Cavitating and Non-cavitating Lumped Vortex Element under a Free Surface

Abstract

In this study, the lift and moment coefficients of two-dimensional cavitating and non-cavitating flat-plate moving with a constant speed under a free surface have been calculated by a closed - form solution. The cavitation (if exists) volume has also been computed in case of cavitating flat-plate. The flat-plate has been modeled by a lumped vortex element under the constraints of potential flow theory. Linearized free surface condition has been applied and then the total velocity potential has been computed by the method of images. Cavitation effect has been included into the calculations by considering an additional angle of attack in the case of fully wetted solution. The wave elevations on the free surface have also been calculated in a closed form solution. The lift coefficients by the present solution have been validated with those of Plotkin’s method. The effects of Froude number, submergence depth of flat-plate from calm free surface, angle of attack and cavitation number on the results (namely lift and moment coefficients, cavitation volume and free surface deformations) have been discussed in a detailed manner