OPTIMIZATION OF THORIUM-BASED SEED-BLANKET
FUEL CYCLES FOR NUCLEAR POWER PLANTS
by
Martin Busse
M.S., Nuclear Engineering
Instituto Balseiro, University of Cuyo, Argentina, 1995
Submitted to the System Design and Management Program in
Partial Fulfillment of the Requirements for the Degree of
Master of Science in Engineering and Management
at the
Massachusetts Institute of Technology
May 2000
© Martin Busse. All rights reserved.
The author hereby grants to MIT permission to reproduce and to distribute publicly paper and electronic copies of
this thesis document in whod nr in nmr+
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George M. Bunker Professor of Management
LFM/SDM Co-Director
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Professor of Aeronautics & Astronautics and Engineering Systems
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MASSACHUqETTS INSTITUTE
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JUN 1 4 2000
LIBRARIES
OPTIMIZATION OF THORIUM-BASED SEED-BLANKET
FUEL CYCLES FOR NUCLEAR POWER PLANTS
by
Martin Busse
Submitted to the System Design and Management Program on
May 5, 2000 in Partial Fulfillment of the Requirements for the Degree
of Master of Science in Engineering and Management
ABSTRACT
From the inception of nuclear power, thorium-based fuels have been of interest
due to the abundance of thorium ore and to potential neutronic advantages in
the efficiency of creating new fissile materials in the core. Early reviews of
nuclear fuel cycles tended to conclude that the uranium cycle, currently used in
nuclear power plants, was more preferable than the thorium cycle, partly
because of its simpler reprocessing and fabrication. The conditions of the
nuclear industry have changed, focusing on high burnup once-through fuel
cycles (no reprocessing). This creates incentives for further analysis of the
thorium-based cycle to assess improved economic performance and safety
margins in addition to the expected reduced waste production and enhanced
proliferation resistance.
This thesis analyzes alternative thorium-based fuel approaches from a thermalhydraulics point of view. The proposed cycle's performance is optimized given
constraints that will facilitate the implementation of the concept in typical
commercial power plants. The new designs are based on a seed and blanket
configuration, where the seed region is rich in uranium fuel (U-235), thus is the
2
supplier of neutrons, and the blanket region is a net neutron absorber to
generate new fuel (U-233) from thorium.
Two different designs are analyzed: the Seed and Blanket assembly as one
Unit (SBU) and the Whole assembly as a Seed or Blanket (WSB). These
designs are optimized from a thermal-hydraulic perspective and their economic
performance is compared to the current fuel cycle. The optimization involves
extracting the maximum energy without violating the limits on heat flux from fuel
rods to the coolant.
The proposed best approach for improving fuel thermal-hydraulics performance
is based on the use of grids that allow differential loss coefficients between the
seed and the blanket regions. This preferred approach to optimization was
found to be more effective in the case of the WSB design because of its power
distribution and the larger spatial separation between regions.
A very important factor in the economics of these designs is the achievable
cycle length, which is a function of the neutronic design. An eighteen-month
cycle is required in order to be economically comparable to the current fuel
cycle.
With comparable length, the fuel cost per unit energy is found
comparable to the current cycle, with slight benefits achieved for all urania or
thoria-based fuel depending on the cost of enrichment.
However, waste
performance and non-proliferation advantages may play an important role in
fuel attractiveness to nuclear power plants and to the government and these
were not factored in the economic analysis.
Thesis Supervisor: Dr. Mujid S. Kazimi
Title: TEPCO Professor of Nuclear Engineering
3
TABLE OF CONTENTS
Chapter 1 Thorium-Based Fuels for PW Rs ................................................
10
1 .1 Intro d u ctio n .........................................................................................
. 10
1.2 Historical Review of the use of Thorium in nuclear reactors..................11
1.3 Alternative designs analyzed...............................................................
12
Chapter 2 Thermal-Hydraulic analysis.......................................................
16
2 .1 Intro d uctio n .........................................................................................
. 16
2 .2 V IP R E cod e .........................................................................................
. 17
2.2.1 VIPRE model capability..................................................................
18
2.2.2 Inputs to the code.............................................................................18
2.3 Thermal Performance Assessment ......................................................
21
2.4 Reference PW R core description ........................................................
24
Chapter 3 Seed Blanket Unit (SBU) design................................................ 27
3.1 Design parameters ...............................................................................
29
3.2 In-core fuel management......................................................................
30
3.3 Inputs to the VIPRE code ......................................................................
33
3.4 SBU Thermal-hydraulics......................................................................
36
3.4.1 BOC, MOC and EOC thermal-hydraulic fuel assembly performance..37
3.5 SBU design optimization .....................................................................
45
Chapter 4 Whole Assembly Seed and Blanket (WSB) design...................51
4.1 Design parameters ...............................................................................
51
4.1.1 W SB metallic seed design ...............................................................
53
4.1.2 W SB uranium dioxide seed pellet design .......................................
54
4.2 In-core fuel management......................................................................
55
4.3 Inputs to the VIPRE code ......................................................................
56
4.4 WSB Thermal-hydraulics modeling results............................................63
4.5 W SB design optimization......................................................................
67
Chapter 5 Thorium-Based fuel thermal-hydraulics : comparison of options ...74
Chapter 6 Economic analysis ....................................................................
76
6.1 Analysis methodology and assumptions.............................................. 76
6.1.1 Front end costs ..............................................................................
76
6.1.2 Operational costs ............................................................................
82
6.1.3 Fuel disposal costs...........................................................................83
6.2 Economic design comparison............................................................... 84
6.3 Sensitivity analysis ..............................................................................
88
Chapter 7 Conclusion .................................................................................
92
7.1 Thermal-hydraulics results ...................................................................
92
7.2 Economic results ...................................................................................
93
7.3 Future research ...................................................................................
94
Appendix A : Annualized Cost Calculation ......................................................
95
4
Appendix B : PW R base design analysis ........................................................
97
106
Appendix C : SBU input file for VIPRE ..............................................................
Appendix D : W SB input files for VIPRE............................................................112
References........................................................................................................130
5
LIST OF FIGURES
Number
Page
Figure 1 Conventional PWR fuel assembly vs. SBU assembly....................... 13
Figure 2 SBU assembly as part of a PWR core .............................................
14
Figure 3 WSB assembly array in a PWR core................................................ 15
Figure 4 Different groups involved in the new product design process ........... 16
Figure 5 Subchannel analysis of a SBU bundle .............................................
19
Figure 6 Subchannel, gap and rod information input.......................................20
Figure 7 Westinghouse PWR fuel assemblies ...............................................
25
Figure 8 PWR Fuel assembly with dimensions ...............................................
26
Figure 9 SBU seed and blanket regions.........................................................
28
Figure 10 SBU radial core power map (cycle 5)............................................. 30
Figure 11 SBU relative pin power distribution .................................................
31
Figure 12 SBU axial power distribution ..........................................................
32
Figure 13 Subchannel, rod and gap definition for the SBU assembly. ............ 34
Figure 14 SBU subchannel identification ........................................................
34
Figure 15 SBU rod identification...................................................................... 35
Figure 16 SBU gap identification....................................................................
36
Figure 17 Hot channel avergage axial temperature profile.............................. 38
Figure 18 Hot channel - hottest subchannel axial temperature profile............ 38
Figure 19 Hottest channel MOC axial temperature and quality profile ............ 39
Figure 20 SBU DNBR analysis for the BOC, MOC and EOC..........................40
Figure 21 SBU MOC exit temperature profile..................................................40
Figure 22 SBU hottest subchannel location ....................................................
41
Figure 23 SBU MOC exit void fraction ............................................................
42
Figure 24 MOC radial temperature profile in the hottest seed rod at an
assembly average q'=25 kW/m ............................................................
44
Figure 25 MOC radial temperature profile in the hottest blanket rod at an
assembly average q'=25 kW/m ............................................................
45
Figure 26 Effect of different blanket local loss coefficient on limiting linear power
and pressure drop for the SBU assembly...........................................
47
Figure 27 Effect of different blanket local loss coefficient on MDNBR for the
S B U asse m b ly ...................................................................................
. . 48
Figure 28 Optimized vs. base design temperature profile for the hottest seed
ro d ......................................................................................................
. . 49
Figure 29 Optimized vs. base design temperature profile for the hottest blanket
ro d ......................................................................................................
. . 49
Figure 30 W S B design ...................................................................................
52
Figure 31 WSB alternative seed rod designs ..................................................
53
Figure 32 WSB-A relative pin power distribution............................................. 57
6
Figure
Figure
Figure
Figure
Figure
Figure
Figure
Figure
Figure
Figure
Figure
Figure
Figure
Figure
Figure
33 WSB-B realtive pin power distribution.............................................57
58
34 Sub-channel analysis of the WSB array design ..............................
58
35 WSB-A subchannel identification ....................................................
59
36 WSB-B subchannel identification ....................................................
37 WSB-A rod identification .................................................................
60
38 WSB-B rod identification .................................................................
61
39WSB-A gap identification .................................................................
62
40 WSB-B gap identification ...............................................................
63
41 WSB axial temperature profile ........................................................
64
42 WSB-A/B DNBR analysis for MOC of the hot seed assembly.........65
43 WSB-A four assemblies coolant exit temperature profile ................ 65
44 WSB-A coolant exit temperature distribution...................................66
45 WSB-B four assemblies coolant exit temperature profile ............... 66
46 WSB-B coolant exit temperature distribution...................................67
47Effect of different blanket local loss coefficient on limiting linear power
and pressure drop for the WSB-A assembly ........................................
68
Figure 48 WSB-B temperature distribution at the hottest seed rod at an
assembly average q'=27 kW/m ............................................................
71
Figure 49 WSB-B temperature profile at the hottest blanket rod at an assembly
average q'=27 kW/m ............................................................................
72
73
Figure 50 WSB-B base design exit temperature profile .................................
Figure 51 WSB-B optimized design exit temperature..................................... 73
77
Figure 52 Front end fuel cycle fowchart ........................................................
Figure 53 Fuel front-end cost calculation ......................................................
81
Figure 54 Annualized cost calculation for one cycle....................................... 83
Figure 55 Contribution of each step of the fuel cycle to total cycle cost..........88
Figure 56 Total cycle cost sensitivity to SWU cost......................................... 89
Figure 57 Total cycle cost sensitivity to total fabrication cost ..........................
90
Figure 58 Total cycle cost sensitivity to refueling outage length......................91
Figure 59 Different economic analysis approaches.........................................96
97
Figure 60 PWR assembly subchannel identification ......................................
Figure 61 PWR assembly rod identification.................................................... 98
Figure 62 PWR assembly gap identification....................................................99
Figure 63 PWR assembly relative pin power distribution .................................. 100
Figure 64 Radial temperature profile in the hottest rod of a PWR assembly.....101
7
LIST OF TABLES
Number
Page
Table 1 Operating parameters of a typical Westinghouse 4-loop PWR .......
25
Table 2 SBU Fuel Assembly Parameters ......................................................
29
Table 3 SBU rod diameter sensitivity analysis ...............................................
46
Table 4 WSB-A assemblies design parameters..............................................54
Table 5 WSB-B assemblies design parameters..............................................55
Table 6 WSB differential loss coefficient optimization results ........................
70
Table 7 Thorium-Based Seed-Blanket fuel design comparison.......................75
Table 8 Thorium-based fuels economic comparison.......................................85
8
ACKNOWLEDGMENTS
The author thanks all the members of the MIT NED Fuel Cycle Group for their
collaboration in this study. Special thanks to my thesis advisor Mujid Kazimi for
his guidance and assistance in the completion of this thesis.
This thesis is dedicated to my parents for all their continual support and
sacrifices during my graduate studies, and specially to my wife Mery. Without
her love and encouragement these two years at MIT would not have been
possible. I cannot truly express my appreciation for her patience and sacrifice in
supporting me through the SDM program.
9
Chapter 1
THORIUM-BASED FUELS FOR PWRS
1.1
Introduction
Thorium-based fuels had been of interest to the nuclear industry due to the
abundance of thorium ore and also because of some important neutronic
advantages. Thorium cycles differ from the conventional uranium cycle in that
thorium-232 (Th 2 3 2 ) produces uranium-233 (U2 3 3 ), which generates neutrons by
fission in the thermal and epithermal neutron fluxes. The different processes are
shown below:
U 2 38
+n _Pu
Th232+n
-+U
23 9
233
This thermal absorption cross section to convert the fertile atom into a fissile
one is higher for Th2 3 2 than for uranium-238 (U2 3 8 ). Thus the in-core fissile
generation capability of thorium-based fuels can be higher, reducing the need of
fuel ore and/or the enrichment per unit of energy generation. The enhanced
proliferation resistant features of the spent fuel complement these potential
economic benefits. This includes the reduced production of plutonium and the
mix of its isotopes that would be less useful in weapons.
The main drawback of the thorium cycle is the lack of U2 3 3 in nature. This
translates in the need for a fissile material such as uranium-235 (U2 35 ) or
plutonium-239 (Pu
23 9
) as a source of neutrons in the early stages of the cycle.
Thus, thorium is used as a part of a thorium-uranium (or thorium-plutonium) fuel
mixture. Although the use of two materials seems as a disadvantage, it is offset
by the significant reduction in plutonium content of the fuel cycle [Ref. 1].
10
Early reviews of nuclear fuel cycles tended to conclude that the uranium cycle
was more preferable than the thorium cycle because of the high cost of the
initial investment in U2 3 5 and the relative reprocessing disadvantages of the
thorium fuel. The conditions of the nuclear industry have changed, focusing on
once-through fuel cycles (no reprocessing). The incentives for further analysis
of fuel alternatives such as the thorium-based cycle given this situation are
clear: economic performance, safety, reduced waste production and enhanced
proliferation resistance.
1.2
Historical Review of the use of Thorium in nuclear reactors
The first core experiments in the use of thorium-uranium oxide fuels date from
the 1960s and 1970s. Two types of designs were analyzed at that time, a
uniform lattice with mixed thorium oxide with highly enriched uranium oxide and
an heterogeneous arrangement of seed and blanket regions, where the blanket
is responsible of producing in-core fissile material while the seed is the source
of neutrons, especially in the early stages of the cycle.
These early approaches to thorium based fuels were done at a time when
reprocessing of the spent fuel for recycling fissile material was the prevailing
expectation and the proscription of a 20% uranium enrichment limit against
proliferation was not an issue. The high gamma energy associated with U-232
in the thorium cycle increases the radiological protection needs during
reprocessing making the use of thorium less appealing.
The Light Water Breeder Reactor (LWBR) program at Shippingport was the first
to demonstrate the seed-blanket concept for commercial power generation in
the late 1970s. Some shortcomings from the LWBR were the lower power
density of the core compared to modern PWRs, and the more complicated
recycling process for two types of fuels containing U and Th compared to
11
recycling one type of fuel in the U and Pu cycle, especially because of the need
of extra shielding in the fabrication process.
Later, in mid 1970s EPRI commissioned a study of the use of thorium in
modern Light Water Reactors (LWRs). The conclusions were that the use of
thorium with recycle can increase the energy output per mined ton of uranium
but with no economic attractiveness (savings occurring later in the cycle).
Additionally the study concluded that thorium fueling was feasible, and no
modifications to a PWR design were needed [Ref. 2].
Reactor types other than LWRs have experimented with the use of thorium, but
no design proved successful enough to justify further investigations [Ref. 3].
Recently, some new characteristics of the thorium cycle attracted the attention
of the nuclear community. The increased cost of management of spent fuel and
the proliferation resistance attributes of spent fuel from US reactors are among
the key reasons for new research initiatives [Ref. 4].
An improved seed-blanket concept was recently proposed by Alvin Radkowsky
based on the ideas of the LWBR program. This once-through light water
thorium
technology,
known
as
RTF
(Radkowsky
thorium
fuel),
is
nonproliferative, provides reduction in fuel waste and is expected to reduce fuel
costs. A key feature is that an RTF design can be implemented in current
PWRs cores [Ref. 5][Ref. 6].
1.3
Alternative designs analyzed
In the present study, heterogeneous seed-blanket designs are analyzed.
Keeping in mind the goals of the new fuel, some design constraints were
applied in order to take into account the context where the fuel is going to be
used. These constraints will facilitate the commercial implementation of the
concept by allowing the use of the new fuel in typical commercial PWRs.
12
The most relevant constraints are:
" Compatibility with existing PWR's
" Comparable Environmental, Safety and Health characteristics
" Economic Competitiveness
Two designs are analyzed: the Seed Blanket Unit (SBU) and the Whole Seed
and Blanket array (WSB). Both approaches are based on the seed and blanket
regions concept. However, while the SBU implements these regions within a
fuel assembly, the WSB has whole assemblies as seeds or blankets. Figure 1
compares a conventional PWR uranium based assembly with the SBU design
approach. The seed region is fissile rich, while the blanket region has low initial
fissile content.
17 rods
17 rods
Figure 1 Conventional PWR fuel assembly vs.
SBU assembly.
13
The SBU is designed to be used in current PWRs, whose core layout is
depicted in Figure 2. Each assembly has two regions; the center is composed
of seed rods while the blanket is surrounding it. These regions should be stand
alone elements as their fuel type and management are very different (this will
be discussed in detailed in the next chapter). Because of its higher power
density, the seed region requires smaller fuel pin diameters and/or fuel material
with higher conductivity than the blanket region. In Chapter
3 a detailed
analysis of the SBU will be given.
Seed region
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Blanket region
PWR core outlay with SBU assemblies
Figure 2 SBU assembly as part of a PWR core
The WSB approach uses a whole assembly as a seed or a blanket. The
resulting core looks like a checkerboard with seed assemblies surrounded by
blankets. In this case each assembly follows different fuel management
policies.
14
The checkerboard approach is very appealing given that the refueling units are
the same as those used in current PWRs. A more detailed analysis of this
design will be given in Chapter 4.
The basic layout of the checkerboard array is shown in Figure 3.
Blanket assembly
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Figure 3 WSB assembly array in a PWR core.
15
Chapter 2
THERMAL-HYDRAULIC ANALYSIS
2.1
Introduction
The thermal-hydraulic analysis is part of the New Fuel Design Process. This
process can be divided in reactor physics, thermal-hydraulics, materials, wastemanagement and overall performance. The relationship between these design
groups is shown in Figure 4.
Thermal-hydraulics
analysis
Physics
-
Power distribution
Moderator/Fuel ratio
FuBurnup
4
MDNBR
Temperature profile
New Fuel
Concept Design
-
c ---
Materials
on Fuel materials t
(oxides, carbides,
nitrides, metals)
-Fission Gas Release
Corrosion
Performance-
Economics
Waste Management
.
a
Fuel materials stability
(oxides, carbides,
nitrides, metals)
Long term
radiotoxicity
Proliferation concerns
Figure 4 Different groups involved in the new
product design process
The fuel design is a feedback process among all these groups as the inputs for
one of them are the outputs from another. For example, the type of material
16
selected will directly affect the fissile material density in the fuel, constraining
some neutronic design parameters. On the other hand, neutronic parameters
will determine the power generation distribution, which drives the fuel thermalhydraulics performance. As a result of the thermal analysis, the materials group
should assess the cladding and fuel temperatures, ending in this way one of the
several feedback loops in the product design process (PDP).
The thermal-hydraulic performance of the different designs was assessed by
the use of a Thermal-Hydraulic Code for Reactor Cores -VIPRE-01-. The
selection of a nuclear reactor modeling code was based on the feasibility to
model heterogeneous assemblies and the verification and prior use for safety
licensing submittals.
Additionally, this code helps to evaluate nuclear reactor core safety limits
including minimum departure from nucleate boiling ratio (MDNBR), critical
power ratio (CPR), fuel and clad temperatures, and coolant properties in normal
operation and assumed accident conditions. Typical coolant, fuel and cladding
physical properties are also included in the code, all of them being largely
previously benchmarked [Ref. 7].
2.2
VIPRE code
VIPRE ( Versatile Internals and Component Program for Reactors; EPRI [Ref.
7]) was developed
for nuclear power utility thermal-hydraulic
analysis
applications.
The code was developed by EPRI in response to the utility industry's need for a
publicly available code for boiling water reactors (BWR) and PWR core
analysis. It predicts the three-dimensional velocity, pressure, and thermal
energy fields and fuel rod temperatures for single- and two-phase flow in PWR
and BWR cores. The code solves the set of finite-difference conservation
17
equations for mass, energy and momentum of the coolant in interconnected
subchannels, assuming incompressible thermally expandable homogeneous
flow. Although the formulation is based on homogeneous coolant for each finite
volume, nonmechanistic models are included for subcooled boiling and
vapor/liquid slip in two-phase flow.
2.2.1 VIPRE model capability
VIPRE modeling structure is based on subchannel analysis. The core, fuel
bundle or any other section of symmetry is defined as an array of parallel flow
channels with lateral connections between adjacent channels. A channel may
represent a small area between fuel rods or a larger area representing several
rod bundles. The shape and size of these subchannels is arbitrary, depending
on the expected level of detail in the analysis. In areas where the fuel design is
expected to be critical, the fuel is analyzed in detail, while in the rest of the core
average values are good enough.
The code is tailored to the utilities' analytical requirements in fuel reload
analysis, allowing for example the use of several Critical Heat Flux (CHF)
correlations, capability to iterate operating conditions to a given MDNBR (safety
requirement), and thermal transport within fuel rods with gap conductance
model.
2.2.2 Inputs to the code
Input to the VIPRE code is organized into several groups. These groups can be
divided in geometry of the problem, physical properties of the coolant, boundary
conditions, models to be used for the flow and heat transfer solutions, and the
numerical method to be used.
18
In order to understand the model used in this study, an example of the
geometry input will be given. The main parts of the geometry are described by
the subchannels, the gaps connecting them, and the rods.
Subchannel 2
Subchannel1
Subchannel 4 Subchannel 5
Subchannel 3
Subchannel 8 Subchanne
l
Subchanne1 6
Subchanne 7
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oo0
0000000
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0oooooooooo
00
00000
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00.ooaoogoo doo o
0000000000000000
00000000000000000)
eQa
o00000000see
000000000000000s
~000000000000>c(
000@000000000@00
030000000000000
00000000000000000
Figure 5 Subchannel analysis of a SBU bundle
Figure 5 shows a typical SBU bundle, with the different kinds of subchannels
that were defined for the analysis. In this case nine different subchannels were
19
identified. Each subchannel has a characteristic flow area, wetted perimeter
and heated perimeter All of the subchannels in the model belong to one of the
types shown in Figure 5. Once this information is supplied to the code, some
additional geometry relationships are needed as gap types (dimensions),
wetted and heated perimeters and distance between centroids of channels.
This information for a specific subchannel is shown in Figure 6.
o O
--
@000
~
O
&~,~i~h%'
information
00
Axial
Gap
0-ebi~
Subchannei area
Wetted perimeter
Heated perimeter
0 Neighbors
Dimension
subchannel:
0)Connecting
* Dimension
00000
Axial power distribution
-
Rods
-
100
0 0 0
*
Subchannel
--
0
1000tc
O OO
Crossfiow
0 Assembly power
-distribution
Pin power distribution
between
subchannels
Figure 6 Subchannel, gap and rod information input
The wetted perimeter is given by the proportional perimeter of the surrounding
rods facing each subchannel, while the heated perimeter is constrained to heat
generating rods (exclusion of control and structural rods).
In the following chapters more detailed inputs for each case will be given, but all
of them are based on the same kind of model: a subchannel analysis of a fuel
bundle. This analysis can be applied to the hot assembly in the core (in order to
analyze safety requirements as MDNBR) and to the average assembly (to for
example analyze exit temperature profiles between the seed and the blanket
region).
20
2.3
Thermal Performance Assessment
In the thermal design analysis, fuel integrity will define the maximum allowable
power level in a nuclear reactor. The most important factors are:
"
Fuel temperature safely below the melting point or phase transition
points
"
Heat flux to coolant below a maximum value allowable by coolant
conditions (under expected operating conditions and under postulated
accidents)
"
Burnup and fission-gas release inside the rod limited to avoid excessive
internal pressure
" Suitable power density for a convenient refueling time and reasonable
fabrication cost
*
Rate of power change limited to prevent excessive local stresses
The first two factors are analyzed in the current study, while the materials and
physics properties for the SBU and WSB were addressed by others at MIT [Ref.
8] [Ref. 9].
The major limitation on the thermal design of a PWR is the necessity to
maintain an adequate safety margin between operating heat generation
conditions and the critical heat flux or critical power. The fuel design criterion in
PWR is usually stated in terms of a departure from nucleate boiling ratio
(DNBR), that is defined as:
correlation
DNBR = DNB heat flux predictedby applicable
local heat flux from fuel claddingto coolant
21
It can be seen that the DNBR is a function of the coolant conditions at a certain
location (numerator) and of the power distribution in the fuel (denominator). It is
the minimum DNBR (MDNBR) in the hottest channel that drives the design
process.
A typical PWR criterion is that the MDNBR > 1.30 at maximum overpower
conditions with high level of confidence. The probability of a PWR reaching this
condition is very small and even then the number of rods in the fuel with DNBRs
close to 1.3 is also small.
It should be noted that the departure from nucleate boiling does not necessarily
lead to fuel damage. Some development tests and reactor tests have shown
that operation at or beyond DNB can proceed for limited periods of time without
adverse effects [Ref. 10]. But the lack of sufficient data to describe the fuel
damage leads to the licensing assumption that fuel damage will occur whenever
the heat flux exceeds the DNB value.
For light water reactors the key thermal-hydraulic design criterion to be satisfied
is [Ref. 11]: "For departure from nucleate boiling ratio (DNBR) or critical heat
flux ratio (CHFR) correlations, there should be a 95% probability, at the 95%
confidence level, that no fuel rod in the core experiences a departure from
nucleate boiling condition during normal operation or transients that are
anticipated to occur with moderate frequency".
In order to satisfy the above licensing criterion, the following is necessary [Ref.
12]:
" To have a correlation to calculate DNB heat flux
" To be able to calculate the parameters that are needed to predict the
DNB
22
*
To express the DNB thermal design criterion in terms of the MDNBR
*
To make allowance for the uncertainties in evaluating the minimum
DNBR
*
To establish which of the anticipated transients is the most limiting for
DNB
Regarding correlations for DNB, a number of different correlations have been
developed. Among them, the most well known and publicly available are the
Westinghouse W-3 CHF correlation, Babcock & Wilcox BAW-2 CHF correlation,
the EPRI correlation, and the Combustion Engineering CHF correlation CE-1.
These correlations were developed for 15 x 15 fuel bundles, but when they
were used for 17 x 17 bundles it was observed that they do not predict the fuel
behavior with sufficient accuracy. New correlations were fitted for this case but
because of the proprietary nature of them, the approach used in this study is
constrained to the previous set of correlations. Although these calculations may
not be highly accurate, the results obtained are expected to be relevant in order
to compare different designs since all have the same boundary conditions and
very similar geometry configurations.
The selected correlation for this study is the Westinghouse W-3L that takes into
account the effects of grids and rod bundle effects on the DNB (L factor). This
correlation is included in the VIPRE code. The W-3 correlation was developed
using Westinghouse' THINC subchannel code. Since VIPRE and THINC have
similar two-phase flow correlations and the benchmarks of VIPRE against
THINC performed by Westinghouse showed good agreement between them,
the use of the W-3 correlation with VIPRE was considered suitable for the
purpose of the present study.
A MDNBR limit must be specified in order to satisfy the 95% probability of not
having any rod experiencing departure from nucleate boiling with 95% of
confidence level. This limit definition depends on the data population used to
23
construct the CHF correlation, the larger the amount of data the more reliable
the correlation. As the estimations are more reliable, the DNBR required limit is
smaller. The limit is also affected by the slope of the correlation in the CHFquality plane [Ref. 13]. As an example of these effects, the W-3 correlation has
a limit for MDNBR of 1.30 while the CE-1 correlations has a limit of 1.13. All the
correlations satisfy the 95% probability at 95% confidence level criterion. All
thermal analysis in this study will use the MDNBR of 1.3 applicable to the W-3L
CHF correlation.
The general design criteria require the consideration of normal operating
conditions and frequent transients. In order to take into account these
situations, a shortcut was used in the design process. DNBR calculations are
taken at 118% rated power, and the MDNBR is required to be above its limit
[Ref. 12]. Additional analysis of transients, such as excessive load increase
transient, uncontrolled control rod assembly withdrawal at power and complete
loss of reactor coolant flow, should be considered for further studies.
2.4
Reference PWR core description
The selected PWR design for analysis of the different fuel arrangements was a
Westinghouse 3400 MWth four loop plant. This core design will constrain fuel
assembly configurations in order to make them compatible and ready to use in
current reactors. The most important boundary conditions for this type of plant
are summarized in Table 1.
The fuel assemblies analyzed were a 17 x 17 array of fuel rods with 24 guide
thimbles for control rods and one guide tube for instrumentation. A photograph
of an assembly is shown in Figure 7 while the most important fuel dimensions
are given in Figure 8. The core is of the open type, this means that the
assemblies are not contained in individual channels. Eight spacer grids were
considered equally spaced in the fuel length and the L-grid with mixing vanes
24
correlation was selected to take them into account in the DNB correlation (W3L).
Table I Operating parameters of a typical Westinghouse 4-loop PWR
Parameter
Value
Reactor Core Heat Output [MWth]
3,400
System Pressure, nominal [MPa]
15.5
Total Flow Rate [Mg/s]
18.63
Effective Flow Rate for heat removal [Mg/s]
17.70
Active Fuel Height [cm]
366
Number of Assemblies
193
Inlet Coolant Temperature [*C]
289
Figure 7 Westinghouse PWR fuel assemblies [Ref. 14]
25
21.5 cm
1.35 cm
-n
Co
-9
00
0.
iU)
0n
0 0 000000
0 000000
0 0 000000 0
0 000000
0 00000 0 0 000000 0
0 000000 0 0 000000 0
0 000000 0 0 000000 0
0 000000 0 0 000000 0
0 000000 0 0 000000 0
0 000000 0 0 000000 0
0 000000 0 0 000000 0
0 000000 000 000000 0
0 000000 000 000000 0
0 000000 000 000000 0
0 000000 000 000000 0
0 000000 000 000000 0
0 000000 000 000000 0
0 000000 000 000000 0
0 000000 000 000000 0
1.26 cm
21.40 cm
t--
N)
0)
0
0 000000 0
0 000000
0 000000
0 0 000000 0
0 000000
0 0 000000 0
0 000000
0 0 000000 0
0 000000 0 0 000000 0
0 000000
0 0 000000 0
0 0 000000 0
0 000000
000000 0
0 000000
010
0
0 000000
000 000000
000000
0 000000
000 000000 0
0
0 000000
000
0
0 000000
000 000000
0
000000
0 000000
000
0 000000
000 000000 00
0 000000
000000
000
000000 0
000000
0
000
0 000000
OOOO 0
Guide Thimble/
Control Rods
(25 per assembly)
Fuel Rods
(264 per assembly)
Chapter 3
SEED BLANKET UNIT
(SBU) DESIGN
In the proceedings for the International Conference On Future Nuclear
Systems, Global 99, Galperin et. al. presented a thorium-based fuel design
approach compatible with existing PWRs
[Ref. 15]. The objectives of this
design were to enhance the proliferation-resistance, reduce waste storage and
disposal requirements and produce fuel cycle cost savings, while keeping
comparable environmental and safety characteristics of current nuclear fuels.
In a conventional PWR fuel assembly, the type of fuel -U0 2 - and rods are
homogenous but within the SBU assembly two different fuel types in two
regions are defined as shown in Figure 9. The central part is called the seed
region because it is the supplier of neutrons for the assembly (supercritical)
while the surrounding area is the blanket which is a subcritical energy and
fissile material generator.
The SBU allows a spatial separation of the seed and the blanket within the fuel
assembly with the possibility of having different core management cycles for
each of them. The seed region (central rods in Figure 9) has a metallic fuel alloy
composed of approximately 45% U (20% enriched) and 55% Zr by weight. This
enrichment is accepted to be nonproliferative and the U235 presence in the seed
fuel is enough to supply neutrons to the blanket in an efficient way. The use of
metallic fuel in the seed region is driven by its better heat conductance
characteristics (hot region with high heat rate generation) and potential
production cost reduction. On the other hand, the blanket fuel consists of oxides
of thorium plus a small amount (-10% in weight) of uranium oxide enriched to
less than 20%.
27
The seed is where most of the power is generated in the early parts of the
cycle. Thus, its power density is higher than in a conventional PWR assembly
with a relative peak power in fuel pins of 1.69.
11 rods
Seed
" Metallic U/Zr alloy
N
(45%/55% in weight)
- U 20% enriched
Blanket
" (U+Th)O
2
(10% UC/90% Thq in weight)
- U 15% enriched
E
&0
ti
1-0
17 rods / 21.4 cm (bundle)
Figure 9 SBU seed and blanket regions
The extra uranium in the blanket is added for two reasons:
*
Natural thorium has no fissile content, so enriched uranium is required to
provide power during the initial period of uranium-233 build up (product
of burning the thorium in the blanket).
28
*
The uranium-238 and other nonfissile uranium isotopes denature the
discharged blanket residual U-233 so that it is also nonproliferative; i.e.
its percentage in total uranium is always below 12%.
3.1
Design parameters
Table 2 shows the SBU design parameters. Notice that seed rods have smaller
diameter than those in the blanket area, increasing the coolant flow in the
central region (taking into account a boundary condition of constant pressure
drop).
Table 2 SBU Fuel Assembly Parameters 15.
Parameter
Seed
21.4 x 21.4
Fuel Assembly Size [cm]
Side Dimensions [cm]
Fue MteralU/Zr
Fuel Material
Composition
Number of Fuel Rods
Fuel Pellet Radius [cm]
inner-outer
Blanket
13.83
21.4
alloy
metal
(45%/55%
in weight)
U 20% enriched
(10% U02/90% 2ThO 2 in
weight)
U 15% enriched
108
156
0.20
-
0.38
(U+Th)0
0.0 - 0.4095
No
0.0085
Cladding material
thickness [cm]
0.04
0.057
Fuel Cell Pitch [cm]
1.26
1.26
Moderator/Fuel Volume
Ratio
3.3
1.7
Volume Fraction [%]
41
59
Fuel-Clad Gap [cm]
29
Although some previous similar designs considered a separating wall between
the seed region and the blanket, the one analyzed in this study has no walls of
this type.
3.2
In-core fuel management
The seed and blanket have different in-core fuel management schemes. The
residence time of the SBU's seeds in the core is about 3 years, leading to a
high burnup (over 75 MWd/kg HM). The residence time for the blankets is quite
long, about 9 years, which achieves a large burnup (above 100 MWd/kg HM).
The seeds follow a multi-batch replacement strategy, similar to the standard
PWR fuels cycle. Approximately one third of the seeds are replaced periodically
(12 to 18 months) by fresh ones, leaving an inventory of fresh, once burned and
twice burned seed assemblies. All seeds are reshuffled with the partially burned
blankets to the required configuration for the next cycle. The reload period for
the seed is planned to be 1 year.
Relative Power Distribution
1.115
1.232
1.268
--
-~
- - B C
MOC
EOC
Fuel Management
---.. ...
Fresh
Once
1.126
1.158
1 212
..
-----
L...41 ...
. .
-
L
..--
.
L..IL.
......S1.244
Ir10[
------- -------- ---....
1.096
1.09
1.246
1.278
1.319
1.339
J1.161
0 0 0 0L...
:
Twice
1.177
1.331
1.323
1.293
1.295
1.246
L.. ---
U
1.115
1.232
1..9. 1.268
1.2 10
1.120
1.192
1.187
Figure 10 SBU radial core power map (cycle 5)
30
A summary of the core relative power map is given in Figure 10. These results,
given in the Global 99 report [Ref. 15], correspond to the beginning of cycle
(BOC), middle of cycle (MOC) and end of cycle (EOC) of the
5 th
cycle (mid life
of the blanket).
The assembly power distribution given in Figure 10 was used in this study to
identify the hot channel in the core and analyze its thermal-hydraulics
performance, since it will be the one to constrain the power level of the reactor.
Within each assembly, the relative pin power distribution was taken from the
same source (see Figure 11). This distribution (assumed equal for every
assembly) represents the seed to blanket relative power generation and will
identify the hottest subchannel in the assembly.
Pin #
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
1 0.600 0.600 0.600 0.668 0.676 0.682 0.678 0.669 0.664 0.669 0.678 0.682 0.676 0.668 0.620 0.620 0.620
2 0.600 0.581 0.581 0.648 0.665 0.685 0.666 0.640 0.622 0.640 0.666 0.685 0.665 0.648 0.601 0.601 0.620
3 0.600 0.581 0.572 0.636 0.666 0.000 0.668 0.620 0.000 0.620 0.668 0.000 0.666 0.636 0.591 0.601 0.620
4 0.655 0.636 0.624 0.000 1.637 1.695 1.656 1.590 1.546 1.590 1.656 1.695 1.637 0.000 0.647 0.659 0.679
5 0.663 0.653 0.654 1.637 1.508 1.473 1.484 1.470 1.441 1.470 1.484 1.473 1.508 1.637 0.678 0.677 0.687
6 0.669 0.672 0.000 1.695 1.473 0.000 1.421 1.424 0.000 1.424 1.421 0.000 1.473 1.695 0.000 0.697 0.693
7 0.666 0.654 0.656 1.656 1.484 1.421 1.446 1.467 1.456 1.467 1.446 1.421 1.484 1.656 0.680 0.677 0.690
0
S-
8 0.657 0.628 0.608 1.590 1.470 1.424 1.467 1.543 1.612 1.543 1.467 1.424 1.470 1.590 0.631 0.651 0.681
9 0.652 0.610 0.000 1.546 1.441 0.000 1.456 1.612 0.000 1.612 1.456 0.000 1.441 1.546 0.000 0.633 0.675
10 0.657 0.628 0.608 1.590 1.470 1.424 1.467 1.543 1.612 1.543 1.467 1.424 1.470 1.590 0.631 0.651 0.681
11 0.666 0.654 0.656 1.656 1.484 1.421 1.446 1.467 1.456 1.467 1.446 1.421 1.484 1.656 0.680 0.677 0.690
12 0.669 0.672 0.000 1.695 1.473 0.000 1.421 1.424 0.000 1.424 1.421 0.000 1.473 1.695 0.000 0.697 0.693
13 0.663 0.653 0.654 1.637 1.508 1.473 1.484 1.470 1.441 1.470 1.484 1.473 1.508 1.637 0.678 0.677 0.687
14 0.655 0.636 0.624 0.000 1.637 1.695 1.656 1.590 1.546 1.590 1.656 1.695 1.637 0.000 0.647 0.659 0.679
15 0.588 0.569 0.560 0.618 0.648 0.000 0.650 0.602 0.000 0.602 0.650 0.000 0.648 0.618 0.573 0.583 0.602
16 0.588 0.569 0.569 0.630 0.646 0.666 0.647 0.622 0.604 0.622 0.647 0.666 0.646 0.630 0.583 0.583 0.602
17 0.587 0.588 0.588 0.649 0.657 0.662 0.659 0.650 0.645 0.650 0.659 0.662 0.657 0.649 0.602 0.602 0.601
Figure 11 SBU relative pin power distribution
31
Finally the axial power distribution for the three stages of the cycle was also
considered in the thermal-hydraulics calculations. This distribution is very
important to identify the location of the MDNBR within the fuel length. As the
peak location is shifted to the outlet of the reactor, the CHF at this peak is
reduced as a result of a higher average temperature in the coolant.
Figure 12 shows the shape of the axial power distribution for the beginning,
middle and end of cycle.
-BOC
1.6
1.4
4:
power distribution
-MOC power distribution
--
-
-
- -
EOC power distribution
1.2
0
'00
1.0
.
0
S0.8
0.06
0.4
0.2
0.0
23
46
69
91
114
137
160 183 206 229
Axial distance [cm]
251
274
297
320
343
366
Figure 12 SBU axial power distribution
The SBU assembly modeling process is discussed in the following section,
where all the power distribution information will be used with the design
32
characteristics of the fuel as an input to the VIPRE code to predict the thermalhydraulics performance.
3.3
Inputs to the VIPRE code
In this section the modeling within the VIPRE code is discussed. As was
mentioned earlier in Chapter 2, VIPRE requires the user to define subchannels
within the model, with their physical characteristics (i.e. flow cross-sectional
area, wetted perimeter, heated perimeter, neighbors). Additional information is
needed for the gaps connecting the subchannels and the rods.
For this study one whole assembly will be modeled assuming that the
boundaries with adjacent assemblies are symmetric. This means that no heat or
mass fluxes between assemblies are considered.
The selected subchannel definition for the SBU assembly is shown in Figure 5.
Nine different types of subchannels were used for modeling the SBU assembly.
A total of 324 subchannels were defined, each subchannel being the flow area
between fuel rods in a regular rectangular array. This kind of channel grouping
by equal flow area is very useful in order to input the required data into VIPRE.
Subchannels, rods and gaps modeled are shown in Figure 13.
Identification of all subchannels, rods and gaps used in the model are given in
Figure 14, Figure 15, and Figure 16 respectively. An example of a VIPRE input
file can be found in Appendix C.
33
Heated / Wetted
peimeter
Subchannel
Gap
1-adg
[1-612]
Seed
fuel rod
Figure 13 Subchannel, rod and gaV definition fbr Whe SBU assembly.
type i
typ 2
one"wet rod
types3
four MWnhut rod
type 4
seed rdS
type6
type 7
typeS
typee
two blenhiel rode
two blukt rode+ two
wnseed rof
we blehis rods onem
sed rode. 0+1
am aro
rod
fte se rods one
nos1,
odson
ft" ww rod *a
Figure 14 SBU subohannel Identification
34
1
10
2
0
1
2
0
2
0
18
19
3 0
0
35
4 0
52
5 0
69
6 0
86
7 0
103
8
0
120
9
0
137
10 0
154
110
171
12 0
188
13 0
205
14 0
222
15 0
239
16
17
0
36
0
53
3
4
5
6
7
8
0
0
0
0
0
0
3
4
5
6
7
8
0
0
0
0
0
0
20
21
22
23
24
25
26
0
0
0
@
0
@
37
38
39
40
42
43
0
@
0e
54
55
56
OO
0
70
0
87
71
73
@ *
88
41
90
0
91
92
93
0
O
0
0
0o0
0
121
122
123
124
125
126
127
0
@
0
138
139
140
143
144
o
o
o
159
160
161
o
110
111
@
0 0
46
47
95
96
e
112
0
128
129
0
0
33
0
34
0
49
50
@
0
0 0
65
66
67
0
0
51
68
0
82
83
@
0
0
@
0 0
97
98
99
100
101
00
114
0
115
0
@
0
147
148
149
162
163
164
165
00
0
116
0
146
o
0
32
17
48
0
131
e
16
81
130
145
0
17
0
80
0
113
16
0
15
31
64
0
79
0
0*
(e
o
158
94
e
108
142
78
0
30
e0
@ e
ee
109
77
0
63
15
0
14
29
e
76
e
157
62
75
107
O
61
74
106
156
45
e0e e 0
105
0
0
44
14
0
13
0
28
0
0
12
0
27
e
104
155
0
13
0
11
e
0O
*
10
59
60
12
0
58
0
141
0
9
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11
oe
e00
@
89
0
10
57
e
72
0
9
132
0
84
0
0
117
118
0
0 0
133
134
@
0
150
151
152
168
169
135
0 00
166
167
85
102
119
0
136
0
153
00
170
0
0
0
0
0
0
0
0
0
0
0
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
0
@
190
0
191
0
192
@
193
0
194
0
195
@
196
0
197
0
198
@
199
0
200
0
201
@
202
0
203
0
204
214
215
189
0
Oe
206
207
208
0
0
223
224
0
0
0
0
0
0o
o
0
0
0
209
210
211
212
213
@
0
0
0
0
0
0
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0
0
@
0
0
0
225
226
227
228
229
230
231
232
233
234
235
236
237
238
0
0
216
0
217
0
218
0 0
219
220
0
221
0
0
0
0
@
0
0
@
0
0
@
0
0
0
0
0
240
241
242
243
244
245
246
247
248
249
250
251
252
253
254
255
267
268
269
270
271
0
256
257
258
259
260
261
262
263
264
265
266
0
0
0
0
0
0
0
0
0
0
0
273
274
275
276
277
278
279
280
281
282
283
0
Seed
0
Blanket
@
Control rod
0
284
0
285
0
286
0
287
0
288
272
0
289
Figure 15 SBU rod identification
35
WON
0
36
0
71
0
106
0
141
0
176
0
211
0
246
0
281
0
316
0
351
0
386
0
421
0
456
0
491
0
526
0
561
0
4 0
38
39 0
73
74 0
108
109 0
143
144 0
178
179 0
213
214 0
248
249 0
23
284 0
318
319 0
33
354 0
6 0
8 0 10 0
42
44
40
41 0 43 0 45 0
75
77
76 0 78 0
8O0
110
111 0
145
148 0
o
12 0 14 0
16 0 18 0
20
46
48
50
52
47 0 49 0 51 0 53 0 55
3
85W
86
%
*
U
U
U
U
U
0
54
0
89
9216M
26 0
60
U
0
61 0
95
0
0
U
S
U
U M 0
Ueoeoe
U
U
U
U
22 0 24 0
56
58
57 0
59 0
91
28 0
30 0 32
62
64
63 0
65 0 67
97
99
98 0 100 0 102
134
0
0 137
169
0
0 172
101
0
136
0
171
0
206
34 0
68
69 0
103
104 0
138
139 0
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208
0 209 0
o e oee
U
U
e
o oe o
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U
U
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21_9;
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J
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0m M
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388
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424 0
458
459 0
493
494 0
528
529 0
563
564 0
0
66
0
mem
-
~'I
* ~6~S~6~~~@~@
0
426 0
0
0
460
0
n0
0
461 0
495
M
496 0 498 0 500
0 506
530
532
534
538
531 0 533 0 535 0 537 0 539 0 541
565
567
569
571
573
566 0 568 0 570 0 572 0 574 0 576
U
U0
13
M
U
I
KI
I
0
0
540
544
U
512
K
M
0
546
0m 518
0 520
241
243
0 244 0
276
278
0 279 0
311
313
240
0 314 0
346
348
0 349 0
381
383
0 384 0
416
418
0 419 0
451
453
0 454 0
486
488
0487 0 489 0
523
521
519
UO221eoeoe
s
0
522
0
524
554
556
0 543 0 545 0 547 0 549 0 551 0 553 0 555 0 557 0 559
575
577
579
581
583
585
589
587
591
0 578 0 580 0 582 0 584 0 586 0 588 0 590 0 592 0 594
550
552
0
558
0
593
0
rod to assembly edge
type 2 blanket to blanket rod
blanket to control rod
seed to control rod
seed to seed rod
blanket to seed rod
* Seed
0 Blanket
* Control rod
Figure 16 SBU gap Identification
3.4
SBU Thermal-hydraulics
In this section, the VIPRE thermal-hydraulics results for the base design given
in the Global 99 report [Ref. 15] are studied for the different stages of a cycle.
Following these results, the highest power level achievable with this fuel will be
calculated based on a more detailed analysis of the most restrictive operating
condition, including temperature profiles and DNB analysis.
36
3.4.1 BOC, MOC and EOC thermal-hydraulic fuel assembly performance
The different power distributions of the SBU fuel during a typical cycle (5 th
cycle) directly impact the fuel performance (see Figure 10 and Figure 12). The
most restrictive condition will constrain the reactor power level, since no
boundary conditions or physical arrangements can be changed during one
cycle.
The core radial power distribution shown in Figure 10 was used to identify the
hottest channel in the reactor. Its power level given the boundary conditions of a
W-PWR (3400 MWth, see Table 1) and the radial peaking factor was used to
analyze the fuel performance at each stage of the cycle.
Figure 17 shows the average coolant temperature in the SBU analyzed channel
(hot channel). The higher peak factors for the MOC and EOC result in higher
average exit temperatures for these parts of the cycle. The plotted temperature
is the average across the whole bundle, but as significant different power levels
can be found in the seed compared to the blanket, the problem must be
analyzed at the hottest spot in the fuel. In this case, the hottest subchannel
shows the higher temperature found in the fuel. The temperature profile for this
critical location is shown in Figure 18. The coolant temperature reaches the
boiling temperature in the region close to the exit, meaning that saturated
boiling is taking place. It should be noted that this situation is found only in a
specific location in some of the hot-channels in the reactor core. The
appearance of positive coolant flow quality' is shown in Figure 19 for the MOC
power distribution (it should be noted that flow quality is differently defined
compared to the thermal equilibrium quality. The flow quality accounts for vapor
present under subcooled bulk coolant conditions, while thermal equilibrium
quality does not. This is the reason why its value decreases close to the exit
'The EPRI correlation developed by Lellouche and Zolotar was used for calculating the flow quality.
37
where heat flux from the fuel is low. For detailed information about the boiling
models used and correlations see VIPRE-01 Mathematical Modeling [Ref. 16]).
350
Boiling temperature
340
330
320
E 310
BOC
. . MOC
300
,..
EOC
290
280
0
23
46
69
91
114
137
160 183 206 229
Axial Distance [cm]
251
274
297
320
343
366
Figure 17 Hot channel avergage axial temperature profile
350
Boiling temperature
340
330
320
E 310
,/
I-
BOC
-
.
MOC
-
- EOC
300
'-
290
280
0
23
46
69
91
114
137
160 183 206
Axial Distance [cm]
229
251
274
297
320
343
366
Figure 18 Hot channel - hottest subchannel axial
temperature profile
38
0.030
350
temperature
-Boilng
340
-0.025
330
0.020
320
-0.015
aa
E 310
-0.010
300
---
Temperature__.5
-0.005
290-
-Quality
280
0.000
0
23
46
69
91
114 137 160 183 206 229 251
274 297 320 343
366
Axial Distance [cm]
Figure 19 Hottest channel MOC axial
temperature and quality profile
An analysis of the DNBR for the hottest subchannel in the fuel can easily show
that some parts of the cycle are more critical than others. Figure 20 shows the
DNBR along the length of the fuel for the three parts of the cycle. The minimum
DNBR found is very similar for the MOC and EOC, because their peaks are
shifted to the exit of the channel, where the coolant temperature is higher and
consequently the DNB is lower.
Since the MOC distribution usually describes a larger period of time of the fuel
in the core, it was selected as the best one to use for fuel performance
evaluation.
The MOC exit temperature profile gives a very good sense of the impact of
different power levels between the seed and the blanket, and also shows the
hot locations within the fuel (see Figure 21 and Figure 22).
39
4.0
-BOC
3.8
- -- EOC
3.8
3.4
3.2
3.0
2.8
I
2.6
2.4
E C_-__
-
__-_
2.2
2,0
A-
-
1,6
1.4
1
-f
1.2
1.0
23
46
69
91
114
137
180
183
206 229 251
274 297 32C 343 366
Axial distance [am]
Figure 20 SBU DNBR analysis for the BOC, MOC and EOC
345
I
338
w og
33 75
- 331
D] U
-
324
- 317
Figure 21 SBU MOC exit temperature profile
40
345
338
33 1L
o ai n f
324
317
Figure 22 SOU hottest subchannel location
Other results from the simulation can give some additional insights of the fuel
thermal-hydraulics performance. The void fraction found at the exit of the
modeled channel (SBU hot channel) clearly shows the location of the most
compromising areas, where two phase flow is taking place, see Figure 23. As
one can expect, these regions are the locations where the coolant temperature
is higher.
41
G 14
.0
10
0
Figure 23 SBU MOC exit void fraction
3.4.1.1 Impact of the fuel's thermal-hydraulics performance on materials temperatures
The temperature condition within seed and blanket rods was analyzed by using
a conduction model for each part of the fuel. The conduction heat transfer
model applied was based on a control volume formulation of the conduction
equation, and was supported by the VIPRE code.
For the class of problems addressed in this study, axial and circumferential
conduction in rods were relatively unimportant, and only radial conduction was
considered. In order to solve the conduction equation, radial nodes are
positioned within the conductor material (fuel and gap) and local radial power
distributions are assigned.
42
Fuel materials properties for the seed rods were taken from the MATPRO
library of thermal conductivity for metallic uranium nuclear fuels [Ref. 17]. The
model does not take into account burnup, fission product appearance or
irradiation and is based on a second order polynomial curve derived from
experimental data:
K = 20.457 +1.204710-
2
-T - 5.736810- 6 *T2
Equation I
where :
K[W /(m "K)] andT ["K]
For the seed's Zr a constant conductivity of 22.7 W/(m 0K).
For the blanket's thermal conductivity, the Belle and Berman correlation was
used [Ref. 17]. This correlation calculates the thermal conductivity of thoriaurania mixtures as a function of temperature:
K=
A =
1
,
1
Equation 2
AO +A1 -M
B = BO + B, -M + B2
M2
where:
AO = 46.958, BO =1.59710-4 ,A= -112.072, B, = 6.73610~4 , B 2 = -2.15610- 3
K[W /(m "K)], T["K] andM[mole fractionof U0 2 ]
A uniform radial power profile for the fuel rod was assumed in order to calculate
the internal temperature distribution.
43
The temperature profile for the hottest seed rod (rod 201, Figure 15) is given in
Figure 24 for an operating condition satisfying the required MDNBR=1.3 (25.09
kW/m average linear power for the hot channel).
At 2.5m from the bottom of the assembly
O6U
550
500
450
400
Il//I00,
350
/
/
/
\II
\
300
1
/.0
///
3
P 1300
4
/
5
6
7
8
9
Nodes
Fluid
Clad
Figure 24 MOC radial temperature profile in the hottest seed rod
at an assembly average q'=25 kWIm
In the case of the hottest blanket rod (rod 117, Figure 15), the same operating
condition was taken, but additionally the fuel-clad gap conductance was taken
into account.
44
At 2.5m from the bottom of the assembly
800
750
700
650
2 600
l 550
E
1 500
450
400
a-
350
3AA
I
/
A
5
Nodes
134
76
7
8
9
/
Fluid
Clad
Figure 25 MOC radial temperature profile in the hottest blanket rod at
an assembly average q'=25 kW/m
3.5
SBU design optimization
In order to optimize the SBU thermal-hydraulics, a MDNBR criteria was used as
a metric for fuel performance. For all cases, the boundary conditions were kept
constant (inlet flow, inlet temperature, power distribution) in order to compare
different designs.
45
Three design alternatives were analyzed to gain insight into the safety margin of
this assembly. The analysis involved:
" Changing the seed rod diameter
" Changing the blanket rod diameter
*
Introduction of differential seed-blanket grid resistance
A sensitivity analysis for the first two alternatives is shown in Table 3. For this
calculation the limiting linear power level for the average pin in the hot assembly
was adjusted in order to meet the MDNBR. From Table 3 it is clear that no
significant improvement can be gained by rod diameter changes without
changing the reactor physics (moderator/fuel ratio).
Table 3 SBU rod diameter sensitivity analysis
Design
Rod diameter [cm]
Moderator/Fuel Limiting power level for MDNBR (=1.3) (1)
BAW 2 Correlation
Blanket Volume ratio
W-3L Correlation
Seed
Clad Fuel out Fuel in Clad
Seed Blanket [kw/m]
[MWth] (2) [kw/m] [MWth] (2)
Global 99
0.840
0.760
0.400
0.950
3.3
1.6 25.09 2,978
base 26.72 3,171
Seed +5% (3)
0.882
0.802
0.496
0.950
3.3
1.6 25.57
1.9% 26.70 3,168 -0.1%
Seed -5%(3)
0.798
0.718
0.275
0.950
3.3
1.6 24.28 2,881 -3.2% 26.38 3,130 -1.3%
Blanket +5% (3)
0.840
0.760
0.400
0.997
3.3
1.4 26.46
3,139
Blanket -5% (3)
0.840
0.760
0.400
0.902
3.3
2.0 23.95
2,842 -4.6% 25.59 3,036 -4.2%
3,034
5.4% 28.03 3,326
base
4.9%
(1) Limit on the hottest rod of the hot channel. Power distribution of MOC.
(2) 18% overpower for transients considered.
(3) Boundary condition: constant inlet effective mass flow of 17.7 Mg/sec
The differential grid resistance option was analyzed by modeling different grid
local loss coefficients for each assembly area (8 grids equally spaced in the
46
assembly). Figure 26 shows the effect on pressure drop and the limiting pin
average linear power of the hot channel for different blanket grid loss
coefficients. The limiting rod moves from the seed to the blanket when the
blanket local loss coefficient is increased above 1.2 (compared to the base 0.86
loss coefficient) as shown in Figure 27. In this case the linear power level is
approximately 5% above the reference design [Ref. 15]. The same linear power
and pressure drop could be obtained by a 5% increase in blanket diameter,
which would impact the reactor physics.
26.50
0.16
26.00
0.15
Seed Grid Local
Loss Coefficient
'.
,
00
1 -2
'25.50 -.
25.00
-
..
-
----
'
-
-___-
-
-
--
---
0.13-
LImitIng average linear
power at hottest channel
rj- .Pressure drop
24.50
0.12
0.8
0.86
0.9
1.0
1.1
1.2
Blanket Local Loss Coefficient
1.3
1.4
1.5
2
Limiting linear power in the hot channel constrained by MDNBR=1 .3 and MOC power distribution
2 8 grids equally spaced in the assembly
1
Figure 26 Effect of different blanket local loss coefficient on limiting linear
power and pressure drop for the SBU assembly
47
1.70 -
A
1.60
1.50
r 1.40
C
2 1.30
-
1.20
.Blanket limiting sub-channel
1.10
e
Seed limiting sub-channel
1.00
0.8
0.86
0.9
1.0
1.1
1.2
1.3
Blanket Local Loss Coefficient
1.4
1.5
Figure 27 Effect of different blanket local loss
coefficient on MDNBR for the SBU assembly
From the three different thermal-hydraulics design optimization alternatives that
were analyzed for the SBU fuel design, the differential local loss coefficient for
the blanket region was found to be the best design improvement approach. It
provided the higher allowable level of linear power with minimal impact on the
reactor physics characteristics. The differential-grid optimized
design
is
compared to the base one in Figure 28 and Figure 29, where the temperature
distribution in the two types of fuel rods (hottest rods of each kind shown) is
shown.
48
55 0
50 0
2
45
E
40
35
30
1
2
3
Optimized
design. 5
4
Nodes
6
--
...-'.
----base design
Figure 28 Optimized4vs.
7
8
9
Base design
temperature profile for the hottest seed rod
800
750
700
650
600
8550
E
(
500
450
400
350
300
1
2
3
4
5
6
7
8
9
Nodes
Figure 29 Optimized vs. base design
temperature profile for the hottest blanket rod
49
In both kinds of rods the temperature could be raised because the coolant flow
was optimally distributed between the two regions: increased in the seed and
lowered in the blanket. It can be seen from the plots that the optimization
allowed a slight increase in the coolant local temperature (aprox. 20C), but most
importantly an increase in the heat flux that results in higher internal
temperatures in the fuel (10 C in the seed and 270C in the blanket).
The maximum power achievable by this design, at an assembly level, comes
from the relative power between the seed and blanket region, and from the pin
power distribution within the same region. The first problem can be solved by
the proposed differential grid loss factor. This optimization allows a 5% increase
in the allowable power level. At this point the design is constrained by the
relative power distribution within the region (seed and blanket) and the location
of the hottest rod in that region.
50
Chapter 4
WHOLE ASSEMBLY SEED AND BLANKET
(WSB) DESIGN
The Seed and Blanket core designs based on the use of thorium fuel, have
attracted the attention of the nuclear community mostly because of the
improved anti-proliferation characteristics of the spent fuel (reduced plutonium
content and worse isotopic content of Pu from a weapon-use point of view). The
SBU design [Ref. 15] is one of this approaches that incorporates these
characteristics to current PWRs. An alternative design has been studied at MIT
addressing the possibility to have a Seed and Blanket approach where each
type of fuel occupies one full-size assembly [Ref. 8]. These two types of
assemblies are arranged in a checkerboard distribution.
This design is also constrained by the requirement of retrofitability into current
PWRs as was discussed for the SBU. The main advantages of this new design
are simpler fabrication, easier in-core management and potentially easier
optimization of the thermal-hydraulic performance. On the other hand, having
the same amount of seed and blanket assemblies becomes a challenge from
the physics point of view, where based on the SBU design a 40%/60% seed-toblanket volume ratio is optimal for fuel performance.
4.1
Design parameters
The seed and blanket regions in this design are made up of whole assemblies.
The checkerboard array distribution in a PWR core is shown in Figure 30 with a
detail of a seed and blanket cluster.
51
Blanket assembly
0000000000000000000000.00000000
300000000OOOOC)DOOOOOOOOO
-o~oooo
OOOOOOOOoooooo
3000
0000000000000000000O00000000
00000000000000000000000000
OOOOOOOOOooooooooooooo0ooooo
OOOOOOOOOO00(OOOoOOOOOOOOOOOOOO
0000000000000000000O00000000000000
m
000000000000000000000000000000000CO
0000000000000000000 0000 000D0 00 000 0
1-
oosoo
ooooooooooooo0oOOeooooooo
OOOOOOOOOOOOOOOOO(OgOOooo
0 C) 00000C)
±
C
000000000000000000000000000000
000
0000000000
000000~0000000000000oooo
0000000000000000000000o0oooooo0ooo
0000000 00000 0000000000000000000000o
000000000*0*000
I
___
000000
0
a000s000mbly
0000000000000000000000Seed0assemb0
000
0
00000
00000
PWR core outlay with WSB assemblies array
Figure 30 WSB design
The fuel pins of each type can be identical to those specified in the SBU design
but arranged in a 17x17 Westinghouse PWR fuel assembly (Design WSB-A) or
the seed pins can be made of U0
2
annular pellets (Design WSB-B).
The blanket fuel pins are assembled into a bundle with just one guide tube at
the center. Given the lower power generation and because it is mainly an area
where neutrons are absorbed, no control rods are considered in this type of
assembly. This design decision should be further assessed from a mechanical
point of view, to see whether guide tubes are needed for structural strength and
grid spacers positioning.
In the case of the seed assemblies, seed fuel pins are bundled together with
adjusted fuel pins (blanket pins located in seed assemblies) and control and
instrumentation rods. These adjusted pins optimize the seed/blanket ratio in the
52
design and also help to reduce the seed's power peak. This is the reason why
they are concentrated in the center of the seed bundle. Although these pins
play the role of the blanket in the design, they are expected to be an integral
part of the seed assembly, thus following the same refueling cycle.
WSB metallic seed pin
WSB UO 2 seed pin
U/Zr alloy
U02
Zircaloy
~2 cm
0.400 CM
07
0.56~4 cm
0.770 cm
0.850 cm
0.77 0 cm
0.85 0 cm
Figure 31 WSB alternative seed rod designs
Two alternative designs were analyzed for the WSB approach. The only
difference between them is the fuel material in the seed region. The first option
has a metallic alloy (U+Zr) that is co-extruded with the cladding Zircaloy in order
to produce seed rods. These seed rods follow the same approach of the
Galperin's SBU assembly. The second option has uranium dioxide pellets as
fuel material in the seed. These WSB options are shown in Figure 31.
4.1.1
WSB metallic seed design
This design (called WSB-A), has the same type of seed pins like the SBU but is
based on a whole assembly arrangement.
53
The most relevant design parameters are given in Table 4.
Table 4 WSB-A assemblies design parameters.
Parameter
Fuel Assembly Size [cm]
Seed assembly
Blanket assembly
21.4 x 21.4
21.4 x 21.4
Fuel MterialU/Zr
Fuel Material
Composition
alloy
(45.3% metal
U, 54.7% Zr)
U 20% enriched (1
Number of Rods
28 adjusted rods 2)
25 control/guide rods
236 seed rods(1
Fuel Pellet Radius [cm]
inner-outer
0.20
Fuel-Clad Gap [cm]
-
0.38
(1%(U+Th)0 2
(10% U0 2/90% ThO 2 in
weight)
U 15% enriched
288 blanket rods
1 guide tube
0.0 - 0.4095
No
0.0085
Cladding material
thickness [cm]
0.04
0.057
Fuel Cell Pitch [cm]
1.26
1.26
(1)
metallic fuel
(2) (U+Th)0
2 fuel
-similar to blanket material-
4.1.2 WSB uranium dioxide seed pellet design
In this design (called WSB-B), the seed rods are filled with uranium dioxide
pellets. The advantage of this option is its proven design and better
performance under some accident scenarios. Additionally, licensing problems
can be minimized as U0
2
pellets are currently used in most commercial PWRs.
The most relevant design parameters are given in Table 5. The design
preserves the same amount of U235 and U238 in the seed and blanket pins.
54
Table 5 WSB-B assemblies design parameters.
Parameter
Fuel Assembly Size [cm]
Fuel Material
Composition
Number of Rods
Fuel Pellet Radius [cm]
inner-outer
Fuel-Clad Gap [cm]
4.2
Seed assembly
Blanket assembly
21.4 x 21.4
21.4 x 21.4
U0 2
U 20% enriched
264 seed rods
25 control/guide rods
0.281 - 0.377
(U+Th)0 2
(10% U0 2/90% ThO 2 in
weight)
U 15% enriched
288 blanket rods
1 guide tube
0.0
-
0.4095
0.0085
0.0085
Cladding material
thickness [cm]
0.04
0.057
Fuel Cell Pitch [cm]
1.26
1.26
In-core fuel management
The fuel management policies are very similar to a typical PWR with the
difference that blanket assemblies have a residence period close to 10 years.
At the present, seed refueling cycle length is one year for the WSB-A
alternative, while a 18 month cycle is achievable with the WSB-B. Both can be
expected to meet the 18 month cycle requirement with careful design.
The refueling process will clearly be simplified for the facilities by the use of any
of these seed and blanket designs because the load units remain the same as
today and no specific training is expected to be required to handle the new fuel.
However, for a 50%-50% seed-blanket division, the number of assemblies
involved in any reload will be cut by 1/3.
55
Physics calculations for the WSB design at the time of this study were available
at an assembly level. Whole core calculations are underway but in order to
analyze and compare the different alternative designs, the core radial and axial
power distribution were taken from the SBU MOC results (please refer to Figure
10 and Figure 12). The relative pin power distribution for the WSB-A seed and
blanket cluster is given in Figure 32. The same distribution but in this case for
the WSB-B option is shown in Figure 33.
4.3
Inputs to the VIPRE code
The thermal-hydraulics modeling of the WSB design using the VIPRE code was
done in a similar way as for the SBU and will be discuss briefly in this section.
Only the differentiating variables are shown as in this case two different types of
assemblies are modeled in the same problem.
In this case, the selected modeling region was taken as the symmetric volume
composed of one quarter each of two seed assemblies and one quarter each of
two blanket assemblies, as shown in Figure 34.
The rods located at the perimeter of the modeled region were analyzed as
shared at halves (in area and power generation) with the surrounding channels.
Subchannels, rods and gaps were also defined in a similar way as was done for
the SBU. The identification used for them (the same in WSB-A/B) is shown in
Figure 35, Figure 37 and Figure 39.
56
% blanket assembly
% seed assembly
2
3
0.000 1.217 1.145
1.217 1.108 1.664
1.145 1.664 1.570
0.000 1.640 1.572
1.091 1.578 1.511
1.081 1.566 1.503
0.000 1.593 1.540
1.063 1.557 1.502
1.058 1.618 1.575
4
1
1
2
3
4
5
6
7
8
9
10' 0.534 0.532
11 0.540 0.542
12 0.559 0.553
13 0.553 0.558
14 0.559 0.564
15 0.580 0.572
16 0.586 0.583
17 0.627 0.604
18 0.000 0.627
0.527
0.540
0.551
0.558
0.563
0.568
0.575
0.583
0.586
5
6
7
8
9
0.000 1.091 1.081 0.000 1.063 1.058
1.640
1.572
0.000
1.537
1.534
1.578
1.511
1.537
1.512
1.546
1.566
1.503
1.534
1.546
0.000
1.593
1.532
1.498
0.000 1.532 1.498 1.436
1.524 1.471 1.438 1.421
1.561 1.546 1.533 1.524
1.471
1.438
1.421
1.429
1.529
1.546:
1.533
1.524
1.529
1.598
0.524
0.538
0.549
0.556
0.561
0.564
0.568
0.572
0.580
0.521
0.536
0.547
0.554
0.558
0.561
0.563
0.564
0.559
0.519
0.533
0.544
0.550
0.554
0.556
0.558
0.558
0.553
0.516
0.529
0.539
0.544
0.547
0.549
0.551
0.553
0.559
0.512
0.521
0.529
0.533
0.536
0.538
0.540
0.542
0.540
0.513
0.512
0.516
0.519
0.521
0.524
0.527
0.532
0.534
1.557 1.618
1.540 1.502 1.575
0.000 1.524 1.561
10
0.534
0.532
0.527
0.524
0.521
0.519
0.516
0.512
0.513
1. 598
11
12
14
0.559
0.564
0.563
0.561
0.558
0.554
0.547
0.536
0.521
1.533 1. b46
13
15
16
17
18
0.580
0.572
0.568
0.564
0.561
0.556
0.549
0.538
0.524
1.561
0.586
0.583
0.575
0.568
0.563
0.558
0.551
0.540
0.527
1.575
1.529 1.429 1.421 1.438 1.471 1.524 1.502
1.524 1.421 1.436 1.498 1.532 0.000 1.540
1.533 1.438 1.498 0.000 1.546 1.534 1.503
0.627
0.604
0.583
0.572
0.564
0.558
0.553
0.542
0.532
1.618
1.537
1.557
1.593
1.566
1.578
0.000
0.627
0.586
0.580
0.559
0.553
0.559
0.540
0.534
1.058
1.063
0.000
1.081
1.091
0.000
1.546
1.561
1.575
1.618
0.540
0.542
0.540
0.538
0.536
0.533
0.529
0.521
0.512
1.529
0.559
0.553
0.551
0.549
0.547
0.544
0.539
0.529
0.516
1.524
0.553
0.558
0.558
0.556
0.554
0.550
0.544
0.533
0.519
1.471 1.532 1.546 1.512
1.524 0.000 1.534 1.537
1.502 1.540 1.503 1.511
1.557 1.593 1.566 1.578
1.511
0.000 1.572
1.572 1.570
1.640 1.664
1.058 1.063 0.000 1.081 1.091 0.000 1.145
1.640
1.664 1.145
1.108 1.217
1.217 0.000
Figure 32 WSB-A relative pin power distribution
1/4
2
3
1 0.000 1.542 1.538
2 1.542 1.494 1.490
3 1.538 1.490 1.488
4 0.000 1.533 1.532
5 1.527 1.480 1.481
6 1.520 1.474 1.476
7 0.000 1.520 1.521
8 1.535 1.491 1.490
9 1.612 1.609 1.609
1
10
11
12
13
14
15
16
17
18
seed assembly
4
0.000
1.533
1.532
0.000
1.536
1.536
0.000
1.536
1.610
5
6
1.527 1.520
1.480 1.474
1.481 1.476
1.536 1.536
1.516 1.556
1.556 0.000
1.543 1.509
1.485 1.452
1.602 1.592
7
8
9
0.000 1.535 1.612
1.520 1.491 1.609
1.521 1.490 1.609
0.000 1.536 1.610
1.543 1.485 1.602
1.509 1.452 1.592
1.444 1.439 1.588
1.439 1.459 1.604
1.588 1.604 1.710
0.491 0.49( 0.49( 0.49( 0.49( 0.495 0.494 0.492 0.495
0.510
0.518
0.522
0.523
0.524
0.530
0.550
0.000
0.510
0.519
0.522
0.523
0.524
0.528
0.537
0.550
0.510 0.511
0.519 0.519
0.522 0.523
0.523 0.523
0.523 0.523
0.525 0.523
0.528 0.524
0.530 0.524
0.510
0.520
0.523
0.524
0.523
0.523
0.523
0.523
0.510
0.519
0.522
0.523
0.523
0.522
0.522
0.522
0.507
0.515
0.519
0.520
0.519
0.519
0.519
0.518
0.500
0.507
0.510
0.510
0.511
0.510
0.510
0.510
0.492
0.494
0.495
0.497
0.497
0.497
0.497
0.497
% blanket assembly
10
11
12
13
14
15
16
0.497 0.5 10 0.518 0.522 0.523 0.524 0.530
0.497 0.5 10 0.519 0.522 0.523 0.524 0.528
0.497 0.5 10 0.519 0.522 0.523 0.523 0.525
0.497 0.5 11 0.519 0.523 0.523 0.523 0.523
0.497 0.5 10 0.520 0.523 0.524 0.523 0.523
0.495 0.5 10 0.519 0.522 0.523 0.523 0.522
0.494 0.5 07 0.515 0.519 0.520 0.519 0.519
0.492 0.5 00 0.507 0.510 0.510 0.511 0.510
0.495 0.4 92 0.494 0.495 0.497 0.497 0.497
1.710 1.604 1.588 1.592 1.602 1.610 1.609
1.604 1.459 1.439 1.452 1.485 1.536 1.490
1.588 1.439 1.444 1.509 1.543 0.000 1.521
1.592 1.452 1.509 0.000 1.556 1.536 1.476
1.602 1.485 1.543 1.556 1.516 1.536 1.481
1.610 1.536 0.000 1.536 1.536 0.000 1.532
1.609 1.490 1.521 1.476 1.481 1.532 1.488
1.609 1.491 1.520 1.474 1.480 1.533 1.490
1.612 1.535 0.000 1.520 1.527 0.000 1.538
17
0.550
0.537
0.528
0.524
0.523
0.522
0.519
0.510
0.497
1.609
18
0.000
0.550
0.530
0.524
0.523
0.522
0.518
0.510
0.497
1.612
1.491 1.535
1.520 0.000
1.474 1.520
1.480 1.527
1.533 0.000
1.490 1.538
1.494 1.542
1.542 0.000
Figure 33 WSB-B realtive pin power distribution
57
000000000000000
000000000000000
0000000000000000
0000000000000000
oooooooooooooooo
oooooooooeoooooo
0000000000000000
0000000000000000
1000e000000000000
100000000000000o0
10000000000000
'oe,,eoe,eseoe
10000000000000000
10000000000000000
Blanket assembly
oooooo0o0000000Z
OO0000000
00000000
seeee
seeee
00000000o o
00000000oo o
@oooOoe
ooee
00000000seE~mmil
000000000000
oeoooooooo
ee
00000000
00000000000000
00000000000000
"MoMoooo
0000000000000
0000000000000
00000000000
Sub-channel
analysis of the
checkerboard array
00000000ec
00000000ee
00000000
00000000
0000006000000
00000000000000
00000000000000
0000000se
10000000100 00000 oo
0000000000000000,
00000000000000
00000000000000
0000000000000000'
000000000000000(),
0000000000000000'
0000000000000000
0000000000000000,
00000000000006001
00000000000000001
4-Seed assembly
Figure 34 Sub-channel analysis of the WSB array design
type I
thsee seed rods + one
conr
rod
type 2
four seed rods
type 3
two seeds + two blanket
three blanket rods + one
*ontrol rod
type 4
type 5
type 6
type 7
type 8
four blanket rods
three seed rods + one
blanket rod
two seeds + one blanket +
tonrl rod
One
three blanket rods + one
seed rod
Figure 35 WSB-A subchannel Identification
58
type 1
three seed rods +one
control rod
type 2
four seed rods
type 3
type 4
two seeds + two blanket
three blanket rods + one
control rod
type 5
four blanket rods
Figure 36 WSB-B subchannel identification
59
2
1
3
1@
0
1
2
0
00
19
20
2
4
0
5
@
0
4
3
6
0
5
6
0
21
7
8
9
10
@
0
0
0
7
8
9
10
0
22
23
24
0
0
0
25
26
27
11
12
0
28
0 0
29
30
0
00
0
0
40
41
42
43
44
45
46
47
48
4 @
0
0
@
0
0
@
0
0
0
0
0 0
55
56
57
58
59
60
61
62
63
64
65
66
5
6
0
0
0
73
74
75
0
0
0
91
92
93
7 @
109
8
9
0 0
76
0
77
0
94
0
0 0
78
79
@
0 0
96
95
80
97
98
0
81
0
99
100
0
0
@
0
0
0
0
0
111
112
113
114
115
116
117
0
0
0
0
0
0
0
0
0
127
128
129
130
131
132
133
134
135
0
0
0
0
146
147
148
10
0
0
163
164
181
182
0
165
0
0
110
12
0
0
199
13
200
0
217
14
236
0
0
237
0
253
254
0
272
0
155
0
0
0
0
0
0
0
0
167
168
169
170
171
172
173
0
0
0
0
0
0
0
0
184
185
186
187
188
189
190
191
0
0
0
0
0
0
0
0
202
203
204
205
206
207
208
209
0
220
0
238
0
307
308
309
0
Seed
0
Blanket
0
310
0
85
86
0
103
0
120
0
138
0
156
121
0
139
0
192
0
210
0
69
0
87
0
0
104
105
0
0
122
123
0
0
140
141
0
0
157
158
159
175
176
0
0
174
51
0
0
0
193
194
0
0
211
212
0
177
0
195
0
52
0
70
0
88
0
106
0
124
0
142
0
160
178
196
214
0
0
0
@
0
0
0
0
227
228
229
230
231
232
0
0
0
0
0
0
0
0
0 0
0
239
240
241
242
243
244
245
246
262
0
@
263
264
249
250
265
266
267
268
0
0
0
0
0
0
0
0
0
0
0
0
276
277
278
279
280
281
282
283
284
285
286
0
0
311
0
35
36
0
0
53
54
0
0
71
72
0
0
89
90
0
0
107
108
0
0
125
126
0
0
143
144
0
0
161
162
0
0
179
180
0
0
197
198
0
©
215
216
0
233
234
251
252
0 0
@
275
293
18
0
00
248
0
@
17
@ 0
213
226
0
0
0
0
247
18
0
225
261
0
0
0
34
0
0
18 @
68
33
0
224
260
0
67
0
17
16
0
0
292
0
0
15
223
0
0
50
0
16
0
259
274
102
0
49
15
222
0
221
0
0
0
166
258
291
137
154
0
0
0
0
136
153
257
290
0
0
32
0
84
0
119
0
0
289
0
118
152
256
0
101
151
0
273
0
0
0
83
0 0
150
255
0
271
17
0
219
0
235
16
0
201
0
218
0
15
183
0
149
0
82
0
110
145
0
0
31
0 0
0
14
0
39
0
0
13
38
0
0
12
37
3
14
0
11
0
13
269
0
287
@
270
0
288
0
0
0
0
0
0
0
0
0
0
0
294
295
296
297
298
299
300
301
302
303
304
0
0
0
0
0
0
@
0
0
@
0 0
@
312
313
314
315
316
317
318
319
320
321
322
324
0
305
323
0
306
@ Control rod
Figure 37 WSB-A rod identification
60
1
2
3
1
2
3
4
@
0
0
@
1
2
3
0
0
19
0
37
5
6
4
5
6
0
0
0
20
21
22
23
0
0
0
38
39
40
55
56
6
0
74
75
0
0
0
92
93
7 @
109
7
8
9
10
0
0
0
0
0
24
25
26
27
28
0
0
0
0
0
0
41
42
43
44
45
46
0*
@
60
61
59
0
76
0
77
00
94
95
0
79
@
0
96
97
0
@
00 0
111
112
113
128
0
129
0
130
0
131
0
62
132
12
100
0
117
0
134
135
0
0
14
0
0
0
0
0
0
85
0
0
0
101
102
103
104
0
0
141
138
139
140
0
0
0
0
0
0
0
0
0
151
152
153
154
155
156
157
158
0
0
0
0
168
169
170
171
181
182
0
110
12
0
0
199
13
200
0
217
14
0
236
253
16
0
17
0
219
0
237
0
254
271
201
0
0
15
0
0
218
235
0
183
0
0
0
290
291
@
0
0
307
308
309
0
0
Seed
176
177
0
0
0
0
0
0
0
0
0
188
189
190
191
192
193
194
195
0
0
0
0
0
0
0
202
203
204
205
206
207
208
209
0
0
196
210
211
212
213
214
0
0
0
0
222
223
224
225
226
227
228
229
230
231
232
0
0
0
0
0
0
0
0
0
0
0
0
0
238
239
240
241
242
243
244
245
246
247
248
249
250
0
0
0
*
@
0
259
260
261
265
266
267
268
0
0
0
0
257
258
00
0
262
0
@
0
@
263
264
0
0
0
0
0
0
0
0
0
0
0
0
0
276
277
278
279
280
281
282
283
284
285
286
0
0
0
0
0
0
293
294
295
296
297
298
0
0
0
0
0
0
310
311
312
313
314
315
0
299
0
316
0
300
0 0
301
302
@e
317
318
0
303
320
162
179
0
321
180
0
198
197
*
@
215
216
233
0
234
0
251
252
269
270
@
0
287
288
00
304
@
319
0
00
275
292
144
161
@
221
274
0
178
220
0
289
175
00
0
00
0
187
0
126
143
0
160
0 0
0
256
0
174
142
0
159
186
0
273
0
0
185
255
0
272
0
00
184
0
108
0
137
173
107
0 0
136
172
90
0
125
150
167
0
0
0
166
0
89
124
149
165
72
0
0
164
0
88
106
0
71
123
148
163
70
54
0
0
0
0
122
0
0
0
0
105
0
53
0
147
0
0
36
121
0
0
87
35
120
146
0
69
18
0
52
0
@
0
0
0
0
0
18
17
34
51
0
145
10
00
16
0 0
86
0
119
00
33
0
68
17
0
0
50
16
15
32
67
84
0
118
0
0
13
0
0
83
0
0
49
66
0
0
0
116
65
15
0
48
0
14
31
0
47
13
0
30
0
82
99
98
0
29
64
0
0
133
11
0
81
0
115
0
12
0
0
63
80
0
114
11
0
0 0
78
0
0
127
9
10
110
0
8
9
@
58
0
73
91
18
57
0
5
8
* ©@
4 @
7
322
305
306
*
@
323
324
Blanket
@ Control rod
Figure 38 WSB-B rod identification
61
0
0
l
0
m
o
m
0
m
0
0
m nm
0
0
nm m
0
0
0
0
0
0
0
0
0
17
19
21
23
25
27
29
31
0 20 0 22 0 24 0 26 0 28 0 30 0 32 0 33
50
52
54
56
58
60
62
64
0
63 0
65 0
66
0 53 0 55 0 57 0 59 0 61 0
83
85
87
89
91
93
95
97
0 n m n mn mm 0 mn am a 0 86 0 88 0 90 0 92 0 94 0 96 0 98 0 99
116
118
120
122
124
126
128
130
0
0 119 0 121 0 123 0 125 0 127 0 129 0 131 0 132
149
151
153
155
157
159
161
163
0 m m m m nm
0 152 0 154 0 156 0 158 0 160 0 162 0 164 0 165
m nm
182
184
186
188
190
192
194
196
0
0 185 0 187 0 189 0 191 0 193 0 195 0 197 0 198
215
217
219
221
223
225
227
229
0 m
0 218 0 220 0 222 0 224 0 226 0 228 0 230 0 231
m m m 11111 m 11111111e o 248
250
252
254
256
258
260
262
0
0251 0 253 0 255 0 257 0 259 0 261 0 263 0 264
mmm m m m m I
0 266 0 268 0 270 0 272 0 274 0 276 0 278 0 280 0 m * m * m * m * m * m * m * m. NO
298
300
302
304
306
308
310
31,
=
m
m mm inm 0
0 299 0 301 0 303 0 305 0 307 0 309 0 311 0 313 0
*u*'in*m
w*in
331
333
335
337
339
341
343
341
_mmm
0 332 0 334 0 336 0 338 0 340 0 342 0 344 0 348 0 m 01
364
366
368
370
372
374
376
371
0
m m m m M m
0 365 0 367 0 369 0 371 0 373 0 375 0 377 0 379 0
0
397
399
401
403
405
407
409
411 m
M-M-M-M-M-M-M-:
0 0 398 0 400 0 402 0 404 0 406 0 408 0 410 0 412 0
*
0 =0
* 0
* * q
430
432
434
436
438
440
442
444
0 431 0 433 0 435 0 437 0 439 0 441 0 443 0 445 0
463
465
467
469
471
473
475
47j
*
0
0
0
0 464 0 466 0 468 0 470 0 472 0 474 0 476 0 478 0
496
498
500
502
504
506
508
51(
0 497 0 499 0 501 0 503 0 505 0 507 0 509 0 511 0 ' F -O 544 528 0
* *n* * 529
530
531
532
533
534
535
531
0 0
0
0
0
0
0
0
0
00
0
0
0
0
0
0
0
seed to seed rod
type
blanket to blanket rod
seed to control rod
blanket to seed rod
blanket to control rod
* Seed
0 Blanket
* Control rod
Figure 39WSB-A gap identification
62
0 0
0
0
0
0
0
0
17
19
21
23
25
27
29
31
S
0 20 0 22 0 24 0 26 0 28 0 30 0 32 0 33
0
60
62
64
50
52
54
56
58
0
0 53 0 55 0 57 0 59 0 61
83
85
87
91
89
*
0
0
0
0 86 0 88 0 90 0 92 0 94 0
96 0
98 0
99
116
118
120
122
124
126
128
130
*
0 119 0 121 0 123 0 125 0 127 0 129 0 131 0 132
149
151
153
159
161
155
157
163
0 152 0 154 0 156 0 158 0 160 0 162 0 164 0 165
182
184
186
188
192
194
196
190
0
*
*
0
0
0M
a
266 0 268 0 270 0 272 0 274 0 276 0 278
298
300
302
304
306
308
299 0 301 0 303 0 305 0 307 0 309 0 311
331
333
341
335
337
339
0 251 0 253 0 255 0 257 0 259 0 261 0
263 0
6
0
6
0
0
0
0
0
0 313 03
343
345
*
0
0
0
0
0
0
0
0
0
0 M 0
0
0
0
398 0 400 0 402 0 404 0 406 0 408 0 410 0 412 o
430
432
434
436
440
442
438
444
431 0 433 0 435 0 437 0 439 0 441 0 443 0 445 0f
463
465
467
469
471
473
475
477
464 0 466 0 468 0 470 0 472 0 474 0 476 0 478 O3
496
498
500
502
504
506
508
510
497 0 499 0 501 0 503 0 505 0 507 0 509 0 511 0f
529
530
531
532
533
534
535
536
0
0
0
0
0
0
0
0
-
0 185 0 187 0 189 0 191 0 193 0 195 0 197 0 198
215
217
219
221
223
225
227
229
0 218 0 220 0 222 0 224 0 226 0 228 0 230 0 231
248
250
254
256
252
258
260
262
0 280 0
310
312
332 0 334 0 336 0 338 0 340 0 342 0 344 0 346 03
364
366
368
370
372
374
376
378
365 0 367 0 369 0 371 0 373 0 375 0 377 0 379 03
397
399
401
403
405
407
411
409
type 2
0 63 0 65 0 68
93
97
95
M S
M
*
0
0
0
264
0
0
M---
M
0M
0M
0M
M
0=
U.e
0=
0=
0=
*
0
-S
- 0 - 0 - M - M - M - M - M - No
0
0
0
0
0
0M
*
seed to seed rod
blanket to blanket rod
seed to coor rod
blanket to seed rod
Figure 40 WSB-B gap Identification
A VIPRE input file for the WSB design can be found in Appendix D.
4.4
WSB Thermal-hydraulics modeling results
The thermal-hydraulics performance of the WSB designs was evaluated based
on the typical boundary conditions found in a Westinghouse PWR plant.
Additionally, the radial hot channel power peak factor and the axial power
distribution was taken from the SBU's MOC calculations as no detailed core
neutronic results were available at the time of this study.
63
Average coolant temperature in the WSB-A cluster is compared to the hottest
spot in it in Figure 41. While the WSB-A has the same average temperature
profile as the SBU, the hottest subchannel peak temperature is reduced in the
WSB design (compare Figure 41 with Figure 18). This lower temperature in the
most constrained region of the fuel leads to a higher MDNBR in both WSB
designs compared to the SBU as shown in Figure 42.
350 -
330
--
320
0~0
E
310
a0
Hot channel average
300
.
Hottest subchannel
290
280
0
23
46
69
91
114
137
160
183
206
229
251
274
297
320
343
366
Axal Distance [cm]
Figure 41 WSB axial temperature profile
Figure 43 shows the coolant temperature distribution at the exit of a WSB-A
cluster of two seed and two blanket assemblies. The same result for WSB-B is
shown in Figure 45. Notice the impact of the adjusted pins (blanket-type pins in
the seed assembly) in flattening the distribution at the center of the seed
assemblies in alternative WSB-A.
64
3.0
2.8
--
2.6
WSB-A
- --WSB-B
2.4
2.2
z0
2.0
1.8
1.6
1.4
1.2
1.0
23
46
69
91
114
137
160 183 206 229
Axial distance [cm]
251
274
297
320
343
366
Figure 42 WSB-A/B DNBR analysis for MOC of
the hot seed assembly
25
346.a
21
17
338. 25
3
4
L
330.50
E
F-
4-7
1
5
0
322.75
T-
7F-
13
17
21
25
29
33
315.00
Figure 43 WSB-A four assemblies coolant exit temperature profile
65
341
4
3M,
E
39
e
.
Figure 44 WSB-A coolant exit temperature distribution
21
346.
17
0
13
333
9
C
a)
I1
5
9
13
17
21
25
29
33
314.
Figure 45 WSB-B four assemblies coolant exit temperature profile
66
345
341
33?
333Q
32
3
E
32
3M
x
314
Figure 48 WSB-B coolant exit temperature distribution
4.5
WSB design optimization
The optimization approach for the WSB designs was done in a similar way to
that of the SBU. Differential loss-coefficients for the two kinds of assemblies
were analyzed because of the possibility to redirect coolant flow into the hot
areas and the minimal impact on the fuel physics.
Coolant temperature and flow boundary conditions were kept constant in all
cases, and the difference in pressure drop in the reactor core was assumed to
be compensated by the reactor's pumps.
As in this design each seed or blanket area is composed of an entire assembly,
the flow distribution was achieved by not only having different loss factors in 8
equally spaced grids but also by having different inlet orifice losses (inlet losses
were modeled as a local loss at the beginning of the fuel). The effect of
increasing the loss coefficient of the grids and at channel inlet in the blanket
67
assemblies while keeping them constant in the seed for the WSB-A alternative
is shown in Figure 47.
27.50 --
0.16
27.00
26.50
26.00
EO
,i
Seed Grid Local
-- --
0.15
0U
Loss Coefficient
0
El'
D 25.50
0. 14-"a
a)
0
S25.00
a)
24.50
,
24.00
..--
Limiting average linear
power at hottest channel
. c. -Pressure drop
,I J
0. 12
23.50
0.86
1.0
2
1.2
1.4
1.6
1.8
2
Coefficient
Loss
Local
Blanket
1 Limiting average linear power constrained by MDNBR=1.3
2 8 grids equally spaced in the assembly + inlet orifice
2.2
2.4
and MOC power distribution
Figure 47Effect of different blanket local loss coefficient on limiting linear
power and pressure drop for the WSB-A assembly
A similar result is found for the WSB-B version with higher loss-coefficient
differences as the power distribution is more limiting in this case (see Figure 33
and Figure 42), and the hottest rod located in the seed region is closer to the
blanket boundary.
In the WSB-A design the hottest rod in the seed assembly is located close to
the center (see Figure 32 and Figure 43). The optimization provided by the
incremental flow in the seed assembly, and consequently decrease in the
blanket, has a direct impact on the achievable average linear power for the
68
WSB cluster and also on the pressure drop. For the range of loss coefficient
studied, the most constrained rod (where the MDNBR was found for the cluster)
was always located in the seed assembly. This result, as opposed to the SBU
where for higher local losses in the blanket the critical rod changed from the
seed to the blanket region, is not surprising because the distance between the
seed and blanket hot rods in the WSB is nearly four times that in the SBU. This
difference allows for higher coolant flow in the seed region without significant
mix with the adjacent blanket.
The same type of flow redistribution optimization can be achieved by reducing
the grids' loss factor in the seed region, with the further benefit of reduced
pressure drop across the core. New grid designs can reach loss factors of
approximately 0.6 [Ref. 18] (compared to the base design of 0.86). The use of
this improved grid design in the seed region was also analyzed. In Table 6 the
optimal values for each region loss coefficient for meeting the required power
level (3400 MWth, with a 18% of overpower buffer and 1.3 MDNBR) is given for
the two possible configurations.
From the results in Table 6 it is also clear to see that the WSB-B has a more
demanding design from the thermal-hydraulics perspective, as the required
differences in loss coefficient are higher than in the WSB-A case. This is the
result of a higher power peak in the seed and a closer location of this hot rod to
the blanket area.
69
Table 6 WSB differential loss coefficient optimization results
Loss coefficient
Pressure Active rods
Blanket drop (3) per modeled
Grids
Seed Blanket Inlet
[MPa]
assembly
Design
Limiting power level for
MDNBR (=1.3) (1)
W-3L Correlation
[kW/m]
[MWth]
(2)
WSB A
0.86
0.86
-
0.123
276
24.07
2,986
WSB-A optimized 1
0.86
2.35
2.35
0.154
276
27.43
3,403
WSB-A optimized 2
0.60
1.80
1.80
0.129
276
27.42
3,402
WSB-B
0.86
0.86
-
0.122
276
23.66
2,935
WSB-B optimized 1
0.86
3.35
3.35
0.167
276
27.44
3,404
WSB-B optimized 2
0.60
2.55
2.55
0.139
276
27.41
3,401
(1) Limit of average linear power on the hottest rod of the hot channel. Power distribution of MOC.
(2) 18% overpower for transients considered.
(3) Boundary condition: constant inlet effective mass flow of 17.7 Mg/sec
An important constraint for the WSB-B design can be the fuel temperature at
the seed rods given their high power generation level and also because the
type of fuel used. This last design variable is the main difference between the
WSB A and B options. Its importance is given because the following reasons:
"
U0
2
fuels have lower conductivity than metallic fuels (i.e. conductivity in
the metallic seed rods was approximately 7 times the one in U0
*
2
rods)
Metallic fuels can be co-extruded with the cladding, avoiding any gap
between them. U0
2
is used in the form of pellets that are inserted in
Zircaloy rods. The existing gap between the pellet and the cladding
generates a significant increase in temperature in the fuel centerline.
70
The physical properties of U0
2
are nearly design independent. On the other
hand, pellet design can be optimized in order to avoid high temperatures in the
U0 2. In the WSB-B design this was done by leaving an empty hole in the pellet
(to be filled by ZrO 2). This design allows the maximum contact area between
fuel and gap/cladding and also avoids high temperatures by limiting the fuel
radial depth.
A detail analysis for this design was done in order to assess its viability. The
WSB-B optimized 2 was selected at the operating condition corresponding to a
MDNBR=1.30. The temperature profiles for the hottest rods in the seed and in
the blanket are shown in Figure 48 and Figure 49.
At 2.5m from the bottom of the assembly
900
800
Fuel temp.
700-
700
600
E
500
400
Clad temp.
-
Fluid temp.
300
1
2
3
4
5
6
7
8
9
Nodes
Figure 48 WSB-B temperature distribution at the hottest
seed rod at an assembly average q'=27 kW/m
71
At 2.5m from the bottom of the assembly
650
600
550
Fuel temp.
10
a
E 450
400
350
-IFluid temp.
Clad temp.
3ann
1
2
3
4
5
6
7
8
9
Nodes
Figure 49 WSB-B temperature profile at the hottest blanket
rod at an assembly average q'=27 kW/m
The nodes were located in fuel subregions of equal radial thickness, from the
central void to the outside diameter.
The hottest point in the seed region (approximately at 850 *C) is safely below
the U0
2
melting point (2,800 *C), leaving enough buffer to consider transients
and possible flux inhomogeneities. These temperature profiles can be
compared to a typical PWR U0
2
based fuel shown in Figure 64, Appendix B.
Exit temperatures for the original and optimized 2 WSB-B designs are
compared in Figure 50 and Figure 51.
It is clear to see that the optimized coolant flow is increased in the seed region,
allowing the required MDNBR, while the decrease in the coolant flow in the
blanket region increases the exit temperature in those channels.
72
346
17
13
338.
9
,
5
1
9
13
17
21
25
29
330.
33
314
Figure 50 WSB-B base design exit temperature profile
346.
17
338.
13
93
CL
E
(D
I-
5
9
13
17
21
25
29
33
314.
Figure 51 WSB-B optimized design exit temperature
73
Chapter 5
THORIUM-BASED FUEL THERMALHYDRAULICS: COMPARISON OF OPTIONS
The thermal-hydraulic analysis for both SBU and WSB fuel designs concluded
in the recommendation of improving the performance by using different types of
grids in the two regions of the fuel.
This optimization is to be implemented in the SBU design by using higher
blanket loss coefficient grids along the whole assembly (8 equally spaced grids
were considered in this study). As the fuel grids are responsible of the structural
strength of the rods, the design of this new type of grids will be a challenging
task mostly because of the need for detachable seed and blanket regions.
In the WSB approach, the advantage of having a whole assembly as a seed or
blanket comes not only from a design perspective but also from an operational
point of view. The design optimization relies on higher loss factor grids in the
blanket (relative to the seeds') and in differential inlet loss coefficients also. As a
result the total localized losses in the channel are at the inlet and in 8 grid
equally spaced grid positions. The operational advantage of the WSB compared
to the SBU will be discussed in Chapter 6 where the economics involved are
assessed.
The thermal-hydraulics performance of the SBU and WSB base and optimized
designs are compared in Table 7. In all calculations a MDNBR of 1.3 was taken
for an 18% overpower condition.
74
Table 7 Thorium-Based Seed-Blanket fuel design comparison
Loss coefficient
Design
Blanket
Grids
Seed
Pressure Active rods
Blanket
Inlet
drop
(3)
[MPa]
per modeled
assembly
Limiting power level for
MDNBR (=1.3) (1)
W-3L Correlation
[kW/m]
[MWth]
(2)
SBU (Global 99)
0.86
0.86
-
0.127
264
25.09
2,978
base
SBU optimized
0.86
1.30
-
0.145
264
26.36
3,128
5.1%
WSB A
0.86
0.86
-
0.123
276
24.07
2,986
0.3%
WSB-A optimized 1
0.86
2.35
2.35
0.154
276
27.43
3,403
14.3%
WSB-A optimized 2
0.60
1.80
1.80
0.129
276
27.42
3,402
14.3%
WSB-B
0.86
0.86
-
0.122
276
23.66
2,935
-1.4%
WSB-B optimized 1
0.86
3.35
3.35
0.167
276
27.44
3,404
14.3%
WSB-B optimized 2
0.60
2.55
2.55
0.139
276
27.41
3,401
14.2%
(1) Limit of average linear power on the hottest rod of the hot channel. Power distribution of MOC.
(2) 18% overpower for transients considered.
(3) Boundary condition: constant inlet effective mass flow of 17.7 Mg/sec
75
Chapter 6
ECONOMIC ANALYSIS
In this chapter, the analyzed thorium-based fuel designs are evaluated from an
economic perspective. The economic competitiveness of thorium-based fuels is
a key goal if this type of fuel is to be used in commercial reactors.
The methodology for the economic assessment of the new designs will be
explained with their assumptions. The final comparison between the base U fuel
cycle and the thorium-based cycles will show the cost drivers and possible
advantages of these fuels under different market scenarios.
6.1
Analysis methodology and assumptions
The fuel cycle cost was divided into three groups: front end costs, operating
costs and disposal costs.
6.1.1
Front end costs
In this part of the cycle four steps were considered: mining, conversion,
enrichment and fabrication. Some of these steps are easily quantifiable as
pricing information is available for current types of fuels. On the other hand,
some estimates were used when new materials or fabrication processes are
used.
A flow chart showing the different material flows for uranium in a PWR is given
in Figure 52. For other materials or types of fuels a similar model was used
based on mass and isotope flow conservation.
76
Mining &
Milling
Waste
U308
0.5% (losses)
(0.25% w/)
UF 6
Feed
Conversion
(U 2350.711%w
pEnrichment
(losses)
t1%
Fabrication
U0
Product
(2% - 20% W/)
UF 6
4
2
o
fPWR
Figure 52 Front end fuel cycle fowchart
6.1.1.1 Mining
Uranium at natural isotopic concentration (0.711 % w/o) is the first cost to be
incurred in the production process. U30 8 or "yellow cake" is delivered to the
conversion (to UF 6 ) plant in sufficient amount to account for the required
enriched final fuel U0 2 and all losses.
The cost was assumed to be proportional to the amount of natural uranium
needed and equal to $50/kg [Ref. 19].
77
The cost for thorium was estimated to be $85/kg [Ref. 20], while for zirconium
the estimated purchase price was $30/kg [Ref. 21].
6.1.1.2 Conversion
In the case of uranium, the conversion process (U30 8 ->UF
6
) is needed in order
to prepare for enrichment. The estimated price for conversion was $8/kg HM
[Ref. 19].
For the other materials (Th and Zr) all preparatory costs are assumed to be
included in the cost of fabrication.
6.1.1.3 Enrichment
This step is only associated with the uranium content of the fuel. The calculation
is based on the Separative Work Units (SWU) required to enrich the uranium
from the natural enrichment to the desired enrichment in the fuel at a specified
enrichment in the waste or tails.
The tails' enrichment can also be optimized depending on the price of a SWU
and the price of the raw material for the process (UF 6). The higher the price of
the SWU compared to the raw material, the more preferable it is to increase the
enrichment of the tails in order to minimize the total cost. The optimal value for
tails enrichment for an enrichment cost of $110/SWU and a natural uranium
plus conversion cost of $58/kg is approximately 0.28%
w/o
(optimization of the
whole cycle cost as a function of tails' enrichment).
If future prices of SWU decrease from the assumed $11 0/SWU, a decrease in
the optimum tails enrichment would be appropriate.
It should be noted that transportation costs are assumed to be included in the
cited prices for each process step. Transportation is licensed for current
enrichment levels and may require special safety and licensing measures to be
78
considered in the case of higher concentrations. A similar situation applies to
the fabrication step, and shipment and storage at the reactor site.
6.1.1.4 Fabrication
Although this step is not the most expensive in the front end fuel costs it is the
principal differentiator between all designs.
The production costs were divided into three categories:
1.
Hardware costs: Including top/bottom nozzles and grids (measured in
$/assembly).
2. Process cost: Fuel rod fabrication including Zircaloy, burnable poisons,
pellet fabrication, final assembly and welding (measured in $/kg Heavy
Metal).
3. QA,
safety
and
administrative:
Quality
assurance,
safety
and
administrative costs (measured in $/assembly).
Given the typical cost of current U0
2 fueled
PWR assemblies (457 kg HM/assy.
X 275 $/kg HM=$125,675), this cost was subdivided into a 20% for hardware
(1), 70% for processing (2) and 10% for QA (3) [Ref. 22].
With these results, the final unit values are:
1.
Hardware costs: $25,135 per assembly.
2. Process cost: $192.5 per kg HM.
3. QA, safety and administrative: $12,568 per assembly.
In the case of hardware costs, a 10% increase in price was taken for the SBU
design ($27,649 per assembly) taking into consideration the additional cost of
79
manufacturing
two different, stand
alone, regions for each fuel. This
requirement comes from the fact that the blanket area is designed to be
separated from their original seed in order to have an average residence time in
the reactor of 10 years (compared to 3 years for a seed).
The processing cost was reduced to 80% of a typical U0
2
assembly for the
seeds' metallic rods. This assumption is based on estimates that the process of
co-extrusion of the uranium-zirconium fuel meat with the Zircaloy cladding will
result in process savings 15.
For QA, safety and administrative cost, an additional 10% was considered for
the SBU design based on the same reasons discussed for the hardware costs.
6.1.1.5 Front end final product cost calculation
All the front end cost were calculated based on the present value of all the
expenses. Each step was discounted forward, in order to estimate the total fuel
cost at the time of its use in the reactor.
For each step this in-service cost was evaluated as follow,
FC = C -(1+r,)'
where the future cost FC at the time of use of the fuel in the reactor, is the
actual cost C, discounted forward at an annual discount rate ry for a period of ty
years (time between actual expense and use of the fuel in the reactor). A
graphical representation for this fuel front end cost calculation is shown in
Figure 53.
80
Fabrication
C,,
0
SW
C.,
4--
0
C)
~0
4-
0
C
0
Conversion
U-
Ore
0
U
Time to'
irradiation
2.0
1.5
0.5
1.0
0
Start of
irradiation
Expenses discounted forward
Figure 53 Fuel front-end cost calculation
This future cost was later annualized based on the residence time in the
reactor. The annual cost was calculated based on:
A
- FC
y-
(I+ y
reinc
+ r,)'residene-1
where the annualized cost A, is calculated on the basis of the future cost FC,
and an annual discount rate ry, during a period of tresidence years (time of
residence of the fuel in the reactor core). This approach was chosen in order to
simplify the calculations of different residence times as is the case of seed and
blanket areas.
81
6.1.2
Operational costs
These costs were calculated based on an estimated cost per reactor refueling
outage of $20M for the material and manpower used [Ref.19]. This cost was
converted into an annualized cost using the following relation:
A = ROC. r,
(1+r)'"""
(1+ r,)'v'" -1
where the annualized cost A, is calculated on the basis of the actual refueling
outage cost ROC, an annual discount rate ry, during a period of tcycle years. As
the economic analysis considered an assembly as the unit for comparison, this
refueling cost was divided by the average number of fuel assemblies changed
in each outage (196 assemblies/3 batchs). The tcycle was taken as the in-core
residence time for the fuel (typically 4.5 years for a 18 month cycle).
Additionally, only seed regions were assumed responsible for paying the
refueling cost, as their shorter residence time is constraining the cycle length.
The annual cost calculation for front end and operational costs is shown in
Figure 54.
Additionally, the refueling downtime was taken into account in order to calculate
the total amount of energy produced by the reactor during one year:
EE = P - 24hay - 365daV",, Plantefficiency -Availability - I-
ref.length
Cycle length
where P is the nominal thermal power of the facility (different for each design
and a function of the safety requirements discussed in Chapter 3, Chapter 4,
and results of Chapter 5); plant efficiency is the thermodynamic efficiency of
transforming thermal into electrical power (taken equal to 1150 MWe/3411
MWth=33.71%). Forced outages were taken into account in the availability
82
(100%-Forced outages rate=95%). The impact of refueling
outages was
calculated by subtracting its relative contribution from the total cycle length.
Seed annualized cost
Refueling
cost *
Fabrication
1
SW
'2,
Conversion
Ore
Year
*
Prorated between the fresh seeds4193/3 assy.)
Blanket annualized cost
Fabrication
SW
Conver sion
WWWWEL~Z-
4"8
"
Ore
I
I
|
I
|
I
z~I1
I
Year
Figure 54 Annualized cost calculation for one cycle
6.1.3 Fuel disposal costs
One of the objectives of thorium-based fuels is the reduction of waste storage
and disposal requirements [Ref. 15]. Current research efforts are focused on
analyzing fuel material stability, long term radiotoxicity and potential proliferation
reduction.
83
Although this advantage can be a very important factor in the decision to
change to thorium-based fuels, it was not taken into account in the economic
analysis. This conservative approach was chosen as no conclusive results
and/or disposal policies are available at the time of the study.
The fuel disposal cost was assumed covered by the Federal waste disposal fee,
equivalent to 1 Mills/kwhre. The same value was used for all fuel types, thus no
economic advantage was taken into account for thorium-based fuels for the
back end costs. On the other hand, the cost to utilities of storing the fuel onsite
may in fact be reduced when spent fuel/kWhr is reduced at the high burnups
reached with the aid of thorium
6.2
Economic design comparison
In Table 8 the economic comparison for each design is shown. For all
alternatives an assembly is taken as the unit of analysis:
" All U: A 17x17 assembly based on U0
*
2
pellets
SBU: A 17x17 assembly where hardware and QA costs were divided
between seed and blanket proportionally to the number of rods (11 x 11
seed).
*
WSB: A cluster of two quarters of a seed assembly and two quarters of a
blanket assembly, as shown in Figure 34. In this case hardware and QA
cost per assembly were evenly divided between seed and blanket.
84
Thorium-based fuels economic compariso
Ore
Fuel
Conversion
Enrich. kg/assy. Unit Cost Total Cost LTI kg/assy. kg/assy. Unit Cost Total Cost LTI
$/kg
$/assy. years (feed) (product
$/kg
$/assy. years
All U
U
-I
0*
w
0.71%
4,287
50 $214,356
2
4,287
4,266
8 $34,126
1.5
U
0.71%
Zr
1
Blanket
U
0.71%
Th
1
2,422
68
50 $121,125
30 $ 2,048
2
2
2,422
68
2,410
68
8 $19,283
0 $
-
1.5
1.5
895
229
50 $ 44,747
85 $ 19,492
2
2
895
229
890
228
8 $ 7,124
0 $
-
1.5
1.5
3,615
$187,412
3,615
3,597
$26,407
2,961
83
50 $148,041
30 $ 2,504
2
2
2,961
83
2,946
83
8 $23,568
0 $
-
1.5
1.5
826
212
50 $ 41,304
85 $ 17,993
2
2
826
212
822
211
8 $ 6,576
0 $
-
1.5
1.5
4,082
$209,841
4,082
4,062
$30,144
3,771
50 $188,526
2
3,771
3,752
8 $30,013
1.5
826
50 $ 41,304
2
826
822
8 $ 6,576
1.5
212
85 $ 17,993
2
212
211
0 $
1.5
4,808
$247,823
4,808
4,784
SBU-
Seed
0I
WSBA
0
(0
0
Seed
U
0.71%
Zr
1
Blanket
U
0.71%
Th
1
WSBB
Seed
U
0.71%
Blanket
U
0.71%
Th
1
Ca,
LTI: lead time to irradiation
-
$36,589
Thorium-based fuels economic comparison
Separative Work
Fuel
Fabrication
Enrich. SWU/assy Unit Cos Total Cost LTI kg/assy. kg/assy. Hardware
$/SWU
$/assy. years (feed) (product)
Cost
$/assy.
All U
U
Process QA + safet Total Cost LTI
Cost
$/assy. years
$/kg
$/assy.
4.51%
3181
110 $349,962
1
462
457
25,135
192.5
12,568
$125,675
0.5
U
20.00%
Zr
1
Blanket
U
15.00%
Th
1
2339
0
110 $257,308
$
-
1
1
56
68
56
67
11,576
154.0
154.0
5,788
$ 8,578
$ 27,722
0.5
0.5
839
0
110 $ 92,254
$
-
1
1
28
228
28
226
16,072
192.5
192.5
8,036
$ 5,304
$ 67,593
0.5
0.5
380
376
27,649
13,824
$109,196
SBU
Seed
$349,563
WSB A
Seed
U
20.00%
Zr
1
Blanket
U
15.00%
Th
1
2859
0
110 $314,487
$
-
1
1
69
83
68
82
12,568
154.0
154.0
6,284
$ 10,484
$ 31,511
0.5
0.5
774
0
110 $ 85,156
$
-
1
1
26
211
25
209
12,568
192.5
192.5
6,284
$ 4,896
$ 58,990
0.5
0.5
388
384
25,135
12,568
$105,881
88
87
12,568
6,284
$ 35,540
0.5
$
$399,643
Seed
U
20.00%
Blanket
U
15.00%
Th
3641
110 $400,491
1
774
110 $ 85,156
1
26
25
1
211
209
12,568
324
321
25,135
1
0
$
-
$485,647
0)
LTI: lead time to irradiation
192.5
192.5
192.5
4,896
0.5
6,284
$ 58,990
0.5
12,568
$ 99,426
Thorium-based fuels economic comparison
Final Product
Fuel
AlUU
Total cost Max.
Total fuel
per assembly Power
cost
MWth Mills/kWhre
Refueling
Cycle
Cost
Length time
Millons months years
Annual
Cost
$ 819,921
3400
4.89 $
20 M
1.50
4.5 $322,859
$
$
436,534
31,637
3128
$
20 M
1.50
3 $311,355
$
$
$
160,709
94,831
723,711
U
$
Zr
$
Blanket
U
$
533,539
36,175
Oper.
Disposal Total cycle
cost
fee
cost
Mills/kWhre Mills/kwhre Mills/kWhre
6.72
1.00
7.72
8.10
1.00
9.10
8.23
1.00
9.23
6.81
1.00
7.81
SBU
Seed
U
Zr
Blanket
U
Th
10 $ 41,588
4.98
$352,943
WSBA
Seed
Th
$
20 M
1.50
148,343
U
$
148,343
Th
$
83,960
$
935,074
3 $352,187
10 $ 37,806
$ 83,960
$ 802,017
WSBB
Seed
U
$ 702,770
Blanket
00
3400
5.33
3400
LTI: lead time to irradiation
$389,993
$
20 M
1.50
4.5 $289,270
10 $ 37,806
4.98
$327,076
The contribution of each step of the fuel cycle for all alternative designs is
shown in Figure 55. The most important components come from the enrichment
process, ore and mining and operation. The last one is largely affected by the
reduction of cycle length. Both designs based on a 12 month cycle suffer this
disadvantage.
$10.0
$9.0
0 Ore
[ Conversion
E] SWU
E Fabrication
M Operati,
$8.0
n
N Disposal
$7.0
(U
$6.0
$5.0
$4.0
$3.0
$2.0
$1.0
$0.0
All U (1)
SBU (2)
WSB A (2)
VVSB B (1)
Design
(1) 18 month cycle
(2) 12 month cycle
Figure 55 Contribution of each step of the fuel cycle to total cycle cost
6.3
Sensitivity analysis
The sensitivity of the total cycle cost to the change in some of the parameters
was analyzed. The most important ones are the SWU price, the total fabrication
price and the refueling outage length.
88
Prices of SWU are expected to fall in the long term; changes can reduce the
case-to-case cost differentials. The total cost sensitivity to the SWU price is
shown in Figure 56.
10.0 --
9.5 1
9.0 8.5
U,
8.0
All U
-
7.5
.. h- SBU
WSB-A
-..
7.0 -
.X..
WSB-B
6.5 70
80
90
100
110
120
130
140
SWU cost
Figure 56 Total cycle cost sensitivity to SWU cost
The impact of fuel fabrication cost on the total cycle cost was also analyzed
because a decline in its value has been observed during the past. The
sensitivity analysis for this factor is shown in Figure 57. In this case the
equivalent cost per kilogram of U HM was modified and all related production
cost were changed proportionally.
89
9.5 -
---
9.0=A
-r--&
-u- All U
i
8.5
W>
S8.0
-....
....
SBU
WSB-A
WSB-B
270
280
7.5
7.0
200
210
220
230
240
250
260
Total fabrication cost [$/kg HM]
Figure 57 Total cycle cost sensitivity to total fabrication cost
The final variable analyzed was the refueling outage length. Although nowadays
core refueling is not in the critical path of a refueling outage, some
improvements in new designs may enable some reductions in the time involved
in refueling. The impact of this period where the plant is not generating energy
in the total cycle cost is shown in Figure 58.
90
9.5
9.3
-
9.1
k-k
8.9
U>
- &-- --
k
8.7
All U
8.5
--.- SBU
_. -.. WSB-A
... WSB-B
8.3
8.1
7.9
7.7
-- --- - I-- --.. ----- - --- - ------X
-.
-
-
K -- ---- - -
7.5
1.0
1.1
1.2
1.3
1.4
1.5
1.6
1.7
Refueling lenght [months]
Figure 58 Total cycle cost sensitivity to refueling outage length
91
Chapter 7
CONCLUSION
As a result of this study several different thorium-based fuels were analyzed
from their thermal-hydraulics and their economic performance. The main
contribution is to clarify the best path to follow in future research on this type of
fuel elements and to identify the key parameters that will enable future
commercial use of these nuclear fuels.
7.1
Thermal-hydraulics results
The most important challenge for all of the analyzed designs was to deal with
the difference in power generation between the seed and the blanket. The best
solution to attack this problem was to use different grids' local loss coefficient in
order to improve coolant flow in the seed region.
After this optimization, there is a limit on the allowable power generated in the
assembly given by the pin peak location in each region. As the seed's and
blanket's peaks are set further apart from each other the better this solution is.
An example can be found in that the SBU design has a limiting average linear
power in the hot assembly of 26.36 kW/m while the same metric in the WSB-B
design can be increased to 27.41 kW/m.
The WSB approach is the most promising design because it separates the two
regions enough to allow differential flow and heat transfer in different locations
of the assembly.
92
It should be noted that this optimization comes at the expense of a higher
pressure drop in the core. Thus, its feasibility should be assessed in case of
implementation in PWRs.
Another important result from the thermal analysis is that there is no specific
need for the use of metallic fuel in the seed region (other than potential
economic savings). The annular pellet solution shows a good performance, with
the additional advantage of being a very well known and benchmarked
fabrication process, and that the fuel licensing is expected to be much shorter
and simpler.
All results are based on SBU core power distribution [Ref. 15]. Peaking factors
for other designs should be analyzed in detail in order to validate this
assumption.
7.2
Economic results
As a result of an analysis of the fuel cycle cost, the most important drivers for
fuel deployment form an economic perspective were identified.
Cycle length (12 vs. 18 months) is by far the most important objective to take
into account for a design. The operational costs involved in each refueling
outages are responsible for a very important part of the whole cycle cost.
A scenario where SWUs prices decline will enhance the SBU and WSB
attractiveness compared to current fuels cycles. This is due to the fact that they
both depend on 20% U enrichment which becomes less costly as the SWU
become less expensive.
Important savings in metallic pin production can potentially improve seed
blanket fuels but a trade-off between the use of this technology and safety and
licensing problems should be assessed in detail.
93
Disposal and non-proliferation incentives were not taken into account in the
economics. Potential benefits for the facilities from this point of view can
become important factors the acceptance of the seed and blanket approach.
7.3
Future research
Future research in this area should be focused on having a detailed analysis of
a whole core for the different designs. Axial and radial peaking factors are very
important in order to assess fuel operating limitations under the safety
requirements.
Detailed analysis of the boundary between the seed and blanket regions is also
an area where some further investigation is needed. Mixed coefficients and fluid
dynamics in these regions of high temperature and velocity gradients can bring
some insights about fuel performance from a thermal perspective and also from
a structural one.
The utilization of just one guide tube in blankets assemblies (WSB designs)
should also be assessed from a structural point of view. Grid and spacers
attachment to the fuel can be a constraint for it.
The utilization of new developed types of grids (with loss coefficients as low as
0.6) should be analyzed and tested in these types of designs.
Pump power and flow distribution within the core should also be assessed in
the case of higher pressure drops.
94
Appendix A: ANNUALIZED
COST CALCULATION
The annualized cost for front end and operational cost was calculated based on
an annuity formula:
A = FC
rY
(1+
(1±rI'
r,)'reirnc
-1
The residence time depends on the part of the fuel considered as seeds are
more often replaced. A graphical representation of how annualized costs were
calculated can be seen in Figure 54.
This type of calculation also applies to an entire cycle for a blanket assembly.
The comparison is shown in Figure 59.
The equal length analysis assumes a total cycle length equal to the blanket
residence time (3L). In this case the annualized cost for the three seeds (S) can
be calculated as follows,
As
r, (1 +r,) 3 L
S'I+
I+r,)L
+
r,2
3L
_
On the year based analysis used in the present study, just one period L is used
to calculate the annual cost. The annual cost calculated by this approach is:
As = S- ry -(1+ry)L
(1+r,)L _
95
Equal lenght analysis
Seed 1
Seed 2
Seed 3
Blanket
0
1
2 3 4 5 6 7 8 9
0 1 2 3 4 5 6 7 8 9
Years of irradiation
Years of irradiation
Investments
Yearly
payments
Year based analysis
tt
Blanket
I
0 1 2 3 4 5 6 7 8 9
Years of irradiation
0
1
2 3 4 5 6 7 8 9
Years of irradiation
Figure 59 Different economic analysis approaches
Mathematical transformations of the above expressions shows that the two
approaches are totally equivalent.
All the calculations are based on real values, and all results should be
understood as evaluated at current prices. Additionally no credit is taken for
possible price decrease due to improve technology, such as isotope separation
methods or machines.
96
Appendix B : PWR BASE DESIGN ANALYSIS
A typical U02 PWR fuel assembly was also modeled in VIPRE in order to
compare all new designs characteristics with this type of fuel.
A 17 x 17 assembly (shown in Figure 8) was modeled based on subchannel
analysis in a very similar way done for the other designs. Subchannel, rod and
gaps identification assignments are shown in Figure 60, Figure 61 and Figure
62.
one rod
type 1
type 2
type 3
*two
rods
four rods
three rods + one contro
type 4 PW b b
Figure 60 PWR assembly subchannel Identification
97
1
1
2
3
4
5
6
7
8
0
0
0
0
0
0
0
0
1
2
3
4
5
6
7
8
0
0
0
0
0
0
0
0
18
19
20
21
22
23
24
0
0
000O
35
36
37
38
4 0
0
0
@ O
O
O
52
53
54
55
56
57
58
59
2
3
@
39
40
41
9
0
9
0
25
26
0
@
42
43
10
0
11
0
10
0
11
0
27
12
0
45
0 0
0
0
60
61
62
0
12
13
0
28
44
13
0
0
0
0
14
0
32
0
0
0
47
48
49
@
00
65
66
0
0
82
83
O@
46
0
64
16
0
15
31
30
63
15
0
29
0
14
17
0
16
0
17
0
33
0
34
0
50
51
0
67
68
0
0
0
0
0
0
0
0
69
70
71
72
73
74
75
76
0
0
@
0
0
@
00
86
87
88
89
90
91
92
0
0
0
0
0
0
0
0
0
0
103
104
105
106
107
108
109
110
111
112
0
0
0
0
0
0
0
0
0
0
120
121
122
123
124
125
126
127
128
129
0
0
@
0
0
@
0
0
@
0 0
@ 0
0
a
0 0
137
138
139
140
141
142
143
144
145
146
147
148
150
151
152
0
0
0
0
0
0
0
0
0
0
0
157
158
159
160
161
162
163
164
167
168
169
0
0
0
184
185
186
5
6
7
8
9
10
0
154
156
0
171
0
172
12
0
188
13
205
0
223
0
0
207
224
240
0
256
0
257
0
0
241
0
258
0
274
0
275
0
Fuel rod
@
Control rod
77
0
78
@ 0
93
94
95
0
0
79
0
113
0
130
97
0
0
0
0
0
0
0
0
176
177
178
179
180
181
182
199
0 0
@
0
0
@
00
193
194
195
196
197
198
192
0
0
0
0
0
0
0
209
210
211
212
213
214
215
0
0
0
0
0
0
228
229
230
231
232
233
226
227
0
@
0
0
@
00
243
244
245
246
247
248
249
250
0
0
0
0
0
0
0
262
263
264
265
0
276
260
261
0
0
134
135
183
200
0
216
0
259
0
133
0
0
242
0
118
@ 0
208
225
0
117
166
0
0
0 0
0
116
0
165
0
0
115
149
0
© 0
100
132
217
0
101
102
0
119
0
136
153
0
170
0
187
0
a
0 0
202
203
0
218
0
0
219
220
© 0
235
0
236
237
0
0
0
251
252
253
254
0
0
0
0
266
267
268
269
270
0
@ 0
85
201
0
234
0
84
99
0
131
175
0
0
98
0
114
0
191
81
@ 0
96
0
0
80
174
0 @
0
239
273
190
0
222
17
0 @
206
0
16
173
189
0
15
0
155
110
14
0
0
0
0
0
0
0
0
0
0
0
0
277
278
279
280
281
282
283
284
285
286
287
0
271
0
288
204
0
221
0
238
0
255
0
272
0
289
Figure 61 PWR assembly rod identification
98
0
36
4 0
6 0
38
8 0
40
0
39 0
41
71
73
0
74 0
76
106
108
0 109 0 111
42
0
43 0
75
77
0
78 0
110
10 0
12 0
14 0
16 0
18 0
20 0
22 0
24 0
26 0
28 0
30 0
32 0
34 0
44
46
48
50
52
54
56
58
60
62
64
66
68
45 0 47 0
49 0
51 0
53 0
55 0
57 0
59 0
61 0
63 0
65 0
67 0
69 0
79
800
114
0 117 0
83
65
0
0 8 0
118
120
119 0 121 0 123
89
91
0
920
124
126
125 0 127 0 129 0
95
0
130
1310
97
99
101
103
98 0
100 0 102 0 104 0
134
136
138
0137
0
139
0
141
143
145
149
151
153
0 144 0 146 0 148 0 150 0 152 0 154 0 156
176
178
182
184
188
0 1790
0i 1850
0W191
155
157
159
161
163
165
169
171
0 158 0 160 0 162 0 164 0 166 0 168 0 170 0 172 0 174
190
194
196
200
202
206
0
0 1970
0 2030
0 209
173
0
208
211
225
243
0
246
0
281
0
316
0
351
0
386
0
421
213
214 0 216 0
248
250
249 0 251 0
283
284 0
318
319 0 321 0
353
355
354 0 356 0
388 M O
389 0
217
219
218 0
252
253 0
287
0
322
323 0
357
358 0
392
0
220 0
254
255 0
289
2900
324
325 0
359
360 0
394
3950
427
429
423
0 424 0
456
458
0 459 0
491
493
0 494 0
526
528
0 529 0
561
563
0 564 0
426 0
460
461 0
495
496 0
530
531 0
565
566 0
223
222 0 224 0 226 0
256
258
260
257 0 259 0 261 0
293
295
0 296 0
328
330
327 0 329 0 331 0
361
363
365
362 0 364 0 366 0
398
400
0 4010
428 0 430 0 432 0
464
466
0 467 0
499
498 0 500 0
532
534
533 0 535 0 537 0
567
569
571
568 0 570 0 572 0
433
229
231
235
237
228 0 230 0 232 0 234
262
264
266
263 0 265 0 267 0 269
299
301
0 3020
334
336
333 0 335 0 337 0 339
367
369
371
368 0 370 0 372 0 374
404
406
0 4070 MO
0 236 0 238 0
268
270
272
0 271 0 273 0
305
307
@
0 308 0
340
342
0 341 0 343 0
373
375
377
0 376 0 378 0
410
412
0 4130
439
445
435
441
241
240 0 242 0 244
274
276
275 0 277 0 279
311
0 314
346
345 0 347 0 349
379
381
380 0 382 0 384
416
O
0 419
447
451
434 0 436 0 438 0 440 0 442 0 444 0 446 0 448 0 450 0 452 0 454
468
470
472
474
476
478
480
0484
486
469 0 471 0 473 0 475 0 477 0 479 0 481 0
0 487 0 489
503
505
509
511
515
519
521
0 506 0
538
540
539 0 541 0 543 0 545
573
575
577
574 0 576 0 578 0 58
0
0
278
0
313
0
348
0
383
0
418
0
453
0
488
0
523
0 512 0
0 518 0 520 0 522 0 524 0
544
546
0 547 0 549 0 551
579
581
583
0 582 0 584 0 586
550
552
0 553 0 555
585
587
0 588 0 590
554
556
0 557 0 559
589
591
0 592 0 594
558
0
593
0
I
rod t assembly edge
type 2 Rod to rod
Rod to contr rod
0 Rod
* Control rod
Figure 62 PWR assembly gap Identification
Operating conditions for this assembly were taken also from Table 1.
Additionally a 1.55 peak to average chopped-cosine axial power distribution
was assumed [Ref. 23]. The peak to average radial assembly ratio was
assumed equal to 1.587 [Ref. 23].
Figure 63 shows the relative pin power distribution used for this assembly.
99
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
1
1.000
0.967
0.965
0.973
0.983
0.991
0.991
0.991
0.994
0.991
0.991
0.991
0.983
0.973
0.965
0.967
1.000
2
0.967
0.934
0.940
0.956
0.978
1.010
0.983
0.983
1.009
0.983
0.983
1.010
0.978
0.956
0.940
0.934
0.967
3
0.965
0.940
0.964
1.012
1.035
0.000
1.021
1.019
0.000
1.019
1.021
0.000
1.035
1.012
0.964
0.940
0.965
4
0.973
0.956
1.012
0.000
1.051
1.038
0.999
0.996
1.024
0.996
0.999
1.038
1.051
0.000
1.012
0.956
0.973
5
0.983
0.978
1.035
1.051
1.027
1.038
1.001
0.999
1.027
0.999
1.001
1.038
1.027
1.051
1.035
0.978
0.983
6
0.991
1.010
0.000
1.038
1.039
0.000
1.030
1.029
0.000
1.029
1.030
0.000
1.039
1.038
0.000
1.010
0.991
7
0.991
0.983
1.021
0.999
1.002
1.030
1.000
1.000
1.028
1.000
1.000
1.030
1.002
0.999
1.021
0.983
0.991
8
0.992
0.983
1.020
0.996
0.999
1.029
1.000
1.000
1.029
1.000
1.000
1.029
0.999
0.996
1.020
0.983
0.992
9
0.994
1.009
0.000
1.024
1.027
0.000
1.028
1.029
0.000
1.029
1.028
0.000
1.027
1.024
0.000
1.009
0.994
10
0.992
0.983
1.020
0.996
0.999
1.029
1.000
1.000
1.029
1.000
1.000
1.029
0.999
0.996
1.020
0.983
0.992
11
0.991
0.983
1.021
0.999
1.002
1.030
1.000
1.000
1.028
1.000
1.000
1.030
1.002
0.999
1.021
0.983
0.991
12
0.991
1.010
0.000
1.038
1.039
0.000
1.030
1.029
0.000
1.029
1.030
0.000
1.039
1.038
0.000
1.010
0.991
13
0.983
0.978
1.035
1.051
1.027
1.038
1.001
0.999
1.027
0.999
1.001
1.038
1.027
1.051
1.035
0.978
0.983
14
0.973
0.956
1.012
0.000
1.051
1.038
0.999
0.996
1.024
0.996
0.999
1.038
1.051
0.000
1.012
0.956
0.973
15
0.965
0.940
0.964
1.012
1.035
0.000
1.021
1.019
0.000
1.019
1.021
0.000
1.035
1.012
0.964
0.940
0.965
16
0.967
0.934
0.940
0.956
0.978
1.010
0.983
0.983
1.009
0.983
0.983
1.010
0.978
0.956
0.940
0.934
0.967
17
1.000
0.967
0.965
0.973
0.983
0.991
0.991
0.991
0.994
0.991
0.991
0.991
0.983
0.973
0.965
0.967
1.000
Figure 63 PWR assembly relative pin power
distribution
The temperature profile for the hottest rod in the assembly, calculated based on
a conduction model is shown in Figure 64. This profile can be taken as a base
point in order to compare new U0
2
based fuel performance.
100
At 2.1m from the bottom of the assembly
1700
1500
1300
Fuel temp.
1100
E 900
700
500
i
300 4
,
Fluid tem p.d
2
m
F~~~-AClad
temp.
3
4
5
6
7
8
9
Nodes
Figure 64 Radial temperature profile in the
hottest rod of a PWR assembly
101
The VIPRE input file for the PWR assembly case follows.
input card images
2
1
card
3
4
1
*
2
*
3
4
*
*
5
*
6
7
8
1,0,0
UO2 homogeneous assembly case( 17x17 )
9
10
5
6
7
8
12345678901234567890123456789012345678901234567890123456789012345678901234567890
*
*
*
*
*
*
*
*
*
*
*
*
*
*
*
*
*
*
*
*
*
*
*
*
*
*
*
*
*
*
*
*
*
*
*
*
*
05/01/00
vipre-01, PWR assembly input
*
*
*
*
*
*
*
*
*
*
*
*
*
*
*
*
*
*
*
*
*
*
*
*
*
*
*
*
*
*
*
*
*
*
*
*
*vipre.1
*vipre.2
assembly geometry = 17x17 rods
*
*4 different compressed geometry input
*geom.1
*geom.2
11
12
geom,324,4,16,0,4
144.,?
13
0.,0.5
14
*
channel dimensions
15
*
type I
16
4,0.03404,0.2937,0.2937
*geom.5
17
18
1,18,307,324
*
type II
*geom.6
19
20
64,0.06808,0.5875,0.5875
2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17
*geom.5
*geom.6
21
19,36,37,54,55,72,73,90,91,108,109,126,127,144,145,162
*geom.6
22
163,180,181,198,199,216,217,234,235,252,253,270,271,288,289,306
*geom.6
23
24
308,309,310,311,312,313,314,315,316,317,318,319,320,321,322,323 *geom.6
type III
*
25
26
27
28
29
30
31
32
33
34
35
36
164,0.13616,1.1750,1.1750
20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35
38,39,40,41,44,47,50,51,52,53,56,57,62,65,70,71
74,75,78,79,80,81,82,83,84,85,88,89,92,95,97,98
101,102,104,107,110,113,114,116,119,121,122,125,128,129,130,131
132,133,134,135,136,137,138,139,140,141,142,143,146,149,152,155
158,161,164,167,170,173,176,179,182,183,184,185,186,187,188,189
190,191,192,193,194,195,196,197,200,203,204,206,209,211,212,215
218,221,223,224,227,228,230,233,236,237,240,241,242,243,244,245
246,247,250,251,254,255,260,263,268,269,272,273,274,275,278,281
284,285,286,287,290,291,292,293,294,295,296,297,298,299,300,301
302,303,304,305
*
default sl = 0.5
*geom.2
(cont.)
*geom.5
*geom.6
*geom.6
*geom.6
*geom.6
*geom.6
*geom.6
*geom.6
*geom.6
*geom.6
*geom.6
*geom.6
type IV
37
*
38
39
92,0.11800,1.2598,0.8812
42,43,45,46,48,49,58,59,60,61,63,64,66,67,68,69
40
41
42
*geom.6
76,77,86,87,93,94,96,99,100,103,105,106,111,112,115,117
*geom.6
118,120,123,124,147,148,150,151,153,154,156,157,159,160,165,166
168,169,171,172,174,175,177,178,201,202,205,207,208,210,213,214 *geom.6
43
44
219,220,222,225,226,229,231,232,238,239,248,249,256,257,258,259
261,262,264,265,266,267,276,277,279,280,282,283
45
* Gap input data
46
612,3,0,18,0,0
47
*
48
49
68,0.061,0.496
1,2,3,5,7,9,11,13,15,17,19,21,23,25,27,29
*geom.8
*geom.9
50
31,33,35,37,70,72,105,107,140,142,175,177,210,212,245,247
*geom.9
51
52
280,282,315,317,350,352,385,387,420,422,455,457,490,492,525,527 *geom.9
*geom.9
560,562,595,596,597,598,599,600,601,602,603,604,605,606,607,608
53
54
55
609,610,611,612
*
gap type II
444,0.122,0.496
*geom.5
*geom.6
*geom.6
*geom.6
*geom.7
gap type I
*geom.9
*geom.8
102
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
*geom.9
4,6,8,10,12,14,16,18,20,22,24,26,28,30,32,34
*geom.9
36,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52
*geom.9
53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68
*geom.9
69,71,73,74,75,76,77,78,79,80,83,85,86,89,91,92
*geom.9
95,97,98,99,100,101,102,103,104,106,108,109,110,111,114,117
118,119,120,121,123,124,125,126,127,129,130,131,134,136,137,138 *geom.9
139, 141, 143, 144, 145, 146, 148, 149,150,151,152,153,154,155,156,157 *geom.9
158,159,160,161,162,163,164,165,166,168,169,170,171,172,173,174*geom.9
176,178,179,182,184,185,188,190,191,194,196,197,200,202,203,206 *geom.9
208,209,211,213,214,216,217,218,219,220,222,223,224,225,226,228 *geom.9
229,230,231,232,234,235,236,237,238,240,241,242,243,244,246,248 *geom.9
*geom.9
249,250,251,252,253,254,255,256,257,258,259,260,261,262,263,264
265,266,267, 268,269,270,271,272,273,274,275,276, 277,278,279,281 *geom.9
283, 284, 287, 289, 290, 293, 295, 296, 299, 301, 302, 305, 307, 308, 311, 313 *geom.9
314,316,318,319,321,322,323,324,325,327,328,329,330,331,333,334 *geom.9
335,336,337,339,340,341,342,343,345,346,347,348,349,351,353,354 *geom.9
355, 356, 357, 358, 359,360, 361, 362,363,364, 365, 366, 367, 368, 369, 370 *geom.9
371,372,373,374,375,376,377,378,379,380,381,382,383,384,386,388 *geom.9
*geom.9
389,392,394,395,398,400,401,404,406,407,410,412,413,416,418,419
*geom.9
421,423,424,426,427,428,429,430,432,433,434,435,436,438,439,440
*geom.9
441,442,444,445,446,447,448,450,451,452,453,454,456,458,459,460
*geom.9
461,464,466,467,468,469,470,471,472,473,474,475,476,477,478,479
*geom.9
480,481,484,486,487,488,489,491,493,494,495,496,498,499,500,503
*geom.9
505,506,509,511,512,515,518,519,520,521,522,523,524,526,528,529
530, 531, 532, 533, 534, 535, 537, 538, 539, 540, 541, 543, 544, 545, 546,547 *geom.9
549,550,551,552,553,554,555,556,557,558,559,561,563, 564,565,566 *geom.9
567,568,569,570,571,572,573,574,575,576,577,578,579,580,581,582 *geom.9
*geom.9
583,584,585,586,587,588,589,590,591,592,593,594
84
*
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
gap type III
100,0.068,0.496
81,82,84,87,88,90,93,94,96,112,113,115,116,122,128,132
133,135,147,167,180,181,183,186,187,189,192,193,195,198,199,201
204,205,207,215,221,227,233,239,285,286,288,291,292,294,297,298
300,303,304,306,309,310,312,320,326,332,338,344,390,391,393,396
397,399,402,403,405,408,409,411,414,415,417,425,431,437,443,449
462,463,465, 482,483, 485,497,501,502,504,507,508,510,513,514,516
517,536,542,548
18,36,54,72,90,108,126,144,162,180,198,216,234,252,270,288
306,324
*geom.8
*geom.9
*geom.9
*geom.9
*geom.9
*geom.9
*geom.9
*geom.9
*geom.10
*geom.10
*
prop,22,1,1,0
203.32,729.1,1800.
*
create table from functions
*prop.1
*prop.3
*
drag,1,0,1
.18,-.2,0.,64.,-l.,0. * axial friction correlation
* pitch = .496, kij = .51/p
.5,.496
*drag.1
*drag.2
*drag.5
*
grid,0,l
*seed, blanket drag factors
.86
*seed channels
-1,8
16.0,1,32.0,1,48.0,1,64.0,1,80.0,1,96.0,1,?
112.0,1,128.0,1,
0,
*
grid loc.
*grid.1
*grid.2
*grid.4
*grid.6
*grid.6
*grid.4
*
corr,1,0,
epri,epri,epri,none,
0.2
ditb
w-31
0.043,0.066,0.986
116
*
117
118
119
120
121
oper,l,l,-1,0,0,1,0,
* iterate to mdnbr=1.30, fcool=1.95, convergence=0.005
-1.0,1.3,1.95,0.005
0
2248.1,552.2,202.186,8.825, * operat. cond. 1.587 radial peak
*corr.1
*corr.2
*corr.3
*corr.6
*corr.9
*corr.11
*oper.1
*oper.2
*oper.3
*oper.5
103
to
SZ*GPOI*
ZZ'GPOJ*
OZ'GPOJ*
OZ'SPO-T*
OZ*SPOI*
6T*SPOI*
S-Spoj*
666'0'8EO'T
Z'TGO*T'000*0'ZTO'T'996*0'E:L6*O'E86'0'8L6'0'GEO*T'TSO*T'LZO'T
6EO'T'ZOO'T
Z'666*0'LZO*T'666*0'ZOO*T'6EO'T'LZO'T'TGO*T'SEO*T'BL6'O'E86*0
T66'O'OTO'T
Z'000*0'8EO*T'8EO'T'000*0'OEO*T'6ZO*T'000*0'6ZO*T'OEO*T'000'0
8EO*T'8EO'T
Z'000'0'OTO"T'T66*0'T66*O'E86'0'TZO'T'666'0'TOO*T'OCO*T'000*T
000*T'8ZO*T
Z'000*T'000*T'OEO'T'TOO*T'666*0'TZO'T'E86'0'T66*0'T66'O'C86*0
6TO*T'966*0
Z'666*0'6ZO*T'000*T'000'T'6ZO*T'000*T'000*T'6ZO'T'666'0'966*0
6TO*T'E86'0
Z'T66*0' 66*0'600*T'000*0' ZO'T'LZO*T'000*0'8ZO*T'6ZO*T'000*0
6ZO*T'8ZO*T
Z'000*0'LZO*T' ZO'T'000*0'600*T' 66*0'T66*O'E86'0'6TO*T'966,0
666'0'6ZO*T
Z'000*T'000*T'6ZO'T'000*T'000*T'6ZO'T'666*0'966*0'6TO*T'C86*0
T66'0'T66*0
-L'E86*0'TZO"T'666*0'TOO'T'OEO*T'000*T'000*T'BZO'T'000*T'000'T
OCO*T'TOO'T
Z'666*0'TZO*T'E86*0'T66'0'T66*0'OTO*T'000*0'8EO*T'8CO'T'000'0
OEO*T'6ZO'T
Z'000*0'6ZO*T'OEO*T'OOO*O'8EO'T'BEO*T'000'0'OTO'T'T66*O'C86*0
8L6*0'GEO*T
Z'TGO*T'LZO*T'6EO'T'ZOO*T'666*0'LZO*T'666*0'ZOO*T'6EO*T'LZO*T
TSO*T'SEO'T
Z'8L6*0'EB6*0'EL6*0'996*0'ZTO*T'000*0'TSO*T'BE:O'T'666*0"966*O
ZO*T'966*0
,L'666'O'8CO"T'TGO*T'000*0'ZTO*T'996'0'EL6"0'996*0'0 6*0' 96*0
ZTO'T'SCO'T
j,'000*0'TZO*T'OZO'T'000'0'OZO'T'TZO*T'000'0'SEO*T'ZTO*T' 96*0
O 6*0'996*0
Z'L96*0' E:6*0'0 6*0'9S6*0'BL6*0'OTO*T'E86*O'E86*0'600*T'C86*0
C86*0'OTO*T
Z'8L6'0'996*0'0 6*0' E6*0'L96*0'000*T'L96'O'S96*0'EL6'0'EB6'0
T66*0'T66'0
Z'Z66*0' 66*0'Z66*0'T66*0'T66*0'E:86*0'EL6*O'S96*0'L96*0'000*T
0
0
OGz
L Z' PZ'SEZ'SZZ'ZOZ'66T'96T'E6T'06T'TST'8 T'S T
Z T'6ET'OOT'L6' 6'T6'88'99'GS'9 'Et,'OP
S'Z'T'SZ
(LTxLT) T@uupT4oqns aoj qnOAPT POJ passaadmoo *
oTqea Npad @b'elaAP oq N-ead * 99-T
Uspoa*
SaPOu 9T JO
We9 JO; AJ4U9
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*
U0T4le3T;Tz)@ds GTTjoid aamod TPPOu *
Z*SPO-T*
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T-sp0j*
spoa uoT4z)npuoo puii? Auimnp paxTiu 4noAPT POI
TT-4uoo*
6 - 4uoz)*
8 - -4uoz)*
L.quoo*
9.4U03*
c - quoz)*
z .4uoz)*
T-4uoo*
ZT*jado*
pa4uiad s4Tnsai qup
OEVEST
6TZ'TOZ'98T
Pa4UTjd sdieb * LOS'E8P'E8T'ZZT'GTT
Pa4uTjd sTauuPT40 *
OCZ'EST'09
"O"O"O"O"O"OOOT
O'T'T'O'O'O'T'T'O'Z'E'S'E:'O
8*0'TO*0'90*0'TO*O'*O"O
uoTqnTOs mOT;dn qoaaTp
T '0 '0 'OZ '0 ' ' 0
4uoz)
suoT4oun; buToao; ou
0
L8T
98T
S8T
BT
C8T
Z8T
TH
08T
6LT
8LT
LLT
9LT
9LT
PLT
ELT
ZLT
TLT
OLT
69T
89T
L9T
99T
99T
P9 T
C9T
Z9T
T9T
09T
6ST
89T
LST
9ST
9ST
GT
EST
Z9T
TST
OST
6PT
8PT
LVT
9 P T
9VT
P T
EPT
Z T
TPT
OPT
6ET
8ET
LET
9ET
GET
PET
CET
ZET
TET
OET
6ZT
8ZT
LZT
9ZT
SZT
PZT
EZT
ZZT
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
0.996,1.024,0.996,0.999,1.038,1.051,0.000,1.012,0.956,0.973,?
0.965,0.940
0.964, 1.012, 1.035,0.000, 1.021,1.020,0.000, 1.020,1.021,0.000,?
1.035,1.012
0.964,0.940,0.965,0.967,0.934,0.940,0.956,0.978,1.010,0.983,?
0.983,1.009
0.983,0.983, 1.010,0.978,0.956,0.940,0.934,0.967,1.000,0.967,?
0.965,0.973
0.983,0.991,0.991,0.992,0.994,0.992,0.991,0.991,0.983,0.973,?
0.965,0.967
1.000
17,17,34,51, 68,85,102,119,136,153,170,187
204,221,238,255,272,289
1,nucl,0.374,0.3225,6,0.0,0.02244
*U02 rods
0,0,0,0,0,3500.0,1.0,0.01 * 3500 btu/hr-ft2-F
2,dumy,0.482,0.0,0
*control rods
endd
*
*
*rods.27
*rods.28
*rods.28
*rods.62
*rods.63
*rods.68
end of input file
105
Appendix C : SBU
INPUT FILE FOR
VIPRE
A reference input file for the SBU design is shown below.
input card images
card
1
2
4
3
5
6
8
7
12345678901234567890123456789012345678901234567890123456789012345678901234567890
1
*
2
3
*
*
4
*
5
*
6
7
1,0,0
RTF homogeneous assembly case(llxll seed 17x17 blanket)
8
*
9
10
11
12
13
14
*
15
*
16
17
4,0.03404,0.2937,0.2937
1,18,307,324
*
*
*
*
*
*
*
*
*
*
*
*
*
*
*
*
*
*
*
*
*
*
*
*
*
*
*
*
*
*
*
*
*
*
*
vipre-01, RTF assembly input
*
*
*
*
*
*
*
*
*
*
*
*
*
*
*
*
10/01/99
*
*
*
*
*
*
*
*
*
*
*
*
*
*
*
*
*
*
*
*
*vipre.1
*vipre.2
assembly geometry = 11 x 11 seed rods 17x17 blanket rods
*
geom,324,9,16,0,9
*9 different compressed geometry input
144.,?
0.,0.5
* default sl = 0.5
*
channel dimensions
*geom.1
*geom.2
*geom.2 (cont.)
type I
18
*
19
20
21
22
23
64,0.06808,0.5875,0.5875
2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17
19,36,37,54,55,72,73,90,91,108,109,126,127,144,145,162
163,180,181,198,199,216,217,234,235,252,253,270,271,288,289,306
308,309,310,311,312,313,314,315,316,317,318,319,320,321,322,323
24
*
25
26
27
28
29
30
31
88,0.13616,1.1750,1.1750
20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35
38,39,40,41,44,47,50,51,52,53,56,57,70,71,74,75
88,89,92,107,110,125,128,129,142,143,146,161,164,179,182,183
196, 197,200,215,218,233,236,237,250,251,254,255,268,269,272,273
274,275,278,281,284,285,286,287,290,291,292,293,294,295,296,297
298,299,300,301,302,303,304,305
32
*
33
34
8,0.14811,1.1071,1.1071
62,65,130,141,184,195,260,263
35
*
36
37
38
39
40
41
68,0.16006,1.0392,1.0392
78,79,80,81,82,83,84,85,95,97,98,101,102,104,113,114
116,119,121,122,131,132,133,134,135,136,137,138,139,140,149,152
155,158,167,170,173,176,185,186,187,188,189,190,191,192,193,194
203,204,206,209,211,212,221,223,224,227,228,230,240,241,242,243
244,245,246,247
42
*
43
44
8,0.123981,1.2258,0.8473
59,68,76,87,238,249,257,266
*geom.5
*geom.6
type II
*geom.5
*geom.6
*geom.6
*geom.6
*geom.6
type III
*geom.5
*geom.6
*geom.6
*geom.6
*geom.6
*geom.6
*geom.6
type IV
type
*geom.5
*geom.6
V
*geom.5
*geom.6
*geom.6
*geom.6
*geom.6
*geom.6
type VI
*geom.5
*geom.6
type VII
45
*
46
47
48
24,0.129959,1.1919,0.8134
60,61,63,64,66,67,94,105,112,123,148,159,166,177,202,213
220,231,258,259,261,262,264,265
49
*
*geom.5
*geom.6
*geom.6
type VIII
106
50
51
52
32,0.13594,1.1580,0.7794
77,86,96,99,100,103,115,117,118,120,150,151,153,154,156,157
168,169,171,172,174,175,205,207,208,210,222,225,226,229,239,248
53
*
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
28,0.11800,1.2598,0.8812
42,43,45,46,48,49,58,69,93,106,111,124,147,160,165,178
201,214,219,232,256,267,276,277,279,280,282,283
* Gap input data
612,6,0,18,0,0
gap type I
*
68,0.061,0.496
1,2,3,5,7,9,11,13,15,17,19,21,23,25,27,29
31,33,35,37,70,72,105,107,140,142,175,177,210,212,245,247
280,282,315,317,350,352,385,387,420,422,455,457,490,492,525,527
560,562,595,596,597,598,599,600,601,602,603,604,605,606,607,608
609,610,611,612
gap type II
*
244,0.122,0.496
4,6,8,10,12,14,16,18,20,22,24,26,28,30,32,34
36,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52
53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68
69,71,73,74,75,76,77,78,79,80,83,85,86,89,91,92
95,97,98,99,100,101,102,103,104,106,108,109,110,111,134,136
137,138,139,141,143,144,145,146,169,171,172,173,174,176,178,179
206,208,209,211,213,214,216,241,242,243,244,246,248,249,250,251
274,276,277,278,279,281,283,284,311,313,314,316,318,319,321,346
347,348,349,351,353,354,355,356,379,381,382,383,384,386,388,389
416,418,419,421,423,424,426,451,452,453,454,456,458,459,460,461
484,486,487,488,489,491,493,494,495,496,498,500,506,512,518,519
520,521,522,523,524,526,528,529,530,531,532,533,534,535,537,538
539,540,541,543,544,545,546,547,549,550,551,552,553,554,555,556
557,558,559,561,563,564,565,566,567,568,569,570,571,572,573,574
575,576,577,578,579,580,581,582,583,584,585,586,587,588,589,590
591,592,593,594
*
gap type III
44,0.068,0.496
81,82,84,87,88,90,93,94,96,112,113,132,135,180,181,204
207,215,239,285,286,309,312,320,344,390,391,414,417,425,449,463
485,497,502,504,508,510,514,516,517,536,542,548
89
*
type
*geom.5
*geom.6
*geom.6
IX
*geom.5
*geom.6
*geom.6
*geom.7
*geom.8
*geom.9
*geom.9
*geom.9
*geom.9
*geom.9
*geom.8
*geom.9
*geom.9
*geom.9
*geom.9
*geom.9
*geom.9
*geom.9
*geom.9
*geom.9
*geom.9
*geom.9
*geom.9
*geom.9
*geom.9
*geom.9
*geom.9
*geom.8
*geom.9
*geom.9
*geom.9
gap type IV
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
56,0.0896,0.496
115,116,122,128,133,147,167,183,186,187,189,192,193,195,198,199
201,205,221,227,233,288,291,292,294,297,298,300,303,304,306,310
326,332,338,393,396,397,399,402,403,405,408,409,411,415,431,437
443,462,465,482,483,501,507,513
*
gap type V
176,0.1653,0.496
117,119,121,123,125,127,129,131,149,150,151,152,153,154,155,156
157,158,159,160,161,162,163,164,165,166,168,182,184,185,188,190
191,194,196,197,200,202,203,217,219,220,222,223,224,225,226,228
229,230,231,232,234,235,236,237,238,252,254,255,256,257,258,259
260,261,262,263,264,265,266,267,268,269,270,271,272,273,287,289
290,293,295,296,299,301,302,305,307,308,322,324,325,327,328,329
330,331,333,334,335,336,337,339,340,341,342,343,357,359,360,361
362,363,364,365,366,367,368,369,370,371,372,373,374,375,376,377
378,392,394,395,398,400,401,404,406,407,410,412,413,427,429,430
432,433,434,435,436,438,439,440,441,442,444,445,446,447,448,464
466,467,468,469,470,471,472,473,474,475,476,477,478,479,480,481
108
*
109
110
111
112
113
114
115
24,0.1436,0.496
114,118,120,124,126,130,148,170,218,240,253,275,323,345,358,380
428,450,499,503,505,509,511,515
18,36,54,72,90,108,126,144,162,180,198,216,234,252,270,288
306,324
*geom.8
*geom.9
*geom.9
*geom.9
*geom.9
*geom.8
*geom.9
*geom.9
*geom.9
*geom.9
*geom.9
*geom.9
*geom.9
*geom.9
*geom.9
*geom.9
*geom.9
gap type VI
*geom.8
*geom.9
*geom.9
*geom.10
*geom.10
*
prop,22,1,1,0
*
create table from functions
*prop.1
107
116
117
118
119
203.32,729.1,1800.
*prop.3
*
drag,1,0,1
.18,-.2,0.,64.,-1.,0.
120
.5,.496
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
*
*
pitch =
* axial friction correlation
.496, kij =
.51/p
grid,0,2
.86,.86
*seed, blanket drag factors
100,8
*seed channels
77,78,79,80,81,82,83,84,85,86,95,96,97,98,99,100
101,102,103,104,113,114,115,116,117,118,119,120,121,122,131,132
133,134,135,136,137,138,139,140,149,150,151,152,153,154,155,156
157,158,167,168,169,170,171,172,173,174,175,176,185,186,187,188
189,190,191,192,193,194,203,204,205,206,207,208,209,210,211,212
221,222,223,224,225,226,227,228,229,230,239,240,241,242,243,244
245,246,247,248
16.0,1,32.0,1,48.0,1,64.0,1,80.0,1,96.0,1,? * grid loc.
112.0,1,128.0,1,
224,8
*blanket channels
1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16
17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32
33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48
49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64
65,66,67,68,69,70,71,72,73,74,75,76,87,88,89,90
91,92,93,94,105,106,107,108,109,110,111,112,123,124,125,126
127,128,129,130,141,142,143,144,145,146,147,148,159,160,161,162
163,164,165,166,177,178,179,180,181,182,183,184,195,196,197,198
199,200,201,202,213,214,215,216,217,218,219,220,231,232,233,234
235, 236, 237,238,249,250,251,252,253,254,255,256,257,258,259,260
261,262,263,264,265,266,267,268,269,270,271,272,273,274,275,276
277,278,279,280,281,282,283,284,285,286,287,288,289,
290,291, 292
293, 294, 295, 296, 297, 298, 299, 300, 301, 302, 303, 304, 305, 306, 307, 308
309,310,311,312,313,314,315,316,317,318,319,320,321,322,323,324
16.0,2,32.0,2,48.0,2,64.0,2,80.0,2,96.0,2,? * grid loc.
112.0,2,128.0,2,
0,
152
*
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
corr,1,0,
epri,epri,epri,none,
0.2
ditb
w-31
0.043,0.066,0.986
176
*
177
178
179
180
181
*
*
*drag.1
*drag.2
*drag.5
*grid.1
*grid.2
*grid.4
*grid.5
*grid.5
*grid.5
*grid.5
*grid.5
*grid.5
*grid.5
*grid.6
*grid.6
*grid.4
*grid.5
*grid.5
*grid.5
*grid.5
*grid.5
*grid.5
*grid.5
*grid.5
*grid.5
*grid.5
*grid.5
*grid.5
*grid.5
*grid.5
*grid.6
*grid.6
*grid.4
*corr.1
*corr.2
*corr.3
*corr.6
*corr.9
*corr.11
*
oper,1,1,-1,0,4,1,0,
* iterate to mdnbr=1.30, fcool=1.95, convergence=0.005
-1., 1.3, 1.95, 0
0
2248.1,552.2,202.186,7.401,
* operating conditions MOC
0
* no forcing functions
*oper.1
*oper.2
*oper.3
*oper.5
*oper.12
*
cont
0.,0,20,0,0,1
* direct upflow solution
0.,0.,0.01,0.05,0.01,0.8
0,3,5,3,2,0,1,1,0,0,0,1,1,0
1000.,0.,0.,0.,0.,0.,
60,153,230
* channels printed
115,122,183,483,507 * gaps printed
185,201,219
153,230
* dnb results printed
rod layout
-
*cont.1
*cont.2
*cont.3
*cont.6
*cont.7
*cont.8
*cont.9
*cont.11
mixed dummy and conduction rods
rods,1,289,1,3,4,0,0,3,
*rods.1
*
0.0,0.0,1
*
nodal power profile specification
*rods.2
108
60M
Z 'Lt'9 0'999 *0'9V9 0 '0S9 0'699'0'69S*0 '88S~' '09'0 'C8S *0 'ELSA 0
8T9*0'879*0
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j,'LE9 '
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91
£61
161
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681
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981
£81
£81
Z8T
248
249
250
251
252
253
254
255
256
257
258
259
260
261
262
263
264
265
266
267
268
269
270
271
272
273
274
275
276
277
278
279
280
281
282
283
284
285
286
287
288
289
290
291
292
293
294
295
296
297
298
299
300
301
302
303
304
305
306
307
308
309
310
311
312
313
0.622,0.604
0.622,0.647,0.666,0.646,0.630,0.583,0.583,0.602,0.587,0.588,?
0.588,0.649
0.657,0.662,0.659,0.650,0.645,0.650,0.659,0.662,0.657,0.649,?
0.602,0.602
0.601
*rods.27
17,17,34,51,68,85,102,119,136,153,170,187
*rods.28
204,221,238,255,272,289
*rods.28
1,nucl,0.3307,0.30315,6,0.1575,0.013775
*seed rods
*rods.62
0,1,0,0,0,1000000.,1.,0.01 *No gap very high btu/hr-ft2-F
*rods.63
2,hrod,0.374,0.0,3
*bkt. rods 3 regions:fuel+gap+clad *rods.68
6,2,0.161,0.99,1,3,0.0034,0.0,3,4,0.02244,0.01*blanket rods
*rods.69
3,dumy,0.482,0.0,0
*control rods
*rods.68
1,25,1183.01,seed
*rods.70
80.33,0.0642,13.1439,?
170.33,0.0642,13.1575
260.33,0.0642,13.1702,?
350.33,0.0642,13.182
440.33,0.0642,13.1928,?
530.33,0.0642,13.2027
620.33,0.0642,13.2117,?
710.33,0.0642,13.2197
800.33,0.0642,13.2267,?
890.33,0.0642,13.2329
980.33,0.0642,13.238,?
1070.33,0.0642,13.2423
1160.33,0.0642,13.2456,?
1250.33,0.0642,13.2479
1340.33,0.0642,13.2493,?
1430.33,0.0642,13.2498
1520.33,0.0642,13.2493,?
1610.33,0.0642,13.2479
1700.33,0.0642,13.2456,?
1790.33,0.0642,13.2423
1880.33,0.0642,13.238,?
1970.33,0.0642,13.2329
2060.33,0.0642,13.2267,?
2150.33,0.0642,13.2197
2240.33,0.0642,13.2117
2,25,638.256,blan
*rods.70
80.33,0.0764,5.356,?
170.33,0.0764,4.902
260.33,0.0764,4.520,?
350.33,0.0764,4.192
440.33,0.0764,3.909,?
530.33,0.0764,3.662
620.33,0.0764,3.444,?
710.33,0.0764,3.251
800.33,0.0764,3.078,?
890.33,0.0764,2.923
980.33,0.0764,2.782,?
1070.33,0.0764,2.655
1160.33,0.0764,2.538,?
1250.33,0.0764,2.432
1340.33,0.0764,2.334,?
1430.33,0.0764,2.243
1520.33,0.0764,2.159,?
1610.33,0.0764,2.082
1700.33,0.0764,2.010,?
1790.33,0.0764,1.942
1880.33,0.0764,1.879,?
1970.33,0.0764,1.820
2060.33,0.0764,1.765,?
2150.33,0.0764,1.712
2240.33,0.0764,1.663
*rods.70
3,1,1.0,bgap
110
314
315
316
317
318
319
320
321
322
323
324
325
326
327
328
329
330
331
1,100,6.8 *gap condty.=2000Btu/hr.ft2.F*0.0034 ft
4,13,409.0,bcld
80.33,0.0671,7.330,?
260.33,0.07212,8.1158
692.33,0.07904,9.8016,?
1502.33,0.08955,13.2923
1507.73,0.11988,13.3211,?
1543.73,0.14089,13.5166
1579.73,0.14686,13.7172,?
1615.73,0.1717,13.9231
1651.73,0.1949,14.1347,?
1687.73,0.18388,14.3519
1723.73,0.1478,14.5752,?
1759.73,0.112,14.8047
1786.73,0.085,14.9810
endd
*
*
end of input file
111
Appendix D : WSB
INPUT FILES FOR
VIPRE
A reference input file for the WSB-A design follows.
input card images
card
1
2
3
4
5
6
7
8
12345678901234567890123456789012345678901234567890123456789012345678901234567890
1
*
2
*
3
*
4
*
5
*
6
7
1,0,0
Checkerboard array case(l assembly seed + 1 assembly blanket)
8
*
9
10
11
12
13
14
15
16
17
18
*
*
*
*
*
*
*
*
*
*
*
*
*
*
*
*
*
*
*
*
*
*
*
*
*
*
*
*
*
*
*
*
*
*.
*
vipre-01, Checkerboard array input Ver 3
*
*
*
*
*
*
*
*
*
*
*
*
*
*
*
*
*
*
*
*
*
*
03/10/00
*
*
*
*
*
*
*
*
*
*
*
*
*
*
*vipre. 1
*vipre.2
assembly geometry = 11 x 11 seed rods 17x17 blanket rods
*
geom,289,8,16,0,8
144.,?
*8 different compressed geometry input
0.,0.5
20
21
22
23
24
* default si = 0.5
channel dimensions
type I
32,0.13445,1.1669,0.7884
37,38,40,41,54,55,57,58,73,74,88,89,90,91,105,106
184, 185, 199,200,201,202,216,217,232,233,235,236,249,250,252,253
*
type II
64,0.15809,1.1669,0.7884
20,21,22,23,24,25,36,39,42,53,56,59,70,71,72,75
76,87,92,93,104,107,108,109,110,121,122,123,124,125,126,127
163, 164, 165,166,167,168, 169,180,181, 182, 183,186, 197,198,203,214
215,218,219,220,231,234,237,248,251, 254,265,266,267,268,269,270
25
*
26
27
28
29
37,0.14712,1.1131,1.1131
5,8,26,43,60,69,77,94,111,120,128,138,139,140,141,142
143,144,145,146,147,148,149,150,151,152,162,170,179,196,213,221
230,247,264,282,285
30
*
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
4,0.11801,1.2598,0.8812
1,17,273,289
*
type V
126,0.13616,1.1750,1.1750
10,11,12,13,14,15,16,27,28,29,30,31,32,33,34,44
45,46,47,48,49,50,51,61,62,63,64,65,66,67,68,78
79,80,81,82,83,84,85,95,96,97,98,99,100,101,102,112
113,114,115,116,117,118,119,129,130,131,132,133,134,135,136,154
155,156, 157,158,159,160,161,171,172,173,174,175,176,177,178,188
189,190,191,192,193,194,195,205,206,207,208,209,210,211,212,222
223,224,225,226,227,228,229,239,240,241,242,243,244,245,246,256
257,258,259,260,261,262,263,274,275,276,277,278,279,280
*
type VI
2,0.15260,1.0821,1.0821
19,271
46
*
47
48
16,0.12897,1.1979,0.8193
3,4,6,7,35,52,86,103,187,204,238,255,283,284,286,287
49
*
19
*
*geom.1
*geom.2
*geom.2 (cont.)
*
*
*geom.5
*geom.6
*geom.6
*geom.5
*geom.6
*geom.6
*geom.6
*geom.6
type III
*geom.5
*geom.6
*geom.6
*geom.6
type IV
*geom.5
*geom.6
*geom.5
*geom.6
*geom.6
*geom.6
*geom.6
*geom.6
*geom.6
*geom.6
*geom.6
*geom.5
*geom.6
type VII
*geom.5
*geom.6
type VIII
112
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116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
121,122,123,124,125,126,127,128,137,138,139,140,141,142,143,144
145,146,147,148,149,150,151,152,153,162,163,164,165,166,167,168
169,170,179,180,181,182,183,184,185,186,187,196,197,198,199,200
201,202,203,204,213,214,215,216,217,218,219,220,221,230,231,232
233,234, 235, 236,237,238, 247,248,249, 250,251,252, 253,254, 255,264
265,266,267,268,269,270,271,272,281,282,283,284,285,286,287,288
289
16.0,1,32.0,1,48.0,1,64.0,1,80.0,1,96.0,1,?
* grid loc.
112.0,1,128.0,1,
128,8
* Blanket channels
10,11,12,13,14,15,16,17,27,28,29,30,31,32,33,34
44,45,46,47,48,49,50,51,61,62,63,64,65,66,67,68
78, 79, 80, 81, 82, 83, 84, 85, 95, 96, 97, 98, 99, 100, 101, 102
112,113,114,115,116,117,118,119,129,130,131,132,133,134,135,136
154,155,156,157,158,159,160,161,171,172,173,174,175,176,177,178
188,189,190,191,192,193,194,195,205,206,207,208,209,210,211,212
222,223,224,225,226,227,228,229,239,240,241,242,243,244,245,246
256,257,258,259,260,261,262,263,273,274,275,276,277,278,279,280
16.0,2,32.0,2,48.0,2,64.0,2,80.0,2,96.0,2,?
* grid loc.
112.0,2,128.0,2,
0,
*grid.5
*grid.5
*grid.5
*grid.5
*grid.5
*grid.5
*grid.5
*grid.6
*grid.6
*grid.4
*grid.5
*grid.5
*grid.5
*grid.5
*grid.5
*grid.5
*grid.5
*grid.5
*grid.6
*grid.6
*grid.4
*
corr,1,0,
epri,epri,epri,none,
0.2
ditb
w-31
0.043,0.066,0.986
144
*
145
146
147
148
149
150
oper,1,1,-1,0,0,1,0,
* iterate to mdnbr=1.00, fcool=1.95, convergence=0.005
-1., 1.3, 1.95, 0
0
7 4
264 276
2248.1,552.2,202.186,7.079,
* ( . 01*
/
)op. cond. MOC
0
* no forcing functions
151
*
152
153
154
155
156
157
158
159
160
161
162
163
cont
0.,0,20,0,0,1
* direct upflow solution
0.,0.,0.01,0.,0.,0.8
2,3,5,0,2,0,1,1,0,0,0,1
1000.,0.,0.,0.,0.,0.,
19,64,254
* channels printed
51,150,271,291,480 * gaps printed
64,254
* dnb results printed
164
*
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
0.0,0.0,1
*
*
*
rod layout
-
*corr.1
*corr.2
*corr.3
*corr.6
*corr.9
*corr.11
*oper.1
*oper.2
*oper.3
*oper.5
*oper.12
*cont.1
*cont.2
*cont.3
*cont.6
*cont.7
*cont.8
*cont.9
*cont.11
mixed dummy and conduction rods
rods,1,324,0,3,0,0,0,0,0,0,0
*rods.1
* nodal power profile specification
*rods.2
* one entry for each of 16 nodes
*rods.3
*
16
*
0.45373,0.81156,1.05758,1.12688,1.13106,1.12223,1.12083,1.13245 *rods.6
1.15524,1.18175,1.19292,1.18175,1.13013,1.00409,0.73761,0.46019
*rods.6
* normal rod layout for checkerboard
1,3,0.00000000,1,1,0.25
2,1,1.21700000,1,1,0.25,2,0.25
3,1,1.14500000,1,2,0.25,3,0.25
4,3, 0.00000000, 1,3,0.25,4,0.25
5,1,1.09100000,1,4,0.25,5,0.25
6,1,1.08100000,1,5,0.25,6,0.25
7,3,0.00000000,1,6,0.25,7,0.25
8,1,1.06300000,1,7,0.25,8,0.25
9,1,1.05800000,1,8,0.25,9,0.25
10,1,0.53400000,1,9,0.25,10,0.25
114
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A reference WSB-B input file for VIPRE is given below.
input card images
card
1
2
3
4
5
6
7
8
12345678901234567890123456789012345678901234567890123456789012345678901234567890
1
*
2
*
3
4
*
*
5
*
6
7
1,0,0
Checkerboard array case(1 assembly seed + 1 assembly blanket)
8
*
9
10
11
12
13
14
15
16
17
18
*
*
19
*
20
21
22
23
24
64,0.15809,1.1669,0.7884
20,21,22,23,24,25,36,39,42,53,56,59,70,71,72,75
76,87,92,93,104,107,108,109,110,121,122,123,124,125,126,127
163,164,165,166,167,168,169,180,181,182,183,186,197,198,203,214
215, 218, 219, 220, 231, 234, 237, 248,251,254,265,266,267,268,269,270
*
*
*
*
*
*
*
*
*
*
*
*
*
*
*
*
*
*
*
*
*
*
*
*
*
*
*
*
*
*
*
*
*
*
*
vipre-01, Checkerboard array input Ver 3
*
*
*
*
*
*
*
*
*
*
*
*
*
*
*
*
*
*
*
*
*
*
03/10/00
*
*
*
*
*
*
*
*
*
*
*
*
*
*
*vipre.1
*vipre.2
assembly geometry = 11 x 11 seed rods 17x17 blanket rods
geom,289,8,16,0,8
*8 different compressed geometry input
144.,?
0.,0.5
* default si = 0.5
*
channel dimensions
*
type I
32,0.13445,1.1669,0.7884
37,38,40,41,54,55,57,58,73,74,88,89,90,91,105,106
184,185,199,200,201,202,216,217,232,233,235,236,249,250,252,253
*geom.1
*geom.2
*geom.2 (cont.)
*geom.5
*geom.6
*geom.6
type II
25
*
26
27
28
29
37,0.14712,1.1131,1.1131
5,8,26,43,60,69,77,94,111,120,128,138,139, 140, 141, 142
143,144,145,146,147,148,149,150,151,152,162,170,179,196,213,221
230,247,264,282,285
30
*
31
32
33
34
35
36
37
38
39
40
41
42
4,0.11801,1.2598,0.8812
1,17,273,289
*
type V
126,0.13616,1.1750,1.1750
10,11,12,13,14,15,16,27,28,29,30,31,32,33,34,44
45,46,47,48,49,50,51,61,62,63,64,65,66,67,68,78
79,80,81,82,83,84,85,95,96,97,98,99,100,101,102,112
113, 114, 115, 116, 117, 118, 119, 129,130,131,132,133,134,135,136, 154
155,156,157,158,159,160,161,171,172,173,174,175,176,177,178,188
189,190,191,192,193,194,195,205,206,207,208,209,210,211,212,222
223,224, 225, 226,227,228,229, 239,240,241,242,243, 244,245,246,256
257,258,259,260,261,262,263,274,275,276,277,278,279,280
*geom.5
*geom.6
*geom.6
*geom.6
*geom.6
type III
*geom.5
*geom.6
*geom.6
*geom..6
type IV
43
*
44
45
46
47
48
2,0.15260,1.0821,1.0821
19,271
*
type VII
16,0.12897,1.1979,0.8193
3,4,6,7,35,52,86,103,187,204,238,255,283,284,286,287
49
*
50
51
52
53
8,0.14164,1.1440,1.1440
2,9,18,137,153,272,281,288
* Gap input data
544,4,0,17,0,0
54
*
55
188,0.1614,0.496
*geom.5
*geom.6
*geom.5
*geom.6
*geom.6
*geom.6
*geom.6
*geom.6
*geom.6
*geom.6
*geom.6
type VI
*geom.5
*geom.6
*geom.5
*geom.6
type VIII
*geom.5
*geom.6
*geom.7
gap type I
*geom.8
120
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
6,8,10,12,14,16,36,37,38,39,40,41,42,43,44,45
46,47,48,49,67,69,70,73,75,76,79,81,82,100,102,103
105,106,107,108,109,111,112,113,114,115,133,135,136,137,138,139
140,143,145,146,147,148,166,168,169,172,175,176,177,178,179,180
181,199,201,202,204,205,206,207,208,209,210,211,212,213,214,232
234,235,236,237,238,239,240,241,242,243,244,245,246,247,284,286
288,290,292,294,296,314,316,317,318,319,320,321,322,323,324,325
326,327,328,329,347,349,350,351,352,353,354,355,356,359,361,362
380,382,383,384,385,388,391,392,393,394,395,413,415,416,417,418
420,421,422,423,424,425,426,427,428,446,448,449,452,454,455,458
460,461,479,481,482,484,485,486,487,488,490,491,492,493,494,512
514,515,516,517,518,519,520,521,522,523,524,525
*
gap type II
260,0.1220,0.496
1,2,17,19,20,21,22,23,24,25,26,27,28,29,30,31
32,33,50,52,53,54,55,56,57,58,59,60,61,62,63,64
65,66,83,85,86,87,88,89,90,91,92,93,94,95,96,97
98,99,116,118,119,120,121,122,123,124,125,126,127,128,129,130
131,132,149,151,152,153,154,155,156,157,158,159,160,161,162,163
164,165,182,184,185,186,187,188,189,190,191,192,193,194,195,196
197,198,215,217,218,219,220,221,222,223,224,225,226,227,228,229
230,231,248,250,251,252,253,254,255,256,257,258,259,260,261,262
263,264,266,268,270,272,274,276,278,280,298,299,300,301,302,303
304,305,306,307,308,309,310,311,312,313,331,332,333,334,335,336
337,338,339,340,341,342,343,344,345,346,364,365,366,367,368,369
370,371,372,373,374,375,376,377,378,379,397,398,399,400,401,402
403,404,405,406,407,408,409,410,411,412,430,431,432,433,434,435
436,437,438,439,440,441,442,443,444,445,463,464,465,466,467,468
469,470,471,472,473,474,475,476,477,478,496,497,498,499,500,501
502,503,504,505,506,507,508,509,510,511,528,529,530,531,532,533
534,535,536,544
*
gap type III
40,0.0877,0.496
5,11,68,71,72,74,77,78,80,104,110,141,142,144,167,170
171,173,174,203,357,358,360,363,386,387,389,390,419,450,451,453
456,457,459,462,483,489,539,542
*
gap type IV
56,0.1417,0.496
3,4,7,9,13,15,18,34,35,51,84,101,117,134,150,183
200,216,233,249,265,267,269,271,273,275,277,279,281,282,283,285
287,289,291,293,295,297,315,330,348,381,396,414,429,447,480,495
513,526,527,537,538,540,541,543
*geom.9
*geom.9
*geom.9
*geom.9
*geom.9
*geom.9
*geom.9
*geom.9
*geom.9
*geom.9
*geom.9
*geom.9
*geom.8
*geom.9
*geom.9
*geom.9
*geom.9
*geom.9
*geom.9
*geom.9
*geom.9
*geom.9
*geom.9
*geom.9
*geom.9
*geom.9
*geom.9
*geom.9
*geom.9
*geom.9
*geom.8
*geom.9
*geom.9
*geom.9
*geom.8
*geom.9
*geom.9
*geom.9
*geom.9
*
17,34,51,68,85,102,119,136,153,170,187,204,221,238,255,272
289
*geom.10
*geom.10
*
prop,22,1,1,0
* create table from functions
203.32,729.1,1800.
*prop.1
*prop.3
*
drag,1,0,1
.18,-.2,0.,64.,-1.,0. * axial friction correlation
.5,.496
* pitch = .496, kij = .51/p
*drag.1
*drag.2
*drag.5
*
grid,0,3
*grid.1
.6,2.3,2.3
* seed, blanket loss coef., blanket inlet
*grid.2
161,8
* Seed and boundary channels
*grid.4
1,2,3,4,5,6,7,8,9,18,19,20,21,22,23,24
*grid.5
25,26,35,36,37,38,39,40,41,42,43,52,53,54,55,56
*grid.5
*grid.5
57,58,59,60,69,70,71,72,73,74,75,76,77,86,87,88
*grid.5
89,90,91,92,93,94,103,104,105,106,107,108,109,110,111,120
121,122,123,124,125,126,127,128,137,138,139,140,141,142,143,144 *grid.5
145,146,147,148,149,150,151,152,153,162,163,164,165,166,167,168 *grid.5
169,170,179,180,181,182,183,184,185,186,187,196,197,198,199,200 *grid.5
201,202,203,204,213,214,215,216,217,218,219,220,221,230,231,232 *grid.5
233,234,235,236,237,238,247,248,249,250,251,252,253,254,255,264 *grid.5
265,266,267,268,269,270,271,272,281,282,283,284,285,286,287,288 *grid.5
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
289
16.0,1,32.0,1,48.0,1,64.0,1,80.0,1,96.0,1,? * grid loc.
112.0,1,128.0,1,
128,8
* Blanket channels
10,11,12,13,14,15,16,17,27,28,29,30,31,32,33,34
44,45,46,47,48,49,50,51,61,62,63,64,65,66,67,68
78,79,80,81,82,83,84,85,95,96,97,98,99,100,101,102
112,113,114,115,116,117,118,119,129,130,131,132,133,134,135,136
154,155,156,157,158,159,160,161,171,172,173,174,175,176,177,178
188,189,190,191,192,193,194,195,205,206,207,208,209,210,211,212
222,223,224,225,226,227,228,229,239,240,241,242,243,244,245,246
256,257,258,259,260,261,262,263,273,274,275,276,277,278,279,280
16.0,2,32.0,2,48.0,2,64.0,2,80.0,2,96.0,2,? * grid loc.
112.0,2,128.0,2,
128,1
* Inlet Blanket channels
10,11,12,13,14,15,16,17,27,28,29,30,31,32,33,34
44,45,46,47,48,49,50,51,61,62,63,64,65,66,67,68
78,79,80,81,82,83,84,85,95,96,97,98,99,100,101,102
112,113,114,115,116,117,118,119,129,130,131,132,133,134,135,136
154,155,156,157,158,159,160,161,171,172,173,174,175,176,177,178
188,189,190,191,192,193,194,195,205,206,207,208,209,210,211,212
222,223,224,225,226,227,228,229,239,240,241,242,243,244,245,246
256,257,258,259,260,261,262,263,273,274,275,276,277,278,279,280
0.0,3
0,
147
*
148
149
150
151
152
153
corr,1,0,
epri,epri,epri,none,
0.2
ditb
w-31
0.043,0.066,0.986
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
*corr.1
*corr.2
*corr.3
*corr.6
*corr.9
*corr.11
*
oper,1,1,-1,0,4,1,0,
* iterate to mdnbr=1.00, fcool=1.95, convergence=0.005
-1.,
1.3, 1.95, 0
0
2248.1,552.2,202.186,7.079, * ( 7 . 4 01* 2 6 4 / 2 7 6 )op. cond. MOC
0
* no forcing functions
*oper.1
*oper.2
*oper.3
*oper.5
*oper.12
*
cont
0.,0,750,50,3,0
*0.,0,20,0,0,1
*0.,0.,0.01,0.,0.,0.8
* iterative upflow solution
* direct upflow solution
0.,0.,0.001,0.,0.,0.3,1.5,0.8
5,3,5,0,2,0,1,1,0,0,0,1,1
1000.,0.,0.,0.,0.,0.,
17,64,254
* channels printed
51,150,271,291,480 * gaps printed
17,254
* dnb results printed
174
*
*
*
175
rods,1,324,1,3,4,0,0,0,0,0,0
176
*
177
0.0,0.0,1
178
*
179
180
181
182
183
184
185
186
187
16
173
*grid. 5
*grid.6
*grid.6
*grid.4
*grid.5
*grid.5
*grid.5
*grid.5
*grid.5
*grid.5
*grid.5
*grid.5
*grid.6
*grid.6
*grid.4
*grid.5
*grid.5
*grid.5
*grid.5
*grid.5
*grid.5
*grid.5
*grid.5
*grid.6
*grid.4
rod layout
-
*cont.1
*cont.2
*cont.2
*cont.3
*cont.3
*cont.6
*cont.7
*cont.8
*cont.9
*cont.11
mixed dummy and conduction rods
*rods.1
* nodal power profile specification
*rods.2
* one entry for each of 16 nodes
*rods.3
*
0.45373,0.81156,1.05758,1.12688,1.13106,1.12223,1.12083,1.13245 *rods.6
1.15524,1.18175,1.19292,1.18175,1.13013,1.00409,0.73761,0.46019 *rods.6
* normal rod layout for checkerboard
1,3,0.00000000,1,1,0.25
2,1,1.54200000,1,1,0.25,2,0.25
3,1,1.53800000,1,2,0.25,3,0.25
4,3,0.00000000,1,3,0.25,4,0.25
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TS
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6PV
8PP
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M
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966
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452
453
454
455
456
457
458
459
460
461
462
463
464
465
466
467
468
469
470
471
472
473
474
475
476
477
478
479
480
481
482
483
484
485
486
487
488
489
490
491
492
493
494
495
496
497
498
499
500
501
502
503
504
505
506
507
508
509
510
511
512
513
514
515
516
517
269,2,1.53300000,1,237,0.25,238,0.25,254,0.25,255,0.25
270,3,0.00000000,1,238,0.25,255,0.25
271,1,0.53000000,1,239,0.25,256,0.25
272,1,0.52800000,1,239,0.25,240,0.25,256,0.25,257,0.25
273,1,0.52500000,1,240,0.25,241,0.25,257,0.25,258,0.25
274,1,0.52300000,1,241,0.25,242,0.25,258,0.25,259,0.25
275,1,0.52300000,1,242,0.25,243,0.25,259,0.25,260,0.25
276,1,0.52200000,1,243,0.25,244,0.25,260,0.25,261,0.25
277,1,0.51900000,1,244,0.25,245,0.25,261,0.25,262,0.25
278,1,0.51000000,1,245,0.25,246,0.25,262,0.25,263,0.25
279,1,0.49700000,1,246,0.25,247,0.25,263,0.25,264,0.25
280,2,1.60900000,1,247,0.25,248,0.25,264,0.25,265,0.25
281,2,1.49000000,1,248,0.25,249,0.25,265,0.25,266,0.25
282,2,1.52100000,1,249,0.25,250,0.25,266,0.25,267,0.25
283,2,1.47600000,1,250,0.25,251,0.25,267,0.25,268,0.25
284,2,1.48100000,1,251,0.25,252,0.25,268,0.25,269,0.25
285,2,1.53200000,1,252,0.25,253,0.25,269,0.25,270,0.25
286,2,1.48800000,1,253,0.25,254,0.25,270,0.25,271,0.25
287,2,1.49000000,1,254,0.25,255,0.25,271,0.25,272,0.25
288,1,1.53800000,1,255,0.25,272,0.25
289,1,0.55000000,1,256,0.25,273,0.25
290,1,0.53700000,1,256,0.25,257,0.25,273,0.25,274,0.25
291,1,0.52800000,1,257,0.25,258,0.25,274,0.25,275,0.25
292,1,0.52400000,1,258,0.25,259,0.25,275,0.25,276,0.25
293,1,0.52300000,1,259,0.25,260,0.25,276,0.25,277,0.25
294,1,0.52200000,1,260,0.25,261,0.25,277,0.25,278,0.25
295,1,0.51900000,1,261,0.25,262,0.25,278,0.25,279,0.25
296,1,0.51000000,1,262,0.25,263,0.25,279,0.25,280,0.25
297,1,0.49700000,1,263,0.25,264,0.25,280,0.25,281,0.25
298,2,1.60900000,1,264,0.25,265,0.25,281,0.25,282,0.25
299,2,1.49100000,1,265,0.25,266,0.25,282,0.25,283,0.25
300,2,1.52000000,1,266,0.25,267,0.25,283,0.25,284,0.25
301,2,1.47400000,1,267,0.25,268,0.25,284,0.25,285,0.25
302,2,1.48000000,1,268,0.25,269,0.25,285,0.25,286,0.25
303,2,1.53300000,1,269,0.25,270,0.25,286,0.25,287,0.25
304,2,1.49000000,1,270,0.25,271,0.25,287,0.25,288,0.25
305,1,1.49400000,1,271,0.25,272,0.25,288,0.25,289,0.25
306,1,1.54200000,1,272,0.25,289,0.25
307,3,0.00000000,1,273,0.25
308,1,0.55000000,1,273,0.25,274,0.25
309,1,0.53000000,1,274,0.25,275,0.25
310,1,0.52400000,1,275,0.25,276,0.25
311,1,0.52300000,1,276,0.25,277,0.25
312,1,0.52200000,1,277,0.25,278,0.25
313,1,0.51800000,1,278,0.25,279,0.25
314,1,0.51000000,1,279,0.25,280,0.25
315,1,0.49700000,1,280,0.25,281,0.25
316,1,1.61200000,1,281,0.25,282,0.25
317,1,1.53500000,1,282,0.25,283,0.25
318,3,0.00000000,1,283,0.25,284,0.25
319,1,1.52000000,1,284,0.25,285,0.25
320,1,1.52700000,1,285,0.25,286,0.25
321,3,0.00000000,1,286,0.25,287,0.25
322,1,1.53800000,1,287,0.25,288,0.25
323,1,1.54200000,1,288,0.25,289,0.25
324,3,0.00000000,1,289,0.25
0
2,nucl,0.3346,0.2967,6,0.22126,0.01575 *U02 seed rods
0,0,0,0,0,3500.0,.97,0.0
1,hrod,0.374,0.0,3
*bkt. rods 3 regions:fuel+gap+clad
6,2,0.161,0.99,1,3,0.0034,0.0,3,4,0.02244,0.01*blanket rods
3,dumy,0.482,0.0,0
*control rods
1,25,1183.01,seed
80.33,0.0642,13.1439,?
170.33,0.0642,13.1575
260.33,0.0642,13.1702,?
*rods.9
*rods.62
*rods.63
*rods.68
*rods.69
*rods.68
*rods.70
127
518
519
520
521
522
523
524
525
526
527
528
529
530
531
532
533
534
535
536
537
538
539
540
541
542
543
544
545
546
547
548
549
550
551
552
553
554
555
556
557
558
559
560
561
562
563
564
565
566
567
568
569
570
571
572
573
574
575
576
577
578
579
580
581
582
583
350.33,0.0642,13.182
440.33,0.0642,13.1928,?
530.33,0.0642,13.2027
620.33,0.0642,13.2117,?
710.33,0.0642,13.2197
800.33,0.0642,13.2267,?
890.33,0.0642,13.2329
980.33,0.0642,13.238,?
1070.33,0.0642,13.2423
1160.33,0.0642,13.2456,?
1250.33,0.0642,13.2479
1340.33,0.0642,13.2493,?
1430.33,0.0642,13.2498
1520.33,0.0642,13.2493,?
1610.33,0.0642,13.2479
1700.33,0.0642,13.2456,?
1790.33,0.0642,13.2423
1880.33,0.0642,13.238,?
1970.33,0.0642,13.2329
2060.33,0.0642,13.2267,?
2150.33,0.0642,13.2197
2240.33,0.0642,13.2117
2,30,638.256,blan
80.33,0.0764,5.356,?
170.33,0.0764,4.902
260.33,0.0764,4.520,?
350.33,0.0764,4.192
440.33,0.0764,3.909,?
530.33,0.0764,3.662
620.33,0.0764,3.444,?
710.33,0.0764,3.251
800.33,0.0764,3.078,?
890.33,0.0764,2.923
980.33,0.0764,2.782,?
1070.33,0.0764,2.655
1160.33,0.0764,2.538,?
1250.33,0.0764,2.432
1340.33,0.0764,2.334,?
1430.33,0.0764,2.243
1520.33,0.0764,2.159,?
1610.33,0.0764,2.082
1700.33,0.0764,2.010,?
1790.33,0.0764,1.942
1880.33,0.0764,1.879,?
1970.33,0.0764,1.820
2060.33,0.0764,1.765,?
2150.33,0.0764,1.712
2240.33,0.0764,1.663,?
2420.33,0.0767,1.573
2600.33,0.0770,1.492,?
2780.33,0.0772,1.419,
2960.33,0.0774,1.352,?
3140.33,0.0776,1.292
3,1,1.0,bgap
1,100,6.8 *gap condty.=2000Btu/hr.ft2.F*0.0034
4,13,409.0,bcld
80.33,0.0671,7.330,?
260.33,0.07212,8.1158
692.33,0.07904,9.8016,?
1502.33,0.08955,13.2923
1507.73,0.11988,13.3211,?
1543.73,0.14089,13.5166
1579.73,0.14686,13.7172,?
1615.73,0.1717,13.9231
1651.73,0.1949,14.1347,?
1687.73,0.18388,14.3519
*rods.70
*rods.70
ft
128
584
585
586
587
588
589
1723.73,0.1478,14.5752,?
1759.73,0.112,14.8047
1786.73,0.085,14.9810
endd
*
*
end of input file
129
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N.
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A. Radkowsky, A. Galperin. "The Nonproliferative Light Water
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A. Radkowsky. "Using Thorium in a Commercial Nuclear Fuel Cycle:
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Ref. 7 -
VIPRE-01: A Thermal-Hydraulic Code for Reactor Cores. Volume 1:
Mathematical Modeling (Revision 3). Subcooled Boiling Models pp. 299, 1989.
Ref. 8 -
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Engineering Department, December 1999.
Ref. 9 -
Dean Wang, Xianfeng Zhao, M. J. Driscoll and M. S. Kazimi, "Fuel
Assembly PWR Seed and Blanket Core Performance", ANS Annual
Meeting, San Diego, CA June 2000.
Ref. 10 -
McDonald P.E. et. al., "Performance of Unirradiated and Irradiated
PWR Fuel Rods Tested Under Power-Cooling-Mismatch Conditions",
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Gaithersburg, Maryland, November 1977.
Ref. 1 1-
USNRC, "Standard Review Plan for the Review of Safety Analysis
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Ref. 12 -
Sorenson M. et. al., "The Reactor Analysis Support Package (RASP),
Vol. 1: Introduction and Overview", Report NP-4498, April 1986.
Ref. 13 -
Hejzlar P. and Todreas N. E.., "Considerations for CHF Margins by
Subcooled or Low-Quality CHF Correlations", Nuclear Engineering
and Design, 163, June 1996, pp. 215-223.
Ref. 14 -
Westinghouse Nuclear Fuel Business Unit, PWR Nuclear Fuel
Assembly Fabrication.
Ref. 15 - A. Galperin, A. G. Morozov, M. Todosow, M. Kazimi, A. Radkowsky."
A Thorium-Based Seed-Blanket Fuel Assembly Concept to Enhance
PWR Proliferation Resistance", Proc . Int. Conf. On Future Nuclear
Systems, Global 99, Jackson Hole, Wyoming, August 1999.
Ref. 16 -
VIPRE-01: A Thermal-Hydraulic Code for Reactor Cores. Volume 1:
Mathematical Modeling (Revision 3). Subcooled Boiling Models pp. 299, 1989.
131
Ref. 17 -
C.M.Allison, G.A. Berna, R.Chambers, E.W.Coryell, F.L. Davis, et al.
"SCDAP/RELAP5/MOD3.1
Code Manual Volume IV: MATPRO
A
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November 1993.
Ref. 18 -
Pavel Hejzlar, private conversation, MIT, February 11, 2000.
Ref. 19 -
C.S. Handwerk, M. J. Driscoll, N. E. Todreas and M. V. MaMahon.
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Cycle in Existing PWRs", Program for Advanced Nuclear Power
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D. Kim, M. S. Kazimi,, N. E. Todreas and M. J. Driscoll. "Economic
Analysis of the Fuel Cycle of Actinide Burning Systems", Nuclear Fuel
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J. Lahoda,
Westinghouse Science & Technology Department, April 2000.
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