A method for optimum cavitating ship propellers

A practical design method was applied to obtain optimum cavitating ship propellers by combining a vortex lattice lifting line method (propeller design program) and a lifting surface method (propeller analysis program). The optimum circulation distribution that gives the maximum lift-to-torque ratio was computed for given thrust and given chord lengths along the radius of the propeller by a vortex lattice solution to the lifting line problem. The section details of the blades, such as pitch-to-diameter ratio and camber ratio, were then found to obtain the desired (optimal) circulation distribution automatically by a lifting surface method. In order to get the optimum circulation distribution, the radius of the blades was divided into a number of panels extending from hub to tip. The radial distribution of bound circulation could be computed by a set of vortex elements that have constant strengths. A discrete trailing free vortex line was shed at each of the panel boundaries with strength equal to the difference in strengths of the adjacent bound vortices. The vortex system was built from a set of horseshoe vortex elements, each consisting of a bound vortex segment of constant strengths and 2 free vortex lines of constant strengths. An algebraic equation system could be formed by using these vortex systems. Once this equation system for unknown vortex strengths was solved with a specified thrust, the optimum circulation distribution and the forces could be computed by the Betz-Lerbs method. When the radial distribution of optimum circulation and chord length were reached, the lifting surface method could be applied to determine the blade pitch and camber in order to produce the desired circulation automatically. The lifting surface method also accounts for cavitation, which is an avoidable physical phenomenon on the blades. The cavity effects in the present method were represented by using cavity sources and cavitating velocities, which were evaluated on the blade surface beneath the cavity. The practical design technique was applied both to noncavitating and cavitating DTMB 4119 and DTMB 4381 propellers, for which the hydrodynamic characteristics are given in the literature, and the results were compared with those given in the literature. A very good level of satisfaction was obtained for practical applications.