Unsteady RANS simulation of the ship forward speed diffraction problem

The forward speed diffraction problem for a surface ship is analyzed numerically, using a RANS approach with a single-phase level set method to compute the free surface and a blended k–ε/k–ω model for the turbulent viscosity. Simulations were run for a DTMB 5512 model under head incident waves at two speeds and two wavelengths with the same wave amplitude (a = 0.006L, with L the ship length). The medium speed case (Fr = 0.28) with long wavelength incident waves (λ = 1.5L) behaves linearly and has been extensively compared against available experimental data for resistance and heave forces and pitching moment, unsteady free surface elevations, and unsteady velocity fields at the nominal wake plane (x/L = 0.935). Quantitative verification and validation was performed for this case by running three grids and three time steps with refinement ratio of 2 and the flow field analyzed in detail. The behavior of the boundary layer is analyzed to explain the origin of large first harmonic amplitudes on the axial velocity observed both experimentally and numerically. The high speed case (Fr = 0.41) with short wavelength incident waves (λ = 0.5L) exhibits non-linear behavior on the forces and moment with a strong second harmonic component and an unsteady breaking bow wave. The second harmonic has been reproduced by the CFD computations and the breaking wave predicted. Analysis of the flow indicates that the breaking wave could be responsible for the non-linear behavior on the forces and moment.