Abstract
An experimental and numerical study was made of converging cylindrical shock waves. The goal of the present study was to clarify the movement and instability of the converging cylindrical shock waves. Experiments were conducted in an annular shock tube of 230 mm o.d. and 210 mm i.d. connected to a cylindrical test section of 210 mm diameter. Double exposure holographic interferometry was used to visualize the converging cylindrical shock waves. Incident shock Mach numbers ranged between 1.1 and 2.0 in air. A numerical simulation was conducted using the TVD finite difference scheme. It was found in the experiments that although the initial shock wave configuration looked cylindrical, it was gradually deformed with propagation towards the center and finally showed mode-four instability. This is attributable to the existence of initial disturbances which were introduced by the struts which supported the inner tube of the annular shock tube. This trend was significant for stronger shock waves indicating that at the last stage of shock wave convergence the initial perturbations of the converging cylindrical shock wave were amplified to form the triple point of Mach reflection. The numerical results correctly predicted the experimental trend.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
Caulfield HJ (1979) Handbook of optical holography. Academic Press New York
Demmig P, Hehmsoth HH (1989) Model computation of converging cylindrical shock waves: Initial configurations, propagation, and reflection. In: Kim YM (ed) Proc 17th Int Symp Shock Wave and Shock Tube, pp 155–160
Gardner JH, Book DL, Bernstein IB (1982) Stability of imploding shocks in the CCW approximation. J Fluid Mech 114:41–58
Guderley G (1942) Starke kugelige und zylindrische Verdich-tungsstösse in der Nähe des Kugelmittelpunktes bzw. der Zylinderachse. Luftfahrtforsch 19:302–312
Harten A (1983) High resolution scheme for hyperbolic conservation law. J Comp Phys 49:357–393
Itoh T, Abe K (1984) Simulation of instability of cylindrically converging shock waves. In: Proc 4th Int Conf Applied Numerical Modelling, Taiwan, pp 666–671
Itoh K, Takayama K (1987) Transonic shock tube flow over an NACA 0012 aerofoil and elliptical cylinders. In: Bershader D, Hanson RK (eds) Proc 16th Int Symp Shock Tubes and Waves, Stanford Univ Press Stanford, pp 693–699
Perry RW, Kantrowitz A (1951) The production and stability of converging shock waves. J Appl Phys 22:878–886
Takayama K, Kleine H, Grönig H (1987) An experimental investigation of the stability of converging cylindrical shock waves in air. Exp Fluids 5:315
Takayama K, Ben-Dor G (1986) Reflection and diffraction of shock waves over a circular concave wall. Rept Inst High Speed Mech, Tohoku Univ 51:43–52
Takayama K (1983) Application of holographic interferometry to shock wave research. Proc. SPIE 398 pp 174–181
Takayama K, Honda M, Onodera O (1977) Shock propagation along 90 ∘ bends. Rept Inst High Speed Mech, Tohoku Univ 35:83–102
Takayama K (1990) Proceedings of international workshop on shock wave focusing, Shock Wave Research Center, Institute of Fluid Science, Tohoku Univ
Watanabe M (1989) Stability of converging cylindrical shock wave. Master Thesis, Tohoku Univ in Japanese
Wu JHT, Neemeh RA, Ostrowski PP, Elabdin MN (1977) Production of converging cylindrical chock waves by finite element conical contraction. In: Hertzberg A, Russell D (eds) Proc 11th Int Symp Shock Tubes and Waves, Washington Univ Press Seattle, pp 107–112
Author information
Authors and Affiliations
Additional information
This article was processed using Springer-Verlag TEX Shock Waves macro package 1990.
Rights and permissions
About this article
Cite this article
Watanabe, M., Takayama, K. Stability of converging cylindrical shock waves. Shock Waves 1, 149–160 (1991). https://doi.org/10.1007/BF01414910
Received:
Accepted:
Issue Date:
DOI: https://doi.org/10.1007/BF01414910