation Model</a></span></dt></dl></dd><dt><span class="section"><a href="cfxMultTurbPhas.html#cfxMultPhasEqua1">5.10.1.3. Two-Equation Models</a></span></dt><dt><span class="section"><a href="cfxMultTurbPhas.html#cfxMultPhasReyn1">5.10.1.4. Reynolds Stress Models</a></span></dt></dl></dd><dt><span class="section"><a href="i1306662.html">5.10.2. Turbulence Enhancement</a></span></dt><dt><span class="section"><a href="cfxMultTurbHomo.html">5.10.3. Homogeneous Turbulence for Multiphase Flow</a></span></dt></dl></dd><dt><span class="section"><a href="i1411696.html">5.11. Additional Variables in Multiphase Flow</a></span></dt><dd><dl><dt><span class="section"><a href="cfxMultAddiAddi.html">5.11.1. Additional Variable Interphase Transfer Models</a></span></dt><dd><dl><dt><span class="section"><a href="cfxMultAddiAddi.html#i1306767">5.11.1.1. Particle Model Correlations</a></span></dt><dt><span class="section"><a href="cfxMultAddiAddi.html#cfxMultAddiMixt1">5.11.1.2. Mixture Model Correlations</a></span></dt></dl></dd><dt><span class="section"><a href="i1306806.html">5.11.2. Homogeneous Additional Variables in Multiphase Flow</a></span></dt></dl></dd><dt><span class="section"><a href="i1306824.html">5.12. Sources in Multiphase Flow</a></span></dt><dd><dl><dt><span class="section"><a href="i1409102.html">5.12.1. Fluid-specific Sources</a></span></dt><dt><span class="section"><a href="i1409114.html">5.12.2. Bulk Sources</a></span></dt></dl></dd><dt><span class="section"><a href="i1306836.html">5.13. Interphase Mass Transfer</a></span></dt><dd><dl><dt><span class="section"><a href="cfxMultInteSeco.html">5.13.1. Secondary Fluxes</a></span></dt><dt><span class="section"><a href="i1306909.html">5.13.2. User Defined Interphase Mass Transfer</a></span></dt><dt><span class="section"><a href="i1306928.html">5.13.3. General Species Mass Transfer</a></span></dt><dd><dl><dt><span class="section"><a href="i1306928.html#i1306940">5.13.3.1. Equilibrium Models</a></span></dt><dd><dl><dt><span class="section"><a href="i1306928.html#cfxMultEquiRaou">5.13.3.1.1. Raoult’s Law</a></span></dt><dt><span class="section"><a href="i1306928.html#cfxMultEquiHenr">5.13.3.1.2. Henry’s Law</a></span></dt></dl></dd><dt><span class="section"><a href="i1306928.html#i1307005">5.13.3.2. Two Resistance Model with Negligible Mass Transfer</a></span></dt></dl></dd><dt><span class="section"><a href="i1307110.html">5.13.4. The Thermal Phase Change Model</a></span></dt><dd><dl><dt><span class="section"><a href="i1307110.html#i5h85n85">5.13.4.1. Wall Boiling Model</a></span></dt><dd><dl><dt><span class="section"><a href="i1307110.html#i4g8785564">5.13.4.1.1. Partitioning of the Wall Heat Flux</a></span></dt><dt><span class="section"><a href="i1307110.html#i8ch238gf">5.13.4.1.2. Sub-models for the Wall Boiling Model</a></span></dt><dd><dl><dt><span class="section"><a href="i1307110.html#i75gf74ft">5.13.4.1.2.1. Wall Nucleation Site Density</a></span></dt><dt><span class="section"><a href="i1307110.html#if8388544">5.13.4.1.2.2. Bubble Departure Diameter</a></span></dt><dt><span class="section"><a href="i1307110.html#i47fh6845">5.13.4.1.2.3. Bubble Detachment Frequency</a></span></dt><dt><span class="section"><a href="i1307110.html#i5f7356fy">5.13.4.1.2.4. Bubble Waiting Time</a></span></dt><dt><span class="section"><a href="i1307110.html#i85gu58xnvf">5.13.4.1.2.5. Area Influence Factors</a></span></dt><dt><span class="section"><a href="i1307110.html#iy57g8456">5.13.4.1.2.6. Convective Heat Transfer</a></span></dt><dt><span class="section"><a href="i1307110.html#i9644kd9n">5.13.4.1.2.7. Quenching Heat Transfer</a></span></dt><dt><span class="section"><a href="i1307110.html#i955jd832">5.13.4.1.2.8. Evaporation Rate</a></span></dt></dl></dd><dt><span class="section"><a href="i1307110.html#sect_det_wall_heat_flux_part">5.13.4.1.3. Determination of the Wall Heat Flux Partition</a></span></dt></dl></dd></dl></dd><dt><span class="section"><a href="cfxMultInteCavi.html">5.13.5. Cavitation Model</a></span></dt><dd><dl><dt><span class="section"><a href="cfxMultInteCavi.html#i1307195">5.13.5.1. The Rayleigh Plesset Model</a></span></dt><dt><span class="section"><a href="cfxMultInteCavi.html#i1307259">5.13.5.2. User Defined Cavitation Models</a></span></dt></dl></dd><dt><span class="section"><a href="cfxMultInteDrop.html">5.13.6. The Droplet Condensation Model</a></span></dt></dl></dd><dt><span class="section"><a href="i1307272.html">5.14. Free Surface Flow</a></span></dt><dd><dl><dt><span class="section"><a href="cfxMultFreeImpl.html">5.14.1. Implementation</a></span></dt><dt><span class="section"><a href="i1307284.html">5.14.2. Surface Tension</a></span></dt></dl></dd></dl></dd><dt><span class="chapter"><a href="i1308252.html">6. Particle Transport Theory</a></span></dt><dd><dl><dt><span class="section"><a href="i1335625.html">6.1. Lagrangian Tracking Implementation</a></span></dt><dd><dl><dt><span class="section"><a href="cfxPartLagrPart.html">6.1.1. Calculation of Particle Variables</a></span></dt><dt><span class="section"><a href="i1338669.html">6.1.2. Interphase Transfer Through Source Terms</a></span></dt></dl></dd><dt><span class="section"><a href="i1333220.html">6.2. Momentum Transfer</a></span></dt><dd><dl><dt><span class="section"><a href="i1333156.html">6.2.1. Drag Force on Particles</a></span></dt><dt><span class="section"><a href="i1333105.html">6.2.2. Buoyancy Force on Particles</a></span></dt><dt><span class="section"><a href="i1332922.html">6.2.3. Rotation Force</a></span></dt><dt><span class="section"><a href="BABGFJFB.html">6.2.4. Virtual or Added Mass Force</a></span></dt><dt><span class="section"><a href="BABBFAFD.html">6.2.5. Pressure Gradient Force</a></span></dt><dt><span class="section"><a href="i1339007.html">6.2.6. Turbulence in Particle Tracking</a></span></dt><dt><span class="section"><a href="i1336132.html">6.2.7. Turbulent Dispersion</a></span></dt></dl></dd><dt><span class="section"><a href="i1308531.html">6.3. Heat and Mass Transfer</a></span></dt><dd><dl><dt><span class="section"><a href="i1308547.html">6.3.1. Heat Transfer</a></span></dt><dt><span class="section"><a href="i1335681.html">6.3.2. Simple Mass Transfer</a></span></dt><dt><span class="section"><a href="i1308585.html">6.3.3. Liquid Evaporation Model</a></span></dt><dd><dl><dt><span class="section"><a href="i1308585.html#cfxPartLiquExte">6.3.3.1. Extension of the Liquid Evaporation Model</a></span></dt><dd><dl><dt><span class="section"><a href="i1308585.html#cfxPartExteExam">6.3.3.1.1. Examples of ideal mixtures</a></span></dt></dl></dd><dt><span class="section"><a href="i1308585.html#cfxPartLiquDete">6.3.3.2. Determination of the Total Vapor Pressure of an Ideal Mixture</a></span></dt><dt><span class="section"><a href="i1308585.html#cfxPartLiquDiff">6.3.3.3. Diffusion Regime (Non-Boiling Particles)</a></span></dt><dt><span class="section"><a href="i1308585.html#cfxPartLiquBoil">6.3.3.4. Boiling Particles</a></span></dt></dl></dd><dt><span class="section"><a href="i1321934.html">6.3.4. Oil Evaporation/Combustion</a></span></dt><dd><dl><dt><span class="section"><a href="i1321934.html#i1308616">6.3.4.1. Light Oil Modification</a></span></dt></dl></dd><dt><span class="section"><a href="i1321938.html">6.3.5. Reactions</a></span></dt><dd><dl><dt><span class="section"><a href="i1321938.html#arrh_rxns6351">6.3.5.1. Arrhenius Reactions</a></span></dt><dt><span class="section"><a href="i1321938.html#heat_rel6352">6.3.5.2. Heat Release</a></span></dt><dt><span class="section"><a href="i1321938.html#cfxPartCoalChar">6.3.5.3. Char Oxidation</a></span></dt><dd><dl><dt><span class="section"><a href="i1321938.html#i1308695">6.3.5.3.1. Field</a></span></dt><dt><span class="section"><a href="i1321938.html#i1308729">6.3.5.3.2. Gibb</a></span></dt></dl></dd><dt><span class="section"><a href="i1321938.html#i1308793">6.3.5.4. Radiative Preheating</a></span></dt><dt><span class="section"><a href="i1321938.html#i1308621">6.3.5.5. Coal Combustion</a></span></dt><dd><dl><dt><span class="section"><a href="i1321938.html#cfxPartCoalCoal">6.3.5.5.1. Coal Combustion - Gas Phase</a></span></dt><dt><span class="section"><a href="i1321938.html#cfxPartCoalCoal1">6.3.5.5.2. Coal Decomposition</a></span></dt><dt><span class="section"><a href="i1321938.html#i1308638">6.3.5.5.3. Devolatilization</a></span></dt></dl></dd></dl></dd><dt><span class="section"><a href="i1335683.html">6.3.6. Hydrocarbon Fuel Analysis Model</a></span></dt></dl></dd><dt><span class="section"><a href="i1308809.html">6.4. Basic Erosion Models</a></span></dt><dd><dl><dt><span class="section"><a href="i1308811.html">6.4.1. Model of Finnie</a></span></dt><dd><dl><dt><span class="section"><a href="i1308811.html#i1346839">6.4.1.1. Implementation in CFX</a></span></dt></dl></dd><dt><span class="section"><a href="i1308876.html">6.4.2. Model of Tabakoff and Grant</a></span></dt><dd><dl><dt><span class="section"><a href="i1308876.html#cfxPartModeImpl">6.4.2.1. Implementation in CFX</a></span></dt><dd><dl><dt><span class="section"><a href="i1308876.html#cfxPartImplMapp">6.4.2.1.1. Mapping of CFX to Original Tabakoff Constants</a></span></dt><dt><span class="section"><a href="i1308876.html#cfxPartImplCons">6.4.2.1.2. Constants</a></span></dt></dl></dd></dl></dd><dt><span class="section"><a href="i1321974.html">6.4.3. Overall Erosion Rate and Erosion Output</a></span></dt></dl></dd><dt><span class="section"><a href="i1337133.html">6.5. Spray Breakup Models</a></span></dt><dd><dl><dt><span class="section"><a href="spray_primary_breakup.html">6.5.1. Primary Breakup/Atomization Models</a></span></dt><dd><dl><dt><span class="section"><a href="spray_primary_breakup.html#BABJCDBH">6.5.1.1. Blob Method</a></span></dt><dt><span class="section"><a href="spray_primary_breakup.html#BABBCEAD">6.5.1.2. Enhanced Blob Method</a></span></dt><dd><dl><dt><span class="section"><a href="spray_primary_breakup.html#cfxPartEnhaInpu">6.5.1.2.1. Input Parameters for the Enhanced Blob Method</a></span></dt></dl></dd><dt><span class="section"><a href="spray_primary_breakup.html#BABDICGH">6.5.1.3. LISA Model</a></span></dt><dd><dl><dt><span class="section"><a href="spray_primary_breakup.html#BABIFBHC">6.5.1.3.1. Film Formation</a></span></dt><dt><span class="section"><a href="spray_primary_breakup.html#BABFFBGA">6.5.1.3.2. Sheet Breakup and Atomization</a></span></dt><dt><span class="section"><a href="spray_primary_breakup.html#cfxPartLISAUser">6.5.1.3.3. User Input Data for the LISA Model</a></span></dt></dl></dd><dt><span class="section"><a href="spray_primary_breakup.html#primary_breakup_turbulence">6.5.1.4. Turbulence Induced Atomization</a></span></dt><dd><dl><dt><span class="section"><a href="spray_primary_breakup.html#cfxPartTurbUser">6.5.1.4.1. User Input Data for Turbulence Induced Atomization</a></span></dt></dl></dd><dt><span class="section"><a href="spray_primary_breakup.html#cfxPartPrimUsag">6.5.1.5. Usage and Restrictions for Primary Breakup Models</a></span></dt></dl></dd><dt><span class="section"><a href="spray_secondary_breakup.html">6.5.2. Secondary Breakup Models</a></span></dt><dd><dl><dt><span class="section"><a href="spray_secondary_breakup.html#cfxPartSecoBrea">6.5.2.1. Breakup Regimes</a></span></dt><dt><span class="section"><a href="spray_secondary_breakup.html#cfxPartSecoNume">6.5.2.2. Numerical Approach to Breakup Modeling</a></span></dt><dt><span class="section"><a href="spray_secondary_breakup.html#BABBHHEB">6.5.2.3. Reitz and Diwakar Breakup Model</a></span></dt><dd><dl><dt><span class="section"><a href="spray_secondary_breakup.html#cfxPartReitBrea">6.5.2.3.1. Bag Breakup</a></span></dt><dt><span class="section"><a href="spray_secondary_breakup.html#cfxPartReitStri">6.5.2.3.2. Stripping Breakup</a></span></dt></dl></dd><dt><span class="section"><a href="spray_secondary_breakup.html#cfxPartolin">6.5.2.4. Schmehl Breakup Model []</a></span></dt><dd><dl><dt><span class="section"><a href="spray_secondary_breakup.html#cfxPartBrea">6.5.2.4.1. Breakup Process for Schmehl Breakup Model</a></span></dt></dl></dd><dt><span class="section"><a href="spray_secondary_breakup.html#cfxPartolin1">6.5.2.5. Taylor Analogy Breakup (TAB) Model []</a></span></dt><dt><span class="section"><a href="spray_secondary_breakup.html#cfxPartolin2">6.5.2.6. ETAB []</a></span></dt><dt><span class="section"><a href="spray_secondary_breakup.html#cfxPartSecoCasc">6.5.2.7. Cascade Atomization and Breakup Model (CAB)</a></span></dt></dl></dd><dt><span class="section"><a href="i1338540.html">6.5.3. Dynamic Drag Models</a></span></dt><dd><dl><dt><span class="section"><a href="i1338540.html#cfxPartolin3">6.5.3.1. Liu []</a></span></dt><dt><span class="section"><a href="i1338540.html#cfxPartolin4">6.5.3.2. Schmehl []</a></span></dt></dl></dd></dl></dd><dt><span class="section"><a href="ppcm.html">6.6. Particle Collision Model</a></span></dt><dd><dl><dt><span class="section"><a href="ppcm_intro.html">6.6.1. Introduction to the Particle Collision Model</a></span></dt><dd><dl><dt><span class="section"><a href="ppcm_intro.html#cfxPartIntrBack">6.6.1.1. Background Information</a></span></dt></dl></dd><dt><span class="section"><a href="ppcm_implementation.html">6.6.2. Implementation of a Stochastic Particle-Particle Collision
Model in ANSYS CFX</a></span></dt><dd><dl><dt><span class="section"><a href="ppcm_implementation.html#ppcm_theory">6.6.2.1. Implementation Theory</a></span></dt><dd><dl><dt><span class="section"><a href="ppcm_implementation.html#ppcm_coefficients">6.6.2.1.1. Particle Collision Coefficients Used for Particle-Particle
Collision Model</a></span></dt><dt><span class="section"><a href="ppcm_implementation.html#ppcm_variables">6.6.2.1.2. Particle Variables Used for Particle-Particle Collision Model</a></span></dt><dd><dl><dt><span class="section"><a href="ppcm_implementation.html#ppcm_variables_1">6.6.2.1.2.1. Particle Number Density</a></span></dt><dt><span class="section"><a href="ppcm_implementation.html#ppcm_variables_2">6.6.2.1.2.2. Turbulent Stokes Number</a></span></dt><dt><span class="section"><a href="ppcm_implementation.html#ppcm_variables_3">6.6.2.1.2.3. Standard Deviation of Particle Quantities</a></span></dt><dt><span class="section"><a href="ppcm_implementation.html#ppcm_variables_4">6.6.2.1.2.4. Integration Time Step Size (User Fortran Only)</a></span></dt></dl></dd></dl></dd></dl></dd><dt><span class="section"><a href="ppcm_limitations_1.html">6.6.3. Range of Applicability of Particle-Particle Collision Model</a></span></dt><dt><span class="section"><a href="ppcm_limitations_2.html">6.6.4. Limitations of Particle-Particle Collision Model in ANSYS CFX</a></span></dt></dl></dd><dt><span class="section"><a href="particle_wall_interaction.html">6.7. Particle-Wall Interaction</a></span></dt><dd><dl><dt><span class="section"><a href="particle_wall_interaction_intro.html">6.7.1. Introduction to Particle-Wall Interaction</a></span></dt><dd><dl><dt><span class="section"><a href="particle_wall_interaction_intro.html#particle_wall_interaction_background">6.7.1.1. Background Information</a></span></dt></dl></dd><dt><span class="section"><a href="Theory_Elsaesser_model.html">6.7.2. The Elsaesser Particle-Wall Interaction Model</a></span></dt><dd><dl><dt><span class="section"><a href="Theory_Elsaesser_model.html#Theory_Elsaesser_model_regimes">6.7.2.1. Classification of Impact Regimes</a></span></dt><dd><dl><dt><span class="section"><a href="Theory_Elsaesser_model.html#cfxPartsubs">6.7.2.1.1. Cold Wall with Wall Film (T<sub>Wall</sub> &lt;
T<sub>PA</sub>)</a></span></dt><dt><span class="section"><a href="Theory_Elsaesser_model.html#cfxPartsubs1">6.7.2.1.2. Hot Wall with Wall Film (T<sub>PA</sub> &lt; T<sub>Wall</sub> &lt; T<sub>RA</sub>)</a></span></dt><dt><span class="section"><a href="Theory_Elsaesser_model.html#cfxPartsubs2">6.7.2.1.3. Hot Wall Without Wall Film (T<sub>Wall</sub> &gt;
T<sub>Ra</sub>)</a></span></dt></dl></dd><dt><span class="section"><a href="Theory_Elsaesser_model.html#cfxPartElsaWall">6.7.2.2. Wall Roughness</a></span></dt><dt><span class="section"><a href="Theory_Elsaesser_model.html#cfxPartElsaRang">6.7.2.3. Range of Applicability, Input Data and Restrictions</a></span></dt></dl></dd><dt><span class="section"><a href="Theory_stick_to_wall_model.html">6.7.3. Stick-to-Wall Model</a></span></dt><dt><span class="section"><a href="Intro_vwm.html">6.7.4. The Sommerfeld-Frank Rough Wall Model (Particle Rough Wall
Model)</a></span></dt></dl></dd><dt><span class="section"><a href="Theory_wall_film.html">6.8. Quasi Static Wall Film Model</a></span></dt><dd><dl><dt><span class="section"><a href="cfxPartQuasAssu.html">6.8.1. Assumptions</a></span></dt><dt><span class="section"><a href="cfxPartQuasDete.html">6.8.2. Determination of Flooded Regime</a></span></dt><dt><span class="section"><a href="cfxPartQuasEner.html">6.8.3. Energy Transfer to and from the Wall Film</a></span></dt><dd><dl><dt><span class="section"><a href="cfxPartQuasEner.html#Theory_wall_film_heat_cond">6.8.3.1. Conductive Heat Transfer</a></span></dt><dd><dl><dt><span class="section"><a href="cfxPartQuasEner.html#cfxPartCondfloo">6.8.3.1.1. Non-flooded Regime</a></span></dt><dt><span class="section"><a href="cfxPartQuasEner.html#cfxPartCondFloo1">6.8.3.1.2. Flooded Regime</a></span></dt></dl></dd><dt><span class="section"><a href="cfxPartQuasEner.html#Theory_wall_film_heat_conv">6.8.3.2. Convective Heat Transfer</a></span></dt><dd><dl><dt><span class="section"><a href="cfxPartQuasEner.html#cfxPartConvfloo">6.8.3.2.1. Non-flooded Regime</a></span></dt><dt><span class="section"><a href="cfxPartQuasEner.html#cfxPartConvFloo1">6.8.3.2.2. Flooded Regime</a></span></dt></dl></dd><dt><span class="section"><a href="cfxPartQuasEner.html#Theory_wall_film_temperature">6.8.3.3. Calculation of the Average Wall Film Temperature</a></span></dt><dt><span class="section"><a href="cfxPartQuasEner.html#Theory_wall_film_evaporation">6.8.3.4. Evaporation from Film</a></span></dt><dd><dl><dt><span class="section"><a href="cfxPartQuasEner.html#Theory_wall_film_evaporation_non_flooded">6.8.3.4.1. Non-flooded Regime (Non-boiling)</a></span></dt><dt><span class="section"><a href="cfxPartQuasEner.html#Theory_wall_film_evaporation_flooded">6.8.3.4.2. Flooded Regime (Non-boiling)</a></span></dt><dt><span class="section"><a href="cfxPartQuasEner.html#Theory_wall_film_evaporation_flooded_and_non">6.8.3.4.3. Flooded and Non-flooded Regime (Boiling Particles)</a></span></dt></dl></dd></dl></dd><dt><span class="section"><a href="cfxPartQuasMass.html">6.8.4. Mass Transfer to and from the Wall Film</a></span></dt><dt><span class="section"><a href="cfxPartQuasWall.html">6.8.5. Wall Film Thickness</a></span></dt><dt><span class="section"><a href="cfxPartQuasWall1.html">6.8.6. Wall Film in Moving Mesh Applications</a></span></dt><dd><dl><dt><span class="section"><a href="cfxPartQuasWall1.html#cfxPartWallWall">6.8.6.1. Wall Film Moving with Mesh</a></span></dt><dt><span class="section"><a href="cfxPartQuasWall1.html#cfxPartWallWall1">6.8.6.2. Wall Film Moving Relative to Underlying Mesh</a></span></dt></dl></dd><dt><span class="section"><a href="cfxPartQuasUser.html">6.8.7. User Control for Heat and Mass Transfer Terms of Wall Particles</a></span></dt></dl></dd></dl></dd><dt><span class="chapter"><a href="i1309239.html">7. Combustion Theory</a></span></dt><dd><dl><dt><span class="section"><a href="BABDHEAD.html">7.1. Transport Equations</a></span></dt><dt><span class="section"><a href="BABHAJCA.html">7.2. Chemical Reaction Rate</a></span></dt><dt><span class="section"><a href="BABDBGDH.html">7.3. Fluid Time Scale for Extinction Model</a></span></dt><dt><span class="section"><a href="i1309340.html">7.4. The Eddy Dissipation Model</a></span></dt><dd><dl><dt><span class="section"><a href="i1309349.html">7.4.1. Reactants Limiter</a></span></dt><dt><span class="section"><a href="i1309356.html">7.4.2. Products Limiter</a></span></dt><dt><span class="section"><a href="cfxCombEddyMaxi.html">7.4.3. Maximum Flame Temperature Limiter</a></span></dt></dl></dd><dt><span class="section"><a href="i1309364.html">7.5. The Finite Rate Chemistry Model</a></span></dt><dd><dl><dt><span class="section"><a href="i1309405.html">7.5.1. Third Body Terms</a></span></dt></dl></dd><dt><span class="section"><a href="i1309484.html">7.6. The Combined Eddy Dissipation/Finite Rate Chemistry Model</a></span></dt><dt><span class="section"><a href="i1309497.html">7.7. Combustion Source Term Linearization</a></span></dt><dt><span class="section"><a href="i1347579.html">7.8. The Flamelet Model</a></span></dt><dd><dl><dt><span class="section"><a href="i1309526.html">7.8.1. Laminar Flamelet Model for Non Premixed Combustion</a></span></dt><dt><span class="section"><a href="BABFDJGE.html">7.8.2. Coupling of Laminar Flamelet with the Turbulent Flow Field</a></span></dt><dt><span class="section"><a href="i1309704.html">7.8.3. Flamelet Libraries</a></span></dt></dl></dd><dt><span class="section"><a href="i1309768.html">7.9. Burning Velocity Model (Premixed or Partially Premixed)</a></span></dt><dd><dl><dt><span class="section"><a href="cfxCombBurnReac.html">7.9.1. Reaction Progress</a></span></dt><dt><span class="section"><a href="thry_comb_weightedreactionprogress.html">7.9.2. Weighted Reaction Progress</a></span></dt></dl></dd><dt><span class="section"><a href="BABEAHAF.html">7.10. Burning Velocity Model (BVM)</a></span></dt><dd><dl><dt><span class="section"><a href="cfxCombBurnEqui.html">7.10.1. Equivalence Ratio, Stoichiometric Mixture Fraction</a></span></dt></dl></dd><dt><span class="section"><a href="BABGIFCF.html">7.11. Laminar Burning Velocity</a></span></dt><dd><dl><dt><span class="section"><a href="cfxCombLamiValu1.html">7.11.1. Value</a></span></dt><dt><span class="section"><a href="BABDBJDB.html">7.11.2. Equivalence Ratio Correlation</a></span></dt><dd><dl><dt><span class="section"><a href="BABDBJDB.html#BABHBAHD">7.11.2.1. Fifth Order Polynomial</a></span></dt><dt><span class="section"><a href="BABDBJDB.html#BABEFGJE">7.11.2.2. Quadratic Decay</a></span></dt><dt><span class="section"><a href="BABDBJDB.html#BABBFAHC">7.11.2.3. Beta Function</a></span></dt><dt><span class="section"><a href="BABDBJDB.html#cfxCombEquiResi1">7.11.2.4. Residual Material Dependency</a></span></dt><dt><span class="section"><a href="BABDBJDB.html#BABDJAFG">7.11.2.5. Metghalchi and Keck</a></span></dt></dl></dd></dl></dd><dt><span class="section"><a href="BABDFAGE.html">7.12. Turbulent Burning Velocity</a></span></dt><dd><dl><dt><span class="section"><a href="cfxCombTurbValu1.html">7.12.1. Value</a></span></dt><dt><span class="section"><a href="cfxCombTurbZimo1.html">7.12.2. Zimont Correlation</a></span></dt><dt><span class="section"><a href="cfxCombTurbPete1.html">7.12.3. Peters Correlation</a></span></dt><dt><span class="section"><a href="cfxCombTurbMuel1.html">7.12.4. Mueller Correlation</a></span></dt></dl></dd><dt><span class="section"><a href="thry_ecfm.html">7.13. Extended Coherent Flame Model (ECFM)</a></span></dt><dd><dl><dt><span class="section"><a href="cfxCombExteTurb.html">7.13.1. Turbulent Flame Stretch</a></span></dt><dt><span class="section"><a href="thry_comb_ecfm_flamethickness.html">7.13.2. Laminar Flame Thickness</a></span></dt><dt><span class="section"><a href="cfxCombExteWall.html">7.13.3. Wall Quenching Model</a></span></dt></dl></dd><dt><span class="section"><a href="cfxCombResi.html">7.14. Residual Material Model</a></span></dt><dd><dl><dt><span class="section"><a href="cfxCombResiExha.html">7.14.1. Exhaust Gas Recirculation</a></span></dt><dt><span class="section"><a href="cfxCombResiPrin.html">7.14.2. Principal Variables and Transport Equation</a></span></dt><dt><span class="section"><a href="thry_comb_resmat_mixture.html">7.14.3. Mixture Composition</a></span></dt><dt><span class="section"><a href="cfxCombResiRein.html">7.14.4. Reinitialization for Subsequent Engine Cycles</a></span></dt><dt><span class="section"><a href="cfxCombResiEqui.html">7.14.5. Equivalence Ratio and Conditional Fresh/Residual Mixtures</a></span></dt></dl></dd><dt><span class="section"><a href="BABHAJFB.html">7.15. Spark Ignition Model</a></span></dt><dt><span class="section"><a href="cfxCombAuto1.html">7.16. Autoignition Model</a></span></dt><dd><dl><dt><span class="section"><a href="cfxCombAutoIgni1.html">7.16.1. Ignition Delay Model</a></span></dt><dt><span class="section"><a href="cfxCombAutoKnoc.html">7.16.2. Knock Model</a></span></dt><dt><span class="section"><a href="cfxCombAutoIgni2.html">7.16.3. Ignition Delay Time</a></span></dt><dd><dl><dt><span class="section"><a href="cfxCombAutoIgni2.html#cfxCombIgniDoua">7.16.3.1. Douaud and Eyzat</a></span></dt><dt><span class="section"><a href="cfxCombAutoIgni2.html#cfxCombIgniHard">7.16.3.2. Hardenberg and Hase</a></span></dt></dl></dd></dl></dd><dt><span class="section"><a href="EFIHENIM.html">7.17. Phasic Combustion</a></span></dt><dt><span class="section"><a href="i1310041.html">7.18. NO Formation Model</a></span></dt><dd><dl><dt><span class="section"><a href="cfxCombFormForm.html">7.18.1. Formation Mechanisms</a></span></dt><dd><dl><dt><span class="section"><a href="cfxCombFormForm.html#cfxtheory_thermal_no">7.18.1.1. Thermal NO</a></span></dt><dt><span class="section"><a href="cfxCombFormForm.html#cfxCombFormProm">7.18.1.2. Prompt NO</a></span></dt><dt><span class="section"><a href="cfxCombFormForm.html#cfxCombFormFuel">7.18.1.3. Fuel Nitrogen</a></span></dt><dt><span class="section"><a href="cfxCombFormForm.html#cfxCombFormRebu">7.18.1.4. NO Reburn</a></span></dt><dt><span class="section"><a href="cfxCombFormForm.html#cfxCombFormTurb">7.18.1.5. Turbulence Effects</a></span></dt><dt><span class="section"><a href="cfxCombFormForm.html#cfxCombFormTemp">7.18.1.6. Temperature Variance Equation</a></span></dt><dt><span class="section"><a href="cfxCombFormForm.html#cfxCombFormMode">7.18.1.7. Model Control</a></span></dt><dd><dl><dt><span class="section"><a href="cfxCombFormForm.html#BABECBGE">7.18.1.7.1. Adjusting Model Coefficients</a></span></dt><dt><span class="section"><a href="cfxCombFormForm.html#cfxCombModeUser">7.18.1.7.2. User Defined NO Formation Mechanisms</a></span></dt></dl></dd></dl></dd></dl></dd><dt><span class="section"><a href="BABGHIDJ.html">7.19. Chemistry Postprocessing</a></span></dt><dt><span class="section"><a href="i1310261.html">7.20. Soot Model</a></span></dt><dd><dl><dt><span class="section"><a href="cfxCombSootSoot.html">7.20.1. Soot Formation</a></span></dt><dt><span class="section"><a href="i1310507.html">7.20.2. Soot Combustion</a></span></dt><dt><span class="section"><a href="cfxCombSootTurb.html">7.20.3. Turbulence Effects</a></span></dt></dl></dd></dl></dd><dt><span class="chapter"><a href="i1310759.html">8. Radiation Theory</a></span></dt><dd><dl><dt><span class="section"><a href="BABDDIJA.html">8.1. Radiation Transport</a></span></dt><dd><dl><dt><span class="section"><a href="cfxRadiBlac.html">8.1.1. Blackbody Emission</a></span></dt><dt><span class="section"><a href="cfxParticRadiTrans.html">8.1.2. Particulate Effects to Radiation Transport</a></span></dt><dt><span class="section"><a href="cfxRadiQuan.html">8.1.3. Quantities of Interest</a></span></dt><dd><dl><dt><span class="section"><a href="cfxRadiQuan.html#i1310958">8.1.3.1. Optical Thickness</a></span></dt></dl></dd><dt><span class="section"><a href="BABDDIJJ.html">8.1.4. Radiation Through Domain Interfaces</a></span></dt></dl></dd><dt><span class="section"><a href="i1311019.html">8.2. Rosseland Model</a></span></dt><dd><dl><dt><span class="section"><a href="cfxRadiWall.html">8.2.1. Wall Treatment</a></span></dt></dl></dd><dt><span class="section"><a href="i1311072.html">8.3. The P1 Model</a></span></dt><dd><dl><dt><span class="section"><a href="cfxRadiModeWall.html">8.3.1. Wall Treatment</a></span></dt></dl></dd><dt><span class="section"><a href="i1311101.html">8.4. Discrete Transfer Model</a></span></dt><dt><span class="section"><a href="i1311130.html">8.5. Monte Carlo Model</a></span></dt><dd><dl><dt><span class="section"><a href="moncarlstat.html">8.5.1. Monte Carlo Statistics</a></span></dt></dl></dd><dt><span class="section"><a href="i1311144.html">8.6. Spectral Models</a></span></dt><dd><dl><dt><span class="section"><a href="cfxRadiGray.html">8.6.1. Gray</a></span></dt><dt><span class="section"><a href="cfxRadiMult.html">8.6.2. Multiband Model</a></span></dt><dt><span class="section"><a href="cfxRadiWeig.html">8.6.3. Weighted Sum of Gray Gases</a></span></dt><dd><dl><dt><span class="section"><a href="cfxRadiWeig.html#cfxRadiWeigWeig">8.6.3.1. Weighted Sum of Gray Gases Model Parameters</a></span></dt></dl></dd></dl></dd></dl></dd><dt><span class="chapter"><a href="ch_mhd.html">9. Electromagnetic Hydrodynamic Theory</a></span></dt><dd><dl><dt><span class="section"><a href="cfxElecElec.html">9.1. Electromagnetic Models</a></span></dt><dd><dl><dt><span class="section"><a href="cfxElecElecCons.html">9.1.1. Constitutive Relationships</a></span></dt><dt><span class="section"><a href="cfxElecElecMagn.html">9.1.2. Magnetohydrodynamics (MHD)</a></span></dt><dt><span class="section"><a href="cfxElecElecElec.html">9.1.3. Electrohydrodynamics (EHD)</a></span></dt><dt><span class="section"><a href="cfxElecElecFerr.html">9.1.4. Ferrohydrodynamics (FHD)</a></span></dt><dt><span class="section"><a href="cfxElecElecElec1.html">9.1.5. Electromagnetic Basics: Potential Formulation in ANSYS CFX</a></span></dt><dt><span class="section"><a href="cfxElecElecBoun.html">9.1.6. Boundary Conditions</a></span></dt><dt><span class="section"><a href="cfxElecElecTran.html">9.1.7. Transformed Equations</a></span></dt><dt><span class="section"><a href="cfxElecElecCond.html">9.1.8. Conductive Media Approximation</a></span></dt></dl></dd><dt><span class="section"><a href="cfxElecFlui.html">9.2. Fluid Dynamics Model</a></span></dt></dl></dd><dt><span class="chapter"><a href="ch_th_rigidbody.html">10. Rigid Body Theory</a></span></dt><dd><dl><dt><span class="section"><a href="cfxRigiEqua.html">10.1. Equations of Motion of Rigid Body</a></span></dt><dt><span class="section"><a href="cfxRigiRigi1.html">10.2. Rigid Body Solution Algorithms</a></span></dt><dd><dl><dt><span class="section"><a href="thry_rb_translationalEOM.html">10.2.1. Translational Equations of Motion</a></span></dt><dd><dl><dt><span class="section"><a href="thry_rb_translationalEOM.html#thry_rb_newmark">10.2.1.1. Newmark Integration</a></span></dt></dl></dd><dt><span class="section"><a href="thry_rb_rotationalEOM.html">10.2.2. Rotational Equations of Motion</a></span></dt><dd><dl><dt><span class="section"><a href="thry_rb_rotationalEOM.html#thry_rb_backward_euler">10.2.2.1. First Order Backward Euler</a></span></dt><dt><span class="section"><a href="thry_rb_rotationalEOM.html#thry_rb_simo_wong">10.2.2.2. Simo Wong Algorithm</a></span></dt></dl></dd></dl></dd></dl></dd><dt><span class="chapter"><a href="i1311629.html">11. Discretization and Solution Theory</a></span></dt><dd><dl><dt><span class="section"><a href="i1311644.html">11.1. Numerical Discretization</a></span></dt><dd><dl><dt><span class="section"><a href="i1311648.html">11.1.1. Discretization of the Governing Equations</a></span></dt><dd><dl><dt><span class="section"><a href="i1311648.html#cfxDiscDiscOrde">11.1.1.1. Order Accuracy</a></span></dt><dt><span class="section"><a href="i1311648.html#cfxDiscDiscShap">11.1.1.2. Shape Functions</a></span></dt><dd><dl><dt><span class="section"><a href="i1311648.html#cfxDiscShapHexa">11.1.1.2.1. Hexahedral Element</a></span></dt><dt><span class="section"><a href="i1311648.html#cfxDiscShapTetr">11.1.1.2.2. Tetrahedral Element</a></span></dt><dt><span class="section"><a href="i1311648.html#cfxDiscShapWedg">11.1.1.2.3. Wedge Element</a></span></dt><dt><span class="section"><a href="i1311648.html#cfxDiscShapPyra">11.1.1.2.4. Pyramid Element</a></span></dt></dl></dd><dt><span class="section"><a href="i1311648.html#cfxDiscDiscCont">11.1.1.3. Control Volume Gradients</a></span></dt><dt><span class="section"><a href="i1311648.html#i1311959">11.1.1.4. Advection Term</a></span></dt><dd><dl><dt><span class="section"><a href="i1311648.html#i1311980">11.1.1.4.1. 1st Order Upwind Differencing Scheme</a></span></dt><dt><span class="section"><a href="i1311648.html#cfxDiscAdveSpec">11.1.1.4.2. Specified Blend Factor</a></span></dt><dt><span class="section"><a href="i1311648.html#i1312006">11.1.1.4.3. Central Difference Scheme</a></span></dt><dt><span class="section"><a href="i1311648.html#sect_cfx_bcds">11.1.1.4.4. Bounded Central Difference Scheme</a></span></dt><dt><span class="section"><a href="i1311648.html#cfxDiscAdveHigh">11.1.1.4.5. High Resolution Scheme</a></span></dt></dl></dd><dt><span class="section"><a href="i1311648.html#cfxDiscDiscDiff">11.1.1.5. Diffusion Terms</a></span></dt><dt><span class="section"><a href="i1311648.html#cfxDiscDiscPres">11.1.1.6. Pressure Gradient Term</a></span></dt><dt><span class="section"><a href="i1311648.html#cfxDiscDiscMass">11.1.1.7. Mass Flows</a></span></dt><dd><dl><dt><span class="section"><a href="i1311648.html#i1312pvc">11.1.1.7.1. Pressure-Velocity Coupling</a></span></dt><dt><span class="section"><a href="i1311648.html#cfxDiscMassComp">11.1.1.7.2. Compressibility</a></span></dt></dl></dd><dt><span class="section"><a href="i1311648.html#i1311805">11.1.1.8. Transient Term</a></span></dt><dt><span class="section"><a href="i1311648.html#CHDIIIEB">11.1.1.9. Mesh Deformation</a></span></dt></dl></dd><dt><span class="section"><a href="cfxDiscNumeCoup.html">11.1.2. The Coupled System of Equations</a></span></dt></dl></dd><dt><span class="section"><a href="i1312078.html">11.2. Solution Strategy - The Coupled Solver</a></span></dt><dd><dl><dt><span class="section"><a href="cfxDiscSoluGene.html">11.2.1. General Solution</a></span></dt><dt><span class="section"><a href="i1312256.html">11.2.2. Linear Equation Solution</a></span></dt><dd><dl><dt><span class="section"><a href="i1312256.html#cfxDiscLineAlge">11.2.2.1. Algebraic Multigrid</a></span></dt></dl></dd><dt><span class="section"><a href="i1312559.html">11.2.3. Residual Normalization Procedure</a></span></dt></dl></dd><dt><span class="section"><a href="i1312572.html">11.3. Discretization Errors</a></span></dt><dd><dl><dt><span class="section"><a href="CHDIAJDD.html">11.3.1. Controlling Error Sources</a></span></dt><dt><span class="section"><a href="CHDCFHAJ.html">11.3.2. Controlling Error Propagation</a></span></dt></dl></dd></dl></dd></dl></toc>