Unsteady, Symmetrical, Supercavitating Flows Past a Thin Wedge in a Jet

Abstract

Problems of symmetrical two-dimensional supercavitating flow about a thin wedge in a finite fluid with two free surfaces are solved by means of a linearized method utilizing the complex acceleration potential. Taking advantage of the symmetry, the otherwise doubly connected region is divided into two identical simply connected regions. Conformal mapping technique is then applied to the upper half of the flow region. An oscillatory-type motion as well as general types of unsteady motions are considered. The solution contains no singularity and, as a result, pressure is everywhere finite. The mathematical condition required for the existence of a singularity-free solution leads to an equation which gives the relationship between the cavity length and the cavitation number. The theoretical results are in good agreement with experimental data for the steady-flow case, but data for the unsteady case are not yet available.