Abstract
Despite the intensive development of computer technology and methods of solving the Navier-Stokes and Reynolds equations, the unsteady problems of the three-dimensional boundary layer are of significant interest in aerodynamics. So far these problems have been little studied as a result of objective difficulties related with the large dimensionality of the system of equations and the complexity of its investigation [{xc1}]. Therefore, analytic results in this field are important. In the present study the unsteady three-dimensional boundary layer equations are investigated in the case of small cross flows using the perturbation method. An intermediate system of equations, which includes the basic three-dimensional effects but is significantly simpler than the initial system is derived. The features of the formulation considered are studied in relation to the important practical problems of boundary layer flow past slender wings and weakly asymmetric bodies at small angles of attack.
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References
D.P. Telionis, Unsteady Viscous Flows (Springer, N.Y., 1981).
P.D. Smith, “Numerical Calculation of Three-Dimensional Boundary Layer,” in Three-Dimensional Turbulent Boundary Layers, Ed. by H. Fernholts and E. Krause (Springer-Verlag, Berlin-Heidelberg-N. Y., 1982), 257–275.
V.V. Struminskii, Aerodynamics and Molecular Gas Dynamics (Nauka, Moscow, 1985) [in Russian].
F.K. Moore, “Theory of Three-Dimensional Boundary Layers,” in Advances in Applied Mechanics, Vol. 4, Ed. by H. Dryden and T. von Kármán (Acad. Press, N.Y., 1956), 159–228.
V.Ya. Neiland, V.V. Bogolepov, G.N. Dudin, and I.I. Lipatov, Asymptotic Theory of Supersonic Viscous Gas Flows (Fizmatlit, Moscow, 2004) [in Russian].
A. Mager, “Three-Dimensional Laminar Boundary Layers,” in Theory of Laminar Flows, Ed. by F. K. Moore (Princeton University Press, Princeton, 1964), 286–394.
E.A. Eichelbrenner, “Three-Dimensional Boundary Layers,” Ann. Rev. Fluid Mech. 5, 339–360 (1973).
J.C. Cooke, “An Axially Symmetric Analogue for General Three-Dimensional Boundary Layers,” Atronaut. Rts. Council. Rept. and Mem., No. 3200 (1961).
A.D. Khon'kin and V.I. Shalaev, “Laminar Non-Separated Flow Past Slender Bodies,” Tr. TsAGI, No. 2265, 95–112 (1985).
T.K. Fannelöp, “A Method of Solving the Three-Dimensional Laminar Boundary-Layer Equations with Application to a Lifting Re-Entry Body,” AIAA Journal 6, No. 6, 1075–1084 (1968).
Yu.D. Shevelev, Three-Dimensional Problems of the Theory of the Laminar Boundary Layer (Nauka, Moscow, 1977) [in Russian].
V.I. Shalaev, “Boundary Layer on Slender Wings in a Supersonic Gas Flow,” in Numerical Methods of Continuum Mechanics, Vol. 17, No. 5 (Siberian Branch of the Academy of Sciences of the USSR, ITPM, Novosibirsk, 1986) [in Russian], 127–134.
V.I. Shalaev, “Boundary Layer on Quasi-Cylindrical Surfaces,” in Abstracts of 4th All-Union School “Methods of Aerophysical Research” (Siberian Branch of the Academy of Sciences of the USSR, ITPM, Novosibirsk, 1986) [in Russian], 69.
V.I. Shalaev, “Three-Dimensional Boundary Layer on Slender Wings and Bodies at Small Angles of Attack,” in Simulation in Mechanics, Vol. 2(19), No. 5 (Siberian Branch of the Academy of Sciences of the USSR, ITPM, Novosibirsk, 1988) [in Russian], 148–153.
A.D. Khon'kin and V.I. Shalaev, “Three-Dimensional Boundary Layer on Slender Wings of Finite Span,” Dokl. Akad. Nauk SSSR 307, No. 2, 312–315 (1989).
V.I. Shalaev, “Boundary Layer on Slender Short-Span Wings,” Zh. Prikl. Mekh. Tekh. Phys., No. 1, 71–78 (1992).
V.V. Lunev and E.A. Senkevich, “Method of Meridional Sections in Problems of a Three-Dimensional Boundary Layer,” Fluid Dynamics, 21, 394–400 (1986).
A.D. Khon'kin and V.I. Shalaev, “Three-Dimensional Boundary Layer on Bodies with Slight Cross-Section Asymmetry at Small Angles of Attack,” Dokl. Akad. Nauk SSSR, 313, No. 5, 1067–1071 (1990).
V.I. Shalaev, “Unsteady Boundary Layer with Small Three-Dimensional Perturbations,” in Investigation of Certain Problems of Aerodynamics and Dynamics of Aircraft Flight (Moscow Physical and Technical Institute, Moscow, 1989) [in Russian], 67–74.
M.D. Van Dyke, “Higher Approximations in Boundary Layer Theory. P. 2. Application to leading edges,” J. Fluid Mech. 14, Pt. 4, 481–495 (1962).
M.A. Hislet and G. Lomax, “Theory of Small Perturbations at Supersonic and Transonic Flight Speeds,” in High Speed Aerodynamics and Jet Propulsion. Vol. 6. General Theory of High Speed Aerodynamics. Chapter D, Ed. by W. R. Sears (Princeton Univ. Press, Princeton, New Jersey, 1961).
M.D. Van Dyke, Perturbation Methods in Fluid Mechanics (Academic Press, New York, 1964).
G. Gess and S. Folkner, “Exact Power Values Determining a Potential Flowfield over Semi-Infinite Cones,” AIAA J. 3, No. 4, 239–240 (1965).
A.V. Voevodin and G.G. Sudakov, “Solution of the Problem of Ideal Fluid Flow in the Neighborhood of Apexes of Bodies andWings,” Zh. Prikl. Mekh. Tekh. Phys., No. 3, 60–63 (1990).
L.P. Howart, “The Boundary Layer in Three-Dimensional Flow. II. The Flow near a Stagnation Point,” Philosophical Magazine, Ser. VII 42, 1433–1440 (1951).
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Original Russian Text © V.I. Shalaev, 2007, published in Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, 2007, Vol. 42, No. 3, pp. 71–83.
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Shalaev, V.I. Unsteady boundary layers with small cross flows. Fluid Dyn 42, 398–409 (2007). https://doi.org/10.1134/S0015462807030088
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DOI: https://doi.org/10.1134/S0015462807030088