Skip to main content
SpringerLink
Log in

Analysis of molten metal spreading and solidification behaviors utilizing moving particle full-implicit method

  • Research Article
  • Published:
Frontiers in Energy Aims and scope Submit manuscript

Abstract

To retrieve the fuel debris in Fukushima Daiichi Nuclear Power Plants (1F), it is essential to infer the fuel debris distribution. In particular, the molten metal spreading behavior is one of the vital phenomena in nuclear severe accidents because it determines the initial condition for further accident scenarios such as molten core concrete interaction (MCCI). In this study, the fundamental molten metal spreading experiments were performed with different outlet diameters and sample amounts to investigate the effect of the outlet for spreading-solidification behavior. In the numerical analysis, the moving particle full-implicit method (MPFI), which is one of the particle methods, was applied to simulate the spreading experiments. In the MPFI framework, the melting-solidification model including heat transfer, radiation heat loss, phase change, and solid fraction-dependent viscosity was developed and implemented. In addition, the difference in the spreading and solidification behavior due to the outlet diameters was reproduced in the calculation. The simulation results reveal the detailed solidification procedure during the molten metal spreading. It is found that the viscosity change and the solid fraction change during the spreading are key factors for the free surface condition and solidified materials. Overall, it is suggested that the MPFI method has the potential to simulate the actual nuclear melt-down phenomena in the future.

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

Similar content being viewed by others

Abbreviations

A :

Surface area of particle

C ps :

Specific heat for solid/(J·(kg·K)−1)

C pl :

Specific heat for liquid/(J·(kg·K)−1)

D :

Nozzle diameter/mm

M :

Molten metal amount/g

MPFI:

Moving particle Full-implicit method

MPS:

Moving particle Semi-implicit method

Nu :

Nusselt number

P :

Pressure/Pa

Pr :

Prandtl number

Q :

Heat source/J

Re :

Reynolds number

T :

Temperature/°C

T e :

Environment temperature/°C

T m :

Melting temperature/°C

T s :

Stainless steel temperature/°C

X :

Falling height/mm

a :

Parameter for surface tension calculation

d ij :

Distance between particle i and particle j/m

g :

Gravity acceleration/(m·s−2)

h :

Enthalpy/J

h 1 :

Liquefying enthalpy/J

h 0 :

Solidifying enthalpy/J

k :

Thermal conductivity/(W·(m·K)−1)

q radiation :

Heat flux from radiation/(W·m−2)

r e :

Effective radius/m

t :

Time/s

u :

Fluid velocity/(m·s−1)

w ij :

Weight function

γ :

Solid fraction

η :

Emissivity

κ :

Compressibility/(N·m−2)

μ 0 :

Initial viscosity/(Pa·s)

μ 1 :

Viscosity/(Pa·s)

ρ :

Density/(kg·m−3)

σ :

Stephan-Boltzmann constant

ω :

Angular velocity/(rad·s−1)

References

  1. TEPCO. Unit 3 Primary Containment Vessel Internal Investigation. 2017, available at the website of http://tepco.co.jp

  2. TEPCO. Fukushima Daiichi Nuclear Power Station Unit 2 primary containment vessel internal investigation results. 2018, available at the website of http://tepco.co.jp

  3. Pellegrini M, Dolganov K, Herranz E, et al. Benchmark study of the accident at the Fukushima Daiichi NPS: best-estimate case comparison. Nuclear Technology, 2016, 196(2): 198–210

    Article  Google Scholar 

  4. Sehgal B R. Nuclear Safety in Light Water Reactors-severe Accident Phenomenology. USA: Academic Press, 2012

    Google Scholar 

  5. Veteau J M, Wittmaack R. CORINE experiments and theoretical modelling. In: Van Goetem G, Balz W, Della Loggia E, eds. FISA 95 EU Research on Severe Accidents, Office Official Publ. Luxembourg: Europ. Communities, 1996, 271–285

    Google Scholar 

  6. Green G A, Finrock C, Klages J, et al. Experimental studies on melt spreading, bubbling heat transfer, and coolant layer boiling. In: Proceedings of 16th Water Reactor Safety Meeting, Gaithersburg, MD, USA, 1988

  7. Dinh T N, Konovalikhin M J, Sehgal B R. Core melt spreading on a reactor containment floor. Progress in Nuclear Energy, 2000, 36(4): 405–468

    Article  Google Scholar 

  8. Suzuki H, Matsumoto T, Sakaki I, et al. Fundamental experiment and analysis for melt spreading on concrete floor. In: Proceedings 2nd ASME/JSME International Conference 1, San Francisco, USA, 1993, 403–407

  9. Eppinger B, Fieg G, Schuetz W, Stegmaier U. KATS experiments to simulate corium spreading in the EPR core catcher concept. In: Proceedings of the 9th International Conference on Nuclear Engineering (ICONE-9), Nice Acropolis, France, 2001, 32068804

  10. Alsmeyer H, Cron T, Messemer G, et al. ECOKATS-2: a large scale experiment on melt spreading and subsequent cooling by top flooding. In: Proceedings ICAPP’04 (International Congress Advances in Nuclear Power Plants), Pittsburg, USA, 2004

  11. Alsmeyer H, Crin T, Foit J J, et al. Test report of the melt spreading tests ECOKATS-V1 and ECOKATS-1. Constract FIKS — CT 1999 — 003. Ex-vessel core melt stabilization research. Karlsruhe: Wissenschaftliche Berichte, 2004, SAM-ECOSTAR-D15/FZKA 7064

    Google Scholar 

  12. Steinwarz W, Alemberti A, Häfner W, et al. Investigations on the phenomenology of ex-vessel core melt behavior (COMAS). Nuclear Engineering and Design, 2001, 209(1–3): 139–146

    Article  Google Scholar 

  13. Tromm W, Foit J J, Magallon D. Dry and wet spreading experiments with prototypic materials at the FARO facility and the theoretical analysis, 2000, Germany. FZKA, 2000, 6475: 178–188

    Google Scholar 

  14. Journeau C, Boccaccio E, Brayer C, et al. Ex-vessel corium spreading: results from the VULCANO spreading tests. Nuclear Engineering and Design, 2003, 223(1): 75–102

    Article  Google Scholar 

  15. Alsmeyer H, Albrecht G, Fieg G, et al. Controlling and cooling core melts outside the pressure vessel. Nuclear Engineering and Design, 2000, 202(2–3): 269–278

    Article  Google Scholar 

  16. Ogura T, Matsumoto T, Miwa S, et al. Experimental study on molten metal spreading and deposition behaviors. Annals of Nuclear Energy, 2018, 118: 353–362

    Article  Google Scholar 

  17. Matsumoto T, Sakurada K, Miwa S, et al. Scaling analysis of the spreading and deposition behaviors of molten-core-simulated metals. Annals of Nuclear Energy, 2017, 108: 79–88

    Article  Google Scholar 

  18. Ogura T, Matsumoto T, Miwa S, et al. Experimental study on molten metal spreading and deposition behaviors on wet surface. Progress in Nuclear Energy, 2018, 106: 72–78

    Article  Google Scholar 

  19. Sahboun N, Miwa S, Sawa K, et al. A molten metal jet impingement on a flat spreading surface. Journal of Nuclear Science and Technology, 2020, 57(9): 1111–1120

    Article  Google Scholar 

  20. Yokoyama R, Suzuki S, Okamoto K, et al. Scale effect of amount of molten corium and outlet diameters on corium spreading. Progress in Nuclear Energy, 2020, 130: 103535

    Article  Google Scholar 

  21. TEPCO. Locating fuel debris inside the unit 3 reactor using a muon measurement technology at Fukushima Daiichi nuclear power station. 2017-9-28, available at the website of http://tepco.co.jp

  22. Huppert H. The propagation of two-dimensional and axisymmetric viscous gravity currents over a rigid horizontal surface. Journal of Fluid Mechanics, 1982, 121: 43–58

    Article  Google Scholar 

  23. Foit J J. Spreading under variable viscosity and time-dependent boundary conditions: estimate of viscosity from spreading experiments. Nuclear Engineering and Design, 2004, 227(2): 239–253

    Article  Google Scholar 

  24. Farmer T, Sienicki J, Chu C, et al. The MELTSPREAD-1 computer code for the analysis of transient spreading and cooling of high temperature melts. Report EPRITR-103413,1993

  25. Wittmaack R. Coreflow: a code for the numerical simulation of free-surface flow. Nuclear Technology, 1997, 119(2): 158–180

    Article  Google Scholar 

  26. Spindler B, Veteau J M. The simulation of melt spreading with THEMA code. Nuclear Engineering and Design, 2006, 236(4): 415–424

    Article  Google Scholar 

  27. Allelein H, Breest A, Spengler C. Simulation of core melt spreading with LAVA: theoretical background and status of validation. In: Proceedings of the OECD Workshop on Ex-vessel Debris Cool-ability, Karlsruhe, Germany, 1999, FZKA6747

  28. Koshizuka S, Oka Y. Moving particle semi-implicit method for fragmentation of incompressible fluid. Nuclear Science and Engineering, 1996, 123(3): 421–434

    Article  Google Scholar 

  29. Kawahara T, Oka Y. Ex-vessel molten core solidification behavior by moving particle semi-implicit method. Journal of Nuclear Science and Technology, 2012, 49(12): 1156–1164

    Article  Google Scholar 

  30. Li G, Oka Y, Furuya M. Experimental and numerical study of stratification and solidification/melting behaviors. Nuclear Engineering and Design, 2014, 272: 109–117

    Article  Google Scholar 

  31. Chai P, Erkan N, Kondo M, et al. Experimental research and numerical simulation of moving molten metal pool. Mechanical Engineering Letters, 2015, 1: Paper No.15-00367

  32. Yamaji A, Li X. Development of MPS method for analyzing melt spreading behavior and MCCI in severe accident. Journal of Physics: Conference Series, 2016, 739: 012002

    Google Scholar 

  33. Chai P, Kondo M, Erkan N, et al. Numerical simulation of MCCI based on MPS method with different types of concrete. Annals of Nuclear Energy, 2017, 103: 227–237

    Article  Google Scholar 

  34. Jubaidah D G, Duan G, Yamaji A, et al. Investigation on corium spreading over ceramic and concrete substrates in VULCANO VE-U7 experiment with moving particle semi-implicit method. Annals of Nuclear Energy, 2020, 141: 107266

    Article  Google Scholar 

  35. Kondo M. A physically consistent particle method for incompressible fluid flow calculation. Computational Particle Mechanics, 2021, 8(1): 69–86

    Article  Google Scholar 

  36. Kondo M, Ueda S, Okamoto K. Melting simulation using a particle method with angular momentum conservation. In: Proceedings of the 2017 25th International Conference on Nuclear Engineering, Shanghai, China, 2017

  37. Monaghan J J. Simulating free surface flows with SPH. Journal of Computational Physics, 1994, 110(2): 399–406

    Article  Google Scholar 

  38. Spencer D B, Mehrabian R, Flemings M C. Rheological behavior of Sn-15 Pct Pb in the crystallization range. Metallurgical and Materials Transactions B, Process Metallurgy and Materials Processing Science, 1972, 3(7): 1925–1932

    Article  Google Scholar 

  39. Joly P A, Mehrabian R. The rheology of a partially solid alloy. Journal of Materials Science, 1976, 11(8): 1393–1418

    Article  Google Scholar 

  40. Ramacciotti M, Journeau C, Sudreau F, et al. Viscosity models for corium melts. Nuclear Engineering and Design, 2001, 204(1–3): 377–389

    Article  Google Scholar 

  41. Kondo M. Development of surface tension model with many-body potential. In: International Conference on Particle-based Methods — Fundamentals and Applications (Particles 2017), Hannover, Germany, 2017, 461–470

Download references

Acknowledgements

This study was partially supported by the Mitsubishi Heavy Industry (MHI).

Author information

Authors and Affiliations

  1. Department of Nuclear Engineering and Management, The University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo, 113-8656, Japan

    Ryo Yokoyama

  2. Research Center for Computational Design of Advanced Functional materials (CD-FMat), Department of Materials and Chemistry, National Institute of Advanced Industrial Science and Technology (AIST), Central 2, 1-1-1, Umezono, Tsukuba, Ibaraki, 305-8568, Japan

    Masahiro Kondo

  3. Institute of Engineering Innovation, School of Engineering, The University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo, 113-8656, Japan

    Shunichi Suzuki

  4. Nuclear Professional School, The University of Tokyo, 2-22 Shirakata, Tokai-mura, Ibaraki, 319-1188, Japan

    Koji Okamoto

Authors
  1. Ryo Yokoyama
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Masahiro Kondo
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Shunichi Suzuki
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Koji Okamoto
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Ryo Yokoyama.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Yokoyama, R., Kondo, M., Suzuki, S. et al. Analysis of molten metal spreading and solidification behaviors utilizing moving particle full-implicit method. Front. Energy 15, 959–973 (2021). https://doi.org/10.1007/s11708-021-0753-0

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11708-021-0753-0

Keywords

Search

Navigation