VALIDATION OF BATAN'S STANDARD
DIFFUSION CODES ON IAEA BENCHMARK
STATIC CALCULATIONS
Sembiring, T.M. and Liem P.H."
ABSTRACT
VALIDATION
OF BATAN'S
STANDARD
CODES
ON lAEA
BENCHMARK
STATIC CALCULATIONS.
Extensive benchmark calculations using the combination of
Batan's standard diffusion code and WIMSID4 have been conducted to check the validity and
accuracy of the codes, and to obtain proper cell modeling for MTR type fuel and control
elements which will be used in designing the next high loading silicide fuel of RSG-GAS.
The benchmark object and parameters to be calculated are defined by the IAEA in the IAEATECDOC-233 and IAEA-TECDOC-643.
In general, the combination of Batan's standard
diffusion code, Batan-2DIFF, and WIMSID4 gave very satisfactory results which proved the
validity of the proposed WIMSID4 cell model and the accuracy of the Batan's diffusion code
used in the benchmark calculations. Four-energy-group, multiplate options of WIMSID4 were
sufficient to give accurate results in term of infinite multiplication factors, fuel depletion
results and diffusion constants for whole core calculations. Two-dimensional,
four-group
diffusion model supplied with a correct axial buckling value can be considered accurate
enough for the MTR whole core calculations.
INTRODUCTION
Research activities with high priority in the Center for Multipurpose
Reactor (PRSG), National Atomic Energy Agency (Batan), include
RSG G.A. Siwabessy core conversion program from oxide to silicide fuel
(both utilize low enriched uranium - LEU, i.e. 19.75 w/o). This activity has
been coordinated with research and development programs in Nuclear Fuel
Element Center (PEBN-Batan) and presently four experimental silicide fuel
elements, with 250 gram 235Uloading per fuel element, have been irradiated
in the oxide core of RSG-GAS. Among other advantages of silicide fuel, its
high loading of fissile material is expected to increase the operation cycle of
RSG-GAS, hence, higher capacity factor and utilization of RSG-GAS
can be achieved.
Historically, the RSG-GAS was designed and commissioned by
Interatom/Siemens as the vendors, while the first batch of RSG-GAS fuel
elements were supplied by NUKEM. However, the next RSG-GAS core
conversion program, which consists of:
Center for Multipurpose
Reactor - BA TAN
73
(a)
Preliminary parametric survey on the neutronic and thermal-hydraulic
aspects of silicide core, followed by
(b) Final neutronic
and thermal-hydraulic
designs of RSG-GAS
silicide core,
(c) Safety design and accident analyses, and supported by
(d) Silicide fuel element development program ofPEBN,
is expected to be conducted mainly throught Batan's own efforts.
In order to support those efforts, from the neutronic design aspects of
the RSG-GAS silicide core, several Batan's standard codes have been and are
being developed:
(a)
Multidimensional
multigroup neutron diffusion codes for solving
criticality and fixed source problems, calculations of integral kinetic
parameters and application of perturbation theory for rapid calculation
of reactivity change (Batan-2DIFF & -3DIFF codes (1,2))
(b) Computer codes for operational in-core fuel management and for
obtaining an equilibrium core condition (Batan-FUEL and -EQUIL-2D
codes (3,4))
Batan-2DIFF and -3DIFF codes have several features which are not
always available in other generic diffusion codes. These are: (1) special
treatment of the (n,2n) neutron scattering which is significant for beryllium
reflected RSG-GAS core, (2) option for directional diffusion constants, (3)
up-scattering, and (4) power peaking factor calculation based on flux on the
mesh edge which is more conservative than the one based on mesh center.
The codes supports safety and transient analyses by providing integral
kinetic parameters, i.e. the effective delayed neutron fractions, prompt
neutron life time and neutron generation time. They can also be used to
compute, in a fast and efficient way, small reactivity changes and various
feedback reactivity coefficients using the perturbation theory. The validation
and accuracy of these codes have been checked and verified by using
2DBUM (5) and 3DBUM (6) codes, generic diffusion codes developed by
Battelle North West Laboratory and later modified by University
of Michigan.
Batan-EQUIL-2D code has been developed to obtain directly the
equilibrium condition of the RSG-GAS silicide core which will serve as the
typical working core (TWC) for further thermal and safety analysis.
In addition to the validity and accuracy of the above-mentioned Batan's
standard codes, another important factor influencing the accuracy of the
74
neutronic design results is proper modeling of the fuel and control elements
in the cell calculations for generation of the diffusion cross section set. As
widely known, WIMS/D4 cell calculation code (7) has been verified and
used by neutronic communities in various institutions/organizations.
This
code has also been independently verified in Batan and it is expected to be
one potential code for generation of the diffusion cross section set of the
RSG-GAS silicide fuel elements. WIMS/D4 and the above stated Batan's
standard codes were installed and executable on VAX 8550 and VAX 2100
mainframe computers in the Informatics Development Center of Batan
(PPI-Batan). However, our codes were designed as machine independent as
possible so that those codes in principle are also executable even on a
personal computer with relatively slower computation speed and for some
cases with smaller dimension of problem.
In order to properly conduct the neutronic design of the new RSG-GAS
silicide core using the combination ofWIMS/D4 and Batan's standard codes,
a series of benchmark calculation must be done first. In this paper, the results
of the static part of the safety-related benchmark calculation proposed by
IAEA are reported and discussed.
A typical 10 MWth Material Testing Reactor (MTR) with LEU core
defined by the International Atomic Energy Agency (IAEA) in the Appendix
F of IAEA- TECDOC-233 (8) is taken as the benchmark core. This core is
suitable for our benchmarking problem since it is an MTR core and its fuel
element configuration is considerably close to the one of the RSG-GAS.
The benchmark calculations cover almost all aspects of neutronic design
such as: criticality, various types of power peaking factor, isothermal
feedback reactivity coefficients, fuel element and control rod worths, etc.
Seven countries with their own code systems have participated in this
benchmark calculation project, hence, they provided results which can be
directly compared to calculation results of the Batan's code system.
Therefore, the present work reported here has twofold goals:
(a)
Obtaining a proper neutronic modeling of the LEU silicide fuel and
control elements of RSG-GAS in both cross sections generation and
diffusion calculation phases.
(b) A means of evaluating the performance and accuracies of Batan's
standard codes for neutronic design and to find ways to improve those
codes systematically.
The organization of this paper is as follows. First, the IAEA benchmark
problem definition is briefly reviewed. This is followed by discussions of
neutronic modeling proposed in the WIMS/D4 cell calculations for the
75
benchmark core. Then, the diffusion calculation results by Batan's codes are
presented and compared to the ones of other countries. Conclusion and
suggestion concerning the proper neutronic modeling. for the RSG·GAS
silicide fuel elements and core will be given in the last part of this paper.
BENCHMARK
PROBLEM
DEFINITION
The present work consists of two phases, i.e. benchmark calculations
based on IAEA· TECDOC-233 (8) followed by safety-related benchmark
calculations based on [AEA- TECDOC-643 (9).
IAEA-TECDOC-233
The
aim
of
Benchmark
these
Calculations
benchmark
(7 participants)
calculations
defined
in
IAEA-
TECDOC-233 is comparison of the different calculation methods and cross
section data sets used in different laboratories, limited conclusion for real
core conversion problem. The reactor used for these benchmark calculations
described in the Appendix F of IAEA- TECDOC-233 is a 10 MWth reactor
with MTR type fuel. The reactor primary data and configuration are shown
in Table I and Fig.l, respectively. As depicted in Fig.l, the reactor consists
of core and reflectors made of graphite or water. In the core, besides
standard fuel elements, there are four control fuel elements (fuel element
with absorber plates).
The participants are obliged to provide the multiplication factor; flux
and flux ratios along the two symmetry-axes of the core in three groups and
for begin of life (BOL) and end of life (EOL), respectively.
IAEA- TECDOC-643
Safety-Related
Benchmark
Calculations
(5 participants)
For the safety-related benchmark problem, the reactor description is the
same one utilized for the benchmark problem solved in the previously
discussed IAEA-TECDOC-233, except for a change in the description of the
central flux trap (See Fig.l). The water in the central flux trap in the original
core is replaced with a 7.7 cm x 8.1 cm block of aluminum containing a
square hole 5 cm on each side in order to compute more realistic radial and
local power peaking factors for the limiting standard fuel element.
The safety-related benchmark calculations are divided into two main
groups, i.e., static and transients calculations. However, this paper merely
discusses the static calculations since only neutronics modeling and codes
are involved (for transient calculations, neutron dynamics, time-dependent
thermal-hydraulics modeling and codes are involved which are out of the
76
scope of our discussion). Furthermore,
conduct the following static calculations:
the participants
are obliged to
1. Isothermal Reactivity Feedback Coefficients
a). Change of Water Temperature Only - 38, 50, 75, 100 0c.
b). Change of Water Density Only - 0.993, 0.988, 0.975, 0.958 g/cc.
c). Change of238U Temperature Only - 38, 50, 75, 100,200 0c.
d). Core Void Coefficient - Change Water Density Only - 10, 20 %
Void.
e). Local Void Coefficient - Change Water Density Only - 5, 10 % Void
separately in SFE-2, SFE-3 and SFE-4 (this is optional).
2. Radial and Local Power Peaking Factors
a). Replace burned CFE-I with fresh CFE.
b). Replace burned SFE-l with fresh SFE.
c). Note reactivity changes for all cases.
Note that (a) SFE and CFE stand for standard fuel element and control
fuel element, respectively; (b) The beginning of life (BOL) core, shown in
Fig.I, contains fission products; and (c) fresh SFE and CFE contain no
fission products.
PROPOSED NEUTRONICS
MODELING
The neutronics modeling proposed for the present static calculations
consists of two main parts, i.e., cross sections generation using WIMS/D4
cell calculation code and neutron diffusion theory calculations using Batan's
standard neutron diffusion code, Batan-2D1FF.
Cross Sections Generation with WIMSill4
Cross sections in four energy groups (Table 2) for core materials as a
function of 235U burnup were generated using 1-D lattice cell calculation
code, WIMS/D4. No detailed explanations on WIMS/D4 code is given here
and readers can find them in relevant references. It should be emphasized
here that cell calculations in WIMS/D4 consist of two main parts. The first
part is eigenvalue transport calculation in a simplified geometry, i.e. fuelcladding-moderator-extra region, to determine the neutron spectra for those
four regions. In this.case, the transport calculation is conducted in 69 energy
group but without considering the detailed mesh division in each region.
77
All regions of fuel are collected in the fuel region and similarly for cladding,
moderator and extra regions. The four kinds of neutron spectra obtained are
then used to collapse the cross sections into few group (for our benchmark
calculation is a four-energy group). Then the second part of the WIMS/D4
cell calculation is conducted. [n the second part, another transport calculation
is conducted in few group by considering the real unit cell geometry and the
fine mesh division prescribed by user. Finally, the space dependent group
neutron fluxes accross the unit cell are used for generating the effective cross
sections of the unit cell by volume weighting.
The proposed model for standard fuel element, SFE, is depicted in
Fig. 2. The 2-D SFE geometry is approximated by 1-0 cell calculation
model (WIMS/D4 cell calculation code can only treat 1-0 cell model).
For SFE, the multiplate model is chosen. The unit cell consists of eleven and
a half identical fuel regions and one extra region where each fuel region is
divided further into fuel meat, aluminum cladding, water moderator regions.
The extra region in WIMS/D4 is used to include regions which are not
covered
by
meat-cladding-moderator
fuel
plate
configurations.
Those regions are side plates, small parts of aluminum cladding adjacent to
side plates. and water gaps between fuel elements. After cell calculation
completion W[MS/04
homogenizes the effective cross sections for the
whole equivalent unit cell of the SFE by spectrum and volume weighting.
For a control fuel element, CFE, (see Fig. 3) careful modeling for the
CFE unit cell is needed. The following method is proposed for CFE.
The CFE is divided into two parts, i.e., regions for fuel and absorber,
respectively, where the cross sections for each part are generated separately.
The cross sections for fuel region part are generated with multiplate option in
the same way as for SFE (Fig. 3). Since the present benchmark calculation
does not include the control worth and kinetic calculation, we only consider
the case where in the absorber region the absorber blade is not inserted
(fully withdrawn). Therefore, the cross sections for absorber region are
generated in the same way as for other structural or reflector materials.
For non-fuel (reflector) regions (i.e., graphite, water and aluminum) and
absorber region of CFE, cross section sets are generated with the model
shown in Fig. 4. Three and a half fuel plate regions are included to simulate
the core spectra which are expected to influence the extra region where the
structural parts exist. To some extent this modeling can be justified for
structural parts which are located inside the core or in the core periphery.
However, the authors doubt that the model can be used for reflector regions
which are far (in term of neutron mean free path length) from the core
periphery. For those regions, a higher order method such as 1-0 or 2-D
transport codes must be used to obtain more accurate results. Fortunately, the
effective multiplication factor and the neutron flux and power distributions
78
across the core are not strongly affected by the accuracy of the reflector's
cross sections which is not located adjacent to the core. For our benchmark
calculations, the cross sections of the graphite and water reflectors which are
located directly adjacent to the core region are generated consideraing that
the core neutron spectra will interact with the graphite and water reflectors.
The best way one can do with WIMSID4 cell calculation code is by the
modeling shown in Fig. 4. For the cross sections of the outest water
reflectors the same set of cross section for the inner water reflector are used.
Even with this modeling the calculation
agreement with other institution's results.
results suprisingly
show good
Diffusion Calculations with Batan-2DIFF
Similar to other institutions/organizations,
the neutron transport
problems are treated with few group 2-D diffusion theory. For calculations
of reactor criticality, flux and power peaking factor distributions, and
reactivity changes, Batan-2DIFF code is used.
Batan-2DIFF code adopts the placing of flux on the mesh center rather
than in the mesh boundary (edge). However, conservative power peaking
factor has to be evaluated at the mesh edge, therefore, based on the
continuity condition of neutron flux at the medium interface, a relationship
between fluxes calculated at the centers of mesh intervals and the
corresponding values at the mesh boundary or edge has been built into the
code. It should be emphasized here that not all diffusion codes (for e.g.
CITATION code) have the capability to calculate power peaking factor
based on the edge mesh flux. Contrast to the more homogeneous core of
power reactors, the research and test reactors usually have cores with strong
heterogenity, not only in term of different fuel element bum up levels but
also in the existence of various irradiation positions. Furthermore, to
minimize the core critical mass excellent reflector materials are used.
In the interface boundaries between a fuel element and reflector then a large
gradient of (especially thermal) neutron flux and consequently a high power
peaking factor will appear. Estimation of local power peaking factor by
center mesh flux will give an under-estimated value. This is the reason that
the IAEA benchmark problem required the participants to produce the power
peaking factor calculated by mesh edge flux. Another advantage of using
mesh edge flux for calculating power peaking factor is that the calculated
power peaking factor is relatively insensitive to the mesh widths used in the
calculation.
For most calculations, in general, one block SFE, CFE or reflector with
dimension of 8.] x 7.7 cm2, is divided uniformly into 4 x 4 meshes. It has
79
been checked that these mesh widths produced enough accuracy in the
calculation of criticality and power peaking factors.
BENCHMARK CALCULATION RESULTS & DISCUSSIONS
IAEA- TECDOC-233 Benchmark Calculation Results
The criticality calculation results (multiplication factor, keff) for the
fresh, BOL and EOL cores are tabulated in Table 3. Hereinafter, figures in
the parentheses show the relative difference (%) from the values calculated
by ANL. The ANL results were chosen since they provided also some values
calculated by the continuous energy Monte Carlo method. It should be
emphasized here that those figures are not relative error since IAEA did not
determine which one is the best estimate.
For the fresh core, ANL deliberately provided keff value calculated with
the continuous energy Monte Carlo method, which in our opinion can be
considered to be the most accurate result. It can be observed that the
combination
of WIMS/D4 and Batan-2DIFF codes can give the
multiplication factors with high accuracy since they were inside the range of
the values calculated with the Monte Carlo method.
The accuracy of the criticality calculations for the BOL and EOL cores
depend strongly also on the accuracy of the WIMSID4 bum up calculations
during the cross section set generation. Even for these cases, very accurate
estimation for keffof both BOL and EOL cores can be produced.
As required by the IAEA, the group neutron flux distributions at the
midplane of the reactor calculated with Batan-2DIFF code are shown in
Fig. 5, while the flux ratio distribution (against thermal neutron flux) are
shown in Fig. 6. In the interface boundaries between flux trap (Al+water)
and fuel element regions the thermal neutron flux distribution shows a very
steep gradient and the neutron spectra (in term of flux ratio shown in Fig. 6)
also change significantly. In the fuel region, the neutron spectra are
determined by the moderator to heavy metal atomic ratio and fission process
while in the flux trap region the neutron spectra are attributed by slowing
down process of fast neutrons leaking from fuel region. Hence, the neutron
spectra in the fuel region are much harder than the flux trap region. It can be
understood that the power peaking factors for the adjacent fuel elements
have to be calculated by mesh edge flux.
Table 4 shows the thermal neutron flux in the flux trap region. It can be
observed that Batan-2DIFF code produced thermal neutron flux close to
other institutions' results. It should be noted that the relative differences
among the participants' results are expected to occur in the vicinity of flux
trap region where the neutron flux peak appears.
80
Table 5 summarized
the calculated
results for various
isothermal
temperature
and void reactivity
coefficients
defined
previously.
Three temperature ranges in which MTRs are commonly operated were
investigated. In addition, reactivity coefficients arised from water density
changes which simulates the moderator void or boiling phenomena were also
investigated. In general, the combination of WIMSID4 and Batan's code
provided very close calculated values to other institutions'
results.
The largest relative difference compared to ANL results appeared in
the reactivity coefficient
of water moderator
in the temperature
o
range of 50 - 100 C.
Table 6 gives the calculated results for the local void coefficients in
some prescribed standard fuel elements. The benchmark calculation results
for this case were only provided by ANL. It can be observed from the table
that not only for whole core void reactivity coefficients shown in the
previous table but our calculation results for local void reactivity coefficients
were very close to the ANL results.
The calculated power peaking factors for some prescribed fuel and
control elements when they are substituted with their fresh compositions are
shown in Table 7. These values are very important parameter in the thermal
and safety design of an MTR for e.g. in simulating operator' error in
refueling operation. As already discussed earlier, the power peaking factors
are conservative, that is, the values at the edge of the mesh interval with
highest power, and not the value at the center of the mesh interval with
highest power. Normally, there is a sharp rise in the power density at the
edge of a fuel element facing moderator or reflector region. It can be
observed from the table that even for those severe flux gradients our
calculation results either for local, radial power peaking factors and their
product values were very close the ANL results. This results also proved that
the edge-mesh power peaking factor calculations in Batan-2DIFF are valid.
CONCLUDING
REMARKS
AND FUTURE WORKS
Extensive benchmark calculations using combination of WIMSID4 and
Batan's standard diffusion code have been conducted to check the validity,
accuracy of the codes, and to obtain proper cell modeling for MTR type fuel
and control elements which will be used in designing the next high loading
silicide fuel ofRSG-GAS.
The object and parameters of the benchmark calculations are defined by
the IAEA in the IAEA-TECDOC-233 and IAEA-TECDOC-643. In general,
the combination of WIMS/D4 and Batan's standard diffusion codes gave
very satisfied results which proved the validity of the WIMSID4 cell model
proposed and the accuracy of the Batan's diffusion code used in the
8]
benchmark calculations. Four energy group, multiplate options of WIMSID4
are sufficient to give accurate results in term of infinite multiplication
factors, fuel depletion results and diffusion constants for whole core
calculations. Two-dimensional, four group diffusion model supplied with a
correct axial buckling value can be considered accurate enough for the MTR
whole core calculations. Of course, 3-D few group diffusion model will be
necessary for further refined analyses which can be done by our
Batan-3DIFF diffusion code. The capability of Batan-2DIFF code to
calculate power peaking factors in a conservative way, that is, based on the
mesh edge flux, widens the code applicability for safety analyses especially
on heterogenous cores such as research or test reactors' cores.
As future works, the second part of the benchmark calculations will be
elaborated in which the reactor kinetic parameters, control rod worths, axial
power distributions used in those calculations have to be calculated first.
These works will require other Batan's standard codes such as BatanADJOINT-2D and Batan-3DIFF codes.
ACKNOWLEDGMENTS
The
authors
express
their
gratitude
to Ir. Bakrie
Arbi,
Ir. Alfahari Mardi M.Sc., Ir. Iman Kuntoro, and all staff member
of Reactor Physics Division, Center for Multipurpose Reactor, for their keen
interest and encouragement given for the present work.
REFERENCES
1.
LIEM, P.H., "Development and Verification of Batan's Standard, TwoDimensional Multigroup Neutron Diffusion Code (Batan-2DIFF)",
Atom Indonesia, 20 ( 1), Jakarta (1994)
2.
LIEM, P.H., "Pengembangan Program Komputer Standar Batan Diffusi
Neutron Banyak Kelompok 3-D (Batan-3DIFF)", Risalah Komputasi
dalam Sains dan Teknologi Nuklir V, PPI-Batan, Jakarta (1995)
3.
LIEM, P.H., "Batan-FUEL: A General In-Core
Code", accepted to be published in Atom Indonesia
4.
LIEM P.H., et al., "Development of algorithm for searching equilibrium
core condition of a nuclear reactor", Proceeding of Workshop on
Computation
in Nuclear Science and Technology
IV, Batan,
Jakarta (1994)
5.
LITTLE, Jr., W.W. and HARDIE, R.W., "2DB User's Manual Revision I", BNWL-831 REV 1. See also 2DBUM (2DB University of
Michigan) documentation on tape
82
Fuel Management
6.
LITTLE, Jr., W.W. and HARDIE,
documentation on tape
7.
ASKEW, lR., FAYERS, FJ. and KEMSHELL, P.B., "A General
Description of the Code WIMS", Jour. of Brit. Nuc. Energy Soc.
5 (1966)
8.
IAEA, "Research Reactor Core Conversion from the Use of Highly
Enriched Uranium to the Use of Low Enriched Uranium Fuels Guide
Book", IAEA-TECDOC-233,
9.
R.W., "3DB User's
Manual",
Vienna (1980)
IAEA, "Research Reactor Conversion Guide Book - Volume
Analytical Verification ", IAEA-TECDOC-643, Vienna (1992)
3:
10. FOWLER, T.B. and VONDY, D.R., "Nuclear Reactor Core Analysis
Code: CITATION", ORNL-TM-2496, Rev. 2 (1971)
83
Tabel 1. Data and specification agreed for benchmark problem (8).
Active core height 600 mm
Extrapolation length 80 mm (in 80 mm distance from the core,
the cosine-shaped flux goes to zero)
X-Y calculation only
Space at the grid plate per fuel element 77 mm x 81 mm
Fuel element cross-section
76 mm x 80.5 mm including support plate
76 mm x 80.0 mm without support plate
Meat dimensions
63 mm x 0.51 mm x 600 mm
Aluminum-canning
with p A12.7 g/cc
Thickness of support plate 4.75 mm; p AI 2.7 glee
Number of fuel plates per fuel element:
23 identical plates, each 1.27 mm thick
Number of fuel plates per control element:
17 identical plates, each 1.27 mm thick
Identification of the remaining plate positions of the control element:
4 plates of pure aluminium pAl 2.7 g/cc, each 1.27 mm thick in the position
of the first, the third, the twenty-first, and the twenty-third standard plate
position; water gaps between the two sets of aluminum plates.
Specifications of the (UAlx-AI Fuel) for LEU corresponding to the previous
definitions:
· Enrichment 20 w/o U-235
.390 gram U-235 per fuel element (23 plates)
· 72 w/o of uranium in the UAlx-AI
· only U-235 and U-238 in the fresh fuel
Total power: 10 MWth (power buildup by 3.1 x
Thermal hydraulic data:
o
Water temperature 20o C
Fuel temperature 20 C
Pressure at core height 1.7 bar
84
1010
fission/joule)
Table 2. Four group structure for cross section generation by WIMS/D4 cell
calculation code.
63
ance
6(eV)
36
Energy
Region
-
10.000
x10
10 Bound
0.625
0.821
10
5.530
0.821
xxxEnergy
0.000
5.530
0.625
10
Upper Lower
(eV)
Energy
Bound
Table 3. Calculation results of the effective multiplication
TECDOC-233).
factor (lAEA-
- 1.168±0.003
1.
]683
1.0120
1.0320
1.0091
1.0014
1.0278
1.0213
1.1683
EOL
BOL
Fresh
Core
Core
1.0000
1.0178
1.1594
1.1813
1.0191
1.0130
1.0394
1.0332
1.1870
1.1815
1.0412
1.0019
1.0578
1.0216
1.1834
1.1681
((-)Core
(+0.026)
)1.768)
(-0.140)
(-0.343)
(-0.762)
(+
(-1.059)
(+1.772)
(+
1.048)
(+1.113)
(+1.60])
(+0.029)
(+0.050)
(+3.974)
(+1.]58)
(+1.165)
(+
(0.0)
1.292)
(+0.026)a
(+3.574)
1.130)
(+0.636)b
INSTITUTION (+0.769)b
ANL
a) Relative difference from MC (%)
b) Relative difference from ANL (%)
85
x Average
Icrn-2s-l)
Tabel 4. Calculated thermal neutron
(IAEA- TECDOC-233) .
(10
j
fern s )
••••...•••••.
.
2.3800
·2-1
-14
2.5113
2.3668
2.4920
3.1033
3.2898
2.0250
1.9862
1.7220
2.5852
1.9017
3.1200
Flux
3.3896
Center
(-)
(-8.4)
(-8.4
)the
(-7.9)
((-2.9)
(-2.9)
((-8.0)
-)
)(-at
(10
)Flux
fern
(+6.5)a
(-3.6)
I·••.
at s)
the
a) Relative difference from ANL (%)
86
flux
in
the
flux
trap
regIOn
..
Cent~rMi~fl.~~
.
Table 5. Isothermal reactivity coefficients (IAEA-TECDOC-643).
0344
0305
2.52
20.4
123
18.6
83
8.1
7.8
2.58
26.4
2.63
16.5
8.2.. ATOM
9.6
11.2
7.9
7.5
18.9
9.2
18.9
14.3
8.2
9.7
11.7
18.1
7.8
19.9
29.8
26.4
19.6
6.2
7824.7
7.8
19.5
2.12
0316
0.232
1.89
2.19
0337
0.513
2.94
0322
2.55
INTERANL
2.]9
15.8
2.17
24.6
15.9
22.5
1.94
1.92
237
2.16
17.0
25.9
20.7
3.08
3.15
2.73
lEN
0.280
0.299
0.490
0.289
8.5
7.1
17.]
7.7
63
88.2
13.6
6.8
.5
11.7
17.5
8.2
.0
lAERI
36.0
2.68
16.2
Batan
0.237
...
(-8])
(-16)
(+3.7)
(0.0)
(-3.8)
(+5.1)
(-21)
(0)
(-77)
(-4.9)
(-8.1)
(-7.4)
(+14)
(-23)
(+
(-2.7)
(-2.5)
(+60)
(+29)
(-16)
1.2)
(-3.7)
(-5.9)
(-4.4
)
(-25)
6)
(-13)
(+17)
(+1.2)
React.(_3.7)a
(-6.8)
(-]
(-26)
7)
(-1.9)
(-10)
(+20)
(+36)
(+3.8)
(-8.9)
(-4.8)
(-21)
(-24)
(+2.4)
(-4.9)
(+59)
(-4.9)
(-3.6)
(-33)
(+49)
(-6.4)
(-4.2)
(-3.6)
(+3.0)
(-16)
(+19)
(+2])
(+3.9)
(-8.2)
(-22)
(-2.0)
(+61)
(-5.2)
(-13)
(-7.4)
(-1.8)
(-15)
(+64)
(+17)
.................
ture -Range:
20 - (38
°C(-t.pPC
x 105)
0.958
glee
-t.p
38 -- 100°C
50°C
xx /105)
50
(-t.pPC
05) ))
0.998
-0.900
0.958 (-t.pPC
glee arw
(arw
-t.p
a"
/]t.pw
t.pw
a"
aTw
EIR>I.
Notes
aT'!;
a
a 7j
a"
Dw
= Reactivity
= Reaclivity
= Reactivity
= Reactivity
coeff. of water temperature
coeff. of water density
coeff. of fuel temperature
coeff. of void in terms of water density
a) Relative difference from ANL (%)
87
Table 6.
ElementNoided
void
coefficients
(~P
x
1000)
1.200
1.200
0.887
0.844
1.190
(0.0)
Ii(+0.84)a
(+0.36)
ANt
(USA)
Batan(Indonesia)
(-)
(-))
(-
SFE-4
SFE-3SFE-2
aNone
Local
U
None
adialNone
x Local
Calculated local
TECDOC-643).
a) Relative difference from ANL (%)
Table 7. Power peaking factor (IAEA-TECDOC-643).
1.26
1.24
1.48
1.56
1.04
1.57
1.66
1.12
2.13
1.15
1.10
1.85
1.06
1.12
1.97
1.23
0.99
1.60
1.29
1.24
1.56
1.14
1.32
1.80
1.58
1.02
1.71
1.10
1.31
1.58
1.75
1.02
JEN
EIR
1.52
1.58
1.51
1.72
1.72
1.36
1.55
ANt
1.55
1.56
1.33
(+24.6)
(+19.4)
(+24.7)
(-15.8)
(-16.0)
(-29.7)
(+4.55)
(-1.53)
(+
(+0.58)
(-6.77)
(+3.64)
(-2.94)
(-2.58)
((+0.76)
(+2.26)
(+2.86)
.1.11
(+
(+0.58)
(+0.91)
(0.0)
\.27)
\.28)
1.28)
Element INTER(+18.6)
(-8.57)
(+3.92)
I
Batan
....
Radial
ATOM
a) Relative difference from ANL (%)
b) Calculated by mesh edge flux
88
(IAEA-
-45%
FE
WW 45%
25%
FE
FE
25%
FE
AI
SFE-2
G
25%
FE
W
45%
G
G
CE
25%
5%
W
45%
45%
SFE-3
CE
CFE-l
FE
45%
SFE-l
W
5%
HP
I FE
FE I
W : Water
Figure].
: Standard Fuel Element
: Control Element
FE,SFE
CE,CFE
G : Graphite
IAEA 10 MW benchmark reactor configuration (BOL) as defined
in IAEA-TECDOC-233.
.-------------
1/2
Reflective
Fuel
FuelMeat
Meal
BC
Modera.or
Moderator
Clad
(AI)
(H2O)
0.02~~
0.038 0.038-_ ..
0.223
O.O~I
0.2230.038
On. Fuel Plate
Dimension
(0.33885)
EQUIV ALENT
UNIT CELL OF SFE
lOx
lOx
0.33885
One Fuel Plate
0.925
Extra Region
(AI & H20)
(em)
Reflective BC
Figure 2.
WIMS/D4
equivalent
multiplate option.
unit
cell
model
for
FE
with
89
Reflective
j0,0255
i
0,038
'
0,223
i
-
BC
-
-
1/2 Fuel Meat
Clad (AI)
~
I
Moderator
0,038
(H20)
Clad (AI)
II ---~
Fuel Meat
i
0,051
0.Q38
0.223
i
,
i
One Fuot Plate
DimenSion
(0,33885)
I
,
,_._. __ Clad (AI~
Moderator (H20)
___ J\il
7x
0,33885
EQUIVALENT
UNIT CELL OF CFE
7x
One Fuel Plat.
0,4611
Extra Region
(AI & H20)
,
1.
(em)
Rcflective BC
Figure 3.
WIMS/D4 equivalent unit cell model for CE with multiplate
option (absorber region is treated separately).
~0.223 0,038
(C. AI or 0.33885
H2O)
0.0255
0.038
8.0
Clad.-(AI)
Moderator
0.051
Extra
Region(H2O)
!
- i
Structural
Dimensionandi Reflector
1/2
One
Fuel
Fuel
2x
Fuel
Meat
Meat
Plate
Moderalor
Clad
(H2O)
(AI)
Materials
Homogenized
Reflective
BC
/!\
(0.33885)
-----,---- (em)
Macroscopic
Sections
Reflective
BC
0,038
One
Fuel PlateCross
\"
0,223
11\
____t ~
\11
- ---K
----fj
2x
Figure 4.
90
WIMSID4 cell model for structural and reflector materials cross
section generation.
-
3
'.."
.,::3
0d)C8c 014]
::3
!;:
c.:J
0..
~[xl
~•...
><E 2
I
H20
I
I
I
I
H20
:FE:FE:~AI+:~FE:FE:
,-...
g=4
a
100
X-direction (cm)
Figure 5.
X-direction group neutron flux distributions at the reactor center
(2-D geometry).
6
H20
!FE i FE
i~A,+i~ FE! FE!
H20
H20
o
50
100
X-direction (cm)
Figure 6.
X-direction fast to thermal neutron flux ratio at the reactor center
(2-D geometry).
91