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Flow in the exit of open pipes during acoustic resonance

Published online by Cambridge University Press:  19 April 2006

J. H. M. Disselhorst  and
L. Van Wijngaarden
J. H. M. Disselhorst
Affiliation:
Twente University of Technology, Enschede, The Netherlands
L. Van Wijngaarden
Affiliation:
Twente University of Technology, Enschede, The Netherlands
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Abstract

The flow near the mouth of an open tube is examined, experimentally and theoretically, under conditions in which resonant acoustic waves are excited in the tube at the other end. If the edge of the tube is round, separation does not occur at high Strouhal numbers, which enables us to verify theoretical predictions for dissipation in the boundary layer and for acoustic radiation. Observation with the aid of schlieren pictures shows that in the case of a sharp edge vortices are formed during inflow. The vortices are shed from the pipe during outflow. Based on these observations a mathematical model is developed for the generation and shedding of vorticity. The main result of the analysis is a boundary condition for the pressure in the wave, to be applied near the mouth. The pressure amplitudes in the acoustic wave measured under resonance are compared with theoretical predictions made with the aid of the boundary condition obtained in the paper.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 99 , Issue 2 , 25 July 1980 , pp. 293 - 319
Copyright
© 1980 Cambridge University Press

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References

Batchelor, G. K. 1967 An Introduction to Fluid Dynamics. Cambridge University Press.
Chester, W. 1964 Resonant oscillations in closed tubes. J. Fluid Mech. 18, 44.Google Scholar
Chu, B. T. & Ying, S. J. 1963 Thermally driven nonlinear oscillations in a pipe with travelling shock waves. Phys. Fluids 6, 11.Google Scholar
Clements, R. R. & Maull, D. J. 1976 The representation of sheets of vorticity by discrete vortices. Prog. Aero. Sci. 16, 129.Google Scholar
Cruikshank, D. B. 1972 Experimental investigations of finite amplitude acoustic oscillations in a closed tube. J. Acoust. Soc. Am. 52, 1024.Google Scholar
Disselhorst, J. H. M. 1978 Acoustic resonance in open tubes. Ph.D. thesis, Twente University of Technology, Enschede.
Disselhorst, J. H. M. & Van Wijngaarden, L. 1979 Oscillatory flow around the edge of a flat plate. J. Engng Math. 13, 271.Google Scholar
Jimenez, J. 1973 Nonlinear gas oscillations in pipes. Part 1. Theory. J. Fluid Mech. 59, 23.Google Scholar
Lettau, E. 1939 Messungen an Gasschwingungen grosser Amplitude in Rohrleitungen. Dtsch. Kraftfahrtforsch. 39, 1.Google Scholar
Levine, H. & Schwinger, J. 1948 On the radiation of sound from an unflanged pipe. Phys. Rev. 73, 383.Google Scholar
Lighthill, M. J. 1978 Waves in Fluids. Cambridge University Press.
Maxworthy, T. 1977 Some experimental studies on vortex rings. J. Fluid Mech. 81, 465.Google Scholar
Merkli, P. 1973 Theoretische und experimentelle thermoakustische Untersuchungen am Kolbengetriebenen Resonanzrohr. Ph.D. thesis, Eidgenössische Technische Hochschule Zürich.
Prandtl, L. 1961 Collected Works, vol. II., pp. 703–704. Springer.
Rayleigh, J. W. S. 1945 The Theory of Sound, cha. 19. Dover.
Saffman, P. G. & Baker, G. R. 1979 Ann. Rev. Fluid Mech. 11, 95.
Seymour, B. R. & Mortell, M. P. 1973 Nonlinear resonant oscillations in open tubes. J. Fluid Mech. 60, 733.Google Scholar
Sturtevant, B. 1974 Nonlinear gas oscillations in pipes. Part 2. Experiments. J. Fluid Mech. 63, 97.Google Scholar
Sturtevant, B. & Keller, J. J. 1978 Subharmonic nonlinear resonances in open tubes. Part II: Experimental investigation of the open-end boundary condition. Z. angew. Math. Phys. 29, 473.Google Scholar
Temkin, S. 1968 Nonlinear gas oscillations in a resonant tube. Phys. Fluids 11, 960.Google Scholar
Van Wijngaarden, L. 1968 On the oscillations near and at resonance in open pipes. Proc. A.S.C.E., J. Engng Math. 2, 225.Google Scholar
Van Wijngaarden, L. & Wormgoor, W. 1974 Investigations on resonant acoustic waves in open pipes. In Finite Amplitude Wave Effects in Fluids (ed. L. Bjorne), p. 75. IPC Science and Technology.