Hostname: page-component-cd9895bd7-lnqnp Total loading time: 0 Render date: 2024-12-28T21:24:22.261Z Has data issue: false hasContentIssue false
  • English
  • Français

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

Published online by Cambridge University Press:  05 May 2011

J. J. Liu
J. J. Liu*
Affiliation:
Department of Engineering Science, National Cheng Kung University, Tainan, Taiwan 70101, R.O.C.
*
* Professor
Get access

Abstract

Strong pseudo-steady Mach reflections in sulfur hexafluoride (SF6) are analyzed using the three-shock and local three-shock theories, where both the vibrationally-frozen (γ = 1.333) and -equilibrated (γ = 1.093) perfect-gas models are used to compare with existing experiments. The ranges of the incident shock Mach number and reflecting wedge angle studied are 1.49 ≤ Ms ≤ 5.95 and 10° ≤ θω ≤ 42°, respectively. It is found that predicted angles between the incident and reflected shocks from the local three-shock theory using the vibrationally-equilibrated fictitious perfect-gas model (i.e., γ = 1.093) agree closely with those, currently available in literature, measured experimentally; while these predicted angles obtained using the vibrationally-frozen perfect-gas model (i.e., γ = 1.333) differ significantly from the existing experiments. Taking the convex Mach stem curvature at the triple point into consideration, it is shown that both the triple point trajectory angle and the angle between the incident and reflected shocks of strong pseudo-steady Mach reflections in SF6 can be more accurately determined for wide ranges of Ms and θω from the three-shock theory using the vibrationally-equilibrated fictitious perfect-gas model than those without considering this effect.

Keywords

Pseudo-steady Mach reflectionsTriple point trajectory anglesSF6.
Type
Articles
Information
Journal of Mechanics , Volume 17 , Issue 1 , March 2001 , pp. 1 - 12
Copyright
Copyright © The Society of Theoretical and Applied Mechanics, R.O.C. 2001

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

1Mach, E., “Uber den Verlanf von Funkenwellen in der Ebene und im Raume,” Sitzungsber. Akad. Wiss. Wien, 78, pp. 819–838 (1878).Google Scholar
2Neumann, J. von. “Refraction, Interaction and Deflection of Shock Waves,” NAVORD Rep. 203-45, Navy Dept., Bureau of Ordinance, Washington, DC. (1945).Google Scholar
3Ben-Dor, G. and Glass, I. I., “Domains and Boundaries of Nonstationary Oblique Shock Wave Reflections: 1. Diatomic Gas,” J. Fluid Mech., 92, pp. 459–496 (1979).CrossRefGoogle Scholar
4Ben-Dor, G. and Glass, I. I., “Domains and Boundaries of Nonstationary Oblique Shock Wave Reflections: 2. Monatomic Gas,” J. Fluid Mech., 96, pp. 735–756 (1980).CrossRefGoogle Scholar
5Lee, J. H. and Glass, I. I., “Pseudo-Stationary Oblique-Shock-Wave Reflections in Frozen and Equilibrium Air,” Prog. Aerospace Sci., 21, pp. 33–80 (1984).CrossRefGoogle Scholar
6Ando, S. and Glass, I. I., “In Proc. Intl. Symp. on Military Aspects of Blast Simulations,” DRES, Alberta, Canada, I, 3.6–1-3.6-24 (1994).Google Scholar
7Shirouzu, M. and Glass, I. I., “An Assessment of Recent Results on Pseudo-Stationary Oblique- Shock-Wave Reflections,” UTIAS Rep. 264 (1982).Google Scholar
8Shirouzu, M. and Glass, I. I., “Evaluation of Assumptions and Criteria in Pseudo-Stationary Oblique Shock-Wave Reflections,” Proc. R. Soc. Lond, A 406, pp. 75–92 (1986).Google Scholar
9Hu, T. C. J., “Pseudo-Stationary Oblique-Shock-Wave Reflections in a Polyatomic Gas — Sulfur Hexafluride,” UTIAS TN 253 (1984).Google Scholar
10Hu, T. C. J. and Glass, I. I., “Pseudo-Stationary Olique Shock-Wave Reflections in Sulfur Hexafluride (SF6): Interferometric and Numerical Results,” Proc. R. Soc. Lond., A 408, pp. 321–344 (1986).Google Scholar
11Bleakney, W. and Taub, A. H., “Interactions of Shock Waves,” Rev. Mod. Phys., 21, pp. 584–605 (1949).CrossRefGoogle Scholar
12Griffith, W. C., “Shock Waves,” J. Fluid Mech., 106, pp. 81–101 (1980).CrossRefGoogle Scholar
13Colella, P. and Henderson, L. F., “The von Neumann Paradox for the Diffraction of Weak Shock Waves,” J. Fluid Mech., 213, pp. 71–94 (1990).CrossRefGoogle Scholar
14Liu, J. J., “Sound Wave Structures Downstream of Pseudo-Steady Weak and Strong Mach Reflections,” J. Fluid Mech., 324, pp. 309–332 (1996).CrossRefGoogle Scholar
15Hamsen, C. F., “Molecular Physics of Equilibrium Gases: A Handbook for Engineers,” NASA SP-3096 (1976).Google Scholar
16Law, C. K. and Glass, I. I., “Diffraction of Strong Shock Waves by a Sharp Compressive Corner,” CASI Trans., 4, pp. 2–12 (1971).Google Scholar
17Olim, M. and Dewey, J. M., “A Revised Three-Shock Solution for the Mach Reflection of Weak Shocks (1.1 < Mi < 1.5),” Shock Waves, 2, pp. 167–176 (1992).CrossRefGoogle Scholar
18Henderson, L. F., “On the Confluence of Three Shock Waves in a Perfect Gas,” Aero. Quart., 15, pp. 181–197 (1964).CrossRefGoogle Scholar
19Ben-Dor, G., “A Reconsideration of the Three-Shock Theory of a Pseudo-Steady Mach Reflection,” J. Fluid Mech., 181, pp. 467–484 (1987).CrossRefGoogle Scholar
20Glass, I. I., “Some Aspects of Shock-Wave Research,” AIAA J., 25, pp. 214–229 (1987).CrossRefGoogle Scholar