A Study of the Hydroelastic Instabilities of Supercavitating Hydrofoils

Abstract

Presented herein are the results of a theoretical study of the static and dynamic hydroelastic instabilities of rigid supercavitating hydrofoils on elastic supports. A two-dimensional theory is used to define the unsteady hydrodynamic force and moment acting on the oscillating foil, which is assumed to be elastically restrained in translation normal to the free-stream direction and in rotation about a prescribed axis which is normal to the plane of flow. All other motions are neglected. The effects of variation in the elastic and inertial properties, as well as the effect of varying the position of the upper surface flow-separation point on the possibility of either form of instability, are determined. Also, the effect of cavitation number over a small range near zero is hypothesized. The theory predicts that dynamic instability (bending-torsion flutter) is possible at the density ratios typical of supercavitating operation. This is in contrast to the results for fully-wetted flow, where the occurrence of flutter is unlikely at the structural-to-fluid density ratios typical of hydrodynamic operation. The flutter possible in supercavitated operation is also more severe than that indicated for fully-wetted flow. Furthermore, it is shown that for the supercavitating hydrofoil, static instability (torsional divergence) and dynamic instability are of equal importance which again differs from the results in fully-wetted flow where static instability was shown to be the more important practical problem. Recommendations are made for experimental studies to verify these theoretical results.