Abstract
A solution to the problem of local separation of a three-dimensional boundary layer from an arbitrary smooth surface is constructed. Separation takes place along the limiting streamline at the points of which the component of the surface friction (calculated from the boundary-layer equations) that is orthogonal to this streamline has a break. An asymptotic expansion of the solution of the Navier-Stokes equations that describes the flow field in the separation region is found. The conclusions for the two-dimensional and self-similar theory of local separation are generalized to the three-dimensional case.
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Literature cited
M. Tobak and D. J. Peake, “Topology of three-dimensional separated flows,” Ann. Rev. Fluid Mech.,14, 61 (1982).
E. C. Maskell, “The significance of flow separation in the calculation of a general fluid flow,” Ninth Congr. Int. Mecanique. Appl., Vol. 3, Brussels (1957), p. 226.
M. J. Lighthill, Laminar Boundary layers, Oxford University Press, Oxford (1963), Chap. 2, p. 79.
A. I. Ruban, “A singular solution of the boundary-layer equations that can be continuously extended through a point of zero surface friction,” Izv. Akad. Nauk SSSR, Mekh. Zhidk. Gaza, No. 6, 42 (1981).
A. I. Ruban, “Asymptotic theory of short separation regions at the leading edge of a slender airfoil,” Izv. Akad. Nauk SSSR, Mekh. Zhidk. Gaza, No. 1, 42 (1982).
S. N. Brawn, “Singularities associated with separating boundary layers,” Philos. Trans. R. Soc. London, Ser. A:25, 409 (1965).
J. Buckmaster, “Perturbation technique for the study of three-dimensional separation,” Phys. Fluids,15, 2106 (1972).
S. Goldstein, “On laminar boundary-layer flow near a position of separation,” Q. J. Mech. Appl. Math.,1, 43 (1948).
V. B. Zametaev, “Singular solution of boundary-layer equations on a thin cone,” Izv. Akad. Nauk SSSR, Mekh. Zhidk. Gaza, No. 2, 65 (1987).
V. B. Zametaev, “Local separation on a thin cone preceding the appearance of a vortex sheet,” Izv. Akad. Nauk SSSR, Mekh. Zhidk. Gaza, No. 6, 21 (1987).
V. B. Zametaev, “Formation of singularities in a three-dimensional boundary layer,” Izv. Akad., Nauk SSSR, Mekh. Zhidk. Gaza, No. 2, 58 (1989).
A. E. Perry and M. S. Chong, “A series-expansion study of the Navier-Stokes equations with applications to three-dimensional separation patterns,” J. Fluid Mech.,173, 207 (1986).
S. N., Brawn, “Marginal separation of a three-dimensional boundary layer on a line of symmetry,” J. Fluid Mech.,158, 95 (1985).
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Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 3, pp. 39–47, May–June, 1991.
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Vilenskii, G.G. Three-dimensional local separation. Fluid Dyn 26, 349–356 (1991). https://doi.org/10.1007/BF01059003
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DOI: https://doi.org/10.1007/BF01059003