Toward modeling of turbulent flow over surfaces of arbitrary roughness

The problem of Reynolds-averaged modeling of turbulent boundary-layer flow over surfaces of arbitrary roughness is studied using the results of direct numerical simulations of turbulent flow over many different rough surfaces. The complexity of flow in the roughness sublayer is such that the most effective general strategy appears to be to model it as a prescribed velocity profile, either at a coarse level as a conventional roughness-specific log-linear wall function, or at a fine level as a modeled roughness-specific velocity profile across the roughness sublayer, together with a standard Reynolds-averaged closure in the outer flow. Calculations made with sandgrain roughness wall functions and velocity-profile models were in excellent agreement with channel-flow simulation data and, after correction for effects of Reynolds number and roughness height, were in good agreement with friction coefficients for a wide range of reference pipe-flow data. Equally good predictions of friction coefficients were made of flows over wavy walls, walls with spaced arrays of semi-ellipsoids, and walls with roughness elements of random size and orientation, when either sublayer velocity profiles or wall functions for the corresponding roughnesses were used. This modeling approach is made possible by the availability of relevant data from a library of roughness-sublayer velocity profiles from simulations of flow over many different kinds of rough surfaces.