Investigation of the Level of Action on Wall Shear Stress and the Law of the Wall for Rough Wall Turbulent Boundary Layer

Abstract

The discussion on the law of the wall has been performed for turbulent boundary layer over rough surface under a zero pressure gradient. The wall shear stress was directly measured with a drag balance of a floating element device. The center of the wall shear stress, which is calculated from the moment of the pressure drag acting on a roughness element, is well consistent with the vertical origin estimated with the assumption of the log law profile. The distance from the crest of the roughness element to the center of the wall shear stress normalized with the roughness height increases with increasing roughness density λs. The value approaches to zero less than λs=0.5 and tends to 0.5 in the limit of λs=1. The roughness function is formulated as function of Reynolds number based on the distance from the crest to the center of the wall shear stress and the friction parameter, which is the ratio of friction velocity to the free stream velocity, for the equilibrium boundary layer over the rough surface. Experimental data collapses on the formula in the case of the constant friction parameter.