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Heating of Two-Layer Thermal Protection Coating at Hypersonic Flow around a Spherical Blunting

  • AIRCRAFT AND ROCKET ENGINE THEORY
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Abstract

The nonstationary problem of thermal conductivity in a two-layer thermal protection coating is under consideration. The solution is given for a metal hemispherical shell with axisymmetrical distribution of the heat flux density over the outer surface of the coating.

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REFERENCES

  1. Osnovy teploperedachi v aviatsionnoi i raketno-kosmicheskoi tekhnike (Fundamentals of Heat Transfer in Aeronautical and Space Technologies), Avduevskii, V.S. and Koshkin, V.K., Eds., Moscow: Mashinostroenie, 1992.

    Google Scholar 

  2. Nikitin, P.V., Teplovaya zashchita (Thermal Protection), Moscow: MAI, 2006.

    Google Scholar 

  3. Surzhikov, S.T., Raschetnoe issledovanie aerotermodinamiki giperzvukovogo obtekaniya zatuplennykh tel na primere analiza eksperimental’nykh dannykh (Numerical Simulation of Aerothermodynamic Properties of the Hypersonic Flow over Blunted Bodies: Analysis of Experimental Data), Moscow: IPMekh RAN, 2011.

    Google Scholar 

  4. Antuf’ev, B.A. and Konovalov, A.V., Effect of Heating on the Dynamic Behavior of a Shell with Partially Damaged Thermal Insulation, Izv. Vuz. Av. Tekhnika, 2014, vol. 57, no. 1, pp. 3–6 [Russian Aeronautics (Engl. Transl.), vol. 57, no. 1, pp. 1–5].

    Google Scholar 

  5. 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].

    Google Scholar 

  6. Gimbitskii, A.V., Gil’fanov, R.N., Dezider’ev, S.G., and Karimova, A.G., Influence of Thermal Protection on the Temperature State of the Screen and Casing, Izv. Vuz. Av. Tekhnika, 2015, vol. 58, no. 4, pp. 62–66 [Russian Aeronautics (Engl. Transl.), vol. 58, no. 4, pp. 426–430].

    Google Scholar 

  7. Formalev, V.F. and Kuznetsova, E.L., Teplomassoperenos v anizotropnykh telakh pri aerodinamicheskom nagreve (Heat and Mass Transfer in Anisotropic Bodies under Conditions of Aero-Gas-Dynamic Heating), Moscow: MAI-Print, 2010.

    Google Scholar 

  8. 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].

    Google Scholar 

  9. Leonov, V.V. and Zarubin, V.S., Uneven Heating of the Anisotropic Spherical Layer of the Heat-Protective Coating, AIP Conference Proceedings, 2019, vol. 2171, article no. 030004.

    Article  Google Scholar 

  10. Formalev, V.F., Kolesnik, S.A., and Selin, I.A., About Coupled Heat Exchange in a Case of Aerodynamic Heat of Bodies with High Degree of Anisotropy, Teplovye Protsessy v Tekhnike, 2016, vol. 8, no. 9, pp. 388–394.

    Google Scholar 

  11. Zarubin, V.S., Zarubin, V.S., Jr., and Leonov, V.V., Uneven Heating of the Surface of Anisotropic Spherical Layer, Teplovye Protsessy v Tekhnike, 2019, vol. 11, no. 3, pp. 115–123.

    Google Scholar 

  12. Komkov, M.A. and Tarasov, V.A., Tekhnologii namotki kompozitsionnykh konstryktsii raket i sredstv porazheniya (Technology of Winding of Composite Structures of Missiles and Destruction Facilities), Moscow: Izd. MGTU, 2015.

    Google Scholar 

  13. Zarubin, V.S., Kuvyrkin, G.N., and Savel’eva, I.Yu., Thermal Conductivity of Fibrous Composites: Conclusions, Validity Check, and Parametric Analysis of Computational Formulas, Saarbrücken: LAMBERT Academic Publishing, 2013.

    Google Scholar 

  14. Zarubin, V.S., Kuvyrkin, G.N., and Savel’eva, I.Yu., Thermal Conductivity of the Textured Composite with Anisotropic Lamellar Inclusions, Kompozity i Nanostruktury, 2015, vol. 7, no. 2, pp. 97–108.

    Google Scholar 

  15. Urazbakhtin, F.A., Kharinova, Yu.Yu., and Urazbakhtina, A.Yu., Optimization of Forming Parameters for Fiberglass Shells of Rocket Nose Cones by a Criticality Criterion, Izv. Vuz. Av. Tekhnika, 2017, vol. 60, no. 1, pp. 135–142 [Russian Aeronautics (Engl. Transl.), vol. 60, no. 1, pp. 141–149].

    Google Scholar 

  16. Zarubin, V.S., Leonov, V.V., and Zarubin, V.S., Jr., Temperature State of an Anisotropic Spherical Layer during Convective Heat Exchange with the Environment, Vestnik MGTU im. N.E. Baumana. Seriya Estestvennye Nauki, 2019, no. 4, pp. 40–55.

    Google Scholar 

  17. Fialkov, A.S., Baver, A.I., Sidorov, N.M., Chaikun, M.I., and Rabinovich, S.M., Pyrographite. Production, Structure, Properties, Uspekhi Khimii, 1965, vol. 34, no. 1, pp. 133–153.

    Google Scholar 

  18. Graphite, URL: http://www.xumuk.ru/encyklopedia/1145.html.

  19. Vaganov, A.V., Dmitriev, V.G., Zadonskii, S.M., Kireev, A.Yu., Skuratov, A.S., and Stepanov E.A., Estimations of Thermal Regime of Small-Sized Winged Re-Entry Vehicle at the Stage of Design, Fiziko-Khimicheskaya Kinetika v Gazovoi Dinamike, 2006, vol. 4, pp. 443–463.

    Google Scholar 

  20. Shafeeque, A.P., CFD Analysis on an Atmospheric Re-Entry Module, International Research Journal of Engineering and Technology, 2017, vol. 4, no. 1, pp. 587–594.

    Google Scholar 

  21. Tikhonov, A.N. and Samarskii, A.A., Uravneniya matematicheskoi fiziki (Equations of Mathematical Physics), Moscow: Izd. MGU, 1999.

    Google Scholar 

  22. Kartashov, E.M., Analiticheskie metody v teorii teploprovodnosti tverdykh tel (Analytical Methods in Theory of Thermal Conductivity of Solids), Moscow: Vysshaya Shkola, 2001.

    Google Scholar 

  23. Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables, Abramowitz, M. and Stegun, I.A., Eds., New York: Dover Publications, 1964.

    MATH  Google Scholar 

  24. Zaitsev, V.F. and Polyanin, A.D., Spravochnik po lineynym obyknovennym differentsial’nym uravneniyam (Handbook on Linear Ordinary Differential Equations), Moscow: Faktorial, 1997.

    Google Scholar 

  25. Formalev, V.F., Teploprovodnost’ anizotropnykh tel. Analiticheskie metody resheniya zadach (Thermal Conductivity of Anisotropic Bodies. Analytical Methods for Solving Problems), Moscow, Fizmatlit, 2014.

    Google Scholar 

  26. Vlasova, E.A., Zarubin, V.S., and Kuvyrkin, G.N., Priblizhennye metody matematicheskoi fiziki (Approximate Methods of Mathematical Physics), Moscow: Izd. MGTU, 2001.

    Google Scholar 

  27. Galanin, M.P. and Savenkov, E.B., Metody chislennogo analiza matematicheskikh modelei (Methods of Numerical Analysis of Mathematical Models), Moscow: Izd. MGTU, 2018.

    Google Scholar 

  28. Tauber, M.E., Some Simple Scaling Relations for Heating of Ballistic Entry Bodies, Journal of Spacecraft and Rockets, 1970, vol. 7, no. 7, pp. 885–886.

    Article  Google Scholar 

  29. Shevelev, Yu.D. and Syzranova, N.G., Influence of Chemical Reactions on Heat Transfer in a Boundary Layer, Fiziko-Khimicheskaya Kinetika v Gazovoi Dinamike, 2010, vol. 10, no. 2, pp. 91–126.

    Google Scholar 

  30. 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.

    Google Scholar 

  31. Tauber, M.E., A Review of High-Speed, Convective Heat Transfer Computation Methods, Technical Paper no. 2914, NASA, Washington, 1989.

  32. Konstruktsionnye materialy: Spravochnik (Structural Materials: Handbook), Moscow: Mashinostroenie, 1990.

  33. GOST (State Standard) 4401-81: Standard Atmosphere: Parameters, Moscow: Izd. Standartov, 2004.

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ACKNOWLEDGEMENTS

This work was supported by the Russian Foundation for Basic Research, project no. 18-38-20108.

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Correspondence to V. V. Leonov.

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Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Aviatsionnaya Tekhnika, 2021, No. 1, pp. 81 - 89.

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Zarubin, V.S., Zimin, V.N., Leonov, V.V. et al. Heating of Two-Layer Thermal Protection Coating at Hypersonic Flow around a Spherical Blunting. Russ. Aeronaut. 64, 87–96 (2021). https://doi.org/10.3103/S1068799821010116

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  • DOI: https://doi.org/10.3103/S1068799821010116

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