FLUENT Fluent Software Trainin Ncct⊙tLD TRN-99-003 Two Equation Model: rNG k-8 .k-c equations are derived from the application of a rigorous statistical technique(Renormalization Group Method)to the instantaneous Navier Stokes equations Similar in form to the standard k-E equations but includes additional term in s equation that improves analysis of rapidly strained flows the effect of swirl on turbulence analytical formula for turbulent Prandtl number differential formula for effective viscosity Improved predictions for high streamline curvature and strain rate ● transitional flows wall heat and mass transfer DI6 c Fluent Inc. 2/20/01
D16 © Fluent Inc. 2/20/01 Fluent Software Training TRN-99-003 Two Equation Model: RNG k-e u k-e equations are derived from the application of a rigorous statistical technique (Renormalization Group Method) to the instantaneous NavierStokes equations. u Similar in form to the standard k-e equations but includes: l additional term in e equation that improves analysis of rapidly strained flows l the effect of swirl on turbulence l analytical formula for turbulent Prandtl number l differential formula for effective viscosity u Improved predictions for: l high streamline curvature and strain rate l transitional flows l wall heat and mass transfer
FLUENT Fluent Software Trainin Ncct⊙tLD TRN-99-003 Reynolds Stress model Reynolds stress auu P.+①-E+ Transport Egns aU eneration uu +uu (computed) Pressure-Strain Redistribution (modele u. du Dissipation E=2 u (related to a) X dx Turbulent (modeled) Diffusion J=1l4l+pD(64+ Turbulent Pressure/velocity transport fluctuati (equations written for steady, incompressible flow w/o body forces) DI7 C Fluent Inc. 2/20
D17 © Fluent Inc. 2/20/01 Fluent Software Training TRN-99-003 Reynolds Stress Model k ijk ij ij ij k i j k x J P x u u U ¶ ¶ = + F - + ¶ ¶ r e Generation k i j k k j ij i k x U u u x U P u u ¶ ¶ + ¶ ¶ º ÷ ÷ ø ö ç ç è æ ¶ ¶ + ¶ ¶ F º - ¢ i j j i ij x u x u p k j k i ij x u x u ¶ ¶ ¶ ¶ e º 2 m Pressure-Strain Redistribution Dissipation Turbulent Diffusion (modeled) (related to e) (modeled) (computed) (equations written for steady, incompressible flow w/o body forces) Reynolds Stress Transport Eqns. Pressure/velocity fluctuations Turbulent transport ( ) ijk uiujuk p jkui iku j J = + ¢ d + d
FLUENT Fluent Software Trainin Ncct⊙tLD TRN-99-003 Reynolds stress model RSM closes the Reynolds-Averaged Navier-Stokes equations by solving additional transport equations for the reynolds stresses Transport equations derived by reynolds averaging the product of the momentum equations with a fluctuating property Closure also requires one equation for turbulent dissipation Isotropic eddy viscosity assumption is avoided Resulting equations contain terms that need to be modeled RSM has high potential for accurately predicting complex flows Accounts for streamline curvature. swirl rotation and high strain rates a Cyclone flows, swirling combustor flows a Rotating flow passages, secondary flows D18 c Fluent Inc. 2/20/01
D18 © Fluent Inc. 2/20/01 Fluent Software Training TRN-99-003 Reynolds Stress Model u RSM closes the Reynolds-Averaged Navier-Stokes equations by solving additional transport equations for the Reynolds stresses. l Transport equations derived by Reynolds averaging the product of the momentum equations with a fluctuating property l Closure also requires one equation for turbulent dissipation l Isotropic eddy viscosity assumption is avoided u Resulting equations contain terms that need to be modeled. u RSM has high potential for accurately predicting complex flows. l Accounts for streamline curvature, swirl, rotation and high strain rates n Cyclone flows, swirling combustor flows n Rotating flow passages, secondary flows
FLUENT Fluent Software Trainin Ncct⊙tLD TRN-99-003 Large Eddy simulation arge eddies Mainly responsible for transport of momentum, energy, and other scalars directly affecting the mean fields Anisotropic, subjected to history effects, and flow-dependent, i.e., strongly dependent on flow configuration, boundary conditions, and flow parameters ◆ Small eddies Tend to be more isotropic and less flow-dependent o more likely to be easier to model than large eddies LES directly computes(resolves) large eddies and models only small eddies(Subgrid-Scale Modeling) Large computational effort Number of grid points, NLes oC RE Unsteady calculation D19 c Fluent Inc. 2/20/01
D19 © Fluent Inc. 2/20/01 Fluent Software Training TRN-99-003 Large Eddy Simulation u Large eddies: l Mainly responsible for transport of momentum, energy, and other scalars, directly affecting the mean fields. l Anisotropic, subjected to history effects, and flow-dependent, i.e., strongly dependent on flow configuration, boundary conditions, and flow parameters. u Small eddies: l Tend to be more isotropic and less flow-dependent l More likely to be easier to model than large eddies. u LES directly computes (resolves) large eddies and models only small eddies (Subgrid-Scale Modeling). u Large computational effort l Number of grid points, NLES µ l Unsteady calculation 2 Reut
FLUENT Fluent Software Trainin Ncct⊙tLD TRN-99-003 Comparison of raNs turbulence models Model Strengths Weaknesses Spalart- Economical (1-eq, ); good track record Not very widely tested yet lack of Allmaras for mildly complex B L type of flows lbmodels(e.g. combustion buoyancy Robust economical, reasonably Mediocre results for complex flows STD k-8 accurate; long accumulated nvolving severe pressure gradients, strong streamline curvature swirl performance data and rotation Good for moderately complex Subjected to limitations due to RNG K-8 behavior like jet Impingement, separating flows, swirling flows, and isotropic eddy viscosity assumption secondary fI Realizable offers largely the same benefits as Subjected to limitations due to RNG resolves round-jet anomaly isotropic eddy viscosity k-8 assumption Reynolds Physically most complete model Requires more cpu effort (2-3x) Stress (history, transport, and anisotropy of turbulent stresses are all accounted tightly coupled momentum and Model for turbulence equations D20 C Fluent Inc. 2/20/01
D20 © Fluent Inc. 2/20/01 Fluent Software Training TRN-99-003 Comparison of RANS Turbulence Models Model Strengths Weaknesses SpalartAllmaras Economical (1-eq.); good track record for mildly complex B.L. type of flows Not very widely tested yet; lack of submodels (e.g. combustion, buoyancy) STD k-e Robust, economical, reasonably accurate; long accumulated performance data Mediocre results for complex flows involving severe pressure gradients, strong streamline curvature, swirl and rotation RNG k-e Good for moderately complex behavior like jet impingement, separating flows, swirling flows, and secondary flows Subjected to limitations due to isotropic eddy viscosity assumption Realizable k-e Offers largely the same benefits as RNG; resolves round-jet anomaly Subjected to limitations due to isotropic eddy viscosity assumption Reynolds Stress Model Physically most complete model (history, transport, and anisotropy of turbulent stresses are all accounted for) Requires more cpu effort (2-3x); tightly coupled momentum and turbulence equations