Analysis of the MOX critical experiments BASALA by pin-by-pin core analysis method using three-dimensional direct response matrix

Figures & data

Figure 1. Schematic illustrations of sub-response matrices. (a) Transmission probability. (b) Neighbor-induced production probability. (c) Self-induced production probability. (d) Escape probability.

Figure 2. Schematic illustration of sub-surfaces and angular segments.

Table 1. Core characteristics and fuel assembly specifications of BASALA experiments.

Items	Core 1	Core 2
Core configuration	Hot operation condition of BWR	Cold stand-by condition of BWR
Hydrogen to heavy metal atomic ratio (H/HM)	5.0	9.0
Volumetric moderator ratio	1.7	3.1
Fuel rods
Cladding outer diameter (mm)	9.5	9.5
Over-cladding outer diameter (mm)	10.2	10.2
Fuel pin pitch (mm)	11.3	13.5
Fuel effective  length (mm)	800	800
Water rods
Outer diameter (mm)	10.2	10.2
Inner diameter (mm)	8.3	8.7
Fuel assembly pitch (mm)	114.1	135.5
Water gap half width (mm)	6.2	7.0

Figure 3. Configuration of reference core for core 1. The percentages are wt % of Pu total content and the numbers are the numbers of each type of rod.

Figure 4. Configuration of reference core for core 2. The percentages are wt % of Pu total content and the numbers are the numbers of each type of rod.

Figure 5. Configuration of 8Gd core for core 1. The percentages are wt % of Pu total content and the numbers are the numbers of each type of rod.

Figure 6. Configuration of 16Gd core for core 1. The percentages are wt % of Pu total content and the numbers are the numbers of each type of rod.

Figure 7. Configuration of 8Gd core for core 2. The percentages are wt % of Pu total content and the numbers are the numbers of each type of rod.

Figure 8. Configuration of 16Gd core for core 2. The percentages are wt % of Pu total content and the numbers are the numbers of each type of rod.

Figure 9. Configuration of 2D void core for core 1. The percentages are wt % of Pu total content and the numbers are the numbers of each type of rod.

Figure 10. Configuration of water rod core for core 1. The percentages are wt % of Pu total content and the numbers are the numbers of each type of rod.

Figure 11. Configuration of control blade inserted core for core 2. The percentages are wt % of Pu total content and the numbers are the numbers of each type of rod.

Figure 12. Illustrations of sub-surfaces and angular segments. (a) Number of sub-surfaces and angular segments : 4 × 4 and 4. (b) Number of sub-surfaces and angular segments : 4 × 4 and 16.

Table 2. Energy group structure for sub-response matrices.

Energy group		Energy (eV)
3-group	9-group	Upper	Lower
1	1	1.0000 × 10^7	1.5335 × 10^6
	2	1.5335 × 10^6	2.3518 × 10^5
	3	2.3518 × 10^5	3.6066 × 10^4
	4	3.6066 × 10^4	5.5308 × 10^3
2	5	5.5308 × 10^3	2.4301 × 10^2
6	2.4301 × 10^2	1.0677 × 10^1
	7	1.0677 × 10^1	6.2500 × 10^−1
3	8	6.2500 × 10^−1	1.0000 × 10^−1
9	1.0000 × 10^−1	1.0000 × 10^−5

Table 3. Critical k-effective values for reference cores.

Number of angular segments	Number of energy groups	Critical k-effective value
		Core 1	Core 2
4	3	1.0238	1.0228
16		1.0174	1.0162
	9	1.0100	1.0082

Figure 13. Fuel rod fission rate distribution of reference core for core 1 (diagonal direction).

Figure 14. Fuel rod fission rate distribution of reference core for core 2 (diagonal direction).

Table 4. Root mean square and maximum differences of fuel rod fission rate distribution between calculation and measurement in diagonal direction for reference cores (unit:%).

Number of angular segments	Number of energy groups	Root mean square difference		Maximum difference
		Core 1	Core 2	Core 1	Core 2
4	3	1.6	2.2	3.9	4.7
16		1.5	1.7	3.6	3.4
	9	1.4	1.0	3.2	2.4

Figure 15. Fuel rod fission rate distribution of reference core for core 1 (test assembly).

Table 5. Root mean square and maximum differences of fuel rod fission rate distribution between calculation and measurement in test assembly for reference cores (unit:%).

Number of angular segments	Number of energy groups	Root mean square difference		Maximum difference
		Core 1	Core 2	Core 1	Core 2
4	3	1.3	1.2	3.4	2.7
16		1.3	1.1	3.5	2.5
	9	1.4	1.1	3.9	2.4

Figure 16. Fuel rod fission rate distribution of reference core for core 2 (test assembly).

Table 6. Critical k-effective values.

Core	Core 1	Core 2
Reference	1.0100	1.0082
8Gd	1.0100	1.0090
16Gd	1.0108	1.0112
2D void	1.0096	–
Water rod	1.0108	–
Control blade	–	1.0126
Average	1.0102	1.0102
Standard deviation (%)	0.05	0.20

Figure 17. Fuel rod fission rate distribution of 8Gd core for core 1 (diagonal direction).

Table 7. Root mean square and maximum differences of fuel rod fission rate distribution between calculation and measurement in diagonal direction (unit:%).

Core	Root mean square difference		Maximum differences
	Core 1	Core 2	Core 1	Core 2
Reference	1.4	1.0	3.2	2.4
8Gd	2.5	2.1	6.6	3.4
16Gd	2.2	1.8	8.0	5.6
2D void	1.2	–	2.6	–
Water rod	1.9	–	4.8	–
Control blade	–	1.6	–	3.9

Figure 18. Fuel rod fission rate distribution of 16Gd core for core 1 (diagonal direction).

Figure 19. Fuel rod fission rate distribution of 8Gd core for core 2 (diagonal direction).

Figure 20. Fuel rod fission rate distribution of 16Gd core for core 2 (diagonal direction).

Figure 21. Fuel rod fission rate distribution of 2D void core for core 1 (diagonal direction).

Figure 22. Fuel rod fission rate distribution of water rod core for core 1 (diagonal direction).

Figure 23. Fuel rod fission rate distribution of control blade inserted core for core 2 (diagonal direction).

Figure 24. Fuel rod fission rate distribution of 8Gd core for core 1 (test assembly).

Table 8. Root mean square and maximum differences of fuel rod fission rate distribution between calculation and measurement in test assembly (unit: %).

Core	Root mean square difference		Maximum differences
	Core 1	Core 2	Core 1	Core 2
Reference	1.4	1.1	3.9	2.4
8Gd	1.6	1.4	4.8	3.4
16Gd	1.8	1.6	4.9	4.7
2D void	1.3	–	3.3	–
Water rod	1.5	–	4.0	–
Control blade	–	1.6	–	4.3

Figure 25. Fuel rod fission rate distribution of 16Gd core for core 1 (test assembly).

Figure 26. Fuel rod fission rate distribution of 8Gd core for core 2 (test assembly).

Figure 27. Fuel rod fission rate distribution of 16Gd core for core 2 (test assembly).

Figure 28. Fuel rod fission rate distribution of 2D void core for core 1 (test assembly).

Figure 29. Fuel rod fission rate distribution of water rod core for core 1 (test assembly).

Figure 30. Fuel rod fission rate distribution of control blade inserted core for core 2 (test assembly)

Table 9. Comparison of reactivity worth between calculation and measurement.

Core	Measurement (pcm)	Calculation (pcm)	C/E value
Core 1
8Gd	−2085 ± 134	−2067	0.99
16Gd	−2187 ± 142	−2208	1.01
2D void	−1314 ± 81	−1438	1.09
Water rod	761 ± 35	800	1.05
Core 2
8Gd	−3913 ± 238	−3921	1.00
16Gd	−5282 ± 324	−5290	1.00
Control blade	−9699 ± 592	−9743	1.00