OpenFOAM® Implementation of an Incompressible Eddy Viscosity Turbulence Model with Zero Wall Boundary Condition Elliptic Relaxation Function

OpenFOAM Implementation of an Incompressible Eddy Viscosity Turbulence Model with Zero Wall Boundary Condition Elliptic Relaxation Function Mirza Popovac*#1 and Peter Benovsky2 1,2 AIT Austrian Institute of Technology, Energy Department Giefinggasse 2, 1210 Vienna, Austria March 15, 2012 The z − f 0 turbulence model, wall-bounded turbulent flows. 1. Introduction The model of turbulence presented in this paper is based on Durbin's v − f 2 model [1], which brings improvements in the quality of results (e.g. compared to the standard k −e model) by introducing only two additional transport equations. Although the v − f 2 model captures the most important near-wall flow effects, it proved to cause numerical stabilities, especially in the calculations on meshes of poor quality. Aiming at improving the robustness and computational stability of Durbin's original model, the z − f model was derived by Hanjalić and Popovac [2], where the eddy viscosity was defined as: C k T t n z μ = (1) with v k 2 z = being the ratio between the fluctuating velocity component normal to the streamlines and the turbulent kinetic energy, = 0.22 μ C being the turbulent viscosity constant, and T being the turbulent time scale. In the original z − f model, however, the elliptic-relaxation function has a non-zero wall boundary condition. This aspect is particularly important when considering the implementation of this model into a general purpose RANS-based CFD fluid flow solver. Therefore the accent in the present paper is the modification of the original # Corresponding Author: Mirza Popovac ([email protected]) 7th OpenFOAM Workshop Center of Smart Interfaces, Technische Universität Darmstadt, Germany 25-28 June, 2012 z − f model, in the manner explained by Lien and Kalitzin [3], so that the zero wall boundary condition for the relaxation function = 0 w f is obtained (hence the name 0 z − f proposed for this new model). In addition to the model modification, the present paper gives details of the implementation of this model in OpenFOAM, and shows the results obtained with this model. 2. Results In order to test the turbulence model presented in this paper, a set of generic test cases have been calculated with the simpleFoam incompressible turbulent flow OpenFOAM solver: the plane channel flow, impinging and massively separating flow. For the brevity, however, Fig. 1 shows only the results for the impinging jet simulations, obtained with the k −e and 0 z − f models. One can clearly see the over-prediction of k (typical for the k −e model) being reduced with the 0 z − f model, consequently causing also the change in the jet spreading (velocity magnitude). The only price for this improvement in the quality of the obtained results is approximately 15 ÷ 20 % increase in the computation time. Fig. 1: the comparison between the k −e (left) and 0 z − f (right) results for impinging jet flow (above: velocity magnitude, below: the turbulent kinetic energy). REFERENCES [1] P.A. Durbin, Near-wall turbulence closure modelling without damping functions. Theor. Comput. Fluid Dyn., 3, pp. 1-13, (1991). [2] K. Hanjalić, M. Popovac and M. Hadziabdić, A robust near-wall elliptic-relaxation eddyviscosity turbulence model for CFD. Int. J. Heat and Fluid Flow, 25/6, pp. 1047-1051, (2004). [3] F.S. Lien and G. Kalitzin, Computations of transonic flows with the v2-f turbulence model, Int. J. Heat Fluid Flow, 22, pp. 53-61, (2001).