Abstract
The mechanism of shock wave focusing in a two-dimensional log-spiral duct has been investigated here numerically using a finite volume method. This approach is based on a MUSCL TVD scheme with flux-vector splitting applied to the Euler equations. The isopycnics determined from the calculations are compared with the experimental results obtained by use of holographic interferometric photography and are found to be in excellent qualitative agreement with the experiments. The computational results clarify the details of the wave interactions very near to the focus. In particular, phenomena such as the formation of secondary shock waves prior to the implosion, their interaction with the reflected shock and the formation of vortices after the implosion have been examined.
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Grönig H (1990) Past, present and future of shock focusing research. In: Takayama K (ed) Proc. Int. Workshop on Shock Wave Focusing, Institute of Fluid Science, Tohoku University, Sendai, Japan. pp 1–37
Inoue O, Takahashi N, Takayama K (1993) Shock wave focusing in a log-spiral duct. AlAA Jnl. 31:1150
Milton BE, Archer RD (1969) Generation of implosions by area change in a shock tube. AlAA Jnl. 7:779
Milton BE, Takayama K, Archer RD (1988) An evaluation of two-dimensional and axi-symmetric focusing of a plane shock wave. In: Grönig H (ed) Shock tubes and waves, Proc. 16th International Symposium on Shock Tubes and Waves, Aachen, West Germany, July 26–31, 1987. VCH Verglagsgesellschaft, West Germany, pp 567–573
Milton BE (1990) The focussing of shock waves in two-dimensional and axi-symmetrical ducts. In: Takayama K (ed) Proc. International Workshop on Shock Wave Focussing, Institute of Fluid Science, Tohoku University, Sendai, Japan. pp 155–192
Takayama K (1983) Application of holographic interferometry to shock wave research. Proc. SPIE 398:174
Takayama K, Inoue O (1991) Shock wave diffraction over a 90 degree sharp corner. Shock Waves 1:301
van Leer B (1982) Flux-vector splitting for the Euler equations. Proc. 8th ICNMFD, Lecture Notes in Physics 170:507–512
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Inoue, O., Imuta, S., Milton, B.E. et al. Computational study of shock wave focusing in a log-spiral duct. Shock Waves 5, 183–188 (1995). https://doi.org/10.1007/BF01435526
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DOI: https://doi.org/10.1007/BF01435526