Abstract
The two-dimensional flow of a viscous incompressible fluid near the leading edge of a slender airfoil is considered. An asymptotic theory of this flow is constructed on the basis of an analysis of the Navier—Stokes equations at large Reynolds numbers by means of matched asymptotic expansions. A central feature of the theory is the region of interaction of the boundary layer and the exterior inviscid flow; such a region appears on the surface of the airfoil in a definite range of angles of attack. The boundary-value problem for this region is reduced to an integrodifferential equation for the distribution of the friction. This equation has been solved numerically. As a result, closed separation regions are constructed, and the angle of attack at which separation occurs is found.
Similar content being viewed by others
Literature cited
Incompressible Aerodynamics, Clarendon Press, Oxford (1960), p. 636.
I. Tani, “Low-speed flows involving bubble separations,” Prog. Aeronaut. Sci.,5, Pergamon Press, Oxford (1964).
R. N. Herring and W. L. Ely, “Laminar leading edge stall prediction for thin airfoils,” AIAA Paper, No. 1222, 12 (1978).
V. V. Sychev, “Laminar separation,” -Izv. Akad. Nauk SSSR, Mekh. Zhidk. Gaza., No. 3, 47 (1972).
V. Ya. Neiland, “Theory of separation of a laminar boundary layer in a supersonic stream,” Izv. Akad. Nauk SSSR, Mekh. Zhidk. Gaza, No. 4, 53 (1969).
K. Stewartson and P. G. Williams, “Self-induced separation,” Proc. R. Soc. London Sect. A,312, 181 (1969).
V. Ya. Neiland, “Asymptotic problems in the theory of viscous supersonic flows,” Tr. TsAGI, No. 1529, 124 (1974).
K. Stewartson, “Multistructured boundary layers on flat plates and related bodies,” Adv. Appl. Mech.,14, 145 (1974).
A. I. Ruban and V. V. Sychev, “Asymptotic theory of the separation of a laminar boundary layer in an incompressible fluid,” Usp. Mekh.,2, 57 (1979).
A. I. Ruban, “Singular solution of boundary-layer equations that can be extended continuously through a point of zero surface friction,” Izv. Akad. Nauk SSSR, Mekh. Zhidk. Gaza, No. 6, 63 (1981).
J. D. Cole, Perturbation Methods in Applied Mathematics, Blaisdell, Waltham, Mass. (1968).
M. D. Van Dyke, “Second-order subsonic airfoil theory including edge effects,” NACA Report, No. 1274, 23 (1956).
X. Stewartson, “Is the singularity at separation removable?” J. Fluid Mech.,44, 347 (1970).
G. N. Watson, A Treatise on the Theory of Bessel Functions, Cambridge (1922).
Author information
Authors and Affiliations
Additional information
Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 1, pp. 42–51, January–February, 1981.
I thank V. V. Sychev and Vik. V, Sychev for assistance.
Rights and permissions
About this article
Cite this article
Ruban, A.I. Asymptotic theory of short separation regions on the leading edge of a slender airfoil. Fluid Dyn 17, 33–41 (1982). https://doi.org/10.1007/BF01090696
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF01090696