CFD calculation of turbulent flow with arbitrary wall roughness

Wall functions are used in CFD calculations of turbulent flow to handle the no-slip boundary condition at solid surfaces without an unacceptably-large number of grid cells. Recent work in the Turbulence Mechanics Group at the University of Manchester has been aimed at developing wall functions suitable for non-equilibrium flows - primarily for smooth walls. For environmental fluid-mechanics problems, however, there is a need to extend the new wall-function concepts to arbitrary wall roughness. Suga, Craft and Iacovides (Extending an analytical wall function for turbulent flows over rough walls, 6th International Symposium on Engineering Turbulence Modelling and Measurements, Sardinia, 2005) have shown how this may be achieved by making the zero-eddy-viscosity height, y(nu) , a function of roughness. Their function is, however, largely empirical, and this paper goes further by demonstrating that the zero-eddy-viscosity height can be more satisfactorily determined by appealing to higher-order consistency with the log law. Roughness-dependent changes are also made to the near-wall prescription of the turbulent kinetic energy dissipation rate, epsilon. The wall function for arbitrarily-rough surfaces is developed in detail and its ability to reproduce the Darcy friction factor in rough-walled pipes is tested. Some computational results for the more complex application which stimulated this work - sediment transport and sandbank morphodynamics - are then given. The application of the wall function to the Reynolds-stress transport equations and modifications for streamwise pressure gradients are also discussed.