A single formula for the law of the wall and its application to wall-modelled large-eddy simulation

TL;DR

This paper introduces a unified logarithmic-exponential formula for the law of the wall and employs a neural network trained on this formula to improve wall-modelled large-eddy simulations of turbulent flows, outperforming existing models.

Contribution

It presents a novel single formula for the law of the wall and a neural network approach trained on it for enhanced wall-modelled LES accuracy.

Findings

The LOG-EXP formula effectively predicts mean velocity profiles.

The neural network trained on the formula improves Reynolds stress predictions.

The FNN outperforms the Werner-Wengle model in WMLES.

Abstract

In this work, we propose a single formula for the law of the wall, which is dubbed as the logarithmic-exponential (LOG-EXP) formula, for predicting the mean velocity profile in different regions near the wall. And then a feedforward neural network (FNN), whose inputs and training data are based on this new formula, is trained for the wall-modelled large-eddy simulation (WMLES) of turbulent channel flows. The direct numerical simulation (DNS) data of turbulent channel flows is used to evaluate the performance of both the formula and the FNN. Compared with the Werner-Wengle (WW) model for the WMLES, a better performance of the FNN for the WMLES is observed for predicting the Reynolds stresses.