227 



THE MOTION AND SHAPE OF THE HOLLOW PRODUCED BY AN 

 EXPLOSION IN A LIQUID 



G. I. Taylor and R. M. Dtviej 



February 1943 



Summary , 



It is shown in a previous paper by one o' us that the gas-filled hollows produced By explosions 

 in water cannot Be reproduced on a small scale unless the pressure eDove the water Is correspondingly 

 reduced. in the experiments here described, which are on a very small scale, bubbles were produced by 

 sparking under a liquid contained In an evacuated vessel. In this way It seems that wt can reproduce, on 

 a '^ery small scale, the changes in form and motion o' the gas bubble produced by a large explosion. it 

 is worth noticing that, in small-scale explosions at atmospheric pressure, the ef'ect of the free surf.^ce 

 is so great that the bubble hardly rises at all, even when it gets to 3 fuet diameter, yet these bubbles 

 of 6 cm. maximum diameter showed the riso under gravity which is expectud in lirgo-scjle explosions. 



One of the objects of these experiments was to see how far the assumption that the explosion g.is 

 OuBBle Is spherical is justified. This assumption has been mada to facilitate calculation of the rate 

 of rise of the bubble, and our experiments show that it is correct o\i6r the greater part of the first 

 pulsation of the bubble. The photograi^hs also vprify tho theorotical conclusion that the surface of th° 

 bubble should be smooth and stable during the first expansion and the early part of the first contraction. 

 But should bccc«iie unstable when the bubble tes contracted tii near its minimum volume. 



Introduction , 



In Report ("Vertical motion of a spherical bubble and the pressure surrounding it'^, hereafter 

 called Report *, the affect of gravity on a bubble Is calculated, assuming that the bubble is maintained 

 spherical by internal constraints which do no work on the surrounding fluid apart from that whicn is done 

 by the gas contained in it during the expansion and contraction of Its volume. This assumption Imposes 

 a severe limitation on the accuracy with which the calculated results may be expected to apply to resl 

 explosion gas bubbles. On the other hand it does enable calculations to be made which may be expected to 

 be reasonably significant in cases where analysis in which the whole motion is taken as a small perturbation 

 of a pulsating bubble referred to u fixed centre cannot be used. 



In the calculation of Report a the effect of the free surface or of a horizontal rigid surface on 

 the motion of the bubble was not considered though, as Conyers Herring' showed, it may in some cases be 

 comparable or even greater than that of gravity. Photographs, taken by Edgertc«i i at the Taylor Model 

 tesin, of the Bubble produced by exploding a detonator cap at a smaVl depth btjlow a frea surface do in 

 fact show that during its first period, at any rate, the effect of the free surface is greater than that 

 of gravity, so that the Bubble sinks instead of rising. This is, qualitatively at any rate, in accordance 

 with the theoretical prediction of Herring. 



In Report a it is shown that large upward displacements of the bubole, due tc gravity, nay be 

 expected when its .laximum diameter is comparable with the head of water necessary to produce the hydrostatic 

 pressure at the level of its centre. This condition occurs when an explrsion produces in water a bubble 



wh.. se . , 



U.S. Report n:. CU-sr 2O-O1O, "The theory rf the pulsati. ns .-f the gas bubble produced 

 by an underwater explcsii-m", octcbtr nm. 



U.S. Rep- rt, "A photographic study of underwater explcsions", October 19U1 



