On the collapse of an empty cavity in water
On the collapse of an empty cavity in water
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水中空腔的塌陷
DOI：
10.1017/s0022112060000578
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发表时间：
1960
影响因子：
3.7
通讯作者：
C. Hunter
中科院分区：
文献类型：
--
作者：
C. Hunter
本文研究了水中空腔的球对称坍缩问题。忽略了粘性和表面张力的影响，但考虑了水的可压缩性，并假定了水的适当状态方程。这样做的目的是通过孤立地考虑可压缩性对流动的影响来澄清它，从而描述由崩溃及其随后的传播形成的压力脉冲。精确的流动方程的数值积分，它被发现，非常高的流速发展在附近的崩溃点。对于小的t，空洞的半径与（-t）n成正比，其中t = 0是坍缩的瞬间，n是小于1的某个正数。在崩溃点附近的流动可以通过相似解来描述，并且n的值由相似解的规律性性质来确定（n的值取决于假定的水的状态方程）。相似理论只适用于非常高的压力和速度，但可以在坍缩瞬间之后继续下去，以描述坍缩完成后激波的形成和激波的初始传播。
This paper is concerned with the spherically symmetric collapse of an empty cavity in water. The effects of viscosity and surface tension are neglected, but the compressibility of the water is allowed for and a suitable equation of state for the water assumed. The object of this is to clarify the effect of compressibility on the flow by considering it in isolation and thus to describe the formation of a pressure pulse by the collapse and its subsequent propagation. The exact flow equations are integrated numerically and it is found that very high flow speeds develop in the neighbourhood of the collapse point. The radius of the cavity is found to be proportional to (-t)n for small t, where t = 0 is the instant of collapse, and n is some positive number less than unity. The flow in the neighbourhood of the collapse point can be described by means of a similarity solution, and the value of n is determined by regularity properties of the similarity solution (the value of n depends on the equation of state assumed for the water). The similarity theory, which is valid only at very high pressures and velocities, can be continued beyond the instant of collapse to describe the formation of a shock wave after the collapse is completed, and the initial propagation of this shock.