The Effect of a Linear Free Surface Boundary Condition on the Steady-State Wave-Making of Shallowly Submerged Underwater Vehicles

Near-surface simulation methods for shallowly submerged underwater vehicles are necessary for the population of a variety of free-surface-affected, coefficient-based maneuvering and seakeeping models. Simulations vary in complexity and computational costs, often sacrificing accuracy for simplicity and speed. One particular simplifying assumption, the linearization of the free surface boundary conditions, is explored in this study by comparing the steady-state wave-making characteristics of a shallowly submerged prolate spheroid using two different simulation methods at several submergence depths and forward speeds. Hydrodynamic responses are compared between a time-domain boundary element method that makes use of a linearized free surface boundary condition and an inviscid, volume of fluid Reynolds-Averaged Navier–Stokes computational fluid dynamics code that imposes no explicit free surface boundary condition. Differences of up to 22.6%, 32.5%, and 33.3% are found in the prediction of steady state surge force, heave force, and pitch moment, respectively. The largest differences between the two simulation methods arise for motions occurring at small submergences and large wave-making velocities where linear free-surface assumptions become less valid. Nonlinearities that occur in such cases are revealed through physical artifacts such as wave steepening, wave breaking, and high-energy waves. A further examination of near-surface viscous forces reveals that the viscous drag on the vessel is depth dependent due to the changing velocity profile around the body.