Investigation of two-dimensional transom waves using inviscid and viscous free-surface boundary conditions at model- and full-scale ship Reynolds numbers

Abstract

Two-dimensional transom waves are computed using inviscid and viscous free-surface boundary conditions at model- and full-scale ship Reynolds numbers. The computations are carried out solving the steady Euler or RaNS equations with the Navier-Stokes solver, FINFLO. The viscous free-surface boundary conditions are obtained from a flat-surface approximation. Different numerical schemes used when evaluating the free-surface deformation are presented. Their effect on the evaluated transom waves and the flow field is discussed at model and full scale. Further, computations of turbulent free-surface flows carried out at full-scale ship Reynolds numbers using the moving-grid technique and no wall functions are presented and discussed. An improved extrapolation method combining model testing and CFD is proposed.

The simulations in this work demonstrate the significant effect of the numerical realization of the free-surface boundary conditions and the decreasing Froude number on the computed transom waves, the flow field and the total resistance. At full-scale ship Reynolds numbers, multigridding will speed up the convergence. The free-stream dissipation of the turbulent kinetic energy has to be treated like a material property when using Chien's low-Reynolds number k-ε turbulence model. The scaling of the computed results is in excellent agreement with the modified ITTC-78 method. The convected turbulent kinetic energy is amplified by the transom waves. At the vicinity of the transom, a significant increase of the nondimensional vorticity is obtained at full scale.