A New Wall Function Model for RANS Equations Based on Overlapping Grids

Abstract

This paper presents a new numerical method for the modeling of turbulent flows based on a new wall model for computing Reynolds-Averaged-Navier-Stokes (RANS) equations with the Spalart-Allmaras (SA) turbulence model. The basic objective is the reduction of the total central processing unit (CPU) cost of the numerical simulation without harming the accuracy of the results. The main idea of this study is based on the use of two overlapping computational grids covering the two distinct regions of the flow (i.e., the boundary layer and the outer region), and the implementation of appropriate (different) numerical schemes in each case. The seamless cooperation of the grids in the iterative algorithm is achieved by defining an alternative wall function concept. The unstructured grid (UG) covering the outer region consists of mixed type elements (i.e., quadrilaterals and triangles), with relatively small degrees of anisotropy, on which the full set of Navier-Stokes (NS) along with the turbulent model (TM) equations are relaxed. The inner structured grid (SG), which aims at resolving the boundary layer, is a body-fitted mesh with high element density in the normal to the wall direction. The slow relaxation of the governing equations on anisotropic SGs is alleviated by using the Tridiagonal Matrix Algorithm (TDMA) and a block Lower Upper Method (LU). These prove to be quite suitable for the relaxation of the discretized equations on SGs, which consist of banded arrays in tensor form. The application of the proposed algorithm in a couple of benchmark cases proves its superiority over the High-Reynolds SA model with standard wall functions when both methods are compared with the (more costly) Low-Reynolds SA turbulence model and experimental results.

Keywords:

• Wall function model
• RANS equations
• High-Reynolds numbers
• Hybrid grids