Wall-Roughness Eddy Viscosity for Reynolds-Averaged Closures*

An approach to modeling the effect of rough surfaces on turbulent boundary-layer flow is presented.  It is based on the concept of a rough-wall eddy viscosity, in which the pressure and viscous drag forces which arise on account of flow past roughness elements are recast as an equivalent viscous shear force
within the roughness sublayer at the surface.  This shear force can be modeled as an apparent body force or as a wall-roughness eddy viscosity and carries information on both the flow Reynolds number and the roughness height.  The modeling approach is developed and evaluated as part of k--ε and k--ε--v^' closures.   When the wall-roughness eddy viscosity is modeled in proportion to k⁺_s^3/4 where k⁺_s is the sand-grain roughness in wall units, it yields predictions of drag coefficients which are in excellent agreement with those from reference data for flow in rough-walled pipes, over a wide range of surface-roughness heights and Reynolds numbers.  Its predictions are also in good agreement with experimental data for zero and favorable pressure gradient boundary layers over fully-rough surfaces.