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ΔΣ
a g
p
a g
( r)
= Σ ( r)
− Σ ( r)
a g
(7.6-15)
ΔΣ
s g→g'
p
s g→g'
( r)
= Σ ( r)
− Σ s g g'
( r)
→
(7.6-16)
g
p
g
ΔD
( r)
= D ( r)
− D ( r)
g
(7.6-17)
2
g
ΔB
( r)
= B
2 p
g
( r)
− B
2
g
( r)
(7.6-18)
The superscript p denotes the perturbed state.
7.6.2 Finite-difference Equation for Leakage Term
below.
The term appearing in the leakage term
*
∇ϕ
g ( r)
ΔDg
( r)
∇ϕ
g ( r)
dV
is approximated as shown
∑
j
A
j
2
1 ⎪⎧
ΔiD
jg ⎪⎫
} in the bulk of the system
Δ
i
⎨
⎪⎩
ΔiD
jg
+ Δ
j
D
ig
⎬
⎪⎭
* *
{ ϕig
−ϕ
jg
}{ ϕig
−ϕ
jg
∑
j
A
j
1
Δ
i
⎪⎧
Δ iCsg
⎨
⎪⎩ Δ iCsg
+ Δ
j
D
ig
⎪⎫
⎬
⎪⎭
2
ϕ *
ig
ϕ
ig
at the black boundary of the system
where the subscript i denotes a flux point, j the neighboring flux point, A j the leakage area, Δi the
distance between the flux point i and the leakage surface, Δj the distance between the flux point j and
the leakage surface, and C sg the black boundary constant. At the reflective boundary the above term is
null.
7.7 Cell Burn-up Calculation
In the cell burn-up calculation, two kinds of time-step units are adopted in the SRAC code. One
is the burn-up step unit with a relatively broad time interval, and the other is the sub-step unit in each
burn-up step. While the burn-up step interval is specified by input, the sub-step interval is determined
in the code. At each burn-up step, flux calculation is carried out with a selected code. As a result,
one-group collapsed flux distribution and collapsed microscopic cross-sections for burnable nuclides
are obtained. The depletion equation for the interval of the n-th burn-up step [t n-1 , t n ] can be expressed
by Eq. (7.7-1), under the assumption that the relative distribution of the microscopic reaction rates for
capture, fission and (n,2n) reactions does not change during the time interval of the burn-up step.
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