Modification of the $k-\omega_0$ model for roughness

TL;DR

This paper extends the k-omega0 turbulence model to account for surface roughness by introducing an effective origin, linking it to sandgrain roughness, and ensuring consistency with the fully rough flow limit.

Contribution

The authors modify the k-omega0 model by incorporating an effective origin to better predict flows over rough surfaces, establishing a link with sandgrain roughness and the fully rough limit.

Findings

The model includes an effective origin for rough surfaces.

A formula for the virtual origin in fully rough flow is derived.

The extended model aligns with the fully rough flow limit.

Abstract

Surface roughness plays a substantial role in many flows for which Reynolds averaged prediction is needed. The transformation used in the k-omega0 model is extended to rough surfaces by adding an effective origin. The log-layer offset is computed as a function of this effective origin, thereby creating a correspondence between effective origin and equivalent sandgrain roughness. A formula is derived for the virtual origin of the fully rough log law. It is shown how the present model is consistent with the fully rough limit.