MASSACHUSETTS INSTITUTE OF TECHNOLOGY
Department of Nuclear Engineering
Cambridge, Massachusetts
DESIGN OF CENTRAL IRRADIATION FACILITIES FOR THE MITR-1
RESEARCH REACTOR
P. C. Meagher, D. D. Lanning
September, 1976
MITNE - 190
MASSACHUSETTS INSTITUTE OF TECHNOLOGY
Department of Nuclear Engineering
Cambridge, Massachusetts
DESIGN OF CENTRAL IRRADIATION FACILITIES
FOR THE MITR-II RESEARCH REACTOR
by
P. C. Meagher, D. D. Lanning
September, 1976
MITNE-190
2
DESIGN OF CENTRAL IRRADIATION
FACILITIES FOR THE MITR-II RESEARCH REACTOR
by
Paul Christopher Meagher
Submitted to the Department of Nuclear Engineering
on September 30, 1976 in partial fulfillment of the
requirements for the degree of Master of
SCIENCE
ABSTRACT
Design analysis studies have been made for various in-core irradiation
future use
facility designs which are presently used, or proposed for
core
effects,
The information obtained includes reactivity
in the MITR-II.
and
limits
flux and power distributions, and estimates of the safety
limiting conditions for operation. A finite-difference, diffusion theory
computer code was employed in two and three dimensions, and with three and
fifteen group energy schemes. The facilities investigated include the
single-element molybdenum sample holder, a proposed double-element
irradiation facility and a proposed central irradiation facility design
In
encompassing most of the area of the three central core positions.
been
has
materials
addition, a comparison of the effects of various absorber
dummies.
solid
made for a core configuration which includes three
Flux levels in the molybdenum holder facility and in the beam ports were
calculated for both three and five dummy cores. Flooding the sample tube in
these cases was found to increase the safety and operating limits, but not to
unacceptable levels for an 8 inch blade height. For the five dummy case, the
operating limit in the C-ring was predicted to reach its maximum allowed value
at a blade bank height of 13.6 inches. The reactivity effect of flooding was
for the five dummy case, in direct agreement with
calculated to be 0.19%AK
the measured value. Flooging the large sample channel in the double element
6
and also to cause
facility was found to increase the reactivity by 1.5 %AK ff
an unacceptable powerpeaking.
The proposed central irradiation facility is a thermal flux-trap which
2
could produce thermal flux values of up to 2.0 x 1014 n/cm sec. Computer
estimates show that flooding this facility's central sample tube would increase
2
this value to 2.5 x 1014 n/cm sec, without resulting in an unacceptable
power peak.
Thesis Advisor:
Title:
D. D. Lanning
Professor of Nuclear Engineering
3
TABLE OF CONTENTS
Page
ABSTRACT
2
LIST OF FIGURES
5
LIST OF TABLES
7
ACKNOWLEDGEMENTS
8
CHAPTER 1
INTRODUCTION
9
CHAPTER 2
CALCULATIONAL METHODS
16
2.1
The Computer Code, CITATION
16
2.2
Cross Section Data
17
2.2.1
Fuel Cross Sections
18
2.2.2
Control Blade Cross Sections
20
2.2.3
Steel and Molybdenum Cross Sections
29
CHAPTER 3
SAFETY LIMIT AND LIMITING CONDITION FOR OPERATION
32
3.1
Safety Limit
32
3.2
Limiting Condition for Operation
34
3.3
Evaluation of the Safety and Operating Limits
35
CHAPTER 4
SINGLE ELEMENT IRRADIATION FACILITIES
44
4.1
Original In-Core Sample Assembly
44
4.2
Molybdenum Sample Holder
46
CHAPTER 5
DOUBLE ELEMENT IRRADIATION FACILITY
54
5.1
Fifteen Group CITATION Study
56
5.2
Three Group CITATION Study
61
4
CHAPTER 6
CENTRAL IRRADIATION FACILITY STUDIES
6.1
Effect of Various Materials in the Central Facility
6.2
Proposed Central Irradiation
CHAPTER 7
Facility Design
CONCLUSIONS AND RECOMMENDATIONS FOR FURTHER WORK
68
69
77
87
REFERENCES
96
APPENDIX A
CONTROL BLADE HOMOGENIZATION AND MESH CORRECTION
APPENDIX B
THREE DUMMY CORE CALCULATIONS
102
APPENDIX C
THE COMPUTER CODE, LIMITS
114
APPENDIX D
SAMPLE CITATION OUTPUT
121
-
5
LIST OF FIGURES
Page
1-1
Cross Section of the MITR-II Facility
10
1-2
Vertical Cross-section of the MITR-II Core
11
1-3
Horizontal Cross-section of the MITR-II Core
13
1-4
MITR-II Fuel Element
14
2-1
Horizontal Section of the Fixed Absorber Spider
with Hafnium Inserts in Place
24
4-1
Original In-core Sample Assembly Design
45
4-2
Molybdenum Sample Holder Design
47
4-3
Horizontal Section Showing Core Model for
Molybdenum Sample Holder
49
5-1
Horizontal Section of A-ring Core Positions with
Double Element Facility in Place
55
Two-dimensional Core Model used for Fifteen Group
Steel Sample Calculations
57
Fast Flux (Radially Averaged Across Steel Sample)
as a Function of Axial Position
60
Horizontal Section Showing Core Model for Double
Element Irradiation Facility
62
5-2
5-3
5-4
5-5
Fast and Thermal Fluxes along Centerline of
Steel Sample
5-6
Fast and Thermal Fluxes across Steel Sample at a
Point Halfway Up Sample
6-1
66
Thermal Flux Along Centerline of Central Irradiation
Facility Filled with Various Materials
6-2
65
74
Epithermal Flux Along Centerline of Central
Irradiation Facility Filled with Various Materials
75
6
6-3
6-4
6-5
6-6
6-7
6-8
B-1
B-2
B-3
B-4
B-5
B-6
Thermal Flux Plotted Radially from Centerline
of Central Facility for Various Materials
76
Vertical Cross Section of Proposed Central
Irradiation Facility
78
Horizontal Cross Section of Proposed Central
Facility with Rectangular Molybdenum Sample Regions
79
Horizontal Cross Section of Proposed Central
Facility with Cylindrical Molybdenum Sample Regions
86
Two-dimensional Core Model used for Proposed
Central Facility Calculations
82
Vertical Section of Proposed Central Facility
Showing Lines of Constant Thermal Flux
85
Core Power Peaking as a Function of Axial
Position for Element A-2 (plate 1)
107
Core Power Peaking as a Function of Axial Position
for Element B-15
108
Core Power Peaking as a Function of Axial Position
for Element C-8 (plate 1)
109
Thermal Flux as a Function of Axial Position for
Element A-2
110
Thermal Flux as a Function of Axial Position for
Element C-8
111
Thermal Flux as a Function of Axial Position for
Corner Hole #2.
112
7
Page
LIST OF TABLES
2-1
Energy Structure of the Three and Fifteen Group Cross
Section Sets
19
2-2
Boron-Stainless-Steel Control Blade Composition
27
2-3
Composition of A533 (Type B) Steel Sample
31
3-1
Factors used in Safety and Operating Limit Evaluation
36
3-2
Values of Plenum Flow Disparity (dFP) for Three and
Five Dummy Core Configurations
3-3
Comparison of Experimentally Determined and ComputerGenerated Values of FR, FA, and Z for a THREE-DUMMY
Core Configuration
39
3-4
Comparison of Experimentally Determined and ComputerGenerated (with old Cd Cross Section Data) Values of
and Z for a FIVE-DUMMY Core Configuration
FR, F ,
4-1
Results of Limit Calculations for the Molybdenum Sample
Holder
4-2
Results of CITATION Thermal Flux Calculations for the
Molybdenum Sample Holder
53
5-1
Zone Compositions for 15 group Steel Sample Calculation
58
5-2
Results of Three Group Double Element Facility
Calculation
64
6-1
Results of Two-dimensional CITATION Study of Various
Materials in the Central Facility
71
Results of CITATION Flux Calculations for Various
Materials in the Central Facility
72
6-2
6-3
7-1
Zone Compositions for 3 group Flux-trap
Calculations
51
Facility
Results of CITATION Flux Calculations for Various
Core Configurations
B-1
Results of 3 Dummy+ Core Study
B-2
Beam Port Thermal Flux Values Generated by CITATION
for the Three Dummy Core Study
83
90
103
105
8
ACKNOWLEDGMENTS
The author wishes to thank Dr. D. D. Lanning for his guidance
and advice, without which this study could not have been accomplished.
The help of Dr. A. F. Henry, especially in the development of neutron
cross section data, has also been greatly appreciated.
Mr. R. Chin and Dr. G. Allen have taken much of their time to
explain various aspects of the MITR-II, and the techniques used to
study this facility.
invaluable.
Their advice and encouragement have been
Thanks also go to Rachel Morton for her assistance with
computer codes, and to Cindi Mitaras for her part as typist.
The computations for this report have been done at the MIT
Information Processing Center.
9
CHAPTER I
INTRODUCTION
The nuclear reactor facility at the Massachusetts Institute
of Technology has been a valuable asset to student instruction and
research for many years.
of the MITR-I core.
Operation began in 1958 with the criticality
This design produced a maximum thermal power
of 5 MW with a fully enriched uranium-aluminum alloy fuel, and a
heavy water coolant and moderator.
The MITR-I performed well during
its planned lifetime and was shutdown in 1974 for a complete core
revision.
The new design, called the MITR-II, was developed to provide
increased reliability and higher neutron flux levels at the beam
ports.
Like the MITR-I, the rated thermal power is 5 MW, but the
new core is more compact, with a higher power density.
of the facility is shown in Figure 1-1.
A cross section
Light water flows down around
the outer edges of the core, and then up through the fuel elements to
a large upper plenum.
The region surrounding the core tank contains
a heavy water reflector which can be dumped as a safety shutdown
mechanism.
Beam ports extend through the reactor's concrete
shielding into the reflector region below the core.
These ports
allow for sample irradiation in this high flux region or can provide
a neutron beam path to instruments located outside the shielding.
Figure 1-2 is
a vertical cross section of the MITR-II core.
As shown, fixed neutron absorbers may be positioned in the upper
fueled region.
These serve to push the maximum reactor power toward
10
FIGURE 1-1. Cross section of the MITR-II facility.
11
FIGURE-1-2. Vertical cross section of the
MITR-II core.
fixed
absorber
region
shim
blade
lower
spider
assembly
D2 0
core
tank
12
the bottom of the core, enhancing the thermal flux obtained from
the beam ports.
fuel is reduced.
elements,
In addition, burnup in the upper half of the
By inverting and reusing once-burned fuel
a longer fuel life can be obtained.
Normal reactivity control is accomplished by the motion of
six shim blades and one smaller regulating rod.
These absorbers
essentially form a ring which shields the core from the surrounding
reflector.
This orientation can be seen in the horizontal core
section of Figure 1-3.
The core itself is hexagonal in cross section, with a 15.0
inch span across the flats.
It is composed of up to twenty-seven
fuel elements which form three concentric rings.
Three positions
form the innermost, or A-ring, while the B and C-rings contain nine
and fifteen positions, respectively.
in Figure 1-4.
A single fuel element is pictured
Each contains fifteen finned fuel plates held in place
by the rhomboid body of the element.
The plates consist of an alloy
of thirty-five weight percent uranium (93% enriched) in aluminum,
surrounded by an aluminum cladding.
The MITR-II can be operated with several non-fueled core positions.
This allows space for the placement of various experimental facilities
into the core in order to hold materials such as irradiation samples
or a neutron source.
This research report deals with the evaluation
of the experimental facilities which have been used in the MITR-II
core.
In addition, an investigation is made into the feasibility
of several other facilities which have been proposed for future use.
13
core
-hexagonal fixed absorber region
radial fixed absorber region
FIGURE 1-3. Horizontal cross section of the MITR-II core.
-
-__
r
1
A.,,
1
49.
--
-
-
...
- ---
- -.L
+--
-
--
-----
__
-+.
-
---
Za
-"
Zb.
MEF.
PYaEL CA LNtTh
-I
-
0
0
1P7
%Mri
'.LL ".%6%
H-
"~'
1
t.ATEMT
FV96.
frp
.mt
wo".u
,t-
e*
rye t. PPiy Saame.
IIiI
am
.110
VIALL
N401iVA
$ELr'tum
FIGURE 1-4.
MITR-II fuel element.
-b
ILTAM.
15
Chapter 2 deals with some of the considerations involved in
analyzing in-core facilities and includes the calculational methods
required for the neutronic portion of such an analysis.
An explanation
and description of the safety limit and limiting condition
are contained in Chapter 3.
for operation
These two technical specification limits
place restrictions upon reactor operation in order to avoid power
peaking which could produce an adverse effect on fuel cladding
integrity.
Chapters 4, 5 and 6 explain the various facilities studied,
the procedures employed in their evaluation, and the results obtained.
Chapter 7 summarizes and draws conclusion about the results, and then goes
on to suggest paths which future work might take.
16
CHAPTER 2
COMPUTATIONAL METHODS
The evaluation and design of an incore assembly for a
reactor such as the MITR-II must include consideration of
various neutronic effects.
For example, the introduction
of too great a volume of water into the core can produce an
unacceptable power peaking in adjacent fuel elements.
The
effect of an assembly on the thermal neutron flux obtained
from the beam ports is also an important factor.
In addition,
reactivity effects must be investigated in this type of analysis,
due to reactor control and safety considerations.
Each of
these constraints must be balanced against the desire for
attaining the maximum possible neutron flux with the most
useful energy spectrum.
In order to perform these evaluations of limiting
conditions and optimum designs, information such as the core
power and flux distributions, and K
values for various
core configurations, must be known.
The tool which was most
often used in this research study to find the required information
was the computer code CITATION (Ref. 1).
2.1
THE COMPUTER CODE, CITATION
This code is a finite-difference, diffusion theory code
which was developed at the Oak Ridge National Laboratory.
Beyond those capabilities previously mentioned, CITATION can
17
be used to determine the solution of perturbation and depletion
problems, calculate the adjoint flux, and generate flux-weighted
macroscopic cross sections.
CITATION was run in both the two-dimensional (R,Z) and
three-dimensional (RO,Z) modes, depending upon the core
configurations being modelled and the degree of accuracy
required.
This code has the ability, however, of handling
various other geometries.
The neutron energy structure employed for the majority
of the cases was a three group scheme.
Fifteen group calculations
were also performed in order to flux-weight fifteen group
cross section sets to a three group structure.
The result
of such a "collapse" run is a set of three group macroscopic
cross sections for each different mixture of materials.
These
three and fifteen group cross section sets are further described in
the next segment of this chapter.
The core models and finite-difference mesh spacings used
to mockup various core configurations are detailed throughout
later
2.2
chapters.
CROSS SECTION DATA
The three group cross section set used for MITR-II calculations
was originally developed by Kadak (Reference 2) and Addae (Reference 3).
This set was collapsed from the previously mentioned fifteen group
set which had been modelled after that of Hansen and Roach
(Reference
4).
Collapsing was accomplished by use of the finite
18
difference, diffusion theory code, EXTERMINATOR-II (Reference
5).
The energy structure of the three and fifteen group sets is
listed in
2.2.1
Table 2-1.
Fuel Cross Section
In the energy range above 1 ev, the neutron diffusion
length is long enough such that the fueled core regions can
be considered as homogeneous.
In the thermal range, however,
the diffusion length is on the same order as the fuel plate
thickness.
It was therefore necessary to consider the hetero-
geneity of the fuel elements in the development of the fuel's
thermal cross sections.
This was accomplished by iteratively
using the transport theory code, THERMOS (Reference
6).
The
first step homogenized a single fuel cell (fuel plate and
surrounding moderator), while the second went on to homogenize
a series of cells into a full element.
Fuel placed in different regions of the core will experience
different neutron energy spectrums.
This is largely dependent
upon nearness to the reactor's reflector.
Additional THERMOS
calculations were therefore performed by Kadak to obtain
homogenized fuel cross sections averaged over the neutron
spectrum radially and axially throughout the core.
The
resulting thermal cross sections then formed the lowest two
groups of the modified Hansen and Roach set, which was
subsequently collapsed to the final three group set.
19
TABLE 2-1
ENERGY STRUCTURE OF THE THREE AND FIFTEEN GROUP CROSS-SECTION SETS
Three Group Set:
Group
Energy Range (ev)
1
.00025 - .40
2
3
.40 - 3.00 x 103
3.00 x 103
-
10.00 x 10
Fifteen Group Set:
Group
Energy Range (ev)
1
3.00 x 106 - 10.00 x 106
2
1.4o x 10 6
-
3
.90 x 106 -
4
.40 x 10 6
5
.10 x 10 6
6
-
3.00 x 106
1.40 x 106
.90 x 106
.4ox1o66
17.00 x 103 -100.00 x 103
7
3.00 x 103
17.00 x 103
8
.55 x 103
3.00 x 103
9
100
-
550
10
30
-
100
11
10
-
30
12
3
-
10
13
1
-
3
14
.4
15
-00025
1
.4
20
Control Blade Cross Sections
2.2.2
Great care must be taken to ensure the accurate representation
of a strongly absorbing control material in a diffusion theory
The diffusion theory approximation to the transport
calculation.
Therefore,
equation breaks down in the presence of such a material.
equivalent diffusion theory parameters must be found which
approximate the actual absorption taking place in the control
This can be done by the use of blackness theory,
material.
which is detailed in a paper by Henry (Reference 7).
Blackness theory can be readily applied to control blades
which approximate an infinite slab, and in which scattering may
The theory first defines blackness coefficients in
be neglected.
terms
of the net current and fluxes at either side of the slab:
+
a(E)
-
(2-1)
(E
where
j
and
j+
j
j-
are the currents at the right and left, respectively.
+ and $~ are the similarly defined fluxes.
The transport equation is then solved inside the slab in order
to find the surface fluxes and currents, producing the following
equations for the blackness coefficients:
21
1 - 2E
(Z)
2[l + 3E 4 (Z)]
(2-2)
1 + 2E
(Z)
2[l - 3E 4(Z)]
where Z = 2t a(E), and t is the slab's half-thickness.
E3 and E
are the exponential integrals defined as:
En2Z
(Reference
=
0p nexp[-
(2-3)
-]dy
8 contains tables of these integral functions.)
For the thermal range,
the functions a(E) and
S(E)
are then
averaged over the energy spectrum:
E
fa(E)* o(E) dE
th
E
fc
o
(E) dE
(2-4)
E
c
{S(E)$o(E)de
th
E
c
o o(E) dE
22
is the thermal cut-off energy, and
where E
4o(E)
is the flux
C
spectrum in the surrounding medium, away from the slab's surface.
The value of <a>th provides a measure of the absorption ability
of the slab.
A value near zero would be very lightly absorbing,
while the maximum value of 1/2 would represent a totally black
absorber.
The equivalent diffusion theory parameters, Za and D, are
obtained from the spectrum-weighted blackness coefficients by the
use of the following equations:
-
a
<-a><>
2t
1 + /<a>/<>
1
-<>/<,>
(2-5)
a
When the blade is composed of layers of different materialsa
homogenization correction must be considered.
This was the case
for the original design of the absorbers in the MITR-II, which
were cadmium clad with aluminum.
Values of
Za and D were found
for each material region, then combined in a manner which equated
the thermal fluxes and currents at each internal interface.
The
result of this correction was to produce homogenized equivalent
diffusion theory parameters for the blade as a whole.
Before inclusion into a finite-difference code such as
CITATION, one additional correction must be made to the Ta and D
values.
This correction compensates for the effect that the mesh
23
spacing which mocks up the blade region has on the blade's absorption.
The methods used to apply these two corrections were generated
9).
and written into a small computer program by Emrich (Reference
The segment of this program which deals with these corrections was
isolated and modified for the following work.
A listing and
description of the required input of the modified code is given
in Appendix A.
The original aluminum-clad, cadmium absorbers of the MITR-II
were used successfully for approximately the first five months of
the core's operation.
After this period, swelling of the fixed and
moveable absorbers was noted.
It was therefore decided that the
core would be operated for a time without fixed absorbers, and then
eventually be refitted with hafnium fixed absorbers.
The six
moveable cadmium blades were replaced one by one with plates of 1.1%
natural boron in stainless-steel.
To accurately model prospective
core configurations, it became necessary to develop equivalent diffusion
theory parameters for the hafnium fixed absorbers, and boron-stainless
steel
moveable absorbers.
Hafnium Fixed Absorbers
The new fixed absorber design consists of twelve pure hafnium
slab inserts held in position by the central spider assembly, as
shown in Figure 2-1.
Each slab is 0.1 inch thick, by 2 inches wide,
by 12.3 inches long.
With these absorbers in place, the active
(unpoisoned) core height is twelve inches.
Values of <a> th and < >th were determined by employing the
previously outlined method of weighting a(E) and
S(E)
over the flux
hafnium inserts
FIGURE 2-1. Horizontal section of the fixed absorber spider with hafnium inserts
in place.
25
spectrum in the thermal range.
Z
and
I
were then found by use of
the modification of Emrich's code which considered homogenization
and mesh-spacing corrections.
It was also necessary to apply blackness theory in the epithermal
energy range, due to the significant amount of resonance capture in
The technique used here was that of Henry, as detailed
hafnium.
in Reference
<a>
7. In this work, <c>epi is shown to be given by:
. =
(2-6)
3 x 103
epi
3 x 103
where I
=
a(E)dE
[1 + Y3 (E)]E
(2-7)
The problem was then reduced to that of determining a value for I.
To accomplish this, the epithermal energy range was broken up into
three segments.
The neutron absorption of each one was considered
separately, and the contribution of each segment to the integral
(I) was found.
In the first segment, .4 ev to 10 ev, BNL data (Reference 10)
was applied to the first of equations (2-2) to obtain the function
a(E).
This function was then used to numerically integrate equation
(2-7) over the .4 to 10 ev range.
For the second segment, 10 ev to 100 ev, the integration
considered absorption due to isolated resonances through the use
of Stein's method (Reference 11).
The resonance parameters employed
26
in this analysis by Henry were obtained from Reference 10.
Hf
(.0253ev) = 105 b.,
Additionally, a 1/v contribution based on a
a
was included in this segment.
In the third segment, from 100 ev
to 3 x 103 ev, only a 1/v cross section was considered.
The individual contributions to I from the three segments
were summed to give a total I.
The value of <a> epi was determined
from equation (2-6), then the homogenization and mesh-spacing
corrections were applied to obtain the final values of T
and D.
Blackness theory was not required to accurately determine
the fast neutron cross sections.
A flux-weighting CITATION
collapse run, as described in Section 2.1, was used in this
energy range.
Boron-Stainless-Steel Control Blades
The new boron-stainless-steel shim blades are of the same
outer dimensions as the old cadmium blades.
Internally, each
blade consists of two plates separated by a 0.05 inch water gap.
Both plates are composed of 1.1 weight percent natural boron in type
304 stainless steel; Table 2-2 lists the blade's constituents and
their densities.
In developing the group cross-sections, the
elements B, Fe, Cr, Ni, Mn, Si, and C were considered.
The others
were assumed to have a negligible effect due to their very low
concentrations.
The blackness theory technique described in the
first part of section 2.2.2 was employed in the thermal range.
Simple flux-weighting, by use of a CITATION collapse run, was
adequate for the epithermal and fast groups.
27
TABLE 2-2
BORON-STAINLESS STEEL CONTROL BLADE COMPOSITION
Element
Weight Percent
B*
1.100
Fe
64.280
Cr
18.450
Ni
13.660
MN
1.750
Si
.710
C
.040
P
.008
S
.004
*The 1.1% Boron consists of 18.41 atom percent B-10.
28
Aluminum-Clad Cadmium Absorbers
The original design of the control materials for the MITR-II
consisted of aluminum-clad cadmium for both the fixed and moveable
absorbers.
The hexagonal fixed absorber, which surrounded the A-ring
of elements was composed of a 0.020 inch thich cadmium plate covered with
aluminum.
The three radial fixed absorbers, and six moveable shim blades
each consisted of a 0.040 inch thick plateof cadmium clad with aluminum.
The group cross sections for the cadmium absorbers were originally
developed well before operation of the MITR-II reactor (References 3 & 17).
In the epithermal and fast energy ranges, a fifteen group cadmium cross
section set was collapsed into three group form in an EXTERMINATOR-II run.
For the thermal range, a modified blackness theory approach was used.
When using the cross section set obtained in this manner, it was noted
that CITATION was consistently low in predicting K ff
CITATION also
underpredicted the thermal flux and power levels of the upper core region,
which is the area most affected by the cadmium absorbers.
These facts
suggested that the cadmium absorption cross sections were too large,
A
causing an unrealistically strong flux depression in the upper core.
new three group cadmium cross section set was therefore generated.
For the
epithermal and fast energy ranges, a new fifteen group cadmium cross section
set was used in a CITATION collapse code.
This procedure produced a
significantly smaller fast neutron absorption cross section, and a slightly
smaller epithermal absorption cross section.
For the thermal range, the
blackness theory method presented at the beginning of section 2.2.2 was
employed.
The result was a greatly reduced thermal absorption cross section.
29
in
It was found that the new three group set produced a K
closer agreement with experiment than the old set.
For a representative
case*, the new Keff prediction was low by 1%, as compared with an
underprediction of
4.2% with the old cross section set.
The new
set also resulted in more realistic axial power and flux distributions
in the core.
The thermal flux levels in the beam ports were also
affected by the change; the newly calculated flux showed a 12%
drop from the old predictions.
Appendix B contains additional comparisons between results
obtained with the old and new cadmium cross section sets, and compares
these results with empirically determined data.
It also includes
the results of a calculation which mocks up an expected future
core configuration of three aluminum dummies in place, and hafnium
fixed absorbers at a height of 12 inches.
2.2.3
Steel and Molybdenum Cross Sections
Chapters 4, 5 and 6 are concerned with the analysis of facilities
which will allow the in-core irradition of various samples.
Two of the
materials envisioned for irradiation in these facilities are molybdenum
and steel.
Molybdenum-98 undergoes a neutron capture reaction which
produces the gamma emitter technetium-99m, a nuclide useful in cancer
detection.
The irradiation of steel samples is useful in the
study of neutron damage on steel's material properties.
*24 fueled elements, 2 aluminum dummies, and old in-core sample
assembly in place. Fixed cadmium absorbers at a height of 10
inches, and cadmium blades at a height of 10 inches.
30
In order to represent these materials in the CITATION code,
it was necessary to develop their three group cross-sections.
The
epithermal and fast cross sections were generated by a CITATION
collapse run from a fifteen group set.
The thermal cross sections
were flux-weighted over the flux spectrum obtained from the THERMOS
code.
A533 (Type B) steel, which is used for light water pressure
vessels, was the steel sample modeled; its composition is noted in
Table 2-3.
31
TABLE 2-3
COMPOSITION OF A533 (TYPE B) STEEL SAMPLE
Element
Weight Percent
Fe
97.10
Mn
1.30
Ni
.55
Mo
.50
C
.25
Si
.22
P
.04
S
.04
32
CHAPTER 3
SAFETY LIMIT AND LIMITING CONDITION FOR OPERATION
The safety limit and limiting condition for operation
provide a conservative means of insuring that incipient boiling
will not occur at any point in the core.
If boiling is prevented,
burnout can not occur, and the structural integrity of the fuel
cladding will be maintained.
Derivations of these limits can be found in the MITR-II Safety
Analysis Report (Reference 12).
The definitions and evaluation
procedures which are contained in the following sections have been
drawn from the MITR-II Technical Specifications (Reference 13),
and a report by Allen entitled "The Reactor Engineering of the MITR-II
Construction and Startup" (Reference 14).
3.1
SAFETY LIMIT
The safety limit is defined as:
Safety Limit
FHC FP/FF dF
where FHC = FH(FR max,
and dF =FCdFP'
33
The meanings of the various terms are as follows:
FH
- Hot channel enthalpy factor.
This term considers uncertainties
in reactor power and power density measurement, fuel density,
eccentricity, and flow measurement.
FR
- Radial peaking factor, the ratio of the power produced in a
particular plate to the power produced in the average plate
in the core.
FHC - Hot channel factor, the ratio of the power released into the
hottest channel to the power released into the average core
channel.
FF
- Fraction of the primary coolant which actually cools the fuel.
F
- Fraction of the total power generated by the fuel.
dFC
-
Channel flow disparity.
This term considers the maldistribution
of flow among the channels of a single element.
dFP - Plenum flow disparity.
This considers flow maldistribution
among the fuel elements for a particular core configuration.
dF
- Flow disparity, the ratio of the coolant flow through the
hot channel to the flow through the average channel in the core.
The safety limit must always be less than or equal to 2.9 at all points
in the core.
34
LIMITING CONDITION FOR OPERATION
3.2
The limiting condition for operation, or operating limit, is
defined as follows:
Operating
Limit
.
_
[W
.2
T
To
F FRZF'
PR 0
dF
G
- 1
-
P FF
- .466
A
A
where
G=FRFAFP 8
=
Gj F FdF.8
rn(FFdF)
ToC
F
h A
F 0 , anddF
and
dd
FCFP
The terms are defined as follows:
WT
-
Total coolant flow rate in gallons/minute.
WTo - Two pump coolant flow rate (1800 gallons/minute).
- Axial location factor.
Z
This is the ratio of the power
released into the channel containing the hot spot between
the inlet and the hot spot, to the total power released
into the channel.
F
P
'
-
Uncertainty factor in determining FR Z and in the flow
o
measurement.
-
Limiting safety system setting of the reactor power (MW).
Axial peaking factor, the ratio of the power density in a
FA
plate at a certain height to the average power density in the
plate.
-
Cladding fin effectiveness, ratio of finned plate heat transfer
to unfinned plate heat transfer.
35
A
- Total heat transfer area of the fuel meat (not cladding
surface) in ft2 .
CP
- Coolant heat capacity in BTU/lb-*F.
ho
- Normalized heat transfer coefficient for a particular
core configuration in BTU/hr-ft 2 -*F.
F0
- Uncertainty factor in fuel density tolerances and in
determining the reactor power, power density, flow, heat
transfer coefficient, and fin effectiveness.
The maximum value of the operating limit in the core must be
less than or equal to 3.72 in order to allow operation above a
reactor power of 1 KW.
3.3
EVALUATION OF THE SAFETY AND OPERATING LIMITS
The various factors needed to determine the safety and operating
limits were evaluated by Allen (Reference 14).
Table 3-1 lists these
factors for three dummy and five dummy core configurations, and for
one and two pump operation.
Table 3-2 shows the experimentally
determined value of dFP for each fueled position in the three and
five dummy cores used in the MITR-II.
In order to find values for the remaining factors (FR, FA, and Z),
the power distribution of the core must be known.
A CITATION calculation
or a plate gamma-scanning procedure can be used to gain this information.
Care must be taken however, when CITATION data are used.
It has been
found that the FR, FA, and Z values predicted by CITATION are, in some
36
TABLE 3-1
FACTORS USED IN SAFETY AND OPERATING LIMIT EVALUATION
Factor
FH
Value for 3-Dummy Core
Value for 5-Dummy Core
1.211
1.211
1.0
1.0
Ff
.9487
.9205
dfC
.887
.887
8.91x10 5 lbm/hr
WT
8.91x10
5
lbm/hr
0
WT/WT (for 2 pump
operation)
o
1.0
1.0
WT/WT (for 1 pump
operation)
o
.5
.5
F'
0
A
1.122
1.122
1.9
1.9
2
232.9 ft
2
213.5 ft
PT(for 2 pump operation)
6.0 MW
6.o MW
P T(for 1 pump operation)
3.0 MW
3.0 MW
CP
h
0
F0
.9985 BTU/lb-4F
.9985 BTU/lb0 F
2585 BTU/hr-ft2 _oF
2771 BTU/hr-ft 2 .OF
1.55
1.55
37
TABLE 3-2
) FOR THREE AND FIVE
VALUES OF PLENUM FLOW DISPARITY (d
DUMMY CORE CONFIGUPKIONS:
3 dummy core - dummies in positions A-1,
5 dummy core - dummies in positions A-2,
B-2, and B-8
A-3, B-3, B-6 and B-9
Core Position
Value for 3-Dummy Core
A-1
A-2
A-3
B-1
B-2
B-3
B-4
B-5
B-6
B-7
B-8
B-9
C-1
C-2
C-3
*
1.009
1.017
*
C-4
Value for 5-Dummy Core
.986
1.o49
1.074
*
1.049
.997
1.007
1.057
1.073
i.o82
1.032
1.058
*
1.032
1.092
.942
*
.989
.960
.930
.981
.977
.951
.949
1.o84
C-5
*
*
C-6
*
*
C-7
C-8
C-9
C-10
C-il
C-12
C-13
C-14
C-15
.945
1.011
.938
.981
.985
.946
.997
1.025
1.001
954
.993
.953
1.019
1.009
.944
.944
.972
1.036
*Aluminum dummy location or above-core obstruction prevented values
being taken for these positions.
38
instances, below the more reliable gamma-scan values.
These
underpredictions are most pronounced in areas where local conditions
influence a single plate, such as near a water-filled channel.
This is mainly due to the fact that the computer models which are employed
can only approximate the true shape of the core power distribution.
can not give
They
detailed power densities at each point in the core, such as
can be obtained by a gamma scan procedure.
More detailed CITATION
results can be obtained by increasing the number of core mesh points,
but if carried too far, the limitations of computer costs and computer
memory size are eventually encountered.
The degree by which CITATION underpredicts the three power distribution
factors depends upon the core configuration and core region being considered.
Core power data, some of which have been obtained from Reference 14, are
listed in Tables 3-3 and 3-4.
The first compares experimentally determined
(gamma-scan) values with those obtained from CITATION calculations, for
two positions in a three dummy core.
For the A-ring, the configuration
which is compared includes the old in-core sample assembly (the old
cadmium cross section set was used in the CITATION calculation).
C-ring,
For the
the
the three solid aluminum dummy configuration was considered;
new cadmium cross section set was used here.
The second table considers
a five dummy core and compares FR values developed from a conservative
combination of gamma-scan data and CITATION data, with values from
CITATION data only.
"CITATION-only" estimates of FA and Z are compared
against gamma-scan values for these factors.
Listed for each pair of
ratio of the
FyR, FA, and Z values is a prediction factor which is the
experimental value to the "CITATION-only" value.
39
TABLE 3-3
Comparison of experimentally determined, and computer generated
values of FR, FA, and Z for a THREE-DUMMY core configuration*.
Core Position A-2, next to old in-core sample assembly:
= 2.13
= 1.571
= 1.356
gamma-scan valuev+ ue
"CITATION-only" value
prediction factor
FR:
FA
Height above
fuel bottom
(inches)
Gam-+
Scan
0
1.573
1.211
1.174
1.329
1.1
2.1
6.1
8.0
10.0
14.0
1.451
1.413
.864
.690
.498
.291
16.0
19.0
24.0
z
Pred.
Factor
Pred.
Factor
GamScan+
1.988
1.813
.791
.668
.000
.068
.000
1.000
.084
.810
1.685
1.645
.697
.122
.345
.161
.758
.866
.946
.413
.553
.679
.834
.888
.945
.835
.837
.875
.954
.975
1.000
1.000
CIT
1.617
1.335
.738
.570
.388
.263
.808
.897
1.058
1.171
1.211
1.284
1.106
.463
.594
.796
CIT
1.001
1.000
An average of the inner two CITATION channels (for 0=6) was used to obtain
the "CITATION-only" values (old Cd cross sections were used in CITATION run).
Core Position C-8, at edge of core:
FR:
= 1.527
gamma-scan value+
"CITATION-only" value = 1.341
= 1.139
prediction factor
Height above
fuel bottom
(inches)
0
1.1
2.1
6.1
8.0
10.0
14.0
16.0
19.0
24.0
FA
GamScan+
.000
.339
.902
.742
.865
1.063
1.222
1.295
1.216
1.142
.947
.254
.669
1.000
Scan
CIT
2.200
1.611
2.440
1.755
1.846
1.630
1.224
.687
.514
.321
.170
z
Pred.
Factor
Gam- +
2.172
2.028
1.736
1.334
.945
.565
.450
.076
.146
.453
.591
.711
.866
.916
.968
CITN
Pred.
Factor
.000
.102
1.000
.745
.192
.760
.871
.906
.520
.652
.739
.858
.899
.947
.962
1.009
1.019
1.000
1.000
1.022
The outer CITATION channel (0=11) was used to obtain the "CITATION-only"
values (new Cd cross sections were used in CITATION run).
(Footnote explanations on following page)
40
*Dummies in A-1, B-2, and B-8, Cd fixed absorbers at
Many of these data are from Reference 14.
1 0 ".
+Experimental data from gamma-scanning, blade height = 7.6 inches.
++"CITATION-only" values obtained from computer analysis, blade height
= 8.0 inches.
41
TABLE 3-4
Comparison of experimentally determined, and computer-generated
(with old Cd cross section data) values of FR, FA, and Z for a
FIVE-DUMMY core configuration*.
Core Position A-1, next to solid dummy:
FR:
R
gamma-scan & CITATION value+ = 1.430
= 1.250
"CITATION-only" value++
= 1.144
prediction factor1
FA
Height above
fuel bottom
(inches)
GamScan**
0
1.1
2.1
6.1
8.0
10.0
14.0
16.0
19.0
24.0
1.250
1.000
.980
1.075
1.085
1.145
1.150
1.035
.730
.715
z
CIT'
Pred.
Factor
GamScan**
CIT-++
Pred.
Factor
1.709
1.516
1.341
1.027
1.015
1.038
1.023
.953
.831
.727
.731
.660
.731
1.047
1.069
1.103
1.124
1.086
.878
.983
.000
.062
.110
.295
.388
.492
.720
.877
.949
1.000
.000
.071
.134
.307
.391
.474
.655
.738
.849
1.000
1.000
.866
.821
.961
.992
1.038
1.099
1.188
1.118
1.000
(An average of the inner two CITATION channels (for 0=5) was used to obtain
the "CITATION-only" values.)
Core Position C-13, at edge of core:
FR:
R
gamma-scan & CITATION value+ = 1.54
"CITATION-only" value++
= 1.191
prediction factorl
= 1.293
Height above
fuel bottom
(inches)
0
1.1
2.1
6.1
8.0
10.0
14.0
16.0
19.0
24.0
FA
GamScan**
1.79
1.35
1.43
1.61
1.58
1.42
.82
.65
.39
.28
z
CIT
Pred.
Factor
GamScan*
CIT
Pred.
Factor
2.238
1.977
1.833
1.576
1.259
.965
.667
.567
.460
.370
.800
.683
.780
1.022
1.255
1.426
1.229
1.146
.848
.757
.000
.067
.126
.382
.510
.636
.825
.887
.953
1.000
.000
.093
.175
.469
.590
.676
.809
.859
.923
1.000
1.000
.720
.720
.814
.910
.966
1.020
1.033
1.033
1.000
(The outer CITATION channel (0 = 5) was used to obtain the "CITATION-only"
(Footnote explanations on following page)
values.)
42
*Dummies in A-2, A-3, B-3, B-6, & B-9, no fixed absorbers.
of these data are from Reference 14.
**Experimental data from gamma-scanning,
Many
blade height = 8.6 inches.
+Values obtained from a conservative combination of gamma-scan and
CITATION data.
++"CITATION-only" values obtained from computer analysis, blade
height = 8.0 inches. (Old cross section set used.)
'These prediction factors include the conservatism used in combining
the gamma-scan and CITATION Information.
43
A larger A-ring prediction factor for FR is seen to result in the
three dummy core as compared to the five dummy core.
This is
partly
due to the different mesh spacing arrangements employed in modelling
these configurations.
The widths of the fueled mesh regions which are
used in developing the three-dummy factors are approximately three times
as large as for the five dummy case.
Therefore, the three-dummy
"CITATION-only" value averages further into the cooler region toward
the centerline of the element.
When this CITATION prediction is
compared against the experimental value for the hot plate at the
element's edge, a large prediction factor for FR results.
A short code was written to estimate the safety and operating limits
by using computer-generated power density data and the prediction factors
given in Tables 3-3 and 3-4.
The CITATION information provides estimates
These factors are then
of the three core power distribution factors.
multiplied by the correct prediction factors (depending upon the core
geometry and core location considered) before they are used in the safety
and operating liruit equations.
Appendix C presents a listing of this
code and explains the required input procedure.
44
CHAPTER 4
SINGLE ELEMENT IRRADIATION FACILITIES
The two initial designs of in-core sample holders were
developed to make use of a single core position.
This chapter
provides a description and evaluation of the original single
element assembly designed by Soth (Reference 15), and of the
subsequent modification made to this design.
4.1
ORIGINAL IN-CORE SAMPLE ASSEMBLY
The original in-core sample assembly (ICSA) had been designed
and constructed before the completion of the reactor modification.
This assembly is pictured in Figure 4-1.
Its external dimensions
are those of a typical fuel element, allowing installation
into any of the twenty-seven core positions.
Internally, it
consists of a 1.25 inch O.D. sample tube reaching partway down
its length, and surrounded by a .425 inch thick annular coolant
gap.
Below the sample tube is a 1.25 inch diameter coolant channel.
The assembly's body is composed of aluminum.
This ICSA was used to hold a neutron source during startup
testing of the MITR-II.
It was later in place for some of the
low power physics tests, including the initial gamma-scanning
procedures.
During these tests however, it was determined that
the ICSA's water channel was producing an unacceptable power
peaking in adjacent fuel plates.
This analysis was performed
.1.O.WELD
As
\
LtEms rot&Ac sm .P
aw PsEEA PJNL3s.s
4r0
nori
asm.
L
Pde
- A SIP P.,r
MOB , S'
0
-A
IP
/
SLA
ON
NOZZLE
Ai
0"V,
-
to"
"IMf
-a.#**
LET
e,L
ENO
&S fer
y/f
W
JAe&M
P
/fNr
MeszL.
,v
c-ar
VI/EW
-IS Nor
Re* C&AIrTi.
sH*N
U,.
FIGURE 4-1,
Original in-core sample assembly design
46
His work showed that
by Allen and is detailed in Reference 14.
a safety limit of 2.88 was reached.
This is very close to, but
still below the maximum allowed value of 2.9.
However, the
operating limit reached a value of 5.07, well above the 3.72
limit allowed for operation above 1 KW.
Therefore, the initial
ICSA design could not be employed at higher reactor powers.
In
order to alleviate this power peaking problem, the ICSA was modified
into an assembly called the molybdenum sample holder.
4.2
MOLYBDENUM SAMPLE HOLDER
The design of the molybdenum sample holder eliminated much
of the coolant volume which the old ICSA contained.
This was
accomplished by adding aluminum to the assembly's body and
lengthening the sample tube to a point slightly below the fuel
bottom.
is
Figure 4-2 shows this new design.
surrounded by a .05
of the assembly.
The central sample tube
inch annular coolant gap running the length
An aluminum insert was placed into the upper portion
of the original ICSA's housing to reduce the coolant gap to the
desired size.
Several three-group CITATION calculations were performed to
determine if power peaking would be a problem with the molybdenum
sample holder design.
tube was also found.
The reactivity effect of flooding the sample
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FIGURE 4-2. Molybdenum sample holder design.
-
5
48
The core configuration for which this computer analysis
was conducted was that of a five dummy core (four solid dummies
plus the sample holder), without fixed absorbers.
A three-dimensional
(R, 0, Z) core model was used; this mockup was based on work by
Yeung (Reference 16), and is depicted in Figure 4-3.
This figure
shows a horizontal cross section of the core with the radial
and azimuthal mesh spacings.
Only one-half of the core is mocked
up; a plane of symmetry is assumed through the regulating rod
and core centerline.
nine planes.
Axially, the fueled region is divided into
Two more planes are located above these nine to
model the structure and coolant located above the fuel.
planes are located below the fuel.
The
Nine
moveable cadmium control
blades in this study were mocked up by the use of the original set
of cadmium blade cross sections as described in Section 2.2.2.
The reactivity effect of flooding the sample tube was found
first.
Although the sample assembly would be physically located
in either core position A-2 or A-3, it was impossible to represent
this situation with the half-core computer model being used.
The sample tube was therefore mocked up as being located halfway
between the midpoints of core positions A-2 and A-3.
Two CITATION
cases were then run with the cadmium control blades'at a height
of 8 inches and a core power of 5 MW.
The first mocked up a voided
sample tube and resulted in a Keff of .9550.
In the second run,
the void was replaced by water, resulting in a K
of .9569.
49
gcore
core tank
10
9
7
3
regulating
rod
6
5
shim blade
corner hole #2
Hexagonal fixed absorber region
Radial fixed absorber region
FIGURE 4-3.
Horizontal section showing core model for
molybdenum sample holder.
50
The reactivity effect of flooding was therefore estimated to be
0.19% AK.
This prediction was confirmed when low power testing
of the assembly took place.
The reactivity effect of removing
the voided sample tube and leaving a water-filled channel in the
center of the assembly was measured to be 0.19% AK, the same as
the predicted value.
The technical specification limits for the voided tube mockup
were calculated from the CITATION power density output; this
information is listed as case 1 of Table 4-1.
It can be seen
that for this computer mdckup, the limits are within their allowed
ranges.
The maximum safety limit of 2.19 occurred in position A-1,
next to the sample assembly,
while the maximum operating limit of
3.17 occurred at the edge of the core in position C-13.
The
prediction factors for a five dummy core (Table 3-4) were used
in this analysis.
CITATION calculations were also performed to evaluate the
technical specification limits for the sample holder in a flooded
condition at two shim blade heights.
A slightly different
approach was used in modelling these computer runs.
Because
of the symmetry condition imposed by the half-core model, the
equivalent of one-half of a flooded sample tube was included in
both positions A-2 and A-3.
The first case run with this core
mockup positioned the blades at a height of 8 inches.
case was for a 14 inch blade height.
The second
The results of these calculations
are shown as the second and third cases in Table 4-1.
TABLE 4-1
RESULTS OF LIMIT CALCULATIONS FOR THE MOLYBDENUM SAMPLE HOLDER
Max. Safety Limit
Core
++
K
eff
|I
I
Case
Configuration
1*
4 dummies & voided sample
holder, Cd blades at 8"
2*
4 dummies & flooded sample
holder, Cd blades at 8"
3
4 dummies & flooded sample 1.0314
holder, Cd blades at 14"
2.71
C-13, at edge 3.891
of core
+
2 dummies & flooded sample
holder, B-SS blades at 8",
Hf fixed at 12"moyhlemlyodr
2.74
moly holder
.9550
.9938
value
Max. Operating Limit
height
FR
R
position
(inches)
value
position
2.19
A-1, next to
moly holder
3.17**
C-13, at edge
of core
A-1, next to
moly holder
326**
3.40**
FA
zZ
8
1 .52
1.84
.51
A-1, next to
moly holder
16
1.76
1.06
.87
C-2, at edge
of core
10
1.58
1.83
.64
moly holder
10
1.88
1.35
.56
*The technical specification limits obtained for these cases have been estimated by use of the
prediction factors listed in Table 3-4.
+The technical specification limits obtained for this case have been estimated
by use of the
prediction factors listed in Table 3-3.
+Different core mockups were used for these cases (except for cases 2 & 3),
not strictly appropriate to compare these values.
it is therefore
**For 5MW (2 pump) operation.
1
This value is the predicted 2.5 MW (1 pump) operating limit, the predicted
shim blade height
at which the 3.72 limit is reached is 13.6 inches.
H
52
The "CITATION-only" results generated from these computer calculations
showed the safety and operating limits for both cases to be below the
maximum allowed values of 2.9 and 3.72, respectively.
However, when the
prediction factors from the five dummy core (Table 3-4) are applied to
the "CITATION-only" results, the operating limit for the 14-inch case
exceeds its maximum allowed value of 3.72.
The condition at which the
operating limit is predicted to reach 3.72 is with the blades raised
to a height of 13.6 inches.
Cases 1, 2, and 3 were performed for a core containing the molybdenum
sample holder, four aluminum dummies, cadmium shim blades, and no fixed
absorbers.
In order to evaluate the power peaking effect of introducing
hafnium fixed absorbers and boron-stainless-steel shim blades, a fourth
case was performed.
This calculation positioned dummies in positions
B-2 and B-8, with a flooded sample assembly in position A-1.
The fixed
and moveable absorbers were at heights of 12 and 8 inches, respectively,
and the reactor power was again set at 5 MW.
The coremodel used for this
case was based on previous work by Allen (Reference 14) and is similar to
the model described earlier in this section.
The output of this computer
run, along with an updated listing of the CITATION three group cross section
library is provided in Appendix D.
The results of this calculation are shown as case 4 of Table 4-1.
The prediction factors employed are from the three dummy configurations
of Table 3-3.
Maximum values of each limit occurred in the A-3 position,
adjacent to the flooded sample assembly.
The safety limit reached a
value of 2.74, which is below the maximum allowed limit of 2.9.
The
53
largest estimated operating limit was 3.40, which is below its maximum
allowed value of 3.72.
(In obtaining these limits, the power densities
of the two inner CITATION channels which border the facility were
averaged.)
Table 4-2 shows the thermal flux levels at two locations for the
four cases considered.
The first column lists the flux values at a point
along the core centerline at the height of the beam ports.
the magnitude of the flux which drives the beam ports.
This indicates
The second column
shows the maximum thermal flux encountered within the sample assemblies.
Table 4-2
Results of CITATION thermal flux calculations
for the molybdenum sample holder
Case
Description
Beam Port
Thermal Flux
(n/cm2 sec)
Max. Sample Assembly
Thermal Flux
(n/cm2 sec)
1
4 dummies & voided sample
holder, Cd blades at 8"
8.5 x 1013
5.4 x 1013
2
4 dummies & flooded sample
holder, Cd blades at 8"
8.4 x 1013
7.8 x 1013
3
4 dummies & flooded sample
holder, Cd blades at 14"
7.5 x 1013
6.8 x 1013
4
holder, B-SS blades at 8",
Hf fixed at 12"
2 dummies & flooded sample
13
9.3 x 10
13
8.5 x 10
This peak occurs at the bottom of the sample tube for each case.
These results demonstrate the influence that the control materials
exert in pushing the thermal flux toward the bottom of the core.
The
maximum flux values at lower core positions are obtained when fixed
absorbers are present, and the moveable absorbers are at the lower height.
54
CHAPTER 5
DOUBLE ELEMENT IRRADIATION FACILITY
The single element facilities discussed in the previous chapter
allow for the irradiation of samples only up to 1.13 inches in
diameter.
Larger samples can be inserted into the beam ports, but
the flux there is lower and much more thermalized than in the core.
A larger facility was therefore investigated which would make use
of two A-ring core positions.
This facility was designed to include a channel for the
irradiation of a large rectangular sample, and a smaller channel
containing a 1.25 inch O.D. sample tube.
The layout can be seen in
the horizontal cross section of the A-ring positions as shown in
Figure 5-1.
The aluminum body of the facility consists of two
individual pieces.
When placed together into adjacent A-ring positions,
they form a large channel that is about 2.2 inches by 2.5 inches in
cross section.
The smaller sample channel is entirely contained by one
of the aluminum pieces.
A steel sample is initially envisioned for irradiation in the
large channel as part of a study of radiation damage effects.
The
smaller channel will be useful for the irradiation of molybdenum samples.
These two materials were therefore included in the analysis of the
double element facility in regard to reactivity effects, power peaking,
and attainable fluxes.
large sample
channel
fuel element
IJ1
Ln
FIGURE 5-1.
Horizontal cross section of A-ring core positions with double element
facility in place.
56
5.1
FIFTEEN GROUP CITATION STUDY
The fast neutron flux is important to the investigation of
radiation damage.
It was therefore decided to perform a fifteen
group study in order to obtain a detailed picture of the high energy
flux spectrum.
Two CITATION cases were considered, each using a
two-dimensional (R,Z) core model.
The first was a base case in which
the three central elements were replaced by a mixture of 90% aluminum
and 10% water.
Fuel was placed in all other core positions.
The
second case included a 90% steel and 10% water, cylindrical sample, equal
in cross sectional area to a single fuel element.
It was located
along the core centerline and ran the length of the fuel.
Hafnium
fixed absorbers were included at a height of 12 inches, and the
boron-stainless-steel moveable blades were placed at 8 inches for
both cases.
The mesh spacing and zone compositions employed are shown
in Figure 5-2.
Table 5-1 lists the materials contained in each zone.
The base case K
was found to be 1.063.
With the introduction
of the steel sample, this value fell to 1.051, showing a reactivity
effect of 1.2%AK.
The steel sample also produced an 8% drop in the
thermal flux levels near the tips of the beam ports.
The component of the neutron flux above .9 mev is plotted in
Figure 5-3 for the steel sample region.
This curve shows the radial
average of the fast flux across the steel sample as a function of axial
position.
2
The peak of 5.2 x 1013 n/cm sec occurs at a point approximately
half-way up the active core.
57
FIGURE 5-2.
Two-dimensional core model used for
fifteen group steel sample calculations.
(not to scale)
58
TABLE 5-1
ZONE COMPOSITIONS FOR 15 GROUP STEEL SAMPLE CALCULATION
Zone
Nuclide Number
Nuclide Name
Number Density (atoms/cm-b)
10
1010-2
102
4.390
3.359
3.183
1.545
x
x
x
x
5
6
7
8
U-235
U-238
Al
H 0
2
U-235
U-238
Al
H20
4.390
3.359
3.183
1.545
x 10
x 10x 10 2
x 102
3
9
10
11
12
U-235
U-238
Al
H 20
4.390
3.359
3.183
1.545
x
x
x
x
4
13
14
Al
H20
3.012 x 10 2
1.655 x 10 2
5
13
14
15
1.621 x 10
1.645 x 10-2
3.275 x 10 2
6
16
Al
H20
D20
2
Al
7
17
Al
6.023 x 10o 2
8
13
14
Al
H20
3.012 x 10 2
1.655 x 1o2
9
18
C
8.344 x 10-2
10
13
15
Al
D20
3.120 x 10 2
1.654 x 10 2
11-13
14
H20
3.340 x 10-
14
13
19
Al
Hf
4.455 x 10 2
3.188 x 102
15
14
17
H 0
Ai
3.340 x 10-3
5.421 x 10- 2
1
1
2
3
4
2
10
1010-2
10 2
6.023 x 10-
2
2
59
Zone
Nuclide Number
Nuclide Name
Number Density (atoms/cm-b)
10-2
10- 2
10- 2
102
16*
20
21
22
23
B
Fe
Cr
Ni
9.745
5.543
1.710
1.121
x
x
x
x
17**
14
18
21
23
H20
C
Fe
Ni
3.340
7.561
8.900
3.800
x 10x 10 2
x 10_
x 104
*The collapsing run to 3 groups for the B-SS blades also included
the nuclides: Mn, Si, and C.
**The collapsing run to 3 groups for the steel sample also included
the nuclides: Mn, Si, and Mo; also, it excluded H2 0
FIGURE 5-3. Fast (above .9mev) flux (radially averaged across steel sample) as a function
of axial position.
U
U
C.,
H
0
H
a
5
10
HEIGHT ABOVE BOTTOM OF SAMPLE (inches)
15
- 20
o%
61
5.2
THREE GROUP CITATION STUDY
Following the fifteen group study, a three group, three-dimensional
model was used to allow for a detailed spatial analysis of the double
element facility.
Estimates of the safety and operating limits, fluxes,
and reactivity effects were found.
Due to the asymmetric nature of the facility, it was decided to
abandon the half-core
three-dimensional runs.
model which had been used in all previous
A full core model was employed as shown in the
horizontal cross section of Figure 5-4.
The core configuration assumed
for this analysis consisted of the double element facility located in
core positions A-1 and A-3.
The A-2 position was fueled, and the B-4
position was filled with a solid dummy.
The hafnium fixed absorbers
were at a height of 12 inches, while the boron-stainless-steel blades
were at 8 inches.
The first CITATION case included steel and molybdenum samples in
the large and small channels, respectively.
In the axial direction,
the steel sample extended upward ten inches from a point two inches
above the fuel bottom.
The major part of the channel above the steel
was filled with aluminum, and below the steel was an aluminum-water
mixture.
A molybdenum sample, in the form of MoO3 at its theoretical
density, extended upward 10.75 inches from a point .75 inch below the
fuel bottom.
The sample tube volume above the molybdenum was voided.
Two additional cases were computed.
The first of these considered
the removal of the steel sample and aluminum plug above the sample,
and replaced these volumes with water.
This run modeled the hypothetical
62
12
______14
2
regulating
rod
3
shim blade
corner hole
#2
hexagonal fixed absorber region
radial fixed absorber region
FIGURE, 5-4.
Horizontal section showing core model for double
element irradiation facility.
63
case of steel sample ejection from the core and resulted in
reactivity increase of 1.56%AK
.
a
The final case determined
the reactivity effect of replacing the molybdenum sample with a
void.
The result was a reactivity increase of .25%A K
.
Since
the sample contained 382 gm. of molybdenum metal, the estimated
reactivity effect per gram of metal is 6.54 x 10
4
%AKeff*
results of the first run are recapped in Table 5-2;
The
prediction
have been used to
factors from the three dummy core
estimate the technical specification limits shown.
The predicted safety and operating limits for this case are
well below their maximum allowed values.
It would therefore be
possible to safely operate the core with this orientation.
The
maximum limits for this case occur in the outer ring of fuel, not
in the area immediately adjacent to the experimental facility.
With flooding of the large sample channel, however, an unacceptable
power peak would occur in core position A-2, immediately adjacent to
the flooded channel.
To prevent this, a secured filler plug would
be required for the large channel if a sample was not being irradiated.
For case 1, the thermal flux in the molybdenum sample ranged
from a low of 1.9 x 10 13n/cm 2sec at the top, to a high of 5.7 x 1013
at the sample's bottom. The epithermal flux reached 6.2 x 1013 near
the top, and dipped to 4.3 x 1013 at the lower tip.
the steel are plotted in Figures 5-5 and 5-6.
The fluxes in
The first figure shows
the fast (above 3 kev) and thermal fluxes through the sample's center
TABLE 5-2
RESULTS OF THREE GROUP DOUBLE ELEMENT FACILITY CALCULATION
Max. Safety Limit
Case
1
Description
dummy & double
element facilitysteel and moly
samples in place
eff
.9884
value
position
value
2.05
A-2, adjacent
to facility
3.10
Max. Operating Limit
height
F
R
(inches)
position
C-i, at edge
of core
6
1.28
+The dFP values used are from the 3 dummy case as shown on Table 3-2. These technical
specification limits have been estimated by the use of prediction factors obtained by
comparing experimental three-dummy data with CITATION predicted data. For the C-ring,
the factors listed in Table 3-3 were used; for the A-ring the prediction factors were
obtained by comparing experimental data for the hottest Dlate (plate 1, A-1) to the
hottest A-ring CITATION channel.
F
A
1.89
Z
.48
1.8 .
FIGURE 5-5.
Fast (above 3kev)
and thermal fluxes along centerline of steel sample.
1.6 -
fast flux (X 1014)
1.4
1.2
thermal
(X 1013)
1.0
.6
C%
*0
1
2
3
4
5
6
HEIGHT ABOVE BOTTOM OF SAMPLE (inches)
7
8
9
L,
1.78
FIGURE 5-6. Fast (above 3kev) and thermal fluxes across
steel sample at a point half-way up sample.
1.76
,.zj
x
0
ci'
0
0
0
1.
1.T2
1.70L0
DISTANCE ACROSS SAMPLE (inches)
CN
67
as a function of axial height in the core.
The next figure is a
plot of the same fluxes across the sample at a fixed axial position
half-way up the sample.
This curve shows that the fast flux near
the sample's center is approximately 2.5% lower than that at the
edge.
The depression found in the thermal flux is much greater,
about 45%.
Under the condition of case 3, the thermal flux reached a
peak of 1.8 x 10 14n/cm 2sec at the center of the large channel, 7
inches above the fuel bottom.
As noted, however, the power peaking
is unacceptable and this flux level is therefore unattainable with
this facility.
The thermal flux seen along the core centerline at the height
of the beam ports was found to be 8.7 x 10 13n/cm 2sec.
was essentially the same for all three cases.
This value
In comparison with
other facilities, this flux level is about 6% lower than the
predictions obtained for other core configurations employing hafnium
fixed absorbers.
However, it is higher than that found in cases
where no fixed absorber is present.
68
CHAPTER 6
CENTRAL IRRADIATION FACILITY STUDIES
During the initial criticality testing of the MITR-II it was
determined that the optimum core configuration included three non-fueled
positions.
By fueling the entire B and C-rings, the three A-ring
positions would be freed for other purposes.
A facility could be
developed for this region which would allow much more space and
flexibility than found in the previously studied sample assemblies.
The size of such a facility is restricted, however, by a regulation
which limits the cross-sectional area of any in-core facility to
within 16 square inches for research reactors (Reference 17).
Since
the MITR-II is licensed by the Nuclear Regulatory Commission as a
research reactor, the full 20.3 square inches of the A-ring can not
be used.
Probably the best way to restrict the facility size is to
include a separate aluminum structure which would fit just inside of the
core spider assembly.
This would be supported by the lower grid plate
and restrained by the top hold down plate.
Such a structure would
surround a cylindrical volume with a 16 square inch cross-sectional area.
This central region could be a useful place for the irradiation
of large samples at a high flux.
of a thermal "flux-trap".
Another possibility is the development
This could be accomplished by correctly
orienting a moderating material in the central area.
Fast neutrons
entering from the surrounding fuel would be thermalized, producing
a high thermal flux.
The present chapter investigates some of the
69
potentials of this central region and proposes a "central irradiation
facility" design based on the flux-trap concept.
This design is
capable of producing a high thermal flux while limiting power peaking
to acceptable levels.
6.1
EFFECT OF VARIOUS MATERIALS IN THE CENTRAL FACILITY
CITATION calculations were first performed to investigate
the effects of several different materials in the central facility.
The materials used were fuel, water, and mixtures of aluminum and
water.
A neutron poison, in the form of an annular ring of boron-
stainless-steel, was also included in certain cases to prevent
excessive power peaking.
These cases were run using a three group energy structure,
and a two-dimensional core model similar to that described in
Section 5-1.
Hafnium fixed absorbers were positioned at a height
of 12 inches, and the boron-stainless-steel blades were at 8 inches.
Five cases were considered; each is described as follows:
Case
Material in Central Facility
1
fuel
2
90% aluminum - 10% water mixture
3
100% water, with a ring of boron-stainless-steel
poison at lower outside edge of facility, poison
density is 12.5% of the shim blade density
4
100% water with a ring of boron-stainless-steel
poison at lower outside edge of facility, poison
density is 6.3% of the shim blade density
5
10% aluminum - 90% water mixture, with a ring of
boron-stainless-steel poison at lower outside edge
of facility, poison density is 6.3% of the shim
blade density
70
Some of the results for these cases are listed in Table 6-1.
The "CITATION-only" estimates of the safety and operating limits
for each situation can be seen to be within acceptable boundaries.
The operating limits for cases 4 and 5 are the only ones which
come close to their maximum allowed value.
purposely approached in
This maximum was
order to determine the largest thermal
flux which could be obtained in the central facility, while still
avoiding unacceptable power peaking.
The highest predicted operating
limit of 3.35 (case 4) is 10% below the maximum allowed value of
3.72.
The 10% margin was allowed in order to account for the approximate
nature of the CITATION predictions, especially when a two-dimensional
core model is
used.
The poison employed for cases 4, 5 and 6 was in the form of
a
0.25 inch thick cylindrical ring of material equivalent to that
which makes up the boron-stainless-steel shim blades, but of a reduced
density.
It was positioned just inside the fixed absorber spider
assembly and reached up 10 inches from the fuel bottom.
An equivalent
poisoning strategy would be to use a higher concentration of boron
in stainless-steel and a thinner poison region.
Table 6-2 lists the thermal flux levels located near the
tips
of the beam ports, and the value of the maximum thermal flux attained
in each facility.
These predictions are not as accurate as those
which would be obtained from a three-dimensional calculation.
However,
they can be used to gain a rough idea of the expected fluxes.
Beam
port flux values for the fuel and the 90% aluminum - 10% water mixture
TABLE 6-1
Results of two-dimensional CITATION study of various materials in the central facility
Max. Safety Limit*
Material in Facility
Keff
value
position
1
Fuel
1.0929
1.50
at core CL 1.62
2
90% Al - 10% H20
mixture
1.0286
1.65
at edge
of core
3
100% 1120 with B-SS
poison (density =
12.5% blade density)
.9620
1.81
4
100% 1120 with B-SS
poison (density =
6.3%blade density)
.9782
5
10% Al - 90% 1120
mixture with B-SS
poison (density =
6.3% blade density)
.9829 +
Case
value
Max. Operating Limit*
height above fuel
FR
position bottom (inches)
FA
_Z
at core CL
9
.98
1.52
.65
2.44
at edge
of core
5
1.08
2.02
.53
B-ring,
near
spider
2.98
B-ring,
near
spider
11
1.18
1.80
.84
2.06
B-ring,
near
spider
3.35
B-ring,
near
spider
11
1.35
1.65
.87
2.04
B-ring,
near
spider
3.29
B-ring,
near
spider
11
1.34
1.64
.87
*These are "CITATION-only" values computed with a blade height of 8 inches; fixed hafnium absorbers were
at 12 inches. All values of dFP were taken to be .94, the lowest measured value for the 3 dummy core.
+A different mesh spacing arrangement was used for this case, it is therefore not appropriate to compare
this value with the previous Kef f values.
H
72
TABLE 6-2
RESULTS OF CITATION FLUX CALCULATIONS FOR
VARIOUS MATERIALS IN THE CENTRAL FACILITY
Case
Material in Facility
Beam Port Ihermal
Flux(n/cm sec)
Max. Thermal Flux
in Facility(n/cm sec)
1
Fuel
7.3 x 1013
3.3 x 1013
2
90% Al - 10% H20
mixture
7.9 x 10 13
5.9 x 1013
100% H 20 with B-SS
poison (density
= 12.5% blade density)
8.4 x 10 13
2.6 x 1014
100% H20 with B-SS
poison (density = 6.3%
blade density)
8.8 x 10
13
2.7 x 1014
10% Al - 90% H20 with
B-SS poison (density
= 6.3% blade density)
8.8 x 10 13
2.5 x 1014
3
4
5
73
are the lowest seen in any of the computer calculations performed
for this work.
However, the results for cases 4 and 5 are among
the highest found for any irradiation facility; only the flooded
single element sample holder with fixed absorbers produced a higher
beam port flux.
A maximum thermal flux of 2.7 x 10
in case 4.
n/cm2 sec was developed
This configuration positioned 100% water in the facility
and boron-stainless-steel (of lower density) at the edge of the
facility.
Increasing the poison density was found to decrease the
magnitude of the thermal flux (case 3); reducing the water density
also had the same effect (case 5).
Plots of the fluxes in the central facility for cases 1, 2 and
4 are given in the next several figures.
Figures 6-1 and 6-2 show
the thermal and epithermal fluxes axially along the centerline of
the core.
The water-filled region produced the highest thermal flux
reaching its maximum of 2.7 x 1014 n/cm2 sec at a height of about
7 inches up the facility.
However, it also produced the lowest
epithermal flux levels of the three cases considered.
With fuel in
the central facility, the epithermal flux was optimized, but the
thermal flux was the lowest over the active core length.
The fluxes
obtained in the active core for the 90% aluminum - 10% water mixture
were intermediate between the other two cases.
Figure 6-3 plots the thermal flux radially outward from the
centerline at a height of 7 inches above the fuel bottom.
For the
water case, the thermal flux can be seen to drop sharply at the
region containing the boron-stainless-steel poison.
74
H2 0 with 6.3% B-ss
i11I
90%
920 mixture
fuel
10133
FIGURE
103
0
2
6-1.
Thermal flux along centerline of
central facility filled with
various materials.
4
6
6
10
12
14
16
1
HEIGHT ABOVE BOTTOM OF THE FACILITY (inches)
75
fuel
90% Al-10% H20 mixture
H2 0 with 6.3% B-ss
1013-
FICURE 6-2.
0
2
Epithermal flux alon6 the centerline of the
central facility filled with various
materials.
18
16
14
12
10
8
6
4
HEIGHT ABOVE BOTTOM OF THE FACILITY (inches)
20
22
24
76
FIGURE 6-3. Thermal flux as a function of distance from
the centerline of the central facility
filled with various materials.
(Height is 71n. above fuel bottom.)
V&
H20 with 6.3% B-ss
cenra
Aixture
H2
facilit
20
101-
90/0 Al-10% H20 mixture
fuel
centerline
0
2.0
1.5
.5
1.0
RADIAL DISTANCE FROM CENTERLINE OF FACILITY (inches)
2.5
3.0
3.5
77
6.2
PROPOSED CENTRAL IRRADIATION FACILITY DESIGN
In developing an effective central irradiation facility
design, the thermal flux levels should be optimized while holding
the core's maximum safety and operating limits to acceptable values.
As seen previously, power peaking can be reduced by excluding water,
by introducing a poison region, or both.
Each of these options,
however, can degrade the thermal flux levels.
The design proposed in this section employs both means of
reducing power peaking.
First, it places aluminum near the botton
and outside edges of the facility to exclude water.
Second, it
includes a ring of molybdenum oxide samples in the lower outside
area of the facility to act as a poison.
Since resonance capture
accounts for a large fraction of the neutron absorption in molybdenum,
the positioning of these samples in this high epithermal flux region
should be suitable.
Periodic removal and replacement of the molybednum
samples will allow the recovery of the valuable technetium produced by activation of molybdenum -
99m isotope
98.
A vertical cross section of the proposed facility is shown in
Figure 6-4.
The central sample tube extends down to a point that is
4 inches above the fuel bottom.
It is immediately surrounded by
a wide water region, which will produce a high thermal flux in the
tube.
volume.
Regions of aluminum and molybdenum oxide surround the water
In the actual core setup, the molybdenum could be in the
form of samples with a rectangular cross section, set side by side
as shown in Figure 6-5.
Another possibility is the use of small
cylindrical samples as shown in Figure 6-6.
78
FIGURE 6-4. Vertical cross section of proposed central
irradiation facility. (approximately onehalf scale)
aluminum
support
structure
central
sample tube
aluminum
filler
plug
molybdenum
sample
regions
aluminum
inner
structure
nozzle
central sample
tube,
aluminum
support
structure
molybdenum
sample
regions
inner
aluminum
structure
FIGURE 6-5.
Horizontal cross section of proposed central irradiation facility with
rectangular molybdenum sample regions.
central sample
tube ,
aluminum
support
structure
inner
aluminum
structure
molybdenum
sample
regions
0
FIGURE 6-6. Horizontal cross section of proposed central irradiation facility with
cylindrical molybdenum sample regions.
81
The two-dimensional core model and zone compositions used
to mock up this facility are depicted in Figure 6-7.
Table 6-3
lists the materials associated with each zone composition.
The
hafnium fixed absorbers and boron-stainless-steel shim blades were
positioned at 12 inches and 8 inches, respectively, and aluminum
was placed in the sample tube for this calculation.
Estimates of the technical specification limits provided by
this computer run are well below the maximum allowed values.
The
largest "CITATION-only" safety limit of 2.00 occurs in the B-ring
of elements, adjacent to the central spider.
The maximum operating
limit of 3.09 also occurs in the B-ring, at a height of 7 inches
above the fuel bottom.
The thermal flux predicted to occur near the tips of the beam
ports is 8.65 x 1013 n/cm 2sec.
This is higher than the estimate
for the voided molybdenum sample holder in a core without fixed
absorbers.
However, it is less than or equivalent to the values
obtained for the other facilities which employ fixed absorbers.
The thermal flux in this proposed central irradiation facility
reaches a maximum value of 1.97 x 10
the sample tube's lower tip.
n/cm2 sec at a point just below
The flux levels remain high in the
lower half of the aluminum sample and in the water surrounding the
sample.
This can be noted in the thermal flux map of Figure 6-8.
The epithermal flux is found to be fairly constant throughout the
lower section of the facility,always close to a value of 6.0 x 10 13n/cm 2sec.
The fast (above 3 KEV) flux dips significantly in the central facility,
as would be expected with a "flux-trap" design.
The lower half of the
82
FIGURE 6-7. Two-dimensional core model used for proposed
central facility calculations.
(not to scale)
2
83
TABLE 6-3
ZONE CONPOSITIONS FOR 3 GROUP FLUX-TRAP
FACILITY CALCULATIONS
(Omitted numbers were not used)
Zone
Nuclide Number
Nuclide Name
Number Density (atoms/cm-b)
x 10~x 105
x 102
x 10-2
U-235
U-238
H 0
Ai
4.390
3.359
1.545
3.183
32
33
H 0
Ai
1.655 x 10 2
3.012 x 10 2
5
15
16
14
13
U-235
U-238
H 0
Ai
4.390
3.359
1.545
3.183
x
x
x
x
6
17
18
19
20
U-235
U-238
H2 0
Al
4.390
3.359
1.545
3.183
x 10
-5
x
x 10-2
x 10
7
21
22
47
D20
Al
H2 0
3.275 x 104
1.621 x 104
1.646 x 10
10
38
Al
6.023 x 10-
11
53
Al
6.023 x 10 2
14
28
29
31
30
U-235
U-238
H20
Al
4.390
3.359
1.545
3.183
1
1
2
3
4
2
x
x
x
x
1010-2
102
10-2
2
10
10-2
10 2
10
84
Zone
Nuclide Number
Nuclide Name
Number Density (atoms/cm-b)
2
15
39
40
H20
Al
1.655 x 10
3.012 x 10-
16
41
C
2
8.334 x 10
17
42
43
D2 0
Al
1.654 x 103.120 x 10-
18
44
H20
2
3.340 x 10
20
47
H 20
3.340 x 10-2
21
48
H20
2
3.340 x 10
25
32
H20
2
3.340 x 10
27
35
60
Al
Hf
4.455 x 103.188 x 10-
31
62
B-SS
9.026 x 10-
33
32
53
H2 0
Al
1.336 x 105.782 x 10-
34
32
59
H 0
Mg
1.670 x 10- 32
1.864 x 10-
85
FIGURE 6-8. Vertical section of proposed central facility
showing lines of constant thermal flux.
(valnes in 10-14n/cm 2 sec)
K)>
.
86
sample sees a fast flux of approximately 1.1 x 10 14n/cm2 sec.
Another CITATION calculation was performed to investigate
the effects of flooding the central sample tube.
this flooded case is 1.0117;
calculation) is 1.0136.
-0.19%A&K
The K
for
the voided value (from the previous
This results in a reactivity change of
due to flooding.
The thermal flux in the flooded
sample tube reaches a peak of 2.5 x 10 14n/cm 2sec at a point about
2 inches above the bottom of the tube.
The beam port thermal flux
levels remain almost unchanged.
The technical specification limits for the flooded case occur
at the same locations, but increase in magnitude.
The maximum
"CITATION-only" value of the safety limit increases by 2% to a value
of 2.04 , while the operating limit increases 4% to a value of 3.21.
Suppression of the power peaking in this design is due largely
to the exclusion of water by the molybdenum samples and the aluminum
structural material.
The absorption effect of the molybdenum plays
only a minor role in reducing the safety and operating limits.
Therefore, it would most likely be possible to use the molybdenum
sample positions for any materials which must be irradiated.
This
would provide greater flexibility in the management of in-core
irradiation samples than would be available with a single sample tube
alone.
87
CHAPTER 7
CONCLUSIONS AND RECMMNDATIONS FOR FUTURE WORK
This work is an investigation of the neutronic effects of
one, two, and three element sample assemblies for the MITR-II.
Before much of this work could be carried out, various three and
fifteen group cross section sets had to be generated and prepared
for input into the CITATION computer code.
in this work are described in Chapter 2.
The procedures involved
In addition, an updated
listing of the three group CITATION cross section library is
provided at the beginning of the sample computer run of Appendix D.
The safety and operating limits have been estimated for
various core configurations of the assemblies.
Prediction factors,
as described in Section 3.3, have been used to compensate for the
fact that CITATION generally underpredicts these limits.
The results
of the calculations have shown that in the five dummy core, the
molybdenum
saiple holder can be safely operated in either a voided or
flooded condition with a shim blade height of up to 13.6 inches at a
core power of 2.5 MW.
A three dummy case, which includes the flooded
molyb d enum sample holder, hafnium fixed absorbers at 12 inches,
boron-stainless-steel shim blades at 8 inches, was also studied.
and
This
configuration was found to result in safety and operating limits which are
within acceptable margins.
The technical specification limits for the
88
double element facility are far below the maximum allowed values,
but flooding of the large sample channel is not acceptable.
(As
more information becomes available about the hafnium poisoned core,
the validity of the underprediction factors used in these estimates
should be checked.)
The "CITATION-only"
limits for the central irradition facility
proposed in Chapter 6 are well within their allowed ranges.
However,
these values were obtained from a two-dimensional calculation which
does not provide adequate detail for accurate limit evaluation.
A
three-dimensional computer analysis of this facility should be undertaken for more precise predictions.
The B-ring underprediction factors
should also be evaluated and applied for this core configuration.
When calculating the technical specification limits, the value
of the plenum flow disparity(ratio of the coolant flow through the
element in question to the average element's flow) is of considerable
importance.
Measured values from the three and five dummy cores
were used in analysis of the single and double element assemblies.
For the work in Chapter 6, however, a conservative plenum flow disparity
of 0.94 was assumed for each channel.
This number is well below the
B-ring values measured for the three and five dummy cores.
In addition,
it is likely that introduction of the proposed flux-trap would divert
additional flow to the B-ring, producing larger dFp values than
those measured.
This would result in much lower "CITATION-only" safety
and operating limits than shown in Chapter 6.
Maintenance of high thermal flux levels in the beam ports is an
important consideration when developing a sample assembly design.
The
89
largest calculated beam port flux value was 9.3 x 10 13n/cm 2sec
(excluding the unrealistic case in Appendix B which used the old
cadmium cross section set).
This value of 9.3 x 10 13n/cm 2sec
was reached in the hafnium poisoned core with the flooded molybdenum
sample tube (Chapter 4), and in the three-dummy fixed-absorber
cores described in Appendix B.
The proposed three-element flux-trap and double element sample
facility both produce beam port fluxes of 8.7 x 10 13n/cm 2sec.
8.5 x 10 13n/cm 2sec was the lowest value generated in any of the
functional sample assembly configurations.
This occurred for the
voided molybdenum sample assembly in a core without fixed absorbers.
Table 7-1 contains the beam port flux values obtained for various
core configurations; the maximum fast and thermal flux values seen
in each setup are also listed.
The maximum thermal flux predicted to occur for any core
configuration was 2.7 x 1014 n/cm 2sec.
This value was attained
with a completely flooded central core region (16 square inches
in horizontal cross section) and boron-stainless-steel poison
at the core bottom.
Of the irradiation facilities studied, the
proposed flux-trap produced the greatest thermal flux, reaching
2.0 x 10 1n/cm 2sec.
With flooding of the central sample tube,
this value increased to 2.5 x 10 14n/cm2sec.
The remainder of
the experimental facilities developed much lower thermal flux levels.
For example, the maximum achieved with the flooded molybdenum
sample holder with hafnium fixed absorbers was 8.5 x 1013 n/cm2sec,
and the double element facility reached a value of only 5.7 x 10 13n/cm 2sec.
TABLE 7-1
RESULTS OF CITATION FLUX CALCULATIONS FOR VARIOUS CORE CONFIGURATIONS
Thermal Beam
Port Flux (n/cm2 sec)
Max. Thermal Flux
in the Facility
Max. Fast (>3 KEV) Flux
in the Facility
4 dummy core & voided
moly sample holder Cd
blades at 8"
8.5 x 10 3
5.4 x 10 13
1.6 x 1014
2 dummy core & flooded
moly sample holder, Hf
fixed at 12", B-SS
blades at 8"
9.3 x 1013
8.5 x 1013
1.7 x 1014
Double element facility
with steel & moly in
place, Hf fixed at 12",
B-SS at 8"
8.7 x 1013
5.7 x 1013
1.7 x 1014
Fully flooded central
facility with B-SS
poison (6.3% of blade
density)
8.8 x 1013
2.7 x 1014
1.2 x 1014+
a)voided central tube
8.7 x 1013
2.0 x 1014
1.2 x 1014
b)flooded central tube
8.7 x 1013
2.5 x 1014
1.1 x 1014*
Core
Configuration
Proposed flux trap
Occurs at edge of facility
*Maximum values in the central sample tube
'.0
0
91
CITATION showed that the optimum assemblies for producing a
fast flux were the double element facility and the molybdenum
sample holder (with fixed absorbers in place).
The maximum values
obtained for the flux component above 3 kev.were close to 1.7 x 10 14n/cm 2sec
for each facility.(The flux above .9
MEV was found to peak at
5.2 x 10 13n/cm 2sec in the steel sample of the double element facility.)
The flux-trap design of Chapter 6 produced a fast flux of only 1.2 x 1014
in its central sample tube.
It should be noted that the central region of the core is
potentially useful for many other types of facilities besides the
proposed flux-trap design.
A central facility might be designed
to place a region of fuel material immediately adjacent to a
sample tube.
This would allow an ideal place for the irradiation of
samples in a fast flux.
Another possibility is a facility which
Larger
would provide space for the irradiation of very large samples.
samples could be allowed for in the design of the flux-trap facility,
simply by the use of a larger sample tube.
manner would reduce the thermal flux levels.
Excluding water in this
However, operation of the
tube in a flooded condition would help to alleviate this problem.
Flooding some of the sample tubes in the proposed flux-trap might
be a useful way to increase the thermal flux attained.
For example,
if specimens were placed in the molybdenum sample regions, the central
sample tube might be flooded.
The calculations performed in Chapter 6
determined that this procedure would increase the thermal flux levels
in the specimens by up to 5%, and by slightly higher percentages
in the aluminum filler region above the specimens.
Conversely, it
92
may be possible to flood some of the molybdenum sample regions in order
to maximize the thermal flux in the central sample tube and remaining
molybdenum regions.
Further calculations would be necessary to assure
that the safety and operating limits would be acceptable for these
conditions.
It has been seen that a large part of the analysis of potential
core configurations and irradiation facilities deals with predicting
the technical specification limits.
make this work
cases.
The present computer models
difficult by underpredicting these limits in most
A more desirable prediction scheme has been suggested by
Allen (Reference 14).
He proposes that a full core analysis first
be performed in order to find the relative power
each core position.
produced in
This would point out several potentially troublesome
elements in which the worst peaking might occur.
A more detailed
calculation would then be performed for each of these elements.
Only the element itself would be considered in this computer model,
and artificial boundary conditions would be employed to simulate the
environment surrounding a particular element.
If it is known with some certainty where the power peak will occur,
an alternative procedure may be suitable.
This would be to increase
the number of mesh lines, but only in the region of the expected
peak.
A more detailed power density map would be generated in this
way, and the accuracy of the limit predictions would improve.
This
scheme would be useful for investigating effects such as peaking
adjacent to a flooded sample holder, or the peaking for a well-understood
core configuration.
93
Another consideration in determining the future use of a flux
trap facility is that of the reactivity worth in the core.
It was
found during the startup testing of the MITR-II that a core
configuration employing three solid aluminum dummies would be
the most useful at that time.
However,
three-dimensional CITATIONruns
have shown that switching from this original three dummy core
(dummies in A-1, B-2, and B-8 with cadmium absorbers) to one with
the same absorbers but a completely flooded central facility and
with fuel in each B and C-ring position, would result in a reactivity
decrease of approximately 1.35%
AK
.
(Since the proposed flux trap
is not completely water filled, the reactivity drop would not be this
great, but a decrease would still occur).
The contral blades would
have to be raised to compensate for this effect, causing the thermal
flux levels in the beam ports to decrease.
In addition, fuel burnup
and fission product poisoning will decrease the reactivity worth of
the core even further.
It has been measured that these effects
decrease Keff by about .08% for an average week of scheduled operation
at 2.0 MW to 2.5 MW.
Therefore, it may eventually be desirable to
increase the fuel loading over the three-dummy core loading in order
to allow operations at lower shim blade heights.
This could not be
accomplished with the flux-trap facility and fixed absorbers both
in place.
94
REFERENCES
1.
Fowler, T. B., Vondy, D. R., and Cunningham, G.- W.,
CITATION",
"Nuclear Reactor Core Analysis Code:
ORNL-TM-2496, (Revision 2, 1971).
2.
Kadak, A. C., "Fuel Management of the Redesigned MIT
Research Reactor", Ph.D. Thesis, MIT Department of
Nuclear Engineering, (1972).
3.
Addae, A. K., "The Reactor Physics of the Massachusetts
Institute of Technology Reactor Redesign", Ph.D. Thesis,
MIT Department of Nuclear Engineering, (1970), MITNE-118.
4.
Hansen, G. E. and Roach, N. H., "Six and Sixteen Group Cross
Section for Fast and Intermediate Critical Assemblies",
LAMS-2543.
5.
A Fortran IV Code for
Fowler, T. B., et al, "EXTERMINATOR-II:
Solving Multigroup Diffusion Equations in Two Dimensions",
ORNL-4078 (1967).
6.
A Thermalization Transport Theory
Honeck, H. C., "THERMOS:
Code for Reactor Lattice Calculations", BNL-5826, (1961).
7.
Henry, A. F.,
"A Theoretical Method for Determining the Worth
of Control Rods", WAPD-218, (1959).
8.
Case, K. M., et al, "Introduction to the Theory of Neutron
Diffusion (Volume I), "Los Alamos Scientific Laboratory,
(1953).
9.
10.
Emrich, W. J., "Reactivity Studies of the MITR-II", S. M. Thesis,
MIT Department of Nuclear Engineering, (1974).
Hughes, D. J. and Harvey, J. A.,
"Neutron Cross Sections",
BNL-325, (1955).
11.
Stein, S.,
"Resonance Capture in Heterogeneous Systems",
WAPD-139, (1955).
12.
MITR Staff, "Safety Analysis Report for the MIT Research
Reactor (MITR-II)", MITNE-115, (1970).
13.
MITR Staff, "Technical Specifications for the MIT Research
Reactor (MITR-II)", MITNE-122, (1973).
14.
Allen, G. C., "The Reactor Engineering of the MITR-II
Construction and Startup", Ph.D. Thesis, MIT Department
of Nuclear Engineering, (1976), MITNE-186.
95
15.
Soth, L. G., "An In-Core Irradiation Facility for the MIT
Research Reactor Redesign", S. M. Thesis, MIT Department
of Nuclear Engineering, (1972).
16.
Yeung, M. K., "Reactivity Studies of the MITR-II for
Initial Loading", 22.90 Special Report, MIT Department
of Nuclear Engineering, (1975).
17.
Code of Federal REgulations, Title 10, Chapter 1, Part 50,
United States Nuclear Regulatory Commission, (1975).
18.
Hove, C. M., "Extra Power Peaking in MITR-II Due to
Manufacturing Tolerances in the Length of the Fuel Plates",
22.90 Special Report, MIT Department of Nuclear Engineering,
(1973).
96
APPENDIX A
CONTROL BLADE HOMOGENIZATION AND MESH CORRECTION
This appendix describes a short computer program which
provides two corrections to the equivalent diffusion theory
parameters
(I
and D) which are used in modelling a control
blade region in a finite difference code.
The first correction
considers homogenization of the control blade (if it consists
of multi-layered materials) by equating the fluxes
at each internal material interface.
(and currents)
The second correction
compensates for the effect which the mesh spacing of the control
region (in the diffusion theory code) has on the blade's absorption.
The mesh correction scheme employed here is applicable if the
parameters are going to be used in a code which uses the same
finite-difference approximation as CITATION.
These correction procedures were generated by Emrich (Reference 9),
as based on work by Henry (Reference 7).
The code presented here is
a modification of a program originally written by Emrich which performs
the same function.
An infinite slab approximation is assumed for the control blade
in this work, therefore only a one-dimensional view is considered.
97
Input Variables
The variables which must be entered into the code are as follows:
Variable
Variable name
in code
(1) number of
Comments
This is equal to the number of
material regions which make up
the blade. For example, a blade
consisting of material A, clad
on each side with material B,
would have a value of 3.
blade regions
N
(2) region widths
z
These variables designate the
thickness of each blade region;
one is required for each region.
(Units are cm)
(3) number of regions
in diffusion theory
blade mockup
M
This equals the number of mesh
regions which will model the blade
when the diffusion theory parameters
are used in a code such as CITATION.
In generating values to be used in
the present CITATION models of the
MITR-II, this number will equal 1.
(4) equivalent
macroscopic
absorption cross
section (Ia)
(5) equivalent
diffusion
SA2
D2
One of these variables must be
entered for each material region.
If a material is heavily absorbing,
blackness theory (see Section 2.2.2)
must be used to develop the D2 value.
(Units are cm)
NCT
This equals the number of different
cases to be considered. If any of
the variable numbers 2, 4, or 5 are
charged, a new case must be input.
If the variable numbers 1 or 3 are
changed, a whole new run must be
accomplished with the present logic
setup.
coefficient
(6) number of
cases
One of these variables must be
entered for each material region,
starting at either side of the
blade. If a material is heavily
absorbing, blackness theory (see
Section 2.2.2) must be used to
devilop the SA2 value. (Units are
cm )
98
Input Order
Variables are input on cards in the order outlined below.
The
format for each card is also listed.
CARD 1 (3I2)
N (columns 1-2)
M (columns 3-4)
NCT (columns 5-6)
CARD(S) 2 (6E11.5)
N=1
N=2
Z (columns 1-11)
(columns 12-22)
SA2
D2 (columns 23-33)
Z
SA2
D2
etc.
Values of Z, SA2, and D2 are repeated in this manner until
values for each blade region have been specified. As many
cards as needed should be used to input the (3xN) values
for these card(s) 2.
To start a new case, a new set of card(s)2 is included
immediately after the previous card(s)2 set. Do not mix
two cases on a single card, but start each new case on a
fresh card.
This code is presently dimensioned to handle up to ten material
regions.
There is no limit to the number of cases that can be
accomplished per run.
be self-explanatory.
The output of this code is labelled so as to
IMPLICIT REAL*8(A-HO-Z)
DIMENSION R]K1(10),TK(1C),AR(2,2),BR(2,2),CR(2,2),Z(10),D2(10),
1SA1 (10) ,SA2(10)
RFAD(5,1)N,M,NCT
1 FORMAT(3I2)
DO 950 MCT=1,NCT
READ(5,900)
(Z(I),SA2(I),E2(I),I=1,N)
9C0 FORMAT(6E11.5)
DO 4 J=1,N
RK1 (J) =DSQE' (SA2 (J)/U2 (J))
WRITE (6, 375) JSA2 (J) , L2 (J) ,Z (J)
375
FORMAT($
BEG NO= ',12,1
SA2= ',E11.5,'
D2= ',
+E11.5,'
BEG SIZE= ',E11.5)
4 TK(J)=RK1(J)*Z(J)/2.
C HCMOGENIZES THE VARIOUS MATERIAL REGIONS
AR (1,1) =DCOSH (TK (1))
AR (1,2)=-DSINH (TK (1)) /(L2 (1) *RK1 (1))
AR (2,1) =-D2 (1) *RK1 (1) *LSINH (TK (1))
AR (2,2)=DCCSH(TK(1))
DO 6 K=2,N
BR (1,1) =rcosH (TK (K))
BR (1,2)=-DSINH (TK (K)) /(D2 (K) *RK1 (K))
BR(2,1)=-D2(K)*RK1(K)*ESINH(TK(K))
BR (2,2)=DCOSH (TK (K))
DO 5 I=1,2
DO 5 J=1,2
5 CR(IJ)=AR (I,1)*BR(1,J)+AF(I,2)*BR(2,J)
AR (1,1)=CR (1,1)
AR(1,2)=CR(1,2)
AR(2,1)=CR (2,1)
6 AR (2,2)=CR (2,2)
DO 380 I=1,2
DO 380 J=1,2
385
WRITE(6,385) I,J,AR(I,J)
FORMAT(' MATRIX ELEMENT ',I2,'-',I2,'
=',E11.5)
380
CONTINUE
C CALCULATES THE INVERSE CCSE
X1=25.0
X2=.1D-10
7 X3=(X1+X2)/2.
Y1=DCOSH (X1)-AR (1,1)
Y3=DCOSH (X-3)-AR (1, 1)
IF (DABS (Y3)-. COC0001) 11,11,8
8 IF(Y1*Y3)9,11,10
9 X2=X3
GO TO 7
10 X1=X3
GO TO 7
11 ZK2=X3
DK2=DSQRT (AR (2, 1)/AR (1,2))
C CALCULATES THE BlACKNESS CCEFFICIENTS AND TEE MACROSCOPIC ABSORPTION
C CROSS-SECTION AND DIFFUSICN CCEFFICIENT TO EE USED IF THE HOMOGENIZED REGION
C WERE TO BE DIVIDED INTO AN INFINITE NUMBER OF SECTIONS
T= 0.0
DO 12 1=1,N
12 T=T+Z(I)
RK2= (ZK2/T)*2.
D3=DK2/RK2
SA3=D3*RK2*RK2
A2=DSQRT (D3*SA3) *DTANH (RK 2*1/2.)
B2=DSQRT(D3*SA3)/DTANIN4Rg2*T/2.)
WRITE(6,390) ZK2,DK2,rFK2,L3,SA3
390
FORMAT(' ZK2= ',E11.5,'
DK2= ',E11.5,'
RK2= 1,
+E11.5,'
L3= ',E11. 5, "
SA3= ',E11. 5)
WRITE(6,40C) A2,B2
400
FORMAT('
A2= ',E11.5,'
B2= ',E11.5)
C CALCULATES THE EFFECTIVE MESH CORRECTED ABSCRPTION CROSS- SECTION AND DIFFUSION
C CCEFFICIENT
H=T/M
SA4= (2.*A2*E2)/ (H* (B2-A2))
D4=H*B2/2.
H
0
0
WRITE (6, 13) SA4, D4
13 FORMAT('
SIGA = ',E11.5,'
950 CONTINUE
STOP
END
1/C
I',/,'ID
=
I ,E11.5,' CM')
I-A
0
H
102
APPENDIX B
THREE DUMMY CORE CALCULATIONS
This appendix gives a comparison of the results of several
CITATION calculations of three dummy core configurations with
experimental data obtained from the original three dummy core.
The configurations studied all
include solid aluminum dummies
in
the A-1, B-2, and B-8 positions, with fixed absorbers in place
in the central spider.
The cases considered are:
Case 1 -
Experimental results of original three dummy
core; fixed cadmium absorbers at 10" and
cadmium shim blades at 7.6".
Case 2 -
CITATION results using old cadmium cross
section set; fixed cadmium absorbers at 10"
and cadmium shim blades at 8".
Case 3 -
CITATION results using new cadmium cross
section set; fixed cadmium absorbers at
10" and cadmium shim blades at 8".
Case 4 -
CITATION results of potential core setup;
fixed hafnium absorbers at 12" and boronstainless-steel shim blades at 8".
The experimental data for Case 1 were obtained during the
startup testing of the MITR-II, as described by Allen in Reference 14.
The CITATION results were generated by use of a three-dimensional
core model similar to that described in section 4.2 of the present
work.
The reactor power for
each CITATION case was 5 MW.
The reactivity and technical specification limit "CITATION-only"
results are listed in Table B-1.
As stated in Chapter 2, the old
cadmium cross section set greatly overpredicted the reactivity worth
TABLE B-1
RESULTS OF 3 DUMMY+ CORE STUDY
Max. Safety Limit
Case
Case Description
Keff
value
position
Max. Operating Limit
height
(inches)
position
va lue
F
R
FA
Z
1
Experimental Data
Cd fixed at 10"
Cd blades at 7.6"
1.0000
2.17
C-8, at edge
of core
3.53
C-9, at edge
of core
5.4
1.27
2.29
.51
2
CITATION Data
with old Cd
cross section set
Cd fixed at 10"
Cd blades at 8"
.9468
1.94
C-9, at edge
of core
3.84
C-9, at edge
of core
6.1
1.26
2.38
.62
3
CITATION Data
with new Cd
cross section set
Cd fixed at 10"
Cd blades at 8"
.9830
1.91
C-8, at edge
of core
3.30
C-9 at edge
of core
6.1
1.24
2.16
.56
4
CITATION Data
Hf fixed at 12"
B-SS blades at 8"
.9879* 1.91
C-9, at edge
of core
3.27
C-9, at edge
of core
6.1
1.24
2.14
.55
+Dummies in core positions A-1, B-2, B-8
4+ These are "CITATION-only" values, no prediction factors have been applied
*A slightly different axial mesh spacing was required to model this configuration, therefore,
direct comparison of this value with the Case 2 & 3 values is not strictly appropriate.
I-.
104
of the cadmium fixed absorbers and cadmium shim blades.
This can
be seen by the low Keff prediction of .9468 for Case 2.
Case 3,
with the new cadmium cross section data, still underpredicts the
K
,
but comes closer to the experimental result.
The predicted operating limit of 3.84 for Case 2 is the only
limit which exceeds its maximum allowed value.
However, the
experimental value (Case 1) for this position was found to be
3.53, well below the maximum allowed operating limit of 3.72.
The
CITATION operating limit prediction was therefore conservative in
this particular situation.
CITATION was not conservative in predicting
the safety limit for this case, and both limits are underpredicted by
an even greater margin in Case 3.
The radial peaking factors (FR) at the maximum operating limit
for the first three cases are quite close.
however, vary considerably.
The axial peaking factors,
The maximum predicted Fa value of the
three is 2.38 for Case 2, while the smallest is 2.13 for Case 3.
The experimental value lies between these two.
Table B-2 shows the calculated thermal fluxes along the core
centerline at the height of the beam ports.
As would be expected,
the largest value is for Case 2 in which the artificially high
absorption in the cadmium forces the power and flux toward the core
bottom.
Case 2.
Cases 3 and 4 predict values approximately 13% lower than
105
TABLE B-2
BEAM PORT THERMAL FLUX VALUES GENERATED BY
CITATION FOR THE THREE DUMMY CORE STUDY
Case
Beam Port Thermal Flux (n/cm sec)
2
1.08 x 1014
3
9.37 x 1013
4
9.33 x 1013
106
Figures B-1 through B-3 compare the power distributions
along the core at three different locations.
They show the product
of the axial and radial peaking factors as a function of core
height for positions A-2, B-5, and C-8.
The experimental
data which is presented was derived from the gamma-scanning of fuel
plates.
The CITATION calculations generally underpredicted the power
produced in the upper part of the core for the A and C-ring channels.
The B-ring results for the four cases are fairly close in the
upper core, but CITATION overpredicts the power density for most
of the lower part of this element.
The CITATION power peak results
for the bottom edge of the core are consistently underestimated
for the A and B-ring positions, but overestimated for the C-ring
element.
The effect of increasing the active core height to 12
inches can be seen in the Case 4 curves on Figures B-2 and B-3.
For these B and C-ring core positions, the highest power density halfway
up the core occurred for Case 4.
The next set of figures compare the thermal neutron flux
distributions for each case.
The experimental data (Case 1) was
generated from a wire scan procedure as detailed in Reference 14.
The magnitude of the flux was originally obtained in the units of
counts per minute; a conversion was therefore needed to produce
values of the flux.
A factor of 186.5 counts/minute = 10 13n/cm 2sec
(at 5 MW) was chosen by Allen after comparing the wire scan and CITATION
results at the incore locations where the confidence in CITATION
predictions is greatest.
3
FIGURE B-1. Core power peaking as a function of
axial position for element A-2.
F FA
Case 1
Case 4
Case 3
15
HEIGHT ABOVE FUEL BOTTOM (inches)
H
0
W,
3.0
2.5
FIGURE B-2. Core power peaking as a function of
axial pcsition for element B-5.
F F
R A
Case 2
2.0
1.5
Case 4
Case 1
1.0
Case 3
.5
0
0
10
HEIGHT ABOVE FUEL BOTTOM (inches)
15
20
I-A
FIGURE B-3. Core power peaking as a function of
axial position for element C-8.
Case 2
3
FR A
Case 1
2
Case 4
1
Case 3
0
10,
HEIGHT ABOVE FUEL BOTTOM (inches)
20
10
7
6
FIGURE B-4. Thermal flux as a function of axial
position for element A-2.
Nj
H
4
0
2
3 -Case
2
LCase
4
Case
0
1
5
10
HEIGHT ABOVE FUEL BOTTOM (inches)
15
20
8
7
FIGURE B-5. Thermal flux as a function of axial
position for element C-8.
U
>5
Case 2
Ea
.- 3
2
Case
4
Case 3
1
Case 1
0
5
HEIGHT
10
ABOVE FUEL BOTTOM (inches)
15
20
HJ
H
12
FIGURE B-6. Thermal flux as a function of axial
position for corner hole #2.
C\)n1
E)
Qn-
0'
2
Case 1
Case 3Case
4
2
0
5
10
HEIGHT ABOVE FUEL BOTTOM (inches)
15
20
H
H
113
The core locations considered are the A-2 and C-8 core positions
and the water filled corner hole #2, which is adjacent to core
position C-3.
At the two in-core locations, the CITATION calculations
of cases 2 and 3 present a good approximation to the measured flux
shape over most of the core's length.
In the corner hole however,
the CITATION values are consistently low.
Once again, the CITATION
calculations underpredict the peaking effect at the lower edge of
the core.
This is especially true in the corner hole positions.
114
APPENDIX C
THE COMPUTER CODE, LIMITS
This appendix describes a short computer code called LIMITS,
which estimates the safety limit and the two-pump operating limit
for the MITR-II.
This program uses CITATION power density
information to produce values for the radial peaking factor (FR)
the axial peaking factor (FA),
and the axial location factor (Z).
Each of these factors are then multiplied by prediction factors
which were developed by comparing experimental data with CITATION
data
(as shown in Tables 3-3 and 3-4).
The choice of prediction
factors depends upon the core configuration and the core location
Corrected values of FR, FA, and Z are then used in
considered.
the equations which appear in Chapter 3 to find the predicted safety
and operating limits.
Certain factors are written into this code as constants since
they do not normally change from run to run.
These are as follows:
Constant Value
Factor
1.211
FH
F,P1.000
dFC
.887
W
8.91 x 10
WT
To
lbm/hr
1.000 (since this code considers 2 pump operation)
C
.9985 BTU/lb-*F
F0
1.55
n
1.9
F'
1.122
PT
6.0 MW (since this code considers 2 pump operation)
0
115
Input Variables
The variable factors which must be input into the code are
as follows:
Variable
Comments
Variable name in Code
(1)
plenum flow
disparity
DFP
A separate value must be
input for each channel
considered. These numbers
have been empirically
determined for 3 and 5
dummy cores, as listed in
Table 3-2.
(2)
plane power
densities
PD
These values are obtained
from CITATION output, one
is input for each fueled
plane (starting at the core
bottom) in each channel.
3
(Units are w/cm )
(3)
number of
fuel planes
NP
This is the number of axial
segments into which the fuel
is partitioned.
(4)
heat transfer
coefficient - h
0
XHT
Values for 3 and 5 dummy cores
are listed in Table 3-1.
Values for other core configurations are determined by
use of the following equation:
XHT
=
BTU
(32857.12hrft2oF
1 .8
N
where N = number of fueled
core positions.
(5)
surface area of
PA
fuel meat - A
Values for 3 and 5 dummy cores
are listed in Table 3-1. Values
for other core configurations
are determined by use of the
following equation:
PA = (9.70 ft 2)N.
(6)
average power
per square cm
APD
This factor equals the total
reactor power divided by the
fueled area in a horizontal
slice across the core.
(Units are w/cm 2 )
116
(7)
fraction of flow
cooling fuel - Ff
FF
Experimentally determined values for
3 and 5 dummy cores are listed in
Table 3-1.
(8)
radial peaking
prediction factor
PFR
This factor compensates for CITATIONS's
error in predicting values for
FR'
(See Tables 3-3 and 3-4.)
(9)
axial peaking
prediction factors
PFA
These factors compensate for CITATION's
error in predicting values for F . One
value is input for each axial mesh
surface in (or bordering on) a fueled
plane. NP+l values must be entered.
(See Tables 3-3 and 3-4.)
(10)
axial location
prediction factors
PFZ
These factors compensate for CITATION's
error in predicting values for Z. One
value is input for each axial mesh
surface in (or bordering on) a fueled
plane. NP+l values must be entered.
(See Tables 3-3 and 3-4.)
(11)
axial plane
thickness
DELH
These are the distances between axial
mesh surfaces within the fueled region
starting with the thickness of the
bottom fueled plane. (NP values must
be entered.)(Units are cm.)
(12)
number of cases
per start
(defined below)
M
Each case is defined as a single
channel investigated in a particular
core configuration (start). A value
for the variable DFP(#l above), and
a series (NP in number) of PD (#2)
values are input for each case.
(13)
number of starts
L
This designates the number of different
core configurations being considered.
The variables NP, XHT, PA, APD, FF,
PFR, PFA, PFZ, DELH, and M (#3 through
12) are input for each new start. If
any of these variables are changed, a
new start must be made. Single values
are input for each of the variable
numbers 3 through 8 and 12. A series
of values (NP+1 in number) must be
input for the variable numbers 9
through 11.
117
Input Order
Variable factors are input on cards in the order outlined below.
The format for each card is also listed.
Card 1 (12)
L (columns 1 -
2)
(A single card 1 is input each time the code is run.)
The following cards (2 - 6) are input for each new start:
Card 2 (212, 4E11.5)
M
NP
APD
FF
PA
XHT
(columns 1 (columns 3 -
2)
4)
(5 - 16)
(17 - 28)
(29 - 40)
(41 - 52)
Card 3 (Ell.5)
PFR (columns 1 - 11)
Card(s) 4 (6E11.5)
PFA
(Values of PFA, starting at the fuel bottom, are input on as
many cards as are needed. NP+l values must be entered.)
Card(s)
5 (6E11.5)
PFZ
(Values of PFZ, starting at the fuel bottom, are input on as
many cards as are needed. NP+l values must be entered.
NOTE: The first and last values of PFZ for any particular
channel will always equal 1.000.)
Card(s)
6 (6E11.5)
DELH
(Values of DELH, starting with the bottom fueled plane, are
input on as many cards as are needed. NP values must be
entered.)
118
The following card(s) is/are input for each new case:
Card(s)
7 (6Ell.5)
DFP (columns 1 - 11)
PD
(Values of PD, starting with the bottom fueled plane, are
input on as many cards as are needed. NP values must be
entered.)
A normal data input begins with a single card 1, followed
by a set of cards 2 through 6 which provide information for the
first start.
One or more sets of card(s) 7 then follow;
each
set provides information concerning a particular channel in the
core described by the start information (cards 2 - 6).
If more
than one start is to be made, a new set of start cards (2 - 6) will
immediately follow the last of the channel information cards (7)
of the previous start.
There is no limitation on the number of starts
which can be made, or on the number of cases that can be included
under each start.
The present dimensioning of the code allows for
up to twelve axial mesh planes in the fueled core region.
The
output of the code is clearly labelled so as to be self-explanatory.
LIMITS develops the safety and operating limits only at specific
points in the core.
By the nature of the computer data which are
available, it is impossible to find the limits at each core location,
such as at every axial position along a hot channel.
It would therefore
be possible for the code to "average-over" a peak which actually
occurs in the core.
This fact must be considered when looking for
the maximum safety and operating limits of a particular core setup.
1
2
100
3
4
20
18
DTMENSION DELH(12),-D(12),FA(12),Z(12),G(12),RRR(12),
+0L (12) ,QDH (12) ,QSUM (12) ,EFfA (12) ,PFZ (12) ,cED (12) ,CFA( 12)
READ (5,1) L
FORMAT(I2)
DO 25 J=1,I
READ(5,2) MNP,APr,FF,PA,XHT
FORMAT (2I2,L4E1l.5)
RFAD(5,100) PiER
FORM AT(E11.5)
READ (5,3) F:AND, (PA (I) ,I=1,NP)
READ (5,3) PF7ND, (PFZ (I) ,1=1, NP)
READ (5,3) (DEL H (I) , I= 1,N P)
FORMAT(6E11.5)
DO 25 JJ=1,,
READ (5,4) D FP, (PE (I) ,I=1,NP)
FORMAT(6E11.5)
SUBSUM=0.0
DO 20 JJJ=1,NP
QDH (JJJ)= (PE (JJJ)) * (DELH (JJJ))
QSUM(JJJ)=SUBSUM+QDH(JiJ)
SUBSUM=QSUM (JJJ)
FR= (QSUM (NP) ) /APL
FR=FR*PFF
DF= (.887) *LFP
SL=(1.211)*FR/(DF*FF)
BUCK=0.0
SEDND=0. 0
DO 18 K=1,NF
SED(K)=BUCK+DELH (K)/2.54
BUCK=SED(K)
FA (K)= (60.b5)*PD (K)/QUM (NP)
DMZ= (DELH (1) ) /2.
DMZZ=DELH(1) +(DELH(2))/2.
FAND=(DMZ*FA (2) -DMZZ*FA (1))/(LMZ-DMZZ)
FAND=FAND*FiAND
ZND=0. 0
212
205
5
8
6
15
101
7
25
PDND=(DMZ*ID (2) -DMZZ*PL (1)) /(EMZ-DMZZ)
GND= ((72577E. 12) *FR*FAND/ (XHT*PA) )/ ( (FF*DF) **.8)
hRRND=2.77*((6.*FR *FANE/(1.9*PA))**.466)
OLND=GND-1 .-RERNI
DO 205 K=1,NP
KPLUS=K+1
TF (K.EQ. NP) CFA (K)=FA (1)
IF (K.EQ. NP) GC TO 212
SEDBK=SEE (K) -DELH (K)/2.C
SEDFO=SED (K) +DELH (KPLUS) /2.O
CFA (K) =FA (K) + (FA (KPLUS) -F (K) ) * (SED (K) -SEDBK) /(SEDFO -SEDBK)
CFA(K)=PFA(K)*CFA(K)
Z (K) =QSU r (K) /CSUM (N P)
Z(K)=Z (K)*PFZ(K)
G(K)=((725778.12)*FR*CFA (K)/(XHT*PA))/((FF*DF)**.8)
RPR(K)=2.77* ((6.*FR*CFA (E)/ (1.9*PA)) **.466)
OL (K)=1. 122*FF*Z (K) /(DF*Ff) +G (K)- 1.0-RPR (K)
WRITE(6,5) JJJ,FRSL
FORMAT(V
START # = ',12,'
CASE # = ',12,'
FR = I,
+E11.5,'
SAFETY LIM = ',E11.5)
WRITE (6,8)
FORMAT('
,/,'
')
WRITE (6,6) SEDND,PDND, FANE, ZNDGND,OLND
FORMAT(V
HEIGHT = ',E11.5,'
P.D. = ',El1.5,
+'
FA
',E1l.5,'
2 = ',El1.5,'
G = ',E11.5,
+'
O.L. = ',E1.5)
DO 15 KK=1,NP
WRITE (6,6) SEE (KK) ,PD(KK) ,FA (KK) ,Z (KK) ,G (KK) ,OL(KK)
CONTINUE
WRITE(6,l01) DFP,APD,Ff,A,XHT
FORMAT("
EFP= ',E1l.5,'
APD= ',E11.,'
FF= ', El 1.5,
+'
PA= ',E11.5,'
11= ',E1l.5)
WRITE (6, 7)
FORMAT(/////)
CONTINUE
STOP
0
121
APPENDIX D
SAMPLE CITATION OUTPUT
This appendix consists of an updated listing of the CITATION
three group cross section set, followed by a sample output of a
CITATION calculation.
The calculation is that of a two dummy
core with the molybdenum sample assembly in a flooded condition.
This calculation is fully discussed in Section 4.2
EDIT OF CITATION CROSS SECTION TAPE FOLLOWS
CROSS SECTION SET
RECORD I
TITLE ****-
I
MICROSCOPIC CROSS-SECTIONS FOR THE MITR-1!
RECORD 2
DATA TYPE. NO.NUCS, NJ.GRPS, OWSCATUPSCAT, EXTRA
-2
63
3
2
0
0
QFCORD 3
GPOUP CHIS
1.003000E+00
0.0
0.0
UPPER ENFRGY or FACH GROUP
1.13000E+06 3.000000E+03
MEAN
rNERGY OF EACH
5.477200E+04
1/V
4.000000E-01
GrOfUP
3.464000F+O1
1.000000E-02
SIGMA FOR FACH GROUP
1.990000E-09 2.778000E-07
DELAYED NFUT. PPFCURSOR DECAY
1.241000E-02 3.059010r-02
0.0
GAMMA ENERGY STRUCTURF
000
0.0
0.0
RECORD
4.247000E-06
CONSTS.
1.11000OF-01
3.010000E-01
1.140000E+00
3.010000E+00
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
4
SIMPLE NUC.NO,
NAME *****
GENERAL DATA
0.0
3.3
0.0
0.0
0.0
6.599999E-04
0.0
OTHER
NUC.NO,
SIGMA INO.SCAT.IND.
0.0
0.0
0.0
0.0
0.0
0.0
0,0
3.225800E-1L
0.0
0.0
0.0
0.0
0.0
0.0
EXTRA
0.0
0.0
0.0
0.0
0.0
0.0
0.0
1
0
0
0.0
0.0
0.0
0.0
0.0
5. 200000F-04
0.0
0.0
0.0
0.0
0
0
0.0
3.460000E-03
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
6.239999E-03
0.0
0.0
0.0
1.82000JE-03
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
3.100000E-03
0.0
0.0
RECORD 5
ISIGA(K), SIGF(K), SIGTR(K), SNU(K). SIGX(K), KulKMAX)/I(SIGS(KK,KKKuL,KMAX),KxL.KMAX)
2.049700E+00 1.745600F+00 6.579100F+00 2.553500F+00 0.0
4.012399E+01
4.325701E+02
0.0
RECORD
2.842900E+01
3.687100E+02
4.755199E-03
2.44930)F+00
2.442000E+00
0.0
0.0
0.0
0.0
4.420899E-03
6
SIMPLE NUC.ND, OTHER
NAME ****+
GENPRA. DATA
0.0
0.)
0.0
0.0
0.0
0.0
0.0
RFCORD
4.452699E+01
4.413899E+02
0.0
NUC.NO,
SIGMA IND.SCAT.IND,
EXTRA
2
0
0
0.0
3.225800E-Ll
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
003
0.0
0.0
0.0
0
0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
7
(SIGA(K), SIGF(K), SIGTR(K).
3.730100E-01
3.007100E+01
1.247600E+00
0.0
SNU(KI,
SIGX(K), K=1,KMAXI/((SIGS(KK,K,KKz1,KMAX),K=1,KMAX)
6.554200E+00
2.641400E+01
1.107900F+00
0.0
0.0
0.0
'-a
1.81360O~t00
0.0
RECORD
8
SIMPLE NUC.NO,
NAME ***
GENERAL DATA
0.0
0.0
0.0
0.0
0.0
0.0
5.706209F-03
9.135000E+00
0.0
OTHER NUC.NO, SIGMA
iNDSCAT.INO,
EXTRA
0.0
0.0
0.0
3
5.305100E-03
0
0
0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
(.0
0.0
0.0
0.0
0.0
0.0
0.0
2.930000E+02
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
000
6.239999E-03
0.0
0.0
0.0
0.0
0.0
1.820000E-J3
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0
0.0
0 .0
0 .0
0 .0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
9
RECORD
(SIGA(K), SIGF(K), SIGTRIK), SNU(K), SIGX(K), K=10KMAX)/((SIGS(KK.K0,KKz1,KMAX),K=1,KMAX)
0.0
0.0
7.495900E+00
0.0
3.945801E-03
0.0
0.0
2.170500E+01
0.0
3.551400E-02
0.0
0.0
6.650301c+01
0.0
5.142500E-01
0.0
4.043600E+00 0.0
0.0
2.116200E+00 0.0
0.0
RFCORD 10
SIMPLE NUC.Nf,
NAME ***A*
GENERAL DATA
3.0
0.2
0.0
0.0
0.0)
0.0
0.0
OTHER
NUC.No,
0.0
0.0
0.0
0.0
0.0
0.0
0.0
SIGMA IND.SCAT.IND,
EXTRA
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
4
0
0
0
0.0
0.0
0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
3.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
RECORD 11
(SIGA(K), SIGF(K), SIGTR(K), SNU(K), SIGX(K), K-L,KMAXI/((SIGS(KK.K),KK=1.KMAXJKz1.KMAXI
0.0
0.0
2.689500E*00
3.696300E-03 0.0
0.0
0.0
0.0
1.373900F+00
1.5825)0E-02
0.0
1.466200r+00
0.0
2.263400E-01
0.0
1.016800E-02
0.0
0.0
0.0
5.991600F-03 0.0
0.0
RECORD 12
SYMPLE NUC.N0, OTHFR NUC.NO.
NAME *GENERAL OATA
0.0
0.3
0.0
0.)
0.0
0.)
0.0
0.3
0.0
0.0
0.0
6.599q999-04
0.0
0.0
SIGMA
INDSCAr.INO, EXTRA
3.225800E-11
0.0
0.0
0.0
0.9
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
5
0
0 .0
0 .0
0 .0
0 *0
5. .200000E-04
0 .0
0. .0
0
0
0
0.0
0.0
0.0
0.0
3.460000E-03
0.0
0.0
0.3
0.0
0.0
0.0
3.10000OE-03
0.0
RFCORD 13
(SIGA(K), SIGF(K), SIGTR(K). SNU(K), SIGX(K). K1,K4AX)/((SIGSIKK,K).KK=1,KMAX),K=1,KMAX)
6.6238001E+00
2.550800E+00
0.0
2.064100E+00 1.755100F+00
4.443300E+01
2.449300C(+00
0.0
4.003101E+01
2. 834500F+01
2.442000Ef00
4.413899E+02
0.0
4.325701E+02
3.687 100E+02
4.365899E-03
0.0
0.0
4.865602E-03
0.0
0.0
). )
RFCORD 14
SIAPLE NUC.Nf,
NAME ***
GENERAL IATA
3.3
0.0
OTHER NUC.N,
SIGMA
IND.SCAT.IND. FXTRA
6
0
0
0
0
1-i
0.0
0.0
3.225800E-11
0.0
0.0
0.0
0 .0
0 .0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0,0
0.0
0.0
2.930000E+02
0.0
0.0
0.0
0.0
0.0
0.0
0.0
RFCORO 15
(SIGA(K), SIGF(K), SIGTR(K), SNU(Kle SIGX(K), K=1,KMAXI/((SIGS(KK.K(,KKAIKMAX),K=LKMAX).
1.252900E+00 6.603700F+00 L.C83700C+00 0.0
3.711200E-01
0.0
0.0
2.644099E+OL
0.0
3 .00 3 0 0 0 E+01
0.0
0.0
9.135001+00
1.813600E+00 0.0
5.833700E-03
0.0
RECORD 16
SIMPLE
NUC.NO,
NAME****GFNERAL OATA
0.0
OTHFR NUC.NO9
5,239099C-03
0.0
0.0
0.0
SIGMA IND.SCAT.IND, EXTRA
7
0
0
0
0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0,0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
RECORD 17
SNUIK), SIGX(K),
STGF(K), SIGTR(K).
(SIGA(Kl,
0.0
7.584200L+00
0.0
3.778100E-03
0.0
2.170000L+01
0.0
3.525600r-02
0.0
6.650301r+01
0.0
5.142500E-0I
0.0
0.0
2.164700F+00
0.0
RECORD 1q
SIMPLE NUC.NO,
NAME *****
GENERAL DATA
0.0
0.0
0.0
0.0
0.0
0.0
0.0
OTHFR NUC.N0,
SIGMA
INO,SCAT.IN,
0.0
0.0
0).0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
K=1.KMAX)/((SIGS(KK.K),KK=IlKMAX).K=1.KMAX)
0.0
0.0
0.0
0.0
FXTRA
0.0
0.0
0.0
0.0
0.0
0.0
0.0
8
4.001300E*00
0
0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0
0
RECORD 19
(SG'A(K), SIGF(K), SIGTR(K), SNU(K), SIGX(K), K=1,K4AX)/((SIGS(KKK),KK=1,KMAX),K=L.KMAX)
0.0
0.0
2.694100F+00
0.0
3.391700E-03
0.0
0.0
1.373800F+00
L.57L600E-02 0.0
0.0
0.0
1.466200E+00
0.0
2.263400C-01
1.004200E-02 0.0
0.0
0.0
0.0
6.130699E-03
0.0
RECORD 20
SIMPLE NUC.N',
NAME *****
GFNFRAL
OTHER
NUC.NO.
SIGMA IND*SCAT.IN.
.9
0
DATA
0.1
0.0
3.225800E-11
0.0
0.0
0.0
0.0
0.0
0.0
0.0
2.0.
6.99999E-04
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
FXTRA
0 .0
0 .0
0 .0
0 .0
5 .2000E-04
0 .0
0
0
0
0
0.0
0.0
0.0
0.0
3.460000F-03
0.0
0.0
0.0
0.0
0.0
0.0
3. 00000E-03
0.0
21
(S1(6K), SIGFIK), SIGTR(K), SNU(K), SIGX(K), Ku1,KMAX)/((SIGS(KKK),KK=1,KM4AX),K3lKMAXI
0.0
2.5506001+00
I.75'9O0F+00 6.633500E+00
2.067')00F+0
REC!Rn
0.0
0.0
0.0
0.0
0.0
0.0
6.239999E-03
0.0
0.0
0.0
0.0
1.820000E-03
0.0
H
"3
3.Q5070+01
3.592230E+02
0.0
2.790500F+01
3.047700F+02
4.888900E-03
4.391400E+01
3.682200E+02
0.0
2.442000E+00
0.0
0.0
0.0
0.0
2.449300E+00
RECORD 22 .
SIMPLF NHC.NO, OTHER NJUC.NO, SIGMA IND,SCATIND,
EXTRA
1I
4.1L4900E-03
0
0
0
0.0
0.0
0.0
000
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0
NAME *****
GENERAL DATA
3.0
0.0
0.0
0.0
0.0
0.0
0.0
0.1)
RFCWR) 23
(SIGA(K),
SIGFIK),
3.722900E-01
2.969701E+01
1.520400E+00
0.0
3.225800F-11
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
3.0
0.0
0.0
0.0
SIGTR(K),
SNU(Kf, SIGXIK),
rECiRD
0.0
0.0
0.0
K=1,KMAX)/((SIGSIKK,KI,KKzlKMAXi9K1,
1.244100F+00
0.0
0.0
6.614000F+00
2.648300E+L
8.989000F+00
1.082800E+00
0.0
0.0
0.0
0.0
0.0
5.R64669F-03
0.0
0.0
0.0
RECORD 24
STMPLF NUC.NO, OTHER NUC.NO, SIGMA INDeSCAT.INO.
NAME ****
GFNFAL DATA
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
3.0
0.0
0.0
0.0
0.0
0.0
0.0
3.0
2.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
EXTRA
11
4.937898E-03
0
0
0
0.0
0.0
0.0
0.0
0.0
0.0)
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
2.930000E+02
0.0
0.0
0.0
0.00
000
0.0
0.0
0.0
0.0
0.0
KMAXI
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
25
(SIGA(Ki, SIGF(K), SIGTR(KJ, SNU(K), SIGX(K), K.1,KMAX)/((SIGS(KK@KI ,KKm1,KMAXItKmlKMAX)
0.0
2.085900L+00 0.0
3.518600E-03 0.0
0.0
1.3768001-+00 0.0
1.5353004-02 J.0
0.0
0.0
1.536600F+00
1.9759001-01 0.0
9.464301E-03 0.0
0.0
0.0
6.159908E-03 0.0
0.
PECOW0 26
SYMPLC NUC.NO, OTHER NUC.NO, SIGMA INO,SCAT.IND, EXTRA
NAME ***
GENERAL
0.0
0.0
0.0
0.0
0.0
0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0 .0
0.0
12
0
DATA
-
0.0
-
0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
000
0.0
0
0
0.0
0.0
0.0
0.0
0.00
0*0
27
(SIGA(K), SIGF(K), SIGTR(K), SNU(K). SIGX(K), K=1.KMAX)/((SIGSIKKK),KK=1.KMAX),K=1,KMAX)
0.0
7.587300E+00 0.0
3.752100E-03 0.0
0.0
0.0
2.167799E+0[
0.0
3.40q6006-02
0.0
5.701700E+01 0.0
4.237100F-01 0.0
3.812000E00 0.0
3.0
0.0
2.175800E+00 0.0
0.0
0.0
0.0
0.00
RrECOP)
RECORD 28
SIMPLE NUC.NU, OTHFR NUC.NO, SICMA IND.SCAT.INn, EXTRA
13
0
0
0
0
F-A
ILn
GFNERAL DATA
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0)
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0.
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
RECD
29
(SIGA(K), S!GF(K), SIGTR(K), SNU(K). SIGX(K), Ka1,KMAX)/( (SIGS(KKK 1,KK=1KMAX )Ku1,KMAX)
0.0
0.0
0.0
2.084200E+00
3.6.08300E-03
0.0
1.524100E-02
0.0
1.373500E+00
0.0
0.0
1.904900E-01 0.0
1.444700E+00
0.0
0.0
9.511098E-03
0.0
0.0
6.065499E-03 0.0
0.0
REVCRD 33
SYMPLE NUC.NC,
NAME **+**
GENERAL DATA
0.0
0.0
0.)
0.0
0.0
0.0
0.'
OTHER NUC.NO. SIGMA
0.0
0.0
0.0
0.0
0.0
INDSCAT.INO, EXTRA
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0
14
0
0.0
0.0
0.0
0.0
0.0
0.0
RECORD 31
(SIGA(K), SIGF(K), SIGTR(K), SNUIX). SIGX(K), K=1.KMAX)/((SIGS(KK,K),KK-L.KMAX),KeL.KMAX)
0.0
3.914699E-03
0.0
7.506800E+00
0.0
0.0
0.0
2.167999F+01
3.418400F-02
0.0
4.291300F-01
0.0
5.757001E+01
0.0
0.0
0.0
0.0
0.0
3.828200E+00
0.0
2.142200E+00
0.0
RECOP0 32
IMPLE NUC.N,
NAME ***
GENERAL DATA
OTHFR
0.0
0.0
0.0
0.0
0.0
6.>59900t'-4
0.0
NJC.NOt SIGMA
0.0
0.0
0.0
0.0
0.0
0.0
0.0
INDSCAT.INO,
3.225800E-11
0.0
0.0
0.0
0.0
0.0
0.0
EXTRA
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0
15
0
0
0
0
.0
.0
.0
.00
5 .200000E-04
0 .0
0 .0
0
0
0.0
0.0
0.0
0.0'
0.0
2.930000E+02
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
3 .460000E-03
0.0
0.0
3.LOOOOOE-03
0.0
6.239999E-03
0.0
1.820000E-J3
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
RECORD 33
(SIGA(K), SIGr(K), SIGTR(K), $NU)(K), SIGX(K), Ko1.KMAXI/ (SIGS(KK.K).KKalKMAX).K1,KMAXI
2.05 7-100E+00
1.751400E+00 6.598000F+00
2.!;53200E+00
0.0
3.953900E+01
2.793401F+01 4.394R00+01 2.449300F+00
0.0
3.6)34900 +02
2.4420OOEt-00
3. 095500E+02
3.724700f;+02
0.0
4.813d98E-03
3.0
0.0
0.0
4.135299F-03 0.0
0.0
0.0
0.0
RFCORD
34
SIMPLE NUC.NO,
NAME *****
GENERAL DATA
0.0
0.0
0.0
0.0
0.0
0.0
0.0
35
(SIGA(Ki,
OTH1ER
NUC.NO. SIGMA IND.SCAT.IND, EXTRA
0.0
0.0
0.0
0.0
0.0
0.0
0.0
3.225800E-11
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
it
0.C
0.0
0.0
0.0
0.0
0.0
0.0
0
0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0
0
0.0
0.0
0.0
0.0
0.0
0.0
RFCORD
SIGF(K),
SIGTR(K),
SNU(K).
SIGX(K)v
Ku.lKMAX)/((SIGS(KK.K .KK=L.KMAX).K=1,KMAX)
3.?48900E-01
2.07 000E+01
1.538700E+0.1
0.0
L.233000F+00
0.0
0.0
5. 776700E-03
6.573500F+00
2.647301F+01
8.S98900E900
0.0
t.105900E+00
0.0
0.0
0.0
0.0
0.0
0.0
0.0
4.962299E-03
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
RECORI 36
SIMPLE NUC.NO, OTHER NUC.NO, SIGMA INDSCAT.IND, EXTRA
17
0
0
0
0
NAMF *****
GENFRA. DATA
0.0
0.0
0.0
0.0
3.225800E-11
0.0
0.0
0.0
0 .0
0.0
0.0
0.0
0.)
6.599999E-04
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0 .0
0 .0
5 .200000E-04
0 .0
.0
0
0.0
0.0
0.0
0.0
3.460000E-03
0.0
0.0
t.239999E-03
0.0
0.0
1.820000E-03
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
3.LOOOOOE-03
0.0
RECORD 37
(SIGA(K), SIGF(K), SIGTR(K), SNU(K). SIGX(K), K=1.KMAX)/I(SIGS(KK,K),KK=L.KMAX)K=1,KMAX)
0.0
6.566700E+00 2.553900F+00
1.741700E+00
2.044000E+00
3.094200+01
4.325701F+02
0.0
RECORD
2.826900E+01
3.687100F+02
4.435500E+01
4.413899F+02
2.449300C+00
2.442000C+00
4.704300F-03
0.0
0.0
0.0
0.0
0.0
4.306901E-03
38
SIMPLF NtUC.ND, OTHER NUC.NO,
SIGMA IND,SCAT.IND, EXTRA
18
0
0
0
0
NA'4E **
GENERAL DATA
0.3
0.0
0.0
0.0
0.0
0.3
).0
0.0
3.225800E-11
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.C
0.0
0.0
0.0
0.0
,0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
2.930000E*02
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
RECORD 39
(SIGA(K),
SIGF(K).
SIGTRIK),
SNU(K), SIGX(K),
Kz1.KMAX)/((SIGS(KK,Kl.KKmlKMAX),Ka1,KMAX)
3.733500E-01
1.246000E+00
C.452200F+00
1.112700E+00
0.0
3.001300E+01
0.0
2.645500E+01
0.0
0.0
1.813600E+01
0.0
0.0
5.645100E-03
9.135000F+00
0.0
0.0
0.0
0.0
0.0
RECORD
5.168300E-03
40
SYMPI.E NUC.NO, OTHER NUC.ND,
NAME *****
GENERAL DATA
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
SIGMA IN%.SCAT.INn,
0.0
0.0
0.0
0.0
0.0
0.0
0.0
EXTRA-
19
0
0
0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
PECORD 41
(SIGA(K), SIGF(K),
3.950201E-03
0.0
3.51010OE-02
0.0
5.142500E-01
0.0
RFCORD
SIGTR(K), SNU(Kl, SIGX(K), Ku1,KMAX)/ I(SIGSCKK.K),KKLvK MAX).KuL.KMAX)
7.471400E+00 0.0
0.0
0.0
2.169501F+01
0.0
0.0
6.650301E+01 0.0
0.0
2.095200E+00 0.0
0.0
0.0
-3.969300E+00 0.0
-4
42
SIMPLE NUC.NO, OTHER NUC.NO, SIGMA INUSCAT.IND,
NA4F **-*"
GENERAL DATA
EXTRA
20
0
0
0
0
0.0
0.0
0.)
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0 0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0. 0.
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
'
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
2.930000E+02
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.00
0.0
0.0
0.0
0.0
0.0
0.00
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.00
0.0
0.0
0.0
0.0
0.0
0.00
0.0
0.0
0.0
0.0
0.0
000
RECORn 43
(SIGA(K), SIGF(K). STGTR(K). SNU(K), SIGX(K), Kul.KMAX)/(ISIGSIKKKlbKKalKMAX)KKNlKMAXI
0.0
2.690700E+00 0.0
3.691600F-03 0.0
0.0
0.0
1.373800E+00
1.564400E-02 0.0
0.0
0.0
-01
0.0
1.466200E+00
2.263500
0.0
.905901E-03- 0.0
0.0
0.0
5.927399E-03
0.0
0.0
0.0
RECORD 44
SIMPLE NUC.NO, OTHER NUC.NO, SIGMA IND.SCAT.IND. EXTRA
21
0
0
0
0
NA'4E ** 'k
GENERAL
0.0
0.0
0.0
0.0
0.0
DATA
0.0
0.0
0.0
0.0
a.0
0.0
0.0'
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
RECORD 45
(SIGA(K), STGF(K), SIGTR(K),
0.0
0.0
0.0
7.064000E+00
8.329600F+00
0.0
0.0
0.0
0.0
1.281600E+01
0.0
6.818800E-01
0.0
0.0
.0.0
0.)
0.0.
0.0
0.0
0.0
0.0
OTHFR
NUC.NO,
SIGMA INo.SCAT.INDO
EXTRA
22
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
6.297100F-01
0
PCCRD) 48
IUMPLc NUC.NO, CTHFR NLC.NO, SIGMA INDvSCAT.INO, EXTRA
NAIF4 *'t
GENERAI. DATA
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
23
0.0
0.0
0.0
0.0
0.0
0.0
0
0
0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.00
000
JIGF(Kle 11GTR(Kle %NU(Kle SICX(Kli KUlKMAXI/((SI(S(KKKl
0.0
1.920000('#0+ 0.0
0.0
1.941IM0.00.0
1.30100r+00 0.0
0.0
0.0
2.A4800E-01 0.0
L.99100+r0o 0.0
0. )
0.0
1.386300E-02 0.0
10.,
0.0
0.0
0.0
0.0
0.0
0.0
0.0
3.368000-0j
0.0
0.0
0.0
0.0
RECORD 4T
(511A(K)t
RFCnRO 49
0.0
SNU(K). SIGX(K), K=1.KMAX)/((SIGS(KK.K).KK.l.KMAX)hK'lKMAX)
2.490700E-03
?.659L01E-05
9.A63300E-04
RPCORn 46
SIMPLF NUC.NO,
NANIF" -*
GENFRAL DATA
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0
KKuLKMAXi
K.LK4AXI
L.376400F-Od
0
0.0
0.0
0.0
0.0
0.0
0.0
000
0
0
00
ISIGAIK), SIOF(K), SIGTRIK), SNUIK). SIGX4K), KoLoKMAX)/ (ISIGS(KKK),KKalKMAX),KelKMAXI
0 .0
7.422000r+00
0.0
3.71300F-03
0.0
0.0
0 .0
3.370600E-02
0.1
2.165900F+0L
0 .0
0.0
5.7000!:+01 0.0
4.237100E-01
3.699400E+00 0.0
0 .0
0.0
2.247600E+00 0.0
0.0
RECORD 50
SIMPLE NUC.NO, OTHFR NUC.NO,
NAME ****ft
GENERA. DATA
SIGMA INO.SCAT.IND, EXTRA
0.0
0.0
3.225ROOF-I
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
6.r,19999E-04
0.0
0.0
0.0
0.0
0.0
0.0
0.0
24
0
0
0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.00
6.239999E-03
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0)
0.0
0.0
0.0
0
0 .0
.0
0 .0
0.0
0.0
0.0
0.0
0.0
0
5 .2000OOE-04
0 .0
0 .0
0.00
0.0
0.0
3.460000E-03. 3.100000E-03
0.0
0.0
0.0
RECORD 51
(SIGA(K), STGF(K), SIGTR(K),
SNU(KI
SIGX(K), Ku1.KMAX)/I(SIGS(KKK).KK=1KKMAX),Ku=.KMAX)
0.0
2.550000E+00
1.771400E+00 6.671900E+00
2.03T000E+00
0.0
4.384100E+01
2.449400E+00
3.937100E+01
2.774200F+01
3.592200 +02
3.047700F+02
3.682200E+02
0.0
2.442000E+00
0.0
f 5.068600E-03
0.0
0.0
0.0
3.865200E-03
0.0
1.820000E-03
RECORD 52
SIMPLE NUC.NO, OTHER NUC.NO. SIGMA INDoSCAT.IN0, EXTRA
NAME **t*
GcNFRAL DATA
0.0
0.0
3.225800E-IL
0.0
0.0
0.0
0.0
3.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.)
0.0
0.0
0.0
0.0
0.0
0.0
0.0
25
0
0 .0
0.0
0.0
0.0
0.0
0
0
0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
RECORD 53
SIGX(K), K=1,KMAX)/((SIGS(KK.K),KK=1,KMAX).K=1.KMAX)
(SIGACK),
SIGF(K), SIGTR(K), SNU(K),
3.752200E-01
1.223900F+00 6.651400F+00
L.077000F+00
0.0
0.0
0.0
2.667799E+01
0.0
2.993100E+01
0.0
0.0
8.989000E+00
0.0
1.52040000
0.0
4.638199E-03
0.0
0.0
1.0
6.082300E-03 0.0
RECORD 54
SIMPLE NUC.NO, OTHFR NUC.NO. SIGMA IND.SCAT.IND, EXTRA
NAME *****
GENERAL DA7A
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.00
0.0
0.0
0.0
0.0
0.0
0.0
26
a
0. .0
0 .0
0 .0
0..0
0.0
0.0
0.0
0
0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
OTHER NUC.NO,
SIGMA IND.SCAT.INO,
EXTRA
27
0
0
0
0.0
0.0
0
REC00 55
(SIGA(K). SIGF(K), SIGTR(K), SNU(K). SIGX(K), Ku1,KMAX)/((SIGS(KKKlKKI1,KMAX),KI1.KMAX)
3.55190OF-03
0.0
2.079200E+00 0.0
0.0
1.515400E-02
0.0
1.376700r+00 0.0
0.0
1.9759000-01
0.0
1.536600F+00
0.0
0.0
6.386399E-03 0.0
0.0
0.0
8.889899E-03 0.0
RFCORD 56
SIMPLE NUC.NO,
NAME ***f**
0.0
0.0
0.0
0.3
0
-
1-9
GFNERAL DATA
0.0
0.0
0.0
1.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0,0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0. a
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
2.930000E+02
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
6.239999E-03
0.0
0.0
0.0
0.0
0.0
1.820000E-03
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
000
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
RECORD 57
SIGF(K), SIGTR(IK), SNU(K), SIGX(K), Ku,KMAX)/((SIGS(KK,K),KKLKMAX),KuLKMAX)
(SIGA(K),
0.0
0.0
0.0
7.622000E+00
3.712300F-03
0.0
0.0
2.165900F+01
0.0
3.370600E-02
0.0
5.701700F+01
0.0
4.23710OE-01
0.0
0.0
0.0
3.699400E+00
0.0
2.247600E+00 0.0
0.)
RECORD 58
SIMPLF NUC.NO,
NAME
***
GENSRAL DATA
0.0
3.0
0.0
2.0
6.599999E-04
0.0
OTHER NUC.NO,
SIGMA INO,SCAT.IND, EXTRA
3.225800F-11
0.0
0.0
0.0
0.0
0.0
0.3
0.0
0.0
0.0
0.0
0.0
0.0
0.0
28
0
00.0
0 .0
.0
0 .0
5 .200000E-04
0 .0
0 .0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0
0
0
0.0
0.0
0.0
0.0
3.460000E-03
0.0
0.0
0.0
0.0
0.0
0. 0
3.100000E-03
0.0
RECnRO 59
(SIGAM(), SIGF(K), SIGTR(K), SNU(K), SIGX(K), KULKMAX)/U(SIGS(KK,KleKK-KMAX),K=LKMAX)
2.553400E+00 0.0
2.064000E+00
1.756000E+00 6.607000E+00
4.405400F+01
2.449300E+00 0.0
2.798500E+01
3.2'62199E+01
3. '47700E+02
3.592200E+02
3.682200E+02
2.442000F+00 0.0
4.099399E-03
4.
0.0
0.0
0.0
190499E-03
0.0
0.0
RECORD 60
SIMPLE NUC.NO. OTHFR NUC.NO,
NAME *****
GENERAL DATA
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
SIGMA IND,SCAT.IND.
3.225800F-11
0.0
0.0
0.0
0.0
0.0
0.0
EXTRA
0.0
0.0
0.0
0.0
0.0
0.0
0.0
29
0
0 .0
0 .0
0.0
0.0
0.0
0.0
0.0
0
0
0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
,
RECORD 61
(SIGA(K), SIGF(K), SIGTR(K), SNU(K), SIGX(K), Kz1,KMAXI/((SIGS(KKK).KK1,KMAX),KIKMAX)
3.769600E-01
1.220700E+00
6.581300F+00 1.108400E+00
0.0
2.990500E+01
0.0
2.653999E+01
0.0
0.0
1.520400E+00 0.0
8.989000E+00 0.0
0.0
0.)
5.8566000-03
0.0
0.0
0.0
4.919302E-03
0.0
RECORD 62
SIMPLF NUC.N',
NAME **&**
qENERAL DATA
0.0
0.0
0.0
0.1
'3.0
0.0
2.0
OTHER
0.0
0.0
0.0
0.0
0.0
0.0
0.0
NUC.NO,
SIGMA IND.SCAT.IND, EXTRA
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
30
0, .0
0
0. .0
0, .0
0. .0
.0
0
.0
0
0
0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0
0
0.0
0.0
0.0
0.0
0.0
0.0
W
RFCORD 63
(%IGA(Kis SIGF(K), SfGTR(K), SNU(K), SIGX(K), K-1.KMAX)/((SIGS(KK@KKKLKMAX),Ku1lKMAX)
0.0
2.081100F+00 0.0
0.0
3.065300F-03
0.0
0.0
1.376900F+00
0.0
1.544900F-02
0.0
0.0
1.536600E+00
0.0
1.975900E-01
9.428699E-03
0,0
0.0
0.0
0.0
6.149400F-03
0.0
RFCORO 64
SIMPLE NUC.NO, OTHER NUC.NO, SIGMA INO.SCAT.IND, EXTRA
NAME A***
GENERAL nATA
0.0
0.0
0.0
0.0
0.0
0.1
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
31
0
0
0
0.0
0
0.0
0.0
0.0
0.0
0.0
2.930000E+02
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0,0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0,0
RFCORn 65
(SIGA(K), SIGF(K), SIGTR(K), SNU(K), SIGX(K), K=1,KMAXI/((SIGS(KK.K),KKulKMAX),KaLKMAX)
7.502300r+00 0.0
0.0
0.0
2.167799E+01 0.0
0.0
3.432500E-02 0.0
4.237100E-01 0.0
0.0
5.701700L+01
0.0
3.830300E+00 0.0
0.0
0.0
2.165000F+00 0.0
0.0
3.904500E-03
RECnRD 66
SIMPLE NUC.NO. OTHFR NlC.NO, SIGMA INDSCAT.IND, EXTRA
NAME **
GENERAL OATA
0.0
0.0
0.0
,.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
32
0
0
0
0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
000
000
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0. .0
0.0
0.0
0.0
0.0
REC00 67
(SIGA(K), SIGF(K), SIGTR(K), SNU(Kle SIGX(K), K=1,KMAX)/((SIGS(KKK),KK.1,KMAX),K=l.KMAX)
0.0
3.779200E-03 0.0
7.721100F+00
0.0
2.196800E+01 0.0
3.o93180E-02 0.0
0.0
0.0
6.127600E-01
0.0
7.769901E+01
0.0
4.414800E+00 0.0
0.0
0.0
2.460200E+00 0.0
0.0
RECORI 68
SIMPLF NUC.ol,
NAME **
GENERAL DATA
0.0
0.3
0.0
00
0.0
0.0
0.0
OTHFR NUC.NC, SIGMA INDoSCAT.IND,
0.0
0.0
0.0
0.0
0.03
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
EXTRA
0.0
0.0
0.0
0.0
0.0
0.0
0.0
33
0
0
0
0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.C
0.0
0.0
RECORD 69
(SIGA(K), SIGF(K), SIGTR(K), SNtJ(K), SIGX(K), K=IKMAX)/((SIGS(KK.KIKK=1.KMAX).K=l.KMAX)
2.059400E+00
0.0
0.0
3.641300E-03
0.0
1.708500E-02
0.0
0.0
1.378500C+00
0.0
0.0
2.645800E-01
0.0
1.599100E+00 0.0
1.125600F-02 0.0
0.0
7.061299E-03 0.0
0.0
0.0
PFCORD
70
SIMPLE
NUC.N
OTHFR
NUC.NO. SIGMA INn.SCAT.IND. EXTRA
34
0
0
0
0
W
NAME*****
OfNERAL DATA
0.0
0.0
0.0
0.00.0.
0.0
0.0
0.0
0.0
0.0
0.0
0.00
0.0
0.0'
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.00
_0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0 :
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
RFCORI 71
(SIGAKN SIGP(K), SIGTRIKh9 SNU(Kh SIOX(Kh
5.880200E+00 0.0
3.L04500-03 0.0
19113400E+01 0.0
8.6130028-03 0.0
1.113000F+01 0.0
4.800000E-02 0.0
0.0
1.456000E-02 0.0
0.0
RECORD 72
C.
1
_f
SIMPLE NUC.NO,
NAME
*40**
GENERAL DATA
0.0
0.0
0.0
0.0
0.0
0.0
0.0
DTHFR
NUC.NO, SIGMA
INOSCAT.IND#
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
K.lKMAX /((SIGS(KK.KhKKLKMAX)1Km.bKMAX)
0.0
0.0
0.0
0.0
L.164000E-0 2 -- 0.-0 - EXTRA
0.0
0.0
0.0
0.0
0.0
35
*
0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0
0
0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0'
0.0
0.0
0.0
0.0
RICORD 73
ISIOA(Kht 610PIie 5leTRIKIh fNU(Khi 610X(Kii KmlKMAX)/( 1M106 KKKhKKhlKMAXI iKaLKMAM)
3,96190OP-0i 0.0
010
P105R000c00 0.o0
1.54L4008-02
2.6458001-01
0.0
II
RECORD 74
SIMPLE NUC.N0,
NAME*****
GENCRAL DATA
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
7.218398a-03
0TI4ER
0.0
0.0
0.0
0.0
0.0
0.0
0.0
l.377000E+00
l.J99100+00
0.0
0.0
0.0
0.0
NUC.NO, SIGMA IN09SCAT.IND, EXTRA
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
a.3319999-03
0.0
36
0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0
0
0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
RECORD 75
(SIGA(KhI SIOPIKI SIOTRIKh, SNU(K), SIGX(IK9 Kh KMAXI/( (SI0S(KK@KhKK1.KMAX).KI.9KMAX)
6.266600F+00 0.0
6.357200E+00 0.0
0.0
1.535400E+01 0.0
1.108100+OL
0.0
0.0
3.003600F+06 0.0
L.408100R+02 0.0
0.0
0.0 ,
. 0.0 .
0.0
-- 0.0
.
0.0
000
,
000
PECORD 76
SIMPLE NUC.NO,
NA4E **0*
GENERAL DATA
OTHER
NUC.NO, SIGMA INDSCAT.IND, EXTRA
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
00
0.0
0.0
0.0
0.0
0.0'
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
37
0 .0
0 .0
0.0
0.0
0.0
0.0
00
0
0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0
0
0.0
0.0
0.0
0.0
0.0
0.0
H
SitTA(KNo SNUlK), SIOX(K), Ks1,KMAX)/t(IGSIKKK),KKULKMAX),K=,KMAX)
0.0
2.021400C+00 0.0
0.0
1e379000E+00 0.0
0.0
1.599100F+00 0.0
1e2221001-02 0.0
0.0
0.0
0.0
8.8942011-03
RECSIO1Kb SIGP(K),
3.734400-03 0.0
1.16400C-02 0.0
2.6458001-01 -.0.0
0.0
F
RECORO 78
SIMPLE NUC.NO, OTHER NUC.NO, SIGMA INDoSCAT.INO,
NAME ****
OENCRAL-AA.. 0
000
0.0
00
0.0
0.0
0.0
0.0
0.0
040
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0
0.00
0.0
0.0
0.0
0.0
0.0
0.0
EXTRA
38
0
0*0
0
0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
00
0.0
000
0.0
.
0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
040
0.0
0.0
0.0
0 .0
0 .0
0.0
0 so
0.0
0
g0
c
E
C
RECORD 79
(SIGA(K)N SIGFIK), SIGTR(K), SNU(K), SIGX(K), KUlKMAX)/((SIGS(KKKhKKLKMAXKaLKMAXI
0.0
2.084500E+00 0.0
2.55700E-03 0.0
1.232900E-02 0.0
1.5807006-01
0.0
0.0
6.16560E-03
l.376900E+00
1.536600F+00
0.0
0.0
0.0
0.0
0.0
RFCORD 80
SIMPLF NUC.NO9 OTHER NIiC.NO@ SIGMA INDSCATeIND,
EXTRA
39
9.499501E-03
0
GENERAL DATA
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
__0.0
0.0
0.0
0
0
0.0
0.0
0.0
0.0
0.0
00
0.0
0.0
0.0
0.0
0.0
0*0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
000
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0
1.-
-. NAME *+***
0.0
-
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
00
0.0
0.0
0.0
060
0.0
0.0
0.0
0.0
0.0
0.0
RFCORn 81
(SIGA(KN1
SIGFI K)h SIGTRIKI SNU(K). SIOX(K)h KulKMAX)/((SIGS(KKK)DKKA1KMAX),K01,KMAX)
0.0
1.075400E+01- 0.0 . ...
0.0
0.00
2.234,099F+01 0.0
5.295200E-02 0.0
0.0
7.769901E+01 0.0
6.127600E-01 0.0
6.543800R+00 0.0
0.0
0.0
6.084400E+00 0.0
0.0
2.313000E-03
RECORD 82
SIMPLE NUC.N0,.0THER NUC.NO, SIGMA INDSCAT.INO9 EXTRA.-
40
0
0
0
0..
0...
NAME ***
c
GENERAL DATA
0,0
0.0
0.0
0.0
--
0.0
0.0
0.0
0,0
0.0
0.0
0-0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
00
0.0
0.0
0.0
0.0
0.0
0.0
000
0.0
0.0
0.0
RECORI 83
SNU(KN1 SIGXK), KslKMAX)/USIGS(KK.KKKuIKMAX).KiI,K=.AX
1 TR4K
P
(SIA (bJ ISIGF(K1
0.0
1.831900E+00 0.0
3.854005-03 0.0
0.0
1.384100F+00 0.0
2.287900P-02 0.0
0.0
1.599100E+00 0.0
2.645800E-01 0.0
1.7907006-02 0.0
0.0
0.0
1.868800E-02 0.0
0.0
RECORD 84
0.0
0.0
0.0
Li3
0.0
0.0
SIMPLE NUC.NC, OTHER NUC.NO, SIGA INCSCAT.INO, EXTRA
41
0
0
0
~
0.0
0.0
0.0
0.0~~~ ~
0.0
0.0
0.0
0
NAME ****
GENERAL DATA
0.0
0.0
0.0
00~~
0.0
0.0
0.0
c.0
0.0
0.0
0
0
0.0
0.0
0.0
0
0.0
0.0
0.0
..
.0~~
0.0
0.C
0.0
0.0
0.0
0.0
~~0.0
0.0
0.0
0.0
C.0
0.0
C.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
00
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
*0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
RECORU 85
(SIGAIK), SIGF(KT SIGTR(K), SNU(K)p SIGX(K)b KmLKMAX)/ ((SIS IKKK 1bKK1,KMAX IKnItKMAX
0.0
0.0
3.O9330C+00 0.0
0.0
0.0
1.017000E-C4 0.0
4.40230c+00 0.0
2.991200E-03 0.0
4.71070C+00 0.0
0.0
1.227400E-01 0.0
0.0
1.099700e-0l 0.0
0.0
0.0
7
.4;
RECORD 86
SIMPLE NUC.NO, OTHER NUC.Nn, SIGMA INCSCAT.INO, EXTRA
AAME *$$$$
N
GENERAL DATA
0.0
0.00
0e.C
0.0
0.0 0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0
42
0.0
0 .0
C.0
0.0
0.0
0.0
0.0
0
0
~
0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
-0.0
0.0
0.0
0.0
0.0
0.0
RFCOR) 87
ISIGAIK), SIGF(K), SIGTRIK), SMU(K), SIGX(K)t Ku1,KMAX)/((S IS(KKKbKKu1,KMAX),K1,KMAX)
3.363100E-03 0.0
6.69220CE+00 0.0
0.0
2.361000E-05 0.0
0.31270CE+00 0.0
0.0
0.0
9.863300E-04 0.0
1.201600E+01 0.0
0.0
4.38890E-01 0.0
0.0
0.0
5.635600E-01 0.0
RECORD 88
SIMPLE NUC.NO,
OTHFR
NUC.NO, SIGMA INCSCAT.IND9 EXTRA
0
43
0
0
0
NAME *****
GENFRAL DATA
0.0
0.0
0.0
0.0
.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
C.C
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0.
00
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
--
*-
0.0
0
0.0
0 .0
0 .0
0.0
0.0 .
0.0 .
.
0.0
0.0
RECORD 89
(SIGA(K), SIGF(K), SIGTR(K), SNU(K), SIGX(K)b KulKMAX)/ ((SIGS(KKK)hKK=1,KMAX),KulKMAX
0.0
2.C2140CE+00 0.0
3.734400P-03 0.0
1.768400E-02 0.0
I.17JC0CF+C0
0.0
0.0
0 .0
1.59910CE+00 0.0
Zi
2.645800E-01 0.0
~0.0~
~
~8.89420'E-0TF 0.*
0.00
1.222100E-02 0.0
.0
RECORD 90
SIMPLF NUC.NO, OTHER NUC.NO, SIGMA INCSCAT.IND, EXTRA
NAME*****
GFNERAL DATA
0.0
~ o0.0~~~
~0.00.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.00
0o0
0.C
44
~ 0.0
0.0
0.0
0.0
0.0
0.0
0
~
0
0.00.0
0.0
0.0
0.0
0.0
0
-
~
0.0
0.0
0.0
-0.0
0.0
0.0
0.0
0.0
0.0
0
~
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
-r_-
0.0
0.00
0.0
0.0
0
0.0 '
RECORD 91
(510AIK), SIGF(iK), SIGTR(K), SNU(K), SIGX(K), KulKMAX)/((SIGS(KKK),KKEIKMAX),MelKMAX)
0.0
7.113900C+00 0.0
4.654299E-03 0.0
0.0
2.2049000+01 0.0
4.238200-02 0.0
0.0
7.7699016401 0.0
6.127600E-0~0.0
4.875800400 0.0
0.0
0.0
2.231700e+00 0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0'
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
95
(SIGAIK), SIGF(K), SIGTR(KI, SNU(K), SIGX(K), K=1,KMAX)/((510S(KKK~ ,KKu1,KMAX),m1,KmAX)
0.0
?.037900E+00 0.0
.9900!5-03 0.0
0.0
1.702600-02 0.0
1.179200+00 0.0
0.0
0.0
1.9991004CF+
.645A006-01 0.0
009-03
0.0
0.0
0.0
1.184100E-02 0.0
7.282 6
0.0
0.0
0.0
2.930000E+0?
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
RCORO 92
SIMPLL NUC.NO, OTHLR NUC.NO, SIGMA INCSCAT.IND
AAME
'
r
S
L
c
EXTRA
0
45
0
0
0
*****
GENERAL
0.0
0.0
0.0
0.0
0.0
0.0
0.0
DATA_
-
0.C
a0.0
0.0
0.0
0.0
C0.
0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
RLCORD 93
SIGF(K), SIGTR(K
(SIGoAIK),
4.190702E-03 0.0
4.107700E-02 _0.0
6.127600E-01 0.0
2.516300E+00
0.0
RCCORD 94
SIMPLL NUC.NC,
NAMP ****
GENFRAL DATA
0.0
0.0
0.0
0.0
0.a 0
0.0
0.0
OTHIRR
, SNU(Kl, SIOX(K)i gelMMAX /I(S
0.0
7.501900F+00 0.0
0.0.
2.200500F+01 0.0
0.0
7.769901P+01 0.0
0.0
0.0
0.0
NUC.NO, SI0A !NCSCA.INI
0.0
0.0
0.0
0.0
c.0
0.0
0.0
0.0
0.C
.0
0.0
0.
0.0
0.0
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7SUB- ZONE INDICATOR
22
1.62100E-04
47
3.275003-02
-~
3
0
3.18300E-02
O~ AND CONTROL OPTION
3.359001-05
7-
66_ 7.416001-03
_
0--
ZONES 6- 6 SUB-ZONE INDICATOR 0 AND CONTROL OPTION 0
17 4.39000E-04
18 3.359001-05
20 3.183002-02
-
_
1.65500E-02
INDICATOR
10
_
NUMBER
- DENSITY)
AND CONTROL OPTION 0
3-~3~SUB-ZONE INDICA Toa0
5 4.39000E-04
6
3.35900E-05
e 3.18300E-02
4
__
0.07A_
1.000000
INDICATOR 0 AND CONTROL OPTION 0
4 3.18300E-02
2 3.359001-05
SUB-ZONk
ZONES 4-
_
I-SECTION
1
3.01200E-02
0
0
0
0
DNSC
,
TITLE
2
NICROSCOPIC CROSS-SECTIONS F01 THE NITR-II
1/V
DIST.FUNCT
MEAN ENERGY
1.990000E-09
1.000000
5.477200E+04
0.0
2.778000E-07
3.464000E+01
1-
4.39000E-04
AL*VOID
AL+D20+VOID
CORE-H20
AL+R20
VOID
H20
H20
CROSS SECTIONS
UPSC
0
INPUT NUCLIDE DENSITIES(NUCLIDE
-ZONES
0
0
0
0
0
0
0
suN
ZONES
CORE+AL-H20
_______________
____
13- 13
ZONES
-
24
SUB-ZONE INDICATOR
25
4.39000-04
14- 14
ZOES3
28
SUB-ZONE INDICATOR
29
4.390001-04
0
26
AND CONTROL OPTION
3.359001-05
30
0
_ -
3.183001-02
31
0
AND CONTBOL OPTION
0
ZONES 11 17 SUB ZONE~INDiCATO 0 AND CONTROL OPTION
42 1.65400E-02
43 3.120001-02
0
ZONES 18- 18 SUB-ZONE INDICATOR
44 3.34000E-02
ZONES 16- 16 SUB-ZONE INDICATOR
41 8.33400E-02
19
ZONES
45
19
SUB-ZONE INDICATOR
46
3.14300E-02
0
0
AND CONTROL OPTION
0
0
AND CONTSOL OPTION
0
0
AND CONTROL OPTION
0
ZONES
21- 21 SUB-ZONE INDICATOR
3.340003-02
0 AND CONTROL OPTION
0
ZONES
22- 22
0
0
28
SUB-ZONE INDICATOR
4.390001-04
29
1.545001-02
------
3.012002-03
ZONES 20- 20 SUB-ZONE INDICATOR
47 3.340001-02
48
1.545001-02
0
3.18300E-02
15- 15 SUB-ZONE INDICA TOR 0 AND CONTROL
3.012003-02
39 1.65500E-02
40
c-
AND CONTROL OPTION
OPTION
ZONES
o
0
3.359001-05
AND CONTROL OPTION
3.359C0E-0S
30
5.404001-02
31
3.09000E-03
14
3.090003-03
ZONES 23-
23 SUB-ZONE INDICATOR 0 AND CONTROL OPTION 0
4.39000E-04
16 3.359003-05
13 5.404001-02
15
ZONES 24- 24 SUB-ZONE INDICATOR 0 AND CONTROL OPTION
52 6.02300E-03
51 3.006001-02
0
ZONES 25-25 SUB-ZONE INDICATOR 0 ANDfCONTROL~OPTION 0
21 1.329201-02
22 5.42160E-03
56 5.100001-01
------
ZONES 26- 26 SUB-ZONE INDICATOR 0 AND CONTROL OPTION 0
21 2.093503-02
22 3.01200E-03
56 3.200001-01
ZONES 27- 27
SUB-ZONE INDICATOR 0 AND CONTROL OPTION
9.036001-03
56 8.200001-01
22
0
ZONES 20- 28 SUB-ZONE INDICATOR 0 AND CONTROL OPTION 0
21 1.528603-02
22 4.819203-03
56 4.60000R-01
3ONIS
21
29-~29 ~SUB-ZONU INDICATOR 0 ANDOCONTROL OPTION 0
9.969003-03
22 3.614401-03
56 3.400003-01
ZONES 30- 30
.0
SUB-ZONE INDICATOR 0 AND CONTROL OPTION 0
1.728001-02
22 4.21660E-03
56 4.100001-01
21
3
21
UA
1.993801-02
ZONES 32- 32
21
22
SUB-ZONE INDICATOR
2.591903-02
soMs3
3.61440E-03
22
PTION0
3.40000E-01_
AND CONTROL OPTION
1.807201-03
56
0
1.900003-01
liT~
3-UB20
5 4.39000E-04
0
56
-
6
0
A-ND
-ClON-TaRCL0-PTION
0
3.35900E-05
8 3.183001-02
ZONES 34- 34 SUB-ZONE INDICATOR 0 AND CONTROL OPTION 0
9 4.390003-04
10 3.35900E-05
11 3.183003-02
------
Un
SONES 35- 35 BUB-ZONE INDICATOP 0 AND CONT8OL OPTION 0
15 4.39000E-04
16 3,359001-05
13 3,183003-02
ZONES 36- 36 SUB-ZONE INDICATOR 0 AND CONTOL OPTION 0
26 3.108300E-02
24 4.39000E-04
25 3.35900E-05
ZINiD~ICATOR 0 AND CONT RCL OPTION
0
ZONE537 37 SIUB-01
28 4.390003-04
29 3.359001-05
30 3.183002-02
ZONES 38- 38 SUB-ZONE INDICATOR 0 AND CONTROL OPTION 0
17 4.390001-04
18 3.35900E-05
20 3.183003-02
ZO1S
39- 39 SUB-ZONE INDICATOR 0 AND CONTROL OPTION 0
4 3.183001-02
2 3.35900E-05
1 4.390001-04
ZONES 40- 40 SUB-ZONE INDICATOR 0 AND CONTRCL OPTION
47 1.407001-02
54 3.49160E-02
0
ZONES
0
57
SI- 41 SUB-ZONE INDICATOR
1.00000B+00
ZONES
42- 42 SUB-ZONE INDICATOR
14 3.340003-02
ZONES 4314
43
SUB-ZONE INDICATOR
3. 340003-02
0 AND CONT0L OPTION
----0
AND CONTROL OPTION _,0_
0
AND CONTROL OPTION
0
ZONES 4%- 44 SUB-ZONE INDICATOR 0 AND CONTROL OPTION
60 1.535003-02
35 4.259001-02
OPTION
0
ANDCONTROL OPTION
0
47 SUB-ZONEINDICATOR O AND CONTROL OPTION
7.416003-03
35 5.060001-02
0
ZONES 4561
0-
45 SUB-ZONE INDICATOR 0 AND CONTROL
8.940003-03
35 3.95600E-02
ZONES 46- 46 SUB-ZONE INDICATOR
62 9.025803-04
0
zoNE5s4766
FISSILE NUCLIDES--8 10 14 16
FERTILE NUCLIDES--6
9 12 15
7 13
INTERAMDIATE NUCLIDES--OTHER NUCLIDES--11 17 18 19 20 21
STRUCTURAL NUCLIDES--26 27 31 32 33 34 35 37 38 39 45 46 47
1
2
3
5 23
SPECIAL NUCLIDES--FISSION PRODUCT NUCLIDES--- 48 49 50 51 52 53 54 55 56 57 58 59
COR3ESTORAGE~DIffERENCE (WORDS)
E
EQUATION CO NSTANTS
I/0
60
61
62
63
64
65
66
11
19 20
3
0
INSTEADOF STOREDb35058
EQUATION CONSTANTS WILL BE STORED ON I/O LOGICAL 15
NulEER0---COLUNSRONS, PLANES, GROUPS, UPSCAT, DONNSCAT, REGIONS,
AND ZONES
24180
47
MEMORY LOCATIONS RESERVED FOR DATA STORAGE--- 118000
MNIORY LOCATIONS USED FOR THIS PROBLEM-----86421
NEORY LOCATIONS NOT USED------------------ 31579
4*******eNARNING*******
INEUT SPECIFIED DOUNSCATTER
2
HAS BEEN CHANGED TO ACTUAL DONNSCATTER
1
C0
ZONE VACROSCOPIC CROSS SECTIONS
-
NARE
ONE
1- CORE
2_
H20.AL
______
c
GRP
D
SIGR
SIGA
BSQ
NUSIGF
POWER/FLUX
2.60717D-14
4.02591E-13
12
.22140R-
1
2
3
1.62978E+00- 3.288831-02- 1.09096E-03. 2.003225-03
1.96769E-02 3.05681E-02
8.34367E-01 6.279931-02
2.05109E-03.95271E-01
2.6Z83_6 -0___0
1
2
1.75611E+00
8.22862E-01
2.49859E-01
_4.09290E-02
7.340391-02
3
0.0
1.72222E-C4
1.16531E-03
1.81103E-02
3.36421E-02
6.21418E-02
0.0
1.08494E-03_2.097EQ_3.0
1.96273E-02 3.04778E-02 0.0
2.05109E-01 3.95271E-01 0.0_
2.62119E-_4
4.01401E-13
5.22140E-12
0.0
1.09028E-03_2.013481-03
3.000463-02 0.0
1.93564E-02
1.705842-01
.26725-0.
0
2.62407E-14
3.95170E-13
4R.315933-1?
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
3
CORE
1
2
3
1.61766E+00
8.34613E-01
2.62836E-01
4
CORE
1
2
3
1.78490E+00 3.381451-02
8.35597E-01
5.91986E-02
3.0531 4E-010,0
5 CORE
1
2
1.79755E+00
8.35722E-01
3.03235E-01
3.32924E-02
1.09130E-03
5.94504E-02 1.93690B-02
0.0
-31.72317E-01
2.00887E-03
3.003583-02
3.30777E- 01
6
1
2
3
1.63257E+00
8.348451-01
2.62836E-01
3.25618E-02
6.16431E-02
0.0
1.08839E-03
1.95829E-02
2.05109E-01
1.99930E-03-0,0
3.039601-02 0.0
3.95271D-01 0.0
0.0
0.0
0.0
2.61380E-14
3.95581E-13
4.369461- 12
0.0
0.0
0.0-
.-
0
c
7
_
CORE
D20+N20+AL
PD
1
2
1.43073E+00
1.204941+00
2.27943E-02
2.138511-02
8.27860E-05
1.059851-05
0.0
0.0
0.0
0.0
0.0
0.0
3
7.70232E-01
0.0
1.76033E-04
0.0
0.0
0.0
1
2
1.72041E+00
9.086001-01
4.797521-04
3.83538E-04
1.02293E-04
2.83798E-04
0.0
0.0
0.0 _
0.0
0.0
0.0
0.0
1
2
3
1.96928E+00
2.04424E+00
1.567321-01
4.17163E-04
4.21599E-04
0.0
1.61449E-03 0.0
8.29796E-02 0.0
4.112191+02. 0.0 --
_ 1
2.655003+00
4.01942E+00
3.601681+00
3.71354E-04
5.721551-04
0.0
1.71999E-04
7.425762-04
9.52056E-03
0.0
0.0
0.0
0.0
0.0
.0.0
0.0
0.0
2.666383+00
4.01738E+00
3.460912+00
3.995001-04
6.035651-04
0.0
1.97850E-04
8.94777E-04
1.46606E-02
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
1
2.71624E+00 4.944521-04
24.01476E006.789121-04
3
3.46091E+00 0.0
2.20117E-04
1.02969E-03
1.59357E-02
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
3
9
10
CD+AL
AL__
2
3
11
u
AL
_
1
2
_3
12
D20
e
2.60148E-14_
4.00325E-13
5.22140E-12
__
9.089262-010.0
_
1.58160-030.0
0.0
-
0.0
0.0
-0.0.
_
CORE
1
2
3
1.781643+00
8.362731-01
3.05314E-01
3.493111-02
5.74405E-02
0.0
1.09921E-03
1.92940B-02
1.705843-01.
2.02727E-03
2.98306B-02
3.267253-01
0.0
0.0
0.0
2.641143-14
3.92862z-13
4.315933-12
14
CORE
1
2
3
1.79914E+00
8.354581-01
3.053143-01
3.364731-02
5.94802E-02
0.0
1.076651-03
1.94206E-02
1.705843-01
2.01382E-03
3.009073-02
3.267253-01
0.0
0.0
0.0
2.618991-14
3.96303E-13
4.315932-12
15
AL+N20
1
1.429663+00
28.92E-01
3
2.49859E-01
1.012601-01
1.55308E-04
1.5671.81103E-02
0.0
0.0
0.0
0.0
0.6
0.0
0.0
0.0
0.0
9.164901-03
1.022911-02
0.0
0.0
8.475683-C6
2.49286E-04
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
16
C
1
1.293011+00
3
8.476241-01
2 - 9.08544E-01
.0
_
_
_
_
_
0.0
0.0
0.0
13
1.0839-01
_
H
a.'
H
1.91839E+00
1.84655E+00
1. 27290100
7.53674E-03
9.702571-03
0.0
1.72139E-04
5.52131E-04
8.271211-03
0.0
0.0
0.0
0.0
0.0
0.0
120
1
2
3
1.39896E+00
4.52630E-01
1.28445E-01
7.46055E-02
1.62852E-01
0.0
1.554542-04
1.41556i-03
2.04662E-02
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
19__&L+820
1
2
3
1.37749E+00
4.79085E-01
1.36227E-01
7.91092E-02
1.463231-01
0.0
1.43090E-04
1.344742-C3
2.00560E-02
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
20
0
1
2
3
1.24040E+00
4.53494-01
1.284451-01
9.34558E-02
1.54211E-01
0.0
1.20477E-04
1.35534E-03
2.04662E-02
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
1
1.24195E+00
4.546091-01
1.28445E-01
9.067431-02
1.144983E-01
0.0
1.16686E-04 0.0
1.299131-03
0.0
2.046621-02 -0.0.0
0.0
0.0
0.0
0.0
0.0
2
1-
2.402121+00
2.062401+00
7.914441-01
7.02450E-03
1.234711-02
0.0
1.09647E-03 2.013823-03 0.0
1.933951-02 3.009071-02 0.0
1.697363-01 _3.26725-1_0.0_9
2.61899E-14
3.963031-13
AL+D20
_
18
21
820
2
E
6
22
CORE3AL-H20,
0.0
0.0
0.0
.
4.3193-12
CO8Z+AL-N20
1
2
3
2.399061+00
2.06529E+00
7.94068E-01
6.949481-03
1.234511-02
0.0
1.123061-03
1.92850E-02
1.71244E-01
2.008873-03 .0.0
3.003581-02 0.0
3.307771-01
0.0
2.61380E-14
3.955811-13
4.369461-12
24
AL+H20
1
2
3
1. 369001+00
4.988021-01
1.421303-01
7.137631-02
1.301211-01
0.0
1.32019-04
1.243972-03
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
1
2
3
2.647228+00
2.375271+00
1.64809E+00
9.13870E-03
8.444731-03
0.0
5.390801-05
1.02350-04
1.44756E-03
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
1 _ 1.993271+00
25
AL+D20+OD
26
AL+020+TOID
28
29
AL+YID
AL+D20+TOID
ALOD20#TOID
_._
1.969441-02
2
3
1.732271+00
1.158623+00
1.43169E-02
1.32244E-02
0.0
6.36992E-05
5.722141-05
8.175631-04
0.0 0.0
0.0
0.0
0.0
0.0
0.0
1
2
3
6.39779E+00
6.93563E+00
6.43429E+00
1.25266-04
1.243721-04
0.0
3.466933-05
1.699942-C4
2.39075E-03
0.0
0.0
0.0
0.0
0.0
0.0
0.0
1
2
3
2.437921+00
2.16531E+00
1.04900E-02
9.692073-03
1.484331+00
0.0
5.656312-05
9.10700E-05
1.290143-03
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
1
2
3.632273+00
3.24308E+00
2.236661+00
6.847773-03
6.327323-03
3.869751-05
6.82628E-05
0.0
0.0
0.0
9.661311-04
0.0
0.0
0.0
0.0
0.0
0.0
0.0
1
2.25930E+00
2-1.989452+00
5.92183E-05
7.979023-05
0.0
0.0
0.0
0.0
0.0
0.0
0.0
3
E
-
_
_
23
27
e
0.0
1
2
3
17
-
0.0 0.0
0.0
-
-
0.0
30
AL+D20+TOID
3
1.35017E+00
1.184131-02
1.093941-02
0.0
1.13272E-03
0.0
0.0
31
AL+D20+TOID
1
2
3
2.055193+00
1.793841+00
1.204261+00
1.364541-02
1.260491-02
0.0
6.352731-CS
6.85279E-C5
9.759633-04
0.0
0.0
0.0
0.0
0.0
0.9
0.0
0.0
32
ALOD20+TOID
1
2
3
1.712791+00
1.470791+00
9.697721-01
1.76987X-02
1.634631-02
0.0
7.149033-05
3.46881E-05
5.037133-04
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
C033-1120
1
3.750251000
1*974721-04
1.026561-03
2.010978-03
0.0
2.62119-14
3
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r
r
2
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5.198401+00
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0.0
1
4.79420E+00 1.98416E-04
2
5.209042+00 3.032211-04
___3.58082+000._0
0.0
0.0
4.014013-13
5.22140E-12
1.032313-03 2.013483-03 0.0
1.882983-02 3.000463-02 0.0
1..64038E-013._26725E-QL0.-0
2.624073-14
3.951702-13
4.31593-32
1.908263-02
1.971641-01
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3.952713-01
34
C033-M20
35
Co8-920
.. 1
2
3
4.79911E+00
5.21641E+00
1.5888CE+00
1.953721-04
3.047201-04
0.0
1.03082E-03
1.884093-02
1.656873-01
0.0
0.0
0.0
2.61380E-14
3.95581E-13
4.36946E-12
36
C083-320
1
2
3
4.80770E+00
5.211373+00
1.580823+00
2.057092-04
2.848181-04
0.0
1.04185-C32.02727E-03-0.0
1.87733E-02 2.983063-02 0.0
1.640383-01 3.267251-01 0.0
2.641143-.14
3.92862Z-13
4.315933-12
37
C013-20
1
2
3
4.80564E400
5.20363E+00
1.580823+00
1.98075E-04
3.020801-04
0.0
1.016333-03
1.889033-02
1640383-01
2.01382E-03
3.009073-02
3.26_72]3-01
0.0
0.0
0.0
2.61899E-14
3.963033-13
4.31593E12
38
CORE-H20
2.00887E-03
3.003583-02
3.307773-01
3.75610E+00
1.90924Z-04
1.02736E-03
1.99930E-03
2
5.20114E+00
3.173691-04
0.0
1.90406E-02
3.039603-02
0.0
0.0
1.384583+00
1.971643-01
3.952713-01
0.0
5.22140E-12
2.00322E-03
3.056813-02
0.0
0.0
2.60717E-14
4.025913-13
_1
__
_
2.601482-14-
4.00325E-13
39
CORE-H20
1
2
3
3.757353+00
5.19513E+00
1.38458E+00
1.929921-04
3.257661-04
1.030003-03
1.91282E-02
0.0
1.97164E-01-3.95271-01
0.0
5.221403-12
40
AL+H20
1
2
3
1.80820E+00
9.316971-01
2.900923-01
3.965733-02
6.535611-02
0.0
1.78356E-04
1.16787E-03
1.78596E-02
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
41
VOID
1
2.730001+00
1.91681E+00
1.584281+00
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
1.32947E+00 7.154951-02 1.30751E-C4
4.60334E-011.27862E-011.14175-03
1.433293-02_
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
2
3
42
820
1
2
3-1-73355E-01
43
44
45
320
M1+AL
W-S
7.15495E-02
1.30751E-04
0.0
0.0
0.0
1.278623-01
0.0
1.14175E-C3
1.43329E-02
0.0
0.0
0.0
0.0
0.0
0.0
1.70715E+00
7.34511E-01
3.715243-01
3.074311-04
3.548601-04
0.0
4.09665E-C3
3.23359E-01
8.738771-01
0.0
0.0
0.0
0.0
2
3
0.0
0.0
0.0
0.0
0.0
1
2
3
2.485111+00 2.85560E-04
1.34400+00 3.29614t-04
7.469361-01 0.0
1.953053-03
1.45286-01
0.0
0.0
0.0
0.0
0.0
0.0
4.082523-01
0.0
0.0
0.0
1
1.161321+00
3.094541-01
4.735433-01
2.12123E-03
1.67298E-03
0.0
2.71066E-03
1.531113-01
2.783293+00
0.0
0.0
0.0
0.0
0.0
0.0
0.0
I47
1 1.969283+00
2
2.044241+00
.3
1.567321-01
4.171633-04
4.215991-04
0.0
1.614491-03
8.297961-02
4.11219EtC2
0.0
0.0
0.0
0.0
0.0
0.0
0.0
1
c
46
1.32947E+00
4.60334E-01
1.73355E-01
1
2
3
H?+AL
_
2
3
2
CDAL
0.0
0.0
0.0
-
0.0
0.0
___
BOLT
SA
LE HOLDER,
HF FIXED AT 12",
B-SS
ELACES AT 8",
24. ELEMENTS
INNER IIERATIONS)
LINE RELAXATION VIIL BE DONE ON BOWS -_3
N0-3
PU-2
N1-1
BETA
ITERATION FLUX CHANGE
0.0
6.08812 -1.99876
1.00000
1
3.044061+00
e
1.87832
1.78304
1.71492
1.66933
1.64014
1.62199
1.61090
1.60420
1.60018
1.59777
1.59634
1.59548
1.59498
1.59467
1.59449
19
1.00000
1.59433
1.59429
-0.25101
2.18258
0.84297
-0.59601
1.55034
0.78612
20
-2.06549E-02
1.59426
-1.02025
-1.24354
21
22
23
24
1.42603E-02
1.156431-02
9.47094E-03
7.78103E-03
1.59425
1.59424
1.59424
1.59424
-0.67615
0.82251
0.82845
0.82935
-0.56275
0.92200
0.92389
0.92609
5.54209E-02
EXTRAPOLATION
17
18
-
_25
26
27
28
29
30
31
32
33
34
35
1.99318E-03
-4.513031-03
3.66211E-03
-4. 27705E-03
2.86484E-03
2.64549E-03
2.450941-03
2.26688E-03
2.56736E-02
-1.280491-03
1.068121-0
8.926391-04
6.3035
ITH_
EXTRAPOLATION
WITH
1.00000
0.25815
1.59423 -2.26875
1.59423 -0.80779
1.59423 -1.17220
1.59423 -0.66695
1.59423
0.92608
1.59423
0.92891
1.59423
0.92717
EXTRAPOLATION WITH
1.00000 -0.56615
1.59423 -0.83308
1.59423
0.83661
OF RIGENVALUE CALCULATION -
ED
6.19160
10.17908
40.82141
4.69094
9.50468
1.87829
2.04866
-0.72387
-0.44146
-0.67612
0.43239
0.80382
0.80491
0.80525
0.80477
1.05165
0.00062
0.10221
0.00323
3.22641
0.01892
0.40719
0.01026
0.44394
0.01194
0.35550
0.15076
0.10096
0.59364
0.50627
-0.58005
0.33337
-0.44791
-0.27918.0.01697
0.91111 -41.58059
0.89703
1.66488
0.91383
1.28418
0.91819
1.14937
0.92139
1.08596
4.660571+00
8.38084E+00
3.646981+01
4.56575E+00
7.79698E+00
1.66477E+00
1.27987E+00
-4.06362E-01
3.021931-01
-1.569033-01
-8.046911-02
-7.03433E-02
-6.09043E-02
-5.22241E-02
-4.434411-02
-2.924872-01
1.16472E-02
2.51284E-02
2.06633E-02
2
3
4
5
6
7
a
9
10
11
12
13
14
15
16
6.80854
0.16151
0.99336
0.94867
0.94417
0.92215
0.91706
0.91582
7.1779
0.23734
7.29220
-1.96562
0.03825
-0.96624
1.02081
-0.88300
0. 97112
-0.79915 __ 0.97234
0.90996
0.94818
0.90695
0.94746
0.91090
0.94078
11.3512
-0.33358
11.44178
-0.23812
0.01689
0.92545
0.99624
ITERATION TINE
K
_.0.353841
0.948672
0.958072
0.965232
0.970448
0.974695
0.978091
0.980897
0.983203
0.985115,
0.-996923
0.996660
0.996229
0.996002
0.995776
0.995564
0.995369
0.995202
0.994035
0.994030 _
0.994055
0.994087
0.994102
0.994104
0.994101
0.994092
8.21730E15
TOTAL LOSSES
AIRAGE FLUXES BI ZONE AND GROUP
ZONE
1-CORE
8.82495E+13
ZONE
3.657971+13
3.74741E+13
5.31499E+12
1.687371+13
5.752383+13
2.771111+13
2--H20+AL
8.853351+12
ZONE
3--CORE
-ZONE
4-CORE
1.509631+14
_
0.993950
0.993936
0.993902
0.993877
1.343 MINUTES
CONI3RGENCE INDzcrIC~DBYININIZING THE SUN OF THE SQUARES OF THE RESIDUES -
LEAKAGE
_
0.826959
0.788136
0.883745
0.913714
0.936362
1.9062211~7
TOTAL PRODUCTIONS
RELATIVE ABSORPTIO8
0.9999909
1.89455Z+17 REACTOR PONER(WATTS)
K .0.9938350
5.00000E+06
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0.31024
0.01103
0.00397 0.01041
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.00226
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
.0.0
0.0
0.00556
0.05159
0.0
0.0
0.0
0.0 0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.00736
0.00791
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.00006 0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.C0014 0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
-SS
0.0
0.0
0.0
0.0
0.0
CE2AL
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.01546
0.31024
+20
H20
HF+AL
HF+A
___
OVERALL
END OF CASE
-
0.0
0.0
0.0
0.0
0.0
0.0
OTHER LOSSES'
0.01103
TOTAL CPU TINE WAS
ENDED
NOR
MALL
0.00137
0.00137
0.00619
00.0
0.0
0.0
0.00633
.0
0.0
0.0
-
0.0
0.0
G.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.02016
0.00013 0.0
0.0
0.00016 0.0
0.01294
0.0
0.0
0.0
0.0
0.11369
0.00001 0.0
0.00350
0.0
EASED 0 START-0F-STEP TOTAL LOSSES
0.0
0.0
0.02029
0.04750
1.00000
0.13413
0.02075
0.41769
TOTAL CLOCK TIME HAS
**.***
***....****..********..********e*.*********
370E
0.0
0.0
0.0
0.0
0.0
0.0
1.61 MINUTES
******THIS
SPECIAL UNSPECIFIED
SUNS CONY. RATIO
0.0
0.01360
0.01312
0.00048
0.0
0.04875
0.0
0.0
0.38778 3._00_505
0.00763_-0.00000
0.0
0.00443
0.01881
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.03380
0.03606
0.0
0.0
0.0
0.0
0.0
0.0
0. 13443 0.13999_0.0
0.0
0.04055
0.09214
0.0
0.00730
0.0
0.0
0.00730
0.0
0.00367
0.00367
0.0
0.0
0.00437
0.00370 0.0
0.0
0.00736
0.0
0.0
0.0
0.0258.0.03312_0.0
0.0
0.0
0.0
0.0
0.00282
0.0
0.0
0.00282
0.0
0.00219 0.00225 0.0
0sAS
E
N
3.10
**********
9/i0776
0.01310
0.11369
0.00351
0.04311
MINUTES
3.00505
-
****************************.*
6N
E II
37065
******
-
----------
POWER(HU)
FISSILE(KG)
1.297181-01 0.0
0.0
0.0
3.580591+00.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
1.28''19
0 0.0
0.0
0.0
0.0
0.0
0.0
0.0
-0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
4.99999E+00
0.0