On the relation between measurable (AHR) and modelled (sand-grain) roughness heights in RANS-based full-scale ship resistance predictions

The surface roughness of ship hulls is usually expressed in terms of an average height of the roughness (AHR), determined from measurements at a large number of locations across a hull. In viscous-flow (RANS-CFD) solvers the sand-grain height, h_R, is used to model surface roughness effects, typically through the adaptation of the wall-boundary conditions in the turbulence model. It is important to realize that these are two very different measures for the surface roughness, and to the best of the author’s knowledge there is no generally valid expression that relates AHR to h_R. Nevertheless, for numerical simulations we are faced with the challenge to translate the texture of a ship’s surface, either newly-built or after some time in service, into an equivalent roughness height.
In the present study it has been investigated how the CFD-predicted ship-resistance increase due to surface roughness compares with a well-known emperical relation that has been used in the determination of the ship resistance for quite some time. From this comparison a factor has been determined that for the present test case results in a good agreement between the two methods at higher roughness values.