Comparison of three roughness function determination methods

Three methods have been used to experimentally determine the roughness function (DU) for several rough surfaces. These include the rotating disk, the towed plate, and the velocity profile methods. The first two are indirect methods in as much as they rely on measurements of overall torque or resistance and boundary layer similarity laws to obtain DU, whereas the velocity profile method provides a direct measurement of DU. The present results indicate good agreement between the towed plate and the velocity profile methods for all of the surfaces tested. Tests for the rotating disk were carried out at much higher unit Reynolds numbers. Using this method, the results for sandpaper rough surfaces agree within their uncertainty with a Nikuradse-type roughness function in the fully rough regime, while a spray painted surface agrees with a Colebrook-type roughness function. Nomenclature B smooth wall log-law intercept, =5.0 CF overall frictional resistance coefficient, 1⁄4 FD ð Þ 1 2 qU 2 e S Cf skin-friction coefficient, 1⁄4 so ð Þ 1 2 qU 2 e Cm torque coefficient, =(2M)/(qR (/x)) FD drag force k arbitrary measure of roughness height K acceleration parameter, 1⁄4 m U2 e dUe dx L plate length M torque N number of samples or replicates R disk radius Ra centerline average roughness height, 1⁄4 1 N PN