Neutronics analysis of full MOX BWR core simulation experiments – FUBILA: Part 2

Figures & data

Figure 1. Picture of a core tank loaded with MOX rods and structures for the control blade core [4]. Note: the number of MOX rods in the driver region is not the same as that of the critical core.

Figure 2. Schematic diagram of core radial configurations of critical cores [3,4]. (a) 9 × 9 reference core (0% void), (b) Control blade core (40% void), (c) UO₂ rod core (40% void), (d) Gd₂O₃-UO₂ rod core (40% void), (e) 10 × 10 assembly core (40% void), (f) Time-elapsed reference core (0% void). Note: “Pu(t) 3.0wt%” means a total-Pu content (include ²⁴¹Am) of MOX pellets is 3.0 wt%, “AG3” is Aluminum alloy.

Table 1. Geometrical and material specifications of the mockup assemblies in the FUBILA cores [3,4]. (Geometrical unit: mm).

	Test assembly						Driver assembly
Item	9 × 9 reference core (0% void)	Control blade core (40% void)	UO2 rod core (40% void)	Gd2O3-UO2 rod core (40% void)	10 × 10 MOX assembly core (40% void)	Time-elapsed reference core (0% void)
Assembly lattice	9 × 9	9 × 9	9 × 9	9 × 9	10 × 10	9 × 9	9 × 9
MOX fuel rod
Pellet outer diameter	9.4	9.4	9.4	9.4	9.4	9.4	8.2
Fuel rod outer diameter	11.0	11.0	11.0	11.0	11.0	11.0	9.5
Thickness of fuel cladding	0.7	0.7	0.7	0.7	0.7	0.7	0.6
Material of fuel cladding	Zry-2	Zry-2	Zry-2	Zry-2	Zry-2	Zry-2	Zry-4
Overcladding outer/inner diameter	12.8/11.3	12.8/11.3	12.8/11.3	12.8/11.3	12.3/11.3	12.8/11.3	12.6/9.8
Material of overcladding	AG3^a	AG3	AG3	AG3	AG3	AG3	AG3
UO2 fuel rod	–	–	–	–	–	–	–
Pellet outer diameter			8.2	8.2
Fuel rod outer diameter			9.5	9.5
Thickness of fuel cladding			0.6	0.6
Materila of fuel cladding	–	–	Zry-4	Zry-4	–	–	–
Overcladding outer/inner diameter			12.8/9.8	12.8/9.8
Materila of overcladding			AG3	AG3
Gd2O3-UO2 fuel rod	–	–	–	–	–	–	–
Pellet outer diameter	–			8.2	–	–	–
Fuel rod outer diameter				9.5
Thickness of fuel cladding				0.6
Materila of fuel cladding			6.7	Zry-4
Overcladding outer/inner diameter			14.9	12.8/9.8
Materila of overcladding				AG3
AG3 rod outer diameter	–	6.7	6.7	6.7	–	–	–
Fuel rod pitch	14.9	14.9	14.9	14.9	13.4	14.9	14.9
Water rod							–
Number	9	9	9	9	9	9
AG3 tube outer/innner diameter	12.8/8.8	12.8/10.2	12.8/10.2	12.8/10.2	12.3/9.6	12.8/8.8
Out-channel water gap
Width of water gap^b	20.9	20.9	20.9	20.9	21.0	20.9	20.9
AG3 rod	13.2	11.4	11.4	11.4	10.4	13.2	–
Assembly pitch	155.0	155.0	155.0	155.0	155.0	155.0	155.0
B4C control blade	–	Figure 2	–	–	–	–	–
Note: ^aAluminum alloy, ^bGap between the outer surfaces of fuel cells, “–”: not applied.

Table 2. Core configurations of the FUBILA cores for critical mass measurement [3,4].

Core	9 × 9 reference core (0% void)	Control blade core (40% void)	UO2 rod core (40% void)	Gd2O3-UO2 rod core (40% void)	10 × 10 MOX assembly core (40% void)	Time-elapsed reference core (0% void)
Measurement date	2005/2/14	2006/2/7	2006/3/24	2006/4/27	2006/1/4	2006/7/12
Number of fuel rods and structures
Test region
MOX 3 wt%	16(4 × 4)	16(4 × 4)	8	–	–	16(4 × 4)
MOX 5 wt%	32(4 × 8)	32(4 × 8)	28	24(4 × 6)	–	32(4 × 8)
MOX 8.5 wt%	112(4 × 28)	112(4 × 28)	92	72(4 × 18)	112(4 × 28)	112(4 × 28)
MOX 11.5 wt%	128(4 × 32)	128(4 × 32)	128	128(4 × 32)	256(4 × 64)	128(4 × 32)
UO2	–	–	32(2 × 16)	32(2 × 16)	–	–
Gd2O3-UO2	–	–	–	32(2 × 16)	–	–
AG3 tube for water rod	36(4 × 9)	36(4 × 9)	36(4 × 9)	36(4 × 9)	32(4 × 8)	36(4 × 9)
AG3 rod	–	400(4 × 100)	400(4 × 100)	400(4 × 100)	–	–
AG3 rod for out-channel	117	117	117	117	129	117
Driver region
MOX 7wt%	598	1474	910	1226	617	661
Safety rod guide tube	20	20	20	20	20	20
Pilot rod guide tube	1	1	1	1	1	1
Fission chamber guide tube	1	1	1	1	1	2
Core temperature (°C)^a	19.8 ± 0.1	20.0 ± 0.1	19.6 ± 0.1	19.9 ± 0.1	20.0 ± 0.1	20.0 ± 0.1
Doubling time (s)^a	39.5 ± 0.2	21.0 ± 0.2	30.4 ± 0.3	28.0 ± 0.3	39.7 ± 0.3	49.3 ± 0.3
Excess reactivity ($)^a	0.143 ± 0.001	0.216 ± 0.008	0.170 ± 0.003	0.180 ± 0.003	0.141 ± 0.003	0.122 ± 0.004
Excess reactivity (pcm Δ k/k)^b	49.7 ± 0.5	71.0 ± 2.5	59.2 ± 1.1	61.6 ± 1.1	49.5 ± 1.1	42.1 ± 1.4
β eff (pcm)^c	348.6	328.0	349.0	342.4	351.8	344.7
Note: ^aError in 1 σ ; ^bExcess reactivity calculated using  β  eff in the bottom low of the table (unit: ×10^−5 Δ k/k); ^cCalculated by three dimensional diffusion calculations (see text).

Figure 3. Schematic drawing of cross-section of cruciform control blade with B₄C absorber rods [7].

Figure 4. Configuration of a mockup fuel assembly with an in-channel void fraction of 40%.

Table 3. Fission rate distribution measurements and measured buckling values.

Core/Measurement	Fission rate distribution measurement	Measurement of buckling
		Buckling (×10^−3 cm^−2)	Error (1σ) (×10^−3 cm^−2)
Control blade core	A	0.982	0.003
UO2 rod core	N/A	–	–
Gd2O3-UO2 rod core	A	1.007	0.002
10 × 10 assembly core	A	1.027	0.003
Time-elapsed reference core	N/A	–	–
Note: A: measurements were applied, N/A: measurements were not applied.

Figure 5. Multi-cell model for out-channel gap inserted with a cruciform control blade. Note: Ex. MOX 5.0wt%: homogenized cell of MOX rod of 5.0 (total Pu) wt%, moderator and structures.

Figure 6. Critical k _eff's calculated with JENDL-3.3 for the FUBILA cores. Note: Critical k _eff's of bold–italic faced cores show the present results and others those in Ref. [9].

Figure 7. Critical k _eff's calculated by MVP. Note: Critical k _eff's of bold–italic faced cores show the present results and others those in Ref. [9].

Table 4. Critical k _eff of the FUBILA cores.

Core		Control blade core (40% void)	UO2 rod core (40% void)	Gd2O3-UO2 rod core (40% void)	10 × 10 MOX assembly core (40% void)	Time-elapsed reference core (0% void)
No. of MOX rods in driver region		1474	910	1226	618	661
Code	Library	Critical k eff
CITATION-2D^a	JENDL-3.3	1.0014	–	1.0000	0.9974	–
CITATION-3D^b		–	0.9974	–	0.9966	0.9980
CITATION-3D (21g)^c		0.9993	0.9980	0.9989	0.9969	0.9980
TWODANT		1.0031	–	1.0001	1.0001	–
THREEDANT		–	1.0010	1.0015	1.0021	1.0025
MVP^d	JENDL-3.3	1.0042	1.0024	1.0034	1.0010	1.0023
	JENDL-4.0	1.0035	1.0024	1.0029	1.0016	1.0022
	ENDF/B-IV.8	1.0025	1.0005	1.0012	0.9986	0.9996
	ENDF/B-VII	1.0071	1.0060	1.0061	1.0040	1.0051
	JEFF-3.1	1.0024	1.0020	1.0024	1.0012	1.0018
	JENDL-3.3 + ^157Gd^e	–	–	1.0038	–	–
Note: ^aTwo-dimensional calculations with 16 neutron energy groups; ^bThree-dimensional calculations with 16 neutron energy groups; ^cThree-dimensional calculations with 21 neutron energy groups; ^dStatistical error is ± 0.0002; ^eCalculated results with the JENDL-3.3 base nuclear data file which adopted the cross sections of ^157Gd of the new measurement data of Leinweber et al. [23].

Figure 8. Deviation of calculated radial fission rates of CITATION-2D calculation from measurements for the test region of the control blade core. Note: Deviation (%): (calculated fission rate −measured fission rate)/(measured fission rate) × 100.

Figure 9. Deviation of calculated radial fission rates of TWODANT calculation from measurements for the test region of the control blade core. Note: Deviation (%): (calculated fission rate −measured fission rate)/(measured fission rate) × 100

Table 5. Root-mean-square (RMS), maximum (Max) and minimum (Mini) values of (calculated–measured)/measured in % for radial fission rates in the test region.

Core	Control blade core (Test region)			Gd2O3-UO2 rod core (Test region)			10 × 10 MOX assembly core
Measurement error (%)	1.2			1.3			1.3
Code^a	RMS	Max	Min	RMS	Max	Min	RMS	Max	Min
CITATION-2D	2.44	5.68	−6.45	3.00	7.24	−8.15	2.28^b	4.55^b	−3.72^b
TWODANT	2.01	4.39	−6.43	2.03	4.59	−4.89	1.48^b	2.89^b	−5.97^b
MVP^c	1.65	4.61	−3.15	2.20	3.47	−7.42	1.17	2.55	−3.24
Note: ^aThe calculations were performed using the nuclear data library JENDL-3.3; ^bThe calculated results of the 10 × 10 assembly core are those calculated using CITATION-3D and THREEDANT; ^cThe statistical errors in the calculated fission rates are about 0.5%.

Figure 10. Comparison between calculated fission rates of CITATION-2D and measurements in the diagonal direction of the test region of the control blade core. Note: The average values of fission rates are normalized to 1.0.

Figure 11. Deviation of calculated radial fission rates of CITATION-2D calculation from measurements for the test region of the Gd₂O₃-UO₂ core [12]. Note: Deviation (%): (calculated fission rate −measured fission rate)/(measured fission rate) × 100. Notation: Brown: UO₂ rod, dark blue: Gd₂O₃-UO₂ rod, light blue, white and yellow: MOX rods.

Figure 12. Deviation of calculated radial fission rates of TWODANT calculation from measurements for the test region of the Gd₂O₃-UO₂ core [12]. Deviation (%): (calculated fission rate −measured fission rate)/(measured fission rate) × 100. Notation: Brown: UO₂ rod, dark blue: Gd₂O₃-UO₂ rod, light blue, white and yellow: MOX rods.

Table 6. Average deviation of calculated fission rates from measurements as (calculated–measured)/measured in % for the Gd₂O₃-UO₂ rod core.

Type of fuel rod	UO2	Gd2O3-UO2	MOX
CITATION-2D (JENDL-3.3)	−5.29	−0.09	0.99
	(−3.37)^a	(0.17)^a	(0.67)^a
TWODANT (JENDL-3.3)	−2.32	−1.98	0.44
	(−1.25)^a	(−1.73)^a	(0.23)^a
MVP (JENDL-3.3)	−1.86	−4.09	0.58
MVP (ENDF/B-VII)	−1.90	−4.61	0.63
MVP (JEFF-3.1)	−2.26	−4.21	0.63
MVP (JENDL-3.3 + ^157Gd)^b	−2.11	−2.59	0.51
Note: ^aCalculated results by using the improved lattice calculation (see text); ^bCalculated results with the JENDL-3.3 base nuclear data file which adopted the cross sections of ^157Gd of the new measurement data of Leinweber et al. [23].

Figure 13. Infinite assembly models in lattice calculations for Gd₂O₃-UO₂ rod cells and UO₂ rod cells in the Gd₂O₃-UO₂ Core. Note: Notation should be referred to Figure 2.

Figure 14. Deviation of calculated radial fission rates of MVP calculation with ¹⁵⁷Gd-modified JENDL-3.3 from measurements for the test region of the Gd₂O₃-UO₂ core.

Figure 15. Deviation of calculated radial fission rates of CITATION-3D calculation from measurements for the 10 × 10 MOX assembly core.

Figure 16. Deviation of calculated radial fission rates of THREEDANT calculation from measurements for the 10 × 10 MOX assembly core.

Figure 17. Comparison between calculated fission rates of CITATION-3D and measurements in the diagonal direction of the 10 × 10 MOX assembly core. Note: The average values of fission rates are normalized to 1.0.

Figure A1. Measured relative radial fission rate distribution in the control blade core [4]. Note: The average value of measured 81 fuel rods in the test region is 1.0 and that of 7 fuel rods in the driver region 1.0.

Figure A2. Measured relative radial fission rate distribution in the test region of the Gd₂O₃-UO₂ rod core [4]. Note: The average value of measured 167 fuel rods in the test region is 1.0.

Figure A3. Measured radial fission rate distribution in the 10 × 10 MOX assembly core [4]. Note: The average value of measured 109 fuel rods in the test region is 1.0.

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