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Zh. Vychisl. Mat. Mat. Fiz., 2006, Volume 46, Number 9, Pages 1692–1703 (Mi zvmmf419)  

This article is cited in 2 scientific papers (total in 3 papers)

The $P_1$ and $P_2$ approximations of the spherical harmonic method as applied to radiative heat transfer computations with allowance for strong blowing from the surface of a vehicle moving in the Jovian atmosphere

V. M. Borisova, A. A. Ivankovb

a Dorodnicyn Computing Center, Russian Academy of Sciences, ul. Vavilova 40, Moscow, 119991, Russia
b Lavochkin Scientific and Production Association, Leningradskaya ul. 24, Khimki-2, Moscow oblast, 141400, Russia

Abstract: The spherical harmonics method in the $P_1$ and $P_2$ approximations is used to analyze radiative heat transfer for a space vehicle entering a planet's atmosphere. Strong blowing of ablated materials from the vehicle surface is taken into account by using a two-layer flow model without allowance for the viscosity and thermal conduction of the gas. The heating and ablation of a multilayered thermal protection system are determined simultaneously with the vehicle's flight trajectory, which is calculated taking into account the mass loss due to the ablation. The approach is illustrated by computing the flight of a space vehicle shaped as a spherical segment or a spherically blunted cone entering the Jovian atmosphere at a speed of 60 km/s and an entry angle of $-5^\circ$.

Key words: heat transfer, radiation, strong blowing, ablation, trajectory, segment, cone, $P_1$ and $P_2$ approximations, spherical harmonic method.

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English version:
Computational Mathematics and Mathematical Physics, 2006, 46:9, 1611–1622

Bibliographic databases:

UDC: 519.631
Received: 01.03.2006

Citation: V. M. Borisov, A. A. Ivankov, “The $P_1$ and $P_2$ approximations of the spherical harmonic method as applied to radiative heat transfer computations with allowance for strong blowing from the surface of a vehicle moving in the Jovian atmosphere”, Zh. Vychisl. Mat. Mat. Fiz., 46:9 (2006), 1692–1703; Comput. Math. Math. Phys., 46:9 (2006), 1611–1622

Citation in format AMSBIB
\Bibitem{BorIva06}
\by V.~M.~Borisov, A.~A.~Ivankov
\paper The $P_1$ and $P_2$ approximations of the spherical harmonic method as applied to radiative heat transfer computations with allowance for strong blowing from the surface of a~vehicle moving in the Jovian atmosphere
\jour Zh. Vychisl. Mat. Mat. Fiz.
\yr 2006
\vol 46
\issue 9
\pages 1692--1703
\mathnet{http://mi.mathnet.ru/zvmmf419}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=2287667}
\transl
\jour Comput. Math. Math. Phys.
\yr 2006
\vol 46
\issue 9
\pages 1611--1622
\crossref{https://doi.org/10.1134/S0965542506090120}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-33748993968}


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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. M. K. Kerimov, “In memory of professor Valerii Mikhailovich Borisov (1939–2008)”, Comput. Math. Math. Phys., 49:6 (2009), 1080–1084  mathnet  crossref  isi
    2. Reviznikov D.L., Sposobin A.V., Dombrovsky L.A., “Radiative Heat Transfer From Supersonic Flow With Suspended Polydisperse Particles To a Blunt Body: Effect of Collisions Between Particles”, Comput. Therm. Sci., 7:4 (2015), 313–325  crossref  isi  elib  scopus
    3. Dombrovsky L.A., Reviznikov D.L., Sposobin A.V., “Radiative Heat Transfer From Supersonic Flow With Suspended Particles To a Blunt Body”, Int. J. Heat Mass Transf., 93 (2016), 853–861  crossref  isi  elib  scopus
  • Журнал вычислительной математики и математической физики Computational Mathematics and Mathematical Physics
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