Single-spiral-vortex Model for a Cavitating Elastic Curvilinear Foil

A two-dimensional nonlinear inverse fluid-structure interaction problem for a curvilinear elastic hydrofoil is considered. A cavity formed behind the foil is modeled according to the single-spiral-vortex model by Tulin. The fluid-structure problem is decoupled by the method of successive approximations. For the cavitation problem, the foil is modeled as a polygon. The method of conformal mappings and the Riemann-Hilbert problem is employed at this stage. The classical detachment mechanism for a smooth arc is satisfied for the polygon approximately. The deformation of the smooth foil is described by the governing equations of the thin shell theory with the clamped-clamped boundary conditions. The loading acting on the middle surface of the foil is prescribed as the difference between the fluid and vapor pressure computed in the fluid problem. Numerical results include those for the cavity profile, the drag coefficient, the pressure distribution, the speed, and the displacements of the elastic foil.