FLUENT Fluent Software Trainin Ncct⊙tLD TRN-99-003 Reynolds stress terms in rans-based models RANS equations require closure for Reynolds stresses au. al Boussinesq Hypothesis:R =-puu =-p=k8+4n+ (isotropic viscosity) turbulent viscosity is indirectly solved for from single transport equation of modified viscosity for One-Equation model For Two-Equation models, turbulent viscosity correlated with turbulent kinetic energy(tKe)and the dissipation rate of TKe Turbulent Viscosity:H+≡pC Transport equations for turbulent kinetic energy and dissipation rate are solved so that turbulent viscosity can be computed for rans equations Turbulent Dissipation rate of au au Kinetic energy k=42 Turbulent Kinetic Energy C Fluent Inc. 2/20,D8 © Fluent Inc. 2/20/01 Fluent Software Training TRN-99-003 u RANS equations require closure for Reynolds stresses. u Turbulent viscosity is indirectly solved for from single transport equation of modified viscosity for One-Equation model. u For Two-Equation models, turbulent viscosity correlated with turbulent kinetic energy (TKE) and the dissipation rate of TKE. u Transport equations for turbulent kinetic energy and dissipation rate are solved so that turbulent viscosity can be computed for RANS equations. Reynolds Stress Terms in RANS-based Models Turbulent Kinetic Energy: Dissipation Rate of Turbulent Kinetic Energy: e m r m 2 k Turbulent Viscosity: t º C Boussinesq Hypothesis: (isotropic viscosity) ÷ ÷ ø ö ç ç è æ ¶ ¶ + ¶ ¶ = - = - + i j j i ij i j ij t x U x U R ruu r kd m 3 2 /2 i i k ºu u ÷ ÷ ø ö ç ç è æ ¶ ¶ + ¶ ¶ ¶ ¶ º i j j i j i x u x u x u e n