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The Quarterly Journal of Mechanics and Applied Mathematics 1954 7(2):247-256; doi:10.1093/qjmam/7.2.247
© 1954 by Oxford University Press
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UNSTEADY COMPRESSIBLE FLOW IN DUCTS

W. CHESTER

( Department of Mathematics, The University Bristol )

A rarefaction wave is produced in a two-dimensional channel by the impulsive retraction of a piston. In a finite section of the channel there is a slight variation in cross-section, and the effect of this variation on the rarefaction wave is considered. It is found that, after passing through the transition section, a perturbation is superimposed on the main wave which tends to decrease the flow velocity by a term which decreases inversely as the time for a point moving with the wave, but increases linearly with the time at a fixed point in the channel. In the transition section the disturbances accumulate and tend to increase the flow velocity if there is a throat, eventually producing a sonic régime. An attempt is made to describe the establishment of steady subsonic-supersonic flow in a converging-diverging nozzle.


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