Continous Formulation of Wall Function with Adverse Pressure Gradient

Abstract

In computational fluid dynamics, wall function boundary conditions are essential for the treatment of solid boundaries. In practice, computational meshes used to be created so that solid boundaries were either located in the laminar sublayer or in the logarithmic region of the boundary layer. In complex geometries, though, it is not straightforward to ensure that the first off-the-wall point satisfies the requirements for either an integration of the governing equations through the viscous sublayer, or that it is always in the logarithmic region of the boundary layer. Therefore, various continous formulations of boundary layer profiles have been proposed, which cover both the sublayer and the buffer layer. These formulations do not generally take into account the effects of pressure gradients on the boundary layer. In this paper, a continous formulation of the boundary layer velocity profile that includes the effects of pressure gradients is presented.