Non-equilibrium wall model for large eddy simulations of complex flows exhibiting turbulent smooth body separation

TL;DR

This paper introduces a non-equilibrium wall model for large eddy simulations that better predicts turbulent flows with separation by accounting for pressure-gradient effects, improving upon traditional equilibrium models.

Contribution

The paper proposes a novel non-equilibrium wall model that incorporates pressure-gradient and convective effects, enhancing LES predictions of separated turbulent flows.

Findings

Model accurately predicts boundary layer separation in complex flows.

Improves LES accuracy over traditional equilibrium wall models.

Successfully tested on NASA-Boeing speed bump and Bachalo-Johnson bump flows.

Abstract

In this work, a non-equilibrium wall model is proposed for the prediction of turbulent flows experiencing adverse pressure gradients, including separated flow regimes. The mean-flow nonequilibrium is identified by comparing two characteristic velocities: the friction velocity (u_tau) and the viscous-pressure gradient velocity (up). In regions where the pressure gradient velocity is comparable to the friction velocity (up \sim u_tau, the near-wall turbulent closure is modified to include the effect of the pressure-gradient and convective terms. The performance of this wall model is evaluated in two canonical flows experiencing smooth body separation: the NASA-Boeing speed bump and the Bachalo-Johnson bump. Improvements in the predictive capabilities of the proposed model for the conventional equilibrium wall model are theorized and then demonstrated through numerical experiments. In particular, the proposed wall model can capture the onset of boundary layer separation observed in experiments or DNS calculations at resolutions where the equilibrium wall model fails to separate.