Pseudostationary oblique shock-wave reflections in sulphur hexafluoride (SF ₆ ): interferometric and numerical results

Abstract

Pseudostationary oblique shock-wave reflections in SF 6 were investigated experimentally and numerically. Experiments were concluded in the UTIAS 10 x 18 cm Hypervelocity Shock Tube in the range of incident shock wave Mach number 1.25 < M s < 8.0 and wedge angle 4° < θ w < 47° with initial pressure 4 < P 0 < 267 Torr (0.53-35.60 kPa) at temperatures T 0 near 300 K. The four major types of shock-wave reflection, i. e. regular reflection (RR), single-Mach (SMR), complex-Mach (CMR) and double-Mach reflections (DMR), were observed. These were studied by using infinite-fringe interferograms from a Mach-Zehnder interferometer with a 23 cm diameter field of view. The isopycnics and the density distributions along the wedge surface are presented for the various types of reflection. The analytical transition boundaries between the four types of shock-wave reflection were established up to M s = 10.0 for frozen and equilibrium vibrational SF 6 . An examination of the relaxation length under the present experimental conditions indicated that a vibrational-equilibrium analysis was required. Comparisons of experiment with analysis for transition-boundary maps, reflection angle δ and the first triple-point trajectory angle X verify that the reflections were in vibrational equilibrium. The excellent agreement between the present interferometric results and the numerical results obtained by H. M. Glaz et al . ( Proc. int. colloq. on dynamics of explosives and reactive systems [ Berkeley ] (1985)) with real-gas effects also supports the vibrational equilibrium hypothesis for shocked SF 6 . The behaviour of the angle between the two triple-point trajectories ( X ' — X ) is discussed and the unique pattern of DMR with X ' = 0 was verified experimentally. A numerical analysis for the second triple-point system is obtained for the first time. It is shown that, for a given incident shock Mach number, the highest wedge-surface pressure is achieved through a DMR instead of an RR at high M s .

Analytical Predictions of Strong Pseudo-Steady Mach Reflections for the Polyatomic Gas: SF6

“…The physical quantities experimentally measured for this chosen pseudo-steady MR, as taken from Hu [9], are χ = 3.0° and ω ir = 117.2°. This is why we perform two series of three-shock calculations for the series of experimentally observed pseudo-steady MR in SF 6 [10] in the following two sections, in order to validate the vibrational equilibrium hypothesis for shocked SF 6 and to verify the applicability and general accuracy of our computed shock polar solutions of strong pseudo-steady MR in SF 6 using the vibrationally-equilibrated fictitious perfect-gas model in the three-shock theory. They are χ = 3.06° and ω ir = 117.16°, which are in remarkably close agreement with the experimentally measured values.…”

“…In the following, the ω ir of strong pseudo-steady MR experiments in SF 6 reported by Hu [9], Hu and Glass [10] is calculated with their measured χ applied in the three-shock theory using the following two different perfect-gas models: γ = 1.333 for vibrationally-frozen SF 6 and γ = 1.093 for vibrationally-equilibrated SF 6 . In the following, the ω ir of strong pseudo-steady MR experiments in SF 6 reported by Hu [9], Hu and Glass [10] is calculated with their measured χ applied in the three-shock theory using the following two different perfect-gas models: γ = 1.333 for vibrationally-frozen SF 6 and γ = 1.093 for vibrationally-equilibrated SF 6 .…”

“…Thus, this result shows that this observed pseudo-steady MR in SF 6 is in vibrational equilibrium. The experimental data, taken from Hu [9], Hu and Glass [10], are marked as solid circles. 4(a) and 4(b).…”

“…The reflected wave of the computed pseudo-steady MR solution is a backward facing weak oblique shock for the shock polar solution given in Fig. Solid circles are measured data of Hu and Glass [10]. 4(b).…”

“…Hu [9] and Hu and Glass [10] investigated pseudo-steady MR in SF 6 experimentally and analytically. Sulphur hexafluoride has 3 transnational, 3 rotational, and 15 vibrational degrees of freedom.…”