Abstract
A solution is derived for the variational problem on the shape of a three-dimensional slender body subjected to a minimal radiation heat flux during its motion in the atmosphere with a constant hypersonic velocity. The distribution of radiation flux over the surface is approximated in the form of dependence on the local surface slope. The limitations on the body shape are provided by the isoperimetric conditions for the bulk of the body, for the area of its wettable surface, for the area of its bottom cross section, and for the perimeter of the bottom cross section, as well as the limitation on the limiting value of the wave drag. It is found that the transverse contour of the optimal body may have the form of a circle, of a star-shaped transverse contour, and of a contour consisting of arcs of a circle and line segments. It is demonstrated that the use of optimal three-dimensional bodies enables one to significantly (by more than 50%) reduce the radiation heat flux to the body surface compared with bodies of revolution which have the same preassigned geometric characteristics.
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REFERENCES
Korchagina, M.A. and Pilyugin, N.N., Kosm. Issled., 1991, vol. 29, issue 2, p. 298.
Arguchintseva, M.A. and Pilyugin, N.N., Ekstremal'nye zadachi radiatsionnoi gazovoi dinamiki (Extreme Problems of Radiation Gas Dynamics), Moscow: Mosk. Gos. Univ. (Moscow State Univ.), 1997.
Seiff, A. and Tauber, M.E., AIAA J., 1966, vol. 4, no. 1. Translated as Raketn. Tekh. Kosmonavt., 1966, no. 1, p. 77.
Perminov, V.D. and Solodkin, E.E., Izv. Akad. Nauk SSSR Mekh. Zhidk. Gaza, 1971, no. 2, p. 94.
Solodkin, E.E. and Pyatnova, A.I., Tr. Tsentr. Aerogidrodin. Inst., 1972, issue 1374, p. 119.
Borodin, A.I. and Peigin, S.V., Teplofiz. Vys. Temp., 1999, vol. 37, no. 1, p. 92 (High Temp. (Engl. transl.), vol. 37, no. 1, p. 87).
Deev, A.A. and Pilyugin, N.N., Izv. Akad. Nauk SSSR Mekh. Zhidk. Gaza, 1978, no. 2, p. 94.
Gil'man, O.A. and Pilyugin, N.N., Prikl. Mat. Mekh., 1991, vol. 55, issue 2, p. 290.
Theory of Optimum Aerodynamic Shapes, Miele, A., Ed., New York: Academic, 1965. Translated under the title Teoriya optimal'nykh aerodinamicheskikh form, Moscow: Mir, 1969.
Vedernikov, Yu.A. and Shchepanovskii, V.A., Optimizatsiya reogazodinamicheskikh sistem (Optimization of Rheogasdynamic Systems), Novosibirsk: Nauka, 1995.
Ostapenko, N.A., Dokl. Akad. Nauk SSSR, 1989, vol. 307, no. 1, p. 62.
Maikapar, G.I., Izv. Akad. Nauk SSSR Mekh. Zhidk. Gaza, 1967, no. 2, p. 38.
Gonor, A.L., Prikl. Mat. Mekh., 1963, vol. 27, issue 1, p. 185.
Gusarov, A.A. and Levin, V.A., Izv. Akad. Nauk SSSR Mekh. Zhidk. Gaza, 1981, no. 6, p. 98.
Ostapenko, N.A. and Yakunina, G.E., Izv. Ross. Akad. Nauk Mekh. Zhidk. Gaza, 1992, no. 1, p. 95.
Arguchintseva, M.A. and Pilyugin, N.N., Kosm. Issled., 1992, vol. 30, no. 5, p. 615.
Arguchintseva, M.A. and Pilyugin, N.N., Prikl. Mat. Mekh., 1992, vol. 56, issue 4, p. 643.
Apshtein, E.Z., Pilyugin, N.N., and Tirskii, G.A., Kosm. Issled., 1979, vol. 17, issue 2, p. 246.
Apshtein, E.Z. and Pilyugin, N.N., Izv. Akad. Nauk SSSR Mekh. Zhidk. Gaza, 1979, no. 2, p. 71.
Apshtein, E.Z., Vartanyan, N.V., and Sakharov, V.I., Izv. Akad. Nauk SSSR Mekh. Zhidk. Gaza, 1986, no. 1, p. 92.
Apshtein, E.Z., Vartanyan, N.V., and Sakharov, V.I., Izv. Akad. Nauk SSSR Mekh. Zhidk. Gaza, 1986, no. 4, p. 183.
Berdichevskii, V.P., Variatsionnye printsipy mekhaniki sploshnoi sredy (Variational Principles of Continuum Mechanics), Moscow: Nauka, 1983.
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Arguchintseva, M.A., Pilyugin, N.N. Optimization of the Shape of a Three-Dimensional Body for Radiation Heat Flux. High Temperature 40, 557–570 (2002). https://doi.org/10.1023/A:1019619331171
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DOI: https://doi.org/10.1023/A:1019619331171