General Formulation of the Gradient Richardson Number for RANS Modelling

Abstract

The present paper deals with a grid-point local and general reformulation of the gradient Richardson number that is used to characterize and quantify mean-streamline curvature and rotation effects inside a fluid flow. In this context, a new computational relation is derived from the classical definition used by Bradshaw. This includes a condition to maintain the directional information which is associated with amplification and damping of turbulence. For this purpose, an in-depth analysis and a comparison with Richardson numbers from the literature are provided. The newly derived equations and terms are eventually verified with the analytical solution using a channel with U-turn test case and a vortex downstream of a delta wing. Moreover, potential areas of applications for the gradient Richardson number in the field of computational fluid dynamics are presented. Besides an application in classical RANS modelling, the usage of the parameter inside the Field Inversion/Machine Learning approach as a flow feature is discussed.