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Theory of producing a single-phase rarefaction shock wave in a shock tube. (English) Zbl 1005.76051
Although predicted early in the 20th century, a single-phase vapour rarefaction shock wave has yet to be demonstrated experimentally. Results from a previous shock tube experiment appear to indicate a rarefaction shock wave. These results are here discussed, and their interpretation is challenging.
Then, in preparation for a new experimental study, the authors construct a global model to investigate the initial conditions required to produce a triple-discontinuity wave field in the incident flow of a shock tube, where one discontinuity is a rarefaction shock wave (RSW). The described procedure provides a starting point for shock tube experiments that produce non-classical phenomena due to negative non-linearity in the vapour phase of dense fluids. For a given experiment, the flow field initial conditions are fixed with the choice of three parameters: the specific volume at a fixed state, and two prescribed non-negative parameters. The adjustment of input parameters enables an approximate maximization of RSW shock strength, thus enhancing the probability of detection. For the fluid FC-70, a finite but small region of initial states exists where the entropy jump and upstream Mach number are satisfactory. The van der Waals model is confirmed using a similar model with Martin-Hou equation of state (MH EOS). This model further demonstrates that the high-pressure state is not close to either the critical point or the coexistence curve. Further analysis of the FC-70 wave field, using an Euler flow solver with MH EOS, provides additional confirmation of the global model.
The analysis predicts a small region of initial states that may be used to unequivocally demonstrate the existence of a single-phase vapour rarefaction shock wave. Simulation results are presented in the form of representative sets of thermodynamic state data (pressure, density, Mach number, and fundamental derivatives of gas dynamics).

76L05 Shock waves and blast waves in fluid mechanics
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