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The oblique wing as a lifting-line problem in transonic flow

Published online by Cambridge University Press:  19 April 2006

H. K. Cheng  and
S. Y. Meng
H. K. Cheng
Affiliation:
Department of Aerospace Engineering, University of Southern California, Los Angeles, California 90007
S. Y. Meng
Affiliation:
Department of Aerospace Engineering, University of Southern California, Los Angeles, California 90007
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Abstract

A transonic-flow theory of thin, oblique wing of high aspect ratio is presented, which permits a delineation of the influence of wing sweep, the centre-line curvature, and other three-dimensional (3D) effects on the nonlinear mixed flow in the framework of small-disturbance theory. In the (parameter) domain of interest, the flow field far from the wing section pertains to a high subsonic, or linear sonic, outer flow, representable by a Prandtl–Glauert solution involving a swept, as well as curved, lifting line in the leading approximation.

Among the 3D effects is one arising from the compressibility correction to the velocity divergence, absent in classical works; this effect also leads to a correction in the outer flow in the form of an oblique line source. More important is the upwash corrections which includes the influence of both the near and far wakes, as well as the local curvature of the centre-line. For straight oblique wings, local similarities exist in the 3D flow structure, permitting the reduced equations to be solved once for all span stations. An analogy also exists between the oblique-wing problem and that of a 2D transonic flow which is weakly time-dependent; this provides an alternative method of solving numerically the inner airfoil problem.

Solutions to the reduced problem are demonstrated and compared with full-potential solutions for elliptic oblique wings involving high subcritical as well as slightly supercritical component flows.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 97 , Issue 3 , 15 April 1980 , pp. 531 - 556
Copyright
© 1980 Cambridge University Press

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References

Ashley, H. & Landahl, M. 1965 Aerodynamics of Wings & Bodies, pp. 137–142 and 227–244.
Ballhaus, W. F. & Goorjian, P. M. 1977 A.I.A.A. J. 15, 1728–1735.
Bauer, F., Garabedian, P., Korn, D. & Jameson, A. 1974 Supercritical Wing Section. II. Lectures notes in economics and mathematical systems, no. 108. Springer.
Boerstoel, J. W. 1974 Nat. Aerosp. Lab. Rep. NLRMP 74024 U. Amsterdam.
Busemann, A. 1935 Luftfahrtforschung 12, part 6.
Cheng, H. K. 1976 Univ. So. Calif., School Engng, Dept. Aerosp. Engng Rep. USCAE 133.
Cheng, H. K. 1978a A.I.A.A. J. 16, 1211–1213.
Cheng, H. K. 1978b Univ. So. Calif., School Engng, Dept. Aerosp. Engng Rep. USCAE 135.
Cheng, H. K. & Hafez, M. M. 1975 J. Fluid Mech. 72, 161–187.
Cheng, H. K. & Meng, S. Y. 1979a A.I.A.A. J. 17, 121–124.
Cheng, H. K. & Meng, S. Y. 1979b Univ. So. Calif., School Engng, Dept. Aerosp. Engng Rep. USCAE 136.
Cole, J. D. 1975 SIAM J. Appl. Math. 29, 763–787.
Cook, P. 1978 Indiana Univ. Math. J. 27, no. 1.
Cook, P. 1979 Quart. Appl. Math., July, 178–202.
Cook, P. & Cole, J. D. 1978 SIAM J. appl. Math. 35, 209–224.
Courant, R. & Hilbert, D. 1965 Methods of Mathematical Physics. II. pp. 551–556.
Ehlers, F. E. 1974 N.A.S.A. Rep. CR-2257.
Fung, K. Y., Yu, N. J. & Seebass, R. 1978 A.I.A.A. J. 16, 815–822.
Hafez, M. M. & Cheng, H. K. 1977a A.I.A.A. J. 15, 329–331.
Hafez, M. M. & Cheng, H. K. 1977b A.I.A.A. J. 15, 786–793.
Hafez, M. M., Rizk, X. & Murman, E. M. 1977 Proc. AGARD Unsteady Transonic & Separated Flows, Lisbon, Portugal.
Jameson, A. 1974 Comm. Pure Appl. Math. 27, 283–309.
Jameson, A. & Caughey, D. A. 1977 New York Univ. ERDA Rep. C00 3077-140.
Jones, R. T. 1946 N.A.C.A. Rep. no. 851.
Jones, R. T. 1971 A.I.A.A. J. 10, 171–176.
Jones, R. T. 1977 Acta Aeronautica 4, 99–110.
Jones, R. T. & Cohen, D. 1957 Aerodynamics of Wings at High Speed. In Aerodynamic Components of Aircraft at High Speed (ed. D.F. Donovan & H. R. Lawrence), pp. 3–236. Princeton University Press.
Kacprzynski, J. J., Ohman, L. H., Garabedian, P. R. & Korn, D. G. 1971 Nat. Res. Counc. Canada, Aero. Rep. LR-554.
Küchemann, N. D. 1969 Aeronautical J. 73, 101–110.
Landahl, M. 1962 Symposium Transsonicum, pp. 414–439.
Murman, E. M. 1974 A.I.A.A. J. 12, 626–633.
Murman, E. M. & Cole, J. D. 1971 A.I.A.A. J. 9, 114–121.
Murman, E. M. & Krupp, J. A. 1971 Proc. 2nd Int. Conf. Numerical Methods in Fluid Dynamics, Lecture notes in physics, vol. 8, pp. 199–206. Springer.
Nieuwland, G. Y. 1967 NLR (Neth.) Tech. Rep. T 172.
Oswatitsch, K. 1962 Symposium Transsonicum, pp. 402–413.
Oswatitsch, K. & Zierep, J. 1960 Z. angew. Math. Mech. Suppl. 40, 143–144.
Prandtl, L. 1918 Nachrichten d.k. Gesellschaft d. Wiss. zu Göttingen. Math-Phys. Klasse, pp. 451–477.
Sprieter, J. R. 1953 N.A.C.A. Rep. 1153.
Timman, R. 1962 Symposium Transsonicum, pp. 394–401.
Traci, R. M., Albano, E. D. & Farr, J. L. 1976 A.I.A.A. J. 4, 1258–1265.
Van dyke, M. D. 1964 Perturbation Methods in Fluid Mechanics, pp. 167–176. Academic.
Whitcomb, R. T. 1974 Paper presented at the 9th Int. Congr. Aero. Sci., Haifa, Israel.
Williams, M. H. 1979 A.I.A.A. J. 17, 394–397.