A method which models two- or three-dimensional cavitating hydrofoils moving with constant speed under a free surface is described. An integral equation is obtained by applying Green's theorem on all surfaces of the fluid domain. This integral equation is divided into two parts:the cavitating hydrofoil problem, andthe free-surface problem. These two problems are solved separately, with the effects of one on the other being accounted for in an iterative manner. The cavitating hydrofoil surface and the free surface are modeled with constant strength dipole and source panels. The source strengths on the free surface are expressed in terms of the second derivative of the potential with respect to the horizontal axis by applying the linearized free-surface conditions. The induced potential by the cavitating hydrofoil on the free surface and by the free surface on the hydrofoil are determined in an iterative sense. In order to prevent upstream waves the source strengths from some distance in front of the hydrofoil to the end of the truncated upstream boundary are enforced to be equal to zero. No radiation condition is enforced at the downstream boundary or at the transverse boundary. The method is applied to 2-D and 3-D hydrofoil geometries in fully wetted or cavitating flow conditions and the predictions are compared with those of other methods in the literature.

Most marine propellers operate in nonaxisymmetric inflows, and thus their blades are often subject to an unsteady flow field. In recent years, due to increasing demands for faster and larger displacement ships, the presence of blade sheet and tip vortex cavitation has become very common. Developed tip vortex cavitation, which often appears together with blade sheet cavitation, is known to be one of the main sources of propeller-induced pressure fluctuations on the ship hull. The prediction of developed tip vortex cavity as well as blade sheet cavity is thus quite important in the assessment of the propeller performance and the corresponding pressure fluctuations on the ship hull. A boundary element method is employed to model the fully unsteady blade sheet (partial or supercavitating) and developed tip vortex cavitation on propeller blades. The extent and size of the cavity is determined by satisfying both the dynamic and the kinematic boundary conditions on the cavity surface. The numerical behavior of the method is investigated for a two-dimensional tip vortex cavity, a three-dimensional hydrofoil, and a marine propeller subjected to nonaxisymmetric inflow. Comparisons of numerical predictions with experimental measurements are presented.

This paper presents two numerical methods, a vortex lattice method (MPUF-3A) coupled with a finite volume method (GBFLOW-3D) and a boundary element method (PROPCAV), which are applied to predict time-averaged sheet cavitation on rudders, including the effects of the propeller as well as of the tunnel walls. The coupled MPUF-3A and GBFLOW-3D determines the velocity field due to the propeller within the fluid domain bounded by tunnel walls. MPUF-3A solves the potential flow around the propeller by distributing the line vortices and sources on the blade mean camber surface and determines the pressure distributions on the blade surface. GBFLOW-3D solves Euler equations with the body force terms converted from the pressure distributions on the blade surface and determines the total velocity field inside the fluid domain. The tunnel walls are treated as a solid boundary by applying the slip boundary condition, and the propeller blades are modeled via body forces. The two methods are solved iteratively until the forces on the blade converge. The cavity prediction on the rudder is accomplished via PROPCAV, which can handle back and face leading edge or mid-chord cavitation, in the presence of the three-dimensional flow field determined by the coupled MPUF-3A and GBFLOW-3D. The present method is validated by comparing the cavity shapes and the cavity envelope with those observed and measured in experiment and computed by another method.

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A low-order boundary element method is applied to predict the trailing wake geometries shedding from hydrofoil and marine propellers in steady and unsteady flows, as well as the vortex motions of the classical lifting line problem with elliptic loading distribution. In order to prevent the numerical instability near the vortex roll-up region, a tip vortex with finite core size is introduced at the end of the vortex line (or at the tip of the wake sheet in the case of a three-dimensional problem), and the induced velocities are evaluated at the displaced control points instead of the actual control points on the vortex (or wake) panels. Green's integral equation with boundary conditions is formulated based on the perturbation potential and solved for the potentials on the lifting bodies and the tip vortex surface. The three-component velocities on the tip vortex surface are computed by numerically differentiating the solution potentials, and the induced velocities on the wake surface are directly determined from the integral equation derived from analytical differentiation of Green's integral equation. The new geometries of the vortex line or the trailing wake as well as the location of the tip vortex core center are then determined by aligning them to the flow so that the force-free condition is satisfied on the wake. The method is applied for the two-dimensional and three-dimensional problems, and validated with experiments and other numerical methods in terms of tip vortex trajectory and blade forces.