The radiation hydrodynamics of a heaving surface effect ship (SES) is examined including the effect of air compressibility on the hydrodynamic forces and surface waves. Of particular focus of the study has been on determining the nonlinear viscous and air compressibility effects at natural frequencies corresponding to the piston and sloshing wave modes between the hulls and at the natural frequency corresponding to the heave motion of a surface effect ship with the restoring force dominated by the compressibility of the air cushion. In the present paper, the air cushion pressure is assumed to be uniform with its variation due to change of volume modeled using the adiabatic gas law pVγ = constant, where p denotes the absolute pressure of the air, V the air volume bounded by the side hulls, the free surface and the wet deck, and γ the ratio of specific heats Cp/Cv which is about 1.4 for air. The incompressible Navier-Stokes equations governing the nonlinear viscous wave-air-body interaction problem is solved in the time domain using a finite-difference method based on boundary fitted coordinates. New results presented in this paper show that air cushion compressibility affects the generation of waves and wave radiation forces significantly even at small amplitude of hull motion. As already well known, the free surface nonlinearity due to hull motion is significant for large amplitude of oscillation. At small amplitude of body oscillation, significant nonlinearity can be caused by air compressibility resulting in the generation of higher harmonic waves and forces. The results also highlight the significance of viscosity and flow separation, in conjunction with air compressibility, in the case of large amplitude hull motion with a small draft.
Numerical investigations of the free surface effect in three-dimensional polycrystalline aggregates
