Characteristics of drag due to streamwise inhomogeneous roughness

Characteristics of the skin friction due to streamwise inhomogeneous roughness are investigated by modeling it in a simplified manner using step changes in equivalent sand grain roughness height k s, denoted as P (k s = 81.25 μm), Q (k s = 325.00 μm) and R (k s = 568.75 μm). The selected k s values represent the common ship-hull roughness, i.e., from light slime to about small calcareous fouling. RANS simulations are performed to study the friction characteristics of various rough surfaces formed by a trio-combination of P, Q and R roughnesses on flat plates with streamwise lengths of 30, 60, 120 and 240 m. The three combinations of roughnesses form either homogeneous (PPP, QQQ or RRR) or inhomogeneous (PQR, PRQ, QPR, etc.) rough walled turbulent boundary layer flow. A step change in roughness height results in a sudden change of the local skin friction coefficient in the form of overshoot or undershoot, followed by a relaxation where the inhomogeneous local skin friction is slowly returning to the homogeneous local one. The sequence of roughness arrangement in a streamwise inhomogeneous roughness pattern plays a key role in the resulting overall skin friction with value increasing in the following order: PQR < PRQ < QPR < QRP < RPQ < RQP. The similarity laws hold for both homogeneous and inhomogeneous rough surfaces.