On the Reynolds analogy for high-speed rough-wall flows: implications for wall modelling

TL;DR

This paper investigates the validity of the generalized Reynolds analogy in high-speed turbulent boundary layers over rough surfaces, showing it holds above the roughness sublayer and proposing a GRA-based wall model for heat transfer prediction.

Contribution

It demonstrates the asymptotic validity of the GRA in high-speed rough-wall flows and develops a new GRA-based wall model for heat transfer prediction.

Findings

GRA validity is confined to the roughness sublayer.

Above the roughness layer, GRA recovers smooth-wall-like similarity.

Proposed a GRA-based wall model for heat transfer over rough surfaces.

Abstract

We study the validity of the generalized Reynolds analogy (GRA) in compressible turbulent boundary layers over prism-shaped roughness by mining direct numerical simulation data of Mach 2 and Mach 4 compressible turbulent boundary layers with adiabatic and cooled surfaces. Although the direct influence of roughness strongly disrupts the near-wall coupling between momentum and energy, we show that this breakdown is confined to the roughness sublayer. Above this layer, the enthalpy and velocity fields recover a smooth-wall-like similarity, and the GRA becomes asymptotically valid by naturally accounting for roughness-enhanced wall shear stress and heat flux. Building on these results, we propose a GRA-based wall model for predicting heat transfer over rough surfaces, which is coupled with a drag-predictive physics-based method developed for prism-shaped roughness by means of compressibility transformations.