A mixing length model for arbitrary geometry: the case of parallel flows

TL;DR

This paper introduces a phenomenological mixing length model that adapts to arbitrary geometries, accurately capturing turbulence characteristics in channel and pipe flows, and aligning well with experimental data.

Contribution

The paper presents a novel mixing length model that inherently accounts for geometry and satisfies Navier-Stokes symmetries, improving turbulence modeling accuracy.

Findings

Accurately models damping in viscous sub-layer

Predicts the log-law of the wall analytically

Aligns with high Reynolds number friction factor data

Abstract

We present a phenomenological model for the mixing length used in turbulence models. It has the advantage of naturally accounting for the object's geometry while satisfying the standard symmetries of the Navier-Stokes equations. We employ the model to study channel flow and pipe flow. We calibrate the three model parameters to recover the damping in the viscous sub-layer, the log-law of the wall, and the outer region behaviors. Our model compares favorably to friction factor measurements in the pipe flow at high Reynolds numbers and gives analytical predictions of the mixing length for several canonical flows.