455 



THE EFFECT OF AN ADJACENT DEFORMING TARGET 

 U PON THE BUBBLE DUE TO ^ SUBMARINE EXPLOSION 



L I. G. Chambers 



November 1946 



Summary . 



Reference is made to previous work on the siCject. An alternative theory is put forward 

 to account for discrepancies which have arisen in Box Model work and calculations are described 

 Based on certain Box Model shots and discussed. It is concluded that the effect of the rigidity 

 of the target on the t>ubDle is small and may, in general, be neglected. 



Notatton and Symbols us ed. 



The suffix indicates values at t = 0. The quantities are non-dimensional. Being defined 

 in terms of the units introduced by G. I. Taylor in the report "Vertical trotion of a spherical 

 bubble and the pressure surrounding it" 



a = radius of bubble, assumed to remain spherical. 



b = equivalent radius of plate. 



c = an explosive parameter. 



d = depth of centre of bubble below target. 



h = central deflection of target. 



K = a constant of integration, chosen to satisfy the initial conditions. 



t = time. 



u = velocity of bubble =-g| 



V = upward velocity of centre of plate. 



z = depth of bubble below virtual surface. 



Introductiott . 



It is well known that the mechanism of danage due to an underwater explosion is extremely 

 complex, even in the comparatively simple case of a single plate rigidly clamped at its edges, and 

 that the phenomena involved are many - for example, the elastic properties of the steel, the 

 occurrence of cavitation eithsr at or away from the steel-water interface, and lastly the effect 

 of the motion of the gas bubble. It is with this last phenomenon that this report is mainly 

 concerned. 



It has been shown by Conyers Herring and Dy others, that the bubble is liable to migrate, 

 the nature of this migratio depending on the nature of adjacent surfaces. On the whole, the 

 bubble is attracted Dy a rigid surface and repelled by a free surface, although there is initially 

 i repulsion away from a rigid surface. Thus, for a given charge and distance, there may be a 

 particular strength of plate such that the bubble migration is negligible during the very 

 important first oscillation of the DuDDle. 



If the plate was weaker than this, the net effect would be a repulsion, so that the first 

 minimum of the buoble would occur farther from the plate than the original explosion. If the 

 plate is stronger, the net effect would be an attraction, which increases rapidly as the distance 

 from the plate decreases, so that the first minimum of the bubble would occur very near to, or 

 even in contact with, the plate, and might thus give a large contribution to damage, while the 

 contribution in the repulsive case would be negligible. 



It was found that in certain Box Model snots inconsistencies arose and this was thought 

 to be due to some intrinsic instability in the dependence of the bubble movement on the movement 

 of the plate. Thus in considering the attraction of the bubble towards the target, it is 

 desirable to know whether the motion of the- target plate in the baffle effects the bubble or 

 whether we can assume with sufficient accuracy the target plate to be rigid. 



