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Linear potential theory of steady internal supersonic flow with quasi-cylindrical geometry. Part 1. Flow in ducts

Published online by Cambridge University Press:  26 April 2006

Andreas Dillmann
Deutsche Forschungsanstalt für Luft- und Raumfahrt, Bunsenstraße 10, D-37073 Göttingen, Germany


Based on linear potential theory, the general three-dimensional problem of steady supersonic flow inside quasi-cylindrical ducts is formulated as an initial-boundary-value problem for the wave equation, whose general solution arises as an infinite double series of the Fourier–Bessel type. For a broad class of solutions including the general axisymmetric case, it is shown that the presence of a discontinuity in wall slope leads to a periodic singularity pattern associated with non-uniform convergence of the corresponding series solutions, which thus are unsuitable for direct numerical computation. This practical difficulty is overcome by extending a classical analytical method, viz. Kummer's series transformation. A variety of elementary flow fields is presented, whose complex cellular structure can be qualitatively explained by asymptotic laws governing the propagation of small perturbations on characteristic surfaces.

Research Article
© 1994 Cambridge University Press

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