XIII 

 HYDRODYNAMICS OF UNDERWATER EXPLOSIONS 



Hans G. Snay 

 U. S. Naval Ordnance Laboratory 



Abstract 



A survey is given of the various hydrodynamic aspects of underwater explosions. 

 The topics selected deal with Shockwave phenomena, the behavior of the bubble, 

 surface phenomena and hydrodynamic problems of damage to structures. 



In particular, the following items will be discussed: 



a. The Shockwave formation by a detonating charge. The long distance propa- 

 gation of Shockwaves. The anomalous surface reflection. 



b. The change of shape of migrating bubbles. The energy dissipation at the 

 bubble minimum. The energy partition of non-migrating and of migrating bubbles. 

 The theoretical treatment of pulsating bubbles. Migration caused by rigid or free 

 boundaries. 



c. The spray dome. The gas break-through of shallow explosions. The surface 

 phenomena of venting and non-venting underwater explosions. The plume formation. 

 The rise of the bubble from deep explosions. 



d. The reloading of an air-backed plate subjected to an underwater explosion. 

 The response of cylindrical shells to a Shockwave. The whipping of ships. 



Introduction 



When an explosive charge is fired under water, a sequence of complex events 

 is started. Out of the great number of phenomena which occur, those have been 

 selected which seem to be of greatest interest from the hydrodynamic point of view. 

 Many of the problems which will be discussed are not completely solved today and 

 more work is necessary until a satisfactory understanding is obtained. 



Summary of the Basic Underwater Explosion Phenomena 



The detonation of the charge converts the solid explosive material into gaseous 

 reaction products which have an exceedingly high pressure. This pressure is trans- 

 mitted to the surrounding water and propagates as a Shockwave in all directions. 



Fig. 1 illustrates the pressure-time history which is observed in the water at a 

 fixed distance from the point of explosion. Upon arrival of the shockwave the pres- 

 sure rises practically instantaneously to the peak value. Subsequently the pressure 

 decreases steadily but at a very fast rate. It takes only a few milliseconds until the 

 pressure has decreased to 1/e or 36.8% of its maximum value. The shockwave peak 

 pressure and the decay constant depend on the charge weight and in the distance of 

 the point of observation. Empirical equations for these as well as other shockwave 

 parameters can be found in the literature [1]. 



Fig. 1 shows that subsequent to the shockwave other pressure pulses occur. 

 These pulses arise from a much slower phenomenon, namely the pulsating of the gas 

 bubble which contains the gaseous products of the explosion. The high pressure of the 

 gas causes an initially rapid expansion of the bubble and the inertia of the outward 



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