Shock dynamics of strong imploding cylindrical and spherical shock waves with real gas effects

Abstract

Strong cylindrical and spherical shock implosion in a monatomic gas is considered. A simple solution is obtained by Whitham’s geometrical shock dynamics approach modified to account for the real gas effects. The real gas effects are introduced by jump relations over the shock and include several levels of ionization, Coulomb interaction as well as internal energy of the excited electrons. It is shown that ionization has a major effect on temperature and density behind the converging shock as well as on the shock acceleration. The temperature and acceleration being substantially reduced and density substantially increased as compared to the ideal nonionizing case. The ionization effect on the pressure behind the converging shock is less pronounced. It is also shown that for the considered test case of initial Mach number M0=8 the gas becomes completely ionized behind the spherical shock at approximately 1% of the initial radius from the focal point and its speed being decreased by a factor of 1.8 as compared to the ideal case.