Scheichl S., Kluwick A.

The coefficient of nonlinearity G=1+B/(2A) is of essential importance for the acoustic wave propagation in single-phase gaseous media in thermodynamic equilibrium. In contrast to the well-known perfect gases, which are characterized by values of G>1, real gases featuring very large values of specific heats and commonly referred to as BZT fluids have the distinguishing property that G is found to become negative over a finite range of temperatures and pressures. The existence of thermodynamic states with G<0 in the dense gas regime leads to the occurrence of phenomena which have no equivalent in ideal gas dynamics. For example, if the equilibrium state of the BZT fluid is chosen to be close to the transition line G=0, the propagation of planar nonlinear sound waves is governed by a Burgers equation extended with a cubic nonlinearity term, which, since dissipation is small, may result in the simultaneous generation of compression and rarefaction shocks. The analysis presented here focuses on the properties of acoustic waves transmitted through a BZT fluid contained in a rigid tube which is connected to an array of Helmholtz resonators in its axial direction. Such a system gives rise to dispersion as well and, thus, the identification of physically acceptable discontinuous solutions in the limit of vanishing dissipation and dispersion has to be approached by a special regularization principle: In contrast to the classical, non-dissipative case where the admissibility of a discontinuity is ensured by the existence of a viscosity dominated inner shock structure, the shocks are now generated as limits of diffusive-dispersive traveling waves. The thus obtained shock admissibility criteria crucially depend on the precise ratio of dispersion to dissipation in the system. This may lead to wave solutions violating the well-known Oleinik entropy criterion since their discontinuities emanate rather than absorb waves. Such shocks are termed “non-classical”.