POD-mode-augmented wall model and its applications to flows at non-equilibrium conditions

TL;DR

This paper introduces a POD-mode-augmented wall model for LES that improves the prediction of non-equilibrium turbulent flows by incorporating multiple modes, capturing extreme events and pressure gradient effects more accurately.

Contribution

The paper develops a novel wall model combining the law of the wall with a POD-based mode, enhancing non-equilibrium flow modeling in LES.

Findings

Better capture of extreme wall-shear stress events

Improved modeling of non-equilibrium effects due to pressure gradients

Accurate prediction of rapid changes in wall-shear stress

Abstract

Insights gained from modal analysis are invoked for predictive large-eddy simulation (LES) wall modeling. Specifically, we augment the law of the wall (LoW) by an additional mode based on a one-dimensional proper orthogonal decomposition (POD) applied to a 2D turbulent channel. The constructed wall model contains two modes, i.e., the LoW mode and the POD-based mode, and the model matches with the LES at two, instead of one, off-wall locations. To show that the proposed model captures non-equilibrium effects, we perform a-priori and a-posteriori tests in the context of both equilibrium and non-equilibrium flows. The a-priori tests show that the proposed wall model captures extreme wall-shear stress events better than the equilibrium wall model. The model also captures non-equilibrium effects due to adverse pressure gradients. The a-posteriori tests show that the wall model captures the rapid decrease and the initial decrease of the streamwise wall-shear stress in channels subjected to suddenly imposed adverse and transverse pressure gradients, respectively, both of which are missed by currently available wall models. These results show promise in applying modal analysis for turbulence wall modeling. In particular, the results show that employing multiple modes helps in the modeling of non-equilibrium flows.