Implementation Methods of Wall Functions in Cell-vertex Numerical Solvers

Two different implementation techniques of wall functions for cell-vertex based numerical methods are described and evaluated. The underlying wall model is based on the classical theory of the turbulent boundary layer. The present work focuses on the integration of this wall-model in a cell-vertex solver for large eddy simulations and its implications when applied to complex geometries, in particular domains with sudden expansions (more generally in presence of sharp edges). At corner nodes, the conjugation of law of the wall models using slip velocities on walls and of the cell-vertex approach leads to difficulties. Therefore, an alternative implementation of wall functions is introduced, which uses a no-slip condition at the wall. Both implementation methods are compared in a turbulent periodic channel flow, representing a typical validation case. The case of an injector for aero-engines is presented as an example for an industrial-scale application with a complex geometry.