Development and application of wall-function treatments for turbulent forced and mixed convection flows

CFD calculations of turbulent flow near smooth walls generally employ one of two broad strategies to resolve the very influential, complex, but thin near-wall viscosity-affected sub-layer. One approach uses a fine numerical mesh and a turbulence model incorporating viscous influences; the other employs "wall functions"- Formulae that attempt to account for the overall resistance of the sublayer to momentum and heat transport. The latter requires only a fraction of the computational effort of the former and is thus strongly favoured for industrial calculations. However, the wall-function performance is often poor, partly because of inappropriate implementations and partly because the schemes themselves have inherent limitations. The present paper reviews the evolution of wall-function strategies. Attention is then given to two new schemes developed by the authors, one based on an analytical treatment and the other on a numerical resolution of the near-wall sub-layer. Several applications are shown of mixed and forced convection.