Predictions of canonical wall bounded turbulent flows via a modified $k-\omega$ equation

TL;DR

This paper introduces a modified $k-$ turbulence model that accurately predicts mean velocity and kinetic energy profiles in wall-bounded turbulent flows across various Reynolds numbers, improving upon existing models.

Contribution

The paper presents a physics-based modification to the $k-$ equation, including new parameters for the overlap region, wake effects, and meso-layer dissipation, enhancing predictive accuracy.

Findings

Achieves over 99% accuracy in MVP predictions for Princeton pipes.

Successfully predicts the outer peak in the SMKP.

Improves original model predictions by up to 10%.

Abstract

A major challenge in computation of engineering flows is to derive and improve turbulence models built on turbulence physics. Here, we present a physics-based modified $k-\omega$ equation for canonical wall bounded turbulent flows (boundary layer, channel and pipe), predicting both mean velocity profile (MVP) and streamwise mean kinetic energy profile (SMKP) with high accuracy over a wide range of Reynolds number ($Re$). The result builds on a multi-layer quantification of wall flows, which allows a significant modification of the $k-\omega$ equation. Three innovations are introduced: First, an adjustment of the Karman constant to 0.45 is set for the overlap region with a logarithmic MVP. Second, a wake parameter models the turbulent transport near the centerline. Third, an anomalous dissipation factor represents the effect of a meso layer in the overlap region. Then, a highly accurate (above 99\%) prediction of MVPs is obtained in Princeton pipes, improving the original model prediction by up to 10\%. Moreover, the entire SMKP, including the newly observed outer peak, is predicted. With a slight change of the wake parameter, the model also yields accurate predictions for channels and boundary layers.