An Integral Solution for Skin Friction in Turbulent Flow Over Aerodynamically Rough Surfaces With an Arbitrary Pressure Gradient

Abstract

The combined law of the wall and wake, with the inclusion of the “roughness depression functionâ€‌ for the inner law in the “Logâ€‌ region, is used as the inner coordinates' velocity profile in the integral form of the x momentum equation to solve for the local skin friction coefficient. The “equivalent sand grain roughnessâ€‌ concept is employed in the roughness depression function in the solution. Calculations are started at the beginning of roughness on a surface, as opposed to starting them using the measured experimental values at the first data point, when making comparisons of predictions with data sets. The dependence of the velocity wake strength on both pressure gradient and momentum thickness Reynolds number are taken into account. Comparisons of the prediction with experimental skin friction data, from the literature, have been made for some adverse, zero, and favorable (accelerating flows) pressure gradients. Predictions of the shape factor, roughness Reynolds number, and momentum thickness Reynolds number and comparisons with data are also made for some cases. In addition, some comparisons with the predictions of earlier investigators have also been made.