TURBULENCE MODELING

TURBULENCE MODELINGREALISABLE k- MODEL

Professor: PhD. NGUYN CH CNG Students: NGUYN THNH VN TRN CH TMOUTLINESTURBULENCE FLOW INTRODUCTION INTRODUCTION TURBULENCE FLOWSTIME AVERAGE EQUATIONS (RANS)TURBULENCE MODELTIME AVERAGED EQUATION TRANSPORT EQUATION FOR K.ETRANSPORT EQUATION FOR REYNOLDS STRESS THE BOUSSINESQ ASSUMTIONTHE k- MODELTHE REALIZABLE k- MODELAPPLICATION (VIDEO)FLOW ARROUND RECTANGLE (CIRCLE) USING OPENFOAMANSYS FLUENTINTRODUCTION TURBULENCE FLOWS

INTRODUCTION TURBULENCE FLOWS

INTRODUCTION TURBULENCE FLOWSINTRODUCTION TURBULENCE FLOWS

INTRODUCTION TURBULENCE FLOWS

TURBULENCE MODELA turbulence model is a computational procedure to close the system of mean flow equations.For most engineering application it is unnecessary to resolve the detail of the turbulence fluctuations, only need to know how turbulence affected the mean flow.Classical models. Based on RANS equations:Zero equation model: mixing length model.One equation model: Spalart - Almaras.Two equation models: k- style models (standard, RNG, realizable), k- model and ASM.Seven equation model: Reynolds stress model.The number of equations denotes the number of additional PDEs that are being solved.

Prediction Methods TURBULENCE MODEL

TIME AVERAGE NAVIER-STOKESContinuity equation and N-S equation of incompressible flow with constant viscosity:

Decompose the instantaneous variables (velocity and pressure) into a mean value and a fluctuating value

Insert to continuity equation and N-S equation, then average whole equation , we obtain:

Reynolds equation when we assume that the mean flow is steady, N-S equation written:

: Reynolds stress tensor

TIME AVERAGE NAVIER-STOKES

TRANSPORT EQUATION FOR KINETIC ENERGYProduct rule backwards

The exact k equation: We subtract equation (2) from equation (1) and divide by density multiply by and time average, we obtained:

I. ConvectionII. Production III. TBL diffusion IV . Dissipation

TRANSPORT EQUATION FOR REYNOLDS STRESSSubtract equation (2) from (1) and divide by density, multiply by and time average. We obtain:

(3)

Write an equation (2) for and multiply this equation by

(4)

Adding (4)+(3) together gives:

Reynolds stress equationTRANSPORT EQUATION FOR REYNOLDS STRESS

THE k EQUATIONTKE is the sum of all Reynolds stresses:

Setting indices i=j of the Re stress equation and dividing by 2, we get the equation for TKE

THE BOUSSINESQ ASSUMPTIONIn the Boussinesq assumption an eddy viscosity is introduced to model the unknown Reynolds stress, contains: vicosity of a flunctation molecular and viscosity of TBL

Kinematic TBL viscosity:

Mean rate of deformation tensorThe production:

Diffusion term in the k-equation in the k- model are modeled using the standard gradient hypothesis: assumes that TBL diffusion act to even out all inhomogeneities:

The bouyancy term: TBL thermal diffusivity

THE BOUSSINESQ ASSUMPTION

THE k- MODELBy inserting the model assumptions for TBL diffusion, the production and the buoyancy term into the exact k equation, we get the modeled equation for k

In the same way, the modeled equation is obtain:

THE k- MODEL DISCUSSION

REALIZABLE k- MODELShares the same turbulent kinetic energy equation as the standard k-e model.Improved equation for Variable instead of constant.Improved performance for flows involving:Planar and round jets (predicts round jet spreading correctly).Boundary layers under strong adverse pressure gradients or separation.Rotation, recirculation.Strong streamline curvature.

Distinctions from standard k- model:Alternative formulation for TBL viscosity

REALIZABLE k- MODEL

REALIZABLE k- MODEL

REALIZABLE k- MODEL

COMPARE k- model

LES velocity

RANS (Realizable k- model)

RANS (RNG k- model)REFFERENCEwww.bakkers.orgFluid Mechanics, Turbulent flow and turbulence Modeling , Lars Davidson