Experimental analyses of bismuth sample reactivity worth at Kyoto University Critical Assembly

Figures & data

Figure 1. Top view of the KUCA A-core in Bi sample reactivity worth experiments (Reference core).

Figure 2. Schematic drawing of fuel assemblies (Figure 1) in the A-core. (a). 1/8”p60EUEU fuel rod; (b). ‘40’ partial fuel rod; (c). ‘14’ partial fuel rod; and (d). Reference fuel rod ‘f’ containing Al plates.

Table 1. Control rod positions at the critical state in reference (Al) and test (Bi) cores shown in Figures 1 and 2, respectively

	Rod position [mm]
Core	C1	C2	C3	S4, S5, S6
Reference (Al)	1200.00	715.57	1200.00	1200.00
Case 1	1200.00	676.77	1200.00	1200.00
Case 2	1200.00	662.37	1200.00	1200.00
Case 3	1200.00	663.32	1200.00	1200.00
Case 4	1200.00	658.28	1200.00	1200.00

1200.00 [mm]: Upper limit.

Figure 3. Patterns of Bi sample reactivity worth experiments (b: test fuel rod; Figure 4). (a) Case 1; (b) Case 2; (c) Case 3; and (d) Case 4.

Figure 4. Schematic drawing of test fuel rod containing Bi.

Table 2. Comparison between the results of measured and calculated (Equation (2)(2) $\begin{array}{c}\mathrm{\Delta }{\rho }_{Al\to Bi}^{MCNP}={\rho }_{Excess}^{MCNP,Bi}-{\rho }_{Excess}^{MCNP,Al}\\ =\left(\frac{1}{k_{Critical}^{MCNP,Bi}}-\frac{1}{k_{Clean}^{MCNP,Bi}}\right)-\left(\frac{1}{k_{Critical}^{MCNP,Al}}-\frac{1}{k_{Clean}^{MCNP,Al}}\right)\end{array}$(2) ; MCNP6.1) excess reactivities in reference (Al) and test (Bi) cores shown in Figures 1 and 2, respectively

Core	Calculation [pcm]	Experiment [pcm]	C/E
Reference (Al)	88 ± 6	87 ± 1	1.01 ± 0.07
Case 1	129 ± 6	143 ± 3	0.90 ± 0.05
Case 2	164 ± 6	165 ± 3	0.99 ± 0.04
Case 3	156 ± 6	163 ± 3	0.96 ± 0.04
Case 4	166 ± 6	171 ± 3	0.97 ± 0.04

β_eff = 798 ± 3 [pcm] and ʌϕ = (3.39 ± 0.01)E-05 [s] by MCNP6.1 with JENDL-4.0.

C/E: Calculation/Experiment.

Table 3. Comparison between the results of measured and calculated (MCNP6.1) control rod worth in reference core (Al reference core) shown in Figure 1

Rod	Calculation [pcm]	Experiment [pcm]	C/E
C1	1005 ± 10	945 ± 32	1.06 ± 0.04
C2	454 ± 10	438 ± 1	1.04 ± 0.02
C3	360 ± 11	350 ± 8	1.03 ± 0.04

β_eff = 798 ± 3 [pcm] and ʌϕ = (3.39 ± 0.01)E-05 [s] by MCNP6.1 with JENDL-4.0.

C/E: Calculation/Experiment.

Table 4. Comparison of measured and calculated Bi sample reactivity worth in Equations (1)(1) $\begin{array}{rl}& \mathrm{\Delta }{\rho }_{Al\to Bi}^{Exp}={\rho }_{Excess}^{Exp,Bi}-{\rho }_{Excess}^{Exp,Al}\\ & =\left(1-\frac{1}{k_{Clean}^{Exp,Bi}}\right)-\left(1-\frac{1}{k_{Clean}^{Exp,Al}}\right)\\ & =\frac{1}{k_{Clean}^{Exp,Al}}-\frac{1}{k_{Clean}^{Exp,Bi}}\end{array}$(1) and (4(4) $\begin{array}{rl}& \mathrm{\Delta }{\rho }_{Al\to Bi}^{MCNP}={\rho }_{Excess}^{MCNP,Bi}-{\rho }_{Excess}^{MCNP,Al}\\ & =\left(\frac{1}{k_{Critical}^{MCNP,Bi}}-\frac{1}{k_{Clean}^{MCNP,Bi}}\right)-\left(\frac{1}{k_{Critical}^{MCNP,Al}}-\frac{1}{k_{Clean}^{MCNP,Al}}\right)\\ & ={\mathrm{\Delta }}_{Critical,Al\to Bi}^{MCNP}+\left(\frac{1}{k_{Clean}^{MCNP,Al}}-\frac{1}{k_{Clean}^{MCNP,Bi}}\right)\end{array}$(4) ), respectively, and criticality bias in Equation (5)(5) ${\mathrm{\Delta }}_{Critical,Al\to Bi}^{MCNP}=\frac{1}{k_{Critical}^{MCNP,Bi}}-\frac{1}{k_{Critical}^{MCNP,Al}}$(5)

Core	Experiment in Equation (1)(1) $\begin{array}{rl}& \mathrm{\Delta }{\rho }_{Al\to Bi}^{Exp}={\rho }_{Excess}^{Exp,Bi}-{\rho }_{Excess}^{Exp,Al}\\ & =\left(1-\frac{1}{k_{Clean}^{Exp,Bi}}\right)-\left(1-\frac{1}{k_{Clean}^{Exp,Al}}\right)\\ & =\frac{1}{k_{Clean}^{Exp,Al}}-\frac{1}{k_{Clean}^{Exp,Bi}}\end{array}$(1) [pcm]	Calculation in Equation (4)(4) $\begin{array}{rl}& \mathrm{\Delta }{\rho }_{Al\to Bi}^{MCNP}={\rho }_{Excess}^{MCNP,Bi}-{\rho }_{Excess}^{MCNP,Al}\\ & =\left(\frac{1}{k_{Critical}^{MCNP,Bi}}-\frac{1}{k_{Clean}^{MCNP,Bi}}\right)-\left(\frac{1}{k_{Critical}^{MCNP,Al}}-\frac{1}{k_{Clean}^{MCNP,Al}}\right)\\ & ={\mathrm{\Delta }}_{Critical,Al\to Bi}^{MCNP}+\left(\frac{1}{k_{Clean}^{MCNP,Al}}-\frac{1}{k_{Clean}^{MCNP,Bi}}\right)\end{array}$(4) [pcm]	Criticality bias in Equation (5)(5) ${\mathrm{\Delta }}_{Critical,Al\to Bi}^{MCNP}=\frac{1}{k_{Critical}^{MCNP,Bi}}-\frac{1}{k_{Critical}^{MCNP,Al}}$(5) [pcm]
Case 1	56 ± 3	41 ± 8	24 ± 6
Case 2	78 ± 3	76 ± 8	6 ± 6
Case 3	76 ± 3	68 ± 8	33 ± 6
Case 4	84 ± 3	78 ± 8	37 ± 6

Figure 5. Comparison between the values of criticality bias at critical state evaluated by Equation (5)(5) ${\mathrm{\Delta }}_{Critical,Al\to Bi}^{MCNP}=\frac{1}{k_{Critical}^{MCNP,Bi}}-\frac{1}{k_{Critical}^{MCNP,Al}}$(5) .

Figure 6. Sensitivity coefficients of inelastic scattering reactions of ²⁰⁹Bi and ²⁷Al in JENDL-4.0. (a) ²⁰⁹Bi and (b)²⁷Al.

Figure 7. Sensitivity coefficients of elastic scattering reactions of ²⁰⁹Bi and ²⁷Al in JENDL-4.0. (a) ²⁰⁹Bi and (b)²⁷Al.

Figure 8. Sensitivity coefficients of capture reactions of ²⁰⁹Bi, ²⁷Al, ²³⁵U and ²³⁸U in JENDL-4.0. (a) ²⁰⁹Bi and (b) ²⁷Al, ²³⁵U and ²³⁸U.

Table 5. Reaction-wise contribution [pcm] to changes in Bi sample reactivity worth (Case 4) induced by covariance data of JENDL-4.0

	Reactions
Isotopes	Capture	Elastic	Inelastic	Fission	(n, 2n)	Total
^235U	19.4	1.9	4.1	9.7	0.1	22.2
^238U	2.6	0.0	0.3	0.1	0.0	2.6
^209Bi	-	-	10.0	-	-	10.0
					Total	24.4

Table 6. Comparison of the results of measured excess reactivities between Bi and Pb test cores

Core	Bi sample [pcm]	Pb sample [pcm] (Ref. [13])
Reference (Al)	87 ± 1	92 ± 5
Case 1	143 ± 3	186 ± 7
Case 2	165 ± 3	202 ± 8
Case 3	163 ± 3	237 ± 9
Case 4	171 ± 3	248 ± 9

Table 7. Comparison of reaction-wise contributions [pcm] between Bi and Pb (Ref [14].) sample reactivity worth (Case 4) induced by covariance data of JENDL-4.0

	Reactions
Isotopes	Capture	Elastic	Inelastic	Fission	(n, 2n)	Total
^204Pb	0.1	−0.4	1.6	-	0.0	1.7
^206Pb	−1.0	−4.9	20.0	-	−0.8	19.4
^207Pb	0.9	−2.6	9.0	-	1.5	8.8
^208Pb	−0.6	2.2	11.3	-	3.1	11.9
^209Bi	-	-	10.0	-	-	10.0

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Pyeon CH, Fujimoto A, Sugawara T, et al. Sensitivity and uncertainty analyses of lead sample reactivity experiments at Kyoto University Critical Assembly. Nucl Sci Eng. 2017;185:460–472.

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