Progress in the generalization of wall-function treatments

Generalized wall functions and their application for simulation of turbulent flows

“…In the HR models, the boundary conditions or near-wall proÿles are represented by wall functions. In most cases, the wall functions are semi-empirical and have very limited applications [1][2][3][4][5]. The wall functions were originally based on the log-law proÿle for the velocity [2,3].…”

“…Wilcox [7] showed that the pressure gradient must be taken into account to avoid the mesh dependence. In more recent approaches [1,4,5] attempts have been made to take into account the pressure gradient and other e ects such as buoyancy forces [1,5]. Numerical comparisons presented in References [1,4,5] showed that such advanced wall functions give substantially better prediction than the standard wall functions.…”

“…Reference [1]. In Reference [5], analytical wall functions are obtained by integrating boundary-layer-type equations in the vicinity of a wall using the assumption that all terms besides the di usive one are constant. At the wall, the boundary conditions are the same as those used in the LR models.…”

Direct Numerical Simulation of Reacting Turbulent Multi-Species Channel Flow

“…Writing equation (1) in terms of non-dimensional variables and integrating it, the following logarithmic approximation is found for the Van Driest transformation [12], [13]:…”

“…The classic logarithmic law is implemented in most of the RANS codes and provides reasonable good results for simple incompressible flows. The trend today is to generalize this wall function to account for more physics [1], [2]. Development of wall functions that take into account strong changes in the density due to strong temperature gradient and fluid non-homogeneity is necessary to simulate parietal heat transfers with a good accuracy and at a moderate cost by using RANS-based design codes.…”