Assessment and Prediction of Friction in ZPG Boundary Layers Over Sand Grain Roughness

Prediction of friction in rough wall boundary layers is of great practical importance. For the same overall Reynolds number, a boundary layer over a rough wall experiences higher friction compared to that over a smooth wall. The degree of departure from the smooth-wall value is expected to depend on the amount of roughness present. We use our previously published smooth wall friction model to assess the departures of dimensionless friction from the corresponding smooth-wall values as a function of roughness Reynolds number. It is found that these percentage departures scale on the sand grain roughness Reynolds number and can be modelled empirically. Using this, a new methodology is presented to estimate friction in a rough wall boundary layer provided the sand grain roughness value is known. Predictions of friction velocity with ±5% accuracy are obtained over three decades of roughness Reynolds number range. The accuracy and limitations of the proposed method are discussed.