The Pros and Cons of Wall Functions

Simulations of viscous flows based on the Reynolds-Averaged Navier-Stokes (RANS) equations have become an engineering tool used on a daily basis. One of the main goals of such calculations is to determine friction forces, which are a consequence of the shear-stress at solid walls.In RANS (and other more sophisticated mathematical models), there are two main approaches for the determination of the shear-stress at a wall: direct application of the no-slip condition, i.e. the velocity gradient is determined directly at the surface; wall functions which determine the shear-stress at the wall from semi-empirical equations applicable up to the outer edge of the so-called “wall layer/log layer”. Although the first option is physically preferable, its numerical requirements may lead to iterative convergence problems and/or excessive calculation times. Therefore, especially at high Reynolds numbers, it is not unusual to use the latter approach.In this paper we discuss the advantages and disadvantages of wall-function boundary conditions. To this end we have calculated the flow around a flat plate, conventional and laminar airfoils and a circular cylinder. The influence of the location where wall functions are applied (distance to the wall) and the effect of the Reynolds number (ranging from model to full scale applications) are discussed. Griding requirements for wall-function boundary conditions are also addressed. The results obtained with wall functions are compared with those obtained from the direct application of the no slip at the wall.The results obtained in this study show that the use of wall functions in viscous flow calculations may be justifiable or completely unacceptable depending on the flow conditions. Furthermore, it is also shown that wall-function boundary conditions also require clustering of grid nodes close to the wall, but obviously less demanding than the direct application of no slip condition.Copyright © 2015 by ASME

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