Reconstruction method of homogenized cross sections

Figures & data

Figure 1 Geometrical configurations of calculated systems

Table 1 Comparison of homogenized macroscopic capture and fission cross sections in the no control rod system

				Present method
				4 divisions^a	No division^a	No division^a
Fuel assembly	Cross section	Energy group	Reference	Fuel rod^b	Fuel rod^b	Cell averaged^b
Low-enriched	Σ c	1	0.00108	0.00109 (0.37)	0.00109 (0.40)	0.00109 (0.39)
		2	0.01179	0.01180 (0.03)	0.01180 (0.04)	0.01180 (0.04)
		3	0.01573	0.01574 (0.09)	0.01575 (0.12)	0.01575 (0.12)
	Σ f	1	0.00097	0.00096 (−0.40)	0.00096 (−0.40)	0.00096 (−0.42)
		2	0.00167	0.00167 (0.02)	0.00167 (0.04)	0.00167 (0.04)
		3	0.01785	0.01786 (0.06)	0.01788 (0.19)	0.01788 (0.18)
High-enriched	Σ c	1	0.00111	0.00110 (−0.30)	0.00110 (−0.32)	0.00110 (−0.30)
		2	0.01430	0.01431 (0.07)	0.01431 (0.06)	0.01431 (0.07)
		3	0.03235	0.03230 (−0.15)	0.03222 (−0.42)	0.03222 (−0.40)
	Σ f	1	0.00115	0.00116 (0.38)	0.00116 (0.38)	0.00116 (0.42)
		2	0.00441	0.00441 (0.00)	0.00441 (−0.01)	0.00441 (−0.01)
		3	0.03557	0.03554 (−0.09)	0.03548 (−0.25)	0.03548 (−0.25)

Table 2 Comparison of homogenized macroscopic capture and fission cross sections with values evaluated by infinite single fuel assembly calculation in the no control rod system

					Present method
					4 divisions^a	No division^a	No division^a
Fuel assembly	Cross section	Energy group	Infinite	Reference	Fuel rod^b	Fuel rod^b	Cell averaged^b
Low-enriched	Σ c	1	0.00108	0.00108 (−0.04)	0.00109 (0.33)	0.00109 (0.36)	0.00109 (0.35)
		2	0.01180	0.01179 (−0.08)	0.01180 (−0.05)	0.01180 (−0.04)	0.01180 (−0.04)
		3	0.01574	0.01573 (−0.06)	0.01574 (0.03)	0.01575 (0.06)	0.01575 (0.06)
	Σ f	1	0.00098	0.00097 (−1.49)	0.00096 (−1.89)	0.00096 (−1.89)	0.00096 (−1.91)
		2	0.00167	0.00167 (−0.14)	0.00167 (−0.11)	0.00167 (−0.10)	0.00167 (−0.10)
		3	0.01769	0.01785 (0.91)	0.01786 (0.97)	0.01788 (1.10)	0.01788 (1.10)
High-enriched	Σ c	1	0.00111	0.00111 (−0.05)	0.00110 (−0.34)	0.00110 (−0.36)	0.00110 (−0.34)
		2	0.01431	0.01430 (−0.02)	0.01431 (0.05)	0.01431 (0.04)	0.01431 (0.05)
		3	0.03299	0.03235 (−1.94)	0.03230 (−2.08)	0.03222 (−2.35)	0.03222 (−2.34)
	Σ f	1	0.00114	0.00115 (1.07)	0.00116 (1.46)	0.00116 (1.46)	0.00116 (1.49)
		2	0.00440	0.00441 (0.09)	0.00441 (0.09)	0.00441 (0.07)	0.00441 (0.08)
		3	0.03585	0.03557 (−0.77)	0.03554 (−0.86)	0.03548 (−1.02)	0.03548 (−1.02)

Table 3 Comparison of homogenized macroscopic capture and fission cross sections in the control rod inserted system

				Present method
				4 divisions^a	No division^a	No division^a
Fuel assembly	Cross section	Energy group	Reference	Fuel rod^b	Fuel rod^b	Cell averaged^b
Low-enriched	Σ c	1	0.00131	0.00131 (0.25)	0.00132 (0.44)	0.00132 (0.44)
(control rod inserted)		2	0.01926	0.01919 (−0.36)	0.01930 (0.21)	0.01930 (0.21)
		3	0.02532	0.02527 (−0.20)	0.02517 (−0.57)	0.02517 (−0.57)
	Σ f	1	0.00091	0.00090 (−1.62)	0.00090 (−1.53)	0.00090 (−1.54)
		2	0.00165	0.00165 (0.02)	0.00166 (0.08)	0.00166 (0.08)
		3	0.01827	0.01828 (0.10)	0.01834 (0.43)	0.01834 (0.43)
High-enriched	Σ c	1	0.00111	0.00110 (−0.37)	0.00110 (−0.40)	0.00110 (−0.38)
		2	0.01432	0.01432 (−0.03)	0.01432 (−0.04)	0.01432 (−0.03)
		3	0.03251	0.03247 (−0.14)	0.03238 (−0.39)	0.03239 (−0.38)
	Σ f	1	0.00116	0.00116 (0.56)	0.00116 (0.56)	0.00117 (0.60)
		2	0.00441	0.00441 (0.03)	0.00441 (0.01)	0.00441 (0.01)
		3	0.03567	0.03564 (−0.10)	0.03555 (−0.33)	0.03556 (−0.33)
Low-enriched	Σ c	1	0.00108	0.00109 (0.30)	0.00109 (0.34)	0.00109 (0.33)
(no control rod)		2	0.01181	0.01180 (−0.05)	0.01180 (−0.05)	0.01180 (−0.05)
		3	0.01573	0.01575 (0.10)	0.01575 (0.11)	0.01575 (0.11)
	Σ f	1	0.00097	0.00097 (−0.03)	0.00097 (−0.10)	0.00097 (−0.13)
		2	0.00167	0.00167 (0.02)	0.00167 (0.01)	0.00167 (0.01)
		3	0.01787	0.01788 (0.08)	0.01791 (0.24)	0.01791 (0.24)

Table 4 Comparison of homogenized macroscopic capture and fission cross sections with values evaluated by infinite single fuel assembly calculation in the control rod inserted system

					Present method
					4 divisions^a	No division^a	No division^a
Fuel assembly	Cross section	Energy group	Infinite	Reference	Fuel rod^b	Fuel rod^b	Cell averaged^b
Low-enriched	Σ c	1	0.00131	0.00131 (0.02)	0.00131 (0.27)	0.00132 (0.46)	0.00132 (0.46)
(control rod inserted)		2	0.01959	0.01926 (−1.71)	0.01919 (−2.06)	0.01930 (−1.50)	0.01930 (−1.50)
		3	0.02506	0.02532 (1.01)	0.02527 (0.81)	0.02517 (0.44)	0.02517 (0.44)
	Σ f	1	0.00095	0.00091 (−4.25)	0.00090 (−5.81)	0.00090 (−5.72)	0.00090 (−5.73)
		2	0.00166	0.00165 (−0.20)	0.00165 (−0.18)	0.00166 (−0.11)	0.00166 (−0.11)
		3	0.01822	0.01827 (0.26)	0.01828 (0.36)	0.01834 (0.70)	0.01834 (0.70)
High-enriched	Σ c	1	0.00111	0.00111 (−0.12)	0.00110 (−0.48)	0.00110 (−0.51)	0.00110 (−0.49)
		2	0.01431	0.01432 (0.10)	0.01432 (0.07)	0.01432 (0.06)	0.01432 (0.07)
		3	0.03299	0.03251 (−1.45)	0.03247 (−1.60)	0.03238 (−1.85)	0.03239 (−1.84)
	Σ f	1	0.00114	0.00116 (1.57)	0.00116 (2.14)	0.00116 (2.14)	0.00117 (2.18)
		2	0.00440	0.00441 (0.03)	0.00441 (0.07)	0.00441 (0.04)	0.00441 (0.05)
		3	0.03585	0.03567 (−0.48)	0.03564 (−0.59)	0.03555 (−0.81)	0.03556 (−0.81)
Low-enriched	Σ c	1	0.00108	0.00108 (−0.13)	0.00109 (0.18)	0.00109 (0.22)	0.00109 (0.21)
(no control rod)		2	0.01180	0.01181 (0.03)	0.01180 (−0.02)	0.01180 (−0.02)	0.01180 (−0.02)
		3	0.01574	0.01573 (−0.04)	0.01575 (0.06)	0.01575 (0.08)	0.01575 (0.08)
	Σ f	1	0.00098	0.00097 (−0.98)	0.00097 (−1.01)	0.00097 (−1.09)	0.00097 (−1.11)
		2	0.00167	0.00167 (−0.11)	0.00167 (−0.09)	0.00167 (−0.10)	0.00167 (−0.11)
		3	0.01769	0.01787 (1.02)	0.01788 (1.10)	0.01791 (1.26)	0.01791 (1.26)

Table 5 Results of neutron infinite multiplication factors (k-infinity) in the no control rod system

	Cross sections		Divided number
	Evaluation	Evaluated by			Response		Difference from
Case	method	the method	Surface	Angle	relation^a	k-infinity	reference (%Δk)
Reference	–	–	–	–	–	1.0941	–
1	Single assembly	All	–	–	–	1.0894	−0.47
2	Present method	Σ a , Σ f , νΣ f	4	4	Fuel rod	1.0941	0.00
3	Present method	Σ a , Σ f , νΣ f	1	1	Fuel rod	1.0946	0.04
4	Present method	Σ a , Σ f , νΣ f	1	1	Cell avaraged	1.0945	0.04
5	Multi assembly^b	Σ a , Σ f , νΣ f	–	–	–	1.0941	0.00
6	Multi assembly^b	All	–	–	–	1.0942	0.00

Figure 2 Fuel assembly averaged fission rate distribution in the no control rod system

Table 6 Results of neutron infinite multiplication factors (k-infinity) in the control rod inserted system

	Cross sections		Divided number
	Evaluation	Evaluated by			Response		Difference from
Case	method	the method	Surface	Angle	relation^a	k-infinity	reference (%Δk)
Reference	–	–	–	–	–	1.0301	–
1	Single assembly	All	–	–	–	1.0245	−0.56
2	Present method	Σ a , Σ f , νΣ f	4	4	Fuel rod	1.0286	−0.15
3	Present method	Σ a , Σ f , νΣ f	1	1	Fuel rod	1.0290	−0.11
4	Present method	Σ a , Σ f , νΣ f	1	1	Cell avaraged	1.0290	−0.11
5	Multi assembly^b	Σ a , Σ f , νΣ f	–	–	–	1.0281	−0.21
6	Multi assembly^b	All	–	–	–	1.0270	−0.31

Figure 3 Fuel assembly averaged fission rate distribution in the control rod inserted system