Approximate analytical solution using power series method for the propagation of blast waves in a rotational axisymmetric non-ideal gas

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 axis of symmetry. 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 shock velocity and speed of 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, a comparison between the numerical solution and the approximate analytical solution are shown. The distributions of flow variables such as density, radial velocity, pressure and azimuthal velocity are analysed. The results for the rotationally axisymmetric non-ideal gas environment are compared to those for the ideal gas atmosphere. The velocity-distance and time-distance curves are also shown to analyse the decaying characteristic of a blast wave.