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Approximation Formulas for the Radiative Heat Flux at High Velocities

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Abstract

The aim of the study is to obtain the analytical expression for the radiative heat-transfer coefficient at the stagnation point of a blunt body as a function of its velocity and size and the atmosphere density over the parameter range characteristic of large meteoroid entering into the Earth's atmosphere. Analytical approximations, available in the literature, of the numerical calculations of the radiative heat flux to the stagnation point of a body with the nondestructible surface obtained over restricted altitude, velocity, and nose radius range are given. These approximation formulas are tested over a wider flow parameter range by comparing with calculations carried out by other authors. A new approximation relation for the radiative heat flux at the stagnation point is suggested on the basis of an analysis of these comparisons and performed correlations for the body velocity and radius and the atmosphere density.

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References

  1. Surzhikov, S.T. and Shuvalov, M.P., Testing of computational data on radiative and convective heating of newgeneration re-entry vehicles, Teplofiz. Vysok. Temp., 2013, vol. 51, no. 3, pp. 456–470.

    Google Scholar 

  2. Surzhikov, S.T. and Shuvalov, M.P., Analysis of radiative-convective heating of four types of re-entry vehicles, Fiz.-Khim. Kinet. v Gaz. Din., 2014, vol. 15, no. 4, pp. 1–18.

    Google Scholar 

  3. El'kin, Yu.G., Hypersonic inviscid radiative gas flow past spherically blunted cones, Uch. Zap. TsAGI, 1971, vol. 3, no. 4, pp. 120–125.

    Google Scholar 

  4. Rumynskii, A.N. and Churkin, V.P., Hypersonic viscous radiative gas flow past blunt bodies, Zhurn. Vychil. Mat. Matem. Fiz., 1974, vol. 14, no. 6, pp. 1553–1570.

    Google Scholar 

  5. Suttles, J.T., Sullivan, E.M. and Margolis, S.B., Curve fits of predicted inviscid stagnation-point radiative heating rates, cooling factors, and shock standoff distances for hyperbolic earth entry, NASA CR-1548, 1974.

    Google Scholar 

  6. Tauber, M.E. and Sutton, K., Stagnation-point radiative heating relations for Earth and Mars entries, J. Spacecraft and Rockets, 1991, vol. 28, no. 1, pp. 40–42.

    Article  ADS  Google Scholar 

  7. Stulov, V.P., Mirskii, V.N., and Vislyi, A.I., Aerodinamika bolidov (Aerodynamics of Bolides), Moscow: Nauka, 1995.

    Google Scholar 

  8. Brandis, A.M. and Johnston, C.O., Characterization of stagnation-point heat flux for Earth entry, in: 45th AIAA Plasmadynamics and Lasers Conf. AIAA 2014-2374, 2014.

    Google Scholar 

  9. Biberman, L.M., Bronin, S.Ya., and Lagar'kov, A.N., Radiative and convective heat transfer in hypersonic flow around a blunt body, Fluid Dynamics, 1972, no. 5, pp. 800–809.

    Article  ADS  Google Scholar 

  10. Belotserkovskii, O.M., Biberman, L.M., Bronin, S.Ya., Lagar'kov, A.N., and Fomin, V.N., Hypersonic gas flow around and heating blunt bodies with regard to radiation transfer, Teplofiz. Vysok. Temp., 1969, vol. 7, no. 3, pp. 529–541.

    Google Scholar 

  11. Rolin, M.N. and Yurevich, F.B., Radiative and convective heat exchange in blowing the graphite ablation products in a hypersonic compressed layer, in: Heat and Mass Transfer. VI. Proceeding of VI All- Union Conf. on Heat and Mass Transfer, Minsk: Lykov Institute of Heat and Mass Transfer, 1980, Vol. 2, pp. 12–23.

    Google Scholar 

  12. Rolin, M.N. and Yurevich, F.B., Estimates of certain indeterminateness of the calculation results of radiative and convective heat exchange in hypersonic flows, Teploflz. Vysok. Temp., 1985, vol. 23, no. 2, pp. 340–345.

    ADS  Google Scholar 

  13. Wilson, K.H. and Hoshizaki, H., Effect of ablation product absorption and line transitions on shock layer radiative transport, NASA CR-1264, 1969.

    Google Scholar 

  14. Chin, J.H., Radiation transport for blunt-body flows including the effects of lines, and ablation layer, NASA CR-73223, 1967.

    Google Scholar 

  15. Chin, J.H., Radiation transport for stagnation flows including effects of lines and ablation layer, AIAA J., 1969, vol. 7, no. 7, pp. 1310–1318.

    Article  MATH  ADS  Google Scholar 

  16. Bogolepov, V.V. and El'kin, Yu.G., Hypersonic inviscid radiative gas flow past spherically blunted cones, Uch. Zap. TsAGI, 1971, vol. 2, no. 2, pp. 24–33.

    Google Scholar 

  17. Kamenshchikov, V.A., Plastinin, Yu.A., Nikolaev, V.M., and Novitskii, L.A., Radiatsionnye svoistva gazov pri vysokikh temperaturakh (Radiative Properties of Gases at High Temperatures), Moscow: Mashinostroenie, 1971.

    Google Scholar 

  18. Avilova, I.V., Biberman, L.M., Vorob'ev, V.S., Zamalin, V.M., Kobzev, G.A., Lagar'kov, A.N., Mnatsakanyan, A. Kh., and Norman, G.E., Opticheskie svoistva goryachego vozdukha (Optical Properties of Hot Air), Ed by Biberman, L.M., Moscow, Nauka, 1970.

  19. Ovsyannikov, V.M., Calculations of destruction of Lost City, Grant, and Příbram meteorites in the entry into the Earth's atmosphere, Astronom. Vestnik, 1976, vol. 10, no. 8, p. 151–157.

    ADS  Google Scholar 

  20. Wilson, K.H., RATRAP — a radiation transport code. 6-77-67-12, Lockheed Missiles & Space Co., Mar. 14. 1967.

    Google Scholar 

  21. ReVelle, D.O., Dynamics and Thermodynamics of large Meteor Entry: a Quasi-Simple Ablation Model. Planetary Sciences SR-76-1. Ottawa: Herzberg Institute of Astrophysics, National Research Council Canada, 1976.

    Google Scholar 

  22. Nicolet, W.E., User's Manual for RAD/EQUIL/1973, a General Purpose Radiation Transport Program, NASA CR132470, 1973.

    Google Scholar 

  23. Suttles, J.T., Comparison of the radiation flux profiles and spectral detail from three detailed nongray radiation models at conditions representative of hypervelocity Earth entry, NASA TM X-2447, 1972.

    Google Scholar 

  24. Johnson, J.E., Starkey, R.P., and Lewis, M.J., Aerothermodynamic optimization of reentry heat shield shapes for a crew exploration vehicle, J. Spacecraft and Rockets, 2007, vol. 44, no. 4, pp. 849–859.

    Article  ADS  Google Scholar 

  25. Goulard, R., The coupling of radiation and convection in detached shock layers, J. Quant. Spectrosc. Radiation Transfer, 1961, vol. 1, pp. 249–254.

    Article  ADS  Google Scholar 

  26. Mazaheri, A., Gnoffo, P., Johnston, C., and Kleb, B., LAURA users manual, Tech. Rep. NASA TM 2010-216836. 2010.

    Google Scholar 

  27. Johnston, C., Hollis, B., and Sutton, K., Spectrum modeling for air shock-layer radiation at Lunar-return conditions, J. Spacecraft and Rockets, 2008, vol. 45, no. 5, pp. 865–878.

    Article  ADS  Google Scholar 

  28. Johnston, C.O., Hollis, B., and Sutton, K., Non-Boltzmann modeling for air shock layers at Lunar return conditions, J. Spacecraft and Rockets, 2008, vol. 45, no. 5, pp. 879–890.

    Article  ADS  Google Scholar 

  29. Avilova, I.V., Biberman, L.M., Vorob'ev, V.S., Zamalin, V.M., Kobzev, G.A., Lagar'kov, A.N., Mnatsakanyan, A. Kh., and Norman, G.E., Optical properties of hot air, J. Quant. Spectr. Rad. Transf., 1969, vol. 9, no. 1, pp. 89–122.

    Article  ADS  Google Scholar 

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Acknowledgment

The work was carried out with financial support from the Russian Foundation for Basic Research (project no. 18-01-00740a).

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Correspondence to I. G. Brykina.

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Russian Text © The Author(s), 2019, published in Izvestiya RAN. Mekhanika Zhidkosti i Gaza, 2019, No. 4, pp. 123–134.

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Brykina, I.G., Egorova, L.A. Approximation Formulas for the Radiative Heat Flux at High Velocities. Fluid Dyn 54, 562–574 (2019). https://doi.org/10.1134/S0015462819040037

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  • DOI: https://doi.org/10.1134/S0015462819040037

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