Study of turbulent boundary layers over rough surfaces with emphasis n the effects of roughness character and Mach number

A Reynolds stress model for turbulent boundary layers on rough walls is used to investigate the effects of roughness character and compressibility. The flow around roughness elements is treated as form drag. A method is presented for deriving the required roughness shape and spacing from profilometer surface measurements. Calculations based on the model compare satisfactorily with low speed data on roughness character and hypersonic measurements with grit roughness. The computer model is exercised systematically over a wide range of parameters to derive a practical scaling law for the equivalent roughness. In contrast to previous correlations, for most roughness element shapes the effective roughness is not predicted to show a pronounced maximum as the element spacing decreases. The effect of roughness tends to be reduced with increasing edge Mach number, primarily due to decreasing density in the vicinity of the roughness elements. It is further shown that the required roughness Reynolds number for fully rough behavior increases with increasing Mach number, explaining the small roughness effects observed in some hypersonic tests.