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Shock diffraction in channels with 90° bends

Published online by Cambridge University Press:  20 April 2006

D. H. Edwards ,
P. Fearnley  and
M. A. Nettleton
D. H. Edwards
Affiliation:
Department of Physics, University College of Wales, Penglais, Aberystwyth
P. Fearnley
Affiliation:
B.P. Research Centre, Sunbury-on-Thames, Middlesex
M. A. Nettleton
Affiliation:
Central Electricity Research Laboratories, Kelvin Avenue, Leatherhead, Surrey, KT22 7SE
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Abstract

A study has been made of how initially planar shocks in air propagate around 90° bends in channels of nearly rectangular cross-section. In shallow bends for which the radius of curvature R is much greater than the radius r of the channel, the shock recovers from a highly curved profile at the start of the bend to regain planarity towards the end of the bend. This occurs on account of the acceleration of the triple point across the channel following its interaction with the expansion waves generated at the convex wall. In sharp bends the shock profiles retain their pronounced curvature for some distance downstream of the bend.

At the start of a shallow bend (R/r ≈ 6) the shock at the concave wall, initial Mach number M0, accelerates to Mw = 1.15M0 and remains at this value until towards the end of the bend it begins to attenuate. At the convex wall, shocks of M0 > 1.7 attenuate to Mw = 0.7M0 and propagate at this value for some distance around the bend. In the early stages of a sharper bend (R/r ≈ 3) the shock at the concave wall strengthens to Mw = 1.3M0, remaining at this value for some distance downstream of the bend. At the convex wall the shock decelerates to 0.6M0.

Whitham's (1974) ray theory is shown to predict with reasonable accuracy the Mach numbers of the wall shocks at both surfaces for both bends tested and the range of incident shock velocities used, 1.2 < M0 < 3. The agreement between the theory and experimental results is particularly close for stronger shocks propagating along the inner bend. Predictions from 3-shock theory (Courant & Friedrichs 1948) of the Mach number at the outer wall are consistently higher than those from Whitham's analysis. In turn, the latter tends to slightly overestimate the strength of the wall shock.

A model is developed, based on an extension of Whitham's analysis, and is shown to predict the length of the Mach stem produced by shocks of M0 > 2 over the initial stages of the bend.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 132 , July 1983 , pp. 257 - 270
Copyright
© 1983 Cambridge University Press

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References

Ben-Dor, G. & Glass, I. I. 1979 Domains and boundaries of non-stationary oblique shock-wave reflexions. Part 1. Diatomic gas J. Fluid Mech. 92, 459.Google Scholar
Bryson, A. E. & Gross, R. W. F. 1961 Diffraction of strong shocks by cones, cylinders, and spheres J. Fluid Mech. 10, 1.Google Scholar
Chisnell, R. F. 1957 The motion of a shock wave in a channel, with applications to cylindrical and spherical shock waves J. Fluid Mech. 2, 286.Google Scholar
Courant, R. & Friedrichs, K. O. 1948 Supersonic Flow and Shock Waves. Interscience.
Edwards, D. H., Fearnley, P., Thomas, G. O. & Nettleton, M. A. 1981 Shocks and detonations in channels with 90 bends. 1st Specialists’ Meeting (Intl) Combust. Inst., p. 431. Section Française du Combust. Inst.
Fearnley, P. & Nettleton, M. A. 1983 Pressures generated by blast waves in channels with 90 bends. Submitted to Loss Prevention and Safety Promotion Meeting, Inst. Chem. Engng.
Gvozdeva, L. G., Lagutov, YU. P. & Fokeev, V. P. 1979 Transition from normal reflection to Mach reflection in the interaction of shock waves with a cylindrical surface Sov. Tech. Phys. Lett. 5, 334.Google Scholar
Henderson, L. F. 1980 On the Whitham theory of shock-wave diffraction J. Fluid Mech. 99, 801.Google Scholar
Hide, R. & Millar, W. 1956 A preliminary investigation of shocks in a curved channel. AERE GP/R 1918.
Itoh, S. & Itaya, M. 1980 On the transition between regular and Mach reflection. In Shock Tubes and Waves: Proc. 12th Intl Symp. on Shock Tubes and Waves (ed. A. Lifshitz & J. Rom), p. 314. Magnes Press, Hebrew University, Jerusalem.
Lighthill, M. J. 1949 The diffraction of blast. 1 Proc. R. Soc. Lond. A198, 454.Google Scholar
Nettleton, M. A. 1973 Shock attenuation in a ‘gradual’ area expansion. J. Fluid Mech. 60, 209.Google Scholar
Skews, B. W. 1967 The shape of a diffracting shock wave J. Fluid Mech. 29, 297.Google Scholar
Sloan, S. A. & Nettleton, M. A. 1975 A model for the decay of the axial shock in a large and abrupt area change J. Fluid Mech. 71, 769.Google Scholar
Sloan, S. A. & Nettleton, M. A. 1978 A model for the decay of the wall shock in a large and abrupt area change J. Fluid Mech. 88, 259.Google Scholar
Whitham, G. B. 1974 Linear and Nonlinear Waves. Wiley-Interscience.