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

doi:10.1007/s11708-021-0754-z

Front. Energy

2021, Vol. 15

Issue (4) : 946-958 https://doi.org/10.1007/s11708-021-0754-z

RESEARCH ARTICLE

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

Reo KAWAKAMI¹(

), Xin LI¹, Guangtao DUAN², Akifumi YAMAJI¹, Isamu SATO³, Tohru SUZUKI³

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
². Department of Nuclear Engineering and Management, The University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo, 113-8656, Japan
³. Department of Nuclear Safety Engineering, Faculty of Engineering, Tokyo City University, 1-28-1 Tamazutsumi, Setagaya-ku, Tokyo, 158-0087, Japan

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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.

Keywords boiling water reactor (BWR) severe accident channel blockage moving particle semi-implicit (MPS) method solidification

Corresponding Author(s): Reo KAWAKAMI

Online First Date: 13 July 2021 Issue Date: 04 January 2022

Cite this article:

Reo KAWAKAMI,Xin LI,Guangtao DUAN, et al. Improvement of solidification model and analysis of 3D channel blockage with MPS method[J]. Front. Energy, 2021, 15(4): 946-958.

URL:

https://academic.hep.com.cn/fie/EN/10.1007/s11708-021-0754-z
https://academic.hep.com.cn/fie/EN/Y2021/V15/I4/946

Fig.1 Unsuccessful calculation of fuel support piece channel blockage with melt freezing.

Fig.2 MPS algorithms for modeling melt solidification.

Fig.3 Experimental geometry.

Tab.1 Experimental cases [15]

Fig.4 Analysis geometry in 2D.

Case	A	B	C	D	E	F
Re	700				1200	2300
$u ¯ m o / (m ? s − 1)$	0.02625				0.045	0.08625
$θ W$	2.5	1.1	0.6	0.4	1.1
$T 0 / ° C$	2.0	4.0	4.0	6.0	4.0
$T W / ° C$	–5.0	–4.4	–2.4	–2.4	–4.4

Tab.2 Analysis cases

Fig.5 Velocity scale perpendicular to the flow direction near the inlet at different particle sizes.

Fig.6 Pressure and viscosity distributions in equilibrium state.

Fig.7 Ice thickness for cases at different dimensionless wall temperatures (Re = 700).

Fig.8 Ice thickness for cases at different Re values (θ_W = 1.1).

Tab.3 Physical properties [10,26]

Tab.4 Analysis cases

Fig.9 Calculation geometry and boundary particles.

Fig.10 MPS simulation results of SS/B₄C flowing down BWR fuel support piece.

Fig.11 MPS simulation results of Zr flowing down BWR fuel support piece.

Fig.12 Comparison of outflow mass evaluation.

$α$	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
l₀	Particle size
L	Row vector
n⁰	Initial particle number density
P	Pressure
Q	Heat source
Re	Reynolds number
r_e	Effective interaction radius
r	Position vector
t	Time
T	Temperature
T₀	Inflow temperature
T_W	Wall temperature
u	Velocity vector
$u ‾ m o$	Inflow rate
w(r)	Weight function
x,y	Position
$γ$	Solid fraction
$θ w$	Dimensionless wall temperature
$λ$	Correction factor
$μ$	Dynamic viscosity
v	Kinematic viscosity
$ρ$	Density
$ϕ$	A scalar quantity
i,j	Particle identification number
I	Liquidus
s	Solidus

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