Development of an improved method for calculating the effective delayed neutron fraction of a core using a structure with only a few collapsed energy groups

Figures & data

Figure 1 Fission spectra of the prompt fission neutrons and delayed neutrons for U-235

Figure 2 Cell calculation model for the fuel lattice

Table 1 Energy group structure

Fast energy group				Thermal energy group
107-group structure				107-group structure
Group	Upper energy (eV)	6-group structure	2-group structure	Group	Upper energy (eV)	6-group structure	2-group structure
1	1.0000E+07	1	1	63	1.8554E+00	6	2
2	7.7880E+06			64	1.6374E+00
3	6.0653E+06			65	1.4450E+00
4	4.7237E+06			66	1.2752E+00
5	3.6788E+06			67	1.1254E+00
6	2.8651E+06			68	9.9312E−01
7	2.2313E+06			69	8.7642E−01
8	1.7377E+06	2		70	7.7344E−01
9	1.3534E+06			71	6.8256E−01
10	1.0540E+06			72	6.0236E−01
11	8.2085E+05	3		73	5.3158E−01
12	6.3928E+05			74	4.6912E−01
13	4.9787E+05			75	4.1399E−01
14	3.8774E+05			76	3.8926E−01
15	3.0197E+05			77	3.6528E−01
16	2.3518E+05			78	3.4206E−01
17	1.8316E+05	4		79	3.1961E−01
18	1.4264E+05			80	2.9792E−01
19	1.1109E+05			81	2.7699E−01
20	8.6517E+04			82	2.5683E−01
21	6.7380E+04			83	2.3742E−01
22	5.2475E+04			84	2.1878E−01
23	4.0868E+04			85	2.0090E−01
24	3.1828E+04			86	1.8378E−01
25	2.4788E+04			87	1.6743E−01
26	1.9305E+04			88	1.5183E−01
27	1.5034E+04			89	1.3700E−01
28	1.1709E+04			90	1.2293E−01
29	9.1188E+03	5		91	1.0963E−01
30	7.1017E+03			92	9.7080E−02
31	5.5308E+03			93	8.5397E−02
32	4.3074E+03			94	7.4276E−02
33	3.3546E+03			95	6.4017E−02
34	2.6126E+03			96	5.4520E−02
35	2.0347E+03			97	4.5785E−02
36	1.5846E+03			98	3.7813E−02
37	1.2341E+03			99	3.0602E−02
38	9.6112E+02			100	2.4154E−02
39	7.4852E+02			101	1.8467E−02
40	5.8295E+02			102	1.3543E−02
41	4.5400E+02			103	9.3805E−03
42	3.5358E+02			104	5.9804E−03
43	2.7536E+02			105	3.3423E−03
44	2.1445E+02			106	1.4663E−03
45	1.6702E+02			107	3.5238E−04
46	1.3007E+02			107 (lower)	1.0000E−05
47	1.0130E+02
48	7.8893E+01
49	6.1442E+01
50	4.7851E+01
51	3.7266E+01
52	2.9023E+01
53	2.2603E+01
54	1.7604E+01
55	1.3710E+01
56	1.0677E+01
57	8.3153E+00
58	6.4759E+00
59	5.0435E+00
60	3.9279E+00
61	3.0590E+00
62	2.3824E+00

Figure 3 Core calculation model

Table 2 Comparison of the effective delayed neutron and multiplication factors

Energy group structure	β eff	Error in β eff (%)	k eff	Error in k eff (Δk/kk′%)
107-group structure	6.9812E−03	−	1.2989	−
6-group structure	6.9828E−03	2.3205E−02	1.2980	−5.1723E−02
2-group structure	7.1607E−03	2.5713E+00	1.2981	−4.3829E−02

Table 3 Fission spectra based on the conventional and proposed methods

Energy group	Total	Delayed 1	Delayed 2	Delayed 3	Delayed 4	Delayed 5	Delayed 6
Conventional method
Fuel 1
1	1.00000	1.00000	1.00000	1.00000	1.00000	1.00000	1.00000
2	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000
Fuel 2
1	1.00000	1.00000	1.00000	1.00000	1.00000	1.00000	1.00000
2	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000
Proposed method
Fuel 1
1	0.98458	0.96277	0.96161	0.96207	0.96186	0.96284	0.96340
2	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000
Fuel 2
1	0.98686	0.95999	0.95879	0.95928	0.95923	0.96028	0.96094
2	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000

Table 4 Comparison of the conventional and proposed methods

Energy group structure	β eff	Error in β eff (%)
107-group structure	6.9812E−03	−
2-group structure (conventional method)	7.1607E−03	2.5713E+00
2-group structure (proposed method)	6.9964E−03	2.1816E−01

Figure 4 Adjoint flux from the B1 calculation