Improvement of a physical model for blockage formation of solid–liquid mixture flow with freezing for core safety evaluation of SFRs

Figures & data

Figure 1. Schematic view of a core fuel subassembly during CDAs.

Table 1. Validation status of the key models for blockage formation of the solid–liquid mixture flow with freezing

Situation
Unmolten fuel	Freezing	Key model	Validation status
No	Yes	Heat transfer (HT)	Complete [8]
		Mass transfer (MT)
		Momentum exchange function (MXF)
Yes	No	MXF with particle viscosity (PV)	Complete [9,10]
Yes	Yes	All of HT, MT, and MXF with PV	Incomplete [13]

Table 2. Fuel components during CDAs and modeled components in the SIMMER code with their simulants in the THEFIS experiment

CDAs	SIMMER	THEFIS
Molten fuel	Liquid component	Molten alumina
Solid nuclei of fuel	Particle component	Solid nuclei of alumina
Unmolten fuel	Chunk component	Particle deposit (alumina)

Figure 2. Change in the particle viscosity factor f against the particle fraction α_p for k = 5.0, α_MP = 0.62, and F = 0.

Table 3. Formulation of the particle viscosity factor for each binary component

	Particle	Chunk	Structure
Liquid	– (*1)	Equation (4)(4) $$\begin{array}{c}\hfill f=\frac{{\alpha }_{\mathrm{L}}}{{\alpha }_{\mathrm{L}}+{\alpha }_{\mathrm{P}}}+\frac{k{\alpha }_{\mathrm{MP}}{\alpha }_{\mathrm{P}}}{{\alpha }_{\mathrm{MP}}\left({\alpha }_{\mathrm{L}}+{\alpha }_{\mathrm{P}}\right)-{\alpha }_{\mathrm{P}}},\end{array}$$(4)	f = 1 (*2)
Particle	–	f = 1 (*2)	Equation (5)(5) $$\begin{array}{ccc}\hfill f& =& 1+MAX[\frac{k{\alpha }_{\mathrm{MP}}{\alpha }_{\mathrm{P}\_\mathrm{all}}}{{\alpha }_{\mathrm{MP}}\left(1-{\alpha }_{\mathrm{S}}\right)-{\alpha }_{\mathrm{P}\_\mathrm{all}}},\hfill \\ & & \times \frac{k{\alpha }_{\mathrm{MP}2}\overline{{\alpha }_{\mathrm{P}}}}{{\alpha }_{\mathrm{MP}2}\left(\overline{{\alpha }_{\mathrm{L}}}+\overline{{\alpha }_{\mathrm{P}}}\right)-\overline{{\alpha }_{\mathrm{P}}}}],\hfill \end{array}$$(5)
Chunk	–	–	Equation (6)(6) $$\begin{array}{c}\hfill f=1+\frac{k{\alpha }_{\mathrm{MP}}{\alpha }_{\mathrm{P}\_\mathrm{all}}}{{\alpha }_{\mathrm{MP}}\left(1-{\alpha }_{\mathrm{S}}\right)-{\alpha }_{\mathrm{P}\_\mathrm{all}}},\end{array}$$(6)

*1: the same velocity field.

*2: without particle viscosity model.

Figure 3. Physical phenomena involved in the freezing and blockage formation during CDAs.

Table 4. Improved formulation of the particle viscosity factor for each binary component

	Particle	Chunk	Structure
Liquid	– (*1)	Equation (7)(7) $$\begin{array}{c}\hfill f=\frac{{\alpha }_{\mathrm{L}}}{{\alpha }_{\mathrm{L}}+{\alpha }_{\mathrm{P}}}+\frac{k{\alpha }_{\mathrm{MP}}{\alpha }_{\mathrm{P}}}{{\alpha }_{\mathrm{MP}}\left({\alpha }_{\mathrm{L}}+{\alpha }_{\mathrm{P}}+{\alpha }_{\mathrm{G}}\right)-{\alpha }_{\mathrm{P}}}.\end{array}$$(7)	Equation (7)(7) $$\begin{array}{c}\hfill f=\frac{{\alpha }_{\mathrm{L}}}{{\alpha }_{\mathrm{L}}+{\alpha }_{\mathrm{P}}}+\frac{k{\alpha }_{\mathrm{MP}}{\alpha }_{\mathrm{P}}}{{\alpha }_{\mathrm{MP}}\left({\alpha }_{\mathrm{L}}+{\alpha }_{\mathrm{P}}+{\alpha }_{\mathrm{G}}\right)-{\alpha }_{\mathrm{P}}}.\end{array}$$(7)
Particle	–	f = 1 (*2)	f = 1 (*2)
Chunk	–	–	f = 1 (*2)

*1: the same velocity field.

*2: without particle viscosity model.

Figure 4. Experimental system and analytical model.

Table 5. Position and height of the particle deposit, and computational mesh size for each case

Run #	Position of particle deposit (mm)	Height of particle deposit (mm)	Mesh size (mm)
#1–6	0	0–80	5, 10, 15
#8	0.31	16	4, 8, 16
#9	0.38	80	5, 10, 20

Figure 5. Relation of the phenomena involved in each run of the THEFIS experiment.

Figure 6. Results of penetration length obtained by the THEFIS experiment [12] and the SIMMER analysis for various computational-mesh sizes for (a) Run #8 and (b) Run #9.

Figure 7. Axial distribution of materials with the melt velocity vector during melt penetration around the particle deposit for the Run #8 analysis with the computational mesh of 4 mm (the vertical axis shows the distance from the lower-end of the tube).

Figure 8. Results of penetration length for Runs #1–#6 obtained by the THEFIS experiment [12] and the SIMMER analysis for various computational-mesh sizes.

Figure 9. Axial distribution of materials with the melt velocity vector at the beginning of melt penetration for particle height of 30 and 15 mm with computational mesh of 5 mm.

Kamiyama K, Brear DJ, Tobita Y, et al. Establishment of freezing model for reactor safety analysis. J Nucl Sci and Technol. 2006;43:1206–1217.

 Web of Science ®Google Scholar

Liu P, Yasunaka S, Matsumoto T, et al. Simulation of the dynamic behavior of the solid particle bed in a liquid pool: sensitivity of the particle jamming and particle viscosity models. J Nucl Sci and Technol. 2006;43:140–149.

 Web of Science ®Google Scholar

Liu P, Yasunaka S, Matsumoto T, et al. Dynamic behavior of a solid particle bed in a liquid pool: SIMMER-III code verification. Nucl Eng Des. 2007;237:524–535.

 Web of Science ®Google Scholar

Yamano H, Tobita Y. Experimental analyses by SIMMER-III on fuel-pin disruption and low-energy disrupted core motion. J Power and Energy Systems. 2010;4:164–179.

 Google Scholar

Maschek W, Fieg G, Flad M. Experimental investigations of freezing phenomena of liquid/particle mixtures in the THEFIS facility and their theoretical interpretation. In: Proceeding International Fast Reactor Safety Meeting; 1990 Aug 12–16; Snowbird, UT. Vol. I, p. 519–529.

 Google Scholar