Boundary layer flow over a bump and the three-dimensional law of the wall

Abstract

Many turbulence theories in use today are based on two-dimensional equilibrium flows and have limitations when applied to three-dimensional flows. A three-dimensional law of the wall would help to improve simulation fidelity, but while several versions have been proposed, none have been widely accepted. In this study, the three-dimensional attached boundary layer flow over the windward side of the BeVERLI (Benchmark Validation Experiments for RANS/LES Investigations) Hill bump model was measured using near-wall laser Doppler velocimetry in the Virginia Tech Stability Wind Tunnel to study the mean flow and turbulence structure. These mean velocity measurements are compared with the predictions of the proposed three-dimensional (3D) law of the wall of van den Berg [A three-dimensional law of the wall for turbulent shear flows. J Fluid Mech. 1975;70(1):149–160.], which incorporates pressure gradients and inertial effects but assumes alignment of the mean flow gradient and shear-stress angles, and to the sublayer momentum equations, which are exact in the limit of wall-normal $x_2^{+}\to 0$. In regions with mild stress/strain misalignment, the van den Berg model compares favourably with the experimental data up to a maximum of $x_2^{+}\approx 800$, and the sublayer momentum relationship compares favourably with the experimental data in the linear sublayer.

Keywords:

• Three-dimensional boundary layer
• turbulent flow
• laser Doppler velocimetry
• BeVERLI Hill
• bump

Acknowledgments

We thank BeVERLI collaborators Dr. Philippe Lavoie, Vignesh Sundarraj, Daniel MacGregor, Tom Hallock, and Thomas Ozoroski for their assistance with wind tunnel testing and thoughtful discussion on the data presented. We also thank Stability Wind Tunnel engineer, Bill Oetjens, for his assistance and expertise during wind tunnel testing, and the Aerospace and Ocean Engineering Machine Shop staff for their assistance in the fabrication and instrumentation of test equipment.

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

This work was sponsored by NASA's Transformational Tools and Technologies Project. The Virginia Tech team gratefully acknowledges the support provided by NASA (Langley Research Center) through an NRA award, grant 80NSSC18M0146 and 80NSSC22M0061, with technical monitor Michael Kegerise and programme manager Mujeeb Malik.