Stability of shock wave reflections in nonequilibrium steady flows and hysteresis

In the present work we have addressed the issue of the stability of shock wave reflection in the presence of vibrational and chemical relaxation phenomena and its relation with the occurrence of the hysteresis. In order to better understand the physics of the shock wave reflections we have first formulated an evolution equation for the entropy of a mixture of gases in thermal and chemical nonequilibrium by invoking the shifting equilibrium assumption and the concepts of irreversible thermodynamics, and assuming (i) that all diatomic molecules behave as harmonic oscillators; and (ii) finite rate chemistry. A perturbation analysis of the total entropy evolution equation has then been carried out to analyze the stability of shock wave configurations (either regular or Mach) both for ideal and real gases. The analysis shows that a Mach reflection is more stable than a regular one; furthermore, its stability is enhanced by nonequilibrium effects. In order to clarify the occurrence of the hysteresis phenomenon in light of the conclusions reached through the stability analysis, we have also carried out multidimensional simulations (both at flight and wind tunnel conditions) by developing a pseudotransient procedure to span a (hysteresis) loop dual solution domain --> Mach reflection domain --> dual solution domain. The simulations show that the total entropy of the system exhibits an abrupt change along the path dual solution domain --> Mach reflection domain, while it is continuous along the reverse path. An argument is then developed to prove that hysteresis is the natural consequence of the different stability properties of regular and Mach reflections and the Prigogine minimum total entropy production principle. (C) 2000 American Institute of Physics. [S1070-6631(00)51612-2].