On the Blast Wave Propagation and Structure in a Rotational Axisymmetric Perfect Gas

Abstract

In this paper, the approximate analytical solution for the propagation of a blast (shock) wave in a rotating perfect gas in the case of cylindrical geometry is studied. The axial and azimuthal components of fluid velocity are taken into consideration, and these flow variables in the undisturbed medium are assumed to be varying according to the power laws with distance from the symmetry axis. The shock wave is considered to be strong one for the ratio $${\left(C/{W}_{S}\right)}^{2}$$ to be a small quantity, where $$C$$ is the sound velocity in undisturbed fluid and $${W}_{S}$$ is the shock wave velocity. The initial density in the undisturbed medium is taken to be constant to obtain the similarity solution. To obtain the approximate analytical solution, the flow variables are expanded in power series in power of $${\left(C/{W}_{S}\right)}^{2}.$$ The first- and second-order approximations to solutions are discussed with the help of power series expansion. The analytical solutions are constructed for the first-order approximation. The distribution of the flow variables for the first-order approximation in the flow-field region behind the blast wave is shown in graphs. A comparison is also made between the solutions obtained for non-rotating and rotating medium. It is shown that the constant quantity $${J}_{0}$$ in the flow field region behind the shock front increases in rotating medium in comparison with its value in non-rotating medium; but an increase in adiabatic exponent causes a decrease in it. Further, it is concluded that shock strength increases with adiabatic exponent and decreases due to the consideration of the rotating medium.