Extensions of the Spalart–Allmaras turbulence model to account for wall roughness

This paper describes extensions of the Spalart–Allmaras model to surface roughness, developed independently by Boeing and ONERA. They are rather simple and numerically benign, yield similar predictions, and are in fair agreement with experiments. They do not provide a description of the flow near the roughness elements, but rely instead on the “equivalent sand grain” approach. In that sense, they are not self-contained. The uncertain accuracy of the separate correlations, such as Dirling’s, needed to determine the sand grain size presents a challenge, as always. The roughness height must be much smaller than the boundary layer thickness, but the full range of roughness Reynolds number is covered. Some test cases reveal an incompatibility between the predicted effect of roughness on heat transfer and on skin friction. i.e. if the sand grain size is adjusted for skin friction, the heat transfer is too high.