The effects of gravitational and magnetic fields on the propagation of cylindrical strong shock waves in a van der Waals gas

Abstract

The present study aims to investigate the effects of non-idealness parameter, gravitation and magnetic fields behind the flow of motion for cylindrical hydro-magnetic strong shock waves travelling through a tube of variable cross-section in a self-gravitating van der Waals gas. The analytical expressions of the flow variables for one-dimensional adiabatic flow behind the hydro-magnetic strong shock waves are obtained using Chester-Chisnell-Whitham’s (CCW) Method. The initial density distribution of the medium is assumed to be ρ0=ρ'r−w where ρ' is the density at the axis of symmetry, w is a constant and r is the distance from the axis of symmetry. The magnetic field, on the other hand, is assumed to have only constant axial and variable azimuthal components. Due to the presence of magnetic and gravitational fields, the uniform density distribution of the medium becomes non-uniform and this becomes an interesting fact to study. It is found that, all flow variables except the pressure rises with the shock propagation distance. It is also demonstrated that the gravitational and magnetic fields cause the numerical values of the flow variables to increase behind the shock wave. Further, research shows that even a small increase in the gravitational field increases the pressure behind the shock wave, whereas a small increase in the magnetic field has a little effect on it. Furthermore, it is found that the flow variables get strengthened behind the shock wave in comparison with ahead of the shock. The trends of the current findings are in good agreement with the existing experimental observations and results.