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A Simplified Theory of Oscillating Aerofoils in Transonic Flow: Review and Extension*

Published online by Cambridge University Press:  07 June 2016

E.H. Dowell
E.H. Dowell*
Affiliation:
Princeton University
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Summary

Significant new results are presented to show to what extent a simplified theory for transonic flow may be used. Solutions are obtained by classical techniques and compared with experiment. Results are given for two-dimensional and three-dimensional, steady and unsteady flow. The effects of flow separation and improvements in Bernoulli’s equation and the surface boundary condition are also briefly discussed.

Type
Research Article
Information
Aeronautical Quarterly , Volume 31 , Issue 4 , November 1980 , pp. 252 - 284
Copyright
Copyright © Royal Aeronautical Society. 1980

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Footnotes

*

This work was supported by NASA Grant NSG-2194 with the Ames Research Center. It is a substantial revision of a paper presented at the AIAA Dynamic Specialists Conference, San Diego, March 1977.

References

1 Stahara, S.S. and Spreiter, J.R., Development of a Nonlinear Unsteady Transonic Flow Theory, NASA CR-2258, June 1973.Google Scholar
2 Oehem, K.H. and Teipel, I., Eine Erweiterung der Parabolischen Methode zur Berechnung schallnaher StrSmungen, Zeitschrift fur Flugwissenschaften 22, Helft 9, 1974, pp 307–313.Google Scholar
3 Rubbert, p. and Landahl, M., Solution of the Transonic Aerofoil Problem through Parametric Differentiation, AIM Journal, Vol. 5, No. 3, 1967, pp 470–479.Google Scholar
4 Beam, R.M. and Warming, R.F.. Numerical Calculations of Two-Dimensional Unsteady Transonic Flows with Circulation, NASA TN D-7605, February 1974.Google Scholar
5 Weatherill, W.H., Sebastian, J.D. and Ehlers, F.E., On the Computation of the Transonic Perturbation Flow Fields Around Two- and Three-Dimensional Oscillating Wings, AIAA Paper 76-99, January 1976 Google Scholar
6 Traci, R.M., Albano, E.D. and Farr, J.L., Small-Disturbance Transonic Flows about Oscillating Airfoils and Planar Wings, AFFDL-TR-75-10, June 1975.Google Scholar
7 Magnus, R. and Yoshihara, H., The Transonic Oscillating Flap, AIAA Paper 76-327, July 1976.Google Scholar
8 Caradonna, F.X. and Isom, M.P., Numerical Calculation of Unsteady Transonic Potential Flow over Helicopter Rotor Blades, AIAA Journal, Vol. 14, No. 4, 1976, pp 482–488.Google Scholar
9 Ballhaus, W.F. and Goorjian, P.M., Implicit Finite-Difference Computations of Unsteady Transonic Flows About Airfoils, Including the Treatment of Irregular Shock-Wave Motions, AIAA Paper 77-205, January 1977.Google Scholar
10 Isogai, K., Calculation of Unsteady Transonic Flow Over Oscillating Airfoils Using the Full Potential Equation, to be presented at AIAA Dynamic Specialists Conference, San Diego, March 1977.Google Scholar
11 Goodman, T.R.. An Integral Approach to Lifting Wing Theory at Mach One, Journal of Engineering Mathematics, Vol. 10, No. 3, 1976, pp 243–261.CrossRefGoogle Scholar
12 Cunningham, A.M. Jr. Further Developments in the Prediction of Oscillatory Aerodynamics in Mixed Transonic Flow, AIAA Paper 75-99, January 1975.Google Scholar
13 Dowell, E.H., A Simplified Theory of Oscillating Airfoils in Transonic Flow, Proceedings of the Symposium on Unsteady Aerodynamics U. of Arizona, Tucson, Vol. II, pp 655–679, 1975.Google Scholar
14 Park, P.C., Unsteady Two-Dimensional Flow Using Dowell’s Method, AIAA Journal, Vol. 14, No. 10, 1976, pp 1345-1346.Google Scholar
15 Goldstein, M.E., Braun, W. and Adamczyk, J.J., Unsteady Flow in a Supersonic Cascade with Strong In-Passage Shocks, J. Fluid Mechanics, Vol. 83, No. 3, 1977, pp 569–604.CrossRefGoogle Scholar
16 Williams, M.H., Unsteady Thin Airfoil Theory for Transonic Flows with Embedded Shocks, Princeton University MAE Report No. 1376, May 1978.Google Scholar
17 Bisplinghoff, R.L. and Ashley, H., Principles of Aeroelasticity, John Wiley and Sons, Inc., New York, 1962.Google Scholar
18 Landahl, M., Unsteady Transonic Flow, Pergamon Press, London, 1961.Google Scholar
19 Knechtel, E.D., Experimental Investigation at Transonic Speeds of Pressure Distributions Over Wedge and Circular-Arc Airfoil Sections and Evaluation of Perforated-Wall Interference, NASA TN D-15, August 1959.Google Scholar
20 Spreiter, J.R. and Alksne, A.Y., Thin Airfoil Theory Based on Approximate Solution of the Transonic Flow Equation, NACA TN 3970, 1957 Google Scholar
21 Isogai, K., Unsteady Transonic Flow Over Oscillating Circular Arc Airfoils, AIAA Paper No. 74-360, 1974.Google Scholar
22 Sills, J.A., Relaxation Solutions for Inviscid Transonic Airfoil Flow Fields, ERR-HT-1359, General Dynamics, Convair Aerospace Division, December 1972.Google Scholar
23 Sisto, F. and Perumal, P.V.K., Lift and Moment Prediction for an Oscillating Airfoil with a Moving Separation Point, ASME Paper No. 74-GT-28, Journal of Engineering for Power, 1974.Google Scholar
24 Garner, H.C., A Practical Approach to the Prediction of Oscillatory Pressure Distributions on Wings in Supercritical Flow, RAE Technical Report 74181, February 1975.Google Scholar
25 Rowe, W.S., Redman, M.C., Ehlers, F.E. and Sebastian, J.C., Prediction of Unsteady Aerodynamic Loadings Caused by Leading Edge and Trailing Edge Control Surface Motions in Subsonic Compressible Flow-Analysis and Results, NASA CR-2543, August 1975.Google Scholar
26 Liepman, H.W. and Roshko, A., Elements of Gas Dynamics, John Wiley & Sons, Inc. 1957.Google Scholar
27 Watkins, C.E. and Berman, J.H., Air Forces and Moments on Triangular and Related Wings with Subsonic Leading Edges Oscillating in Supersonic Potential Flow, NACA Report 1099, 1952.Google Scholar
28 Watkins, C.E. and Berman, J.H., Velocity Potential and Air Forces Associated with a Triangular Wing in Supersonic Flow, with Subsonic Leading Edges, and Deforming Harmonically According to a General Quadratic Equation, NACA TN 3009, 1953.Google Scholar
29 Donato, V.W. and Huhn, C.R. Jr. Supersonic Unsteady Aerodynamics for Wings with Trailing Edge Control Surfaces and Folded Tips, AFFDL-TR-68-30, Air Force Flight Dynamics Laboratory, 1968.Google Scholar
30 Williams, M.H., The Resolvent of Singular Integral Equations, Quarterly of Applied Mathematicst Vol. 35, 1977, pp 99–110.CrossRefGoogle Scholar