Skip to main content
SpringerLink
Log in

Numerical investigation of single bubble dynamics in liquid sodium pool

  • Published:
Sādhanā Aims and scope Submit manuscript

Abstract

The single gas bubble rise dynamics in liquid sodium/sodium-potassium alloy (NaK) pool due to entrainment of argon cover gas/non-condensable fission gas (xenon) have received considerable attention in the safe operation of Sodium-cooled Fast Reactor (SFR). Numerical simulation of single bubble dynamics in liquid sodium/NaK pool is an essential intermediate step for the evaluation of rise velocity and shape changes, which are of utmost importance in areas of reactor safety concerned with source term evaluation and cover gas purification. The interFoam solver of OpenFOAM package is used to evaluate inert gas bubble rise dynamics in stagnant liquid metal pool of sodium and NaK. The governing equations are discretized and solved using the Volume of Fluid (VOF) based solver available in OpenFOAM with appropriate initial and boundary conditions. The VOF module of the solver is validated against numerical benchmark data and experimental results available in literature. The bubble dynamics in liquid sodium/NaK pool are studied in terms of trajectory, shape and rise velocity for diameters ranging from 10 to 20 mm, domain aspect ratios and for different gas-liquid systems. The study shows that the bubble rise velocity increases with diameter for liquid sodium systems. The rise behavior of single inert gas bubble in liquid water and sodium pool are compared. The study supports the use of air-water system as a simulant for studying bubble dynamics in liquid sodium systems as suggested by other researchers. The study is very useful and forms an intermediate step towards the development of an OpenFOAM based computational framework to analyze heat and mass transfer from single bubble rising in liquid sodium pool for reactor safety studies.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Figure 1
Figure 2
Figure 3
Figure 4
Figure 5
Figure 6
Figure 7
Figure 8
Figure 9
Figure 10
Figure 11
Figure 12
Figure 13
Figure 14
Figure 15
Figure 16
Figure 17
Figure 18
Figure 19
Figure 20
Figure 21
Figure 22
Figure 23

Similar content being viewed by others

References

  1. Henry R E, Grolmes M A and Fauske H K 1971 Pressure-pulse propagation in two-phase one- and two- component mixtures. ANL-7792. Argonne National Laboratory Illinois

  2. Pradeep A, Sharma A K 2018 Semiempirical model for wet scrubbing of bubble rising in liquid pool of sodium-cooled fast reactor. Nucl. Eng. Technol. 50: 849–853

    Article  Google Scholar 

  3. Puthiyavinayagam P 2015 Progress in Fast Reactor Programme of India: April 2014-March 2015. In: Proceedings of the 48th Annual Meeting of TWGFR, IAEA IPPE. Obninsk. Russia

  4. Clift R, Grace J R and Weber M E 1978 Bubbles, drops and particles. New York: Academic Press, pp.183–216

    Google Scholar 

  5. Shevchenko N, Boden S, Eckert S, Borin D, Heinze M and Odenbach S 2013 Application of X-ray radioscopic methods for characterization of two-phase phenomena and solidification processes in metallic melts. The Euro. Phys. J. Special Topics 220: 63–77

    Article  Google Scholar 

  6. Han Z and Holappa L 2003 Bubble bursting phenomenon in gas/metal/slag systems. Metallurgical and Materials Trans. B. 34B: 525–532

    Article  Google Scholar 

  7. Guézennec A G et al 2004 Dust formation by bubble-burst phenomenon at the surface of a liquid steel bath. Iron and Steel Institute of Japan Int. 44(8): 1328–1333

    Article  Google Scholar 

  8. Wang X 2015 Numerical simulation of two-dimensional bubble dynamics and evaporation. PhD Thesis. KU Leuven Arenberg doctoral school, Belgium

  9. Wang Z and Tong A Y 2008 Deformation and oscillations of a single gas bubble rising in a narrow vertical tube. Int. J. Therm. Sci. 47: 221–228

    Article  Google Scholar 

  10. Raees F, Heul D R V D and Vuik C 2011 Evaluation of the interface-capturing algorithm of OpenFOAM for the simulation of incompressible immiscible two-phase flow. Report. Department of Applied Mathematical Analysis. Delft University of Technology, Netherlands

  11. Klostermann J, Schaake K and Schwarze R 2013 Numerical simulation of a single rising bubble by VOF with surface compression. Int. J. Num. Methods in Fluids 71: 960–982

    Article  MathSciNet  Google Scholar 

  12. Xu Y, Ersson M and Jönsson P 2015 Numerical simulation of single argon bubble rising in molten metal under a laminar flow. Steel Research Int. 86(11): 1289–1297

    Article  Google Scholar 

  13. Pradeep A et al 2015 Numerical simulation of gas bubble rising in a liquid pool of SFR. Indo-UK workshop on Modelling and Simulation of Safety and Materials for Nuclear Applications MSMNA-2015. Anupuram. Tamilnadu, India

  14. Pradeep A et al 2016 Numerical modelling of inert gas bubble rising in liquid metal pool. Proceedings of the 6th International and 43rd National Conference on Fluid Mechanics and Fluid Power MNNITA. Allahabad. India

  15. Verma A, Babu R and Das M K 2017 Modelling of a single bubble rising in a liquid column. In: Proceedings of the 5th International and 41st National Conference on FMFP 2014. A K Saha, et al Editors, 2017, Springer India, New Delhi, pp. 1059–1068

  16. Miyahara S and Sagawa N 1996 Iodine mass transfer from xenon-iodine mixed gas bubble to liquid sodium pool, (II) development of analytical model. J. Nucl. Sci. Technol. 33(3): 220–228

    Article  Google Scholar 

  17. Dickinson D R and Nunamaker F H 1975 LMFBR source term iodine attenuation test of bubble breakup/coalescence in LMFBR outlet plenum following large fission gas release. No. HEDL-TC-537. Hanford Engineering Development Lab. Richland. Wash. USA

  18. Quarterly Technical Progress Report, Nuclear Safety, Characterization of Sodium Fires and Fast Reactor Fission Products, January-March 1976 AI-ERDA-13172. Atomics International

  19. Umbel M 2011 Containment Source Terms for Sodium-Cooled Fast Reactor Accidents. Master’s Thesis. The Ohio State University, USA

  20. Damián S M 2012 Description and utilization of interFoam multiphase solver. Final Work. Computational Fluid Dynamics http://infofich.unl.edu.ar/upload/3be0e16065026527477b4b948c4caa7523c8ea52.pdf

    Google Scholar 

  21. Greenshields C J 2016 OpenFOAM user guide

  22. Hirt C W and Nichols B D 1981 Volume of fluid (VOF) method for the dynamics of free boundaries. J. Comp. Phys. 39: 201–225

    Article  Google Scholar 

  23. Brackbill J U, Kothe D B and Zemach C 1992 A continuum method for modeling surface tension. J. Comp. Phys. 100: 335–354

    Article  MathSciNet  Google Scholar 

  24. Van Leer B 1979 Towards the ultimate conservative difference scheme. V. A second-order sequel to Godunov’s method. J. Comp. Phys. 32: 101–136

    Article  Google Scholar 

  25. Herreras N and Izarra J 2013 Two-Phase Pipe Flow Simulations with OpenFOAM. Master’s thesis. Norwegian University of Science and Technology, Norway

  26. Rusten E S A 2013 Numerical study of the droplet-interface dynamic related to liquid-liquid separators. Master’s thesis. Department of Physics. Norwegian University of Science and Technology, Norway

  27. Hysing S, Turek S, Kuzmin D, Parolini N, Burman E, Ganesan S and Tobiska L 2009 Quantitative benchmark computations of two‐dimensional bubble dynamics. Int. J. Num. Methods in Fluids 60: 1259–1288

    Article  MathSciNet  Google Scholar 

  28. http://www.featflow.de/en/benchmarks/cfdbenchmarking/bubble/bubble_reference.html

  29. Krishna R and Baten J M V 1999 Rise characteristics of gas bubbles in a 2D rectangular column: VOF simulations vs experiments. Int. Comm. Heat Mass Transf. 26(7): 965–974

    Article  Google Scholar 

  30. Levich V G 1962 Physiochemical Hydrodynamics. Englewood Cliffs. New Jersey: Prentice Hall

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Indira Gandhi Centre for Atomic Research, HBNI, Kalpakkam, 603102, India

    ARJUN PRADEEP & ANIL KUMAR SHARMA

Authors
  1. ARJUN PRADEEP
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. ANIL KUMAR SHARMA
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to ARJUN PRADEEP.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

PRADEEP, A., SHARMA, A.K. Numerical investigation of single bubble dynamics in liquid sodium pool. Sādhanā 44, 56 (2019). https://doi.org/10.1007/s12046-018-1041-5

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1007/s12046-018-1041-5

Keywords

Search

Navigation