A treatment of wall boundaries for (k-epsilon) turbulence modelling within an integral (finite element) formulation

A treatment of wall boundaries uses the two-equation k-epsilon turbulence model where epsilon, the dissipation rate of the turbulence kinetic energy (k), is an equivalent length scale variable. Being self-developing and internal, a turbulence model with a global length scale as a field variable is much preferred over the arbitrary local setting of a length scale. The present formulation clearly demonstrates the normal and shear stress contributions and the role of any given analytical wall function in determining the near wall shear wall stress. The wall function gives the shear velocity directly which then permits the setting of k and epsilon at the boundary in the turbulence model closure. The method is tested and appropriate boundary conditions are generated for the complex system of flow past a backward facing step where a recirculation zone is induced including flow separation, point of reattachment, and reverse flow along a side wall.