Hostname: page-component-848d4c4894-8kt4b Total loading time: 0 Render date: 2024-06-17T15:55:27.775Z Has data issue: false hasContentIssue false
  • English
  • Français

Supercritical flow past symmetrical airfoils

Published online by Cambridge University Press:  20 April 2006

Kon-Ming Li  and
Maurice Holt
Kon-Ming Li
Affiliation:
Department of Mechanical Engineering, University of California, Berkeley, California
Maurice Holt
Affiliation:
Department of Mechanical Engineering, University of California, Berkeley, California
Get access Rights & Permissions [Opens in a new window]

Abstract

A numerical method is developed for computing steady supercritical flow about an ellipse at zero angle of attack. The flow is assumed to be two-dimensional, inviscid, isentropic and irrotational. The free-stream Mach number lies in the high subsonic range so that a shock wave occurs locally near the body. The full potential equations are solved by Telenin's method and the ‘method of lines’. Smooth interpolating functions are assumed for the unknown flow variables in selected co-ordinate directions. The resulting set of ordinary differential equations is then integrated away from or along the body depending upon whether the flow is smooth or discontinuous. Jump conditions of the governing equations are applied across the shock wave so that it is perfectly sharp. A doublet solution for flow past a closed body is used as the farfield boundary condition. Supercritical flow calculations have been performed for ellipses with thickness ratio of 0·2 and 0·4 at various free-stream Mach numbers. The present results are compared with the shock-capturing method, and good agreement is obtained.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 114 , January 1982 , pp. 399 - 418
Copyright
© 1972 Cambridge University Press

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Ballhaus, W. F., Jameson, A. & Albert, J. 1978 Implicit approximate factorization schemes for the efficient solution of steady transonic flow problems. A.I.A.A. J. 16, 573–579.Google Scholar
Bauer, F., Garabedian, P. & Korn, D. 1972 A Theory of Supercritical Wing Sections, with Computer Program and Examples. Lecture Notes in Economics and Mathematical Systems, vol. 66. Springer.
Boerstoel, J. W. 1967 A survey of symmetrical transonic potential flows around quasielliptical aerofoil sections. Nat. Rep. Aerospace Lab., Amsterdam. NRL TR T-136.Google Scholar
Busemann, A. 1949 The drag problem at high subsonic speeds. J. Aero. Sci. 16, 337–344.Google Scholar
Chattot, J. J. 1978 Symmetrical flow past a double wedge at high subsonic Mach numbers. J. Fluid Mech. 86, 161–177.Google Scholar
Chushkin, P. I. 1958 Subsonic flow of a gas past ellipses and ellipsoids. Vychislitel'naia Matematika 2, 20–24.Google Scholar
Fletcher, C. A. J. 1975 GTT method applied to cones at large angles of attack. Proc. 4th Int. Conf. on Numerical Methods in Fluid Dynamics (ed. R. D. Richtmyer). Lecture Notes in Physics, Vol. 35, pp. 161–166. Springer.
Frankl, F. I. 1950 On the formation of shocks in subsonic flows with local supersonic velocities. N.A.C.A. Tech. Memo. 1251 (translation).Google Scholar
Gilinskii, S. M., Telenin, G. F. & Tinyakov, G. P. 1964 A method of computing supersonic flow around blunt bodies, accompanied by a detached shock wave. Izv. Akad. Nauk, S.S.S.R. Mekh. Mash. 4, 9–28. (Also N.A.S.A. Tech. Transl. F297, 1965.)Google Scholar
Gross, M. B. & Holt, M. 1976 Steady supercritical flow past ellipses. IUTAM Symp. Transsonicum II, Göttingen, Germany, 1975 (ed. K. Oswatitsch & D. Rues), pp. 369–375. Springer.
Guderley, G. 1953 Shocks in subsonic — supersonic flow patterns. Adv. Appl. Mech. 3, 145–184.Google Scholar
Holst, T. L. 1979 Implicit algorithm for the conservative transonic full potential equation using an arbitrary mesh. A.I.A.A. J. 17, 1038–1045.Google Scholar
Holst, T. L. & Ballhaus, W. F. 1979 Fast, conservative schemes for the full potential equation applied to transonic flows. A.I.A.A. J. 17, 145–152.Google Scholar
Holt, M. 1977 Numerical Methods in Fluid Dynamics. Series in Computational Physics. Springer.
Holt, M. & Masson, B. S. 1971 The calculation of high subsonic flow past bodies by the method of integral relations. Proc. 2nd Int. Conf. on Numerical Methods in Fluid Mechanics (ed. M. Holt). Lecture Notes in Physics, vol. 8, pp. 243–251. Springer.
Jameson, A. 1974 Iterative solution of transonic flows over airfoils and wings, including flows at Mach 1. Comm. Pure Appl. Math. 27, 283–309.Google Scholar
Jones, D. C., South, J. C. & Klunker, E. B. 1972 On the numerical solution of elliptic partial differential equations by the method of lines. J. Comp. Phys. 9, 496–527.Google Scholar
Krupp, J. A. & Murman, E. M. 1972 Computation of transonic flows past lifting airfoils and slender bodies. A.I.A.A. J. 10, 880–881.Google Scholar
Magnus, R. & Yoshihara, H. 1970 Inviscid transonic flow over airfoils. A.I.A.A. J. 8, 2157–2162.Google Scholar
Milne-Thomson, L. M. 1972 Theoretical Hydrodynamics. Macmillan.
Morawetz, C. 1956 On the non-existence of continuous transonic flows past profiles. Part 1. Comm. Pure Appl. Math. 9, 45–68.Google Scholar
Morawetz, C. 1957 On the non-existence of continuous transonic flows past profiles. Part 2. Comm. Pure Appl. Math. 10, 107–131.Google Scholar
Murman, E. M. & Cole, J. D. 1971 Calculation of plane steady transonic flows. A.I.A.A. J. 9, 114–121.Google Scholar
Nieuwland, G. Y. 1967 Transonic potential flow around a family of quasi-elliptical aerofoil sections. Nat. Aerospace Lab., Amsterdam, Rep. NRL TR T-172.Google Scholar
Powell, M. J. D. 1964 A method for minimizing a sum of squares of nonlinear functions without calculating derivatives. Computer J. 7, 303–307.Google Scholar
Steger, J. L. & Lomax, H. 1972 Transonic flow about two-dimensional airfoils by relaxation procedures. A.I.A.A. J. 10, 49–54.Google Scholar
Tai, T. C. 1974 Transonic inviscid flow over lifting airfoils by the method of integral relations. A.I.A.A. J. 12, 798–804.Google Scholar