An asymptotic model for propeller vortex sheets in rotational flow.

Abstract

Traditionally, propeller design and analysis problems have relied on potential flow techniques and prescribed (or partially prescribed) shed-vortex sheet geometries. These models have generally proven satisfactory for lightly to moderately loaded single-unit propulsors, but are often inadequate for heavily loaded or multi-component propulsors. Since modern design practices dem and high power and high efficiency, more sophisticated vortex-sheet models are necessary. In addition to the shortcomings of existing potential flow vortex-sheet models, the potential flow assumption itself is a source of inaccuracy. Any effort towards improving current vortex-sheet models should therefore incorporate the effects of rotational flow. This dissertation introduces a new feature into the design of propulsors operating in axisymmetric sheared onset flows. Rotational flow effects are incorporated by satisfying the force-free requirement on the sheet using the variable head form of the Bernoulli Equation. The geometry of the sheet is found from a combined free-surface boundary condition that is linearized by exp and ing in an asymptotic series. When the zeroeth and first order terms are retained, a system of two coupled ordinary differential equations results that can be integrated to find the consistent first-order perturbation of the sheet from a known reference surface. The resulting wake geometry is used to calculate perturbation velocities on the propeller for the final blade design. Results show that rotational flow and variable sheet geometry can affect blade-section camber and pitch over the inner radii of moderately loaded propellers. Although no compound propulsor designs were attempted, the effect on the trailing component of a t and em propeller is qualified by showing the sensitivity of the down-stream flow velocities to sheet geometry.