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Thermophysical Properties of Liquid Zirconia Measured by Aerodynamic Levitation at High Temperature

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Abstract

In the frame of severe accident modeling, the knowledge of the so-called-corium thermophysical properties is crucial to obtain reliable simulation. In this work, an aerodynamic levitation technique was used to measure simultaneously surface tension, density and viscosity of liquid zirconia, one phase of corium, at temperature ranging from melting point 2 715 °C to 2 900 °C using acoustic excitation. The volume estimation, initially based on the hypothesis of a spherical shape for the sample, was improved with the use of a second camera placed on top of the sample. This enabled a more precise determination of the volume to estimate density. An original post-treatment method was developed to obtain the surface tension by taking into account multimodal oscillation frequencies. The viscosity may be slightly overestimated due to the multimode oscillation. Measurement uncertainties are estimated based on propagation law for the three thermophysical properties considered.

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References

  1. M. Pellegrini, K. Dolganov, L.E. Herranz, H. Bonneville, D. Luxat, M. Sonnenkalb, J. Ishikawa, J.H. Song, R.O. Gauntt, L.F. Moguel, F. Payot, Y. Nishi, Nucl. Technol. 196, 198 (2016). https://doi.org/10.13182/NT16-63

    Article  ADS  Google Scholar 

  2. M. Pellegrini and al., in Nureth-19 Int. Top. Mtg. Nucl. React. Thermal Hydraulics (Brussels, 2022).

  3. P. Piluso, M. Adorni, G. Azarian, K.-H. Bang, S. Basu, and M. Buck, Status Report on Ex-Vessel Steam Explosion: EVSE (NEA-OCDE, 2017).

  4. J. Delacroix, C. Journeau, P. Piluso, Front. Energy Res. (2022). https://doi.org/10.3389/fenrg.2022.883972

    Article  Google Scholar 

  5. S. Ozawa, S. Takahashi, S. Suzuki, H. Sugawara, H. Fukuyama, Jpn. J. Appl. Phys. 50, 11RD05 (2011). https://doi.org/10.1143/JJAP.50.11RD05

    Article  Google Scholar 

  6. Y. Su, M. Mohr, R.K. Wunderlich, X. Wang, Q. Cao, D. Zhang, Y. Yang, H.-J. Fecht, J.-Z. Jiang, J. Mol. Liq. 298, 111992 (2020). https://doi.org/10.1016/j.molliq.2019.111992

    Article  Google Scholar 

  7. H. Yoo, C. Park, S. Jeon, S. Lee, G.W. Lee, Metrologia 52, 677 (2015). https://doi.org/10.1088/0026-1394/52/5/677

    Article  Google Scholar 

  8. Y. Ohishi, K. Kurokawa, Y. Sun, H. Muta, J. Nucl. Mater. 528, 151873 (2020). https://doi.org/10.1016/j.jnucmat.2019.151873

    Article  Google Scholar 

  9. H. Oda, C. Koyama, M. Ohshio, H. Saruwatari, T. Ishikiwa, Int. J. Microgravity Sci. Appl. 37, 370302 (2020). https://doi.org/10.15011/ijmsa.37.3.370302

    Article  Google Scholar 

  10. D. Grishchenko, P. Piluso, HTHP 40, 127 (2011)

    Google Scholar 

  11. D.L. Price, High-Temperature Levitated Materials (Cambridge University Press, Cambridge, 2010)

    Book  Google Scholar 

  12. D. Langstaff, M. Gunn, G.N. Greaves, A. Marsing, F. Kargl, Rev. Sci. Instrum. 84, 124901 (2013). https://doi.org/10.1063/1.4832115

    Article  ADS  Google Scholar 

  13. D. Manara, C. Ronchi, M. Sheindlin, M. Lewis, M. Brykin, J. Nucl. Mater. 342, 148 (2005). https://doi.org/10.1016/j.jnucmat.2005.04.002

    Article  ADS  Google Scholar 

  14. I.C. Sommerville, W.S. Raw, J. Am. Leather Chem. Assoc. 44, 784 (1949)

    Google Scholar 

  15. P. Hofmann, S.J.L. Hagen, G. Schanz, A. Skokan, Nucl. Technol. 87, 327 (1989). https://doi.org/10.13182/NT-TMI2-146

    Article  ADS  Google Scholar 

  16. S. Kohara, J. Akola, L. Patrikeev, M. Ropo, K. Ohara, M. Itou, A. Fujiwara, J. Yahiro, J.T. Okada, T. Ishikawa, A. Mizuno, A. Masuno, Y. Watanabe, T. Usuki, Nat. Commun. 5, 5892 (2014). https://doi.org/10.1038/ncomms6892

    Article  ADS  Google Scholar 

  17. T. Kondo, H. Muta, K. Kurosaki, F. Kargl, A. Yamaji, M. Furuya, Y. Ohishi, Heliyon 5, e02049 (2019). https://doi.org/10.1016/j.heliyon.2019.e02049

    Article  Google Scholar 

  18. W.K. Kim, J.H. Shim, M. Kaviany, J. Nucl. Mater. 491, 126 (2017). https://doi.org/10.1016/j.jnucmat.2017.04.030

    Article  ADS  Google Scholar 

  19. O.L.G. Alderman, C.J. Benmore, J.K.R. Weber, L.B. Skinner, A.J. Tamalonis, S. Sendelbach, A. Hebden, M.A. Williamson, Sci. Rep. 8, 2434 (2018). https://doi.org/10.1038/s41598-018-20817-z

    Article  ADS  Google Scholar 

  20. T. Kondo, H. Muta, Y. Ohishi, J. Nucl. Sci. Technol. 57, 889 (2020). https://doi.org/10.1080/00223131.2020.1736681

    Article  Google Scholar 

  21. E. Cheremisina, Z. Zhang, E. de Bilbao, J. Schenk, Ceram. Int. 49, 4460 (2023). https://doi.org/10.1016/j.ceramint.2022.09.332

    Article  Google Scholar 

  22. S.J. McCormack, A. Tamalonis, R.J.K. Weber, W.M. Kriven, Rev. Sci. Instrum. 90, 015109 (2019). https://doi.org/10.1063/1.5055738

    Article  ADS  Google Scholar 

  23. B. Glorieux, F. Millot, J.C. Rifflet, Int. J. Thermophys. 23, 1249 (2002). https://doi.org/10.1023/A:1019848405502

    Article  Google Scholar 

  24. T. Ishikawa, P.-F. Paradis, S. Yoda, Rev. Sci. Instrum. 72, 2490 (2001). https://doi.org/10.1063/1.1368861

    Article  ADS  Google Scholar 

  25. J. Canny, IEEE Trans. Pattern Anal. Machine Intell. (1986). https://doi.org/10.1109/TPAMI.1986.4767851

    Article  Google Scholar 

  26. J.W.S. Rayleigh, Proc. R. Soc. Lond. 29, 71 (1879). https://doi.org/10.1098/rspl.1879.0015

    Article  Google Scholar 

  27. S. Hakamada, A. Nakamura, M. Watanabe, F. Kargl, Int. J. Microgravity Sci. Appl. 34, 340403 (2017). https://doi.org/10.15011/ijmsa.34.4_340403

    Article  Google Scholar 

  28. P.V.R. Suryanarayana, Y. Bayazitoglu, Phys. Fluids A 3, 967 (1991). https://doi.org/10.1063/1.857974

    Article  ADS  Google Scholar 

  29. D.L. Cummings, D.A. Blackburn, J. Fluid. Mech. 224, 395 (1991). https://doi.org/10.1017/S0022112091001817

    Article  ADS  Google Scholar 

  30. F. Millot, J.C. Rifflet, G. Wille, V. Sarou-Kanian, B. Glorieux, J. Am. Ceram. Soc. 85, 187 (2002). https://doi.org/10.1111/j.1151-2916.2002.tb00064.x

    Article  Google Scholar 

  31. G. Wille, F. Millot, J.C. Rifflet, Int. J. Thermophys. 23, 1197 (2002). https://doi.org/10.1023/A:1019888119614

    Article  Google Scholar 

  32. V. Sarou-Kanian, F. Millot, J.C. Rifflet, Int. J. Thermophys. 24, 277 (2003). https://doi.org/10.1023/A:1022466319501

    Article  Google Scholar 

  33. F. Millot, V. Sarou-Kanian, J.-C. Rifflet, B. Vinet, Mater. Sci. Eng. A 495, 8 (2008). https://doi.org/10.1016/j.msea.2007.10.108

    Article  Google Scholar 

  34. H. Lamb, Proc. Lond. Math. Soc. S1–13, 51 (1881). https://doi.org/10.1112/plms/s1-13.1.51

    Article  Google Scholar 

  35. JCGM_100, Evaluation of measurement data — Guide to the expression of uncertainty in measurement (2008). https://www.bipm.org/documents/20126/2071204/JCGM_100_2008_E.pdf/cb0ef43f-baa5-11cf-3f85-4dcd86f77bd6

  36. N. Metropolis, S. Ulam, J. Am. Stat. Assoc. 44, 335 (1949). https://doi.org/10.1080/01621459.1949.10483310

    Article  Google Scholar 

  37. S.V. Ushakov, A. Shvarev, T. Alexeev, D. Kapush, A. Navrotsky, J. Am. Ceram. Soc. 100, 754 (2017). https://doi.org/10.1111/jace.14594

    Article  Google Scholar 

  38. V. Sarou-Kanian, J.-C. Rifflet, F. Millot, Ninth International Workshop on Subsecond Thermophysics (Austria, Graz, 2010), pp.249–261

    Google Scholar 

  39. J. C. Delabrouille, Surfusion de Quelques Métaux et Alliages (Faculté des sciences de Paris, Paris, 1969).

  40. T. Kondo, H. Muta, Y. Ohishi, HTHP 00, 1 (2019)

    Google Scholar 

  41. H.G. Kim, J. Choe, T. Inoue, S. Ozawa, J. Lee, Metall. Mater. Trans. B 47, 2079 (2016). https://doi.org/10.1007/s11663-016-0712-z

    Article  Google Scholar 

  42. J. Delacroix, P. Piluso, N. Chikhi, O. Asserin, D. Borel, A. Brosse, S. Cadiou, Steel Res. Int. 93, 2100624 (2022). https://doi.org/10.1002/srin.202100624

    Article  Google Scholar 

  43. T. Iida, R.I.L. Guthrie, The Physical Properties of Liquid Metals (Oxford University Press, Oxford, 1988)

    Google Scholar 

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Acknowledgements

This work was supported by the cross-cutting basic research Program (RTA Program) of the CEA Energy Division.

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Authors and Affiliations

  1. CEA, DES, IRESNE, DTN, SMTA, Severe Accident Experimental Laboratory, Cadarache, 13108, Saint-Paul-Lez-Durance, France

    Caroline Denier, Jules Delacroix & Pascal Piluso

  2. CNRS, CEMHTI UPR3079, Univ. Orléans, 45071, Orléans, France

    Caroline Denier, Zheng Zhang & Emmanuel de Bilbao

Authors
  1. Caroline Denier
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  2. Zheng Zhang
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  3. Emmanuel de Bilbao
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  4. Jules Delacroix
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Contributions

CD, ZZ and EdB carried out the experiments. CD has written the main part of the article. EdB, JD and PP have added some contributions, and reviewed the present article in a collegial manner.

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Correspondence to Caroline Denier.

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Appendices

Appendix 1: High-Speed Camera Calibration: Detailed Parameters and Results

The calibration of the high-speed camera also allowed to define satisfying parameters (size of the drop, gas flow) to optimize the levitation and reduce the standard deviation on measured diameters. For each steel ball, several gas flow were used and the width and the height of the drop were obtained with their standard deviation by using the Python script (Table

Table 4 Measured diameters of calibration steel beads for several gas flows with standard deviation
Full size table

4). Standard deviation was smaller for the biggest diameter, but it was not chosen because the drop with a higher mass is subjected to deformation in its lower part; thus the recommended diameter is around 2 mm for the sample. The standard deviation is always higher on the height, as this diameter is partially extrapolated due to the top of the nozzle hiding the lower part of the drop. Increasing the gas flow enables to see a bigger part of the sample with the high-speed camera, but it may also destabilize the drop and complicates the measurement of its thermophysical properties.

Appendix 2: Raw Data for the Three Thermophysical Properties Measured

The raw data and their uncertainties for the density, the surface tension, and the viscosity measured in this work are given Tables

Table 5 Raw data for the density
Full size table

5,

Table 6 Raw data for the surface tension
Full size table

6 and

Table 7 Raw data for the viscosity
Full size table

7, respectively.

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Denier, C., Zhang, Z., de Bilbao, E. et al. Thermophysical Properties of Liquid Zirconia Measured by Aerodynamic Levitation at High Temperature. Int J Thermophys 44, 127 (2023). https://doi.org/10.1007/s10765-023-03230-1

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