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Numerical Study of Heat Transfer from an Air-Cooled Wall of a Titanium Reactor

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Journal of Applied Mechanics and Technical Physics Aims and scope

Abstract—

This work is devoted to the numerical study of the thermal regime of the retort surface in an apparatus for the production of titanium. The problem of conjugate heat transfer between the wall of a cylindrical retort and the wall of a furnace with heaters is considered. There is a gap with forced air flow between the walls. The purpose of this study is to estimate temperature conditions of the retort wall and the heat transfer coefficient on its surface under various heating or cooling conditions occurring in the apparatus. Data on the distribution of heat fluxes on the retort walls are required for the calculation of turbulent convective flows of liquid magnesium inside the retort, since temperature nonuniformity can have a strong effect on the processes occurring inside it. The computational domain consists of solid walls and an air flow between them. The mathematical model is based on a system of axially symmetric nonstationary Navier–Stokes equations, and the RANS (Reynolds-averaged Navier–Stokes equations) approach is used to describe turbulent fields. In addition to heat transfer by forced convection and thermal conductivity, the model also considers the radiation heat transfer between two opposite walls. Four heating options, which can be used during operation of the reactor, are investigated. The air flow velocity required to keep the retort wall temperature in the allowable working range from 750 to 950°C under all operating conditions, was estimated. The temperature distribution along the investigated segment of the retort wall is demonstrated to be nonuniform. Dependencies for the heat transfer coefficient at the side surface of the retort on the vertical coordinate were constructed. The predictions by these dependencies were compared with the known formula for the heat transfer coefficient on a plane infinite surface with a constant heat flux. It has been established that in this case, which is more intricate, the calculated coefficients are close to those predicted by the known engineering formulas only for a part of the regimes examined in this study. Noticeable differences between the obtained dependencies and simplified estimations were found in a wide range of the studied parameters. The largest difference is observed at the channel inlet where the temperature gradients are maximal.

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REFERENCES

  1. Gartmata, V.A., Petrun’ko, A.N., Galitskiy, N.V., Olesov Yu.G., and Sandler, R.A., Titan (Titanium), Moscow: Metallurgiya, 1983.

    Google Scholar 

  2. Gartmata, V.A., Guoyanitskiy, B.S., Kramnik, V.Yu., Lipkes, Ya.M., Seryakov, G.V., Suchkov, A.B., and Khomyakov, P.P., Metallurgiya titana (Titanium Metallurgy), Moscow: Metallurgiya, 1968.

  3. Sergeev, V.V., Galitskii, N.V., Kiselev, V.P., and Kozlov, V.M., Metallurgiya titana (Titanium Metallurgy), Moscow: Metallurgiya, 1971.

  4. Mal’shin, V.M., Zavadovskaya, V.N., and Pampushko, N.A., Metallurgiya titana (Titanium Metallurgy), Moscow: Metallurgiya, 1991.

  5. Khalilov, R.I., Khripchenko, S.Yu., Frik, P.G., and Stepanov, R.A., Electromagnetic measurements of the level of a liquid metal in closed volumes, Meas. Tech., 2007, vol. 50, pp. 861–866. https://doi.org/10.1007/s11018-007-0163-7

    Article  Google Scholar 

  6. Krauter, N., Eckert, S., Gundrum, T., Stefani, F., Wondrak, T., Frick, P., Khalilov, R., and Teimurazov, A., Inductive system for reliable magnesium level detection in a titanium reduction reactor, Metall. Mater. Trans. B, 2018, vol. 49, pp. 2089–2096. https://doi.org/10.1007/s11663-018-1291-y

    Article  Google Scholar 

  7. Tarunin, E.L., Shihov, V.M., and Yurkov, Yu.S., Free convection in a cylindrical vessel at a given heat flux at the upper boundary, Gidrodinamika, 1975, no. 6, pp. 85–98.

  8. Tsaplin, A.I. and Nechaev, V.N., Numerical modeling of non-equilibrium heat and mass transfer processes in a reactor for the production of porous titanium, Vychisl. Mekh. Splosh. Sred, 2013, vol. 6, no. 4, pp. 483–490. https://doi.org/10.7242/1999-6691/2013.6.4.53

    Article  Google Scholar 

  9. Teimurazov, A.S. and Frik, P.G., Numerical study of molten magnesium convection a titanium reduction apparatus, J. Appl. Mech. Tech. Phys., 2016, vol. 57, pp. 1264–1275. https://doi.org/10.1134/S0021894416070129,

  10. Teimurazov, A., Frick, P., and Stefani, F., Thermal convection of liquid metal in the titanium reduction reactor, IOP Conf. Ser.: Mater. Sci. Eng., 2017, vol. 208, p. 012041. https://doi.org/10.1088/1757-899X/208/1/012041

  11. Karasev, T.O. and Teimurazov, A.S., Modeling of Liquid Magnesium Turbulent Convection in a Titanium Reduction Apparatus Using the RANS and LES Approaches, J. Appl. Mech. Tech. Phys., 2020, vol. 61, pp. 1203–1215. https://doi.org/10.1134/S0021894420070044

  12. Teimurazov, A., Frick, P., Weber, N., and Stefani, F., Numerical simulations of convection in the titanium reduction reactor, J. Phys.: Conf. Ser., 2017, vol. 891, p. 012076. https://doi.org/10.1088/1742-6596/891/1/012076

    Article  Google Scholar 

  13. Khalilov, R., Kolesnichenko, I., Teimurazov, A., Mamykin, A., and Frick, P., Natural convection in a liquid metal locally heated from above, IOP Conf. Ser.: Mater. Sci. Eng., 2017, vol. 208, p. 012044. https://doi.org/10.1088/1757-899X/208/1/012044

  14. Shirokov, M.F., Fizicheskie osnovy gazodinamiki (Physical Foundations of Gas Dynamics), Moscow: Fizmatgiz, 1958.

  15. Kutateladze, S.S., Teploperedacha i gidrodinamicheskoe soprotivlenie (Heat Transfer and Hydrodynamic Resistance), Moscow: Energoatomizdat, 1990.

  16. Fedorov, V.K., An engineering method of calculating convective heat transfer for a body in an attached gas flow, J. Eng. Phys., 1965, vol. 8, pp. 130–134. https://doi.org/10.1007/BF00829051

    Article  Google Scholar 

  17. Bergman, T.L., Lavine, A.S., Incropera, F.P., and de Witt, D.P., Introduction to Heat Transfer, 6th ed., New York: Wiley, 2011.

    Google Scholar 

  18. Modest, M.F., The improved differential approximation for radiative heat transfer in multi-dimensional media, J. Heat Transfer, 1990, vol. 112, pp. 819–821. https://doi.org/10.1115/1.2910468

    Article  Google Scholar 

  19. Howell, J.R., A Catalog of Radiation Configuration Factors, New York: McGraw-Hill, 1982.

    Google Scholar 

  20. Howell, J.R., Menguc, M.P., and Siegel, R., Thermal Radiation Heat Transfer, London: Taylor and Francis, 2015. https://doi.org/10.1201/b18835

  21. Marshak, R.E., Note on the spherical harmonics method as applied to the Milne problem for a sphere, Phys. Rev., 1947, vol. 71, pp. 443–446. https://doi.org/10.1103/PhysRev.71.443

    Article  ADS  MathSciNet  MATH  Google Scholar 

  22. Menter, F.R., Two-equation eddy-viscosity turbulence models for engineering applications, AIAA J., 1994, vol. 32, pp. 1598–1610. https://doi.org/10.2514/3.12149

    Article  ADS  Google Scholar 

  23. Pope, S.B., Turbulent Flows, Cambridge: Cambridge Univ. Press, 2000. https://doi.org/10.1017/CBO9780511840531

  24. Bogdanov, S.N., Burtsev, S.I., Ivanov, O.P., and Kupriyanova, O.P., Kholodil’naya tekhnika. Konditsionirovanie vozdukha. Svoistva veshchestv. Spravochnik (Refrigeration Equipment. Air Conditioning. Properties of Substances. Handbook), St. Petersburg: SPbGAKhPT, 1990.

  25. Fizicheskie velichiny. Spravochnik (Handbook of Physical Quantities), Grigoriev, I.S. and Meylikhov, E.Z., Eds., Moscow, Energoatomizdat, 1991; Boca Raton, NY: CRC, 1996.

  26. Issa, R.I., Solution of the implicitly discretized fluid flow equations by operator-splitting, J. Comput. Phys., 1985, vol. 62, pp. 40–65. https://doi.org/10.1016/0021-9991(86)90099-9

    Article  ADS  MATH  Google Scholar 

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Authors and Affiliations

  1. Perm National Research Polytechnic University, Perm, Russia

    T. O. Karasev & A. V. Perminov

  2. Institute of Continuous Media Mechanics, Ural Branch of the Russian Academy of Sciences (ICMM UB RAS), Perm, Russia

    T. O. Karasev & A. S. Teimurazov

Authors
  1. T. O. Karasev
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  2. A. S. Teimurazov
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  3. A. V. Perminov
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Correspondence to T. O. Karasev, A. S. Teimurazov or A. V. Perminov.

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Translated by T. Krasnoshchekova

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Karasev, T.O., Teimurazov, A.S. & Perminov, A.V. Numerical Study of Heat Transfer from an Air-Cooled Wall of a Titanium Reactor. J Appl Mech Tech Phy 62, 1243–1254 (2021). https://doi.org/10.1134/S0021894421070117

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