Hostname: page-component-848d4c4894-4rdrl Total loading time: 0 Render date: 2024-06-17T06:19:52.809Z Has data issue: false hasContentIssue false
  • English
  • Français

A unified unsteady lifting-line theory

Published online by Cambridge University Press:  26 April 2006

Jean-Luc Guermond  and
Antoine Sellier
Jean-Luc Guermond
Affiliation:
Bassin d'Essais des Carènes, 6 Bd Victor, 75 732, Paris, France Present address: LIMSI-CNRS, BP 133, 91403 Orsay cedex, France.
Antoine Sellier
Affiliation:
Bassin d'Essais des Carènes, 6 Bd Victor, 75 732, Paris, France Present address: LADHYX, Ecole Polytechnique, 91128 Palaiseau, France.
Get access Rights & Permissions [Opens in a new window]

Abstract

A lifting-line theory is developed for wings of large aspect ratio oscillating in an inviscid fluid. The theory is unified in the sense that the wing may be curved or inclined to the flow, and the asymptotic expansion is uniformly valid with respect to the frequency. The method is based on the integral equation formulation of the problem. The technique, pioneered by Kida & Miyai (1978). consists of asymptotically solving the Fredholm equation of the first kind which links the unknown pressure jump and the normal velocity imposed on the wing. Use of the finite-part integral theory introduced by Hadamard (1932) and of a technique developed in Guermond (1987, 1988, 1990) yields an asymptotic expansion of the surface integral in terms of the inverse of the aspect ratio. At each approximation order, the problem reduces to a classical two-dimensional integral equation, whose unknown is the pressure jump, and whose right-hand side depends only on the previous approximation orders of the solution. The first finite-span correction is explicitly calculated. An extensive numerical study is carried out, and comparisons with published results are made.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 229 , August 1991 , pp. 427 - 451
Copyright
© 1991 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

Benjamin, T. B. 1968 Gravity currents and related phenomena. J. Fluid Mech. 31, 209–248.Google Scholar
Bradshaw, P. 1966 The effect of initial conditions on the development of a free shear layer. J. Fluid Mech. 26, 225–236.Google Scholar
Bradshaw, P. 1977 Effect of external disturbances on the spreading rate of a plane jet. J. Fluid Mech. 80, 795–797.Google Scholar
Flora, J. & Goldschmidt, V. 1969 Virtual origins of a free plane turbulent jet. AIAA J. 7, 2344–2346.Google Scholar
Foss, J. F. & Jones, J. B. 1968 Secondary flow effects in a bounded rectangular jet. Trans. ASME D: J. Basic Engng 90, 241–248.Google Scholar
Giger, M. 1987 Der ebene Freistrahl in flachem Wasser. Rep. 26–87. Institut fur Hydromechanik und Wasserwirtschaft ETH Zurich.Google Scholar
Goldschmidt, V. 1964 Two phase flow in a two-dimensional turbulent jet. Ph.D. thesis, Syracuse University.
Goldschmidt, V. & Bradshaw, P. 1981 Effect of nozzle exit turbulence on the spreading (or widening) rate of plane free jets. ASME Publications 81–FE–22.Google Scholar
Goldschmidt, V. & Eskinazi, S. 1966 Two phase turbulent flow in a plane jet. Trans. ASME E: J. Appl. Mech. 33, 735–747.Google Scholar
Goldschmidt, B., Moallemi, M. K. & Oler, J. W. 1983 Structures and flow reversal in turbulent plane jets. Phys. Fluids 26, 428–432.Google Scholar
Gutmark, E. & Wygnanski, I. J. 1976 The planar turbulent jet. J. Fluid Mech. 73, 465–495.Google Scholar
Heskestad, G. 1965 Hot wire measurements in a plane turbulent jet. Trans. ASME E: J. Appl. Mech. 32, 721–734 (and corrigendum 33 (1966), 710).Google Scholar
Hussain, A. K. M. F. & Clark, A. R. 1977 Upstream influence on the near field of a plane turbulent jet. Phys. Fluids 20, 1416–1426.Google Scholar
Kotsovinos, N. E. 1975 A study of the entrainment and turbulence in a plane buoyant jet. W. M. Keck Lab., Hydraul. Water Resources, CIT Rep. KH-R-32.Google Scholar
Kotsovinos, N. E. 1976 A note on the spreading rate and virtual origin of a plane turbulent jet. J. Fluid Mech. 77, 305–312.Google Scholar
Kotsovinos, N. E. 1978a A note on the conservation of the volume flux in free turbulence. J. Fluid Mech. 86, 201–203.Google Scholar
Kotsovinos, N. E. 1978b A note on the conservation of the axial momentum of a turbulent jet. J. Fluid Mech. 87, 55–63.Google Scholar
Kraemer, K. 1971 Die Potentialstromung in der Umgebung von freistrahlen. Z. Flugwiss. 19, 93–103.Google Scholar
Liepmann, H. W. & Laufer, J. 1947 Investigations of free turbulent mixing. NACA Tech. Note 1257.Google Scholar
Lippisch, A. 1958 Flow visualization. Aeronaut. Engng Rev. 17(2), 24–36.Google Scholar
List, E. J. 1982a Turbulent jets and plumes. Ann. Rev. Fluid Mech. 14, 189–212.Google Scholar
List, E. J. 1982b Mechanics of turbulent buoyant jets and plumes. In The Science and Application of Heat and Mass Transfer, Vol. 8 (ed. W. Rodi). Pergamon.
Miller, D. R. 1957 Static pressure distribution in free turbulent jet mixing. Ph.D. thesis, Purdue University.
Miller, D. R. & Comings, E. W. 1957 Static pressure distribution in the free turbulent jet. J. Fluid Mech. 3, 1–16.Google Scholar
Rajaratnam, N. 1976 Turbulent jets. Elsevier.
Rodi, W. 1975 A review of experimental data of free turbulent boundary layers. In Studies in Convection, Theory, Measurements and Applications (ed. B. E. Launder). Academic.
Schlichting, H. 1960 Boundary Layer Theory, 4th edn. McGraw-Hill.
Schneider, W. 1981 Flow induced by jets and plumes. J. Fluid Mech. 108, 55–65.Google Scholar
Schneider, W. 1985 Decay of momentum flux in submerged jets. J. Fluid Mech. 154, 91–110.Google Scholar
Stewart, R. W. 1956 Irrotational motion associated with free turbulent flows. J. Fluid Mech. 1, 593–604.Google Scholar
Taylor, G. I. 1958 Flow induced by jets. J. Aero. Sci. 25, 464–465.Google Scholar
Townsend, A. A. 1976 The Structure of Turbulent Shear Flow. Cambridge University Press.
Van Dyke, M. 1982 An Album of Fluid Motion. The Parabolic Press.
Wygnanski, I. 1964 The flow induced by two dimensional and axisymmetric turbulent jets issuing normally from an infinite plane surface. Aeron. Q. 15, 373–380.Google Scholar