Modeling of Unsteady Blade Sheet and Developed Tip Vortex Cavitation

Abstract

A boundary element method is used for the numerical modeling of unsteady blade sheet and developed tip vortex cavitation on propellers. The objective of this work is to predict more accurately blade sheet and developed tip vortex cavity in the vicinity of the blade tip subject to a non-axisymmetric flow-field. The ultimate goal of this work is to predict more accurately the hull pressures induced by the unsteady cavities on the blade and tip. Initially, we assume that the section of the tip vortex cavity shape is circular and the wake a pure helical surface without contraction and roll-up. Once the fully wetted problem is solved by applying the potential based panel method on the assumed tip vortex cavity and wake geometry, the three-component velocities on the tip vortex cavity are calculated by numerically differentiating the velocity potential, and those on the wake surface are determined from the differentiated Green's formula. The new wake surface and the trajectory of the tip vortex cavity core are determined by aligning the wake surface with the flow velocity, in fully unsteady manner. Once the aligned wake surface is determined in an iterative way, the shape of the blade sheet and tip vortex cavity, having a constant pressure distribution, is determined by applying the dynamic and the kinematic boundary conditions on the cavity surface. The method is applied in the case of simplified 2-D vortex cavity, 3-D elliptic wing, and propeller blades subject to inclined and non-axisymmetric inflows. Comparisons with experiments in terms of unsteady cavity shapes, tip vortex cavity trajectories, and unsteady blade forces, are finally presented.