Super-cavitating or surface-piercing propellers have been considered as an alternative design mode of high speed propulsion in the last three decades. Most of the theoretical studies were carried out during this period. The demand for high speeds at higher efficiencies of propulsion necessitates the improvement of robust, reliable and analytically consistent numerical analysis tools.
In this paper, most of the effort is given to present the development of a new BEM formulation to predict the analysis of hydro-elastic behavior of such super-cavitating hydrofoils. The super-cavitating blade sections are sharp at the leading edge with the maximum thickness attained at the trailing edge. The main scope of designing such a blade section lies on the reduction of the frictional losses which leads to a decrease in total drag force. However, this reduction in drag is offset by an increase in the cavity drag which is roughly proportional to the square of the cavity thickness. Cavitation (boiling of the fluid) happens when the pressure in the fluid domain is equal to or less than the vapor pressure. The suction side of the blade cavitates with cavities that often exceed the chord several times. Thus, the best designs require thin sections, in the order of 5 percent or less, at low angles of attack in order to allow for minimum cavity thickness formation.
The deformations of the blade or hydrofoil section can often be very crucial in the overall assessment and design. We have been studying previously the hydrodynamics of these super-cavitating sections by low-order boundary element methods. These methods predict cavity shapes as well as the pressure distributions on the wetted ( non-cavitating) side of the blade. We recently started an effort to study the hydro-elastic coupling of these sections by coupling the hydrodynamics with the structural analysis of the section by also using a boundary element method.
In this paper the structural analysis of a super-cavitating hydrofoil section under a hydrodynamic loading (often square root or fourth root singular with distance at the leading edge) is studied. An iterative low-order boundary element method is utilized, in which the right-hand side is updated via the so called higher-order ``saw-tooth'' effects. In the past, this iterative process was applied for the treatment of the flow at the sharp trailing edge of a non-cavitating hydrofoil, and was found to converge fast to the desired solution. The extension of this process in the case of a structural BEM is presented in this paper. The method is validated against 2-D beam and hydrofoil geometries. The advantages and disadvantages of the method are summarized.