Thermal Hydraulic Limits Analysis for the MIT Research Reactor
Low Enrichment Uranium Core Conversion Using Statistical
Propagation of Parametric Uncertainties
By
KENG-YEN CHIANG
B.S. Engineering and System Science, 2007
M.S. Engineering and System Science, 2009
National Tsing-Hua University, Taiwan
SUBMITTED TO THE DEPARTMENT OF NUCLEAR SCIENCE
AND ENGINEERING
IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF
MASTER OF SCIENCE IN NUCLEAR SCIENCE AND ENGINEERING
AT THE
MASSACHUSETTS INSTITUTE OF TECHNOLOGY
June 2012
@ 2012 Massachusetts Institute of Technology. All rights reserved.
i
1) 3/
Signature of Author:
Keng-Yen Chiang
Dep
Keng-Yen Chiang
ent of uclear Science and Engineering
May 14, 2012
Certified by: Lin-Wen Hu
Associate Director of MIT Nuc!L~eactor Laboratory
Thesis Supervisor
Assistant Profe
of Dep
e
Benoit Forget
cience and Engineering
Thesis Co-Supervisor
Tom Newton
Associate Director of MIT Nuclear Reactor Laboratory
Thesis Reader
Accepted by:
-
Mujid S. Kazimi
TEPCO P ofess of Nuclear Engineering
ittee on Graduate Students
Chair, Department C
Thermal Hydraulic Limits Analysis for the MIT Research Reactor Low
Enrichment Uranium Core Conversion Using Statistical Propagation of
Parametric Uncertainties
by
KENG-YEN CHIANG
SUBMITTED TO THE DEPARTMENT OF NUCLEAR SCIENCE AND ENGINEERING ON
MAY 14,2012 IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE
DEGREE OF MASTER OF SCIENCE IN NUCLEAR SCIENCE AND ENGINEERING
Abstract
The MIT Research Reactor (MITR) is evaluating the conversion from highly enriched
uranium (HEU) to low enrichment uranium (LEU) fuel.
In addition to the fuel
element re-design from 15 to 18 plates per element, a reactor power upgraded from 6
MW to 7 MW is proposed in order to maintain the same reactor performance of the
HEU core. Previous approaches in analyzing the impact of engineering uncertainties
on thermal hydraulic limits via the use of engineering hot channel factors (EHCFs)
were unable to explicitly quantify the uncertainty and confidence level in reactor
parameters.
The objective of this study is to develop a methodology for MITR
thermal hydraulic limits analysis by statistically combining engineering uncertainties
in order to eliminate unnecessary conservatism inherent in traditional analyses. This
methodology was employed to analyze the Limiting Safety System Settings (LSSS)
for the MITR LEU core, based on the criterion of onset of nucleate boiling (ONB).
Key parameters, such as coolant channel tolerances and heat transfer coefficients,
were considered as normal distributions using Oracle Crystal Ball for the LSSS
evaluation. The LSSS power is determined with 99.7% confidence level. The LSSS
power calculated using this new methodology is 9.1 MW, based on core outlet coolant
temperature of 60 'C, and primary coolant flow rate of 1800 gpm, compared to 8.3
MW obtained from the analytical method using the EHCFs with same operating
conditions. The same methodology was also used to calculate the safety limit (SL) to
ensure that adequate safety margin exists between LSSS and SL. The criterion used
to calculate SL is the onset of flow instability. The calculated SL is 10.6 MW, which
is 1.5 MW higher than LSSS, permitting sufficient margin between LSSS and SL.
Thesis Supervisor: Lin-wen Hu
Title: Associate Director of MIT Nuclear Reactor Laboratory
Thesis Co-supervisor: Benoit Forget
Title: Assistant Professor of Nuclear Science and Engineering
2
Acknowledgements
First and foremost I would like to express my deepest gratitude to my supervisor, Dr.
Lin-wen Hu, who has supported and guided me throughout my thesis with her
patience and knowledge, as well as offering me fantastic opportunity to work with
senior researchers in Argonne National Laboratory. I am also indebted to the many
previous and current contributors to the MITR LEU project for providing the
preliminary analyses, system measurement data and relevant document, guiding me
on the right track all over my research. Dr. Sung Joong Kim, Dr. Erik Wilson, Dr.
Floyd Dunn, Dr. Thomas Newton, and Prof. Benoit Forget have fascinated me with
not only their broad knowledge in nuclear science and engineering, but also their
sense of humor and blissful smiles. In many ways I have learnt how to make life
easier and happier in MIT; thanks to their encouragement.
Thanks also go to the MIT Chapel and Zesiger Sports&Fitness Center, the places
where I always get a warm feeling, making me smile. I experienced peace and
serenity of mind whenever having silence meditation with the Venerable Tenzin
Priyadarshi in the Chapel. The feeling of happiness also comes to me every time
when running and laughing on the basketball court with friends. Special thanks to the
staff (a cool black guy) at Z-Center: I appreciate your friendly smile and a "Yo,
what's up brother" every time we met. Every of these brightened my life at MIT,
thank you.
I have been blessed with my family in Taiwan and California, unconditionally
supporting me went through the tough times. Thanks to my dear family, especially
my younger brother Hsiao-Cheng: words cannot describe the feeling of identifying
the big package sent from Taiwan amid stacking boxes from elsewhere when I was
standing at the front desk. Thanks to the monthly food boxes sent from California by
Louie family: They never realized I immediately finished four packs of Taiwanese
sticky rice after I received their first box.
Finally, thanks to everything, either making me laugh or mad, that I have in MIT. It's
an unforgettable journey that I would cherish for the rest of my life.
3
Table of Contents
Chapter 1
Introduction
1.1 The Reduced Enrichment for Research and Test Reactors Program.................11
1.2 Core Conversion Safety Analyses.....................................................................
13
1.3 Description of the MIT Reactor........................................................................
14
1.4 The Proposed Low Enrichment Uranium Fuel Design of the MITR................21
1.5 Thesis Objectives..............................................................................................
Chapter 2
24
Engineering Hot Channel Factors
2.1 Introduction.....................................................................................................
27
2.2 Historical Review on Engineering Uncertainty Treatment..............................
29
2.3 Introduction to Engineering Hot Channel Factors (EHCFs).............................
30
2.3.1 EHCFs.......................................................................................................
30
2.3.2 Common sub-factors involved.....................................................................
32
2.4 Engineering Hot channel Factors (EHCFs) Used in MITR-II.........................
Chapter 3
35
Limiting Safety System Settings
3.1 Definition of LSSS............................................................................................
3.2 Derivation of LSSS.........................................................................................
41
45
3.2.1 Onset of Nucleate Boiling............................................................................
45
3.2.2 Cladding Temperature.................................................................................
46
3.2.3 General Form of LSSS Equation......................................................................48
3.3 Parameters used in LSSS...................................................................................
49
3.3.1 System Parameters.....................................................................................
49
3.3.2 EHCFs..............................................................................................................
52
3.3.3 Local Properties: Coolant pressure............................................................
53
3.3.4 Local Properties: Axial Power Distribution and Coolant Temperature............55
3.4 Heat Transfer Coefficient.................................................................................
3.4.1 Carnavos Correlation and Geometry Analysis for the MITR.......................
59
61
3.4.2 HTC Computed from D-B Correlation and Carnavos Correlation..............63
3.5 Best Estimate Value of LSSS............................................................................65
3.6 LSSS Calculated Using EHCFs.......................................................................
3.7 LSSS Calculated Using Hot Stripe Approach...................................................
4
68
70
3.7.1 Best estimate ONB using hot stripe technique............................................
73
3.7.2 H ot stripe LSSS using EHCFs.....................................................................
75
3.8 Sum m ary..............................................................................................................77
Chapter 4
LSSS Calculation Using Uncertainty Propagation Technique
4.1 Introduction.....................................................................................................
82
4.2 M onte Carlo Simulation...................................................................................
84
4.2.1 Oracle Crystal Ball.......................................................................................
4.2.2 Validation of Sim ple M odel on Crystal Ball................................................
84
86
4.3 U ncertainty of input param eters for the M ITR.................................................
88
4.3.1 Prim ary Coolant Flow Rate.......................................................................
88
4.3.2 Heat Transfer Coefficient............................................................................
91
4.3.3 Hot Channel M ass Flow Rate.......................................................................
93
4.3.4 Power...............................................................................................................97
4.4 Results...................................................................................................................99
4.5 Summ ary..............................................................................................................100
Chapter 5
Sensitivity Study of LSSS
5.1 Flow D isparity Factor........................................................................................105
5.2 Coolant Density at Channel Inlet........................................................................107
5.3 H eat Transfer Coefficient (HTC)........................................................................109
5.3.1 Errors in Estimating Heat Transfer Coefficients............................................109
5.3.2 Effect of Variation in Viscosity for Heat Transfer Correlation Calculation... 111
5.4 Local Fluid Tem perature.....................................................................................116
5.5 Sum m ary..............................................................................................................118
Chapter 6
Safety Limit Calculation
6.1 Introduction.........................................................................................................120
6.2 Onset of Flow Instability....................................................................................123
6.2.1 Introduction....................................................................................................123
6.2.2 Calculation of OFI for the MITR (Analytical Approach)..............................125
6.2.3 Calculation of OF for the MITR (Uncertainty Propagation Technique).......128
6.3 Critical Heat Flux................................................................................................130
6.3.1 Introduction....................................................................................................130
6.3.2 CHF Correlations (Including Natural Convection and Forced Convection).. 133
5
6.3.3 Calculation of CHF for the M1TR (Analytical Approach).............................135
6.3.4 Calculation of CHF for the MITR (Uncertainty Propagation Technique).....137
6.4 Comparison between OFI and CHF...................................................................140
6.5 Summary.............................................................................................................142
Chapter 7
Natural Convection Analysis Using RELAP5/Mod3.3
7.1 Introduction........................................................................................................144
7.2 RELAP5/M od3.3................................................................................................145
7.3 RELAP5 Input Deck for the M ITR....................................................................146
7.4 Natural Convection LSSS Calculation...............................................................149
7.5 Summary............................................................................................................153
Chapter 8
Conclusions and Recommendations
8.1 Conclusions.........................................................................................................156
8.2 Recommendations for This Study......................................................................157
Appendix
Appendix A RELAP5 Input File for Natural Circulation LSSS of MITR (Steady
State).....................................................................................................159
Appendix B RELAP5 Input File for Natural Circulation LSSS of MITR (Restart
File)......................................................................................................169
6
List of Figures
Figure 1-1 Cutaway schematic of the MITR.........................................................
16
Figure 1-2 MITR Core map showing fuel element position designations and major
core structures.......................................................................................
17
Figure 1-3 Schematic of flow channel configuration of MITR (only 3 fuel plates and
isupporting plate are shown in the schematic).....................................18
Figure 1-4 Forced convection flow circulation path during normal operation........19
Figure 1-5 Natural convection flow circulation path during LOF ...............................
20
Figure 2-1 Thermal design nomenclature..............................................................
28
Figure 3-1 MITR HEU LSSS for forced-flow operation (two-loop).......................44
Figure 3-2 Bottom-peaked LEU axial power profile..............................................57
Figure 3-3 Best-estimate ONB computed for core 189 on each node......................67
Figure 3-4 LSSS power computed using EHCFs for core189 on each node...........69
Figure 3-5 Heat fluxes of strips on MIT LEU core 189EOC..................................72
Figure 3-6 Best estimate ONB using hot stripe technique.......................................74
Figure 3-7 LSSS using EHCFs for 189EOC power profile.....................................76
Figure 3-8 Best-estimate ONB comparison using radial peaking factor and hot stripe
78
Factor......................................................................................................
Figure 3-9 LSSS calculated using EHCFs based on radial peaking factor and hot
stripe factor.............................................................................................
79
Figure 3-10 Hot stripe LSSS calculated using EHCFs and best estimate approach....79
Figure 4-1 Primary coolant flow rate distribution as an input for LSSS calculation...90
Figure 4-2 HTC distribution as an input for LSSS calculation................................92
Figure 4-3 Historical off-normal water gap distance value for HEU collecting from
1994 to 2008..........................................................................................
96
Figure 4-4 HCMFR distribution as an input for LSSS calculation.........................96
Figure 4-5 LSSS power of each node using uncertainty propagation technique.........99
Figure 4-6 LSSS calculated using three different approaches...................................102
Figure 5-1 Sensitivity of LSSS power on HTC..........................................................110
Figure 5-2 Comparison between IAPWS 1995 Formulation and simplified viscosity
F ormula....................................................................................................114
Figure 6-1 Channel pressure drop-mass flow rate behavior......................................122
Figure 6-2 Void fraction variation along a uniformly heated channel........................124
Figure 6-3 Schematic diagram of the demand curve for a heated channel with constant
heating rate...............................................................................................124
Figure 6-4 CHF correlation scheme proposed for research reactors using plate-type
F uel...........................................................................................................132
7
Figure 6-5 Comparison between Sudo CHF prediction and experiment result.........134
Figure 7-1 RELAP5 Nodalization of M ITR..............................................................148
Figure 7-2 Decay power changes with time (initial power is set as 1MW)...............151
8
List of Tables
Table 1-1 Research Reactors that were converted or shut down since May 2004.......12
Table 1-2 HEU and LEU fuel plate and full-channel (interior channel) dimensions...22
Table 1-3 HEU and LEU Fuel plate and side-channel (outside channel) dimensions.23
Table 1-4 Composition and thermo-physical properties of HEU and LEU fuel..........23
Table 2-1 Sub-factors and EHCFs used in MITR-II SAR.......................................37
Table 2-2 Description for sub-factors used in MITR-II SAR..................................38
43
Table 3-1 Parameters used in LSSS calculation.....................................................
Table 3-2 Parameters used for analytical LSSS calculation.....................................51
Table 3-3 Summary for the MITR pressure loss calculation...................................55
Table 3-4 Pressure calculated for each node of the fueled region............................55
Table 3-5 Axial power distribution for the MITR LEU fuel...................................57
Table 3-6 Hot channel coolant temperature calculated for at each node.................58
Table 3-7 Derived Geometry Parameters for MITR..............................................
60
Table 3-8 The LEU geometry parameters in Carnavos correlation and their
62
counterpart in M1TR.................................................................................
Table 3-9 HTC calculated using D-B Correlation and Carnavos Correlation..........64
Table 3-10 T/H conditions used in hot stripe LSSS calculation for each node............72
Table 3-11 Summary for LSSS powers calculated using different approaches...........78
Table 4-1 The input description for the model used to validate Oracle Crystal Ball...87
Table 4-2 Comparison between analytical solution and results using Crystal Ball.....87
Table 4-3 Input parametric distributions used in uncertainty propagation
methodology...............................................................................................101
Table 4-4 Summary for LSSS power obtained using different methodology............103
Table 5-1 Changes in LSSS due to the change in flow disparity factor....................106
Table 5-2 The resulting change in LSSS power when outlet temperature is fixed at
60 0 C............................................................................................................
10 8
Table 5-3 The change in LSSS power with respect to the change in HTC when outlet
temperature is fixed at 60 0C........................................................................110
Table 5-4 Summary for correlations typically used to compute HTC in research
Reactors......................................................................................................112
Table 5-5 HTCs and outlet clad temperatures computed using different
correlations.................................................................................................114
Table 5-6 The change in LSSS power with respect to the change in local temperature
(viscosity) when outlet temperature is fixed at 60*C..................................117
Table 6-1 Parameters used to calculate OFI...............................................................127
9
Table 6-2 Parameters set in a form of distribution for OFI/CHF calculation.............129
Table 6-3 Parameters used in CHF calculation for the MITR....................................136
Table 6-4 Parameters that were set in a form of distribution for CHF calculation.... 139
Table 6-5 Comparison between OF and CHF...........................................................141
Table 7-1 Cladding temperature and temperature inducing ONB at each node (both
the NCVs and ASVs are open)...................................................................151
Table 7-2 Cladding temperature and temperature inducing ONB at each node (Only
N CV s are open)..........................................................................................152
Table 7-3 Calculated Coolant Temperature Rise and Film Temperature Rise for
Natural Convection Operation....................................................................154
10
Chapter 1 Introduction
The MIT Research Reactor (MITR) is evaluating the conversion from highly enriched
uranium (HEU) to low enrichment uranium (LEU) fuel. In addition to the fuel
element re-design, a reactor power upgraded from 6 MW to 7 MW is proposed in
order to maintain the same reactor performance of the HEU core.
1.1 The Reduced Enrichment for Research and Test Reactors Program
As introduced in the fact sheet from the National Nuclear Security Administration
(NNSA) [1], "The National Nuclear Security Administration established the Global
Threat Reduction Initiative (GTRI) in the Office of Defense Nuclear Nonproliferation
to, as quickly as possible, identify, secure, remove and/or facilitate the disposition of
high risk vulnerable nuclear and radiological materials around the world that pose a
threat to the United States and the international community."
The Reduced Enrichment for Research and Test Reactors Program (RERTR) was
placed under NNSA in 2004 as part of GTRI [2, 3] with an aim to better coordinate
several nonproliferation programs jointly under GTRI. To reduce the potential global
nuclear threat, these institutes are converting the existing high enriched uranium
(HEU) fuels with low enrichment uranium fuels (LEU, U-235 enrichment < 19.99%)
in research facilities worldwide, as well as detecting, securing, safeguarding,
disposing, and controlling nuclear materials.
GTRI has made significant contribution in nuclear material threat reduction in recent
years. Twenty-two research reactors have been converted to LEU, including the
HIFAR in Australia in 2004 to the Kyoto University research reactor in Japan in 2010.
Moreover, twelve HEU research reactors were shut down without converting,
including the ZPPR reactor's decommission at Idaho National Laboratories started in
September 2008. These research reactors are summarized in Table 1-1, including the
period they were converted or shut down [1]. Note that these converted research
reactors used dispersion fuel, the fuel design allowing the fuel material to be broken
up into very small pieces that are dispersed into and encapsulated by a matrix material,
making the matrix material stable under irradiation. The dispersion fuel design is
sufficient for these conversions while high performance reactors require high density
fuel. An alternate fuel design, monolithic fuel was selected for the MITR conversion
project, which is discussed in section 1.4.
11
Table 1-1 Research Reactors that were converted or shut down since May 2004 [1]
Twenty-two Research reactors converted
Twelve Research reactors shut down
The HIFAR in Australia converted in October 2004
The VR-1 Sparrow research reactor at the Czech
Technical University in Prague. (This conversion in
October 2005 was the first time a Russian-supplied
research reactor was converted to LEU)
The HFR in Petten, the Netherlands converted in
October 2005
The ZLFR in Germany was shut down in
May 2005 without converting
The FRJ-2 reactor in Germany was shut
down in May 2006 without converting
The ULYSSE reactor in France was shut
down in February 2007 without converting
The IRT critical assembly in Libya converted in
2006
January 2down
The Chinese MNSR-SH at the Shanghai
The 1-megawatt TRIGA reactor at Texas A&M
University converted in late September 2006
The ZPPR reactor at Idaho National
Laboratories began decommissioning in
The University of Florida Training Reactor converted in
late September 2006
The Russian-supplied IRT-1 research reactor at the
Tajoura facility in Libya converted in late October 2006
The Chinese HFETR research reactor at the Leshan
Nuclear Power Institute of China converted in March
The General Atomics research reactor in
San Diego shut down in November 2008
The IRT-2000 research reactor in Bulgaria
shut down in April 2009
The PhS-4, PhS-5, and STRELA reactors in
Russia were confirmed by Rosatom as
2007
The Chinese HFETR Critical Assembly at the Leshan
shutdown in February 2010
The RECH-2 reactor in Chile was shut
Nuclear Power Institute converted in April 2007
The Purdue University 1-kilowatt Reactor (PUR-1)
converted in September 2007
The Dalat research reactor at the Nuclear Research
Institute in Vietnam in September 2007
The 1 Megawatt Portuguese research reactor (RPI)
converted in September 2007
The VVR-SM reactor at the Institute of Nuclear Physics
in Uzbekistan was converted in March 2008
The SAFARI-1 reactor in Pelindaba, South Africa was
converted in September 2008
Argentina's RA-6 reactor in Bariloche was converted in
down in April 2010
The MNSR-Shandong reactor in China
confirmed shutdown in December 2010.
September 2008
The WWR-M reactor at the Kiev Institute of Nuclear
Research in Ukraine was converted in September 2008
Washington State University's research reactor at its
Nuclear Radiation Center was converted in September
2008
The research reactor at Oregon State University was
converted in September 2008
The University of Wisconsin research reactor converted
in September 2009
The Budapest research reactor in Hungary converted in
September 2009
The NRAD reactor at Idaho National Laboratory
converted in September 2009
The Kyoto University research reactor in Japan
converted in March 2010
12
Testing and Research Institute was shut
in March 2007
September 2008
1.2 Core Conversion Safety Analyses
In general, the preferred approach for converting from HEU to LEU fuel is direct
conversion without making modifications in fuel element dimensions or core
configurations, therefore minimizing requirements of altering the safety-related
parameters of the facility. Since the volume of HEU cores and fuel elements remain
the same, the way to achieve the same number of uranium-235 atoms as in the HEU
cores is to increase fuel density. As a matter of fact, additional U-235 is actually
required to offset the resonance absorption in U-238.
While doing core conversion, in the beginning what have to be verified are the
feasibility of fabrication process and the LEU fuels performance under irradiation,
such as the capability to accommodate released fission gases. Moreover, a series of
conversion safety analyses have to be performed. These analyses [4] normally
include neutronics analyses, steady-state thermal-hydraulic analyses, and transient
analyses.
Neutronics analyses in general cover analyses on excess reactivity, shutdown margins,
control rod worths, rod worth profiles, power distribution, kinetic parameters (e.g.
prompt neutron lifetime, effective delayed neutron fraction) and reactivity feedback
coefficients (reactivity temperature coefficient).
Steady-state thermal-hydraulic analyses cover safety margin calculation (e.g. margins
to the onset of nucleate boiling/onset of flow instability/departure from nucleate
boiling), and the identification of engineering hot channel factors. One thing to note,
engineering hot channel factors are almost always used for plate-type-fuel reactors in
safety margin calculation, whereas for TRIGA reactors and reactors with Russian
tubular-type fuel, hot channel factors are not directly included in their analyses [4].
Transient analyses generally include rapid reactivity insertion, runaway rod transient
(e.g. control rods move out from the core at their maximum withdrawal rate), loss-offlow transient and natural convection operation. Natural convection operation is
covered in this study.
13
1.3 Description of the MITR
The MIT Research Reactor (MITR) is a research nuclear reactor that is owned and
operated by the Massachusetts Institute of Technology. Figure 1-1[1] shows the cutaway
schematic of the MITR. The MITR has two tanks. The inner one is for the light water
coolant/moderator while the outer one is for the heavy water reflector, which is
surrounded by a graphite reflector. Reactor control is provided by six boron-impregnated
stainless-steel shim blades and one cadmium regulating rod.
Currently, the MITR is licensed for 6MW. As can be seen in Figure 1-2 [5], the closepacked hexagonal reactor core is designed to be loaded with up to twenty-seven
rhomboidal fuel elements. In general, twenty-four fuel elements are loaded during
normal operations. The remaining three positions are filled with either a solid
aluminum "dummy" element or an in-core experimental facility. A rhomboid-shaped
HEU fuel element consists of fifteen fuel plates and each of them is in the form of
uranium-aluminum matrix and cladded with finned 6061 aluminum alloy to increase heat
transfer area, as depicted in Figure 1-3 [6].
The MITR operates at atmospheric pressure with nominal primary coolant flow rate 2000
gpm. Primary coolant enters the bottom of the core tank through the core shroud, flows
upward through the fuel elements and then exits at the outlet piping at about 2 m above
the top of the core, as shown in Figure 1-4[7]. The compact core has an average power
density of about 80 kW/l, with fast, thermal, and gamma fluxes similar to those of a
commercial light water power reactor (LWR). The primary coolant core inlet temperature
of the MITR is approximately 42 *C and outlet temperature is about 50 *C. The
hexagonal core structure is about 38 cm across and the length of an active fuel length is
about 56 cm.
The MITR is designed passively safe that natural circulation and anti-siphon valves
(NCVs and ASVs) provide natural circulation path for decay heat removal when forced
convection flow is not sufficient to keep these valves closed during transients. Figure 1-5
[7] illustrates the flow path for natural circulation. Four NCVs were located at the bottom
of the core tank while two ASVs were installed inside the core tank at the same elevation
of the primary inlet pipe.
Both the NCVs and ASVs are ball-type check valves. During normal operation, coolant
pressure forces the ball to the top of the shaft, blocks the top aperture of the valves and
therefore valves are closed. However, when primary flow rate decreases to certain level,
14
the ball falls down since under such a circumstance coolant pressure is not enough to
sustain the ball. As a result, valves are open. These configurations make natural
circulation possible.
As shown in Figure 1-5, the hot coolant leaving the core rises within the core tank, mixes
with cold coolant in the outlet plenum, reverses, flows through the NCVs and/or ANVs,
and finally flows back through the core region completing the natural circulation loop.
15
Figure 1-1 Cutaway schematic of the MITR [5]
16
C-13
C-c4
Control blade
-- /absorber
(6)
C1
C1
B3-9
B-8
C-12
B-1
C-141
C-2
A-1
B-2
A-3
C-11
A-2
C-3
Control blade
flow regal hole (6)
B-3
C-4
B-6
entrance channel
B-Coolant
C-5
Fixed absorber
C-8
c-
C-6
-
fixed absorber In
radial arm (3)
Fuel
Element
Core
structure
Core tank
Figure 1-2 M1TR Core map showing fuel element position designations and major
core structures [5]
17
Fuel meat
CL
(d)
CL
Figure 1-3 Schematic of flow channel configuration of MITR (only 3 fuel plates and 1
supporting plate are shown in the schematic) [6]
18
Figure 1-4 Forced convection flow circulation path during normal operation [7]
19
Figure 1-5 Natural convection flow circulation path during LOF [7]
20
1.4 The Proposed Low Enrichment Uranium Fuel Design of the MITR
The high density LEU fuel that MITR currently plans to adopt is the monolithic
uranium and molybdenum (U-Mo) fuel. Currently, the development of U-Mo alloy
monolithic fuel is ongoing at Idaho National Laboratory [3, 8]. The mechanical,
physical, and microstructural properties in terms of both integrated and separate
effects of such a fuel were briefly discussed in a study by Burke et al [9].
A study at MIT [10] has demonstrated that LEU conversion is feasible using this alloy
monolithic fuel, which has a uranium density 15.5 g/cm 3 with 10 wt% Mo. The LEU
fuel element designed for the MITR conversion contains 18 fuel plates so that the heat
transfer area is larger than the current HEU design. This LEU configuration was
suggested by Ko [7], that the core tank pressure loading of LEU core should be
limited to be equal or less than that of the current pressure loading of the HEU core.
Tables 1-2, 1-3, and 1-4 [10, 11] compares the properties, as well as the fuel plate
dimensions of HEU and LEU. The thickness of the fuel meat, cladding and coolant
channel are reduced in the new design.
The MITR has two different flow channel configurations, full flow channel and side
flow channel, as illustrated in Figure 1-3. This is the unique design of the MITR that
a narrow space, which is roughly 50 % narrower than regular coolant channels, is in
between the end of fuel plates and their adjacent elements. These narrower flow
channels are called side channels.
The MITR will employ a transitional core conversion strategy, which means replacing
a few depleted HEU elements with fresh LEU elements for each cycle instead of
replacing all HEU elements at once. A preliminary analysis [12] concluded that in the
mixed core configurations higher Onset of Nucleate Boiling margin is expected in
LEU than that of HEU, therefore allowing the implementation of a transitional core
conversion.
21
Table 1-2 HEU and LEU fuel plate and full-channel (interior channel) dimensions [10]
LEU
Plate and channel dimensions
HEU
Fuel plate length (inch)
23
23
Fuel meat length (inch)
Fuel plates per assembly
Full-channels per assembly
(a) Fuel meat thickness (mil)
22.375
15
14
30
22.375
18
17
20
(b) Fuel meat width (inch)
2.082
2.082
(c) Clad thickness (mil)
(base of fin to fuel meat)
(d) Plate to plate pitch, CL to CL (mil)
(e) Water gap (fin tip-to-tip) (mil)
(f) Effective Channel thickness (mil)
15
158
78
88
10 (9 Al +1
Z
132
72
82
(g) Finned width (inch)
Number of fins per plate
(h) Fin height (mil)
2.2
220
10
2.2
220
10
(i) Fin width (mil)
(j) Width without meat to side plate (mil)
(k) Width without fins to side plate (inch)
10
113
54
10
113
54
(1)Channel width (inch)
2.308
2.308
(m) Side plate thickness (mil)
(n) Side plate flat-to-flat, outer edge of one side
plate to outside of other side plate (inch)
(o) Element flat-to-flat or length of side plate (inch)
Actual flow area (i)
Actual flow area with bypass (m)
Wetted equivalent diameter, D. (m)
Wetted equivalent diameter with bypass, D, (m)
Heated equivalent diameter, Dh (m)
Heated equivalent diameter with bypass, Dh (m)
188
188
2.375
2.375
2.380
1.3103E-4
1.2062E-4
2.1887E-3
2.0174E-3
2.4778E-3
2.2808E-3
2.380
1.2210E-4
1.1239E-4
2.0421E-3
1.8820E-3
2.3089E-3
2.1253E-3
22
Table 1-3 HEU and LEU Fuel plate and side-channel (outside channel) dimensions
[10]
HEU
2
LEU
2
44
38
49
43
7.2962E-5
6.4028E-5
Actual flow area with bypass (m)
Wetted equivalent diameter, D. (m)
Wetted equivalent diameter with bypass, D, (m)
Heated equivalent diameter, Dh (m)
6.7162E-5
1.6643E-5
1.5339E-3
2.5488E-3
5.8938E-5
1.4630E-3
1.3482E-3
2.2367E-3
Heated equivalent diameter with bypass, Dh (m)
2.3462E-3
2.0589E-3
Plate and channel dimensions
Side-channels per assembly
(p) Side-channel water gap for fuel plate to fuel
plate neighboring elements (from fin tip) (mil)
(q) Effective side-channel thickness for fuel plate
to side plate neighboring elements (mil)
Actual flow area (i)
Table 1-4 Composition and thermo-physical properties of HEU and LEU fuel [11]
HEU
LEU
Compound
Fuel compound density
3
(g/cm )
Uranium density (g/cm3)
Thermal conductivity
(W/cm -K)
UAlx
3.4
U-10Mo
17.0
4.6
15.5
0.42
0.17
Heat capacity (J/mol - K)
0.75
0.143
Melting temperature (*C)
1400
1135
23
1.5 Thesis Objectives
Thermal hydraulic limits are established to guarantee there is adequate margin
between normal operations and safety limits, and hence ensure fuel and cladding
integrity. Previous work in analyzing the impact of engineering uncertainties on
thermal hydraulic limits via the use of EHCFs makes meeting the ONB criterion
difficult at sufficient power, due to the large uncertainties introduced by EHCFs. In
addition, those studies are unable to quantify the uncertainty in terms of confidence
level. The objective of this study is to (1) develop a general equation for plate-typefuel research reactors to analyze the thermal-hydraulic limits, and (2) develop a
methodology for MITR thermal hydraulic limits analysis by statistically combining
engineering uncertainties with an aim to eliminate unnecessary conservatism inherent
in traditional analyses. The thermal-hydraulic limit employed for the MITR is called
Limiting Safety System Settings (LSSS), which chooses the avoidance of the onset of
nucleate boiling (ONB) as the criterion.
Chapter 2 introduces the historical review on engineering uncertainty treatment and
the engineering hot channel factors (EHCFs) used in MITR-II. Chapter 3 discusses
the limiting safety system settings (LSSS) for the MITR using analytical approach
whereas chapter 4 proposes using a parametric uncertainty propagation methodology
to calculate LSSS. Chapter 5 provides sensitivity study of several key parameters on
LSSS. Chapter 6 discusses the safety limit chosen for the MITR, and computes this
safety limit using both analytical and parametric uncertainty propagation methodology.
Chapter 7 provides a natural circulation analysis for the MITR using
RELAP5/Mod3.3. Finally, chapter 8 summarizes the results and recommendations
for future work.
24
References
[1-1]
Fact Sheet from National Nuclear Security Administration, "GTRI: Reducing
Nuclear Threats", Feb, 2011.
http://www.nnsa.energy.gov/mediaroom/factsheets/reducingthreats
[1-2]
U.S. Department of Energy, "Reduced Enrichment for Research and
Test Reactors," http://www.nnsa.doe.gov/na-20/rertr.shtml
[1-3]
D. M. Wachs, ""RERTR Fuel Development and Qualification Plan",
INIJEXT-05-01017 Rev.4 August 2009
[1-4]
J.E. Matos, RERTR Program/Argonne National Laboratory, "Safety
Assessment of Core Conversion", Presented at US / IAEA Regional
Workshop on Application of the Code of Conduct on the Safety of Research
Reactors Argonne National Laboratory, 30 April - 11 May 2007.
[1-5]
Lin-Wen Hu, Gordon Kohse, "MITR User's Guide" Rev. 1 June 2008
[1-6]
Sung Joong Kim, Yu-chih Ko, Lin-wen Hu, "Loss of Flow Analysis of the
MIT Research Reactor HEU-LEU Transitional Cores Using RELAP5-3D",
proceedings of ICAPP '10, San Diego, CA, USA, June 13-17,2010 Paper
10224
[1-7]
Y. C. Ko, "Thermal Hydraulic Analysis of the MIT Research Reactor in
Support of a Low Enrichment Uranium (LEU) Core Conversion", Chapter 4,
SM Thesis, MIT NSE Department, January 2008.
[1-8]
D. M. Wachs, C. R. Clark, R. J. Dunavant, "Conceptual Process Description
for the Manufacture of Low-Enriched Uranium-Molybdenum Fuel",
INIEXT-08-13840, Feb., 2008.
[1-9]
D. E. Burkes, D. M. Wachs, D. D. Keiser, J. F. Jue, J. Gan, F J. Rice, R.
Prabhakaran, B. Miller, "Fresh Fuel Characterization Of U-MO Alloys",
RERTR 30th International Meeting ON Reduced Enrichment For Research
And Test Reactors, October 5-9, 2008, Washington, D.C. USA
25
[1-10]
S. J. Kim, "Memorandum: MITR Thermal-Hydraulic Parameters,"
MIT-NRL, June 2011
[1-11]
J.Rest, Y.S. Kim, G. L. Hofman, M. K. Meyer, S. L. Hayes, "U-Mo Fuels
Handbook Version 1.0", RERTR Program, Argonne National Laboratory,
2006.
[1-12]
Y. Wang, L-W Hu, "Evaluation of the Thermal-Hydraulic Operating Limits
of the HEU-LEU Transition Cores for the MIT Research Reactor," Reduced
Enrichment Test and Research Reactors (RERTR) Conference, Beijing,
China, November 1-4, 2009.
26
Chapter 2 Engineering Hot Channel Factors (EHCFs)
2.1 Introduction
Commercial nuclear power reactors are designed to achieve maximum possible
thermal hydraulic performance while maintaining sufficient safety margins. Research
reactors, while not aiming at optimum thermal-hydraulic performance, are also
required to permit sufficient safety margins. Therefore it is important to explicitly
evaluate, and combine all the uncertainties involved in thermal-hydraulic analyses to
maximize the thermal performance without endangering the integrity of fuel and
cladding. In general, several things are taken into consideration in core design
accounting for the variation of thermal conditions: power distribution, engineering
uncertainty and overpower factor. These factors and their corresponding thermal
conditions are depicted in Figure 2-1 [1]. Power distribution refers to the variation in
axial, radial, as well as local heat flux distributions while overpower factor takes into
account the uncertainties in design transient response.
Engineering uncertainty treatment is the main topic of this study. Engineering
uncertainty arises from several effects, such as fabrication tolerances, measurement
errors, instrumentation accuracy, manufacturing, correlation uncertainties and so on.
Engineering hot channel factors (EHCFs) discussed in this chapter are in fact the
factors established to include all kinds of uncertainties involved in the analysis [2].
Systematic methodologies have been developed to compute ECHFs and they are
described in the following section.
27
Failure Limit
Margin for Correlation anc
Monitoring Uncertainties
Limit for Design
Transient
Overpower Factor
Maximum Peak Steady State Condition
(i.e., at hot spot with engineering
uncertainties)
Engineering
Uncertainties
Nominal Peak Steady State Condition
(i.e., at hot spot)
Applicable Axial and
Local Flux Factor (for
LWR)
AxialAverage inRadial Peak Pin
Applicable Radial
Flux Factor
Nominal Steady State Core Average
Condition
Figure 2-1 Thermal design nomenclature [1]
28
2.2 Historical Review on Engineering Uncertainty Treatment
In the very beginning, uncertainties involved in thermal design were addressed either
by directly using their values or using dimensionless factors. Systematic treatments
have been developed and employed in power reactors and research reactors to manage
engineering uncertainties. These methodologies apply different strategy to combine
uncertainties so that they can be categorized as direct deterministic method, semistatistical method, and fully statistical methods.
The direct deterministic method is usually applied in the preliminary stage of core
design, directly taking all the parameters at their worst value assuming their
occurrence at the same time and same location, which is highly conservative.
Another strategy that has been employed in the core design of PWRs is treating
uncertainties using hot spot factors. All the engineering uncertainties are expressed as
dimensionless hot spot sub-factors. Every sub-factor is carefully defined and
represents different kinds of engineering uncertainties. Sub-factors are then combined
either statistically since they are assumed to be independent, or multiplicatively,
therefore resulting in conservative estimates. The statistical combination of these
factors is defined as statistical method while the multiplication of these sub-factors is
defined as deterministic combination.
Between the deterministic combination and statistical method is an intermediate
method called semi-statistical method. In Ref [3], both horizontal semi-statistical and
vertical semi-statistical approach are described in detail.
For current core designs of PWRs, the fully statistical methods are widely employed
for its potential in uncertainties reduction. As summarized in Yang and Oka's study
[4], the methods can be further divided into two categories: the methods applying the
Root Sum Square (RSS) technique [5, 6, 7] and the methods applying Monte Carlo
technique [4, 8, 9]. Han [10] summarizes a general statistical formula used to
combine the uncertainties that the sensitivity of each parameter to departure from
nucleate boiling ratio (DNBR) is incorporated to estimate the overall uncertainties of
a PWR core.
29
2.3 Introduction to Engineering Hot Channel Factors (EHCFs)
2.3.1 EHCFs
Hot channel factors are dimensionless factors used to address the extent to which
actual reactor performance may depart from its nominal performance, owing to the
cumulative effect of variations of all primary design variables from their nominal
values.
Hot channel factors are composed of contributions due to nuclear and
engineering considerations, which are assumed to be separative. Nuclear hot channel
factors, or known as power peaking factors express the peak to average ratio of the
nuclear power distributions radially and axially in the core, which are due to the
variation in neutron flux; engineering hot channel factors (EHCFs), which are
evaluated at constant neutron flux, express the uncertainties in local enthalpy rise,
heat flux and heat transfer coefficient due to the fabrication tolerance and flow
maldistributions [11].
Generally, EHCFs may arise from manufacturing dimensional tolerances on the fuel
elements or coolant channels, or dimensional changes of the fuel elements after
irradiation, or from deviations from an ideal flow pattern in the reactor core and
plenum chambers [3]. EHCFs may be categorized into three parts corresponding to
the change in parameters the uncertainties make contribution to: the heat flux in
reactor core, the film temperature rise in reactor core channel, and the temperature
rise or enthalpy rise in the channel [3, 12]. These three parts are illustrated as follows:
1. Uncertainties that influence the heat flux: Heat flux hot factor, FQ, is defined as
the ratio of the highest heat flux which could possibly occur anywhere in the
reactor core to the average heat flux.
q'h,= F - q"
(Eq. 2-1)
Where the subscript hc refers to hot channel and nc refers to nominal channel.
2. Uncertainties in film temperature rise: film temperature rise hot factor, FAT, is
defined as the ratio of the maximum film temperature rise, which could possibly
occur anywhere in the reactor core channel to the average film temperature rise.
(AT,)c = FAT -(AT,),,
30
(Eq. 2-2)
Where A T, is the increase in surface temperature (i.e. fuel cladding temperature)
3.
Uncertainties in the temperature rise or enthalpy change in the channel: Coolant
temperature rise or enthalpy change in the channel hot factor, FH, is defined as the
ratio of the maximum coolant temperature rise which could possibly occur in any
fuel assembly of the reactor core to the average temperature rise.
(ATb)h, = FH -(MT,,
(Eq. 2-3)
Where A Tb is the increase in bulk temperature rise of between inlet and outlet.
These three components can be further divided into sub-factors, either in
multiplicative way or statistical way, as explained earlier in section 2.2. Taking FQ for
example, multiplicatively it, can be expressed as
F = fQ ' fQ 2 'fQ
3
' f,
(Eq. 2-4)
- 1)2
(Eq. 2-5)
or statistically
FQ =1+
Z(f'
Where fQi are the sub-factors involved in the deviation of heat flux from its nominal
value.
The EHCFs used for the MITR use the latter formula, which is discussed in section
2.4. The selection of sub-factors and EHCFs for the thermal-hydraulic analysis of the
hottest channel can have a significant impact on reactor safety margins. For instance,
the uncertainty in the heat transfer coefficient is a major contributor to the reduction
in thermal-hydraulic safety margins, as indicated by Woodruff in 1997[12].
31
2.3.2 Common sub-factors involved
Some common sub-factors used in uncertainty analyses are summarized below, which
are taken from LeTourneau's study [2], which explicitly defined uncertainties
involved in reactor design. The first six factors contribute to unequal flow
distribution, and the last three are responsible for the changes in heat flux distribution.
In some analyses, although the complete independency of each sub-factor is not
strictly verified, it is convenient and therefore somewhat conservative to consider
them as independent [3].
1. Even though the core geometry is ideal, the particular geometry of the reactor inlet
plenum and the entrances region to the individual coolant channels may give rise
to an unequal flow distribution. This factor is defined as plenum factor.
2. Deviations from the nominal design dimensions of the individual coolant channels
will cause unequal flow distribution among the channels. This is known as
channel tolerance factor.
3. Certain fuel element materials and structures show a tendency to expand or
become misshapen under irradiation or when exposed to severe temperature
gradients. This may cause further deviations in the coolant channel dimensions,
and the factor is labeled irradiation factor.
4. If a considerable variation in surface finish among the fuel elements is there
contributing to unequal flow distribution among the channels, the factor is called
roughness factor.
5. Generally, for a compact coolant channel, such as a round tube, the coolant
enthalpy is taken as the mixing-cup average over the cross section. Perfect fluid
mixing in the channel is thereby implied. However, for a noncompact channel,
like a wide, narrow, rectangular tube, it is convenient to assume perfect mixing
across the narrow direction and no mixing across the wide direction. In such a
channel, one may account for mixing in the wide direction by introducing a hot
channel factor less than unity called mixing factor. A similar interchannel mixing
factor may be defined where coolant channels are interconnected, as is the case
when rods or spheres are used as fuel elements.
6. If local or bulk boiling occurs in some channels due to the spatial variation of heat
32
generation in the reactor, the increased pressure drop per unit flow rate caused by
boiling will affect the flow distribution among the channels. The hot channel
factor is defined as the boiling factor.
7. If the volume of fuel material generating heat removed by a unit of surface area is
not uniform in the reactor core, the heat flux distribution will be affected. This
phenomenon may occur due to manufacturing tolerances applicable to the portion
of the fuel elements containing fissionable material. The hot channel factor is
called fuel element tolerance factor.
8. Similarly, if the number of fissionable atoms per unit volume of fuel material is
not constant in the reactor core, the heat flux distribution will be affected. The
disparity may arise from metallurgical tolerances on fuel material composition and
enrichment. The hot channel factor is named fuel density factor.
9. If the fuel material is separated from the coolant by cladding material, variations
in the thickness of this cladding around the perimeter of the heat transfer surface
of the fuel element due to manufacturing tolerances will cause variations in heat
flux distribution at the heat transfer surface compared to the symmetrical case.
The hot channel factor is defined as eccentricity factor.
The plenum factor, in general, must be determined experimentally on a model of the
entrance chamber under consideration, and may be minimized by proper hydraulic
design of the entrance chamber. The channel tolerance, irradiation, roughness, and
boiling factors may be calculated together, using the basic assumption that pressure
drops across a nominal and a hot channel are equal. This is a good assumption for
forced flow [12]. In addition, if the channels are interdependent rather than
independent as with parallel rod fuel elements, then a zero pressure gradient
perpendicular to the flow may be assumed [3].
The mixing factor may be determined wholly by experiment using dye or other tracer
techniques, or analytically using experimentally determined mixing coefficients. To
finish the calculation, one must know the flow distribution, the channel dimensions
and the coolant velocity. There's seems to be no general expression applicable to any
reactor.
The fuel element tolerance factor, the eccentricity factor, and the fuel density factor,
may be determined by application of the steady-state heat conduction equation to a
33
fuel element of nominal dimensions, and to a fuel element of worst allowable
dimensions which will result in a maximum heat flux, in a region of the same neutron
flux.
34
2.4 EHCFs Used in MITR-II
The sub-factors and statistically combined EHCFs used in the SAR [13] are
summarized in Table 2-1. Table 2-2 summarizes the definition for these sub-factors
[2, 3, 13].
The value of the sub-factors in Table 2-1 corresponds to Eq. 2-6.
f =1.0+ --
(Eq. 2-6)
where n is the number of standard deviation that is incorporated into the sub-factor,
o is standard deviation and p is the nominal value of parameters. However, how
these sub-factors were obtained was not clearly documented in MITR-II SAR [13], or
in the previous version dating back to 1970 [14]. There is no sufficient information
indicating the value of n in Eq. 2-6.
Thorough evaluation on the update or verification of these sub-factors will be
performed either from experts' recommendation or from recently retrieved
experimental data. Therefore, the sub-factors in MITR-II SAR were assumed to
correspond to three standard deviation values in this study. In a study covering the
statistical thermal design procedure of super critical LWR, Yang et al [4] derive the
relevant sub-factors incorporating 3 standard deviations, as stated in his study "the
sub-factors are treated as 3a statistical factors and most of them are evaluated from
the typical data of the preliminary work". Therefore, it is assumed that n equals to
three in this study at this stage.
For example, the uncertainty for heat transfer coefficient is 1.20, according to table 21. If three standard deviations are assumed to be incorporated in this value, the
uncertainty of the heat transfer coefficient distribution is one third of 20%, which is
6.7%. Sub-factors involved in subsequent calculation, as shown in Chapter 4, are
treated in this manner.
EHCFs in Table 2-1 were obtained statistically using Eq. 2-7,
F =1+
1)2
35
((Eq. 2-7)
where fi represents sub-factors and F is EHCF referring to FH, FQ and FAT in Table 2-1.
As can be seen in Table 2-1, sub-factors were categorized into three parts contributing
to the uncertainties in enthalpy rise, film temperature rise, or heat flux respectively.
These EHCFs should be identified in the analyses of thermal-hydraulic safety margin,
as part of MITR core conversion safety analyses. One thing worth noting here is that
EHCFs have been used for plate-type fuel reactors, like the MIT Reactor. As for
those reactors with Russian tubular-type fuel assemblies, they usually do not directly
include hot channel factors in the analyses. Neither do the analyses for TRIGA
reactors, as clearly indicated by Matos [15].
36
Table 2-1 Sub-factors and EHCFs used in MITR-II SAR [13]
Enthalpy Rise
Reactor power measurement
Power density measurement/calculation
Plenum chamber flow
Flow measurement
Fuel density tolerances
Flow channel tolerances
1.050
1.100
1.080
1.050
1.026
Eccentricity
FH Statistical
1.089
1.001
1.173
Film Temperature Rise
Reactor power measurement
1.050
Power density measurement/calculation
Plenum chamber flow
Flow measurement
Fuel density tolerances
Flow channel tolerances
1.100
1.060
1.040
Eccentricity
Heat transfer coefficient
FAT. Statistical
1.003
1.200
1.275
Heat Flux
Reactor power measurement
1.050
Power density measurement/calculation
Fuel density tolerances
1.100
1.050
Eccentricity
F0 , Statistical
1.003
1.123
37
1.050
1.124
Table 2-2 Description for sub-factors used in MITR-II SAR [2, 3,13]
Sub-factor
Plenum factor
(Plenum chamber flow)
Fuel density factor
(Fuel density tolerances)
Channel tolerance factor
(Flow channel tolerances)
Eccentricity factor
(Eccentricity)
Definition
Even though the core geometry is ideal, the
particular geometry of the reactor inlet plenum
and the entrances region to the individual
coolant channels may give rise to an unequal
flow distribution.
If the number of fissionable atoms per unit
volume of fuel material is not constant in the
reactor core, the heat flux distribution will be
affected. The disparity may arise from
metallurgical tolerances on fuel material
composition and enrichment.
Deviations from the nominal design dimensions
of the individual coolant channels will cause
unequal flow distribution among the channels.
If the fuel material is separated from the coolant
by cladding material, variations in the thickness
of this cladding around the perimeter of the heat
transfer surface of the fuel element due to
manufacturing tolerances will cause variations
in heat flux distribution at the heat transfer
-surface compared to the symmetrical case.
38
References
[2-1]
N. E. Todreas, M. S. Kazimi, "Nuclear System I: Thermal Hydraulic
Fundamentals",Publishedby Taylor&Francis Group, 1990.
[2-2]
B. W. LeTourneau, and R. E. Grimble, "Engineering Hot channel factor for
reactor design." Nucl. Sci. Eng. 1:359-369, 1956.
[2-3]
N. E. Todreas, M. S. Kazimi, "NuclearSystems II; Elements of Thermal
HydraulicDesign",Hemisphere Publ. Corp., New York, 353 (1990).
[2-4]
J. Yang, Y. Oka, J. Liu, Y. Ishiwatari and A. Yamaji, "Development of
Statistical Thermal Design Procedure to Evaluate Engineering Uncertainty of
Super LWR", Journal of NUCLEAR SCIENCE and TECHNOLOGY, Vol.
43, No. 1, p. 32-42 (2006)
[2-5]
S. Ray, A. J. Friedland, E. H. Novendstern, "Westinghouse advanced
statistical DNB methodology-The 'revised thermal design procedure',"
Third Int. Topical Meeting on Nuclear Power Plant Thermal Hydraulics and
Operations. Seoul, Korea, Nov., 1988, A5-261 (1988).
[2-6]
L. S. Tong, J. Weisman, "Thermal Analysis of Pressurized Water Reactors"
3rd Edition, America Nuclear Society, USA, 582 (1996).
[2-7]
J. Robeyns, F. Parmentier, G. Peeters, "Application of a statistical thermal
design procedure to evaluate the PWR DNBR safety analysis limits," Ninth
Int. Conf. on Nuclear Engineering ICONE 9, Nice, France, Apr. 8-12, 2001,
(2001).
[2-8]
J. P. Bourteele, J. Greige, M. Missaglia, "The Framatome generalized
statistical DNBR method (MSG)," Sixth Int. Topical Meeting on Nuclear
Reactor Thermal Hydraulics NURETH-6, Grenoble, France, Oct. 5-8, 1993,
v.1-355 (1993).
[2-9]
K. L. Eeckhout, J. J. Robeyns, "MTDP-An optimized MONTE CARLO
method for evaluation of the PWR core thermal design margin," Eighth Int.
Topical Meeting on Nuclear Reactor Thermal Hydraulics NURETH-8, Kyoto,
Japan, Sept. 30-Oct. 4, 1997, v.1-421 (1997).
39
[2-10]
K. I. Han, "Technical Review on Statistical Thermal Design of PWR Core",
Journal of the Korean Nuclear Society, Vol. 16, No.1, March, 1984.
[2-11]
J. H. Rust, "NuclearPower PlantEngineering",Haralson Publishing Co.,
1979
[2-12]
W. L. Woodruff, "Evaluation and Selection of Hot Channel (Peaking)
Factors for Research Reactor Applications" February, 1997
[2-13]
MIT Nuclear Reactor Laboratory, "Safety Analysis Report for the MIT
Research Reactor," MIT-NRL- 11-02, August, (2011)
[2-14]
Safety Analysis Report for the MIT Research Reactor (MITR-II),
MITNE- 115, October 1970.
[2-15]
J.E. Matos, RERTR Program/Argonne National Laboratory, "Safety
Assessment of Core Conversion", Presented at US / IAEA Regional
Workshop on Application of the Code of Conduct on the Safety of Research
Reactors Argonne National Laboratory, 30 April - 11 May 2007.
40
Chapter 3 Limiting Safety System Settings
3.1 Definition of LSSS
As stated in ANSI/ANS- 15.1, "Foreach parameteron which a safety limit is
establishedby the SAR, a protective channel should be identified that prevents the
value of that parameterfrom exceeding the safety limit. The calculatedsetpointfor
this protective action, providing the minimum acceptable safety margin considering
process uncertainty,overall measurement uncertainty,and the transientphenomena of
the process instrumentation,is defined as the limiting safety system setting (LSSS)"
[1].
Similar to the description above, LSSS is defined in NRC Glossary [2] as " settings
for automatic protective devices related to those variables having significantsafety
functions. Where a limiting safety system setting is specifiedfor a variable on which
a safety limit has been placed, the setting will ensure that automaticprotective action
will correct the abnormalsituationbefore a safety limit is exceeded."
Hence, LSSS are limits established to guarantee that there is sufficient margin
between the normal operating conditions and the safety limits. The prevention of
nucleate boiling (ONB) within the coolant channels is chosen to derive LSSS in
thermal-hydraulic analysis [3]. For narrow rectangular coolant channels, such as
those in the M1TR, Sudo et al. [4] suggested to apply the Bergles-Rohsenow
correlation [5] to predict the occurrence of the onset of nucleate boiling (ONB). This
suggestion was based on comparisons of several existing correlations with
experimental data.
The LSSS specifically for the MITR in forced convection mode [6] is set for:
a) The maximum reactor power,
b) The maximum steady-state average core outlet temperature,
c) The minimum primary flow rate, and
d) The minimum coolant level in the core tank.
If operating conditions are in the region below the LSSS curve shown in Figure 3-1
[3], it is guaranteed that boiling will not occur anywhere in the core under all credible
conditions and that means the safety limits will not be exceeded. The safety limits are
established to ensure the integrity of the fuel clad, to prevent fission product release.
41
For the MITR, both CHF and OFI are calculated and the one that would occur first is
adopted as the safety limits for conservatism. The analysis for the safety limit is
included in Chapter 6. The ONB limit is calculated based on the fuel clad
temperature. The analytical expression was presented in the MITR SAR report [3].
Both the best-estimate value for ONB and the LSSS calculated using engineering hot
channel factors (EHCFs) are presented in this section. The best-estimate ONB is the
LSSS obtained at the most limiting coolant channel (or fuel plate stripe for the hot
stripe approach described in section 3.7) that the parameters are taken at their nominal
values, e.g. without taking into account engineering uncertainties. In contrast, LSSS
calculated using EHCFs takes the uncertainties into consideration via the usage of
EHCFs.
There are numerous system parameters and notations involved in LSSS calculation.
Their definitions are summarized in Table 3-1.
42
Table 3-1 Parameters used in LSSS calculation
Symbols
Ff
dr
Definitions
Core coolant flow factor, the ratio of the primary coolant flow that
actually cools the core region to the total flow, which is 0.921 [5]
Flow disparity factor of M1TR, the ratio of (minimum
flow/average flow) for coolant channels within a fuel assembly,
which is 0.93 [6]
WP
N,
Fr
Fs
Fcore
Ffuel
rh
P
AH
PH
Total primary coolant flow rate [3], which is taken as 1800 gpm
for LSSS calculation.
The number of coolant channels in the core region, which is 432
for the proposed LEU fuel design [3].
Radial power peaking factor, which is assumed as 1.76 for LEU
core [3]
Lateral power peaking factor such that FrF, is assumed to be 2.12
[7] for the hot stripe approach.
Core power deposition factor, the fraction of the fission power
deposited in the core region (fuel &coolant) of the core tank,
which is 0.965 [3]
Fuel power deposition factor, the fraction of the core power
deposited in
the fuel elements, which is 0.94 [3]
Hot channel mass flow rate
Reactor operating power
2
Heat transfer area per channel, which is calculated as 0.12357 m
Heat transfer perimeter per coolant channel, which is calculated as
0.2115 m
Tin
Tout
h
p
z
O(z)
q"(z)
FAT
FH
Coolant temperature at channel inlet
Coolant temperature at channel outlet
Heat transfer coefficient
System pressure
Elevation in coolant channel
Normalized axial heat flux distribution factor
Local heat flux
EHCF featuring film temperature rise, which is 1.275 [3]
EHCF featuring enthalpy rise, which is 1.173 [3]
43
9
8-
Primary Flow Rate, Wp=1800 gpm
------
6
-
-
Fcore,
2.0
Fgdf, =0.8
-1.173
FAT = 1.275
-
4
50
- 55
60
65
70
75
80
Reactor Outlet Temperature, Tout (*C)
Figure 3-1 MITR HEU LSSS for forced-flow operation (two-loop) [3]
44
3.2 Derivation of LSSS
The basic idea of LSSS calculation is that the maximum cladding temperature is no
greater than the temperature that induces ONB, as expressed in Eq. 3-1.
Ilad(Z) <dad,ONB(Z)
(Eq.3-1)
3.2.1 Onset of nucleate Boiling (ONB)
For narrow rectangular channels, like channels in MITR-II, Sudo et al. [4] suggested
to apply the Bergles-Rohsenow correlation [5] to predict the occurrence of the onset
of nucleate boiling (ONB).
The Bergles-Rohsenow correlation, which relates the wall temperature with applied
heat flux when ONB occurs, is used for the derivation of LSSS for MITR, as shown in
Eq. 3-2. The original form of correlation can be rewritten if the thermal properties are
specified, as shown in Eq. 3-3. The latter was used in the previous version of MITR
SAR [3] in which pressure was estimated at 1.3 bar corresponding to saturation
temperature 1070 C. This pressure corresponds to a coolant height of 10 feet (3 meters)
above the top of the fuel plates or 4" below overflow.
q
9O.0234
1156) 2.16
1W,ONB
T'lad,ONB
=107
s2
+ 0.0177 [q"(Z)]0.4 6
45
(Eq. 3-2)
(Eq. 3-3)
3.2.2 Cladding Temperature
The cladding temperature in Eq. 3-1 can be obtained using energy balance. The
subscript "hc" for heat flux refers to hot channel heat flux. The description for every
term used in the following equations is summarized in Table 3-1. As written in Eq. 34, the bulk temperature of coolant at certain axial level can be expressed in terms of
inlet coolant temperature and heat flux applied to the channel. The difference in bulk
coolant temperature and cladding temperature can be expanded to include heat
transfer resistance, as shown in Eq. 3-5.
.F
T..,,(z)=7z+
TadZ =TW,+
.F
mhCpf
0
(Eq. 3-4)
fPHqhc(z)dz+
F
mC
h
(Eq. 3-5)
Next, the channel inlet temperature in Eq. 3-5 can be expressed as a function of outlet
temperature and reactor operating power, as can be seen in Eq. 3-6. Substituting all
these terms into Eq. 3-3, the expression for LSSS is obtained as shown in Eq. 3-7.
PF,,,
-
T=
WP f
P -F,e
WPc
F
(Eq. 3-6)
itzhdz+
"
mep
<[1 ]-[ q z1)
1.8 1082p
h
0.4633,234+±T,
=0
(Eq. 3-7)
where
q" (z)=
P
- F ,CFOeF,-O(z)
NcAH
As explained earlier, LSSS is used to set a limit so that ONB does not occur
everywhere in core region. To derive such a limit (upper limit for cladding
temperature), simply equalizing cladding temperature with temperature that induces
46
ONB, as shown in Eq. 3-8.
(Eq. 3-8)
Tclad WTcld,ONB(Z)
As a result, Eq. 3-7 becomes,
P -F,,.
-P-e.
F
-
1.]-[
1.8
qhcz)
h
MC,
WPc,
-Tsat -[
F
-j Pq",e(z)dz+F
q (Z)
1082p 1 5 6
].463P
0234
(Eq. 3-9)
=0
Which can be expanded as
TP.
F. F,,-(
HNPA
0-C,
""'W,-Ci
P
T
F.,,F F,.,(z))dz F -NAH F.,F,yGO(z)
N
-A
h
FrFfd),,FF)
0
A1.8
1082p'
0
F*z)
+463p
(Eq. 3-10)
In Eq. 3-10, the objective is to derive maximum allowable outlet temperature Tour
when operating power P is specified, or to obtain maximum allowable operating
power P when outlet temperature Tot is fixed. In either case, the LSSS curve for
MITR LEU can be obtained similar to that of HEU as shown in Figure 3-1 [3].
47
3.2.3 General Form of LSSS Equation
There are many parameters in Eq. 3-10, which can be categorized into three groups:
system parameters, local properties and engineering hot channel factors. These
parameters can be combined to simplify the LSSS equation. As a result, Eq. 3-10 can
be reduced to,
T.,t=7;at(Z)+C(Z)-PC(Z)+C3 .PC
4 (Z)-P-C 5
(Z)P
(Eq.3-11)
These system parameters, local properties and EHCFs used in LSSS calculation are
described in detail in the following sections. Eq. 3-11 is derived in this study and is
applicable for most of the plate-type-fuel research reactors since ONB is the common
concern for these research reactors of narrow coolant channels and high power density.
Note that the coefficients C 1-C 5 in Eq. 3-11 are different when applying different
methodologies to calculate LSSS. For the best-estimate LSSS in the most limiting
channel, every parameter is taken at their nominal values and EHCFs, the factors
characterizing accumulative uncertainties, are set as unity. For the LEU LSSS
calculated using EHCFs, all parameters are taken at their nominal values, but EHCFs
are set as what they were in HEU analysis [3] to account for the parametric
uncertainties. For the uncertainty propagation methodology, some key input
parameters are set as normal distributions reflecting for the parametric uncertainties
and EHCFs are set as unity since the parametric uncertainties are reflected using
parametric normal distributions in this methodology.
48
3.3 Parameters Used in LSSS Calculation
The system parameters, local properties, and EHCFs used in LSSS calculation are
summarized in this section.
3.3.1 System Parameters
The system parameters used in LSSS calculation can be found in Table 3-2. The LEU
fuel element consists of 18 fuel plates so that the heat transfer area is larger than the
original HEU design (15 plates). This LEU configuration was suggested by Ko et al.
[8] for reason that the core tank pressure loading of LEU core should be limited to be
equal or less than that of the current pressure loading of the HEU core. Total number
of flow channels is 432, which is calculated assuming 18 flow channels per element
and 24 fuel elements in core. Note that the number of channels 432 is obtained
assuming that two half-channels form a full channel. This assumption simplifies the
analyses. Derivation of thermal hydraulic limits for half-channels is not within the
scope of this study.
Since the neutronic analyses for the proposed LEU core were on-going, core power
deposition factor Fcor, fuel power deposition factor Fjei, and radial power peaking
factor Fr are adopted from the previous version of MITR-II SAR[3], which are 0.965,
0.94 and 1.76 respectively. These values were used in the LEU calculations at this
stage. The values will be updated in the near future to reflect the LEU core more
precisely [9].
The primary flow rate (kg/sec) is calculated using 1800 gallon per minute, which is
the current LSSS flow rate, and assuming average coolant temperature is 55 'C in
LEU core. The heat capacity, Cp, was taken at the aforementioned temperature
assuming a pressure of 1.3 bar. This pressure was also used in the uniform heat flux
assumption in [3]. Heat capacity at constant pressure Cp is not sensitive to the change
in pressure. Therefore, the assumption 1.3 bar made in the calculation has negligible
effect for the result.
According to the initial start-up testing of the MITR-II [6], about 92.1% of primary
flow enters core region of the MITR-IL. The flow distribution in the reactor core was
also measured during the MITR-II's initial startup testing. The minimum flow
through a fuel element is 93% of the average core flow rate [6]. The flow distribution
within a fuel element has also been measured experimentally using a dummy element
49
as 92.9% [6]. To calculate the worst case for a flow channel receiving minimum flow,
intuitively all of the three flow disparity factors should be included such that the
minimum flow for a channel is (92.1%x93%x92.9%) of the primary flow. However,
when calculating the mass flow rate used in Eq. 3-10, the factor 92.9% actually is
removed since the EHCFs are included in Eq. 3-10. The exclusion of the factor
92.9% is because the inclusion of EHCFs implies that the discrepancies among the
channels, such as flow rate, heat flux and so on, are taken into account in the
calculations. To avoid double-counting mass flow rate discrepancy among the
channels, the factor 92.9% is therefore removed.
One thing has to be clarified here is that the hot channel does not necessarily receive
minimum channel flow. Instead, it is fairly possible that the channel receive
minimum flow does not possess peaking power. Therefore, the inclusion of flow
disparity for hot channel mass flow rate calculation is a conservative assumption.
Other geometry terms such as flow area and heat transfer area in Table 3-2 are derived
from the fuel geometry of the MITR. These geometry terms are discussed in detail in
section 3.4.
50
Table 3-2 Parameters used for analytical LSSS calculation
*Number of channels NC
432 (18*24)
Feo,,
0.965
FfeI
0.94
Radial power peaking factor
F,
Fr
Heat transfer area (per
channel)
Heated perimeter PH
1.76
0.12357 m 2
0.2115 m
4.18E+03 J/kg (When T=55*C, the average
coolant temperature in channel; P=1.3 bar, the
P
pressure used in [3] for uniform heat flux
assumption.)
Coolant flow area
1.21 le-4 m 2
Thermal hydraulic diameter
2.042e-3 m
a
Heat capacity
Primary coolant flow rate W,
**MFR in hot channel rh
111.938 kg/sec (converted from 1800 gpm
when T =55'C, the average coolant
temperature in channel)
0.2219 kg/sec ((111.938/432)*0.921*0.93)
*Assuming two half-channels form one full-channel
**0.921 = core coolant flow factor, 0.93 = flow disparity factor
51
3.3.2 EHCFs
As can been seen in Eq. 3-10, two EHCFs are included in LSSS calculation: enthalpy
rise factor FH and film temperature rise factor
FAT.
According to the previous version
of the SAR [3], these two factors were the accumulative result of uncertainties
involved respectively in enthalpy rise and film temperature rise. The sub-factors
involved in enthalpy rise and film temperature rise are summarized in Table 2-1 [3].
In this study, the values of EHCFs are directly adopted from [3] and used in one of the
methodologies to calculate LSSS.
52
3.3.3 Local Properties: Coolant pressure
The fueled region of a MITR channel is divided axially into ten equal distance nodes
in several thermal-hydraulic computer models used for steady-state and transient
simulations, as can be seen in Ko's study [8]. Local properties in this study refer to
the fluid temperature, pressure, HTC and axial power distribution factor respectively
for each of these axial nodes. In the following sections, how these properties were
estimated is explained in detail.
The static pressure corresponding to 10 feet of coolant above the top of the fuel is 1.3
bar (which has a saturation temperature 107*C). Therefore, for the bottom node of the
fuel, the pressure is calculated to be the sum of 1.3bar plus the equivalent liquid
pressure of 10 ft water plus the equivalent liquid pressure of 0.5842 meter (fuel height)
water. The pressure of the top node of the fuel is the pressure of the bottom node
minus the pressure loss, where the pressure loss is the sum of frictional, gravitational
and nearly negligible acceleration pressure drop across the core.
The major contribution of the pressure drop is frictional pressure drop, which can be
expressed by Eq. 3-12 [10],
APfricti
=
f
- ) - )pV
2
(Eq. 3-12)
where
f =0.575. (Re)~02
= 0.575- (')~25
= 0.575- (PVD)-02
(Eq. 3-13)
pA
P
Note that the friction factor f is taken from Wong's thesis [11], a friction factor
correlation developed for MIT finned rectangular channel.
The correlations used to calculate gravitational and acceleration pressure drop are
respectively shown in Eq. 3-14 and 3-15 [10].
APgravily = pgh
APPcceeratn
G
(Eq. 3-14)
)out
P
53
P
E(q.
(Eq. 3-15)
where G is mass flux and p is fluid density.
The water properties used for pressure loss calculations are based on the
temperature/pressure assumption described in section 3.3.1. The summary for
pressure loss calculation and pressure at each node, and their corresponding saturation
pressure are summarized in Table 3-3 and Table 3-4. The total pressure loss is
calculated as 35,459 Pa, which is mostly contributed by the frictional pressure drop.
These pressure drops are calculated based on the estimated mass flow rate of the hot
channel, 0.2219 kg/sec, as shown previously in Table 3-2. In pressure drop
calculation, the thermal properties are assumed as constant for simplicity, and are
taken at temperature being 55*C and pressure at 1.3 bar.
54
Table 3-3 Summary for the MITR pressure loss calculation
Term
Frictional pressure loss
Acceleration pressure loss
Gravity Pressure loss
Calculation Result
29750 Pa
66 Pa
5643 Pa
Total Pressure Loss
35459 Pa
Table 3-4 Pressure calculated for each node of the fueled region
Node #
Pressure (bar) Saturation Temperature (*C)
1 (Bottom)
1.65
114.3
2
1.61
113.5
3
1.57
112.8
4
1.53
112.0
5
1.49
111.2
6
1.45
110.4
7
1.41
109.6
8
1.37
108.8
9
1.33
107.9
10 (Top)
1.30
107.1
55
3.3.4 Local Properties: Axial Power Distribution and Coolant Temperature
The preliminary power distribution analyses conducted by ANL indicated that the
most limiting fuel element amongst the core is reference core 189 at the end of cycle
(denoted as 189EOC as follows) [7]. For conservatism, the power profile of this fuel
element is used to calculate LSSS. This LEU fuel axial power is bottom-peaked, as
illustrated in Figure 3-2. The axial power peaking of 189EOC, the ratio of maximumto-average axial nodal power is 1.27.
Coolant temperature increases as coolant flowing through a heated channel, and the
increase in coolant temperature within certain flowing distance is related to local heat
flux. Since the axial power profile is bottom-peaked, the increase in coolant
temperature is expected to be larger in the lower portion of the fueled region. This
trend can be observed in Table 3-6.
In this section, the values of heat capacity at constant pressure and mass flow rate are
assumed constant throughout the calculation. The coolant temperature for each node
is calculated assuming a reactor power of 8.4 MW, which is the presumed LSSS
power for MITR LEU core, and average core outlet coolant temperature of 60'C,
which is one of the specified conditions for LSSS. The inlet coolant temperature can
be obtained using these two assumptions via Eq. 3-6. The inlet temperature is
calculated to be 43C. Once the inlet coolant temperature is determined, the coolant
temperature at each node for the hot stripe can be obtained using the axial power
profile of 189EOC, as summarized in Table 3-5. The sensitivity study of coolant
temperature on LSSS calculation can be found in Chapter 5.
The LSSS for the MITR HEU configuration is 7.4 MW as documented in the SAR [3],
which is 20% larger than 6 MW, the steady-state power of the HEU configuration.
Similarly, the LSSS for the MITR LEU is expected to be 8.4 MW, which is 20%
larger than the target licensing LEU power 7 MW.
56
10
9
8
0
0
5
3210.02
0.06
0.1
0.14
Axial Normalized Power Factor
Figure 3-2 Bottom-peaked LEU axial power profile [7]
Table 3-5 Axial power distribution for the MITR LEU fuel (189EOC) [7]
Node Normalized factor
1
2
3
4
5
6
7
8
9
10
0.117
0.115
0.123
0.127
0.127
0.123
0.109
0.084
0.04
0.02
57
Table 3-6 Hot channel coolant temperature calculated for core189
Node
Coolant
Number Temperature(*C)
1
46.60
50.47
2
54.60
3
4
58.85
63.12
5
6
67.26
7
70.92
8
73.73
75.27
9
10
76.13
58
3.4 Heat Transfer Coefficient
Heat transfer coefficient plays an important role in LSSS calculation. This can be
seen later in Chapter 5 (Sensitivity Study). The purpose of this section is to obtain the
best-estimate value for heat transfer coefficients (HTC) at each node in the fueled
region of the MITR.
As can been seen in the existing studies [8, 11, 12], there are two ways to compute
HTCs for the MITR. One is the conventional Dittus-Boelter correlation [13] in
conjunction with the enlarged heat transfer area; the other is Carnavos correlation [14],
an empirical correlation for finned channel. The enhancement factor for heat transfer
area used in the former approach was calculated as 1.9 by S. Parra [9] and this value
is used for MITR's heat transfer calculation.
The fuel plate geometry of MITR and the notations for each parameter are firstly
introduced for the better understanding of the subsequent calculation of HTCs. Figure
1-3 shows part of the side view of a fuel assembly of the MITR noting that the
proposed design for LEU has 18 plates per assembly [8]. Table 3-7 summarizes some
derived geometry parameters for the MITR and these parameters will be used in
subsequent HTC computation. In this table, the term "nominal" refers to a situation
that geometry parameters are calculated as if the fins were not present, comparing to
the term "actual" calculating geometry parameters taking into consideration the
presence of fins. The coolant properties used for the HTC calculation are summarized
in Tables 3-4 and 3-6.
59
Table 3-7 Derived Geometry Parameters for MITR (LEU)
Derived Geometry
Parameter
Derivation
Value
Nominal Flow Area
Channel Width x (2 x Fin
Height + Water Gap*)
2 x Channel Width
1.3699E-04 m 2
Nominal Heated
Perimeter
Nominal Wetted
.
Penimeter
2 x (Channel Width +
Nominal Hydraulic
Diameter
(4 x Nominal Flow
Area)/ Nominal Wetted
Perimeter
2 x (Channel Width +
Water Gap* + 2x Fin
Height - Fin Height)
Pseudo Wetted Perimeter
Pseudo Hydraulic
Diameter
*
Water Gap*+2x Fin
1.1172E-01 m
1.2191E-01 m
Height)
(4 x Actual Flow Area)/
Pseudo Wetted Perimeter
Water gap refers to fin tip-to-tip distance
60
4.495E-03 m
1.214E-01 m
4.023E-03 m
3.4.1 Carnavos Correlation and Geometry Analysis for MITR
Carnavos correlation is an empirical correlation based on 11 finned tubes of different
number of fins, fin height, fin helix angles and tube diameters [14]. Carnavos
correlated the heat transfer performance of these 11 sets of data within 10% error, as
written in Eq. 3-16:
Nu =0.023 -Rea0 8 * Pr^- (f
A,
Where Nu
=h.Dha
k
)O1
and the predicted value of
)-
-
sec3 a
(Eq. 3-16)
A.
Nu
Pr*.
is within 10% error.
Nu, Re and Pr are Nusselt, Reynolds and Prandtl Number respectively. The subscript
"a" used in Eq. 3-16 represents that actual parameters used to compute for the
hydraulic diameter. The other terms in Carnavos correlation and their counterparts in
the MITR are given in Table 3-9.
Carnavos correlation is applicable for 0<a<30, 10,000<Re<100,000, 0.7<Pr<30, fin
tip diameter ranging from 8.08 to 16 mm, and number of fins ranging from 6 to 38.
The Reynolds number for the hot channel LSSS mass flow of the MITR is roughly
between 7,000 and 10,000 for each node based on hand calculations, which is slightly
out of the applicable range*. The fin tip diameter for the proposed MITR channel is
uncertain at this stage while the number of fins per plate is 220. Although some of the
MITR channel geometry/operating conditions are out of the applicable range,
Carnavos correlation is used for the analyses in this study since there are no other
correlations more suitable for this analysis.
*These Reynolds numbers were calculated based on hot channel flow with primary flow 1800 gpm.
The Reynolds number for average channel flow with primary flow 2000 gpm is between 7,700 and
14,000.
61
Table 3-8 The LEU geometry parameters in Carnavos correlation and their
counterpart in MITR
Meaning
Counterpart in MITR
Value
Afa
Actual free flow
area
Channel width x (water
gap* + 2 x fin height) -
number of fins per channel
x single fin area
5.8623E-02 x (1.8288E-03 + 2x
2.54E-04) -220 x 6.4516E-08
2
Open core free
Channel width x water
Afc
flow area at fin
inner diameter
Nominal heat
transfer area
based on tube
inner diameter as
if fins were not
5.8623E-02 x 1.8288E-03
gap*
=1.072E-04 (m2)
Nominal heated perimeter
x fuel length
1.1172E-01 x0.5842= 0.0653 (m2)
Actual heated perimeter x
2.1153E-01 x 0.5842= 0.12357 (m2
0
0 for a and therefore 1 for sec3 a
(4 x actual flow
4 x 1.2210E-04)/(2.3917E-01)
area)/(actual wetted
perimeter)
= 2.042E-03 (m)
Symbol
=1.2210E-04 (m )
present
A.
a
_______
Dha
*
Actual heat
transfer area
fuel length
Helic angle in
finned tube
Actual hydraulic
diameter
___________
water gap refers to fin tip-to-tip distance
62
3.4.2 HTC Computed from D-B Correlation and Carnavos Correlation
As mentioned earlier, besides Carnavos correlation, Dittus-Boelter correlation in
conjunction with fin effectiveness can be also used to estimate HTC [8, 11, 12]. The
HTC computed from these two correlations is compared in this section.
The Dittus-Boelter correlation (D-B correlation) mentioned in this study refers to the
well-known correlation of Eq. 3-17. It is interesting to know Wintertwon [16]
indicated that this widely-used equation was not originally proposed by Dittus F.W.
and Boelter L.M.K.[13], but was actually introduced by McAdams [17]. However, to
avoid confusion, the name Dittus-Boelter correlation is still kept in this study.
Nu
h-D
=
k
=
0.023. Re*8 -Pr*4
(Eq. 3-17)
Dittus-Boelter correlation is the most widely-used correlation for fully-developed
turbulent flow. Carnavos correlation, an empirical heat transfer correlation for finned
tube, is actually a modified form of D-B correlation with three geometry correction
factors. The three geometry correction factors can be found in Eq. 3-16 and Table 3-
10.
Table 3-10 summarizes three approaches used to calculate HTC. Approach A and
approach B are based on D-B correlation while approach C is based on Carnavos
correlation. In approach A, the actual wetted parameter and flow area were applied
and therefore the area enhancement factor is 1.0.
In contrast, the hydraulic diameter in approach B was calculated as if fins were not
present, and therefore the area enhancement factor is 1.9. There are no geometry
correction factors for D-B Correlation, so geometry correction factors are set as 1.0 in
these two approaches. Approach C calculates HTC using Carnavos correlation, which
is developed for finned channel and therefore the area enhancement factor is 1.0.
In the previous sections, the temperature and pressure for each node has been
estimated. Therefore, HTC for each node can be calculated using approach A, B and
C respectively and are summarized in Table 3-10. The HTCs calculated by approach
C are the lowest among these three approaches. For conservatism, HTCs computed
from Carnavos correlation were taken for LSSS calculation.
63
Table 3-9 HTC calculated using D-B Correlation and Carnavos Correlation
Dittus-Boelter Correlation
(Approach A)
Dittus-Boelter Correlation
(Approach B)
Geometry
Correction
Factor
1.0
1
1.0
Hydraulic
Diameter (m)
The actual wetted
perimeter and flow area
were applied such that
hydraulic diameter is
calculated as
(4 x actual flow
area)/(actual wetted
perimeter) = 2.042E-03 m
Carnavos Correlation
(Approach C)
A1.
(-)
A
The hydraulic diameter was
calculated as if fins were not
present.
(4 x actual flow
area)/(pseudo wetted
perimeter) = 4.023E-03 m
A
sec 3
-(-)
Aa -- sec a
a
(4 x actual flow area)/(actual
wetted perimeter)= 2.042E-03
m
Heat transfer
area1.1.10
Enhancement
1.
1.9
1.0
factor
Calculated HTC
range for node
1.36E04-1.66E04
2.25E04-2.77E04
1.00E04-1.22E04
1-10
2
(W/ m -K)
* These calculations are based on hot channel MFR 0.2219 kg/sec and local coolant
temperatures listed in Table 3-6
64
3.5 Best Estimate ONB
In section 3.2, a general form of LSSS equation was derived. Moreover, in sections
3.3, 3.4 and 3.5, all of the parameters required to obtain LSSS power, including
system parameters, EHCFs and local properties have been introduced. Combining of
all of these parameters, the coefficients in Eq. 3-11 can be computed but note that
these coefficients would vary if different methodologies were used, as explained in
section 3.2.
This section summarizes the best-estimate value for LSSS, which does not take into
account parametric uncertainties. That is, the two EHCFs in Eq. 3-11,
FH
and
FAT,
were set as unity because EHCFs themselves reflect the accumulative result of
parametric uncertainties. The input parameters for LSSS calculation are set as a
single value and nominal values are used. The assumption made to compute the
LSSS for the hot channel is that LEU radial peaking factor is 1.76 [3].
Substitute the local properties of node #7 (as indicated in Table 3-6, pressure is 1.4 bar
and saturation temperature is 109.6*C) into Eq. 3-11, it becomes
(Eq. 3-18)
466
T., = T,, +2.261- PO. -3.93. P
Where coefficients are listed as follows,
1
F reFFf.O(z)
C, =0.556-[ Nc - AH0.463P0234
1 156
=
1082p .
C 2 = 0.463 - p0 0234
F
'r"
C3 -
ZP HC4 =
2.261
= 0.466
= 2.062
F e F,.Ffel(z))dz
N, -A" .
m-cp
= 3.36
1FcorFrFffieio(Z)
cr
C,-NeC5
-AAH= h=
h
.
2.632
Above LSSS calculations are for node #7, other nodes can be computed in a similar
manner. Node #7 is taken as an example above because this node has the most
65
limiting ONB margin, which can be seen later.
As can be expected in Eq. 3-18, when power increases, the negative contribution
brought by the last term on the RHS (3.93P) is larger than the positive contribution
brought by the second term (2.26 1PA6). As a result, when power increases,
allowable outlet temperature decreases. This trend agrees with the intuition that when
operating power increases, the maximum allowable outlet temperature should
decrease to prevent the occurrence of nucleate boiling.
The idea of best-estimate, from the perspective of statistics, is to provide an unbiased
estimate that has minimum variance. For best-estimate ONB, no parametric
uncertainties are taken into consideration thus every input parameter is at their
nominal values. The best-estimate for the hot channel is obtained assuming that radial
power peaking factor is 1.76. The ONB of node #7 when outlet temperature is 60 *C
is 14 MW, which is the most limiting among the nodes and therefore is taken as the
reference value of this methodology as shown in Figure 3-3.
66
16
14
12
node 1
----10-.--
10
node 2
node 3
node 4
8
----
0
6
node 5
-node6
node 7
2
---
--- node 8
---
node 9
----
node 10
0
50
60
70
80
90
100
Tout (*C)
Figure 3-3 Best-estimate ONB computed for core189 on each node
67
3.6 LSSS Calculated Using EHCFs
In this methodology, EHCFs were included reflecting the accumulative parametric
uncertainties when calculating the coefficients in Eq. 3-11. The assumption LEU
radial peaking factor 1.76 is still kept in this methodology when calculating the LSSS
for the hot channel. The values of EHCFs were directly taken from the previous
version of MITR SAR [3], as explained earlier in section 3.3.2.
Similar to best-estimate LSSS methodology, node #7 is also taken as a example due to
its lowest prediction in LSSS power. As a result, Eq. 3-11 is written as,
T,= T, +2.261- Po466 -5.23. P
(Eq. 3-19)
Where
F.,f FydO(z)
C =0.556. [ N, - AH
1 156
1082p .
10.463p0.0
=
2.261
0 2 34
C2 = 0.463 -p0 . = 0.466
F
C3
F C4 -
C5 =
FAT'
core
WP -CP
= 2.062
coreFFfuei(z))dz
N A
3.941
Nc - A=
th -c,
1
F
Fcore rFfueO(z)
- 3.356
c H
h
The trend of Eq. 3-19 is same as Eq. 3-18. When power increases, the negative
contribution brought by the last term on the RHS (5.23P) is larger than the positive
contribution brought by the second term (2.261Po.466). As a result, when power
increases, allowable outlet temperature decreases.
Similar to the best-estimate ONB, the result of node #7 at outlet temperature 60'C was
taken as the reference value (10.48 MW) for this methodology because this node has
the most limiting LSSS power, as demonstrated in Figure 3-4.
68
16
14
12
node 1
10
----
node 2
A
node 3
node 4
8----
-
node 5
CA6
----
node 6
4
----
node 8
2
-
- --
node 9
-
node 10
0
50
55
60
70
65
75
so
Tout (*C)
Figure 3-4 LSSS power computed using EHCFs for corel89 on each node
69
3.7 LSSS Calculated Using Hot Stripe Technique
In general, the thermal power distribution within the core is assumed to be
proportional to the fission reaction rates or the neutron flux distribution that are
calculated by the MCNP computer code [18], since most of the energy is deposited in
the vicinity of where fission reactions take place. As illustrated in previous sections,
the axial power variation is represented by 0(z) while the variation in radial direction
is taken into account by radial peaking factor Fr, which describes how the power of
the hottest flow channel deviates from the average power of flow channel.
However, the power distribution analysis [7] provided by Argonne National
Laboratory indicates that there is a significant power variation within a fuel plate
along the width of a fuel plate or lateral direction, and should be taken into
consideration in thermal hydraulic analyses. Fuel plates are divided into four strips.
The heat flux of these strips was calculated as shown in Figure 3-5. The ratio of the
highest flux of these strips to the average heat flux on this fuel plate is defined as Fs,
the lateral peaking factor. The product of radial peaking factor and fuel plate peaking
factor, FrFs, is defined as hot stripe factor, which is the ratio of the highest flux on a
strip to the average heat flux of the core. The hot stripe factor of the MITR LEU core
is calculated as 2.12 [7].
Given the same conditions, using hot stripe factor leads to more limiting results
comparing to using radial peaking factor because the radial power peaking factor is
replaced with the hot stripe factor, and the latter is roughly 20% larger. Divide one
fuel plate into four strips, adopt the one has the highest flux as shown in Figure 3-5,
and perform LSSS calculation. Similar hot stripe approach has been used in the
thermal hydraulic analyses of Missouri Research Reactor [19].
To apply hot stripe approach to calculate LSSS, recall LSSS derivation,
-Fe
PF.
W,c,
<[
1.8
+
rhc,
q] hc
1082p1
Pjjq'h(z)dz + FT
1(Z)0.463
56
Where
q"c(z)=
h
P
Nc AH
-FfiFc,,corF,-0(z)
70
+sat
=0
he
h
(Eq.
3-7)
Re-write the heat flux term in Eq. 3-7 describing the most limiting hot stripe such that,
P
qhs(z) =
NAH
-F
(z)
FF,-
Where FrFs is 2.12 and subscript hs refers to hot stripe, so that Eq. 3-7 becomes,
P-F'"
re
-
WPc,
<[
1.8
(zhdz+
Zd
+
mc
,q.
h
hS(Z) ].463P0234 +Ta
1082p 1.56
]-[1
=0
(Eq. 3-20)
Table 3-2 summaries the system parameters used in hot stripe LSSS calculation. In
hot stripe approach, it is assumed that there is no lateral mixing and the flow is the
same as that in hot channel approach. Table 3-10 summarizes the thermal-hydraulic
conditions used in hot stripe LSSS calculation for each node. The coolant
temperature for each node is calculated assuming the reactor power is 8.4 MW, which
is the presumed LSSS power for MITR LEU core, and average core outlet coolant
temperature is 600C, which is one of the specified conditions for LSSS. The inlet
coolant temperature can be obtained using these two assumptions via energy
conservation. Once the inlet coolant temperature is determined, the coolant
temperature at each node for the hot stripe can be obtained using the axial power
profile of 189EOC, as summarized in Table 3-10. Note that the coolant temperature
at outlet is higher than the case based on power radial peaking factor, as shown in
Table 3-7. The temperature is higher is because the heat flux of the most limiting
channel calculated based on hot stripe consideration (2.12) is of greater value than
using radial peaking power factor (1.76).
71
Table 3-10 T/H conditions used in hot stripe LSSS calculation for each node
Coolant
Normalized
Power factor Pressure (bar) Temperature
(189EOC)
("C)
Node #
0.117
1.65
47.40
2
0.115
1.61
52.06
3
0.123
1.57
57.04
4
0.127
1.54
62.16
5
0.127
1.50
67.29
6
0.123
1.46
72.28
7
0.109
1.42
76.69
8
0.084
1.38
80.08
9
10
0.045
1.34
81.93
(bottom)
0.025
(top)
_
_
_
_
_
1.30
_
_
_
_
_
_
82.97
_
_
_
_
_
_
_
_
Hot Stripe in 7MW LEU Equilibrium Core Series
(189EOC Element 27, Plate 1)
700
R600
0
t
'ra
3=00
Stripe 1
-Stripe
2
-Stripe
3
-Stripe
4
00
-J100
0
0c.
0
0
2
4
6
8
10
12
14
16
18
Distance from Bottom of Fuel (inches)
Figure 3-5 Heat fluxes of strips on MIT LEU core 189EOC [6]
72
20
22
3.7.1 Best estimate ONB using hot stripe technique
The best-estimate ONB using hot stripe technique is obtained by setting EHCFs in Eq.
3-20 to be unities, since the parameters are taken at their nominal values. The most
limiting ONB occurs at node #7, which is 11.1 MW with outlet temperature being
60*C, as shown in Figure 3-6.
73
16
14
7
node 1
.
4
12
node 2
yAn
10
-~-node
--
8
o
3
M--node 4
-- *--
node 5
6
--
node 6
4
-
node 7
node 8
2
node 9
0
50
55
60
70
65
75
80
Tout (*C)
Figure 3-6 Best estimate ONB using hot stripe technique
74
---
node 10
3.7.2 Hot stripe LSSS using EHCFs
As demonstrated in Figure 3-7, the most limiting node for 189EOC is node #7. The
analytical LSSS for node #7 using hot stripe approach is calculated as 8.36 MW.
75
16
14
12
node 1
node 2
--
10
A
node 3
node 4
8-4i--
node 7
4-
-+-
node 8
-node 9
2
---
0
50
55
60
70
65
75
80
Tout (*C)
Figure 3-7 LSSS using EHCFs for 189EOC power profile
76
node 10
3.8 Summary
It has been shown that node #7 predicts the most limiting LSSS power and therefore
for conservatism, the LSSS power of this node is adopted for the subsequent analyses.
The LSSS powers illustrated in Figures 3-8 -3-10 are all LSSS powers of node #7
obtained based on different approaches. The analytical approach takes into account
the parametric uncertainties via the usage of EHCFs while the best-estimate ONB
does not take into the parametric uncertainties but provides the best-estimate ONB
results. Given the same conditions, the LSSS power calculated using hot stripe
technique predicts much lower LSSS power than the conventional radial power
peaking factor since the heat flux of the most limiting channel calculated based on hot
stripe consideration (2.12) is of greater value than using radial peaking power factor
(1.76).
Figure 3-8 compares the best-estimate ONB based on radial peaking factor and hot
stripe factor. As expected, the one based on hot stripe factor, 11.1MW, is more
limiting than that based on radial peaking factor, 14MW. The similar trend can be
also observed in LSSSs calculated using EHCFs that the one based on hot stripe factor,
8.36MW, is more limiting than that based on radial peaking factor, 10.48MW, as
shown in Figure 3-9. Table 3-12 summarizes these LSSSs calculated using different
approaches. For conservatism, the LSSSs based on hot stripe factor are adopted as the
final results, as shown in Figure 3-10. These analytically obtained LSSSs for node #7
are going to be used for the subsequent analyses in the following chapters.
77
Table 3-11 Summary for LSSS powers calculated using different approaches
LSSS Power at Tout = 60*C [MW]
14.0
11.1
10.48
8.36
Approach to Calculate LSSS
Best-estimate (radial peaking factor)
Best-estimate ( hot stripe factor )
Using EHCFs (radial peaking factor)
Using EHCFs (hot stripe factor)
16
14
12
--
10
-4-BE (radial peaking)
-U-BE (hot stripe)
6
2
0
50
55
60
65
70
75
80
Tout (*C)
Figure 3-8 Best-estimate ONB comparison using radial peaking factor and hot stripe
factor
78
16
14
12
10
I-
8
a
0~
+Using
6
-
U)
U)
U)
4
EHCFs (radial peaking)
Using EHCFs (hot stripe)"
-I
2
0
50
55
60
65
70
75
80
Tout (*C)
Figure 3-9 LSSS calculated using EHCFs based on radial peaking factor and hot
stripe factor
16
14
12
10
I-
8
0
0
-.-
6
U)
U)
U)
BE (hot stripe)
Using EHCFs (hot stripe)
4
-I
2
0
50
55
60
65
70
75
80
Tout (*C)
Figure 3-10 Hot stripe LSSS calculated using EHCFs and best estimate approach
79
References
[3-1]
American Nuclear Society, "The Development of Technical Specifications for
Research Reactors" ANSI/ANS-15.1-1990/2007
[3-2]
International Atomic Energy Agency "Research Reactor Core Conversion
Guidebook, Volume 1: Summary" IAEA-TECDOC-643, 1992.
[3-3]
MIT Nuclear Reactor Laboratory, "Safety Analysis Report for the MIT
Research Reactor," MIT-NRL-11-02, August, (2011)
[3-4]
Y. Sudo et al. "Experimental Study of Incipient Nucleate Boiling in Narrow
Vertical Rectangular Channel Simulating Subchannel of Upgraded JRR-3",
Journal of Nuclear Science and Technology, 23[3-1], Jan. 1986.
[3-5]
A.E. Bergles and W.M. Rohsenow, "Forced-Convection Surface-Boiling Heat
Transfer and Burnout in Tubes of Small Diameter," Trans.ASME, J. Heat
Transfer, Vol. 86, pp. 365-372, (1961); ASME Paper 63-WA-182, (1963)
[3-6]
MITR-II Startup Report, MITNE-198, February 1977
[3-7]
E.H. Wilson, N.E. Horelik, F.E. Dunn, T.H. Newton, Jr., Lin-wen Hu, and J.G.
Stevens, "Power Distributions in Fresh and Depleted LEU and HEU Cores of
the MITR Reactor," ANL-RERTR-TM-12-03, Argonne National Laboratory
(2012).
[3-8]
Y. C. Ko, "Thermal Hydraulic Analysis of the MIT Research Reactor in
Support of a Low Enrichment Uranium (LEU) Core Conversion", Chapter 4,
SM Thesis, MIT NSE Department, January 2008.
[3-9]
S. Parra, The Physics and Engineering Upgrade of the Massachusetts Institute
of Technology Research Reactor, Ph.D. Thesis, MIT Nuclear Engineering
Department, 1993.
[3-10]
N.E. Todreas and M.S. Kazimi, "NuclearSystems I- Thermal Hydraulic
Fundamentals",Hemisphere Publishing, 1990.
80
[3-11]
Susanna Wong, Lin-Wen Hu, Mujid Kazimi, "New Friction Factor
Correlation For The MIT Reactor Fuel Elements", Reduced Enrichment Test
and Research Reactors (RERTR) Conference Beijing, China , November 1-5,
2009
[3-12]
Yunzhi (Diana) Wang, "Evaluation of the Thermal-Hydraulic Operating
Limits of the HEU-LEU Transition Cores for the MIT Research Reactor",
S.M. Thesis at MIT, June. 2009
[3-13]
Dittus, F. W., and Boelter, L. M. K. "Heat transfer in automobile radiators of
the tubular type." University of California, Berkeley, PubL. Eng. 2,
pp.443-461, 1930.
[3-14]
Carnavos, T.C., "Heat Transfer Performance of Internally Finned Tubes in
Turbulent Flow," Heat Transfer Engineering, 1: 4, 32-37, 1980.
[3-15]
Sung Joong Kim, Yu-chih Ko, Lin-wen Hu, "Loss of Flow Analysis of the
MIT Research Reactor HEU-LEU Transitional Cores Using RELAP5-3D",
proceedings of ICAPP '10, San Diego, CA, USA, June 13-17,2010 Paper
10224
[3-16]
R.H.S. Winterton, "Where did the Dittus-Boelter Equation Come From?" Int.
J. Heat Mass Transfer. Vol.41 Nos 4-5, pp 809-810, 1998.
[3-17]
W. H., McAdams, "HeatTransmission, " 2nded., McGraw-Hill, New York,
1942.
[3-18]
X-5 Monte Carlo Team, "MCNP - A General Monte Carlo N-Particle
Transport Code, Version 5, Volume I: Overview and Theory"LA-UR-03-1987
[3-19]
E.E, Feldman, "Implementation of the Flow Instability Model for the
University of Missouri Reactor (MURR) That is Based on the Bernath
Critical Heat Flux Correlation" ANL/RERTR/TM-1 1-28,July 2011
81
Chapter 4 LSSS Calculation Using Uncertainty Propagation
Technique
As discussed in section 3.2.3, the coefficients in Eq. 3-11 would vary if different
methodologies were used. In this chapter, the methodology uncertainty propagation
technique is presented to obtain LSSS.
4.1 Introduction
Traditionally, engineering uncertainties were treated using EHCFs. In the uncertainty
propagation methodology, engineering uncertainties were treated by setting key input
parameters as normal distributions. The mean values of these input parametric
distributions are the values used in the analytical approaches in Chapter 3. The
standard deviations of these input parametric distributions are either obtained based
on the SAR [1] or by uncertainty propagation based upon their interrelationship with
known parametric distributions. How each parametric distribution was obtained is
discussed in section 4.3. The commercial computer software Oracle Crystal Ball [2]
was used in this study to generate these distributions by Monte Carlo method [3] with
specified mean values and standard deviations.
The input parametric distributions used in this methodology were assumed as normal
distributions at this stage due to the insufficient, or the incomplete understanding of
underlying physical mechanism of experimental data. However, more realistic
parametric distributions, i.e. distributions characterizing of skewness and/or kurtosis,
can be used as input distributions in the future if we have prior knowledge on them.
Some key input parameters in Eq. 3-9, such as heat transfer coefficient h, primary
coolant flow rate w,, hot channel mass flow rate rh and reactor power P are set as
normal distributions and denoted as <h>, <Wp>, <rh >, and <P> as follows. Other
input parameters, which are of insignificant importance on LSSS calculation, are
treated as constant values. These parameters are treated in the same manner as
analytical approach and therefore their notations remain unchanged. As a result, Eq.
3-9 becomes,
82
<q"z
z
F
<P>-F
<q",(z)>dz+Fsr
<
,
<h>
'*,+
Tu,- <W >c,
<m>c
[ [<
1.8
Tat
-
h
(
10.463P00234 -0
>
Where < q"h,(z)>=
e,,,F,,,FFO(z)
Nc -AH
Note that EHCFs
(Eq. 4-1)
1082p 1 56
and the subscript hs means hot stripe.
and Fr in Eq. 4-1 were set to unity since the parametric
FH
uncertainties were taken into account by setting key input parameters as normal
distributions. Consequently, Eq. 4-1 becomes Eq. 4-2,
"'<W,> c,
T]-]-
"'
1
1.8
..
< th> c,
(z)
1082p'.
56
<h>
(Eq. 4-2)
463,1.15=0
Re-write Eq. 4-2 by expanding hot channel heat flux in terms of power,
rz
j
______
TW
"
< P > -F,,,,
<W > c,
-
1
1.8
-(
o
NI
. A
<P>
NH A Fco,,Fu,,FFO(z))dz
Nc -AH
< rh > cH
<P>
,,FFO(z)
F ,,F
core f
NC -A
<h>
<>FF FF
core fuel , r
1082p1.156
(z)
].463,0*4=0
(Eq. 4-3)
Solving Eq. 4-3 for LSSS power given input parametric distributions and other singlevalued input as discussed in sections 3.2.3-3.5, LSSS power is obtained in a form of
distribution, representing the accumulative result of input parametric uncertainties.
83
4.2 Monte Carlo Simulation
Monte Carlo simulation is typically used when the model is complex, nonlinear, or
involves several parameters of uncertainties. It is essentially a sampling method with
inputs randomly generated from the probability distributions, which are in good
agreement with the actual data or best represent the current state of knowledge to
simulate the process of sampling from an actual population. The goal of a Monte
Carlo simulation is to simulate realistic situations to make predictions based upon the
given confidence intervals. A simulation can typically involve over 10,000
evaluations of the model so that sufficient data can be gathered. Some variance
reduction techniques, including modifying probability distributions to favor events of
greater interests and splitting/rouletting to change the number of particles in certain
regions, might be applied to approach smaller variances of the prediction results
depending on the situations [4,5]. In this study, none of any variance reduction
techniques were used at this stage.
4.2.1 Monte Caro Simulation on Oracle Crystal Ball
Monte Carlo simulation was performed on Oracle Crystal Ball to generate and
combine normal distributions for several key input parameters. These normal
distributions are randomly sampled with specified mean values and standard
deviations. The mean values of these input parametric distributions are the nominal
values used in the analytical approaches in Chapter 3. The standard deviations of
these input parametric distributions are either obtained based on the SAR [1] or by
uncertainty propagation based upon their interrelationship with known parametric
distributions, such as the fabrication tolerance distribution of water gap distance.
Oracle Crystal Ball is a spreadsheet-based software developed by Oracle. This
software is a prominent spreadsheet-based software package for predictive modeling,
forecasting, Monte Carlo simulation and optimization that has been used in industries
including aerospace, financial services, manufacturing, oil and gas, pharmaceutical
and utilities.
The quality of random number generator is associated with the credibility of Monte
Carlo simulations. As pointed out in Oracle Crystal Ball User's guide [2], "For no
starting seed value, Crystal Ball takes the value of the number of milliseconds elapsed
since Windows started." That is equivalently to say, if no starting seed value is
specified in the Sampling dialog box, the cycle of random numbers may be found
84
repeated after several billion trials. The iteration formula used in the random number
generator is:
r +- (62089911. r)mod(2" -1)
(Eq. 4-4)
This random number generator has a period of length of 231 - 2, or equivalently,
2,147,483,646, according to Eq. 4-4. This means the cycle of random numbers does
not repeat until after several billion trials, which is comparably larger than the sample
size in this study. This formula is discussed in detail in the Simulation Modeling &
Analysis and Art of Computer Programming, Vol. II, references in the Crystal Ball
User's Guide bibliography [2].
85
4.2.2 Model validation on Crystal Ball
Some simple tests were conduct to assess the reliability of this software. In these
simple tests, some models with exact known analytical solutions were chosen to
validate the results computed by Oracle Crystal Ball.
For example, if two normal distributions are multiplied, each of them with mean 1.00
and the standard deviations of 0.10 and 0.05 respectively, the predicted mean and
standard deviation based on analytical solution are respectively 1.00 and 0.01118.
Using a sample size of 10,000 in Monte Carlo Simulation on Oracle Crystal Ball, the
simulated results are in good agreement with the analytical solution: the averaged
mean of 5 runs is 0.999161 and the averaged standard deviation is 0.112184. The
error predicting mean value and standard deviation in this case is respectively 0.08%
and 0.34%.
Next, using the same analytical model but sample size was increased to 100,000. The
error of the predicted mean value and standard deviation are reduced to 0.02% and
0.07% respectively, which are fairly close to the exact analytical solution. However,
the reduction in variation is obtained at the expense of longer simulation time, which
is proportional to 1/sqrt(N), where N is sample size.
Another more complex model with known analytical solution was tested using sample
size 100,000. The model and the test results are described in Table 4-1. The error of
predicted mean value and standard deviation for this model is 0.02% and 0.33%,
which is in good agreement with the exact analytical solution. Therefore, for all
analyses presented in this chapter a sampling size of 100,000 is chosen.
86
Table 4-1 The input description for the model used to validate Oracle Crystal Ball
Standard
Input Parametric Distribution
Mean
Deviation
A
B
C
D
E
1.0
1.0
1.0
1.0
1.0
0.1
0.2
0.03
0.04
0.05
Table 4-2 Comparison between analytical solution and results using Crystal Ball
Model Description
G=0.7xABCDE
Solution
Analytical
Mean
0.7
0.16416
Standard Deviation
Predictionby CrstalBall
Mean
0.69983
0.16470
Standard Deviation
Error
Mean
0.02%
Standard Deviation
0.33%
87
4.3 Uncertainty of input parameters for the MITR
As explained earlier in section 4.1, four input parameters including primary coolant
flow rates, heat transfer coefficient (HTC), hot channel mass flow rate (HCMFR) and
power, were set as normal distributions to obtain LSSS power. To generate normal
distributions, mean values and standard deviations were specified on Crystal Ball first,
and then Monte Carlo simulation was performed. How these mean values and
standard deviations were determined is discussed in this section.
4.3.1 Primary Coolant Flow Rate
The mean value of primary coolant flow rate, 111.38 kg/sec, was converted from 1800
gallon per minute under the assumption that temperature is 55*C, the average coolant
temperature in the core. The primary flow rate 1800 gpm was documented in MITRII SAR as the LSSS. As a result, 111.38 kg/sec is specified as the mean value for the
primary coolant flow rate distribution.
As for the specification for the distribution's standard deviation, the uncertainty for
flow measurement is 1.05 for enthalpy rise and 1.04 for film temperature rise, as
shown in the EHCFs table in MITR-II SAR. These values can be also found in Table
3.3. For conservatism, 1.05 is adopted in the analysis. However, how the sub-factors
were obtained in Table 3-3 was not clearly documented in MITR-II SAR. In a study
covering the statistical thermal design procedure of super critical LWR, Yang et al [6]
incorporated three standard deviations (n=3 in Eq. 2-1 that is recalled in this section)
to obtain the relevant engineering sub-factors. Therefore, in this study, it is assumed
that the sub-factors in SAR were derived in the same manner and that three standard
deviations were incorporated.
Therefore, the sub-factors were assumed corresponding to three standard deviation
values (3o) in this study. Consequently, the uncertainty (1 ) of the primary coolant
flow rate is one third of 5%, which is 1.33%, which corresponds to 1.87 kg/sec.
f =1.0+n.-
(Eq. 2-1)
where n is the number of standard deviation that is incorporated into the sub-factor,
a is standard deviation and p is the nominal value of parameters.
88
Figure 4-1 shows the primary coolant flow rate distribution as one of the input
parametric distributions for LSSS calculation. According to the famous 68-95-99.7
rule, about 99.7% of the value falls within three standard deviations of the mean for a
normal distribution. That is, there is 99.7% probability that the primary coolant flow
rate used in LSSS calculation are within the range of 106.33 and 117.55 kg/sec,
reflecting minor flow fluctuation as well as flow measurement uncertainty in real
situation.
89
NosneW D*iinuion
100.000 Tdils
99.999 Olsplayed
miee
_otforC
Use
3,200
~~~2,800
~~
~-
2,400
8,000
-~-
~-~Std
Dev
110.
3 Std Dev =106.3
400
106.00
Mean 11194
108.00
110.00
112.00
114.00
116.00
118.00
Std. Dev.1.87
Figure 4-1 Primary coolant flow rate distribution as an input for LSSS calculation
90
4.3.2 Heat Transfer Coefficient
The mean values for the HTC distributions are calculated using Carnavos correlation
as illustrated in section 3.4. The uncertainty for heat transfer coefficient estimation is
1.20, as documented in the EHCFs table in the SAR. However, again, how this subfactor was obtained is unclear. Therefore, the sub-factors in MITR-II SAR were
assumed to be three standard deviation values (3a) in this study. That is, the
uncertainty (1Y) of the heat transfer coefficient distribution is one third of 20%, which
is 6.7%.
Figure 4-2 shows the mean value and standard deviation of the HTC estimated for
node #7 for 189EOC core. Note that, the mean value of HTC for each node is
different due to the different local properties, but the standard deviations for them are
all assumed to be 6.7%.
91
99,994 Dispied
Norma Disttion
100.00m Tdals
HTC (W/m2-K)
-
-
~-
- ~
Notfor Comme
i/ Use
3,300
3,000
2,700
2,400
2100
1,800
SdDev
1
3
900o
600
-3 Std Dev =9.943.19
300
10,000.00
9,000.00
Mean 12436.00
11,000.00
13,000.00
12,000.00
14,000.00
15,00.00
Std. Dev.
Figure 4-2 HTC distribution as an input for LSSS calculation
92
0
.
4.3.3 Hot Channel Mass Flow Rate
The mean value of hot channel mass flow rate distribution is 0.2219 kg/sec, which is
obtained from primary coolant flow rate divided by the number of channels, along
with taking into account the core coolant flow factor and flow disparity factor, as
explained earlier in Chapter 3.
The uncertainty for hot channel flow rate is associated to the variations in water gap
distance because of fabrication tolerance. Due to multi-channel core design with
constant pressure drop in core region, when water gap distance is smaller than design
specification, less mass flow pass through the channel; whereas water gap distance is
larger than design specification, more mass flow pass through the channel.
The fabrication data for the LEU core cannot be determined at this stage. Therefore,
it is assumed that the fabrication distribution of LEU water gap is the same as that of
HEU's.
The data for the water gap distance of HEU was collected and analyzed in this study.
The data of channel scanning results of HEU was taken from element #243 to element
#364 (fabricated from 1994 to 2008), fabricated by Babcock & Wilcox [7]. Water gap
tip-to-tip distance was measured at 14 axial levels for each fuel element that total
1708 data entry were analyzed to obtain the fabrication distribution of water gap, as
depicted in Figure 4.3. The abscissa of Figure 4.3 is the deviation from the nominal
distance of water gap distance. The historic standard deviation (3a) for HEU water
gap distance was found as 5.4 mils, according to HEU water gap data analysis in
Figure 4.3. As explained earlier that the fabrication of LEU water gap distance is
assumed to be the same as that of HEU. Consequently, the standard deviation for
LEU water gap distance is 1.8 mil (lo).
The distribution in Figure 4.3, as reexamined by the Oracle Crystal Ball using best-fit
technique, is a normal distribution. Since water gap distance distribution is a normal
distribution, the maximum/minimum possible value of water gap distance is close to
the nominal value of LEU fuel (72 mils) plus/ minus three standard deviations (5.4
mils), which is 77.4 and 66.6 mils respectively.
Given the as-fabricated distribution of water gap distance, the distribution of HCMFR
can be obtained by assuming that frictional pressure drop, a major contributor to total
pressure drop, is the same for all flow channels. That is,
93
(Eq.4-5)
= (AP)OFF-NOR
(AP)NORMN
where frictional pressure drop can be expressed as [8],
p
L
PV
D,
2
p
2
(Eq.4-6)
and the frictional factor developed empirically for the MITR is [9]
f, = 0.316.-(e)-0.2s1
(Eq.4-7)
Next, combining Eq. 4-5 - 4-7, a conclusion can be made that the pressure drop
across channels is proportional to the product of
(h
75
. A-'.75. D,
1.
L-p02.p-1)
where A represents the cross-sectional flow area of a channel. Therefore, Eq. 4-5 can
be expressed as
(i
75
- A-'"
De-1.25 L-
0 2
P-1)NOMVAL _
l.75
-1'.7s.
e-s-
-
L*
02
-P')OFF-NRMAL
(Eq.4-8)
For simplicity, an assumption is made that the pressure drop is independent of Tvg
;
that is, pressure drop are assumed independent of the property terms listed in Eq. 4-8.
In addition, flow area A and hydraulic diameter De are proportional to water gap
distance J
, as can be seen in Eq. 4-9, and L is fuel length.
A=L6
D= 4-L
;'-29
2(L+.5)
if L>>,
(Eq. 4-9)
Therefore, Eq. 4-8 can be simplified as
=
(ln)
)
2
2
94
7
(Eq. 4-10)
Since the distribution for water gap distance is known (99.7% of water gap distance
value falls within the range 72 + 5.4 mils, as discussed earlier), the distribution of
HCMFR can be obtained using Eq. 4-10.
The uncertainty of HCMFR was determined using Monte Carlo Simulation on
Crystal Ball. After analyzing 100,000 samples generated by Oracle Crystal Ball, the
results show that the uncertainty is about 4.26% of the nominal value. The
distribution of HCMFR is shown in Figure 4-4.
95
DatAnalysis: DatSeries
00463
64
6
003
36
32
i
006
-.
24
201
Is
12
-3
Figure 4-3 i-storical off-normal water gap distance value for HEU collecting from
1994 to 2008
100,oTials
Normal Dsnbution
99.993 Diplaye
HCMFR (kg/sec)
Not for
omm cia/Us
-
3,000
2,700
2,400
5
21800
1.500
-2900
600
3 Std Dev -0.193
300
0.1900
Mean
0.2219
0.2000
02100
Std. Dev.
.0.2200
0.2300
0.2400
0.26W0
0.0095
Figure 4-4 HCMFR distribution as an input for LSSS calculation
96
0.2600
0
4.3.4 Power
As shown in Eq. 3-11 and Figure 3-11, LSSS is specified such that average outlet
temperature can be obtained if reactor power is given, or alternatively, a reactor power
(LSSS power) can be obtained if average outlet temperature is given. If the former
approach is used, reactor power is one of the inputs and therefore a power distribution
representative of power measurement uncertainty should be used as one of the input
parametric distributions. If the latter approach is used, reactor power is first solved
from the LSSS equation (Eq. 4-3, but <P> = P), and then the overall uncertainty of
power is obtained by propagating the power measurement uncertainty with the
uncertainties obtained in the previous step. The latter approach is used in this study
since the goal is to calculate the maximum allowable reactor given average outlet
temperature is 60*C.
The standard deviation for power is determined as 3.73%, which is the statistical
combination result (Eq. 2-2) of the uncertainties of reactor power measurement and
power density measurement/calculation listed in the EHCFs table (Table 3.3). Again,
the uncertainties of reactor power measurement and power density
measurement/calculation listed in the EHCFs table are assumed referring to three
standard deviations. Therefore, the one standard deviation for reactor power
measurement and power density measurement/calculation is respectively 1.66% and
3.33%. Combine these two uncertainties using root mean square (Eq. 2-2), the one
standard deviation for power is then obtained as 3.73%.
97
4.4 Results
In Chapter 3, it has been demonstrated that the analytical LSSS calculated based on
hot stripe factor (2.12) is more limiting than that based on radial power peaking factor
(1.76), and for conservatism the former is adopted. Therefore, the methodology
proposed in this Chapter is also focus on calculating LSSS based on hot stripe factor.
Since some input parameters used in LSSS calculation are set as distributions, LSSS
power obtained based on these parameters is also in a form of distribution. For
conservatism, LSSS power at (mean - 3a) value is taken as the reference value for
this methodology. Figure 4-5 shows the (mean - 3o) value of LSSS power for each
node. Like in Chapter 3 node #7 predicts the most limiting LSSS power in this
technique, as depicted in Figure 4-5.
When outlet temperature is specified as 60*C, the LSSS power at (mean - 3a) value
for node #7 is 9.1 MW, as depicted in Figure 4-5. This LSSS power is taken as the
reference value for the uncertainty propagation technique.
The data fitting performed on Crystal Ball indicates that the LSSS power distribution
obtained from Eq. 4-3 is also a normal distribution. Since this LSSS power is a
normal distribution, there is about 99.85% possibility that the actual LSSS power
limitation is higher than the (mean - 3a) LSSS power limitation 9.1MW. That is to
say, the probability of ONB occurrence is roughly 0.15% when operating power is
9.1MW.
98
16
14
*
node 1
-+-
10
8
U-
node 2
A
node 3
x
node 4
node 5
6
-0-
node 6
7
-node
4
--- node 8
2
-+node9
---
0
50
55
60
65
70
75
node 10
80
Tout(*C)
Figure 4-5 LSSS power of each node using uncertainty propagation technique
99
4.5 Summary
The input parametric distributions used in the uncertainty propagation methodology
are summarized in Table 4-3. As explained earlier, these distributions are set as
normal distributions. The most limiting LSSS power calculated using uncertainty
propagation methodology is 9.1MW, on node #7 of 189EOC core.
This study demonstrates a new methodology using direct uncertainty propagation of
several key underlying parameters, such as the water gap fabrication tolerances, heat
transfer coefficient uncertainty etc., to calculate the LSSS power explicitly for the
proposed MITR LEU core design. The advantage of this proposed methodology is
that the statistical uncertainties can be represented explicitly, as demonstrated in
section 4.4 that the probability of ONB occurrence is roughly 0.15% when operating
reactor power is 9.1MW. The LSSS power calculated using uncertainty propagation
methodology indicates that the deregulation in LSSS power limitation is plausible;
since the LSSS power calculated using this methodology (9.1MW) is higher than that
using analytical approach (8.3MW). Figure 4-6 compares the LSSS power obtained
using best-estimate, using EHCFs and using uncertainty propagation methodology.
As can be seen in Figure 4-7 and Table 4-4, the LSSS power obtained using
uncertainty propagation methodology is 0.8 MW higher than that obtained using
EHCFs when outlet temperature is 60*C.
100
Table 4-3 Input parametric distributions used in uncertainty propagation
methodology
Normallydistributed
parameters
Mean value
Uncertainty
Specification
Primary
coolant flow
rate <Wp>
111.938 kg/sec (converted
from 1800 gpm assuming T
=55 *C)
1.00+
0.0167(1a)
Mean+3 or
=-05
0.2219 kg/sec, calculated
from
1.00+
See ECHF table. Subfactors documented in
MITR SAR is assumed
that 3 sigma was
incorporated
This distribution was
derived from water gap
[(111.938/432)*0.921*0.93],
0.0426(10)
distance distribution
MFR in hot
channel
<m>
where core coolant flow
factor =0.921, flow disparity
factor = 0.93, and number of
channels =432
the calculated heat transfer
Heat transfer
coefficient <h>
coefficient ranges from
10094 to 12914 based on
local properties for each
node.
Mean value of LSSS power
LSSS Power
is computed that outlet
coolant temperature and
other parameters are
specified.
101
Source
where mean value is
72.0 mil and (mean +
3y) value are 66.6 and
77.4 mils
1.00+
See ECHFs table. Subfactors documented in
0.067(0)
SAR is assumed
MITR
Mean+3 a
-1.20
that 3 sigma was
~1'0incorporated
The one standard
deviation for reactor
power measurement and
power density
1.00± 0.0373 measurement/calculation
is respectively 1.66%
(lo)
Mean+3 .
and 3.33%. Combine
Mean+3
these two uncertainties
using root mean square
(Eq. 2-2), the one
standard deviation for
power is then obtained
J _as
3.73%.
Mea+28
16
14
~12
10
---
Using EHCFs
8
-+Best-Estimate
6
4_-U-Uncertainty
Propagation
2
0
50
60
70
80
Tout(*C)
Figure 4-6 LSSS calculated using three different approaches
102
Table 4-4 Summary for LSSS power obtained using different methodology
LSSS Power
Methodology
Description
(When Tout is
60"C)
EHCFs were set as 1.0. The input
parameters were set at their
nominal values and as single values
Best-estimate
Uncertainty
propagation
to obtain LSSS power in an
analytical manner. This dataset
shows the results of node #7, the
most limiting among the nodes of
189EOC.
EHCFs were set as 1.0. Some key
input parameters were set as normal
distributions to obtain a LSSS
power distribution. This dataset
shows the LSSS power at (mean3*S.T.D.) value that are calculated
by Crystal Ball based on node #7,
the most limiting among the nodes
11.1 MW
9.1 MW
of 189EOC.
EHCFs were set as what they were
documented in the SAR. The input
parameters were set at their
nominal values and as single values
EHCFs
to obtain LSSS power in an
analytical manner. This dataset
shows the results of node #7, the
most limiting among the nodes of
189EOC.
103
8.3 MW
References
[4-1]
MIT Nuclear Reactor Laboratory, "Safety Analysis Report for the MIT
Research Reactor," MIT-NRL- 11-02, August, (2011)
[4-2]
EPM Information Development Team, "Oracle Crystal Ball User's Guide
Fusion Edition" Release 11.1.1.3.00, 1988
[4-3]
N. Metropolis, , "The beginning of the Monte Carlo Method", Los Alamos
Science (1987 Special Issue): ppl25-130, 1987
[4-4]
J. W. Wittwer, , "Monte Carlo Simulation Basics" From Vertex42.com, June
1,2004,
http://www.vertex42.com/ExcelArticles/mc/MonteCarloSimulation.html
[4-5]
F. B. Brown, "Fundamentals of Monte Carlo Particle Transport" Los Alamos
National Laboratory, LA-UR-05-4983, Spring 2011 MIT Course Material
22.106
[4-6]
J. Yang, Y. Oka, J. Liu, Y. Ishiwatari and A. Yamaji, "Development of
Statistical Thermal Design Procedure to Evaluate Engineering Uncertainty of
super LWR" Journal of Nuclear Science and Technology, vol. 43, No.1, pp
32-42 (2006)
[4-7]
Babcock&Wilcox Nuclear Operation Group, "Certification Report
Massachusetts Institute of Technology Research Reactor Fuel Element," 1994-
2008
[4-8]
N.E. Todreas and M.S. Kazimi, "NuclearSystems I - Thermal Hydraulic
Fundamentals",Hemisphere Publishing, (1990).
[4-9]
S. Wong, L. W. Hu, M. Kazimi, "New Friction Factor Correlation For The
MIT Reactor Fuel Elements", Reduced Enrichment Test and Research
Reactors (RERTR) Conference Beijing, China, November 1-5, (2009)
104
Chapter 5 Sensitivity Study of LSSS
In this chapter, sensitivity of LSSS on several parameters is investigated. The
following sensitivity studies were conducted based on node #7 of core 189 EOC since
this is the most limiting case as concluded in Chapter 3. Some suggestions given by
experts concerning the update of some parameters involved in LSSS calculations are
also presented in this chapter.
5.1 The Update of Flow Disparity Factor
As explained earlier in section 3.3, flow disparity factor is defined as the ratio of
(minimum flow/average flow) for the coolant channels within a fuel element, which
was taken as 0.864 in the previous version of MITR-II SAR[1]. This factor is updated
and used in LSSS calculations based on discussions with experts from MIT-NRL and
ANL.
As documented in the SAR citing experimental results from the start-up test [2], 0.864
is the multiplicative result of the other two factors, 0.93 and 0.929. The first factor
0.93 represents the minimum flow through a fuel element is 93% of the average core
flow rate. The second factor 0.929 represents the ratio of the minimum channel flow
rate to the average channel flow rate within a fuel element is 0.929. As discussed
earlier, it is suggested to take the factor 0.929 out from the flow disparity factor to
avoid double-count. Therefore, flow disparity factor was changed from 0.864 to 0.93,
and the latter was used in this study for LSSS calculation.
Table 5-1 summarizes the calculated LSSS before and after the updating of flow
disparity factor. When the outlet temperature is fixed at 60'C, the update in flow
disparity factor results in approximately 0.4 MW increase in LSSS power. These
results are reasonable. As flow disparity factor becomes larger, it means flow
distribution moves towards closer to uniform distribution, and therefore there is more
coolant for the minimal flow channel. This fact surely gives more room to the upper
bond of safety limits LSSS power, as can be seen in Table 5-1.
105
Table 5-1 Changes in LSSS due to the change in flow disparity factor
106
5.2 Coolant Density Estimation
One of the LSSS criterions is that primary flow is at least 1,800 gallons per minute
(gpm) when the primary coolant pumps on both loops are active. As shown earlier in
Chapter 3, primary flow rate (kg/sec) and hot channel mass flow rate (kg/sec) are
involved in LSSS calculation. Coolant density is required when converting gallon per
minute into kilogram per second.
Table 5-2 shows how LSSS power would change with respect to the change in coolant
density at channel inlet when outlet temperature is fixed at 60*C, which is also one of
the LSSS criterions. The results show that the change in LSSS power due to the
change in coolant density is of insignificant importance. This effect is negligible
when coolant average temperature ranges from 40*C to 60*C with changes in LSSS is
within 0.03 MW.
107
Table 5-2 The resulting change in LSSS power when outlet temperature is fixed
at 60cC
Average
coolant
temperature
Coolant
density
[kg/ m3 ]
Primary flow
rate
[kg/s]
Hot channel
MFR
[kg/s]
LSSS Power
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
992.229
991.843
991.449
991.048
990.64
990.225
989.803
989.375
988.939
988.497
988.048
987.592
987.13
986.661
986.187
985.706
985.218
984.725
984.225
983.72
983.208
112.680
112.636
112.591
112.545
112.499
112.452
112.404
112.355
112.306
112.256
112.205
112.153
112.100
112.047
111.993
111.939
111.883
111.827
111.771
111.713
111.655
0.2234
0.2233
0.2232
0.2231
0.2231
0.2230
0.2229
0.2228
0.2227
0.2226
0.2225
0.2224
0.2223
0.2222
0.2221
0.2219
0.2218
0.2217
0.2216
0.2215
0.2214
8.392
8.391
8.389
8.388
8.386
8.385
8.383
8.382
8.380
8.379
8.377
8.376
8.374
8.372
8.370
8.369
8.367
8.365
8.363
8.362
8.360
108
5.3 Heat Transfer Coefficient (HTC)
5.3.1 Errors in Estimating Heat Transfer Coefficients
Heat transfer coefficient plays an important role in LSSS calculation for its impact on
cladding temperature. Carnavos correlation was used in this study to estimate HTC
due to its conservatism as explained earlier in section 3.4. The HTC calculated for
node #7 at core 189EOC is 12436 W/m 2 -K.
Table 5-3 shows how the LSSS power of node #7 at core 189EOC would change with
respect to the change in HTC when outlet temperature is fixed at 60*C. Figure 5-1
depicts the sensitivity of LSSS power on HTC. As expected, higher HTC means
better heat transfer, and therefore LSSS power, which plays similar role as safety limit
does, is expected to be higher. This trend can be observed in Table 5-3 and Figure 51 that over-estimation of HTC results in larger LSSS power. The results show that
LSSS power is sensitive to HTC so that the error of LSSS power is roughly within
±10 %, or equivalently ±0.9MW, given acceptable estimation error in HTC, say
within + 16%.
109
Table 5-3 The change in LSSS power with respect to the change in HTC when outlet
temperature is fixed at 60'C
HTC
Change in HTC Analytical LSSS Power Resulting Change in LSSS Power
2
-K)]
1%]
[MW]
[%]
[W/(m
-56.3%
-48.2%
-40.2%
-32.2%
-24.1%
-16.1%
-8.0%
0.0%
8.0%
16.1%
24.1%
32.2%
40.2%
48.2%
56.3%
5436
6436
7436
8436
9436
10436
11436
12436
13436
14436
15436
16436
17436
18436
19436
-45.2%
-37.4%
-30.1%
-23.2%
-16.9%
-10.9%
-5.3%
0.0%
5.0%
9.6%
14.1%
18.2%
22.2%
26.0%
29.5%
4.58
5.24
5.85
6.42
6.96
7.46
7.93
8.36
8.78
9.17
9.54
9.89
10.23
10.54
10.84
60%
40%
0
20%
-60%
0
.413%o
0 VO
-20%
20%
40%
-20%
1U
-40Y%
-60%
Error in HTC
Figure 5-1 Sensitivity of LSSS power on HTC
110
60%
5.3.2 Effect of Variation in Viscosity for Heat Transfer Correlation Calculation
Viscosity is strongly dependent on local fluid temperature and therefore is important
for the estimation of heat transfer coefficient (HTC) to obtain film temperature rise
and clad temperature. Dittus-Boelter correlation [3] takes properties from bulk fluid
while some correlations take properties from wall temperature, or the arithmetic mean
of wall temperature and bulk fluid. The effect of radial variation in viscosity for HTC
calculation, and how this effect could affect LSSS power are discussed in this section.
In research reactors, correlations usually used to compute HTC are Dittus-Boelter,
Sieder-Tate, Colburn and Petukhov correlation [3,4,5,6]. Besides these correlations,
Constantine et al. [4] proposed a modified Dittus-Boelter correlation accounting for
the variation of viscosity in radial direction. These correlations treat the variation of
viscosity in radial direction in different manners, as summarized in Table 5-4. A quick
calculation comparing the HTCs from these correlations is as follows. The conditions
used for this quick calculation are:
(1) Inlet coolant temperature Tin is 50*C;
(2) Pressure is 1.3 bar corresponding to saturation temperature 107*C;
(3) Primary flow rate is 1800gpm;
(4) Hot stripe factor is 2.12;
(5) Reactor power is 8.0 MW;
(6) 189EOC axial power distribution;
(7) Entrance effect is ignored since entrance length only accounts for ~10% of heated
length under turbulent conditions. *
* Entrance length for turbulent flow is z/D = 25-40. The diameter of the flow channels in MITR is
2e-3 m, therefore the entrance length is 0.05m-0.08m, which is about one-tenth of fuel rod length.
111
Table 5-4 Summary for correlations typically used to compute HTC in research
reactors
Correlation
Description
Dittus-Boelter
Nu = 0.023- Re0 8 -Pr 0-4
Modified DittusBoelter
Nu = 0.023- Re".-Pr-4 (pb )01
p
Sieder-Tate
Nu = 0.027 -Re
0 8Pr"3
Jub
Nu =0.023. Re08 -Pr0
Colburn
Where fluid properties
are taken from
All properties are taken
at the bulk temperature of
the fluid
All properties are taken
at the bulk temperature of
the fluid, except for the
term P.
All properties are taken
at the bulk temperature of
the fluid, except for the
term p,
)0.14
All properties are taken
at the film temperature,
the arithmetic mean
between the fluid bulk
and surface temperature,
except for the specific
heat that is evaluated at
fluid bulk temperature.
3
All properties are taken
Re. Pr
at the film temperature,
8
Nu=
1.07+12.7
between the fluid bulk
and surface temperature,
except for , except for the
8
Petukhov
where f
1
=
(1.8210g(Re)
Carnavos
the arithmetic mean
- 4 -( -1)p
0 . 0.0231 s
CaP.na o(5 Nu
)sec
"
Nu =0.023-Re-4
Aft
A.
112
term p,, and pb
-1.64)2
3
a
All properties are taken
at the bulk temperature of
the fluid
Since some HTC correlations take properties from wall temperatures, or from the
average of bulk and wall temperatures, iterations are required to compute HTCs based
on wall temperatures using the equation below,
Tfdg
) =7,,+
I~
()=
i
.
PHqh(z)dz +F
rCpf
0
o
h
(Eq. 5-1)
As explained earlier, since HTC is strongly and mostly dependent on viscosity, a
function (Eq. 5-2) correlating viscosities and temperature is used in conjunction with
Eq. 5-1 to compute cladding temperature through iterations. For properties other than
viscosity that are required to compute HTC, they are taken at coolant temperature of
55*C and pressure of 1.3 bar. Viscosities were obtained using an empirical correlation
shown as follows.
S= 0.0217 -T-0.-4
(Eq. 5-2)
Where p is viscosity and T is coolant temperature. The average mean absolute error
of Eq. 5-2 is within 1% in the range shown in Figure 5-2 comparing to the viscosities
computed using the International Association for the Properties of Water and Steam
(IAPWS) 1995 formulation [7], which has been widely used for general and scientific
purposes. Table 5-5 summarizes the HTCs and cladding temperatures at node #7 of
189EOC core using Eq. 5-1 in conjunction with different HTC correlations.
113
0.0008
0.0007
0.0006
M 0.0005
0.0004
--- Equation 5-2
0.0003
''LAPWS
Formulation 1995
0.0002
0.0001
0
0
20
40
60
80
100
120
Coolant Temperature ("C)
Figure 5-2 Comparison between IAPWS 1995 Formulation and simplified viscosity
formula
Table 5-5 HTCs and outlet clad temperatures computed using different correlations
Correlation
HTC (W/m2-K)
Cladding Temp (*C)
D-B
Modified D-B
Sieder-Tate
Colburn
Petukhov
14518
15444
17035
15553
19043
100.3
100.0
99.5
99.9
99.1
Carnavos
10685
102
Note: hydraulic diameter used for correlations above was calculated that (4 x actual
flow area)/(actual wetted perimeter) = 2.042e-3 m.
114
As can be observed in Table 5-5, after taking into account the effect of viscosity
variation in the radial direction, the HTC computed from modified D-B correlation is
6% larger than the original D-B correlation. This 6% increase in HTC, based on
Figure 5-1, could result in roughly 5% in LSSS power, which is of minor importance.
As demonstrated, Carnavos correlation predicts the most limiting HTC and cladding
temperature, and therefore is adopted in LSSS analyses. However, Carnavos
correlation does not have a counterpart incorporating the varying viscosity in radial
direction as the modified D-B correlation does. Consequently, how the varying
viscosity in radial direction could affect the HTC computed based on Carnavos
correlation is unknown at this stage, and it is expected that the ongoing experiment
conducted at the MIT-NRL can bridge this gap afterwards.
115
5.4 Local Fluid Temperature
In previous analyses we realized that LSSS is sensitive to the change in HTC. HTC
was calculated using Carnavos correlation in this study. Among parameters in
Carnavos correlation, viscosity is the one that is strongly dependent on local fluid
temperature. The purpose of this section is to investigate how the measurement error
of fluid temperature could affect the change in HTC and LSSS power.
As can be seen in Table 5-6, measurement error in local temperature has insignificant
impact on HTC, resulting in roughly the same magnitude of change in LSSS power.
As can be seen, 5 *C measurement error in local fluid temperature results in +2.5%
change in HTC, resulting in about +2% change in LSSS power. Consequently, it is
concluded that the change in LSSS power is within 0.3 MW if fluid temperature
measurement error is within 5*C.
116
Table 5-6 The change in LSSS power with respect to the change in local temperature
(viscosity) when outlet temperature is fixed at 60*C
Local Temperature
[*C]
HTC Change in HTC LSSS Power
2
[MW]
[%]
[W/(m -K)J
Change in
LSSS
Power
[%]
65
66
67
68
69
70
71
72
11409
11475
11540
11604
11668
11731
11794
11856
-5.7%
-5.1%
-4.6%
-4.0%
-3.5%
-3.0%
-2.5%
-2.0%
7.91
7.94
7.97
8.00
8.03
8.06
8.09
8.12
-3.7%
-3.4%
-3.0%
-2.7%
-2.3%
-2.0%
-1.6%
-1.3%
73
11918
-1.5%
8.14
-1.0%
74
75
76
77
78
79
80
81
82
83
84
85
11979
12040
12100
12160
12219
12277
12336
12393
12451
12507
12564
12620
-0.9%
-0.4%
0.0%
0.5%
0.9%
1.4%
1.9%
2.4%
2.9%
3.3%
3.8%
4.3%
8.17
8.20
8.22
8.25
8.27
8.30
8.32
8.35
8.37
8.40
8.42
8.45
-0.6%
-0.3%
0.0%
0.3%
0.6%
0.9%
1.2%
1.6%
1.9%
2.1%
2.4%
2.7%
117
5.5 Summary
The sensitivity analyses in this chapter give out a general idea how LSSS power could
change due to the uncertainties in parameters/properties, or due to the update of flow
disparity factor. Conclusions for the sensitivity analyses are summarized below.
(1) The update of flow disparity factor results in roughly 0.4 MW increase in
LSSS power. This updated disparity factor was used in this study for
analytical, best-estimate, and uncertainty propagation LSSS power
calculations.
(2) The estimation uncertainty in coolant density at channel inlet has been
demonstrated to be negligible for LSSS power calculation.
(3)
HTC is important for LSSS calculation. LSSS power is sensitive to HTC so
that the error of LSSS power is roughly within ±10 %, or equivalently
+0.9MW, given acceptable estimation error in HTC, say within + 16%.
(4) The uncertainty in LSSS power is within 0.3 MW if fluid temperature
measurement error is within 5"C.
118
References
[5-1]
MIT Nuclear Reactor Laboratory, "Safety Analysis Report for the MIT
Research Reactor," MIT-NRL- 11-02, August, (2011)
[5-2]
MITR-II Startup Report, MITNE-198, February 1977
[5-3]
Dittus, F. W., and Boelter, L. M. K. "Heat transfer in automobile radiators of
the tubular type." University of California, Berkeley, Publ. Eng. 2, pp.443-461,
1930.
[5-4]
Constantine P. Tzanos, "Heat Transfer Predictions by Turbulence Models and
Heat Transfer Correlations" Transactions of the American Nuclear Society,
Vol. 105, Nov. 2011
[5-5]
[5-6]
S. Kakag, R.K. Shah and W. Aung, Handbook of Single-Phase Heat Transfer,
A Wiley-Inter-science Publications (1987)
Y Sudo, H. Ikawa and M. Kaminaga, "Development of Heat Transfer
Package for Core Thermal-hydraulic Design and Analysis of Upgraded JRR3", International Meeting On Reduced Enrichment for Research and Test
Reactors (RERTR), Petten, The Netherlands, 14-16 Oct. 1985. pp. 363-372.
[5-7]
W. Wagnera. and A. PruBb., "The IAPWS Formulation 1995 for the
Thermodynamic Properties of Ordinary Water Substance for General and
Scientific Use", J. Phys. Chem. Ref. Data, Vol. 31, No. 2, 2002
119
Chapter 6 Safety Limit Calculation
6.1 Introduction
Safety limits are established to secure the integrity of the fuel cladding, that is to say,
to avoid fuel overheating. Critical heat flux (CHF) is normally used as the criterion
for fuel overheating. However, considering the MITR's flow channel is a
multichannel design, flow instabilities could possibly occur prior to reaching CHF
limitations. When onset of flow instability (OFI) occurs, it would have the effect of
reduced flow rate due to flow instability, hence lowering the CHF in the hot channel.
In the safety limit calculations, both CHF and OF are calculated and the lower one is
adopted as the safety limit for conservatism.
Since coolant in the MITR flows through parallel flow channels, Ledinegg instability
[1], or flow excursion instability could be a particular concern in such a parallel flow
path design, especially for research reactors having narrow flow channels. Figure 6-1
shows a demand curve [2, 3] describing the total pressure loss in a heated channel
versus the mass flow rate. As depicted in Figure 6-1, before entering the minimum
point B, which is defined as OFI (the onset of flow instability), the pressure drop
through the channel decreases as mass flow rate decreases. Beyond this point, as
mass flow rate decreases, pressure loss continually increases until fluid becomes
single vapor phase.
Operating between point B and point C in Figure 6-1 is considered unstable. The
trend in the region A-B is reversed at point B because plenty of vapor generation is
there mixing with the liquid core flow. At this point, a small negative perturbation in
mass flow rate at point B could result in the shifting to B' ,which leads to CHF
because the increase in pressure drop in single channel results in flow diversion to
other channels, or even to bypass flow path. As a result, substantial loss of channel
cooling could lead to burnout. The bubble blockage in flow channels is a dominant
cause for pre-mature CHF in low pressure system, such as low-pressure research
reactors due to flow instability.
CHF is essentially a boiling process transiting from nucleate boiling to film boiling.
Typically this transition is accompanied by a large increase in temperature on the
surface due to the sudden decrease in heat transfer performance. This localized
overheating could cause failure of equipment, and therefore it is important to
120
investigate when such a mechanism occurs, if there is any indication prior to its
occurrence, and if possible, any approaches to take to improve heat transfer during
such an undesirable transition.
Due to the extremely complex nature of two-phase flow with heat transfer, in spite
there have been numerous experiments conduct and theoretical models developed, the
mechanism of CHF is still not fully understood. For nuclear industry, design of
reactors therefore requires sufficient margin with regard to CHF to minimize the
possibility of cladding failure due to overheating.
121
constant q'(z)
liquid
Constant h y,
gas
A
I9
IL
a
L
TOE
L
/
B
D
O'region
01
two phase
single phase
liquid
0
Mass Flow Rate,
Figure 6-1 Channel pressure drop-mass flow rate behavior [2,3]
122
q'(z)
6.2 Onset of Flow Instability
Under some circumstances, for safety concerns a limit is set for the maximum
possible channel power due to a phenomenon called excursive-flow instability or
Ledinegg instability if coolant is likely undergoing a transition from single phase to
two-phase conditions when flowing through heated channels.
6.2.1 Introduction
Research reactor is different from power reactor given that research reactor is
primarily designed to generate neutrons for research purposes, instead of achieving
high power conversion efficiency. For this reason, a research reactor usually has
higher power density to attain relatively high neutron flux densities. High power
density is achieved by the compact core structure design with flow channels of small
hydraulic diameters.
For such a narrow channel design, the onset of significant void (OSV), the onset of
flow instability (OFI) and other relevant phenomena could occur. As can be seen in
Figure 6-2 [3], before entering to region I, subcooling prevails in that the flow is
mainly liquid single-phase flow. If heat is continuously applied, the heating surface
temperature increases, eventually exceeding the saturation temperature by a certain
extent, the incipient boiling then occurs, which is also known as ONB, referring to the
incipience of bubble nucleation on the heating surface. At this stage, bubbles do not
detach from the heating surface but grow and collapse before their contact with the
surrounding subcooled liquid. That is, bubbles are restricted to the immediate vicinity
of the heating surface (wall voidage).
In region II, bubbles begin to detach from the heating surface, which is defined as the
onset of significant void (OSV). At this stage, bubbles grow, detach from the heating
surface, and coexist with core flow, but are condensed when encountering the colder
zone in subcooled liquid core flow. The local increase in void content is important to
nuclear reactors because it influences reactivity via the change in neutron moderation
effectiveness, therefore changing the dynamic behavior of reactors.
The point ONB, OSV in Figure 6-2 can be referred in the pressure drop-mass flux
curve in Figure 6-3. OFI refers to the minimum point of the curve in Figure 6-3 [4].
As explained earlier, operating beyond the point OFI is considered unstable because
the trend beyond this point is reversed due to mixing of vapor generation with the
123
liquid core flow, therefore resulting in flow's diversion to other channels leading to
burnout.
Al
FEGION
a
I
REGION 11
OWALL
VIOIO$4E
DETACHED
VODAGE
II-T-
ff.-~
I
THERMODYNAMIC
EOUIUSRNJUM
VOID PROFILE
ACTUAL
g
I
PROFILE
DISTANCE ALONG HEATED SURFACE. Z
Figure 6-2 Void fraction variation along a uniformly heated channel [3]
Superbeated
single-phase
vapor Flow
Wall
voidage
Bulk boiling
Subcooled
single-phase liquid flow
AP
G
Figure 6-3 Schematic diagram of the demand curve for a heated channel with constant
heating rate [4]
124
6.2.2 Calculation of OFI for the MITR (Analytical Approach)
The point OFI was determined using a steady-state energy conservation equation,
which was proposed by J.E. Kowlaski [5],
FI=
R -c,(T., - TO
(Eq.6-1)
where
rhOFI is the channel mass flow rate when OFT occurs (kg/sec)
Q is the channel power (W)
R is the channel outlet subcooling ratio, (T.,- Tm)I(Tw, - T)
c, is the coolant specific heat (J/kg-0 C)
is the saturation temperature (*C)
T, is the channel inlet temperature (*C)
Ta,
T, is the channel outlet temperature (*C)
The channel outlet subcooling ratio, R, can be determined from one of the following
three equations [5, 6],
L
R=
1+25 D,
for 30 < -L<300 [6],
D,
(Eq. 6-2)
0.258, for 70 < 1L< 250 [7],
D,6
(Eq. 6-3)
Lh
R = 0.21 -In DD,)
for 100 < L% <200 [6],
D,
R = 0.697 + 0.00063.
Where for the MITR,
Lh
is the heated length of the coolant channel (m), which is 0.5842 m
D, is the equivalent diameter of the coolant channel (m), which is 2.042e-3 m
Lhis calculated as 286.1
De
125
(Eq. 6-4)
Therefore, we should apply Eq. 6-2 to calculate R. The parameters used in Eq. 6-1 to
calculate OFI is summarized in Table 6-1.
Substitute the parameters of Table 6-1 into Eq. 6-1 to calculate how much channel
power/reactor operating power it takes to induce OFI. The conversion from operating
power to channel power is also summarized in Table 6-1. The result shows that 12.46
MW is predicted to induce OFI.
126
Table 6-1 Parameters used to calculate OFI
Parameter
Channel outlet subcooling ratio, R
Value
0.9196
Source
From Eq. 6-2
At T-60*C P=1
4.18 kJ/ kg-*C
Coolant specific heat, cp
Saturation temperature
corresponds to pressure
1070C
Saturation temperature, Tat
bar,
is 1.3 bar
0
Channel inlet temperature, Ti,
Hot channel mass flow rate rh
42 C
0.2219 kg/sec
Q=( P 1e6).F
Converting reactor operating
power P (MW) to channel power
Q (W)Q(W)
cr
Assumption
See section 3.3
-FF
-F
e
432 )-0.965 -0.94 .2.12
=432
=(4.451e±3).P
=(
127
System parameters
6.2.3 Calculation of OFT for the MITR (Uncertainty Propagation Technique)
The results obtained in the previous section were obtained in a manner that every
parameter used is at their nominal value, without taking into account the parametric
uncertainty. In this section, the uncertainty of water gap distance, which is due to
fabrication tolerance, is incorporated to calculate OFI power.
As documented, the historical fabrication tolerance for HEU water gap distance is 5.4
mil (3a value). The fabrication tolerance of LEU is assumed to be the same as that of
HEU. Since water gap distance is a distribution, the parameters associated with water
gap distance, such as channel subcooling ratio R and channel mass flow rate, are also
distributions based upon the relation between water gap distance.
The equivalent diameter of the coolant channel De is a function of water gap distance.
Therefore, the channel outlet subcooling ratio R also changes with water gap distance.
In addition, as demonstrated earlier in Eq. 4-10, channel mass flow rate is associated
with water gap distance so that water gap of different dimension results in different
mass flow rate. How these parameters correlated with water gap distance and its
relevant geometry dimension are summarized in Table 6-2.
Similar to the uncertainty propagation technique used in LSSS calculation, R and
mass flow rate in Eq. 6-1 are in brackets <>, representing that they are distributions,
as shown in Eq. 6-5.
< rhmR
*F
Where < Q >=
N
>=
Q
<JR>-c,(~T,,-T j)
-FF,and < R >=
(Eq. 6-5)
1
co1+25<D,>
Lh
The uncertainty for reactor power is also taken into account such that 3.73% is used in
the OFT analyses, which is similar to the LSSS analyses.
According to the Monte Carlo simulation on Crystal Ball, the reactor power at (mean3a) value inducing OFI is 10.41 MW. Recall that the most limiting LSSS power
using uncertainty propagation is 9.1 MW, as concluded in Chapter 4. These imply
that the margin between OFT and operating power is sufficient given the fact that the
proposed relicensing power of the MITR is 7 MW.
128
Table 6-2 Parameters set in a form of distribution for OFI/CHF calculation
<R
Outlet subcooling ratio
<P>
____ ____
Relationship to water gap distance 8
Definition
Parameter
1
<De > is associated with <5>. See below
for details.
>=
1+25
____
____Lh
Equivalent diameter
<De>
Actual flow area
<A>
<De> =(4 x actual flow
<De>=(actual w
area)/(actual wetted
perimeter)
<A>= channel width x
( water gap + 2 x fin
height) - number of fins per
channel x single fin area
Actual flow area and perimeter are
associated with <S>. See below for details.
<A>=5.8623E-02x ( <&> +2x 2.5400E-04)
- 220x 6.4516E-08
Actual wetted perimeter
<Pw>= channel width x 4 +
<P,>=5.8623E-02x 4+( <5>+2x 2.5400E-
<P,>
(water gap+2x fin height) x
2
04)x 2
Channel mass flow rate
Mass flow rate inside the
12
<sow>
___________________ __
_
__i__
chiEnel
_
__
_
129
_
- , shown in Eq. 4-10.
4-10
62J
)(=j-I
6.3 Critical Heat flux
6.3.1 Introduction
Critical heat flux (CHF) is the phenomenon accompanied by a large increase in
temperature on the heated surface due to the sudden and substantial decrease of heat
transfer performance. This localized overheating of heating surface could lead to
undesirable increase in fuel temperature that fuel cladding could lose its integrity.
Sudo et al. [8] proposed a CHF correlation scheme for research reactors using flatplate-type fuel, as shown in Figure 6-4. For the MITR, forced convection is the heat
transfer mechanism during normal operation that coolant flows upward through the
vertical rectangular channels.
The CHF correlation used for forced upflow in MITR is a modified version proposed
by Sudo taking into account the effect of channel outlet subcooling [8], that was
applied in high mass flux region as depicted in Figure 6-4,
.
,g.61
5000
.
qCHF =0.005 -G
.(1+
.ATsuo)
G*
where qCHF
CHF
hfg - 2Agpg(pf - pg)
G
G Agp (P, - Pg)
ATs*u,o =
C
a-(T,,
-T,,),
hfg
F
=
10.5
(
-0j
(characteristic length)
g -( p, - p, )
g is the acceleration due to gravity,
hf, is the enthalpy difference fluid and gas phases,
pf is fluid density,
130
(Eq. 6-6)
p8 is gas density,
o is the surface tension
Regarding CHF for natural convection, Sudo suggested the minimum CHF for upflow
forced convection that corresponds to a condition that the flow become stagnant, the
low mass flux region in Figure 6-4, is used as the CHF for natural convection. The
flow is under counter-current flow limitation (CCFL) while the water moving
downward coexists with the steam/bubbles moving upward. CHF is closely related to
CCFL, and the correlation used for such a situation, which also applies to natural
convection, is
.A
vWIA
qCHF=0.7 -
Am [+(,
where A is cross-sectional channel flow area,
AH is heated area of the channel,
W is channel width
131
/Pf )o.2s
(Eq.6-7)
Low mans ffua
Medium mass flux
IHigh mass flux
ase of
A'TUBO
qICIIF
(-)
GG
)
Figure 6-4 CHF correlation scheme proposed for research reactors using plate-type
fuel (adopted from [8])
132
6.3.2 Root Mean Square Error of Sudo's CHF Correlation
The modified CHF correlation (Eq. 6-6) is a best-fit result from experimental data.
Figure 6-5 [8] compares CHF's prediction using Eq. 6-6 and the experiment results.
Both upflow and downflow experiment results are shown in this figure while the
coolant in the core of the MITR flows upwards. As can be seen in Figure 6-5, Sudo's
CHF prediction allows the root mean square error (RMSR) of 33 percent to the lower
limits of the experimental data.
Indeed, some experimental data are 33% outside the upper limits of Sudo's CHF
prediction, as shown in Figure 6-5, but this fact is of insignificant importance to the
safety limit calculation because safety analyses focus on the lower limit of CHF
prediction, instead of the upper limit. Therefore, 33% RMSR is adopted as the basis
for CHF prediction uncertainty for subsequent analyses, as shown in section 6.3.4.
133
100,
100
.
o UPFLOW
o
*DOWNFLOW
6
+33%
E
-33%
000
10
LL0
-
o
10
10 0
q*
(-
Figure 6-5 Comparison between Sudo CHF prediction and experiment result[8]
134
6.3.3 Calculation of CHF for the MITR (Analytical Approach)
Eq. 6-6 is used to estimate the forced convection CHF for the MITR. Table 6-3
summarizes the parameters used in CHF calculation for the MITR. The CHF on the
hottest spot of the MITR is calculated in this section. The hottest spot is node #5 of
189EOC core, which is close to the midplane of the heated region, as can be seen in
Figure 3.2. Therefore, the properties used for CHF calculation is based on the
estimated local condition of this node. The estimated pressure for this node is 1.49
bar and saturation temperature is 111. PC.
The calculated CHF for node#5 is 3.22 x10 6 W/m 2 , which is equivalent to 70 MW
reactor power with a hot stripe factor of 2.12. However, as shown earlier in Sudo's
study [8] that 33% reduction should be made to reflect the uncertainty in Sudo's CHF
correlation. As a result, a conservative estimate of forced convection CHF using
analytical approach is taken as 2.16 x106 W/m.
In contrast, the CHF calculated for the natural convection mode using Eq. 6-7 is
2.307 x 10 4 W/m 2, which corresponds to a reactor power of 504 kW with a hot stripe
factor of 2.12. However, upon taking into account the uncertainties associated with
reactor power measurement (5%) and power density analysis (10%) as documented in
the EHCFs table, the reactor power corresponding to a dry-out condition becomes 448
kW. A reactor power of 400 kW is conservatively adopted as the safety limit as
proposed in this study.
135
Table 6-3 Parameters used in CHF calculation for the MITR
Parameter
Value
Saturation temperature Tsa
111.1 0C
Mass flux of hot channel G
Outlet temperature for hot
channel Tot
1817.36
kg/m2-sec
82.9 0 C
Source
Saturation temperature corresponding to
the estimated pressure at node #5 of
189EOC
Hot channel MFR 0.2219 kg/sec divided
by the actual flow area 1.221E-04 m2
Assuming channel inlet temperature is
43*C, which is the average channel inlet
temperature. Operating reactor power is
8.4MW, which is 120% Of the proposed
relicensing power for the MITR
Normalized axial power shape
at node #5
Heat transfer area for a
channel
0.1275
0.12357 m2
.137mMIRgoer
136
189EOC
M1TR geometry
6.3.4 Calculation of CHF for the MITR (Uncertainty Propagation Technique)
The results obtained in the previous section were obtained in a manner that every
parameter used is at their nominal value, without taking into account the parametric
uncertainty. In this section, the uncertainty of water gap distance, which is due to
fabrication tolerance, along with the correlation error stated in Sudo's study [8], are
incorporated to calculate CHF power.
Analogous to uncertainty propagation technique used in LSSS calculation, G*,
ATUB,
and q*HF in Eq. 6-8 are in brackets < >, representing that they are in a form of
distribution as input to calculate CHF. How these parameters relate to water gap
fabrication tolerance can be found in Table 6-2.
>0611
qCHF
>= 0.005-<G* ><
whr=<T
.
5000
<G>
E
ATsUB,o >)(Eq.
6-8)
6-8)
Cf -(T-<O,>
where < ATSUB,o
in
.(l+
±
hfg
satout
P -FO,,,,- F , -F,.Fs
N .c,-<ih >
<G>
2gp,(p,-p,)
<cm>
<A>
1
Vgp,(pf-pg)
As documented, the historical fabrication tolerance for HEU water gap distance is 5.4
mil (3cy value). The fabrication tolerance of LEU is assumed to be the same as that of
HEU. Since water gap distance is a distribution, the parameters which are directly
linked to water gap distance, such as hot channel mass flow rate and mass flux are
also distributions. Since mass flux changes with water gap distance, coolant outlet
temperature also changes. The latter can be verified by energy balance. How these
parameters correlate with the change in water gap distance is summarized in Table 6-4.
Note that HCMFR is used as the mass flow rate for hot stripe analyses in this study.
The uncertainty of CHF correlation is also included in CHF calculation using
uncertainty propagation methodology. Since all data falls within 33% of the lower
137
limit of Sudo's correlation, assuming 33% corresponds to 3a such that 11% error
corresponds to la. This uncertainty was specified as STD when generating the
normal distribution representing CHF distribution.
The CHF calculated at (mean-3a) value is 2.14 x 106 W/m 2, which is equivalent to
47 MW reactor power with a hot stripe factor of 2.12.
138
Table 6-4 Parameters that were set in a form of distribution for CHF calculation
Relationship to water gap
Definition
Parameter
____
_____
______
____
___
___
___
___
___
8
___distance
12
MFR inside the hot channel
HCMFR, rh
, please see section
4.3.3.
Actual flow area, A
Hot channel mass
flux, G
Outlet temperature,
To'tChannel
CHF, q*
A= channel width x ( water gap + 2 x fin
height) - number of fins per channel x
single fin area
G =(HCMFR)/(actual flow area)
outlet temperature
""_
_
_S
Critical heat flux predicted using Sudo's
correlation
139
A=5.8623E-02 x ( 6 +2 x 2.5400E04) - 220 x 6.4516E-08
Combination result of the above
two
(Channel power/(HCMFR* Cp)) +
Ti., where HCMFR is correlated to
as shown above
Since all data falls within 33% of
the lower limit of Sudo's
correlation, assuming 33%
corresponds to 3a so that 11%
error corresponds to la is used as
the STD for the normal
distribution representing the error
of CHF
6.4 Comparison between OFI and CHF
As concluded and verified in the SAR, OF is actually a more conservative estimate
than CHF when it comes to safety limit for forced convection operating modes. That
is equivalent to saying, CHF occurs after OFI. There has been various research
reactors that take advantage of this phenomenon in how their safety limits are
calculated based on OH instead of CHF. In this section, this conclusion is reexamined for the proposed LEU design. Both the analytical and (mean - 3a) value
of CHF and OFI were calculated, as can be seen in sections 6.2 and 6.3. These values
are summarized in Table 6-5. For conservatism, the CHF and OH at (mean - 3a)
values are adopted.
As summarized in Table 6-5 that the heat flux inducing OFI is about 12 times smaller
than that of CHF. Note that CHF is a localized phenomenon while OFI is a universal
effect within a flow channel. That is, the CHF calculated in Table 6-5 is specifically
for the hottest point of 189EOC and the heat flux inducing OH is calculated for the
whole channel. To take into account this difference, the axial peaking factor of
189EOC, 1.26, should be incorporated into the analysis. As a result, after taking into
account the axial power peaking factor, the heat flux inducing OH is roughly 9.5
times smaller than CHF. Which means, for the transients characterized by ascending
heat flux due to loss of cooling or unexpected power excursion, OH occurs prior to
CHF. Therefore, OH is adopted as the safety limit for the proposed LEU design in
this study for conservatism.
140
Table 6-5 Comparison between OH and CHF
Mean value of OFI
(Mean - 3a) value of OF
Their occurrence with
respect to reactor
power (MW)
12.4
10.4
Mean value of CHF
70
(Mean - 3a) value of CHF
47
OFI/CHF
141
Maximum local heat flux
(kW/m 2)
5.71 x 102
4.78 x 102
3.22 x 10 3
2.14 x 10 3
6.5 Summary
Both CHF and OFI are analyzed in this study to decide which one should be adopted
as the safety limit, which is set to avoid the overheating of fuel cladding, for the
proposed LEU design. These two criterions are calculated respectively using
analytical approach and uncertainty propagation methodology. The CHF and OFI at
(mean-3a) value using uncertainty propagation methodology are adopted for
conservatism.
The CHF calculated at (mean-3a) value is 2.14 x 106 W/m 2, which is equivalent to
47 MW reactor power with a hot stripe factor of 2.12 while the OFT power at (mean3a) value is 10.4 MW. That is, OFT is more limiting than CHF and therefore is
adopted as the safety limit. The margin between the LSSS power using uncertainty
propagation 9.1MW and the calculated OFT power 10.4 MW is 1.3 MW, which is
sufficiently enough from the perspective of safety.
142
References
[6-1]
M. Ledinegg, "Instability of flow during natural and forced circulation." Die
Wirme (translation in USAEC-tr-1861) 61-4: 891-898, 1938.
[6-2]
T. Dougherty, C. Fighetti, E. McAssey, D. G. Reddy, B. Yang, K.F. Chen, and
Z. Qureshi, "Flow Instability In Vertical Down-Flow At High Fluxes" Heat
transfer in high energy/high flux applications, Vol. 119 pp.17-23, 1989
[6-3]
N.E. Todreas and M.S. Kazimi, "NuclearSystems I - Thermal Hydraulic
Fundamentals",Hemisphere Publishing, 1990.
[6-4]
S. M. Ghiaasiaan and R. C. Chedester "Boiling incipience in microchannels"
Int. J. Heat Mass Transfer, International Journal of Heat and Mass Transfer 45
(2002) 4599-4606, April 2002)
[6-5]
J.E. Kowlaski, et al., "Onset of Nucleate Boiling and Significant Void On
Finned Surfaces", ASME, FED 99:405-411, 1990.
[6-6]
R. H. Whittle and R. Forgan, "A Correlation for the Minima in the Pressure
Drop Versus Flow Rate Curves for Sub-Cooled Water Flowing in Narrow
Heated Channel," Nuclear Engineering and Design, Vol. 6, 1967.
[6-7]
T. Dougherty, et. al., Boiling Channel Flow Instability, ASMEJSME Thermal
Engineering Proceedings, Vol. 2, ASME, 1991.
[6-8]
Y Sudo and M. Kaminaga, "A New CHF Correlation Scheme Proposed for
Vertical Rectangular Channels Heated From Both Sides in Nuclear Research
Reactors", Journal of Heat Transfer, Vol.115 pp. 426-434, May 1993
143
Chapter 7 Natural Convection LSSS Calculation
7.1 Introduction
The MITR is designed to be passively safe such that natural circulation and antisiphon valves (NCVs and ASVs) come into play whenever forced convection, the
main heat removal mechanism during normal operation, is not sufficient to remove
heat from the core region during transients. The anti-siphon valves make natural
circulation possible. Figure 1-4 [1] illustrates the flow path for natural circulation
comparing the flow path for forced convection during normal operation, as depicted
in Figure 1-5 [1]. Four NCVs were located at the bottom of the core tank while two
ASVs were installed inside the core tank at the same elevation of the primary inlet
pipe.
Both the NCVs and ASVs are ball-type check valves. During normal operation,
coolant pressure forces the ball to the top of the shaft, blocks the top aperture of the
valves and therefore valves are closed. However, when primary flow rate decreases to
certain level, the ball falls down since under such a condition coolant pressure is not
enough to sustain the weight of the ball. As a result, valves are open enabling natural
circulation.
As depicted in Figure 1-4 [1], the hot coolant leaving the core rises within the core
tank, mixes with cold coolant in the outlet plenum, reverses, flows through the NCVs
and/or ANVs, and finally flows back through the core region completing the natural
circulation loop.
The thermal-hydraulic computer code RELAP5/mod3.3 [2] is used to analyze the
LSSS under natural circulation modes. The input deck [3] that was originally built for
analyzing loss of flow transient (LOF) is slightly modified to calculate the LSSS
under natural circulation mode. Two cases are analyzed in this study: first, both the
ASVs and NCVs are open, second, only the NCVs are open. The first case describing
the low-power operation situation without forced primary flow while the second case
may occur if the coolant level drops below the ASV (about 6.4 feet above top of the
core).
144
7.2 Introduction to RELAP5/Mod3.3
Reactor Excursion and Leak Analysis Program, abbreviated as RELAP, is a series of
computer code designed to simulate the behavior of light water reactor (LWR)
systems during normal operation and postulated accident conditions. The precursor of
RELAP is RELAPSE (Reactor Leak And Power Safety Excursion), which was
released in 1966. RELAPSE, RELAP2[4], RELAP3[5] and RELAP4[6] were all
based on homogeneous equilibrium model (HEM) assuming that velocity, temperature
and pressure are the same in two phases of fluids. In 1976, the development of a nonhomogeneous, non-equilibrium model was undertaken. This process is the beginning
of the RELAP5 project [7].
This code was developed for the U.S. Nuclear Regulatory Commission (NRC) for use
in rulemaking, licensing audit calculations, evaluation of operator guidelines, and as a
basis for a nuclear plant analyzer. In cooperation with several countries and domestic
organizations that were members of the International Code Assessment and
Applications Program (ICAP) and its successor organization, Code Applications and
Maintenance Program (CAMP), the NRC developed RELAP5/MOD3, a code version
suitable for the analysis of all transients and postulated accidents in LWR systems,
including both large and small-break loss-of-coolant accidents (LOCAs) as well as the
full range of operational transients.
The principal new feature of the RELAP5 series was the use of a two-fluid, nonhomogeneous, non-equilibrium, hydrodynamic model for transient simulation of the
two-phase system behavior.
Note that the coolant channel of MITR is finned. However, RELAP5/MOD 3.3 does
not have heat transfer package specifically for finned hydraulic geometry. The
alternative approach taken in this study is, treating finned channel as smooth channel
and adjust some of the geometry parameters accordingly (material thermal properties
were also changed accordingly).
145
7.3 RELAP5 Input Deck for the MITR
The RELAP5 steady-state input deck for the MITR was prepared by S. J. Kim, a
senior researcher at MIT-NRL [3]. Several minor edits were made in the input deck in
this study to calculate LSSS during natural convection.
Several kinds of hydrodynamic components, such as pipes, single volumes, valves,
and time-dependent volumes were deployed, interconnected with junctions or timedependent junctions to simulate the primary flow path geometry of MITR's coolant
system in the input deck. The coolant system consists of cold leg, coolant pump,
downcomer, lower plenum, reactor core, flow shroud, mixing area, and hot leg.
The flow channels of the proposed LEU core are simulated using pipe components.
These pipes are axially divided into ten nodes. Node 1 is the node at the bottom of
the channels and node 10 is the node at the top end. The flow channel receiving the
highest power in the LEU core is defined as the hot channel in RELAP5 input
hydrodynamic model while other flow channels are defined as average channels. Hot
channel model is constructed in accordance with the actual dimension of a single flow
channel in MITR while other flow channels were lumped into a large one simulated as
average channel, as depicted in Figure 7-1 [3].
Heat structure was attached to the hydrodynamic model to simulate the power
generated in fueled region. The power distribution within the models, both in axial
direction and radial direction, were set in accordance with the power distribution in
MITR. The power generated within the hot channel model is featured by hot stripe
peaking factor 2.12 and both the axial power distribution of hot channel and average
model is set using 189EOC core.
Four natural convection valves and two anti-siphon valves were modeled for natural
convective heat removal, which is the heat transfer mechanism during LOF. In the
input deck, these valves were respectively lumped into one for simplicity. This
procedure might not be able to truly reflect the local flow conditions, especially in the
vicinity of the valves, but from the perspective of bulk flow, the result is agreeable.
The schematic nodalization of RELAP5/MOD3.3 input deck for MITR is shown in
Figure 7-1 [3].
Under normal conditions, the MITR operates with a primary coolant flow rate of
146
2,000 gpm. If primary coolant flow rate drops below 1900 gpm, a scram signal is
automatically actuated. Followed by the initiation of low flow scram signal, the shim
blade magnets are de-energized and then all six shim blades drop at the core periphery.
Two events might result in low primary coolant flow rate: loss of off-site electric
power and pump coast down accident due to pump hardware failure. The later might
be caused by malfunctions of motors or failures of pump power supply. In both case,
the MITR loses primary flow via pump coast down. The pump coast down curve
used in RELAP5/mod3.3 is,
Q = -3.36376- t 3 +83.86236 t -
where
698.94871- t + 2004.99719
Q is gallons per minute and t is time in seconds.
(Eq. 7-1)
This new curve fit was
obtained when the heat exchanger outage was performed [8].
To simulate the scenarios of LOF, relevant trips settings and tabulated data in input
deck were constructed. The simulated LOF scenarios begin with reactor scram signal
actuation at 0.0 seconds. In contrast to step reactivity insertion applied in MULCH,
which was mentioned in Ko's study [1], ramp reactivity insertion was applied in
RELAP5/MOD3.3 simulation that -7.5 beta of reactivity was introduced between 1.3
and 2.3 seconds after reactor scram. Shim blade insertion is assumed to have one
second delay to reflect the signal transmission delay in real situation.
The assumption that the shim blade insertion takes 1.3 seconds is based on MITR
shim bank integral curve [9]. The heat removal mechanism during LOF transient is
natural circulation. During which natural circulation valves and anti-siphon valves
are open since the pressure applied on the balls blocking on the aperture of valves
decreases during LOF. In RELAP5/MOD3.3 simulation, these valves were manually
set to open on 4.4 seconds after the scram signal.
Thermo-physical properties, such as thermal conductivity (k) and volumetric heat
capacity (p xCp) of fuel meat and cladding were entered in RELAP5/MOD3.3 input
deck based on Ref. [10, 11]. Thermal conductivity of cladding material Al, and base
of fin and fuel surface material Zr, are set as constants while thermal conductivity and
volumetric heat capacity of fuel meat are temperature-dependent.
147
Hot leg
105
20113
Mixing area 1
107
106
204
108
Flow shroud
02208
210
3011
401
501
.21L ~~~-
FFuel110
bottom
Figure 7-1 RELAP5 Nodalization of MITR [3]
148
7.4 Natural Convection LSSS Calculation
Two cases are analyzed in this study using RELAP5/mod3.3: both the ASVs and
NCVs are open and only NCVs are open. The first case describing the low-power
operation situation without forced primary flow while the second case may occur if
the coolant level drops below the ASV (about 6.4 feet above top of the core).
The calculations are performed assuming that the reactor is at 1 MW before a loss of
primary flow (LOF) occurring at t=300 second and the data required for LSSS
calculation is retrieved at where reactor power is at 100 kW, as depicted in Figure 7-3.
Coolant inlet temperature is assumed as 60 *C, because the resistance temperature
detector (RTD) located at the outlet pipe level cannot measure the instantaneous core
outlet temperature due to slow coolant mixing in the upper core tank region during
natural convection.
The criterion for the LSSS during natural convection is the avoidance of ONB, which
is the same as that in forced convection. Recall that the margin to ONB ATONB can be
calculated using,
ATONB=
TONB-
T
(Eq. 7-2)
Where
( hs
7ONB
Tcla dT
0.0234
)
2.16
1082-p
+
1.8
Tin
ZH
+
mc
q
,(Hqhs)dz+FA
h(Z
hs
h
The difference between calculating LSSS in natural convection and forced convection
is that the HTCs, pressures, and HCMFR are directly retrieved from RELAP5 instead
of using hand calculation. This is because (1) this study mainly focuses on the forced
convection LSSS, which also receives more attention in license application, and (2)
for simplicity.
The margins to ONB for both cases are summarized in Table 7-1 and Table 7-2. To
make sure the HTCs computed by RELAP5 is based on laminar flow condition, which
is expected to occur in natural convection, Reynolds number is also retrieved from the
149
data. As can be seen in Tables 7-1 and 7-2, the Reynolds number for each node is
well below 2,200, indicating that viscous effect are dominant and laminar flow
prevails.
The margins to ONB are adequate during natural convection since the minimum
margin to ONB is about 36.4*C for both cases, as demonstrated in Tables 7-1 and 7-2.
150
1.20E+06
1.OOE+06
8.00E+05
0
6.OOE+05
0
U
M 4.OOE+05
cc
2.OOE+05
O.OOE+00
400
200
0
600
1400
1200
1000
am
1600
Time (s)
Figure 7-2 Decay power changes with time (initial power is set as 1MW)
Table 7-1 Cladding temperature and temperature inducing ONB at each node (both
the NCVs and ASVs are open)
node 1 node 2 node 3 node 4 node 5 node 6 node 7 node 8 node 9 node 10
Reynolds
Number
451
455
458
461
464
467
468
469
468
467
Hot stripe HTC
(W/m 2 -K)
1698
1704
1710
1716
1720
1725
1728
1729
1728
1727
Pressure at hot
1.26
1.26
1.25
1.24
1.24
1.23
1.23
1.22
1.22
1.21
4053
3883
4080
4149
4120
3961
3444
2561
1260
632
64.09
64.96
66.15
67.26
68.30
69.20
69.70
69.71
69.08
68.78
Temperature that 10724
induces ONB ("C)
107.09
107.00
107.0
106.86
10
106.72
40.85
39.60
38.42
stripe (bar)
Heat flux at hot
stripe (W/m2)
Cladding
temperature at
hot stripe (*C)
Margin to ONB
("C)
43.15
42.13
I
I
106.57 106.40 106.15 105.80
_____
37.37
I
151
0
___0
36.70
II
105.51
00
36.44
36.72
36.73
Table 7-2 Cladding temperature and temperature inducing ONB at each node (Only
NCVs are open)
node 1 node 2 node 3 node 4 node 5 node 6 node 7
Reynolds
node 8 node 9 node 10
482
486
489
493
496
498
500
501
500
499
npe HTC
1725
1732
1738
1743
1748
1752
1756
1757
1756
1754
Pressure at hot
stripe (bar)
1.26
1.26
1.25
1.24
1.24
1.23
1.23
1.22
1.22
1.21
Heat flux at hot
4128
3951
4151
4221
4190
4029
3502
2604
1280
642
64.10
64.96
66.15
67.26
68.29
69.19
69.68
69.69
69.06
68.76
107.00 106.87
106.73
106.58 106.40
106.15
105.80
105.51
38.44
37.39
36.46
36.75
36.76
_
_
Number
Hot
stripe (W/m 2)
Cladding
temperature at
hot stripe (*C)
Temperature that 107.27 107.09
induces ONB (*C)
Margin to
ONB(0 C)
43.17
42.14
40.86
39.61
_
_
_
152
36.72
________
I_
7.5 Summary
RELAP5/mod3.3 is used to calculate the LSSS during natural convection mode. In
RELAP5 settings 300 hundred seconds of steady state calculation is performed prior
to the actuation of LOF The initial reactor power is assumed as 1MW and the data
required for LSSS calculation are retrieved when the reactor power drops to 100kW.
The results show that the margin to ONB is adequate for the two cases: both NCVs
and ASVs are open and only NCVs are open. The results of these two cases are very
close. The minimum margin to ONB is about 36.4*C for both cases as summarized in
Table 7-6.
153
Table 7-3 Calculated Coolant Temperature Rise and Film Temperature Rise for
Natural Convection Operation
Parameter
NCV&ASV
NCV only
Flow rate through
0.0133
0.0136
Tin (*C)
60
60
Tclad, max (0C)
69.71
69.69
TONB (*C)
106.15
106.15
Margin to ONB
3644
36.46
hot channel (kg/s)
ATONB (0C)
154
References
[7-1]
Y. C. Ko, "Thermal Hydraulic Analysis of the MIT Research Reactor in
Support of a Low Enrichment Uranium (LEU) Core Conversion",
SM Thesis, MIT NSE Department, January 2008.
[7-2]
Nuclear Safety analysis Division, "RELAP5/MOD3.3 Code Manual
Volume II: Appendix A Input Requirements" Information
Systems Laboratories, Inc. March 2006
[7-3]
S. J. Kim, Memorandum to MIT-NRL, June, 2011
[7-4]
K. V. Moore and W. H. Rettig. RELAP2 - A Digital Program for Reactor
Blowdown and Power Excursion Analysis. IDO-17263. Idaho National
Engineering Laboratory. March 1968.
[7-5]
W. H. Rettig et al. RELAP3 - "A Computer Program for Reactor Blowdown
Analysis", IN-1445. Idaho National Engineering Laboratory. February 1971
[7-6]
K. V. Moore and W. H. Rettig. RELAP4 - "A Computer Program for Transient
Thermal-Hydraulic Analysis. ANCR-1127", Idaho National Engineering
Laboratory. March 1975.
[7-7]
V. H. Ransom et al. "RELAP5/MOD1 Code Manual, Volumes 1 and 2",
NUREG/CR-1826, EGG-2070. Idaho National Engineering Laboratory.
March 1982.
[7-8]
T. Newton, "Pump Coastdown", Memorandum, Nuclear Reactor Laboratory,
May 2011
[7-9]
[7-10]
MITR Staff, "Safety Analysis Report for the MIT Research Reactor
(MITR-III)", Chapter 4, MIT Nuclear Reactor Laboratory, July 1999.
Research reactor core conversion guidebook, Vol. 4: Fuels (Appendices I-K),
IAEA-TECDOC-643, IAEA.
[7-11]
D. E. Burkes, G. S. Mickum, D. M. Wachs, "Thermophysical properties of
U-OMo Alloy", INL/EXT-10-19373, INL, November 2010.
155
Chapter 8 Conclusions and Recommendations
8.1 Conclusions
Thermal hydraulic limits are established to guarantee there is adequate margin
between normal operations and safety limits. Previous works in analyzing the impact
of engineering uncertainties on thermal hydraulic limits via the use of EHCFs makes
meeting the ONB criterion difficult at sufficient power, due to the large uncertainties
introduced by EHCFs. In addition, those studies are unable to quantify the
uncertainty in terms of confidence level. In this study parametric uncertainty
propagation technique was developed and used for the MITR thermal hydraulic limit
and safety limit analyses. The aim of this study is to eliminate part of the
conservatism inherent in uncertainty analyses using EHCFs, as well as providing
uncertainty in terms of confidence level.
In this study, several project accomplishments have been achieved: (1) Propose a
generalized equation that can be used to calculate LSSS for plate-fuel-type research
reactors, (2) Calculate the analytical forced convection LSSS, OFT and CHF for the
MITR, which are respectively 8.3, 12.4 and 70 MW, (3) Quantify coolant channel
fabrication uncertainty, which is the dominant sources of engineering uncertainties,
and based upon which derive associated parametric uncertainties, (4) Develop and use
uncertainty propagation technique for the MITR calculating forced convection LSSS,
OFI and CHF, which are respectively obtained as 9.1, 10.4 and 47 MW using Oracle
Crystal Ball, (5) Calculate the LSSS for the proposed MITR-LEU core for natural
convection modes using RELAP5/mod3 for two cases: both NCVs and ASVs are
open and only NCVs are open, and the minimum margin to ONB is about 36.4'C for
these two cases.
In the uncertainty propagation methodology LSSS was taken at (mean-3o) value. The
calculation shows that the probability of ONB occurrence is roughly 0.15% when
operating power is 9.1MW. This result not only permits 0.8 MW additional margins
comparing to analytical approach, but also indicates the low probability of ONB
occurrence at this power level. Besides, there is adequate margin between 9.1 MW
and the targeting license power of the MITR 7 MW, making possible the proposed
power uprate from 6 MW to 7 MW.
156
8.2 Recommendations for This Study
Several recommendations for future work are discussed below.
(1) Flow and heat transfer behavior at the channel edge would be a concern:
The MITR has narrow rectangular coolant channels and therefore heat transfer
rate at the corner of coolant channel may be lower, comparing to the center region
due to reduced turbulent convection. The flow and heat transfer behavior near the
edge of the channels could be investigated using CFD software. This effect could
have significant influence if power peaking, which requires further neutronic
calculation, is not negligible near the end of fuel meat.
(2) The investigation of heat conduction of fuel plates in lateral direction:
In this study, the heated surface used in the calculation actually includes
non-fueled area, which was adopted from the assumption used in the previous
MITR safety analysis. Therefore, the effect of conduction in lateral direction
through the non-fueled region will need to be investigated.
(3) MITR-based correlations are required to be developed:
At this stage Carnavos correlation is used to calculate heat transfer coefficient and
Bergles-Rohsenow correlation is used to predict ONB. It is expected that the
correlations specifically developed for the MITR could be used in the analyses
after the relevant experiments are completed, and this could reduce the excess
penalties inherent in current analyses, therefore providing additional margin for
power uprate.
(4) Completeness of parametric uncertainties specification:
In this study LSSS is calculated by setting several key input parameters in a form
of normal distribution, and other parameters are at their nominal values. The
completeness of parametric uncertainties specification cannot be achieved before
resolving the issues indicated as follows. First, the parametric uncertainties for
primary coolant flow and heat transfer coefficient are specified by adopting the
values documented in the SAR directly, instead of by independent study. Second,
for those parameters using constant values in the LSSS equation, they do, while
relatively small, have parametric uncertainties. Third, there might be effects not
covered in this study that may be worthwhile to investigate: irradiation effects
such as dimensional change in channels and heat transfer degradation due to crud
formation on cladding.
157
(5) Analyses based on half-channels:
The MITR has a unique design such that there are full-channels and half-channels
in the core. Note that the total number of flow channels 432 used in this study is
based on the assumption that two half channels form a full channel, which
simplifies the analyses. This study only focuses on the full-channels of the MITR
assuming that the most limiting result throughout the core is on one of the fullchannels. For licensing, it is suggested to conduct similar analyses on halfchannels for completeness.
158
Appendix A.
RELAP5 Input File for Natural Circulation LSSS of MITR (Steady State)
=
MIT casel, pump coast-down
*
first 300 seconds is steady-state, pump trip is defined in transient input
*
5/30/2011 Homogeneous core: LEU Power 7.4MW, 24 elements, 18
plates/element
100 new transnt
102 si si * use SI units
105 5.0 6.0 5000. * max computer time = 5000 seconds
*
*
time step
*
201 300. 1.0-9 .005 3 100 1000 500 * SJK 5/12/2010) time step control 3,
minimum time step=0.005 sec
*
*
minor edit variables
*
301 count 0
302 cputime 0
303 dt 0
304 dtcrnt 0
*
*
trips, open ASV and NCV
*
401 time 1 ge null 1 10000. 1* SJK 071409 no ASV trip within specified
operation duration
402 time 1 ge null 1 10000. 1 * SJK 071409 no NCV trip within specified
operation duration
403 time 1 ge null 1 10000. 1 * SJK 071409 no pump trip within specified
operation duration
*
*
hydrodynamic components
*
1000000 snkref tmdpvol * sink reference volume, sets system pressure
1000101 1.0 1.0 1.0 0. 0. 0. .00001 0. 0000000
1000200 103
159
1000201 0. 1.02+5 328.0 * initial p, T, by MULCH S.S. compinent #1 YCK
032207
*
1010000 outlet sngljun
1010101 103010002 100010001 .032 1.0 1.0 100 1.0 1.0 *Word 9 left out (SJK
11/04/2010)
1010201 1 112.5 0. 0.
*
1020000 cldleg tmdpvol * cold leg inlet temperature
1020101 1.0 1.0 1.0 0. 0. 0. .00001 0. 0000000
1020200 103
1020201 0. 1.03+5 333.15 * initial p, T change to be consistent with HEU input
deck SJK 062409
*
1030000 upppln snglvol
1030101 .923 .1 .0923 0. 90. .1.00001 1.1 11000
1030200 103 1.025+5 333.15 * initial p, T
*
1040000 uppjnl sngljun
1040101 105010002 103010001 .5 .01 .01 100 1.0 1.0 *Word 9 left out (SJK
11/04/2010)
1040201 1 112.5 0. 0.
*
1050000 uppl2 snglvol * middle volume for upper plenum
1050101 .923 1.12 1.03376 0. 90. 1.12.00001 1.1 11000 *YCK 022807
1050200 103 1.04+5 333.15 * initial p, T
*
1060000 uppjn2 sngljun
1060101 108010002 105010001 .13 .01 .01 100 1.0 1.0 *Word 9 left out (SJK
11/04/2010)
1060201 1 112.5 0. 0. * initial flow rate
*
1070000 uppjn3 sngljun
1070101 105010001 109010001 .5 .01 .01 100 1.0 1.0 *Word 9 left out (SJK
11/04/2010)
1070201 1 0. 0. 0.
*
1080000 uppl3 snglvol
160
1080101 .130.76 .0988 0.90. .76.00001 .387 11000 *YCK 022807
1080200 103 1.05+5 333.15 * initial p, T
*
1090000 uppl4 snglvol
1090101 .973 .80 .7784 0. -90. -.80 .00001 1.282 11000 *YCK2 022807
1090200 103 1.05+5 333.15 * initial p, T
*
1100000 inltpl snglvol
1100101 .130.0658.008554 0.90. .0658.00001 .387 11000 *YCK 022807
1100200 103 1.10+5 320.4 * initial p, T
*
2010000 pump tmdpjun * pump
2010101 102010002 203010001 .032
2010200 1 403 *SJK 071409
2010201 -1. 112.5 0. 0. *SJK 071409
2010202 0. 112.5 0. 0. * t,w new pump coastdown SJK 5/12/2011
2010203 0.1 108.625 0. 0.
2010204 0.2 104.843 0. 0.
2010205 0.3 101.153 0. 0.
2010206 0.4 97.554 0. 0.
2010207 0.6 90.622 0. 0.
2010208 0.8 84.041 0. 0.
2010209 1.0 77.799 0. 0.
2010210 1.5 63.624 0. 0.
2010211 2.0 51.376 0.0.
2010212 2.5 40.916 0. 0.
2010213 3.0 32.100 0.0.
2010214 3.5 24.788 0. 0.
2010215 4.0 18.837 0. 0.
2010216 4.5 14.107 0. 0.
2010217 5.0 10.456 0. 0.
2010218 6.0 5.823 0. 0.
2010219 7.0 3.807 0.0.
2010220 8.0 3.274 0.0.
2010221 10.0 2.131 0. 0.
2010222 11.0 0.0 0. 0.
2010223 100000.0 0.0 0. 0.
*
161
2020000 ASV valve
2020101 105010002 203010001 .007674 6.90 7.90 100 1.0 1.0 1.0 * 2 valves
2020201 1 0. 0. 0. * initial flow rate
2020300 trpvlv * trip valve
2020301 401 * trip 401
*
2030000 regn1 pipe * region 1
2030001 10 * number of nodes
2030101 .339,10 * area
2030301 .122,10 * node lengths * YCK 022807
2030601 -90.,10 * vertical angles
2030801 .00001,.180,10 * roughness, Dw
2031001 11000,10 * volume control flags
2031101 1020,9 * junction control flags
2031201 103,1.04+5,320.4,0.,0.,0.,10 * initial pressure, temperature
2031300 1 * use mass flows below
2031301 112.5,0.,0.,9 * initial junction flow rates
*
2040000 rgnIto2 sngljun * region 1 to region 2 junction
2040101 203100002 205010001 .111 .3.3 100 *YCK 022807
2040201 1 112.5 0. 0. * initial flow rate
*
2050000 regn2 pipe * region 2
2050001 10 * number of nodes
2050101 .111,10 * area
2050301 .06899,10 * node lengths YCK 022807
2050601 -90.,10 * vertical angles YCK 022807
2050801 .00001,.063,10 * roughness, Dw
2051001 11000,10 * volume control flags
2051101 1020,9 * junction control flags
2051201 103,1.05+5,320.4,0.,0.,0.,10 * initial pressure, temperature
2051300 1 * use mass flows below
2051301 112.5,0.,0.,9 * initial junction flow rates
*
2060000 rgn2to3 sngljun * region 2 to region 3 junction
*2060101 205100002 207010001 .0044 .18 .18 100 * YCK 022807
2060101205100002 207010001 .111 .18 .18 100 * SJK 5/12/2011
2060201 1 112.5 0. 0. * initial flow rate
162
*
2070000 regn3 pipe * region 3
2070001 10 * number of nodes
*2070101 .0044,10 * area * YCK 022807
2070101 .12566,10 * area * SJK 5/12/2011 Downcomer 3 area pi*D*th (D=40
cm, th=10 cm)
2070301
2070601
2070801
2071001
.364,10 * node lengths * YCK 022807
-0.16,10 * vertical angles * YCK 022807
.00001, .22, 10 * roughness, Dw *SJK 05/01/11
11000,10 * volume control flags
2071101 1020,9 * junction control flags
2071201 103,1.06+5,320.4,0.,0.,0.,10 * initial pressure, temperature
2071300 1 * use mass flows below
2071301 112.5,0.,0.,9 * initial junction flow rates
*
2080000 NCV valve * NCV
2080101 109010002 210010001 .029 52.0 46.3 100 1.0 1.0 1.0 * 4 valves
2080201 1 0. 0. 0. * initial flow rate
2080300 trpvlv * trip valve
2080301 402 * trip 402
*
2090000 rgn3to4 sngljun * region 3 to region 4 junction
*2090101 207100002 210010001 .0044.1 .1 100 * YCK 022807
2090101207100002 210010001.029.1 .1 100 * SJK 5/12/2011
2090201 1 112.5 0. 0. * initial flow rate
*
2100000 regn4 pipe * region 4
2100001 10 * number of nodes
2100101
2100301
2100601
2100801
.029,10 * area
.061,10 * node lengths * YCK 022807
-90.,10 * vertical angles
.00001,.040,10 * roughness, Dw
2101001 11000,10 * volume control flags
2101101 1020,9 * junction control flags
2101201 103,1.07+5,320.4,0.,0.,0.,10 * initial pressure, temperature
2101300 1 * use mass flows below
2101301 112.5,0.,0.,9 * initial junction flow rates
*
163
2110000 rgn4toi sngljun * region 4 to inlet plenum
2110101 210100002 110010001 .029 2.05 2.05 100 * YCK 022807
2110201 1 112.5 0. 0. * initial flow rate
*
*
302 represents 329 average core channels
*
402 represents 1 hot channel
*
3010000 avginl sngljun * inlet to the average core channel
3010101 110010002 302010001 .048442 .3 .2 100 * SJK 5/12/2011
3010201 1 103.3 0. 0. * initial flow rate * YCK 032407
*
3020000 avgchn pipe
3020001
3020101
3020301
3020601
3020801
3021001
3021101
3021201
*
average core channel
10 * number of nodes
.048442,10 * area * SJK 5/12/2011
.06478,1 .05683,9 .06478,10 * node lengths
90.,10 * vertical angles
.00001,.0018820,10 * roughness, Dw SJK 05/12/2011
11000,10 * volume control flags
1020,9 * junction control flags
103,1.08+5,320.4,0.,0.,0.,10 * initial pressure, temperature
3021300 1 * use mass flows below
3021301 103.3,0.,0.,9 * initial junction flow rates * YCK 032407
*
3030000 avgout sngljun * outlet from the average core channel
3030101 302100002 108010001 .048442.2.3 100 * SJK 5/12/2011
3030201 1 103.3 0. 0. * initial flow rate * YCK 032407
*
*
average fuel plate
*
13021000 10 10 1 00. 0 0 2 * YCK 658 average half-plates SJK 5/29/2011
13021100 0 2 * mesh flags
13021101 .00005715,3,.0000127,5,.0000635,9 * mesh intervals clad = 0.25 mm,
fuel=0.508mm SJK 5/29/2011
13021201 1,3 2,5 3,9 * compositions SJK 5/29/2011
13021301 0.,5 1.,9 * radial source distribution SJK 5/29/2011
13021401 320.4,10 * initial temperatures SJK 5/29/2011
13021501 302010000,10000,1,0,4.922345,10 * left boundary condition * SJK
072709 LEU 24 elements
164
13021601 0,0,0,0,4.922345,10 * right boundary condition, insulated * SJK
072709 LEU 24 elements
13021701 1000 9.931029e-02 0. 0. 1 * axial source distribution, KYC 2011-12-7:
431 avg. in 24 LEU elements
13021702 1000 1.043853e-01 0. 0. 2 *SJK 062609
13021703 1000 1.119480e-01 0. 0. 3 *SJK 062609
13021704 1000 1.216004e-01 0. 0. 4 *SJK 062609
13021705 1000 1.193117e-01 0. 0. 5 *SJK 062609
13021706 1000 1.134406e-01 0. 0. 6 *SJK 062609
13021707 1000 1.022956e-01 0. 0. 7 *SJK 062609
13021708 1000 9.075249e-02 0. 0. 8 *SJK 062609
13021709 1000 7.035308e-02 0. 0. 9 *SJK 062609
13021710 1000 6.169577e-02 0. 0. 10 *SJK 062609
130218000
13021801 .0021253,10.,10.,0.,0.,0.,0.,1.0,10 * additional left boundary * SJK
5/12/2011
130219000
13021901 .0021253,10.,10.,0.,0.,0.,0.,1.0,10 * additional right boundary * SJK
5/12/2011
*
4010000 avginl sngljun * inlet to the average core channel
4010101 110010002 402010001 1.1239-4 .3 .2 100 * SJK 5/12/2011
4010201 1 .259 0. 0. * initial flow rate * YCK 032407
*
4020000 hotchn pipe * hot core channel
4020001 10 * number of nodes
4020101 1.1239-4,10 * area * SJK 05/12/2011
4020301 .06478,1 .05683,9 .06478,10 * node lengths
4020601 90.,10 * vertical angles
4020801 .00001,.0018820,10 * roughness, Dw *SJK 5/12/2011
4021001 11000,10 * volume control flags
4021101 1020,9 * junction control flags
4021201 103,1.08+5,320.4,0.,0.,0.,10 * initial pressure, temperature
4021300 1 * use mass flows below
4021301 .259,0.,0.,9 * initial junction flow rates * YCK 032407
*
4030000 avgout sngljun * outlet from the average core channel
4030101 402100002 108010001 1.1239-4 .2 .3 100 * SJK 5/12/2011
165
4030201 1 .259 0. 0.* initial flow rate * YCK 032407
*
*
*
peak fuel plate
*
14021000 10 10 1 00. 0 0 2 * YCK 658 average half-plates SJK 5/29/2011
14021100 0 2 * mesh flags
14021101 .00005715,3,.0000127,5,.0000635,9 * mesh intervals clad = 0.25 mm,
fuel=0.508mm SJK 5/29/2011
14021201 1,3 2,5 3,9 * compositions SJK 5/29/2011
14021301 0.,5 1.,9 * radial source distribution SJK 5/29/2011
14021401 320.4,10 * initial temperatures 5/29/2011
14021501 402010000,10000,1,0,.011421,10 * left boundary condition * SJK
072709
14021601 0,0,0,0,.011421,10 * right boundary condition, insulated * SJK 072709
14021701 1000 5.743628e-04 0. 0. 1 * axial source distribution, KYC 2011-12-7,
hot stripe factor=2.12 in 24 LEU elements
14021702 1000 5.673444e-04 0. 0. 2 * SJK 062609
14021703 1000 6.060255e-04 0. 0. 3 * SJK 062609
14021704 1000 6.238675e-04 0. 0. 4 * SJK 062609
14021705 1000 6.257135e-04 0. 0. 5 * SJK 062609
14021706 1000 6.076277e-04 0. 0. 6 * SJK 062609
14021707 1000 5.371655e-04 0. 0. 7 * SJK 062609
14021708 1000 4.124721e-04 0. 0. 8 * SJK 062609
14021709 1000 2.253363e-04 0. 0. 9 * SJK 062609
14021710 1000 1.274972e-04 0. 0. 10 * SJK 062609
140218000
14021801 .0021253,10.,10.,0.,0.,0.,0.,1.0,10 * additional left boundary * SJK
5/12/2011
140219000
14021901 .0021253,10.,10.,0.,0.,0.,0.,1.0,10 * additional right boundary * SJK
5/12/2011
*
5010000 bypini sngljun * inlet to the bypass flow
5010101 110010002 502010001 4.1934-3 .3.2 100 * SJK 5/12/2011
5010201 1 8.91 0. 0. * initial flow rate * YCK 032407
*
5020000 bypass pipe * bypass flow
166
5020001
5020101
5020301
5020601
5020801
10 * number of nodes
4.1934-3,10 * area * SJK 5/12/2011
.06478,1 .05683,9 .06478,10 * node lengthss
90.,10 * vertical angles
.00001,.0018820,10 * roughness, Dw *SJK 5/12/2011
5021001 11000,10 * volume control flags
5021101 1020,9 * junction control flags
5021201 103,1.08+5,320.4,0.,0.,0.,10 * initial pressure, temperature
5021300 1 * use mass flows below
5021301 8.91,0.,0.,9 * initial junction flow rates * YCK 032407
*
5030000 bypout sngljun * outlet from the bypass flow
5030101 502100002 108010001 4.1934-3 .2.3 100 * SJK 5/12/2011
5030201 1 8.91 0. 0. * initial flow rate * YCK 032407
*
*
*
*
tables
*
20100100 tbl/fctn 1 1 * thermal properties table 1 for Al
20100101 97.297 * Al thermal conductivity *SJK 05/12/2011
20100151 1.9615e6 * Al rho*Cp *SJK 05/01/2011
*
20100200 tbl/fctn 1 1 * thermal properties table 1 for Zr
20100201 22. * Zr thermal conductivity *SJK 05/29/2011
20100251 1.8525e6 * Zr rho*Cp *SJK 05/29/2011
*
20100300 tbl/fctn 1 1 * thermal properties table 2 for LEU fuel
20100301
20100302
20100303
20100304
20100305
20100306
20100307
293.
373.
473.
573.
673.
773.
873.
6.108 * thermal conductivity *SJK 5/12/2011
7.135 *
9.243 *
10.973 *
12.811 *
14.919 *
17.243 *
20100308 973. 19.135 *
20100309 1073. 20.270 *
20100351 273.15 1.268e6 * rho*Cp *SJK 5/12/2011
167
1.292e6 *
1.331e6 *
1.387e6 *
1.443e6 *
1.507e6 *
1.542e6 *
20100358 973.15 1.586e6 *
20100352
20100353
20100354
20100355
20100356
20100357
373.15
473.15
573.15
673.15
773.15
873.15
*
20200100 reac-t
*
General table 1, scram reactivity
20200101 0. 0. * SJK 071409
20200102 10000. 0.0 * SJK 071409 no scram during the steady state run
*
* point kinetics
*
30000000
30000001
30000002
30000401
point separabl
gamma-ac 1.0e6 0. 150. 1.0 0.7 *SJK 12/20/2010 7.4 MW LSSS power
ans79-1
1.0e6 52. wk * SJK 12/20/2010 7.4 MW LSSS power
300000111
30000501 500. 0. * moderator density reactivity
30000502
30000601
30000602
30000701
30000801
2000. 0.
300. 0. * doppler reactivity
1000. 0.
302010000 0 1. 0. * Volume weighting factors
3021001 0 1.0 0.
. end of input file
168
Appendix B.
RELAP5 Input File for Natural Circulation LSSS of MITR (Restart file)
=
*
MIT casel, pump coast-down
restart file from steady run: pump trips at t=0
100 restart transnt
102 si si * use SI units
103 60151 *SJK 070209
105 5.0 6.0 10000. * max computer time
=
10000 seconds
*
*
time step
*
201 375. 1.0-9 .000125 23 200 1000 500 * SJK 5/12/2011 time step control 23, max
time step=0.000125 sec
202 1500. 1.0-9.005 23 20 1000 500 * SJK 5/12/2011 time step control 23, max time
step=0.005 sec
*
*
minor edit variables
*
301 count 0
302 cputime 0
303 dt 0
304 dtcrnt 0
*
*
trips, open ASV and NCV
*
403 time 1 ge null 1 0.0 1 * pump trip at restarting, i.e., @t= 0.0 and subsequent
coastdown *SJK 070309
401 time 1 ge timeof 403 4.4 1 * trip ASV at t = 4.4 and latch *SJK 070309
402 time 1 ge timeof 403 4.4 1 * trip NCV at t = 4.4 and latch *SJK 070309
611 403 and 403 n -1. * SJK @Rxtrip*
*
2020000 ASV valve
2020101 105010002 203010001 .007674 6.90 7.90 100 1.0 1.0 1.0 * 2 valves
2020201 1 0. 0. 0. * initial flow rate
2020300 trpvlv * trip valve
2020301401 * trip 401
169
*
*
2080000 NCV valve * NCV
2080101 109010002 210010001 .029 52.0 46.3 100 1.0 1.0 1.0 * 4 valves
2080201 1 0. 0. 0. * initial flow rate
2080300 trpvlv * trip valve
2080301 402 * trip 402
*
*
*
tables
*
20100100 tbl/fctn 1 1 * thermal properties table 1 for Al
20100101 97.297 * Al thermal conductivity *SJK 05/12/2011
20100151 1.9615e6 * Al rho*Cp *SJK 05/01/2011
*
20100200 tbl/fctn 1 1 * thermal properties table 1 for Zr
20100201 22. * Zr thermal conductivity *SJK 05/29/2011
20100251 1.8525e6 * Zr rho*Cp *SJK 05/29/2011
*
20100300 tbl/fctn 11 * thermal properties table 2 for LEU fuel
20100301
20100302
20100303
20100304
20100305
20100306
20100307
20100308
20100309
20100351
20100352
20100353
293. 6.108 * thermal conductivity *SJK 5/12/2011
373. 7.135 *
473. 9.243 *
573. 10.973 *
673. 12.811 *
773. 14.919 *
873. 17.243 *
973. 19.135 *
1073. 20.270 *
273.15 1.268e6 * rho*Cp *SJK 5/12/2011
373.15 1.292e6 *
473.15 1.331e6 *
20100354
20100355
20100356
20100357
20100358
573.15
673.15
773.15
873.15
973.15
1.387e6
1.443e6
1.507e6
1.542e6
1.586e6
*
*
*
*
*
*
170
20200100 reac-t 611 * General table 1, scram reactivity
20200101 0. 0. * t, reactivity ($)
20200102 1.3 0. * SJK 071509
20200103 2.3 -7.5 * SJK 071509
20200104 3.3 -10.0 * SJK 071509
20200105 10000. -10.0 * SJK 071509
*
*
point kinetics
*
30000000 point separabl
30000001 gamma-ac 1.0e6 0. 150. 1.0 0.7 *SJK 071509
30000002 ans79-1
30000401 1.0e6 52. wk *$ SJK 062209: rescaled the total reactor power rather than
taking fuel element power
30000011 1
30000501 500. 0. * moderator density reactivity SJK 062009 wI: mod density w2:
reactivity
30000502 2000. 0.
30000601 300. 0. * doppler reactivity SJK 062009 wI: fuel temp w2: reactivity
30000602 1000. 0.
30000701 302010000 0 1. 0. * Volume weighting factors
30000801 3021001 0 1.0 0.
. end of input file
171