Effect of a dense gas equation of state on the expansion and contraction of an underwater gas bubble

Abstract

At the high pressure believed to occur in underwater explosion gases, and in cavitation gas bubble collapse, deviations from an ideal gas must be considered. A theoretical investigation into the effect of a simplified dense gas equation of state on underwater gas bubble dynamics is presented. Our approach is to make a direct comparison between ideal and dense gas results. First, the lossless, incompressible liquid case is analyzed. The requirement of a realistic equation of state yields some startling results, placing severe bounds on some of the key parameters: the peak bubble pressure, the maximum bubble wall velocity, and the minimum bubble radius. Next, nonviscous energy losses are discussed. A generalization of the Herring method is used for approximate evaluation of the radiation‐loss integral derived from the Kirkwood–Bethe equation. These calculations appear to give physically reasonable loss estimates under both the ideal and dense gas assumptions. Also, an often‐quoted formula for the acoustic radiation loss has been found to be in error and has been corrected. For ease in calculation of some of the important quantities of interest, useful graphs and formulas have been presented.Subject Classification: 30.60, 30.75; 25.60.