Effects of Non-Sphericity and Radiative Energy Loss on the Migration of the Gas Bubble from Underwater Explosions

摘要

An important phenomena associated with the upward motion of a gas bubble from an underwater explosion is the significant departure from sphericity near the times of the minimum bubble radius. Neglecting this change in shape results in the prediction of a much faster upward velocity than actually occurs. Inclusion of this effect in the equations of motion has been exceedingly difficult because of the large magnitude of the departure from sphericity. This report describes the shape of the bubble by an ellipsoid whose axes are allowed to vary independently, thus modelling, to first order, the changes of bubble shape. The Lagrangian equations of motion, incorporating the effects of the change of shape and of energy loss by the radiation of sound, are derived and solved for the case of a spheroidal bubble. Results of these calculations for various initial conditions are compared with analgous cases for a spherical bubble. It is found that the spheroidal bubble model predicts a reduction in the upward translational motion of the bubble by a factor of approximately 2. Comparison of the predicted upward motion of a spheroidal bubble produced by 227.27 kg. of TNT detonated 46 metres below the surface shows good agreement with that which has actually observed. Keywords: Explosion bubbles. (Canada)