Analysis and Experiments on Three-Dimensional, Irregular Surface Roughness

Randomly placed, nonuniform, three-dimensional roughness with irregular geometry and arrangement is analyzed. New correlations are presented for such roughness for determination of magnitudes of equivalent sand grain roughness size $ks$ from a modified version of the Sigal and Danberg parameter $Λs.$ Also described are the numerical procedures employed to determine $Λs$ from three-dimensional profilometry data. The sand grain roughness values determined with this approach are then compared with and verified by$ks$ magnitudes determined using: (i) analytic geometry for uniformly shaped roughness elements arranged in a regular pattern on a test surface, and (ii) measurements made with nonuniform, three-dimensional, irregular roughness with irregular geometry and arrangement. The experiments to obtain these measurements are conducted using this latter type of roughness placed on the walls of a two-dimensional channel. Skin friction coefficients are measured in this channel with three different types of rough surfaces on the top and bottom walls, and agree very well with values determined using the numerical procedures and existing correlations. The techniques described are valuable because they enable the determination of equivalent sand grain roughness magnitudes, for similar three-dimensional roughness, entirely from surface geometry after it is characterized by three-dimensional optical profilometry data.