Abstract—
Significantly inhomogeneous gas flow in the neighborhood of the lower surface of a plain delta wing at an angle of attack in hypersonic stream is considered. The most general case of narrow wing with the bow shock attached to the leading edge or detached from it is studied in the analytical solution of the problem obtained with the use of the asymptotic thin shock layer method. In the solution with the attached shock wave, “singular cross-sections” which are normal to the wing and have breaks of the stream surfaces due to the action of concentrated forces are found. Their input to the aerodynamic characteristics is evaluated. In flow with the detached shock, the distinctive feature of the solution relates to the formation of a thin entropy layer on the wing surface. In this layer the flow is formed under the action of the side pressure gradient. Examples of universal solutions valid for the flow description through the “external” main shock layer part and the “internal” entropy layer are constructed.
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REFERENCES
Chernyi, G.G., Introduction to Hypersonic Flow Theory, New York: Academic, 1961.
Hayes, W.D. and Probstein, R.F., Hypersonic Flow Theory, New York: Academic, 1959.
Lunyov, V.V., Giperzvukovaya aerodinamika (Hypersonic Aerodynamics), Moscow: Mashinostroenie, 1975.
Messiter, A.F., Lift of slender delta wings according to Newtonian theory, AIAA J., 1963, vol. 1, no. 4, pp. 794–804.
Golubinskii, A.I. and Golubkin, V.N., Spatial hypersonic gas flow over a slender wing, Dokl. Akad. Nauk SSSR, 1977, vol. 234, no. 5, pp. 1032–1034.
Golubkin, V.N., Three-dimensional hypersonic gas flow over wings, Fluid Dynamics, 1992, vol. 27, no. 5, pp. 720–730. https://doi.org/10.1007/BF01051615
Hayes, W.D. and Probstein, R.F., Hypersonic Flow Theory, 2nd ed., vol. 1, Inviscid Flows, N.Y.–London: Acade-mic, 1966.
Bullakh, B.M., Nelineinye konicheskie techeniya (Nonlinear Conical Flows), Moscow: Nauka, 1970.
Ladyzhenskii, M.D., Prostranstvennye giperzvukovye techeniya gaza (Spatial Hypersonic Gas Flows), Moscow: Mashinostroenie, 1968.
Golubinskii, A.I., Hypersonic flow past delta wings of a certain class at angle of attack with an attached shock, Fluid Dynamics, 1968, vol. 3, no. 5, pp. 48–51. https://doi.org/10.1007/BF01029536
Golubkin, V.N., Hypersonic gas flow over a plane delta wing, Uchen. Zap. TsAGI, 1976, vol. 7, no. 6, pp. 1–10.
Woods, B.A., Hypersonic flow with attached shock waves over delta wing, Aeronaut. Quart., 1970, vol. 21, no. 4, pp. 319–325.
Golubinskii, A.I. and Golubkin, V.N., Analysis of singularities in the solution of the problem of hypersonic flow over a small-aspect ratio delta wing, Uchen. Zap. TsAGI, 1987, vol. 18, no. 6, pp. 20–29.
Golubkin, V.N. and Negoda, V.V., On calculation of flow over delta wings in the thin shock layer approximation, Zh. Vychisl. Mat. Mathem. Fiz., 1989, no. 10, pp. 1530–1537.
Hida, K., Thickness effect on the force of slender delta wings in hypersonic flow, AIAA J., 1965, no. 3, pp. 427–433.
Shanbhag, V.V., Numerical studies on hypersonic delta wings with detached shock waves, ARC Current Paper, 1974, no. 1277.
Johnson, C.B. and Marcum, D.C., A parametric study of effect of forebody shape on flow angularity at Mach 8, NASA TN D–7768, 1974.
Squire, L.C., Calculated pressure distributions and shock shapes on thick conical wings at high supersonic speeds, Aeronaut. Quart., 1967, no. 2, pp. 185–206.
Bazzhin, A.P., Two new correlation dependences for flow parameters on planar delta wing, Uchen. Zap. TsAGI, 1976, no. 4, pp. 111–114.
Bashkin, V.A., Experimental investigation of flow over plane wings at the Mach numbers M = 3 and 5 in the range of the angles of attack from 0 to 90°, Tr. TsAGI, 1970, no. 1175, pp. 124–162.
Bertram, M.H. and Henderson, A., Recent hypersonic studies of wings and bodies, ARS J., 1961, vol. 31, no. 8, pp. 1129–1139.
Coleman, G.T., Force measurements on caret and delta wings at high incidence, Imperial Coll., London. Dept. of Aeronautics Rept., 1972, no. 16–76.
Minailos, A.N., Similarity of aerodynamic characteristics of delta wings at supersonic speeds, Uchen. Zap. TsAGI, 1979, vol. 10, no. 3, pp. 16–26.
Sorrels, R.S. and Landrum, E.J., Theoretical and experimental study of twisted and cambered delta wings designed for a Mach number of 3.5, 1976, NASATN.D-8247.
Zhdanov, A.V., Experimental investigation of the interference between the wing and the body at supersonic speeds, Tr. TsAGI, 1982, no. 2161, pp. 3–7.
Stallings, R.L. and Lamb, M., Wing-alone aerodynamic characteristics at high angles of attack, J. Spacecraft, 1982, vol. 19, no. 2, pp. 145–149.
Van Dyke, M., Perturbation Methods in Fluid Mechanics, New York, London: Academic, 1964.
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Golubkin, V.N. Singularities of the Flow Field in the Neighborhood of the Windward Surface of a Small Aspect Ratio Delta Wing in Hypersonic Stream. Fluid Dyn 56, 699–717 (2021). https://doi.org/10.1134/S0015462821050037
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DOI: https://doi.org/10.1134/S0015462821050037