A comprehensive method which determines the most efficient propeller blade shapes for a given axisymmetric hull to travel at a desired speed, is presented. A nonlinear optimization method is used to design the blade, the shape of which is defined by a 3-D B-spline polygon, with the coordinates of the B-spline control points being the parameters to be optimized for maximum propeller efficiency, for given effective wake and propeller thrust. The performance of the propeller within the optimization scheme is assessed by a vortex-lattice method (VLM). To account fully for the hull/propeller interaction, the effective wake to the propeller and the hull resistance are determined by analyzing the designed propeller geometry by the VLM, coupled with a Reynolds-Averaged Navier-Stokes (RANS) solver. The optimization method re-designs the optimum blade with the updated effective wake and propeller thrust (taken to be equal to the updated hull resistance), and the procedure continues until convergence of the propeller performance. The current approach does not require knowledge of the wake fraction or the thrust deduction factor, both of which must be estimated a priori in traditional propeller design. The method is applied for a given hull to travel at a desired speed, and the optimum blades are designed for various combinations of propeller diameter and RPM, in the case of open and ducted propellers with provided duct shapes. The effects of the propeller diameter and RPM on the designed propeller thrust, torque, propeller efficiency, and required power are presented and compared with each other in the case of open and ducted propellers. The present approach is shown to provide guidance on the design of propulsors for underwater vehicles, and is applicable to the design of propulsors for surface ships.

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