Hostname: page-component-5c6d5d7d68-wpx84 Total loading time: 0 Render date: 2024-08-22T08:23:06.509Z Has data issue: false hasContentIssue false
  • English
  • Français

The propagation of detonation waves in channels of varying cross-section

Published online by Cambridge University Press:  26 April 2006

F. Bartlmä
F. Bartlmä
Affiliation:
DLR. Institut für Physikalische Chemie der Verbrennung. Pfaffenwaldring 38. D 7000 Stuttgart 80, FRG
Get access Rights & Permissions [Opens in a new window]

Abstract

One-dimensional detonation wave propagation in channels of varying cross-section is reconsidered and studied in detail. Different analytical solutions are given for the case of an accelerated detonation wave in a converging channel and for a decelerated detonation wave in a diverging channel. Separation of the leading shock and the reaction zone in the second case is taken into account. Two- and three-dimensional problems of geometrical detonation wave dynamics can be solved by adapting the well-known approach of Whitham, but Whitham's method is based on a suitable one-dimensional analytical model.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 218 , September 1990 , pp. 225 - 238
Copyright
© 1990 Cambridge University Press

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

Bartlmä, F.: 1971 Detonationsvorgänge in Gasen. In Übersichtsbeiträge zur Gasdynamik (ed. E. Leiter & J. Zierep). Springer.
Bartlmä, F.: 1975 Gasdynamik der Verbrennung. Springer.
Bartlmä, F. & Schröder, K. 1986 The diffraction of a plane detonation wave at a convex corner. Combust. Flame 66, 237–248.Google Scholar
Burcat, A., Liftshitz, A., Scheller, K. & Skinner, G. B., 1971 Shock-tube investigation of ignition in propane–oxygen–argon mixtures. Thirteenth Symp. (Intl) on Combustion, pp. 745–755. The Combustion Intsitute.
Butler, D. S.: 1954 Converging spherical and cylindrical shocks. Armament Res. Establ. Ministry of Supply Rep. 54/54.Google Scholar
Cherny, G. G.: 1973 Lectures on the Theory of Exothermic Flows Behind Shock Waves. Springer.
Chester, W.: 1953 The propagation of shock waves in a channel of non-uniform width. Q. J. Mech. Appl. Maths 6, 440–452.Google Scholar
Chisnell, R. F.: 1957 The motion of a shock wave in a channel, with application to cylindrical and spherical shock waves. J. Fluid Mech. 2, 286–298.Google Scholar
Edwards, D. H., Thomas, G. O. & Nettleton, M. A., 1979 The diffraction of a planar detonation wave at an abrupt area change. J. Fluid Mech. 95, 79–96.Google Scholar
Fickett, W. & Davis, W. C., 1979 Detonation. University of California Press.
Guderley, G.: 1942 Starke kugelige und zylindrische Verdichtungsstösse in der Nähe des Kugelmittelpunktes bzw. der Zylinderachse. Luftfahrtforschung 19, 302–312.Google Scholar
Oppenheim, A. K. & Stern, R. A., 1959 On the development of gaseous detonation. Analysis of wave phenomena. Seventh Symp. (Intl) on Combustion, pp. 837–850. Butterworths.
Schnitzspan, H.: 1976 Die Ausbreitung von Chapman–Jouguet-Detonationen in Rohren veränderlichen Querschnitts. Mech. Res. Commun. 3, 435–440.Google Scholar
Strehlow, R. A.: 1984 Combustion Fundamentals. McGraw-Hill.
Teipel, I.: 1975 Die Ausbreitung von starken Detonationswellen in konvergierenden Kanälen. Abh. Aerodyn. Inst. TH Aachen Nr. 22, pp. 111–115.Google Scholar
Teipel, I.: 1976 Imploding detonation waves. Mech. Res. Commun. 3, 21–26.Google Scholar
Teipel, I.: 1983 Detonation waves in pipes with variable cross-section. Acta Mech. 47, 185–191.Google Scholar
Thomas, G. O.: 1979 Gasdynamic studies of diverging detonations. Ph.D. dissertation, University of Wales.
Whitham, G. B.: 1957 A new approach to problems of shock dynamics. Part 1. Two-dimensional problems. J. Fluid Mech. 2, 146–171.Google Scholar
Whitham, G. B.: 1959 A new approach to problems of shock dynamics. Part 2. Three-dimensional problems. J. Fluid Mech. 5, 369–386.Google Scholar
Whitham, G. B.: 1974 Linear and Nonlinear Waves. Wiley.