A modified Parametric Forcing Approach for modelling of roughness

Surface roughness in turbulent channel flow is effectively modelled using a modified version of the Parametric Forcing Approach introduced by Busse and Sandham (2012). In this modified approach, the model functions are determined based on the surface geometry and two model constants, whose value can be fine tuned. In addition to a quadratic forcing term, accounting for the effect of form drag due to roughness, a linear forcing term, analogous to the Darcy term in the context of porous media, is employed in order to represent the viscous drag. Comparison of the results with full-geometry resolved Direct Numerical Simulation (DNS) data for the case of dense roughness (frontal solidity congruent to 0.4) shows a satisfactory prediction of mean velocity profile, and hence the friction factor, by the model. The model is found to be able to reproduce the trends of friction factor with morphological properties of surface such as skewness of the surface height probability density function and coefficient of variation of the peak heights.