Turbulent boundary layer with strong favorable pressure gradient and curvature effects: Streamline coordinate and scaling analysis

TL;DR

This study uses DNS to analyze a turbulent boundary layer over a Gaussian bump, focusing on pressure gradient and curvature effects, and proposes improved scaling laws for Reynolds stresses.

Contribution

It introduces new integral analysis-based scalings for Reynolds stresses that outperform traditional scalings in complex pressure gradient and curvature conditions.

Findings

Reynolds stress profiles collapse better with proposed scalings.

Flow exhibits complex pressure gradient and curvature effects before separation.

Integral analysis simplifies momentum budget interpretation.

Abstract

Direct numerical simulation (DNS) of a turbulent boundary layer over the Gaussian (Boeing) bump is performed. This boundary layer exhibits a series of adverse and favorable pressure gradients and convex and concave curvature effects before separating. These effects on turbulent boundary layers are characterized and compared to a lower Reynolds number flow over the same geometry. The momentum budgets are analyzed in the streamline-aligned coordinate system upstream of the separation region. These momentum budgets allow the simplification of equations to facilitate an integral analysis. Integral analysis-based scalings for Reynolds stresses in the inner and outer regions of the boundary layer are also formulated. These proposed scalings exhibit a better collapse of Reynolds stress profiles compared to friction velocity scaling and Zagarola-Smits scaling in the strong favorable pressure gradient region and in the mild adverse pressure region that precedes it in this flow.