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Nonlinear gas oscillations in pipes. Part 1. Theory

Jimenez, J. (1973) Nonlinear gas oscillations in pipes. Part 1. Theory. Journal of Fluid Mechanics, 59 (1). pp. 23-46. ISSN 0022-1120. doi:10.1017/S0022112073001400.

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The problem of forced acoustic oscillations in a pipe is studied theoretically. The oscillations are produced by a moving piston in one end of the pipe, while a variety of boundary conditions ranging from a completely closed to a completely open mouth at the other end are considered. All these boundary conditions are modelled by two parameters: a length correction and a reflexion coefficient equivalent to the acoustic impedance. The linear theory predicts large amplitudes near resonance and nonlinear effects become crucially important. By expanding the equations of motion in a series in the Mach number, both the amplitude and wave form of the oscillation are predicted there. In both the open- and closed-end cases the need for shock waves in some range of parameters is found. The amplitude of the oscillation is different for the two cases, however, being proportional to the square root of the piston amplitude in the closed-end case and to the cube root for the open end.

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Additional Information:© 1973 Cambridge University Press. Received 11 September 1972 and in revised form 5 February 1973. Published online: 29 March 2006. This work was motivated by the experiments on nonlinear resonance being conducted by Professor B. Sturtevant of this Institute. The experimental results will be reported in subsequent parts of this series. The work was supported in part by a contract with the office of Naval Research (N00014-67-A-0094-0014) and a grant from the National Aeronautics and Space Administration (NGR 05-002-220) and the author was supported partially by a fellowship from the European Space Research Organization.
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Office of Naval Research (ONR)N00014-67-A-0094-0014
NASANGR 05-002-220
European Space Research OrganizationUNSPECIFIED
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ID Code:32924
Deposited By: Tony Diaz
Deposited On:03 Aug 2012 22:34
Last Modified:09 Nov 2021 21:31

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