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Improvement of solidification model and analysis of 3D channel blockage with MPS method

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Abstract

In a severe accident of a nuclear power reactor, coolant channel blockage by solidified molten core debris may significantly influence the core degradations that follow. The moving particle semi-implicit (MPS) method is one of the Lagrangian-based particle methods for analyzing incompressible flows. In the study described in this paper, a novel solidification model for analyzing melt flowing channel blockage with the MPS method has been developed, which is suitable to attain a sufficient numerical accuracy with a reasonable calculation cost. The prompt velocity diffusion by viscosity is prioritized over the prompt velocity correction by the pressure term (for assuring incompressibility) within each time step over the “mushy zone” (between the solidus and liquidus temperature) for accurate modeling of solidification before fixing the coordinates of the completely solidified particles. To sustain the numerical accuracy and stability, the corrective matrix and particle shifting techniques have been applied to correct the discretization errors from irregular particle arrangements and to recover the regular particle arrangements, respectively. To validate the newly developed algorithm, 2-D benchmark analyses are conducted for steady-state freezing of the water in a laminar flow between two parallel plates. Furthermore, 3-D channel blockage analyses of a boiling water reactor (BWR) fuel support piece have been performed. The results show that a partial channel blockage develops from the vicinity of the speed limiter, which does not fully develop into a complete channel blockage, but still diverts the incoming melt flow that follows to the orifice region.

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Abbreviations

α :

Threshold parameter

C :

Corrective matrix

C p :

Specific heat capacity

CR :

Parameter of Ramacciotti model

d :

Dimension number

f :

Force

g :

Gravity

H :

Half of the flow channel width

h :

Enthalpy

k :

Thermal conductivity

l 0 :

Particle size

L :

Row vector

n 0 :

Initial particle number density

P :

Pressure

Q :

Heat source

Re :

Reynolds number

r e :

Effective interaction radius

r :

Position vector

t :

Time

T :

Temperature

T 0 :

Inflow temperature

T W :

Wall temperature

u :

Velocity vector

ū mo :

Inflow rate

w(r):

Weight function

x,y :

Position

γ :

Solid fraction

θ W :

Dimensionless wall temperature

λ :

Correction factor

μ :

Dynamic viscosity

ν :

Kinematic viscosity

ρ :

Density

ϕ :

A scalar quantity

i,j :

Particle identification number

l:

Liquidus

s:

Solidus

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Acknowledgements

This work was supported by the Nuclear Energy Science & Technology and Human Resource Development Project (through concentrating wisdom), the Advanced Theoretical and Experimental Physics, Waseda University, and the TCU priority promotion research supported by Tokyo City University.

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Authors and Affiliations

  1. Cooperative Major in Nuclear Energy, Graduate School and Advanced Science and Engineering, Faculty of Science and Engineering, Waseda University, 3-4-1 Okubo, Shinjuku-ku, Tokyo, 169-8555, Japan

    Reo Kawakami, Xin Li & Akifumi Yamaji

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

    Guangtao Duan

  3. Department of Nuclear Safety Engineering, Faculty of Engineering, Tokyo City University, 1-28-1 Tamazutsumi, Setagaya-ku, Tokyo, 1580087, Japan

    Isamu Sato & Tohru Suzuki

Authors
  1. Reo Kawakami
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  2. Xin Li
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  3. Guangtao Duan
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  4. Akifumi Yamaji
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  5. Isamu Sato
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  6. Tohru Suzuki
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Correspondence to Reo Kawakami.

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Kawakami, R., Li, X., Duan, G. et al. Improvement of solidification model and analysis of 3D channel blockage with MPS method. Front. Energy 15, 946–958 (2021). https://doi.org/10.1007/s11708-021-0754-z

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  • DOI: https://doi.org/10.1007/s11708-021-0754-z

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