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

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 $R{e}_{{\delta }_2}=570$ to $13800$, with a self-similar region from $R{e}_{{\delta }_2}=10000$ 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.

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