Theory for producing a single-phase rarefaction shock wave in a shock tube

Abstract

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 discussed and their interpretation challenged. In preparation for a new shock tube experiment, a global theory is developed, utilizing a van der Waals fluid, for demonstrating a single-phase vapour rarefaction shock wave in the incident flow of the shock tube. The flow consists of four uniform regions separated by three constant-speed discontinuities: a rarefaction shock, a compression shock, and a contact surface. Entropy jumps and upstream supersonic Mach number conditions are verified for both shock waves. The conceptual van der Waals model is applied to the fluid perfluoro-tripentylamine (FC-70, C15F33N) analytically, and verified with computational simulations. 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 in the form of representative sets of thermodynamic state data (pressure, density, Mach number, and fundamental derivative of gas dynamics) are presented.

Direct numerical simulations of homogeneous isotropic turbulence in a dense gas

“…FC-70 is suspected to be dense enough to possess an inversion region in which its fundamental derivative is negative [2]. All along this study, the initial pressure, temperature and specific volume correspond to the thermodynamic state 4 for the first MAH case in the article of Fergason et al [3] in which the reduced (normalized by the critical values) pressure and specific volume are respectively equal to 0.9866 and 1.5733. All decaying HIT cases proposed in this study are performed for an initial Taylor Reynolds number equal to 75 and simulations are initiated using an incompressible homogeneous isotropic turbulent velocity field following the Passot-Pouquet spectrum with k e the wavelength of maximum initial kinetic energy defined by the relationship Re λ = 2u rms /(νk e ).…”

Bayesian quantification of thermodynamic uncertainties in dense gas flows

“…However, these experiments where questioned by several authors (see, e.g. [29]). Efforts for carrying out new shock tube experiments were done at University of Colorado Boulder [29] and at TU Delft [30], but no data have been made available up to present.…”

“…[29]). Efforts for carrying out new shock tube experiments were done at University of Colorado Boulder [29] and at TU Delft [30], but no data have been made available up to present. A dense gas nozzle facility is presently under construction at Politecnico di Milano [31].…”

Flow in near-critical fluids induced by shock and expansion waves

“…In particular, the MLLS coexistence curve is much closer to experimental values. Portions of the Hugoniot, however, are always below the spinodal curve and the wave must hence contain two-phase fluid states [21], which could manifest itself in an increased shock thickness.…”