Analytical Solutions for Predicting Underwater Explosion Gas Bubble Behaviour


  1. Riley, M.
Corporate Authors
Defence R&D Canada - Atlantic, Dartmouth NS (CAN)
This study describes different analytical models that have previously been developed for predicting the radial growth and collapse of underwater explosion (UNDEX) gas bubbles in a free-field environment. The report describes the implementation of nine analytical gas bubble models, in the form of nonlinear differential equations, and a fourth-order Runge-Kutta solution method. Gas bubble radius time histories calculated with these models are compared to empirical models derived from published experimental data. The analytical models allow for different assumptions such as fluid compressibility, bubble migration coupled to dilatation, and an empirical correction for energy loss. It was found that none of the analytical models fully account for the reduction in the gas bubble radius throughout the growth and collapse cycles. Including compressibility in the fluid and the gas bubble provides the best predictions when compared to experimental fits. The incompressible fluid model requires an empirical energy loss function, as there is no energy loss inherent within the model. Models considering just the compressibility of the surrounding fluid do not account for the full energy loss seen in the experimental fits, and produced similar results. Inclusion of migration effects had no influence on the bubble radius or period because of the large detonation depth.

Il y a un résumé en français ici.

Report Number
DRDC-ATLANTIC-TM-2010-237 — Technical Memorandum
Date of publication
01 Nov 2010
Number of Pages
Electronic Document(PDF)

Permanent link

Document 1 of 1

Date modified: