HOMOGENIZED CROSS SECTION DETERMINATION by ILKER TARI

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HOMOGENIZED CROSS SECTION DETERMINATION
USING MONTE CARLO SIMULATION
by
ILKER TARI
B.S., Hacettepe University, Turkey 1987)
M.S. University of Michigan 1991)
Submitted to the Department of Nuclear Engineering
in Partial Fulfillment of the Requirements for the Degree of
NUCLEAR ENGINEER
and the Degree of
MASTER OF SCIENCE
at the
MASSACHUSETTS INST111M OF TECHNOLOGY
January 1994
0 Ilker Tari, 1994. All rights reserved.
The author hereby grants to MIT and Turkish Ministry of Education permission to reproduce and distribute
copies of this thesis document in whole or in part.
Signature of Author
Department of Nuclear Engineering
January 28, 1994
Certified by
Allan F. Henry
Professor of Nuclear Engineering
Thesis Supervisor
Accepted by
Allan F. Henry
MASSACHLISETT::
WSTITU
-iE
PIT
APR 26
1994
i-loriAWES
cience
Chairman, Department Committee on Graduate Students
HOMOGENIZED
CROSS SECTION DETERMINATION
USING MONTE CARLO SIMULATION
by
ILKER TARI
Submitted to the Department of Nuclear Engineering
on January 28, 1994, in partial fulfillment of the
requirements for the degrees of
NUCLEAR ENGINEER and MASTER OF SCIENCE
ABSTRACT
This thesis is an application of Monte Carlo simulation techniques to homogenized cross section
determination. MCNP Monte Carlo code was used for obtaining homogenized node cross sections for
QUARTZ triangular-z nodal code model of MITR-II (MIT research reactor). According to specifically
developed original scheme, three different MCNP models of MITR-11were generated.'These models were
used in several MCNP runs to obtain cell fluxes and reaction rates. These results were processed using a
homogenization scheme to generate homogenized total, absorption, fission and elastic scattering cross
sections and diffusion coefficients for two energy groups. The accuracy of the specifically developed cross
section processing programs were tested. Axial and radial distributions of the results were investigated. The
general accuracy of the procedure was evaluated and possible sources of error were identified. A simple
problem which is a portion of a MITR-11 fuel element was modeled and used for demonstrating the
suggested one-MCNP-run procedure. 'Me computer facility requirements were evaluated and some
projections about the future requirements were discussed.
Three major outcomes of this thesis are : () threenew MCNP models of MITR-II, 2) two group reaction
rate and flux data for every cell represented in the MCNP model of MITR-H
homogenized cross sections for two groups.
Thesis Supervisor- Prof. Allan F. Henry
Thesis Reader: Prof. David D. Lanning
2
3 Triangular-z nodal
TABLE OF CONTENTS
Page
ABSTRACT
2
TABLE OF CONTENTS
3
LIST OF FIGURES AND TABLES
4
CHAPTER I INTRODUCTION
6
1.1. THESIS OBJECTIVE
6
1.2 BACKGROUND ON MITR-H
7
1.3 A BRIEF BACKGROUND OF MONTE CARLO SMULATION AND MCNP
12
1.4 BACKGROUND ON QUARTZ NODAL CODE
13
1.5. ORGANIZATION OF THE THESIS
15
CHAPTER 2 PROBLEM, SOLUTION STRATEGY AND MCNP MODELS
16
2. 1. WHY MCNP ?
16
2.2. GENERAL STRATEGY AND PROCEDURE
19
2.2.1. QUARTZ Model of M1717R-II
19
2.2.2. Organization and Distribution of the Tasks
21
2.3. MCNP MODELS AND THEIR EVOLUITON
24
2.3.1. Original Model
24
2.3.2. Simplified Model
24
2.3.3. Triangulated Model
32
2.3.4 13 Symmetry Incore Fully Triangulated Model
35
CHAPTER 3 PRE-PROCESSING, PROCESSING AND POST-PROCESSING
38
3. I. MCNP INPUT PREPARATION AND PRE-PROCESSING PROGRAMS
38
3..1. 1. Tally Cards
38
3.1.2. Stochastic Volume Calculation by using MCNP
38
3.1.3. Segmentation
39
3.2. MCNP RUNS FOR OBTAINING CELL FLUXES AND REACTION RATES
39
3.3. THE HOMOGENIZATION SCHEME AND POST-PROCESSING PROGRAMS
41
3.3.1. Homogenization Scheme
41
3.3.2. Calculation of the Statistical Erors
42
CHAPTER 4 RESULTS
43
4.1. INCORE RESULTS
44
4.2. OUT OF THE CORE RESULTS
44
4.2. I. Results for the Nodes Above the Bottom Level of The Fuel
44
4.2.2. Results for the Nodes Below the Bottom Level of ne Fuel
47
3
4.3. SURFACE FLUX AND SURFACE CURRENT RESULTS
47
4.4. GROUP TO GROUP SCATTERING
47
4.5. NEUTRON BALANCE
50
4.6. GENERAL TRENDS OF THE CROSS SECTION RESULTS
51
CHAPTER
CONCLUSION
67
5.1. GENERAL EVALUATION OF THE RESULTS
67
5.2. COMPUTER FACILITY REQUIREMENTS
69
51.1. Required Memory for MCNP runs
69
5.2.2. Relation between CPU Time and the Number of Cells in the Model
70
5.2.3. Relation between CPU Time and the Tallies in the Model
71
5.2.4 Sorage Space Requirement
71
5.3. CONT'RIBLMONS
71
5.4. RECOMMENDATIONS FOR THE FUTURE WORK
72
REFERENCES
73
APPENDIX A INPUT TALLY CARDS
74
APPENDIX
87
PROCESSING PROGRAMS
APPENDIX C SAMPLE CROSS SECTION RESULTS
112
APPENDIX D ONE GROUP NODE BALANCE CHECK RESULTS
131
APPENDIX E THE M T OF HOMOGENICZATIONPROCEDURE
136
LIST OF FIGURES AND TABLES
Page
Figure 11. Artist's rendering of M[TR-H reactor facility
8
Figure 12. N=
9
-11fuel element with its dimensions
Figure 13. MITR-H cote number 2 loading with dummy and 22 fuel elements
10
Figure 14. Scaled x-y view of MITR-II with reflectors
II
Figure 1.5. QUARTZ triangular
14
mesh geometry
Figure 2.1.Azimutal enlarged CITATION model of MITR-11
17
Figure 22. The 3-D representation of QUARTZ model of M1TR-II
20
Figure 23. Tix oganization of the tasks in the development of MCNP model
22
Figure 24. The tasks after the model was generated
23
Figure 25. Original Model of MITR-11(y-z view)
25
Figure 26. Original Model of MITR-II (x-y view)
26
Table 2 1 'Me comparison of CPU time and k-effective results for different runs of two models
27
Figure 27. One of the bottom detectors in guide tube
29
4
Figure 28. Simplified Model before graphite reflector changed to hexagonal prism (x-y view)
30
Figure 29. Simplified Model after graphite reflector changed to hexagonal prism (y-z view)
3
Figure 210. Triangulated Model (x-y view)
33
Figure 21 1. Triangulated Model (y-z view)
34
Figure 212 'Me 13 symmetry boundaries
36
Figure 213. The 13 symmetry triangulated core model (x-y view)
37
Table 3 1 'Me comparison of CPU time and k-effective results for
MCNP tally runs
40
Figure 41. 2-D nodal map of QUARTZ model showing the I and J indices
45
Table 4 1. The smple results for the radial distribution of the cross sections and flux
46
Table 42. Axial distribution of flux and cross sections for triangular node 1=I 1, J= 1
48
Table 43. Axial distribution of flux and cross sections for triangular node 1=17,J=7
49
Figure 42. Radial flux distributions
52
Figure 43. Radial distributions of homogenized croaa.sections
53
Figure 44. Radial distribution of statistical errors
54
Figure 45. The axial distribution of fluxes for the 2 energy groups in node 17,7)
55
Figure 46. The axial distribution of homogenized cross section results in node 17,7)
56
Figure 47 'Me axial distribution of statistical error for the 2 energy groups in node 17,7)
57
Figure 48. MCNP axial thermal flux distribution for Aluminum of A-3
60
Figure 49. MCNP axial fast flux distribution for Aluminum of A-3
61
Figure 410. MCNP axial thermal flux distribution for Plate I of B-7
62
Figure 41 1. MCNP axial fast flux distribution for Plate
63
of B -7
Figure 412. MCNP axial thermal flux distribution for Pate 15 of B-7
64
Figure 413. MCNP axial fast flux distribution for Plate 15 of B-7
65
Table 5. 1. Summary of the data relevant to the computing resources
69
5
CHAPTER
INTRODUCTION
1.1. THESIS OBJECTIVE
This thesis is an integrated part of the department wide effort to obtain tools for real time transient analysis
of nuclear rectors. The real time determination of spatial power distribution in the core and the total core
reactivity is the key issue to improve the safety and control of the nuclear reactors. 'Me real time
calculations and analysis requires accurate and faster methods to determine reactor physics parameters. The
theoretical, and experimental nodal synthesis methods are the promising candidates for this task. Recently
a quadratic nodal code for triangular-z geometry QUARTZ) is developed by T.F. DeLorey [D-1] and tested
against several static and transient benchmark cases. Application of QUARTZ to calculation of a real reactor
for the first time, requires homogenized cross section data for every node in its defined mesh. The thesis
project of W.S. Kuo [K-1] involves this kind of application of QUARTZ to Massachusetts Institute of
Technology Research Reactor (MITR-H), therefore the homogenized cross sections for triangular-z mesh
model of MITR-11 for QUARTZ are required. The main objective of this thesis is to generate the required
cross section data by using a Monte Carlo simulation. The MCNP Monte Carlo code developed at the Los
Alamos National Laboratory is chosen for this job, it being the only readily available code that can provide
enough flexibility to obtain satisfactory results. Some unique characteristics of the MITR-Il makes reactor
analysis impossible without using a Monte Carlo simulation. During the course of this thesis work, a
consistent and original approach was developed by the author and Kuo. Since the application of the
procedure by one person was impossible to complete within the time limitations, the task was divided
between the author and Kuo. The task division and the approach will be discussed-in the next chapter.
Sections 12 through 14 briefly describe MITR-Il, MCNP and QUARTZ for the unfamiliar reader. More
detail about MITR-II and MCNP is presented as required for the understanding of the related topics. For
more information on those topics, references [M-11 and [B-1] are very good sources of information for
MITR-H and MCNP, respectively.
6
1.2. BACKGROUND
MITR-11 is a
ON MITR-11
MWth research reactor at the Massachusetts Institute of Technology which has been in
operation since 1975. It serves as an interdepartmental research and education facility. It is a unique design
created by MIT Nuclear Engineering Department students, faculty and staff. Figure 11 shows the general
view of the entire reactor and the associated research facilities.
MITR-II has a very compact core design involving 27 rhomboid assembly locations. These locations can be
filled with fuel assemblies, A6061 dummy elements or with special experimental apparatus. Each fuel
element consists of 15 highly enriched (-93% U-235) UAIxfuel plates as shown along with dimensions in
Figure 12
The Core elements form three separate rings with some parts of the core divided by boron
inserts. Figure 13 shows the MITR-H fresh Core-2 loading arrangement with
dummy elements and 22
fuel assemblies. This is the case for which the homogenized cross sections will be obtained. In this case,
the A-ring consists of two
y elements and a fuel element occupying the small hexagonal section in
the middle of the core. The B-ring is a hexagonal ring surrounding the A-ring. It includes 3 dummy and 6
fuel elements. Ile A-ring and B-ring are divided by a hexagonal structure called a spider which is partly
Aluminum, partly water, and some parts of which include boron inserts. The outer ring which includes 5
fuel elements is called as the C-ring. Some elements in 13-ringand C-ring are separated by 3 other structures
called arms, and some parts of these ams include boron inserts.
The reactor core is surrounded by a hexagonal Aluminum structure in which the control blades, water holes
and regulating rod are nested. 'Me six boron control blades are located at the edges of the hexagon. Each
comer of the hexagon has a cylindrical hole called a water hole or water vent hole. 'Me main function of the
water holes is the ventilation of the water replaced by control blades during the control blade insertion. 'Me
water hole on the right corner in Figure 13 includes the regulating rod which uses Cadmium as a control
material and functions as a mechanism for fine reactivity adjustments and flux shape regulation. All
constituents of the core are numbered starting rom the position of the regulating rod and numbering in a
clockwise dection. For example A-1 is the fuel element in the A-ring nearest the regulating rod where is in
water hole 1. MITR-11 core is cooled with light water. 'Me core tank which holds the core itself and the
coolant, is placed in another tank fled with heavy water which acts as both moderator and reflector. The
reflector tank is also surrounded by an approximately 60 cm thick graphite reflector. As can be seen from
Figure 14, MITR-II core is a very compact design and is neutronically highly coupled.
The MITR-II facility also includes several neutron beam ports, thimbles and pneumatic tubes for both
incore and out of core irradiation and a medical therapy facility at the bottom of the reactor. Incore
experiments can be conducted by replacing a dummy element with a rhomboid shaped experimental
apparatus.
7
(1)
LU
Q
C
LL.
.j
z
cc
LLJ
CL
x
z
z
w
z
0
0.
2
00
cc
0
cc
cc
LLI
1-:
U.
0
Figure 1.I Artises rendering of N=-II
reactor facilitY (ad-Vted ftm [M-21)
8
A-A CROSS SECTION
----i
A
A
A
C
T
I
v
56.83-4 cm
E
F
66 i7 cm
n
U
E
L
0.4 cm
Figure 12 MITR-11 fuel element with its dimensions
9
10
Absorber Plate
RR: Regulating Rod
CB: Control Blade
WH: Water Hole
Figure 13 MrM-II core number 2 loading with
10
dummy and 22 fuel elements
C
C
i
-I
i
L
II
L
C
-7 -
i
I
I
CD -
0 ,
Ln I
CD
0
I
. I. I. . I. . . .I -I - - I- - - I- I- - - -I I---- -I I- I---I I- I I I . . . ... .. .I . . . . . . . . . . . . .
.
-
100
-50
0
50
Figure 14 Scaled x-y view of MITR-11with reflectors.
Ii
.
.
.
.
.
.
.
.
.
.
100
.
.
1.3 A BRIEF BACKGROUND OF MONTE CARLO SIMULATION AND
MCNP
Parts of this paragraph are taken directly from the MCNP Manual [B-1]. Monte Carlo methods are very
different from deterministic transport methods. Deterministic methods solve the transport equation for the
average particle behavior. By contrast, Monte Carlo does not solve an explicit equation, but rather obtains
answers by simulating individual particles and recording some aspects (tallies) of their average behavior.
The average behavior of particles in the physical system is then inferred (using the central limit theorem)
from the average behavior of the simulated particles. The central limit theorem says that for sampling from
almost any distribution, the distribution of the smple mean is approximately normal provided the sample
size is large enough
-1]. Not only are Monte Carlo and deterministic methods very different methods of
solving a problem even what constitutes a solution is different. Deterministic methods typically give fairly
complete information (for example, flux) throughout the phase space of the problem, whereas Monte Carlo
supplies information only about specific tallies requested by the user. Monte Carlo can be used to
theoretically duplicate a statistical process (such as the interaction of nuclear particles with materials) and is
particularly useful for complex problems that can not be modeled by computer codes of deterministic
methods[B-1].
MCNP is a general-purpose,
continuous-energy,
neutron/photon/electron Monte Carlo =sport
generalized-geometry,
time-dependent,
coupled
code. MCNP is widely used and its accuracy has been tested
throughout these years of heavy usage. To use the code, the user creates an input file that is subsequently
read by MCNP. This file which is referred to as the MCNP model in this thesis, contains information
about the problem in areas such as the geometry specification, the description of materials, which crosssection evaluations to use, the location and characteristic of the source, and the type of answers or tallies
desired. A more detailed description of MCNP options can be found in User's Manual [B-1] and its
supplements [B-2].
Some definition's of the terms used in this thesis related to MCNP are the following.
surface and surface definition In MCNP input geometry of the model is defined by using surfaces. MCNP
has several surface definition tools that can be used to define fst- and second-degree surfaces and some
special fourth-degree surfaces.
cell and cell definitigIL Cells are the units that are used to define geometry. They are defined as the volumes
bounded by the defined surfaces.
12
tally and LaUYdefinitions as mentioned earlier, MCNP results are obtained by following histories in the
defined geometry. Tallies are the statistical results of that procedure and they can only be obtained for
defined surfaces and cells. MCNP can tally seven major quantities. The ones used in this project are
Fl:surface current, F2:surface flux and F4:track length estimate of cell flux.
source definitions and Thecritical
MCNP has several source definitions to generate the histories and
introduce them to the geometry. 'Me ones used are the surface source and the criticality source. 'Me
criticality source runs are the ones that starting with the initial source points, create source points for the
next group of initiating particles. Each group of particles is called a cycle, and each cycle is introduced at
the source points created by the previous one. One can think of source points as the points where the
fission events take place.
he criticality run gives as a result the eigenvalue (criticality) of the reactor
model.
universe-fl1l and =ated
structures definitions Some repeated structures in the geometry can be defined
easily by using the special options of MCNP introduced in the recent versions of the code. The newest and
the most frequently used of these options is the universe-fill scheme. In this scheme several cells-can be
defined as a universe and the universe can be used in some other cell definitions with fill command. These
filled cells act as windows that the universe viewed from.
Detailed descriptions of all these definitions can be found in the manual [B-1].
1.4. BACKGROUND ON QUARTZ NODAL CODE
QUARTZ is a =dratic
polynomial Reactor code for 3:nangular-Z geometry developed by DeLorey [D-11.
This in-house code solves the quadratic nodal equations using a non-linear iteration scheme, based on the
corrected, mesh-centered finite difference equations. These equations are forced to match the quadratic
equations by computing discontinuity factors iteratively during the solution [13-I].
QUARTZ uses an equilateral triangle-z geometry. The triangle side length is variable, but the triangle must
be equilateral. An example of the nodal mesh geometry of QUARTZ is given in Figure 1.5. his mesh
structure is especially suitable to represent the core elements of MITR-II that are rhomboids with equal
sides.
More information about QUARTZ can be found in references [D-1],[D-2] and [K-1].
13
TRIANGULARNMESH
a
1=1
1=2
I
Z-MESH:
I
K increases from bottom to top
I
Figure 1.5 QUARTZ triangular-z mesh geometry
14
1.5. ORGANIZATION OF THE THESIS
After this introduction chapter, in Chapter 2 the overall problem and the approach used for its solution are
discussed with respect to the MCNP models created to obtain the data for homogenization.
Chapter 3 gives some information about the pre-processing software written to prepare input data and other
data gathering processes. It also discusses the MCNP runs and the homogenization schemes for incore and
out of core homogenized cross section calculations, including post-processing procedures and the software
written to implement them.
In Chapter 4 results are presented and the procedure for using them in QUARTZ is discussed. The large
volume of data obtained is summarized to give the general trends in the forms of tables and graphics.
The thesis conclude with Chapter
discussing the validation of the cross section results and evaluation of
the general solution scheme. A discussion of computer facility requirements for this End of job, a summary
of the contributions made in this thesis and recommendations for the future work are also given in this
chapter.
15
CHAPTER 2
PROBLEM, SOLUTION STRATEGY AND MCNP MODELS
2.1. WHY MCNP ?
MCNP is the most suitable Monte Carlo code available for the case at hand, as offered, for example KENO
Monte Carlo code which has been tested by Kuo was found unsuitable. New versions of MCNP have
enough generality for most reactor physics applications. However, we have found no application of MCNP
to homogenized cross section generation in the literature. Although the MCNP manual includes some
hints, its application to that area requires creative approaches and sometimes tricks to fake the code. During
the course of this work, among some other tricks tried -such as using the surface source read-write option
instead of a criticality run for larger numbdr of histories- the approach discussed in the next section is
chosen eventually. It seems to be the best approach possible.
Most of the commercial and research oriented computer codes were developed for commercial nuclear plants,
and therefore generally use Cartesian or r-O-z geometry along wiih fixed geometrical shapes convenient for
the representation of BWR and PWR cores. Since the MITR-II core has a very unique geometry, it is
impossible to represent it by these codes without major approximations to the geometry. Calculations for
reactor operations for the MIIR-II have been done regularly by the reactor staff using the CITATION code
[F-1]. But CITATION is in r-O-z geometry which, as seen in Figure 21 does not conform well to the
MITR design. On the contrary, MCNP allows the definition of almost any possible geometric shape that
can be associated with an open or closed form polynomial function. Such generality is required for a good
representation of MrIR-II.
16
AZIMUTHAL MESH:
CORE
SECTION
ENLARGED MODEL
M.I.T.Ft.11
Figtwe 21 Azimuthal enlarged CITAMN mdel OfMITR-11
17
MCNP has some other advantages over deterministic transportcodes that can be itemized as
•
It has the inherent characteristic of a Monte Carlo simulation that the accuracy of the results is not
limited by any theoretical approximation.
•
The continuously-updated, continuous-energy cross section libraries allows calculations to be made
without any energy group approximation, and by using the most recent cross section data sets.
•
The model geometry plotting tool that comes with the package aows the user to check the model at
every step of the development process. Most of the figures included in this thesis were generated by
using this tool.
On the other hand, MCNP has some limitations and inconvenient characteristics The accuracy of MCNP
results is limited by the statistical nature of the model. Results can be obtained with any desired statistical
certainty, provided that a sufficient number of histories is followed. The larger the number of histories, the
better the results, however, also, the longer MCNP runs. Thus to obtain the desired accuracy may be very
expensive. MCNP has some variance reduction options for increasing the accuracy without increasing the
number of histories. However they are not recommended for the kind of applications associated with this
research CB-11.
Some other limitations of MCNP are:
•
MCNP can provide only the reaction rates and fluxes for each defined cell in the model. To obtain cross
sections, post processing is required.
•
Tallying is possible only over the defted cells and surfaces of the model. If the desired cells can not be
modeled, the post processing of the data is required.
•
MCNP does not provide group-to-group scattering reaction rates. Therefore it is impossible to obtain
group-to-group scattering cross sections directly from MCNP results.
Another reason for the selection of MCNP is the existing MCNP model of MITR core number 2 for which
the accuracy has been tested oginally by Redmond [R-2] and by several users including the author [T-11.
The model is a very detailed representation of MITR-II with its research facilities including the beam ports
and the medical therapy room. Since it was originally developed for more general purposes (in particular for
BNCT research), it includes some unnecessary portions of the facility when the primary interest is in the
core and reflector area. A more detailed description of this model will be given in Section 23. 1.
18
2.2. GENERAL STRATEGY AND PROCEDURE
The major goal of the thesis is to represent the Wmgular-z nodes of the QUARTZ model of MITR-11by an
MCNP model and using this MCNP model to obtain required homogenized cross sections for each node of
the QUARTZ model.
I
MCNP calculations raise two major difficulties: long CPU (Central Processing Unit) time, and large
computer RAM (Random Access Memory) requirements. These are the major concerns of the present
project As mentioned above the MITR-11model of Redmond is geometrically more detailed than required
and includes some parts of the reactor that are not of interest for a core-related reactor physics study.
Nevertheless it is reasonable to assume as a starting point, that Redmond's model is a good representation
of the MITR-11 reactor geometry itself. Its accuracy has been proven several times by both Redmond [R2][R-3], and the author [T-1]. Its geometric complexity is a drawback with respect to CPU time and RAM,
but this complexity is the characteristic of the reactor itself and must be kept as it is, to get reliable results.
By keeping the iportant
parts of the model and changing some definitions to simplify the geometric
representation of MITR-H a simplified model was obtained from the original. Taking this simplified model
as a basis, a new model consisting of triangular-z cells used for the QUARTZ model of the MITR-11,was
developed Mom detailed descriptions of these QUARTZ and MCNP models are given in Section 22.1 and
Section 23.
2.2.1. QUARTZ Model of MITR-II
The QUARTZ model of MITR-11 includes
Oxl6 nodes as shown three-dimensionally in Figure 22
(adapted from reference [K- I]). The 24 nodes in the center represents the core portion of the reactor, and the
outer boundary of the graphite is modeled as a hexagonal prism. The number of axial nodes was originally
set as 12 sarting from the bottom of the fuel to the top of the fuel. However, initial results showed that a
constant albedo boundary condition at the bottom (required by QUARTZ) was not correct because of the
D20 reflector effects, a portion of the bottom reflector 4 more axial layers of nodes) was added to the
model.
The energy group structure was set at 2 groups, one from
MeV.
19
to 0625 eV and the other from 0625 eV to 20
z
I
I
1
,b
i
Figure 2.2 The 3-D representation of QUARTZ model of MITR-H.
20
2.2.2. Organization and Distribution of the Tasks
As mentioned earlier the project was divided between the author and Kuo as shown in Figure 23 and Figure
2.4. Details of the division of work are given in the next section. Basically, the node-homogenized cross
sections and node-averaged fluxes wereobtained by the author, and surface fluxes and currents were obtained
by Kuo. Since MCNP does not have the required options to obtain cross section results, the homogenized
cross sections were obtained by processing MCNP reaction rates and fluxes by volume-averaging as will be
discussed in Section 33. However, surface fluxes and surface currents can be obtained from MCNP results
directly. Since to obtain the surface currents and surface fluxes is the easier and less time consuming part of
the process, Kuo also obtained the group-to-group scattering cross sections and discontinuity factors for
each node by putting together the results from both parts of the process. A more detailed description of the
portion of the work executed by Kuo can be found in his thesis [K-11.
2-1
Original Model
MITR-H Core-2
I
I
I
rI
Remove neutron beam ports and
every cell below the bottom of
the reflector tank (IT)
Small Model
I
I
I
I
I
I
I
I
I
I
I
I
Replace graphite reflector with
I
30 cm thick cylindrical sel
I
(M
I
I
I
I
I
Modify cells at the upper part of
the core tank and bottom water hole
support flanges WSK)
I
I
I
I
I
I
I
I
I
Add 9 detectors to water holes
Z 4 and 6 according to given
specifications by Shelby (IT & WSK)
Detector Model
I
I
I
L
rI
I
Graphite shape is changed to hexagon (WSK)
I
I
I
I
I
I
I
-
I
Separate cells,between top and bottom levels
of fuel from the rest of the cells (IT & WSK)
I
I
I
I
I
I
I
I
I
Simplified Model
I
I
Triangulated Model
I
Triangulatethe separatedout of core cells M
I
I
I
L
I
IT: Ilker Tari
WSK: Weng-Sheng Kuo
Figure 23 The organization of the tasks in the development of M(NP Model
22
Simplified Model
A
Tally surface currents and
surface fluxes after partitioning the tangles with
universe-fill (WSK)
Tally Reaction rates and
cell fluxes M
OUT-OF-CORE (ABOVETHE BOTTOM OF FUEL)
Triangulated Model
Tally control blade ring
surface currents and by
segmenting the cells
physically (WSK)
Tally Reaction rates and
cell fluxes M.
OUT-OF-CURIF, (BELOW THE BOTTOM OE FURL)
I TriangulatedModel
I
Extent triangulation 4 layers below 5
Tally surface currents
by segmenting (WSK)
Tally Reaction rates and
cell fluxes M
IT: Ilker Tari, WSK: Weng-Sheng Kuo
Figure 24 The tasks after the model was generated.
23
2.3. MCNP MODELS AND THEIR EVOLUTION
During the model development stages,.the original model (Redmond's model) which includes features not
needed for present purposes was simplified and then tested for consistency against the original model. 'Men
from the simplifted model by a tangulation process discussed below, the triangulated model was generated.
This final model was used for tallying in different ways by both the author and Kuo A 13 triangulated core
model developed for a stochastic volume calculation is also discussed below.
2.3.1. Original Model
The Original model as discussed above was developed and tested by Redmond. Details concerning the model
and its preparation can be found in references [R-21 and [R-31.The model represents the fresh core-2 with
control blades positioned such that the reactor is critical, therefore MCNP runs of the model give k-effective
very close to 1.00. The difference if any is a result of statistics and some minor approximations in the
model.
Figure 25 and Figure 26 shows two different views of the original model.
2.3.2. Simplified Model
Since the present research is concerned only with the parts of the reactor included in the QUARTZ model,
the original model of MITR-II includes more detail than needed. By making several simplifications and
getting rid of the unnecessary prts, the CU time requirement can be reduced. The modifications made were
the following:
The beam tubes, medical therapy facility and everything below the reflector tank bottom hemisphere
were removed. The resultant model is called the Sall
Model. This model was tested and the results
showed that ftuther simplification was possible. By using this model, the difference between reflective
and no-incoming-flux boundary conditions was tested. The results from the several runs to obtain cross
sections for assemblies A 1, B 4, C-8 and C- 11 showed that the reflective boundary condition has little
effect on the cross section and criticality results, but increases CPU time as compared to the noincoming-flux condition.
herefore the boundary condition selected was the no-incoming-flux
condition.
24
tTs
Figure 25 Original Model of MITR-H (y-z view)
25
Figure 26 Original Model of MUR-11 (x-y view)
26
As a further simplification the bottom hemisphere of the reflector tank was removed and reflector
thicimess was reduced by almost half to 30 cm. This model was named the Simplified Graphite Model
or simply: Simplified Model. Tests showed that, without loss of accuracy, the CPU time requirement
was reduced 30% compared to the original model. Table 21 shows the fdings
from criticality runs
to obtain fluxes for assemblies C-11, C-8, B-4 and A-1 for 35 cycles of 3000 neutrons and for 205
cycles of 3000 neutrons (no tallies being made for the first
cycles). Although the problem is the
same in all cases, because of the limitations of the model, a separate run has to be made to edit each
individual assembly. 'Me reason for the k-effective difference among the runs for the same model and
size is that different source files were used everytime.
Model and number of cycles
CPU time used
of 3000startingparticles
(minutes)
K-effective
Original 35 cyclesfor C-11
322.97
0.98688
Original 35 cyclesfor C-8
320.72
0.99379
Original 35 cyclesfor B-4
325.93
0.99427
Original 35 cyclesfor A-1
329.88
0.99470
Original 205 cycles
1610.36
0.99281
Simplified 35 cycles for C11
204.50
0.99164
Simplified 35 cycles for B-4
209.79
0.99111
Simplified 35 cycles for A -
211.88
0.98593
Simplified 205 cycles
1205.72
0.99094
Simplified 205 cyclesfor WHs
1157.53
0.99338
Table 21 The comparison of CPU time and k-effective results for different runs of two models.
27
The similar eigenvalue and the similar cross section results suggest that the Simplified model is as good as
the original model. Using this simplified model, the following cell modifications were made by Kuo:
The comer cells of the control blade hexagon (the Al supporting structure where the control blades are
located) and the cells in the curvbd part of the upper portion of core tank were homogenized as a
mixture of the materials originally modeled.
In addition to these modifications the final model includes 9 detectors and paced in the water holes 24 and
6 as suggested by Shelby [S-11. The geometry and material specifications of the detectors were obtained
from Shelby's thesis. According to his suggestions, each water hole has 3 detectors axially located in
different positions in a guide tube immersed in the water hole. One of the detectors as defined for the model
is shown in Figure 27. The specifications for these fission chamber detectors can be found in Shelby's
thesis [S-1]. After the addition of the detectors, this model is used for incore runs.
For the incore triangular nodes and for out of core nodes, two different paths were followed. For incore
nodes, after voiding the repeated sructure procedure, cell reaction rates and fluxes were obtained for each cell
in the core hexagon. Since the ells of interest are the fuel plates and water channels making up a rhombic
assembly, it is necessary to assume that cross sections found from homogenizing a given fuel with its
associated moderator are partially constant, then, when a given rombic element is cut into triangles we can
take the cross sections for the portions of a fuel plate belonging to different triangles to be that of the plate
itself. The homogenization process is discussed further in Section 33. For out of core nodes another model
is created.
Figure 2.8 and Figure 2.9 shows two different views of the model after these modifications.
28
i
i
i
I
II
I
I
I
I
0-
I
CN
I .
rl)
I
I,I-
-4
-3
-2
1
0
1
Figure 27 One of the bottom detectors in guide tube
29
2
3
4
f
Figure 28 Simplified model before graphite reflector changed to hexagonal prism x-y view)
30
D20
Figure 2.9 Simplified model after graphite reflector changed to hexagonal prism (y-z view)
31
2.3.3. The Triangulated Model
As mentioned earlier MCNP can not tally energy group cross sections. Rather it can provide energy group
cell fluxes by using 4 tallies and cell reaction rates, again by using F4 along with microscopic cross
section and atom, density multipliers. Atom densities can be obtained from the Table 50 of MCNP output
and the multiplier indicators for different microscopic cross sections are given in MCNP manual. Thus, by
running MCNP, the reaction rates and fluxes for each ell can be obtained, and then by using these data a
homogenization process can be applied to get homogenized cross sections for triangles that include MCNP
cells.
To obtain cross sections for Wangles, they must be defined in the MCNP model. In the Simplified Model,
most of the defined cells fall into core hexagon (hexagonal region of 27 elements). 'Mat part of the
geometry is the most complicated part. The Simplified Model incore cells are defined by using repeated
structures option. This procedure reduces the number of cell definitions very significantly. However for
triangulation, the repeated structures need to be removed, and this removal causes the number of cells in the
core to increase by a factor of 12. Since triangulation process also divides the cells, the total effect of
triangulation in the core region is to increase the number of cells by a factor of 24. As a result the number
of incore cells becomes more than 4000. Since CPU time and RAM requirements increase with increasing
number of cells, this kind of triangulation was estimated to be too expensive (if not impossible) to run,
because of the RAM limitation of the available computers. Accordingly the triangulation process was
applied only to the cells outside the core hexagon.
Before the triangulation of the out of core cells, the graphite definition is changed from cylinder to
hexagonal prism as in QUARTZ model. The triangulation of the out of core cells is a very long, and
tedious job which required more than 60 hours of work. In this process triangle surfaces defined according to
the QUARTZ model and all the out of core cells are redefined by using these definitions, and previous
surface definitions of Simplified model. At every stage of the development geometry integrity checks were
done to insure the accuracy and consistency of the model as compared to the Simplified Model. The result is
called the Triangulated Model; it is a combination of the Simplified model and the QUARTZ model. Figure
2.10 and Figure 211 show two different views of the triangulated model. This triangulation was done only
for the initial 12 axial segments; four additional axial segments were added to the bottom later on for
obtaining the constant albedo at the bottom. Two test were applied to the triangulated model, a geometry
test with 100 million histories showed that there is no gap between cell definitions and that all of the cell
definitions are correct. In addition, criticality calculation was made and the k-eff obtained was 099719 very
close to 1.00. These tests support the integrity and accuracy of the model.
32
AAA
Z/T T11\7)6II\VVV\1VVV
V\/\\Vv\
/VL/\
I
VV\/\/\
\/V\AVV
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VVLzl
A
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&LL
V\\AVVVVV\/\/VV/A/V
A
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\-
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A
\
Vv_/
VVVVV
A/VVV\AAA
VVVV
Figure 2.10 Triangulated Model (x-y view)
33
\
Figure2.11 Triangulated Model (y-z view)
34
2.3.4 13 Symmetry Incore Fully Triangulated Model
As mentioned in the previous section, to triangulate incore cells is not an attractive option. As will be
discussed in Section 33, for incore cross section homogenization, the volume fractions of MCNP model
cells falling into each triangle are required and there is only one tractable way to obtain these volumes
which is to use the MCNP volume calculation capability and the stochastic volume calculation option after
triangulation of the cells. As seen from Figure 212 there is amost a 13 symmetry for incore triangles By
using this symmetry all the volume fractions can be obtained by triangulating 13 of the core. Figure 213
shows the 13 symmetry triangulated model. In this model every small subregion (portions of fuel plates,
water channels etc.) of a triangle is an individual ell. The model was geometry tested for 100000 and 100
million histories and passed both tests.
As will be discussed in Chapter 5, this model is a very pron-dsingframework for the future research.
35
ir--
D-
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Figure 213
I
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0
.
I
.
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:
.
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2
The 13 symmetry boundaries (note that this is not an exact symmetry because A-ring has
only one fuel element and 2 dummy elements)
36
Figure 2.14 The 1/3 symmetry trianguhdal core model (x-y view)
37
CHAPTER 3
PRE-PROCESSING9 PROCESSING AND
POST-PROCESSING
3.1.
MCNP
INPUT
PREPARATION
AND
PRE-PROCESSING
PROGRAMS
MCNP input preparation involves two parts: the model dermition and the preparation of tally cards. After
the Triangulated Model is generated, it is used in separate ways for cross section generation and tallying of
the surface flux and currents.
his section discusses the tallying process related to homogenized cross
section generation part.
3.1.1. Tally Cards
To tally the required data for homogenization, only the 4 type tally cards of MCNP are used. Without any
multipliers, the 4 cards provide the track length estimate of MCNP cell fluxes. For reaction rate tallies the
atom density data obtained from the Triangulated Model criticality test run output is also required. By using
these atom densities and multipliers for absorption, total, elastic scattering, and fission cross sections, and
for vEf, reaction rate tally cards are prepared. To tally for axial nodes over portions of the MCNP cells, tally
segmentation cards are used.
3.1.2. Stochastic Volume Calculation using MCNP
MCNP calculates cell volumes and surface areas as one of the fu-st stages of the run, but it cannot calculate
the volumes and areas of asymmetric, nonpolybedron, or infinite cells. Since most of the cells in
Triangulated Model are asymmetric, the volumes of this cells are required for 4 tallies. These volumes are
found by hand calculations if the geometry is simple, but if not, the stochastic volume estimation of
MCNP is used. The stochastic estimation is simply a ray tracing process. 'Me procedure is described in
detail in the MCNP manual [B-11. Since the process is stochastic, the limiting factor on the accuracy of the
results of this calculation is the number of histories followed. For the stochastic volume calculations in
38
this thesis 100 million histories were used and less than 2
statistical eror was obtained for most of the
cell volumes. Since only part of the volumes are obtained this way, this statistical eror is not included in
the final error calculations described in Section 33.2.
3.1.3. Segmentation
As mentioned before, the Triangulated Model is segmented in 12 axial layers, but subsequently
anged and
4 more layers added to the bottom of the lower tangle layer. These segmentations and the segmentations
for incore tallies are done by using the FS4 taHy segmentation cards. The required segment volumes for
asymmetric cells are obtained by partitioning the volumes found using the methods discussed in the
previous section.
3.2. MCNP RUNS FOR OBTAINING CELL FLUXES AND REACTION
RATES
The input files for MCNP runs are ready after the model implementation and preparation of the tally cards.
Because of memory lmitations, these input files must be used for
separate MCNP runs, of which 6 runs
are for tallying all the ells in the core hexagon, one for the out of core portion of the original Triangulated
Model and one for the four additional layers starting from the bottom of the fuel cells. All MCNP cases
were run on the SIN Sparcstation called mitrsun, using the same initial source file (SRCTP) to repeat the
same simulation a number of times. Since mitrsun is not a dedicated machine for this research, most of the
time, the runs were made sharing the time with other jobs running on the machine. This time and memory
sharing limits the size of the MCNP jobs in that, if the required RAM is larger tan the available RAM at
that time, the job cannot be submitted. Also if the time sharing is done without any niceing, time is shared
among the submitted jobs equally. Tis was the case most of the time. Since during all the runs, there was
at least one other job, the CPU times given on Table 31 must be multiplied by 2 or 3 to get the elapsed
time for one run. Table 31 shows the resulting CPU times and k-effective values for each MCNP run. As
seen, k-effective results for all the incore runs are the same except of Run
1. During this run the process
was interrupted as a result of a power surge, and MCNP used a different source file when the process was
restarted.
39
Model with 260 cycles of
CPU time used
3000 starting particles
(minutes)
K-effective
Incore Run # 1
1978.25
0.99916±0.0011
Incore Run 2
1979.47
0.99714+-0.0011
Incore Run
3
2183.69
0.99714±0.0011
Incore Run 4
2099.01
0.99714+-0.0011
Incore Run # 5
2103.12
0.99714+-0.0011
Incore Run
6
2003.21
0.99714-+0.0011
Out of core runfor 12 layers
3196.00
0.99719+-0.0012
Runfor 4 a"tional layers
2308.26
0.99524±0.0010
Table 31 The comparison of CPU time and k-effective results for
40
MCNP tally runs
3.3. THE HOMOGENIZATION
PROGRAMS
SCHEME AND POST-PROCESSING
The node-homogenized cross sections are obtained by flux weighted volume averaging using the computer
programs written to process the MCNP tally output files (MCTAL files). For this job, 13 programs to
process incore data, and 2 programs to process 12 and 4 segment out of core data were developed. Some of
these programs are given in Appendix B.
3.3.1. Homogenization Scheme
The flux weighted volume averaging formula for homogenization can be given as the following:
g
R,9' VOID
IJ
( VD
09",
where,
9
homogenized cross section for energy group g and triangular-z node j,
Rg
= MCNP reaction rate per unit volume for cell i,
01i)
= volume of the portion of cel i that is in triangular-z node j
O(Y)
= MCNP flux density for energy group g and for the portion of cell i in node j.
9
To find the volumes for incore homogenization, the 13 symmetry model of the core was run using the
stochastic volume estimation and the resulting values were used as the volumes in the equation above. For
the out of core cases, volume values are the segment volumes of the cells given as a part of the input.
The homogenized cross sections computed are the total cross sections(l,
absorption cross sections(l),
fission cross sections(l? and fission neutron production cross sections K?.
The edited MCNP absorption
cross sections do not include either the fission cross sections or the (n,2n) cross sections. The group-togroup scattering cross sections cannot be tallied. They must be obtained from neutron balance. Details of
that procedure can be found in the thesis of Kuo [K- I].
41
3.31. Calculation of the Statistical Errors
Since every MCNP result is accompanied with a statistical effor, the calculated cross sections also have
statistical erors. Since each MCNP result is a mean value, to calculate the standard deviation associated
with the cross sections the following NW formulae [K-21can be used:
If
u=x+y
or u=x-y
then a2 u =02 x +2
If
u=x*y
or u=x/y
then (au/u)2=(Ox/x)2+(Cy
Y
Y/
2
where x and y are the means of two different quantities having statistical uncertainties and the a s are the
standard deviations. If u = c * x where c is a constant, au can be obtained by multiplying ox with the
constant c.
42
CHAP'TER 4
RESULTS
The results presented in this chapter are divided into two parts: incore results, and out of core results. To
indicate how nodes are identified a 2-D map of the quartz model is shown in Figure 4. I. Indices I and J
specify the location of the triangular nodes. The index K specifies the z4ocation of the nodes (K goes from
bottom to top). To be consistent with the results obtained before addition of 4 layers (Appendix Q, the
nodes above surface 85 are numbered 112 srting
from that surface and going up. Below surface 85, K is
negative and decreases from the surface downward (as 1,-2,-3,-4). The flux results are normalized to one
starting particle (fission source) and to obtain the fluxes in units of neutrons/cm2/sec the MCNP flux
results should be multiplied by the number of fission neutrons per second corresponding to the power level
of the reactor. That factor is given by:
PN = P
I Q
v
I ken)
where,
P
Reactor power level Watts
Q
Energy generated per fission ( J / fission
v
Average number of neuuxm generated per fission
kef =
eutron Multiplication Factor.
If both the numerator and denominator of homogenization formula are multiplied with the same constant,
the result does not change. Therefore the flux results presented in this chapter are not normalized to power.
43
4.1. INCORE RESULTS
The incore homogenized cross section results along with the calculated statistical erors for the 12 layers of
24 triangles are obtained by using the scheme discussed previously. The complete set of results are
presented in Appendix C under the fe name xchonOn where group is the fast and group 2 is the thermal
group, and group boundaries are 0.625eV to
MeV and
to 0.625eV, respectively, also errors are given as
the ratio of error to mean value (the result). These results were obtained by using the specially written
programs named as xg*.f and xg**.f. The accuracy of the results and the reliability of the software were
tested by regenerating the same results with an entirely different logic which is reliable because of its
simplicity. The software written for comparison, sibelf and the results labeled rslts are given in Appendix
B. The results given in rsIts and those of Appendix C match to at least
significant digits after the floating
point. This test process is a strong evidence that the processing of the MCNP results i correct.
4.2. OUT OF THE CORE RESULTS
The out of the core results are discussed in two parts: the initial 12 segment Triangulated model results for
regions above the bottom level of the fuel and the 4 segment part below the bottom level of fuel (which
from this point on wl
be referred to surface 85 or simply 85 the reference being to its MCNP surface
number).
4.2.1. ResWts for the Nodes Above the Bottom Level of The Fuel (above 85)
This part of the results was obtained by running the program prohxlnf
of which listing is given in
Appendix B. The complete list of cross section results is extremely long and therefore is not given in this
thesis. However the results have been saved in a file named hxIn.ou and packed with all the files in the
same directory for possible future use.
Some sample results are given in Table 41. These results display radial change of the cross sections and
flux starting from the graphite reflector, crossing the D20 reflector and core radially, and ending at the other
comer of the graphite reflector hexagon at axial node K6. Statistical erors are given as fractions of the
results.
44
1.11 J.)
17 J7
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Figure 41 2-D nodal map of QUART7, model showing the I and J indices user in the representation of the
results, also K is the index for the z-direction
45
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4.2.2. Results for the Nodes Below the Bottom Level of The Fuel (below 85)
The homogenized cross section results for the nodes below surface 85 (which is the bottom surface of the
fuel) are also extremely long. Some sample results are included in Tables 42 and 43 which show the axial
distribution of flux and cross sections for two tangular nodes: Triangle
1,J = (1 1, 1).and Triangle 2 IJ)
= 17,7). (See Figure 41)
4.3. SURFACE FLUX AND SURFACE CURRENT RESULTS
'Me results for surface fluxes and surface currents were obtained by Kuo and the description of the procedure
used to obtain these results can be found in his thesis. 'Me results are voluminous and are presented neither
here nor in his thesis. The general srategy used to obtain the results was to trick MCNP by filling exactly
defined triangle surfaces with the universe of the entire model for incore cells and by tallying the surface
fluxes and currents directly for these triangulated portions of the model.
4.4. GROUP TO GROUP SCATTERING
Since MCNP can not provide group-to-group scattering cross sections, they need to be determined from
neutron balance. his portion of the data gathering process for QUART7 was done by Kuo and is presented
in his thesis [K-1]. Also CNEFDdiscontinuity factors were found by Kuo. Some difficulties encountered
with the group-to-group cross section and discontinuity factor calculations, which for some cases come out
negative. The problems and possible causes of these negative results are, as in his thesis
•
Negative fast to thermal group scattering cross sections were found. This phenomenon may be caused
by statistical fluctuation in the net currents or the absorption cross sections, or from the failure to
include up-scattering and n-2n cross sections in two-group neutron balance equations.
•
Negative CMFD discontinuity factors were found. The negative discontinuity factors can result in loss
of the diagonal dominance of the matrices used in QUART7, which can cause the solution to diverge.
One way was found to avoid the negative discontinuity factors, namely to increase arbitarily the
diffusion coefficients so that the factors which cause a match with the reference leakages will be
positive.
Some additional discussion of these problems is given in the next section and in Chapter .
47
h
C,4
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49
4.5. NEUTRON BALANCE
The programs to calculate the two group neutron balance were written by Kuo, originally to obtain group
to group scattering cross sections. Because of the inconsistency of the results, another program was written
to obtain one group cross sections, fluxes, surface fluxes and surface currents from the two-group results
and to check neutron balance for one energy-group. The procedure and program were also tested by the
author. For both incore and out of the core results this balance check is failed (Some of the results of this
balance check are given in Appendix D). It is important to recognize that, for incore results, neutron balance
should not be expected.7he surfacefluxesand surface currentswereobtainedfor the surfacesof triangles,
but the cross sectionsand nodeflux were obtainedfrom a homogenizationschemewhich uses MCNPflux
resultsfor group of cells not bounded by the triangle surfaces. The lack of balance suggests that either there
are invalid approximations involved in the process or that some of the data obtained is either incorrect or
includes too much statistical error. These possibilities must be investigated for incore and out of the core
separately, because the procedures for these two cases have some major differences.
Incore results
The accuracy of the homogenized cross sections was established by regenerating the same results semimanually for an arbitrary triangle using an entirely different programming logic. The results had very low
statistical effors. These findings suggest that the eor
comes from these results it is related to the
assumption that the flux distribution is very similar for the neighboring rhomboid core assemblies and does
not change much throughout the assembly.
According to Kuo, the processing of his results are also correct, therefore; again only the MCNP results can
be questioned. In his tallying process, Kuo had to make several rims for different surfaces of different cells
because the universe-fill scheme does not allow him to obtain all the results together from the same run.
This might have caused some inconsistency in the neutron balance, because the model is changed slightly
for every run. To expect a neutron balance in the end, all of the separate MCNP runs should be the
repetitionsof the same simulation,otherwisethe resultscome out irrelevant.
Out tcore results
Again the models used for the homogenized cross section part and the surface part have some differences.
Kuo explicitly divided the cells into segments to obtain node top and bottom surface results while the
author used the Triangulated model directly. These differences might have affected the simulation results.
50
For the ells and surfaces in the graphite nodes, the statistical errors are very high; even zero flux results are
obtained for some of the triangles because of lack of sampling. Therefore; it is hard to expect any balance in
this region of the core.
4.6. GENERAL TRENDS OF THE CROSS SECTION RESULTS
This section aims to present some portion of the data in a meaningful format and investigate possible
causes of filure of the general procedure. The distributions presented in Table 41, Table 42 and Table 43
are represented graphically in Figures from
42 through47. Figure41 shows the locationof the traverses
in the radial direction.
By looking at the results presented in Appendix C, Table 41, Table 42, Table 43, and the figures, some
general observations about the triangular node fluxes and homogenized cross sections can be made. They are
itemized as the following:
Incore homogenized cross section results (Appendix Q have very small errors. Average and maximum
statistical errors are (the first number is for fast and the second is for thermal group):
Flux
Total Xsection
Average error
0.5% - 09%
0.6% -1.8%
2.0%
Maximum error
0.9%
1.3% - 28%
3.1% - 26%
Ile eors
1.7%
Absorb. Xsection
1.7%
Fission Xsection
1.8% - 29%
4.2
- .1%
for the flux results are very small; because of the high value of fast flux in the core, the
percent error for the fast flux is smaller. Statistical errors are higher for the cross sections -especially
for fission- due to the fact that sampling is lower for these quantities. Te absorption cross section
percent erors are lower for the thermal group, because the thermal absorption cross section is higher
then the fast absorption cross section. These are the expected results for a very compact core with the
boundary between the energy groups set to 0.625eV. Another observation is that most of the total
cross section consists of the scattering cross section.
5-1
N
3)
-
- --------
--
m
----------
rl(D
Ln
10,
ol------
----------
0C
(1)
S
C\j
W"
II
2
-
.c
-0
W)
-
C:)
-----------
X
U)
'a
10
a
-
Wm
a
1;
0
-- ----------
W
------------
cm
v
0(b
9in
IT
(h
,W
(b
C
IT
9M
0
0
0(b
9cm
v
0(b
9
uo.qnau aajnos jad xnjj
Figure 42 Radial flux distributions (axial node K=6).
52
O
000
6
n
W
10
O
c
I-j
N
0)
rn
t
CC)
cj
fl-
CA
V)
A
CD
C.d
U')
0I-
1-1
.a,.
N
C
C..
L.
j
CI)
a
04
P"
11
:111
-
V)
W
A
.
I=
10
.-
la
la
0
W
N
.
Qj
a
0
E
0
-
W
W
IC
0
r.
U')
4"d
0
r.
0
4"
Z
CM
IC
4"
W)
0
10
C
Ln
-
0
1-:
LO
6
0
6
1;
I=
M
(w:)/I) suoilaas sswa pazwagotuoq apoN
9
Figure 43 The radial distribution of homogenized cross sections (axial node K=6).
53
09
-1
Ij
m
00
CD
A
0I-
LO
1-1
1.
C.10
'IT
-3
j
CO
0
.4"
I"
CV
.11%
I
-
VI
-
Q
W2
w
la
0
C
la
la
aj
64
100
U"
0
fl-
C
0
.0
Le)
la
(A
10
CI)
la
0
0
0
(D
1"Up
&
UI)
UU
U
SOJJ3
W
a
OAT;RJOH
Figure 4.4 The radial distribution of statistical errors (axial node K=6).
54
de
w
------------
0
rr-
1-1
11
1-1
17
m
11
.d
w
Iz
-------------------
r.
N
m
Q
.10
0
--------------
.
L.
12
co
'R
W)
W
X
c
46.d
0
c
0
16.6
CI)
r.
.0
,
I
CA
la
CM
7;
X
Iw
(h
0(b
904
0
9
(umiInau aamos
0
(D
8
ci
ad) xnl,4
Figure 45 The axial distribution of fluxes for the 2 energy groups in node (17,7).
55
C\j
-----------
---------0
rrZ
M
11
- -- --- --------- --
--------
C-4
co
;d
N -
.,=w
Z Z
fl-
r
a
=
- C
Ir-
4j
.%
11
-9
A
w
10
0
----- ------
-
S.
CD
'a
(A
= C
0 .0
.
U')
*W
rj
%- w
0 M
r
V)
CA
C 0
"W
= Q
:2
CI)
Cj
.!: ,FL
.n0
Cj
-----------
---
---- -----
-0 'n
04
0L.
-
.1:4 Ci
X
(M
-,etE
co
6
aIP
C
0
0
0
6
(wa/1) S01133S SSOj;) anuagOWOH
Figure 46
The axial distribution of homogenized cross section results for the 2 energy groups in node
(17,7).
56
r-
r:
11
0
I--,
-It
a)
C
6.
co
11
A
z
6.
S-
r-
A
W
0
4i
C
to
. Li
'7
(A
Q
(m
Qj
L.
CI)
4.0
0
C
O
.C
4"
n
Ii
0,
CIj
Ci
SJOJ13
6
0
Ci
11831jSIjRjS aAI.7131all
X
Figure 4.7 The axial distribution of statistical error for the 2 energy groups in node (17,7).
57
Table 41 shows that the cross sections for graphite -especially the fast group and those for outer
triangles- are accompanied with unacceptably large eors. Values of 141
eor mean hat there are
only one or two interactions occurring for the approximately 250*3000 srting
particles. Since the
flux is low at those areas, they can be used (cautiously) in subsequent calculations. However they can
not satisfy the nodal balance. Erfors in D20 region are much lower because of the higher fluxes
(especially thermal). The triangle samples from J=8 and J= 13 correspond to the Control Blade Ring
where the control blades and water holes are present in the Al blocks. Te errors for this ring are as low
as the ones for the incore portion. The gradual increase in the ratio of thermal flux to fast flux with the
radius can be seen nicely from Figure 44.
Table 42 and Table 43 shows the axial distributions for two triangles: the one given as Triangle I
(node i=1 1, j= 1 of Table 42) is in the outer graphite ring but is on the side of the hexagon so that it
sees the core much bet ter than the corner triangles. Hence it has much better statistics than the comer
ones. However, the fast energy group results are still unacceptable with their more than 50
eor
'Me
thermal energy group results have acceptable errors. 'Me non-zero thermal flux values suggest that there
is some leakage from the sides of the graphite which might bring the arbitary assignment of a
hexagonal boundary into question. However the k-effective is not affected, indicating that the coupling
of the neutrons in the outer parts of the graphite to the core is negligible. Ile flux distribution is given
in Figure 45. It is higher at the bottom and lower at the top nodes, probably because of the higher
absorption cross section of the H20 at the top next to the core hexagon (wider portion of the core tank)
comparing to that of D20 in the reflector tank surrounding the bottom portion of the core tank.
The other triangle
node i=17, j=7 of Table 43) goes through heavy water at the bottom nodes and
light water at the top four nodes. Figures 45 and 46 show axial distribution of fluxes and cross
sections. Ile
thermal flux shows a distribution similar to that of Triangle I but drops more
significantly because of the light water existing at the top portion. 'Me fast flux is also higher at the
bottom. Fast absorption cross sections are much higher in the top 4 nodes 2 to 4 times), although the
total cross section is only slightly higher at the top (D20 balances the effect of H20 microscopic
absorption cross section with its scattering cross section). The thermal total cross section is higher at
the top because of two orders of magnitude higher thermal absorption cross section. One thing to
remember about the cross section behavior is that the fast group starts at 0.625eV a rather low cut
point.
The distributions of eror for both triangular nodes increase as the flux decreases. Errors in both energy
groups for Triangle 2 are acceptable, also the eors
in Triangle
for thermal energy group are
acceptable (around 10%). However, again, this kind of eror affects neutron balance significantly if all
the data is not obtained from the same simulation run.
58
These observations show that the cross section distributions are consistent and match with the expectations.
Ibis is an eidence about their accuracy.
As mentioned, there is a suspicion about the initial assumption that flux shapes among portions of a
rhombus shows similar behavior. To test that flux distributions in two different fuel plates of a rhombus
and in one of the dummy elements compared with each other. For this comparison, fuel element B-7 and the
neighboring dummy element A-3 were selected (both contributes to triangle (IJ)=(4,2) denoted in core
coordinates). Figures 48 through 413 show MCNP axial flux distributions for Aluminum of A-3 and two
fuel plates of B-7 of which Plate
is the closest plate to A-3 and it is completely in the selected triangle,
Plate 15 is the farthest fuel plate to A-3 and it is completely out of the triangle. In these figures, according
to MCNP convention the segment nmbers increase from top to bottom. These flgures show that the axial
flux distribution differs significantly among the portions of same element, and among the neighboring
elements.
After these observations, one other investigation for incore results can be made: Is the assumption that flux
distribution is the same throughout a rhomboid shaped element, and the flux distribution does not change
significantly between two neighbor incore elements? For these investigations by considering that if there is
a significant difference exists, it is between fuel and dummy elements.
59
FL',JX
li N
DUMMY
1
n0
0
[,I
U
ry
Idi
<
O 0
I
__j
I
Ln
I
0
0
2
4
6
8
SEGMENT
BIN
10
2
4
6
NUMBER
Figure 4.8 MCNP axial thermal flux distribution for Aluminum of A-3 (segments are numbered from top
to bottom).
60
11
0
A
N
U MM Y
A- 3
. . . .
. I . . .
.
I
i
-j
U
rf,
aI
__j
I
,II
- - - -
CD
0
2
- - - - - - - - -
I
4
4
6
a
SEGMENT-BIN
10
2
.
I
.
NUMBER
Figure 49 MCNP axial fast flux distribution for Aluminum of A-3 (segments are numbered from top to
bottom)
61
6
FLUX
IN FUE:-
3-7
,I-
0
L.L-j
-.- I
U
r,
a_
.1
I
I
Ln
0
0
2
4
6
8
SEGMENT
BIN
10
2
NUMBER
Figure 4 10 MCNP axial themml flux distribution for Plate I of B-7 (the closest fuel plate to A-3)
62
4
FL!,!X IN FE1C)
0 I.
CD
. . . . . . . . I . . . .
I . .
B-7
I I I . . . . .
I
i
iI
I
I
L.Ij
U
Of
aI
I
14I
. . . . . II I I I I
. . . . . . . . . . . .
Ili
0
2
4
8
6
SEGMENT
BIN
10
2
NUMBER
Figure 4.11 MCNP axial fast flux distribution for Plate I of B-7 (the closest fuel plate to A-3)
63
4
F L UX
N
5_
FUE-
7
0
L.J
I
U
ry
a.
-j
-j
Ul
I
(-j
I . I II .1 . . .. .. .1 . . .I . .I .
.
0
2
4
.I .I .I .I . . . . . . . I . . I
.
SEGMENT
I
.
a
6
BIN
I
10
I
2
NUMBER
Figure 4.12 MCNP axial thermal flux distribution for Plate 15 of B-7 (the farthest fuel plan to A-3)
64
4
FLUX
CD
0
-1
O
I
FUEL B-7
IN
. . . . . . . . . . . . . . . . . . . . . . .
j
L.I.J
- i
L)
Of
CL
11-1
I
--I
I
41
1
C)
.
0
2
4
.
I
I
I
I- I
I
6
I
I
I
-
1
10
8
SEGMENT
BIN
I
2
NUMBER
Figwr 413 MCNP axial fast flux distribution for Plate 15 of B-7 (the farthest fuel plate to A-3)
65
4
These observations about axial flux shapes suggests tat the assumption was not a gotodow, but it is the
only path the
an be followed without tangulating
the, entire
re. On the other hnd,
without a
triangulation, the homogenization process sould work for a rhombus providing that the surface currents
out of the rhombus can be obtained from the same run. For testing the homogenization scheme, a model
consisted of only one fuel element (wiih smaller length to save from runtime) was created. With only one
nm surface currents, reaction rates and fluxes were tallied. for one energy group and these results were
processed to-obtain cross sections and leakage out of the rhombus. The MCNP results and the proce
program is given in Appendix E. The resultsof the processing program are.Average rhombus flux
: 1.34163E-02
Absorption cross section : 3.46784E-03
Total cross section
: 3.75824E-01
v
sigma fission
: 6.14328E-03
Fission cross section
: 2.46291E-03
Neutron balance results are:
Total eakage
:2.45090E-03
Total loss
:2.49743E-03
Total source
: 2.50364E-03
Therefore, the residual from these was found as:
Residual
:6.21402E-06
The ratio of the residual to total loss and total source are very low:
Residual Tota km
: 2.49817E-03
Residual / Total source
: 2.48199E-03
These results are the indication of neutron balance. This shows that the procedure can satisfy neutron
balance, if the complete triangulation can be achieved and surface currents can be allied with the reaction
rates in the same run.
66
CHAPr-R 5
CONCLUSION
5.1. GENERAL EVALUATION OF THE RESULTS
In previous chapters, the homogenized cross sections, calculated for each node of triangular-z mesh
QUARIZ model of MIT-H, were presented. Comments about the results and thek accuracy, and about the
neutron balance results were made. The lack of neutro blance was discussed and some of the
mystery surrounding it was removed. U present chapter
.
i tese discussions.
Evidencesupportbigthe'accuracyof the cross section and node averagedflux results (at least within the
limits of the procedure) can be
•
.
I as:
Past experience with the original model and tests at every step of the model development sow that, the
MCIVPmodel Triangulated Model) represents MrM-II correctly Section 23).
•
•
The reliabilityof the processingsoftwareis demonstrated(Section4 ).
begeneralbehavkwotbotbfluxandcrosssection&stributionsmatchesexpectations(Sectwn4.6).
Despite this evidence, nodal neutron balance could not be otained. Since homogenized cross sections and
fluxes were obtained fim te same group of runs and same proven processing programs, the mismatch
must be betwom them and the sur6ce-currenttsurface-flux results.
11hereare several points in the pocedure that are believed to be the reason for the mismatch:
•
he model usedfor sur.faceflux and currents differs in some aspectsfirom the model used for cross
sections. herefore the simulation cannot be repeated exactly (Section 45).
•
For the incoreportion, unlessflux shapesthroughouta given rhombuswereflat, exact nodal balance
cannot be expected.
67
•
Sow Ponions of the out of core resultshaveunacceptablyhigh statisticalerrors thittcm only be fixed
by increasing the MCNP simulation run tme by at least a factor of 100 (Section 46).
•
Some oher portions of the out of core results have moderate eors
(5%-10%), but the total effect of
these erors and the ones fim surface flux/current causes unbalanced results (Section 46).
Unfortunately the total effect of al tese contributors cannot be estimated.
Some other points about the unbalance can be made:
•
To repeat a simulation (MCNP run) exactly, the model, the number of histories waked and the initial
source points should be the same. Evidence that some repeated runs were not exact is that the keffective of the run differed slightly between Wcore and the out of core runs and also between tose and
the surface current and surface flux runs. This shows that the use of the same basic model and the same
initial source points does not guarantee exact repetition. On the other hand, five icore runs resulted
with the same k-effective. Thus simulation can be repeated only by satisfying all of the given
conditions. The sampling size 250*3000
750000) of starting particles may not have been Lge
enough to compensate for tins lack of exact repetition, and balance may have been affected.
•
Even if the lack of repetition is only a few percent for each cycle, after a smal nmber of cycles, the
simulation become totally different leading to an avalanche effect, since succeeding source points are
the outcome of previous cycles.
To get rid of the lack of repetition was not possible with the process used in this thesis. Te tallying jobs
were done by following the only path found after a careful search and investigation of possible alternatives.
Generally, the paths chosen represent the only practical solution as far as the author and Kuo consider
within the capabilities of MCNP.
To repeat a simulation exactly requires that tallying should be made without modifying any of the cells.
However it was necessary to repeat the calculation several times at least by changing the universe numbers.
The obvious way to avoid this is to do the simulation only once and to tally everything from this one
simulation. Unfortunately tis procedure is beyond the capabilities of MCNP at present.
In the following section, computer facility requirements are estimated both to get rid of unacceptable
statistical erors, and to complete this kind of MCNP run in a easonable time.
68
5.2. COMPUTER FACILITY REQUIREMENTS
The comments about the facility requirements given in this section takes the SUN Sparcstation mitrsun as
reference. Therefore requirements can be translated as the nmber of times current capacity.
Table 5.1 shows a summary of the data relevant to the computing resources used during and after each
MCNP run. This data is used for making the estimates given in the following subsections. The runs with
name Run#* and Vol Run are for incore cells; mit8c is for the 13 symmetry model; outhexy, outhxt2 and
outhlOt are for the out of core cells.
MCNP RUN
#of cells
& run date
CpU time
k-,ffective OUTPTfile
(minute
RUNTPE
MCTAL
size (MB)
-rilesize (B)
file size(B)
Run #1
913
1978.25
0.99916
2.59
5392939
669872
Run 2
913
1979.47
0.99714
2.58
5392959
669872
Run 3 715)
1210
2183.69
0.99714
5.08
6724855
1586514
Run 4 719)
1210
2099.01
0.99714
5.10
6705367
1565800
Run #5 723)
1210
2103.12
0.99714
5.10
6705367
1565800
Run 6 726)
1012
2003.21
0.99714
3.69
5906727
280.11
n/a
Volume run for 10 million articles
1
1051704
Vol Run 82)
.913
mit8c run
1173
3.62
n/a
100000 particle run to check geometry
outhexv
2706
6004.5
n/a.
Volume run for 100 million articles
outhxt2 919)
2706
3196.0
0.99719
13.9
10731259
3314861
outh I Ot ( 12)
3341
2308.26
0.99524
6.21
9557675
350221
(8/8)
Table 5.1 Summary of the data relevant to the computing resources used during and after each MCNP run.
The following subsections ahn to evaluate the computer resources used for this thesis project and to make
the required facility estimates for an exactly triangulated model involving 600*16 triangular-z nodes.
5.2.1. Required Memory for MCNP runs
Each incore run used 2500,000 words of memory and each one of the out of core runs used 5,000,000
words of memory. The total memory available on mitrsun is approximately 15,000,000 words, but
experience indicates that, even if only 10,000,000 words of RAM are used, the system starts to create
problems and this affects all functions of the system adversely. For example the system may not allow a
69
user to login. The largest size run with approximately 4000 cells were made by Kuo, and this run tied up
the machine for about a week. Since it was a 10,000,000-word-run, the upper limit of the RAM may be
taken as that value.
The number of cells for the entirely trangulated model may be estimated from the number of cells of 13
triangulated incore model and the number of cells of the out of core models. Thus with 913 large incore
cells used in the outhxt2 model and 2706 cells used for the rest of the reactor in the model for the lower four
layers,
# of incomecells
of axial layers)* 3
# of out of core ells for top 12 layers
1/3 model cells) = 12
12
3
42228
(out of core ells of outhxt2
12 * ( outhxt2 cells - 913
# of out of core cells for below 4 layers
1173
4 *(3341 - 2706
12
2706 - 913
21516
2540
Thus the total number of cells required becomes 66248.
The definition and run of that large job is impossible for the available machine. Thus another estimate for a
model that gathers the required data with only few runs 2 or 3 by using tally segmentation was made. In
this case the number of cells adds up to 3519
1793
635 = 5947, making it is a very large job by itself
As mentioned a 4000 ell run uses -10 Mwords of RAM. Assuming linear dependence the required RAM
for these 2 or 3 runs becomes around 15 Mwords, which exceeds the RAM capacity of mitrsun. The
assumption in this second scenario is that tally segmentation can be done without segmenting the actual
cells physically. Tis is the case for the cell reaction rate and flux runs, but may not work with surface flux
and current runs. Methods for accomplishing such segmentations need to be investigated.
5.2.2. Relation between CPU Time and the Number of Cells In the Model
The total CPU time used during the homogenized cross section part alone was approximately 2000
minutes. Since the relation between the number of cells and the CPU time is not linear, being affected by
the size of the cells, only a rough estimate for a 260 cycle run with 6000 cells can be made. The result is
8000 minutes based on taking 25 times the CPU time of the outhxt2 run. If statistical errors are to be
decreased by a factor of 2 the number of cycles must be increased 4 times. Iberefore, assuming a linear
relation, the CPU time becomes 32000 minutes. As mentioned this run must be repeated at least 2 or 3
times to tally everything, since MCNP has a limit on the number of tally cards that can be used.
70
5.23. Relation between CPU Time and the Tallies In the Model
Present results and past experience suggest that tallying is not the major factor determining CPU time.
Obviously it has some effect, but it is negligible compared to the effect of cell definitions.
5.2.4. Storage Space Requirement
During this project MCNP output files (OUTYI), run tracking fes (RUNTPE) and tally files (MCFAL)
were saved on hard disks. The total storage space for these files for the given runs in Table 5. is
approximately 113 MB. This storage space requirement may be decreased by file compression. However,
since RUNTPE files are binary files, the compression ratio is around 66 which is very low, compared to
the other text files that have compression ratios around 5. Assuming that the storage space will be the same
for a totally triangulated small number of runs, the required space is estimated as 100 MB after
compression. If the RUNTPE files were removed, it would drop significantly to 50 MB, but this is not
recommended since the RUNTPE files are required for possible restart runs. During the project some space
was also used for processing the results. But this was minor compared to the MCNP files. hus; 200 MB
of disk space should be enough for both cross section and surface current runs.
5.3. CONTRIBUTIONS
The contributions of this thesis project can be summarized as the following:
•
Although nodal balance for the results could not be obtained (indicating possible erors in nodal fluxes
for the triangles) a complete set of homogenized cross section results for the triangular-z nodes were
obtained, and in accord with the discussion in Section 46, are believed to be acceptably accurate.
•
From the MCNP runs of 260 cycles of 3000 neutrons, a tremendous amount of data for the 2 energy
groups was obtained. The major portions of that information are:
L Flux and reaction rates for every cell (pure material) in the core with 12 equal axial segments.
This complete iformation for the MITR-H model of MCNP was obtained for the first time.
ii. Flux and cross sections obtained for out of core triangles give valuable information about the
distribution of cross sections and fluxes in that portion of the model. The same kind of
information was also obtained for surface flux and currents by Kuo)
W. Since all RUNTPE files were saved, statistical erors may be decreased by restarting the MCNP
jobs using these files.
71
•
The computer facility requirements were identified, and some estimates for more accurate analysis were
given.
•
The 13 symmetry fully triangulated model is a very good srting
point for future research if the
triangulation of incore cells is the intention. One might get a feeling about how the tangulation
can
be done, by looking at the cell definitions for that model. Also that model with some cell additions can
be used for tallying and perhaps the recently introduced symmetry boundary condition for MCNP can be
used to obtain results with many fewer number of cells.
5.4. RECOMMENDATIONS FOR THE FUTURE WORK
In the future, different approaches should be found to obtain homogenized cross sections, fluxes and surface
currents. Some suggestions for these approaches are:
•
The use of a smaller triangular mesh including only the D20 reflector (the flux in graphite reflector is
significantly low).
•
The triangulation of incore cells with the use of the 13 symmetry triangulated incore model.
•
The creation of a less detailed model for the MITR-II core, by lumping neighboring cells together
through material homogenization.
Also options related to MCNP:
•
Apply the recently introduced symmetry boundary condition,
•
Make use of the newly added prallel computing capability to reduce run time.
In the future, if MCNP has options for tallying group-to-group scattering reaction rates or tallying
homogenized cross sections for groups of cells directly, many inherent problems of this project will be
solved automatically.
Other suggestions would be the use of a CRAY for faster runs or the use of a dedicated and faster computer.
To write an in-house code especially for MITR-II may not be an option. Developing a code like MCNP
requires thousands of man-hours of programming and years of heavy usage testing.
72
REFERENCES
[B-1]
Briestneister, J F, Ed., MCNP
A General Monte Carlo Codefor Neutron and Photon Transport,
Version 3A, LA-7396-M, Los Alamos National Laboratory, 1991.
[B-2]
Briesmeister, J , MCNP3B and MCNP4 Newsletters, Los Alamos National Laboratory, 1988
and 1991.
[D-1] DeLorey,T F, A Transient,QuadraticNodalMethodfor Triangular-ZGeometry,PhD. Thesis,
Department of Nuclear Engineering, Massachusetts Institute of Technology, Cambridge, MA,
1993.
[D-2]
DeLorey, T F QUARTZ Users Manual, Department of Nuclear Engineering, Massachusetts
Institute of Technology, Cambridge, MA, 1993.
[F-1]
Fowler, T B, Vondy, D R, and Cunningham G W, Nuclear Reactor Core Analysis Code:
CITATION, ORNL-TM-2496, Rev.2, Oak Ridge National Laboratory, 1971.
[F-2]
Fraser, D A , Statistics: An Introduction, Wiley, New York, 1958.
[H-1]
Henry, A , Nuclear Reactor Analysis, MIT Press, Cambridge, MA, 1982.
[K-1]
Kuo, W S Te General Evaluation of the Nodal Synthesis Method in Nuclear Reactor Transient
Analysis, PhD.Thesis, Department of Nuclear Engineering, Masachusetts Institute of
Technology, Cambridge, MA, 1993.
[K-21
Knoll.,G F, Radiation Detection and Measurement, Wiley, New York, 1989.
[M-11
MIT Reactor Staff, Facility Description Manualfor the MITR-11,Department of Nuclear
Engineering, Massachusetts Institute of Technology, Cambridge, MA, 1979.
[M-21 MIT Reactor Staff, MITR-11brief description brochure.
[R-1]
Redmond, E L, Monte Carlo Methods, Models and Applicationsfor the Advanced Neutron Source,
MS Thesis, Department of Nuclear Engineering, Masachusetts Institute of Technology,
Cambridge, MA, 1990.
[R-2]
Redmond, E L, Monte Carlo Modelling of MITR-11,22.39 term project report, Department of
Nuclear Engineering, Massachusetts Institute of Technology, Cambridge, MA, 1990.
[R-31
Redmond, E L, Yanch, J C, Harling, 0 K, Monte Carlo Simulation of the MIT Research Reactor,
1993.
[S-1]
Selby, L C, Experimental Evaluation of an Instumented Synthesis Methodfor the Real-Time
Estimation of Reactivity, NE/MS Thesis, Department of Nuclear Engineering, Massachusetts
Institute of Technology, Cambridge, MA, 1993.
[T-11
Tari, 1, 22.39 Term Project and 22.901 Special Problem Report, Department of Nuclear
Engineering, Massachusetts Institute of Technology, Cambridge, MA, 1992.
73
APPENDIX A
INPUT TALLY CARDS
74
c
c TALLY CARDS
c
eO
0.625e-6 20.0
fqO
c
c
c
e s m
f 4:n
4
FLUX TALLIES
4
4902
4912
4 92 0
49322
49422
49502
4
49
4 902 9 49040 49049
49129 4913 4 913 9
4 9209 49210 49219
49326 493 42 4 93 46
4 9426 49432 49436
4 9506 49512 4 9516
4962 6 49627 49646 49647
49726 49727 49736 49737
49806 49807 49816 49817
44405 44408 44409 4 4 410
4 4 42 3 44426 44427 44428
44503 44 505 44 509 44510
44522 44 526
4 4 5 1 8 44 52
44603 44604 44605 44608
446
44613 44614 44617
44701 4 4702 44703 4 4705
447 16 44717 447 8 44719
4 4803 4 4804 44805 4 4808
4481 44813 44814 44817
4 4901 4 4902 44903 4 4 90
44916 44917 44918 44919
45403 4 5404 45405 4 5408
45411 4 54 13 45414 4 5417
4 5501 4 5502 45503 45504
4551.1 4 5512 4 5513 45514
4 52
473 2 4
47 422
47 521.
47 622
4 5522
4 5523
4732
47328
47 428 47429
47 52 4 47 52
47 623 4762 6
47721. 47722 47723
4782 47826 47827
20201. 2 0202 20203
2 02 1 202 12 20213
20223 2 0224 20225
2 04
204 67
2 047 9
7 87 0
2 04 56 204 57
204 68 20469
4 5409
4 5418
4 5410
4 5420
49080 49089 49090 49099
4917 4 917 9
492
0 492 59
493 86 49392 49396
49382
49472
49552
49686
49776
49856
49476
49556
49687 49696 49697
49777
49857 44403 44404
4 4418 44420 44421 44422
44517
44621 44622 44623 44626 44627 44628
44709 447 0 44712 44713 44714 44715
4472 4 4472
44726 44728 44729 44730
4482 44822 44823 44826 44827 44828
44909 44910
44912 44913 44914 44915
4492 4 4492
44926 44928 44929 44930
45422
45508
45518
45528
473S9
45426 45427 45428
45509 4 5510
45519 4552
4 5423
4 552 9
473 64
47 4 0 47 462
47 556 47 561
4 5530
473 65
47 468
47 564
47657 47662 47 663
477 59 47761 47762
47850
20208
20218
20230
2 0462
2047 4
473 68
47 469
47 565
47 666
473 69
47 460
47 566
47667
47763 47769
47865 47866 47867 47 860
202 09 2 02 0
2 0219 20220 20221 2 0222
20451 2 04 52 2 0453 204 54
2 0463 20464 20465 2 0466
20475 2 0476 2 0477 2 0478
2 0480
7 87 1 78752 78753 78754 78755 78756
7 8776 78777 78778 78779 78780 78781 78782 78783 78784 78785 78786
78868
78880
7 8903 78904
7891 78916
7 8936 78937
7 8948 78949
7 97 1 79752
7977 6 79777
7 8867
78878 7 8879
7 8902
7 9 4
7 893
7 947
7 97 0
7 977
7 97 87
44514
4452
44609 4 4610
44618 4462
4 4706 44707
44721 44722
4 4809 44810
44818 4482
44906 4 4907
44921 44922
4 4513
4542
45505 45506 4 5507
4 5515 45516 45517
4552 4 4552
45526 4 5527
47329 473 54 473 5 473 8
47 420 47 452 47 458 47459
47 526 47S51 47 554 47 555
47 627 47 652 47653 47656
4772 9 477 1 477 52 47753
47 82
47 855 47856 47857
20204 2 0205 20206 20207
202 14 202 5 20216 20217
2 0226 20227 2 0228 2022 9
20458 20459 20460 20461
20470 20471 2 0472 20473
7877
78787
78802 78803 78804 78805
7 8814 78815 78816 78817
78833
78841 78842 78843 78844
7 8853
7 8866
49050 49059 49060 49069
49140 49149 49160 49169
49220 4922 9 492 40 49249
493 52 493 56 49362 49366
49442 49446 49462 49466
49522 49526 49542 49546
49656 49657 49666 49667
497 46 49747 497 66 49767
49826 49827 49846 49847
44411 44413 44414 44417
78869
78881
78905
78917
78938
78950
79753
79778
78806
78818
78834
78845
78870
78882
78906
78918
78939
78807 78808 78809 78810 78811 78812 78813
78819
78835 78836 78837 78838 78839 78840
78846 78847 78848 78849 78850 78851 78852
78871
78883
78907
78919
78940
78872 78873 78874 78875 78876 78877
78884 78885 78886 78887 78888
78908 78909 78910 78911 78912 78913
78941 78942 78943 78944 78945 78946
79754 79755 79756
79779 79780 79781 79782 79783 79784 79785 79786
75
fc4
c
fl4:n
79802 79803 79804 79805 79806 79807
79814 79815 79816 79817 79818 79819
79833 79834 79835
79841 79842 79843 79844 79845 79846
79853
79866 79867 79868 79869 79870 79871
79878 79879 79880 79881 79882 79883
79902 79903 79904 799Q5 79906 79907
79914 79915 79916 79917 79918 79919
79935 79936 79937 79938 79939 79940
79941 79942 79943 79944 79945 79946
** cells without segmentation **
46103 46104 46105 46108 46109 46110
46111 46113 46114 46117 46118 46120
46201 46202 46203 46204 46205 46206
46211 46212 46213 46214 46215 46216
46221 46222 46223 46224 46225 46226
46301 46305 46306 46309
46314 46315 46318 46319
46321 46324 46328 46329
46402 46403 46407 46410
4641.2 46413 46416 46417
46422 46425 46426 46430
79808 79809 79810 79811 79812 7 9813
79820
79836 79837,79838
79839 79840
79847 79848 79849 79850 79851 79852
79872 7 9873 7 9874 7 9875 79876 79877
79884 79885 7 9886 7 9887 7 9888
79908 7 9909 7 9910 7 9911 7 9912 7 991-3
79947 79948 79949 79950
46121
46207
46217
46227
46122
46208
46218
46228
fc14
** segmentation I
fs14
c
f24:n
204 208 212 216 220 224 228 232 236 240 244
46123
46209
46219
46229
46126 46127 46128
462 10
46220
46230
* l(SO-85),5(80-1125),12(80-1153)
20351 20352 20353 20354 20355 20356 20357 20358 20359 20360 20361 20362 20363
2 03 64 2 0365 20366 203 67 20368 20369 20370 20371 20372 20373 20374 20375
2037 6 20377 20378 20379 20380
647 0 647 1 647 52 647 53 647 54 647 5 64756 64775 64776 64777 64778 64784
6478 647 86 64787 64 802 64803 64804 64805 64817 64818 64819 64820 64833
6483 4 64852 64853 64866 64867 64887 64888 64902 64903 64918 64919 64935
6493 6 64949 64950
657 0 657 1 657 52 657 53 657 54 657 5 657 56 6577
65776 65777 65778 65784
6 578
6 5786 657 87 65802 65803 65804 65805 65817 65818 65819 65820 65833
6583 4 65852 65853 65866 65867 65887 65888 65902 6 5903 65918 65919 65935
6 593 6 65949 6 5950
6667 66672 66673 66674 6667 66676 66677 66678 66679 66680 66681 66682
66683 66684 66685 66686 66687 66688 66689 66690 66691 66692 66693 66694
66695 66696 66697 66698 66699 66700 66701 66702 66703 66704 66705 66706
667 07 66708 66709 66710 66711 66712 667 13 667 14 66715 667 16 66717 66718
66719 66720 66721 66722 66723 6672 4 6672 66726 66727 66728 66729 66730
66731 66732 66733 6673 4 6673 66736 66737 6673 66739 667 40 667 41 66742
667 43 66744 667 45 66746 66747 667 48 66749 667 0 667 1 667 52 667 53 667 54
667 5 667 56 667 57 667 8 667 59 66760 66761 66762 66763 66764 66765 667 66
66767 66768 66769 66770 66771 66772 66773 6677 4 6677S 66776 66777 66778
667 84 667 5 667 86 66787 667 8 667 89 667 90 66791 667 92 667 93 66794 6679S
66796 66797 66798 667 99 66800 66801 66802 66803 66804 66805
66817 66818 66819 66820 66821 66822 66823 6682 4 66825 66826 66827 66828
6682 9 66830 66831 66832 66833 66834
66852 66853 66854 66855 66856 668 57 66858 66859 66860 66861 66862 66863
66864 66865 66866 66867
66887 66888 66889
66890
66891 66892 66893 66894 66895 66896 66897 66898 66899 66900 66901 66902
6 6 90.3
66918 66919
66 93 O 6693
6 6 94 9 66950
67671 67672
6692
66932
66951
67673
6 7 6 83 67 684 67685
6769 67696 67697
677 07 677 8 67709
66921 66922 66923 66924 66925
66933 6693 4 6693 66936
66952 66953 66954 66955 66956
6767 4 67 67
67 676 67677 67678
67 686 67687 67688 67689 67690
67698 67 699 67700 67701 67702
677 0 677 1 67712 677 13 67714
76
66926 66927 66928 66929
66957 66958
67 679
67 691
67 680 67 681 67 682
67692 67 693 67 694
67703 67704 677 5 677 06
67715 67716 67717 67718
67719
67731
67743
67755
67767
67784
67796
67817
67829
67852
67864
67887
67899
6791.8
67930
67949
f c24
fs24
sd24
67720
67732
67744
67756
67768
67785
67797
67818
67830
67853
67865
67888
67900
67919
67931
67950
67721
67733
67745
67757
67769
67786
67798
67819
67831
67854
67866
67889
67901
67920
67932
67951
67722 67723 67724
67734 6773 67736
677 46 67747 67748
677 8 677 59 67760
67770 67771 67772
6772 6 67727 67728 67729 67730
677 87 677 8
677 99 67800
677 91 677 92 677 93 67794 67795
67803 67 804 67 805
67824 67825 67 826 67827 67828
67 820 67821
67 832 67833
67 855
67 856
6772
67737
677 49
67761
67773
677 89 677 90
67801 67802
67822 67823
67834
67857 67858
67738 67739
677 0 67751
67762 67763
6777 4 67775
67740 67741 67742
677 52 677 53 67 7 54
67764 677 65 677 66
67776 67777 67778
67859 67860 67861 67862 67863
67867
67 890 67 891
67 902 67 903
67892 67893 67894 67895 67896 67897 67898
67921 67922 67923 67924 67925 67926 67927 67928 67929
67 933 67 93 4 67935 67936
67 952 67 953 67954 67955 67956 67957 67958
** segmentation I ** J(j30-85),5(80-1125),12(80-1153)
204 208 212 216 2,20 224 228 232 236 240 244
(10.76
(74.55
(10.76
(59.17
(59.17
(10.76
(10.76
(59.17
(10.76
(59.17
lOrlO.06)
lOr69-68)
lOrlO.06)
lOr55-31)
lOr55.31)
lOrlO.06)
lOrlO.06)
lOr55.31)
lOrlO.06)
lOr55.31)
(35.44 l1r)
(35.44 l1r
lOrIO.06)
lOr55.31)
lOr69.68)
5 lOr69.68)
17 lOr55.31)
17 lOr55.31)
74.55 lOr69.68)
74.55 lOr69.68)
59.17 lOr55.31)
10.76 lOrlO 06)
(10
(59
(7 4
(7 4
(59
(59
76
17
12.27 l1r)
(34.61 l1r)
(59.17
(10.76
(59.17
(10.76
(10.76
(59.17
(59.17
(10.76
(74.55
(10.76
300 l1r) (38.00 l1r)
lOr 55 3 )
lOr 10 06)
lOr 55 3 )
lOr 10 06)
lOr 10 0)
lOr 55 3 )
lOr 55 3 )
lOr 10. 06)
lOr 69 68)
lr 10.06)
17.34 l1r)
34.61 l1r)
12.27 l1r)
41 l1r) (8.76 l1r) (8.76 l1r)
12.27 l1r) 35.44 l1r) 876 l1r)
38.00 l1r) (38.00 l1r)
41 l1r) (8.76 l1r) 35.44 l1r) 12.27 l1r) 17.34 l1r)
(34.61 l1r) 34.61 l1r) (17.34 l1r) 12.27 l1r) 34.61 l1r) 34.61 l1r)
(12.27 l1r) (35.44 l1r) (8.76 l1r) (8.76 l1r) (35.44 l1r) (38.00 l1r)
(4.81. l1r) (4.81 l1r) 38.00 l1r)
(35.44 l1r) (12.27 l1r) 34.61 l1r) 17.34 l1r) 34.61 l1r)
(12.27 l1r) (35.44 l1r) 38.00 l1r) 38.00 l1r)
41 l1r)
(8.76 l1r) (8.76 l1r)
(4.81 l1r) (38.00 l1r) 38.00 l1r) 12.27 l1r) 35.44 l1r)
(8.76 l1r) (4.81 l1r)
41 l1r) (8.76 l1r) 35.44 l1r)
(12.27 l1r) (17.34 l1r)
(34.61 l1r) (34.61 l1r) 17.34 l1r) 12.27 l1r) 34.61 l1r) 34.61 l1r)
(8.76 l1r) (8.76 l1r) 35.44 l1r) 38.00 l1r)
(12.2.7 l1r)
(3 5.44 l1r)
(4.81. l1r)
(4 .81 l1r) (38.00 l1r)
(248.076 l1r) (248.076 l1r) (248.076 l1r) (248.076 l1r) (248.076 l1r)
(2 4. 07 6 l1r) (248.076 l1r) (248.076 l1r) (248.076 l1r) (248-076 l1r)
(2 48. 07 6 l1r) (248.076 l1r) (248.076 l1r) (248.076 l1r) (248.076 l1r)
(248 . 076 l1r) (248.076 l1r) (248.076 l1r) (248.076 l1r) (248.076 l1r)
(2 48. 076 l1r) (248.076 l1r) (248.076 l1r) (248.076 l1r) (248.076 l1r)
(248.,07 6 l1r) (248.076 l1r) (248.076 l1r) (248-076 l1r) (248.076 l1r)
(248. 076 l1r) (248.076 l1r) (248.076 l1r) (248.076 l1r) (248.076 l1r)
(2 48. 07 6 l1r) (248.076 l1r) (248.076 l1r) (248.076 l1r) (248-076 l1r)
(248. 076 l1r) (248.076 l1r) (248.076 l1r) (248-076 l1r) (248.076 l1r)
(2 48. 076 l1r) (248.076 l1r) (248.076 l1r) (248.076 l1r) (248.076 l1r)
(248. 076 l1r) (248.076 l1r) (248.076 l1r) (248.076 l1r) (248.076 l1r)
(248 076 l1r) (248.076 l1r) (248.076 l1r) (248.076 l1r) (248.076 l1r)
(2 48 076 l1r) (248.076 l1r) (248.076 l1r) (248.076 l1r) (248.076 l1r)
(2 48 076 l1r) (248.076 l1r) (248.076 l1r) (248.076 l1r) (248.076 l1r)
(2 4 076 l1r) (248.076 l1r) (248.076 l1r) (248.076 l1r) (248.076 l1r)
(2 48 076 l1r) (248.076 l1r) (248.076 l1r) (248.076 l1r)
(182.31 l1r)
(22 6 36 l1r)
(98.885 l1r) (208.94 l1r) (98.885 l1r) (226.36 l1r)
(182 31 l1r) (248.076 l1r) (248.076 l1r) (248.076 l1r) (248.076 l1r)
(2 4 076 l1r) (248.076 l1r) (248.076 l1r) (248.076 l1r) (248.076 l1r)
(2 48. 07 6 l1r) (248.076 l1r) (248.076 l1r) (248.076 l1r) (248.076 l1r)
(4.81 l1r)
(4-81 l1r)
77
(248.076 l1r) (248.076 l1r) (248.076 l1r) (248.076 l1r) (113.32 l1r)
(113.32 l1r)
(3.06 l1r)
(5.35 l1r)
(5.35 l1r)
(3.06 l1r)
(113.32 l1r) (113.32 l1r) (248.076 l1r) (248.076 l1r) (248.076 l1r)
(248.076 l1r) (248.076 l1r) (248-076 l1r) (248.076 l1r) (248.076 l1r)
(248.076 l1r) (248.076 l1r) (248-076 l1r) (248.076 l1r) (248.076 l1r)
(248.076 l1r) (226.36 l1r) (182.31 l1r)
(5.35 l1r)
(3.06 l1r)
(3.06 l1r)
(5.35 l1r) (182.31 l1r) (226.36 l1r) (248.076 l1r)
(248.076 l1r) (248.076, l1r) (248.076 l1r) (248.076 l1r) (248.076 l1r)
(248.076 l1r) (248.076 l1r) (248.076 l1r) (248.076 l1r) (248.076 l1r)
(248.076 l1r) (208.94 l1r) (98.885 l1r) (98.885 l1r) (208.94 l1r)
(248.076 l1r) (248.076 l1r) (248.076 l1r) (248.076 l1r) (248.076 l1r)
(248.076 l1r) (248.076 l1r) (248.076 l1r) (248.076 l1r) (248.076 l1r)
(248.076 l1r) (248.076 l1r) (226.36 l1r) (98.885 l1r) (98.885 l1r)
(226.36 l1r) (248.076 l1r) (248.076 l1r) (248.076 l1r) (248.076 l1r)
(248.076 i1r) (248.076 l1r) (248.076 l1r) (248.076 l1r) (248.076 l1r)
(248.076 l1r) (248.076 l1r) (248.076 l1r) (248.076 l1r) (182.31 l1r)
(5.35 l1r)
(5.35 l1r) (182.31 l1r) (248.076 l1r) (248.076 l1r)
(248.076 l1r) 248.076 l1r) 248.076 l1r) 248.076 l1r) 248.076 l1r)
(248.076 l1r) 248.076 l1r) 248.076 l1r) 248.076 l1r) 248.076 l1r)
(248.076 l1r) (248.076 l1r) (248.076 l1r) (113.32 l1r)
(3.06 l1r)
(3.06 l1r)
113.32 l1r) 248.076 l1r) 248.076 l1r) 248.076 l1r)
(248.076 l1r) (248.076 l1r) (248.076 l1r) (248.076 l1r) (248.076 l1r)
(248.076 l1r) (248.076 l1r) (248.076 l1r) (248.076 l1r) (248.076 l1r)
(248.076 l1r) (248.076 l1r) f248.076 l1r) (248.076 l1r) (248.076 l1r)
(248.076 l1r) (248.076 l1r) (248.076 l1r) (248.076 l1r) (248.076 l1r)
(248.076 l1r) (248.076 l1r) (248.076 l1r) (248.076 l1r) (248-076 l1r)
(248.076 l1r) (248.076 l1r) (248.076 l1r) (248.076 l1r) (248.076 l1r) (248.076 l1r) (248.076 l1r) (248.076 l1r) (248.076 l1r) (248.076 l1r)
(248.076 l1r) (248.076 l1r) (248.076 l1r) (248.076 l1r) (248.076 l1r)
(248-076 l1r) (248.076 l1r) (248.076 l1r) (248.076 l1r) (248.076 l1r)
(248.076 l1r) (248.076 l1r) (248.076 l1r) (248.076 l1r) (248.076 l1r)
(248.076 l1r) (248.076 l1r) (248.076 l1r) (248.076 l1r) (248.076 l1r)
(248.076 l1r) (248.076 l1r) (248.076 l1r) (248.076 l1r) (248.076 l1r)
(248.076 l1r) (248.076 l1r) (248.076 l1r) (248.076 l1r) (248.076 l1r)
(248.076 l1r) (248.076 l1r) (248.076 l1r) (248.076 l1r) (248.076 l1r)
(248.076 l1r) (248.076 l1r) (248.076 l1r) (248.076 l1r) (248.076 l1r)
(248.076 l1r) (248.076 l1r) (248.076 l1r) (248.076 l1r) (248.076 l1r)
(248.076 l1r) (248.076 l1r) (248.076 l1r) (248.076 l1r) (182.31 l1r)
(22:6.36 l1r) (98.885 l1r) (208.94 l1r) (98.885 l1r) (226.36 l1r)
(182.31 l1r) (248.076 l1r) (248.076 l1r) (248.076 l1r) (248-076 l1r)
(248.076 l1r) (248.076 l1r) (248.076 l1r) (248.076 l1r) (248.076 l1r)
(248.076 l1r) (248.076 l1r) (248.076 l1r) (248.076 l1r) (248.076 l1r)
(248.076 l1r) (248.076 l1r) (248.076 l1r) (248.076 l1r) (113.32 l1r)
(113.32 l1r)
(3.06 l1r)
(3.06 l1r)
(5.35 l1r)
(5.35 l1r)
(113.32 l1r) (113.32 l1r) (248.076 l1r) (248.076 l1r) (248.076 l1r)
(248.076 l1r) (248.076 l1r) (248.076 l1r) (248.076 l1r) (248.076 l1r)
(248.076 l1r) (248.076 l1r) (248.076 l1r) (248.076 l1r) (248.076 l1r)
(3.06 l1r)
(248-076 l1r) (226.36 l1r) (182.31 l1r)
(5.35 l1r)
(3.06 llr
(5.35 l1r) (182.31 l1r) (226.36 llr (248.076 l1r)
(248-076 l1r) (248.076 l1r) (248.076 l1r) (248.076 l1r) (248.076 l1r)
(248.076 l1r) (248.076 l1r) (248.076 l1r) (248.076 l1r) (248.076 l1r)
(248.076 l1r) (208.94 l1r) (98.885 l1r) (98.885 l1r) (208.94 l1r)
(248.076 l1r) (248.076 l1r) (248.076 l1r) (248.076 l1r) (248.076 l1r)
(248.076 l1r) (248.076 l1r) (248.076 l1r) (248.076 l1r) (248.076 l1r)
(248.076 l1r) (248.076 l1r) (226.36 l1r) (98.885 l1r) (98.885 l1r)
(226.36 l1r) (248.076 l1r) (248.076 l1r) (248.076 l1r) (248.076 l1r)
(248.076 l1r) (248.076 l1r) (248.076 l1r) (248.076 l1r) (248.076 l1r)
(248.076 l1r) (248.076 l1r) (248.076 l1r) (248.076 l1r) (182.31 l1r)
(5-35 l1r)
(5-35 l1r) (182.31 l1r) (248.076 l1r) (248.076 l1r)
(248.076 l1r) 248.076 l1r) 248.076 l1r) 248.076 l1r) 248.076 l1r)
(248.076 l1r) 248-076 l1r) 248.076 l1r) 248.076 l1r) 248.076 l1r)
(248.076 l1r) (248.076 l1r) (248.076 l1r) (113.32 l1r)
(3.06 l1r)
(3.06 l1r)
113.32 l1r) 248.076 l1r) 248.076 l1r) 248.076 l1r)
(248..076 l1r)
248.076 l1r)
248.076 l1r)
78
248.076 l1r)
(248.076 l1r) c
f34:n
48195
88750
88775
88787
88802
88814
48199 48115 4119 48135 48139 4815S 48159 48165 48169
88751 88752 887S3 88754 88755 88756
88776 88777 88778 88779 88780 88781 88782 88783 88784 88785 88786
88803 88804 88805
88815 88816 88817
88833
88841 88842 88843 88844
88853
8886.6 88867 88868 88869
88878 88879 88880 88881
88902 88903 88904 88905
88914 88915 88916 88917
fc34
88806
88818
88834
88845
88807 8808 88809 88810 88811 88812 88813
88819 88820
88835 88836 837 88838 88839 88840
88846 88847 88848 88849 88850 88851 88852
88870
88882
88906
88918
88871 88872 88873 88874 88875 88876 88877
88883 88884 88885 88886 88887 88888
88907 88908 88909 88910 88911 88912 88913
88919
88935 88936 88937 88938 88939 88940
88941 88942 88943 88944 88945 88946 88947 88948 88949 88950
89750 89751 89752 89753 89754 89755 89756
89775 89776 89777 89778 89779 89780 89781 89782 89783 89784 89785 89786
89787
89802 89803 89804 89805 89806 89807 89808 89809 89810 89811 89812 89813
89814 89815 89816 89817 89818 89819 89820
89833 89834 89835 89836 89837 89838 89839 89840
89841 89842 89843 89844 89845 89846 89847 89848 89849 89850 89851 89852
89853
89866 89867 89868 89869 89870 89871 89872 89873 89874 89875 89876 89877
89878 89879 89880 89881 89882 89883 89884 89885 89886 89887 89888
89902 89903 89904 89905 89906 89907 89908 89909 89910 89911 89912 89913
89914 89915 89916 89917 89918 89919
89935 89936 89937 89938 89939 89940
89941 89942 89943 89944 89945 89946 89947 89948 89949 89950
** segmentation II * 280-1120),15(80-890),17(80-892)
fs34
204 208 212 216
sd34
(2.81 3r 1.4)
(2.81 3r 1.4)
(1.415 3r 0326)
(1.94 3r 0.97)
1415 3r 0326)
(1.94 3r 0.97)
283 3 141)
23
3 141)
(3.0 3 1494) 30 3 1494)
(30.26 3r 2761) 926 3 084) 115.2 3r 10.52) 22.18 3r2.01)
(115.2 3rlO.52) 926 3 084) 30.26 3 2761) 95.16 3r8.67)
(95.16 3r 867)
243.21 3r 22.2) 239.63 3r2l.87)
248.075 3r 22.63)
(248.075 3r 22.63) 248.075 3r 22.63) 248.075 3r22.63)
(248.075 3r 22.63) 239.63 3r 21.87) 243.21 3r 22.2) 95.16 3 867)
3r 867)
(243.21
(248.075
(248.075
(248.075
926 3 084)
3r 22.2)
3r 22.63)
3r 22.63)
3r 22.63)
30.26 3r2.761)
(248.075
248.075
(248.075
(248.075
3r
3r
3r
3r
22.63)
22.63)
22.63)
22.63)
(243.21 3r 22.2) (239.63 3r2l.87)
239.63 3r 21.87)
(248.075
248.075
(248.075
(248.075
3r22.63)
3r22.63)
3r22.63)
3r22.63)
(30.26 3r2.761) (9.26 3r 0.84)
(22.18 3r 2.01) (115.2 3r 10.52)
(248.075 3r22.63)
(248.075 3r 22.63) (248.075 3r 22.63) (248.075 3r22.63)
(248.075 3r 22.63) (248.075 3r 22.63) (248.075 3r22.63)
(248.075 3r 22.63) (248.075 3r 22.63) (248.075 3r22.63)
(248.075 3r 22.63) (248.075 3r22.63) (248.075 3r22.63)
(248.075 3r 22.63) (248.075 3r22.63) (248.075 3r22.63)
(248.075 3r 22.63) (115.2 3r 10.52) (22.18 3r 2.01) (9.26 3r 0.84)
(115.2 3rlO.52)(248.075 3r22.63)
248.075 3r22.63)
(248.075 3r 22.63) 248.075 3r22.63)
248.075 3r22.63)
(248.075 3r 22.63)
205.85 3r 18.79) 205.85 3r 18.79) 40.497 3 3692)
(140.5 3rl2.8)
40.497 3r3.692)
205.85 3r 18.79) 205.85 3r 18.79)
(248.075 3r 22.63)
248.075 3r22.63)
248.075 3r22.63)
(248.075 3r 22.63)
248.075 3r22.63)
248.075 3r22.63)
(115.2 3rlO.52)
926 3 084)
30.26 3 2761)
239.63 3r 21.87)
(248..075 3r 22.63)
248.075 3r22.63)
248.075 3r22.63)
(248..075 3r 22.63) (248.07S 3r22.63)
(140..5 3rl2.8)
40.497 3r3.692)
40.497 3 3692)
140.5 3r 12.8)
(248..075 3r 22.63)
248.075 3r22.63)
248.075 3r22.63)
(248.075 3r 22.63)
248.075 3r22.63)
79
95.16
(239.63 3r 21.87)
(30.26 3r 2761)
95.16 3r8.67)
(248.075 3r 22.63)
(248.075 3r 22.63)
(40.497 3r3.692)
243.21 3r 22.2)
248.075 3r22.63)
205-85 3r 18.79)
248-075 3r22.63)
40-497 3 3692)
205.85 3r 18.79)(248.075 3r22.63)
(248.075 3r 22.63) 248.075 3r22.63)
248.075 3r22.63)
(243.21 3r 22.2) 95.16 3r8.67)
(30..26 3 2761) (9.26,3r 084)
115.2 3r 10.52) 22.18 3 201)
(115.2 3rlO.52)
926 3 084)
30.26 3 2761)
95.16 3 867)
(95.16 3r 867)
243.21 3r 22.2) 239.63 3r 21.87) 248.075 3r 22.63)
(248.075 3r 22.63) 248.075 3r22.63)
248.075 3r22.63)
(248.075 3r 22.63) 239.63 3r 21.87) 243.21 3r 22.2) 95-16 3 867)
(95.16 3r 867) 926 3 084) 30.26 3r2.761) 239.63 3r 21.87)
(243.21 3r 22.2)(248.075 3r22.63) 248.075 3r22.63)
(248.075 3r 22.63)
(248.075 3r 22.63)
(248.075 3r 22.63)
248.075 3r22.63)
248.075 3r22.63)
248.075 3r22.63)
248.075 3r22.63)
248.075 3r22.63)
248.075 3r22.63)
(243.21 3r 22.2) 239.63 3r 21.87) 30.26 3r 2761)
(22.18 3 201) 115.2 3rlO.52)(248.075 3r22.63)
(248.075
(248.075
(248.075
(246.075
(246.075
(248.075
3r
3r
3r
3r
3r
3r
22.63)
22.63)
22.63)
22.63)
22.63)
22.63)
(248.075 3r22.63) (248.075
(248.075 3r22.63) (248.075
(248.075 3r22.63) (248.075
(248.075 3r22.63) (248.075
(248.075 3r22.63) (248.075
(115.2 3r 10.52) (22.18 3r
(115.2 3rlO.52)(248.075 3r22.63)
926 3 08'4)
3r22.63)
3r22.63)
3r22.63)
3r22.63)
3r22.63)
2.01) (9.26 3r 0.84).
248.075 3r22.63)
(248.075 3r 22.63)
248.075 3r22.63)
248.075 3r22.63)
(248.075 3r 22.63)
205.85 3r 18.79) 205.85 3r 18.79) 40.497 3 3692)
(140.5 3rl2.8)
40.497 3r3.692)
205.85 3r 18.79) 205.85 3r 18.79)
(248.075 3r 22.63)
248.075 3r22.63)
248.075 3r22.63)
(248.075 3r 22.63)
248.075 3r22.63)
248.075 3r22.63)
(115.2 3rlO.52)
926 3 084)
30.26 3 2761)
239.63 3r 21.87)
(248.075 3r 22.63)
248.075 3r22.63)
248.075 3r22.63)
(248.075 3r 22.63)
248.075 3r22.63)
(140.5 3rl2.8)
40.497 3r3.692)
40.497 3 3692)
140.5 3r 12.8)
(248.075 3r 22.63) 248.075 3r22.63)
248.075 3r22.63)
(248.075 3r 22.63)
248.075 3r22.63)
(239.63 3r 21.87)
(30.26 3r 2761)
95.16 3r8.67)
243.21 3r 22.2)
(248.075 3r 22.63)
248.075 3r22.63)
248.075 3r22.63)
(248.075 3r 22.63) 205.85 3r 18.79) 40.497 3 3692)
(40.497 3r3.692)
205.85 3r 18.79)(248.075 3r22.63)
(248.075 3r 22.63)
(243.21 3r 22.2)
c
f44:n
fc44
248.075 3r22.63)
248.075 3r22.63)
95.16 3r8.67)
48280 48289 48384 48385 48482 48486 48582 48581 48686 48687 49010 49019
49270 49279
49312 49316
49572 49576
49616 49617
49876 49877
47314 47315 47318 47319
47412 47418 47419 47410
47511 47514 47515 47516
47612 47613 47616 47617
47711 47712 47713 47719
47815 47816 47817 47810
** segmentation III ** 680-1147),19(80-1147),20(80-5237)
fs44
204 208 212 216 220 224 228 232
sd44
(9.0 7r9.7) (9.0
(9.0 7r9.7) (9.0
(9.0 7r9.7) (9.0
(1.357 7rO.743)
(1.357 7rO.743)
7r 9.7)
7r 97)
7r 97)
1357 7
1357 7
(11.999 8r) (11.999 8r)
11.999 8r) 11.999 8r)
0743)
0743)
12186 7 07798)
12186 7 07798)
80
12186 7r 07798)
12186 7r 07798)
(1.357 7rO.743) 1357 7 0743) 12186 7r 07798) 12186 7r 07798)
(7.055 7r7.056) 17.31 r) 7055 7 7056) 17.31 r)
(7.055 7r7.056) 7055 7 7056) 17-31 r) 17.31 r)
(7.055 7r7-056)
c
f54:n
f c54
f s54
sd54
17-31
r)
17.31
r
(17.31 Sr)
7055 7 7056)
17.31 r)
(17.31 Sr)
(17..31 Sr)
7055
7055
7055
7
7
7056)
7056)
7
7055
7
7056)
7055 7 7056)
7056)
17.31 r)
7055 7r7.056)
17.31 Sr)
20151 20152 20153 20154 20155 20156 20157 20158 20159 20160 20161 20162 20163
20164 20165 20166 20167 20168 20169 20170 20171 20172 20173 20174 20175
20176 20177 20178 20179 20180
68750 68751 68752 68753 68754 68755 68756
68775 68776 68777 68778 68779 68780 68781 68782 68783 68784 68785 68786
68787
68802 68803 68804 68805 68806 68807 6808 68809 68810 68811 68812 68813
6881.4 68815 68816 68817 68818 68819 68820
68833 68834 68835 68836 68837 68838 68839 68840
6884 68842 68843 68844 68845 68846.68847 68848 68849 68850 68851 68852
68853
68866 68867 68868 68869 68870 68871 68872 68873 68874 68875 68876 68877
6887 6887 9 68880 68881 68882 68883 68884 68885 68886 68887 68888
68902 68903 68904 68905 68906 68907 68908 68909 68910 68911 68912 68913
68914 68915 68916 68917 68918 68919
68935 68936 68937 68938 68939 68940
68941 68942 68943 68944 68945 68946 68947 68948 68949 68950
697 0 697 1 69752 69753 69754 69755 69756
6977 6977 6 69777 69778 69779 69780 69781 69782 69783 69784 69785 69786
69787
69802 69803 69804 69805 69806 69807 69808 69809 69810 69811 69812 69813
69814 69815 69816 69817 69818 69819 69820
69833 69834 69835 69836 69837 69838 69839 69840
69841 69842 69843 69844 69845 69846 69847 .69848 69849 69850 69851 69852
69853
69866 69867 69868 69869 69870 69871 69872 69873 69874 69875 69876 69877
69878 69879 69880 69881 69882 69883 69884 69885 69886 69887 69888
69902 69903 69904 69905 69906 69907 69908 69909 69910 69911 69912 69913
69914 69915 69916 69917 69918 69919
69935 69936 69937 69938 69939 69940
69941 69942 69943 69944 69945 69946 69947 69948 69949 69950
** segmentation IV * 41120-1125)
220 224 228 232 236 240 244
(14.9716.47 5rl5.40) (14 97 16 47
(20.3122.35 5r2O.89) (1 69 12 86
(14.9716.47 5rl5.40) (20 3 22 3
(11.6912.86 5r12 02) (20 31 22 3
(11.6912.86 5rl2.02) (11 69 12 86
(14.9716.47 5rl5 40) (1 69 12 86
(14.9716.47 5rl5.40) (20 31 22 3
(11.6912.86 5rl2.02) (20 3 22 3
(14.9716.47 5ri5.40) (11 69 12 86
(11.6912.86 5rl2.02) (14 97 16 47
(27.68 30.46 5r 28.48) 847 932
5rl5.40) (11.69 12.86 5rl2.02)
5rl2.02) (14.97 16.47 5rl5.40)
5r2O.89) (11.69 12.86 5rl2.02)
5r2O.89) (14.97 16.47 5rl5.40)
5rl2.02) (14.97 16.47 5rl5.40)
5rl2.02) (11.69 12.86 5rl2.02)
5r2O.89) (11.69 12.86
5r 20.89) (14.9716.47
5r 12.02) (20.3122.35
5r 15.40) (14.9716.47
5r 8.71) 104.73115.24
(20.0922.1 5r 20.66) 104.73 115.24 5r 107.73) 8479.32
(27.683.0.46 5r28.48) (86.82 95.53 5r 89.3) (86.82 95.53
(220.73 242.89 5r 227.05) 217.3239.12 5r223.52)
(225.45 248.08 5r 231.9)
(225.45 248.08 5r 231.9)
5rl2.02)
5r 15.40)
5r 20.89)
5r 15.40)
5r 107.73)
5r 871)
5r 89.3)
225.45248.08 5r231.9)
(225.45 248.08 5r 231.9)
(225.45 248.08 5r 231.9) 217.3 239.12 5r 223.52)
(220.73 242.89 5r 227.05)
(86.8295.53 5r89.3)
86.82 95.53 5r 89.3)
847 932 5r 871)
(27.6830.46 5r28.48)
217.3 239.12 5r 223.52)
(220.73 242.89 5r 227.05)
(225.45 248.08 5r 231.9)
225.45248.08 5r231.9)
81
(225.45
(225.45
(225.45
(225.45
(225.45
(225.45
(220.73
248.08
248.08
248.08
248.08
248.08
248.08
242.89
5r
5r
5r
5r
5r
5r
5r
231.9) (225.45248.08
231.9)
231-9) (225.45248.08
231.9)
231.9) (225.45248.08
231.9)
227.05) (217.3239.12
5r231.9)
5r231.9)
5r231.9)
5r223.52)
(27.6830.46 5r28.48)
(8.47 932 5r
(225.45 248.08
(225.45 248.08
(225.45 248.08
(225.45 248.08
(225.45 248.08
(225.45 248.08
(225.45 248.08
(225.45 248.08
(225.45 248.08
(225.45 248.08
(225.45 248.08
(225.45 248.08
(104.73 115.24
(104.73 115.24
(225.45 248.08
(225.45 248.08
(225.45 248.08
(225.45 248.08
(171.14 188.32
8.71) 20.0922.1 5r 20.66) 104.73 115.24 5r 107.73)
5r 231.9)
5r 231.9) (225-45248.08 5r231-9)
5r 231.9)
5r 231.9) (225.45248.08 5r231.9)
5r 231.9)
5r 231.9) (225.45248.08 5r231.9)
5r 231.9)
5r 231.9) (225.45248.08 5r231.9)
5r 231.9)
5r 231.9) (225.45248.08 5r231.9)
5r 231.9)
5r 231.9)
5r 107.73) (20.09 22.1 5r 20.66) (8.479.32 5r 8.71)
5r 107.73)
5r 231.9) (225.45248.08 5r231.9)
5r 231.9)
5r 231.9) (225.45248.08 5r231.9)
5r 231.9)
5r 176.04) (171.14 188.32 5r 176.04)
(25.1327.65 5r25.85)
(107.99 118.82 5r 111.08) (25.13 27.65 5r 25.85)
(171.14 188.32 5r 176.04)
(171.14 188.32 5r 176.04)
(225.45 248.08 5r 231.9) (225.45248.08 5r231.9)
(225.45 248.08 5r 231.9)
(225.45 248.08 5r 231.9) (225.45248.08 5r231.9)
(225.45 248.08 5r 231.9)
(104.73 115.24 5r 107.73) (8.47 9.32 5r 8.71) (27.6830.46 5r 28.48)
(217.3 239.12 5r 223.52)
(225.45 248.08 5r 231.9) (225.45248.08 5r231.9)
(225.45 248.08 5r 231.9)
(225.45 248.08 5r 231.9) (225.45248.08 5r231.9)
(107.99 118.82 5r 111.08) (25.13 27.65 5r 25.85) (25.1327.65 5r25.85)
(107.99 118.82 5r 111.08)
(225.45 248.08 5r 231.9) (225.45248.08 5r231.9)
(225.45 248.08 5r 231.9)
(225.45 248.08 5r 231.9) (225.45248.08 5r231.9)
(217.3 239.12 5r 223.52)
(27.6830.46 5r28.48)
86.82 95.53 5r 9.3)
(220.73 242.89 5r 227.05)
(225.45 248.08 5r 231.9) 225.45248.08 5r231.9)
(225.45 248.08 5r 231.9)
(22,5.45 248.08 5r 231.9)
171.14188.32 5r176.04)
(25.1327.65 5r25.85)
(25.1.327.65 5r25.85)
171.14 188.32 5r 176.04)
(225.45 248.08 5r 231.9)
(225.45 248.08 5r 231.9) 225-45248.08 5r231.9)
(225..45 248.08 5r 231.9)
(220..73 242.89 5r 227.05) 86.82 95.53 5r 9.3)
(27.6830.46 5r28.48) (8.47 932 5r .71) 104.73 115.24 5r 107.73)
.(20.0922.1 5r 20.66) 104.73 115.24 5r 107.73) 847 932 5 871)
(27.6830.46 5r28.48)
86.82 95.53 5r 9.3) 86.82 95.53 5r 9.3)
(220.73 242.89 5r 227.05) 217.3239.12 5r223.52)
(225.45 248.08 5r 231.9)
(225.45 248.08 5r 231.9) 225.45248.08 5r231.9)
82
(225.45 248.08
231.9)
(225.45 248.08
231.9) 217.3 239.12
223.52)
(220.73 242.89
227.05)
(86.8295.53 5r89.3)
86.82 95.53
89-3) (8.47 932
(27.6830.46 5r28.48)
217.3 239.12
223.52)
(220.73 242.89 Sr 227.05)
(225.45 248.08 Sr 231.9) (225-45248.08 5r231.9)
(225.45 248.08 Sr 231.S) (225-45248.08 5r231.9)
(225.45 248.08 Sr 231.9)
(225.45 248.08 Sr 231.9) (225-45248.08 5r231.9)
(225.45 248.08 Sr 231.9)
(225.45 248.08 Sr 231.9) (225.45248.08 5r231.9)
(225.45 248.08 Sr 231.9)
(220.73 242.89 Sr 227.05) (217.3239.12 5r223.52)
871)
(27.6830.46 5r28.48)
(8.47 932
(225.45 248.08
(225.45 248.08
(225.45 248.08
(225.45 248.08
(225.45 248.08
(225.45 248.08
(225.45 248.08
(225.45 248.08
(225.45 248.08
(225.45 248.08
(225.45 248.08
(225.45 248.08
(104.73 115.24
(104.73 115.24
(225.45 248.08
(225.45 248.08
(225.45 248.08
(225.45 248.08
(171.14 188.32
871)
20.0922.1
20.66) 104.73 115.24
107.73)
Sr 231.9)
Sr 231.9) (225-45248.08 5r231.9)
Sr 231.9)
Sr 231.9) (225-45248.08 5r231.9)
Sr 231.9)
Sr 231.9) (225.45248.08 5r231.9)
Sr 231.9)
Sr 231.9) (225-45248.08 5r231.9)
Sr 231.9)
Sr 231.9) (225-45248.08 5r231.9)
Sr 231.9)
Sr 231.9)
Sr 107.73) (20.09 22.1 Sr 20.66) (8.47 9.32 Sr 8.71)
Sr 107.73)
Sr 231.9) (225.45248.08 5r231.9)
Sr 231.9)
Sr 231.9) (225.45248.08 5r231.9)
Sr 231.9)
Sr 176.04) (171.14 188.32 Sr 176.04)
(25.1327.65 5r25.85)
(107.99 118.82 Sr 111.08)
(171.14 188.32 Sr 176.04)
(171.14 188.32 Sr 176.04)
(22
4
2 48. 08 Sr 23
(225.45 248.08
(225..45 248.08
(225..45 248.08
(104..73 115.24
(217.3 239.12
(225.45 248.08
(225.45 248.08
(225.45 248.08
(107.99 118.82
(107.99 118.82
(225.45 248.08
(225.45 248.08
Sr
Sr
Sr
Sr
9
231.9)
231.9)
231.9)
107.73)
223.52)
Sr 231.9)
Sr 231.9)
Sr 231.9)
Sr 111.08)
Sr 111.08)
Sr 231.9)
Sr 231.9)
(225.45248.08 5r231.9)
(25.13 27.65 Sr 25.85)
(225.45248.08
5r231.9)
(225.45248.08
5r231.9)
(8.47 9.32 Sr 8.71)
(225.45248.08 5r231.9)
(225.45248.08 5r231.9)
(25.13 27.65 Sr 25.85)
225.45 248.08 5r231.9)
(86.82 95.53 Sr 89.3)
5r227.05)
5r231.9) (225.45 248.08 5r231.9)
5r231.9)
5r231.9) (171.14 188.32 5r176.04)
(25.13 27.65
25.85)
(25.1.3 27.65 Sr 25.85)
(25.1327.65
(225.45248.08 5r231.9)
(217.3 239.12
223.52)
(27.68 30.46 Sr 28.48)
(220.73242.89
(225.45248.08
(225.45248.08
(225.45248.08
(27.68 30.46 5-r 28.48)
(171.14188.32
Sr 176.04)
(225.45248.08 5r231.9)
(225.45248.08 5r231.9) (225.45 248.08 5r231.9)
(225.45248.08 5r231.9)
83
5r25.85)
(220.73242-89 5r227.05)
c
f64:n
46503 46504 46505 46508 46509 46510
46511 46513 46514 46517 46518 46520
46803 46804 46805 46808 46809 46810
46821 46822 46823 46826 46827 46828
47111 47113 47114 47117 47118 47120
fc64
fs64
c
f74:n
86.82 95.53 5r
segmentation
46521
46811
47103
47121
9.3)
46522
46813
47104
47122
46523
46814
47105
47123
46526
46817
47108
47126
V ** 10(80-872)
46603 46604 46605 46608 46609 46610 46611 46613 46614 46617 46618 46620 46621
46622 46623 46626 46627 46628
** segmentation VI ** 11(872-1153)
fs74
224 228 232 236 240 244
sd74
(1.03 8.35 26.19 27.12 2r 20.3) (0. lr 7.3629.926 2r 7.43)
(1.03 835 26.19 27.12 2r 20.3) (0. lr 73629.926 2 743)
(1.03 835
26.19 27.12 2r 20.3)
(0. 'r 7362 9926 2 743)
(1.03 835
(1.03 835
(1.03 835
103
103 835 26.19 27.12 2r 20.3)
(0. lr 73629.926 2 743)
103 835 26.19 27.12 2r 20.3)
103 835 26.19 27.12 2r 20.3)
103 835 26.19 27.12 2r 20.3)
44103 44104 44105 44108 44109 44110 44111 44113 44114 44117 44118 44120 44121
44122 44123 44126 44127 44128
45101 45102 45103 45104 45105 45106 45107 45108 45109 45110 45111 45112
45113 45114 45115 45116 45117 45118 45119 45120 45121 45122 45123 45124
45125 45126 45127 45128 45129 45130
fc84
** segmentation VII ** 13(80-1150)
fs84
c
f94:n
204 208 212 216 220 224 228 232 236
48105 48109
fc94
** segmentation VIII ** 16(890-1147)
fs94
220 224 228 232
sd94
(6.02 12.0 3r) (6.02 12.0 3r)
44203 44204 44205 44208 44209 44210 44211 44213 44214 44217 44218 44220 44221
44222 44223 44226 44227 44228
44303 44305 44309 44310 44313 44314 44317
44318 44321 44322 44326 44328
45201 45202 45203 45204 45205 45206 45207 45208 45209 45210 45211 45212
45213 45214 45215 45216 45217 45218 45219 45220 45221 45222 45223 45224
45225 45226 45227 45228 45229 45230 45301 45302 45303 45304 45305 45306
45307 45308 45309 45310 45311 45312 45313 45314 45315 45316 45317 45318
45319 45320 45321 45322 45323 45324 45325 45326 45327 45328 45329 45330
47334 47335 47338 47339 47344 47345 47348 47349
47432 47438 47439 47430 47442 47448 47449 47440
47531 47534 47535 47536 47541 47544 47545 47546 47632 47633 47636 47637
47642 47643 47646 47647 47731 47732 47733 47739 47741 47742 47743 47749
47835 47836 47837 47830 47845 47846 47847 47840
fclO4
fslO4
sdlO
835 26.19 27.12 2r 20.3)
103 835 26.19 27.12 2r 20.3)
26.19 27.12 2r 20.3)
26.19 27.12 2r 20.3)
26.19 27.12 2r 20.3)
(0. lr 7362 9926 2 743)
(0. lr 7362 9926 2 743)
c
flO4:n
46528
46820
47110
47128
204 208 212 216 220
fc74
c
f84:n
46527
46818
47109
47127
segmentation
240 244
3
X ** 8(1150-1125)
82.39 77.02) 455 982 918)
38.282.3977.02) 455 982 918)
(38.2 82.39 77.02) (38.282.39 77.02)
(38.2 82.39 77.02) (38.282.39 77.02)
(38.2 82.39 77.02) (38.282.39 77.02)
(4.559..829.18)
38.2 82.39 77.02)
(0.130,280.27)
(0.13 0.280.27) (0.13
(0.130.280.27)
(0.13 0.280.27) (0.13
(0.130.280.27)
(0.13 0.280.27) (0.13
(0.290.620.58)
(0-29 0.620.58) (8.03
(8.03 17.32 16.18) (0.29 0.62 0.58)
(8.03 17.32 16.18) (8.0317.32 16.18)
84
(4.55 9.829.18) (38.282.39 77.02)
(38.2 82.39 77.02) (4.55 9.82 9.18)
(4.55 9.829-18) (38.282.39 77.02)
0.28 0.27) (0.13 0.280.27)
0.28 0.27) (0.13 0.280.27)
0.28 0.27) (0.13 0.280-27)
17.32 16.18) (5-15 11.11 10.38)
(0.29 0.62 0.58) (5.15 11.11 10.38)
(5.15 11.11 10.38) 029 062 0.58)
(8.03 17.32 16.18) 80317.32 16.18) 029 0620.58)
029 062 058)
(8.03 17.32 16.18) (8.0317.32 16.18) 029 0620.58)
(5-1511.11 10.38)
(8.03 17.32 16.18) (8.0317.32 16.18) (5.15 11.11 10.38) 029 062 0.58)
(0.290.620.58)
(8.03 17.32 16.18) (5.1 1511-1110.38) (8.0317.32 16.18)
(0.290.620.58) 029 0620.58)
(0.440.950.88)
(2.2 474 443)
(2.2 4.74 4.43)
(0.44 0.950.88)
(2.2 4.74 4.43)
(0.071 0.153 0.143)
044 095 0.88) 044 095 0.88) 0071 0153 0143)
(2.2 4.744.43)
(0.071 0.153 0.143)
(0.44 0.95 0.88)
(2.2 4.74 4.43) (2.2 4.744.43)
(0.440.950.88)
(2.2 4.74 4.43)
(0.071 0.153 0.143)
(0.071 0.153 0.143)
(0.44 0.95 0.88)
(2.2 4.74 4.43)
(2.2 4.74 4.43) (2.2 4.744.43) (0.440-950.88) (0.440.95 0.88)
(2.2 4.74 4.43) (2.2 4.744.43) (0.440.950.88) (0.071 0.1530.143)
(0.440.950-88) 044 0950.88)
(3.11 6.71 6.27) (6.55 14.1213.19) (3.116.71 6.27) (6.55 14.1213.19)
(0.15 0.33 0.31) (7.2315.614.58) (0.150.33 0.31) (7.2315.614.58)
(3.11 6.71 6.27)
(3.11 6.71 6.27)
(6.55 14.12 13.19)
(6.55 14.1213.19)
(0.15 0.33 0.31) (0.15 0.33 0.31) (7.2315.6 14.58) (7.2315.614.58)
(3.11 6.71 6.27) (6.55 14.1213.19) (6.55 14-12 13.19) (3.116.716.27)
(0.15 0.33 0.31) (7.2315.614.58) (7.23 15.6 14.58) (0.150.330.31)
(6.55 14.12 13.19)
(7.23
(6.55
(7.23
(3.11
(0.15
c
fll4:n
fc114
sd114
3116.716.27)
655
14.12 13.19)
3116.716.27)
15.6 14.58) (0.15 033 031)
723 15.614.58)
0150.330.31)
14.12 13.19) 655 14.12 13.19) 311 671 627) 3116.716.27)
15.6 14.58)(7.23 15.6 14.58) (0.1 033 031) 0150.330.31)
6.71 627) 655 14.1213.19) 655 14.12 13.19) 3116.716.27)
0.33 031)
72315.614.58)
723 15.6 14.58) (0.150.330.31).
49300 49309
49602 49606
49906 49907
46703 46704
46721 46722
46911 46913
47203 47204
47221 47222
46705
46723
46914
47205
47223
** segmentation
XI *
0076 0424 0223)
(0.076 0424 0223)
(0.076 0424 0223)
46708
46726
46917
47208
47226
46709
46727
46918
47209
47227
46710
46728
46920
47210
47228
46711
46903
46921
47211
9872-860),45(5245-5232)
00760.4240.223)
46713
46904
46922
47213
46714
46905
46923
47214
fs114
46717
46908
46926
47217
46718
46909
46927
47218
224 228
00760.4240.223)
00760.4240.223)
(2.53.580.27) 114 1650.27) 25 358 027) 114 165 027)
(2.53.580.27) 25 358 027) 114 165 027) 253.58 027)
(2.53,.580.27) 25 358 027) 253.580.27) 1141.65 027)
(2.53.580.27) 25 358 027) 114 165 027) 253.58 027)
(1.14 165 027) 25 3580.27)
(6.02 864 0.8) 31 4570.74) 602 864 0.8) 31 457 074)
(6.028.640.8) (6.028.640.8) (3.184.570.74) (6.02 8.64 0.8)
(6.028.640-8) (6.028.640.8) (6.028.640.8) (3.18 4.570.74)
(6.028.640.8) (6.028.640.8) (3.184.570.74) (6.02 8.64 0.8)
(3.184.570.74) 602 864 0.8)
(6.459.250.5)
(6.459.250.5)
(6.459.250.5)
(6.459.250.5)
(2.633.770.6)
c
fl24:n
fc124
sd124
(2.633.770.6)
(6.459.250.5)
(6.459.250.5)
(6.459.250.5)
(6.459.250.5)
(6.459.250.5)
(2.633.770.6)
(6.459.250.5)
(2.633.770.6)
(2.63
(6.45
(2.63
(6.45
3.770.6)
9.250.5)
3.770.6)
9.250.5)
49030 49039
49332 49336
49636 49637
49070 49079 49100 49109
49372 49376 49402 49406
49676 49677 49706 49707
segmentation
XII ** 22(5233-5234),26(5240-5241)
01043 00904) 010430.0904)
(0.1043 00904) 010430.0904)
(0.1043 00904) 010430.0904)
85
fs124
232
46720
46910
46928
47220
(l.l.le-4 9.6e-5) 1lle-4 9.6e-S) 009 0078) 009 0078) 1lle-4
(l.l.le-4 9.6e-5) 009 0078) 009 0078) 1.11e-4 9.6e-5) 1lle-4
(0.09 0078) 009 0078)
c
fl34:n
9.6e-5)
9.6e-5)
49110 49119 49150 49159 49180 49189
4941.2 49416 49452 49456 49482 49486 49716 49717 49756 49757 49786 49787
fc134 ** segmentation XIII ** 29(5243-5244),33(5250-5251)
fs134
sd134
c
fl44:n
220
0032 0163) 0032 0163) (3.39e-5 1.73e-4) (3.39e-5 1.73e-4) 00275 01405)
(0.02750.1405)
(0.032 0163) 0032 0163) (3.39e-5 1.73e-4) (3.39e-5 1.73e-4) 00275
0.1405) 002750.1405)
(0.032 0163) 0032 0163) (3.39e-5 1.73e-4) (3.39e-5 1.73e-4) 00275
0.1405) 002750.1405)
49190 49199 49230 49239 49260 49269
49492 49496 49532 49536 49562 49566 49796 49797 49836 49837 49866 49867
fc144 ** segmentation XV** 36(5253-5254),40(5260-5261)
fs144
sd144
212
0187 7.7e-3) (0.1877.7e-3) (1.987e-4 8.26e-6) (1.987e-48.26e-6)
(0.161 0007) 0161 0007)
(0.187 7.7e-3) (0.1877.7e-3) (1.987e-4 8.26e-6) (1.987e-48.26e-6)
(0.161 0007)
0161 0007)
(0.187 7.7e-3) (0.1877.7e-3) (1.987e-4 8.26e-6) (1.987e-48.26e-6)
(0.161 0007) 0161 0007)
c
fl54:n
49280 49289
49582 49586
49886 49887
fc154 ** segmentation XVI ** 43(80-5252)
fs154
204 208
sd154
(0.424 Ir 0.069)
c
fl64:n
(0.424 lrO.069)
(0.424 lr 0069)
(0.424 lr 0069)
0424 lrO.069)
0424 lrO.069)
49290 49299
49592 49596
49896 49897
fc164 ** segmentation XVII ** 44(5255-5242)
fs164
sd164
216
(0.3649 0.3578)
(0.36490.3578)
(0.3649 03578)
(0.3649 03578)
036490.3578)
036490.3578)
86
APPENDIX
PROCESSING PROGRAMS
The following program and file listings are given in this Appendix
xcgOln.f
incore flux, tally processing program
xcgln.f
incore homogenized cross section processing program
prohxln.f
out of core flux and cross section processing program
prohx2n.f
version of prohxln.f for the cells below surface 5
sibel.f
the program written to prove accuracy of processing programs
rs___
the results of sibel.f
87
Program : xcgOln.f
character*8 kodver
character*19 probid
character*79title
character*4ntalvals
character*5 tallykcode
character*2fdusmc,,et
character*3 tfc
character*75
c
fcomment
integer indllupflindfnff
integer rnrpbnameptypecellntallyn
real cellvxdatatrf
dimension ebin(3)
dimension celln(62),tallyn(35),xkeff(3)
dimension tf(8)
c
common/datv/cellv(3659),indl(3659,5),lupfl(2),indf
common/datc/nff(3S)
common/datx/xdata(2,35,3,5,14,62)
common/rslt/trf(2,24,12,3)
c
c
xdata(2,35
3
514,70)
c
c
c
c
(2, nt, ne, nm, ns, n f
nt
tally no :
ne
energy bin no.
rim
multiplier
no.
c
c
ns
nf
c
trf
segment no.
cell no.
2, 24, 12,
3,
5)
c
(i, ni, ns, ne, nm)
c
c
c
ni
: triangle
no
open(unit=13,file=lmcxllform=lformattedl,status=loldl)
open(unit=19,file=lvol7l,form=lformattedl,status=loldl)
open(unit=llfile=lxcllform=lformattedl,status=lunknown')
open(unit=20,file=ltrrllform=lformattedl,status=lunknown')
open(unit=22,file=ltrfllform=lformattedl,status=lunknown')
c
c Start to read cell volume data from vol, file
c
ind=O
do 101 i=1,3659
read(19,103)(indl(i,k),k=1,2),cellv(i),(indl(i,i),j=3,5)
103
101
format(i6,xi6,1pe13.5,3(xi2))
continue
501
format(2a8,a19,i5,i11,i15)
502
format (1x, a7 9)
503
format(aCi6)
600
format(16i5)
read(13,501)kod,ver,probid,knod,nps,rnr
write(11,5011)kod,ver,probid,knod,nps,rnr
5011 format(ITally file:'/,Imcxll,2x,2a8,al9,i5,illil5)
c
read(13,502)title
c
read(13,503)ntalnt
c
read(13,600)(ta1lyn(i),i=1,nt)
c
c ***** Start
ally
loop
c
88
do 100 n=lnt
read(13,504)tallypbnameptype
504
format(a5,2i5)
read(13,505)fcomment
505
format(5xa75)
506
format(a2,i8)
507
format(11i7)
read(13,506)fnff(n)
nf=nff(n)
read(13,507)(ce1ln(i),i=1,nf)
read(13,506)didumm
read(13,506)uidumm
read(13,506)sns
read
( 3, 5 6 m, nm
if(nm.'eq.O)rim=l
read(13,506)cnc
if(nc.eq.O)nc=l
508
509
format(a2,iBi4)
format(lp6el3.5)
510
format(a4)
read(13,506)ene
read(13,509)(ebin(i),i=1,ne) read(13,506)tidumm
read(13,510)vals
c
c Read list of tally/error
c
data pairs
read(13,511)(((((xdata(it,n,ie,im,is,ic),it=1,2),
x ie=lne),im=lnm),is=lns),ic=lnf)
511
1025
format(4(1pe13.5,Opf7.4))
format(i3,xi5,Ip1Oe1O.3)
c
c Read tally
c
fluctuation
data
read(13,512)tfc,nfc,(jtf(i),i=1,8)
512
format(a3,i5,8i8)
do 150 j=lnfc
read(13,513)npsxtallyxerrfom
513
150
format(i11,1p3e13-5)
continue
c
c ***** End of tally
100
continue
loop
c
c Read kcode data
c
read(13,3000,end=999)kcode,ncycle
3000 format(a5,i5)
c
do 200 ncy=1,ncycle
read(13,3010,end=998)(xkeff(k),k=1,3),dummyl,dummy2
200
continue
3010 format(lp5el2.5)
c
998
continue
999
continue
c
c
• Processing xdata and frac and cellv to get triangle
•
call parameters (imatl1w,1upititnca11n)
sections c
c
•
•
•
•
imat:
l1w
lup
it
material number to fetch from cell volume array
starting line number cell volume to be found the array
final line number to find cell volume
order of tally in mcx file no. iu
89
•
itn
problem number of tally(only used in if statements)
calln: variable to count no of calls from main
•
c
indf-1
call flux(4,1,152,3,24,1)
call.
call.
call.
call
call.
call.
call
call
flux(1,1,152,4,34,2)
flux(2,1,152,5,44,3)
flux(0,153,511,1,4,4)
flux(5,155,514,2,14,5)
flux(4,292,510,12,124,7)
flux(1,292,510,13,134,B)
flux(2,292,510,14,144,9)
flux(7,2,0,18,194,10)
do ilk=1,2
write(22,556)(((trf(ilk,i,jk),k=1,3),j=1,12),i=1,24)
555
556
format(lp5el3.5)
format(lp3el3.5)
end do
c
stop
end
c------------------------------------------------------------------------c
SUBROUTINE FOR FLUX CALCULATION
c------------------------------------------------------------------------subroutineflux(imatllwlupititnjale)
c
integer indllupflindfnff
real cellvxdatatrf
common/datv/cellv(3659),indl(3659,5),lupfl(2),indf
common/datc/nff(35)
common/datx/xdata(2,35,3,5,14,62)
common/rslt/trf(2,24,12,3)
c
I
write(11,1001)imat,llw,lup,it,itn,jale
1001 format(5xlflux
,6i8)
c
ic=O
idmat=1
iflagd=O
iflags=O
nseg=12
nm=3
c
c ---
check for dummyelements
that have 14 segments,
if(itn.ge.4.and.itn.le.14)iflagd=1
ignore 1st
last
c
c --- check for fuel materials
c
if(itn.eq.24.or.itn.eq.124)then
lupfl(indf)=lup
indf=indf+l
endif
c
c --- check for aluminum tallies
c
to separate
a1200, a1300, and a1600
if(itn.eq.44.or.itn.eq.144)idmat=3
c
c --c
check for tally
4 and 14 to separate
2 cells
if(itn.eq.4.or.itn.eq.14)idmat=2
c
c --- check for imat=7 to separate the cells of tally 194
c
if(imat..eq.7)idmat=llw
c
90
c
llup=lup
lllw=llw
c
c do loop to separate cells in same tally
c
do 500 jj=lidmat
if(imat.eq.7)then
lup=lupfl(jj)
l1w=1up-12
if(ii.eq.2)ic=4
else
if(idmat.eq.3)then
if(jj,.eq.l)then
imat=2
endif
if(ii.eq-2)then
imat=3
ic=30
endif
if(jj.eq.3)then
imat=6
ic=60
endif
endif
c
c
c
if tally4 and 14 then take llw of both cells from call parameters
if(itn.eq.4)then
if(ii.eq.l)then
lup=lllw+l
endif
if(ii.eq.2)then
ic=1
llw=llup
lup=llup+2
endif
endif
if(itn.eq.14)then
if(jj.eq.l)then
lup=lllw+4
endif
if(ii.eq.2)then
ic=4
llw=llup
lup=llup+9
endif
endif
endif
c ----------------------------------------------------------------------CALCULATION OF TRIANGLE FLUX
c
TOTALS
c -----------------------------------------------------------------------do 410 ii=llwlup
imt=indl (ii, 5)
if(imat.eq.imt)then
if(ind.eq.O)then
ic=ic+l
ni 1=indl (i i, 4)
ni2=indl(ii+1,4)
ni3=indl(ii+2,4)
nct=indl(ii,3)
do 400 ie=1,3
imn=1
do 400 is=lnseg
c ignore lst segment ----------------------
iss=is
91
ind=O
isg=is+iflagd
c fmm = total
cellv
segment volume
fmm=12.
if(iflags.eq.l)then
iss=iss+5
fmm=6.4357647
if(isg.eq.1)fmm=14.768897
endif
if(iflags.eq.2)then
fmm=5.5642353
if(isg.eq.6)fmm=9.8615507
endif
cvl=cellv(ii)/fmm
cv2=cellv(ii+l)/fmm
cv3=cellv(ii+2)/fmm
if(nct.eq.O)then
c
x
x
trf(l,nil,iss,ie)=trf(l,nil,iss,ie)
+xdata(litieimnisgic)*cvl
trf(2,nil,iss,ie)=trf(2,nil,iss,ie)+
(xdata(l,it,ie,imn,isg,ic)*xdata(2,it,ie,imn,isg,ic)*cvl)**2
ind=O
c
elseif(nct.eq.l)then
c
x
x
trf(.lnil,iss,ie)=trf(l,nil,iss,ie)
+xdata(litieimnisgic)*cvl
trf(l,ni2,iss,ie)=trf(l,ni2,iss,ie)
+xdata(litieimnisgic)*cv2
x
trf(2,nil,iss,ie)=trf(2,nil,iss,ie)+
(xdata(l,it,ie,imn,isg,ic)*xdata(2,it,ie,imn,isg,ic)*cvl)**2
trf(2,ni2,iss,ie)=trf(2,ni2,iss,ie)+
x
(xdata(l,it,ie,imn,isg,ic)*xdata(2,it,ie,imn,isg,ic)*cv2)**2
c
ind=1
elseif(nct.eq.2)then
c
x
x
x
x
x
x
trf(l,nil,iss,ie)=trf(l,nil,iss,ie)
+xdata(litieimnisgic)*cvl
trf(l,ni2,iss,ie)=trf(l,ni2,iss,ie)
+xdata(litieimnisgic)*cv2
trf(l,ni3,iss,ie)=trf(l,ni3,iss,ie)
+xdata(litieimnisgic)*cv3
trf(2,nil,iss,ie)=trf(2,nil,iss,ie)+
(xdata(l,it,ie,imn,isg,ic)*xdata(2,it,ie,imn,isg,ic)*cvl)**2
trf(2,ni2,iss,ie)=trf(2,ni2,iss,ie)+
(xdata(l,it,ie,imn,isg,ic)*xdata(2,it,ie,imn,isg,ic)*cv2)**2
trf(2,ni3,iss,ie)=trf(2,ni3,iss,ie)+
(xdata(l,it,ie,imn,isg,ic)*xdata(2,it,ie,imn,isg,ic)*cv3)**2
ind=2
endif
imark=ii+nct
400
continue
else
ind=ind-1
endif
endif
410
500
600
if(imark.eq.lup.and.jj.eq.2)goto
continue
continue
continue
600
return
end
92
c
Program : xcgln.f
character*8 kodver
character*19 probid
character*79title
character*4ntalvals
character*5 tallykcode
character*2
fdusmcet
character*3 tfc
character*75
c
fcomment
integer indllupflindfnff
integer rnrpbnameptypecellntallyn
real cellvxdatatrr
dimension ebin(3)
dimension celln(62),tal1yn(35),xkeff(3)
dimension jtf(8)
c
common/datv/cellv(3659),indl(3659,5),lupfl(2),indf
common/datc/nff(35)
common/datx/xdata(2,35,3,5,14,62)common/rslt/trr(2,24,12,3,5)
c
c
xdata(2,35,
3, 5,14,70)
c
c
c
c
(2 nt, ne I ran, ns, nf
nt
tally
no :
ne
energy bin no.
nm
multiplier
no.
c
c
ns
nf
c
segment no.
cell no.
trr(2,24,12,
c
c
i
c
ni
c
c
3,
5)
(ininsnenm)
value, stdev pair
triangle
no
open(unit=13,file=lmcxllform=lformatted',status='old')
open(unit=19,file=lvol7l,form=lformatted',status='old')
open(unit=llfile=lxcl',form='formattedl,status='unknown')
open(unit=20,file=ltrrllform=lformattedl,status=lunknown')
c
c Start to read cell volume data from 'vol' file
c
ind=O
103
101
do 101 i=1,3659 read(19,103)(indl(i,k),k=1,2),cellv(i),(indl(i,j),j=3,5)
format(i6,xi6,1pel3.5,3(xi2))
continue
502
format(lxa79)
503
format(aCi6)
600
format(16i5)
read(13,501)kod,ver,probid,knod,nps,rnr
501 format(2a8,a19,i5,il1,i15) write(11,5011)kod,ver,probid,knod,nps,rnr
5011 format(ITally file:,/,Imcxll,2x,2a8,al9,i5,illil5)
c
read(13,502)title
c
read(13,503)ntalnt
c
read(13,600)(tallyn(i),i=lnt)
c
c ***** Start
tally
loop
c
do 100 n=lnt
read(13,504)tallypbnameptype
504
format (a5, 2 i5)
read(13,505)fcomment
505
format(5xa75)
read(13,506)fnff(n)
93
506
nf =nf f (n)
format(a2,i8)
507
format (1 1 i7)
read(13,507)(celln(i),i=1,nf)
read(13,506)didumm
read(13,506)uidumm
read(13,506)sns
read(13,506)mnm
if(nm.eq.o)nm=l
read(13,506)cnc
if(nc-eq.O)nc=l
508
509
format(a2,i8,i4)
format(lp6e13.5)
read(13,506)ene
read(13,509)(ebin(i),i=1,ne)
read(13,506)tidumm
read(13,510)vals
510
format(a4)
c
c Read list of tally/error
c
data pairs
read(13,511)(((((xdata(it,n,ie,im,is,ic),it=1,2),
511
1025
x ie=lne),im=lnm),is=lns),ic=lnf)
format(4(1pe13.5,Opf7.4))
format(i3,xi5,1p1Oe1O.3)
c
c Read tally
c
512
fluctuation
data
read(13,512)tfc,nfc,(jtf(i),i=1,8)
format(a3,i5,8i8)
do 150 j=lnfc
read(13,513)npsxtallyxerrfom
513
150
format(illlp3e13.5)
continue
c
c ***** End of tally
100
continue
loop
c
c Read kcode data
c
read(13,3000,end=999)kcode,ncycle
3000 format(a5,i5)
c
do 200 ncy=1,ncycle
read(13,3010,end=998)(xkeff(k),k=1,3),dummyl,dummy2
200
continue
3010 format(lp5el2.5)
c
998
continue
999
continue
c
c
• Processing xdata and frac and cellv to get triangle
•
call parameters (imatllwlupititncalln)
sections c
c
•
•
•
•
•
•
imat:
llw
lup
it
itn
calln:
material number to fetch from cell volume array
starting line number cell volume to be found the array
final line number to find cell volume
order of tally in mcx file no. iu
problem number of tally(only used in if statements)
variable to count no of calls from main
c
indf=1
call tri(4,1,152,6,64,1)
94
call tri(1,1,152,7,74,2)
call tri(2,1,152,8,84,3)
call tri(0,153,511,9,94,4)
call
call
call
call
call
tri(5,155,158,10,104,5)
tri(5,514,521,11,114,6)
tri(4,292,510,15,164,7)
tri(1,292,510,16,174,8)
tri(2,292,510,17,184,9)
call tri(7,2,0,19,204,10)
do ilk=1,2 write(20,555)((((trr(ilk,ijk,l),1=1,5),k=1,3),j=1,12),i=1,24)
555
format(lp5e13.5)
end do
c
stop
end
subroutinetri(imatl1w,1upititnncall)
c
integer indllupflindfnff
real cellvxdatatrr
common/datv/cellv(3659),indl(3659,5),lupfl(2),indf
common/datc/nff(35)
common/datx/xdata(2,35,3,5,14,62)
common/rslt/trr(2,24,12,3,5)
c
write(11,1001)imat,llw,lup,it,itn,jale
1001 format(5xltri
,6i8)
c
ic=O
idmat=1
iflagd=O
iflags=O
nseg=12
nm=3
c
c ---
check for dummy elements that
have 14 segments,
if(itn.ge.94.and.itn.le.114)iflagd=1
ignore
1st
last
c
c --- check for fuel materials to assign no. of multipliers
c
if(itn.eq.64.or.itn.eq.164)then
nm=5
lupfl(indf)=lup
indf=indf+l
endif
c
c --c
check for aluminum tallies
to separate
a1200, a1300, and a1600
if(itn.eq.84.or.itn.eq.184)idmat=3
c
c --- check for tally 94 to separate 2 cells
c
if(itn.eq.94)idmat=2
c
c --- check for imat=7 to separate the cells of tally 204
c
c
if(imat.eq.7)idmat=llw
llup=lup
lllw=llw
c
c do-loop to separate cells in same tally
c
do 500 jj=lidmat
if(imat.eq.7)then
lup= lupf 1 (j j )
95
c
llw=lup-12
else
if(jj.eq-2)ic=4
if(idmat.eq.3)then
if(j1j.eq.1)then
. imat=2
endif
if(ii-eq-2)therk
imat=3
ic=30
endif
if(ji.eq.3)then
imat=6
ic=60
endif
endif
c
c
if tally94 then take llw of both cells from call parameters
c
if(itn.eq.94)then
if(jj-eq.1)then
lup=lllw+l
endif
if(ji.eq.2)then
ic=1
llw=llup
lup=llup+2
endif
endif
endif
c ----------------------------------------------------------------------c
CALCULATION OF TRIANGLE REACTION RATE TOTALS
c -----------------------------------------------------------------------ind=O
do 410 ii=llwjup
imt=indl(ii,5)
if(imat.eq.imt)then
if(ind.eq.O)then
ic=ic+l
nil=indi(ii,4)
ni2=indl(ii+1,4)
ni3=indl(ii+2,4)
nct=indl(ii,3)
do 400 ie=1,3
do 400 im=lnm
do 400 is=lnseg
• ignore 1st segment ----------------------
iss=is
isg=is+iflagd
• fmm
total
cellv
segment volume
fmm=12.
if(iflags.eq.1)then
iss=iss+5
fmm=6.4357647
if(isg.eq.1)fmm=14.768897
endif
if(iflags.eq.2)then
fmm=5.5642353
if(isg.eq.6)fmm=9.8615507
c fuel multiplier
endif
adjustment
imn=iM
if(imat.eq.4.and.im.le.3)imn=im+2
if(imat.eq.4-and.im.gt.3)imn=im-3
96
cvl=cellv(ii)/fmm
cv2=cellv(ii+l)/fmm
cv3=cellv(ii+2)/fmm
if(nct.eq.O)then
c
x
x
trr(.Inil,iss,ie,im)=trr(l,nil,iss,ie,im)
+xdata(litieimnisgic)*cvl
trr(2,nil,iss,ie,im)=trr(2,nil,iss,ie,im)+
(xdata(l,it,ie,imn,isg,ic)*xdata(2,it,ie,imn,isg,ic)*cvl)**2
c
ind=O
elseif(nct.eq.l)then
c
x
x
x
x
trr(l,nil,iss,ie,im)=trr(l,nil,iss,ie,im)
+xdata(litieimnisgic)*cvl
trr(l,ni2,iss,ie,im)=trr(l,ni2,iss,ie,im)
+xdata(litieimnisgic)*cv2
trr(2,nil,iss,ie,im)=trr(2,nil,iss,ie,im)+
(xdata(l,it,ie,imn,isg,ic)*xdata(2,it,ie,imn,isg,ic)*cvl)**2
trr(2,ni2,iss,ieim)=trr(2,ni2,iss,ie,im)+
(xdata(l,it,ie,imn,isg,ic)*xdata(2,it,ie,imn,isg,ic)*cv2)**2
c
ind=1
elseif(nct.eq.2)then
c
x
x
x
x
x
trr(l,nil,iss,ie,im)=trr(l,nil,iss,ie,im)
+xdata(litieimnisgic)*cvl
trr(l,ni2,iss,ie,im)=trr(l,ni2,iss,ie,im)
+xdata(litieimnisgic)*cv2
trr(l,ni3,iss,ie,im)=trr(l,ni3,iss,ie,im)
+xdata(litieimnisgic)*cv3.
trr(2,nil,iss,ie,im)=trr(2,nil,iss,ie,im)+
(xdata(l,it,ie,imn,isg,ic)*xdata(2,it,ie,imn,isg,ic)*cvl)**2
trr(2,ni2,iss,ieim)=trr(2,ni2,iss,ie,im)+
(xdata(l,it,ie,imn,isg,ic)*xdata(2,it,ie,imn,isg,ic)*cv2)**2
trr(2,ni3,iss,ieim)=trr(2,ni3,iss,ie,im)+
x
(xdata(l,it,ie,imn,isg,ic)*xdata(2,it,ie,imn,isg,ic)*cv3)**2
c
ind=2
endif
imark=ii+nct
400
continue
else
ind=ind-1
endif
endif
410
500
600
if(imark.eq.lup.and.jj.eq.2)goto
continue
continue
continue
600
return
end
Program : prohxln.f
program prohx1n
c This program processes mctal file of input file outhx2
character*8 kodver
character*19 probid
character*79title
character*4ntalvals
character*5 tallykcode
character*2
fdusmcet
97
character*3 tfc
character*75
c
fcomment
integer tal1yn(56),pbnameptypenff(90)
dimensionxkeff(3),ebin(3),jtf(8)
c
dimension celln(10000),fldat(2,3,12,5000),rrdat(2,3,5,12,5000)
dimensiontrf(2,40,20,12,3),trr(2,40,20,12,3,5)
dimension nj(9),kl(9),k2(9),jj(9,32),il(9,32),i2(9,32),nseq(9,32)
itri(40,20)
dimension cvo1(5,2166),no(5,2166),nom(5)
dimension cvol2(5,2166),no2(5,2166),nom2(5)
dimension voltr(40,20,12,3)
dimension flx(40,20,12,3),totxs(40,20,12,3),absxs(40,20,12,3)
dimension elsct(40,20,12,3),diffc(40,20,12,3),fisnu(40,20,12,3)
dimension fisxs(40,20,12,3)
c
rea1*8 stflx,sttxs,staxs,stels,stfxs,stfnu
dimension stflx(40,20,12,3),sttxs(40,20,12,3),staxs(40,20,12,3)
dimension stels(40,20,12,3),stfxs(40,20,12,3),stfnu(40,20,12,3)
c
open(unit=llfile=lhxln.oul,form=lformattedl,status=lunknown')
open(unit=12,file='inpt',form='formattedl,status=loldl)
open(unit=13,file=lmcxohl,form--'formattedl,status=loldl)
open(unit=14,file=ltlistall,form='formatted',status=lunknown')
open(unit=15,file=ltri6OO.l',form='formattedl,status=loldl)
open(unit=16,file='vale',form='formattedl,status=loldl)
open(unit=17,file='vale2l,form=lformattedl,status=loldl)
open(unit=18,file=ltlista3l,form='formatted',status=lold')
open(unit=20,file=ldebug.ol,form='formattedl,status='unknown')
c
• Sequential reading from mctal file, first fluxes then reaction rates
• After data has been read subroutines process the data and add it to the
• triangle totals of fluxes or reaction rates.
write(11,10)
10
format(///5x,'PROHX1.F
- AN MCNP TALLY PROCESSING PROGRAM',//)
c
c Reading the general info about tallies
c
(not to be processed)
read(13,501)kod,ver,probid,knod,nps,rnr
501
format(2a8,a19,i5,i11,i15)
502
format(lxa79)
write(11,5011)kod,ver,probid,knod,nps,rnr
5011 format('Tally file:,/,'mcxohl,2x,2a8,al9,i5,illil5)
c
read(13,502)title
write(11,502)title
c
c
nt=56
read(13,503)ntalnt
503
format(a5,i5)
600
format (16i5)
c
read(13,600Htallyn(i),i=1,nt)
c
c ***** Start
tally
loop
c
nfkeepl=l
nfkeep2=0
nfkeep3=1
nfkeep4=0
do 100 n=lnt
read(13,504)tallypbnameptype
504
format(a5,2i5)
98
dimension
read(13,505)fcomment
505
506
format(5xa75)
read(13,506)fnff(n)
format(a2,A)
nf=nff(n)
if(n.le.17)then
nfkeepl=nfkeep2+1
nfkeep2=nfkeep2+Df
endif
if(n.gt.17)then
nfkeep3=nfkeep4+1
nfkeep4=nfkeep4+nf
endif
if(n.le-17)read(13,507) (celln(i),i=nfkeeplnfkeep2)
if(n.gt.17)read(13,507) (celln(i),i=nfkeep3,nfkeep4)
507
format(11i7)
read(13,506)didumm
read(13,506)uidumm
read(13,506)sns
if(ns.eq.O)ns=l
read(13,506)mnm
if(nm.eq.O)nm=l
509
read(13,506)cnc
if(nc.eq.O)nc=l
read(13,506)ene
read(13,509)(ebin(i),i=1,ne-1)
format(lp6el3.5)
read(13,506)tidumm
read(13,510)vals
510
format(a4)
c
c Readlist of tally/error data pairs
c
if(n.le.17)then
read(13,511)((((fldat(it,ie,is,ic),it=1,2),
511
x ie=1,3),is=lns),ic=nfkeepl,nfkeep2)
format(4(1pe13.5,Opf7.4))
endif
if(n..gt.17)then
read(13,511)(((((rrdat(it,ie,im,is,ic),it=1,2),
x ie=1,3),im=lrim),is=lns),ic=nfkeep3,nfkeep4)
endif
c
c Read tally fluctuation
c
data
read(13,512)tfc,nfc,(jtf(i),i=1,8)
512
format(a3,i5,8i8)
do 150 j=lnfc
read(13,513)npsxtallyxerrfom
513
150
format(illlp3el3.5)
continue
c
c ***** End of tally
loop
100 continue
c
c Read kcode data
c
read(13,3000,end=999)kcode,ncycle
3000 format(a5,i5)
do 200 ncy=lncycle
read(13,3010,end=999)(xkeff(k),k=1,3),dummyl,dummy2
99
200 continue
3010 format(lp5el2.5)
999 continue
c
c Multiplier
sequence change for detector uranium coatings c
do 778 ic=1,2166
if((ic.ge.
213.and.ic.le. 248).or.
x
(ic-ge.2107.and.ic.le.2112).or.
x
(ic.ge.2125.and.ic.le.2130).or.
x
(ic.ge.2143.and.ic.le.2148))then
do 777 it=1,2
do 777 ie=1,3
do 777 is=1,12
xxl=rrdat(itielisic)
777
continue
778
continue
xx2=rrdat(itie,2,isic)
rrdat(it,ielis,ic)=rrdat(it,ie,3,is,ic)
rrdat(it,ie,2,is,ic)=rrdat(it,ie,4,is,ic)
rrdat(it,ie,3,is,ic)=rrdat(it,ie,5,is,ic)
rrdat(itie,4,isic)=xxl
rrdat(itie,5,isic)=xx2
endif
c
c Read segment volume data from vale
c
do 413 ill=1,2166
read(16,1(2i6,5(lpel3.5,i3))I)ic,noc,cvol(l,ill),no(l,ill),
x cvol(2,ill),no(2,ill),cvol(3,ill),no(3,ill),cvol(4,ill),
x no(4,i.11),cvol(5,ill),no(5,ill)
413 continue
c same for trr from vale2
do 531 ill=1,2166
read(17,1(2i6,5(lpel3.5,i3))I)ic,noc,cvol2(l,ill),no2(l,ill),
x
vol2(2,ill),no2(2,ill),cvol2(3,ill),no2(3,ill),cvol2(4,ill),
no2(4,ill),cvol2(5,ill),no2(5,ill)
531
continue
c
c Read cell number to triangle
number conversion data from inpt
c
read(12,301) (nj(n),n=1,9)
read(12,301) (kl(ik),ik=1,9)
read(12,301)
301
k2(ik),ik=1,9)
format(9i3)
do 101 ii=1,9
read(12,302)(jj(iiij),ij=lnj(ii))
101 continue
do 102 ii=1,9
read(12,302)(il(iiiin),iin=lnj(ii))
read(12,302)(i2(iiiin),iin=lnj(ii))
302
102
format (23i3)
continue
do 103 isq=1,9
read(12,303) (nseq(isqiin),iin=1,nj(isq))
303
103
format(14i5)
continue
do 110 ng=1,9
do
1 1 0 nn= 1, n
(ng)
do 110 ie=1,2
do 110 i=il(ngnn),i2(ngnn)
do 110 k=kl(ng),k2(ng),-l
100
x
j=jj (ng,-)
ic=nseq(ngnn)+i-il(ngnn)
is=kl(ng)+l-k
nom(1)=no(1,ic)
nom(2)=no(lic)+no(2,ic)
nom(3)=no(l,ic)+no(2,ic)+no(3,ic)
nom(4)=no(l,ic)+no(2,ic)+no(3,ic)+no(4,ic)
nom(5)=no(l,ic)+no(2.,ic)+no(3,ic)+no(4,ic)+no(5,ic)
if(is.le.nom(1))cvlm=cvo1(1,ic)
if(is.gt.nom(l).and.is.le.nom(2))cvlm=cvol(2,ic)
if(is.gt.nom(2).and.is.le.nom(3))cvlm=cvol(3,ic)
if(is.gt.nom(3).and.is.le.nom(4))cvlm=cvol(4,ic)
if(is.gt.nom(4).and.is.le.nom(5))cvlm=cvol(5,ic)
x
110
trf(l,ijk,ie)=trf(l,i,jk,ie)+fldat(l,ie,is,ic)*cvlm
voltr(ijk,ie)=voltr(ijk,ie)+cvlm
trf(2,ijk,ie)=trf(2,ijk,ie)+(fldat(l,ie,is,ic)*cvlm*
fldat(2,ieisic))**2
continue
c
c
the same thing for trr data from vale2 and inpt
c
read(12,301) (nj(n),n=1,9)
read(12,301) (kl(ik),ik=1,9)
read(12,301) (k2(ik),ik=1,9)
do 191 ii=1,9
191 continue
read(12,302)(jj(iiij),ij=1,nj(ii))
do 192 ii=1,9
read(12,302)(i1(iiiin),iin=Inj(ii))
read(12,302)(i2(iiiin),iin=1,nj(ii))
192 continue
do 193 isq=1,9
read(12,303) (nseq(isqiin),iin=1,nj(isq))
193
continue
do 111 ng=1,9
do
1 1 1 nn= 1, nj (ng)
do 111 ie=-1,2
do 111 i=il(ngnn),i2(ngnn)
do 111 k=kl(ng),k2(ng),-l
ic=nseq(ngnn)+i-il(ngnn)
is=kl(ng)+l-k
nom2(1)=no2(lic)
nom2(2)=no2(lic)+no2(2,ic)
nom2(3)=no2(l,ic)+no2(2,ic)+no2(3,ic)
nom2(4)=no2(l,ic)+no2(2,ic)+no2(3,ic)+no2(4,ic)
nom2(5)=no2(l,ic)+no2(2,ic)+no2(3,ic)+no2(4,ic)+no2(5,ic)
if(is.le.nom2(l))cvlm=cvol2(l,ic)
if(is.gt.nom2(l).and.is.le.nom2(2))cvlm=cvol2(2,ic)
if(is.gt.nom2(2).and.is.le.nom2(3))cvlm=cvol2(3,ic)
if(is.gt.nom2(3).and.is.le.nom2(4))cvlm=cvol2(4,ic)
if(is.gt.nom2(4).and.is.le.nom2(5))cvlm=cvol2(5,ic)
do 111 im=1,5
trr(l,i,jk,ie,im)=trr(l,i,jk,ie,im)+rrdat(l,ie,im,isic)*cvlm
trr(2,i,jk,ieim)=trr(2,i,jk,ie,im)+(rrdat(l,ie,im,is,ic)*
x
111 continue
cvlm* rrdat(2,ieimisic))**2
c
c
Read the rest of the conversion data for flux from tlistal
c
do 312 loop=1,846
read(14,1(i6,i6,4i3,i6)',end=313)isqn,ncl,i,jktopkbot,idm2
nom(l)=no(lic)
nom(2)=no(lic)+no(2,ic)
101.
ic=isqn
nom(3)=no(l,ic)+no(2,ic)+no(3,ic)
nom(4)=no(l,ic)+no(2,ic)+no(3,ic)+no(4,ic)
nom(5)=no(l,ic)+no(2,ic)+no(3,ic)+no(4,ic)+no(5,ic)
do 312 ie=1,2
do 312 k=ktopkbot,-l
is=ktop+l-k
if(is.le.nom(l))cvlm=cvol(lic)
if(is.gt.nom(l).andis.le.nom(2))cvlm=cvol(2,ic)
if(is.gt.nom(2).and.is.le.nom(3))cvlm=cvol(3,ic)
if(is.gt.nom(3).and.is.le.nom(4))cvlm=cvol(4,ic)
if(is.gt.nom(4).and.is.le.nom(5))cvlm=cvol(5,ic)
trf(l,,i,jk,ie)=trf(l,i,jkie)+fldat(l,ie,is,ic)*cvlm
voltr(ijk,ie)=voltr(ijk,ie)+cvlm
x
312
trf(2,,i,jk,ie)=trf(2,i,jk,ie)+(fldat(lie,is,ic)*cvlm*
fldat(2,ieisic))**2
continue
c
c
end tlistal
c
313
continue
c
c
Continue for trr data from tlista3
c
do 412 loop=1,846
read(18,'(i6,i6,4i3,i6)1,end=433)isqn,ncl,i,jktopkbot,idm2
nom2(1)=no2(lic)
nom2(2)=no2(lic)+no2(2,ic)
ic=isqn
nom2(3)=no2(l,ic)+no2(2,ic)+no2(3,ic)
nom2(4)=no2(l,ic)+no2(2,ic)+no2(3,ic)+no2(4,ic)
nom2(5)=no2(l,ic)+no2(2,ic)+no2(3,ic)+no2(4,ic)+no2(5,ic)
do 412 ie=1,2
do 412 k=ktopkbot,-l
is=ktop+l-k
if(is.le.nom2(l))cvlm=cvol2(l,ic)
if(is.gt.nom2(l).and.is.le.nom2(2))cvlm=cvol2(2,ic)
if(is.gt.nom2(2).and.is.le.nom2(3))cvlm=cvol2(3,ic)
if(is.gt.nom2(3).and.is.le.nom2(4))cvlm=cvol2(4,ic)
if(is.gt.nom2(4).and.is.le.nom2(5))cvlm=cvol2(5,ic)
do 412 im=1,5
trr(l,i,jk,ie,im)=trr(l,i,jk,ie,im)+rrdat(l,ie,imisic)*cvlm
trr(2,i,jk,ieim)=trr(2,i,jk,ie,im)+(rrdat(l,ie,im,is,ic)*
412
x
continue
cvlm*rrdat(2,ieimisic))**2
c
c
end tlistal
c
433
continue
c
do 882 j=1,20
read(15,881,end=882)(itri(i,i),i=1,40)
881
882
format(4Oi4)
continue
c
c
c
Final processing to get volume averaged flux and cross sections
also diffusion coefficient
c
do 911 j=1,20
do 911 i=1,40
if(itri(ij).ne.O)then
do 912 k=1,12
do 912 ie=1,3
c if the flux is not zero, process cross sections
if(trf(lijkie)
ne. 0.0)then
102
flx(ijk,ie)=trf(l,i,jk,ie)/voltr(i,jk,ie)
totxs(ijk,ie)=trr(l,ijk,ie,2)/trf(l,i,jk,ie)
absxs(ijk,ie)=trr(l,ijk,iel)/trf(l,i,jk,ie)
elsct(ijk,ie)=trr(l,ijkie,3)/trf(l,ijk,ie)
diffc(i,jk,ie)=l/(3*totxs(ijk,ie))
fisnu(ijk,ie)=trr(l,i,jk,ie,4)/trf(l,i,jk,ie)
fisxs(I.,jk,ie)=trr(l,ijk,ie,5)/trf(l,i,jk,ie)
stflx(ijk,ie)=(sqrt(trf(2,i,jk,ie)))/trf(l,ijk,ie)
c
sttxs(ijk,ie)=sqrt(trr(2,i,jk,ie,2)/
• trr(l,i,jk,ie,2)**2+trf(2,i,jk,ie)/trf(l,i,jk,ie)**2)
staxs(ijk,ie)=sqrt(trr(2,i,jk,iel)/
• trr(l,ijk,iel)**2+trf(2,ijk,ie)/trf(l,ijk,ie)**2)
•
if(fisnu(ijkie).ne.0.0)then
stfnu(ijk,ie)=sqrt(trr(2,i,jk,ie,4)/
trr(l,i,jk,ie,4)**2+trf(2,i,jk,ie)/trf(l,i,jk,ie)**2)
stfxs(ijk,ie)=sqrt(trr(2,i,jk,ie,5)/
• trr(l,ijk,ie,5)**2+trf(2,ijk,ie)/trf(l,i,jk,ie)**2)
endif
endif
912
continue
911
continue
endif
c
c
Write the results
to the file hxl.out
c
write(11,466)
466
format(/,,Note:
gp#1 = fast gp and, gp#2
thermal gp.,,/)
write(11,461)
461
formatP
•
•
I
J
K -,9x,-FLUX
TT.XSECTION stdev
stdevl,2x,'DIFF.COEFF.
ABS.XSECTION stdevllx,
NU*FISS.XSECstdevl,2x,'FISS.XSECT
stdev')
do 894 j=1,20
do 894 i=1,40
if(itri(ij).ne.O)then
do 896 k=1,12
kplus=k+4
write(11,462)ijkplus
896
894
• totxs(ijk,2),sttxs(ijk,2),absxs(i,jk,2),staxs(i,jk,2),
write(11,463)flx(ijk,2),stflx(i,jk,2),diffc(i,jk,2),
fisnu(i,jk,2),stfnu(i,jk,2),fisxs(i,jk,2),stfxs(i,jk,2)
write(11,464)flx(ijk,l),stflx(ijk,l),diffc(i,jk,l)I
x
x totxs(i,jk,l),sttxs(i,jk,l),absxs(i,jk,l),staxs(i,jk,l),
x
fisnu(ijk,l),stfnu(i,jk,l),fisxs(i,jk,l),stfxs(i,jk,l)
continue
endif
continue
c
462 format(3i4,1
g#.)
463
format(14x
1
464
format(14x
2 ',lpel3.5,Opf6.3,lpel3.5,4(lpel3.5,Opf6.3))
stop
lpel3.5,Opf6.3,lpel3.5,4(lpel3.5,Opf6.3))
end
Program : prohx2n.f
program prohx2n
c This program processes mctal file of input file outhx2
character*8 kodver
character*19 probid
character*79title
character*4ntalvals
character*5 tallykcode
103
c
character*2
fdusmcet
character*3 tfc
character*75
c
fcomment
integer tallyn(56),pbnameptypenff(90)
dimensionxkeff(3),ebin(3),jtf(8)
c
dimension celln(10000),fldat(2,3,12,5000),rrdat(2,3,5,12,5000)
dimension trf(2,60,30,4,3),trr(2,60,30,4,3,3)
dimension itri(40,20),itribig(60,30)
dimension cvol(5,2166),no(2),nom(2)
dimension voltr(60,30,4,3)
dimension flx(60,30,4,3),totxs(60,30,4,3),absxs(60,30,4,3)
dimensionelsct(60,30,4,3),diffc(60,30,4,3)
c
real*8 stflxsttxsstaxsstels
dimensionstflx(40,20,12,3),sttxs(40,20,12,3),staxs(40,20,12,3)
dimension stels(40,20,12,3)
c
open(unit=llfile=lhx2n.oul,form=lformattedl,status=lunknown')
open(unit=13,file=lmclOtlform=lformattedl,status=loldl)
open(unit=14,file=ltccl.c2l,form=lformatted',status=lunknown')
open(unit=15,file=ltri6OO.2',form='formatted',status=loldl)
open(unit=16,file=lvvva.c2l,form=lformatted',status=lold')
c
• Sequential reading from mctal file, first fluxes then reaction rates
• After data has been read subroutines process the data and add it to the
• triangle totals of fluxes or reaction rates.
write(11,10)
10
format(///5x,'PROHX2.F
- AN MCNP TALLY PROCESSING PROGRAM',//)
c
c Reading the general info about tallies
c
(not to be processed)
read(13,501)kod,ver,probid,knod,nps,rnr
501 format(2a8,al9,i5,illil5)
write(11,5011)kod,ver,probid,knod,nps,rnr
5011 format(ITally file:,/,ImclOtl,2x,2a8,al9,i5,illil5)
c
read(13,502)title
502
format(lxa79)
write(11,502)title
c
c
nt=56
read(13,503)ntalnt
503
format(aSi5)
600
format(16i5)
c
read(13,600)(tallyn(i),i=1,nt)
c
c ***** Start tally loop
c
nfkeepl=l
nfkeep2=0
nfkeep3=1
nfkeep4=0
do 100 n=lnt
read(13,504)tallypbnameptype
504
format(a5,M)
read(13,505)fcomment
505
506
format(5xa75)
read(13,506)fnff(n)
format(a2,A)
nf=nff(n)
if(n.le.18)then
104
nfkeepl=nfkeep2+1
nfkeep2=nfkeep2+nf
endif
if(n.gt.18)then
nfkeep3=nfkeep4+1
nfkeep4=nfkeep4+nf
endif
if(n.le.18)read(13,507) (ce11n(i),i=nfkeep1,nfkeep2)
ifi:n.gt.1S)read(13,507) (celln(i),i=nfkeep3,nfkeep4)
507
format(110)
read(13,506)didumm
read(13,506)uidumm
read(13,506)sns
if(ns.eq.O)ns=l
read(13,506)mnm
if(nm.eq.O)nm=l
read(13,506)cnc
if(nc.eq.O)nc=l
read(13,506)ene
read(13,509)(ebin(i),i=1,ne-1)
509
format(lp6e13.5)
read(13,506)tidumm
read(13,510)vals
510
format(a4)
c Readlist of tally/error
c
data pairs
if(n.le.18)then
read(13,511)((((fldat(it,ie,is,ic),it=1,2),
511
x ie=1,3),is=lns),ic=nfkeepl,nfkeep2)
format(4(1pe13.5,Opf7.4))
endif
if(n.gt.18)then
read(13,511)(((((rrdat(it,ie,im,is,ic),it=1,2),
x ie=1,3),im=lnm),is=lns),ic=nfkeep3,nfkeep4)
endif
c
c Read tally
c
fluctuation
data
read(13,512)tfc,nfc,(jtf(i),i=1,8)
512
format(a3,i5,8i8)
do 150 j=lnfc
read(13,513)npsxtallyxerrfom
513
150
format(illlp3el3.5)
continue
c
c ***** End of tally
100 continue
loop
c
c Read kcode data
c
read(13,3000,end=999)kcode,ncycle
3000 format(a5,i5)
do 200 ncy=1,ncycle
read(13,3010,end=999)(xkeff(k),k=1,3),dummyl,dummy2
200 continue
3010 format(lp5el2.5)
999 continue
c
c Read segment volume data from vvva.c2
c
x
do 413 ic=1,1210 if((ic.le.36).or.(ic.gt.78.and.ic.le.300).or.
(ic.gt.540.and.ic.le.570).or.
105
x
(ic.gt.642.and.ic.le.846).or.
x
(ic.gt.846.and.ic-le-1102))then
read(16,*,end=417)ic,cvol(l,ic),cvol(2,ic)
endif
if((ic.gt.36.and.ic.le.78).or.
x
x
x
(ic.gt.300.and.ic.le.462).or.
(ic.gt.570.and.ic.le.642).or.
(ic.gt.462.and.ic-le-540).or.(ic.gt.1102))then
read(16,*,end=417)iccvol(lic)
endif
413 continue
417 continue
c
c
Read the rest of the conversion data for flux from tccl.c
c
do 312 loop=1,1210
if((loop.le.36).or.(loop.gt.78.and.loop.le.300).or.
x
x
(loop.gt.540.and.loop.le.570).or.
(loop.gt.642.and.loop.le.846))then
no(1)=1
no(2)=l
ktop=4
kbot=3
endif
if(loop.gt.36.and.loop.le.78)then
no(1)=1
ktop=4
kbot=4
endif
if((loop.gt.300.and.loop.le.462).or.
x
(loop.gt.570.and.loop.le.642))then
no(1)=1
ktop=3
kbot=3
endif
if((loop.gt.462.and.loop.le.540).or.(loop.gt.1102))then
no(l)=4
ktop=4
kbot=1
endif
if(loop.gt.846.and.loop.le.1102)then
no(1)=1
no(2)=2
ktop=3
kbot=l
endif
nom(l)=no(l)
nom(2)=no(l)+no(2)
read(14,'(i6,i6,2i3)',end=313)isqn,ncl,ij
ic=isqn
do 312 ie=1,2
do 312 k=ktopkbot,-l
is=ktop+l-k
if(is.le.nom(l))cvlm=cvol(lic)
if(is.gt.nom(l).and.is.le.nom(2))cvlm=cvol(2,ic)
x
trf(l,ijk,ie)=trf(l,i,jk,ie)+fldat(l,ie,is,ic)*cvlm
voltr(i,jk,ie)=voltr(ijk,ie)+cvlm
trf(2,ijk,ie)=trf(2,ijk,ie)+(fldat(l,ie,is,ic)*cvlm*
fldat(2,ieisic))**2
if(ic.eq.918)then
trf(1,19,8,k,ie)=trf(1,19,8,k,ie)+fldat(l,ie,is,ic)*cvlm
vo.itr(19,8,k,ie)=voltr(19,8,k,ie),+cvlm
trE(2,19,8,k,ie)=trf(2,19,8,k,ie)+(fldat(l,ie,is,ic)*cvlm*
fldat(2,ieisic))**2
106
x
endif
do 312 im=1,3
trr(l,i,jk,ie,im)=trr(l,ijk,ie,im)+
x
rrdat(lieimisic)*cvlm
trr(2,i,jk,ie,im)=trr(2,i,jk,ie,im)+(rrdat(l,ie,imis,ic)*
cvlm* rrdat(2,ieimisic))**2
x
if(ic.eq.918)then
trr(1,19,8,k,ie,im)i=trr(1,19,8,k,ie,im)+
x
rrdat(lieimisic)*cvlm
trr(2,19,8,k,ie,im)=trr(2,19,8,k,ie,im)+(rrdat(l,ieim,is,ic)*
endif
312
x
cvlm* rrdat(2,ieimisic))**2
continue
c
c
end tccl.c
c
313
continue
c
c
c
read triangle
mesh from tri6OO.2
c
do 882 j=1,20
read(15,881,end=882)(itri(i,j),i=1,40)
881
882
format(4M)
continue
do 885 j=21,30
read(15,886,end=885)(itribig(i,j)li=41,60
886
format(2M)
885 continue
c
•
Final processing to get volume averaged flux and cross sections
•
also diffusion coefficient
c
do 911 j=1,20
do 911 i=1,40
if(itri(ij).ne.O)then
do 912 k=1,4
do 912 ie=1,3
c if the flux is zero set xsections to zero automatically
if(trf(lijkie)
ne. 0.0)then
flx(ijk,ie)=trf(l,i,jk,ie)/voltr(i,jk,ie)
totxs(ijk,ie)=trr(l,ijk,ie,2)/trf(l,ijk,ie)
absxs(i,jk,ie)=trr(l,i,jk,iel)/trf(l,i,jk,ie)
elsct(ijk,ie)=trr(l,ijkie,3)/trf(l,ijk,ie)
if(totxs(ijkie).ne. 0.)diffc(i,jk,ie)=l/(3*totxs(ijk,ie))
c
stflx(i,jk,ie)=(sqrt(trf(2,i,jk,ie))-)/trf(l,ijk,ie)
sttxs(i,jk,ie)=sqrt(trr(2,i,jk,ie,2)/
• trr(l,i,jk,ie,2)**2+trf(2,i,jk,ie)/trf(l,i,jk,ie)**2)
staxs(ijk,ie)=sqrt(trr(2,i,jk,iel)/
• trr(,li,jk,iel)**2+trf(2,i,jk,ie)/trf(l,i,jk,ie)**2)
endif
912
continue
911
continue
endif
c
c
Write the results
to the file hx2.ou
c
write(11,466)
466
formatU,'Note:
gp#l = fast gp and, gp#2
thermal gp.',/)
write(11,461)
461
format('
x
I
i
K 1,9x,'FLUX
TT.XSECTION stdev
stdevl,2x,'DIFF.COEFF.
ABS.XSECTION stdevl)
107
,
do 894 j=1,20
do 894 i=l
40
if(itri(ij).ne.O)then
do 896 k=1,4
write(11,462)iik
write(11,463)flx(ijk,2),stflx(ijk,2),diffc(ijk,2),
write11,464)flx(ijk,;),stflx(i,jk,l),diffc(i,jk,l),
• totxs(ijk,2),sttxs(ijk,2),absxs(i,jk,2),staxs(i,jk,2)
• totxs(i,j;k,l),sttxs(i,jk,l),absxs(i,jk,l),staxs(i,jk,l)
896
continue
endif
894
continue
c
c
graphite reflector
c
do 941 j=21,30
do 941 i=41,60
if(itribig(ij).ne.O)then
do 942 k=1,4
do 942 ie=1,3
c if the flux is zero set xsections to zero automatically if(trf(lijkie)
.ne. 0.0)then
flx(ijk,ie)=trf(l,ijk,ie)/voltr(ijk,ie)
totxs(ijk,ie)=trr(l,ijk.,ie,2)/trf(l,i,jk,ie)
absxs(i,jk,ie)=trr(l,i,jk,iel)/trf(l,i,jk,ie)
elsct(ijk,ie)=trr(l,ijkie,3)/trf(l,ijk,ie)
if(totxs(ijkie).ne. 0.)diffc(i,jk,ie)=l/(3*totxs(ijk,ie))
c
stflx(ijk,ie)=(sqrt(trf-(2,i,jk,ie)))/trf(l,ijk,ie)
sttxs(ijk,ie)=sqrt(trr(2,i,jk,ie,2)/
• trr(l,i,jk,ie,2)**2+trf(2,ijk,ie)/trf(l,ijk,ie)**2)
staxs(ijk,ie)=sqrt(trr(2,i,jk,iel)/
• trr(l,ijk,iel)**2+trf(2,ijk,ie)/trf(l,ijk,ie)**2)
endif
942
continue
941
continue
c
c
endif
Write the results
to the file hx2.ou
c
do 994 j=21,30
do 994 i=41,60
if(itribig(ii).ne.O)then
do 996 k=1,4
imin=i-40
jmin=j-20
write(11,465)iminjmink
write(11,463)flx(ijk,2),stflx(ijk,2),diffc(i,jk,2)I
write(11,464)flx(ijk,l),stflx(i,jk,l),diffc(i,jk,l),
• totxs(i,jk,2),sttxs(i,jk,2),absxs(i,jk,2),staxs(i,jk,2)
• totxs(i,jk,l),sttxs(i,jk,l),absxs(i,jk,l),staxs(i,jk,l)
996
continue
endif
994
continue
462
463
464
format(3i4,1
format(14x
format(14x
gp#')
1
pel3.5,Opf6.3,lpel3.5,2(lpel3.5,Opf6.3))
2
lpel3.5,Opf6.3,lpel3.5,2(lpel3.5,Opf6.3))
465
format
B-
c
c
3 (i3,
gp#')
stop
end
108
Program : sibell
character*6titl
character*1
+
+
adum
integer cnumvnum
dimension cnum(3,1000),flx(3,2,12,1000),abx(3,2,12,1000),
tox(3,2,12,1000),elx(3,2,12,1000),fnu(3,2,12,1000),
fis(3,2,12,1000),vnum(200),vol(200),indt(3,1000)
dimension tabx(12,2),ttx(12,2),telx(12,2),tfnu(12,2),
+
c
c
c
c
3
2
12
100
tfis(12,2),tf1x(12,2)
nf 1=8, 2=9, 3=10
ie
is
cell number
ifile
open(unit=Bfile=lmcn2.inpl,form=lformatted',status='old')
open(unit=9,file=lmcn5.inp',form=lformattedl,status=loldl)
open(unit=10,file=lmcn4.inpl,form='formatted',status=lold')
open(unit=llfile=lvol.outlform='formattedl,status=lold1)
open(unit=12,file=lrsltslform=lformattedl,status=lunknown')
c
do
8 nf=1,3
ifile=nf+7
icn=O
10
read(ifile,,(a6,i6,/)',end=88)titl,numl
if(titl.eq.lltallyl)then
if(numl.eq.124.or.numl.eq.334.or.numl.eq.214)itype=1
if(numl.eq.134.or.numl.eq.344.or.numl.eq.224)itype=1
if(numl.eq.144.or.numl.eq.354.or.numl.eq.234)itype=1
if(numl.eq.164.or.numl.eq.364.or.numl.eq.244)itype=2
if(numl.eq.174.or.numl.eq.374.or.numl.eq.254)itype=3
if(numl.eq.184.or.numl.eq.384.or.numl.eq.264)itype=3
if(numl.eq.194)itype=l
if(numl.eq.204)itype=3
elseif(titl.eq.,
cell )then
icn=icn+l
cnum(nficn)=numl
indt(nficn)=itype
if(itype.eq.l)then
read(ifileI(a)I)adum
do is=1,12
read(ifile,*)idum,flx(nflis,icn),rdum,flx(nf,2,is,icn)
c
c
+
write(12,1(3h #0,2i7,1p2e13.5)1)cnum(nficn),
enddo
icn,flx(nflis,icn),flx(nf,2,is,icn)
read(ifile,'WI)adum
if(itype.eq.2)then
read(ifileI(a,/)I)adum
endif
do is=1,12
read(ifile,*)idum,fnu(nflis,icn),rdum,fis(nflis,icn),
rdum,abx(nflis,icn),rdum,tox(nflis,icn),
+
+
rdumelx(nf,1,isicn),rdum
enddo
read(ifi1eI(a,////)I)adum
do is=1,12
read(ifile,*)idum,fnu(nf,2,is,icn),rdum,fis(nf,2,is,icn),
rdum,abx(nf,2,is,icn),rdum,tox(nf,2,is,icn),
rdumelx(nf,2,isicn),rdum
+
+
enddo
read(ifile,,(a,/////////////////)')adum
endif
if(itype.eq.3)then
read(ifileI(a,/)')adum
read(ifile,*)idum,abx(nflis,icn),rdum,tox(nflis,icn),
do is=1,12
109
+
rdumelx(nflisicn),rdum
read(ifile,,(a,////)')adum
enddo
do is=1,12
read(ifile,*)idum,abx(nf,2,is,icn),rdum,tox(nf,2,is,icn),
rdumelx(nf,2,isicn),rdum
+
enddo
endif
c
read(ifile,'(a,/////////////////)Iend=88)adum
write(12,*)nficncnum(nficn)
endif
goto
88
0
continue
do i=.1,193
read(ll,*)idumvnum(i),vl
vol(i)=vl/12.
c
write(12,*)idumvnum(i),vol(i)
end do
do 90 =,193
tvol=tvol+vol(i)
if(i.le.37)then
nconv=vnum(i)-71000
nf=l
elseif(i.gt.37.and.i.le.113)then
nconv=vnum(i)-11000
nf=2
elseif(i.gt.113)then
nconv=vnum(i)-81000
nf=3
endif
do 90 j=1,1000
if(nf.eq.l)ncmp=cnum(nfi)-81000
if(nf.eq.2)ncmp=cnum(nfj)-42000
if(nf.eq.3)ncmp=cnum(nfi)-82000
if(ncmp.eq.nconv)then
write(12,*)i,vnum(i),cnum(nf,i),nconvncmp,nf
do is=1,12
do ie=1,2
if(indt(nfi).eq.l)then
tflx(is,ie)=tflx(is,ie)+flx(nf,ie,isj)*vol(i)
endif
if(indt(nfj).eq.2)then
tfnu(is,ie)=tfnu(is,ie)+fnu(nf,ie,isj)*vol(i)
tfis(is,ie)=tfis(is,ie)+fis(nfie,isj)*vol(i)
tabx(is,ie)=tabx(is,ie)+abx(nf,ie,isj)*vol(i)
ttox(is,ie)=ttox(is,ie)+tox(nfie,isj)*vol(i)
telx(is,ie)=telx(is,ie)+elx(nf,ie,isj)*vol(i)
endif
if(indt(nfj).eq.3)then
tabx(is,ie)=tabx(is,ie)+abx(nf,ie,isj)*vol(i)
ttox(is,ie)=ttox(is,ie)+tox(nfie,isj)*vol(i)
telx(is,ie)=telx(is,ie)+elx(nf,ie,isj)*vol(i)
endif
enddo
enddo
endif
90
19
continue
write(12,19)
format('
x
K gp#1,5x,'FLUX',4x,'TOT.XSECTIONI,2x,
'ABS.XSECTION',lx,'NU*FISS.XSECI,2x,'FISS.XSECTI)
nn=O
do 91 is=12,1,-l
nn=nn+l
do 91 ie=2,1,-l
if(ie.eq.2)iee=l
110
if(ie-eq.l)iee=2
flux=tflx(isie)/tvol siga=tabx(isie)/tflx(isie)
sigt=ttox(isie)/tflx(isie)
sige=telx(isie)/tflx(isie) sigf=tfis(isie)/tf1x(isie)
sfnu=tfnu(isie)/tflx(isie)
write(12,20)nn,iee,flux,sigt,siga,sfnu,sigf
20
format(2i3,lp5el3.5)
91
continue
write(12,*)nniee,fluxsigt,siga,sfnu,sigf
c
write(12,1(13h
stop
total vol = lp5el3.5)1.)tvol*12
end
File : rsits
K
1
1
2
2
3
3
4
4
5
5
6
6
7
7
8
8
9
9
10
10
11
11
12
12
total
gp#
1
2
1
2
1
2
1
2
1
2
1
2
1
2
1
2
1
2
1
2
1
2
1
2
FLUX
3.64298E-04
7.13615E-05
4.47630E-04
6.83401E-05
5.13602E-04
7.25782E-05
5.45928E-04
7.66283E-05
5.36221E-04
7.25827E-05
5.04040E-04
5.97613E-05
4.49893E-04
4.91919E-05
3.92346E-04
4.20241E-05
3.41173E-04
3.55777E-05
2.81711E-04
2.96850E-05
2.32209E-04
2.47867E-05
1.69892E-04
2.40555E-05
vol =
TOTASECTION
ABS.XSECTION NU*FISS.XSEC
5.54066E-01 2.29585E-03
1.87641E+00 3.3620SE-02
5.62481E-01 2.28250E-03
1.81449E+00 3.16205E-02
5.64775E-01 2.23828E-03
1.78767E+00 3.141OOE-02
5.70975E-01 2.32829E-03
1.79394E+00 3.16111E-02
5.69695E-01 2.25072E-03
1.78241E+00 3.18629E-02
5.77033E-01 2.26380E-03
1.74026E+00 3.17982E-02
5.78575E-01 2.32567E-03
1.72769E+00 3.18037E-02
5.80923E-01 2.39860E-03
1.71519E+00 3.19280E-02
5.78941E-01 2.47606E-03
1.69937E+00 3.17879E-02
5.79020E-01 2.47141E-03
1.70773E+00 3.20984E-02
5.79536E-01 2.43172E-03
1.74561E+00 3.35301E-02
5.75283E-01 2.38011E-03
1.77757E+00 3.56112E-02
2.97691E+03
ill
9.05881E-03
2.85794E-01
9.16390E-03
2.66815E-01
9.00610E-03
2.65587E-01
9.42292E-03
2.68949E-01
9.20519E-03
2.75376E-01
9.28217E-03
2.80191E-01
9.42908E-03
2.85593E-01
9.52839E-03'
2.87597E-01
9.80863E-03
2.87257E-01
9.63444E-03
2.93157E-01
9.80162E-03
3.06559E-01
9.59636E-03
3.31846E-01
FISS.XSECT
3.68822E-03
1.1728BE-01
3.73346E-03
1.0949BE-01
3.66894E-03
1.08994E-01
3.84006E-03
1.10374E-01
3.7512BE-03
1.13012E-01
3.78327E-03
1.1498BE-01
3.84369E-03
1.17205E-01
3.88470E-03
1.18027E-01
3.99929E-03
1.17888E-01
3.92791E-03
1.20309E-01
3.99709E-03
1.25809E-01
3.91062E-03
1.36187E-01
APPENDIX C
SAMPLE CROSS SECTION RESULTS
'Me sWisticals effors are given as ftwtions of the mean values (not percent).
112
OD
-4
C
14
x(1)
C
En
H
r-
E-
U
w
(n
x
a
0
:
1
1
C)
0
CD
0
()
C)
I
-4
C)
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(In 1-4
0
C)
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I
d.
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I'm
1-4
r-4
Ln
C,)
ON
(1)
ON
Iq
Cq
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al
1-4
CD
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r-1
OD
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1
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C
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C
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C)
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C)
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C)
-4
0
C,) -4
C) 0
10
C)
CN
0
(n
C)
1-4
0
()
a
1-4
rn -4
C) C)
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C) CD
() -4
C) a
1 114
;:r ON
r14 1
0 ol
WI C
1-4 10
'IC q
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Ln
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APPENDIX D
ONE GROUP BALANCE CHECK RESULTS
The ratios of residual to total loss and total source are given in percent.
131
I
17
J
9
K
5
18
9
5
19
20
21
17
18
19
20
21
22
23
18
19
20
21
22
23
24
20
21
22
23
24
9
9
9
10
10
10
10
10
10
10
11
11
11
11
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11
11
12
12
12
12
12
5
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5
17
18
19
9
9
9
6
6
6
20
21
9
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
6
17
18
19
20
21
22
23
18
19
20
21
22
23
24
20
21
22
23
24
10
10
10
10
10
10
10
11
11
11
11
11
11
11
12
12
12
12
12
9
6
17
18
19
20
21
17
18
19
20
21
22
23
18
19
20
21
22
23
24
20
21
22
23
24
9
9
9
9
9
10
10
10
10
10
10
10
11
11
11
11
11
11
11
12
12
12
12
12
7
7
7
7
7
17
18
19
20
21
9
9
9
9
9
8
8
8
8
8
17
18
19
20
21
22
23
18
19
20
21
22
23
10
10
10
10
10
10
10
11
11
11
11
11
11
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
8
8
8
8
8
8
8
8
8
8
8
8
8
TOTAL LEAKAGETOTAL ABSORP TOTAL LOSS
1.08633E-05
2.095OOE-05
3.18133E-05
2.041OOE-05 1.12020E-05
1.16479E-05
1.35869E-05
1.31283E-05
-5.79491E-06 1.29490E-05
-4.01155E-06 7.78670E-06
-9.12188E-06 2.16344E-06
-4.6260SE-06 8.06749E-06
1.32212E-05 7.81022E-06
-7.42257E-06 8.37898E-06
-9.59164E-06 1.15940E-05
-8.24828E-06 1.26277E-05
-7.19076E-06 1.20575E-05
6.60932E-06 7.38191E-06
2.45990E-05 2.09609E-06
2.42193E-05 1.30372E-05
-8.61004E-06 1.27270E-05
-1.08853E-05 1.18032E-05
1.97611E-05 1.10101E-05
2.07099E-05 1.13918E-05
-8.03719E-06 7.94306E-06
-4.61657E-06 1.32087E-05
2.36130E-05 1.32678E-05
2.44444E-05
9.58311E-06
2.36080E-05
1.03622E-05
-6.60220E-06
1.08546E-05
-2.72485E-06 1.25576E-05
2.65776E-05
1.22816E-05
-5.90344E-06
1.23370E-05
-6.49261E-06
6.8717SE-06
-2.37293E-05
1.79280E-06
-1.51755E-05
7.16104E-06
5.04393E-06 6.92675E-06
-7.47699E-06 7.61885E-06
-8.67323E-06
1.03229E-05
-8.95884E-06
1.20642E-05
-9.8910SE-06
1.09255E-05
-2.86092E-06
6.46613E-06
1.33206E-05 1.85618E-06
2.12792E-05 1.20845E-05
-9.98156E-06 1.19053E-05
-1.33766E-05 1.05066E-05
2.31005E-05 1.00783E-05
2.35470E-05 1.01177E-05
-9.84199E-06 7.26927E-06
-3.23655E-06 1.28250E-05
2.77566E-05 1.24779E-05
2.60302E-05
1.10048E-05
2.57992E-05
1.17673E-05
-7.86799E-06
1.23152E-05
-3.07869E-06
1.40929E-05
2.99518E-05
1.35498E-05
-7.00036E-06 1.32243E-05
-7.36828E-06 7.56406E-06
-2.50965E-05 1.84115E-06
-2.02804E-05 7.48752E-06
4.76907E-06 6.96884E-06
-7.80465E-06 8.20889E-06
-9.92454E-06
1.10832E-05
-9.56595E-06
1.33377E-05
-1.10068E-05
1.24710E-05
-5.05634E-07
6.7802SE-06
1.27223E-05 1.86113E-06
1.94527E-05 1.28591E-05
-1.24551E-05
1.33408E-05
-1.41471E-05
1.14762E-05
2.67750E-05 1.12103E-05
2.61484E-05 1.08184E-05
-1.10486E-05 7.86604E-06
-3.90860E-06
1.36494E-05
3.07936E-05 1.40726E-05
2.66442E-05
1.14001E-05
2.66448E-05
1.13212E-05
-5.60382E-06
1.23475E-05
-2.59271E-06
1.4320SE-05
3.06421E-05
1.42429E-05
-5.72001E-06 1.42476E-05
-7.66642E-06 8.08838E-06
-2.84972E-05 1.85003E-06
-2.42442E-05 7.42888E-06
6.94965E-06 7.29730E-06
-7.99573E-06 8.38803E-06
-9.30556E-06 1.14444E-05
-9.71859E-06 1.41975E-05
-9.93786E-06 1.31872E-05
-5.43385E-06 7.18465E-06
1.38520E-05 1.86351E-06
2.25806E-05 1.31591E-05
-1.21486E-05 1.37786E-05
-6.42744E-06
-3.57556E-06
2.27540E-05
TOTAL SOURCE
1.94863E-05
3.16120E-05 2.01796E-05
5.22051E-06 2.12275E-05
1-00113E-05 2.49896E-05
3.58823E-05 2.40741E-05
7.1540SE-06 2.3762SE-05
3.77515E-06 1.32785E-05
-6.95844E-06 1.41621E-06
3.44140E-06 1.35546E-05
2.10314E-05 1.32766E-05
9.56404E-07 1.47099E-05
2.0023SE-06 2.09093E-05
4.37944E-06 2.33096E-05
4.86677E-06 2.22283E-05
1.39912E-05 1.22043E-05
2.66951E-05 1.35015E-06
3.72565E-05 2.36150E-05
4.11694E-06 2.33770E-05
9.1782SE-07 2.13508E-05
3.07712E-05 1.98968E-05
3.21017E-05 2.04877E-05
-9.41279E-08 1.35962E-05
8.59213E-06 2.42926E-05
3.68809E-05 2.44539E-05
3.40275E-05 1.70681E-05
3.39702E-05 1.85004E-05
4.25236E-06 1.95216E-05
9.83276E-06 2.28537E-05
3.88592E-05 2.2182SE-05
6.43356E-06 2.24003E-05
3.79167E-07 1.16329E-05
-2.19365E-05 1.28631E-06
-8.01443E-06 1.19420E-05
1.19707E-05 1.16540E-05
1.41853E-07 1.3103SE-05
1.64963E-06 1.83260E-05
3.10539E-06 2.20103E-05
1.03446E-06 1.97556E-05
3.60522E-06 1.06424E-05
1.51768E-05 1.46716E-06
3.33637E-05 2.16485E-05
1.92369E-06 2.15582E-05
-2.87001E-06 1.86833E-05
3.31789E-05 1.79478E-05
3.36647E-05 1.80175E-05
-2.57272E-06
1.23813E-05
9.58847E-06 2.32752E-05
4.02345E-05 2.28011E-05
3.70350E-05 1.96793E-05
3.75664E-05 2.10515E-05
4.44726E-06 2.22223E-05
1.10142E-05 2.57593E-05
4.35016E-05 2.45186E-05
6.22393E-06 2.39699E-05
1.95785E-07 1.29726E-05
-2.32553E-05 1.509OOE-06
-1.27929E-05 1.25701E-05
1.17379E-05 1.16602E-05
4.04248E-07 1.4185SE-05
1.15862E-06 1.97253E-05
3.77171E-06 2.43609E-05
1.46423E-06 2.26040E-05
6.27465E-06 1.12659E-05
1.45835E-05 1.58005E-06
3.23117E-05 2.31253E-05
8.85691E-07 2.42177E-05
-2.67093E-06 2.04681E-05
3.79853E-05 2.00733E-05
3.69667E-05 1.93066E-05
-3.18259E-06 1.34951E-05
9.74077E-06 2.47310E-05
4.48662E-05 2.57638E-05
3.80442E-05 2.03562E-05
3.79660E-05 2.0237SE-05
6.74371E-06 2.22633E-05
1.17281E-05 2.61152E-05
4.48850E-05 2.58394E-05
8.52760E-06 2.58272E-05
4.21957E-07 1.38704E-05
-2.66472E-05 1.54710E-06
-1.68153E-05 1.25024E-05
1.42469E-05 1.22491E-05
3.92297E-07 1.45339E-05
2.1388SE-06 2.04160E-05
4.47895E-06 2.58520E-05
3.24929E-06 2.38041E-05
1.75080E-06 1.19919E-05
1.57155E-05 1.63858E-06
3.57397E-05 2.35882E-05
1.62999E-06 2.49782E-05
132
RESIDUAL
1.23269E-05
1.14325E-05
1.60070E-05
1.49783E-05
1.18082E-05
1.6608SE-05
9.50331E-06
8.37465E-06
1.01132E-05
7.75482E-06
1.37535E-05
1.89069E-05
1.89301E-05
1.73616E-05
1.7868SE-06
2.53449E-05
1.36415E-05
1.92601E-05
2.04330E-05
1.08744E-05
1.16140E-05
1.36904E-05
1.57005E-05
1.24270E-05
1.69594E-05
1.54699E-05
1.52693E-05
1.30209E-05
1.66764E-05
1.59667E-05
1.12537E-05
2.32228E-05
1.99565E-05
3.16644E-07
1.29619E-05
1.66764E-05
1.89050E-05
1.87212E-05
7.03719E-06
1.37097E-05
1.17152E-05
1.96345E-05
2.15533E-05
1.52310E-05
1.56472E-05
1.49540E-05
1.36867E-05
1.74334E-05
1.73557E-05
1.65149E-05
1.77750E-05
1.47451E-05
1.89830E-05
1.77460E-05
1.27769E-05
2.47643E-05
2.53630E-05
7.77308E-08
1.37816E-05
1.85666E-05
2.05892E-05
2.11398E-05
4.99124E-06
1.30034E-05
9.18645E-06
2.33320E-05
2.31390E-05
1.79120E-05
1.76601E-05
1.66777E-05
1.49903E-05
1.91025E-05
1.76881E-05
1.77283E-05
1.55196E-05
1.43871E-05
1.90457E-05
1.72996E-05
1.34485E-05
2.81943E-05
2.93178E-05
1.99783E-06
1.41416E-05
1.82771E-05
2.13731E-05
2.05548E-05
1.02411E-05
1.40769E-05
1.21515E-05
2.33482E-05
RESID/LOSS
3.87478E+01
3.61650E+01
3.06617E+02
1.49614E+02
3.29081E+01
2.32158E+02
2.51733E+02
-1.20352E+02
2.93868E+02
3.68725E+01
1.43804E+03
9.44221E+02
4.32250E+02
3.56737E+02
1.27714E+01
9.49423E+01
3.66151E+01
4.67824E+02
2.22623E+03
3.53395E+01
3.61789E+01
-1.45444E+04
1.82731E+02
3.36950E+01
4.98403E+01
4.55394E+01
3.59078E+02
1.32424E+02
4.29149E+01
2.48178E+02
2.96801E+03
-1.05864E+02
-2.49007E+02
2.64517E+00
9.13758E+03
1.01092E+03
6.08780E+02
1.80975E+03
1.95195E+02
9.03329E+01
3.51135E+01
1.02067E+03
-7.50983E+02
4.59058E+01
4.64796E+01
-5.81253E+02
1.42741E+02
4.33295E+01
4.68631E+01
4.39620E+01
3.99685E+02
1.33874E+02
4.36375E+01
2.85125E+02
6.52597E+03
-1.06489E+02
-1.98258E+02
6.62220E-01
3.40918E+03
1.60247E+03
5.45884E+02
1.44374E+03
7.95461E+01
8.91655E+01
2.84307E+01
2.63433E+03
-8.66330E+02
4.71551E+01
4.77730E+01
-5.24029E+02
1.53892E+02
4.25765E+01
4.64934E+01
4.66951E+01
2.30134E+02
1.22672E+02
4.24321E+01
2.02866E+02
3.18716E+03
-1.05806E+02
-1.74351E+02
1.40229E+01
3.60482E+03
8.54518E+02
4.77189E+02
6.32594E+02
5.84938E+02
8.95735E+01
3.40001E+01
1.43241E+03
RESID/SOURCE
6.32595E+01
5.66538E+01
7.54068E+01
5.99382E+01
4.90494E+01
6.98938E+01
7.15694E+01
5.91344E+02
7.46108E+01
5.84096E+01
9.34982E+01
9.04235E+01
8.12119E+01
7.81056E+01
1.46413E+01
1.87719E+03
5.77663E+01
8.23889E+01
9.57012E+01
5.46539E+01
5.66879E+01
1.00692E+02
6.46306E+01
5.08181E+01
9.93631E+01
8.36191E+01
7.82172E+01
5.69751E+01
7.51771E+01
7.12791E+01
9.67406E+01
1.80538E+03
1.67111E+02
2.71704E+00
9.89175E+01
9.09984E+01
8.58912E+01
9.47637E+01
6.61240E+01
9.34436E+02
5.41154E+01
9.10768E+01
1.15361E+02
8.48629E+01
8.68446E+01
1.20779E+02
5.88039E+01
7.64585E+01
8.81930E+01
7.84502E+01
7.99874E+01
5.72418E+01
7.74228E+01
7.40344E+01
9.84908E+01
1.64111E+03
2.01773E+02
6.66635E-01
9.71503E+01
9.41262E+01
8.45173E+01
9.35222E+01
4.43040E+01
8.22977E+02
3.97248E+01
9.63428E+01
1.13049E+02
8.92331E+01
9.14717E+01
1.23583E+02
6.06131E+01
7.41447E+01
8.68928E+01
8.76000E+01
6.97093E+01
5.50908E+01
7.37079E+01
6.69821E+01
9.69579E+01
1.82239E+03
2.34496E+02
1.63100E+01
9.73008E+01
8.95235E+01
8.26747E+01
8.63499E+01
8.54001E+01
8.59091E+02
5.15154E+01
9.34743E+01
24
20
21
22
23
24
17
18
19
20
21
17
18
19
20
21
22
23
18
19
20
21
22
23
24
20
21
22
23
24
17
18
19
20
21
17
18
19
20
21
22
23
18
19
20
21
22
23
24
20
21
22
23
24
17
18
19
20
21
17
18
19
20
21
22
23
18
19
20
21
22
23
24
20
21
22
23
24
17
18
19
20
21
17
18
19
20
21
22
23
18
19
11
12
12
12
12
12
9
9
9
9
9
10
10
10
10
10
10
10
11
11
11
11
11
11
11
12
12
12
12
12
9
9
9
9
9
10
10
10
10
10
10
10
11
11
11
11
11
11
11
12
12
12
12
12
9
9
9
9
9
10
10
10
10
10
10
10
11
11
11
11
11
11
11
12
12
12
12
12
9
9
9
9
9
10
10
10
10
10
10
10
11
11
8
8
8
8
8
8
9
9
9
9
9
9
9
9
9
9
9
9
9
9
9
9
9
9
9
9
9
9
9
9
10
10
10
10
10
10
10
10
10
10
10
10
10
10
10
10
10
10
10
10
10
10
10
10
11
11
11
11
11
11
11
11
11
11
11
11
11
11
11
11
11
11
11
11
11
11
11
11
12
12
12
12
12
12
12
12
12
12
12
12
12
12
-1.483613E-05
2.82614E-05
2.76984E-05
-1.28208E-05
-3.71709E-06
3.20848E-05
2.53011E-05
2.58040E-05
-8.5015SE-06
-1.98645E-06
3.00989E-05
-4.40SOOE-06
-8.674OIE-06
-3.19039E-05
-2.426OOE-05
2.01653E-06
-8.89770E-06
-8.7574SE-06
-1.00787E-05
-1.403OIE-05
-3.34667E-06
1.26131E-05
1.82155E-05
-1.45835E-05
-1.30334E-05
2.62798E-05
2.54790E-05
-1.17250E-05
-2.28317E-06
3.01876E-05
2.15189E-05
2.20032E-05
-8.24839E-06
1.37552E-06
2.60188E-05
-2.92867E-06
-1.03184E-05
-3.25172E-05
-2.76469E-05
-5.85201E-07
-1.07706E-05
-5.590OOE-06
-6.46345E-06
-1.2809SE-05
-6.20587E-06
2.80865E-06
1.52782E-05
-1.35496E-05
-9.7311SE-06
2.21699E-05
2.3168SE-05
-1.55968E-05
1.28050E-06
2.62574E-05
1.90871.E-05
1.97922E-05
-8.90223E-06
2.87152E-06
2.28087E-05
-1.13411E-06
-9.56722E-06
-3.44563,E-05
-2.67593E-05
-8.43806E-07
-1.02465E-05
-5.31105E-06
-4.85946E-06
-1.28959E-05
-1.17102E-05
2.66142E-06
1.32990E-05
-1.26924E-05
-8.0241SE-06
1.94999E-05
1.95974E-05
-1.34105E-05
1.86110E-06
2.25413E-05
1.67038E-05
1.62438E-05
-9.44742E-06
1.77768E-06
2.06611E-05
-2.05727E-06
-9.16003E-06
-2.99752E-05
-2.82826E-05
-2.04286E-06
-1.03722E-05
-6.19429E-06
-4.47586E-06
-1.20159E-05
1.22933E-05
1.19469E-05
1.16609E-05
8.20863E-06
1.43853E-05
1.46471E-05
1.00849E-05
1.10184E-05
1.25221E-05
1.36102E-05
1.35784E-05
1.37338E-05
7.91776E-06
1.81442E-06
7.42659E-06
7.3443SE-06
8.43079E-06
1.1062SE-05
1.35430E-05
1.33476E-05
7.34757E-06
1.78577E-06
1.28045E-05
1.34109E-05
1.15210E-05
1.10075E-05
1.06175E-05
7.84928E-06
1.33574E-05
1.33693E-05
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1.35181E-05
1.26672E-05
8.46297E-06
8.66087E-06
1.29244E-05
1.09410E-05
1.17323E-05
1.14492E-05
7.26716E-06
9.11206E-07
8.10246E-06
7.56602E-06
8.26217E-06
8.08059E-06
1.04406E-05
1.36174E-05
7.44219E-06
8.61147E-07
1.35761E-05
1.34410E-05
8.51509E-06
8.73194E-06
8.45974E-06
7.47030E-06
1.19071E-05
1.05332E-05
6.86659E-06
6.37630E-06
1.00115E-05
8.51620E-06
9.58646E-06
9.90293E-06
6.14974E-06
7.17610E-07
6.98088E-06
6.25301E-06
6.81737E-06
6.96771E-06
9.15116E-06
1.12445E-05
6.12796E-06
8.15055E-07
1.15974E-05
1.11171E-05
7.03670E-06
7.31745E-06
6.38798E-06
5.69928E-06
9.15837E-06
8.51116E-06
6.16232E-06
6.76772E-06
I.0337SE-05
8.40210E-06
9.19736E-06
9.64063E-06
6.21895E-06
7.41015E-07
6.53018E-06
6.46775E-06
134
1.11115E-05
2.02790E-06
4.01976E-06
2.15448E-05
1.44492E-05
1.15277E-05
1.28731E-05
1.69731E-05
4.7493SE-06
1.31714E-05
1.10416E-05
1.11174E-05
1.55625E-05
4.12563E-06
1.15646E-05
8.09830E-06
1.29328E-05
2.59587E-05
2.77441E-05
6.79091E-06
1.32369E-05
7.67507E-06
9.70106E-06
1.897OOE-05
1.15050E-05
1.32138E-06
2.29434E-06
1.80876E-05
1.16199E-05
1.01122E-05
1.13173E-05
1.50687E-05
4.54090E-06
1.22337E-05
1.00932E-05
9.8943SE-06
1.34215E-05
3.22862E-06
9.070OIE-06
6.4628SE-06
9.86507E-06
2.26046E-05
2.48993E-05
4.35962E-06
1.21583E-05
6.64212E-06
8.13713E-06
1.5085SE-05
1.09641E-05
2.21230E-06
2.65660E-06
1.57694E-05
9.75430E-06
8.46774E-06
8.78075E-06
1.33512E-05
3.79764E-06
1.01457E-05
6.73583E-06
6.27738E-06
1.12296E-05
2.12759E-06
7.63932E-06
4.76073E-06
9.34570E-06
1.91503E-05
2.04004E-05
3.55282E-06
9.45081E-06
5.19739E-06
6.56070E-06
1.31443E-05
9.66216E-06
1.0234SE-06
2.84682E-06
1.34097E-05
6.91409E-06
6.63438E-06
7.32532E-06
1.02480E-05
2.91947E-06
8.22427E-06
4.85713E-06
4.61702E-06
9.67536E-06
2.81865E-06
4.09717E-06
5.51543E-06
6.72945E-06
1.09095E-05
9.83614E-06
1.16349E-06
-8.03269E+02
6.00607E+01
1.73416E+01
-7-46256E+02
-7.69021E+02
4.76297E+01
5.28785E+01
-2.47391E+02
4.11815E+01
4.62035E+01
5.31340E+01
5.24886E+01
-2.40716E+03
4.61276E+01
4.50226E+01
1.47055E+02
-2.79255E+02
-1.04465E+02
-1-46889E+02
3.74256E+02
-3-70651E+02
3.93973E+02
3.36860E+02
-6.67759E+02
-3.69275E+02
5.47313E+01
1.21265E+01
-6.88565E+02
-1.20601E+03
4.87895E+01
5.47905E+01
-2.28734E+02
5.05827E+01
4.91295E+01
5.43928E+01
5.33239E+01
-2.69993E+03
4.18627E+01
4.36010E+01
1.29611E+02
-3.79730E+02
-1.04200E+02
-1.48238E+02
1.35967E+02
-3.12059E+02
4.61751E+02
3.53257E+02
-1.02734E+03
-3.11311E+02
7.19811E+01
1.63658E+01
-6.77259E+02
-7.87139E+02
4.92320E+01
5.09310E+01
-2.27026E+02
4.68295E+01
4.90631E+01
4.95194E+01
4.96091E+01
-9.21919E+02
3.33027E+01
4.43482E+01
9.25815E+01
-2.92423E+02
-1.03893E+02
-1.52020E+02
1.31577E+02
-3.58876E+02
2.93584E+02
2.53264E+02
-6.91856E+02
-2.73390E+02
5.56681E+01
1.97091E+01
-5.84906E+02
5.63889E+03
4.75521E+01
5.34176E+01
-2.25295E+02
4.67946E+01
4.91429E+01
4.40778E+01
4.05545E+01
1.46046E+03
5.04821E+01
3.08184E+01
1.33701E+02
-1.31823E+03
-1.07287E+02
-2.97528E+02
2.19351E+01
1.14219E+02
1.50380E+02
2.09798E+01
1.15474E+02
1.14947E+02
9.09480E+01
1.12218E+02
1.67847E+02
2.91692E+01
8.58858E+01
1.13374E+02
1.10476E+02
1.04334E+02
3.15666E+01
8.18928E+01
5.95232E+01
1.55786E+02
2.33984E+03
3.13271E+02
7.89143E+01
1.36948E+02
7.97560E+01
7.71094E+01
1.17613E+02
1.37137E+02
1:20903E+02
1.37999E+01
1.16990E+02
1.09042E+02
9.52724E+01
1.21192E+02
1.77680E+02
3.35913E+01
9.65776E+01
1.19263E+02
1.14242E+02
1.03846E+02
2.95093E+01
7.73080E+01
5.64481E+01
1.35749E+02
2.48073E+03
3.07306E+02
5.76211E+01
1.47157E+02
8.21985E+01
7.79375E+01
1.10783E+02
1.47324E+02
2.56902E+02
1.95683E+01
1.17323E+02
1.14553E+02
9.69744E+01
1.03795E+02
1.78724E+02
3.18938E+01
9.63213E+01
9.80958E+01
9.84486E+01
1.12167E+02
2.49828E+01
7.96886E+01
4.80739E+01
1.51969E+02
2.66862E+03
2.92233E+02
5.68178E+01
1.38628E+02
7.45925E+01
7.16925E+01
1.16896E+02
1.57673E+02
1.25571E+02
2.45471E+01
1.20623E+02
9.82575E+01
9.06652E+01
1.14673E+02
1.79812E+02
3.18776E+01
9.66293E+01
7.88198E+01
6.82213E+01
9.35916E+01
3.35469E+01
4.45472E+01
5.72102E+01
1.08209E+02
1.47224E+03
1.50626E+02
1.79891E+01
22
23
18
19
20
21
22
23
24
20
21
22
23
24
10
10
11
11
11
11
11
11
11
12
12
12
12
12
16
16
16
16
16
16
16
16
16
16
16
16
16
16
-5.75871E-06
-2-71754E-06
-1.72124E-06
-5.91484E-06
-1.73394E-06
6.32173E-06
8.12292E-06
-6.43806E-06
-4.07764E-06
7.42412E-06
7.40386E-06
-6.70992E-06
1.04669E-06
8.96014E-06
Core total loss
Core total source
Core total residual
Residual/Loss
M
Residual/Source
4.0063SE-06
3.92732E-06
4.44976E-06
5.92040E-06
3.94821E-06
1.40224E-06
7.01344E-06
6.07438E-06
3.84284E-06
3.95819E-06
3.94784E-06
3.36894E-06
4.79825E-06
4.39318E-06
=
=
=
=
(%) =
-1.75233E-06
1.20978E-06
2.72852E-06
5.55773E-09
2.21427E-06
7.72397E-06
1.51364E-05
-3.63684E-07
-2.34803E-07
1.13823E-05
1.13517E-05
-30409SE-06
5.84494E-06
1.33533E-05
6.75721E-06
6.47830E-06
8.09392E-06
1.08377E-05
6.13564E-06
8.23216E-07
1.24116E-05
1.11407E-05
6.84582E-06
7.09508E-06
6.46655E-06
5.67047E-06
8.79883E-06
7.97567E-06
2.46031E-03
4.04258E-03
1.58228E-03
6.43122E+01
3.91402E+01
135
8.50954E-06
5.26852E-06
5.36539E-06
1.08321E-05
3.92137E-06
6.90075E-06
2.724SOE-06
1.15044E-05
7.08062E-06
4.28722E-06
4.88515E-06
9.01146E-06
2.95389E-06
5.37765E-06
-4.85613E+02
4.35494E+02
1.96641E+02
1.94901E+05
1.77095E+02
8.93421E+01
1.80017E+01
-3.16329E+03
-3.01556E+03
3.76657E+01
4.30345E+01
-2.69725E+02
5.05375E+01
4.02720E+01
1.25933E+02
8.13257E+01
6.62892E+01
9.99487E+01
6.39113E+01
8.38268E+02
2.19537E+01
1.03264E+02
1.03430E+02
6.04253E+01
7.55449E+01
1.58919E+02
3.35714E+01
6.74256E+01
APPENDIX E
THE TEST OF HOMOGENIZATION PROCEDURE
The files given in this Appendix are:
hesap
: MCNP results for one fuel element test run in which
mult 1 = absorption reaction rate
mult 2 = total reaction rate
mult 3 = elastic scattering reaction rate
inult 4 = ny) reaction rate
mult
=n
sigma fission reaction rate
inult 6 = fission reaction rate
hes.f
Cross section proccesing and neutron balance calculation program for the test.
136
Program:
c
hes.f
c
this program calculates neutron balance for a separated individual
c
fuel
lement rhomboid.
c
character*1 adum
character*18 adum2
integer celln
real
keff
dimension fl(100),rra(100),rrt(100),rre(100),rrg(100)
dimension rrn(100),rrf(100)
dimensionscur(4),sflx(4)
dimension are(2),vol(6),celln(100)
c
open(unit=8,file=lhesapl,form=lformattedl,status='old')
open(unit=9,file=lhes.oul,form=lformatted',status=lunknown')
c
keff=0.03292
c
c
reading hesap
c
read(8,'(a)')adum
do i=l.,2
+
read(8,*)celln(i),fl(i),rdum,rra(i),rdum,rrt(i),rdum,
rre(i),rdumrrg(i),rdum
end do
do i=3.,17
read(E.,*)celln(i),fl(i),rdum,rra(i),rdum,rrt(i),rdum,
+
rre(i),rdum,rrg(i),rdum,rrn(i),rdum,rrf(i),rdum
end do
do i18,93
read(g,*)celln(i),fl(i),rdum,rra(i),rdum,rrt(i),rdum,
+
rre(i),rdumrrg(i),rdum
end do
read(8,1 (a) )adum
do i=1,4
read(8,*)idum,scur(i),rdum,sflx(i),rdum
end do
read(8,1(a),)adum
do i=1,2
read(BI(alB,4xlpel3.5))I)adum2,are(i)
end do
read(8,'(a)')adum
do i=1,6
read(8,'(al8,lpel3.5))Iend=99)adum2,vol(i)
end do
99
continue
flx=O.
absr=O.
totr=O.
fnur=O.
fisr=O.
tvol=O.
do i=1,93
if(i.ge.1.and.i.lt.3)vl=vol(1)
if(i.ge.3.and.i.lt.18)vl=vol(2)
if(i.eq.18.or.i.eq.33)vl=vol(3)
if(i.ge.19.and.i.1t.33)vl=vol(4)
if(i.ge.34.and.i.1t.64)vl=vol(5)
if(i.ge.64)vl=vol(6)
flx=flx+fl(i)*vl
absr=absr+rra(i)*vl
totr=totr+rrt(i)*vl
137
fnur=fnur+rrn(i)*vl
fisr=fisr+rrf(i)*vl
tvol=tvol+vl
end do
avgfl:K=flX/tVol
siga=(absr+fisr)/flx
sigt=totr/flx
signu:=fnur/flx
sigf=:Eisr/flx
tleak:=(scur(l)+scur(2)+scur(3)+scur(4))/tvol
tloss:=tleak+siga*avgflx
tsour(-e=(l./keff)*signu*avgflx
resid=abs(tloss-tsource)
write(9,101)flx,absr,totr,fnur,fisr,tvol
101 format(2xlflx :,,lpel3.5,/,2x,
+
+
+
+
+
c
labsr
Itotr
Ifnur
Ifisr
ltvol
:,,lpel3.5,/,2x,
:,,lpel3.5,/,2x,
:Ilpel3.5,/,2x,
:Ilpel3.5,/,2x,
:,,lpel3.5,/)
writei:9,100)avgflx,siga,sigt,signu,sigf,tleak,tloss,tsource,
+
residresid/tlossresid/tsource
100 format(2x,'avgflx :',lpel3.5,/,2x,
+
Isiga:,,lpel3.5,/,2x,
+
'sigt:,,lpel3.5,/,2x,
+
Isignu:',lpel3.5,/,2x,
+
'sigf :Ilpel3.5,//,2x,
+
Itleak:,,lpel3.5,/,2x,
+
Itloss:',lpel3.5,/,2x,
+
Itsource:,,lpel3.5,/,2x,
+
'residual:,,lpel3.5,//,2x,
+
+
stop
'resid/tloss:',lpel3.5,/,2x,
Iresid/tsource
:lpel3.5)
end
138
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