Application of correction technique using leakage index combined with SPH or discontinuity factors for energy collapsing on pin-by-pin BWR core analysis

Figures & data

Figure 1. Overview of the calculation procedure of LI correction technique with SPH factor and DF.

Figure 2. 8×8 BWR fuel assemblies used in present study.

Table 1. Energy group structure.

4-group structure	8-group structure	Lower energy boundary (eV)
First group	First group	2.2313E+06
	Second group	8.2085E+05
	Third group	9.1188E+03
Second group	Fourth group	1.3007E+02
	Fifth group	3.9279E+00
Third group	Sixth group	6.2506E−01
Fourth group	Seventh group	1.4572E−01
	Eighth group	1.0000E−04

Figure 3. Geometry of 4×4 colorset assemblies.

Figure 4. Treatments of spatial and energy dependences in lattice physics and core calculations.

Table 2. Types of calculation results used in the present verifications.

	LI correction	SPH
	technique	factor	DF
None	–	–	–
LI	○	–	–
SPH	–	○	–
DF	–	–	○
LI + SPH	○	○	–
LI + DF	○	–	○

Note: –: not applied, ○: applied.

Table 3. Summary of 4-group calculation results considering errors due to spectral interference effect and energy collapsing.

		None	LI	SPH	DF	LI + SPH	LI + DF
Control rod: withdrawn
$\Delta k_{inf}$ (pcm)	Average	106	87	57	44	37	20
	Maximum	403	310	172	142	81	45
ΔRf, RMS (%)	Average	1.19	1.01	0.77	0.59	0.49	0.26
	Maximum	1.51	1.16	1.28	1.01	0.82	0.47
Control rod: inserted
$\Delta k_{inf}$ (pcm)	Average	137	95	100	89	46	31
	Maximum	465	328	221	196	90	63
ΔRf, RMS (%)	Average	1.28	1.06	0.85	0.71	0.53	0.33
	Maximum	1.60	1.23	1.37	1.12	0.86	0.58

Table 4. Summary of 8-group calculation results considering errors due to spectral interference effect and energy collapsing.

		None	LI	SPH	DF	LI + SPH	LI + DF
Control rod: withdrawn
$\Delta k_{inf}$ (pcm)	Average	29	33	14	16	8	3
	Maximum	135	110	60	70	24	8
ΔRf, RMS (%)	Average	0.59	0.50	0.29	0.30	0.20	0.07
	Maximum	0.78	0.63	0.45	0.52	0.35	0.13
Control rod: inserted
$\Delta k_{inf}$ (pcm)	Average	36	38	13	13	6	6
	Maximum	151	115	62	70	24	12
ΔRf, RMS (%)	Average	0.62	0.52	0.31	0.35	0.21	0.08
	Maximum	0.82	0.65	0.48	0.55	0.35	0.14

Table 5. Summary of 4-group calculation results only considering spectral interference effect in previous study [6].

		None	LI
Control rod: withdrawn
$\Delta k_{inf}$ (pcm)	Average	40	20
	Maximum	143	48
ΔRf, RMS (%)	Average	0.48	0.13
	Maximum	0.79	0.23
Control rod: inserted
$\Delta k_{inf}$ (pcm)	Average	75	23
	Maximum	187	52
ΔRf, RMS (%)	Average	0.55	0.16
	Maximum	0.86	0.28

Table 6. Summary of 8-group calculation results only considering spectral interference effect in previous study [6].

		None	LI
Control rod: withdrawn
$\Delta k_{inf}$ (pcm)	Average	17	1
	Maximum	72	4
ΔRf, RMS (%)	Average	0.29	0.02
	Maximum	0.51	0.04
Control rod: inserted
$\Delta k_{inf}$ (pcm)	Average	13	1
	Maximum	73	5
ΔRf, RMS (%)	Average	0.33	0.02
	Maximum	0.54	0.04

Table 7. Breakdown of calculation errors by LI correction technique, SPH factor, and DF in 4-group.

		Spectral interference effect		Energy collapsing
			With correction		With correction	With correction
	Total	Uncorrected	by LI	Uncorrected	by SPH	by DF
Control rod: withdrawn
$\Delta k_{inf}$ (pcm)	106	40	20	66	17	0
ΔRf, RMS (%)	1.19	0.48	0.13	0.71	0.36	0.13
Control Rod: Inserted
$\Delta k_{inf}$ (pcm)	137	75	23	62	23	8
ΔRf, RMS (%)	1.28	0.55	0.16	0.73	0.37	0.17

Table 8. Breakdown of calculation errors by LI correction technique, SPH factor, and DF in 8-group.

		Spectral interference effect		Energy collapsing
			With correction		With correction	With correction
	Total	Uncorrected	by LI	Uncorrected	by SPH	by DF
Control rod: withdrawn
$\Delta k_{inf}$ (pcm)	29	17	1	12	7	2
ΔRf, RMS (%)	0.59	0.29	0.02	0.30	0.18	0.05
Control rod: inserted
$\Delta k_{inf}$ (pcm)	36	13	1	23	5	5
ΔRf, RMS (%)	0.62	0.33	0.02	0.29	0.19	0.06

Figure 5. Geometry of 2×2 colorset assemblies.

Figure 6. Difference of pin-by-pin fission rate distribution (Cases 1 and 2).

Figure 7. Difference of pin-by-pin fission rate distribution (Cases 3 and 4).

Figure 8. Difference of pin-by-pin fission rate distribution (Cases 5 and 6).

Fujita T, Endo T, Yamamoto A. A new technique for spectral interference correction on pin-by-pin BWR core analysis. J Nucl Sci Technol. 2014;51:783–797.

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