Self-similar solution for the flow behind an exponential shock wave in a rotational axisymmetric non-ideal gas with magnetic field

Abstract

The propagation of a cylindrical shock wave driven out by a piston moving with time according to an exponential law, in a rotational axisymmetric non-ideal gas with azimuthal magnetic field is investigated. It is assumed that the ambient medium possess radial, azimuthal and axial components of fluid velocity. The magnetic field and the component of fluid velocity are assumed to be varying according to an exponential law. The solutions are obtained for both the cases of adiabatic and isothermal flows between the piston and the shock by considering the components of vorticity vector. The effects of variation of ambient magnetic field, non-idealness of the gas and adiabatic exponent are worked out in detail. It is shown that the increase in the non-idealness of the gas or the adiabatic exponent of the gas or presence of magnetic field have decaying effect on the shock wave. The zero temperature gradient assumption decreases the shock strength and brings a profound change in the density, the magnetic field and the non-dimensional axial components of vorticity vector distributions as compare to those of the adiabatic case. Also, a comparison between the solutions obtained in the case of isothermal and adiabatic flows is done.