Shock and Detonation Dynamics in Non-Ideal Gases

Shock and detonation dynamics in a non-ideal van der Waals gas are studied in the presence of classical and anomalous waves. Anomalous waves are admissible in a single gas phase material when isentropes are non-convex, rendering the sound speed to have the unusual feature of decreasing with increasing temperature. The second law-satisfying anomalous waves considered include rarefaction shock waves, continuous compression fans, and composite waves. To study detonations behind anomalous waves, a foundational understanding of anomalous wave dynamics in inert flows must be established. Analysis of steady wave dynamics in an inert van der Waals gas reveals that the viscous shock solution is required to discern which among multiple second law-satisfying anomalous waves are achieved in an initial value problem. Shock tube solutions are used for verification of numerical simulations. Highly resolved viscous solutions are obtained with a simple explicit Euler time advancement scheme coupled with a second order central spatial discretization. Inviscid simulations are done with a third order Runge-Kutta method in time and a fifth order Mapped Weighted Essentially Non-Oscillatory (WENO5M) discretization. The WENO5M method is supplemented with a novel use of global Lax-Friedrichs flux-splitting in space, as local flux-splitting methods fail when changes in the sound speed are non- monotonic. New analysis is done of steady detonation dynamics in a van der Waals gas for classical and anomalous behavior. Understanding of anomalous steady wave dynamics in inert flows is used to identify potential complications with Chapman- Jouguet and ZND analysis in and around the anomalous region. Non-convexities of Hugoniot curves in the anomalous region are found to render steady solutions predicted by CJ and ZND analysis inadmissible. Numerical predictions of stable unsteady detonations driven by an anomalous wave are presented, and the detonation dynamics are shown to be consistent with the structure of piston-driven detonations. The van der Waals model is shown to delay the transition to instability of detonations in the classical regime.