The converging shock wave from a spherical or cylindrical piston
The converging shock wave from a spherical or cylindrical piston
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DOI：
10.1017/s0022112082002845
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发表时间：
1982-07
影响因子：
3.7
通讯作者：
M. V. Dyke;A. Guttmann
中科院分区：
文献类型：
--
作者：
M. V. Dyke;A. Guttmann
含有静止气体的球形或圆柱形空腔开始以高恒定径向速度收缩，驱动轴对称激波向内在中心坍缩。我们对流场进行了时间幂次展开的分析，并将算法委托给计算机计算了40项。对激波半径级数的分析证实了Guderley聚焦的局部自相似解，包括他的相似指数最近的精炼值，并在他的局部展开中得到更高的项。在证明Guderley解不唯一的绝热指数范围内，根据Gel’fand的一个猜想，我们发现了最小的可容许的相似指数。
A spherical or cylindrical cavity containing quiescent gas begins to contract at high constant radial speed, driving an axisymmetric shock wave inward to collapse at the centre. We analyse the flow field by expanding the solution in powers of time, and calculate 40 terms by delegating the arithmetic to a computer. Analysis of the series for the radius of the shock wave confirms Guderley's local self-similar solution for the focusing, including recent refined values for his similarity exponent, and yields higher terms in his local expansion. In the range of adiabatic exponent where the Guderley solution has been shown not to be unique we find, in accord with a conjecture of Gel'fand, that the smallest admissible similarity exponent is realized.