Evaluation of numerical wall functions on the axisymmetric impinging jet using OpenFOAM

Abstract

Two new robust numerical wall functions are evaluated and the effect of different approximations used in earlier numerical wall functions by Craft et al. (2004) and by Bond and Blottner (2011) are demonstrated. A standard low-Reynolds-number turbulence (LRN) model is used as reference but with different meshing strategies. The objective is to considerably reduce the total central processing unit (CPU) cost of the numerical simulations of wall bounded flows while maintaining the accuracy of any LRN model.When calculating turbulent flow problems, a tremendous speed-up may be achieved by decoupling the solution of the boundary layer from the bulk region by using a wall function. However, most wall functions are quite limited and based on assumptions which are not valid in complex, non-equilibrium flows.The present wall functions solve full momentum and energy equations on a sub-grid, using face fluxes of advection and diffusion to transfer the solution to and from the sub-grid. The evaluation was carried out on an axisymmetric impinging jet using the turbulence model of Launder and Sharma (1974) with the correction of Yap (1987).Compared to standard LRN calculations, the results show perfect agreement to less than one-sixth of the computational cost. However, the reason for the speed-up is shown to come mainly from the meshing strategy, and none of the evaluated wall functions add much additional value.