In this paper, the propagation of cylindrical shock wave in rotating non-ideal gas under adiabatic flow condition using Lie group of transformation method is investigated. The density is assumed to be constant and azimuthal fluid velocity is assumed to be varying in the undisturbed medium. The arbitrary constants appearing in the expressions for the infinitesimals of the Local Lie group of transformations bring about two different cases of solutions i.e. with a power-law and exponential-law shock paths. Numerical solutions are obtained for both the cases. Distribution of gasdynamical quantities is illustrated through figures. It is obtained that the reduced flow variables pressure and azimuthal fluid velocity decrease in general, whereas density and radial fluid velocity increase in case of power-law shock path. The reduced azimuthal fluid velocity decreases, whereas reduced density, pressure and radial fluid velocity increase in case of exponential-law shock path. Also, it is obtained that shock strength decreases with increase in value of adiabatic exponent or gas non-idealness parameter, whereas it increases due to increase in ambient azimuthal fluid velocity exponent.

中文翻译：

---

基于李群理论的旋转非理想气体中圆柱激波的相似性解

本文利用李群变换方法研究了绝热流动条件下圆柱激波在旋转非理想气体中的传播。假设密度是恒定的，并且假设流体方位角速度在未受干扰的介质中是变化的。出现在局部李变换群的无穷小表达式中的任意常数带来了两种不同的解，即幂律和指数律冲击路径。这两种情况都得到了数值解。气体动力学量的分布通过图来说明。结果表明，在幂律冲击路径下，减小的流动变量压力和方位流体速度普遍降低，而密度和径向流体速度增加。在指数规律冲击路径的情况下，降低的方位流体速度降低，而降低的密度、压力和径向流体速度增加。此外，得出的结论是，冲击强度随着绝热指数或气体非理想参数值的增加而降低，而由于环境方位流体速度指数的增加而增加。