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Bubble Size Measurement in a Continuous Casting Mold Using Physical Modeling and Shadowgraphy

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Abstract

Argon gas injection into a continuous casting mold (vessel with moving liquid) helps in increasing the casting sequence length by avoiding SEN clogging. Bubble formation may create bubble-related steel defects at specific operating conditions. Parametric estimation of bubble size distribution (BSD) and mean bubble diameter may identify the type of unforeseen defect in cast slab. Physical modeling experiments were performed to estimate Sauter mean diameter (SMD) of the bubbles for different input parameters such as gas/liquid flow rates and liquid properties. High-speed high-resolution imaging and advanced image processing were used to capture images from the physical model. Four different simulating liquids were used in the physical modeling experiment. Bubble characteristic data were used to measure the SMDs (output data). Different values of SMDs were correlated with the input parameters using direct multilinear regression (DMR). Experimental and predicted values were found well in agreement with high R2. A dimensionless equation was also determined using the same data and compared with the DMR correlation. DMR correlation was compared and validated with the previous work related to the bubbly flows in stagnant and moving liquid flow regimes. As a result, it was concluded that an increasing gas flow rate, a decreasing liquid flow rate, an increasing surface tension, and an increasing viscosity increase the SMD of bubbles formed in the mold.

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Abbreviations

F g :

Gas fraction in liquid

Q L :

Liquid flow rate

Q G :

Gas flow rate

d 32 :

Sauter mean diameter of the bubbles

d i :

Diameter of ith bubble

n i :

Number of ith bubble diameter (same bubble diameter)

b :

Coefficient of lnQL

σ :

Surface tension of the liquids

µµ L :

Viscosity of the liquid

ρ L :

Density of the liquid

H :

Submerge Depth of the Submerged Entry Nozzle

λ :

Scale Factor, Dimension of model/dimension of prototype mold (real mold)

Q Liquid- n :

Liquid flow rate for nth liquid

ρ Liquid - n :

Density of Liquid-n

d ni :

Internal Diameter of the injection nozzle

d o :

Outer Diameter of the injection nozzle

D :

Diameter of the bubble column (Akita and Yoshida)

d n :

Nozzle diameter (Sada et al.)

u g :

Gas velocity (Sada et al.)

u l :

Liquid velocity (Sada et al.)

f :

Bubble detachment function (Luty and Pronczuk)

b :

Ratio of major to minor bubble diameter

D h :

Diameter of gas injection hole

T :

Temperature of liquid

Regas :

Reynolds number of gas

Reliq :

Reynolds number of liquid

µ g :

Viscosity of gas

d :

Nozzle diameter of gas injection port

U :

Liquid velocity

References

  1. B. Thomas, A. Dennisov, and H. Bai, in Proc. of ISS Steelmaking Conf., Chicago 1997, 80, pp. 375–84

  2. C. C. Maier, U. S. Bur. Mines Bull., 1927, No. 260, p. 62

  3. T. Tadaki and S. Maeda: Chem. Eng., 1963, vol. 27, pp. 147–55. https://doi.org/10.1252/kakoronbunshu1953.27.147.

    Article  Google Scholar 

  4. L. Davidson and E.H. Amick Jr.: AIChE J., 1956, vol. 2, pp. 337–42. https://doi.org/10.1002/aic.690020309.

    Article  CAS  Google Scholar 

  5. I. Leibson, E.G. Holcomb, A.G. Cacoso, and J.J. Jamic: AIChe J., 1956, vol. 2, pp. 300–06.

    Article  Google Scholar 

  6. A. Mersmann, VDI-Forschllngshift 491, 1962, Vol. 28B, pp.1–39

  7. M. Sano, K. Mori, and T. Sato: Tetsu-to-Hogane., 1974, vol. 60, pp. 348–60.

    Article  Google Scholar 

  8. K. Akita and F. Yoshida: Ind. Eng. Chem. Process Des. Dev., 1974, vol. 13(1), pp. 84–90.

    Article  CAS  Google Scholar 

  9. M. Sano and K. Moil: Trans. JIM (Japan)., 1976, vol. 17, pp. 344–52.

    Article  Google Scholar 

  10. A. Kumar, T.E. Degaleesan, G.S. Laddha, and H.E. Hoelscher: Can. J. Chem. Eng., 1976, vol. 54, pp. 503–08.

    Article  CAS  Google Scholar 

  11. M. Iguchi, T. Chiara, N. Takanashi, Y. Ogawa, N. Tokumitsu, and Z. Morita: ISIJ Int., 1995, vol. 35, pp. 1354–61.

    Article  CAS  Google Scholar 

  12. R. Pohorecki, W. Moniuk, P. Bielski, P. Sobieszuk, and G. Dabrowiecki: Chem. Eng. J., 2005, vol. 113, pp. 35–39. https://doi.org/10.1016/j.cej.2005.08.007.

    Article  CAS  Google Scholar 

  13. G.A. Irons and R.I.L. Guthrie: Metall. Trans. B, 1978, vol. 9B, pp. 101–10.

    Article  CAS  Google Scholar 

  14. K. Mori, M. Sano, and T. Sato: Trans. ISIJ, 1979, vol. 19, pp. 553–58.

    Article  CAS  Google Scholar 

  15. M. Iguchi, T. Chihara, N. Takanashi, Y. Ogawa, N. Tokumitsu, and Z. Morita: ISIJ Int., 1995, vol. 35, pp. 1354–61.

    Article  CAS  Google Scholar 

  16. K. Akita and F. Yoshida: Ind. Eng. Chem. Proc. Des. Dev., 1974, vol. 13, pp. 84–91.

    Article  CAS  Google Scholar 

  17. L. L. van Dierendonck, Ph.D. Thesis, Chapter 2, University Twente, 1970

  18. P. Bielski, Ph.D. Thesis, Warsaw University of Technology, 2002

  19. G.A. Hughmark: Ind. Eng. Chem. Proc. Des. Dev., 1967, vol. 6(2), pp. 218–20.

    Article  CAS  Google Scholar 

  20. K. Idogawa, K. Ikeda, T. Fukuda, and S. Morooka: Int. Chem. Eng., 1986, vol. 26, pp. 468–74.

    Google Scholar 

  21. K. Idogawa, K. Ikeda, T. Fukuda, and S. Morooka: Int. Chem. Eng., 1987, vol. 27, pp. 93–99.

    Google Scholar 

  22. E. Sada, A. Yasunzshz, S. Katoh, and M. Nzshioka: Can. J. Chem. Eng., 1978, vol. 56, pp. 669–72.

    Article  CAS  Google Scholar 

  23. Y. Kawase and J.J. Ulbrecht: Ind. Eng. Chem. Process. Des. Dev., 1981, vol. 20(4), pp. 636–40.

    Article  CAS  Google Scholar 

  24. C. Muilwijk and H.E.A. Vanden Akker: Chem. Eng. Sci., 2019, vol. 202, pp. 318–35.

    Article  CAS  Google Scholar 

  25. P. Luty and M. Pronczuk: Processes, 2020, vol. 8, p. 999.

    Article  CAS  Google Scholar 

  26. P.F. Wace, M.S. Morrell, and J. Woodrow: Chem. Eng. Commun., 1987, vol. 62, pp. 93–106.

    Article  CAS  Google Scholar 

  27. I. Kim, Y. Kamotani, and S. Ostrach: AIChE J., 1994, vol. 40(1), pp. 19–28.

    Article  CAS  Google Scholar 

  28. Y. Sahai and T. Emi: Tundish Technology for Clean Steel Production, 1st ed. World Scientific Publishing, Singapore, 2008, pp. 20–21.

    Google Scholar 

  29. H. Bai and B.G. Thomas: Metall. Mater. Trans. B, 2001, vol. 32B, pp. 1143–59.

    Article  CAS  Google Scholar 

  30. R. Banderas, R. Morales, R. Sanchez-Perez, L. Demedices, and G. Solorio-Diaz: Int. J. Multiphase Flow, 2005, vol. 31, p. 643.

    Article  Google Scholar 

  31. J. Klostermann, H. Chaves, and R. Schwarze: Steel Res. Int., 2007, vol. 78(8), pp. 595–601.

    Article  CAS  Google Scholar 

  32. S.M. Cho, B.G. Thomas, and S.H. Kim: ISIJ Int., 2018, vol. 58(8), pp. 1443–52.

    Article  CAS  Google Scholar 

  33. M. Burty, M. Larrecq, C. Pusse, and Y. Zbaczyniak: 13th PTD Conf., Nashville, TN, 1995, vol. 13, pp. 287–92.

  34. R. Sanchez-Perez, R. Morales, L. Demedices, J. Palafox-Ramos, and M. Díaz-Cruz: Metall. Mater. Trans. B, 2004, vol. 35B, pp. 85–99.

    Article  CAS  Google Scholar 

  35. R. Sanchez-Perez, R. Morales, M. Diaz-Cruze, O. Olivares-Xomet, and J. Palafox Ramos: ISIJ Int., 2003, vol. 43, pp. 637–46. https://doi.org/10.2355/isijinternational.43.637.

    Article  CAS  Google Scholar 

  36. K. Jin, S. Vanka, and B. Thomas: Metall. Mater. Trans. B., 2018, vol. 49B, pp. 1360–77.

    Article  Google Scholar 

  37. T. Zhang, Z. Luo, H. Zhou, B. Ni, and Z. Zou: ISIJ Int., 2016, vol. 56(1), pp. 116–25.

    Article  CAS  Google Scholar 

  38. K. Timmel, N. Shevchenko, M. Roder, M. Anderhuber, P. Gardin, S. Eckert, and G. Gerbet: Metall. Mater. Trans B, 2015, vol. 46B, pp. 700–10.

    Article  Google Scholar 

  39. K. Timmel, S. Eckert, G. Gerbeth, F. Stefani, and T. Wondrak: ISIJ Int., 2010, vol. 50, pp. 1134–41.

    Article  CAS  Google Scholar 

  40. A. Srivastava, R. Wang, S.K. Dinda, and K. Chattopadhyay: MLWA, 2021, vol. 6, p. 100180.

    Google Scholar 

  41. P. Kowalczuk and J. Drzymala: Particul. Sci. Technol., 2016, vol. 34, pp. 645–47. https://doi.org/10.1080/02726351.2015.1099582.

    Article  CAS  Google Scholar 

  42. A. Srivastava and K. Chattopadhyay: Metall. Mater. Trans. B, 2022, vol. 53B, pp. 1018–35. https://doi.org/10.1007/s11663-021-02396-z.

    Article  CAS  Google Scholar 

  43. V. Singh, S. Dash, J. Sunitha, and S. Ajmani: ISIJ Int., 2006, vol. 46, pp. 210–18. https://doi.org/10.2355/isijinternational.46.210.

    Article  CAS  Google Scholar 

  44. W. Chen, Y. Ren, L. Zhang, and P. Scheller: JOM, 2019, vol. 71, pp. 1158–68.

    Article  CAS  Google Scholar 

  45. A. Srivastava, S. K. Dinda, K. Chattopadhyay, and J. Sengupta, AISTech 2021, Proc. of the Iron & Steel Tech. Conf. Nashville, https://doi.org/10.33313/382/172

  46. S. K. Dinda, A. Srivastava, K. Chattopadhyay, and J. Sengupta, AISTech 2021, Proc. of the Iron & Steel Tech. Conf. Nashville, https://doi.org/10.33313/382/171

  47. A. Asgarian, Z. Yang, Z. Tang, M. Bussmann, and K. Chattopadhyay: Exp. Fluids, 2020, vol. 61, p. 14. https://doi.org/10.1007/s00348-019-2847-6.

    Article  Google Scholar 

  48. A. Srivastava, R. Wang, D. Li, and K. Chattopadhyay, Proc. Of AISTech 2020, pp. 803–13, https://doi.org/10.33313/380/085

  49. P.M. Wilkinson, PhD Thesis, University of Groningen, Groningen, The Netherlands, 1991

  50. Q. Wu, X. Wang, T. Wang, M. Han, Z. Sha, and J. Wang: Can. J. Chem. Eng., 2013, vol. 91, pp. 1957–63.

    Article  CAS  Google Scholar 

  51. G. Besagni, F. Inzoli, G. Deguido, and L.A. Pellegrini: Chem. Eng. Sci., 2016, vol. 158, pp. 509–38. https://doi.org/10.1016/j.ces.2016.11.003.

    Article  CAS  Google Scholar 

  52. D. Laupsien, C.L. Men, A. Cockx, and A. Linè: Chem. Eng. Res. Des., 2021, https://doi.org/10.1016/j.cherd.2021.09.025.

    Article  Google Scholar 

  53. P. Zahedi, R. Saleh, R.M. Atanasio, and K. Yousefi: Korean J. Chem. Eng., 2014, vol. 31(8), pp. 1349–61.

    Article  CAS  Google Scholar 

  54. F. Liu, H. Zhou, L. Zhang, C. Ren, J. Zhang, Y. Ren, and W. Chen: Steel Res. Int., 2021, vol. 92, p. 2100067. https://doi.org/10.1002/srin.202100067.

    Article  CAS  Google Scholar 

  55. Y. Liao and D. Lucas: Chem. Eng. Sci., 2009, vol. 64, pp. 3389–406.

    Article  CAS  Google Scholar 

  56. Y. Liao and D. Lucas: Chem. Eng. Sci., 2010, vol. 65(10), pp. 2851–64.

    Article  CAS  Google Scholar 

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Acknowledgments

The authors thank the Natural Sciences and Engineering Research Council of Canada (NSERC), ArcelorMittal, and the University of Toronto Dean’s Catalyst Professorship for funding this research.

Conflict of interest

The authors declare no conflict of interest in publishing this manuscript.

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Authors and Affiliations

  1. Process Metallurgy Research Lab, Department of Materials Science and Engineering, University of Toronto, 184 College Street, Toronto, ON, M5S3E42, Canada

    Amiy Srivastava, Soumitra Kr. Dinda, Ali Asgarian & Kinnor Chattopadhyay

  2. ArcelorMittal Global Research and Development, Hamilton, ON, L8H3N8, Canada

    Joydeep Sengupta

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  1. Amiy Srivastava
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Correspondence to Kinnor Chattopadhyay.

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Appendix

Appendix

Effect of Flow Rates on Bubble Coalescence

To understand the effect of flow rates on the bubble coalescence, a parameter called rate of bubble coalescence (fc) is used in this study.

$$ f_{c} \, = \,{\text{Frequency}}\,{\text{of}}\,{\text{bubble}}\,{\text{coalescence}}\,{\text{per}}\,{\text{second}}\, = \,{\text{Number}}\,{\text{of}}\,{\text{coalescence}}\,{\text{events}}\,{\text{per}}\,{\text{second}}. $$

Figure A1 shows the effect of liquid flow rate on the rate of coalescence at different gas flow rates. Liquid flow rate is dominating over gas flow rate and becomes a responsible factor for bubble coalescence as on increasing QL, fc increases significantly but on increasing Qg, it does not increase significantly.

Fig. A1
figure 13

Rate of coalescence for different liquid flow rates and gas flow rates

Full size image

An increased liquid flow rate provides energy to the bubbles for coalescence to take place. Bigger bubbles produced after coalescence are responsible for the occurrence of slag–gas interaction-related defects such as open eye formation and slag layer shearing.

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Srivastava, A., Dinda, S.K., Asgarian, A. et al. Bubble Size Measurement in a Continuous Casting Mold Using Physical Modeling and Shadowgraphy. Metall Mater Trans B 53, 2209–2226 (2022). https://doi.org/10.1007/s11663-022-02521-6

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