A novel method for the determination of frictional resistance coefficient for a plate with inhomogeneous roughness

Ship performance is largely influenced by roughness on immersed surfaces, which is mostly inhomogeneous. Therefore, the prediction of the effects of roughness on ship performance is of crucial importance. Even though it has several drawbacks, the Granville similarity law scaling method is widely reported in the literature for predicting the frictional resistance coefficient of a rough surface. Lately, the CFD approach based on a modified wall function approach has also been used, since it allows for a more comprehensive analysis of the effects of roughness. In this paper, a novel method for assessing the frictional resistance coefficient for rough surfaces is proposed. The proposed method can take into account the non-uniform distribution of friction velocity, as well as the roughness Reynolds number, and thus the non-uniform distribution of roughness function values can be predicted along a rough surface. Additionally, the proposed method can consider the non-uniform distribution of roughness and its effect on the frictional coefficient of a flat plate. Based on the proposed method, an in-house numerical code is developed, allowing for the rapid and accurate assessment of the frictional resistance coefficient for a rough surface. The applicability of the proposed method is demonstrated by comparison with the CFD approach for several surface conditions defined with different roughness function models and the longitudinal position of roughness. A comparison is made of two flat plates representing one containership and one tanker at two different speeds. The obtained relative deviations in the predicted frictional resistance coefficients for all surface conditions are lower than 2.5%. Therefore, it is demonstrated that the proposed method can be used for estimating the frictional resistance coefficient of various surface conditions defined with roughness function models and the longitudinal positions of roughness.