A parametrized non-equilibrium wall-model for large-eddy simulations

TL;DR

This paper introduces a new parametrized wall-model for large-eddy simulations that incorporates non-equilibrium effects, such as pressure gradients, by extending wall-normal ODE-based models to better predict complex boundary-layer phenomena.

Contribution

It develops a novel approach to include non-equilibrium effects in wall-models while maintaining computational efficiency with wall-normal ODEs.

Findings

Successfully modeled adverse pressure-gradient boundary layers.

Accurately predicted shock/boundary-layer interactions.

Improved wall shear stress predictions in non-equilibrium flows.

Abstract

Wall-models are essential for enabling large-eddy simulations (LESs) of realistic problems at high Reynolds numbers. The present study is focused on approaches that directly model the wall shear stress, specifically on filling the gap between models based on wall-normal ordinary differential equations (ODEs) that assume equilibrium and models based on full partial differential equations (PDEs) that do not. We develop ideas for how to incorporate non-equilibrium effects (most importantly, strong pressure-gradient effects) in the wall-model while still solving only wall-normal ODEs. We test these ideas using two reference databases: an adverse pressure-gradient turbulent boundary-layer and a shock/boundary-layer interaction problem, both of which lead to separation and re-attachment of the turbulent boundary layer.