ML20138L562
| ML20138L562 | |
| Person / Time | |
|---|---|
| Site: | University of Michigan |
| Issue date: | 12/31/1980 |
| From: | Kerr W MICHIGAN, UNIV. OF, ANN ARBOR, MI |
| To: | |
| Shared Package | |
| ML20138L505 | List:
|
| References | |
| FOIA-85-587 NUDOCS 8512190301 | |
| Download: ML20138L562 (193) | |
Text
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$g-d MARCH 1981
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Low Enrichment Fuel Evaluation
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and Analysis Program
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Summary Report for the Period January,1980 - December,1980 WILLIAM KERR, Project Director
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a MU Department of Nuclear Engineering g y p, l _,
and the o
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Michigan-Memorial Phoenix Project I
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j PROJECT PARTICIPANTS Di
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3 William Kerr John S. King
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John C. Lee
.t William R. Martin t-Reed R. Burn
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Forrest B. Brown
!:t David C. Losey
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Joao Moreira James Rathkopf
- j James Sheridan i
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Gayle Stankiewicz
)f John Tucker i-hi David Wehe
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a Roger wisent L
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q TABLE OF CONTENTS y]
LIST OF FIGURES.
iv O.!
LIST OF-TABLES.
O v
Pd I. INTRODUCTION.
y 1
N II. DEMONSTRATION EXPERIMENTS PROGRAM.
(2 A. Spatial Measurements...
4 yI B. Spectral Measurements.............
4
{
7 C. Reactivity Measurements............
8 O
III. GENERIC METHODS DEVELOPMENT AND VERIFICATION.
10 A. Generation of Few-Group Constants.......
10
- 3. Global Diffusion Theory Calculations.
29 O
C. Specialized Methods and Applications..
33 D. Data Bank.
38
.j IV. ANALYSIS OF CURRENT FNR CORE AND COMPARISON WITH i
EXPERIMENT...................
40 A. Power Defect.
40 B. Void Coefficient of Reactivity.
40 1
4 C. FNR Fuel Burnup Calculation's..
45 L3 D. Control Rod worth................
46 m
j E. Reactor Kinetics Parameters....
47 V. ANALYSIS AND OPTIMIZATION OF LEU FUEL.
49 71 A. Equilibrium Core Void Coefficient of
?q Reactivity.
49 il-B. Control Rod Effects.....
50 C. Alternative Fuel Designs.
55 D. Optimized Core Loading Scheme.
58 1
6]
E. Temperature Coefficient of Reactivity and Power Defect..................
59 3
i VI. SAFETY ANALYSIS REPORT.
i 60 N
]
VII. THERMAL HYDRAULICS.
61
- t
- f VIII.
SUMMARY
AND CONCLUSIONS.
63 REFERENCES.
65 Q
y APPENDIX A. "The RERTR Demonstration Experiments p]
Progras'at the Ford Nuclear Reactor" a
y APPENDIX B. " Core Physics Analysis in Support of the h@5 FNR HEU-LEU Demonstration Experiment"
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APPENDIX C. Documentation for Data Bank i
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LIST OF F L*URES
.i Page I
fj 1.
LEOPARD Library Comparison:
U Capture Cross-I d
Section vs.
Lethargy.............................
13 2.
LEOPARD Library Compaiison 23'50 Fission Cross-g
?d Section vs.
Lethargy.............................
14
- 1) 27 3.
LEOPARD Library Comparison:
Al Capture Corss-j'!
q Section vs.
Lethargy.............................
15 i
16 4.
LEORRD Library Comparison:
O Capture Cross-3 Section vs.
Lethargy.............................
16 5.
Effective Multiplication Factor vs. Fuel ti Depletion........................................
24 6.
Difference in the Effective Multiplication Factor
, }.
Due to Different Libraries vs. Fuel Depletion....
25
.O 7.
Calculated Tranverse Bucklings...................
34 8.
Axial Geometry for 3-Dimensional VENTURE j
Calculation......................................
35 s
9.
Core Configuration for Void coefficient of Reactivity Experiment............................
43
- i 10.
Void Coefficient of Reactivity for FNR Cycle l
169B Core........................................
44 0
11..
Void Coefficient of Reactivity Calculated for
]
the Equilibrium Cores............................
51 i
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h:i 1.
HEU Microscopic Cross-Sections Important to the
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Infinite Multiplication Factor.
18 3
3' 2.
TRZ Rodded 00
- 4 (W/F=2.35)
- 2. Critical Lattice Results 20 A
7 4
]
3.
Two-Group constants for 93% Enriched FNR Fuel.
21 j.,.
1')
a, 4.
HEU FNR Burnup Effect on LEOPARD Results.
23
- y 5.
Flux and Eigenvalue Comparisons for 2-and 3-i, D ime ntional Geome try............................
35
,j 1;
6.
Cross sections for the Void Coefficient G
Calculation.....
41
- id 7.
Comparison of 2x2 and 6x6 Mesh / Element for Control Rod Worth Calculations in FNR Equilibrium Core Model........
47 8.
Void Reactivity Components for Equilibri'um Cores 52 y
,1 9.
Neutron Balance for Control Rod Ef f acts in the
.i HEU Batch Test Core.
53
- 10. Neutron Balance for Control Rod Effects in the
_ i
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LEU Batch Test Core.
54 c;
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- 11. Equilibrium Core Fuel Design Comparisons.
57
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L I. INTRODUCTION
}
- j The University of Michigan Department of Nuclear L. '.
Engineering and the Michigan-Memorial Phoenix Project have been engaged in a cooperative effort with Argonne National
- j. l Laboratory to test.and analyze low enrichment fuel in the je Ford Nuclear Reactor (FNR).
The effort was begun in 1979, b)I as part of the Reduced Enrichment Research and Test Reactor
-}
(RERTR) Program, to demonstrate, on a whole-core basis, the
(
j3j feasibility of enrichment reduction f rom 934 to below 204 in MTR-type fuel designs.
Testing of lov enrichment uranium 3
(LEU) fuel in the FNR core is currently scheduled to begin j
in September, 1981.
y, The key technical basis of the LEU fuel is to reduce
],
the uranium enrichment while increasing, at the same time, the uranium loading of each fuel element in order to yj compensate for the reactivity loss due to the larger 238g The required uranium loading can be achieved by content.
~
i increasing the uranium density in the fuel meat and by d
increasing the fuel volume fraction.
At the same time it is necessary to insure that fuel elements operate within their thermal-hydraulic limits.
]
The first phase in our investigation performed in ug preparation for the LEU fuel testing at the FNR core K
included (a) initiation of development of experimental and analytical techniques applicable for neutronic evaluation of the MTR-type fuel elements, (b) selection of a LEU design e9 for the FNR, (c) preparation of a preliminary FNR license dy amendment, and (d) a thermal-hydraulic testing program for L
the MTR-type fuel elements.
These initial efforts
[.]
undertaken in our LEU project are summarized in our first j
Annual Summary Report for the year 1979.
A g
In continuation of these initial ef forts, further y
improvements and validation of the experimental and 3
analytical methods were carried out in 1980.
The experimental work was centered around spatial flux 9ri e.
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q measurements in and out of the core, and ex-core flux A,
spectrum measurements.
The analytic offorts included y'
improvement of various computer codes and development of
j calculational models for reactivity coefficients as well as j.l further analysis of I.EU fuel designs.
During the present reporting period, a series of thermal hydraulics tests were 2
performed for the.MTR-type fuel elements.
Amendments t,o a m
M]
safety analysis submitted as part of a requested license amendment to permit the use of I.EU fuel in the FNR were also
]
submitted to the U. 5. Nuclear Regulatory Commission in 1980.
Approval was granted in February, 1981.
1 Detailed papers on the experimental and analytical d
ef forts performed under the I.EU project for the FNR core 1
p;t were presented at the International Meeting on Development, 1
Fabrication and Application of Reduced-Enrichment Fuels for a
l Research and Test Reactors, held on November 12-14, 1980 at-
~,
Argonne National Iaboratory, and are included here as Appendices A and B.
Hence, this report aims primarily at 1
summarizing those efforts performed during 1980, which were adequately covered in the papers, and at providing a nos y
brief review of the project status.
We begin with a review
].
of the activities related to the I.EU demonstration 9
]
experiments in Section II.
Various efforts undertaken in j
support of the development and verification of the neutronic
,d methods for generic analysis of MTR-type fuel elements are
>g then summarized in Section III, while comparisons between
[..j the calculational results and the FNR experimental data are wg presented in Section IV.
Design analysis of the I.EU fuel Ij
'and comparisons between the IEU and high enrichment uranium
]
(HEU) fuels are presented in Section V.
A review of the
[]
activities related to the FNR license amendment is then g
given in Section VI, followed by a summary of the thermal-hydraulics test results in section VII.
A summary of the h
project activities for the year 1980 and a brief review of ro pj the project status are then presented in Section VIII.
In y
addition to Appendices A and B discussed earlier, a limited
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O II. DEMONSTRATION EXPERIMENTS PROGRAM A
f4 The Demonstration Experiments Program, designed to M
measure.the significant dif ferences between HEU and I.EU k-f cores, was continued in order to characterize the HEU t'NR j
core.
The work performed through January of 1980 is
{'
9 described in'the first Annual Summary Report. The work performed during the period January, 1980 - December, 1980
- {l has involved primarily the implementation and extension of
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the concepts developed in Reference 1.
Appendix A, "The y
RERTR Demonstration Experiments Progras'at the Ford Nuclear 1, l p
Reactor," contains many of'the results from the experiments which have been performed during the past year.
These
('
etforts, summarized below, are by no means completed and y
work is continuing in all areas at this time.
- )
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a
']
A. Sostial Measurements
.g L,
- 1. Rhodium Self-Powered Neutron y
Detector Thermal Flux Mapping
}5 The two major problems with the rhodium detector j
thermal flux mapping identified.in Reference 1 have been p]
addressed and are described below.
9 a) Epitberaal Neutron Contribution to Detector Signal
21 g
Analysis of the epithermal neutron contribution to the v
detector signal for the HEU core has continued during this h.1 s.
q period.
The results of the measurements performed during h
1979 and the analysis in 1980 were presented at the June f
j 1980 ANS meeting.
While the major part of this offort is
]
completed, it would be helpful to repeat some of these
{
pj measurements using beta counting in our 4-r proportional counter, at various reactor power levels, and at the 3
beginning, middle, and end of the operating cycle.
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b) Time Delay to Reach Fquilibrium Signal i
ij This problem was identified in Reference 1 as one of
_]4 the more serious drawbacks in using the rhodium detector for J.),
extensive flux mapping.
A technique was developed at the
- S,
dj University of Michigan to determine the fluz at a particular time (and hence, position) from the detector current known
.h at all previous times.
The technique has been codified in 3
'{'
the RHODI computer program and has been applied to data l}
taken at various positions and detector speeds through the ia FNR.
'I The results were quite acceptable, and were presented at the November 1980 ANS meeting.
Further work in this 4
/,,j area has led to a dramatic simplification of the governing equations, but at' the price of a surprising decrease in
!{
accuracy.
While the techniqun has been developed adequately k*-
for use on the FNR, it would be useful to " fine tune" the codes by varying K, the prompt sensitivity of the detector, p
i.
and to continue work on simplifying the analysis.
These two efforts should yield increased accuracy and decreased
.: [
computational requirements.
- 2. In-core Power Distribution Measurements
- )
./
In order to measure the axial temperature rise of the j
h water flowing through each fuel assembly in the FNR core, a thermocouple probe was designed, built, and tested.
The probe consisted of a copper and constantan thermocouple that
]
was designed so that N
it could be inserted into the regular A
tuel elements of the FNR,
S il Two nearly complete and two partial core maps were made using the probe.
f The temperature difference across a given f,3 fuel assembly was taken as the difference between the temperature readings one inch above and one inch below the a
y fuel region of the assembly.
Readings were taken at regular time intervals for several minutes and were averaged.
}
Typical measurements had a variation of about 0.6 degrees Fahrenheit.
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As mentioned above, the temperature drop across some h
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elements was measured on four separate occasions.
The data h
indicates that the reproducibility of the measured
]
tempera'ture drop across an element is good for the majority
]
of these elements (i.e., less than 10 percent variation from u
the average temperature drop measured on that element).
c; d
However, there were a few elements where a measured value differed by more than 20 percent from the average
(
- )
.a temperature drop measured across that element.
h The temperature differences were also compared to the f
{
midplane thermal flux measured by the rhodium detector in 1
y order to compare the radial power distribution that each
{
- 'j predicts.
We assume, in our preliminary discussion, that ki the mass flow rates and macroscopic fission cross sections 3
are-constant in the regular fuel elements so that the tj normalized temperature differences can be directly compared
,f
- j with the measured normalized fluxes.
Again, agreement in g
most cases is good (less than 10% difference), although 4'
there were cases cf serious disagreement (more than 204 difference).
In addition, the averace coolant temperature
~
7 rise in the elements measured was approximately twice as
<=
i large as the readings taken by the FNR control' room system J
instrumentation.
A possible source of this error is h'est
.]
conduction from the fuel cladding to the tip of the probe.
[
This would cause an error in the measurement of the outlet g
temperature, which 1,1 where the principal disagreements
{
exist.
In addition, there is uncertainty concerning the bypass flow around the active core and the relative flow p
pj through the regular and special ele'ments.
As a result, we L
f.j presently view the temperature difference data with some 7
skepticism.
f (6
- 3. In-core Wire Activation Experiments
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I In-core wire activation experiments were also made during this reporting period to provide additional
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verification of earlier results for axial flux ji distributions.
The equipment and data analysis techniques j
are presented in detail in Reference 1.
The recent ij measurements yielded results which do not dif f er
- [
significantly from those presented there.
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1-j' B. Spectral Measurements is J
- 1. In-core Spectral Measurements
- 1..,
This phase of the experimental program was first addressed in Reference 1.
Additional work has continued along those lines.
In addition to the SAND-II code, we have also acquired and implemented the SANDANL, WINDOWS, and FERRET code packages.
These codes are much more recent, and provide additional unfolding capabilities, including sophisticated error analysis subroutines.
New ENDF-IV R$
-v cross sections were obtained f rom Brookhaven National Laboratory, along with the INTEND code which is required to.
i
' j, formulate the cross section libraries into a standard SAND-j II compatible format.
In addition, a complete set of foils was acquired in order to carry out the experimental program l
on both the HEU and LEU cores.
~
l:
L The results of unfolding a set of measurements made D
with five trial foils activated in the FNR are presented in Appendix A.
The lessons learned from this experiment led to 1
the design and construction of an in-core sample holder 7
d which fits into a special fuel element, and displaces nearly all of the water in the central hole.
Experiments are continuing in this area.
1
- 2. Excore Spectral Measurements 1
1" a) Crystal Diffraction Measurements Yj The initial measurements performed on the crystal q
spectrometer to determine the beam port thermal flux 1
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spectrum are summarized in Reference 1.
Since measurements q
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of the neutron temperature are strongly dependent on the M
crystal' mosaic vidth, a secondary spectrometer was set up in order to do double crystal rocking measurements of the jj mosaic width.
A perfect crystal was initially borrowed from j
the. University of Missouri for this purpose.
The results of d
f' the experiment gave an effective mosaic width which is too
~
1arge to be consistene with a realistic neutron temperature.
d Because of this problem and the difficulty in accurately
]
determining the crystal reflectivity, a perfect crystal was
..{
ordered from the University of Missouri.
We have just t1 received this crystal and are redesigning the spectrometer h
for a new set of measurements.
't
!y b) Thermal Spectrum Unfolding from Foil-Activations In theory it should be possible to unfold the thermal spectrum at a beam port by foil activations in the manner 11 discussed in Section B.1 above.
Cross sections for non-1/v 1
materials were obtained from Brookhaven National Laboratory,
{
j)]
and some initial experiments have been done.
The activation gj data have been unfolded using tht FERRET and 5ANDANL codes gj and comparisons are just now being made.
While this is the 1:
- i first time thermal spectrum unfolding has been attempted j.
through foil activations, the preliminary results obtained seem to warrant additional work.
As with the experiments
,jj mentioned above, considerable work still remains to be done S!
in this area.
M O!
[q C. Reactivity' Measurements m
h'.
Besides the standard rod worth measurements which are done routinely on the FNR, we also performed a menon h
transient experiment this past year to determine the
[j equilibrium xenon worth in the FNR.
The results agreed well
)
d.
with the values measur4d in previous experiments.
In addition, a number of other conventional experiments (suca l
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as critical loading and reactivity coefficient measurements) were performed in conjunction with our nuclear reactor laboratory course.
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h III. GENERIC METHODS DEVELOPMENT AND VERIFICATION la v.
The basic calculational model used to analyze both HEU ik and LEU fuels has been fully described in Reference 1 and
(;
ij Appendix 3.
The following sections describe completed and i
j current offorts to extend and improve the model.
These
{
j efforts fall into four general areas: First, our methods and Ih data base for the generation of few group diffusion theory M
constants have undergone continuing development and l
h improvement.
We continue to rely upon the LEOPARD and U
EPRI-HAMMER codes for routine calculations, although two h
new codes-- the EPRI-CINDER code and the RCD code-- have 0
oj h
extended our computational capabilities.
A new ENDF/B-IV p
data base has been developed for the LEOPARD code.
Test
]
results appear promising, although general use of the new library awaits the updcting of many physical constants
" hardwired" into the LEOPARD code.
Second, many of the 1
previous extensions of the two-dimensional diffusion theory
>1, 9
capsbilities of the 2DB code have been consolidated into p
the 2DBUM code, with particular emphasis on user convenience
,I and computational speed.
New modifications of the 2DBUM 7
code have been made to accomodate new and specialized g
applications.
Third, new calculations 1 methods have been L)i investigated for both reducing computer costs and extending I,
the model to particularly difficult FNK problems.
- Fourth, u,
j significant effort has been expended on the documentation of
[i our LEOPARD-LINX-2DBUM code system and on the development of a reference data bank for the FNR.
W A. Generation of Few-Grous Constants b
t.-
HQ
- 1. Modifications to the LEOPARD Code l'i M
Recent changes in LEOPARD have involved primarily h
improvements or corrections to previous capabilities.
The t
L l.;
restart capability has been generalized to permit the
')
generation of derivative cross-sections for power defect b,.
u ik' e
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W calculations (see Section II.E in Appendix B). The thermal if. i expansion effects on uranium number density were changed to j,
allow for expansion of input isotopic uranium densities.
d,-
Previously, LEOPARD corrected uranius densities only when E
present in 00.
To allow for the effects of flux peaking 2
j"-
variations due to depletion on the spectrum, an additional j'
input option has been added to provide for burnup-dependent q=
non-lattice peaking factors (NLPF's).
The binary few group
}b,,,
cross-section burnup library passed to LINI was improved by including more complete identifying parameters.
- Finally, i
improved printout has made interpretation of LEOPARD results
],
much easier.
j" d
- 2. New ENDF/B-IV LEOPARD Library
'j 1
Differences (for analyses of MTR-type fuels) between 71 the results of the LEOPARD code and those of more h
sophisticated codes, such as the EPRI-HAMMER code, are h
primarily due to differences in the libraries used.10 The d.)
LEOPARD code uses an early industrial data set while the other codes employ the ENDF/B-IV data.
In order to remedy this inherent' difference, a new library for LEOPARD was
[
assembled from the ENDF/B-IV data.
Ii
[
A new code SPITS, a heavily rewritten version of the SPOTS code, processed data supplied by W.B. Henderson11 of
.h Westinghouse Electric Corporation into a form compatible
- p with the LEOPARD code.
The Westinghouse data were created h
from the original ENDF/B-IV files by the ETOT-5 12 13 and ETOG-5 codes.
The SPITS code copied data for three of the
],
25 LEOPARD nuclides from *he original LEOPARD library.
Data y
for the remaining 22 nuclides were read from the Westinghouse tape.
Cross-sections for deuterium and the
- q lumped fission products were taken from the old library
.io because they are not included in the Westinghouse data; the new Westinghouse hydrogen data were not used because the 3Q scattering cross-sections are based on free rather than the i
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desired bound hydrogen.
Plots for the various cross-sections versus energy for the 23 standard nuclides were 3
made, both for the 54 group fast library and the 172 group i
j thermal library.
Figures 1-4 illustrate the differences j
8 between the two libraries for some important nuclides.
4ij The original LEOPARD library includes bias factors i
i which allow results of LEOPARD analyses of critical and j
experimental lattices to agree with the experimentally obtained parameters.
The bias is implemented in the SPOTS
)
)
ec..e by increasing the number of neutrons released per fission by 0.364.
A second bias is introduced by decreasing k
235 the number of neutrons released by 0 undergoing fast l
)
fission by 1.224.
Although the latter effect is minor, the 3
former effectively biases the calculated multiplication
'f factor by 0.364.
Comparison of the LEOPARD results obtained
- j k
using a new library incorporating these biases and those calculated using a new library without the biases with the corresponding results of more sophisticated codes indicate l,
l-{__
that the biases are not needed in the new LEOPARD library
{
ij because both the library and the codes used for comparison d
consistently use the ENDF/B-IV data.
N j
i In order to determine the usefulness of the new library
'i and its differences from the old library, extensive
- .)
comparisons and studies were made.
The two LEOPARD h1 libraries were compared with benchmark codes, the important
]
differences between the two libraries were deduced using a l
sensitivity method.
In addition, an experimental critical j
L-lattice was analyzed, and both HEU and LEU FNR fuel L3 qs depletion studies were performed with the 2DBUM code.
n t
The benchmark codes used for comparisons between the I
LEOPARD results using the old and new libraries were the di EPRI-HAMMER, VIM
, and EPRI-CELL codes.
The sample cases t
10 15 analyzed were typical HEU and LEU plate-type MTR fuels.10 f
M Comparison of the microscopic cross-sections generated by
-l siy these codes indicate that for the fast energy range those
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t
,-:.u...
mus ce w
.m..
-.- ' ~ - - _
=-
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,_.:. a :. a. ~... + w ~ = ;
^ = ' ' - " "
u u
t, r
8.
[V i.
I s
[
MOLD LEO. FAST LIB.
t ;.
OENDF/8-N FAST LIB.
i 4
1
.'s a
b i,
"'y 8
.d
- 4 d
.I 1
1 W
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l 1
i h
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=
f-t 3.se 4Ae tas aos mas sLas MAe asAs nas asse j
i LETHARGY i
l 1
i i
Figure 1.
LEOPARD Library Comparison: 235 t
i U Capture Cross,Section vs. KAthttgy
.(
t f
o h
i i
l 1-s
T.:13 h % Lab uL M EOD:4WA%UO u u2 ' " = ~' F $W'
^ #^
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{
I
{,...
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?
j s
j.
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'I l
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t
- q L
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am f
I l
h l.
i L
5 A
A
- ^
i b
.T
~
0
~
stes las 4as see s.ee mas stas use asas mas anse e
LEI %RGY Figure 2.
LEOPARD Library Comparison O Fission Crosse 3ection vs. Isthargy
- [
j.
[^
.e
y_
,3_-7._-,,,---;;7;,m___----.----,---_
_i
-_.w...u.-.,=..
~na=~ n-
= =-
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- i.>
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p 5
MOLD LEO. FAST LIB.
6ENDF/8-IV FAST LIB.
- jf j.
~
5-
- +
'T\\
Yg i
g t-in :. *.
.r
,h 3
f
'a
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- n i
i f
1
\\
A
,I
-~ O.
?. :
bes les 4se s.es Ese ase
. ras nas Ese mee anse LETHARGY 27 Figure 3.
LEOPARD Library Comparison:
Al Capture Cross-Section vs. Lethargy i
. u..,a. -.:., w.
,.:-,., s,....:.,..
- ...... m,. u :. :., u... _... :..... ;.... a w.:c...a.a _u:
a..;... w... a w.==
~-
~- >
_.{
,r s
i:-
Ih i
(G-n g,
p t:
-.n
(~.
'~
4 5.
MOLD LEO. FAST LB.
U 6ENDF/8-N FAST LB.
t:
5-5-
T.
si r.
e af I
5-5 l.
2 mm
- e. =
sm am
==
.am um um am um LETHARGY 16 Figure 4.
IJOPARD Library Comparisona O Capture Cross Section vs. Isthargy
..j i
.a
=
m-me ammme ammme
.. _.v a. -
g L _.
j
..m.,
- a. 7 generated using the new library generally agree more' closely with those of the benchmark codes than do those generated j
using the old library.
In the thermal energy range, g
however, the microscopic cross sections of the old library Il compare more favorably with the benchmark cross-sections.
fj -
Before any conclusions can be made, however, the j
importance of the various cross-sections must be evaluated.
To do this, a code incorporating a sensitivity technique was y
used to determine the contributions of differences in er.oss-
]
section'of the two LEOPARD libraries to the infinite d
multiplication factor.
The contribution of a particular aj difference was calculated by multiplying the difference in 1
the macroscopic cross-section by the importance of that
]
cross-section to kint. values of the most important cross-j]-
sections in the new library are generally in better p
agreement with the corresponding values generated by the benchmark codes than are those of the old library as seen in Table 1.for the HEU case.
The materials for which the differences between cross-l i
sections of the two libraries have the largest influence on inf are 0, 27A1, and U.
The differences between the 235 k
j values of these cross-sections of the two libraries can be seen in figures 1-4. Although indi.vidually the contributions may be as much as 0.64 ak/k, they tend to cancel one g-another resulting in a much smaller net difference.
The net j
difference calculated directly by LEOPARD was 0.12% a k/k.
j The sensitivity method code calculated a slightly different 03 value, 0.144, as a consequence of the approximate nature of the technique, however, this difference is acceptable and verifies the basic approach of the method.
ti In an effort to determine how well the new library f,~
simulates experimental data, the TRX rodded 00 lattice l 2
[
with water / metal ratio of 2.35 was analyzed using both the p,
old and new cross-section data sets.
Both libraries predict p
the experimental results quite well, but in most cases the 1
21n
4
,..s.
f'., D; '. v.
i>.%s J.-...c
_w mLu M d ~. ' -...u.__
+
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+ e et.
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= SP fe
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e.
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a g
de g g g 4 =. n e.
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9 89 e.
gg T SS g *
- 9 e.
SG T Se u a e w
e e = e e e.
e = e e e e Ce 9 r?
tfD G G 9 9 9 9 9 9 9 9 9 9
= = n
- tft a
b e
l*
8 4
Ce a
w e
O
= e e C = >
e e e 0 e l.
0 0=0 u
k n
a l
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i 4 i i.
3 O.=.=
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l
.N
'a.I e
l e I.\\r*
F
+
f.
- . g 3
- t t-
=
q v
I
_ _ _ _. _ _ _ _ _, _ +.m.ew.m
-e---'--~
=-
g N'
A hy,, A km ew M e J - *.
De-"""'h-^
y,
.n -
r
.n.:-
- =
~. ~f *" "
- [^
"V t
19 L:
l old library provides slightly better accuracy (see Table 2).
j. *.
It is difficult to draw a conclusion from this result t
because one cannot be sure if the errors are introduced by the calculational scheme or by the cross-section data base.
h i In addition, the error in the experimental data which may be as much as 2% must be considered.
1 J
Two group macroscopic constants for the 934 enriched FNR fuel generated by the LEOPARD and HAMMER codes are compared in Table 3.
In most cases the parameters 9
calculated incorporating the new library agree more closely with the HAMMER parameters.
The thermal diffusion coefficient and thermal absorption cross-section calculated using the old library are exceptions because, as indicated i
eerlier, microscopic thermal constants in the.old library
["
are generally in better agreement with those of the HAMMER
[
code.
Comp 1ete burnup cross-section table sets of both the b
HEU and LEU FNR fuel have been produced by the LEOPARD code using the new library for comparison with the sets previously generated using the old ' library.
By using each batch core depletion studies have been inade with the
- set, 2DBOM code.
In addition, a HEU critical experiment of the FNR core was simulated by the 2DBUM code using the old and 3
- f new cross section data sets.
- 1 The infinite multiplication factor of the fresh fuel s
f calculaced by the LEOPARD code incorporating the new library j}
is higher than that obtained with the old library; as much as 0.26% for the HEU case and 0.22% for the LEU fuel.
As the fuel is depleted the two values are closer to one ij another (see Table 4). This is a consequence of the higher j
absorption cross-section of 2350 in the new library f,
resulting in an increased burnup rate for that nuclide.,
The f
value of the effective multiplication factor which was 4
calculated using"a constant buckling of 0.00914 cm shows
-2 h
a larger difference.
j.
The discrepancy in k,gg can be N
1
[ MGO:.w*inLM__...
c
- .; y i
i 5 O'
\\hia. _...
' w 2,...
a a..
. c L.-...
a.-
.i d
20
.W N' d
'l' I$
Table 2.
TRX Rodded 00 Critical Lattice Results (w/F = 2.35) 2 k
-11]
old LEOPARD New LEOPARD Parameter Experiment l
j (a)
(b) value 4 diff.
vabe 4 diff.
8 9
28 ed 1.311 1.2698
-3.1 1.2843
-2.0
'N 25
']
0.098L 0.0994
+1.3 0.1061
+4.2 L' 8 28 Ji.
0.0914 0.0890
-2.6 0.0847
-3.0 3
.J CR*
0.792 0.7668
-3.2 0.7607
~4.0 2
3 0.0057 0.00564
-1 1 0.00562
-1.4 k *'
1.0 0.9984
-0.16 0.9977
-0.23 I
co' U
28, U-238 epithermal capture Notes: (a)
U-238 thermal capture 25,0-235 epithermal fission U-235 thermal fission m.1 28 U-238 fissions
=
f3 U-235 fissions 2
,U-238 captures U-235 fissions
,A
- 1 5
= critical buckling s
iJ (b) MkPD-TM-931 (1970)
L 1'
[
(c) Measured value assmed to be 1.0; b
calculated value is based on a LEOPAID run with measured critical g
. buckling input l
l.1 l%
I.",
e
.(-,
A I.?
a l.1 llig e.'l a4 i
1
-~""
O
~ - -
- m-, :; 9 m:a ~ * " ~ ^
.. ? ' 2.~
~~
- -g-
,~
\\1.
- 4. ;
q-Table -3. Tro-Group Constants of 93% Enriched' FNR Fuel n.
)
m
.i 1-Old LEOPARD New LEOPARD a
Parameter HAMP.ER
{,
value value 4 diff.
Value 4 diff.
y.
M k.
1.5556 1.,5415
-0.91 1.5455
-0.65 1
h/$
2.460 2.439
-0.~B4 2.457
-0.13 i
t.'
/.ge 50.79 52.01
+2.46 51.26
+0.99 D
1.3S56 1.4455
+3.58 1.4126
-i.22 i
I.S.
1.8578-3 2.0697-3 +11.41 1.8359-3
-1.18
%,i 2.5621-2 2.5722-1
+0.39 2.5719-2
+0.38 ia
- I,i 2.2663-3 2.0874-3
-7.39 2.2241-3
-1.86 i
D2 2.7607-1 2.8677-1
+3.88 2.3960-1
+4.90 I.2 5.9558-2 6.0115-2
+3.01. 6.0469-2
+3.62
-j,
aIra 9.3737-2 9.5112-2
+1.47 9.4850-2
+1.19 4,
~
4 ia d
G
[,
9 i.
-5,
.a
".)
j.I
^
a, J
u s
Q,
- f d
a d 1
' ' - ~ ~~
~~
,.,C*
7., __ j7 u d.C'
~ -
- =
- LUb,,u
.'.2 s w.iEb s14" +
u.
n
};
.i 22
.+
q 15:
3 attributed to the large difference in the fast non-leakage 49 f].;
probability, P At the beginning of life the difference NU.
in k,gg.is 0.89% decreasing to 0.754 for the HEU case after f
500 days of depletion.
For the LEU case, the difference is j
initially 0.82% and decreases to 0.59% af ter 700 days.
The
]$
new library yields higher values of k,gg and kinf throughout j
the depletion steps.
pg To further assess the impact of the new LEOPARD library l
.2 on fuel depletion calculations, the HEU and LEU batch core f
d configurations were analyzed for the FNR core.
In the 2DBUM
(
depletion calculations covering the fuel depletion from
[l beginning of life through 200 days of full power operation, g.i differences in k,gg for the HEU and LED cores obtained with the two LEOPARD cross-section libraries stay nearly constant q
with depletion.
Again, the new library predicted the higher value (see Fig. 5). For the f resh HEU core, tihe dif ferencir is 0.834.
Af ter about fif teen days of fuel burnup, it peaks
]
to about 0.904.
With time the ditierence gradually
{
y decreases to 0.80% at 200 days (see Fig. 6). The LEU core
,g behaves in a similar manner.
Initially the dif ference in
)
eigenvalue is 0.744.
After a peak difference of 0.80% at
[
]
about 20 days, the difference slowly decreases to 0.69% at N-200 days.
The decrease, as before, can be attributed to the faster depletion of U with the new library.
235
'l M
The eigenvalues calculated in the 2DBUM simulation of
- .j the HEU critical experiment performed on June 13, 1971 M.
during FNR cycle 147B are 1.0024 and 1.0102 for the old and H
new libraries, respectively.
The difference of 0.784 is l
f consistent with that found in the cases mentioned above.
This case is not a completely independent evaluation of the j
(?
dif ferences between the two libraries because the data input m;;
to establish the middle-of-life core (i.e., fuel burn-up
["j distribution) were calculated for both cases using the old
.4 Ik') -
LEOPARD library.
M i
!.y In summary, the new ENDF/B-IV library shows better i
Ik
(~b 1
i-s,
.c_
.-r p x,.yg " c - :; m -
y"
^7
'~
e JJ e
\\
a s
E
.)
O
- 1 me,e O-n.,
1 m
M..,. e. p e..
=
- .I 2
0000000 34 3
+++++++
-f
=
8
-en-
~~ene3
.a en eeeeee
=
+
2
.O W e. e. d. e. W. e.
g em a
O000000 s'
i 8
i De see
-s
>>>> es s
Oc y <
- o. w. e. s. e. e. d.
3 a
O000000 e....e.
- e. m. e. e. e. k. r=.
1, 3
9 0000000 p
+++++++
e a
O
'1 a
= e r= p= >
.1 e
3e r=--Oe as
-pe,aem 2
O O.. e. e. e. e. e.
e w
Js a
=OOOOOO
- a Ga
-Owen>-
De
-en.en=e n-ee l
i O
.. e. m. e. e. e.
es w
j u
.a
-O00000 e
b eMon-e, b
h.
M. M.M.M.M.
w M
0000000 N
+++++++
e.
3.2 5
6
....e 2
,e e
8 I
w b.
1
=
2 e,...,
6 3.
.,e,e,,e-o,..,
O ens a
e 3O O mes.e g
-,.e...
o.
2.o
=
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O n
.=
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, e. e.. e..
- a,
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m
.a u
d.
O...
-,8...
~
0 3.~
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-en e
s g
1 4
288 8 ~
a
-~,
- =
a i
II f
a I'.;
H
'a d
i 5
w-...
~ :L;.
..> cl A&k:> :
. - :e
.:.~....
24 es o
-t
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.g a
6:
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- 3
- d
.g.j m, s A
s, 1'
+
1.06 g au
- .n
.3 IEC Flet Batett Core 2DacK Calculation
- y A new LEOPARD library 1.04 o old LEOPARD library t '.9 w
i
.I we
.J M
~
p 1
houo
]
., 1.02 4,
s u
e u
w
.d Os.
- 1.00
.a
,)
3 z
<.?
e
-s
.,n
'M a
o 4
e t 0.98 M
h*
y!
- )
m
- - ]
?!
0.96 h
a_
i:
-=
Q i
50 100 150 200 y:
r 4
Figure 5.
Effective Multiplication Factor vs. Fuel Depletion a
3H l3
- 1 2.
If b,
r,
=>
4 a._
m
..u-_. -
.._2
__ i
.3 I
I 4
0.90 EEU Flut Batch Core 2DBUM calculation e
4 )
l O
8 e
$0.85 u
e 9
a e
1ii it
.a
. t.
4 E
.)
i
- i 4
O.90 l
i 50 100 150 200 Equivalent Full Power Days of Operation
)
1 al Figure 6.
Difference in the Effective Multiplication Factor Dve to Different Libraries vs. Fuel Depletion I'in
- 4
.~
l1
'i I3 li 1,
s
\\
-- Q " "' ' " -
.aww
-w - -
-~
~~
a
~j 26 5L M
agreement with the results of more' sophisticated codes on
'l d
both the macro and microscopic levels.
Cores analyzed with j
the new library are predicted to deplete slightly faster but j
]
with a' higher initial multiplication factor than are cores Tj studied using the old library.
I{l q.j Currently, efforts are underway to update a number of g
physical constants used in the LEOPARD code.
These include
']
fission yields, decay constants, elemental densities, and l
atomic masses.
Efforts will be made also to further explain
(
the difforences in kggg and k,gg between the new and old
}
LEOPARD libraries.
di l
l
- 3. The ROD Code The computational sche:ae for FNR control rod worth l
l analysis presented in Reference 1 requires the use of the lf HAMMER code to generate special assembly cross-sections both
')
with and without a control rod.
To include the effects of fuel depletion on control rod worth, HAMMER calculations g
i must be done for several special assembly burnups.
Two I
s schemes were considered for accomplishing this: The first, adding a depletion capability to HAMMER, was clearly q
unacceptable due to the extremely high computer costs, long L,.l development time, and major rewrite of HAMMER that would be N
required.
The second, linking the LEOPARD and HAMMER codes h
to allow HAMMER calculations at any LEOPARD burnup step, was fij implemented via the development of the RCD code.
This code
[-(
is a sophisticated supervisor program which dynamically H
loads and runs the LEOPARD code for a special or regular h.;
" assembly depletion run, saves the resulting isotopic number densities at each burnup step, sets up HAMMER input for user-specified burnup steps, dynamically loads and runs the 7
HAMMER code, and then reformats the HAMMER generated cross-d sections into a burnup library suitable for the 2DBUM code.
[
Since the HAMMER code performs the spectrum calculation only
((
for a specified input buckling (passed from the LEOPARD code w
.N u
- p n
I
,o i
f -[
(1 tl
g.=__,..
m,g,,.g. g 27 by the ROD code) and does not iterate to criticality, the
(-. :
ROD code checks the HAMMER eigenvalue.
If the HAMMER eigenvalue is not sufficiently close to 1.0, the ROD code
[q, interactively asks the user for a new buckling and then reruns the HAMMER code.
y,-
This interactive iteration approach was chosen to avoid the high cost of modifying HAMMER to perform criticality searches.
For the case of a special assembly with control rod inserted, the ROD code makes a
}
normal LEOPARD depletion run (i.e., no rod), estimates the critical buckling of a rodded special assembly using an k
empirical correlation, and then runs the HAMMER code for a
$a rodded special assembly.
1
[j The entire calculational sequence of the ROD code is moderately expensive (about an order cf magnitude greater
[1 than a standard LEOPARD depletion run) but has been used to
!.;1 generate cross-section burnup libraries for use in both HEU si f
and LEU control rod worth analysis.
I Comparisons of 3
predicted and measured rod worths are presented in Section r
3, III.3 of Appendix B, and a comparison of HEU and LEU rod worths in Section III.F of Appendix 3.
The ROD code performs many system-dependent functions related to disk file manipulation, dynamic program loading
't
()
and linking, and interaction with the user via terminal input / output.
As such, the code is not l J exportable to other
[j computer systems not having both IBM Fortran and the Michigan u[
Terminal System (MTS) operating system.
Additionally, certain
.]
features of the FNR fuel assembly geometry are hardwired into j.
the code, precluding its general use.
4 lt
~,
- 4. The EPRI-CINDER Code
[.
The EPRI-CINDER code calculates fission product o
concentrations, effective cross sections, and other f
quantities based on fuel composition, fluxes and power level bas'ed on a point isotopic depletion model.
The user chooses between two options, an 84 chain fission product library and a
- i
L - ___:
~
a.
- +
L' n ~~-- - -
--a
[
- l.. l
>:3 U !.
28 1
+1
[.g a 12 chain fission product library, which accounts for the 42 eleven most predominant chains and creates a twelfth
}j
" effective" fission product chain to account for the jj remaining chains.
The 12-chain library is intended for use pj in spatial depletion calculations.
In general, the 12-chain di.
library gives results almost identical to the 84-chain
(,j library, except for calculated effective resonance integrals.
wi
- Ay, The code has been modified to run on the Amdahl 470V/8 a;z computer at'the University of Michigan.
Originally written
- q for a CDC 6600 machine, the code is designed for greater 3.. ;
exponent capacity then the Amdahl permits.
The algorithm 7j used to calculate nuclide concentrations includes intermediate products which are accumulated over several
'i nuclides.
These products become so small as to be outside ay the limits of the machine.
Since the algorithm is complicated by extensive roundoff controls, the simplest
[;
solution was to multiply the time step length, power and g
---decay constants by a constant factor at the time they are f
read as input.
Thus, the intermediate quantities become i
manageable while the calculated number density remains 5
unchanged.
n lg To determine the accuracy of this 'fix' sample cases f
will be run, using the unaltered code, on the CDC 6600 m2 machine at Michigan State University, through the MERIT
.qg Computer Network.
The results of these cases will be 2<
2d compared with the results of identical cases run with.the gj modified code.
In addition, comparisons between the altered
"!j code and the summary tables printed in the EPRI-CINDER code J
.;3 manual have been made.
Small differences occurred in ng several quantities, none greater than 0.2% in magnitude, q
while other results were unchanged.
However, we consider fj the final verification must await the CDC-6600 results.
4 l(j With the magnitude of any errors introduced by the code
$]
modifications thus determined, the next step will be to
"',T.
3 b
]
Do
-.; s l..
_. = ~. - -. -
-n.
29
.J ' :
j.-
compare results calculated by the EPRI-CINDER code with
^ l, available experimental data sets to determine how well the Z,
code performs.
The current effort is focused on identifying d*
applicable experimental data on fission products for both 4
Upon verification of the sample
] '.*
lumped fission product correlation for LWR fuel currently 1
used in the LEOPARD code, the EPRI-CINDER code will be f
utilized to generate an equivalent fission product correlation for the HEU and LEU fuel designs.
.f B. Global Dif fusion Theory Calculations 44 E,-
- 3
- 1. 2DBUM Code Modifications l
The 2DB code has continued to be our principal code for
~
h multidimensional diffusion theory analysis of the FNR.
a 1
As noted previously, many local modifications were made to improve the usability of the code (link to LEOPARD, k,
additional options, etc.) and to, allow detailed FNR analysis h,
(macroscopic cross-section interpolation on burnup, space
},. '
dependent zenon, etc.).
Early in 1980 it became apparent that an overall updating of the 2DB code was necessary in order to consolidate and clarify both the original coding and the diverse modifications made by various project y
3 1 members.
Additionally, an overall updating would facilitate
?1 al many major modifications to improve the code.
Consequently,
};
the code was largely rewritten and improved, with very large gains in computational speed and user convenience.
The new j
version is denoted 2DBUM, and some of the major changes are
{
discussed below.
-.y I
- The names of all variables in the code were changed to mnemonics which resemble their purpose.
For example, the A
G old "K7" fission spectrum array is now denoted " CHI".
This j~
has greatly simplified checking and modifying the code.
3
- The FI.DO free-format input processor (used by ANISN, at DOT, MORSE, etc.)
- d. _
was incorporated to simplify input setup i
1 s
'l
... + -
"a
~ ~ =
' m "" *
' ' ~* ". "~~.~~~
- a s
- ~
d 30
.1 and reduce input errors.
M
'}
- Memory storage space was reduced by a factor of about 1
two for many problems through rearrangement and
.l sj consolidation of many large arrays.
All array storage is j
j' now in one large container array which is created f.j dynamically by 2D50M during execution.
(2 START, a
[j previously used separate code to acquire storage U
}
dynamically, is now obsolete.)
3j
= The inner iteration coding was rewritten to follow the procedure outlined for the DIF3D code 18 p
Also, cross-6ld section subscripts were interchanged to avoid the need to 4%
copy cross-sections to a temporary array for the inner l
-s c
lg$
iterations.
These changes resulted in decreases in total CPU time by factors of 2-4 for typical problems.
As yet,
't
?.;
improvements in the outer iteration acceleration scheme have
]
not been made.
,.1
- The edit capabilities of the previously used 2DBED 5
p; code were generalized and included in 2DBUM as a standard
/
edit module.
With only minimal additional input, a user can
.j obtain detailed absolute and relative reaction rate edits ff for one or more combinations of code zones.
This allows j
both global and local detailed results to be obtained easily Q;
from only one computer run.
j.y
- The format of. the 2DBUM binary cross-section burnup
!:}}
library created by the LEOPARD /LINI package was modified to g
increase its generality and reduce the 2DBUM user input.
[ij All information pertinent to the burnup library (such as f0 number of burnup steps, group structure, etc.) is now k.3 included in the library and need not be entered in the 2DBOM p.. (
['J input.
This reformatting facilitated such improvements as j
allowing different numbers of burnup steps for different g
materials, allowing direct access reading rather than 3
sequential, the inclusion of both two and four group cross-sections in the same library, and' reducing the core storage 1.
d.
requirements for the 2DBOM code.
?.'
h,H
^
l4:
, la l
_ 1=,
1
=.s
-.v.c,.,.-~.,,..-
c.
-.-v~
a 31 q
Verification of correct code operation following all of
}.i the above changes was accomplished by detailed comparisons of output from both the new and old versions of the code for
~
many standard FNR problems.
A preliminary version of an input and reference manual for 2DBUM was written.
Currently, this manual describes all s
necessary and optional input to the 2DBUM code, without detailing the theory or computational methods.
6 S
- 2. Three-dimensional capability t
1I j'
The 3DB code is operational on MTS and is being g
.k compared with.2DBUM results for various FNR configurations.
since the 3DB code does not include the various capabilities j
1},
that have been incorporated into the 2DBUM code during the i
course of this project, it has been decided that future effort will be to incorporate three-dimensional capability f
into the 2DBUM code rather than attempting to implement the j-various 2DBUM options into the 3DB code. This effort, however, has not been initiated.
]
- 3. Albedo Boundary Conditions 1
e" An experimental veision of the 2DBUM code has been j
modified to accept position-dependent two group albedo i
boundary conditions as an option along with the usual
]
boundary conditions.
M The input albedo is actually a matrix g, relating the incoming (reflected) partial current 2
]
to the outgoing partial current g*,
^
M d
where 11 12 I
a.
ee g
j and o -
, ai,
_r,
c a-2 s
U
.i
i:..
~
a au...~ l.~
- 7...
a... ;..
=. -.
s G
i 32 i
y e
a It has been assumed that upscatter in the reflector is I
h) negligible, hence e21=0.
l f.
The advantage with using an albedo boundary condition i.i is that the reflector nodes, which account for 60% of the I
mesh, can be eliminated.
This will then allow the officient h
use of the 2DBUM code for fuel cycle calculations which j
involve a large number of time steps and many iterations in y
order to arrive at an optimum scheme.
The albedo option has j
been coded into the 2DBUM code and has been thoroughly I
i
-1 checked.
The results indicate a savings in CPU time by a 1
)
factor of 2.5, which is less than expected on the basis of
.g mesh number reduction but understandable when one takes into il account the 2DBUM " overhead".
The only aspect of this n
effort that remains in question is the calculation of the i
0 l
albedos.
If pointwise albedos from full-core 2DB
}
calculations are utilized, the relative power errors (albedo g
option vs. full-core option) are quite high, especially for the fuel elements adjacent to the D20 tank, where discrepancies in excess of 54 were observed.
In addition the al2 albedo term varied significantly along the D20 tank.
To remedy this n' constant a for the D20 tank was 12 f
determined on the basis of minimizing the RMS power error in
[
the adjacent fuel elements.
With this albedo, the full-core 5
and albedo 2DacM calculations agreed very well, within.02%
j for k,gg and within 14 for the maximum' power error.
In (c;
addition, a 38-step 2DBUM depletion calculation, with g
alternating time steps and fuel shuffling" steps, was y
performed with the above albedos (assumed constant over the Ij depletion) and compared with a corresponding full-core 2DBUM
)~4 depletion run.
The maximum eigenvalue difference for the f.g entire cycle was less than.034.
Thus the albedos appear to
[;
be insensitive to core average depletion as well.as spatial h
variations in the loading pattern.
Effort is still being
(.(
expended to examine the optimum procedure for computing the
'6 q
I 4
5 l
. e_ _r - e -
-.m.udese,#,w..n#w.2..
m - -
A..a
=, _ _ _,. -
33 albedos and to automate the procedure in order to eliminate
- ,i the considerable amount of hand manipulations and al calculations to arrive at an optimum albedo set.
2 jl
- 4. Power Defect
=,'-.
d, I The 2DBUM code can be used to analyze the ef fect of non-uniform temperature effects, such as for calculation of the i
power defect, by utilizing " derivative" cross sections taken
,I!
f rom a particular combination of base and restart LEOPARD "I
runs.
No changes were made to the 2DBOM code because
~,
existing " mixing" routines in 2DB were utilized. See Section II.E of Appendix B for further explanation.
i
- 5. Transverse Buckling Calculations to determine appropriate bucklings for 2-Y geometry FNR calculations have yielded a set of zone and group dependent bucklings that give good agreement between j.
two and three-dimensional calculations.
These bucklings, shown in Figure 7, were edited from three-dimensional 20 VENTURE flux profiles calculated for the FNR Cycle 175D 1
The VENTURE axial geometry geometry had 28 planes core.
}
with 14 planes in the core region.
The bucklings were
- .3
}]
edited by an integration over the central 6 core planes as illustrated in Figure B.
Integration over this particular j
volume gave slightly better agreement between two and U
three-dimensional flux profiles at the core midplane and i
lj calculated core eigenvalues.
The results of the two-and L
three-dimensional flux and eigenvalue calculations are
{
compared in Table 5.
1*
l
'~
7 C. Specialized Methods and Applications
!.~
- 1. Monte Carlo Code Development
-.m, Extensive research effort has been directed toward the
!j l
development of a very fast and inexpensive Monte Carlo code.
S
!.4 hi l
,... _ =.
u_,_.... ;.; _ - _ a - EU-i'"C"..
+-
- i 2
34
~
af
';j ij 3:
d l
}
q Fast Group Bucklings (m" )g) n
- 1 Bernal Group 3991Ws (m m
tl!.i j
E 0 Reflector D O Reflector 2
g a
17.1 c1 16.6 1
16.7 11.6 l
l ij g
sl s
16.8 16.6 16.7 16.8 16.9 li.
16.8 16.9 I
'A 15.9 15.6 15.8 16.0 16.1 16.1 15.9 16.1
[
\\
- )
r n
c 17.1 17.2 17.3 17.5 17.5 17.4 17.3 17.2 y
(
i..
17.0 17.0 17.2 17.4 17.4 17.4 17.1 16.9
..l 17.3 17.4 17.7 17.9 17.7 17.6 17.4 17.2 17.1 17.2 17.6 17.8 17.6 17.5 17.1 17.1 t
E i
17.3 17.5 17.9 18.1 17.8 17.6 17.3 17.2 17.2 17.4 17.8 18.4 17.8 17.4 17.2 17.1 N
r
- N 17.4 17.6 17.8 17.9 17.7 17.4 17.3
?7.3
[
!N, 17.3 17.5 17.7 17.9 17.6 17.3 17.2 17.2 g
s
.d N
T m
L' 17.2 17.5 17.7 17.6 17.5 17.3 17.3 17.2 N
s
'l
!i 17.0 17.4 17.6 17.5 17.3 17.2 17.2 17.1 L1 t it
~
L. s
[l G
Regular Special M ty d
11amant
! Elaeont
- Location c.,
d FNR Cycle 175D
/d I.1 VENTURE Calculation r1[j Figure 7.
Calculated Transverse Bucklings
$}
i.;
hj H.,
I.5
-f i
s I
a mes. we-
w.: 4.
a a.: u -.
i'.-
35 j
d
)
4 Plane n
j 26 S
Buckling Edit 24 y
- 22
- .4 2
20 De j-av g.
37
- 18 2
vol
-i 1
B =
2=
Z l
Edit
- 16
',I Volume
/
Core 4 dY b.
- 14 vol y
12 10 g4
.i dA f,
BZ 4,
n 8
sur g 50 4
2 6
U Grid Plate 4
a edV
.s 1
vol 2
E0 y
2 it Figure 8.
Axial Geometry for 3-Dimensional VEICURE Calculation i
~
?,
e j f h
2 i:
j Table 5.
{
Flux and Eigenvalue Comparisons for 2-and 3-Dimensional Geometry RMS Deviation in Midplane Core a
Code Geometry Thermal Flux Eigenvalue a
2, VDCURE X-Y-Z Raferance 1.0258 I
2DBUM X-Y
.10%
1.0256 A.
e b
.}
- s M
't a
tt
.1 2
. xu,
1
,~
36 5
J.
4 g
It is anticipated that such a code, running 1-2 orders of j;
magnitude faster than standard production codes, will be j
useful for many specialized problems including the j
determination of errors introduced by cell homogenization,
.j estimation of the effects of performing unit cell spectrum f])
calculations for flat rather than curved plates, and analysis of leakage flus for the difficult D 0 tank 2
geometry.
h3 Work is near completion on a general geometry,
[
multigroup Monte Carlo code incorporating many novel l
tg features to enhance computational speed and accuracy.
h Foremost among these are a new discrete conditional sampling 1
method which eliminates the need for table searches when Yj analyzing collisions 21, a moment preserving equiprobable step fune. tion treatment of exit directions from collisions (which avoids both table searches and negative weights)22 3
j and the generalized surface segment geometry treatment of I
]
the ANDY code 23, w
Ji f
- 2. Reactor' Kinetics Parameters The utilization of the point kinetics equation for f
g reactivity measurements requires accurate values of the
[jl kinetics parameters, e.g., the effective delayed neutron l
l fraction p,gg and the neutron generation time t.
In order
{
to assess the accuracy of the p,gg value currently in use j.,
for the FNR core and as a first step in evaluating the y
I changes in the kinetics parameters due to the use of the y
proposed IJ:0 fuel, calculation of p,gg for the present FNR f
- i configurations has been performed.
The calculation to date has been based on the definition 24 of p,gg in the form:
1 2
4 y
e n =
- 8Xd'*"
'(1) f
- e a
<$*,X P$>
14 where
+ is the neutron flux, is the adjoint neutron
{
jj flux, and F is the production operator.
The fission 1
%a
[
q-q
.. - ~
- ..Lw..a
- u. :-.......-
a3 37
{.1 neutron spectrum x(E) may be written in terms of the
.i a
y prompt spectrum x (E) and the delayed spectrum xd(E) p as:
?
d]
x (E)
(1-8)x (E) p 8xd(8)
=
+
9 E
where p is the physical delayed neutron fraction.
We have
?q tried to evaluate p,gg based on Equation (1) through (a) a di first order perturbation analysis and (b) explicit a
p eigenvalue calculations.
In the first approach, standard 3,
first-order perturbtion theory calculations were performed 3
i with the forward and adjoint neutron fluxes calculated for
[
the normal fission spectrum x(E).
In the second approach, f
following Kaplan and Henry ", we assume that the effect of
]i the delayed neutrons is confined to the production operator p.
term and write the reactivity perturbation o
due to 1
delayed neutrons as:
J
<e*,6(xPle>
(3) i
).(.
<$*,xP$>
'v ',
where 6(xP) = p X p
. With the perturbed production e
operator
( X P)' as:
(xP)' = xP +
8X P d
.s
..j one calculates the eigenvalue k' for the perturbed system.
[
Together with the unperturbed eigenvalue k for the normal
[
spectrum x(E), one obtains; n.
i i5 4
i
. x.x
$.i 0 "
x.x (4) i Q*
Our calculation of the effective delayed neutron 9
fraction p,gg has so far been based on the four group structure of the LEOPARD code, and six delayed neutron l
groups.
We have used the fractional yields of delayed neutrons in each of the six delayed groups and the total 4,
- _c..
a.n. -. -...
[.
3 38 n
'4
)
d" yield recommended by R. J. Tuttle
, while the delayed 26 I i q$
235 neutron spectrum for 0 is taken from Saphier et al.27 y;
Spatial calculations were performed with the 2DBUM code in j
X-Y geometry with a (6x6) mesh for each fuel element.
The f
first order perturbation calculations of p'If were ic) performed with the vsd r code based on the four group S8 if, fluzes produced by the 2DBOM code.
l
?
l
- 3. Ex-Core Neutron Fluz Analysis 4
y
}
For calculating the neutron fluz in the core reflectors j
and the neutron beam tubes a number of code packages have been adapted to the NTS computing system and tested in
[
. preliminary calculations.
The SCALE-0 code package g,
29
(
being used to generate few group cross sections for the encore calculations.
Initial SCALE-0 calculations to f
q collapse a 27 group (14 fast / 13 thermal group) master l
library used the NITAWL code.with the Nordheim resonance R
treatment for the resonance self-shielding calculations.
A The spectral-spatial effects were modeled in a one-
{
~
i dimensicnal full-core transport calculation using either the r
a ISDRN or ANISM codes.
y f
Collapsed cross sections from the SCALE-0 system may be
.4 used in both full-core transport and diffusion theory pj calculations.
A number of schemes are being investigated f
Id for calculating local fluz profiles in regions such as the I
.: <j heavy water tank or neutron beams tubes.
First and last l
b]..
flight transport codes have been used in preliminary tests
[]
to calculate the neutron streaming through the beam tubes.
y' p
^!
t
[
..y;*
D. Dg,t,a Bank-ta ci
[
t y
A collection of standard code input and documentation
[
{
has been assembled in computer files to form a data bank for f
.] i our LEOPARD-LINX-2DBUM code system.
The purpose of the data
[
/h bank is to allow standardization in testing and verifying
(
d!
our codes, as well as standardization of input for our y
r j.. 4 1 '1
?
f
, ~ -. _
-.m
l
... J.
A* *' iL: \\
.-. n..
.., ~.... -
g 39 jo f e
1 j,.
routine FNR calculations.
When codes are modified the test 2:j i
files are used to verify the accuracy of the calculation.
.1 J
For routine FNR calculations the data bank files make it 1.j "
convenient for someone unfamiliar with our calculations to
+
set up a particular case.
Standardized input to the cross jj.','
section codes is especially valuable for comparison of subsequent core calculations.
A limited selection of the standardized LEOPARD input and output is presented in
?),
Appendix C.
-a i.j,
Documentation for our LEOPARD-T,INX-2DBUM code system is
]
also being developed.
The documentation includes complete g}
input instructions and sample problems that are stored in
-J1 computer files for convenience in modifying the data and in j
7: 1 transmitting the codes and code manuals to other facilities.
't.,
W
].
s..
u' e
t e
k
. ab eit
.19.
t
- Mb ll 3'
d-n s'
l
'q e
t, C7.
ad l' l 9
d Si
. ;.s u
1
, - a K1 a
T 40
- a l*
IV. ANAI.YSIS OF CURRENT FNR CORE AND COMPARISON WITH EXPERIMENT M
i To test and verify the accuracy of our analytic methods used fo'r predicting the neutronic characteristics of the FNR i
many calculations have been made and compared with experimental data.
These calculations include core criticality, fluz and power distributions, control rod worth, power defect, void coefficient of reactivity, fuel burnup, and reactor kinetics parameters.
The results of 3
many of these calculations have been summarized in Part III N
of Appendix B.
In this section we describe those additional calculations not included in the appendix.
?
'j A. Power Defect 3
.g Using the methods described in section II.E of Appendix
~
B, a preliminary calculation of the FNR power defect yielded
.164 Ak/k, which may be compared with the experimental value of
.21% Ak/k.
We are currently attempting to improve 4
our model.
See section III.B of Appendix B for further
~
J discussion.
f j
B. void Coefficient of Reactivity a
g To predict the impact of I.EU fuel on the void fj coefficient of reactivity a calculational method has been d
developcf.
7d compared with void coefficient measurements
]
for the FNR.
In the void coefficient experiments performed yi as part of the Nuclear Engineering Department reactor d
laboratory course the void is simulated by inserting an L.
aluminum blade into the core.
Because the cross sections j
for aluminum are finite the experiment does not truly a
9 measure the void coefficient of reactivity, but for our 4
]
purposes the experiment and calculation can provide a valid j{
basis for comparing the HEU and I.EU fuels.
f In the experiment an aluminum blade measuring.040" x f:
2.25" x 24.0" is inserted vertically into the central' water
~
3
~
'n
.__.--->.=_L u-.
- _- ~z-m + a m;w k-
~'~L""~~""~'~~
_g 41
}i
+t
^ - >
channel of the fuel elements.
Once the blade is inserted 53 and reactor power stabilized at the initial level the core il reactivity change is calculated from the chpnge in
^
3 regulating rod position.
g, 4gg.
To calculate the FNR void coef ficient of reactivity a h*
two group diffusion and perturbation theory analysis was
/. l used.
In this analysis the forward and adjoint fluz aa distributions were calculated with the 2DBUM code using a n
f4 tj 10 x 10 or 12 x 12 mesh / element. The two group cross
}=
sections for the fluz calculations were from our standard
'j,
burnup dependent LEOPARD cross section libraries.
In the perturbation theory analysis the insertion of the aluminum
), "
blade is represented by a change from water to aluminum cross sections.
These cross sections, compared in Table 6,
- ]
were generated with the HAMMER code, rather than through the less accurate LEOPARD code, because the results of the perturbation analysis depend heavily on the accuracy of these cross sections.
I l-'
1..
I
_s Table 6.
Cross sections for the void j
Coefficlent Calculation i _'
i Cross Section Water Aluminum Change J
j E,,3 (ca~1)
.00043
.00039
.00004 l
E,1-2 (cm
)
.0462
.0002
.0460 s
}
[a,2 (ca'1)
.0166
.0102
.0063 D
(ca)
.907 2.35 1.44 y
D (cm)
.173 4.33 4.16 2
s ll.
!j 1 The first order perturbation theory analysis performed h,
with the PERTV code calculates the void reactivity change h...
ast 11
.q -
, #.4
.i,
- \\
t.-
~
c, z.2.,
- ......r
~
~ ~ ~ ~ '
1
~~ '~
- ~~ -~ ~
~~ '
~~~
~'
$1.
iGO.
~
'Y i
b g
[1 42 t-N
?.4 l #ry M
f;
= (( {(T$ T$p AD (I+2* 'I'"2
+
t t
k s*
' $ +{AI.t
'2'5'"2,
$*E'Ea2
- 1*I'"1s
+
8
+
+
t 2
p) e
[
+ $ (${-4j) Ar,g4 - f $ ($ avI
+ $ Avt 3k %
t 1 t gt 2
r2 d,
d W [ [ *[(+1"En + +2vr 1 dY s2 if 7
J 1,, -
/
The first order approximation is appropriate for this
]
calculation because the aluminum blade is only.040' thick b]
compared to the thermal diffusion lengths which are
(,
typically 3-5 ca.
Therefore, the blade cannot significantly l
perturb the flux distributions.
l 'i f
To verify our methodology for predicting the void j
coefficient of reactivity the experiment performed during
[]
y Cycle 1695 was simulated.
The core configuration and
]
/
blade positions during the experiment are shown in Figure 9.
?
/
tt
(
The comparisions of calculated and seasured void coefficient Jia of reactivity in Figure 10 indicate reasonable agreement
[,j when uncertainties in measurements are considered.
The
[]
{
uncertainties in the measured void coefficients of li reactivity in Figure 10 represent the variation in the n
bt measurements taken by three students during this reactor
$y.
laboratory experiment.
i
(
e a
I L3 i
g r
p i
p I
a r
'p
_ _m, _, m o w.
. ~ ~ -
~~ -
z.,..-
,i:.
.. Y
.,'7,;,,.~.,..,..
43 j. !-
I.l.
T I'
1.-
1 FNR Cycle 1695 i
February 19, 1979 5eavy Water Tank
,b 1,
1 2'
1i 16.0 10.8 6.1 1.6 6.1 5.9 1
k C
12.4 13.2 6.2 20.3 2.5 3.1 6.4 14.2 1
1 16.4 9.2 25.9 5.1 2.5 5.1 12.3 17.0
.1,
(_L-77 7 L L-67 7 L L-57 7 L L-47 7 (L-37 3 C L-27 3 L L-173 (L-07 3
E 17.5 15.4 5.5 11.2 3.0 3.1 12.9 17.1 4
(
10.8 9.2 19 7 12.4 14.7
.jg 3\\
l j.
1.5 10.1 11.0 1.4
'l;j lf
-b il Alloy Dispersion Regular Special Einpty Regular
'j Element Element Location Element ti s
Penn Fuel Void Coefficient
)
State Element
( L-x3 Measurement m
Element Burnup(%)
Locations d
- p.
- Figure 9.
Core Configuration for Void Coefficient of Reactivity Experiment it
~
-.._.---n_.:.s--a.;e,.c I.-. ;;.:--.::-- n -~
7 '.,, ;--.
n w ct;
_ _ _ c. 7 9 x g;en :,, 2,n.c ; cus.tm.2.;,..c.m.ca u.
?
.V
- tl.
- p...
( -1.60 =
t'a
.:i:
%, -1. 40-s LK-
/ ~De 'N
. %(i 7
N
-1. 20P
/
9~
/
j k -1.00.
j g
\\
i 0
vb l
/
N o
.,/
\\
.86 =
3 N
e 8
f
\\
lG
\\
s o
/
f O
\\
G.Ysg l
\\
l
\\
- c
.44
/
5
\\
t b
l l
6 1.
\\
/
\\
d
.M O
g y/
w 8
U
, Calculated
.00 =
'N O nseeuroa D
+. 20-i I
I t,M-a a
a a
a a
.a
,m F-e w
w w
w a
Core Position I,-77 L-67 le-57 6 47 L-37 L-27 L-17 Is-07 Element Type A117 Alloy Special Alloy Dispersion Alloy Alloy
&1loy Void Coefficient co w.8E (tak/k/*AV/v) i calculated
.28
.48 I
.12
.75
-1.30
-1.13
.86
,37
~
un sured
.21
.,.46
+.20
.sa
-1.23
.sa
.55
.2a s.
Measurement t
tk.:e rtainty 1 07 1 13 1 23 1 32 1 02 1 01 1 04 1 01 Figure 10. Void Coefficient of Reactivity for FNR Cycle 169B Core l
i l
t I
l
- c '
= -..- ::.ua : s.; :-
Law-c,
~
j C. FNR Fuel Burnuo Calculations
)'
Several fuel b" nup calculations have been performed for the FNR core to determine accurate fuel burnup
]-
distributions for other calculations and to assess the j
accuracy of different calculational schemes.
These 1
-],-
calculations and che results are briefly described in this section.
j To provide burnup distribution data f6r the more recent i
FNR cores a 2DBUM burnup calculation has been performed to
]
simulate FNR operation from October 10, 1978 to May 1, 1980.
i This calculation used a 2x2 mesh / element and 105 time steps j
to simulate 330 full power days of operation.
The calculated fuel element burnups have been used in other more a
detailed calculations, such as control rod worth 1
calculations for the FNR core.
Fuel burnup calculrtions using a 2x2 homogenous mesh structure have been compared with a 6x6 heterogenous mesh for the HEU equilibrium core.
The purpose of these f-calculations was to determine the adequacy of the 2"z2 mesh structure which we have relied upon for nearly all fuel burnup calculations.
The conclusion of the study was that the 2x2 mesh calculation overpredicts the special element fuel burnup by about 7 to 8% as compared with the 6x6 mesh
[
calculation.
A likely reason for the difference is that in F
the 6x6 calculation the flux will peak in the waterhole region of the special element and not so much in the special element fuel region.
In the 2x2 homogenous calculation, however, the flux will be enhanced throughout the smeared fuel element.
For regular fuel elements there were negligible differences between 2x2 and 6x6 calculations.
p, Equilibrium core fuel-burnup calculations, in which the zenon build-up is explicitly modeled in 2DBUM, have been compared with our more standard calculations without xenon
- ~
build-up.
The conclusion of this study was that the 7
calculated fuel burnup distribution is not significently b,
(..
li l
4._
m c.
.<v.
-a_._.x m
a <~
w<
. 2. m m... _ _
_.a.._,.
h)I
'l 1
f-46 NT
$4 difforent eithough the computing costs of modeling the xenon
.- J Q
build-up are significantly higher because of the large flux
.c p;j perturbations from time step to time step.
c.9 D. Control Rod Worth P.
The development of the rod code, described in section III.A.3, has provided the capability to ine'iude special 4
d assembly fuel depletion effects on control rod worth.
f comparison of measured and calculated control rod worth for
(
six different FNR configurations are presented in Section j
III.B of Appendix B.
The results verify the validity of our y
calculational model for control rod effects, and also seen to indicate that depletion of the boron in the rods causes a small but noticeable decrease in rod worth over a period of 1
several years.
q q
In addition to our standard control rod worth analysis
[?
using a 6x6 mesh / element in full core calculations, we have a
also investigated the use of rod worth calculations with L
only a 2x2 mesh / element.
The purpose of this investigation j
was to find an inexpensive, although not necessarily highly 0
accurate, scheme for calculating rod worth.
The scheme Ij would be necessary for realistic survey type calculations to
[
determine optimal fuel loading strategies for the FNR.
The I
quantitative results of this investigation are summarized in j
Table 7.
The table shows that 2x2 mesh / element calculations j
may be used to predict control rod worth with a slight loss
[
in accuracy, but a considerable savings in computing cost.
il In general 2x2 mesh / element calculations may be used for survey calculations and verified with 6x6 mesh / element J-calculations when necessary..
L.1 d
9 o
a
~
m.
o
~
m -
i
., g;.,g um.,. g g.
g.,
a ~ m
~
47 a
I J
i Table I.
Comparison of 2x2 and 6x6 Mesh / Element for Control Rod Worth Calculations in FNR Equilibrium Core Model 1
?
oi 6x6 Mesh 2x2 Mesh 1 Error
$g Rod Worth (%Ak/k) t b
Rod A
-2.14
-2.27 5.9 4 kM Rod B
-2.15
-2.21 2.6 %
3 Rod C
-1.96
-1.89
-3.8 4
?1,
.i ij E. Reactor Kinetics Parameters Using the methods presented in Section III.G.2, two different FNR configurations were analyzed to date in our
- j p,gg calculations
- a full-core model simulating an actual M'
FNR configuration and a half-core model representing a batch
]
~~-
l ~,
beginning-of-life configuration.
The perturbation theory calculation for the full-core FNR configuration yielded p,gg
= 0.77% with p,gg/p = 1.11.
Values of 1.13 for f]
p,gg/p and p,gg=.7854 were obtained in a similar y
calculation f or a batch half-core configuration.
In I
contrast, the eigenvalue method applied to the batch half-jj core configuration yielded p,g g/ p = 1.08, or p,gg =
3 0.751%.
The physical fraction p was taken to be 0.69554 as
)
recommended by Tuttle All of these estimates for p,gg 26 f]
are in reasonable agreement with a value of 0.755% for p,gg Q-currently in use for the FNR core.
l T.
N Parametric calculations have also been performed with a
the 2DBUM code in cylindrical geometry to assess the adequacy of our I-Y geometry model in representing neutron s
leakage in the axial direction through a transverse buckling
]
term.
These parametric calculations suggest that our I-Y fla b
t_
! - --. +.,..
$?
'5
-....N.~. L.;
' = ~~--..
l-]
'o
'1 48 2..j a.a 4,
simulations are acceptable for the purpose of p,gg g
calculations.
Further work is underway to resolve the
]
differences in the values of p,gg/p, 1.13 versus 1.08, for
-1 the batch core calculated.with the two different W:
- .j calculational schemes.
In addition, alternative methods of
}
calculating p,gg will be studied in an effort to reconcile Lij larger values of the ratio 4,gg/P reportet 7;
earlier 30. Future of forts-under consideration also include Fj experimental determination of the ratio p,gg/p in the current FNR configurations.
Comparison between the Q-
.s m
s a
'l Is
'm
-5 Li Q
l1 p
i u
.)
l':
l*
.n
!n
!4l
'}
L!'Ia 8
l
_ A -,,-.
. m. ~.~. ~ - n q. ~ m O % ' Y i
- ~ ~ ~
'~~
._.-~
L-V. ANALYSIS AN*J OPTIMIZATION OF LED FUEL 3:
}
Extensive analyses have been perforned comparing the
,s.
_ current HEU and proposed LEU fuels.
The analyses were i
i performed in both batch and equilibrium core configurations g.
and are summarized;in Section VI of Appendia 3.
In this' l'
section we present additional comparisons between the HEU f
and LEU fuels in regard to tiie void coef fihient of
(
reactivity and control rod worth.
He also present the j
f important results from analyses that have been~ performed to determine optimized core coniigurations and'to study i
f.
alternative fuel designs.
The main purpose of these p
analyses was to find effective means of increasing the 1
discharge fuel burnup for the FNR core.
Presently' fuel is
)
discharged at approximately 174 fissile depletion which is it relatively low in comparison with that achieved at other r
~
research reactors.
The most important conclusion of our analysis has been that small increases in core reactivity s
can result in large increases.in fuel burnup.
These offects are esplained more fully in Appendia 3.
~
A. Ecuflibrium core MV Coefficient St. Reactivit?
~
The void coefficient of reactivity was calculated for
]
the HEU and LEU equilibrium cores using the methods i
described in section IV.B.
In these calculations the void i
j is simulated by aluminum and therefore is not a truly voided region.
The calculated void coefficients for the two cores
]
are cempared in Figure 11 and the individual components corresponding to the terms of the first order perturbation theory expression for the reactivity change are compared in j*
Table 8.
These reactivity components may be interpreted as i
representing the cause of the reactivity change in oer-two-A group diffusion theory analy' sis-The diffusion theory i
analysis should not be expected to predict accurately the reactivity offects caused by a change in neutron leakage, j
but the effects of the chango in absorption and slowing down q
-x
~~~; %l@g 3;,
G--
" ' ^ ~ '.
. =. q ~= +
-..w
\\
c3 50 3
should be more accurately predicted.
These calculations ij show practically no differences in the void coefficient of
LEU core the void coefficient is slightly more peaked in the m
l
();
center of the core.
5 E. Control M Effects
]
In an effort to identify significant differences p
between control rod effects on HEU and LEU fueled cores, Ik; detailed studies have been made of the neutronic offacts caused by rod insertion.
Using the methods described in ig Reference 1, the batch fresh test cores of Reference 1 were ij analyzed with and without control rods for both HEU and LED Q
fuels.
Since a half-core symmetric model was used, results 3 i aust, be interpreted in terms of 3w.c inserted rods in the wo scuth half of the cores.
Neutron balance tables obtained' from 2DBUM are presented in Tables 9 and 10.
Study of these
!i and other similar results has led to several qualitative conclusions outlined below, i '
The FNR control rods are black to thermal neutrons and grey to fast neutrons.
There is extreme flux depression l) near the rods for the thermal group and little flux j
depression for the fast group, resulting in a significant
!j change in the whole-core fast / thermal fluz ratio.
These u
spectral effects (caused by absorption) are a major l
la contributor to the overall control rod worth.
As can be seen from the neutron balance tables, the dominant effects
]
(in order) are increased fast neutron leakage from the j
core, increased fast absorption, and increased thermal eksorption.
- j A detailed comparison of the HEU and LED core neutron f
[
balance shows that although there are different amounts of j
fast absorption and leakage induced by rod insertion, the b
chances in fast absorption and leakage due to rod insertion P.
y are nearly identical for both cores.
This is reasonable,
)
i e
q%
yya W
MA***
. a ase 1ks vo..' ; - i.
4,.<.,;,_........;,,-~,-.ag+,
_,g,
, ;;g g,,;, g,,g ;,, g,
g,,
,,s, e
Y Y
- 'd 4
t t
h Core Positions
\\
\\
>\\
l
~
~
r,-
L. 2 L.
L.
L.
L.
N 77 67 57 47 YL. 27 17 07 N -1
(
g
,40-.
~
-1. 2 0 -
-1.00-
.g
.80 o
2
.60-ce eu
.40-44 E
.20'-
k u
t3y 00 8 HEU Equilihrium Core
+.20' O
LEI Equilibrium Core L-77 L-67 L-57 L-47 L-37 L-27 L-17 L-07 Core Position Figure 11.
Void Coefficient of Reactivity Calculated for the Equilibrium Cores
,c i
r L.----
.awre
._' K L A L :EiL LLU.tiaa.h
.3 _ _';~. L ul ^
.. L eA-: :'s t : -;.::-.i:' TL E - v.'.'J u
.n 4SllM = u '. w-
- a..
f*.
}.
=
1 t
f t-
- w,.
Table S.
i Vold Reactivity components for aquilibrium cores (tak/k/tA v/V)
D Core Position L-77 L-57 L-37 Ie17 Reactivity C-
__ts t
with source i
Element Type Regular special Regular mogular normalisatice ee ($ vt Fuel um Lau um LW um LW um LW 1 1 fl + p vtf2) - 1 2
Fast Group 4
Absorptica
.00
.00
.00 00
.00
.00
.00
.00
((A T g
l E I4akage
.03"
.03
.10
.10
.18
.18
.09
.09 g (4 p, l
X-Y Leakage
.12
.11
.04
.04
.02
.01
-.10
-.10
( %. 5() A D, Downscatter
.15
.16
.10
.16
-1.24 -1.29
.60
.63
- p,) g,
.e a1 cro,
l un u
j Absorption
.04
.04
.23
.22
.24
.21
.13
.11 p,
a g,,
l 3 Isakage
.05
.04
.23
.22
.28
.24
.15
.13 p g,*A D 5, 8
g 3
f X-Y Isakage
.00
.04
.08
.09
.18
.19
.10
.07
~
(%.g')AD, a
1 Total
.30
.27
.16
.21
-1.30 -1.33
.91
.91 Ak/k *.
I
- y t.
.O 1
C i
4 9
k I
-r h
4
\\
s i
n.
m n
m
~
a..--
,---.- - ~;
- p ;
.3w;< ;
- 3. ' v l~.<? r'**'
$3 i...
.i.
?
l.I G Table 9.
'(
Meutron Balance for control Rod Effects in IED Batch Test Core
- a b
moutron a=1 = ce for Core Regica l
(4 of total fission source)
'I 3
mod out mod In (In-out)
Fast Group i
a.
l absorption 4.1 5.5*
1.4 3
leakage" 30.3 32.3 2.0 Thernal Group
- j-absorption 64.4 65.7*
1.3 leaksee"
-2.3
-2.5
.2
~
Total Losses 96.5 101.0 4.5
- 1 l.
"l J Rod out Rod In Core-averaged (W /W ) :
1.98 2.14 y 2 i
13 13
.)
Core-average A 3.06 x 10 3.19 x 10 t
ei Core-averaged W :
1.54 x 10 1.49 x 10 2
4 3..
k) *
- Core / Rod Breakdown:
?J f ast abe. (core)-4.3 fast abs. fred) - 1.2 therm. abs. (core)-63.4 thern. abs. (rod) - 2.3 i
q "Imakage includes Ds, losses L.
'r'-
lN a}
[.
k '~
l 2.-
~~ ~
~
. _..n. ;m > a.., t :
au
' ' - - ~ ' ' ~
- 3. ]
$4
,!s
.t it t1
- 1 3d'/
-b Table 10.
r y
Neutron Balance for Centrol mod Effects in LEU Batch Test Core b
'e.t, s
!d T
Neutron Balance for Core Region
[A
(% of total fission source) 0
?.;
.j
.a Rod out Rod In (In-out)
?)
0 f.
Fast Group 4..
absorptica 7.5 8.9*
44
.)
leakage **
29.4 31.3 1.9 Thornal Group absorption 62.2 63.3*
1.1 i
leakage **
-2.7
-2.9
.2 i
Total Losses 94.4 100.6 4.2 2
i bg Rod out Rod In Core-averaged (d /p 1:
2.23 2.42 t 2 3
Core-averaged W :
3.00 x 10 3.12 x 10 g
3 13 Core-averaged W
- 1. 35 x 10 1.29 x 10 2
hs b.
VJ
- Core / Ecd Breakdown:
q fast abs. (core)- 7.7 fast abs. (rod)~ 1.2 therm. abs. (core)-61.2 therna. abs.(rod) - 2.1 T
- Imakage include DB, losses g
D i
lt-
...-n--
.___..,3._--
s.,,
...e
~
55 1
J.
since the fast flux distribution is sensitive mainly' to J
gross chang'es in the fission source distribution or core l
1yj geometry.
A similar comparison of chances in thermal neutron q,,
losses due to rod insertion shows that the extra change in Q*
thermal absorption is responsible for the decreesed rod j
worth in the LEU core.
Examination of thermal absorption in
- j '
both cores (see the table and footnotes) shows that thermal j] i absorption in the non-rod portion of the core deeresses for both HEU and LED when the rod is inserted.
This decrease is the same for both cores, about 1% of the total, source, indicating that global ef fects on the thermal flux are quite similar; i.e.,
changes in global thermal fluz are determined
]
primarily by core geometry for black rods.
The major l["
difference in control red effects between the two cores is 1
the increased thermal absorption in the rod itself-- 2.3% of the total source for the HEU core versus 2.1% for the LEU core.
This effect seems to be due to the lower thermal flux q
in the LEU core, offset somewhat by the smaller diffusion 7
length in material surrounding the rod.
1 C. Alternative Fuel Designs
.{
d The core physics analysis presented in Appendix B q'
g compares HEU and LEU fuels, in both batch and equillerium j'
core configurations.
In addition, the final section of the
].
appendix compares LED fuel with an alternative design of
].
higher fissile loading.
In this section we describe
'j,
additional equilibrium core studies for the HEU dispersion fuel and a LEU oxide fuel.
The results of these studies are summarized in Table 11.
The data for the HEU, LEU, and 175 gram LEU fuels have also been included in the table for ease l
of comparison.
In all of our equilibrium core studies l
comparing dif f erent fuel types, the primary constraints have been to preserve the end of cycle reactivity and core size.
These constraints along with our equilibrium core model are k
- d d
l
_..i.
i e
a
.g
]
- Q E.1 56
/
.3 uy 9
described in detail in Appendix B.
J.l f
The HEU dispersion fuel has been analyzed because the f,j fuel is. currently being used in the FNR and thus, there is
.Q..
an opportunity to compare analytic predictions of discharge i.
j fuel burnup with actual core data.
The conversion from HEU j.
j*f,j alloy to HEU dispersion regular fuel elements has taken place gradually starting in December 1978, with the last of l-Gj the alloy fuel expected to be discharged from the core
'i during the summer of 1981.
.i n
ll j
As shown in Table 11, our equilibrium core calculations
]
are predicting a significant increase in fuel burnup with
,]
the conversion from alloy to dispersion fuel.
The reason for this change is that with the thinner fuel clad and
]
hence, the larger moderator fraction in the dispersion elements, the fuel is more reactive.
Because~of the higher o
I reactivity, the dispersion fuel can be depleted longer in our equilibrium core model while maintaining end-of-cycle i
reactivity.
The discharge fuel burnup is predicted to g
increase from 17% fissile depletion with the alloy fuel to yl nearly 22% with the dispersion fuel.
The predicted change in fuel burnup must be int'erpreted p;
with considerable care, because discharge burnup is j
extremely sensitive to core criticality in our equilibrium model.
A relatively small error in the calculated k,
criticality for the two cores creates a significant error in
~
,7] '
the predicted discharge burnup.
Our prediction of a M
significant increase in fuel burnup with the conversion to b;
dispersion fuel has not yet been confirmed ce disproven with I~*
data from the FNR.
The actual fuel loading data indicates E.h some change with dispersion fuel.
On the average, core 1issile loading seems to have decreased and the core average j.j fuel element burnup has increased.
But, at this time the
$.I discharge fuel burnup has increased from the 17% fissile h
depletion achieved with the alloy cores to only about 18% in de,
the elements currently being discharge from,the FNR.
nj >
j,e,
,j is ij
d G:: n... rcr.;c:aratun:: u aa.c._
su
.. :.- a A.:s '.' -
n.
% GM' ' ' ~ ~ - '
h.
J Q
6J LJ 6J n,a 6J,u 6J w
w 6J w
,w LJ LJ L -
. 6. J I
j i
t i
Table 11.
Equilibriunt Core Fuel Design Comparisons I
HI!U LEI Naminal
- UA1, Noudnal UO IMgm 3g Enrichment 93%
934 19.54 19.5%
19.5%
..l Regular element fissile loading (gn) 140.6 139.9 167.3 167.3 175.0 Uranium density in fuel meat 14.1%
14.1%
42.0%
42.0%
43.9%
Equilibrium cycle length (days) 11.0 14.85 16.5 17.75 20.8 Core fissile loading. (ge)
Beginning of cycle 4549 4351 6315
'5262 5327 End of cycle 4522 4314 5274 5218 5277 1.
Discharge burnup (HWD/ element)
L8 Regular 19.2 26.0 28.7 30.7 36.4
,' O Special 16.9 21.8 25.9 27.6 32.5
'.I Burnup reactivity change reto(tak/k/ day) f l
A Rod 2.20 2.14 2.15 1
i B Rod 2.21 2.15 2.14 3'
C Rod 2.00 1.96 2.00 d
Total 6.41 6.25 6.29 S'
Excess reactivity required (tek/k)
Xenon poisoning 2.26
.2.17 2.15 I
Burnup of fact
.31
.37
.43 i
Power defect
.21
.24
.24 Total 2.78 2.78 2.82 Shutdown margin (tak/k) 3.63 3.47 3.47 k
i j
i r
t l
?
. _. ~.,
3 r
58 j
j The physical characteristics of the oxide fuel--
S including clad material, plate spacing, etc.-
are identical bi to the LEU fuel.
The fuel meat consists of 42 w/o uranium, p
in the form of U 0, and is clad with aluminum.
38 a
4 For the oxide fuel, changes in fluzes and power density
.d
. ;;a are negligible except in'the special elements where greater
,d burnup occurs.
The longer cycle. length and corresponding increase in discharge burnup can be attributed to the
]
presence'of oxygen, which decreases the fraction of aluminum j
in the fuel and has a lower absorpti.on cross section than 4
- a Q
9.
An important conclusion of these studies is that, in each case, relatively small changes in fuel design caused
- 119 significant gains in discharge burnup.
Gains of this "i
magnitude ar's possible only because of the low discharge burnup of the FNR core, which is a constraint imposed by FNR operating conditions as discussed further in Appendix 3.
!..t D. Cotimized Core Loadina Scheme Improved core loading schemes have been investigated as
?
a means of increasing core reactivity.
The incentive for y
this preliminary analysis has been the realization that even
(
slight increases in core reactivity may allow the fuel
- p. '
elements to be depleted to substantially higher burnups.
In y
this study, as in cur standard equilibrium. core analysis, several important constraints have been imposed, including a jij W
constant end-of cycle core reactivity and core size.
n The basic idea behind our loading scheme was to load
".j the least depleted fuel elements into the core locations j
having the highest neutron importance.
l(')
reactivity can be maximized.
Although these optimization In this way core
'j techniques have been attempted and are believed to be a valid approach to the problem, no definite results are available at this time.
~.
93n w
i:
- _____m,
,,,emm.---
~--~
- ^
w _....
as
' ^ '.
e 4
E. Temperature Coefficient of Reactivity and Power Defect
[;
The RAMMER and 2D8DM codes were used to compute the isothermal temperature coefficient of reactivity for the batch fresh core model, yielding -8.4 pcm/*F for the HEU fuel and -12.6 pcm/*r for the LEU. fuel.
The dominant i
contributor in both cases is the effect of moderator density changes on leakage and moderation, with the difference due almost exclusively to Doppler effects in the LEU fuel.
As the calculational method for the power defect is 4
still undergoing development, the difference in the isothermal temperature coef ficients was used to estimate the difference in power defect between HEU and LEU fuels.
As g
discussed further in Section' VI.C of Appendix B, this results in a power defect estimate of.24% Ak/k for the LEU batch f resh test core vs.
21% Ak/k f or the HEU.
e
.I '
3 i
i I '.4
~
d
,d
'f:!
,c
-w-e
R.
_. __T.
L' M
.d
- =
- ,1 60 9-
=
'..y VI. SAFETY ANALYSIS REPORT
' I O
t.4 r
a The safety analysis, Utilization of LEU Fuel in the 1
Ford Nuclear Reactor, and accompanying license amendment
(
[]L requesting authorization.to use LEU fuel were submitted for
,]
NRC approval in October, 1979.
In June, 1980 a second
{
]
license amendment was submitted requesting an increase in 4
the total number of kilograms of contained uranium on-site l h.
from 16.1 to 25.
Both amendments were approved in February, j
Jj
- 1981, h
Authorized LEU fuel asse;nblies consist of plates 0j containing uranium aluminide (UA1 ) in the following
/
3 loadings:
3
.1
'J
.9 Number Maximum Pl 3s L**dia9 Maxi =u" ^5139 )7 L
- dias
[!
t b1 of plates (grams of D) 4-(grams of U
.]
18 9.28 t 2 4 167 t 2 4 I
9 9.28 2 2 4 84 2 2 %
I
- i (2
The increased on-site inventory will permit temporary
(;
storage during the testing of LEU elements.
Along with' f.
approval of the license amendments came a requirement j
p.
to
]
submit a loss of-coolant accident (LOCA) analysis by N
September, 1981.
The LOCA model described in Section VIII k
will form a basis for the accident analysis submittal.
2
[i 1
x fd
~
r!
Ap tU
\\?
)
P*"
6.,
[l E
t.
b i.5
.. ~a
'b
~; d l ^!
T.1 1
\\
f
't
=
I!
h + a
_a w.a
-.. - ~....
a w aa a- +~ ~ \\
,z
= -
- .u -
~
61
~
p,;
jj 1
VII. THERMAL HYDRAULICS Tests related to a loss of coolant' accident calculation j
were undertaken at the FNR to determine the peak fuel g.
3, temperature at the hottest spot in the reactor core
],
following loss of coolant and to determine the maximum M'
reactor power below which melting would not occur subsequent j'
to loss of coolant.
Previous test results from the Low 4"
Intensity Training Reactor (LITR) and the Oak Ridge Reactor (ORR) are not directly applicable to the Ford Nuclear 3
f; Reactor because of differences in construction and heat i]
transfer mechanisms between the facilities.
Analytical calculations leave uncertainties as to their applicability
[]
because of significant uncertainties in heat transfer
[j}
coefficients and characteristics in narrow channel flow situations similar to natural convection flow in FNR fuel li}
elements.
l The FNR plate model simulates two flow channels and b 4 three fuel plates in a fuel element.
Electric heating
?j.
t elements provide the fission product decay heat input to 7*.
each plate.
The center heater simulates the plate of g
interest; the two outer plates act as guard heaters to minimize radial conductive and radiative heat losses.
y Two distinct sets of test runs were conducted.
- One,
~
with the fuel plates insulated from a base plate which simulates the core grid and heavy water tank heat sinks, permits heat dissipation by natural convection up the c:
N.
channels and radiation out the ends of the plates.
The second in which the base plate insulator is removed includes t
3 g
heat dissipation by conduction to the base plate.
Decay (j
input values are based upon the ANS 5.1 fission product heat f
decay heat time profile.
These values were increased by 20%
dj '
because of uncertainties as to their accuracy.
d.
Eased on a series of eight test runs 31, the peak fuel
~
temperature in the FNR core as t;he result of a loss of coolant accident following prolonged 2 MW operation is Ti '
n i.
i
.-..:~.
x.--
h ~-'-
.j p
1 62 i
'j calculated to be 800*F. Test results also indicate that the hj.
FNR could be operated continuously up to power levels of
- j 4.0 MW without exceeding a peak fuel temperature of 1200*F,
.a 10, the mel' ting point of aluminum, after suffering a loss of
- A coolant accident.
Without the core grid and heavy water
.]
.,']
tank heat sink, the values would be 965F for 2 MW operation fj and 3.17 MW without exceeding 1200'F.
- .1'.)f
~
-j
~~
a r
if
' i.
_i a
e
~1
.t t
.j
- )
.N
,-)
9 4
M i..i e:
,4 l: 3ff e
a I-
[.-
!ii r.;lq LN P.l i
4 i
~--
x,,
a z ms.,
-m --
-mm+-~.-r%.--~-~-=-
. ;,.. o
.=...a.,.
" '~'" ~""
'C
~
~ ~~
~ ' ~ ~ ' ~ ~
- J. '
j 63 3
,1 }~
e l
[",r VIII.
SUMMARY
AND CONCLUSIONS l
In support of the whole-core demonstration of LEU fuel i*
in the FNR core scheduled to begin in September, 1981, efforts continued during 1980 both in the experimental and l[j,-
analytic areas. A request for an amendment to the FNR i) license which would permit utilisation of LEU fuel was submitted to the U. S. Nuclear Regulatory
- Commission, and a M
provisional. approval has recently been granted.
A series of
]
thermal-hydraulic tests for MTR-type fuel elements was also 1
conducted in 1980.
?
- 1 In the area of the demonstration experiment program, Ol -
considerable progress was made during the past year in the
.4 rhodium flux mapping experiments, and the major problems in y
l
- [
that area are nearing solution.
While substantial progress was made in the areas of thermocouple power mapping, incore spectral unfolding, and excore spectral measurements, significant work still remains to complete these 9
experiments.
Further efforts will also be required in improving the accuracy in the measurements of control rod
~
worths and other reactivity parameters.
n Considerable progress was also made in the analytic
{,,
areas including generic ~neutronic model development and Q,
neutronic analysis of LEU fuel designs.
Major improvements
]q-were made in the multi-dimensional diffusion theory analysis involving the 2DBUM code, together with the implementation a
of the ENDF/B-IV cross section library in the LEOPARD code.
Initial efforts were also made during 1980 for development Y>
of calculational models for reactivity coefficients, a
},
including power defect and void coefficient of reactivity.
g,}
Similar efforts for calculation of reactor dynamics j
parameters were initiated with models for the effective delayed neutron fraction p,gg.
Emphasis was also placed on
.h "
providing efficient links among various computer codes, with 4
I
- 3 special applications to control rod worth calculations.
Lj Further comparison between the calculated results and the
)-
L~
1.
[ w.
- o. = x. n
.~..
~.,
m __
~
y j
s4
~
~
Q g
3l FNR data continued during 1980, including a simulation of l
330 full power days of operation with the 2DBUM code.
- 2 hI In confirmation of fuel specifications for the LEU fuel
(
}l selected for testing at the FNR, further comparisons between
{;
Q the LED and HEU fuels were performed in 1980.
This included j
comparison of the calculated void coefficients of reactivity and control. rod worths.
Equilibrium core analysis of g
?
alternative LEU fuel designs was also undertaken during the L
e j
year.
[
a d
Efforts are continuing for development of methods for L'
accurately predicting ex-core neutron flux distribution in j
the FNR.
Improvements will also be required in analytic, as f
j]
well as experimental, determination of reactivity lj coefficients, control rod worth and reactor dynamics
{
}
parameters for the FNR core.
Future refinements in the y
computer code system will include development of a three-g j
dimensional capability within the 2DBUM code, and I
h consolidation of the ENDF/E-IV library, new fission product y
poisoning correlation and updated physical constants in the q
form of a new version of the LEOPARD code.
In preparation g
for the LEU testing in September, 1981, actual detailed loading calculations and optimal equilibrium core f
calculations are expected to be initiated some time during L;
this summer.
r p
Thermal-hydraulic testing of simulated FNR fuel
]
elements performed to date suggests that there would be an I.]
adequate margin for the FNR operation at 2 Mut, even in.the case of a postulated loss-of-coolant accident.
Some further j
analysis will be necessary in the near future to supply d
information to the U. S. Nuclear Regulatory Commission in I$
connection with the design basis accident analysis required
~36 in our latest license amendment.
g f':
k!R si.
b!
l.c AII h_
_,~
s
-.-_ 'N w,
.u.
L.L.m L aaa..a =-
- ...'~
d' REFERENCES te
~
- 1. Low Enrichment Fuel Evaluation and Analysis Program, Summary Report for the Period January, 1979 -
- ,;p-December, 1979, Department of Nuclear d'
Engineering and Michigan-Memorial Phoenix h
Project Report, University of Michigan 3
(January,1980).
A.
W-
- 2. D. K. Wehe and J. 5. King, Trans. Am. Nucl. Soc.,
34,,
s,1 746 (June 1980).
r
- 3. J. M. Carpenter, R. F. Fleming, and H. Bozorgmanesh, j
Trans. Am. Nucl. Soc., 22,, 606 (November 1975).
o.
[(*j -
- 4. D. K. Wehe and J. S. King, Trans. Am. Nucl. Soc., 25, 571 (November 1980).
/.h
- 5. J. E. Tucker, " Thermocouple Probe Report for the Low j,
Enrichment Project," Department of Nuclear y
Engineering Internal Report, University of q.
Michigan (January 31, 1981).
- r
- i, -
- 6. R. F. Barry, " LEOPARD-A Spectrum Dependent Non-Spatial Depletion Code", WCAP-3269-26, Westinghouse Electric Corporation (Sept. 1963).
j
- 7. J. Barhen, W. Rothenstein, E. Taviv, "The HAMMER Code System", NP-565, Electric Power Research a
Institute (October 1978).
- 8. T. R. England, W. B. Wilson, and M. G. Stamatelatos, i
" Fission Product Data f or Thermal Reactors, Part d.
2-Users Manual for EPRI-CINDER Code and Data",
3 EPRI-NP-356, Electric Power Research Institute j-(Dec. 1976).
M 9.
W. W. Little, Jr. and R. W.
Hardie, "2DB User's Manual-
'1 Revision I",
BNWL-831 REV1, Battelle Pacific Northwest Laboratory (February 1969).
. <[
- 10. F. B. Brown, D. C. Losey, D. K. Wehe, J. C. Lee, and 4-W. R. Martin, Trans. Am. Nucl. Soc., 33, 746 (1979).
a
.,.:q.
- 11. Private Communication, W. D. Henderson, Westinghcuse Electric Corporation, to J. C. Lee, University Ji of Michigan (August 1, 1980).
0-
- 12. C. L. Beard and R. S. Dannels, "ETOT-A FORTRAN IV t'.
Program to Process Data from the ENDF/B File to 4-Thermal Library Format", WCAP-7363,
?j.
ENDF-146, Westinghouse Electric Corporation j
(1971).
n-11 I;'
65 s
.i$
,1 -
1 t
- ' " ~ " " " " - "
l
- - ', -,' "[ '
_m w.m.c l
!i
- 4.. "
- i 66 L
- ./w Q:
S
- 13. D. E. Kusner and R. S. Dannels, "ETOG-1, A FORTRAN IV h
Program to Process Data from the ENDF/B File to e
the MUFT,' GAM, and ANISH Format", WCAP 3845-1, Westinghouse Electric Corporation (1969).
f3
- 14. R. E. Prael and L. J. Milton, "A User's Manual for the d
Monte Carlo Code VIM", FRA-TM-84 (1976).
- 15. Advance Recycle Methodology Program System Documentation, EPRI-CELL Code Description, Part II, Chapter 5 by Electric Power Research Institute (1977).
- 16. W. L. Woodruff, " Comparison of EPRI-CELL and VIM (Monte Carlo) Generated' Microscopic Cross-section Data for a Slab Cell Representative of MTR-type Research and Test Reactors UFing Highly-enriched and Reduced-enrichment Uranium Fuels", Argonne h
National Laboratory Internal Memorandum (January 3, 1979).
- 17. J. Hardy, D. Klein, and J. J. Volpe, "A Study of Physics Parameters in Several Water-Moderated Lattices-F of Slightly Enriched and Natural Uranium", WAPD-TM-931, Westinghouse Electric Corporation b
(March, 1970).
M
- 18. D. R. Ferguson and K. L. Dersti'ne, Nucl. Sci. Eng., 64 l
593 (1977).
i
- 19. R. W. Hardie and W. W. Little, Jr., "3DB, A Three-f Dimensional Diffusion Theory Burnup Code",
t si BNWL-1264, Battelle Northwest Laboratory (1970).
Y,
- 20. D. R. Vondy, T. B. Fowler, and G. W. Cunningham, pl
' VENTURE: A Code Block for Solving Multigroup
[.
Neutronics Problems Applying the Finite-W ji Difference liffusion Theory Approximation to
]
Neutron Transport", 03NL-5062, Oak Ridge National Laboratory (1975).
i
- 21. F. B. Brown, W. R. Martin, D. A. Calahan, *A Discrete p;
Sampling Method for Vectorized Monte Carlo p
Calculations", Trans. Am. Nucl. Soc. (To be j
published June, 1981).
}
11
- 22. L. L. Carter and C. A. Forest, Nucl. Sci. Eng., 59 27
]Q (1976).
~,
- 23. D. R. Harris, "ANDYMG3, the Basic Program of a Series of i.] -
Monte Carlo Programs for Time-Dependent L
Lj Transport of Particles and Photons", LA-4539, Los Alamos Scientific Laboratory (1970).
??
t
~
, iG ' e
- u. a.a
.........l
.. w..
4=;
- - y.
W.,~n y m;st e n :.
m~ M r ";~~~ **,
J
}
67 i
l Jj w
^k s
- 24. A. F. Henry, "The Application of Reactor Kinetics to n-c, M'
Analysis of Experiments", Nucl. Sci. Eno., 3, 52 (1958).
Q i
- 9,,
25.
S'. Kaplan and A. F. Henry, "An Experiment to Measure i
I b
Effactive Delayed Neutron reaction", WAPD-TM-209, Westinghouse Electric Corporation j
Ji y (1960).
R*
2
?j.,
- 26. R. J. Tuttle, " Delayed Neutron Data for Reactor
\\
i Analysis", Nucl. Sci. Eno., jg, 37 (1975).
N 3]
- 27. D. Saphier, et al., " Evaluated Delayed Neutron Spectra U
and Their Importance in Reactor Calculations",
]
Nucl. Sci. Eno., g, 660 (1977).
j
[. 'l i.l.J
- 28. R. W. Hardie and W. W. Little, Jr., "PERTV-A Two Q
Dimensional Code for Fast Reactor Analysis,"
BNWL-1162, Battelle Pacific Northwest Laboratory g
(Sept.
1969).
i
- 29. R. M. Westfall et al., " SCALE: A Modular Code System for Performing Standardized Computer Analysis for i
Licensing Evaluation," NUREG CR-0200,
- 4.
Distributed by the Radiation Shielding J]
Information Center, Oak Ridge National Laboratory (1980).
=
- 30. P. N. Cooper et al.,"Some Measurements of Reactivity in 4
a Light-Water Moderated Highly Enriched Uranium Assembly", React. Sci. Tech., 16, 65 (1962).
M J
5
- 31. " Ford Nuclear Reactor Loss of Coolant Accident Tests
?
Utilizing an Electrically Heated Fuel Plate Model", The University of Michigan, Ann Arbor, Vj "
Michigan (September, 1980).
?)
I*) "
d, t
L, l'M
(
U. -
i 0
I 5
/,
.)
l A
r-f l*g i
iN
-- - ' ' - - ~ - ~ ~ ~ ~ ~ ~ ~ - ~ ~ ~ ~ ~ ~ ~ ~ ~
.r j; * *,, ;
y'.. >
.-' w.
.j.
i l
nt 4,
- .):
APPENDIX A
'?
3 e
.:n (q
The RERTR Demonstration Experiments Program bli 7%
at the
.- 3 Ford Nuclear Reactor
~
l a?
- -4 47
',b
,-n
' ;4 (A5j
\\
e
'I 4 e
e
.i 3
2<
- 1..
i 3
0 1.R l.V l..,
^d';
i.*
\\.*
t..
,,j j.-l l3 cI.
l 1:
.d a <
l.? -
- 1 i LN,5
- 1 9
,,k
, ' 4, i
! M
_ m _,, w. -
~ ~.
~. - - - -
,7
.a-...
- -. 3.n.,, :a m.,.g
, _.4,,,,~,, 7.
Dy1 y
,3 l,
s The RERrR Demonstration Experiments Program at the Ford Nuclear Reactor 13*
5 by
).
D.K. Nehe and J.S. King j-Department of Nuclear Engineering 4
University of Michigan d
Ann Arbor, Mich. 48109 t
9 The purpose of this paper is to highlight a major part of the experimental work which is being carried out at the Ford Nuclear Reactor i
(FNR) in conjunction with the RERTR program. A demonstration experiments program has been developed to:
J
- 1) characterise the FNR in sufficient detail to discern
.1 9.
and quantify neutronic differences between the high.
A and low enriched cores.
- 2) provide the theoretical group with asasurements to 4
y bene h==* their calculations.
As with any experimental program associated with a reactog, stringent y-constraints limit the experiments which pan be performed. Some experiments a
]-
are performed routinely on the FNR (such as control rod calibrations), and auch data is already available. Unfortunately, the accuracy we da==nd precludes using much of this earlier data. And in many cases, the requirement of precise (and copious) data has led to either developing 1
i" new techniques (as in the case of rhoditan mapping and neutron diffraction) l?
or to further refinements on existing methods (as in the case of spectral j
unfolding). Nevertheless, we have tried to stay within the realm of recognized, well-es*=h1 * =hed experimental methods in order to assuage any 1.a
[.
doubts about measured differences between NEC and LIU core parameterr.
r' With these caveats in mind, the experiments which have been chcsen to i'
accomplish these tasks are:
O A.
Wire activation measurements to provide absolute flux noz:aaliza-L i
ll tion (limited spectral and spatial information).
B.
Rhodium detector flux maps to provide absolute thermal (in-core
-3 and ex-corel. fluxes, j
C.
':hermoccuple 6T maps to 3. ovide absolute power distributions.
r
- [3 rY J
^ ~ ~ ^ ~
~
'~~
~
~
i<.wu,& s....,
a
- a. -...
- .~
= =.
}
n q
-l
~.a A-2 I
,4'q 3
3 9
D.
Unfolded foil activation measurements to determine the in-cors
?ii fluz s 6 -.
pe d
E.
Neutron diffraction measurements to determine the fluz spectrum A
in the D 0 **I1******
g 2
1-F.
Shim and control zod worth (th, void coefficient, n.y power defect, menon worth, and temperature coefficient measure-n
@Q monts to detszminereactivity parameters.
tay h following sections of this paper describe the principal results j
of the N W -ats performed so far. Nowever, the reactivity measurements a
1
'j use such traditional techniques (such as the a.1 rh period method, to a
'f asasure the control rod worth) that they are not described here. The paper is written with the ah81% that the reader is f amitin with standard "a W.
It should be emphasised that the experimental program has not been finished. AddiH anni ref 4=====t and repetition of the experiments l
(particularly C, D, and E above is continuing!. Regarding the rhodium fluz
]
ager, application of the zhodim detector transfer function analysis Ndhd later) askeer full-oose rhodium fluz amps a mustL q=_4cker process.
3 Zastly, scue of the estual,.
- tal wozk. associated with, the spectral
{}:
unfolding still remains to be completed. Neverthelesa, the results
- j detailed in this paper represent a major part of the emperimental charac-si terisation of the highly enriched FNR core.
1 o
A.
Wire Activations for Abeslute Flus Nom =1f== tion S
1.
Purpose The purpose of this phase of the -e-tal progzan van two-fold
.s
[{
11 to provide measured values of the thezuel fluz in the core and 1l D o tank for comparison with the results being generated by the 2DE code.
g
,j ill to provide a means of absoluta detezadaation of the sensitivity of the rhodia detector (to be discussed in the next sectioni.
S 2.
Asial F1 tat Detezzination 3
1 a) Thezmal fluz detennination d
In order to obtain a measured value of the thezmal flux, bare and cadeium covered iron wires were irradiated. The iron reaction:
$j 39M
[3 i;
l n
nn..,
<f:5.~
+
i-L D. i.e. -. 9 J~
.?
. w q *- '
--~~-e-
-- > p t,,
e
- ~
- 3 n n,:um; *.9*} > l
^
J..
A-3 3,,,.
,'a N(n,y) fen l-Fe
!.l
%a was used since the cross section varies as 1/v below 0.1 ke7. The j<
analysis closely follows that of Beckurts and Wirtz.
n
}'.
h fact that the cross section varies as 1/v makes the evaluation q) s of the themal cutoff energy, the cadmim cutoff energy, and cadmium J,
correction factor very straightfonward, and yields q
g, =
- h==mt cutoff energy = 0.089 e7
- a E,
caenia cutoff energy = 0.55 eV
=
1~
and F
=
2.5 = caenim cr..ction factor.
cc It should be mentioned that for all activations performed, we have
=
neglected corrections for self shielding, flux depression, and scattering in the foils, assuming they are small. Co-Li detectors, calibrated with 3
an NES standard, were used in the counting.
],
h tha==1 flu de*= mined by wire activations.done axially along q
the core center is shown in Figure 1.
h data " points" are shown as
. bars since the l* long wire segmenta actually integrate the flux over thir distance. Note that the thezmal flus reflector peaking is respon-
!!' ~
sible for the increased values near the ends of the fuel plate. The i
fact that the flux peaks sHP+1y below the core midplane is attributable a
p-to the location of the sata rod bank.
Th. resu.lts have d.en ~ - w to earlier measurements on the FNR, and were found to be in good agreement.
1 h3 Inte-ediate thema1 na h results generated by the ccamputer codes, (such.as j
LEOPARD and 2DEJ will not agree with, the resulta presented in Figure 1.
f:'
W reason for this lies in their definition of the thezumi Cuz.
It is t,.
i a common practice to define the thermal fluz using the caMum cutoff energy E as the upper limit. For thin reason, we define an "intazzo-a diate themal flux", as:
.-s a'
q s
{a Ecc MM L
- g; * {tc p;
l,; a In this energy region, the flux is assumed to behave as 1/E. Then the orj
" intermediate themal flux" may be evaluated as:
d M
b 1
- i f
m
___.,,_,_._.__-_.r.,
,~,_...--.__,.mr,_y,,
uew=w as.2,n.. c.
..e a =. ~ x n,
. u.;.w
=x a. aa.a..uwanz. maw
==.a.
p;;
r
=
24
- i.
To 3
s.
a w
f-la.
.+.
t 22
..2 1.
20 b
L 0
18
.i 16 f
.,- (,g3 b
i, 14
- 1,8 9
+
1 1
p 12
-+ -.-j
- -+-
e-a 10 e.
+. -
8
-+-
-+-
6
-+
p 4
L:
r 2
r i h I
I I
I I
I I
I I
I I
I O
I 0
2 4
6 8
10 12 14 16 18 20 22 24 26 e
INCHES INTO FUEL PLATE
\\.
=
r.
Wire Activation Results for + th
- i I
rigure 1.
-tocation te37-
.f
.s e
e r
p
[.. g
': m..
3...
y.
- --.-,,.. c.y....
y.
A-5 b
- c. u %)
r
-Ai i
h activity from the cadmim covered iron wf.re Fe58 (n, I )Fe59reaction
}
can be used to determine' %., and hence %u (or any integral flux D
in the 1/E range).
t h correct flux from tHe iron wiTe results to ccupare wit!s the ccm-puter generated " thermal flut is t5ar Figure 2 presents ke kgv for the axial center-of-core irradia-j ticas described above. h addition of hp adds as mud as 10%, at the core center, to the value of 44, and brings camputer calculated fiumes closer to the measured fiuses. Also presented on rigure 2 are the results of an axial rhodium detector flux map made on the same fuel element. h rhodium points are based on the manufacturar's detector L
s.n.mvity.ad are. correct.d,or e,ie.rma1 neumns. N 1ar,e disagreements in the values of the fluz are attributable to these
)
epithermal neutron contributions to the rhodium detector signal, and
{
are discussed in detail in section R.
h re the measured values of
~
@A + (27 are used to calculate the==nettivity of the rBodius detector in th. run.
.1 c) Fast Flux An additional benefit from activating iron is the threshold reaction:
]-
Fe ** (a,el % '4 1'"
[
which has a threshold at 4 3.75 Nov.
[~
Defining a fast flux as:
1 f o.
?-
@p 3 i QlfDdli g
3- -
4 wey Ig.
one can obtain k
.i F'
th
~
e-R 54 54 where g = saturated Mn activity per unit Fe
- nucleus, a
1
2' i-
' A",
~~
B=-~-'"
d a
A-s A
4
.\\
n:
d,
?
c,i P
si (land a^!43v) WO1106 m
n.
i o
v
- A o
x N
M
~!1 34, x
h 3."
1 N
Il e>
x y
m a
o=
f ii E 'iii w
e O
3 o ae x
o 1
m a
'i G..e e x
T LaJ s
- ww i
e e *g
.g
- j, 3 e
x 7
H' E" I g x
o I
"1 f' a W 4 cr s
x E..
- i 7
w x
_o 1
o LsJ G.5, 8 x
}{
]3
.g 9
T
..l A
~
s
- Li,
=a
?:
x s
a k
'E o
_. {
N. g x
g t
l; c
2 1,3 q
x o
f
.h Om j.
x I
f ti.
a
~1 -
l' I
g f
U x
CD O 5
l/.
2 x
x o
n c
1 I
-{
x o
f e
r..
x v
r f.i x
o 0
h x
N o
(land ad!4av) 401 x
O x
i 1
x X
I I
I I
I I
l l
8 1
-li x
a:
o e
e e
N o
e N
o i.
N (s.,uJo/ou,ot)4%
y-r
!i -
l
.i).
1,
..~
q....
,,g.
.,.s.
_..n.,
.7.._.,_.
,7
.m._,.
g.
i h*T 1
3 9'
7 54 S us, from the measurement of the Mn activity, one can obtain a measure 3
of the fast fin, as defined above. Figure 3 shows the results of the measurement. Note that the flux scale is an order of magnitude y==11er a
than for figuzes 1 and 2, indicating the smaller size of this fast flux.
The noticeable shift of the flux towards the bottom of the core has been 1
j discussed earlier.
J Additional measurements of the fast fluz usin'g the threshold reaction:
M Ma h 4.
with a threshold of *8.15 nov weze made. S e analysis was perfamed as g
outlined above, and yielded the energy integrated fluz above 8 MeV. As might be expected, the results look like Figure 3 on a smaller scale.
d) Ratio of fast to thermal flux
{
Lastly, it is expected that the ratio of fast to thermal i
flux will change with the introduct.ica of low-enriched fuel. One measure of this, (besider taking ration of Figures 1, 2, and 31 is the cadmium ratio.
g The iron cadmiist ratio remained approximately constant in the core (except near the edges of the fuel) at about 9.7.
He fact that the spectrtan does not vary signifi'cantly throughout the normal fuel elements in this care greatly simplifies-the measurements of the zhodium detector correction factors, d
as described in section E.
i 3.
Radial Flux Determinaticn i
7 i
N one of the difficultima encountered in attempting to compute a-ij.
the fluz in the D 0 reflector is the cceplex structure M4de the tank.
2 In order to provide benchmark. values of the fluz, bare and cadatum www.a
}
iron wire irradiations were perfarmed in the vertical penetrations of the l!
D 0 **""*
2 A photograph. of the D 0 tank is sht.n a 'n Figure 4.
Se vertical 2
}
~
penetrations-into the D 0 tank are the 1* small,1" inner d4===ter, pipes 2
on the tank'r top. Sase pipes extend dwn to within a few inches of the
-)"
core midplane, and are filled with E 0.
Figure 5 shows the spacing 2
between penetrations, and the names associated with them, (e.g., D 0 tank 2
)
position s I.
His nomenclature will be used throughout the rest of the j]
paper for specifying locations in the D 0 tank.
2 2
j a]
a
b' 1d ?
,I
, '.N 7, lih6 i
b: h h I:
.i;!t
>.. f i, i'
<h e:
t4 -
2
.m 6
I s.m
- ! =.g
- m 2
i n
4
.u.
+
2 I
.c
_a..
2
_y 2
I
. u..
=
0 I
,.m.
2 8 E I
T 1
A F
L f
^
6 P I
r 1
.m L
o f
E s
m 4 U t
I l
1 u-F
. s..
o7 e3 p.
2 O E
I n
T on 1
N io ti I
at o
va 8
m S
ic w
t o t
E cl A -
H
-v e
8C I
r i
N W
I
_v 6
I 3
e r
d I
4 g
_m ir
_ w 2
I
_. m.
- g'.> = # - ot
,u.
O 3
,a,
.-w.
.m_
0 8
6 4
2 0
8 6
4 2
O 2
1 1
1 1
1 e
u_
_O"x
~_.
l t
,>,i
'.., e
. ;. 7..
.y..,-.,..
.....p.
- --u l-s.,
l:
],
l*
f.
Y EM
}
! f$ 'h ' '.*....
~f,
'?
a,.
.~
< j,
/
l' l
b.
,,f,.,
~
p.
j-L.. '-
))s o
- R$-Q.,
~
1
% L
.y Core side
[f ^)
';,.. i" g in.-'
~
a N*
$,],. '
U<
b tu gf1 North side
']t ij
-n i.
- [.
. :' ; 1 V-
' $lM..'
i 7".,C'
~ ~
' '=
. re* v. l
= c
+
x.
e',.;: /7),,
~
.~
.i' ;.
E:!:-T.::.
'j T 4.e.
,sf
~
m D "t
(
'[ -[0[ '
- r.i -
[3 ig? jff -~
y.
j,
_ i.v '
,. v-y
)
Q<, f
(["
I' 4'
t-
,1 r;,
i p.
Figura 4.
D 0 Tank a
2
?-
N P
I 1
l!
=...
=
- [
't 't % 5 'j
- f. p.
l'.
(
gi V iL
- i. 65IItg,tti.h 4
,9 e
G.
e e
8 I O
s e
O v
O 1
e ih 5
~
5 E.
T2
=
2 i
3
==
6 n'
y r 2i a
i 2
j7 W
L a.
~
u U
u
.D
~.
O L.
a c
i @
t u
R oya 2
l kn a
t 0
S O
y i.
d.
D 5
eru g
G.
iF L.
P T
Y iT x
E.
Y.
d'.
W Q
Z 5LC
~.
E ni W
J' k5 M2 M
f t
f_q
}';
..g.4, ;p,..w,.a.. +
A 11
- sj
.o J '.
~
Bars and cadmium covered iron wires were irradiated in D 0 **""
2 positions o and X.
The results for the core center, and for D 0 **"k 2
[
positions o and I at an axial position 2" above the core midplane, axe
(;'
presented in Table 1.
The thermal fluzis seen to fall off such slower lj,
in the D 0 tank as compared to an E 0 reflector (see rhodium detector 2
2
},
fluz mapping data, section 5).
This is exactly what ir expected.
g.
Further, the themmal flus quoted for D 0 tank position I is in good 2
j, agreement with previously asasuzed values. m values of M e {rT
-(
are being used by the analytical group to fix the D 0 tank parameters 2
for the computer calculations. The iron casknim ratios are presented i
- ~
l for future ecsW=== with low enriched fuel.
.t y
4.
Conclusion L;'
Ittile the results pensented in this section provide infozma-tica on the fast and thermal fluxar for computer calculation 0 ; =%r y
and position dependent spectrsma variations, they will also play an essential role in the calibration of the rhodium detector discussed in 1(
the next section.
, f..
j E.
Rhodium Detector Mamal Fluz Mapping o.
j 1.
Purpose and Introduction "j
h purpose of this phase of the experimental program was to measure the thermal flux
- at many locaticas in the core and reflectors, in order to:
7 il provide measured values to the analytic group perfo:: ming
' l, the computer calculations. This ensures the coder are' generating 1,(
realistic results and provides additional confidence in their projections u
to low-enriched fuel.
j ill characterize the thezmal fluz profile asraciated with.
- highly enriched fuel in order to quantitatively discern the changer
'~
associated with. switching to low enriched fuel.
A zhodium self-powered neutron detector was chosen to accomplish.the goale a
(
- In contrasgte Section A, the "themaal flux
- in this section is defined ast kt [0 ggM6 where the value of the upper integrand har Been c5anged to t5e cadmium cut-off energy.
c.
i
.e.
,m,,
s
.,,...,e,
,.-_....,,,,,.....,#,q,,
.,,m
.t...
,-_-_..a.m....
a-
=
w.
4 A-12 S
.i 4
')
.,1
- i ti
.u L,ii.
i4
,.]
- 'i e
- s'u
[.)
Table 1.
'" T "L*on of Energy Ia W 1-3 Flumas
,c
?!
a;
'.)
.,'j Core Center D 0 Position X D 0 Position O 2
2 13 L3 13 1.21x10
.913x.to
.287x10 e
th A
(0.117x1013)
T IT
(.45121012)
(.169 x1011)(+13%)
j h,
0.172x10 0.139x10 negligible ( < 10').
I j
RyFe) 9.72 16.67 128 l
..d 4
Ml
>1 e
F.*
r
Jl.
2 i "4 l ~d
- o. !
il pt 1"
,2 lik-;
F.j
[$
. ' ?.
'a.4
.3 d
i?l
..j
-,g.
g....yn.
- -. ~.
g,
.. ;.,,, q,.
m..
A-13 p
a
- .N'.
fJ-k-
b.caus.,
a
- 1) its size, mobility, and sensitivity are such that it can measure
.'(-
the thermal flux at any axial point in almost any core lattice position, 11) the time required to obtain a measured flux, once the sensitivity 4;.
Q*
is known, is such less than for a wire activation, and
]!.'
111) the uncertainty in the measured value is comparable to that obtained g"
from wire activations.
]
.).
This section briefly describes the physics associated with the rhodium self-
-I.
powered neutron detector, the eguipment used to perform the measurements, da and the determination of the detector amaattivity. The results of axial q
and radial measurements are then presented. Finally, a technique being
.s q
developed which may eliminate the most serious drawback in using the
[
rhodium detector for full-core thermal flux amps is addressed.
2.
Theoretical Description of Rhodium Detectors'
[, ~1 The operation of a rhodium self-powered. neutron detector is
.dcj bas.4 on the rhodium anc1.ar reaction, j.
('
goda ie a.m gQ4
=
y]
A closer examination of the rhodium decay scheme (Figure 6) brings to w
y light two important factors of the rhodium detector.
First, the relatively high rhodium absorption cross section implies a relatively high neutron y
sensitivity. Indeed, rhodium has the highest sensitivity of any type of A
- 3. -
self-powered neutron detector. For the FNR, it is the only commercially (1
available material which will yield large enough signals to give precision j.
data. In Figure 7, the energy dependence of the rhodium absorption cross j,
section is shown. The large resonance at 1.25 ev implies that the detector is also measuring neutrons in the epithermal range.
Since the thermal flux
.,q..
}
is required, epithermal corrections need to be applied to the detector current, and are described later. Secondly, the presence of the metastable 4
i
,'l state of Rh-104, with its 4.4 minute half life, implies that the current "J
y may take several minutes to re'ach its equilibrium value after a change in l
h-flux. This can be seen more precisely by writing the appropriate rate 39*
l
\\
_--.?~.-,..--.------
.,a. :i u L : u.:...nw=.
.-. - e 5:.r...a:: n... ;u a. h..... u,. 2. J.. h.a ls.e a..J u au.a. L ;u i
. = w.:..s:
.'.,.8
'-.:c e. : a : = ~<. ' -
t 4
i
,,, u W
e J
b Nb 103 11 sh 45 g
104.
(4 * *I 0~
139b 45 (0.18%) N 1 r o.7 v
45""I43 "I (0 0 'I t
P 8
i l
EC 1,9 y y (0.5%)
(g,ggy Q 6
l 8-2.5 nov U
i (986) l0.56 nev
' ' (2.0%)
M@
f Ru 104 Pd 46 Figure 6.
Rhodium Decay Scheme i
t,.
i I
{
i
l l
l
..1.
e-w, y _.:
- o., 6:w.
s
~
.,.s
.m-g.
4,.
J e
A-15
- 1. a
.q, W'"
> h-;;,Y.*, **t, -*"I.
9". ytTEmm.G*M*IMi*"M Ud'~an*MEs,.. a
,i ile.sm.N d_4. *_$ ~JfM
- WEE t
\\, e G i.M s.q gV-p% al fr.k.W R: 4
' 4 ft Kr h.L A-b.ph.d 't_ %" d',&
1... r. c a. _.,e.
J,. -
=.i
.:. :'=. + = W:-... 3,z.e, _., m...,.a.._ r. s_.. a. g. z a=.=: M:- - ".
- 3. #,
"a,p t r
.z_=,.. m.
w -- ; = s '."I W^*i.
.;:...a a... c._un.: u
- ., s.=:.m.a.- - -
F
-. m..%.
P-i ur t-r4--*r,.
~'.
a n-N =
- = = =~xC"==.g:7. =.=. z :
e,: -
x.:s
-r
=r-b' M I' " l'-!.N'.h;E, hc-NN$d DAD-bh Y N,N-N Y.F-M Ed M M %d2FA M M dMNROW.N*'h,b P
. ' 2i -M M 5'iN b :so m ed 6 k 'Fgp { E QM.- E E Er y 7.. _ :=_I. e i..:.:-:.:;a. f-siL'=h...
- l,f- -fs-E * @
a
- a.
Ei u
--==-
~
. s e tE=.= =.=
l p'
m.Ei e.;:. a a r::
--::.==.she s - - -
==.=-_- - - _ s
- - - - '. mis- --==
+ =,.j:5 =:==;-
i- _--" _Ti,'E_'j.,j=E
=:= + _;=-
i
- ' ~dA
.=?:::--
A
_.:g-t:= =
r J.
Y _"=dh--
_,.,.-.~a 29 F+
+
-w
~
_:.r y
i a[
e,_s %n....
mdE %%1u-meegt-=cuedIIRGuerP.ss.csswwtiuL c._ - #=ift:WiM pun.:..5 T= rv I
- s-
- .-r f. Mit &m!M 85mR'NGB'W8 7a."In m iMTmW-EM"I'mM." --
"PN M M WW-f
]c
. @ E - M.p:~is! il.:G.-.
-.v i - _f 4 l
D 3"'. 3""."zEH227s'li,N.,P,.-8r*8:=GC _ __ w.;
l
'"%Q@s".E"wi""i~=.~i a
> 4. m_= :=.-- ---_
3.___..,,,.,
- a. g -, _,=_;7
)
=.w:.-
une zu m -:
aww
.=.
r%%#6_w:3.' 3 _;:s:aws:w-was;m tn.m;a : -
e mmww-m,rwr.bwm
,1 n.m.,s.:: m.'r_pa n i ennsbub 7--%'w m M PM 1
- i.F_r# > J up-LetsP_e M ma'.muuam%urdEs m'#-
P N
W4"- MJ.:.;t" _ E.r-rw B4.E C W !ss. -
" + nr.PcP e m #.1usu Ir Jum mmP E D 8-E ##.n; A.
WRf 3CE@
l'.54 RN D 6 3
' N MI
~
_ _.s_ar-mar r_.- --== _ - -
g;
_. ; A
- a. _..:
i "I
-=. -. - - -
"as_g_i@. fg
,a, g g-
- y.j. k.,-.;_. i=gg
_-_..- - - ' g- * ;.3.. R. 3.im -'. Ii i
ma'
-- #" 7. l' gr :,,agt?g7.,.-
u
.,, I a*
p.
q
.~.
,. g WWW 3
L=1 " _ ras as m
=..
.,S
. - sria amm a
maen_ ms 2* -
.S.:l l
M-ll1
.~,
)
.g=na w
-.=-
w_-
_- =
3.
_ =. _..
"""2 2
J~
(,
. _ - ~
10 i_
i=.
]
v-;'mm_=is=6tr-7,_,.=r.s uns__
_ m_ s w%fs.usemus,wur
_-'w.c. -6w
%,.mAbr.
1
- 9.5t_ m-c a, wwr rm,sw m_1=_-=_ --in e-ausa z.E---e_nN gn_ _w,.,5 s, N.E_
...,.!'E n._= r_.
r.
_m..
___a_,_,,.
.f_a.n._m. _n.;; H=E _. _e_
._ _:. =. _
s _ z:m z = w,_ __
__'h___
. _a.
a.
_ __ zz.-- :-
=a.
L. u
=
.r
.... =a _ s
-r
-.m.==_-.
-.3.--_g r-----
._.=r.._=:=---.
=-
w.
_9-eM, w,,,_,,;=.....-
\\. =. 2.g. - -..
=
. = - -
1'
- s.
= : _, se e w. r w= m
,=.= ee.,.#. m m. r e
w.u -_ m
-sci.ca r. M. -
. P-'"
_- gaci ;ah; u Na-< - -
= w - _ _. =_.-
ix.a.-
_ wrJm. -e w-APw : h-i
_-aff. _A;pk._ _ _mmu -
.=m__= - - - -m_.5;
_-_--a
=-
e_--
_-w.n a a.am_wa_.imung,5; L
j' h:.am-q,_.
a-g
_r
- ,,.
- ,..=
. k--.
=. r e s e = - w. c 9Em=J > :e
- E:E' _.
- _i.- :cias M r-m.a 'a a; u,;,.y,,,
h i+- _..:i=w - W_
~~
_ _ riErJ_=
'ji::.i e=
= -"
= : --
i-
-E-r-3.__.i
?:WiA&H%U55-55$NNE$$QW_iW WE
~
' - gg$$5 b
d.3.@. %_QM_ g-M.. _.[M.. _.Q<hEffyp.
- Har - cs I o Har-ac I 4.=_I J._.=N!;.G.,i- #,.MM-ilb,d,E._5 e,:M.=._. gi=gia
- p!- l
==dar"t"gigw s.
_f
.= :.:r =r m
W M. :.
I.a.:.=.g. 41 iigi
- a
~
u..:.
_ _, u.2... : =_.::. g.. = _- ;.,.:-. :_.. n..: =.:..:=_=_-
tc BNL - cs 3
..=:-
T=:
ear.
g,
. _. _ =. _.. _,
=._
= - i =.,. :q.._.: =_....
P m :: = = = p :.:: j:_:j==. :: :.=_==. 9
- -- m: :: ; =r = z c:. ; := _; :... :::= g
= gnu _:.p_..,_;: =:
3,-
- =
-- =.;=
.:. ::::a=:
- ::.=..
- -=.:::..
_2
. = =.
- -~
m.y_m._.=.f_*:t:,;::.1 LO - ~ g...:
- =... = ---
r:
-r= _
_ U -- -; I 2 3 ' ~ ~ * ~ ~ "7..A *U"
C1! ~J'~~
- T ;';;' '
k
,.4~.
W.'~10 0
- s. d
~ - ~ "
i i i i & i OJ i
i i
i i ) i i 1.0 i
j i
i i t i ilo -
H, r,.
Energy (ev)
\\;*
4 Figure 7 modiuan 2 sorption Cross Section q-(from BNL-325 - Second F.ditical
,,, ss I.i l.
l-i Y
l
\\
~
. ~.
.. -..... ~...
- " G '- " - - - " -
A A-16 J
~
1
- ]
h},
equations and current equation for one energy group, and solving for the
- e current.
It can be shown that, following a step change in the flux at t=o,
- .1
},@1 the time dependence of the current can be approximated by:
4 "9
-Li Lt\\
- i]
~ Its t, L - 1.7t4.cyEa
. 912 6 * /
- T. + :M'.$.E 3
.g
.h.r. z,. initiat.guilinrium na. of currene f.= t 4 o.
\\f I = dange in the equilibrim value of the current as the result a
l-j of the step change in fluz
}'*j
= decay constants for the Rh ground and metastable states.
104 f(t) = the time dependent function contained in parenthesis.
b Using the above relationship yields:
'E1 Ittb T, j
MM)
Ag
.q a)>
1 584 2
81%
.a 3
904 S
M 5
Mt
- y
+
7 97%
p d
9 984
,5, 10 904 d
O Ip In constructing this table, it is clear that the 4.4 minute half life of W
loda
}
Ilh leads to the requizament of *10 minute waittimes for ~984 of the q
current dange to occur. Bowever, the quantity of interest is===*=11y the M
error in the measured current, which is damad as:
q]
.~
_4, i
N' S' g i
t.
1 A
ij where I is defined as the equilibrium value of the curzent after the flux g
a.
~;
change.
ls 4
Using the above relations, algebra yields:
iO l}
L ia
':1 a
s T
w-em..
^
f
=-.---a.---
_ y e' t " =*'~
7 n q;. e: ;.,;
- j ).
A-17 w
d3
@r (1-Gd) i- )' ' = @-%d W
4
/;
g-1)
.l J.
y The second expression is useful for on-line estimates of the detector g
current error as a function of time. Using the first relationship for a fixed value of the wait time, one can tabulate (.itl. For a wait time of H
3 minutes, for example, we obtain C
)
a, Iff.)
]
l
.38 1.7%
i!
1.2 24
- -g
- 1 k
.5 5%
l r
~l J 2
10 %
i
.1 9%
10 90 %
d.
q
=>
U This shows that, for a given wait time, the detector should be moved into regions of increasing flux to =4n4=4== the error in the current. Or con-versely, longer wait times are required for a given error in the current g
if the detector is moved in the direction of decreasing flux. Thus, while
~l wait times on the order of several minutes are expected, the actual wait times required for a given error in the current cannot be predicted a priori *,
but can be =4n4=4 *ed through a judicial choice of detector measurement s,
j positions.
I 3.
Equipment Description
']
- In order to carry 'out this experimental program, several pieces j
q of equipment were designed and fabricated. These are briefly discussed 3
below.
j, The rhodina'self-powered neutron detector (SPMD) is shown in Figure 8.
j A bare lead, parallel to the emitter lead, is not shown on the figure, but was used to measure the current background. The detector was mounted on a j
- The easily derivable expression:
7
- 1. * ( tI(10)[2It)-I.]
4
}}
cannot be repeatedly used to shorten the wait time since I, represents an
]J equilibrium current prior to the step flux change. Techniques to eliminate
,1 the wait times are discussed later.
,4J n-. ---a-
l,
.. ~....
-.L, G
s
.qp A-18 i
9 fl:
paddle designed to minimize flux perturbations, and can be accurately post-
.h tiened at any axial location in a regular or special fuel element.
UT Special adapters were built to allow the SPtfD assembly, to be used in the vertical penetrations into the D 0 tank (see Figure 4),
2 ese adapters
]
sit on the vertical D 0 tank pipes, and provide a reference height and 2
}i centering har for the SPIED assembly.
f,4j A special adapter was designed and built to.aeasure the flux in the E 0 reflector south of the core. This adapter looks very similar to a 2
f requiar fuel elenee,t, escept that it has four vertical channels for
,]
the detector specifically located to bracket the anticipated narrow 1
thermal flux peaking in the reflector. Se adapter fits into an extension
,;'j of the core grid plate, and rests snugly against a regular fuel element.
Inconel
.s Core Aluminua oxide Inconal Insulator Collector s
o
_ _ _ y,
- u. u :w.we c., w t, m me
.i
/
Epitter Insulation Inconel Sheath Figure 8.
SPND Construction b
4.
De*= =4 nation of Detector Sensitivity h.[
In order to transfozz the measurements of currmat into flux values,
/ *j
?3 the sensitivity of the detector, s, must be known, i.e.
h
- y bq L
mis parameter plays a crucial role in the data analysis, and its accurate i.
dotazaination is the subject of this section.
One technique to determine S is based on the theoretical calculations f
Ll
, of itarren.3 Me model he proposes includes the effects of 2200 m/sec neutron self-shielding in the emitter wire, the energy loss of the electrons o
i in traversing the insulator and emitter, and correction for space-charge f
w.}
buildup on the insultator.
A prescription is presented for dete=4a4ag the sensitivity of various types of detectors with diffarent insulators and geometries.
In general, the model is said to give reasonable agreement e
t W
e i.1 4
i
,,..w
~-~.
~
n
. 4._. _.-
- u..._
_.y p._ 2. y,j g..
q';-
A-19
.N;
.g.
j between asasured and calculated sensitivities. Men applied to our detector, 0
-21 d
warren's model yields 2.97 x 10 amps /nv. h manufacturer's quoted j%
sensitivity is 3 x 10 ampe/nv, close to the calculated value.
-21
[
4 In a more recent work, Laaksonen points out that "several simplifying 9, '
assumptions wem made in (Warren's) model which, in the case of a rhodia a
'i-SPMD in a relatively hard spectztat might be too rough. For example, it was
")
,cj.
assumed that the electron source in the emitter wire is spatially flat, and j,
only 2200 m/sec neutrons were considered."
T==han=== shows that the sensi-
'[g tivity can be strongly spectral dependent, and hence brings into question the validity of the sensitivity which is calculated above. Furthermore,
- l he notes thatthe manufacettrer's quoted sensitivities are usually given as electric current per unit 2200 m/sec fluz. For reactors with a spectrum dif-1 forent than that used in the calibration of the sensitivity, the manufac-
]
turer's value may not be appropriate. Tinally, when the manufacturer's 1
sensitivity was applied to the Fint rhodium detector data, the fluxes did 6
not agree with the iron wire data presented earlier.
?
As a result of these uncsA6es, a progran to de*=rmine the absoluta f,
senaitivity of the rhodium detector used in the FIGL spectrum was developed.
o.finet
= position vector x
fg (x)
= fraction of detector current which is attributable
~
to neutrons with energy below the cadmium cutoff energy, (E
).
w
" epithermal correction factor"
=
Ig(p
= " therma 2" detector current = detector current which is h
attributable to neutrons with energy below E,,.
Itot(x) = total not detector current
[,y g a(p = ther==1 flux p
o ung.eese - u us., es sene uv ay o, ee detector to eer.u neutrons
[
can be written as:
TSP e
3 yp.
r p
b (N
((O%A(D u
D>
l dr r
~ f_
b,
l
.i lQ l3 A-20 F,1 If the thermal current per unit thermal fluz is assumed position inde-
~
- og pendente, and defia.d as s, then tr.
y j
- !ioMc r%
4(U y
q 2 determine s, wuere A
I s,. n<
C. (3T h ( d 4M y
% <c j
=asured values of ((gt, gw, and r w are neided.
a me inn vi a u
^j data of section A 13 used to provide h g(g)**, the measurement of fg(g) i
))
is disucssed belor, and g(p caos from t'se rhodia detector. Using s;j several axial positions at the core oester, we find
-B d(lwraa f amer T, - 3.m io a
M hF a
I
- c. !-j which represents a 94 increase over the annufacturer's quoted sensitivity.
. - j:
21 thezzal anos M e plots which follow use Sg=M g,,,1 gg, sh thh Wed
,4 valus was not available at the time the plots were drwn. Hence, all plot values abould be corrected to account for this 94 ditfarmace.
by Sus, to dotaraine the *h==al sensitivity of es detector requires l
an evaluation of fth(3), the fraction of detector carrant attributable to
(
thamal neutres absorption in the rhodia emitter. 21s quantity was measured ij at various positions, in and around the core, by activation of bare and
{
cadmim covered zhodium wires. From the count rates of wires irradiated at
)
position I, one can detezzine fg ($ as:
l
}, f.
ko(bb
.i kdbO g(3 2) = W"4 activity at time t of the cadmium covered zhodium where A
[}-
wire irradiated at positica 3 q
and A (1,2) = 8Pecific activity at time t of the bare rhodium wire irradiated b
t]
at position 3 y
- It has been shown that the thermal current per unit thermal fluz is strongly il dependent on the effective neutron temperature due to the non-1/v behavior of shodium in the thermal energy region. 1hus, the assumption is that the s '.
effective neutron tamperature is position independent.
Se results obtained p.;
from spectral unfolding la the thermal region (described in section D) j2 he used to check the validity of this approximation and make any needed will d-corrections.
~
@t
]i I
~
. n
~. a..
~
a
' r --
e
~- -
'{,-
a.21
)d 1
4 secause the rhodium wire activates so easily, has.a short half-life, and.
m.
.i -
long-lived impurities, the irradiations were performed at 100 kw to reduce a-y their saturated activities.* Even so, t'he wires needed to be cut remotely o
i j
(to 3/8") for tasshielded counting and handling. The experimental group
'ti found that, with experience, the wires could be counted within ten minutes 4
after the irradiation. A similar experimental technique has been used by 7;*
5 Q
3aldwin and nogers to study the effect of varying boron concentrations on the rhodium detector response. While they chose to count the emitted elec-3 trens with proportional counters, the present experiments used GELL i
1 detectors to count the.555 MeV gamma rays (see Figure 6).
\\
3
/
The eaperimental results for fth(1) are Presented in Table 2.
Radial locations are keyed to Figure 9.
As can be seen from the data for L-37
- ?
(conter of core), L-40 (core edge), and L-67 (regular fuel element next to a special fuel element), the value of fth *I 1* *A* **** d*** *** '**7 I
JJ great 1/*(with the exception of special fuel elements). This is consistent q
with computer code predictions. As a result, a single value of fth(*} % *s could have been applied to all requiar fusi elements in the core without I. 4 substantial error. Values for the epithermal correction factor are also
[-
presented for the E U **f1*****' 8pecial fuel element, and two D 0 tank 2
2 locations. Values of fth(x) in locations which were not directly meausured were interpolated from these measured results. For the E 0 reflector, the 2
y value of fg(x) measured in the second r*manal (outward from the core) 'is g
assumed. applicable for all four channels. This is probably an acceptable g
approximation since the measured value of fg (x) =.93 is already close to unity and should not vary by more than a few percent either way in the other channels.
Thm, with values of fg (x) defined for all points in the core, south 5 0 reflect r, and D 0 tank, the thermal sensitivity of the detector, 2
2 N
k
[i]
gg. D
- i becomes a known function of position, and the thermal flux can be determined a
from rhodium detector not current readings as Y.,
g.
N
- Throughout this section, it is assumed that the spectr.ma does not change f
significantly as a function of FNR core loadings or power level. All
3d
- The epithemal correction factor is also assumed constant axially. This will
. be true except within a couple of inches at the ends of the fuel plates, as h
was shown by iron wire cadmium ratio measurements (section A).
ekd 1
- m..
4.._,4
^ ^ '
. --- -e -- :: =
- -.}
y.
A-22
'4' e
ej
)
, ~.
g.e
- h. 4
.x4
..Q Ti
- .b E-Beavy Water Tank M
y, tw h^
l.lO m.:g 6;
L-45 L-55 L-45' L-35 L-25 L-15 9
E k
C
. L-76 L-44 L-54 L-36 L-16 L-4 l--
- )
I:
f-L-77 L-47 L-57 L-47 L-37 L-27 L-17 L-7 s
g,.
E
/2 L-78 L-44 L-58 L-38 L-is L-a C'"t*'l '
.t
..J j.1 L-49 L-59 L-49 L-39 L-29 L-19 7.I) d
);'
h.1 L-40 L-So L-4o L-so
[,8 (J
(.s
- S'b]
[b.
War special myty nement nement L. cation
('.d
.q' d, w' Figtare 9 Key to Lattice Positions
- 1
-Q e
k i:
1, i.?
U;.
a 6 i e
I
--m
", *,J k '. "
4,s.,e V--
r --
Sew H*
^^
- ;- ;;.nhMI*._
- r.... cu:ma..
.s c se... u m..; _
,f.-
...;a nce.t i D.ci.;L;.:a lai.y.,e s u.L a,
U t___f L'
W L.J 1J t_ J
',. L.
m.
U W'
W
- = = = ' -
j d
4
'i Table 2.
Epitheriaal Correction Factors f
i f
Correlation coefficiente Csanium covered activity "I-I
-Lattice Location Description to straight line fite Bare activity th D-O D O tank penetration O
.9999,.9999
.0282 2
L-67 Regular fuel element
.9999,.9999
.1677 p
L-37 segular fuel element
.9999, 1.0000
.2093 y
au
- r..
u L-40 Regular fuel element adjacent to H O reflector
.9997, 1.0000
.1703 2
..}-
L-40-A Channel 2 in N O
.0726' '
t 2
reflector element
.9994,.9998 r
D-X D 0 tank penetration X
.9998, 1.0000
.1052 3
i hI special fuel element
.0874 i
L-39 (measured in waterhole)
.9999,.9999
[..
Y.,s
- f,'j, t,m tm tL p
n.
Ij V'
.9.,wc m _
a w -
q f
C A-24 9
d L.(0
- 'l
@ll s
- jf 66 @
L
(>*
Tg N
k(x)), are 2e radial and axial measurements of Ig(g) (and hence q
4is.ss.d n. t.
[1 S.
Rhodium Detector Flux Maps k
a) Asial Profiles 7.#
Axial profiles have been measured in elements L-37, L-40, Ay L-35, the E 0 reflector, and D 0 tank position 3 (See Figure 5). A typical 2
2 M
axial. rhodium detiector fluz map is shown in Figure 10 for L-37.
So
'n
{'g axial measurements have not yet been point-by-point corrected for variations J.
in the detector's epithermal rignal, whictL implies the thermal flux in the s
Q reflectors is too high by lot. S e values of k in the active fuel region h
are approximately 84 higher than predicted by the iron wire data. This is h..
directly attributable to the choice of sensitivity,. as discussed previously.
n,j A7aan of axial profiles in L-35, L-37, L-40 and channel 2 in the.
a B
E o reflector is shown in Figure 11. Se appropriate epithammi correction g
j.j factor, fg(g), was appued to each e& ament. By taking the ratios of measured points, it is seen that the axial profile remains constant for lG L-37 and L-40, but flattens close to the D 0 tank (L-35). Computar calcu-l'%
2 q
1ations also predict a constant axial profile throughout the core except l,
3 near the D 0 tank. Channel 82 in the E 0 reflector shows a curvature com-2 2
f.]
parable to that in L-35.
Rese profiles provida valuable information on the axial buckling, as well as the axial correction factors needed later.
Il b) endini profiles r,
N Se rhodium detector was also used to provide radial flux h}
profiles. Because of the long wait times associated with the use of the
[
detector (discussed earlier), radial psofiles were seasured along caly a h
few horisontal planes. In addition, reactor equipment (such as control rod q
Q:..
drive actors, vertical beam tubes, etc) blocked the access to 14 of the fuel g
elements and several of the D 0 tank penetrations. Measurements in the E 0 2
2 reflector were made with the adapter always positioned south of L-40, so j
that a complete north-south traverse of the core could be plotted.
Each of the two radial' flux amps which were measured is discussed below.
t '.'
A 9
'~~^' -
.L_. :W c.:
- v;= W 4 - n ~ -
w.
~ ~ ~ ~^
~ ~ ~ ^ ^ ^ ^
~
~
.zc.a w = w r.w w.2.7 :
= x x.2.u w t.
m;aana.msa 2.sm:a..uuu..n:ua u:n...u.
j u
n:
L>
a-i _i u
a_ i
- a__,
u.
4 I
t L
- .c.
l wl n.
g$l
$l 6.00 1.528 a.I a.1
-l 1450 l
5.50
'l
.p'l lI l
e 2
a.1 1.318 5.00 1,
OI yl l.E,
^
n
, l 1.187
%"' 4.50 l
os a
m l
n 1.055 M
T 4.00 B
ET SIGNAL _
l g
g 3.50 I
I O.923@
%y y
0.7 91 ti lll 9 3.00 1
I 1
I g
1 l
s 0.659
,i
- 2.50 d
I i."
i
%2 d 2.00 l
l O.527 1
N
'b g
i N
O.396 5
[
i.50 l
1 I
O.264 1.00 I
y i
O.50 I
l 0.132 J
\\
l v
l0
-S'4 L
I l'
O O
0 24 20 16 12 8
f
[
ani.1 ni.e a.>
QQ, h./f &
A'[
Figure 10.
Axlal Pro e for llegular Fuel Element in on L-37
..Aegg,.
.f 3
..f
.(
't
.i a-2.
j s
c.,;
').J dj 2.6 t_37 L-35 l1 d
2.4
~
.;j
--- L - 40 T4 H O Reflector (Channel 2) l 2
p!
2.2
?
l l
l I) 2.0 i
l l$
li 1.8
- j q
lg I
9 d56
'=o I
1 l
a s
g*4 d
l-4 c
I S
1.2 o
3
- ,,s.a==
l
=
l:
.g; 1.0
,/
-lAgK l
w
[.
g
-6.-
e
/
'/
i w
H 0.8
,1,.~ %.,'s f'.
s/
l v'/.#,s-
_j O.6 l
I 1
l O.4 1
1 1
i O.2 i
I j
oI ii,i,I,I i i, i, iii i, t, I ii,I,i 1
0 2
4 6
8 10 12 14 16 18 20 22 24 26 28 e
?
AX1AL DETECTOR POSITION (inches)
[.i F,d Figiare 11.
Ewi mi profiles in %C, L 39, and L-40 Lattice
!1 ;
Imcations e
q-l1 i.
't
. n.
c..;.. s c
- m
,,a,
gg 4m a
- c
- m.,
/.
A-27 dl '
m.-
yW*
The first radial fluz map (denoted as map 41) measured the fluz in all accessible fuel elements, the E 0 reflector, and two D O tank penetrations.
2 2
.J-The data was taken at three axial levels:
1/4.into the fuel, the core mid-k.["
plane, and 3/4 into the fuel element. North-south traverses through the core center (L-37) are plotted in Figure 12 for the 1/4, midplane, and 3/4 5;
mj planes. The curves which are drawn between the data points are subject to
?l interpretation, but are probably not far from the actual profile. Also shown
.I9 on the plot is the core midplane data without the epithermal correction factor applied. Not only is the absolute value of the fluz reduced by a
}]c aiseable amount, but the shape also changes due to the different values I
of fth *I*
g y
For this map, core position L-39 contains a special fuel element *, which explains the large thermal peak asasured in the waterhole. These measured 9
values contain some additional uncertainty due to the inability to accurately 17 position the detector r=" ally.
In the core, the 3/4-position fiumes remain higher than the 1/4-position fiumes. This is consistent with the iron wire data, and rhodium amial profiles discussed earlier. Bowever, in the E 0
- q, 2
reflector, the opposite is true. This may be due to a large neutron absorber 73*
which was adjacent to the bottom of the E 0 adapter element. Regarding the 2
'~
points in the D 0 tank, it should be noted that neither position T nor 2
position W is directly on a line con +=4=ia-the other elements for which the g
I?f data is plotted. Position W is quite close to the line, but position T is a;f about six inches west of the line. Bence the value for T is estimated (on D;-
the basis of the sacand radial map discussed later) to be about 9% low.
The second radial flux map, denoted as map 42, measured the flux in all 7
accessible fuel elements, the 5 0 reflector, and seven D 0 tank locations.
2 2
The additional D 0 tank measurements (relative to the first map) were made 2
{,
possible by the removal of a vertical beam tube. The measurements were made at the core midplane, and at the 1/4-and 3/4-planes for a few selected l
elements along the north-south line through L 37.
The D 0 tank measurements 2
were made on the 1/4-plane, and extrapolated to the core midplane. For l,"
scue of the regular fuel elements in the core, the detector would not fit
.3,?
in the channel normally used (just south of the fuel bail). Measurements were 4
J;"
- The special fuel element has several of the center fuel plates removed to allow lJ.,
room for shin or control rods. For this map, lattice positions L-39 and L-57 1
contain special fuel elements.
Z.
9 L
4 Y
i*
b.
,. _ _. _.. _ -, ~., _
__.s._:,-.__..___,,,_.
- a
- ::2..:..
- . a.u.s.1.w,.... s :. a
. :. s a::. _ m.:...
.a. w. a. a a z w:a m a== u s.,.a. m =..
I
[
I.-
2.6 Core Midplane
--- 1/4 into Fuel 24 t
-- 3/4 into Fuel
~
2.2 A
-- Core Midplane (epithermally uncorrected) i!
\\
\\
2.0 0
/_
g;:
\\
in 1.8 i
\\
?
1.6 y
\\
i "a
'l
}
1.4 l 4 /
]
\\
/
\\
N._,. /
l I
i2
/
II
-*' ~ ~ *
\\
Y a
ll
- y. C
- - -* C,s
,. A
\\
l n
1.0 v
s s s.
p
)
t-G **.-
Q
./.
6 t"
o s
h-g,*~'e s
j N
/
O.8
'\\,
l 9
an
/.s
-6~
s\\
/
9/
0.6 -
i O.4 -
E O.2 -
i l
i 0
L-40A L-40 L-39 L-38 L-37 L-36 L-35 W
T i
SOUTH NORTH.-
t Figure 12 North-South Traverse Through L-37
.. j Map 81 i
}
.e
. a
,,w.
,m.
-,.. - - -. - l y._.,
- % N n'
m.
w._...
ll j.
A-29 g,e q
taken in a channel just north of the bail in these cases. The difforences n
.i in the fluz values between these two points is less than 24 as shown by measurements taken on both sides of the bail in L-37.
The c. ore loading.
ki '
is slightly diffarent than during the first map. A regular element replaced i
i j
the special element that was in L-39, and the fuel element that was in L-50
]}
was removed and r.ot replaced. All other locations retained the same type i
jJ of fuel element, although the individual fuel asamblies had been shuffled
]
since the first map.
d A north-south traverse through fe37 for the core midplane is shown in j.]
Figure 13. The thamm1 fluz is seen to behave mud more smoothly without the special element in L-39.
The D 0 tank data is much more complete in this 2
plot, and shows a flux peak which is comparable to that at the center of i
a 4A core.
['i The data which has been acquired provides valuable information on the thermal flux in the FNR core. The data is currently being used to benchmark the computer codes used by the analytical group to predict thermal fluses.
In ' addition, the data also provides information on the offacts of the special.
fuel elements on the thermal flux distribution in the core and D 0 tank.
2 It further suggests that the current shuffling pattern of regular fuel elements does not significantly alter the thermal flux shape. Lastly, the "j
data will be used to determine the changes which are attributable to the W'
introduction of low enriched fuel to the FNR.
6.
Rhodium Detector Transfer Function Analysis
=
I
,J As described earlier, one of the major drawbacks associated with Jd.
using a zhodium SPMD is the several minute wait time required after a change d,
in flux. This long wait time makes full-core flux maps impractical. Even the
.j limited data presented in map 91 and map 02 involved substantial offort. An
/
analytical technique which would eliminate the majority of the delay is being developed at The University of Michigan, and is briefly described in References 6 and 7.
The analysis centers on developing the transfer function O
for the rhodium detector.
If the transfer function is known, then the flux a
can be determined from the current without having to wait for the current to
.;j reach its equilibrium value. A full core flux map could be performed in a 9d.
few hours, instead of a few days, should the technique prove sufficiently o
i accurate.
a]
- t
,~
_... _ _.,. -..,. -.. - _ - _ -. - - -,. ~., -..,
'. p
. c' i.;.. a.m.:
.u :2.
..a w-.
.. -.G.i..
.a 2:
' +,
i
- 4..
I<
,g O
Z (>.
- li a
N q
y A-30 r,
( *,' 3 3
spano M 43 i <>
a
.e}
l ct:
w my,
.a.;
X ei I.
i>
3 *4 M
Q n..
i
.]
p in 9
7
- 4 a
.d u..s c
-n to
,s i
ii J
&c s
g o.
o(
i J
p g
Q.,:
co 5-to I
- Q.
L',
J j1 1
h J,d R,
1.;-
a a
.)
Ir h1 M*
g) o L.
t t.
i (f,
e_
J.
c
-ce -
.s =
i.,
- c. 6 o
o 5
3 ou N
T 2,s r
i
..-l.
.T e
s LN p'b e a
- tm
- )
I i
i i
i i
i i
i i
i i
i U
o o o o.o O o o o o o o o o
W
- N oe eN oee eN g
N N
N a
-a c6o6
(?j, (s.,um/ ou ol) Wp g
l1 (l
F
.e-,e m--w--vw.-----.%-----,--e-.-M--
b--,-
c,w,_h---
4MJwha h
_gE wi-w,.
7~. y..g,y j
....:_ ~
__.y,,,..
m
,.m..
- g....g.3..
1,...
a
]g l
J.
In order to develop the theory, first define (see Figure 6):
- .t.
it N, = number density of 2-104m states i*
N = number density of 2-104 is M states j
g I = not detector current Y"*
I 7,,g
= cross sections for production of m-104m and 2-104g I
g states, respectively l
j N = number density of m -103 y.
x,,x,
= s.n itivity of det.ctor to szad and metastable d. ears j
f x
= sensitivity of detector to conversion electrons from P
m-103*
l Y = fraction of metastable decays going to ground f
j Then the kinetic equations can be written as e* % M - ) M4 l
(1) f]
4= 9M4* Na-hAIS n3 I
- Ya Nm + k Kp N (To,+7d @ -
l 1
1 p
Thus, given N,(0), N (0), and $t), one can calculate I(t) from equations f
~
(1) - (3).
Pictorially, the equations are in the form:
'2' "t*#**
5(t) runction
' I(t)
=
4,;'
In practice, I(t) is measured, and Q(t) is the desired quantity. Thus, jt,1 these equations are inverted by taking the Laplace transform, solving
.jy for
@(s), and re-inverting to obtain M(t). The detailed and lengthy
{
algebra is emitted, and the solution is presented below.
l oerine s, c.4%
q@
l k'*
~8 s ( y %,) ~
1..
UNa*T )
S I h ( W 'd % % + T. b
~.,
C, r W f.
L
% (.%
- 7,s s
'.d S1
- 8 ** ) ~6'- 4C.
i I
d
~
2
?
$ ?. :. '.l '. ^., ' -
- o
-s
.: L
.i 93 1
ci A-32 i
e qjj U:1 It can be shown that the inversion of equations (1)-(3) yields:
a$
e e,*
- Y I' f 14T. c
- 6.i T
l
+
+
git)..
- }1
}\\-KIS'.
i A
gt
[
d 1
F'8,,(t*) 01(**)"Figg), Qi[i,,.
ii f;
I t'(%q's/(f,,-5) y-l
+
-6 p
e t
A 1m5k,,
+
i}
5 with T(0) deterimined by I(0) from equations (1)-(3). Note that the a]
intagrals in (4):
v.
y 4
I O"kftu.V(Y= lim + hM"I du.
8
]
g(t)=,
e g,
1
'I il i
- i I
d
'A can be further moduced to:
(.'
I I1 st f tl+T. YIF) g d(Ile-eboh + d 8
E du-s I:\\.:
4
- n With b'. J C? E Sg + A
- Sar R
g y
Q s 4 - y DeLT
- hh
!l.
Thus defining
%i 1
6 - 6,i
%t it M
.yl FN) E kL.
- L
+
k l-ACl$'
a h-
= =..
- b *- * -* 7 ;
.-"(."..*-'==g e**'*'"**.4 4
mu
- i '1 q, -
- ****A'
~~*
4
.,7
- .;.4..+(*.
','_e_..e.,.
_f a
-..s ite.
s
- 4. c -
n then equation (4) can be rewritten as 3
3c.
glty &lC)fll0 9 C {$lt)~ "Y q/
4 I
j J and the burden is apparently placed on evaluating the (1 erms. Either t
bA 14 1
equation (5) or (6) can be used to de+==w A-(t), and both approaches are equivalent.
i?
In order to evalute j,1(t), we first consider the form of equation (5).
We assume the data is taken at equal time intervals, that is:
l,.4 u
f a {l-ih bt e
Further, we assume that the current I(t) can be approximated by a cubic
- } y polyn einal during the time dt between readings:
~fft) % Yit) E Galir ) { k~1k Y The a,(t ) are detemined by the cubic spline routine SM00TE obtained g
}"'
from AML. Then le.tting x = u-t, splitting the integral into a sum of g
.1
- integrals over time stape At, and after a litt1,e algebra yields:
d, me i
df/6) - g t ((
0(a[t.)In i
gg) vt aro 1 o' N
where 46
]
J. a 6
x" dx ij o n J
~
y' and 0(,(h ). contains the a,(t l and constants from the derivatives.
g g
j "',
Note that equation (S) is not a purely "on-line" scheme since it d
uses values of I(u) with u ') t, to find I(t). This turns out to be i
f e-an advantage when only a limited amount of discrete data is available.
].-
As mentioned. above, equation (6) can also be used to evaluate M (t).
In fact, note that when taking [d in equation (7) to find f(t), the Il I(t1 term drops out completely. Thus, one is only left with numerically
- )
ev.1uat eg:
i
n a..
a
.. _ m_.W E, -
_ _......._._. a
- .s
, g.
1 s.
)
d::
a.34
- 1 v
st C
1(tddw
]
si 1
?2
-g Note that this scheme does have the promise of being "on-line" if one l
sy uses a numerical integration scheme such as the trapezoidal rule or il Simpson's rule. We have found that the trapezoidal rule, Simpson's rule, and a smoothing scheme exactly analogous to that, described above, give 3
the same results for $t).
]
= cot.too m is.ed for ee.va1= tion of th. Ati tote, rats in a(
the antarial which follows. S e technique was first tested using a calculated current from equations (1)-(3), assuming a two-fold step change
{
in the fluz. S e calculated current is shown in Figure 14, the resoonse of the code to this input current is shoun in figure 15.
Both the as:'
re=hte ahitity (within 3 one-second time steps) to resolve the change,
[
and the solution stability for 1 cog times are quite evident.
Se code has also received eatensive testing based on data taken on l
p the FWR. M a code response is compared to data which is taken using the a
conventional *"-49 described in section 3.2.
Figure 16 shows the
- 1 resulta of a, test where the detector is run smoothly through the center 21' of the core at a rate of 1*/ minute. Se vertical scale is exaggerated in order to show the charactaristic lag of code response probably associated
[1 with, valuer of St,slightly off. Nevertheless, calculations shows that the q;
magnitude of the diffarence between eqnitihdun (solid linel and code l1 response predictione (astaricisi averages only about it, within the esperi-mental acertainty of the data. A similar test using a 2"/ninute action j
through the core yielded difihrences which averaged only about 2%, and a
]
shows the characteristic lag to be slightly worse. h e, using either a
4 1*/mia or 2*/mia detector motimes yields good agreement compared to the ij equilibrita data, witiL the possibility of supesh agreement by slightly j
tuning s; and s, to account for the moertainty ia x,.
Se response of the code was also tasted in the reflector regions.
c.;
Ma equi 14h=4um data there is estimated to have an average uncertainty of 24 based upon its syE Mhmty. Figure 17 compares the code response L
to 1*/niante data takaa overy 30 seconds, to eq=414hdum data takaa i
!1 every inch. Similar results were obtained for the top reflector. Nota that the largest difference occurred at the sharp reflector peak and was s
.1 i
~,.-.
.,,.,. __..,_,._.,..-.....,,.._.m-.,.
~
CURRENT RESPONSE i
i's a
a'
.n' d,
g m
'l l
S
..)
g
.1, lt i
3 g
.,t b.
e'i 3
s, j-
- g; Lu Q::
i
{
0,..
N r
e
?
,a l
d.
-e e
v,.
I-4 8
0.00 80.00 160.00 240.00 320.00 400.00 480.00 TIi1E(SEO
~
Figure 14.
Calculated detector current following a three-fold
(,
step change in flux.
1 I
4d f
- - -. ~.
... ~ -.
.==1-n-w i
FLUX RESPONSE
~
-i
.t
'.s, o-
- ..b a..
g..
.)
g
- i u
_i'.
5-e
-Y M,
3 g
I 'j a
(
w x
3 a
LL.
~
S.
a n.
,t
(,t Fl a
a i.i t
l'
- t. s I'
u ci a
h c
1 a
w
{-
a as tsa.co 2am sam 4ca.co 4 mon 3
TI!1E(SEO 4
Figure 15.
Code response to input data from rigure 14.
S f
5-r
(
. m.,.,..g,,gm _. g.3.,...a... e. r-pu y.
a s,.,,
.a, R-0 3 -1 ('"/k N) 9 a..
g n
m a
.i 5..
a
- 1.. -
f 11 s.
4 J.
~
a
~
yt
'I D
- 5 u
.i:'
a
---equilibrium data
=
1 a
'I 4
is n
c t
m
.i.
i
't m..-
,.,,\\,
J,
.s-t-
a
- 3 14 m is.r "3
-sm
-:m 2m am zum *
?,*
-in.no 3
POSITION GNCHES) l-Figure 16.
Equilibrium data compared to code response for data thkon axially at 1*/ minute through the centar 21" of L-37.
i i]
t
,f l -.
~ ~ ~,
~
,y
'O l
=c_.,
8 u
a 3
l
~
s
- n r
1, R-LECTOR DA A
- A
.p
.4 2..
a s
a rhod.t
[
Q o equilibrium t.
- 4 R..
L a
- )
f 4
a L
M.
o 7
.4 a
i.
4 x
r 3
-(
a t.L. a "
a s
~
8 f
.1 N II
>4 c
s H0 FUEL-i I
d::
+
i l'
3..
s t
a ri
- 2 i
5 W
l 4
i -4 E
8
[
.. ]
n l' y
?!
3 d
d 4.no 4.m s.so a.4e 7.2n s.an s.so s.s POSITION (INCHES)
Figure 17.
14I001 code response to data taken axially in N O reflector 2
Q below L-37 is compared to equilibrium data 1,.
i e
g
- _ - ~
z r-. n Mw--
w
- - ~ - - - - -
e,e ^*
ma..- - =~~
=a--
_s.
.. ~..,., - -
j.
.....,,,.g q
A-39 e+
tt,
i e
y
- 5 s.7%, while the uncertainty of the equilibrium data there was 3s. wien the experiment was repeated with a 1/2*/ninute movement, the difforence y
at the reflector peak was reduced to 2.54.
s-M Thus, the technique has been demonstrated to yield reasonable results with n-4 speeds of tg to 2"/ min through the cue and 1*/afa through the asial i
.e
- j reflector regions. Even better agreement has re'oently been achieved i
by reducing g from 54 to 14 In the core, the data which was low is increased by about 0.54, and,the data which was too high is decreased by 1
a similar amount. In summary, as the code is
- tuned" to the proper value of h
{
K,, even greater speeds should be possible Nth negligible differsacos "J
y when coopered to equilibrius data. This will a13mv full core maps to be
];
made in a reasonable anotutt of time.
N C.
The -- +: =le ( AT) Measurements for Power Distributions b
f l
't 1.
Purpose g
The purpose of this phase of the experimental program is to t.p provide aradial core man of the asially-integrated power distribution. This is
- {
used as a theoretical benctusark for the analytic groupq at well as pro-viding additional EED-LED comparisons. The data can also be' used to
.e obemin infozzation about spectzally and spatially averaged fluxes, as
'l*
s-well at being useful in the caleclation of reactivity effects, such as power defects.
h-2.
Equipment hl A Cu-Constantan thermocouple is used for the AT measumments.
I The *h==-byle sheath is enclosed in a stainless steel tube which can he extended intoor retracted from the core by means of a plunger-type
- g i
arrangement. The tha- --- -_ -;-le leads are carweted to a digital meter j
whictL reads temperature directly. Positive alignment is assured by a
- j special mounting heed which rests on the fust bail.
3.
Fuel Assembly Flow Rate Measurements A
y' In order to convert AT measurements into power, the flow i
rates through each. assembly must be known. Pressure drops across indivi-
,",i dual assamh11es have baan ande and have shown:8 r
An FNR with 32 standard elements, 4 control elements,with
],
shim rods in place, and 2 open control elements Oased as irradiation positions). has a measured core pressure drop of 2.lf 2 inches of water. This variation was observed by t
t
- k
-w t-
-r***"
",eW_ - eg a
- t1" 9ev.,-.
=9+,
9 g g 9 -- p,, y p, _*p e yg ; pg.w.pyg g,
~
.a......-
- m. _
w.
w
. 1 3
.]
l 4
A-40
't
, I'
- l
,1
{j making measurements in different core locations. The
}
asasurements in each element shove a fluctuation of not
'j more than 3,1/16 indt.
~
- i'j Me tests perfoamed on the fuel elements show that sj
.I the pressure drop across the element varies as the square
[
t, J
of the flow rate through the element. Mis is confirmed m
<e
.j by similar flow testa performed on an elene'at s4=M==
h to the FNR standard element by AMF Atmics in 1959.g l~
..?
~
q Further measurements made in a plesiglass test tank yielded fumi assembly
{
[j flow rates as a function of pressure drop for tutzodded special, rodded L
N, special, and regular fuel elements. These are summarized below for a f
s,,'
2.1* core pressure drop.
['
t 3
'i Element Tvoe Flow rates (goal
[(
?!
modded special element 18.0 t
Unrodded special element 29.0
- [
2 L
J 3equia, fuel element 20.5 1
a Tahle 3.
Measured flow rates j.a
~
L.a1
? :2 Ji zt should be noted that it is also possible to calculate the flow rates 41 mad o== - drop tf the total con flo ste is amo. za practica, I
ha
(
total core flor zate g ccmtinually monitored, and g known to a precision 1 Tr of about 1-29.
um have not yet had the opportunity to make these com-
[
a paris
, no o t
3 4.
Thezzocotyle Maps
!3Q Se results from one partial 9=- :=4 c mapara shown la i
1
'g 44 Table 4.
The values which are presented are the AT in '? and the nor-
'j anlized assembly powers. Nozmalized core midplane thermal fluz obtainedl from a zhodium amp is presented also. The relative uncertainty in the AT zeadings is calculated to be 3.54 ce the basis ok repeated measurements. i .j rig
- 3
"!:a 1 b n i m -_n w :,r - xm _ _, c- -- --
L.- ---.. L' ..,..m .,a --a . < ~ ~ - ~. ~ - A'-41 ..e -.i ,J Table 4. Results of Partial Hermocouple Map I* ma== 14 *= d Noamalised I,- Element AT Power h ,,g L-40 19.51 4 .51 .43 j!* L-39 28.5.5 .74 .71 1 .i - i! L-33 34.01 3 .39 .91 ..i ' L-37 38.41 3 1.0 1.0 -1]- L-36 35.21 3 .92 .97 al.' L-35 27.1.+ 4 .71 .30
- q,
L-7 20.31 6 .53 .63
- i.,
L-17 26.0+.3 .63 .36 ]' L-27 36.91 6 .96 .97 d L-47 41.0+.7 1.07 .99 -l, " 1 L-67 20.9_+.4 .54 .63 3 + r, L-77 17.3+.3 .45 .46 1 a
- 1 Li 9 itile the thermal flux is measured on a slightly different core, Td =ca of the fluz and power does seem to indicate that the thermocouple measure-nonts need to be repeated ud a careful analysis made to determine the sources of the differencer aBove.
1 ! m' D. Neutron Flux Spectra by Activation Analysis 1. Purpose The purpose of this phase of the demonstration emperiments is to define the in-core spectrum..The technique chosen is known as (j " pal _ Analysis by N,eutron _ Detection
- or "SAMD" and involver the l
unfolding of the neutron sp-from activation measurements of many ]*i feils. >]-
===2. Background=== [] The concept of unfolding neutron spectra is based on the fact that at saturation, the activity can be assumed proportional to: 1 r" Q., q(e~)1(EW J g o q C"g(Z). is the cross section for the reaction being studind. If one wiiare assumes the cross sections are well known, then with. many dif forent activa-2 c.s '. 1,
- 'j
,a '. 5
l -- ~ " * * ' ~ i 4 n
- ]
a *\\ j A-42 14 q li = lily tions, it may be possible to detezatae 3 (3). 2 1s process of finding d(s) d gives the saturated activities of several different fails represents the "a L1 mfoletag. d 3 me afolding of neutzen spectra has been a problem of serious interest for more than a decade, and yet the frequency of articles la the current "i3 literature meerscores the importance of tho' t 6.tauer. to Ostar has b omtalogued the various generic syyzoaches used la unfolding, and listed over (, 20 miolding camputer pungzaar usiaq these methods. sipj has empared C. three of the more standazd computer codes, including CIrsnL anZZ. and i .( snac-II. In the past, we have used the snaD=II code 12 and snlIDnEL codes S as our miolding wo*k-== . In addition to the snND-IZ and snNDalIL codes, the WINDONB17, N1s, W N '5L ' miolding codes have been 1 acquired. mese codes are newer and see t--h=4 nes which aze more mathemat-d loally rigorous, such as linear p,. ^=- for optimal solutions. Se -4q 32nt'sL code also has the===-k"ity of noing the EEtr covaziance flies i mentioned above to assess the significanos of the known errors la the i czoos secticos on the unfolded spectrum. SIEF-T cross sectices, written i iI La a salm-IZ ompatible format, are available fzm Escokhaven National Lab and have replaced the original cross sections la our packages. ] n e selection of a set of fetis plays a critical role in the O ee-- May of the unfolding procese. For the afolding process, one desizes h { at many reacticas as possible, as auch enezTy coverage as _possible, and.asmuch overlap in energy coverage as possible. In additica, the irradiation-handling and counting processes impose additional constraints. For example, the folla J cannot be." Z together, as is acasally done, and still fit in the w ?) 81/5' slot between fast plates. And moestaiaties in the irzadiation time . :3 %] make i==d4=*4 - less than 10 minutes inadvisable. Sese and other con = L siderations seks the foil set selection passedere a difficnit oma. To aid in the selection, the FRED ande was writtaa to predict the d cemhinations of izradiation and weit times required to achieve the optimal .1y count rate (including the ensagy d.;-" - of the detector efficiency) s y: on the timed gemetry, GeLi detector to he need. Yazying foil thickness
- t D,
and diameters were consionzed, as well as the br==-h4=~ ratios for the b variour gammer to be counted, and isotopic abundances. i) S e resulta yielded I, a set of six foil antarials covering 17 reactions, and are summarized in p M Table 5. I-Ai4 lB %) J F m
..:; u - .a. .A2 ,. g.. g...,* g.g.;2 zc g .. g... gs c.g. s.g '..f.. l' j i t: Table 5. selected Trial Folle i I {.- Fo11 Reactions E Region Irradiatten Time Fo!! $ 64 63(n,TICu .0072eV -*- 7.6 kev 1/2 hr 1 - l A. Copper Cu 63(n *( )Co60m 5.9--+ 11 MeV 1/2 hr 1 'a Cu 62 63 (n,2n)Cu 11.9 -416. 3MeV 1/2 hr 1 Cu 63 (n, T )Cu64(Cd) .5ev--& 9.6 kev 1 hr 2 Cu i. l
- 3. Aluminum A127(n p)Mn27(Cd) 3.4 --e-9.2MeV -
1/2 hr 3 j 27,,,L3,,24(Cd) 6.4.-+ 11.eMeV ' 3 T g A1 s se C. Iron Fe (n,I )Fe .0076eV +. 36 kev 45 minutes 4 ss,,,3,,56 5.4 -+ 10.9MeV 4 g Fe i 54(n p)Mn
- 2. 3 ---D. 7.7MeV 4
,j 54 Fe %.'t Fe (n,Y)Fe (Cd) .525ev-+- 2. 8 kev 5 t 51 59(n, at )Cr Fe .t. I Sy 46 D. Titanium T146(n,p)Sc 3.4 4 9 MeV 1 hr 6 r.,.-( 47 47(n,p)Sc 2.1-4 6.9MeV 6 j - r T1 48 Ti48(n.p)Sc 6.6 --4 12. 7MeV 6 I N 64 64(n p)Cu 2.3 -4 7.7 MeV 1 hr 7 + E. Zinc En llha F. Indium In115(n,n')In 1.2 -4 5.8 MeV 1 hr S ,[ {' In (n,I )In .040eV-+ 3.8eV 8 r t i e ,i i
__ _..... _. w - - L.. w w ~.
- f=.
- .y g
A-44 i .i W* U ij .j 2 e results of the unfolding of data taken in L-37 using this trial j d fois set and the SANDAML code are shown in Figure 18. D e indium foil .s!q yielded data which was suspect and was not included in the unfolding. Se M.,. siac foil was not available at the time of the irradiation, and a nickel i ] foil was substituted. Se figure shows the unfolded flux bounded above 1 9.. i and below by one standard deviation. me lack of foil sensitivity in the .Q 10 kav to 2 Nov is apparent from the segnitude of the uncertainty in the afolded flux la this region, while de tharsal fluz energy mesh appears ,i crude, it shoald be noted that the integral tha==1 fluz agrees well with ._i results presented earlier. Two lessoas which were leazned from this unfolding were
- 1) Five foil materials are insufficient to determine j
the spectra accurately over eleven decadesof energy, and ? 21 intzoduction of cadmium covers into a regular fuel channel . Produces substantial pertuzbations in the flus. At a result, additional foils have been added to the in-core irradia-tica plans. Also, an alumiassa sample bolder shich fills the special fuel '1 element center hole has been designed and Built for more convenient incere ~ -1 irradiations. S e unfolding of the incore spectr e has been demonstrated 'to be a more difficult probier, than originally envisioned, and will repre-m sent a significant part of our future efforts. , V; , m$ j E. Measurement of the Mammi Neutrea Spectrum at Beast Port Exits j na sha,e and t.m,er.ture of th. me-ezuan-uh. thezzaz neut=on i; i spectrum is an important daaracteristic of the reactor, both, in core and n [.a at the bens part azita. To detezzine if s4_-4 *4-=-t changes will be intro-ta 4.1 deced hr the low adeh===t design, the experimental program has included a seasuremmets of the been port azit spectru Ming a crystar diffractometer. ]$ Se initial resulta **=4 a=4 are described below. m ese measurements will be repeated to refine the technique, and this will be repeated before and r.. Q after the new core is lastalled. ob 1. czystal ciffractometer Method ,.9 Data have been obemin=d on the FER crystal diffractemeter, located at the exit of beam port I. Figure S is a drawing of the 'spectrca-
- . tj i;
etar and beam port geometry. The effective source plane is naar the contar' ) of the D 0 reflector. con ting data is normally obtained using caly the 2 .-W - n + -' -;- - ~~ ~ '~'
- m. m.m m... : <mmm_.,;m.,m.=_
- -. ~. l I, )_, 1 p-
- g. _. q 1-l'
)_ 'j i J ': ). e )_ ?
- }
c:. 8 b ( us it '\\ )_ <;1 1-1 l g. a ~ 1-j g g 3 a a i i I I I I ..?, 1 l l 1 I i 1 I I I I I <hi ,,,,-.,,.-...-e i,.-i ..-e..-s .wr4 ,,s.ra are i .e 9o l ENERGY (t1EV) gl l ,+ Figure 18. Unfolded in-core fluu spectruun using five trial foils, .T' j along with upper and lower bounds on the solution.
- r-a'
- {.
ma -. t 9 . N. 3. - b.e ut.ma
- & e d-
,.i A 46 c;j q@t il 00 I, n: / ll y Ti 1a.:,. l 3 SOURCE il COLLIMATION a ..iil __:1 / I(*: r 3-PRIMARY -l f fi>i SAMPLE' j FISSION -% MONITOR j SECOND J 't/ SAMPLE BF2 l.:,1 .) ,1 i n; i h.!
- i. -i f 'I t.j A
j a d n-a. SPECTROMETERS ~ 'a %) u L '. f /, 1 d y; R. n> l ?;i l l'l ~i. 8 J e 7 --__; m4 1 ___
,;,.r - ? .....,._..J,_.
- a.---.-.
^ MM -, a n-<, 1 i 2 4 e 4 i x RUN 1 x oRUN 2
- j e
x 2 x o i 3 a x i x j j @E) o x -) 2 3 1 W 4 a,
- 1..
y F f x m_ 1 .5 1 m 4 s 4 l' e 'a,t, ' o O l i eI '4 i 0 f' .03 ' .06 .09 .12 15 sr 4, ENERGY (eV) - 1, 4 O Figure 20. Thermal flux spectr.un. 'A i = g. i ,d'
I I ~ .,,j i it' ..r -I e f,t a-40 n s .m G i. d} fission diamber annitor detector and a single crystal in the primary N sample position, as shown in Figure 19. Conting rater are obtained as AN* this -*W crystat is rocked through Bragg angles about a gives f detector posities 2 9,, for a sequenon of 2 9, positions. a silicon crystal // of narrow mosaic, is used La (111) transmission reflection, which has the s f ashutages of no second order reflective con *=8a=*4=, " constant
- crystal y
G geomatric profila, and relatively reliable prediction of reflectivity versus L ,=.! e,. 3. coast rate at.a.h. e, is, after background correction, viven g hr p= { ?1 CMG ) = a. sieA(Gabkia)de
- 1 s
r ] [ i4 5; where a is a constant gemetry factor, 6@)is the fission clussber effi-ciency versos # (i.e., versus energyL and 1(61 is the crystal reflectivity. n.ca.e em 1 attar term is sharply peaked ta. ngl., as co.at rate is 3 i simply related to the flus by l CW = a.s(OQ!OT(9,3 R M a angular counting rate is converted to energy dependent flux 3 (El i; aring the Bragg law. Figure 2Q gives the results of points taken in two v :; I h separate emperiamats. It should be noted that the accuracy of the deduced f(31 depends q directly on the accuracy of the calculated reflectivity. un have followed 4 ] the well-known kimaantie diffraction theory for ammais crystals in ] + -*=i-- at 4,113'113, hat this requires a priori knowledge of the mosai= E, width. of me crystal, q. mile we have asesumed the mosaic width. using a two-silican crystal rocking - ; -+_ 7, the calsuistion of tSe reflectivity of a single perfect crystal is, in theory, an h more straigtLtforward. Mur, while it is only the shift in the neutron tempera-4 ture that is required, it is our philosophy that if the data also produces an ac-g curate absolutevalua of the neutron temperature, our confidence in the shift ,l is reinforced. As sudt, we are in the process of repeating the measure-
- 43, monts of the neutron temperature using a perfect silicon crystal.
j>. 2ns, in conclusion, the saperimental program has progressed far in ]' characterizing the EIt! core. Additional messerements still need to be J _=_
U ...i., m. :.h8Mc.:.,~.4 .) .; J ii ..,:l " made, particularly in the areas of in-core and escore spectra. But the ,$ *= program itself is somd and couplete, and should quantify the significant Q* differences which are associated with the enrichment change. These results -d., should prove useful to other NTR reactors wRich are also conridering up- .j, grading their facility. 4
- j. as Refe: ences i,
q 1. J. Duderstadt and L. EkmCiton, Nuclear Reactor Analysis, John Wiley t 1u and Sons (1976). .)
- j 2.
L E. Beckurts and K. Wirtz, Neutron Physics, Springer-Verlag (1964). (" 3.
- 5. D. Narren, Nuc. Sci. Eng., 48, 331 (1972).
- )
4. T. Laaksonen and J. Sasstamoinen, Proceedings of IAEA Specialists' N= Meeting on In-core Instrumentation and Failed Fuel Detection and y Location, pp. 111-131, kECL-5124, Atomic Energy of Canada Limited i t. (May 1974). 5. M. N. Baldwin and J. E. Rogers, Physics Verification Program, SAN-3647-23, Babcock and Wilcox Co. (December 1971). 'l..- 6. J. M. Carpenter, R. F. Fleming, and E. Bozorgaanesh, Trans. Am. Nucl. i Soc., 22, 606 CNov.1975). 7. D. K. Nahe and J. S. Elng, Trans. A's. Nucl. Soc., g, 571, (Nov. 1980). 8. R. D. Martin, "A Low-cost Shim-Safety Rod for Pool-Type Reactors", j PML internal report, (July 19671. 3y j 9. American Machine and Foundry Co., Engineering Report No. 7527, 1 " Hydraulic Flow Test of an 18 Plate Dunsuy Fuel Element". 1" 10. W C. A. ostar, " Review of Unfolding Methods Used in the U.S. and d Their Standardization for Dosimetry", BMWL-SA-6503, Battelle Pacific -] j Northwest Laboratory (Detober 1977). W. L. Zipj, Proceedings of the Se cond ASTH-EURATCM Symposium on 11. 4 Reactor Dosimetry, pp. 1333-1365, NUREG/CP-0004, National TechM'**1 0 Information Service Coct. 19771. 3 I' 12. W. N. McElroy, S. Berg, T. Crockett, and R. Hawkins, "A Computer-Autcunated Iterative Method for Neutron Flux Spectra Determination by h. Foil Activation", AFWL-TR-67-41, Atomics International (Sept.1967). 7 13. W. E. Zachariasen, Theory of X-ray Diffraction in Crystals, Dover, N.Y. (1945 14. G. E. Bacon and R. D. Lowds, Acta. Crysta.,1, 303 (1948). 4 15. !L G. E. Bacon, Neutron Diffraction, Clarendon Press, London (1962). Sie a I,} i 1
a x w... _....... _ _... m_.._, 4.j 8' 4 J1 1 J'.1 ~ <A APPENDIX 3 (;]3 9 $q Core Physics Analysis in Support of i, Vif the FNR HEU-LEU Demonstration Experiment
- 3.
>.,1 G.J, il '(; A n i)Je ?,1 o 9 l s.i h e 5.^ r-. 8 e -] ,8 [. w.
- k c:.1
.-r %e t-.(* .a y te, [D iOgI
- -)
Nf 7-e ' e; 1 .M fN ';:.i
- 1.)
o 2g
- T ts
. :. 9 r., / <. 4 ., s 'd I',' UJ ~G -1
= - =. -. ~.....-. --
_ D. 1.hgj.h,- .. m 1_g e..[..;EUA- _.( . :;.2. J 3-1
- 2. -
1. 3, [ Co$e Physics Analysis in Ewn of the i,* FNR EEU-LEU Demonstration Esmeriment c.. 4.% c'; by ?,
- David c. Losey, Forrest s. Brown, ML111am R. Martin i.%
t and John C. Lee Department of Ihaclear Enginesiing 4" Se University of Michigan j aan arbor, Michigan 4stos 3 .slj Abstract .,f A core neutronics analysis has been undertaken to assess the impact h of low-enridsment fuel on the perfomance and wi14== tion of the Fum. as part of this analytic effort a computer code system has been assembled [ which will be of general use in analysing research reactors with MTR-type i.\\ fuel. Ma code system has been aztensively tasted and verified in calcu- -j lations for the present high enrichment core. Se analysis presented here 8 compares the higband-law enrichment fuels in batch and egn414hdina core i.) configurations which model the actual Fsut ope==+i=; conditions. The two ,) ' ~ fuels are compazed for cycle length, fuel burnup, and flux and power dis- }* tributions, as well as for the reactivity effects which are important in assessing the impact of LEU fuel on reactor shutdown margin. n' ~; i ao ? e,, a 'f Presented at the International Meeting Meeting on Development, Fabrication and Application of Iteduced-Enrichment Fuels for Research and Test Reactors, T held on November 12-14, 1980 at Argonne National Laboratory. ~ 4 d I3 M l'I m _ _ _.. _ _ _. ,.- m _., m _m. - ~
i~a.~ A s_a.m g [ >-2 q T. O.3 ..jk yj 1. INTECDUCTION d 'Q S e University of Michigan Department of Nuclear Engineering and the i l
- j Nietgan-namorial va-t-pros.ct are engag.d in a cooperatire.ffort with.
+ 's ,-] ' Argonne National Laboratory to test and analysa low enrichment fuel in the w .4 p.* Ford Nuclear Reactor. Se effort is one element of the Enduced Enrichment [;,4..d Research, and Test Reactor OttarR1 Program, which it itself one facet of A S.f . the overall U.S. policy seeking to =faf=f== the risk. of nuclear weapons f.') proliferation.- A near-tars objective of the REarR program is to demonstrate 4 '] and 1,glement enricBaent reductions from Ds to less than 20% or, where that is impractical, to 454 within the next two years, based on currently quali-fled fuel fabrication technology. A part of the effort to meet this objec-tive is a whole-core amanstration with, rednad enrichment fuel, whien will H ? allow detailed testing and evaluation of the low enrichment fuel and an l'. l. assessment of its ispect on researd, and test reactor perfoznance and C) util4 ration. ( ~] Me Ford Nuclear Beactor (FMRL at Me University of Michigan has been [,-g 1 j selected for the low power whole-core demonstration. His demonstration r.a project includes development of methods to analyze MTR-type fuel and core {d ( configusatione, assisting in the design and analysis of the low enrichment p,; uranium (LEU) fuel, preparation of fuoi procurement specifications, pre-M paring the requisite safety analysis s p revision and license amendment Idd application, procuring the operating license amenchment, planning and con-hNp ducting the emperimental program, and analyzing the results of the experi-inj
- nents, including compariscas with. analytical predictions, a
hl) q M - - - - - ~
L w a d -..+,.- W E:r &. k QsX6 S & :.- Y KW. Q...'- {} m A s.. (; 3 The demonstration project at h University of Michigan has been divided g
- 4, 4
into several phases.
- 5 N initial phase, which is essentially ccuplete, j
includes the work necessary to design and specify the fuel and obtain the 6 3 '., necessary license==== h ate. h FJD fuel has been designed and is pre-m f,) sently being frabricated By two European vendors, NUM and CIRC 1. ~. NW 3 fuel elements have 2157.3 gram *==f1= loading, which is 19.5% higher than
- J 1;)
the present high aa***==at urantun (REU1 feel. N initial phase of the demon-fi I .E stration project has also included an.eaperimental program to characterize the current M core to provide a basis for ocaparison with the' W core. 4 ', t ,.p In addition, emperimental techniques and equigment are being tested and fl O refined during'this phase. A companion paper 1 presented at this conference provides furtMar discussion of the emperimental portions of this project. The major task of the project will be the actual whole-core testing of the m fuel along with the necessary messarements and analysis of experimental s results and comparison with, analytied predictions performed prior to core loading. h present project =^*= calls for actual loading of m fuel 4 A~ elements in April 1981. i Further verification and improvement of our calcu-h lational methods will also be performed along with the whole-core testing
- ?
O program. Thus at the conclusion of the demonstration project, the impact is of m fuel on the FMR performance and =*414-= tion will be assessed emperi-mentally and compared with analytic predictions using methods developed and implemented during thir investigation. N, This paper presents a detailed review of the analytical effort per-a' fossed at h University of Michigan at a part of the demonstration project
- k 1
While many of our analytic resultr and methods have been summarized if Mg '3 + AA 4 ?. -,,,m4 .m ~_ ~ =
V l...... ) ' u ~.. ; _ .jh._ ;.. gr. a. - u ; ._a y .. ~ 'I 3 .s ni 3-4 'a ..,d a ~ ..laj
- 1 A) 2-4 in earlier conference and project reports
,.a detailed a - ry of the effort to date should Be of use to the research reactor commstitT. It 18 T hoped that this review will provide guidance to othere planning similar b$ enzteh= mat reducticar and an appreciation of the pra'ctical consideratione .i M in performing detailed reattor analyses which cannot be addressed'la 1 f) generic studier. m following sectione present a description of tBe cal-g 61 calational.etaode used in the pa =ler analr=ir, and m -r- - of the r d G analysis and usasurements used to validate the calculational inode1~ for the 1 7? present high enrichment uranium fuel. Wit also present 7 - @ ons of the. physics analyserfor tBe IID and I.EU fusis, a sumanary of current efforts, and )I our conclusions to date. .;n h Fut currently user highly enriched uranium MrR-type fuel. i To provide the means for a valid prediction of the impact -of LID fuel on FtER operation, safety, and researctL usage, a generic neutronier model has .d; ' d been developed. 1his model is Based on standard, well m rified 3,Mwt.ica Ci '] codes which are routinely used in reactor analyser. h se codes have been 'i' modified only when necessary to accommodate the special characteristica [; of small lone-power research reactors with, plate-type fuel. As such, the O methods of analysis should Be applicable to a large amber of research. ,i reactors and accessible to anny ccuputing installations. h following a 4 j sections provide a brief description of the calculationa'l model and its di .2 verification. 3 q.j II. CAICUIATICIEAI. IGTHG)S q ri A. e v er Coder c: (.) All analyservers performed with the standard, well-verified pro-duction coder I.ICPARD, EPRI-HAMIER*, 2DS', ANIS 3I , TtIDTItAM , and VEtrIURE.l I } i. 1 i
.... -Mh0kU ~ c AM --~=-' - & n-~ vMn- -hm, : ;6 mew ':v . a.. v ,. e b$ [j u ,. 4 's a. 't i., ?j Brief descriptions of code capabilities arms 14 /'.1; 11 LEOPARD - a zero-dimensional unit-cell code using the MUFT/ L.4 a. gj SorockTE scheme (54 fast and 172 thermal groupsis has deple-q tion e=.W11tys cross-section library consfsts of an early r.1 !i, _ industrial data set. [".1 )
- 2) EPRZ-ERMNER - a one-dimensional integral L'-.-W 5.t d
theory code using 54 fast and 30 the==1 groupes crose bg section library constructed from ENDF/5-ZY data. m '_L 3) 2ns - a too-dimensional multi-group diffusion theory n 9 code with depletion capability, s i
- 4) ANISM - a one-dimensional discrete ordinates transport j,.
theory code.
- 5) TWOTRAN-II - a two-afhansional discrete ordinater j
transport theory code. ,j
- 6) VENTURE - a three-dimensional multi-group diffusion
- ..I
-i theory code. I O B. Code Modifications 9 The LEOPARD code originally performed a spectrum calculation L for lattices eensisting of cylindrical fuel rode. The code was modified c.
- i to allow slab geometry and separate f= ww.y edits for both lattice and
.,..Q-non-lattice regions. '!he principal modification was in the calculation u,s - L' of thermal disadvantage factors by the AEE method for slab geometry.13 A k,..i L> commercial reactor, minor input dange fission product buildup correlation in code must be l factor extended s i. option for burnup dependent incorporate spectral offacts minor input changes L. NLPF input of flus peaking variations due to burnup f,
- p-a r l!
t n
m; g. .J.a e a 4.
- a.... a. _;.,,..
. +., y,,...ggf 7, y. 2,.y., 37 lj l 9 j 0 3* Q The modified LEOPARD code camparts satisfactorily with the EPRZ=,
- 1 l
EMosER coda, an accurate, well-varified' oods rsed in the analysis of bench-V mark, critical 7 - ' nts. A typtoal -:-. _-I .of ( and ^mw para-h matarr in Table
- 2. shove that despite the many engineerin'g approximations 4
in the IJOPAED code, it compares quit.s umil with the nors accurate IMOGl= Differences in fe m constants are due
- == M y to differencer
] code. f.j 3 in tha -sett.11mraries -===Em -/.-rv data.hizo tao,ano f uses an early industrial data set. [ The 2Ds code has been nodified to alleur a macroscopic depletion cape-f i] bility via interpolation of sa - wric cross sections as a function of I d depletion. In addition, tha isotopic balance equations for menon and iodine have been included to alloir the correct menon leveld within the core as a b function of position 42 time (and maczemoopic absorption czoss sections are appropriately modified). Other modifications to 2DE have been aimed at j automating data handling, improving fuel shuffling and edit ~M414 tier, and l 1 y greatly decreasing the computer re -time costs. These modifications are 'g d summarized in Table 3. H 1 l d C. Basic Calculation Method .lj The LEOPARD and 2DB codes were used for routine calculations of M, core reactivity, depletion effects, and power and flux distributions. W 4=1 e methods for control rods and core leakage fluz are described in subsequent -4, ?1 sections. For both HED and the proposed LED fuel, the following scheme war 1 d' aY q.. 1 c
. : z u.:. :....:. .:e -a-u. d j pg N ..i
- . i
.1 +'
- P 1
ri '?H ' }f s 3 Id Table 2. Comparison of LIDPARD asui EMcGR AM Rasults for NTR-type Fuel ryg) i.' e 2, ".s 934. Alley 19.5% Onl, 4,. 120 PARD ENGG1 LEDPARD EM04ER r,j. l '.! 4 1.5477 1.5500 1.5150 1.5116 2.41 2.40 2.76 2.75 l. E $,4 ' ~, Me 51.5 ~. 49.9 .49.1 47.5 D 1.434 1.372 1.424 1.360 i. T 4, 1 [I L 0.00204 0.00182 0.0035s 0.00344 0.0258 0.0257 0.0254 0.0253 Ij.) g,3 0.00206 0.00223 0.00256 0.00274 i. ggg D 0.2s4 0.272 0.280 0.269 2 0.0597 0.0594 0.Os7s 0 06ss ij g,, 0.09 4s 0.0925 0.110 0.10s yg t l.y lh., iIs ',j l.
- ]
e .e D I l,'. 4 P 'r* 'e I li. i 'e," M 4.1 1 I:4-a 'N: J
- 4
.J w
.=w.,2 wax ai.x.n.na w t MK.saCWEL M :M "' MW" M ~ .I i .t. 1. Table 3. Modifications to 2DB Modification Purpose Method .] determine macroscopio cross-sections model fuel number density quadratic Lagrangian inter- ] by interpolation based on local fuel changes and spectrum effects polation in cross-sectica burnup due to local fuel depletion tableset from LacrAmo at each depletion step j major input options added, extra scratch file and / i memo:y s i !{ Xe space-dependent uenon menon fee &ack N determined face local r and flux levels q interpolated as faction .] of local fuel depletion l added to Xe-free f, h I, i s l dynamic memory allocation reduced core storage system routines acquire only 'l .g requirements needed space i i p 6 interface with LaOPARD, reduced input setup & special preprocessor (LIMI) I converte LaGrnmo crees section sets to the 2Ds .0 input formet l j FIDO input processor free-foumat input with total revisica of impet U j many options moutines recoding of inner iteration reduce Cru time by factor use of preocaputed cometant t routines of 4 arrays to eliminate redun-dant calculations t improved edits and output detailed analysis of reaction neutron conservation equations 'l rates, neutron balance complete recoding and updating improve and clarify coding, enamonio variable names, i of entire code reduced storage and CPU time, structured programming, consolidate all changes i improved code logic. j l
- _..da l!Y!$O. - -
-l.u.. .n.: .. n-u ha 3-10 34 s N@N [,j 11 The LEOPARD code was used to generate few-group creer sections. Q p; For most applications, two energy groups (fast and themail were l?! ] used, althoogtL four energy groups were chosen for several detailed N mi calculations. '.) h geometry citosen was a unit cell in slab geometry con-s Q sisting of a lattice region and a non-la' ttice or extra region. f? h lattice region was composed of fuel meat, clad and water +1
- d J-j eh====1.
For regular assemE11er, tAs extra region consisted of -a A.] the side plater, non-activa portions of fuel' plater, and inter - l' 1 ' cJ assembly water gaps, wlLictL are 17 =t==4 on a volums Basir.. E j/ For special fuel assemblies, the central water Bole war also included in the extra WLm. Few-group macroscopic cross-section sets were generated ae functions, of depletion fortaa lattice and l3 non-lattice regions and the total assembly. r1 .-p For the water reflector and heavy water tank, the extra (.; [ij region was chosen as E 0 or D 0 with a.25% H O contant and a 2 2 2 dj 13 volume fraction arbitrarily set equal to that of the lattice N f3 region. h extra region few group cross sections obtained in ['] ] this menner were used for the reflector and heavy water tank in V A. ] the =-* wr. global calculation. 21 Global diffusien theory calculations were performed with the 2Da w d code. Three spatial mestL descriptions were used la av geoeetry. o A Romogeneous description, witB a 2x2 mesh per assembly, was used y l' L< for survey calculations, equilibrium core studies, and cycle mi ~ a ?!?f length. studier. A discrete representation, wing a 6xt laesh per
- s
,1 ll u t . L ~ ~ - -
== ... r,n x g.y:m w.g:;ny.p,;..,.p,%
- ...gy..; ;.y.pm.; n; 3
, ~ - - >11 y-e 1,. 'l j assembly with the latties and non-lattice portions of an 1 l j assembly explicitly represented, was used for detailed
- i
.i .j analysis of power and fluz distributions, temperature i s 3 coefficient, and control rod reactivity worth. A discrete i i n, 8 1 ij representation with, a 1212 mesh per assembly war used for 7 a verifying the adequacy of the 2s2 and Ga6 representations, and for 7_*4=en with the measuzed flux distributions. j h various aesh structures are presented in Figure 1. ] 1 Depletion war accatuited for en the assembly level 4 by interpolating macroscopic croer sections as a function of depletion Oe DArf1 for each. assembly. ne fuel shuffling ): ,t. arm 11ty in the 2DE code allowed actual FHR operation to be simulated. The axial w 1 W team for*the 2Ds code used to [ approximate transversa leakage was based on a he+1f"g and '4 samal Buckling modtfiere eBtained frce three-dimensional in VEtrfURE calculations. l. 3y D. Control Rod Wtarth Calculations a FNR control (shial rods are boron stainless steel containing s 1.5 w/o natural borca. May are essentially black to thermal neutrons and cause a drastic thermal fluz depressica when inserted. Se presence of such. strong localized absorbers necessitater the use of transport theory -J codes to adequately describe the large fluz gradients. However, in a small P high. leakage core like the FN2, control rod effects are not strictly local; 1,: [j therefore, whole core calculations are needed, but are prohibitively expensive Li Q for transpc..t theory codes. To accurately treat both local and global g., 1i i j!- _ _ _ _ _.. _.. _. -., _ _ _ _ _ _ _,... - _ m _,
.u..._.. . nu 1 4 .a = 1 3-12 11 ,1 -1 -et .-;j
- 'd
. 4 l
- . J b
- s 1
-] ylgt Fuel Assemblies
- 4
-_ _= Q w = h N
- 'b' W
i3 V .j pl W w - 1, M, W- ' 'i m' W j Ed E i ' i. i ai 2D3 Mesh Per Assembly a., j{ e i 1 1 ln1 (a. v.. i. l: p ri 1 2x2 6x6 12x12 J d. ID0 GEE 00S DISGETE DISCETE ,.fl r3 l' " Figure 1. 2DB Mesh Description 3 I = - m
sp. .,;.,,,,,,._...y.. ~,,. .. j jy .~_ _ - _s,,,,7,.,,_.. =* a, r. ,u
- 1 effects, transport theory codes were used for assembly level calculations y
to develop effective diffusion theory constants for global calculations. ~ j Few-gEcup constants for the control red and surroundlag water wars .: n
- j ;
obtained from the DRI-ENGER code for a cylindricized special asssably. 0 =* a,, Due to the strong spectral / spatial coupling in the rod it was necessary. to j obtain fee-group cross sections for three control zod regices - a surface J -' layer.1 cm thick, a second layer.3 en tBick, and the central region. .. i j" Since few thermal neutrona zeach, tem central region, the control rod ].. q perimeter, rather taan values, was preserved in the gw' sic representation. Few-group constants for the special element lattice and side regions were obtained from the DRI-EAMMER calculations for one half of a special ele-ment in slah ge<ssetry. To accurately model the local effects of an inserted rod, the two-dimensional transport code TMDTRAN war used in fine-eesh. calculations for a .i.
- j special assembly surrounded on all sider by one half of a as W assembly.
.j-j, Three regions of the rod and the surrounding water were emplicitly repre-a., seated, while the surrounding lattice regions were k7 ahad. To develop effective few-group diffusion theory constants for use in 1 global 2D3 calculations, the 2Ds code was used for the same gecmetry as in TWOTRAN calculations, except that the control rod and surrounding water were ~ =)j, hcmogenized. Both fast and thermal absoEption cross sections were varied h ', 3 - until the 2DB calculatilon yielded the same relative absorption in the control
- .j -
region as the TWOTRAN result in each group. The resulting few-group con-O 1' stants for the control region were then used in global 2DE' calculations. J 4 Although the flux distribution within the control region differed from the "i.
- 1.1
.Il.. -3 4 V
.._._. a
- a...
.= - - L - ~ :- l ^ 2.'.. a Li 8-14 L3 e. lu! i Ih A ?:I [; transport theory results, we believe the relative absorption in the control A [.) region and the fluz in the surrounding fuel is accurately predicted in this l]
- '.2 scheme.
f Ja control rod worth was then determined by comparing global 2Ds calcula-a P tions for the 6m6 mesh / assembly description with and without control rod .. s ./! inserted. a.d sil f-] E. Calculation Methods for Temperature Coefficient of Reactivity and
- c Xenon Reactivity Werth, g
Calculationsof the temperature coefficient of ' reactivity and 'of a O reactivity worth of=== pois ningwere performed with global 2Ds calcula-61 !e tions with a 6m6 mesh / assembly description. The t m crose secticar for these 2Ds casar were obtained from unit-cell calculations with the ay LEDPARD or the EPRI-EMOEER coda, essentially follouring the basic scheme U outlined in Section II.C. To facilitate the calculation of the various p coefficients, several modifications Eave Been made to 2Ds and LEOPARD. A f F aicroscopic menon calculation has been added to 2Ds which allowr the calcu-l '. ] lation of spatially dependent menon concentrations and corresponding adjust- !4 d ment of the local macroscopic cross sections in the 2DE calculation. .:lj The calculation of the isothammi coefficient-of reactivity does not ?j, F require any additional modifications because cross sections are simply b $1 generated at a different temperature input to LEDPARD. Ebwever, the power Hq } defect of reactivity represents t5a total of all reactivity effects induced W [y. by taking the reactor from a cold zero-power condition to normal operating A 7 conditions. Due to tus spatially nonuniform temperature and density changer ,4 T= m=ememarmh e mme-m--am.
- -.w.: m~? '":~.f.&,.gv q[S' ~-- ~ ' ~" m. d, ~ ~ j' involved,'the power defect cannot be predictedsolely on the basis of an d iso *h==1 temperatura coefficiant, h rafore, additional changer were d. necessary. In particular a restart capability has,been added to LEOPARD q ~ q to alleur the reca3=ulation of the spectrum at any depletion step. 5 1 with one or more variables ahW from tBe base depletion calculation.-
- J k
i.; LEDPARD than calcib.ister W resultant deviation KZ in all cross sections S. 2 divided by the varia51e change di and outputs the ' derivative" czoes section J j (hasafunctionofdepletion. m 2DE code than calculates the local d j i change in the variable, e.g., tBa cEange la the moderator temperature from 4 ,j the n =+==1 temperature, and multiplSes the Interpolated derivative crost 4 q section by tais change and ador the incrouvait-to the base macroscopic cross j section, whiatrir itself Interpolated as a function of d'opletion and fuel. J type. Extensive i d m to 2ns were not a eded because==*-*+ ; mixing j g routines in 2Ds were utilized. m dE-creer section is treated se a micro-J scopic cross section, 41ctL is multiplied by the " density" di and added to {~~~~~ theM macroscopic crosv.section I,e I = I,+(h A 5 N l! lt ,1 l III. VERIRICATICRI CF ANALYTICAL ME21E:lDS q< g A. Spectrum Calculatione s ql1 ) The two cross section generation codes that have been ef' H M, a, ~ 48 41 LEOPARD and IAMMER, are %11-verified codes and further effort to verify the 1} was not warranted except 'for the'applicatir.a of LED?ARD to slab geometry. 1 s O' Since LEOPARD ir a prod' action code for pin cell gecmetry it inar necessary j. j 1 j to compare pur modified version with. a code capaBis c;f treating slan geometry. In particular we compared the slab version of LIOPARD with the EAMIER code for ].. both. LED and' EIU MTR-type fuel. Table
- 2. contains a comparison of the various-hr!.
v i.e d I . 4 w - w .,,y,. .mm.m ,,,,,-%,yy,.,- nm,,,.,y,.
. ~..... u:.w ~ -..l .c a .2 1 j 14-16 .+ s 4
- l v.'
k 'l .,}! neutronics parameters and macroscopic cross sections for a vnit cell calculation. In addition, the LEOPARD code has been verified against several critical assemblies, incluling the TRI redded 002 ""d "*****1 ru 1 it uranium slab lattices.4 h agreement has been reasonable, and har further f,, f;j increased our confidence in the use of LEOPARD for routine calculatione n ij for lern-type fuel configurations. 1 'j (1 i W I 9 s. clonal calculatione A ~ To verify the accuracy of tem analytic methods used in pre- ,} dicting core physter parametare for the EEU and LIU fuels the calculated - 1 i' results have been capared with, emperimental data from the Bulk. shielding 1 Reactor M and for var $dms FIER core configurations. The 7 =4 - I h for several FIER configuratione sumarized in Table. 4. Indicates } ~~ the adequacy of the methods for calculating core criticality, power and ~ (l} thermal fluz dis + N i , and control rod worth. Results of preliminary ,f a(j calculations simulating the power datect of reactivity dataare also presented
- v. i in this section.
M ' :j The results presented in Table
- 4. indicate that more criticality is r.qH predicted accurately in our calculations. These calculations have revealed rdaj that considerable attention must Be given to an accurate representation v.
W of the fuel geometry and of trace isotopes, such ar U-236. Leakage in the
- .3
.a. 9, axial direction in our two-dimensional Cr yl 2D5 calculations was represented [j through. the use of zone-dependent axial buckling obtained from three-dimensional N 3 VEttTURE calculations. The resultant 2DR calculations are quita sensitive ,i h to the input du, n <ag distrihation and care muse de taken when dete-4-4 g 7 1 .r. -.. ^ --,s1
<. y.. ..,...m. 3 e.. p...,__ ;;g y ~-7.,..,, ~.. -w.... -- v.ma.y r - . w.:. 3, z r,7 .2 j< 3-17 ~ r; e g s 3 j Table 4 Emperimental and Calculated Results for FNR Cores N j Core criticality 4 FNR Cycle Mesh / Assembly Measured Calculated P / 144 Sm6 1.000 1.003 k, 1833 Sze 1.000 1.001 1 4 .1 Assembly power and Thermal Fluz Distribution 1 Fun Cycle Mesh / Assembly Measurement Locations Measured EMS T.eviatiori j 57 62 power - 35 9.5% 1 i i 152A 2x2 Thezmal Fluz 33 6.2% 5 157B 2x2 unezmal Fluz 30 7.7% 159 2x2 15:ernal Fluz 34 7.1% q. y ]* 167A 2x2 h==1 Fluz 33 4.5% e. 175D 2x2 thermal Fluz 12 7.2% 175D Sze Tha==1 Fluz 22 7.4% 175D 12x12 Thermal Fluz 22 8.0% i g j 1775 2x2 Thermal Fluz 22 5.5% q el Total Coatrol and Worth. (% Ak/k) ] l} FNR Cycle Mash / Assembly Measured Calculated Deviation aj 17 6x6 6.57 6.41' -2.4% 3* q 67 6m6 6.24 6.30
- J. 9 %
a y. 91* 6m6 6.39 6.31 -1.1% 1' N-119 6x6 6.42 6.37 -0.7% Eh Li H 144 6x6 5.81 6.07 +4.5% ) e l,1 178 6x6 5.66 6.26 +10.4% a i 'New control rods installed l* i
.... _ _. _. _ 4. ___ _ _ _, c 1-a _ 2._. a m._._..___. _ 2. a. u _ j I j s-le 4 l1 4 ,G M L, f the transverse buckling for 2Ds. h comparison of the ediculated flux and 7 4 indicator reasonable .;) power distributions with, the FHR data gi:ven in Table 's i c; agreement with EES deviations in the range 4-104, h comparison is based J y on the *h===1 flux data obtained with, self-powered rhodium detectory at the 1 [1 core midplane and center of regular fuel elements. For Cycle.67, the power j distribution was obeminM from the asasured temperature rise across each j fuel assembly. 1 4} Control zod reactivity worth calculations were perfazmed for six q y different FMR configurations. h metBod for 'ob*=*=H the rod worths-1 I r !.9 was discussed in Sec. II.D, except tBat the fuel depletion in the special i fuel elements was also modeled. Accordingly, isotopic number densit es for the lattice regions were taken frca a LacFAnD depletion calculation i 'l for a special element at tSe corresponding Buznup points. h se n1 amber densities were then used in place of nG. ntmber densities, and the sequence of EMOIER calculations described in Sec. II.D was repeated. Full-core j.a 6m6 2D3 calculations were then perfozmed with all rods out and than 4 separate runs were made with eac5. of the three rods fnam-ted. N calculated b i J and measured rod worths are compared in Tatse 4. N M h messamed zod worths were da+amf nad from period====numents for rod T-- d positions in the upper half of tBe core. Considerable unceztainty exists in M d' the measured worths due to the ocaversion from half rod to full rod worth Md i and due to the use of an assumed effective delayed neutron fraction of.755d6 3.a 1, h calculated worths are in good agreement, although. the increasing differences N3 suggest that neglect of Beren depletion over many yearr of operation may be a at source of error. Despite these uncertainties, the basic approach for computing control rod worth appears valid for ing zod worths in EED and LED cores. 1 'i lI, ' 1 ,.,1
2- --z w w.- w + sp.n ~ "" " "~
- .w -~.
.- ~.~.,. b.., m,. : ,,4 .n . t.- D-19 g .e l, '.
- q..
3
- 4 q
J A pr*U=4==v calculation of the FMR power defect has been performed using the rethode 4escribed above. Eswever, the 2D5 calenlation,being a two~ l** dimensional calculation, cannot emplicitly account for the effect of axial j variations in fuel and moderator temperatures. Therefore, as a first attempt u. we have neglected ~ axial variations and have represented radial temperature profiles by assuming an average temperature for each, fuel assembly, which was determined on the basis of a 2Ds calculation (to deta-f na relative power d' factors) and measured FMR core temperature drops and flow rates. With this ?.} ' model, the power defect was calculated to be.164 f, which may be compared with the experimental value of.21% Ak We are currently-attempting to improve k. our model, by including a typical axial power distribution into the analysis 1,. by weighting the calculated temperature changes in an a y-,.iate fashion. r , 'l .a N' IV n m MTION OF EATCE AND EQUILIBRIUM CCgtE MODELS i.2 d;.j To provide maaningful and comprehensive evM6ns of M and pro- ~: posed LED fuels, it is necessary to model Both the intrinsic fuel properties 48 and the FNR operating conditions. For this purpose, two core configurations it nj. were analyzed for both fuels. The first configuration is a batch, core con- 'I-sisting of fresh fuel assemblies, while the second configuration is an equili-brium core. The batch. core configuration allous a 7d m of undepleted M 3, ~ and LED fuels, while the equi 14Mun core allows 7d m of depletion a characteristics and shutdown margin for conditions typical of FNR operation. 1W,' The batch. core model illustrated in Figure 2. Rhs 31'fre h. fuel assenhlies, n hj with, four special ass==h14== at control rod locations. The configuration is a. .j. ,y symmetric about the north /soutE midplane and was analyzed using Half-core ts. j calculations. a.. 1 j de a + , -.. _,,,,. _, _ _..,, - -, _,,,.,,,,,,,., _,,,, _ _ ~ _,. _,,.,, _.
y It i ,.r j'! i)'J>f 1 ' m l ' : 3: ,g l. II ' I e .s , u. 8 ,s _ s. 6 1 3 r..c L 7 8 7 s e m_ ,s n 6 5 4 3 5 o m a S 4 4 4 6 7 g n ., a. i 2 2 d 2 g 2 4, a C 4 g 3 6 7 o L 9 3 5 1 2 4 4 e r 3 2 1 2 s 5 o C . s. m u u 1 2 3 5 i 5 A 3 d. B r lt 5 g 3 8 4 6 b an i i e G cm l i ee pl 3 6 5 1 2 1 u _u SE q 5 5 s 4 5 6 E .=L 1 1 6 4 3 5 7 6 6 en u g 4 3 2 i F u. 7 4 8 ~ .a:. f o e nY n ir o lt i e yt dm n t a em o p my i mm us t a EI C s ar s A u g \\ i e fn \\ 9 o C e r A B o rt C o an l e h um c t ge a el nE B 2 2 .2 e a r .n N u g i _h F 4 g.-< S< do ,. f,' ; ,l. l lj!>; j i
. -. _ -.u.;s.. t._., . c. ,I,, f' e y A1** % the FMR core configuration and fusi shaffling pattern are, k in,racu, d.ter.ined my o,emionaz regersa.nt., an.e-- - i b model was developed to alleur a, meaningful comparison of operating characteristics for the IID and the proposed LED coreer. The v 't M m i core _ pig.re ,.se. -out , mag -e.a.i - 4 31 elements loaded at tBe core conter and moved outward to the core edge. a This schens==^f==- the reactivity worth at the oore conter' that maxi-c: ) mising the control rod wort 5. to achieve tBe required 3% Ak/k shutdown 1j aargin. To compare different fuel types in the equiti.hrium core,the end q ,} of cycle (EOC) k,gg was preserved'.Setween different casar. Preserving
- tj EDC k,gg provides the most realistic 7 M P of different fuel types, because it attempts to model actual FMR operation where g.
a core is depleted until the shim.rodar are nearl.y fully. withdrawn. [1-Along with. preserving the EDC k.g the core size is also maintained constant. These two criteria essentia11y as*= =4na the maxianan fuel o i burnup for a given fuel design. To achieve any Mah-- burnup would kj require that the core size be increased in order to maintain critica11ty. once the maximum fuel buznup is de+==4nad by preserving k with a fixed df core size, calculations must be performed to verify that the core confi-j A 3 guration has the required 3.0% Ak/k shutdown margia. Al*h e the fusi j burnup and power distribution are roughly constant during each equili-3 l l i. brium cycle, our eqn41Mun core configuration is chosen la such a way c 1 that the core configuration repeats every sixth cycle. / 1 0j The shuffling pattern in the equilibritna cycles divides 'the 33 regular 2 fuel element locations into eight loading zones as shown in Figure 3. 8 l Each regular element loading zona corresponds to core locations having a l i! Eu... 7 1. . ~
l - - - ~ ' L----- n.:..L w. L n ~
- r.,..
1 ,,k O ~ B-22 i .'. S 'i f nearly. equal fuel burnup, al* ~ P not necessarily equal burnup rates. f u Mes fusi is loaded into zone 1 and depleted fuel is discharged from Zone S. At the start of each cycle, one new element is loaded into zone 1, and the element in zone 1 is moved to zons 2. N fuel shuffling ,j continues to zone 8, where elemente are discharged. h.eight-sone 7 shuffling pattern for the regular elements is shown in Figure 4. h shuffling pattern forthe special fuel elements is different because there are six special element locations. A new special element t is added and a depleted element is discharged only every sixth. cycle. 4 i Mith this shuffling pattern a new special element is placed in special-4 l j zone 1 at the start ed cycle 1. h elment removed from Special-Zone 1 i is placed in ex-core storage for one cycle and then placed in W =1-I j zone 2 at the start of cycle 2..h sequence continues 1mtil the start of cycle 6 when the element from storage is placed into special-Zone 6 p]i and a depleted special element is discharged frum the core. This shuffling j i [q pattern for special elements is shown also in Figure 4. l ^ 7. N1N9e6'CF TEE.EQUILIBRI!2t CORE MCCIZ, AMD FNR OPERATIW l j h equilibrium core model was designed to be typical of the actual l
- I
. ~, FMR operation. Many characteristics of the FNR operation are well J represented in the equilibrium core analysis. In fact, a modified version of .0 1 the equilibriumcore shuffling scheme has been implemented at the FNR and has proven to be a practical and efficient scheme for loading fuel k. elements. Nonethelesa there are differences between the equilibrium j core model and actual FNR operation. These differences exist mainly ti j because FNR operation is more flexible than the equilibrium model. Fuel '1 i - ~..
t : hhl's .. l =._ ~.
== ~_ ' w- _ -wa-
- ^ ~
u. ~ . h-23 ,4 Figure 4. Equilibria Core Shuffline Sdiese y t ,i.., Regular Fuel Elements Core E M M sons cwle 1 2 3 4
- 5. -
6 7 e fj new Fuel -j 1 ~ i 1-1 + 2-1
- 3-1 + 4-1 + S-1 + 6-1
- 7-1 + S-1
- d<
2 1-1 + 2-2 + 3-2 + 4-2
- 5-2 + 6-2. + 7-2 + S-2 a e
3' 3 + 1-1
- 2-1
- 3-3 + 4-3 + 5-3
- 6-3
- 7-3,* 8-3 a 4
+ 1-1 + 2-2 + 3-1 + 4-4 + 5-4 + 6-4 + 7-4 + s -1 a }i 5 + 1-1 + 2-1 + 2 + 4-5 + 5-5 + 6-5 + 7-5
- 8-2 =
6 1-1 + 2-2 + 3-3 + 4-6 + 5-4 + 6-6 + 7-6 + S-3 a 'd e k l. q f. Dise ars. 0 _ _, _. - - _...... - ~ - I G I9_-. b 4... j e t-1 Fuel xlements. ] Cycle storage core zonding storage } some .e h +
- l 2
x 1 s-2 + x, 3 x 2 8 -2 23 L. 4 x .-4 x 3 4 5 2 + 35 + .x 4 5 6 2 5 S-4 + Discharge g 4 .1 i \\ f 1 i e i i
,L _ _..-_._..s__n..___m..- l U ~ 3-24 ~ y .y
- d Si
.( /q4 d elements need not be shuffled in any fiand pattern and the core confi-
- p p
guratim door not repeat periodically. This section describes charac-teristics of the equilibrium model'and actual FNR core configurations, 5 <sy and also explains important differences between t.he equilibritm analysis II lt; and actual operation.
- .7)
To verify the practicability of the equilibrium model, Table 5. l:y presente a comparison of the calculated dtp1111brium core parameters and r., 2 actual core parametere basedon FNR operation.. h comparisons indicate ti
- {
that the proposed equilibrium cycle represents a reasonably practical ] configuration for comparing the EED and IJD fuel desigar. On the average 'l fuel elemente are shuffled just as often in both cores. The calculated 1 i control rodworths for ten eqat'Mdum core compare well with the rod worths measured in Se FNR.
- f
'j The cycle length compariscar for the equilibrius andoperating cores i3 [ in Table
- 5. point out a difference between analytic models and actual i
operations. In the equiliBritna core model, cycle length is determined - j t t j by the discharge fuel burnup averaged over the regular and special fuel elements. In contrast, the FNR operating cycle length is the time interval c r;: between shim rod calibrations,which are required By technical specifica-m i tions whenever more than three fuel elemente are ahn M 44. In calculations ( p.} comparing the EEU and I20 fusis the parameter most indicative of the time y between control rod calibrations or operating cycle length is the burnup [h i [ reactivity change rata, rather than.the equilibritsa core cycle length, with 3 a constraine on the allowable core excess reactivity, the length of } /$ time the core can be maintained critical without shuffling more than .i f three fuel elements, thereby requiring rod recalibratias, is detezzined r 2 i r I I . n.2 m.
i: .?
- Q
- .
_,, ;d.; :;: 2 w. .4 . - %:g.,. a. ;guv. t3 >x n..i. as...x. m-25 ~ 4 .4 00 4 i4 Table 5 Comparison.of Equilibritan Core and Actual FtOL ly - Parameters. operating EED Experience
- Eauilibritan a
/ operating cycle length (.dayst 17.6 l} 0) aquilibrium cycle length (days-f 11.0 Average nismber of element [j shuffles / day .82 .90
- o.. ;
.j Average discharge burnap OSID/ element) negular 19.4 19.2 y' special 19.5 16.9 j' 5 Calculated koff ,Ij Range 1.022-1.026 1.020-1.032 4i ..i Average 1.024 '1.025 .i. a. j shin zod worth (4&k/k) '.] ' Rod A 2.20 2.08 !) mod 3 2.21 2.24 .i .j' Rod C 2.00 2.17 j Total 6.41 6.49 i$ I.:l t l-( L3, ';. tg Lj ' ' Averaged from Oct. 78 to Nov. 79 5 o, ' II dp, ['- p N.. l.I. l N .t 3 , - - _, -. ~. _ _. c-
.:w -= -.. .- ~_ .~. .a iy 3-26 v1 a 3 a N by the. fuel huanup reactivity change rate. v 10 m l1 ? vr. CORR BEUFEC2fEU A30G.YSES FOR TER BED AND LED FUELED CDRES na h important neutronics parameters analysed'for the EEU and LED q fueled corer are the temperature coefficients of reactivity, zonen 5 reactivity, control zod worth, dischaage buznup, and the shutdown n? y margin. W dmoor of these Nutzonic parameters for the batch core n ( and ega41** Mum core configuratione sEculd provide a basis for assessing ,[j the impact of LED fuel' on FMR perf-a= and utilization. Before N dis===fM the resulty of t5ase wisant; t5e actual IED and LEU fuel configurations will Be discussed. 49 A. LEU and IEU Foal Descriptica i1 e selecticaof tHe LED fuel design var based on extensive generic studier and survey calculations cazzfad out by Argonne National LaboratorN The I2niversity of =f"p=, and others. In addition, j l2 constrainer was 'v--' on the final design as a result of the specific ll l- ] FNR system configuration, FNR operational ennefAmrations, and the need to l %j aktain approval fram tRa Bac of an - d===t to the cazzent FNR operating L] license. These constraints, which. are unique to the FNR, Bad to Be ,f factored into the final LED design. $4 q 3amed on the above considerationa, the LEU fuel design selected for (,'] the FNR was identical in all axemmal dimensions to the EEU fuel as shown 4lf in Tahla 6 M conversion to LED fuel results in an increase in U-238 A-e.d loading by a factor of nearly 5 and an increased U-235 loading te overcome the jj increased capture in U-238. To accommodate the additional uranium ' loading, the v_3 g fuel anat thickness was increased'50% with a cozze r -diag reduction in the N
- s:
i I N -m,--,.. m ---w-m.___
- e +. " ~^~ -' : ' ". :' ' " --- ; ^ - ' ' ~ . -:.w.2. i ' : -. u. ..~.n.~, x: m -,,.,y,:y g.:7. a.,.. ?- .,: e. _ w.,... _ w, e a..:. g.~ v. 9-27 ~' ~ ti
- 1 3
S.. (!U-(j Table 6 EED and LED Fusi Designs ,. 4 ,3.
- 4 3
J. EEU
- LED 4
Fissile enrichnent 934 19.5% 4 !d mogular element fissile loading (gn) 140.0 147.3 .j Uranium density in fuel meat (w/@^d 14.1% 424 s } Fuel plates Per element is is Fusi neat thickness (in! .020 .030 4 i Clad thickness (in) .020 .015 I ,i Fuel plate thickness (ini .060 .060 a Water Channel thickness (in) .117 .117 lie l s A 2 ll* N' ) d. 1 t. A .~ a 1 1 i' r.
- d -
e e ' l, ll
l $~e.~.li k%d.ke\\ d.A .e ' vAs + ~ -- +- '1
- 1 6
- 4 Y
3-28 g g .d c c:y d h cladding thickness, hence keeping a constant fuel plate thickness. The d D FNR licensing considerations dictated the use of fuel with at most 42.0 w/o 3 f) uranium loading, which is considered to be an acceptable fuel design based aq on experianos and testing to date. Using 19.5% enriched uranium, the above LED design has 167.3 g of U-235' per fuel element, and results in y y the same excess reactivity for the batch core as the EED fuel design, aM as desired. D -1: Nd) ~ R. Fluz and Power Distributiona ] Calculated power distriMutions for both EEU and LED cores are - s compared in Figures
- 5. and
- 6. for batch cores and equilibrium cores, n
respectively. Examination of these figures reveals only minor hv M F. between LEU and EED cores. h largest change in assembly power, a 34 s. N. ?.y. relative increase, occurs ior special element locations. Additionally, l.ry there is a small shift in the power distribution away from the heavy ~ p;j water tank and toward a slightly improved overall symmetry about the j Q_ N.s center. There is no evidence of changes which would required detailed + thermel-hydraulic analysis in fact, the ratio of peak to average v op - !. e assembly powerikislightly reduced. N ] The calculated fast and thamat flux distributions are compared in eq - Figures 7. and
- 8. for the batch and equilibrium cores, respectively.
i }d ' j. The figures indicate that the fast fluz distribution is perturbed very E. dl little with LED fuel. This is to 5e expected because the fast neutron FI 4 production and removal rates are nearly equal for the two cores. h i. {k fast neutron production is approxDaataly constant because the core power Ji ' ,a
- T-Y T
T. - _ m-L a_. a c-va.c....... ; ;,. a,, ;;a au,,,g-. _ m j .gj. U N h, W W lamed bened W tuned ta==d named tw w w -p e o* I j e '. 1 1 } 1 , f-Assead21y Power (t) Assembly Fower (t) i
- s _
g:. A HEU Fuel A NW Fuel 3., B LW Fuel 5 LW Fuel r L e I 2.82 3.31 3.50 2.07 2.54 2.96 3.12 2.00 2.39 ~.: 2.79 3.28 3.47 2.08 2.54 2.98 3.15 2.83 2.43 l 2.57 3.53 2.56 4.68 1.72
- 2. 32 3.35 2.15 4.15 2.18 2".91 1.99 s,,
3, 2.57 3.50 2.62 4.66 1.11 2.28 3.34 2.16 4.16 2.22 2.90 1.99 'l = 2.62 3.70 4.59 4.83 1.67 2.62 1.87 4.27 4 32 3.96 3.02 1.98 g i 2.60 3.67 4.58 4.81 1.64 2.59 1.85 4.28 4.31 3.95 2.99 1.95 2.44 3.36 2.43 4.47 1.52 2.42 3.26' 2.20 4.24 1.94 2.72 1.90 l a 2.45 3.37 2.50 4.~49 1.52 2.41 3.25 2.23 4.27 1.94 2.70 1.90 j .r I 2.59 3.09 3.31 2.51 3.02 1.59 2.70 2.20 2.61 3.12 3.32 2.50 3.02 1.53 2.69 2.20 4 1 i 1.66 1.94 2.08 1.00 1.67 1.94 2.09 1.01 } l Figure 5. Astenbly Power Distribution for N W Figure 6. Assembly Power Distribution for NW j and LW Batch Cores and LEU Equilibriusa Cores ~ i j e ve j i e i h I
.._.__L..ZAM.lii e J.J. ; Z.1 " !. ~..
- , E T. C_. ' Z.. ~
i 2._.
- . z :. a.e. d!.. L.l.,.r ;..,;. i.< 2_. c.
i l' s f fE p Cove D0 uo 3 2 2 ~ i. r t S i t t i t b { t t { i i t t 1 i 80 raet 8 i i S l n a core t 1 t t i ,,,..r. 1 i LEU $ 8E**1 l s su i).I I 1 s i i s t.g3 rest. J g g I I a s j a I I' t. N. 8 } t t Y i o et 1 } e g i 8 g i f till b. a f c d I
- f. d s
g 9 l I 3 i k 1 I 1 8 s 't 4 { 8 { 'l 1 i I t t i 1 [ ? t { } 'l ~' t ^ o 40 60 80 100 120 140 0 20 Positiost (cut) .i s Firjure 7. Neutron Flux Distribution for Batch cores b h j
fa b f, K" s~r ~.,. ,e;4,- g1.~ , _ _. ~..yy .p. 7, g. c., .e ,,,y. a.,. 3-31 ..3 i e 4.. s \\4 t':b 4 1 IIII v 3 1 ~ n e 1 O o 5 , w g .e-.= x 2 . I 2 6 I,. c, o a i q l l l l u o a l ,a 3 w ww 1 A.4 i
- i
==-e
== _ a.m. e e e a.= j I O. "8 h u o I Q m. g O u Y 1 3^ + EEEEEEEEEE 'M M EEEEM'h k 1 r 94 ,.e 5 g g o w T' e .a u, w o a gn. 2, z s me* e t .) e ) h. C 'N M M ? z gM gN n x a a C 1 89 0F CE PC 91 g 0 i (s.EIc/u
- 01) xnt,g uos4n*N ET e
5 .W i Q
. -. _. -. - - - - --.-- -- - ~- -- -, --- - - - - - - - - - - - - - - - -
. Jai.... - ~.._u. . g-n .m.. ..r-- .. ~. ) C e u .= a-32 ($ ,i V:: t. 1 is held constant at 2 MW, w' ile the fast neutron removal rate is nearly h Il Fj ifi constant due to the similar moderatirg properties of the two cores. That -sg is, the water channel dimensions are the same. d y Bowever, one espects to see significant changes in the incere thermal W flux distributions between the IEET and LED fuels. a For a well-moderated
- h=== 1 d..
reactor at constant power, the thermal flux is nearly inversely h proportional to the fissile la-dW, hence one espects a reduction in thermal
- t. :
,'0.] flux for the LED core. ld This ei'fect is readily apparent in Figures 9. and 10 9d deze the *h==-1 flux in regular fuel elements is seen to decrease by ?! about 184 For special fuel elements, the reduction in thermal flux l is only about 124 1lhis mitigation in the thermal flux decrease results from the effect of the thamal flux peaking in the large waterhole. This 4 ' d. peak is _*--M_y dependent on the fast flux, dich is not significantly different between the LEET and EED fuels. Since the thermal fluz level '] within the speelmi element will be affected by the waterhole peaking, the overall effect is to mitigte the decrease in thermal flux. 1, L.4 As noted cha L] for the power distribution, there is a slight shift in them=1 flux away bl from the heavy water tank toward a slightly improved overall symmetry i about the center. l1 i, b Excore thermal flux levels are important in the FNR because samples -a e are generally irradiated in the reflector regions. l~. In particular the heavy water reflector is of greatest interest because thermal a , e. neutron beam tubes extend from the tank to the laboratory areas. Coe-Q parisons of the thermal flux levels in the light water reflector show ] a flux depression varying from zero to 64 ll At distances well into the !j light water reflector, there is no change because the primary source for ,ye ) ~ te z. w=
id O - O u %ECYm.:.z;G L M ;-w' apm_gr y
- ,e
,. - y t j- ' l':' r Assembly-Awaraged h ermal Flux (10 m/m -sec) Assembly-Averaged hermal Flux (10 n/cm sec) A HM Fuel . ]' A HEU Fuel 1 B Iml Fuel 3 5 LEU Fuel ..!I3 ) 1.01 1.19 1.38 1.37 1.29 1.09 [ 1.22 1.40 1.4e 1.05 1.20 1.26 .87 1.02 1.19 1.18 1.11 .95 /C 87 1.16 1.57 2.40 1.84 2.23 1.33 1.00 ,7:. 1.11 1.51 2.44 2.00 .96 1.30 2.21 1.74 .75 .98 1.33 2.15 1.58 1.99 1.14 86 d .86 1.27 2.20 1.92 1.84 1.74 1.37 1.02 (( 1.13 1.55 1.93 2.03 w -i i l .97 1.33 1.66 1.74 .73 1.00 1.97 1.65 1.56 1.48 1.16 .87 p ) 1.05 1.44 2.34 1.92 .79 1.16 1.5J 2.37 1.88 2.20 1.34 .97 i l .92 1.25 2.14 1.67 .69 1.00 1.31 2.12 1.61 1.97 1.14 .83 j! 1.21 1.39 1.92 1.34 1.11 p,,[ 1.13 1.32 1.41 1.04 1.19 1.73 1.15 .96 \\ .99 1.14 1.22 s., .83 .94 .98 .93 ..2 .72 .81 .84 81 j 7p i Figure 10. Hermal Flux Distribution for NW and + '.e f Figure 9 hermal Fluz Distribution for NEU and LEU Equilibrium Cores s, LEU Batch Cores fd' i j .a n i .s l 1 )
- 4; 4
-{
..-. w.N a.:-;.. u. : L! $? 2, ~
- a. u.
~ ~- ..:s. n n J, e-34 ~ z: 1 C1 i6'sj %-at neutrons is the slowing down of fast neutrons leaking from Mj the core. ht locations closer to the ooze the contribution to the
- =
,] thermal fluz due to h==1 leakage from the core,1,s larger and, since '3 the thermal leakage is decreased by.the increased fuel
- loading, there
,s. i !] is a corresponding 1T freater decrease in the theamal flux. Consistent m d with this explanation, the relative thezmal flaz in the heavy water y tank is depressed somewhat more (4-44) than la the light water reactor [a due to the increase in tBe relative contribution of thezmal leakage to { the heavy water tank,thezmal fluz. C. Temperature Caefficient of Reactivity and Power Defect
- q
[ Se isothermal temperature coefficient of reactivity was com-puted forthe batch core model to be -0.4 pcm/4 for the EED fuel and b -12.6 pcm/4 for the I20 fuel. Se large increase is due almost a p>. exclusively to the fuel Doppler effects. For the EEU fuel, fuel . ') Doppler effects are negligible due to the small amotait of U-238 present. J 71 For the Z20 fuel, the large amount.ofU-238 increases resonance absorp-o L1 tions in*U-238,resul' ting in much larTer sensitivity to fusi temperature. l3 [ 2e principal contribution to the temperature coefficient of reactivity for .t ] both the EEU and 125 configurations is, howeWor, the effect of the reduction in moderator density on leakage and moderation. a L' As discussed ea rliar, the procedure for calculating the power defect q I.) has not been fntly developed, and a compariada of the difference in the p) Power defect for the EED and I20 cores has not been made. Eowever, N ].) a pret M=q estimate has been made based on the observation that the d 1 increase in the fuel Dcpplar effect is the principal difference in the temperature effects 1$stween the EIU and the IJU designs. The change la
j. _;.- -....,,..-...,1_,., ,x.y,g.;..g.g. .._7 . y.e u, ,.1 .-3s l3N L1 c:e, power defect of reactivity is estimated in the present analysis on the dfi.] Based on an average basis of calculated temperature coefficients. s .gi core temperature rise of 7'F, the power defect for the LEU fuel is e ,a '.t )y-estimated to be about.03% Ak/k larger in magnitude than for IEU fuel. s 'd For a typical FNR configuration, the excess reactivity required to 2 overcome thepower defect would thus change from a measured value of '4 i 7 .21% Ak/k for EED to.24% Ak/k for LED. a1 ~ D. Xenon Reactivity Worth The zenon reactivity worths of the EED and LED fuels are r.y compared in Tables 7. and 8. for the batch and equilibrium core models, For these cores the menon worth is 4-44 lower for the respectively. There are two competing effects responsible ,7 LEU than the EEU fuel. ' ~ First, the larger U-235 loading for the LED core for this decreases .A results in lower incore thermal flux levels, with a greater (10-124) I Second, the increased fuel loading gives the ? xenon concentration. F, As total core LID core a larger neutron absorption cross section. ,J 2S' ], absorption is increased, the fractional absorption in menon, and thus the xenon reactivity worth, is decreased. Although these two effects
- 1
]4 =- tend to cancel one another, the latter effect dead. nates and menon reacti-dr g vity worth is lowered by about.1% ak/k. 1'i],- 2 1 m. M E. Fuel Cycle Analyses 11,.* 4 Equilibrium fuel cycle analyses have been performed for the 4 T. I . e The compari- ,i HEU and LED cores and the results are presented in Table 9. j-son of discharge fuel burnup,which indicates a 50% increase for LED fuel, 1a d should be viewed with some care because of the extreme sensitivity of s-d a
- l. s l-qr
!i T
u. e ._ub:..,..w..n.. m % ;;... w.. ua l-L~.. p l. 1 ...i L4 3-34 ! "a. e Idl .n -1 Table 7. Batch Core Reactivity Comparisons 4 ~ use ..t.m chano. p.] Ud., Cycle length (days) 12.0 10.0 c<., p], Burnup reactivity change rate (tak/k/ day) .028 .02 -284 ,j Y shin zod worth (4&k/k) j A mod 2.37 2.26 ! '.4 5 Rod 2.22 2.12 i ..j C mod 2.'37 2.26 +k y Total 4.97 4.64 -4.7% 4 Excess reactivity required (%4k/k) xenon poisoning 2.50 2.40 -4.04 'i
- j Burnup effact 0.28 0.21 Power defect 0.21 0.24
-l Total 2.99
- 2.85
-4.7% h shutdown.margia (tek/k) 3.94 3.79 -4.0% 3 ' s 5 Table S. Equilibrium Core Reactivity Comparisons t EED TJU Chance ~ Cycle length (days) 11.0 16.5 50% s: Buznup reactivity change rate (%Ak/k/ day) .028 .021 -24% ,.1 shia rod worth (%Ak/k) ':l 2.20 2.14
- ^
A mod a med 2.21 2.15 Ef C mod 2.00 1.94 I. : t l'; ' Total 4.41 4.25 -2.5% L.;. Excess reactivity required (%Ak/h) xenon poisoning 2.24 2.17 -4.0% Burnap effect .31 .37 Power defect .21 .24 j'h Total 2.78 2.78 0% (1 shutdown margiA (%Ak/k) 3.63 3.47 -4.4% (2 L.', E!
- u4 f$
y;3 r'.(; ! j i E t i I
, _ ;. - L - .. m nq 33.g. ;q.y-vr...y. a.u-vg y ; g 3 .-.3.;.;g, g ;g- _ - ~ -r n-37 s
- ?
1' Table
- 9. Equilibrium Core Fusi Cycle 1
3 1 W W OnanGe s Q Cycle length (daysl 11.0 16.5 50% l '.l Dt..n.ng. buzn, s'j OerD/ element) Regular 19.2 28.7 49% 7 4=1 16.9 25.9 534 Regular element Fissile loading (gal
- s. -
Fresh 140.6 167.3 204 '.i Discharge 116.6 134.3 15% Core 1~=M ng ] Beginning of cycle (gal Fissile 4550 5320 17% I' U-235 .4549 5260 16% Burnap reactivity change rate (4 Ak/k/ day) .0279 .0211 -24% 2 9 I i 1 I. I ,l 4 4 .j d P A]. a ' l l .3 1 '0 s 1 .,d W y'j,. ys I
C m. a. a.... __,,,_,,. < ; b, ~..--..~._....,a. 7 m l'
- 4 3-38 O
l
- 3..
f.-j 01 ,1 discharge fust burnup to core reactivity for the Fim core. For example, 4 S in an equilibrium core analysis comparing two LED core configurations, Tj a 0.5.4 Ak/k diange in eigenvolue resulted in a 15% increase in the y This sensitivity is a consequence of the relatively M discharrJe burnup. i low fissile depletion ob*= M in the FIR core. Typically only 17% of ' i, the initial fissile inventory is depleted from the IED fuel elements +i? t; before discharge. A significant change in the discharge fissile v'.; depletion con be achieved with only a small relative change in the total .1 c, core fissile inventory, which is, of course, proportional to core ~ t iA criticality. Thus, the predicted dischazgo burnup is very sensitive, 4 to the calculated core criticality. In addition, this sensitivity N This d is magnified by the in/out shuffling pattern used at the F15. .i l[ shuffling scheme loads the depleted fusi elements into regions of I lower neutron importance. Thus, changes in the discharge burnup have a ri 4tively smaller effect on core criticality than with otRar' shuffling [. j 4 schemes. Because core size and core criticality are directly related, a Y dischaage fuel burnup is also sensitive to core size. Thezefore, to provide valid camparisons a fized core sise was used in our equilibrium core analysis. Calculations for both the batch and equilibrium cores f.j f indicate a decrease in the burnup reactivity change rate with m fuel. The decrease in reactivity change rate is a consequence of two factors. 4 K V Most importantly, the core fissile loading is higher with LEU fuel, U hj so that the fractional fuel depletion rate, and the burnup reactivity I.4 ~ j4 change rate, are lowered. Production of Pu-239 in the LEU fuel also causes u 4 a decrease in the burnup reactivity change rate. Funi depletion calcu-q lations indicate that the Po-239 production rata is approximately 84 l 2 ,u of the U-235 loss rate in the. LED core. This may translate into a l 10-15% decrease in the burnup reactivity change rate, depending on the - _ =.
.,., g. _ .g... g ,;A.;a.~ w. A L 7, ]'b a =39 4 9 n. .1 j reactivity worth of Pu-239 vs. U-235. Caparisons of reactivity .I] changes in the M' and LED batetL cores show that during the first 50 1 1 full power days of operation reactivity is lost more rapidly than at 14 later times due to the effects of annon and samarium, as well as fuel )
- 1 N.
depletion. Once this initial transient has passed the burney reactivity 2 change rates are nearly constant and,,.htely 25 to 30% lower in the LEU core. In the eq=414hdum core calculations the burnup reactivity change rate is affected by the fuel burnup distribution as well as total Y core fissile inventory. For this equi 14h d e core model the burnup .i 4 reactivity change rate is decreased by 244 with the LED fuel. Thus, l as explained earlier a 30% increase in the TAR operating cycle length is e cted. 3 F. Centrol Rod Worth t -- ~ ~ ~ shim rod reactivity worth 7 M acas for the A, 3, and C rods 'l are given in Tables 7. and 8. The LED batch core comparison shows a j 5% relative decrease in shim rod worth. This decrease in rod worth T may be explained qualitatively by noting that, to a good approximation, -.f j the FNR rods are black and, for a black rod control, rod worth is nearly proportional to the product of the control surface area and the thermal diffusion 1ength in the surrounding fueled region.20 gg,,, t the thermal diffusica length in the LED core is 2.05 cm vs. 2.18 cm in the .a l. EED core, this simple model predicts a decrease in rod worth of approxi-p Q mately 64, which may be compared with the calculated 5% decrease in rod worth for the baten core configuration. In the equilibrita configuration i's the total rod worth decreases by only 34 This smaller decrease in rod Y worth indicates that factors other than the shorter thermal diffusion ?) 1.nge are.1so.,,.ct e g ee ca1cu1at.d rod. ore. ,od were ca1 _ y, l .. -.- ? '._*? T.~......_..,.._...,.._. -....: 2 *_._ _ ~ -_
...u--_.-_. . _.,4-..,2, ,22 I t ? .1 a
- j c
.-4o b9d lations for various equilibrium cores show that rod worth is also fdy affected by the discharge fuel burnup. As discharga burnup in the N 43 outer fuel elements is increased, the core fissile loading and core -l '.J S reactivity worth distribution shift toward the core center causing the 34 M fp rod worth to increase. S us the higher M =>h= M e burnup in the LED 7 equilibrium. core has a mitigating effect on the decretase in rod worth, 'a 'i and the net of fact is a. 3% decrease in total worth. ) s.. t [.j G. W dman of Shutdown Margin he most significant safety parameter related to core physics analysis is the shutdown margin. 21s parameter is obtained by sub-tracting the positive como excess reactivity required to overcome annon pod==W, fnel depletion, and the power defect from the total control rod reactivity worth. Se present technical specifications y L require that the shutdown margin be at least 3.0% Ak/k. Any difference between the estimated shutdown margin and the limiting value represents emeess reactivity available for = W = ts. a. [ For the LED batch core, it is seen from Table 7. that the lower excess
- I, reactivity requirement is overshadowed by the decrease in control zod reactivity worth. S e shutdown margin of 3.79% A k/k is lower than for the EEU core, but is still well above the 3% Ak/k requirement.
Addi-tionally, with the most reactive rod fully withdrawn, the shutdown margin 1: b, is 1.53% Ak/k, well in = === of the.75% ak/k required. y ] Coupering the EEU and LIU egm W= core results in Table 8. i< [ shows that the shutdown margin decreaser slightly for the LED core. The computed value of 3.47% Ak/k is well in, excess of the 3.0% Ak/k require-u +4 meat. Also, the shutdown margin witB. the mort reactive control rod fu&ly withdrawn in 1.32% Ak/k., well.above the.75% Ak/k required. 1-3.. _. _ _... _-g
.._ m,.g.,y. _.m. a,,w,3. _ _ -. ,.___ w..g _ u.._..y.7 _ s..s. 4._;,,, ,;.r_.. ~ .... ~... n... ~ _., , gy
- . 4 3-41
,j { VII. ALTENIATIVE LED FUIZ. DESISits /; } The LED fuel design was selected for the full cors' demonstration )n based on a criterion of czesting miniamm perturibations in reactor perfor-d} mance. To determine effective umys of laproving core performance, e.g., .a s M the core fuel burnty, control rod worth, and exoore flus levels, several
- 3 i
dteznative LED fuel designs haya also been studied. R p this section pzemente zesnits of an -" Mun ones study c---*= d, } the LEU fuel with an alternative higher loaded fuel design. h two fuel designe are compared in Tabla la. h fissila laad*== for the alterna-tive fuel design has been increased to 175 gm: by increasing the uranium \\ density in the fuel amat, wit &out changing element dimensions. h impor-I tant conclusion of thin alteznatira. fuel design stadr'IE. tBat it anar Ba a. possible to significantly increase fuel buznup without degrading,other reactor performance charac*=-+=** = The egn" Mum core power and thermal fluz distributions for the o f two fuels are compared in Figurer 11, 12 and 13. M power distribution ] comparisons show only a slight shift for the higher loaded fuel, 4 p despite the increase in fuel 'buznup at the core edges. A anziata n g increase of about 2% in assembly power occus ar the core center and .,j the heavy water tant h ^=== 1 flux distribution comparison shows a >] anziatas decrease of lest than 34, suggesting that the flux depression .1
- 4 j
caused by the higher loading is partially mitigated by the highar fissile t ,j depletion. g. j, Equilibrium cora calculations predict a 26% inczwase in cycle length F;, and discharge burnup for the 175 ga fuel. As explained earlier, the Nj higher discharge burnup results because the fuel can be depleted longer ~ tdLile Raintaining a critical eq.11111rium configuration. The 175 ga fuel 'j '. s i 5 l
.,.. _. 2m - E:, , [:; \\ .....s-- B-42 .f ,( i Table 10. LEU Fuel Design Comparisons Reference Alternative 3 Design Design Otance ..' ) Enrichment 19.5% 19.5% 0% }l} Regular element fissile loading (gal 167.3 175.0 4.64 Uranium density in fuel seat 42.0% 43.9% '4.6% Element dimensions 0% .e aquilibrium cycle length (daysl 16.5 20.8 264 =1 <l Discharge beanup (MND/elementl Regular 28.7 36.4 27% W al 25.9 32.5 24% Burnup reactivity change rate (%Ak/k/ day) .0211 .0207 -2% shia rod worth (44k/k1 ~ c )J A mod 2.14 2.15 B nod 2.15 2.14 I C mod 1.96 2.00 l Total 6.25 6.29 0.6% 4 Excess reactivity required (%dk/k) !:l Zenon poisoning 2.17 2.15 Burnup offact .37 .43 Power defect .24 .24 Total 2.78 2.82 1.4% shutdown margin (.%dk/kl 3.47 3.47 0% I' [: i-r. !)i'. n., let a l "'.}
- +
u
- b
.g
- a k
1 I ** I a e
T zG Guw ..;. c z.w&.:.:.2sa 1.:.k:h.. - * '- _ .u n ..L:
- x...i;,.&%
LL.,him M:W :..:.t: :w al.km.a u. '.i i ~. ' M ' head W W '~ f f -4 I t i 1 Assembly Power- (%) Assembly'-Aweraged Wernal Flum(10 m/m secb. 2 ,r. [ j 1 ) \\ A 167.3 gm L8U ~ A 167.3 gm LEU B 175 gm L W g l175gmLEU B' r f: b 1 i q 'I 3.15 2.83. 2.43 .87 1.02 1.* 9 1.18 1.11 .95 '2.08 '2.54 2.98 i a e t 2.07 2.55 3.01 3. 2,2 2.88 2.48 -I .86 1.01 1.18 1.17,1.10 .95 1.71 2.28 3.34 2,16 4.16 2.22 2.90 1.99 .75 I.I'.94jl.33 2.15 1.58 1.99' 1.14 86 ? 1.68 2.24 3.36 2.14 4,23 2.26 2.95 1.99 .73 .96 1.31 2.14 1.56 1.98 1.12 .86 ).g 'l 1.64 2.60 1.85 4.28 4.31 3.95 2.99 1.95 .73 1.08 1.97 1.65 1.56 1.48 1.16, 87 9 3 I 1.59 2.56 1.79 4.34 4_an 4_n1 3 nl 1_e1 71 1.05 1.96 1.62 1.53 1.46 1.14 86_ h ) 1.52' 2.41 3.25 2.23 4.27 1.94 2.70 1.90 .69 1.00 1.31 2.12 1.61 1.97 1.14 .83 .m. i 1.48 2.38 3.25 2.22 4.34 1.90 2.68 1.87 .67 -.97 1.29 2.10,1.58 1.96 1.13 .82 y, i 4 y 's i I ) 1.04 1.19 1*73 1.15 .96 2.50 3.02 1.53 2.69 2.20 1.02 1.16 1.72 1.13 .95 2.48 3.02 1.46 2.66 2.17 a .72 81 .84 81 q i j 1.67 1.94 2.09 1.81 .71 .79 .83 .79 .[ l 1.65 1.92 2.08-1h77 t 4 1 Figure 12. Hermal Flux for 167.3 and 175 ga Im j l Figure 11. Power Distribution for 167.3 and 175 gm Sydlibrium cores LEU Equilibrium cores 4 k j I
- j J
2 i d.
- 6L.-;:..1 El..--- L BLXXJ hC. IL,.&. rW..
. :a.. l..l.-.n., .ha.. c... '.:.1 t'.'.:D.. : :... G'? T< ' di: .i ,/-.- I f 1 ,i j. -q se f 3 467 + 175 rest i l l E i ~ S s E 2 l l 8 8 5 i n d, I 8 5 i .e I 8 8 8 5 1 i gN 8 I l g g o l 8 HA i l !.Ijl~ - e$lj E D.0 i j i j I E I put g, i ,! :a i a. = ~ 8 8 i I. e i 8 167 + 175 j a .e -.1 p i g i y ~ E i i i i l. E i lIII i i a e s l 8 ,i 5 8 e s l E i i l l i m I o I 0 23 40-60 80 100 120 140 I Positlost (on) f f ? Figure 13 Dieutron Flux Distribution for 167.3 and 175 gen LEU Fuels ,-( k
.t.: .a g-. r _, ;._,,,..., ;. y.,,,..., ,.y. -. -. - ~:w = J '. ./ D-45 s e is initially more reactive Becanon of the higher fissile loading, and loses reactivity due to fuel Buanup at a clouer rate; as'seen by the 2% decrease 3 3<. in burnup reactivity change rate. As noted earlier, however, care must be s.1 taken in laterpreting these results because of the extreme, sensitivity of discharge fuel buzngp to core reactivity for the FNR. d' Calculations of the reactivity effects for the two LED fuels a ) n
- s predice no change in santdoun margiu with, the highar loaded fuel. h
,,lj oontrol rod worth increasesbyan almost insignificant amont because s .; } ,, j the higher core edge ampletion toads to increase core contar teactivity j worth. Thas tan shntaoun margin, er well as tRa core power and thammel flux -on, are not e~_tzr grad.d even og th. -a ,e d,,, burnup is coneta=6y EigEar' for tbs 175 gm foal Ame4-n d. o .I vm.==== 4 A 19.5% enriched fusi Amefy ygg gg1ggged ggd ig being fabrigated [] as part of the FNR 6mmonstration project. h fuel har a 167.3 gram h)I fissile loading and 18 fusi plater per assembly. To accommodata the y \\ L increased uranium contentwit5 cut eManging fuel plate or assembly dimen-l; siens, the uranita loaaing in the fuel seat has been increased to 42 w/o ia 1
- =
and the fuel thicknese har been increased 50% while decreasing the clad thickness. Extensive efforts have been devoted to developing calculational .h methods for analyzing EED and LED fueled research reactore. These methods make use of existing well verified computer codes whenever ]i possible and have been verified by comparison with data free several 4P research reactor esafigurations. s $e ijl. n !H' Li A_ '4
l w. <.--.u. ( D-46 H l -l 6 l ,;j To study all sapected effects, the EEU fuel and LED fuel were analyzed {.] and compared in both batch and equilibrium core models. h se comparisons yj serve to quantify predictions made on physical grounds h higher' q 74 fissile loading required to overums the additiona10-238 absorptions a m 'l results in a large decrease in the in-core thermal fluz. h umal flux
- i,j(
levels in the reflector are depressde to a lesser degree because the t y fast neutron leakage is nearly constant. h power distribution is not "it I! perturbed to a significant degros. m eq= tht= cycle length, and f.! w g Af Mm9 gggi gggggp are predicted' to increase because t5a LID core ? can be depleted longer utLtle maintaining core criticality. THare is a ,3 small decrease in the :xmnon wortE.and control rod worth. caused ~ Br Mf=* h, j U core absorption. Comparisonst for tBa equilthrium corer indicata that the reductica in rod worth, aar Es aitigated By the increased fual Burnup +4 j of tEs LED core. Most Deportantly the comparisont predic't no significant, 'i change in the core sEntdown margin. 1 h analytic metBoda descri5ed in t5e paper Have provided a reasonable U h) assessment of tBe Depacts of LED fM1 ca FNR performance. Ebutver, there remain areas which deserva further study ens additional refinement. g 1,. i; some specific itens currently Leing investigated at '::he University of p
- d ij Michigan are a
3 1) Development of a new data library for the LEDPARD coda d L:!j based upon ENDF/D=IV data. 2) Investigation of optimal equilibrtim core configurations using
- m l-i linear / dynamic programming concepts.
In [ 3) Continued investigation of discrepancies between measured and l:: !.i predicted rod wortiss, with a careful examination of possible s
- t boron depletion effects.
A r j 4) Calculation of 8,gg, the effective delayed neutron fraction, i' for both RED and LEU cores. 7 _% - .u 4-
m-,,.. n_. . _ _,_........ -. 9. g.. y,7.. _r.,.,...,. ., - ~.. _. 3-47 l i 51 Reft - t of the power defect calculation to include non-1 miform axial effects. .3 i 6) Refinements in the determination and use of burn g dependent j non-lattice peaking factors for the LEOPARD oods. 71 Extensive analysis of the leakage flus levels in the Fim m heavy water tank and beam port locations. Calculations I are planned using both discrete ordinates and Monte Carlo i methods. I 1 B 9 9 I J e } 1- .k' .i i m Li l 1 !) '.i J ,.q ) s J e 'e I. le hG il't t cj
- ].
1 4 .I i: 1 .I v.7
.._.2. .. w.w c, 1 3-48 ~ ,1 .a
- .'a:
REFERENCES ? 1. D. Wehe and J. S. King, "The FNR HEU-LEU Demonstration Experiment", (to be presented at this coeference). d 2. E. Ecmoriya, J. C. Lee, and W. R. Martin, Trans. Am. Nucl. Soc., 32,, .y Suppl.1, 31 (1979). ]l 3. F. B. Brown, D. C. Losey, D. K. Wehe, J. C.* Lee and W. R. Martin, Trans. Am. Nucl. Soc., 33, 746 (1979). a y j 4. D. C. Losey, F. B. Brown, W. R. Martin, J. C. Ime, and R. Komoriya, .j Trans. Am. Nucl. Soc., 33,, 748 (1979). 3 .i f 5. W. Kerr, et al., " Low Enrichment Fuel Evaluation and Analysis Program, !j Stammary Report for the Period January 1979-December 1979", University j 't of Michigan Report (Jan. 19801. -d 4 6. D. C. Losey, F. B. Brown, J. C. Lee and W. R. Martin, Trans. Am. Nucl. Soc., 34, 569 (19801. 7. R. F. Barry, " LEOPARD - A Spectrian Dependent Non-Spatial Depletion Code", WCAP-3269-26', Westinghouse Electric Corporation (Sept. 1963). 4 8. J. Barhen, W. Rothenstein, E.' Taviv, "Se HAMMER Code System", NP-565, Electric Power Research Institute (betober 1978). 9. W. W. Little, Jr. and R. W.* Ehrdia, "2DB User's Manual-Revision I*, } BNNL-831 REV1, Battelle Pacific Northwest Laboratory (Pehruary 1969). 10. W. W. Engle, Jr., *1 User's Manual for ANISN, a One-Dimensional j.j Discrete. cxdinates Transport Code with Anisotropic Scattering", .;,j K-1693, Oak Ridge Gaseous Diffusion Plant (March 1967). .3 r y 11. K. D. Lathrop and F. W. Brinkley, TmdMN-II - An Interf aced Expor-table version of the TWOTRAN Code for Two-Dimensional Transport", d Los Alamos Scientiffc Laboratory, LA-4848-MS (1973). i 12. D. R. Vondy, T. B. Fowler, and G. W. Ceningham, " VENTURE: A Code L; Block for Solving Multigroup Neutronics Problems Applying the Finite-Difference Diffusion Theory Approximation to Neutron Transport", ORNL-l 5062 (19751. i-13. M. R. ':heys, Nucl. Sci. Eng., ,7,,, 58 (1960). q 14. J. Hardy, D. Klein, and J. J. Volpe, "A Study of Physics Parameters in g Several Water-ModeratedLattices of Slightly Enriched and Natural E Uraniums, WhPD-TM-931, Westinghouse Electric Corporation (March 1970). l-fi 15. E. B. Johnson, " Power Calibration for BSR Loading 33", CF-57-11-30, cak Ridge National Laboratory (19577. ~ L 16. J. L. Shapiro, "he void Coefficient in an Enriched, Water Reactor", b. ' fuel. Sci. Eng., 12, 449 C19621. l1: lt ,U ~ -
..: A. w :
- m. _
-I MT 1 i 17.
- 3. Eamoriya to J. L. Snelgrove, " Reduced Enrichment Fusi Element i
Loading calculations for the Ford Nuclear Reactor *, Argonne National
- I Laboratory Internal Memorar.dum (Februazy 14, 1979).
i t 13. J. E. Natos and K. E. Freese, Trans. Am. Nucl. Soc., 33, 739 (1979). 9 .. Aj 19. E. Eamoriya, Trans. Am. Nucl. Soc., 3)3, 745 (1979). If 20. J. J. Duderstadt and W. R. Martin, Transport Theory, wiley-Interscience, ( New York (1979). 1 ) .1 i Au i 'l l \\ l i I i J ' i ]' ? .i. lI { IT i J 1 .i f i 1 I! ^ O L 4
. =.... S . = &cLA $z u O A i'l-51 3 y e' ) j, APPENDIX C A h DOCUMENTATION FOR DATA BANK 1 In this appendix we present a limited selection of the h data describing the current and proposed FNR fuel elements. I These data are included to provide documentation for our
- C' calculations and hopefully are sufficiently detailed to f'
allow others to make similar calculations. Vendor drawings 4" of both the HEU and LEU fuels and also the FNR control rods j] J are presented first. By using information gathered from
- j vendor drawings, fuel specifications, and a number of other j
sources, Table C-2 has been made which summarizes the fuel element dimensions and composition..There is considerable uncertainty in the entries of this table because of the f large tolerances in the fuel element specifications and '], because there is very little information describing actual
- J as-built fuel element geometry and composition.
The data ti. represent our best estimates of actual fuel element geometry and composition, and are consistent in that different fuel element types are compared on an equal basis. We also include a limited selection of a reference j cross section library in Table C-4. The library was generated with the LEOPARD code using the data from Table [" ' C-2. describing fuel element dimensions and composition. j. 2 d* 2 3*
- $s1 1
o /W b v, N J ?. < y< c' 4 3 1' i g 9-A L L
... __ _._ _ n,g. 3 2 ,- a Table of 'ontents for Appendix C C 3 A;.j
- .1
[q Figure C-1. HEU Alloy Special Element il Figure C-2. HEU Dispersion Regular Element a j Figure C-3. HEU Dispersion Special Elemedt a Figure C-4. HEU Dispersion Fuel Plate %e Figure C-5. LEU CERCA Regular Element Figure C-6. LEU CERCA Fuel Plates Figure C-7. LEU CERCA Side Plate f Figure C-8. LEU NUKEM Regular Element Figure C-9. LEU NUKEM 5pecial Element L H Figure C-10. LEU NUKEM Fuel Plates Figure C-ll. LEU NUKEM Side Plates a Figure C-12. FNR Shim Safety Rod Figure C-13. FNR Fuel Element Schematics G! d Table C-1. fMR Shim Safety Rod Geometry and Composition M gj Table C-2. FNR Fuel Element Dimensions and Composition 1.. [ff Table C-3. Chemical Composition of Aluminum Alloys Table C-4. Two-Group Cross Sections Generated with the L, LEOPARD Code M l^ '.. l (: o P, [j li I$ dx ,g 4 i'b LiJ'l =
..y .c. 4,.,.3.,, s, #...... t. e 4 .cr.._...:. ... -..,,. _,, s f. 3' e-
- .'s Pi g
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- s a
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- .h.i.
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- j
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- 3 3
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==dy.,_._ ym a v v w w t t t s }- I i t l ACTIVE Oc FUEL t a r l- ~- - 7 p k_.- - - ,y7 N 7l i g s i sc=== i m x\\ f, I 7 l N / i s\\ 8 p
==::a: / ', , \\ C -W k i \\ C D T\\\\\\\\ M M\\ M \\ M M u u RW u\\unu\\Mg i I / ' I 8 C 4 g i N / ! l i s m 2 gi l t l 1 I \\ T 2 N '1 N r ,- / i / l h W J = u t 3=189" I g 5, /[ NATERGAP \\ ~ E \\ \\\\\\\\ \\\\\\ \\ \\ \\\\\\ \\\\\\ \\\\\\\\\\\\U N s'1 1 3 \\ J ,i$ ~ r - / n n , y t h. l e -: M s N r 'y' ~ / x F Ng e l g p l g [ / e y F I ~ 8 ' N / ' si g :r r ' s -f .2 a g h - - -f- -,,,,,- - - - - m g j - l t _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _e Q I I p C C::::::::m I 4 j. ut g 5: [ CLAD THICKNESS V i } y '. E *2* ..o FUEL THICKNESS 1-l - [, Itegular Element Special Element ..: 6" . e' IFig.C-13. ' {j.. l. FNR Fuel Element Schematic e r;: ..P Tin g._
t --.g,- s .g, t.._.. i ,i .l}
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y2.: Table C-1, 'c;.. ]' ', FNR Shia Safety Rod Geometry and Composition ef composition baron stainless steel,1.5 w/o natural boron k number densities * ( 10 24,g,,,f,,3) -d. 10 .001108 fi B ~ 11, .005184 ', ~ Fe .05644 s L j' .. i Ni .0113
- i h
Cr .0164 q 4B . -l < I e y f.
- besed on ecmposition and density of baron stainless steel fzca :
i!;
- w. K. Anderson, R. L. Riahi er, R. A. Earlow, and G. J. Geogrove,
" Boron-Stainless Steels", Meutron Absorber Materials for Reactor ,Ir l Control, W. K. Anderson and J. S. Tb=41 d-, Eds., p. 235-269 [l U.S. Gov. Printing office (1962). I Csl NB 2.198cm t it J.s c d '.i L., n Eds. f P-3.470cm 'J 5.66Scm 3... O .t T. n 1 P N Q 15: TJl n em.
y- .c ..u,,,m.. 2.?.. "N .. - ~ s. r e.. .. _'. c. e,G._m' ~o.- - - - n .,. 2,._.;1. --.' -~. ..J...,.. f. : 2 4 2.._ '.,... ; i ;;f _7.....~ ;,. - - - - - .' 7 .w. . o42 ..,......aa... m,w., .m s \\ I 3 T 7etsle C-2. FNR Fuel Element Olsenelone and Compeeltfen
- 4f u [s
- j ' j.'
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h!.f.. f.,- lg l = y p. HEU 64EU HEU Penn l.2 Alley AIIey Staperelen State LEts game Reguler' Special Seguler* Regular Septer w s.g I, ! p. Fuel seest Length (in) 22.S' 22.58 23.O' 23.5' 23.5* 33.5* Fuel toest Width
- 2.40' 2.40' 2.26' 2.40*
3.eO* 3.e0* Fuel toest Thtchnese* .022 .022 .028 .022 .032 .022 Water Omp .485' .llS' .422' .257 .193* .3esa Clod thictiness' .020 .020 .005 .020 .005 .Oss Smit Cell Ihf46peces .gyy ,gyy ,gy; ,333 , gyy ,gyy Nel Pf also 18 8 se t0 to e t f ale Pf ale Iffeithe u INI 3.170 3.150 3.12e 3.s50 3.850 $1de Plate thiclinesee ,938 .489 .let .4015 .las .see $1de Plate to Plate Specing' 2.562 3.562 2.564 3.694 2.564 3.564 Fuel Curvature Sedile 5.5 5.8 5.5 5.5 5.5 5.5 2.862 2.S64 Special Osttdo Plate widthe .025 .425 Special Outdo Plede Thickneene FueI Iteet Composition (syn) ee*U 940.68 48.84'* $29.8888 944.78 947.3'* S3.65 eseg 1.59 .75 .82 S.79 .00 .00 eeau .75 .34 .62 .00 .00 .00 eseg e.04 4.00 0.58 S.84 Gel 34.5 Aluminum SOS 489 878 434 1980 SSO tron 3.7 88 3.8 8.7 83 48 Weight X Uranium In Fuel seest** 14.25 14.25 84.851 29.$1 43.01 42.0E Croce Sectional Arose (In') Total Element
- 8.466 S.666 S.664 S.644 S.666 S.646 Lettice 7.654 3.827 7.207 7.654 7.654 3.827
.) Non-Lettice 2.082 5.840 2.469 2.082 2.092.
- 5.840
( i Metal in Non-Letticees g,333 g,330 3.380 g.30g g,374 g,334 fj Water in Non-Lettice ,64L4 - 3.980 .848 .707 .638 3.996 bl 9. F051 core grid spacing le 3.888* m 3.035" 2. New regular fuel elemente added to the FNR core af ter Decestner 4 4878 pere dispereton fuel elemente. The last alloy regular fuel elemente are empacted to t>e discharged from the core during the summer of $988. As of April 1988 no disperelon special elemente have t>een pieced in the core, although a few of these elemente are on ette. 3. Fuel plate dimenolone measured from redlographs of 7 elloy and IT dispersion fuel plates. f 4. Olsenelone chosen to tse coneletont with HEU regular fuel element date. S. Fuel meet width to for a flat fuel plate. 6. Fuel meet thtchnese calculated est unit cell thicknese - 2 m clad thlchnees - water gap e.g. HEU alley. .177* - 2 x.020* -.t85* =.022* 7. Water gap width everaged from vencbr measuremente of the actual fuel plate spectng. 3. Data represente the nominal dimenolon on vendor drawings. S. Unit cell thtchnese calculated as: Fleet grid epocIng/ nuatzer of fuel plates e.g. HEU elloy. 3.889*/98=.977* $0. Uranium mese taken from vendor measurement date. 88. Uranium mese teken from fuel specifications. 12'. Modeling trace elemente In the aluminum alloy le Ieport9nt. -.. e s )
'i.71 Zil AC24 ET;-Liht.Enh i.na; 4. 'i-
- e. 4.: MS% Lum r. nELN ! ve ;+.A.wdElk lE dda*.0C b:ws LR.:._.. _
..st s s f-i Table C-3. Chemical Composition of Aluminum Alloys Used in Fuel Element Manufacture by United states, French (CERCA), and German (NUEEN) Supp11ere I Fuel Core Powder _ Fuel Plate Covers Fuel Element Structure 'i .l. 1100 5214 A5HE 6061 AG2NE AL MG-1* 6061 AG3NE AIAGG-314 1-(US) (US) (CERCA) (NUKEN) (US) (CERCA) (NUEEM) Maximum Percentage _ _ (US) (CBBCA) (NUKIM) cr Alloy Range i A1 0 ~ ~ ~ ~ ~ ~ ~ ~ ~ 23 i Boron 001 001 001 001 001 001 001 Cadmium 002 001 001 001 001 001 001 Chromium ~ .15.35 .10 15.35 25 j C:balt 001 003 003 j Cooper .20 20 008 .008 .15.40 .000 .000 .15.40 000 .05 05 40 .20.40 .70 .20.40 45 70 .20.40 50 Iran Lithium 008 001 .001 .001 001 001 .001 015 00-1.2 1.8-2.3 .70-1.1 80-1.2 2.5-3.0 .60-1.2 Magnesium Hanganese .05 .15 .15 .15 40-1.0 Cil and Grease 20 t- ~ 30 30 40.80 30 30 .[0.00 .30 70-1.3 l silicon i S11 con and Iron 1.0 25 .50 20.50 20.50 i 'i .10 i Titanium 02 .15 15 l .10 i vslatiles zinc 10 10 03 03 25 03 05 25 03 .05' [ .t others .15 0.0 03 0.0 .15 03 15 15 03 15 Minimum Percentage 1 i Aluminum 99.0 99.7 99.4 98.5 Remainder Remainder i 1 ? A
-w s cu. E -! ( 4 'y ,.3 Table C-4. ~i [ ).i Two-Group Cross Sections Generated with the LEOPARD Code l; b;.! R l s.a!(i i TABLE FORMAT 3 s i Gr Fissile b []i v (g Depletion f a er s1 2 s l G \\ N5-t lg:5 i .q } j,Af L s,. LIGHT WATER REFLECTOR 1 i 0.0 8.691-4 0.0 2,776-1 2 0.0 1.853-2 0.0 2.112 5.267-2 { .r 'N i '?.s Li [ [# t o.d t HEAVT WATER REFLECTOR [ aw i Il 1 2.729-4 4.698-4 5.478-4 1.803-1
- c. +
2 0.0 6.651-5 0.0 3.075-1 5.466-3 L, fcM ld i y .z } p q i 73
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n: . g.;n v ' ~ - - -. iks ,d* e. i l5 <u .a b I', A ji HEU DISPERSION REGULAR FUEL ELEMENTS
- J j
1 0.004 8.629-4 2.074-3 2.109-3 2.328-1
- g 2
3.965-2 6.099-2 9.670-2 1.225 2.710-2 1 0.104 8.651-4 2.080-3 2.114-3 2.323-1 2 3.949-2 6.220-2 9.630-2 1.2235 2.725-2 ]i 1 10.004 7.876-4 2.055-3 1.923-3 2.311-1 2 3.590-2 5.918-2 8.756-2 1.2285 2.762-2 d 1 20.004 7.074-4 2.023-3 1.728-3 2.299-1 0 2 3.226-2 5.554-2 7.868-2 1.234 2.796-2 O
- 4;;
dsi M Q HEU ALLOT REGULAR FUEL ELIGNTS ,j 1 0.004 8.512-4 2.066-3 2.079-3 2.305-1 3 2 3.890-2 6.000-2 9.487-2 1.163 2.574-2 i; 1 0.104 8.533-4 2.072-3 2.084-3 2.300 2' 3.874-2 6.119-2 9.448-2* 1.1611 2.588-2 1 1 10.004 7.771-4 2.047-3 1.900-3 2.290-1 3 ' 2 3.522-2 5.823-2 8.590-2 1.1660 2.623-2 !-) 1 20.004 6.981-4 2.016-3 1.706-3 2.279-1 2 3.164-2 5.466-2 7.719-2 1.172 2.656-2 g.; b / b h
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] HEU ALLOT SPECIAL FUEL ELEMENTS u Tcj 1 0.004 4.454-4 1.462-3 1.085-3 2.320-1 h 2 1.858-2 3.750-2 4.530-2 1.374 3.169-2 1 1 0.104 4.458-4 1.465-3 1.086-3 2.315-1 j; 2 1.852-2 3.803-? 4.517-2 1.373 3.179-2 71 1 18.004 3.717-4 1.443-3 9.034-4 2.280-1 ]. 2 1.538-2 3.525-2 3.750-2 1.379 3.245-2
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1 36.004 2.951-4 1.416-3 7.147-4 2.294-1 g 2 1.216-2 3.192-2 2.966-2 1.386 3.317-2 ). ) .i,I s 1
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? b; ~ 4 {.'1 I.'$ e [j a LEU REGULAR FUEL ELEMENTS /I d 1 0.00% 1.056-3 3.622-3 2.606-3 2.315-1 2 4.544-2 6.812-2 1.108-1 1.157 2.472-2 D 1 0.104 1.059-3 3.634-3 2.613-3 2.310-1 d 2 4.524-2 6.946-2 1.103-1 1.155 2.487-2 ] 1 10.00% 9.706-4 3.633-3 2.401-3 2.299-1 H 2 4.143-2 6.652-2 1.013-1 1.161 2.518-2 @} 1 20.00% 8.794-4 3.636-3 2.180-3 2.289-1 2 3.749-2 6.284-2 9.201-2 1.167 2.538-2 g A i l] "d LEU SPECIAL FUEL ELEMENTS
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1 0.00% 5.562-4 2.275-3 1.370-3 2.337-1 2 2.198-2 4.167-2 5.360-2 1.366 3.078-2 Lj 1 0.10% 5.569-4 2.280-3 1.371-3 2.332-1 t 2 2.191-2 4.233-2 5.343-2 1.365 3.089-2 1 18.00% 4.702-4 2.272-3 1.159-3 2.300-1 b, 2 1.832-2 3.925-2 4.482.2 1.372 3.152-2 8 1 36.004 3;806-4 2.271-3 9.426-4 2.276-1 / 2 1.461-2 3.549-2 3.589-2 1.379 3.219-2 9 h (.. I;/j '1,i W b*i r W ? []! l~ k\\ w sq .m ...}}