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Physical and Mathematical Modeling of Argon Flow and Distribution Around a Ladle Shroud-Collector Nozzle (LS-CN) Assembly

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Abstract

Injection and distribution of argon in a ladle shroud-collector plate nozzle (LS-CN) assembly have been investigated for three different argon gas delivery designs popularly used in the industry and to these ends, physical and mathematical modeling has been carried out. It is shown that flow and distribution of argon around isolated and perfect LS-CN assembly can be effectively studied through water modeling, by introducing water, in lieu of argon, in a corresponding submerged set-up, maintaining equivalence of Reynolds number at the inlet ports. Accordingly, argon flow and distribution around LS-CN assembly were mapped via water modeling experiments and towards these, video recording as well as electrical conductivity measurement techniques were applied. Results thus obtained indicate that circumferential distribution of argon, around LS-CN assembly, in different gas delivery designs, is substantially different and largely non-uniform. Parallel to such, a steady state, two-component, homogeneous, turbulent flow model has been developed and argon flow and distribution in different LS-CN assemblies predicted numerically, embodying ANSYSTM, version 18.0. Mathematical model predictions agree reasonably well with water modeling observations, and confirm inhomogeneous argon distribution in different isolated and perfect LS-CN assembly systems. In addition to these, progressive heating of argon in transit, following injection, has been investigated computationally and it is shown that trends of results derived from isothermal and non-isothermal simulations are very similar. Finally, the role of natural aspiration on the flow and distribution of argon around LS-CN assembly has been investigated computationally and it is shown that within the range of conditions investigated, flow and distribution of argon in LS-CN assemblies, having different designs, are not largely affected by suction/aspiration phenomena.

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Notes

  1. In a perfect LS-CN set-up, ladle shroud is assumed to be mounted perfectly on to collector nozzle without any physical gap and consequently phenomena such as air ingression, gas–liquid steel, two-phase flows in shroud in such a set-up are irrelevant.

Abbreviations

g :

Acceleration due to gravity (= 9.8 m/s2)

CN:

Collector nozzle

\(C_{i}\) :

Conductivity at flow inlet

x :

Coordinate axes

P :

Dimensionless dynamic pressure referenced to the local hydrostatic pressure

U :

Dimensionless velocity

p :

Dynamic pressure

\(D_{{{\text{eff}}}}\) :

Effective mass diffusivity

K eff :

Effective thermal conductivity

Fr:

Froude number

Gr:

Grashoff number

\(C_{t}\) :

Instantaneous local conductivity

LS:

Ladle shroud

D sh :

Ladle shroud diameter

\(m_{{{\text{Ar}}}}\) :

Local mass fraction of Argon

\(\dot{m}\) :

Mass flow rate of liquid steel

O:

Origin of coordinate axis

\(r_{{{\text{CN}}}}\) :

Radial distance of collector nozzle wall from centerline of shroud

\(r_{{\text{LS, in}}}\) :

Radial distance of shroud internal wall from centerline of shroud

Re(inlet) :

Reynolds number at argon inlet nozzle

\(u_{\theta }\) :

Rotational component of fluid velocity

\(C_{{\text{P}}}\) :

Specific heat capacity

\(u_{i,m}\) :

Time averaged mixture velocity in ith direction

\(u_{j,m}\) :

Time averaged mixture velocity in jth direction

\(C_{1} , C_{2}\) :

Turbulence model constants

\(C_{\mu }\) :

Universal dissipation rate constant

\(Q_{{\text{G}}}\) :

Volumetric gas flow rate of gas

\(Q_{{{\text{Liq}}}}\) :

Volumetric liquid flow rate of liquid

\(\rho_{s}\) :

Density of species ‘s’ (where, s = air, argon)

\(\mu_{{{\text{eff}}}}\) :

Effective dynamic viscosity

\(\vartheta_{t}\) :

Turbulent kinematic viscosity (or momentum eddy diffusivity)

\(\sigma_{k}\) :

Turbulent Prandtl number for k

\(\sigma_{\varepsilon }\) :

Turbulent Prandtl number for ε

\(\alpha_{t}\) :

Turbulent thermal diffusivity (or heat transfer eddy diffusivity)

β :

Volumetric aspiration ratio (= QG/QLiq.)

References

  1. L. Wang, H.G. Lee, and P. Hayes: Steel Res. Int., 1995, vol. 66(7), pp. 279–86.

    Article  CAS  Google Scholar 

  2. J. Zhang, Q. Liu, S. Yang, Z. Chen, J. Li, and Z. Jiang: ISIJ Int., 2019, vol. 59, pp. 1167–77.

    Article  CAS  Google Scholar 

  3. M.K. Fishler (Vesuvius Crucible Co), U.S. Patent 4836508, 1989.

  4. P.K. Singh and D. Mazumdar: Metall. Mater. Trans. B, 2018, vol. 49B, pp. 1945–62.

    Article  Google Scholar 

  5. R. Tiwari, P.K. Singh, A. Agnihotri, and D. Mazumdar: AIST Trans., 2019, vol. 16(2), pp. 1–16.

    Google Scholar 

  6. P.K. Singh and D. Mazumdar: Metall. Mater. Trans. B, 2019, vol. 50B, pp. 1091–1103.

    Article  Google Scholar 

  7. S. Chang, X. Chao, and Z. Zou: Metall Mater. Trans. B, 2018, vol. 49B, pp. 953–57.

    Article  Google Scholar 

  8. D. Mazumdar: Metall Mater. Trans. B, 2021, vol. 52B, pp. 23–29.

    Article  Google Scholar 

  9. L. Wang, H.-G. Lee, and P. Hayes: ISIJ Int., 1996, vol. 36, pp. 17–24.

    Article  CAS  Google Scholar 

  10. K. Chattopadhyay, M. Hasan, M. Isac, and R.I.L. Guthrie: Metall. Mater. Trans. B, 2010, vol. 41B, pp. 225–33.

    Article  CAS  Google Scholar 

  11. K. Chattopadhyay, M. Isac, and R.I.L. Guthrie: ISIJ Int., 1996, vol. 51(4), pp. 573–80.

    Article  Google Scholar 

  12. S. Chatterjee and K. Chattopadhyay: ISIJ Int., 2015, vol. 55(7), pp. 1416–24.

    Article  CAS  Google Scholar 

  13. S. Chatterjee and K. Chattopadhyay: Metall Mater. Trans. B, 2016, vol. 47B, pp. 508–21.

    Article  Google Scholar 

  14. S. Chatterjee, A. Asad, C. Kratzsch, R. Schwarze, and K. Chattopadhyay: Metall Mater. Trans. B, 2017, vol. 48B, pp. 17–21.

    Article  Google Scholar 

  15. Z. Gong, W. Song, and Y.L. Ma: Adv. Mater. Res., 2011, vol. 194, pp. 179–84.

    Article  Google Scholar 

  16. C. Zhang, Y. Bao, M. Wang, and L.C. Zhang: Int. J. Min. Metall. Mater., 2017, vol. 24, pp. 47–54.

    Article  CAS  Google Scholar 

  17. ANSYS-Fluent, Theory Guide, Version 15.0, ANSYS, Inc., Canonsburg, 2013.

  18. Eutech 2700 Benchtop series (Instruction manual, 2013) http://www.eutechinst.com/manuals/english/bench/2700_r2.pdf. Accessed 15 Nov 2021.

  19. Y.A. Cengel and A.J. Ghajar: Heat and Mass Transfer: Fundamentals and Applications, 5th ed. McGraw-Hill Education, New York, 2015, p. 926.

    Google Scholar 

  20. T.-H. Shih, W.W. Liou, A. Shabbir, Z. Yang, and J. Zhu: Comput. Fluids, 1995, vol. 24, pp. 227–38.

    Article  Google Scholar 

  21. O. Davila, R.D. Morales, and L.G. Demedices: Metall. Mater. Trans. B, 2006, vol. 37B, pp. 71–87.

    Article  CAS  Google Scholar 

  22. A. Kumar, D. Mazumdar, and S.C. Koria: ISIJ Int., 2008, vol. 48(1), pp. 38–47.

    Article  CAS  Google Scholar 

  23. S.V. Patankar: Numerical Heat Transfer and Fluid Flow, 1st ed. Hemisphere Publishing, New York, 1982, pp. 126–56.

    Google Scholar 

  24. R.I.L. Guthrie: Engineering in Process Metallurgy, 1st ed. Oxford University Press, New York, 1992, p. 106.

    Google Scholar 

  25. D. Mazumdar and J.W. Evans: Modeling of Steelmaking Processes, CRC Press, Boca Raton, 2009, p. 102.

    Book  Google Scholar 

  26. A.K. Bin: Chem. Eng. Sci., 1993, vol. 48, pp. 3585–3630.

    Article  CAS  Google Scholar 

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  1. Department of Materials Science and Engineering, Indian Institute of Technology, Kanpur, 208016, India

    Suvam Mukherjee & Dipak Mazumdar

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  1. Suvam Mukherjee
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Mukherjee, S., Mazumdar, D. Physical and Mathematical Modeling of Argon Flow and Distribution Around a Ladle Shroud-Collector Nozzle (LS-CN) Assembly. Metall Mater Trans B 53, 2600–2617 (2022). https://doi.org/10.1007/s11663-022-02554-x

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