We study the role of the wall-normal Reynolds stress in hypersonic boundary layers and consider implications for RANS modeling. In low-Mach-number, zero-pressure-gradient boundary layers, the contribution of the wall-normal Reynolds stress to the wall-normal momentum equation is negligible. As a result, the wall-normal momentum equation indicates that pressure is uniform throughout the boundary layer. However, in hypersonic boundary layers, analysis indicates that the wall-normal Reynolds stress becomes significant compared to mean pressure, and the wall-normal momentum equation indicates that pressure must balance the wall-normal Reynolds stress. We validate this hypothesis using direct numerical simulation data of supersonic and hypersonic boundary layers. The results show that the wall-normal Reynolds stress balances with pressure, resulting in non-negligible pressure deficits in the log layer. We consider implications for RANS modeling and show that errors in standard models for the wall-normal Reynolds stress have a noticeable impact (upward of $5\%$ for a Mach 14 cold-wall flow) on wall quantities of interest, such as skin friction.

Close

PrevNext

View figure in article

• Boundary layers
• Compressible flows
• High-speed flow
• Turbulence
• Turbulence modeling
• Turbulent boundary layers