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A first order theory for Newtonian flow over two-dimensional airfoils

Published online by Cambridge University Press:  04 July 2016

Hamdi T. Hemdan
Hamdi T. Hemdan*
Affiliation:
Mathematics Department, King Saud University, Riyadh, Saudi Arabia
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Summary

A simple closed-form formula for the coefficient of surface pressure, Cp is given in this paper. The formula is based on first and second approximations of the full problem and can be used for the Newtonian flow past two-dimensional thin airfoils at small angles of attack and with attached shock waves. It thus extends Cole's zero order theory to the effects of non-zero (γ – 1) and finite values of Mx where γ is the ratio of the specific heats of the gas and Mx is the free stream Mach number. The analysis presented relies on a previous recent formulation of the hypersonic small disturbance theory which has proved to be more advantageous than the hypersonic small disturbance theory. The results are compared with other approximate methods and the agreement is found to be generally good.

Type
Research Article
Information
The Aeronautical Journal , Volume 91 , Issue 910 , December 1987 , pp. 471 - 478
Copyright
Copyright © Royal Aeronautical Society 1987 

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References

1. Hayes, W. D. and Probstein, R. F. Hypersonic flow theory, 1966, 1, Academic Press, New York.Google Scholar
2. Chernyi, G. G. Introduction to hypersonic flow, Academic Press, New York, 1961.Google Scholar
3. Cole, J. D. and Aroesty, J. Hypersonic similarity solutions for airfoils supporting exponential shock waves, AlAA J, 1970, 8, 308–315.Google Scholar
4. Hui, W. H. A solution for hypersonic flow past slender bodies, JFM, 1971, 48, 23.Google Scholar
5. Hui, W. H. and Hemdan, H. T. Higher order similarity solutions tor hypersonic flow past airfoils, Proceedings of the symposium on symmetry, similarity and group theoretic methods in mechanics, University of Calgary, Canada, May 1974.Google Scholar
6. Cole, J. D. Newtonian Theory for Slender Bodies, J. of Aero Sciences, June 1957, 448–455.Google Scholar
7. Hui, W. H. On axisymmetric and two-dimensional flow with attached shock waves, Astronautica Acta, 1973, 18, 35–44.Google Scholar
8. Hemdan, H. T. A Newtonian theory for the compression surface of two-dimensional airfoils at moderate or large incidence, AlAA J, Sept 1987, 25.Google Scholar
9. Hemdan, H. T. Steady supersonic flow over Delta wings and Two-Dimensional Airfoils, L Aerotecnica Missili E Spazio, June 1986, 1-2, 36–45.Google Scholar
10. Hemdan, H. T. On Steady Supersonic Flow over Two- Dimensional Airfoils, Transactions of the Japan Society for Aeronautical and Space Sciences, 1987, 30, 111–129.Google Scholar
11. Hemdan, H. T. Dynamic stability of oscillating two-dimensional supersonic airfoils, L Aerotecnica Missili E Spazio, September 1986, 65, 3, 99–109.Google Scholar