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ORNL-CF-61-10-39.txt
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ORNL-CF-61-10-39.txt
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UCN-2383
(3 11-60)
OAK RIDGE NATIONAL LABORATORY
Operated by For Internal Use Only
UNION CARBIDE NUCLEAR COMPANY ’
Division of Union Carbide Corporation 0 R N l
uee | CENTRAL FILES NUMBER
Post Office Box X
Oak Ridge, Tennessee | | 6 l _ 1 O ",i__g....
DATE: October 11, 1961 COPY NO. j /
SUBJECT: Delayed Neutron Losses in Circulating Fuel
Reactors — MSCR Memo No. 6
TO: Distribution
FROM: T. W. Kerlin, Jr.
Abstract
Equations which describe delayed neutron losses in external
loops of circulating fuel reactors were derived. A working equation
- | and the necessary input data for calculating delayed neutron losses
' by an equilibrium reactor code such as ERC-5 are given.
NOTICE
: This document contains information of a preliminary nature
and was prepared primarily for internal use at the Oak Ridge
National Laboratory. It is subject to revision or correction
and therefore does not represent a final report. The information
is not to be abstracted, reprinted or otherwise given public
dissemination without the approval of the ORNL patent branch,
Legal and Information Control Department.
DELAYED NEUTRON LOSSES IN CIRCULATING FUEL REACTORS
Circulating fuel reactors lose neutrons because some of the delayed
neutrons are emitted outside of the core. These losses depend on core
residence time, external loop residence time, and decay characteristics of
the precursors.
A symbolic representation of the system is
MVefeVe MV ETRE
Tl 1
Core > Heat
& Exchanger
~
Bivzf¢fcvc
where
)ij = decay constant of the ith precursor from fissionable material j,
Bij = number of ith precursors formed per fission neutron from fis-
sionable material j,
Nijc = atoms of ith precursor per unit volume of fuel stream in the
core resulting from fissions in material j, |
NijE = gagtoms of ith precursor per unit volume of fuel stream in the
external loops resulting from fissions in material j,
fc = volume fraction of fuel in the core,
fE = volume fraction of fuel in the external loops,
V. = core volume,
¢
VE = eXternal loop volume,
pjzfj¢finflz = rate of production of fission neutrons in the core from
fissionable material J.
The precursor concentrations are described by these equations:
dN, .
I [ .
e Pig¥ P - Mige > (1)
dNi‘E
dt, - MisE 2 (2)
where
tc = +time in the core,
tE‘ = +time in the external loops.
The boundary conditions are:
Nijc(TC) = NijE(O) , (3)
where
Tc = time for the fuel stream to pass through the core,
TE = +time for the fuel stream to pass through the external loops.
The solutions to Egs. (1) and (2) are:
B, V.20 A, st “A o b
_ 1 J 1’ _ ij e ij ¢
...)\ t
_ ij E
Note that the precursor production rate is assumed constant for the fuel
stream during its stay in the core. This idealized case would exist only
for uniform power density along the fuel stream or for core residence times
which are short compared to the half-life of the precursor.
The boundary conditions become:
B, V. 2.0 -A; ;T -A; T
_i%zfi—gi—(mR‘ e 1Y ) + Nijc(o) e C - NijE(O) ’ (7)
-A; 5T |
Nijc(o) = NijE(O) e 1IE (8)
Eliminating Nijc(o) in Egs. (7) and (8) and substituting the result in
Eq. (6) gives:
=N ;T -\ .t
Pl o e MY WE
ijE Aij [1 ] e-Rij(Tc + TE)] |
. (9)
The rate of decay of precursors in the external loops is:
LN B, .w 2, PV (1 - e-%%fiTé)(l - efixijTE)
EE TE *
A (T + T )
ijt e E
xijTE[l - e ]
The total rate of precursor decay (at equilibrium)is Bijvjzfj¢fcvc' Thus
the fraction of the delayed neutrons which appear in external loops is:
N f_V
"1JEE'E A 5T, N TR
T, £ Vp(l - e (1 -2 ) (11)
_ _ S 11
B. V.2 . QT V “As AT+ To)q °
13t e _ ij e E
'fcvcxijTE [l e }
£V, T
Since Ez-fig , Eg. (11) becomes:
c
TV
“ce
g 5T AT
PigE _ (1-e MYOG@-e T (12)
B, Ay (T + T)
13 Nl [1 L 13te E]
ij c
For using these results in an equilibrium reactor code such as ER.C-B,l
the term.vjzfj¢ may be replaced by a neutron production rate given by
f
N.C’
3 3¥3
where
Cf = reaction rate coefficient for fissions in material j.
J
Using this in Eq. (12) gives the following result for the number of neutrons
lost in the external loops per neutron produced:
-A, T N, T
Bij(l - € 1J C)(l - € ij E)
£
losses = Z Njijj Z ' (T % T (13)
3 1 [ 13 e E]
Ki.T 1 -e
Jgc
The necessary constants for Th252, U235, U235, U238, and Pu259 arez2
Group A (sec-l) ’ _ |
o Th232 233 P PP 239
1 0.0128 0.00085 0.00020 0.0003 0.00015 0.0001
2 0.0315 0.003%5 0.00075 0.0018 0.0017 0.0006
3 0.125 0.0045 0.00105 0.0022 0.0028 0.00045
L 0.325 0.0120 0.00075 0.0023 0.0071 0.00085
5 1.55 0.0045 0.00025 0.0007 0.0042 0.0003
6 4.5 0.0009 - 0.0002 0.0015 -
0.02625 o;ooso 0.0075 0.01745 0.0023%
L. G. Alexander, ERC-5 Program for Computing the Equilibrium States
of Two-Region, Thorium Breeder Reactors, ORNL-CF-60-10-87 (Oct. 20, 1960).
?A. M. Weinberg and E. P. Wigner, The Physical Theory of Neutron Chain
Reactors, p. 1%6, The University of Chicago Press, Chicago, 1958.
DISTRIBUTION
1-10. L. G. Alexander 3. J. A. Lane
11. S. E. Beall 37. J. L. Lucius
12, L. L. Bennett 38. R. N. Lyon
135, A. L. Benson, ORO 39. H. G. MacPherson
14, E. S. Bettis 40, W. B. McDonald
15. A. L. Boch 41. R. P. Milford
16, F. E. Blankenship 4o, A. M, Perry
17. R. B. Briggs 43, D. Scott
18. D. 0. Campbell 4. E. P. Self, ORO
19. W. L. Carter 45, M, J. Skinner
20. R. H. Chapman 46. 1I. Spiewak
21, F. L. Culler Y7, J. A, Swartout
22, J. G. Delene 48. W. C. Thurber
2%3. D, E. Ferguson 49, J. W. Ullmann
24k, H. E. Goeller 50. R. Van Winkle
25. W. R. Grimes 51. G. M. Watson
26. C, E. Guthrie 52. A. M. Weinberg
27. dJ. P, Hammond 53. dJ. H, Westsik
28, F. E. Harrington 54-55. Central Research Library
29, W. H., Jordan 56. Document Reference Section
30. P. R. Kasten 57-59. Laboratory Records
31-35, T, W. Kerlin 60. Laboratory Records (LRD-RC)