Hydrodynamic characteristics and heat exchange characteristics computing at direct movement of two streams of liquid metals


Аuthors

Yachikov I. M., Kartavtsev S. V., Matveev S. V.*

,

*e-mail: matveev_s_v@inbox.ru

Abstract

According to the World Steel Association report, the steel production demonstrates a stable tendency to increase. In 2016, the world’s steel production reached 1,673 billion tons a year. Steel production inevitably passes through the melting stage, after which the liquid steel should be cooled. Almost all the heat is lost without active use, which reduces the energy efficiency of the process. One of the ways to utilize the liquid steel heat is to use liquid metal coolants for this purpose. With this, the liquid steel stream is cooled by the flow of another liquid metal or alloy. The purpose of the presented work consists in creating a mathematical model to determine the hydrodynamic and heat exchange characteristics in the direct flow of two flows of liquid metals. The article de‑ scribes the step‑by‑step developing of heat exchange mathematical model at laminar movement of the two liquid metals flow and presents the main modeling results. The distribution of the velocity profile for the motion of two immiscible metals with different properties was obtained for their various speed ratio and thicknesses of the boundary hydrodynamic layers on the example liquid steel and C‑13 alloy (55.5% Bi and 44.5% Pb). For a liquid steel while its moving at a velocity of U2 = 0.001–1 m/s, the results of approximate estimates revealed that the critical coordinate of the laminar‑to‑turbulent transition lies over a rather wide range of xcr = 86–0.086 m. With this, the dimensional thickness of the boundary layer lies in the range of δ1 = 0.195–0.195·10–5 m (at σ2 = 0.716, x ≈ xcr, λ0 = 1.5). For the C‑13 alloy at U1 = λ0U2 m/s, the critical coordinate of the laminar flow to turbulent flow lies within the limits of xcr = 28.05–0.028 m, the boundary layer thickness in the range of δ1 = 0.063–6.35·10–5 m (at σ2 = 0.716, x ≈ xcr, λ0 = 1.5).

Keywords:

liquid steel, pouring into liquid layers, heat energy utilization, liquid‑metal coolants, laminar flow, boundary layer, heat transfer coefficient

References

  1. World Steel Association. Available at: https://www.worldsteel.org/steel‑by‑topic/statistics/monthly‑crude‑steel‑and‑iron‑production.html.

  2. Coxe C. D. Formation of metal shapes. Bridgeport, Conn., assignor to Remington Arms Company, Ins., a corporation of Delaware. Patent US, no. 2298348, 1940.

  3. Leghorn G. R. Method of forming structural shapes from molten material by stream casting. Patent US, no. 3430680, 1969.

  4. Palm J. V. O., Salzman G. S. Method of producing bimetallic strips. Clevelend Heights, Ohio, assignors to The Clevelend Graphite Bronze Company, Cleveland, Ohio, a corporation of Ohio. Patent US, no. 2022571, 1933.

  5. Magat E. E., Strachan D. R. Formation of films and filament directly from polymer intermediates. Wilmington, Del., assignors to E. I. du Pont de Nemours & Company, Wilmington. Del., a corporation of Delaware. Patent US, no. 2708617, 1955.

  6. Fromson H. A. Method for the casting of sheets of a fusible material. Weston, Conn. Patent US, no. 2754559, 1956.

  7. Lindemuth L. B. Centrifugal casting. N. Y. Patent US, no. 1831310, 1927.

  8. Kartavtsev S. V., Strogonov K. V. Sposob proizvodstva ploskikh izdeliy [Method of production of flat products]. Patent RF, no. 2239515, 2004. In Russ.

  9. Bigeev A. M., Milyaev A. F., Shirshov Yu. P., Vagin A. G., Sokorchuk V. A., Fayzullin V. G. Sposob nepreryvnoy razlivki metallov [Method of continuous casting of metals]. Patent USSR, no. 782951, 1980. In Russ.

  10. Kovytin A. A., Kalyagin Yu. A. O problemakh i perspektivakh utilizatsii teploty, vydelyayushhejsya pri razlivke stali [On problems and perspectives of utilization of heat released during the casting of steel]. Promyshlennay energetika – Industrial power engineering, 2007, no. 8, pp. 36–39. In Russ.

  11. Alovadinova H. N., Demin Yu. K., Matveev S. V., Kartavtsev S. V. Povyshenie energeticheskoj effektivnosti protsessa nepreryvnoj razlivki stali [Increasing the energy efficiency of the continuous steel casting process]. Promyshlennaya energetika — Industrial power engineering, 2015 no. 2, pp. 8–11. In Russ.

  12. Lukin S. V., Poselyuzhnyy D. N., Kibardin A. N. Ispol’zovanie teploty okhlazhdeniya stali, razlivaemoj na mashinakh nepreryvnogo lit’ya zagotovok, v sisteme teplosnabzheniya predpriyatiya [The steel cast cooling heat utilization from continuous casting machines, in the heat supply system of the industrial plant]. Promyshlennay energetika – Industrial power engineering, 2013, no. 5, pp. 7–9. In Russ.

  13. Strogonov K. V., Kartavtsev S. V. Zhidkaya stal’: ispol’zovanie teploty i skoroctnaya razlivka [Liquid steel: unused heat and rapid casting]. Magnitogorsk, NMSTU Publ., 2006. 147 p. In Russ.

  14. Kartavtsev S. V. Intensivnoe energosberezhenie i tehnicheskiy progress chernoy metallurgii [Intensive energy saving and technical progress of ferrous metallurgy]. Magnitogorsk, NMSTU Publ., 2008. 311 p. In Russ.

  15. Shlihting G. Teoriya pogranichnogo sloya [Boundary layer theory]. Moscow, Nauka, 1974. 712 p. In Russ.

  16. Lee F. A. Mixing of two streams at different densities. Fifth Australasian Conference on Hydraulics and fluid mechanics. 1974, Christchurch, New Zealand, 913 December.

  17. Samokhin V. N. On a laminar mixing layer at the boundary between two flows. USSR Computational Mathematics and Mathematical Physics, 1985, vol. 25, iss. 2, pp. 186–188.

  18. Jachikov I. M., Matveev S. V., Kartavtsev S. V. Identifikatsiya parametrov laminarnogo pogranichnogo sloya na granitse razdela dvukh potokov pri razlivke stali v “zhidkij” kristallizator [Identification of the parameters of the laminar boundary layer on the border of the two streams during steel casting in a “liquid” crystallizer]. Matematicheskoe i programmnoe obespechenie system v promyshlennoy i sotsial’noy sferakh – Software of systems in the industrial and social fields, 2017, vol. 5, no. 2, pp. 1218. In Russ.

  19. Lessen Martin. On stability of free laminar boundary layer between parallel streams. Report, January 1, 1950; (digital.library.unt.edu/ark:/67531/metadc60317/m1/4/: accessed April 6, 2017), University of North Texas Libraries, Digital Library, digital.library.unt.edu; crediting UNT Libraries Government Documents Department.

  20. Chirkin V. S. Teplofizicheskie svojstva materialov yadernoj tekhniki. Spravochnik. [Thermophysical properties of nuclear engineering materials. Handbook]. Moscow, Atomizdat, 1968. 484 p.

  21. Elanskii G. N., Kudrin V. A. Struktura i svojstva rasplavov na osnove zheleza [Structure and properties of iron‑base melts]. Vestnik YuUrGU. Serija "Metallurgiya”–Bulletin of the SUSU. Series “Metallurgy”, 2015, vol. 15, no. 3, pp. 11–19. In Russ.

  22. Ryabov A. V. Rastvorimost’ vismuta i svintsa v zhidkom i tverdom zheleze [Solubility of lead and bismuth in liquid and solid iron]. Vestnik YuUrGU. Serija "Metallurgiya”–Bulletin of the SUSU. Series “Metallurgy”, 2013, vol. 13, no. 2, pp. 27–32. In Russ.

  23. Borishanskiy V. M., Kutateladze S. S., Novikov I. I. Zhidkometallicheskie teplonositeli [Liquidphase metals as a heat agents]. Moscow, Atomizdat, 1967. 299 p. In Russ.

  24. Isachenko V. P., Osipova V. A., Sukomel A. S. Teploperedacha [Heat transfer]. Moscow, Energiya, 1975. 488 p. In Russ.

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