Cylindrical shock waves in a rotating van der Waals gas under the variable viscosity and heat conduction

This study investigates a self-similar solution as intermediate asymptotics describing cylindrical shock waves driven by a piston in van der Waals gas under solid-body rotation. The solution is obtained for the exponential variations in the ambient density and the shock radius. The viscous stress follows Newton’s law of viscosity, while heat flux obeys Fourier’s law of heat conduction. The viscosity and thermal conductivity coefficients follow power-law dependencies on temperature and density. The solutions exist with pressure correction for increasing ambient density, while with volume correction for constant ambient density. The viscosity and volume corrections tend to weaken the shock, whereas the pressure correction and the specific heat ratio enhance it. Shock-induced compression intensifies with increasing viscosity, pressure correction and specific heat ratio, but decreases with increasing volume correction. The temperature and density exponents in the viscosity coefficient significantly affect shock compression, shock strength and the distribution of flow variables. Reduced density and radial velocity decrease with viscosity and heat conduction. Viscosity enhances tangential velocity while heat flux affects the normal and tangential stresses. The total energy behind the shock scales as the sixth power of the shock radius for pressure correction and the fourth power for volume correction. Solid body rotation is coupled with shock Mach number and ratio of specific heats. The reduced density, radial velocity and heat flux decrease, while pressure and normal viscous stress increase with pressure correction. Volume correction leads to decreases in density and pressure, but increases in tangential velocity and heat flux.