Unsteady RANS method for ship motions with application to roll for a surface combatant

An unsteady Reynolds-averaged Navier–Stokes method is developed to compute motions and the resulting flow and wave fields around surface ships. Although the formulation and RANS code are generalized for six-degree-of-freedom motions, the method is demonstrated here for the viscous phenomenon of roll decay motion for a surface combatant. The method is based on an extension of CFDSHIP-IOWA (a general-purpose code for computational ship hydrodynamics) to predict ship motions with larger amplitude and non-slender geometry, in comparison to traditional linearized methods. The flow solver uses higher-order upwind discretization, PISO method for pressure–velocity coupling, a blended k–x/k–e two-equation turbulence model, free surface tracking approach, and structured multi-block grid systems. As an initial step, unsteady simulations of a modern surface combatant with predicted roll decay and prescribed sinusoidal roll motion are performed. Roll decay motion is simulated by releasing the model from an initial roll angular displacement and by computing the resulting roll motion. Verification of the time history of the roll motion is performed using iteration, grid, and time step studies and numerical uncertainties are shown to be less than 1%. Validation is performed by comparison with available experimental data with the predictions validated at 1.7% and 1.5% for the uncorrected and corrected solutions, respectively. For simulations with prescribed motions, the periodic response of the boundary layer to the rolling motion is described and quantified using a Fourier analysis. A spring–mass-damper system is used to compare the current non-linear predictions to traditional linear strip theory results. The method is shown to accurately predict the natural rolling frequency and roll decay rate at multiple ship speeds both without and with bilge keels, which demonstrates the ability to assess seakeeping characteristics for practical geometries. � 2005 Elsevier Ltd. All rights reserved.