High-speed submerged and surface piercing cavitating hydrofoils, including tandem case

The iterative method that is originally developed before both for two- and three-dimensional single cavitating hydrofoils moving with a constant speed under free surface is applied to the case of high-speed (Froude number up to 6.5) and some figures are given. The method is also extended to include the surface piercing hydrofoils (vertical struts) and the case of tandem hydrofoils into the calculations. The iterative nonlinear method based on the Green's theorem allows separating the cavitating hydrofoil problem(s) and the free surface problem. These two (or three in the case of tandem hydrofoil) problems are solved separately, with the effects of one on the other being accounted for in an iterative manner. The cavitating hydrofoil surface(s) and the free surface are modeled with constant strength dipole and constant strength source panels. The source strengths on the free surface are expressed in terms of perturbation potential by applying the linearized free surface conditions. No radiation condition is enforced for downstream and transverse boundaries. The cavitation number is expressed in terms of Froude number and the submergence depth of the hydrofoil from the free surface. An algebraic grid on the free surface has been described to get a smooth transition between the panels along the direction of uniform inflow and to have a long distance in the downstream direction depending on the wave-length (or Froude number) while keeping the number of panels fixed. First, the method is validated in the case of surface piercing hydrofoil. Then, the effects of high Froude number and the submergence depth of the hydrofoil from free surface on the results are discussed and some figures are given for interested engineers and designers. The method is later applied to the case of tandem hydrofoils and the effects of one hydrofoil on the other are discussed.