Mechanism of Momentum Exchange near a Roughness Element for Rough Wall Turbulent Boundary Layer (Flow Visualization of Eddy Formed in a Two-Dimensional Square Cavity)

Abstract

Flow visualization has been performed in the vicinity of a roughness element for boundary layers developing over rough surfaces with roughness pitch ratios p of 2 and 4 at low Reynolds number. The momentum thickness Reynolds numbers at streamwise distance x =865 mm for p =2 and 4 are 300 and 500, respectively. For the rough surface of p =2, typical eddy structures are classified into 4 patterns that are consistent with the results of Townes et al., whereas for the rough surface of p =4, three patterns are recognized. As compared with the rough surface of p =2, the rough surface of p =4 takes a larger value of occurrence frequency normalized with respect to the cavity width and the friction velocity. Occurrence frequency is equal to the sum of the frequency of each pattern, and is closely related with momentum exchange. This quantitative result can suggest that the pressure drag acting on a roughness element for the rough surface of p =4 is larger than that of the rough surface of p =2.