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Thermal analysis of hypersonic reactive flows on the SARA Brazilian satellite reentry trajectory

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Abstract

Numerical simulations of hypersonic flows are presented for the Brazilian satellite SARA undergoing atmospheric reentry. The Navier–Stokes equations are numerically solved by the finite volume method with the inclusion of chemical source terms to model the effects of dissociation and ionization. The two-temperature model proposed by Park is employed to analyze the translational–rotational and vibrational–electronic temperature modes. Despite the low density conditions, which lead to high mean free paths, a comparison of the present results against those obtained by DSMC shows that the present calculations are sufficiently accurate even at the highest altitude considered. Moreover, estimates of the Knudsen numbers for the present test cases indicate that they are sufficiently low to justify the continuum model. A mesh refinement study is carried out in order to evaluate the influence of near-wall mesh spacing and the number of volumes in the normal and longitudinal directions of the flow on the calculation of the heat flux over the satellite surface. Analysis of the results shows that thermodynamic non-equilibrium occurs along the entire reentry trajectory of the satellite. While for high altitudes the flow density is extremely low, at lower altitudes supersonic conditions are achieved and, in both cases, chemical reactions are not relevant. On the other hand, for some intermediate altitudes of the reentry trajectory, thermodynamic non-equilibrium is severely affected by the chemical reactions. In these cases, a weak ionization occurs besides dissociation of the gas species and the accurate prediction of the surface heat flux requires a reactive gas model.

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References

  1. Alladadi FA, Rongier I, Wilde PD (2013) Safety design for space operations. Elsevier, Amsterdam, Netherlands

    Google Scholar 

  2. Annaloro J, Galera S, Thiebaut C, Spel M, Van Hauwaert P, Grossir G, Paris S, Chazot O, Omaly P (2020) Aerothermodynamics modelling of complex shapes in the debrisk atmospheric reentry tool: methodology and validation. Acta Astron 171:388–402

    Article  Google Scholar 

  3. Bouyahiaoui Z, Haoui R, Zidane A, Nouiri A (2020) Prediction of the flow field and convective heating during space capsule reentry using an open source solver. Int J Heat Mass Transf 148:119045

    Article  Google Scholar 

  4. Jawahar P, Kamath H (2000) A high-resolution procedure for Euler and Navier-Stokes computations on unstructured grids. J Comput Phys 164(1):165–203

    Article  MathSciNet  Google Scholar 

  5. Karimi MS, Oboodi MJ (2019) Investigation and recent developments in aerodynamic heating and drag reduction for hypersonic flows. Heat Mass Transf 55:547–569

    Article  Google Scholar 

  6. Kim JG, Kang SH, Park SH (2020) Thermochemical nonequilibrium modeling of oxygen in hypersonic air flows. Int J Heat Mass Transf 148:119059

    Article  Google Scholar 

  7. MacCormack RW, Candler G (1989) The solution of the Navier-Stokes equations using Gauss-Seidel line relaxation. Comput & fluids 17(1):135–150

    Article  Google Scholar 

  8. Martin A, Scalabrin LC, Boyd ID (2012) High performance modeling of atmospheric re-entry vehicles. J Phys Conf Ser 341:012002

    Article  Google Scholar 

  9. Moreira FC, Wolf WR, Azevedo JLF (2021) Thermal analysis of hypersonic flows of carbon dioxide and air in thermodynamic non-equilibrium. Int J Heat Mass Transf 165:120670

    Article  Google Scholar 

  10. Niu Q, Yuan Z, Dong S, Tan H (2018) Assessment of nonequilibrium air-chemistry models on species formation in hypersonic shock layer. Int J Heat Mass Transf 127:703–716

    Article  Google Scholar 

  11. Palharini RC, Azevedo JLF (2017) Thermochemical nonequilibrium computations of a brazilian reentry satellite. J Spacecr Rockets 54(4):961–966

    Article  Google Scholar 

  12. Park C (1988) Assessment of a two-temperature kinetic model for dissociating and weakly ionizing nitrogen. J Thermophys Heat Transf 2(1):8–16

    Article  Google Scholar 

  13. Park C (1989) Assessment of two-temperature kinetic model for ionizing air. J Thermophys Heat Transf 3(3):233–244

    Article  Google Scholar 

  14. Park C (1993) Review of chemical-kinetic problems of future NASA missions. i-Earth entries. J Thermophys Heat Transf 7(3):385–398

    Article  Google Scholar 

  15. Park C (2010) The limits of two-temperature kinetic model in air. 48th AIAA Aerospace Sciences Meeting Including the New Horizons Forum and Aerospace Exposition. AIAA Paper No. Orlando, FL, pp. 2010–0911

  16. Qu F, Chen J, Sun D, Bai J, Zuo G (2019) A grid strategy for predicting the space plane’s hypersonic aerodynamic heating loads. Aerosp Sci Technol 86:659–670

    Article  Google Scholar 

  17. Rahmanpour M, Ebrahimi R, Shams M (2011) Numerically gas radiation heat transfer modeling in chemically nonequilibrium reactive flow. Heat Mass Transf 47:1659–1670

    Article  Google Scholar 

  18. Santos WF (2012) Aerothermodynamic analysis of a reentry brazilian satellite. Braz J Phys 42(5–6):373–390

    Article  Google Scholar 

  19. Scalabrin LC (2007) Numerical simulation of weakly ionized hypersonic flow over reentry capsules. Ph.D. thesis, University of Michigan

  20. Steger JL, Warming RF (1981) Flux vector splitting of the inviscid gasdynamic equations with application to finite-difference methods. J Comput Phys 40(2):263–293

    Article  MathSciNet  Google Scholar 

  21. Tahani M, Karimi MS, Mahmoudi Motlagh A, Mirmahdian S (2013) Numerical investigation of drag and heat reduction in hypersonic spiked blunt bodies. Heat Mass Transf 49:1369–1384

    Article  Google Scholar 

  22. Venkatakrishnan V (1995) Implicit schemes and parallel computing in unstructured grid cfd. Tech. rep., NASA Report 195071

  23. Vincenti W, Kruger C (1982) Introduction to physical gas dynamics. Krieger, Ann Arbor, MI, USA

    Google Scholar 

  24. Wang XY, Yan C, Zheng YK, Li EL (2017) Assessment of chemical kinetic models on hypersonic flow heat transfer. Int J Heat Mass Transf 111:356–366

    Article  Google Scholar 

  25. Wilke CR (1950) A viscosity equation for gas mixtures. J Chem Phys 18(4):517–519

    Article  Google Scholar 

  26. Yang X, Gui Y, Xiao G, Du Y, Liu L, Wei D (2020) Reacting gas-surface interaction and heat transfer characteristics for high-enthalpy and hypersonic dissociated carbon dioxide flow. Int J Heat Mass Transf 146:118869

    Article  Google Scholar 

Download references

Acknowledgements

The authors gratefully acknowledge the support for the present research provided by Conselho Nacional de Desenvolvimento Científico e Tecnológico, CNPq, under the Research Grants No. 309985/2013-7, 304335/2018-5 and 407842/2018-7. The work is also supported by computational resources of the Center for Mathematical Sciences Applied to Industry (CeMEAI), funded by Fundação de Amparo à Pesquisa do Estado de São Paulo, FAPESP, under the Research Grant No. 2013/07375-0. The authors acknowledge the National Laboratory for Scientific Computing, LNCC/MCTI, Brazil, for providing HPC resources of the SDumont supercomputer, under the HFWBTF project, which have contributed to the research results reported in the present paper. FAPESP Research Grant No. 2013/08293-7 is further acknowledged by the authors. Support to the first author under the FAPESP Scholarship Grant No. 2021/02705-8 and additional support to the third author under FAPESP Research Grant No. 2013/07375-0 are also gratefully acknowledged.

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Authors and Affiliations

  1. Instituto Tecnológico de Aeronáutica, São José dos Campos, SP, 12228-900, Brazil

    Farney Coutinho Moreira

  2. Faculdade de Engenharia Mecânica Campinas, Universidade Estadual de Campinas, Campinas, SP, 13083-860, Brazil

    William Roberto Wolf

  3. Instituto de Aeronáutica e Espaço, Divisão de Aerodinâmica, São José dos Campos, SP, 12228-904, Brazil

    João Luiz F. Azevedo

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  1. Farney Coutinho Moreira
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  2. William Roberto Wolf
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  3. João Luiz F. Azevedo
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Correspondence to Farney Coutinho Moreira.

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Technical Editor: André Cavalieri.

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Moreira, F.C., Wolf, W.R. & Azevedo, J.L.F. Thermal analysis of hypersonic reactive flows on the SARA Brazilian satellite reentry trajectory. J Braz. Soc. Mech. Sci. Eng. 44, 36 (2022). https://doi.org/10.1007/s40430-021-03336-3

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  • DOI: https://doi.org/10.1007/s40430-021-03336-3

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