Abstract
An experimental study was made of the stability of converging cylindrical shock waves. The experiments were conducted on annular shock tubes equipped with a double exposure holographic interferometer in the Stoßwellenlabor, RWTH Aachen, and in the Institute of High Speed Mechanics, Tohoku University, Sendai, for shock Mach numbers of 1.1 to 2.1 in air. By comparing these two different shock tube experiments, it is found that in the former facility the mode-three instability is predominant at the center of convergence, whereas the mode-four instability appears in the latter setup. The instabilities are denoted in this way because the shock and the flow field behind it reveal a remarkable triangular and quadrangular symmetry, respectively. It is concluded that the converging cylindrical shock wave is always unstable and sensitive to the structure of the annular shock tube. Usefulness of holographic interferometry to this kind of shock wave research is also demonstrated.
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References
Butler, D. S. 1954: Converging spherical and cylindrical shocks. Rep. No. 54/54 Armament Research and Development Establishment, Ministry of Supply, Fort Halstead, Kent, GB
Duong, D. Q.; Milton, B. E. 1985: The Mach-reflection of shock waves in converging, cylindrical channels. Exp. Fluids 3, 161–168
Fong, K.; Ahlborn, B. 1979: Stability of converging shock waves. Phys. Fluids 22, 416–421
Fujiwara, T.; Sugimura, T.; Mizoguchi, K.; Taki, S. 1973: Stability of converging cylindrical detonation. J. Jpn. Soc. Aero. Space Sci. 21, 8–14
Gardner, J. H.; Book, D. L.; Bernstein, I. B. 1982: Stability of imploding shocks in the CCW approximation. J. Fluid Mech. 114, 41–58
Glass, I. I.; Sagie, D. 1982: Application of explosive-driven implosions to fusion. Phys. Fluids 25, 269–270
Glass, I. L.; Sharma, S. P. 1976: Production of diamonds from graphite using explosive-driven implosions. AIAA J. 14, 402–404
Guderley, G. 1942: Starke kugelige und zylindrische Verdichtungsstöße in der Nähe des Kugelmittelpunktes bzw. der Zylinderachse. Luftfahrt Forsch. 19, 302–312
Itoh, T.; Abe, K. 1984: Simulation of instability of cylindrically converging shock waves. Proc. 4th Int. Conf. Applied Numerical Modeling, 666–670
Kleine, H. 1985: Time resolved shadowgraphs of focusing cylindrical shock waves. Study treatise at the StoBwellenlabor, RWTH Aachen, FRG
Knystautas, R.; Lee, B. H. K.; Lee, J. H. S. 1969: Diagnostic experiments on converging detonations. Phys. Fluids. Suppl. I, 165–168
Lazarus, R. B. 1982: One-dimensional stability of self-similar converging flows. Phys. Fluids 25, 1146–1155
Mishkin, E. A.; Fujimoto, Y. 1978: Analysis of a cylindrical imploding shock wave. J. Fluid Mech. 89, 61–78
Nakamura, Y. 1983: Analysis of self-similar problems of imploding shock waves by the method of characteristics. Phys. Fluids 26, 1234–1239
de Neef, T.; Nechtman, C. 1978: Numerical study of the flow due to a cylindrical implosion. Comput. Fluids 6, 185–202
Payne, R. B. 1957: A numerical method for a converging cylindrical shock. J. Fluid Mech. 2, 185–200
Perry, R. W.; Kantrowitz, A. 1951: The production and stability of converging shock waves. J. Appl. Phys. 22, 878–886
Saito, T.; Glass, I. 1. 1979: Applications of random-choice method to problems in shock and detonation wave dynamics. UTIAS Rep. No. 240
Sod, G. A. 1977: A numerical study of a converging cylindrical shock. J. Fluid Mech. 83, 785–794
Stanyukovich, K. P. 1960: Unsteady motion of continuous media. Oxford: Pergamon Press
Takayama, K. 1983: Application of holographic interferometry to shock wave research. Proc. SPIE 398, 174–180
Takayama, K.; Honda, M.; Onodera, O. 1977: Shock propagation along 90 degree bends. Rep. Inst. High Speed Mech. Tohoku Univ. 35, 83–111
Takayama, K.; Onodera, O.; Hoshizawa, Y. 1984: Experiments on the stability of converging cylindrical shock waves. Theor. Appl. Mech. 32, 117–127
Terao, K.; Sato, T. 1973: A study of a radially divergentconvergent detonation wave. In: Recent developments in shock tube research (eds. Bershader, D.; Griffith, W.), pp. 646–551. Stanford: Stanford Univ. Press
Van Dyke, M.; Guttmann, A. J. 1982: The converging shock wave from a spherical or cylindrical piston. J. Fluid Mech. 120, 451–462
Wang, J. C. T. 1982: On the theory of imploding shocks. J. Appl. Math. Phys. 33, 53–62
Wu, J. H. T.; Neemeh, R. A.; Ostrowski, P. P.; Elabdin, M. N. 1977: Production of converging cylindrical shock waves by finite element conical contractions. In: Shock Tubes and Shock Wave Research, Proc. Eleventh Intern. Symp. on Shock Tubes and Waves, pp. 107–114, Seattle: Univ. Washington Press
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To Prof. Dr. sq. techn. Dr.-Ing. e.h. Fritz Schultz-Grunow on the occasion of his 80th birthday
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Takayama, K., Kleine, H. & Grönig, H. An experimental investigation of the stability of converging cylindrical shock waves in air. Exp. Fluids 5, 315–322 (1987). https://doi.org/10.1007/BF00277710
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DOI: https://doi.org/10.1007/BF00277710