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MICROCOPY RESOLUTION TEST CHART
NATIONAL BUREAU OF STANDARDS - 1963
.ORNO fir 2600
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NOV 2 9 1966
MONTE CARLO CALCULATIONS OF FAST MULTICOMPONENT CRITICAL SYSTEMS*
CON4-667019-7
J. T. Thomas
Oak Ridge National Laboratory
Oak Ridge, Tennessee 37830
7:00; w.50
ABSTRACT
Criticality studies have been made of three dimensional cuboidal
systems of uranium metal cylinders enriched to 93.2 wt% -37. The systems
were composed of near identical, individually subcritical components
spaced in air. The dependence of the system critical mass upon the mass
and shape of the components was examined by utilizing units ranging in
mass from 10.5 to 26.2 kg of uranium and with height-to-diameter ratios
from 0.47 to 1.17.
The calculation of such assemblies by usual analytic techniques 18
not practicable, but the systems are ideally suited to Monte Carlo methods.
The multiplication factors of a number of the experiments have been com-
puted by several codes and the results compare favorably. The one most
extensively employed, however, has been the British GEM Monte Carlo code.
A brief description of the geometry input and those features of the code
applicable to the experimental systems investigated will be given in the
paper as well as the results of typica? experiments and comparison with
computation. The computed values of ken agree with experiment to within
1 1/2%.
*Research sponsored by the U. S. Atomic Energy Commission under contract
with the Union Carbide Corporation.

RELEASED FOR ANEUROLMENTE
IN NUCLEAR SCIENCE ANETRACTS
LEGAL NOTICE
This report was prepared as an account of Government sponsored work. Noither the United
· States, nor the Commission, nor any person voting on behalf of the Commissions
A. Makes any warranty or ropresentation, expressed or implied, with respect to th, accola
racy, completoners, or usohulnois of the information contained in this report, or that the uso
of any information, apparatus, method, or process disclosed in this roport may not infringe
privately owned rights; or
B. Assumes any liabilities with respect to the use of, or for damages resulting from the
use of any information, apparatus, method, or proceso disclosed in this report.
As used in the above, "person acting on behalf of the Commission" Includes any om-
ployee or contractor of the Commission, or employee of such contractor, to the extent that
such employee or contractor of the Commission, or employoe of nuch contractor propares,
disseminates, or provides access to, any information pursuant to his employment or contract
with the Commission, or his employment with such contractor.
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INTRODUCTION
A continuing program in support of nuclear criticality safety lu the
handling of accumulations of individually subcritical units of Pissile
materials 18 being coniucted at the Critical Experiments Facility of the
Oak Ridge National laboratory. A significant portion of this program deals
with the criticality of uranium metal systems. The uranium metal enriched
to 93.2 wt% in 255U was utilized in the form of cylinders with masses
ranging from 10.5 to 26.2 kg V. Arrays were constructed to be as near
ideal as was possible commensurate with assembly requirements. As a con-
sequence, the experiments serve as a suitable set to evaluate models and
methods used to compute the criticality of such systems.
constant, k, and in establishing the reliability of Monte Carlo codes which
can then be used in safety evaluations. A summary of a number of critical
experiments 18 followed by a brief description of three codes and their
application to the data. A comparison of the calculative results is of
particular interest because of the different cross section input data.
EXPERIMENTS
The units constituting these arrays consisted of one or more cylinders
of uranium metal enriched to 93.2 wt% in 2330, designated as U(93.2).
The 2340, 2360, and 2380 content were 1.0, 0.2, and 5.6 wt%, respectively.
The units were supported, with their axes vertical, on stainless steel
rods passing through 0.508-cm-diam holes in each cylinder parallel to the
axis and located 8.547 cm apart on a diameter. The vertical separation of
the cylinders was established by spacers of appropriate length cut from
.
Inconel tubing closely fitting the support rode. The rods were mounted
in sections of aluminum Unistrut attached to the two parts of a split table
apparatus. The horizontal position of the rods was adjustable. The aseem-
blies were designed to provide a minimum of support structure and control
was by means of table separation only. A typical assembly of eight 26.2
kg V units, illustrating the support features described, 18 shown in Fig. 1.
Presented in Table 1 is a summary of a number of critical assemblies
of various sized units. The surface separation was equal along the three
directions of an array which centered the units at the corners of a rectang-
ular parallelepiped and gave a cuboidal shape for the array as a whole.
The description of the units represents the average dimension of the units
in an array. The slight variation of mass among the units and the achuracy
in spacing within an array resulted in an estimated error for k of + 0.003.
MONTE CARLO CODES
It is evident that the usual analytic techniques are difficult to appiy
to the systems described above. Monte Carlo techniques, on the other hand,
are particularly suited to the problem. The GEM code originating in the
Health and Safety Branch of the UKAEA was initially written to explore and
evaluate just such systems in the interest of nuclear criticality safety.
The GEM program is written for the IBM 7090, accepts a number of standard
geometries, allows for a fair degree of geometrical freedom and computes
directly a measure of criticality with a speed and accuracy comparable to
other similar programs.
The GEM program input is a simple description of the material, unit,
cell, and reflector. The density, the number of nuclides, their names, and
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Table 1. Critical Arrays on Unterlocted Unmoderated U(93.2)
Metal Cylinders in Thrue Dimensi inal cuboidal a netry.
Unit
Desig-
astion
Number of Units
Along mach Direction
Height-to.
Diameter
Autio
Mussa
kg U
Dinn
Surnace
Sepantion
ng
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10.480
10.484
10.458
10.434
10.489
15.692
15.683
20.360.
20.877
26.218
26.113
0.47
0.47
0.47
0.47
O.H
0.70
3
11.506
11.50g
11.494
11.481
9.116
11.494
11.490
11.506
11.484
11.509
11.486
N
w now now now iwwn
1.349
2.007
3.442
3.952
2.436
0.902
4.2014
2.248
6.363
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0.70
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0.94
0.94
1.17
1.17
3.543
a
3.
8.494
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a. me uraniuma meli density is 18.76 g/cm.
b. Errors on all surface se rostlions + 0.013 cm.
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their proportions by atoms is given for each material present. The basic
element of geometry used to specify a unit or cell 18 the region. A region
• 18 that portion of the system described by associated region boundaries.
These boundaries are closed nested surfaces which may touch or coincide but
must not intersect. The system is divided in two super regions by a neu-
tronically important surface separating a 'core' from a 'reflector' which
may not necessarily correspond to the true core-reflector boundary. In
the program tracking is done by stages, where a stage begins with the pas-
sage of a preselected number of neutrons into the core and terminates when
all the decendants of those neutrons reenter the core. The numbers of
neutrons leaving, crossing and returning to this boundary yielä an estimate
of the core multiplication M and the reflection R of the reflector. The
parameter MR 18 an output of the code, is unity for critical systems, and
is the principal measure of criticality.
Each cell in the core has its own origin of coordinates and can be
divided into any number of regions by a set of nested surfaces. Cells with
different geometries or material content are given different type numbers.
The complete core is specified by listing the type numbers to give an
arrangement of the celis and the position of each cell 18 defined by a set
of three integral coordinates. When the outer boundary of the system is
cuboidal, as is the case with the experiments described above, it is possible
17
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to specify reflection parameters on the six outer faces. The specified
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percentage of neutrons reaching any given face will be specularly reflected.
This option permits one to make use of any symmetry present in the lattice
and may also be used to avoid tracking neutrons in a reflector if its albedo
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As an example of input to GEM, consider the array shown in Fig. 1.
Following a title card, the required input 18 the following:
-] 111 000111
1 Cylinder 1 5.742
211
+ 6.7295 - 6.7295
Core 3
Reflector 4
2
Cuboid
Cuboid
TEPLB
0
0
TEX5
+15.052 + 15.052 + 17.002 - 15.052 - 15.052 - 17.00
+15.052 + 15.052 + 17.002 - 15.052 - 15.052 - 17.00
18.76 93.2 6.8
The minus otse specifies this as a reflected lattice with only one type of
unit. The next three digits are the number of cells along the three co-
ordinates. The next sisi digits represent the degree of reflection on the six
outer boundaries. Instead of the entire array being utilized, use is made
cf the three planes of symmetry by having 100 percent reflection of neutrons
on the planes. The remaining three digits give the number of regions in the
cell, the number of regions in the reflector, and the number of materials
present, respectively. The next line describes region 1 as a cylinder of
material 1 with a radius of 5.742 cm and a height of + 6.7295 relative to
the cell coordinates. The second cell region has no material and its six
coordinate boundaries are given. The third region given is that of the core
reflector boundary. The fourth region defines the reflector boundary, in
this case of no material and zero thickness. The last line ives the two
material and atomic proportions. An additional line of input, not given above,
would specify the number of neutrons to be used per stage and the number of
stages to be run.
The simple descriptions given are adequate for the experiments pre-
sented. The cude has capabilities not touched on here that make it useful
for reactor analyses where the geometries and materials can be much more
complex.3
A second code used was the O5R, General Purpose Monte Carlo Neutron
Code.“ Unlike GEM the geometry input to OSR 18 burdensome in that all the
surfaces in the array must be described with respect to a single reference
coordinate frame. Multiple meida, however, may be treated having arbitrary
shapes which can be described by quadric surfaces. A second distinctive
Peature 18 that an eigenvalue is sought for a volume distribution whereas
in GEM a surface distribution provides the solution. No analysis 18 per-
formed by 05R. Its output consists of one or more collision tapes. Separate
routines must be used to extract the desired information. The multiplication
constant is determined from the life history of neutrons run in batches.
The fission-source distribution in each batch 1s obtained from the f18sion
distribution generated by the previous batch; the initial batch being a
selec'ced spacial distribution. The multiplication constant 18 computed
for each batch as the ratio of the number of neutrons born in the P18sions
produced by that batch to the number of source neutrons for the batch. The
average taken over all the batches run is the constant for the system. It
is usual to exclude from the averaging the first few batches which are still
affected by the initial source distribution.
A third code used originates with the Oak Ridge Computing Science
Center.? This Monte Carlo code computes the multiplication constant in a
fashion similar to 05R but has the attractive feature of simple geometry
input quite similar to that of GEM. The coordinate frame is used in a
cell and the cells are given three integral coordinates. When a neutron
leaving a cell reaches a cell boundary the sign of the coordinate 16 changed
and the cell integral coordinates permuted. The present version of this
code uses the 16-group cross-section set of Hansen and Roach, while
05R and GEM utilize available point cross-section data and have options
for modified data.
APPLICATION TO EXPERIMENT
The three codes have been used to compute the multiplication constan't
of the critical arrays given in Table 1. These results are presented in
Table 2. The multiplication constant reported for the GEM code is a close
estimate of kope obtained directly from the code output. The code computes
the keep from the relation
.
S(M-l.) (M-1/R)
kete = 1 + -
MuF (1/R-6)
where
M is the core multiplication;
R is the reflection factor;
S 18 the number of neutrons entering the core;
d. is the number of neutrons leaving the core without having fissioned
divided by S; and
MF 18 the sum of fissions for all neutrons leaving the core.
This is a valid measure of reactivity whl.ch for practical applications can
be used in place of the usual definition of kopi
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• Table 2. Computed Multipiiration Constants for Experimental
Arrays of U(93.2) Metal Cylinders
Unita
Ai'ray
Compurad Multiplication Constant, k
GEM
05RC
Casca
س
2
3
3
2
3
3
4
3
5
1.00%
س
0.987
1.003
1.008
م
0.971
س
et ma
0.975
. 3
1 2
3
2
3
2
- 3
ج س
1.000
1..002
0.992
0.994
0.992
1.034
0.284
1.005
0.996
0.999
0.995
3
2
3
2
3
2
3
no w now NW.I
0.997
0.995
:
3
2
3
a. See Table 1 for descriptior. Of average unit in array.
b.
The standard deviation for 10,000eutron histories does not exceed
+ 0.015 for all three codes.
Monoenergetic group of riclitrors used.
d. Sixteen-group Hansen-Roach cross-section set used.
for 10,000 100 unit in area
Monoene for all three
11
It has been shown that when only the multiplication factors of un-
reflected homogeneous assemblies such as these are desired, a simpler Monte
Carlo treatment of monoenergetic neutrons is sufficient. This one velocity
treatment was used to obtain the results presented in the table for the O5R
code.
When one considers the error in spacing of the unite coupled with slight
variations in sizes of the pieces within an array, the agreement between
experiment and calculation may be considered as good. It is also evident
that there need not be a strong dependence on cross-section structure wed
when only the multiplication constant is sought.
ACKNOWLEDGEMENTS
Appreciation is expressed to G. E. Whitesides and 0. W. Herman of
the Computing Science Center at Oak Ridge for their operation of the GEM
Code.
**
12
*
**
1.
·
3.
REFERENCES
H. C. Paxton et al., "Critical Dimensions of Systems Containing US,
Pu239, and v233, ** TID-7028, pp. 132-135 (June 1964).
E. R. Woodcock et al., "Techniques Used in GEM Code for Monte Carlo
Neutronics Calculations in Reactors and Other Systems of complex
Geometry," Proceedings of the Conference on the Application of
Computing Methods to Reactor Problems, ANL-7050, pp. 551-579 (May 17-19,
1965).
I. C. Longworth, "The GEM Monte Carlo Code and Its Use in Solving
Criticality Problems," Criticality Control of Fissile Materials,
IAEA, Vienna (1966).
D. C. Irving, R. M. Freestone, Jr., and F. B. K. Kam, "05R, A General-
Purpose Monte Carlo Neutron Code," ORNL-3622. (Feb. 1965).
G. E. Whitesides, G. W. Morrison, and E. C. Crime, "rew-Group Monte
Carlo Criticality Calculations," Trans. Am. Nucl. Soc. 2, 133 (1966).
G. E. Hansen and W. H. Roach, "Six and Sixteen-Group Cross Sections
for Fast and Intermediate Critical Assemblies," LAMS-2543 (1961).
J. T. Mihalczo, "One-Velocity Monte Carlo Calculations of Uranium-
Metal Critical Geometries," Trans. Am. Nucl. Soc. 8, 201 (1965).
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DATE FILMED
12/ 29 / 166






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