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A note on ‘Lifting three-dimensional wings in transonic flow’ by M. S. Cramer

Published online by Cambridge University Press:  20 April 2006

M. S. Cramer
M. S. Cramer
Affiliation:
Department of Engineering Science and Mechanics, Virginia Polytechnic Institute and State University, Blacksburg, Virginia 24061
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Abstract

The purpose of this note is to clarify the discrepancy between the results of Cramer (1979), Barnwell (1975) and Cheng & Hafez (1975). These authors have all derived the boundary-value problem governing the flow far from a three-dimensional lifting wing in transonic flow. The results of both Cramer and Barnwell will provide the lowest-order solution in the far field. The results of Cheng & Hafez are not only accurate to lowest order but to first order as well. That is, the theory of Cheng & Hafez is an order-of-magnitude more accurate than those of Barnwell and Cramer. This is the reason for the discrepancy between the boundary condition derived by Cheng & Hafez and that of Cramer and Barnwell. Because Cheng & Hafez correctly derive the first-order results, the lowest-order theories of Cramer or Barnwell cannot correct those of Cheng & Hafez. It should be recognized that the main contribution of Cramer's work was to clarify the structure of the problem and to simplify the analysis rather than correct the basic results.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 109 , August 1981 , pp. 257 - 258
Copyright
© 1981 Cambridge University Press

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References

Barnwell, R. W. 1975 N.A.S.A. TR R-440.
Cheng, H. K. & Hafez, M. M. 1975 J. Fluid Mech. 72, 161–188.
Cramer, M. S. 1979 J. Fluid Mech. 95, 223–240.