P2M Simulation Exercise on Past Fuel Melting Irradiation Experiments

Figures & data

TABLE I Main Characteristics of the As-Manufactured Fuel Rods

	xM3	HBC4
Rodlet
Rod length (mm)	522	1136
Pellet stack length (mm)	441	996
Plenum length (mm)	44	95
Diametral gap (μm)	170	200
Fuel Pellet
Outer diameter (mm)	8.2	8.0
Height (mm)	10	12.3
Enrichment (%)	4.5	8.2
Grain size (μm)	30	11
Cladding
Outer diameter (mm)	9.5	9.5
Thickness (mm)	0.57	0.63

Fig. 1. Power histories and axial power profiles during the xM3 base irradiation and power ramp.

TABLE II Main Characteristics of the Simulated Power Ramps

Rodlet name	xM3	HBC4
Fuel	UO2	$\mathrm{U}{\mathrm{O}}_2$
Cladding type	SR Zirlo	CWSR Zircaloy-4
Base irradiation reactor	Vandellos-II (Spain)	BR3 (Belgium)
MTR	R2 (Sweden)	BR2 (Belgium)
Year	2005	1987
Burnup ($\mathrm{GWd}\mathrm{t}{\mathrm{U}}^{-1}$) average/peak	27/27	48/61
Conditioning power ($\mathrm{kW}.{\mathrm{m}}^{-1}$)	20	40
Conditioning power duration (h)	18	20
Ramp step ($\mathrm{kW}.{\mathrm{m}}^{-1}$)	5	—
Ramp step rate ($\mathrm{kW}.{\mathrm{m}}^{-1}\mathrm{mi}{\mathrm{n}}^{-1}$)	10	—
Ramp step holding time (h)	1	—
RTL ($\mathrm{kW}.{\mathrm{m}}^{-1}$)	70	66
RTL step rate ($\mathrm{kW}.{\mathrm{m}}^{-1}\mathrm{mi}{\mathrm{n}}^{-1}$)	10	72
RTL holding time	1 h 13 min	40s
Uncertainty on RTL	$\pm$5%	$\pm$7%
Clad failure	No	Yes

Fig. 2. Power histories and axial power profiles during the HBC4 base irradiation and power ramp.

Fig. 3. Transverse cross section of the unfailed xM3 rod after the power ramp.

Fig. 4. Rod diameter profile after the HBC4 power ramp with the location of the transverse (CT) and longitudinal (CL) cross sections and of the central holes.

Fig. 5. HBC4 rodlet. Transverse cross section CT1. Clad failure is visible on the right side.

Fig. 6. HBC4 rodlet. Transverse cross section CT1’, obtained by grinding and polishing downward CT1.

Fig. 7. HBC4 rodlet. Transverse cross section CT2.

Fig. 8. HBC4 rodlet. Longitudinal cross section CL1.

TABLE III Melting Fuel Radii Based on the Available xM3 and HBC4 Cross Sections

	xM3	HBC4-CT1	HBC4-CT1’	HBC4-CT2
Axial position/BFC (mm)	180	362 to 368	362 to 368	334 to 340
RTL ($\mathrm{kW}.{\mathrm{m}}^{-1}$)	70	63.6	63.6	64.4
Local burnup ($\mathrm{GWd}\mathrm{t}{\mathrm{U}}^{-1}$)	27	60.7	60.7	57.9
Central hole radius (mm)	0.15	0.31 to 0.38	0.15 to 0.2	0.61 to 0.77
Melt radius (mm)	0.4 to 1.2	0.8	0.8	1.1

Fig. 9. Calculated clad diameters and pellet-clad gaps at the end of xM3 and HBC4 base irradiations compared to available measurements.

Fig. 10. Calculated fuel centerline temperature evolution at PPN during the xM3 power ramp.

Fig. 11. Calculated axial profiles of the fuel centerline temperature at RTL, calculations at nominal power.

Fig. 12. Calculated and measured residual strain, pellet diameter, and gap axial profiles at the end of the xM3 power ramp.

Fig. 13. Calculated and measured rod elongations during the xM3 ramp (the results are normalized with respect to the clad length at the end of the conditioning plateau).

Fig. 14. Calculated and measured clad axial profiles after the HBC4 power ramp.

Fig. 15. Calculated and measured FGR after the xM3 power ramp.

Fig. 16. Axial profiles of calculated melting radii at RTL compared to measurements.

Fig. 17. Calculated melting fuel melting radii and centerline temperatures at PPN and RTL in the simulations of xM3 (power uncertainty $\pm$5%) and HBC4 (power uncertainty $\pm$7%).

Fig. A.1 Setup for the gap measurements.

TABLE B.I Main Models and Criteria in the Codes

Organization	Code	Dimension	Thermal Analysis	Thermal Conductivity Model	Heat Capacity Model	FGR Model	Fuel Gas-Induced Swelling	Clad Stress Corrosion Cracking Failure Criterion	Impact of Clad Failure on Thermal Analysis	Fuel Melting Model
INL	BISON	1.5D, 2D (r,z)	Transient	[62]	[33]	Yes	Yes	No	No	No
PSI	FALCON v1.5.0	2D (r,$\mathit{\theta }$), 2D (r,z)	Transient, steady state	[63]	[32]	Yes	Yes	Stress	Yes	[32]
NRC	FAST v1.0.1	1.5D	Transient	[35]	[35]	Yes	Yes	No	No	[35]
JAEA	FEMAXI-8 (v8.1)	1.5D	Transient, steady state	[64], [65]	[32]	[43]	[43]	No	No	Internal
CIEMAT	FRAPCON-4.0	1.5D	Steady state	[30]	[30]	Yes	Yes	No	No	No
ALVEL	FRAPCON-4.0/FRAPTRAN-2.1	1.5D	Steady state	[31], [33]	[31], [33]	Yes	Yes	Strain, stress	No	[31]
CRIEPI	FRAPCON-4.0/FRAPTRAN-2.0	1.5D	Transient	[32]	[32]	Yes	Yes	No	Yes	[32]
UJV	TRANSURANUS	1.5D	Transient	Internal	Internal	Yes	Yes	No	No	Internal
VTT	FINIX	1.5D	Transient, steady state	[33]	[33]	Yes	Yes	Strain	Yes	No
EDF	CYRANO3 v3.7.4	1.5D	Transient, steady state	Internal	Internal	Yes	Yes	Stress, SED	No	Internal
GRS	TESPA-ROD	1.5D	Transient	Internal	Internal	Yes	No	Stress	Yes	Internal
SCK‧CEN	TRANSURANUS v1.1	1.5D	Transient, steady state	Internal	Internal	Yes	Yes	Othera	No	[26]
CEA	ALCYONE v2.1	1.5D, 2D (r,$\mathit{\theta }$), 3D	Transient, steady state	Internal	Internal	Yes	Yes	Strain, stress	Yes	Internal

^aIntegrated crack length larger than wall thickness.

TABLE B.II Main Models for Fuel Melting in the Codes*

Organization	Code	Dimension	Melting Temperature	Melting Radius	Fuel Expansion upon Melting	Latent Heat of Melting	Impact on FGR Model	Central Hole Formation Model	Validation Data for Fuel Melting
INL	BISON	1.5D, 2D (r,z)	Tsol = Tliq	R${ }_{\mathit{melt}}$ = R(T${ }_{\mathit{liq}}$)	No	No	No	No	No
PSI	Falcon v1.5.0	2D (r,$\mathit{\theta }$), 2D (r,z)	Tsol = Tliq (burnup)		No	No	No	No	No
NRC	FAST 1.0.1	1.5D	Tsol = Tliq (burnup)	R${ }_{\mathit{melt}}$ = R(T${ }_{\mathit{liq}}$)	Yes	Yes	No	No	[35]
JAEA	FEMAXI-8 (V8.1)	1.5D	Tsol = Tliq (burnup)	R${ }_{\mathit{melt}}$ = R(T${ }_{\mathit{liq}}$)	No	No	No	No	No
CIEMAT	FRAPCON-4.0	1.5D	Tsol = Tliq (burnup)	R${ }_{\mathit{melt}}$ = R(T${ }_{\mathit{liq}}$)	No	No	No	No	No
ALVEL	FRAPCON-4.0/FRAPTRAN 2.1	1.5D	Tsol = Tliq (burnup)	R${ }_{\mathit{melt}}$ = R(T${ }_{\mathit{liq}}$)	Yes	Yes	No	No	No
CRIEPI	FRAPCON-4.0/FRAPTRAN 2.0	1.5D	Tsol = Tliq (burnup)	R${ }_{\mathit{melt}}$ = R(T${ }_{\mathit{liq}}$)	Yes	Yes	No	No	[32]
UJV	TRANSURANUS	1.5D			Yes	Yes	Yes	Yes (disabled)	Internal
VTT	FINIX	1.5D	Tsol = Tliq (burnup)	R${ }_{\mathit{melt}}$ = R(T${ }_{\mathit{liq}}$)	No	No	No	No	No
EDF	CYRANO3 v3.7.4	1.5D	Tsol = Tliq (burnup)	R${ }_{\mathit{melt}}$ = R(T${ }_{\mathit{liq}}$)	No	No	Yes	No	Internal
GRS	TESPA-ROD	1.5D	Tsol = Tliq	R${ }_{\mathit{melt}}$ = R(T${ }_{\mathit{liq}}$)	No	Yes	No	No	No
SCK‧CEN	TRANSURANUS v1.1	1.5D	[27], [28]	R${ }_{\mathit{melt}}$ = R(T${ }_{\mathit{sol}}$)	Yes	Yes	No	Yes	Internal
CEA	ALCYONE v2.1	1.5D, 2D (r,$\mathit{\theta }$), 3D	Tsol $\ne$ Tliq from Gibbs energy minimization^Citation38,Citation40	R${ }_{\mathit{melt}}$ = R(T${ }_{\mathit{sol}}$)	Yes	Yes	Yes	No	No

*T_sol = solidus temperature; T_liq = liquidus temperature.

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