497 



THE OSCILLATION OF THE GAS-BUBBLE FORMED BY A 

 DETONATOR EXPLODING UNDERWATER. DETAILED 

 COMPARISON OF THEORY WITH EXPERIMENT 



H. N. V. Temperley 



March 1944 



Summa ry. 



The discussion of the Oehaviour of gas-buDDles from large charges has been extended to detonators, 

 for which we possess the nrnch more detailed evidence given by actual photographs of the bubbles. 

 Calculations have tnerefore been made for the reprseentat ive case of a gram charge of T.N.T. 3 feet 

 below th« Surface cf the water, and the results have been compared both with experiment and also with 

 the approximate formulae developed by Herring and Bryant. The agreement of the exact calculations with 

 the approximate formulie is found to be such that, with one exception, the latter can be applied to 

 detonators even though auite a high value of Taylor's non-dimensional parameter z is involved. The 

 following quantities are compared with experiment :- 



in 



(a) The r^dius-i iine curve for the bubble : Agreement is already known to be satisfactory, except 'j 

 near the minima where energy is being lost in various ways. ir> 



II 



(b) The trajectory cf the centre of the bubbl e: 3c th under gravity and in the presence of a „ 

 single free ^r rijio surface. AQreement is it any r.^le qualitative up to the first minimum. n 



;i 



(c) The shape of the bubble : Agreement is satisfactory. j| 



* 



(d) The behavicu s of the bubble from a charge fired in contjct with a steel pl^t e: F 

 Agreement is only rough, tw_ serious discrepancies (which may be different aspects of the 



fact that a steel plate can hardly be regarded as rigid for 3 contact charge) have been fcund. 



(e) Th e behav i ous uf the bubble from a charge fired between tw^. steel plates : Agreement 

 is as good as «ne could reasonably expect. 



Taken as a whole, the position seems to be very similar to that found for large charges. 

 Phenomena which depend on the behavious of the bubble near its minimum radius, (such as the minimum 

 radius itself, or the secondary pressure-pulses) cannot be predicted, while phenomena such as the period 

 of the bubble, and the rise or fall of its centre up to first minimum can be predicted fairly accurately. 



Intrcducticn . 



up to the present time, practically all underwater photography of the gas-bubble has been of 

 Charges not larger than a detonator. Hmi it is known that, unless the pressure of the atmosphere above 

 the surface of the water can be reduced, such experiments give an indication of the behaviour to be 

 expected if full-scale charges are fired at depths of the order of 500 feet, whereas we are most interested 

 from a practical point of view in charges fired at depths of up to 200 feet. By working under a partial 

 vacuum, Taylor and Oavies h3ve obtained scale models of the bubbles from charges fired at depths of this 

 order, but the remaining work with detonators seems to lack direct application to the problem of damage 

 to ships by explosions underneath them, and to be more uf the nature of fundamental research. up to 

 the present time alsc, theory has concerned itself m.;stly with the behaviour of the bubble at these 

 relatively shallow depths, which can only be inferred experimentally frcm i very Ung scaling-up ^f 

 Taylor and Oavies' results, -r indirectly fr m pressure-gauge meosurements on the full scale. The rather 

 an^maljus position has tnus arisen that the m re recent dovtlopmonts in the the:."y have n,^t been applied 



t. that 



