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Transonic equivalence rule: a nonlinear problem involving lift

Published online by Cambridge University Press:  29 March 2006

H. K. Cheng  and
M. M. Hafez
H. K. Cheng
Affiliation:
University of Southern California, Los Angeles, California 90007
M. M. Hafez
Affiliation:
University of Southern California, Los Angeles, California 90007
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Abstract

The inviscid transonic flow past a thin wing having swept leading edges, with smooth lift and thickness distributions, is shown to possess an outer nonlinear structure determined principally by a line source and a line doublet. Three domains (the thickness-dominated, the intermediate, and the lift-dominated), representing different degrees of lift control of the outer flow, are identified; a transonic equivalence rule valid in all three domains is established. Except in one domain, departure from the Whitcomb-Oswatitsch area rule is significant; the equivalent body corresponding to the source effect has an increased cross-sectional area depending nonlinearly on the lift. This nonlinear lift contribution results from the second-order corrections to the inner (Jones) solution, but produces effects of first-order importance in the outer flow. Of interest is an afterbody effect dependent on the vortex drag, which is not accounted for by the classical transonic small-disturbance theory.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 72 , Issue 1 , 11 November 1975 , pp. 161 - 187
Copyright
© 1975 Cambridge University Press

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