A scaling law for form drag coefficients in incompressible turbulent flows

Abstract

We present a similarity law for form drag coefficients, which is obtained by a judicious utilization of an energy dissipation equation due to eddy viscosity for incompressible turbulent flow, the steady-state κ–ω turbulence model, and the Kolmogorov turbulence dissipation length scales. It is shown that the form drag coefficients of three geometrically similar vessels subjected to turbulent flows are scaled according to C¯p={c1+c2Re¯−1/3+c3Re¯−1} where (C¯p,Re¯,ci(i=1,2,3)) are the form drag coefficient ratio, the mean flow Reynolds number ratio, and ci are closure coefficients to be determined from existing geometrically similar vessels, respectively. The present theoretical form factor methodology is applied to predict the full scale form factor from the scaled towing tank experiment based on three simulation results, which show improved correlations compared to the empirical least-squares prediction methods.