Direct numerical simulation of a self-similar adverse pressure gradient turbulent boundary layer at the verge of separation

TL;DR

This paper presents DNS results of a self-similar adverse pressure gradient turbulent boundary layer at the verge of separation, analyzing its properties and comparing with zero and mild pressure gradient flows.

Contribution

It provides detailed DNS data and analysis of a high adverse pressure gradient TBL near separation, including self-similarity conditions and flow property comparisons.

Findings

Flow becomes more like a free shear layer with increasing pressure gradient.

Self-similarity conditions for APG TBL are derived and validated.

Mean and Reynolds stress profiles collapse under appropriate scaling.

Abstract

The statistical properties are presented for the direct numerical simulation (DNS) of a self-similar adverse pressure gradient (APG) turbulent boundary layer (TBL) at the verge of separation. The APG TBL has a momentum thickness based Reynolds number range from $Re_{\delta_2}=570$ to $13800$, with a self-similar region from $Re_{\delta_2} = 10000$ to $12300$. Within this domain the average non-dimensional pressure gradient parameter $\beta=39$, where for a unit density $\beta=\delta_1 P_e^\prime / \tau_w$, with $\delta_1$ the displacement thickness, $\tau_w$ the mean shear stress at the wall, and $P_e^\prime$ the farfield pressure gradient. This flow is compared to previous zero pressure gradient (ZPG) and mild APG TBL ($\beta=1$) results of similar Reynolds number. All flows are generated via the DNS of a TBL on a flat surface with farfield boundary conditions tailored to apply the desired pressure gradient. The conditions for self-similarity, and the appropriate length and velocity scales are derived. The mean and Reynolds stress profiles are shown to collapse when non-dimensionalised on the basis of these length and velocity scales. As the pressure gradient increases the flow has properties less like a ZPG TBL and more akin to a free shear layer.