Analysis of high-order velocity moments in a strained channel flow

TL;DR

This study validates model expressions for fifth-order velocity moments in turbulent flows using DNS data, highlighting the effects of flow deformation and grid resolution on model accuracy.

Contribution

It introduces validated model expressions for high-order velocity moments applicable to non-Gaussian turbulent flows, with insights into flow deformation and grid sensitivity.

Findings

Flow deformation improves model-DNS agreement.

Odd velocity moments are sensitive to grid resolution.

A new length scale criterion aids in grid generation near walls.

Abstract

In the current study, model expressions for fifth-order velocity moments obtained from the truncated Gram-Charlier series expansions model for a turbulent flow field probability density function are validated using data from direct numerical simulation (DNS) of a planar turbulent flow in a strained channel. Simplicity of the model expressions, the lack of unknown coefficients, and their applicability to non-Gaussian turbulent flows make this approach attractive to use for closing turbulent models based on the Reynolds-averaged Navier-Stokes equations. The study confirms validity of the model expressions. It also shows that the imposed flow deformation improves an agreement between the model and DNS profiles for the fifth-order moments in the flow buffer zone including when the flow reverses its direction. The study reveals sensitivity of particularly odd velocity moments to the grid resolution. A new length scale is proposed as a criterion for the grid generation near the wall and in the other flow areas dominated by high mean velocity gradients when higher-order statistics have to be collected from DNS.