Wall functions for the k - [epsilon] turbulence model in generalized nonorthogonal curvilinear coordinates

Abstract

<p>Wall functions are often employed to model turbulent flow near solid walls. A method has not been available, however, for the application of wall functions to generalized curvilinear coordinate systems, particularly those with nonorthogonal grids. A general method for this application is developed herein;A k-[epsilon] turbulence model suitable for compressible flow, including the new wall function formulation, has been incorporated into an existing compressible Reynolds-averaged Navier-Stokes code, F3D. The low-Reynolds-number k-[epsilon] model of Chien (1982) was added for comparison with the present method. A number of features were also added to F3D, including improved far-field boundary conditions and viscous terms in the streamwise direction;A series of computations of increasing complexity was run to test the effectiveness of the new formulation. Flow over a flat plate was computed using both orthogonal and nonorthogonal grids, and the friction coefficients and velocity profiles compared with a semi-empirical equation. Flow over a body of revolution at zero angle of attack was then computed to test the method's ability to handle flow over a curved surface. Friction coefficients and velocity profiles were compared to test data. The same case was also computed using the Chien (1982) low-Reynolds-number k-[epsilon] model and the Baldwin-Lomax (1978) algebraic model for comparison. All three models gave good results on a relatively fine grid, but only the wall function formulation was effective with coarser grids. Finally, in order to demonstrate the method's ability to handle complex flowfields, separated flow over a prolate spheroid at angle of attack was computed, and results were compared to test data. The results were also compared to the computation of Kim and Patel (1991), in which a k-[epsilon] model with a one-equation model patched in at the wall was employed. Both models gave reasonable solutions, but they require improvement for accurate prediction of friction coefficients in the separated regions.</p>