Determining an equivalent sandgrain roughness height for turbulent boundary layers developing over streamwise heterogeneous surfaces

Biofouling buildup is a prevalent issue in marine vehicle operation which can result in enormous drag penalties. This naturally occurring roughness is often distributed unevenly, both in the spanwise and streamwise extent. An estimate of the equivalent sandgrain roughness height, k_s, is required for predictive simulations of the rough surface drag penalties. However, a challenge arises to characterize an average k_s over the heterogeneous surface where the local drag will fluctuate due to the topographical changes. Recent work by Hutchins et al. (2023) implemented the power-mean approach to define an equivalent homogeneous k_s for spanwise varying heterogeneous surfaces. The present work extends this method to also include streamwise varying surfaces by considering area- and streamwise-weighted distributions in the power mean. Roughness parameters are computed from several thousand iterations of heterogeneous roughness conditions over a plate with length and velocity parameters representative of a naval destroyer. The results from the power-mean approach are then compared using different roughness function models (i.e. Nikuradse and Colebrook) to formulate a cohesive error analysis of the predicted drag.