Airfoil Design in Subcritical and Supercritical Flows

[+] Author and Article Information
W. C. Chin, D. P. Rizzetta

Aerodynamics Research Group, Boeing Commercial Airplane Co., Mail Stop 3N-29, P. O. Box 3707, Seattle, Wash. 98124

J. Appl. Mech 46(4), 761-766 (Dec 01, 1979) (6 pages) doi:10.1115/1.3424650 History: Received February 01, 1979; Revised May 01, 1979; Online July 12, 2010


The “inverse” or “design” problem in aerodynamics, which solves for the airfoil shape that induces a prescribed chordwise surface pressure subject to additional requirements on trailing edge closure, is considered in the transonic small-disturbance limit. A new formulation for the stream function ψ is suggested which uses well-set Neumann conditions on the chordwise slit, with the degree of closure dictated by a specified jump in ψ across the downstream slit emanating from the trailing edge. The boundary-value problem is solved by a type-dependent relaxation method that automatically generates closed airfoils on convergence. Computed airfoil shapes using subcritical and supercritical pressure distributions obtained from existing finite-difference analysis codes, in the latter case, with and without shockwaves, give results in reasonable agreement with the original specified shapes, and validate the basic ideas.

Copyright © 1979 by ASME
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