Title: Approximate Analytical Solution using Power Series Method for the Propagation of Blast Waves in a Rotational Axisymmetric non-ideal Gas Show Chinese title

Title: 利用幂级数法求爆炸波在旋转轴对称非理想气体中传播的近似解析解

Abstract: In this paper, the propagation of the blast (shock) waves in non-ideal gas atmosphere in rotational medium is studied using a power series method in cylindrical geometry. The flow variables are assumed to be varying according to the power law in the undisturbed medium with distance from the symmetry axis. To obtain the similarity solution, the initial density is considered as constant in the undisturbed medium. Approximate analytical solutions are obtained using Sakurai's method by extending the power series of the flow variables in power of ${\left( {\frac{{{a_0}}}{U}} \right)^2}$, where $U$ and $a_0$ are the speeds of the shock and sound, respectively, in undisturbed fluid. The strong shock wave is considered for the ratio ${\left( {\frac{{{a_0}}}{U}} \right)^2}$ which is considered to be a small quantity. With the aid of that method, the closed-form solutions for the zeroth-order approximation is given as well as first-order approximate solutions are discussed. Also, with the help of graphs behind the blast wave for the zeroth-order approximation, the distributions of variables such as density, radial velocity, pressure and azimuthal fluid velocity are analyzed. The results for the rotationally axisymmetric non-ideal gas environment are compared to those for the ideal gas atmosphere. Show Chinese abstract

Abstract: 本文研究了非理想气体在旋转介质中圆柱几何结构下爆炸（冲击）波的传播，采用幂级数法进行分析。 假设流场变量在未扰动介质中沿对称轴方向的距离按照幂律变化。 为了获得相似解，在未扰动介质中初始密度被设定为常数。 利用 Sakurai 方法，通过扩展流场变量关于 ${\left( {\frac{{{a_0}}}{U}} \right)^2}$ 的幂级数（其中 $U$ 和 $a_0$ 分别为未扰动流体中的冲击波速度和声速），得到了近似解析解。 强冲击波的情况对应于小量 ${\left( {\frac{{{a_0}}}{U}} \right)^2}$ 的比值。 借助该方法，给出了零阶近似的封闭形式解，并讨论了一阶近似解。 此外，借助零阶近似后爆炸波后的图形，分析了诸如密度、径向速度、压力和环向流速等变量的分布。 将旋转轴对称非理想气体环境下的结果与理想气体大气环境下的结果进行了比较。