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Shocks and singularities in the pressure field of a supersonically rotating propeller

Published online by Cambridge University Press:  21 April 2006

C. J. Chapman
Affiliation:
Institute of Sound and Vibration Research, University of Southampton, Southampton S09 5NH, UK

Abstract

When linear acoustic theory is applied to the thickness noise problem of a supersonic propeller, it can give rise to a surface on which the pressure is discontinuous or singular. A method is described for obtaining the equation of this surface (when it exists), and the pressure field nearby; jumps, logarithms and inverse square roots occur, and their coefficients may be calculated exactly. The special case of a blade with a straight radial edge gives a cusped cone, whose sheets, each with a different type of discontinuity or singularity in pressure, are separated by lines of cusps; the coefficients in formulae for the pressure near the surface tend to infinity as a cusp line is approached, in proportion to the inverse quarter power of distance from the line. These results determine regions of space where nonlinear effects are important, and they suggest a strong analogy with sonic boom.

Type
Research Article
Copyright
© 1988 Cambridge University Press

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