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Introduction on Near-wall Physics Wall Functions in OpenFOAM 4.0 New Wall Functions Implementation Case Test Implementation of a Complete Wall Function for the Standard k- ǫ Turbulence Model in OpenFOAM 4.0 Shengnan Liu Offshore Technology, Department of Mechanical and Structural Engineering and Materials Science University of Stavanger, Stavanger, Norway 2016-12-05 Shengnan Liu New Wall Function Implementation in OpenFOAM 4.0 2016-12-05 1 / 35

Introduction on Near-wall Physics Wall Functions in OpenFOAM 4.0 New Wall Functions Implementation Case Test Contents Introduction on Near-wall Physics Wall Function Implementation for Standard k − ǫ Model in OpenFOAM 4.0 New Wall Function Implementation for Standard k − ǫ Model in OpenFOAM 4.0 Test Cases (Verification) Shengnan Liu New Wall Function Implementation in OpenFOAM 4.0 2016-12-05 2 / 35

Introduction on Near-wall Physics Wall Functions in OpenFOAM 4.0 New Wall Functions Implementation Case Test 1 Introduction on Near-wall Physics Shengnan Liu New Wall Function Implementation in OpenFOAM 4.0 2016-12-05 3 / 35

Introduction on Near-wall Physics Wall Functions in OpenFOAM 4.0 New Wall Functions Implementation Case Test Influence of the wall Wall effects are common seen in practical flows such as channel flow, pipe flow and flow around all kinds of structures. Some effects of the wall are shown here. Low Reynolds number - the turbulence Reynolds number Rel = k 2 / ( ǫv ) decreases as the wall is approached. High shear rate - the highest mean shear rate ∂ < U >/∂y occurs at the wall. The velocity changes from the no-slip condition at the wall to its stream value. Wall blocking - the impermeability condition V=0 (at y=0) is considered and it affects the boundary layer flow. Shengnan Liu New Wall Function Implementation in OpenFOAM 4.0 2016-12-05 4 / 35

Introduction on Near-wall Physics Wall Functions in OpenFOAM 4.0 New Wall Functions Implementation Case Test Near Wall Treatment In numerical simulation, two ways can be chosen for wall treatment. DNS resolves eddies in all scales. It required very fine mesh in the near-wall region so that it can be integrated. RANS and LES involve the model to simplify the simulation. They introduce the wall function to give first layer http://www.bakker.org/dartmouth06/engs150/10rans.pdf cell information. Shengnan Liu New Wall Function Implementation in OpenFOAM 4.0 2016-12-05 5 / 35

Introduction on Near-wall Physics Wall Functions in OpenFOAM 4.0 New Wall Functions Implementation Case Test Wall Function Profile Linear viscous sub-layer ( y + < 5 )- Dominated by viscous shear Buffer layer ( 5 < y + < 30 ) - Mix of viscous layer and inertial layer Log-law layer ( 30 < y + < 100 ) - Both viscous and Wall functions for different layers turbulent effects are y + = ( u ∗ y ) /ν ; u + = u/u ∗ , important http://www.computationalfluiddynamics.com.au/tag/wall-functions/ Shengnan Liu New Wall Function Implementation in OpenFOAM 4.0 2016-12-05 6 / 35

Introduction on Near-wall Physics Wall Functions in OpenFOAM 4.0 New Wall Functions Implementation Case Test Viscous Layer ( y + < 5 ) The fluid very close to the wall is dominated by viscous shear in absence of the turbulent shear stress effects. In this region u + = y + , ν T = f µ C µ k 2 /ǫ (Jones and Launder (1972) ), f µ = 1 − exp ( − 0 . 0002 y + − 0 . 00065 y +2 ) (Rodi and Mansour (1993) ), the following equation set is used in the viscous near wall region: y + = u ∗ y/ν   u + = u/u ∗      u + = y +     (1) k = u ∗ 2 / � C µ    ǫ = C 3 / 4 k 3 / 2 /κy   µ     ν T = f µ C µ k 2 /ǫ  Shengnan Liu New Wall Function Implementation in OpenFOAM 4.0 2016-12-05 7 / 35

Introduction on Near-wall Physics Wall Functions in OpenFOAM 4.0 New Wall Functions Implementation Case Test Buffer Layer ( 5 < y + < 30 ) The intersection of viscous and log-law wall funnction is at y + = 11 . That is, y + < 11 linear approximation is more accurate and after y + > 11 the logarithmic approximation works better. Considering both the linear and logarithmic approximation by a weighting factor ω = ( y + − 5) / 25 (Ong et al., (2009)).The equation set is: y + = u ∗ y/ν    u + = u/u ∗       1  u + =    ln ( Ey + ) ) + ( 1 − ω κω  ( y + ) (2) k = u ∗ 2 / �  C µ      ǫ = C 3 / 4 k 3 / 2 /κy   µ    ν T = f µ C µ k 2 /ǫ   Shengnan Liu New Wall Function Implementation in OpenFOAM 4.0 2016-12-05 8 / 35

Introduction on Near-wall Physics Wall Functions in OpenFOAM 4.0 New Wall Functions Implementation Case Test Log-law Layer ( 30 < y + < 100 ) In this region viscous and turbulent effects are both important. The relationship between y + and u + is logarithmic, the equation set to be used in the log-law region is: y + = u ∗ y/ν    u + = u/u ∗       u + = 1  κln ( Ey + )    (3) k = u ∗ 2 / � C µ      ǫ = C 3 / 4 k 3 / 2 /κy   µ    ν T = f µ C µ k 2 /ǫ   Shengnan Liu New Wall Function Implementation in OpenFOAM 4.0 2016-12-05 9 / 35

Introduction on Near-wall Physics Wall Functions in OpenFOAM 4.0 New Wall Functions Implementation Case Test 3 Wall Functions Implementation for Standard k − ǫ Turbulence Model in OpenFOAM 4.0 Shengnan Liu New Wall Function Implementation in OpenFOAM 4.0 2016-12-05 10 / 35

Introduction on Near-wall Physics Wall Functions in OpenFOAM 4.0 New Wall Functions Implementation Case Test Overview on k − ǫ model The k − ǫ belongs to the two-equation models(Launder and Spalding (1972); Rodi (1993)). ∂k ∂k ∂ ( ν T ∂k ) + ν T ( ∂u i + ∂u j ) ∂u i ∂t + u j = − ǫ (4) ∂x j ∂x j σ k ∂x j ∂x j ∂x i ∂x j ǫ 2 ∂ǫ ∂ǫ ∂ ( ν T ∂ǫ ǫ kν T ( ∂u i + ∂u j ) ∂u i ∂t + u j = ) + C 1 − C 2 (5) ∂x j ∂x j σ ǫ ∂x j ∂x j ∂x i ∂x j k Model transport equations are solved for two turbulence quantities. Turbulent kinetic energy k , which determines the energy in the turbulence. Turbulent dissipation ǫ , which determines the rate of dissipation of the turbulent kinetic energy. The turbulent viscosity is specified as ν T = C µ k 2 /ǫ and C 1 = 1 . 44 , C 2 = 1 . 92 , C µ = 0 . 09 , σ k = 1 . 0 , σ ǫ = 1 . 3 . Shengnan Liu New Wall Function Implementation in OpenFOAM 4.0 2016-12-05 11 / 35

Introduction on Near-wall Physics Wall Functions in OpenFOAM 4.0 New Wall Functions Implementation Case Test k − ǫ turbulence model code in OpenFOAM 4.0 The k − ǫ turbulence calculation process is: Calculate turbulent kinetic energy production term G by ”epsilon .boundaryFieldRef().updateCoeffs()” and correct the value of G at first layer mesh by updateCoeffs() function of ǫ . With the updated G, the ǫ equation is revised by ”epsEqn.ref().boundaryManipulate(epsilon .boundaryFieldRef());” . Solve ǫ equation and obtain the updated ǫ field. Solve k equation using the new ǫ , and k field is renewed. Calculate ν T , and update the ν T at wall by ”correctNut();”. Shengnan Liu New Wall Function Implementation in OpenFOAM 4.0 2016-12-05 12 / 35

Introduction on Near-wall Physics Wall Functions in OpenFOAM 4.0 New Wall Functions Implementation Case Test k wall functions in OpenFOAM 4.0 kqRWallFunction is used for high Reynolds numbers and kLowReWallFunction can be used for both low Reynolds numbers and high Reynolds numbers. Type name kqRWallFunction kLowReWallFunction ∗ Available scope Log-law region Viscous and log-law region (first layer cell) Foam::kqRWallFunction- Foam::kLowReWall- Class FvPatchField FunctionFvPatchField Foam::zeroGradient Foam::fixedValue Inherit from FvPatchField FvPatchField Other references zeroGradient fixedValue Table: Available k wall functions in OpenFoam 4.0 * new k wall function is modified based on this Shengnan Liu New Wall Function Implementation in OpenFOAM 4.0 2016-12-05 13 / 35

Introduction on Near-wall Physics Wall Functions in OpenFOAM 4.0 New Wall Functions Implementation Case Test Code framework of kLowReWallFunction in OpenFOAM 4.0 yPlusLam function is used to calculate the intersection of viscous layer and log-law layer updateCoeffs() is the main function of calculating k . ( C k /κln ( y + ) + B k ) ∗ � C µ ∗ k c , y + > yPlusLam k w = { (6) 2400 ∗ C f /C 2 � e ps 2 ∗ C µ ∗ k c , y + < yPlusLam Code Framework Shengnan Liu New Wall Function Implementation in OpenFOAM 4.0 2016-12-05 14 / 35