On imploding cylindrical and spherical shock waves in a perfect gas
On imploding cylindrical and spherical shock waves in a perfect gas
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关于完美气体中内爆的圆柱形和球形冲击波
DOI：
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发表时间：
2006
影响因子：
3.7
通讯作者：
C. Mouton
中科院分区：
文献类型：
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作者：
N. Ponchaut;H. Hornung;D. Pullin;C. Mouton
本文在不使用强激波近似的情况下，研究了初始静止流中圆柱形或球形内爆和反射激波的问题。维数参数首先用来表明，这种流动承认一个一般的解决方案，从无穷大的无穷小弱冲击加强，因为它收敛到原点。对于理想气体状态方程，这个解只取决于流动的维数和比热比。Guderley幂律结果可以解释为在内爆中心原点附近有效的首阶强激波近似。我们改进了Guderley的解决方案，增加了两个进一步的条款，在一系列的扩展解决方案的传入和反射的冲击波。一个级数展开，有效的冲击仍然很弱，非常远离原点，也构造。通过适当地改变变量和使用精确的激波跳跃条件，得到了一个数值的、基于特征的解，描述了从几乎无穷大到非常接近反射点的一般激波运动。比较之间的系列扩展，特性的解决方案，并使用欧拉求解器得到的结果。这些表明，向Guderley解添加两项显着扩展了强冲击级数展开式的有效性范围。
The problem of a cylindrically or spherically imploding and reflecting shock wave in a flow initially at rest is studied without the use of the strong-shock approximation. Dimensional arguments are first used to show that this flow admits a general solution where an infinitesimally weak shock from infinity strengthens as it converges towards the origin. For a perfect-gas equation of state, this solution depends only on the dimensionality of the flow and on the ratio of specific heats. The Guderley power-law result can then be interpreted as the leading-order, strong-shock approximation, valid near the origin at the implosion centre. We improve the Guderley solution by adding two further terms in the series expansion solution for both the incoming and the reflected shock waves. A series expansion, valid where the shock is still weak and very far from the origin, is also constructed. With an appropriate change of variables and using the exact shock-jump conditions, a numerical, characteristics-based solution is obtained describing the general shock motion from almost infinity to very close to the reflection point. Comparisons are made between the series expansions, the characteristics solution, and the results obtained using an Euler solver. These show that the addition of two terms to the Guderley solution significantly extends the range of validity of the strong-shock series expansion.