Derivation, implementation, and initial testing of a compressible wall-layer model

Abstract

Traditional wall functions have been used successfully for decades to decrease the computational cost for obtaining solutions to incompressible flows with equilibrium turbulence. However, these traditional, analytic wall functions are poorly suited for more complex flows. The present work describes an alternative approach named the ‘diffusion model’. The diffusion model is a subgrid model developed by Blottner and Bond that solves a system of ODEs in the near-wall region instead of assuming an analytic profile. The diffusion model has previously been shown to reproduce profiles of various turbulence models through the log layer with fixed outer boundary conditions. This paper documents the implementation and the testing of the diffusion model fully coupled with a 3-D Reynolds-averaged Navier–Stokes (RANS) algorithm, using the Spalart–Allmaras model. The results indicate that the coupled algorithm is valid when the interface between diffusion model and the 3-D RANS algorithm is below the outer edge of the log layer. Although the current work focuses on using steady 3-D RANS outside of the log layer, modeling assumptions introduced in the current work could be used to derive a diffusion model for coupling with a large eddy simulation region. Published in 2010 by John Wiley & Sons, Ltd.