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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).

MSC:
76L05 Shock waves and blast waves in fluid mechanics
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