Second-type self-similar solutions to the strong explosion problem
Second-type self-similar solutions to the strong explosion problem
复制标题
强爆炸问题的第二类自相似解
DOI：
10.1063/1.858668
复制
发表时间：
1993
影响因子：
4.6
通讯作者：
D. Shvarts
中科院分区：
文献类型：
--
作者：
E. Waxman;D. Shvarts
在理想气体球中心的强爆炸产生的流动，其密度随着离原点的距离r下降为r−ω，假设渐近地接近Sedov和Taylor的自相似解。结果表明，仅对ω≤5存在的Sedov-Taylor（ST）解可能是第一类自相似解最常见的例子，但它不能描述对3≤ω≤5所得到的渐近流。给出并分析了新的第二类自相似解，它们描述了3≤ω≤5以及ω≥5的渐近流。由这些解描述的激波是加速的，而由ω≤3的ST解描述的激波是减速的。新的解与Guderley映射中的一个新奇点有关。它们只存在于ω值小于某个取决于气体绝热指数的ωc时。对于ω≥ωc所得到的渐近流将在随后的文章中讨论。
The flow resulting from a strong explosion at the center of an ideal gas sphere, whose density drops with the distance r from the origin as r−ω, is assumed to approach asymptotically the self‐similar solutions by Sedov and Taylor. It is shown that the Sedov–Taylor (ST) solutions that exist only for ω≤5 and are probably the most familiar example for self‐similar solutions of the first type fail to describe the asymptotic flow obtained for 3≤ω≤5. New second‐type self‐similar solutions that describe the asymptotic flow for 3≤ω≤5, as well as for ω≥5, are presented and analyzed. The shock waves described by these solutions are accelerating while the shock waves described by the ST solutions for ω≤3 are decelerating. The new solutions are related to a new singular point in Guderley’s map. They exist only for ω values smaller than some ωc that depends upon the adiabatic index of the gas. The asymptotic flow obtained for ω≥ωc is discussed in a subsequent paper.