Fluent Software Training：《Modeling turbulent Flows》学习资料

FLUENT Fluent Software Trainin Ncct⊙tLD TRN-99-003 Modeling turbulent Flows c Fluent Inc. 2/20/01

D1 © Fluent Inc. 2/20/01 Fluent Software Training TRN-99-003 Modeling Turbulent Flows

FLUENT Fluent Software Trainin Ncct⊙tLD TRN-99-003 What is Turbulence? Unsteady, aperiodic motion in which all three velocity components fluctuate mixing matter, momentum, and energy Decompose velocity into mean and fluctuating parts U1=U1+l1( l1) U1(0) Similar fluctuations for pressure, temperature, and species concentration values C Fluent Inc. 2/20

D2 © Fluent Inc. 2/20/01 Fluent Software Training TRN-99-003 u Unsteady, aperiodic motion in which all three velocity components fluctuate ’ mixing matter, momentum, and energy. u Decompose velocity into mean and fluctuating parts: Ui (t) º Ui + ui (t) u Similar fluctuations for pressure, temperature, and species concentration values. What is Turbulence? Time U i (t) Ui ui (t)

FLUENT Fluent Software Trainin Ncct⊙tLD TRN-99-003 Why model Turbulence? Direct numerical simulation of governing equations is only possible for simple low-Re flows Instead, we solve Reynolds averaged Navier-Stokes(RANS equations aU Op aU aR p k ai ardr y(steady, incompressible flow +u w/o body forces where Rii=- pu;ul (Reynolds stresses) Time-averaged statistics of turbulent velocity fluctuations are modeled using functions containing empirical constants and information about the mean flow Large Eddy simulation numerically resolves large eddies and models c Fluent Inc. 2/20/01

D3 © Fluent Inc. 2/20/01 Fluent Software Training TRN-99-003 Why Model Turbulence? u Direct numerical simulation of governing equations is only possible for simple low-Re flows. u Instead, we solve Reynolds Averaged Navier-Stokes (RANS) equations: where (Reynolds stresses) u Time-averaged statistics of turbulent velocity fluctuations are modeled using functions containing empirical constants and information about the mean flow. u Large Eddy Simulation numerically resolves large eddies and models small eddies. (steady, incompressible flow w/o body forces) Rij = - ruiu j j ij j j i k i i k x R x x U x p x U U ¶ ¶ + ¶ ¶ ¶ + ¶ ¶ = - ¶ ¶ 2 r m

FLUENT Fluent Software Trainin Ncct⊙tLD TRN-99-003 Is the flow turbulent? External flows where Re,s pUl Re25×103 along a surface L=xDD. etc Re>20000 around an obstacle Other factors such as free-stream turbulence surface conditions and Internal flows disturbances may cause earlier Ren22300 transition to turbulent flow Natural convection Ra≥103-100 where Ra≡ gBaTLp c Fluent Inc. 2/20/01

D4 © Fluent Inc. 2/20/01 Fluent Software Training TRN-99-003 Is the Flow Turbulent? External Flows Internal Flows Natural Convection 5 ³5´10 Rex along a surface around an obstacle where m rUL Re where L º Other factors such as free-stream turbulence, surface conditions, and disturbances may cause earlier transition to turbulent flow. L = x, D, Dh , etc. ³ 2,300 Dh Re 8 10 Ra ³10 -10 ma b r 3 g TL Ra D º ³ 20,000 ReD

FLUENT Fluent Software Trainin Ncct⊙tLD TRN-99-003 How Complex is the flow ◆ Extra strain rates Streamline curvature Lateral divergence Acceleration or deceleration Swirl Recirculation (or separation) Secondary flow ◆3 D perturbations Transpiration(blowing/suction Free-stream turbulence g Shear layers C Fluent Inc. 2/20

D5 © Fluent Inc. 2/20/01 Fluent Software Training TRN-99-003 How Complex is the Flow? u Extra strain rates l Streamline curvature l Lateral divergence l Acceleration or deceleration l Swirl l Recirculation (or separation) l Secondary flow u 3D perturbations u Transpiration (blowing/suction) u Free-stream turbulence u Interacting shear layers

FLUENT Fluent Software Trainin TRN-99-003 Choices to be Made Flow Computational Physics R esources Turbulence model & Computational Near-Wall Treatment Grid Turnaround Accuracy Time R equired Constraints C Fluent Inc. 2/20

D6 © Fluent Inc. 2/20/01 Fluent Software Training TRN-99-003 Choices to be Made Turbulence Model & Near-Wall Treatment Flow Physics Accuracy Required Computational Resources Turnaround Time Constraints Computational Grid

FLUENT Fluent Software Trainin Ncct⊙tLD TRN-99-003 Turbulence Modeling approaches Zero-Equation Models RANS-based , models One-Equation Models Spalart-AlImar Include iTwo-Equation Models Increase More Standard k-8 Computational Physics RNG K-8 Cost Realizable k-8 Per Iteration Available Revnolds-Stress model In fluent 5 Large-eddy simulation Direct Numerical simulation C Fluent Inc. 2/20

D7 © Fluent Inc. 2/20/01 Fluent Software Training TRN-99-003 Zero-Equation Models One-Equation Models Spalart-Allmaras Two-Equation Models Standard k-e RNG k-e Realizable k-e Reynolds-Stress Model Large-Eddy Simulation Direct Numerical Simulation Turbulence Modeling Approaches Include More Physics Increase Computational Cost Per Iteration Available in FLUENT 5 RANS-based models

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

FLUENT Fluent Software Trainin Ncct⊙tLD TRN-99-003 One equation Model: Spalart-Allmaras Turbulent viscosity is determined from =P1 /v)+ .v is determined from the modified viscosity transport equation DI pCa SV+al Dy u+pv t oc b2 Generation Diffusion Destruction The additional variables are functions of the modified turbulent viscoSity and velocity gradients C Fluent Inc. 2/20

D9 © Fluent Inc. 2/20/01 Fluent Software Training TRN-99-003 u Turbulent viscosity is determined from: u is determined from the modified viscosity transport equation: u The additional variables are functions of the modified turbulent viscosity and velocity gradients. One Equation Model: Spalart-Allmaras ( ) 1 2 2 2 ~ 1 ~ ~ ~ ~ ~ 1 ~ ~ d c f x c x x c S Dt D w w j b j j b n r n r n m rn s r n n r n - ú ú û ù ê ê ë é ÷ ÷ ø ö ç ç è æ ¶ ¶ + ïþ ï ý ü ïî ï í ì ¶ ¶ + ¶ ¶ = + ( ) ( ) ú û ù ê ë é + = 3 1 3 3 / ~ / ~ ~ n n n n n m rn c t n ~ Generation Diffusion Destruction

FLUENT Fluent Software Trainin Ncct⊙tLD TRN-99-003 One-Equation Model: Spalart-Allmaras Designed specifically for aerospace applications involving wall bounded flows boundary layers with adverse pressure gradients turbomachinery t Can use coarse or fine mesh at wall Designed to be used with fine mesh as a low-Re "model, i. e, throughout the viscous-affected region Sufficiently robust for relatively crude simulations on coarse meshes DIO c Fluent Inc. 2/20/01

D10 © Fluent Inc. 2/20/01 Fluent Software Training TRN-99-003 One-Equation Model: Spalart-Allmaras u Designed specifically for aerospace applications involving wall￾bounded flows. l Boundary layers with adverse pressure gradients l turbomachinery u Can use coarse or fine mesh at wall l Designed to be used with fine mesh as a “low-Re” model, i.e., throughout the viscous-affected region. l Sufficiently robust for relatively crude simulations on coarse meshes