Converging Cylindrical Shock Waves in a Nonideal Gas With an Axial Magnetic Field

Abstract

This paper analyses the propagation of converging cylindrical shock waves in a nonideal gas, in the presence of an axial magnetic field. Chester-Chisnell-Whitham’s method has been employed to determine the shock velocity and the other flow-variables just behind the shock in the cases, when (i) the gas is weakly ionised before and behind the shock front, (ii) the gas is strongly ionised before and behind the shock front, and (iii) nonionised gas undergoes intense ionisation as a result of the passage of the shock. The effects of the nonidealness of the gas, the conductivity of the gas, and the axial magnetic field have been investigated. It is found that in the case (i), an increase in the value of parameter ( ) characterising the nonidealness of the gas accelerates the convergence of the shock. In the case (ii), the shock speed and pressure behind the shock increase very fast as the axis is approached; and this increase occurs earlier if the strength of the initial magnetic field is increased. In the case (iii), for smaller values of the initial magnetic field, the shock speed, and pressure behind the shock decrease very fast after attaining a maximum; and for higher values of the initial magnetic field, the tendency of decrease appears from the beginning. This shows that the magnetic field has damping effect on the shock propagation. In the case (iii), it was also found that the growth of the shock in the initial phase and decay in the last phase were faster when it was converging in a nonideal gas in comparison with that in a perfect gas. Further, it has been shown that the gas-ionising nature of the shock has damping effect on its convergence.