Abstract
The paper presents a solution of a nonlinear nonstationary problem of thermal conductivity in a two-layer heat-protective coating of a metal hemispherical shell when distribution of the heat flux density over the outer surface of the coating is axisymmetric.
REFERENCES
Afanas’ev, V.A., Baloev, A.A., Degtyarev, G.L., and Meshchanov, A.S., Adaptive Algorithm for Controlling the Soft Vertical Landing of an Unmanned Return Spacecraft, Izv. Vuz. Av. Tekhnika, 2021, vol. 64, no. 2, pp. 17–24 [Russian Aeronautics (Engl. Transl.), vol. 64, no. 2, pp. 189–196].
Leonov, V.V. and Grishko, D.A., Estimates of the Trajectory Parameters and Thermal Loads for a Ballistic Capsule Returning from the Moon with Multiple Dives into the Earth Atmosphere, Journal of Engineering and Applied Sciences, 2019, vol. 14, no. 6, pp. 1775–1780.
Leonov, V.V., et al., Multiple Entry Trajectory Scenarios for Returning from the Moon: Advantages and Disadvantages, Proc. of the International Astronautical Congress, 2019, IAC-19_C1_IP_3_x49850.
Zarubin, V.S., Leonov, V.V., and Zarubin, V.S. Jr., Heating of an Anisotropic Insulation Layer with Hypersonic Flow Past a Spherical Blunting, Izv. Vuz. Av. Tekhnika, 2019, vol. 62, no. 1, pp. 73–80 [Russian Aeronautics (Engl. Transl.), vol. 62, no. 1, pp. 81–88].
Zarubin, V.S., Zimin, V.N., Leonov, V.V., and Zarubin, V.S. Jr., Heating of Two-Layer Thermal Protection Coating at Hypersonic Flow Around A Spherical Blunting, Izv. Vuz. Av. Tekhnika, 2021, vol. 64, no. 1, pp. 81–89 [Russian Aeronautics (Engl. Transl.), vol. 64, no. 1, pp. 87–96].
Zemlyanskii, B.A., Lunev, V.V., Vlasov, V.I., Gorshkov, A.B., Zalogin, G.N., et al., Konvektivnyi teploobmen letatel'nykh apparatov (Convective Heat Exchange of Aircraft), Moscow: Fizmatlit, 2014.
Zarubin, V.S., Zarubin, V.S., Jr., and Leonov, V.V., Heating of a Segment of Spherical Layer of Anisotropic Thermal Protective Coating, Teplovye Protsessy v Tekhnike, 2019, vol. 11, no. 12, pp. 556–563.
Svoistva konstruktsionnykh materialov na osnove ugleroda: spravochnik (Properties of Carbon-Based Structural Materials: Handbook), V.P. Sosedov, Ed., Moscow: Metallurgiya, 1975.
Vaganov, A.V., Dmitriev, V.G., Zadonskii, S.M., Kireev, A.Yu., et al., Estimates of the Thermal Mode of a Small-Sized Winged Return Vehicle at the Stage of Its Design), Fiziko-Khimicheskaya Kinetika v Gazovoi Dinamike, 2006, vol. 4, pp. 443–463.
Walker, S.P., Daryageigi, K., Samareh, J.A., Armand, S.C., and Perino, S.V., Preliminary Development of a Multifunctional Hot Structure Heat Shield, Proc. the 55th AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics, and Materials Conference, 2014, AIAA Paper 2014-0350.
Glazunov, S.G. and Moiseev, V.N., Konstruktsionnye titanovye splavy (Structural Titanium Alloys), Moscow: Metallurgiya, 1974.
Gofin, M.Ya., Zharostoikie i teplozashchitnye konstruktsii mnogorazovykh kosmicheskikh apparatov (Heat-Resistant and Heat-Protective Structures of Reusable Spacecraft), Moscow: Mir, 2003.
Gusarova, I.A., High-Temperature Thermal Insulation Material Based on Ceramic Fibers, Kosmicheskaya Nauka i Tekhnologiya, 2017, vol. 23, no. 2, pp. 24–31.
Shevelev, Yu.D. and Syzranova, N.G., Influence of Chemical Reactions on Heat Transfer in Boundary Layer, Fiziko-Khimicheskaya Kinetika v Gazovoi Dinamike, 2010, vol. 10, no. 2, pp. 91–126.
Reviznikov, D.L. and Sukharev, T.Yu., Hypersonic Flow Around Blunted Bodies in Atmosphere of Earth and Mars. Comparative Analysis of Mathematical Models, Teplovye Protsessy v Tekhnike, 2018, vol. 10, nos. 1–2, pp. 5–15.
Eliseev, A.N., Minenko, V.E., Yakushev, A.G., and Agafonov, D.N., Design Aerodynamic and Thermoballistic Analysis of a Descent Vehicle of “Bearing Body” Class, Nauka i Obrazovaniye: Nauchnoe izdanie MGTU imeni N.E. Baumana, 2015, no. 10, pp. 88–125.
Urazbakhtin, F.A., Kharinova, Yu.Yu., and Urazbakhtin, V.F., A Mathematical Model of Heat Shielding for a Nose Cone Taking into Account Critical Flight Situations, Izv. Vuz. Av. Tekhnika, 2014, vol. 57, no. 1, pp. 73–77 [Russian Aeronautics (Engl. Transl.), vol. 57, no. 1, pp. 100–106].
Kutateladze, S.S., Osnovy teorii teploobmena (Fundamentals of the Theory of Heat Exchange), Moscow: Atomizdat, 1979.
Tauber, M.E., Palmer, G.E., and Prabhu, D., Stagnation Point Radiative Heating Relations for Venus Entry, URL: https://ntrs.nasa.gov/api/citations/20120001655/downloads/20120001655.pdf.
Golomazov, M.M. and Ivankov, A.A., Software Package for the Development of Thermal Protection Systems for Spacecraft Launched into the Atmosphere of Planets, Vestnik NPO imeni S.A. Lavochkina, 2017, no. 3, pp. 41–53.
Provotorov, V.P. and Stepanov, E.A., Approximate Dependences for Calculating Heat Transfer on Body Streamlined by Hypersonic Gas Flow, Uchenye Zapiski TsAGI, 1992, vol. 23, no. 2, pp. 25–29.
Galanin, M.P. and Savenkov, E.B., Metody chislennogo analiza matematicheskikh modelei (Methods of Numerical Analysis of Mathematical Models), Moscow: MGTU imeni N.E. Baumana, 2018.
ACKNOWLEDGEMENTS
The work was supported by the Ministry of Science and Higher Education of the Russian Federation (project 0705-2020-0047).
Author information
Authors and Affiliations
Corresponding author
Additional information
Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Aviatsionnaya Tekhnika, 2022, No. 3, pp. 35 - 42.
About this article
Cite this article
Zarubin, V.S., Zimin, V.N., Leonov, V.V. et al. Thermal Mode of Two-Layer Heat-Protective Coating of a Ballistic Capsule When It Is Returning to the Earth with Parabolic Velocity. Russ. Aeronaut. 65, 474–482 (2022). https://doi.org/10.3103/S1068799822030059
Received:
Revised:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.3103/S1068799822030059