Numerical study of molten magnesium convection in the apparatus for titanium reduction
DOI:
https://doi.org/10.7242/1999-6691/2015.8.4.37Keywords:
convection, turbulence, low Prandtl numbers, liquid metal, magnesium, metallothermic titanium reductionAbstract
Numerical study of the structure of convective flows of molten magnesium in the apparatus for metallothermic reduction of titanium is performed for different configurations of vessel cooling and heating zones. A mathematical model is based on the Boussinesq equations for thermogravitational convection of a single-phase fluid. The LES (Large Eddies Simulations) technique is used for turbulence modeling. Simulations were carried with a non-uniform numerical grid consisting of 5 million points. Three-dimensional nonstationary simulations allow one to get instant and average characteristics of the process and to study the fields of velocity and temperature pulsations. It is shown that axisymmetric stationary flows exist under moderate Grashof numbers (Gr ~ 107-108), but nonstationary turbulent flows are established under Grashof numbers, which correspond to the actual titanium reduction process (Gr ~ 1012). Analysis was performed for uniform and non-uniform heat emission provided on the magnesium surface by the reaction of titanium reduction, as well as for two configurations of the system of apparatus heating rate control: with furnace heaters operating at full capacity and with furnace heaters switched off. The principal differences in the convective flow structure in these two cases are revealed. An estimate is made for the maximal velocity of magnesium flows in the reactor. It is shown that more intensive velocity and temperature pulsations occur near the interface between the cooled and heated parts of the lateral surface of the vessel.
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Ahlers G., Grossmann S., Lohse D. Heat transfer and large scale dynamics in turbulent Rayleigh-Benard convection // Rev. Mod. Phys. - 2009. - Vol. 81. - P. 503-537. DOI
2. Zajcev A.M., Semenov V.N., Svecov U.E. Matematiceskoe modelirovanie smesenia raznotemperaturnyh struj metodom CABARET // Vycisl. meh. splos. sred. - 2013. - T. 6, No 4. - C. 430-437. DOI
3. Rogozkin S.A., Aksenov A.A., Zluktov S.V., Osipov S.L., Sazonova M.L., Fadeev I.D., Sepelev S.F., Smelev V.V. Razrabotka modeli turbulentnogo teploperenosa dla zidkometalliceskogo natrievogo teplonositela i ee verifikacia // Vycisl. meh. splos. sred. - 2014. - T. 7, No 3. - C. 306-316. DOI
4. Frick P., Khalilov R., Kolesnichenko I., Mamykin A., Pakholkov V., Pavlinov A., Rogozhkin S. Turbulent convective heat transfer in a long cylinder with liquid sodium // Europhys. Lett. - 2015. - Vol. 109, no. 1. - 14002. DOI
5. Kolesnicenko I.V., Mamykin A.D., Pavlinov A.M., Paholkov V.V., Rogozkin S.A., Frik P.G., Halilov R.I., Sepelev S.F. Eksperimental’noe issledovanie svobodnoj konvekcii natria v dlinnom cilindre // Teploenergetika. - 2015. - No 6. - S. 31-39. DOI
6. Vasil’ev A.U., Kolesnicenko I.V., Mamykin A.D., Frik P.G., Halilov R.I. Rogozkin S.A., Paholkov V.A. Turbulentnyj konvektivnyj teploobmen v naklonnoj trube, zapolnennoj natriem // ZTF. - 2015. - T. 85, No 9. - S. 45-49. DOI
7. Mamykin A., Frick P., Khalilov R., Kolesnichenko I., Pakholkov V., Rogozhkin S., Vasiliev A. Turbulent convective heat transfer in an inclined tube with liquid sodium // Magnetohydrodynamics. - 2015. - Vol. 51, no. 2. - P. 329-336.
8. Garmata V.A., Gulanickij B.S., Kramnik V.U., Lipkes A.M., Serakov G.V., Suckov A.B., Homakov P.P. Metallurgia titana. - M.: Metallurgia, 1968. - 643 s.
9. Garmata V.A., Petrun’ko A.N., Galickij N.V., Olesov U.G., Sandler R.A. Titan. - M.: Metallurgia, 1983. - 559 s.
10. Halilov R.I., Hripcenko S.U., Frik P.G., Stepanov R.A. Elektromagnitnye izmerenia urovna zidkogo metalla v zamknutyh ob"emah // Izmeritel’naa tehnika. - 2007. - No 8. - S. 41-44. DOI
11. Sergeev V.V., Galickij N.V., Kiselev V.P., Kozlov V.M. Metallurgia titana. - M.: Metallurgia, 1971. - 320 s.
12. Mal’sin V.M., Zavadovskaa V.N., Pampusko N.A. Metallurgia titana. - M.: Metallurgia, 1991. - 208 s.
13. Tarunin E.L., Sihov V.M., Urkov U.S Svobodnaa konvekcia v cilindriceskom sosude pri zadannom teplovom potoke na verhnej granice // Ucen. zapiski Permskogo un-ta, No 327, sb. <>. - 1975. - No 6. - S. 85-98.
14. Zimin V.D., Lahov U.N., Sorokin M.P. Konvekcia v vertikal’nom cilindre pri podogreve sverhu // Ucen. zapiski Permskogo un-ta, No 327, sb. <>. - 1975. - No 6. - S. 73-84.
15. Caplin A.I., Necaev V.N. Cislennoe modelirovanie neravnovesnyh processov teplomassoperenosa v reaktore dla polucenia poristogo titana // Vycisl. meh. splos. sred. - 2013. - T. 6, No 4. - S. 483-490. DOI
16. Smagorinsky J. General circulation experiments with the primitive equations. I. The basic experiment // Mon. Wea. Rev. - 1963. - Vol. 91, no. 3. - P. 99-164. DOI
17. Kolesnichenko I., Khripchenko S. Surface instability of the plane layer of conducting liquid // Magnetohydrodynamics. 2003. - Vol. 39, no. 4. - P. 427-434.
18. Issa R.I. Solution of the implicitly discretised fluid flow equations by operator-splitting // J. Comput. Phys. - 1985. - Vol. 62, no. 1. - P. 40-65. DOI
19. Ferziger J.H., Peric M. Computational methods for fluid dynamics. - Berlin: Springer Verlag, 2002. - 423 p.
20. Sweby P.K. High resolution schemes using flux limiters for hyperbolic conservation laws // SIAM J. Numer. Anal. - 1984. - Vol. 21, no. 5. - P. 995-1011. DOI
21. Versteeg H.K., Malalasekera W. An introduction to computational fluid dynamics: The finite volume method. - Pearson Education Limited, 2007. - 504 p.
22. Fletcher R. Conjugate gradient methods for indefinite systems // Lect. Notes Math. - 1976. - Vol. 506. - P. 73-89. DOI
23. Ejdenzon M.A. Magnij. - M.: Metallurgia, 1969. - 352 s.
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