AN ABSTRACT OF THE THESIS OF
Christopher Jordan Bowser for the degree of Master of Science in Nuclear Engineering
presented on June 13, 2012.
Title: RELAP5-3D Modeling of ADS Blowdown of MASLWR Facility
Abstract approved:
Brian G. Woods
Oregon State University has hosted an International Atomic Energy Agency (IAEA)
International Collaborative Standard Problem (ICSP) through testing conducted on the
Multi-Application Small Light Water (MASLWR) facility. The MASLWR facility features
a full-time natural circulation loop in the primary vessel and a unique pressure suppression
device for accident scenarios. Automatic depressurization system (ADS) lines connect
the primary vessel to a high pressure containment (HPC) which dissipates steam heat
through a heat transfer plate thermally connected to another vessel with a large cool
water inventory. This feature drew the interest of the IAEA and an ICSP was developed
where a loss of feedwater to the steam generators prompted a depressurization of the
primary vessel via a blowdown through the ADS lines.
The purpose of the ICSP is to evaluate the applicability of thermal-hydraulic computer codes to unique experiments usually outside of the validation matrix of the code
itself. RELAP5-3D 2.4.2 was chosen to model the ICSP. RELAP5-3D is a best-estimate
code designed to simulate transient fluid and thermal behavior in light water reactors.
Modeling was conducted in RELAP5-3D to identify the strengths and weaknesses of the
code in predicting the experimental trends of the IAEA ICSP. This extended to nodalization sensitivity studies, an investigation of built-in models and heat transfer boundary
conditions. Besides a qualitative analysis, a quantitative analysis method was also performed.
c
Copyright by Christopher Jordan Bowser
June 13, 2012
All Rights Reserved
RELAP5-3D Modeling of ADS Blowdown of MASLWR Facility
by
Christopher Jordan Bowser
A THESIS
submitted to
Oregon State University
in partial fulfillment of
the requirements for the
degree of
Master of Science
Presented June 13, 2012
Commencement June 2013
Master of Science thesis of Christopher Jordan Bowser presented on June 13, 2012
APPROVED:
Major Professor, representing Nuclear Engineering
Head of the Department of Nuclear Engineering and Radiation Health Physics
Dean of the Graduate School
I understand that my thesis will become part of the permanent collection of Oregon State
University libraries. My signature below authorizes release of my thesis to any reader
upon request.
Christopher Jordan Bowser, Author
ACKNOWLEDGEMENTS
I would like to thank my advisor, Dr. Woods, for his encouragement and understanding through this process and the opportunities that I had as a student that he made
possible.
I would also like to thank a few people who made the road a little easier including Dr. Galvin with his LATEX knowledge, Dr. Marcum for the use of his post-processing
scripts, and my roommates, Seth Cadell and Brian Jackson, for listening to my many
questions .
I would also like to acknowledge the Department of Energy’s Nuclear Energy University Program for their fellowship funding.
Thanks Mom, Dad, Seth and Hannah. I am so blessed to have you as my family.
TABLE OF CONTENTS
Page
1. INTRODUCTION . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1
1.1.
IAEA ICSP . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
7
1.2.
Objective . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
8
1.3.
Limitations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
9
1.4.
Content Description . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10
2. LITERATURE REVIEW . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
2.1.
RELAP5-3D: New Uses and Comparing with Experimental Data . . . . . . . 11
2.1.1 FFTBM . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
12
2.2.
Similar Experiments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16
2.3.
Condensation in the Presence of Noncondensables . . . . . . . . . . . . . . . . . . . . . . 19
2.4.
Standard Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31
3. MASLWR RELAP5-3D MODEL . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33
3.1.
Reactor Pressure Vessel. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33
3.1.1
3.1.2
3.1.3
3.1.4
3.1.5
3.1.6
3.1.7
Core Region . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Electrical Core Heat Structure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Hot Leg . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Hot Leg to Cold Leg Conduction and Ambient Heat Loss . . . . . . . .
Upper Plenum and Pressurizer . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Pressurizer Heater Rods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Cold Leg . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
33
35
35
39
40
41
41
3.2.
High Pressure Containment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41
3.3.
Secondary Side . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44
3.4.
ADS Lines . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46
3.4.1 Choked Flow Modeling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.4.2 Trips and Control Systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
49
52
TABLE OF CONTENTS (Continued)
Page
4. CALCULATION MATRIX . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55
4.1.
Initial Calculation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57
4.2.
Second Calculation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68
4.2.1
4.2.2
4.2.3
4.2.4
4.2.5
4.2.6
4.3.
ADS Nodalization Sensitivity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Choked Flow Recommended Options . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Choked Flow Discharge Coefficients . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Motor Valve Open/Close Rate . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
HPC Nodalization Sensitivity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Steady State Comparison . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
68
68
71
72
74
80
Third Calculation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82
4.3.1 Stand-alone Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
82
5. CONCLUSIONS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93
5.1.
Future Work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 94
LIST OF FIGURES
Figure
Page
1.1
MASLWR Concept Schematic . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3
1.2
MASLWR Facility Rendering . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
6
3.1
RELAP5-3D Nodalization Diagram . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
34
4.1
Initial Calculation: RPV Pressure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
59
4.2
Initial Calculation: HPC Pressure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
60
4.3
Initial Calculation: Containment Level . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
60
4.4
Initial Calculation: RPV Pressure - 1st Window . . . . . . . . . . . . . . . . . . . . . . . . .
62
4.5
Initial Calculation: HPC Pressure - 1st Window . . . . . . . . . . . . . . . . . . . . . . . . .
63
4.6
Initial Calculation: Containment Level - 1st Window . . . . . . . . . . . . . . . . . . . .
63
4.7
Initial Calculation: RPV Pressure - 2nd Window . . . . . . . . . . . . . . . . . . . . . . . .
64
4.8
Initial Calculation: HPC Pressure - 2nd Window . . . . . . . . . . . . . . . . . . . . . . . .
64
4.9
Initial Calculation: Containment Level - 2nd Window . . . . . . . . . . . . . . . . . . .
65
4.10 Initial Calculation: RPV Pressure - 3rd Window . . . . . . . . . . . . . . . . . . . . . . . .
65
4.11 Initial Calculation: HPC Pressure - 3rd Window . . . . . . . . . . . . . . . . . . . . . . . .
66
4.12 Initial Calculation: Containment Level - 3rd Window . . . . . . . . . . . . . . . . . . . .
66
4.13 PCS-106A Vent Line Nodalization Study: Primary Pressure . . . . . . . . . . . . .
69
4.14 PCS-106A Vent Line Nodalization Study: Containment Level . . . . . . . . . . .
69
4.15 Choked Flow Discharge Coefficients: HPC Pressure . . . . . . . . . . . . . . . . . . . . .
73
4.16 Henry-Fauske Study: HPC Pressure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
73
4.17 Ransom-Trapp Study: RPV/HPC Pressure . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
74
4.18 RPV Pressure, Motor Valve 1.0 s Closure Rate . . . . . . . . . . . . . . . . . . . . . . . . . .
75
4.19 RPV Pressure, Motor Valve 0.5 s Closure Rate . . . . . . . . . . . . . . . . . . . . . . . . . .
75
4.20 HPC Nodalization Sensitivity: Containment Level . . . . . . . . . . . . . . . . . . . . . .
78
4.21 HPC Nodalization Sensitivity: Primary Pressure . . . . . . . . . . . . . . . . . . . . . . . .
78
4.22 HPC Nodalization Sensitivity: Noncondensable Transport . . . . . . . . . . . . . . .
79
LIST OF FIGURES (Continued)
Figure
Page
4.23 HPC Nodalization Sensitivity: Condensation Rate . . . . . . . . . . . . . . . . . . . . . .
79
4.24 Experimental Heat Transfer Plate Temperatures . . . . . . . . . . . . . . . . . . . . . . . .
80
4.25 Steady State Initialization: Primary Pressure . . . . . . . . . . . . . . . . . . . . . . . . . . .
81
4.26 Steady State Initialization: Containment Level . . . . . . . . . . . . . . . . . . . . . . . . . .
82
4.27 Stand-alone Model: Containment Pressure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
90
4.28 Stand-alone Model: Containment Temperatures . . . . . . . . . . . . . . . . . . . . . . . . .
91
4.29 Initial Calculation: HPC Ambient Heat Loss - 100 − 6000 s . . . . . . . . . . . . .
91
4.30 Initial Calculation: HPC Ambient Heat Loss - 0 − 100 s . . . . . . . . . . . . . . . . .
92
LIST OF TABLES
Table
Page
3.1
Differential Pressure Tap Elevations (Woods et al. (2010)) . . . . . . . . . . . . . . .
36
3.2
Reactor Pressure Vessel Geometry . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
42
3.3
Pressurizer Geometry . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
43
3.4
Containment Thermocouple and ADS Penetration Elevations (Woods
et al. (2010)) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
44
3.5
High Pressure Containment Geometry . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
45
3.6
Automatic Depressurization System Vent Lines Geometric Data (Woods
et al. (2010)) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
47
Automatic Depressurization System Sump Return Lines Geometric Data
(Woods et al. (2010)) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
48
3.8
ADS Vent Line Leg ‘A’ Geometry. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
49
3.9
ADS Vent Line Leg ‘A’ Geometry. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
54
4.1
RELAP5-3D Calculations Performed . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
56
4.2
Manufacturer Provided Instrumentation Uncertainty (Woods et al. (2010)) 57
4.3
Weighting Factor Components, Prosek et al. (2002) . . . . . . . . . . . . . . . . . . . . .
67
4.4
Initial Calculation Average Amplitudes from FFTBM . . . . . . . . . . . . . . . . . . .
67
4.5
PCS-106A Vent Line Nodalization Study . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
70
4.6
High Pressure Containment Nodalization Study . . . . . . . . . . . . . . . . . . . . . . . . .
77
4.7
Initial Heat Transfer Plate Wall Temperatures for Containment Simulation 87
3.7
RELAP5-3D MODELING OF ADS BLOWDOWN OF MASLWR
FACILITY
1.
INTRODUCTION
In March of 2011, the worst nuclear disaster since Chernobyl followed on the heels
of a massive earthquake and subsequent tsunami that destroyed homes and took lives in
the northeastern coastal region of Japan. After the devastation of this two-fold natural
disaster, the loss of offsite AC power and the flooding of backup diesel generator buildings
began a chain of events that led to core meltdown and radioactive release. For many of the
native Japanese who lived near the Fukushima Dai-ichi plants, the hardships caused by the
earthquake and tsunami were increased by the radioactive release which necessitated the
displacement from their homes for the near and possibly distant future. Along with the
global response of aid for the affected Japanese, a renewed pessimism and public outcry
against the expansion and current use of nuclear produced electricity was raised worldwide. Countries such as Switzerland and Germany now look to phase out their operating
reactors and Italy once again declares a post-mortem on their nuclear energy program
even with their consistent contributions to nuclear engineering and their costly electricity
importation, (ANS, June 2011), (ANS, July 2011). In the United States, the Nuclear
Regulatory Commission (NRC) now has their hands full with a public concerned about
the safety of domestic plants such as those situated on the seismically active California
coast at San Onofre Nuclear Generating Station and the important decisions that will
need to be made when more information is gathered from the affected Fukushima nuclear
power plants. The NRC was also in the final stages of reviewing the design certifications
2
of Westinghouse’s AP1000 and General Electric-Hitachi’s Economic Simple Boiling Water
Reactor when the Fukushima accident happened, (ANS, April 2011), (ANS, May 2011).
Also, budgetary planning was already taking place to begin receiving licensing documents
from potential Small Modular Reactor (SMR) designs in the next couple of fiscal years,
(ANS, July 2011). Best laid plans aside, the safety requirements for loss of offsite power
accidents and multiple plant sites may need to be reexamined and reevaluated and existing
design certifications may need to undergo a few more warranted amendments. Or, the
industry shift towards passive safety systems and the increased use and understanding
of natural circulation in new nuclear plant designs will be validated as the appropriate
direction for increasingly safer power plant operations.
As mentioned, the tragedy in Japan has caused the nuclear industry to intensify
the spotlight on the existing nuclear safety culture and question the efficacy of current
mandates in the United States such as four hour battery backup for critical components
and assumptions regarding the number of hours until offsite power is restored, (ANS, June
2011). However, new and proposed designs have already been shifting towards so called
inherently safe designs, minimal operator actions, and increased utilization of natural
forces during accident scenarios. This shift has materialized in the Multi-Application
Small Light Water Reactor (MASLWR) facility at Oregon State University (OSU) which
was funded by the Nuclear Energy Research Initiative (NERI) program through the United
States’ Department of Energy (DOE) to test a conceptual design of a light water SMR.
The MASLWR facility is an integral test facility of a full-time natural circulation reactor
with feedwater supplied to an integral helical coil steam generator located near the top
of the downcomer and below the integral pressurizer. A shell within a shell design is
employed for the long term cooling during an accident where the pressurizer steam space
is vented into the air space of a partially wet high pressure containment (HPC) through
3
FIGURE 1.1: MASLWR Concept Schematic Modro et al. (2003)
the upper automatic depressurization system (ADS) vent lines to depressurize the primary
vessel. Lower ADS lines also remove heat from the primary vessel and inject hot water into
the water space of the HPC. The containment structure which encapsulates the reactor
pressure vessel (RPV) is itself immersed in the containment cooling pool which serves
as the ultimate heat sink as accomplished through conduction heat transfer. Figure 1.1
features a schematic of the conceptual design.
The details and motivations for this project are discussed in Modro et al. (2003).
One motivation was for a more easily deployed reactor that would minimize the strain
on a developing energy infrastructure through its considerably smaller size compared to
4
existing several hundred up to 1000+ MW nuclear power plant designs. The wave of new
SMR designs is primarily fueled by this benefit of the economy of small which is unfortunately made possible through the financial burdens and construction hurdles necessary
for new large nuclear power plant construction. However, the potential certification of an
SMR design may provide new avenues for nuclear energy use and increase the member
population of countries with operating nuclear power plants. Several perceived benefits
of SMR designs are listed in Ingersoll (2009) including improved ease of fabrication and
construction, a more flexible safety platform with the decrease of the source term and
increase in heat transfer effectiveness, less financial strain, etc. Some of the safety features listed in Ingersoll (2009) are also present in the MASLWR concept design such as
minimal RPV penetrations, utilization of heat conduction through the vessel walls, and
decay power removal with fully passive technologies.
In Reyes and King (2003), the scaling of the OSU MASLWR facility is described.
The time scale of the MASLWR facility is 1:1 with respect to the full-size plant concept
and basic geometric ratios include a 1:3.1 length ratio and 1:254.7 volume ratio for the
reduced height facility. However, distortions do exist because of the scaling difficulties
of the metal mass to internal surface area ratio which interferes with the RPV wall time
constants. Another obstacle was overcome by scaling the area of a heat transfer plate
between the HPC and the RPV and installing trace heaters in the upper air volume of the
HPC to simulate an adiabatic surface to maintain the integrity of the shell within a shell
design. The heat transfer coefficient used for the scaling of the containment pressurization
was that of Uchida et al. (1964). To actually construct the facility, the shell within a shell
design is achieved through insulating separate vessels and insulating the connecting ADS
lines between the vessels. In Figure 1.2, a cut-away of the three vessels is depicted with
the RPV on the right side of the figure, the HPC in the middle and the cooling pool vessel
5
(CPV) on the left hand side. The scaled heat transfer plate runs the length of the HPC.
The electrical heater rods are depicted with the color red in the bottom of the RPV. The
upper part of the riser section is wrapped by the helical coils in the downcomer and the
integral pressurizer is separated from the natural circulation circuit with a baffle plate at
the top of the RPV. One of the upper ADS lines is pictured as well as one of the lower
ADS lines which connect the downcomer with the lower fluid volume of the HPC.
Although the MASLWR design concept is phenomenologically similar in many ways
to existing light water reactor designs, there are a number of non-technical issues that
have been identified by the United States NRC that concern the design certification of
a SMR, NRC (2010). One of the proposed benefits of SMRs is the ability to order an
appropriate amount of modules to fit a specific energy need with the allowance to add
more modules later to fit demand. Possibly sharing components between different modules
raises questions on how to determine the source term and the correct level of staffing for
multiple module sites is another debatable issue as noted by the NRC. Possible technical
issues revolve around more prominent roles for existing technologies. Two cases in point
for the MASLWR concept are the use of natural circulation as the driving head for core
cooling during all operations and the containment playing a more central role in core
depressurization at higher pressures where identifed phenomena have been given much
less attention. In Papini et al. (2010), a proposed containment design for the International
Reactor Innovative and Secure (IRIS) concept prompted researchers to explore coupling
the GOTHIC code with RELAP5/MOD3 because traditional containment phenomena
were an area of low importance for the validation of the RELAP thermal hydraulic engine.
The mixing of saturated steam with non-condensable gas was treated with dedicated
containment codes which was reasonable because the pressure response of containment
had negligible two-way interaction with the reactor fluid circuits.
6
FIGURE 1.2: MASLWR Facility Rendering
7
1.1.
IAEA ICSP
The intimate coupling between containment and reactor vessel which is a salient
feature of the MASLWR facility has attracted the interest of the International Atomic
Energy Agency (IAEA) and ultimately culminated in the hosting of an International Collaborative Standard Problem (ICSP) at OSU. The IAEA ICSP is adopted from the International Standard Problem (ISP) format of the Organisation for Economic Co-operation
and Development’s Nuclear Energy Agency. These collaborations could be described as
opportunities to study unique problems and take advantage of unique facilities while inviting international expertise and perspective to fill in pertinent knowledge gaps such as those
identified by IAEA Coordinated Research Programs. One of the goals would be to push
the operational envelopes and increase the understanding of current computational tools
and identify areas of improvement or validate new uses. To accomplish this, an ICSP progresses in three distinct stages. After the initial meetings to determine the test sequences
and familiarize the participants with the test facility and layout, double blind calculations
are submitted using the preferred computational tool of the researchers. Double blind
refers to the fact that the participants are given no actual experimental data but only
the expected test procedures and expected initial conditions. For the second phase which
consists of the blind calculations, the true initial conditions are given as well as other
bounding considerations such as the time stamps of valve openings, the power input to
electrical systems such as an electric core, ambient air measurements, etc. During the
third and final phase, modeling will be done with all of the specified experimental measurements released to the participants for a final fine-tuning of participant models. This
format allows for interesting insights into the effect that the user has modeling the same
problem with oftentimes the same modeling tool. In Aksan et al. (1993), the results from
various ISPs were studied with special emphasis placed on such user inputs as dynamic
8
pressure losses, the specification of different models or correlations, and the simulation of
the initial and boundary conditions through steady-state calculations. The authors also
state that difficult user decisions pertinent to integral test facilities include the modeling
of the large metal mass (previously mentioned in the discussion of the MASLWR scaling
distortions), increasingly important heat loss to ambient, and flow losses in constrained
and atypical geometries. The ICSP provides a platform for not only studying pertinent
phenomena and modeling practices for small-scale facilities but also better understanding the somewhat whimsical nature of the free nodalization format of the best estimate
thermal hydraulic codes.
1.2.
Objective
The purpose of this work is to evaluate the applicability of an industry accepted
best estimate thermal hydraulic code to the modeling of the MASLWR blowdown transient
through a qualitative and quantitative analysis with different nodalization complexities.
A format similar to that of the ICSP timeline has been adopted to perform the
modeling calculations. The first phase of modeling calculations will be initiated by the
actual experimental data that is measured right before the beginning of the blowdown
and will also include the experimental power input to the electric core in a similar fashion
to the blind calculation phase of the ICSP. The second phase of modeling calculations
will investigate the sensitivity of the RELAP5-3D solution to the salient features of the
blowdown transient and the MASLWR facility by toggling available models and changing
nodalization volume sizes. The final phase of calculations will include more widespread use
of the experimental data including but not limited to valve opening times which dictate
the fluid/thermal communication between vessels and the lessons learned from running
9
the sensitivity calculations.
To model the MASLWR facility, RELAP5-3D 2.4.2 was chosen to simulate the loss
of feedwater transient for the ICSP test. Though it has the capability to perform neutronic analysis, only the hydrodynamic modeling capabilities of RELAP5-3D were needed
to model the MASLWR facility. In the hydrodynamic model, eight field equations are
solved with a partially implicit numerical scheme to solve for eight variables: pressure,
phasic specific internal energies, vapor/gas volume fraction, phasic velocities, noncondensable quality and boron density, INL (2005a). The noncondensable model is particularly
important because of the presence of air in the upper portion of the HPC. The control
system module of RELAP5-3D will be used to key valve openings and input the decay
power curve of the electric heater rods. The heat structure module will play an important
role in simulating the aforementioned difficulties in modeling scaled integral test facilities.
Conclusions will be drawn on the capabilities of RELAP5-3D to model the predicted phenomena through subsequent analysis. Besides the traditional qualitative analysis mainly consisting of graphing and comparing the generated data, a quantative method
will also be selected through literature review to provide more insight into the strengths
and weaknesses of the code and the user defined free nodalization.
1.3.
Limitations
The chosen code is deemed accurate and no attempt will be made to attain the source
files and investigate discretizations of conservation laws and closure relations. In regards to
the nodalization, the available reference material for the physical description of the facility
is treated as the true description of pertinent dimensions such as lengths, diameters, areas,
10
etc. Although there is more circuitry and equipment in the data collection path, only the
manufacturer provided instrumentation uncertainty will be treated in the presentation
of the recorded data. No attempt will be made to quantify the total system biasing or
other similar endeavor. With respect to the expected dominant phenomena, it is not
the intent to develop new empirical or physics based models to describe choked flow or
condensation in the presence of non-condensables. The selected code’s built-in models
will be used and described and a literature review will be performed to gain insight into
possible discrepancies or expected results based upon the use of these already existent
models.
1.4.
Content Description
Chapter 1: Introduction The introduction to the conducted study as well as its guiding principles and limitations.
Chapter 2: Literature Review An overview of related work and similar efforts with
the chosen thermal hydraulics code as well as a discussion on published works regarding important expected phenomena.
Chapter 3: MASLWR RELAP5-3D Model An in-depth accounting of the decisions
for the construction of the MASLWR facility model in RELAP5-3D.
Chapter 4: Calculation Matrix The work conducted in RELAP5-3D is described including the full model calculations, sensitivity and nodalization studies, and standalone HPC calculations.
Chapter 5: Discussion
11
2.
LITERATURE REVIEW
With the thermal hydraulic systems code chosen, recent literature was inspected
which highlighted new uses for the code and ways to compare the experimental and calculational data. Published parallels to the MASLWR test were sought as well as papers
discussing condensation in the presence of noncondensables. Finally, the beginnings of the
IAEA ICSP was investigated.
2.1.
RELAP5-3D: New Uses and Comparing with Experimental Data
Because of the widespread use and acceptance of the RELAP modeling engine for
nuclear applications, there has been much interest in extending its use beyond its validation matrix which is the case for the current application of the coupled reactor pressure
vessel/containment as noted in Papini et al. (2010). Much of this interest consists of using
one of the members of the RELAP family to model nuclear power plants that differ from
the typical western pressurized water reactor (PWR) design. A recent, oft-published example would be the use of RELAP to model the Russian-designed VVER nuclear power
plants because of the availability of full scale plant data from Unit 6 at the Kozluduy
Nuclear Power Plant. In Groudev and Pavlova (2007), a benchmark validation problem
for RELAP5/MOD3.2 was constructed to determine the code’s ability to predict natural
circulation transients for the VVER1000. The aforementioned Unit 6 was brought to 5%
full power which is roughly decay power and the main coolant pumps were then tripped.
Subsequent operator interaction was then limited to removing a control rod group out
of the core to maintain the 5% full power initial condition. Overall, the ability of RELAP to predict loss of electrical power natural circulation conditions in the VVER100 was
deemed sufficient. In Salah et al. (2006), a main coolant pump transient was studied with
12
RELAP5/MOD3.3 coupled with the neutronics coding capability of PARCS/2.6. The RELAP5 nodalization was developed as part of a sensitivity study with adjustments made to
better incorporate the feedback effects as calculated through the PARCS/2.6 model with
the positive reactivity induced by the start-up of one of the main coolant pumps. The
agreement between the available data and the coding results was declared acceptable. In
Mousavian et al. (2004), RELAP5/MOD3 was used to study natural circulation phenomena in the VVER1000, particularly the reflux condensation mode. A simplified model
of a single loop of the VVER1000 was used to analyze the effect of elevation on natural
circulation by varying the height of the steam generators above the reactore core. Also,
reactor power was varied to show its significance in affecting the mass flow rate and reflux
condensation was identified by flow reversal in the geometric nodalization and declared to
only occur during a small break Loss of Coolant Accident (LOCA). In Mousavian et al.
(2004), an external method is also introduced to quantify the comparison between the
coding results and the data collected from the nuclear power plant. The previously cited
comparisons were more typical of traditional presentations of code calculations and experimental data in that visual representations of data graphs and usually percent deviations
from the measured value are given to show acceptability. With the prevalence of best estimate code use for design certification and licensing applications, alternative methods have
been proposed such as the quantitative Fast Fourier Transform Based Method (FFTBM)
which was used in Mousavian et al. (2004).
2.1.1
FFTBM
The FFTBM has its origin in the Mechanical and Nuclear Engineering Department
at the University of Pisa spurred by the work of a task group of the Committee on the
Safety of Nuclear Installations in the 1980s. In Ambrosini et al. (1990), the FFTBM was
introduced as a method with a sound mathematical basis which also could be used to provide a total evaluation of a code’s accuracy. In Prosek et al. (2002), the FFTBM is intro-
13
duced and its use illustrated in comparisons of collaborative problem results/calculations
which were the forerunners of the IAEA ICSP. The method hinges on the transformation
of the data presented in the time (t) domain into the frequency (f) domain via fast Fourier
transform equations (all FFTBM equations reproduced from Prosek et al. (2002))
Z
∞
F (t)e2πif t dt
(2.1)
F̃ (f )e−2πif t df
(2.2)
F̃ (f ) =
−∞
Z
∞
F (t) =
−∞
A discrete sum approximation of the integrals with an evenly spaced sampling interval τ
and N sampled values yields
Z
∞
2πifn t
F̃ (fn ) =
F (t)e
∞
dt ≈
N
−1
X
Fk e
2πifn tk τ
=τ
k=0
N
−1
X
Fk e2πikn/N
(2.3)
k=0
where fn ≡ n/N τ . However, in most cases the number of actual points must be supplemented by interpolated values to satisfy the sampling theorem. With the sampling
frequency known according to 1/τ , the number of points needed is computed as follows
1
N
2m+1
= fs = 2fmax =
=
τ
Td
Td
(2.4)
where Td is the calculational/experimental transient time. To apply the FFTBM, the
known calculational and experimental signal values in the time domain and the discrepancy
between the two values are then transformed using the previous equations. Two variables
are computed: the Average Amplitude (AA) and the Weighted Frequency (WF).
m
AA =
2
X
n=0
m
!
˜ (fn )|
|∆F
÷
2
X
n=0
!
|F̃exp (fn )|
(2.5)
14
m
WF =
2
X
n=0
m
!
˜ (fn )|fn
|∆F
÷
2
X
!
˜ (fn )|
|∆F
(2.6)
n=0
where ∆F (t) is the difference between the calculated value in the time domain and the
experimental value in the time domain. The AA gives the magnitude of the averaged
single value discrepancy of calculated and measured variables with respect to the measured variable. The WF gives additional information with respect to the type of error.
However, the method is not completely objective as performance indices are used with
additional weighting factors that are user defined to place more emphasis on the figures of
merit for the experimental/coding comparison. Three considerations have been proposed
for developing these weighting factors: the instrinsic instrumental uncertainties from the
experimental set-up, a safety relevance factor to place more importance on critical measurements such as clad temperature and pressure, and a normalization of all weighting
factors to the penultimate parameter (e. g. primary pressure). Application of the FFTBM
is declared more fruitful with a dose of engineering judgement and these understandably
arbitrary weighting factors. Actual numerical values are still needed with this quantative
method to bound results and define windows that characterize good or poor agreement.
These values were suggested after the FFTBM was applied to several test cases. The
authors of Prosek et al. (2002) also note that this quantitative comparison method is not
meant to supercede the traditional qualitative analysis. Instead, the FFTBM is to be
performed after a qualitative analysis to provide more insight into what may be improved
in a coding calculation. With this short introduction, a few potential problems are already
apparent where the user or insufficient information may adversely affect the use of this
quantitative analytical tool.
In the review article of Prosek et al. (2002), an early application of the FFTBM
to the results of ISP 21 was performed without the benefit of the user-defined weighting
15
factors, so every variable studied was given the same weighting and importance. Using
the referenced weighting table in a subsequent analysis, the total accuracy was affected
marginally though it was noted that “considerable improvements achievable in accuracy
by the tuning of variables affecting code behavior during post-test analysis was further
interesting outcome (190).” The most desirable post-processing method would be objective and free of any such tuning. In the conclusion to Prosek et al. (2002), it was noted
that one way to combat the arbitrary nature of the weighting factors is “when a sufficient
number of variables is used in FFTBM analysis the influence of engineering judgement (in
the specification of weighting factors) on the results is less important (201).” Although
a less arbitrary method would be desired it is not required and this method is straightforward. In Prosek et al. (2002), a pre- and post-test analysis of the IAEA’s SPE-4 test
was quantified with two code assessment methods, the FFTBM as well as the Stochastic
Approximation Ratio Based Method (SARBM). In the SARBM, second order moments
are taken about the calculated signal, error signal and difference between the two signals
and then plugged into an equation to compute the stochastic approximation ratio. The
two methods were compared according to a total accuracy equation with weighting factors
and two different sets of acceptability criteria. Two additional measures concerning the
acceptability criteria were proposed: the minimal variable accuracy and the number of
discrepancies. Ultimately, these two new variables were used to show the supremacy of
the FFTBM over the SARBM. These variables were not seen in other available literature.
In Muellner et al. (2005), a thermal hydraulic model using the RELAP5 engine
was developed to model a scaled VVER-1000 facility. The flow volumes were modeled
using the sliced approach because this “is suitable for a better code response, especially
in natural circulation and/or low flow rate regimes (5).” Besides the FFTBM analysis
that has already been described, the method was also used to qualify the nodalization by
16
changing the code inputs to measured values to show that the true values produced the
best comparison between experiment and code calculations. For the transient modeled in
the paper, the facility and break sizes were input greater than and less than the true measurements in RELAP5 to show that the chosen nodalization performed better according
to the FFTBM because the actual values were more accurate. In Shahedi et al. (2010), the
FFTBM was used to qualify the RELAP5/MOD3.2 nodalization of an integral test facility
that is a scaled version of the VVER-1000. A sensitivity study of the steam generator
nodalization was performed and the FFTBM provided single values for each nodalization
to guide the decision for the best nodalization scheme. Both of these papers illustrate the
extra information available from the application of the FFTBM in the development of an
accurate nodalization.
2.2.
Similar Experiments
As mentioned, the high pressure containment of the MASLWR concept is singular
in the current state of the nuclear industry and coupling of reactor pressure vessel and
containment thermal hydraulics has been unnecessary in past and present safety analyses.
However, there are a few parallels in the published studies of the IRIS concept. In Oriani
et al. (2004), the passive safety systems that respond to a small break LOCA in the
IRIS concept are described. In the IRIS design, coolant mass inventory is maintained
during a LOCA transient through a depressurization mechanism similar to the MASLWR
facility. After a break, coolant from the RPV is lost to a containment vessel where the
pressure begins to rise as a result of the heated mass increase. Further coolant inventory
is preserved through condensation in the steam generators and a pressure equalization
between the RPV and the containment vessel. Consequently, the interaction between the
two vessels is very important in conserving the coolant inventory in the RPV and keeping
17
the core covered. After pressure equalization, break flow rate reverses and begins flowing
back into the RPV. However, the authors explain that this is more due to the activity
of a high elevation suppression pool than the reversed break flow from the containment.
Nevertheless, a shortcoming in the present set of analysis codes was identified. A single
code program does not exist to model containment and pressure vessel cooperation.
In a companion paper to Oriani et al. (2004), the coupling of the RELAP5/mod3.3 and
GOTHIC 3.4e codes is described as a solution to the modeling issue. In Grgic (2004),
the authors describe the current PWR analysis strategy of treating the flow of coolant
analysis and the mass loss to the containment separately due to their time dependence and
spatial effects. As an alternative to developing and verifying a new analytical code, the
decision was made to couple existing codes and frequently update the boundary conditions
predicted by the mass and energy release of the best estimate thermal hydraulic code to a
containment analysis code instead of waiting until the end of the LOCA transient to supply
information to the containment tool for analysis. The results of the GOTHIC analysis
would then be fed into the RELAP5 model to initialize the next RELAP5 iteration. This
presented some difficulties because the two codes supply different variable properties.
GOTHIC supplies mixture mass flow rate, mixture enthalpy, total pressure, liquid volume
fraction, steam pressure ratio, and gas pressure ratios for each of the non-condensable
gases. RELAP5 produces total pressure, liquid and vapor specific internal energy, vapor
void fraction, and non-condensable gas quality quantities. The vessel interaction locations
where the two codes will swap information are at the postulated break, the automatic
depressurization system and the makeup flow path from the elevated suppression pool.
Since there is no physical facility and the concept was still being ironed out, the authors
presented calculations done with RELAP5 only and the coupled code set-up to show that
the data conversions were being done correctly. The two strategies gave similar results and
it was noted that RELAP5 was used alone to evaluate a similar scenario at the PANDA
18
experimental facility. It was noted that duplicating the PANDA experimental results with
the proposed coupling scheme would be useful for assessment.
An alternative coupling scheme was also investigated for the IRIS concept. In del Nevo
et al. (2004), RELAP5, MELCOR and FUMO was used to evaluate the small break
LOCA transient discussed earlier. MELCOR was designed to follow the progression of a
severe accident although it also can be used to model design basis accidents. FUMO is a
simpler, more efficient code originally designed to model dry containments. The geometric
model of the containment in RELAP5 was nodalized in a similar manner to the GOTHIC
nodalization of the containment from Grgic (2004) to have confidence in comparing the
results of the two coding analyses. The MELCOR balance of plant nodalization included
detailed modeling of the integral steam generators and the emergency safety elements of
the IRIS design. The containment was nodalized similar to the GOTHIC scheme. A
simpler schematic of the balance of plant was built in FUMO to allow for a reduced
computational time. One of the interesting features from many of the figures presented in
the paper is that the RELAP5 stand-alone and RELAP5/GOTHIC models closely mirror
each other. One of the exceptions is the containment pressure during the transient. The
authors note that even though the stand-alone RELAP5 model predicts a similar mass
and energy discharge through the break compared to the coupled code, the pressurization
in the containment is slower. This prompted an additional comparison between the four
coding schemes. The containment schemes were all supplied the same input data from the
RELAP5/GOTHIC calculation to be used as boundary conditions. Comparison between
FUMO, MELCOR and GOTHIC was presented first to illustrate that the differences
seen in the earlier analysis was due to different break discharge models. Using identical
boundary conditions, the codes supplied similar curves with a higher pressure predicted
by MELCOR. Further differences are discussed such as dry containment non-condensable
19
gas dynamics. During the RELAP containment analysis, it was noted that by slicing up
the containment model in RELAP an unintended thermal stratification was induced even
though it is postulated that the suppression pool should be strongly mixed. The paper
concluded by identifying possible culprits for code discrepancies.
2.3.
Condensation in the Presence of Noncondensables
The pioneering work in condensation with noncondensables present was published
by Colburn and Hougen in 1934. As described in the publication, a few methods had been
proposed that modified the log mean temperature difference approach for heat exchanger
calculations, but the authors note that no uniform temperature may be used because of the
uneven concentration of vapor and noncondensables throughout the condensation process.
A new method was proposed that treated the heat transfer through the condensate, gas
film, and piping as a series of resistances. An energy balance was constructed with the
unknown variables consisting of the interface temperature between the gas and condensate
as well as the partial pressure of the condensate. The balance is achieved by guessing the
interface temperature which supplies the partial pressures at the interface and iterating
until it is satisfied. The ad hoc model used in RELAP5-3D is based upon this iterative
approach (INL (2005c), 4-123ff). The heat flux from the liquid film to the wall is set equal
to the heat flux due to condensation of vapor mass flux.
q00l = q00v
(2.7)
20
where the heat flux from the liquid film to the wall is determined by
q00l = hc (Tvi − Tw )
hc = condensation heat transfer coefficient
Tvi = interface saturation temperature
Tw = wall temperature
(2.8)
To determine the condensation heat transfer coefficient, a modification is made to the
volumetric condensation heat transfer coefficient that is used without the presence of
noncondensables. As outlined in Appendix 4A of INL (2005c), the maximum value of the
Shah (turbulent flow) and Nusselt (laminar flow) correlations are modified by functions of
the noncondensable gas mass fraction for subcooled liquid and subcooled vapor/gas. and
the heat flux due to condensation of vapor mass flux is determined by
q00v = hm hfgb ρvb ln
1−
1−
Pvi
P
Pvb
P
!
hm = mass transfer coefficient
hfgb = vapor minus liquid saturation specific enthalpy based on Pvb
ρvb = saturation vapor density at bulk vapor partial pressure
Pvb = vapor partial pressure in the bulk
Pvi = vapor partial pressure at the liquid-vapor/gas interface
P = total pressure
(2.9)
The iterated value is the interface saturation temperature (Tvi ) which in turn determines
an interface partial pressure (Pvi ).
Another option to the reduction factor approach peformed in RELAP5-3D would be
21
the use of one of the more widely used correlations for a noncondensable-specific condensation heat transfer coefficient from the work of Uchida et al. (1964). Interestingly, this
conference proceedings was primarily focused on non-uniformities in core spray systems
and how this would affect the release of fission products during accident scenarios. Tucked
away at the end of the publication is a discussion of experimental work with condensation
on a rectangular vertical surface in the presence of air, nitrogen and argon separately.
Pressure is around atmospheric and the weight ratio of steam to the different noncondensables was varied to produce a data graph which has been used to develop a heat transfer
coefficient correlation. In Corradini (1984), the data is correlated as
htot = 379(mg /mv )−.707 (W/m2 · K)
mg /mv < 20
(2.10)
where mg and mv refer to the mass of the noncondensables and the mass of the steam
respectively. Furthermore, the author of Corradini (1984) states in his introduction that
the work of Uchida et al. (Uchida et al. (1964)) and his colleague Tagami were the most
relevant experimental treatment of condensation with noncondensables, but additional
confirmation would be wise with data from experimental apparatus with different scales
and/or different techniques for determining the heat transfer coefficient. Such an experiment was mentioned in Peterson et al. (1993) that verified the data of Uchida et al. and
Tagami.
The work of Colburn and Housen (1934) and that of Uchida et al. (1964) represent
the foundation for much of the systems code calculation of condensation in the presence
of noncondensables (as opposed to the more computationally intensive boundary layer
approaches). This relatively light and simple treatment of the effect of noncondensables
on condensation was merited because of the low importance of the phenomena for tra-
22
ditional light water reactors. Consequently, the importance of the phenomena for the
depressurization of the reactor pressure vessel in the MASLWR concept was one of the
features that led to the formulation of the ICSP test. A review of improvements to the
Colburn and Hougen method was conducted to provide insight into the expected results
of the RELAP5-3D compared to the experimental results.
In Peterson et al. (1993), the authors suggest that an effective condensation thermal
conductivity may be determined and applied to a balance equation that stipulates that the
heat flux through the condensate film and condensing wall equal the sum of the sensible
and latent heat transfer through the noncondensable diffusion layer. The method for
combining the condensation heat transfer coefficients appears to be rooted from a footnote
in Colburn and Housen (1934) which states that heat transfer coefficients for saturated
mixtures may be derived from the Clausius-Clapeyron equation and a heat balance. A
modified Clausius-Clapeyron equation is used along with Fick’s law and the ideal gas law
to develop an effective condensation thermal conductivity with the Sherwood number.
The result is a total heat flux equation which manuevers around iterating on the interface
temperature
qt00 =
hc (Tbs − T∞ ) + hs (Tb − T∞ )
s
1 + hch+h
w
hc = condensing heat transfer coefficient
Tbs = saturated bulk temperature
T∞ = bulk cooling medium temperature
hs = sensible heat transfer coefficient
hw = wall, film and external resistance heat transfer coefficient
(2.11)
The gain is somewhat logistical in that it improves the iteration speed, but this method
23
also does not neglect the sensible heat transfer which is an assumption made in the condensation calculation performed in RELAP5-3D, INL (2005c). In Peterson et al. (1993),
the work of Mori and Hijikata (1973) is cited to highlight the influence of sensible heat
transfer when the gas concentration is higher through mist formation. In Mori and Hijikata (1973), a boundary layer approach was applied to saturated vapor conditions in the
presence of noncondensables on a vertical plane. This analytical study mainly involved
treating the equilibrium condition and investigating the effect of small and large temperature differences. The authors do not explicitly state that mist formation at low gas
concentrations affects the heat transfer solution. This conclusion is not easily deduced.
In Liao and Vierow (2007), a generalized diffusion layer model is derived from a
mass basis and a similiar statement to that of Peterson et al. (1993) is made by declaring
that for high gas concentrations fog formation effects multiply the sensible heat transfer and increase its magnitude to bring it on par with the latent heat transfer. The fog
formation study was described in Brouwers (1996) where the author showed that the formulation of Peterson et al. (1993) included the effects of suction/blowing and that fog
formation correction factors may also be applied. A graphical depiction of the effect of
the correction factors as a function of interface temperature for a specific case was also
presented. The authors of Liao and Vierow (2007) go on to state that the mass based
formulation of the diffusion layer model is more appropriate when applied with the heat
and mass transfer analogy. This statement is also supported by the work of Ambrosini
et al. (2006). In Ambrosini et al. (2006), the application of the heat and mass transfer
analogy to condensation heat transfer problems is studied with respect to the underlying
assumptions and boundary conditions that are necessary for the development of different
models. The authors proceed to show the different critical assumptions for the molar and
mass bases. The mass basis assumes that temperature variations along the boundary layer
24
have a negligible effect on properties that are temperature dependent and the molar basis
assumes that that there is a constant mixture density even when there may be a considerable difference in molecular weight between the gas and the vapor. The authors show that
the difference between the molar and mass bases depends on the definition for the average
molar weight of the mixture. The difference between the two formulations is most evident
at large dissimilarities between molar fractions and the mass approach typically provides
mass flux values of greater magnitude than the molar approach. Reverting back to the
discussion of Liao and Vierow (2007), the importance of variable mixture weight, a massbased quantity, is captured with this generalized methodology. The authors show that the
condensation thermal conductivity is similar to that presented by Peterson et al. (1993)
and that both formulations include the effect of suction. The justification that this new
model is general is conducted by demonstrating that if the underlying assumption in Fick’s
law for the molar basis is applied to the new condensation thermal conductivity then the
new kc is equal to the kc of Peterson et al. (1993). A similar vein of logic is used to show
through of Fick’s law of diffusion and the kinetic theory of gases for mass diffusion that
the mass diffusion formulation is more appropriate because it represents the diffusive flux
under the limiting case for constant mixture molecular weight through the diffusion layer.
Because the mass basis takes into account the difference in mixture molecular weights
through the boundary layer an additional term in the diffusive condensation mass flux is
present which should help to correct the stated underprediction of experimental data by
the model of Peterson et al. (1993). In the comparison with experimental data, a single
log-log graph is used to illustrate that the data is mostly within a band of ±20% off of the
linear slope. Deviation is largely ascribed to film waviness effects which were not treated
due to lack of knowledge. Only condensation in vertical tubes with noncondensables was
compared and there was no visual comparison between this proposed generalized model
and that of Peterson et al. (1993).
25
Experimental investigation into the effect of noncondensable gas on condensation
was prompted by the proposed design of the Westinghouse AP600 passive containment
cooling systems. This work spawned the publication of Anderson et al. (1998) and Herranz
et al. (1998) which describes the experimental and condensation model accomplishments,
respectively. In Anderson et al. (1998), the experimental test section representations of
radial slices of the AP600 containment design are described along with some of the experimental results. The authors state that one of the goals of the experimental testing
would be to determine the effect of major and minor variables on the condensation with
noncondensable process and to provide a venue for evaluating heat transfer correlations.
Two methods were used to experimentally determine heat transfer coefficients. An array of thermocouples and a specially designed probe was used to determine a heat flux
measurement according to
hi =
k(dTi /dx)
Tb,i − Tw,i
(2.12)
where the subscripts ‘b’ and ’w’ refer to the gas/vapor bulk and wall temperatures respectively. The other method used a coolant energy balance according to
hi =
ρl Cp V̇i ∆Tcoolant,i
Ai (Tb,i − Tw,i )
(2.13)
where the coolant channels in the test section were fed water with a known temperature.
The energy balance was performed on this liquid to determine the energy removed by
the condensing plate. The results presented in Anderson et al. (1998) were used in the
validation of a diffusion layer model modified from Peterson et al. (1993) and developed
as described in Herranz et al. (1998). The total heat flux from the bulk to the condensing
wall was presented as a series of resistances
qbw = ht (Tb − Tw ) =
hfilm (hconv + hcond )
(Tb − Tw )
hfilm + hconv + hcond
(2.14)
26
One of the key departures from the model of Peterson et al. (1993) is the treatment of the
condensation conductivity and consequently the application of Clausius-Clapeyron equation. The authors state that the approximation used in the integration of the ClausiusClapeyron equation
hfg
∆P
=
∆T
Tavg vfg
(2.15)
has substantial property deviations for the range of temperatures expected during accident
scenarios in the AP600 containment. To account for the deviations, the ideal gas law is
applied to the specific volume change term (vfg ). Other modifications include treating
the suction effect and the influence of light noncondensables such as helium. It was
noted during the discussion of differing wall subcooling margins that oft-used correlations
such as Uchida’s, Tagami’s and Kataoka’s were developed from experimental data with
constant wall temperatures. Also, a section was devoted to examining the effects of
pressure which affects concentrations and properties in the gas/vapor bulk. A total heat
transfer coefficient was developed without the contribution from sensible heat transfer
while using ideal gas law assumptions and agreeing with the kinetic theory of gases. The
authors surmised that the pressure dependence of the heat transfer coefficient is prominent
only in that it changes the mass fraction which is the primary contributor to changes in
heat transfer.
With the development of new methods for predicting condensation in the presence
of noncondensables, there was an understandable interest in the implementation of new
models in systems codes. In Hassan and Raja (1993) and Hassan and Banerjee (1996),
the U. S. Nuclear Regulatory Commission maintained RELAP5/MOD3 thermal hydraulic
code along with a modified version is compared with various separate effects facilities to
investigate its ability to model condensation in the presence of noncondensables. The
earlier reference, Hassan and Raja (1993), is primarily a scoping study to either show
27
that the current models in RELAP5/MOD3 were adequate or that they needed updating.
A containment type experimental set-up was modeled in RELAP5/MOD3 and results of
the experiments performed were compared with the computational results. A sufficient
amount of graphics were presented to illustrate deficiencies in the present model. One
graphic illustrated the variation of the heat transfer coefficient with different air mass
fractions and two different pressures (1.5 atm and 4.5 atm). Noticeably different experimental values are shown, especially at low air mass fractions, but RELAP5/MOD3
predicted essentially identical heat transfer coefficients for the different pressures. The
pressure of 4.5 atm (66 psi) is typical of the higher end of expected pressures in traditional containment designs during accidents, but the HPC design of the MASLWR concept
will operate at pressures between 200-250 psi(gauge) during the initial blowdown sequence
of the ICSP test as well as much lower pressures during the long term cooling portion of
the testing.
With the scoping study completed, the work presented in Hassan and Banerjee
(1996) was conducted to improve the condensation model’s response to noncondensables
in RELAP5/MOD3. The goal was to implement a condensation model similar to that of
Peterson et al. (1993) and evaluate this model against data from several separate effects
test facilities. As described previously, the authors assert that the current models rely
on very narrow assumptions and correlations as opposed to a physics based approach.
A model similar to Peterson et al. (1993) with previously proposed correlations for heat
transfer coefficients, the Nusselt number, and the Sherwood number was developed and
compared once again with the seperate effects test facilities used for the scoping study.
Two open tank facilities were used which have some similarities to the MASLWR HPC.
One of the facilities was developed to simulate a pressurizer where nitrogen was injected
into the pressurizer tank and pressure was monitored as steam condensed inside the vessel
28
until a prescribed water level was reached. Tests at 3% and 10% nitrogen gas by weight
were performed and the pressure histories were graphed with the modified and unmodified
RELAP5 runs and the experimental data points. The trends of the 3% results were well
modeled by both RELAP5 runs although there was an underprediction of the pressure
by the unmodified code. However, the modified RELAP5 model was shown to be clearly
superior for the 10% nitrogen run. The authors note that the correlations used in the model
were developed with tube experiments although they are being applied to an open tank
facility and that forced convection conditions were also used for correlation development
though some of the experimental validation was done with natural circulation facilities.
The open tank style facility used in the scoping study was also investigated to provide more
data for comparison, yet one of the drawbacks of this facility noted in both sources is that
the air mass fraction is not precisely known. The figures provided in the publication both
have air mass fraction on the abscissa. It is also interesting that the previously mentioned
heat transfer coefficient plot from Hassan and Raja (1993) showcases considerably different
trends although the parameters listed in the two publications (air mass and total pressure)
are the same. More information would be helpful.
In Hogan et al. (2010), a generalized diffusion layer model is input into the MELCOR code to determine the possible improvements in predicting tube condensation of
steam with noncondensables with an improved version of the stagnant film theory already
employed in MELCOR. The authors note the structure of the MELCOR solver limits the
calculation of temperature and pressure to one average value per control volume. The
implementation of the new model must consider this artifact of the MELCOR solution
method. The stagnant film model used in MELCOR has many familiar features such as
a molar based formulation, determination of the Sherwood number with a heat transfer
correlation, use of the ideal gas law to calculate the vapor mole fraction and a subsequent
29
underprediction of the condensation mass flow rate as referenced by the authors to Ghiaasiaan and Eghbali (1997) which described the limitations and assumptions of the model
of Peterson et al. (1993) such as its molar-based formulation. The generalized diffusion
layer model of Liao and Vierow (2007) is used because of its calculation of the mass average
mixture velocity which accounts for disparate molecular weights between the noncondensable gas and steam vapor. The experimental data used to validate the new MELCOR
model included flat plate and tube condensation experiments. The flat plate data was
taken from the experimental apparatus of Anderson et al. (1998). Total system pressure
was equal to atmospheric pressure for each of the tests used for the validation of the updated MELCOR model. The visual representation of the results using the experimental
data of Anderson et al. (1998) showed the averaged experimental heat transfer coefficient
on the abscissa and the averaged heat transfer coefficient calculated by MELCOR at six
different positions along the vertical plate condensing surface. A slight improvement was
also shown in a tabulation of the standard deviation of the two MELCOR models. The
authors do note however that the MELCOR calculations were subject to user effects from
the chosen free nodalization scheme.
Other recent model developments include the work of Kim et al. (2009) where a theoretical study of the thermal hydraulic characteristics of the steam-nitrogen pressurizer
of the REX-10 (SMART concept) is undertaken prompted by the lack of work done with
condensation heat transfer at high pressure for natural convection in the presence of noncondensables. The experimental apparatus was run at pressures ranging from 0.1 MPa all
the way up to 2.0 MPa which represents some of the highest pressures seen in experimental work on condensation with noncondensables. A model was expounded which applied
the heat and mass transfer analogy along the same lines as the diffusion layer model. It
assumes that there are two main heat transfer mechanisms: convective heat transfer in
30
the diffusion layer and the condensation heat transfer carried by mass transfer from the
vapor to the interface. Seen as a circuit of resistances, the total heat transfer coefficient is
htot =
1
1/hf + 1/hcond + hconv
(2.16)
Previously cited studies have used the ideal gas assumption though the authors of Kim
et al. (2009) note that the compressibility of a steam/gas mixture at 2.0 MPa (290 psi) is
0.8865 as opposed to 0.9852 at 0.1 MPa (approximately atmospheric pressure at sea level).
A comparison between the model of Peterson et al. (1993), the model developed by the
authors and the experimental data illustrated the benefits of accounting for compressibility
though the models were similar.
In Ganguli et al. (2008), the diffusion layer model popularized by Peterson et al.
(1993) undergoes another iteration with a focus on the condensation conductivity and
the effective mass diffusivity. The authors identified various parameters and ranked their
importance as follows: primary variables consist of the noncondensable gas mass fraction,
the subcooled temperature difference and pressures, etc. which are used to calculate heat
transfer coefficients, secondary variables are phenomena such as the suction effect, mist
formation, and film waviness, and tertiary variables are parameters such as the type of
noncondensable and the orientation of the condensing surface. The heat flux balance is
similiar to previous models (exactly the same as Herranz et al. (1998))
q 00 = ht (Tb − Tw ) =
hfilm (hconv + hcond )
hfilm + hconv + hcond
(Tb − Tw )
(2.17)
The primary variables are used to calculate the film heat transfer coefficient with the
Kutateladze correlation for treating the ripple effect, the Churchill and Chu correlation
is used for the convective heat transfer coefficient, and the condensation heat transfer
31
coefficient is determined through
hcond =
Sh0
L
kcond
(2.18)
where a new formulation of the effective thermal conductivity is proposed.
kcond =
ρavg DHfg
(Tb − Ti )(Wnc,i − Wnc,b )/Wnc,i
(2.19)
More emphasis is placed upon the interface than the formulation of Peterson et al. (1993)
and the interface temperature is the iterated variable as it was for the model of Colburn
and Housen (1934).
2.4.
Standard Problems
The origin of the IAEA ICSP can be traced back to the efforts of the Committee on
the Safety of Nuclear Installations (CSNI) that operated underneath the Nuclear Energy
Agency of the Organisation for Economic Co-operation and Development. In the 1970s,
the CSNI began organizing standard problems with the following objectives as replicated
from the LOCA specific content of CSNI (1977)
1. To contribute to a better engineering understanding of the postulated LOCA event
in a nuclear reactor and the interaction of the ECC systems.
2. To provide a comparison of best-estimate computer code calculations to experimental
data under controlled conditions.
3. To evaluate the capability of computer codes in adequately predicting the consequences of postulated LOCA events in a nuclear reactor.
4. To provide the participating countries with information for adequately quantifying
32
the safety margins in LOCA analysis with respect to their current licensing criteria.
These problems which were not limited to LOCA events eventually became known as
International Standard Problems (ISPs) and from these problems, the ICSPs have inherited the terms “blind problem” referring to the release of experimental results after the
submission of calculated results and “open problem” where experimental results are made
available before calculations are evaluated. In Prosek et al. (2002), a list of ISPs where the
FFTBM was applied for post-processing analysis gives a glimpse of the scope of problems
that were performed. LOCA events were studied for ISP 18 at the LOBI test facility, ISP
21 at the PIPER-ONE test facility and ISP 27 at the BETHSY test facility. A loss of
feedwater transient was studied at the SPES test facility for ISP 22. More recent ISPs
include more exotic tests including the ISP 35 hydrogen mixing test for containment code
calculations and the ISP 39 severe accident fuel coolant interaction and quenching test.
The history of the IAEA ICSP has a much shorter timeline. The only other ICSP that
has been completed was a study of large break LOCA with the RD-14M heavy water test
facility.
33
3.
MASLWR RELAP5-3D MODEL
The RELAP5-3D 2.4.2 nodalization has been performed to resemble the geometric
data presented in Woods et al. (2010). In Figure 3.1, a diagram of the nodalization is
depicted.
3.1.
3.1.1
Reactor Pressure Vessel
Core Region
The electrical core region has been modeled with pipe elements in RELAP5-3D with
the total length of 63.01 cm from Woods et al. (2010) approximated as 6 equal segments
of 10.5 cm. The area of each element has been input as 8.422 × 10−3 m with a hydraulic
diameter of 9.59 × 10−3 m. In the preliminary model, a forward and reverse loss coefficient
of 10.0 was input for the junction to simulate the frictional losses due to the core grid wires
which momentarily decrease the flow area by a factor of 2. Also, an additional turbulent
friction equation was input because the core section is not a smooth pipe but rodded. A
user-input friction factor may be input in RELAP5-3D in the following form
f = A + B(Re)−C
(3.1)
In Todreas and Kazimi (1990), a friction factor correlation is presented for a rod bundle
in a square array for turbulent flow on pgs. 384-386. The pitch to diameter ratio for the
MASLWR electrical core is 1.17 so the appropriate correlation for interior flow is
fiT ≡
0.1339 + 0.09059(1.17 − 1) − 0.09926(1.17 − 1)2
(Re0iT )0.18
(3.2)
34
High Pressure
Containment
ADS Vent Lines
#420-421
#430-431
Cooling
Pool
Vessel
#607
#302
PCS-106A
#301
#606
Pressurizer
#605
#604
#800
#300
Cold Leg
#201
#603
Hot Leg
#602
ADS Sump Lines
#401-402
#411-412
#110
#601
#600
Insulation
HS #101
#100
HL/CL Heat
Transfer
HS #102-105
Heat Transfer
Plate
HS #800
Insulation
HS #601-605
FIGURE 3.1: RELAP5-3D Nodalization Diagram
#202
Core
HS #130-135
35
3.1.2
Electrical Core Heat Structure
To model the 56 electrical heater rods which supply the heat input to the MASLWR
facility, a heat structure was created for each of the six pipe elements that comprise the
core region. Each rod has a heated length of 0.597 m. Consequently, five out of the
six core pipe elements have a heated length equal to the fluid volume length times the
number of heater rods ((0.105 m)×(56) = 5.88 m). The upper core pipe element has an
abbreviated heat input. A control variable is used to control the heat input to each of the
heat structures. Geometry type 110 is specified for a vertical bundle without crossflow
with the twelve word option specified for the additional right boundary options to instruct
RELAP5-3D that the heat structure is a natural convection cell with the pitch to diameter
ratio of the MASLWR electrical core.
3.1.3
Hot Leg
One of the important considerations in nodalizing the hot leg is to match up ele-
vations of elements with the differential pressure taps that penetrate the hot leg. Also,
the differential pressure taps across the steam generator and into the downcomer must
be considered because the heat that conducts through the hot leg into the downcomer is
modeled by matching up elevations between the two legs and creating a heat structure to
connect the flow volumes. The core region ends at 0.63 cm above the reference elevation.
The next significant penetration is at 5.08 cm for the low pressure tap for DP-101 and
the high pressure tap for DP-102. This is followed by the elevation of the core outlet
thermocouple (TF-106) at 16.51 cm above the reference. These two parameters dictate
the length of the first few elements of the hot leg. The first segment of pipe element 110
has an elevation change of (5.08 - 0.63) = 4.45 cm. The next two elements are set equal
to each other to maximize their elevation changes while centering a pipe element around
the aforementioned core outlet thermocouples. This was determined according to (16.51
36
TABLE 3.1: Differential Pressure Tap Elevations
DP-101 (high
(low
DP-102 (high
(low
DP-103 (high
(low
DP-104 (high
(low
DP-105 (high
(low
DP-106 (high
(low
LDP-106 (high
(low
LDP-301 (high
(low
FDP-131 (high
(low
Instrument
pressure tap)
pressure tap)
pressure tap)
pressure tap)
pressure tap)
pressure tap)
pressure tap)
pressure tap)
pressure tap)
pressure tap)
pressure tap)
pressure tap)
pressure tap)
pressure tap)
pressure tap)
pressure tap)
pressure tap)
pressure tap)
Elevation
-0.6482 m
0.0508 m
0.0508 m
0.400 m
0.400 m
0.695 m
0.695 m
2.991 m
1.540 m
2.991 m
-0.6482 m
1.540 m
-0.6482 m
3.115 m
3.115 m
3.745 m
1.486 m
1.540 m
37
- 5.08)/1.5 = 7.62 cm segments. The slight decrease in flow area and slight increase in
wetted perimeter due to the thermocouple rod was ignored. The hydraulic diameter of
the Hot Leg Regions 1 and 2 (using the notation of Woods et al. (2010)) is
hD =
4 × 305.13 cm2
1m
×
= 0.1971 m
61.92 cm
100 cm
(3.3)
and Hot Leg Region 2 ends at 42.55 cm. The remaining elevation change will be split into
two pipe elements with an elevation change of (42.55 - 20.32)/2 = 11.115 cm each or one
length of 11.11 cm and one of 11.12 cm. The next hydrodynamic volume of the MASLWR
facility is the conical reducer section of the hot leg. This section represents a linear area
change between the lower hot leg and the narrower chimney portion of the hot leg. The
conical section has been split up into two pipe elements with average values for the area
and the hydraulic diameter taken for each section as follows.
average segment =
(305.1 − 82.13) cm2
= 74.32 cm2
3
flow area1 = 305.13 − 74.32 = 230.8 cm2
flow area2 = 230.80 − 74.32 = 156.5 cm2
average segment =
(3.4)
(61.92 − 32.13) cm
= 9.93 cm
3
wetted perimeter1 = 61.92 − 9.93 = 51.99 cm
wetted perimeter2 = 51.99 − 9.93 = 42.06 cm
4 × 230.8 cm2
1m
×
= 0.1776 m
51.99 cm
100 cm
4 × 156.5 cm2
1m
hydraulic diameter2 =
×
= 0.1488 m
42.06 cm
100 cm
(3.5)
hydraulic diameter1 =
(3.6)
38
In regards to the instrumentation taps, the high and low pressure taps for DP-103 do not
match up exactly with the elevation change of the reducer section which is the section
of the pressure loss that it is measuring. The two elements that have been developed
for the conical reducer section in the thermal-hydraulic model will be compared with the
instrumentation data. The lower chimney section has no instrumentation until it nears
the steam generator coils where there are instrumentation taps and the v-cone flow meter.
The high pressure tap for the v-cone is at 148.6 cm above reference. The next several
element lengths will be (148.6 - 67.01)/8 = 10.1988 cm. This will be simplified to seven
elements with a length of 10.2 cm and one element with a length of 10.19 cm. The
hydraulic diameter for this section is
hD =
4 × 82.13 cm2
1m
×
= 0.1022 m
32.13 cm
100 cm
(3.7)
The low pressure tap is at an elevation of 154.0 cm which will determine the length of the
next pipe element (154.0-148.6 = 5.4 cm). The next stretch in the chimney is crowded
with areas of hydrodynamic interest because of the v-cone flowmeter on the chimney and
the beginning of the steam generator (SG) coils on the cold leg side. The region with
the v-cone flowmeter traverses the hot leg from a heigh of 154 cm to 165.1 cm. On the
cold leg side, the SG coil outlet ends at 157.8 cm and begins at 167.95 cm. The v-cone
flowmeter section represents a pressure loss which could be represented over multiple flow
elements if necessary. Matching pipe elements would require two relative small elements of
(157.84 − 154) = 3.84 cm and (167.95 − 165.11) = 2.84 cm. A somewhat arbitrary decision
has been made to forego the 2.84 cm length and keep the 3.84 cm length because of the
lower elevation section in the hot leg that represents the distance between the pressure
taps of FDP-131. The decrease in flow area and increase in wetted perimeter due to the
v-cone flowmeter will be neglected and in the form of compensation, flow losses will be
input at the junction of the pipe element to account for the pressure loss. The nodalization
39
to the top of the cold leg is only dependent on the SG coil sections in the cold leg because
the next pressure tap penetration is above the riser. The lengths of the remaining hot leg
elevation will be divided up as follows
FDP-131 low pressure tap to SG Coil Outlet = 3.84 cm
SG Coil Outlet = 10.11 cm
SG Coil Section =
94.66 cm
= 10.51778 cm
9
SG Coil Inlet = 10.11 cm
Upper Cold Leg = 14.33 cm
(3.8)
The geometric details for the natural circulation flow circuit can be seen in Table 3.2.
3.1.4
Hot Leg to Cold Leg Conduction and Ambient Heat Loss
The riser section of the natural circulation circuit is not thermally insulated from
the downcomer as evidenced from the rendering of Figure 1.2. Because the ICSP test will
begin at steady state conditions with a large heat input (≈299 kW) and then decay from
a fraction of the starting power (≈36 kW), conduction through the stainless steel riser
may influence the experimental testing. In a 2-D numerical stability conducted by the
authors of Misale et al. (2000), pipe thermal capacity and axial conduction was included
in a finite differencing solution scheme of the conservation equations of a rectangular
natural circulation loop. The study was limited to laminar flow only, but the observation
of the transient calculations was that adding the pipe thermal capacity served to stabilize
the solution during heat-up. The default convection boundary condition was used which
selects a heat transfer correlation developed for internal vertical pipe flow based upon the
flow regime such as the Churchill-Chu or McAdams correlation for natural convection flow.
Also, the built-in stainless steel material properties were used to simulate the conduction
through the riser to the downcomer.
40
Because the shell within a shell design concept is maintained through insulated
vessels, the modeling of the ambient heat loss will be critical in determining the operating
conditions and simulating the cooldown of the facility after the loss of feedwater initiating
event. The thermal properties of the insulation as well as the thickness is available from
Woods et al. (2010). The thermal conductivity and heat capacity of the insulation was
input into a table in RELAP5-3D which uses linear interpolation in between temperature
values to determine the inputs into the heat structure models in the code. The default
convection boundary condition was used on the left boundary (downcomer, pressurizer,
etc.) again and a table was created to input the ambient air temperature on the right
boundary of the heat structures.
3.1.5
Upper Plenum and Pressurizer
To model the upper plenum, the branch component in RELAP5-3D is used to attach
multiple fluid flows to the same face of a component. The length was chosen as 12.05 cm
which is the remaining elevation change until the low pressure tap for DP-105 and DP104. The pipe element that represents the pressurizer also contains a portion of the upper
plenum, the baffle plate, and the pressurizer volume that occupies the upper portion of
the reactor pressure vessel. The start of the pressurizer pipe element is at 2.9917 m. This
leaves (307.98 − 299.17) = 8.81 cm of vertical length until the beginning of the baffle plate.
Other important elevations to consider in the pressurizer are the instrumentation tap at
311.5 cm, the pressurizer heaters at 314.3 cm, and the ADS vent lines plus instrumentation
tap at 374.5 cm. To divide up the dimensions of the pressurizer, the first length will be
made to the beginning of the baffle plate. The next vertical travel will be made to center
the pressurizer heaters in the middle of the element and then incremental elements will
be made up the length of the pressurizer. The top of the pressurizer will be treated as
having an elevation of 369.5 cm. This is done to insert a branch component on top of the
41
reactor pressure vessel which will serve as the ADS vent line connection. The dimensions
of the reactor vessel cap are not explicitly stated in the engineering drawings of the facility.
Another item worth considering is the initial condition for the test which states that there
is 14±2 in. of water in the pressurizer from the level reading of LDP-301. This will dictate
the element length which separates the liquid and steam environments. The geometric
description of the pressurizer is tabulated in Table 3.3.
3.1.6
Pressurizer Heater Rods
Three 4 kW heater rods are used to maintain the pressure in the MASLWR RPV.
Though the pressurizer (PZR) heater rods are energized during the intial condition set-up,
they are not active during the blowdown transient. Consequently, the PZR heater rods
were not included in the model.
3.1.7
Cold Leg
The elevation changes for the cold leg are already set by the hot leg because the
heat transfer between legs is to be modeled by a heat structure. Also, the only real area
changes are for the elements that have reduced area due to the SG coils and the reducer
cone which is well set-up from the hot leg side.
3.2.
High Pressure Containment
Considerations in nodalizing the high pressure containment include the location of
the containment thermocouples, the water/air interface and the penetration of the ADS
valves. In Table 3.4, the elevations of the six thermocouple banks that span from the
HPC through the heat transfer plate to the CPV are given along with the elevations
of the ADS valve penetrations and the four wall temperature thermocouples that are
associated with the HPC heaters (which were not used for the IAEA ICSP). Although
42
TABLE 3.2: Reactor Pressure Vessel Geometry
Component # (Type)
#100 (Pipe)
1
2
3
4
5
6
#110 (Pipe)
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
#300 (Branch)
Region (Woods et al. (2010))
Elevation (m)
Length (m)
-0.6237
-0.5187
-0.4137
-0.3087
-0.2037
-0.0987
0.105
0.105
0.105
0.105
0.105
0.105
Hot Leg Region 1
Hot Leg Region 1
Hot Leg Region 1 and 2
Hot Leg Region 2
Hot Leg Region 2
Hot Leg Region 3
Hot Leg Region 3
Hot Leg Region 4
Hot Leg Region 4
Hot Leg Region 4
Hot Leg Region 4
Hot Leg Region 4
Hot Leg Region 4
Hot Leg Region 4
Hot Leg Region 4
Hot Leg Region 4
V Cone Flow Meter
V Cone and Hot Leg Region 5
Hot Leg Region 5
Hot Leg Region 5
Hot Leg Region 5
Hot Leg Region 5
Hot Leg Region 5
Hot Leg Region 5
Hot Leg Region 5
Hot Leg Region 5
Hot Leg Region 5
Hot Leg Region 5
Hot Leg Region 5
0.0063
0.0508
0.127
0.2032
0.3144
0.4255
0.5478
0.6701
0.7721
0.8741
0.9761
1.0781
1.1801
1.2821
1.3841
1.486
1.54
1.5784
1.6795
1.7847
1.8899
1.9951
2.1003
2.2055
2.3107
2.4159
2.5211
2.6261
2.7272
0.0445
0.0762
0.0762
0.1112
0.1111
0.1223
0.1223
0.102
0.102
0.102
0.102
0.102
0.102
0.102
0.1019
0.054
0.0384
0.1011
0.1052
0.1052
0.1052
0.1052
0.1052
0.1052
0.1052
0.1052
0.105
0.1011
0.1433
Upper Plenum
2.8705
0.1205
Core
Core
Core
Core
Core
Core
Region
Region
Region
Region
Region
Region
1 & Flow Plate
1
1
1, 2 and 3
3
3 & Core Plate
43
TABLE 3.3: Pressurizer Geometry
Component # (Type)
#301 (Pipe)
1
2
3
4
5
6
7
8
#303 (Branch)
Region (Woods et al. (2010))
Elevation (m)
Length (m)
Baffle Plate & PZR
Center on Instrument Tap
Center on PZR Heaters
PZR Liquid Volume
PZR Liquid Volume
PZR Liquid Volume
PZR Steam Space
PZR Steam Space
2.991
3.0791
3.1143
3.1703
3.2871
3.4039
3.5207
3.6075
0.0881
0.0352
0.056
0.1168
0.1168
0.1168
0.0868
0.0868
PZR Steam Space
3.6943
0.1
the upper ADS valves emit steam from the RPV perpendicularly, the lower valves turn
down inside the interior of the HPC and terminate vertically down. The lower ADS valves
terminate 0.21 m below their penetration into the HPC. The initial water level of the HPC
is 110 inches which translates to an elevation of 1.87 m using the reference point of Woods
et al. (2010). The simulation of the HPC has the potential to stress the code calculations
as referenced to a few notes from the provided RELAP5-3D manuals concerning the use
of the noncondensable model. In Schultz (2005), low void fractions or the appearance and
disappearance of noncondensables in calculational cells was noted as causing calculational
problems and sometimes even prompted the user to manually interfere. This may occur
during the initial blowdown when steam enters volumes previously inhabited by air only
and at the water/air interface as steam condensenses and the water level changes. However,
the speed with which the blowdown displaces air will be much greater than the speed
at which condensed steam displaces air from the volumes near the water/air interface.
Consequently, the upper containment volumes have a greater area as a consequence of
the facility design and a longer nodal length than the lower containment volumes near
the water/air interface. Also in INL (2005b), it is recommended that for containment
44
volumes the initialization option #4 is used with a static quality of 1.0 for noncondensable
specifications. This recommendation was followed.
TABLE 3.4: Containment Thermocouple and ADS Penetration Elevations
Instrument
Lower ADS Valves
Thermocouple Bank (T-81x)
Thermocouple Bank (T-82x)
Thermocouple Bank (T-83x)
Wall Temperature (TW-891)
Thermocouple Bank (T-84x)
Wall Temperature (TW-892)
Upper ADS Valves
Thermocouple Bank (T-85x)
Wall Temperature (TW-893)
Thermocouple Bank (T-86x)
Wall Temperature (TW-894)
3.3.
Elevation
0.0508 m
0.0699 m
1.5716 m
2.2701 m
2.3400 m
3.1718 m
3.2036 m
3.7450 m
4.1688 m
4.2196 m
4.6704 m
4.7276 m
Secondary Side
For the ICSP blowdown test, the secondary side plays a minimal role because the
initiating event is a loss of feedwater. Ultimately, the steam generator modeling will only
affect the initial condition set-up and provide a minor heat sink during the transient.
Therefore, modeling of the secondary side has been avoided in favor of starting the modeling from the stopping of the main feed pump and using the actual experimental initial
conditions.
45
TABLE 3.5: High Pressure Containment Geometry
Component # (Type)
#600 (Pipe)
1
2
#601 (Branch)
#602 (Pipe)
1
2
3
4
5
6
–
7
#603 (Pipe)
1
2
–
3
4
#604 (Pipe)
#605 (Pipe)
–
1
#606 (Pipe)
1
#607 (Pipe)
1
–
2
3
–
Region
Elevation (m)
Length (m)
HPC below lower ADS Valves
HPC below lower ADS Valves
-0.92390
-0.60267
0.32123
0.32123
Lower ADS Valve Exit
-0.28144
0.1
Lower HPC water volume
Lower HPC water volume
Lower HPC water volume
Lower HPC water volume
Lower HPC water volume
Lower HPC water volume
midpoint elevation
Lower HPC water volume
-0.18144
0.14856
0.47856
0.80856
1.13856
1.44656
1.57156
1.69656
0.33
0.33
0.33
0.33
0.308
0.25
—
0.1737
Lower HPC air volume
Lower HPC air volume
midpoint elevation
Lower HPC air volume
Lower HPC air volume
1.87026
2.12036
2.27036
2.42036
2.67036
0.2501
0.3
—
0.25
0.276
HPC eccentric cone transition
2.94636
0.51
midpoint elevation
HPC below upper ADS Valves
3.20136
3.45636
—
0.23807
Upper ADS Valve Exit
3.69443
0.3382
Upper HPC
midpoint elevation
Upper HPC
Upper HPC
midpoint elevation
4.03263
4.16818
4.30373
4.51473
4.67048
0.2711
—
0.211
0.3115
—
46
3.4.
ADS Lines
The geometric data for the ADS lines are reproduced in Tables 3.6 and 3.7 from
Woods et al. (2010). As evidenced in the tables, the dominant characteristics of the ADS
lines are the multiple elbows, the small area to length ratio, and the orifices which are sized
according to the scaling presented in Reyes and King (2003). Each leg of the ADS lines
have multiple elbows and the lower lines have a submerged exit. Also, each pair of lines
originate from a single line from the RPV which is fitted with a tee to split the flow. In
RELAP5-3D, forward and reverse flow loss coefficients may be entered to simulate minor
flow losses. In White (2003), conservative flow losses are tabulated for elbows, branch
flow from tees and exit losses. These have been input into the RELAP5-3D model of
the MASLWR ADS lines. The 135◦ elbows were approximated as 90◦ elbows because
information in White (2003) did not include 135◦ elbows and the initial calculation is
serving as a starting point. The tee has not been modeled and in its place, the loss
for branch flow has been input into the junction that connects the ADS lines with the
RPV. The elbows have also not been simulated in their respective places but have been
spread out along the total length of the nodalization. In White (2003), sudden expansions
(subscript “SE”) and contractions (subscript “SC”) are treated as minor losses based upon
the velocity head in small pipes which may be applied before and after the orifice in the
ADS lines from the equations below.
KSE =
KSC
d2
1− 2
D
2
d2
≈ 0.42 1 − 2
D
(3.9)
(3.10)
In both cases, “d” represents the smaller diameter and “D” represents the larger diameter.
In this way, the orifice is not explicitly modeled. The pipe lengths and areas before the
47
b leg
a leg
TABLE 3.6: Automatic Depressurization System Vent Lines Geometric Data (Woods
et al. (2010))
Component
From
RPV
tee
PCS-106A
orifice
elbow
elbow
elbow
HPC interior
tee
PCS-106B
orifice
elbow
elbow
elbow
HPC interior
Component
To
tee
PCS-106A
orifice
4d 90◦ elbow
4d 90◦ elbow
4d 135◦ elbow
HPC exterior
termination
PCS-106B
orifice
4d 90◦ elbow
4d 90◦ elbow
4d 135◦ elbow
HPC exterior
termination
OD
(cm)
2.67
1.27
1.27
1.905
1.905
1.905
1.905
2.67
1.27
1.27
1.905
1.905
1.905
1.905
2.67
ID
(cm)
1.885
0.940
0.636
1.57
1.57
1.57
1.57
1.885
0.940
0.636
1.57
1.57
1.57
1.57
1.885
L
(cm)
10
17
5
17
98
25
26
22
17
5
50
98
25
26
22
valves are also not modeled explicitly. Instead, an approximation was made by weighting
the area of the two different pipe sizes before the valves.
π(1.885 cm)2
= 2.7907 cm2
4
π(0.940 cm)2
= 0.6940 cm2
4
10 × 2.7907 cm2 + 17 × 0.6940 cm2
= 1.4706 cm2
27
(3.11)
48
b leg
a leg
TABLE 3.7: Automatic Depressurization System Sump Return Lines Geometric Data
(Woods et al. (2010))
Component
From
RPV
tee
PCS-108A
orifice
elbow
elbow
elbow
elbow
HPC interior
elbow
tee
PCS-108B
orifice
elbow
elbow
elbow
elbow
HPC interior
elbow
Component
To
tee
PCS-108A
orifice
4d 90◦ elbow
4d 90◦ elbow
4d 90◦ elbow
4d 90◦ elbow
HPC exterior
4d 90◦ elbow
termination
PCS-108B
orifice
4d 90◦ elbow
4d 90◦ elbow
4d 90◦ elbow
4d 90◦ elbow
HPC exterior
4d 90◦ elbow
termination
OD
(cm)
2.67
1.27
1.27
1.905
1.905
1.905
1.905
1.905
2.67
2.67
1.27
1.27
1.905
1.905
1.905
1.905
1.905
2.67
2.67
ID
(cm)
1.885
0.940
0.636
1.57
1.57
1.57
1.57
1.57
1.885
1.885
0.940
0.636
1.57
1.57
1.57
1.57
1.57
1.885
1.885
L
(cm)
10
18
5
44
76
38
61
33
22
21
18
5
60
71
25
66
38
22
21
49
TABLE 3.8: ADS Vent Line Leg ‘A’ Geometry
Component # (Type)
#474 (Junction)
Length
Minor Loss
Origin
2.4
Branch Flow
7.73
Valve and KSC
2.7
2.0
2.0
No loss
90◦ elbow and KSE
90◦ elbow
135◦ elbow
Not submerged
#420 (Pipe)
0.27 m
#472 (Motor Valve)
#421 (Pipe)
1
2
3
4
3.4.1
0.57
0.57
0.57
0.22
m
m
m
m
Choked Flow Modeling
In INL (2005c), the choked flow modeling options in RELAP5-3D are discussed
including the standard model developed by Ransom and Trapp and a more recent addition
called the Henry-Fauske model. In Trapp and Ransom (1982), the Ransom and Trapp
model is described which is suited for implementation into the RELAP5-3D engine because
fine spatial noding (potential for violation of the Courant limit) is not required because
of the use of a choked-flow criterion which is a function of local flow conditions. Choked
flow occurs when the mass flow rate becomes independent of the downstream conditions
when acoustic signals can no longer propagate upstream because the fluid velocity has
reached the propagation velocity. A system of first-order, quasi-linear, partial differential
equations with the form of
A(U )[∂U/∂t] + B(U )[∂U/∂x] + C(U ) = 0
(3.12)
50
are developed which have characteristic roots according to
det(Aλ − B) = 0
(3.13)
where the choked condition occurs when information can no longer reach a solution region
such that a boundary point exists when
λj = 0 for some j ≤ n
(3.14)
λ ≥ 0 for all i 6= j
(3.15)
The model assumes that density and entropy are only pressure dependent and that each
phase undergoes a reversible process. The authors note that for the development of the
nonequilbrium, mass-exchange model, the gas mass exchange and the phasic heat transfer
rates are set as a function of state properties which is not a physical representation of
the problem but a simplification that is dependent on the resistance to heat flux being
minimal. The end product as stated in INL (2005c) is that this approach is less effected
by computing interval so that computational time may be saved by this choked-flow approach. The subcooled choking model used in RELAP5-3D is more applicable to break
modeling for loss of coolant accidents where a subcooled liquid changes phase through the
break because of the large pressure difference between the reactor primary or secondary
sides and the containment structure. The other component of the standard Ransom and
Trapp model is the two-phase one-component choking model developed for nonhomogeneous, nonequilibrium flow which would be more applicable to the ADS blowdown of the
MASLWR facility because the liquid is saturated in the pressurizer space instead of subcooled. According to INL (2005a), some of the complex roots are ill-posed and require the
addition of small, second-order viscous effects which is described in Ramshaw and Trapp
(1978) which addresses the treatment of analytical and numerical problems that possess
51
complex eigenvalue roots. In Ramshaw and Trapp (1978), the method for addressing
complex roots during the time of their publication was scattered and non-uniform with
many schools of thought. Insteading of treating the roots as unwanted and not representative of the physical problem studied, the authors used a two-phase separated flow
between parallel plates as the example problem to illustrate their position on a problem
with complex characteristics. Their position was that these complex roots may actual
describe physical instabilities. In their study, surface tension was the physical phenomena
added to the two-phase separated flow study to damp instabilities at short wavelengths.
Surface tension was chosen because of the ease of the theoretical development although
it was noted that viscosity would be more appropriate as it is a dissipative effect which
would serve to damp the problem solution as has been noted in INL (2005a). Also stated
in the manual, the critical flow model assumes choking at the most constricted area of
a flow path. This would be the orifice which scales the flow between the HPC and the
RPV but this is not modeled explicitly because of its small area and length. Alternative
locations include activating the model at the same location as the Henry-Fauske model
or at the ADS valve which has the smallest area in the flow channel. This is discussed
further in the part outlining the calculation matrix.
According to INL (2005c), the Henry-Fauske critical flow model was developed because of shortcomings identified with the standard Ransom and Trapp model during experimental testing of the Westinghouse AP600 design. The virtual mass effect is not
considered for this model as phasic velocities are considered equal in lieu of dominating
thermal nonequilibrium effects. The reasoning is that for nozzles and orifices there is minimal time for mass nonequlibrium effects to occur. The authors of INL (2005c) note that
for the case of single-phase vapor critical flow (initial MASLWR blowdown) the HenryFauske critical flow model utilizes an ideal gas formulation that breaks down at higher
52
pressures. This results in the inclusion of a different equation for stagnation pressure that
features a vapor specific volume term to improve the accuracy at higher pressures. It is
also noted that the Henry-Fauske model was primarily developed to be called at boundaries either into a time dependent volume or into a large volume that simulates a system
such as a containment structure. In the model, the choking option is only activated at the
exit to containment for the single ADS line, PCS-106A, which is used for the depressurization blowdown. The Henry-Fauske model also allows for “tuning” parameters where a
discharge coefficient and a nonequilibrium constant may be input.
3.4.2
Trips and Control Systems
The trip logic for the modeling of this transient has been limited to the operation
of the ADS valves and the power input to the system in the simulated electric core heater
rods. The blowdown is initiated by opening up one of the upper vent valves (PCS-106A)
once the pressure in the RPV has risen to 1300 psig and the pressurizer heaters have been
deenergized. This valve is then cycled according to pressure setpoints in the HPC until
the pressure between the two vessels is equalized (within 5 psi). PCS-106A is modeled as a
motor valve with an approximated closure time of 1.0 s. In RELAP5-3D, motor valves are
controlled by separate open and close trips which vary the valve position according to the
user input valve change rate. The open logic trip has two distinct branches. One of the
branches controls the initial valve opening with a trip that latches once the containment
pressure makes its initial rise to 250 psig and another trip that latches once the pressure
in the RPV rises to 1300 psig. PCS-106A remains open after the RPV pressure trip is
latched until the containment trip latches true. The open signal for the continuation of
the valve cycling is controlled by a combination of trips and a control variable. The valve
will open whenever the containment pressure is below 200 psig and will remain open as
long as the pressure rises until it reaches a value of 250 psig. The pressure rise/decrease
is tracked by a “Lag” control variable which holds the value of the containment pressure
53
from the previous half a second and this value is subtracted from the current calculated
pressure with a “Sum-Difference” control variable.
To input the actual power wattage into RELAP5-3D, control variables were developed for the core heat structures instead of using a table with a large amount of data.
The power history for the transient was collected in EXCEL and then graphed. Using the
trendline fit feature in EXCEL 2007, several different trendline functions were graphed.
Through trial and error, it was decided to split the power history in two and use two
different functions to approximate the data. For the first 5000 s of the power history, a
logarithmic trendline was fit to the data and a second order polynomial fit was applied to
the remaining power history. Various control system components were used to model the
two equations and then a time trip was used to multiply each of the equations so that a
control variable would switch to the polynomial fit equation after 5000 s.
Control variables were also used to determine the collapsed levels in the RPV and
HPC. RELAP5-3D stores variable quantities for the geometric volume of a hydrodynamic
volume as well as the liquid void fraction. A liquid level in a volume can be determined by
multiplying these two quantities together and then dividing by the area of the hydrodynamic volume. Merely repeating this process for the desired volumes and then summing
them up yields the collapsed liquid level.
54
TABLE 3.9: ADS Vent Line Leg ‘A’ Geometry
Type #
Variable Trip # 411
Logical Trip #605
Logical Trip #612
Control Variable #3
Control Variable #8
Control Variable #13
Control Variable #81
Control Variable #102
Purpose
Open PCS-106B, PCS-108A, PCS-108B
Open PCS-106A
Close PCS-106A
Logarithmic Core Power Fit Equation
Polynomial Core Power Fit Equation
Core Power Control
RPV Collapsed Liquid Level
HPC Collapsed Liquid Level
55
4.
CALCULATION MATRIX
For the benefit of the participants of the IAEA ICSP, the testing proceeds from
specified initial conditions and progresses as outlined in a procedure which may be duplicated with a chosen thermal hydraulics code. Initial conditions include the power to
the core heaters, the primary and secondary pressure, the water level in the RPV, HPC
and CPV and the secondary steam superheat. Steady state conditions are achieved at the
specified core power (≈299 kW) with a subcooled core exit temperature and the steam
superheat setpoint (≈15 ◦ F) before proceeding with the transient. The transient begins
when the main feed pump (MFP) is deenergized and a remotely operated valve on the
main feed line is closed from the operator console. With the loss of the heat sink, the
pressure in the RPV begins to rise. Once the pressure has risen from the starting point
of 1250 psig to 1300 psig, the decay power simulation is activated and the core heater
power is decreased from ≈299 kW to ≈36 kW. The power input to the core heaters then
decays from the 36 kW startpoint. 15 s after the pressure on the primary side has reached
1300 psig, the blowdown commences. The initial interaction between the cold and depressurized containment and the RPV is limited to the operation of a single ADS vent
valve. The operation of this single valve proceeds until the pressure difference between
the HPC and the RPV is less than 5 psi. To keep the HPC pressure well within its design
limits, the open/close logic input into the operator console for the single ADS vent valve
was designed to keep the containment pressure below 250 psig at all times. After the
steam condensation in the HPC lowered the containment pressure to 200 psig, the vent
valve was opened once more until the HPC pressure rose again to 250 psig. This cycling
was handled automatically by the programmed software. After the pressure equalization,
all four of the ADS valves are opened for the remaining duration of the test. The test
will either terminate once the RPV pressure has lowered to 75 psig or the total elapsed
56
TABLE 4.1: RELAP5-3D Calculations Performed
#
R-01
R-02-01
R-02-02
R-02-03
R-02-04
R-02-05
R-02-06
R-02-07
R-02-08
R-02-09
R-02-10
R-02-11
R-02-12
R-02-13
R-03-01
R-03-02
Description
Initial Calculation
User Input Study: Nodalizations, Model Decisions, Valve Closure Rate, etc.
Finely Noded PCS-106A Vent Line
Coarsely Noded PCS-106A Vent Line
Discharge Coefficient of 1.5 for Henry-Fauske Choked Flow Model
Discharge Coefficient of 0.5 for Henry-Fauske Choked Flow Model
Experimental Valve Opening Times, Henry-Fauske activated
Same as R-02-05 with Full Abrupt Area Change Model
Same as R-02-06 with 0.25 Discharge Coefficient
Same as R-02-07 except Partial Abrupt Area Change Model used
Experimental Valve Opening Times, Ransom-Trapp activated
Same as R-02-09 with 0.25 used for all Discharge Coefficients
Motor Valve Closure Rate of 0.5 s
Coarsely Noded HPC
Steady State Initiated Calculation
Condensation Study: Containment Stand-alone Model
RELAP5-3D built-in models used
User Input Heat Flux Boundary Condition
transient time is 5 hours.
The RELAP5-3D modeling conducted for this ICSP test proceeded in different
stages as outlined in Table 4.1. The initial calculation starts much like the second phase
of the ICSP format where limited experimental data is input such as initial temperatures
and pressures and the actual power data. The goal of the second step is then to analyze
the effect that different user decisions have on the calculational results. This includes
nodalization sensitivity studies, built-in model toggling, adjusting the ADS vent line valve
open/close rate and initiating the transient calculation from steady-state. After identifying
the dominant mechanism for the pressure equalization between the two vessels, a focused
study on the HPC condensation was performed.
57
In the presentation of the experimental data, error bars are only shown on a limited
basis because of the low manufacturer provided uncertainty as tabulated in Table 4.2 and
the statement made in the limitations that this would be the extent of the error analysis.
TABLE 4.2: Manufacturer Provided Instrumentation Uncertainty (Woods et al. (2010))
Instrument
RPV Pressure Meter (PT-301)
HPC Pressure Meter (PT-801)
Thermocouple (All temperatures presented)
HPC Level Differential Pressure Meter (LDP-801)
4.1.
Uncertainty
±1.2 psig
±0.45 psig
±1.1◦ C
±0.1875 inches H2 O
Initial Calculation
An initial comparison between the RELAP5-3D calculational results and the experimental data was performed with limited experimental input into the RELAP5-3D input
deck. As mentioned previously, it was decided to leave out the modeling of the secondary
side for this work and the thermal hydraulic code was started from experimental data
one second before the blowdown commencement. Experimental temperature, pressure
and level data was used to initialize the fluid volumes. Because the fluid in the natural
circulation loop was single-phase before opening the upper ADS valve and the subsequent
rapid pressure drop, the mass flow rate through the primary loop was also input from
the experimental data. The real experimental power data was input as described in the
RELAP5-3D model chapter. In Figures 4.1-4.3, the RPV and HPC pressures and the
HPC liquid level are plotted, respectively. From Figure 4.1, it is apparent that the time
58
to pressure equalization predicted by RELAP5-3D is nearly 2000 s longer than the actual
experimental time. The initial RPV pressure drops are similar for the experiment and the
calculation, but then RELAP5-3D predicts a rise in pressure where the experiment shows
a steady decline until pressure equalization. Yet, the RELAP5-3D calculation predicts a
considerably quicker time to the test termination with a difference of over 3000 s. Once
the ADS valves have all opened at pressure equalization, the RELAP5-3D predicts a much
more efficient heat removal than was seen in the experiment. In Figure 4.2, the graph of
HPC pressures shows that the calculation predicted a higher peak containment pressure
during the cycling phase. This higher peak pressure will be addressed by adjusting the
valve closure time of the motor valve component that was used to model PCS-106A. Also,
the sharp decline in pressure for the two vessels after equalization is more evident in the
graph of the containment pressure. The RELAP5-3D predicted pressure intersects the experimental trend well before test termination even with the nearly 2000 s head start. Near
the end of the RELAP5-3D calculation, the pressure trend does seem to imitate the slope
of the experimental data. The cause of the overprediction is then in the early stages of the
long-term depressurization stage after the opening of all the ADS valves. The depiction of
the HPC level in Figure 4.3 seems to be contrary to expectations based upon the time to
pressure equalization. Because more steam is condensed in the RELAP5-3D containment,
the time to pressure equalization should be faster in the RELAP5-3D calculation since this
is the primary agent of pressure suppression. The cause of this misperception seems to be
a consequence of the intial level spike in the RELAP5-3D calculation. The experimental
pressure equalization occurs at a containment level of over 3.6 m. The RELAP5-3D pressure equalization occurs at a containment level of nearly 4.0 m. This difference is similar
to the difference between the RELAP5-3D initial level spike compared to the experimental
data. This initial spike did bring the primary pressure down to the experimental value
as shown in Figure 4.1, but then the pressure in the RPV began to rise. RELAP5-3D
59
9.0
Exp
R−01
8.0
7.0
Pressure (MPa)
6.0
5.0
4.0
3.0
2.0
1.0
0.0
0
2000
4000
6000
8000
10000
12000
14000
16000
Time (s)
FIGURE 4.1: Initial Calculation: RPV Pressure
seems to be overpredicting the condensation rate initially and then underpredicting the
condensation rate or the heat transferred out of the primary vessel.
Figures 4.4-4.12 highlight the RPV/HPC pressure trends as well as the HPC liquid
level rise with a quantitative element added. The time windows shown were chosen because
the application of the FFTBM which limits the data points to a power of 2. There are two
distinct phases for this ICSP test: the single vent valve cycling to equalize pressure between
vessels and the opening of all the ADS valves for long-term cooling. To encapsulate the
first phase, the maximum allowed number of points, 212 or 4096, is necessary. The longterm cooling phase cannot be quantified through a single application of the FFTBM so
two windows of 4096 s were chosen. A tabulation of the average amplitude for a selection
of facility instrumentation is presented in Table 4.4. As explained in Prosek et al. (2002),
60
2.0
Exp
R−01
1.8
1.6
Pressure (MPa)
1.4
1.2
1.0
0.8
0.6
0.4
0.2
0.0
0
2000
4000
6000
8000
10000
12000
14000
16000
Time (s)
FIGURE 4.2: Initial Calculation: HPC Pressure
4.0
HPC Liquid Level (m)
3.5
3.0
Exp
R−01
2.5
0
2000
4000
6000
8000
10000
12000
14000
Time (s)
FIGURE 4.3: Initial Calculation: Containment Level
16000
61
the total weighted average amplitude (AAtot ) is computed by
AAtot =
N
var
X
(AA)i (wf )i
(4.1)
i=1
and the individual weighting factors for each quantity is determined through
(wexp )i (wsaf )i (wnorm )i
(wf )i = PNvar
i=1 (wexp )i (wsaf )i (wnorm )i
(4.2)
These individual weighting factors are tabulated in Table 4.3 and were determined by the
developers of the FFTBM to determine the importance of each quantity based upon the
experimental accuracy (wexp ) and safety relevance (wsaf ) while normalizing each variable
to the primary pressure, (wnorm ). In Prosek et al. (2002), it is acknowledged that there is
a degree of arbitrariness in selecting these numbers. There are no wall temperature values
that are listed in the table of weighting factor components so the heat transfer plate
temperatures were set to be half as important as fluid temperatures. This places the heat
transfer plate temperatures as less important than cladding temperatures and having a
similar weighting factor to secondary pressure. Since the heat transfer plate is the primary
heat sink for this test, a weighting factor comparable to the secondary pressure which is the
system responsible for heat removal during normal operations is reasonable. The AAtot
values listed in Table 4.4 characterize very good code predictions according to Prosek et al.
(2002) but as illustrated in the figures and the high AA values for the pressure trends in
the reactor and containment vessels, the most important quantities are not simulated well
at all. In the second phase of calculations, various potential causes will be investigated to
determine the source of these discrepancies. This second phase will be limited to the first
two time windows of the FFTBM study (0-8192 s) due to the low occurence of interesting
phenomena at the back end of this long experiment and the acceptable agreement between
the code and experimental results as evidenced in Figures 4.10-4.12 and the third column
62
AA = 0.38
9.0
Exp
R−01
8.0
Pressure (MPa)
7.0
6.0
5.0
4.0
3.0
2.0
1.0
0.0
0
500
1000
1500
2000
2500
3000
3500
4000
4500
Time (s)
FIGURE 4.4: Initial Calculation: RPV Pressure - 1st Window
in Table 4.4. Also of interest, the selection of the time windows seems to be very important
for this very long transient. Although the experimental data has nearly transitioned to the
long-term cooling period, the calculational results have not during the second time window.
In Figure 4.9, the value of 0.35 for average amplitude suggests good agreement between
the data and the calculational results. However for roughly the first 2000 s, the figure
shows poor agreement and then once the valves have all opened, the agreement between
the liquid levels is nearly perfect. Care should be taken in selecting the time windows. For
the third window of calculations (Figures 4.10-4.12), the instrumentation uncertainty has
been included. Even though the method predicts a very good agreement, the calculational
results are not within the uncertainty band of the instruments. On a facility by facility
basis, this method does not account for the precision of the installed instrumentation. It
is embedded on a general basis in the weighting factors for the calculation of the total
average amplitude.
63
AA = 0.66
2.0
1.8
1.6
Pressure (MPa)
1.4
1.2
1.0
0.8
0.6
0.4
Exp
R−01
0.2
0.0
0
500
1000
1500
2000
2500
3000
3500
4000
4500
Time (s)
FIGURE 4.5: Initial Calculation: HPC Pressure - 1st Window
AA = 0.18
4.0
HPC Liquid Level (m)
3.5
3.0
Exp
R−01
2.5
0
500
1000
1500
2000
2500
3000
3500
4000
Time (s)
FIGURE 4.6: Initial Calculation: Containment Level - 1st Window
4500
64
AA = 0.68
3.0
Exp
R−01
2.5
Pressure (MPa)
2.0
1.5
1.0
0.5
0.0
4000
4500
5000
5500
6000
6500
7000
7500
8000
8500
Time (s)
FIGURE 4.7: Initial Calculation: RPV Pressure - 2nd Window
AA = 0.49
2.0
1.8
1.6
Pressure (MPa)
1.4
1.2
1.0
0.8
0.6
0.4
Exp
R−01
0.2
0.0
4000
4500
5000
5500
6000
6500
7000
7500
8000
Time (s)
FIGURE 4.8: Initial Calculation: HPC Pressure - 2nd Window
8500
65
AA = 0.35
5.0
4.8
4.6
HPC Liquid Level (m)
4.4
4.2
4.0
3.8
3.6
3.4
Exp
R−01
3.2
3.0
4000
4500
5000
5500
6000
6500
7000
7500
8000
8500
Time (s)
FIGURE 4.9: Initial Calculation: Containment Level - 2nd Window
AA = 0.14
1.5
Exp
R−01
1.4
1.3
Pressure (MPa)
Pressure (MPa)
1.2
1.1
1.0
0.9
0.8
0.7
0.6
0.5
0.8
0.85
0.9
0.95
1
1.05
Time (s)
1.1
1.15
1.2
1.25
4
x 10
Time (s)
rd
FIGURE 4.10: Initial Calculation: RPV Pressure - 3 Window
66
AA = 0.10
1.5
Exp
R−01
1.4
1.3
Pressure (MPa)
Pressure (MPa)
1.2
1.1
1.0
0.9
0.8
0.7
0.6
0.5
0.8
0.85
0.9
0.95
1
1.05
Time (s)
1.1
1.15
1.2
1.25
4
x 10
Time (s)
rd
FIGURE 4.11: Initial Calculation: HPC Pressure - 3 Window
AA = 0.024
4.0
3.9
3.8
Liquid Level (m)
HPC Liquid Level (m)
3.7
3.6
3.5
3.4
3.3
3.2
3.1
3.0
0.8
Exp
R−01
0.85
0.9
0.95
1
1.05
Time (s)
1.1
1.15
1.2
1.25
4
x 10
Time (s)
rd
FIGURE 4.12: Initial Calculation: Containment Level - 3 Window
67
TABLE 4.3: Weighting Factor Components, Prosek et al. (2002)
Pressure drops
Mass inventories
Flowrates
Primary pressure
Secondary pressure
Fluid temperatures
Clad temperatures
Collapsed levels
Core power
wexp
0.7
0.8
0.5
1.0
1.0
0.8
0.9
0.8
0.8
wsaf
0.7
0.9
0.8
1.0
0.6
0.8
1.0
0.9
0.8
wnorm
0.5
0.9
0.5
1.0
1.1
2.4
1.2
0.6
0.5
TABLE 4.4: Initial Calculation Average Amplitudes from FFTBM
Instrumentation Tag
PT301
PT801
TF102
TF104
TF106
TF892
LDP801
Core Power (KW101,KW102)
TW822
TW823
TW824
TW832
TW833
TW834
TW842
TW843
TW852
TW853
TW854
TW862
TW863
TW864
0-4096 s
AAtot =0.21
0.38
0.66
0.15
0.14
0.17
0.41
0.18
0.32
0.16
0.16
0.16
0.15
0.038
0.086
0.28
0.17
0.29
0.19
0.080
0.21
0.28
0.13
4097-8192 s
AAtot =0.23
0.68
0.49
0.18
0.17
0.27
0.14
0.35
0.31
0.24
0.18
0.13
0.21
0.14
0.13
0.21
0.14
0.099
0.12
0.062
0.41
0.34
0.17
8193-12288 s
AAtot =0.094
0.21
0.14
0.060
0.061
0.069
0.13
0.027
0.45
0.022
0.032
0.059
0.056
0.025
0.013
0.19
0.13
0.11
0.073
0.069
0.17
0.055
0.10
68
4.2.
4.2.1
Second Calculation
ADS Nodalization Sensitivity
To gauge the influence of the ADS vent line nodalization that is responsible for the
steam flow during the blowdown transient, the fluid volumes that represent the piping
from the orifice to the HPC exterior as detailed in Table 3.6 were changed in separate full
time scale RELAP5-3D runs. The differences between the noding of the different runs
are documented in Table 4.5. For this study, the Henry-Fauske model was used and is
activated as described in Section 3.4.1. As shown in Figure 4.13, there is a slight difference
between these nodalizations. This difference can also be seen in the depiction of the
containment liquid level in Figure 4.14. On the basis of the mass error printed out in the
major edits, the base nodalization was chosen. According to INL (2005a), the mass error
computed by RELAP5-3D involves taking the difference between the density computed
by the continuity equation and the total density determined by the state relationship
and multiplying by the geometric volume of a specific hydrodynamic volume. Summing
all of the mass errors for each hydrodynamic volume in a system yields the mass error
which is printed out in the major edits. Several statements are made in INL (2005a)
concerning a relation between reduced mass error and improved code performance. The
two fluid systems in the RELAP5-3D model are the coupled RPV/HPC and the cooling
pool vessel. The coarse nodalization had a mass error of several kilograms around the
time of pressure equalization for the coupled system. This nodalization was not chosen.
The fine and base nodalization had similar mass errors, but the base nodalization was
chosen because the initial mass error was lower at the start of the transient.
4.2.2
Choked Flow Recommended Options
In Schultz (2005), a discussion of the available hydrodynamic components touches
upon the single junction input options and the choked flow models. For the Henry-
69
R−01
R−02−01
R−02−02
9.0
8.0
Pressure (MPa)
7.0
6.0
5.0
4.0
3.0
2.0
0
1000
2000
3000
4000
5000
6000
Time (s)
FIGURE 4.13: PCS-106A Vent Line Nodalization Study: Primary Pressure
4.5
Liquid Level (m)
4.0
3.5
3.0
R−01
R−02−01
R−02−02
2.5
0
1000
2000
3000
4000
5000
6000
Time (s)
FIGURE 4.14: PCS-106A Vent Line Nodalization Study: Containment Level
70
TABLE 4.5: PCS-106A Vent Line Nodalization Study
Component # (Type)
#421 (Pipe)
1
2
3-8
Length (m)
R-02-01
0.21375
0.21375
0.21375
Length (m)
R-01
0.855
0.855
—
Length (m)
R-02-02
1.71
—
—
Fauske model, the full abrupt area change model or the partial abrupt area change model
is recommended to be activated along with this specific choking model. Leaving these
options out is only recommended for no area changes (there is a large change from ADS
vent line to HPC) or smooth area changes. It is also noted that when a containment is
modeled with hydrodynamic components other than a time-dependent volume that the
energy transferred through a choked junction would be underestimated and the junction
flag which applies an energy correction term should be activated. After deciding to use the
base nodalization (R-01), the recommended options were activated and the full calculation
was re-run without any additional changes. For the calculation with the energy correction
term activated and the partial abrupt area change, the RELAP5-3D run stalled after
1241.06 s while still in the PCS-106A vent valve cycling phase. No error was reported.
With the energy correction term activated along with the full abrupt area change option,
the RELAP5-3D run stalled after 149.625 s with no error message. Re-running with
only the energy correction term activated resulted in an identical primary pressure trend.
Subsequently, the full model calculation in the third round of calculations does not have
either of the recommended abrupt area change models activated but the energy correction
term is activated.
71
4.2.3
Choked Flow Discharge Coefficients
According to INL (2005c), there are additional options for tuning the choked flow
models to specific geometries via the discharge coefficients for the different models and
different flow scenarios. Using the standard Ransom-Trapp model, a user-input discharge
coefficient is available for subcooled liquid, two-phase and superheated vapor/gas choked
flow. For the Henry-Fauske model, a discharge coefficient for all applicable flows may be
input as well as a thermal nonequilibrium constant which was added for additional tuning
capabilities, INL (2005c). The stated range of the discharge coefficients in INL (2005d) are
between 0.0 and 2.0. The thermal nonequilibrium constant of the Henry-Fauske model has
a much wider range of input bounds, but according to INL (2005c), the thermal equilibrium
constant does not affect the calculation for high quality flows (> 20%) which is the case
for the ADS blowdown. The discharge coefficient for the Henry-Fauske model was set to
0.5 and 1.5 for separate calculation runs to determine if they had an affect on the time
to pressure equalization. In Figure 4.15, it is evident that merely changing the discharge
coefficient has only quickened the time to pressure equalization by a single vent valve
cycle. The previous calculation was performed with the control logic still in place which
controls the valve cyling of PCS-106A between the pressure setpoints outlined in the test
procedure. Yet in theory, the transient may be modeled without the pressure setpoint logic
if the valve timing is known and the major phenomena is treated perfectly in RELAP53D. A table was constructed to mimic the actual experimental opening/closing times of
PCS-106A and the calculation was run without the PCS-106A pressure constraints. In
Figure 4.16, several attempts at adjusting the available inputs to the Henry-Fauske model
are shown. For runs R-02-05 - R-02-08, the Henry-Fauske model is activated in the same
location as the base model with none of the recommended options, the full abrupt area
change model is activated with the Henry-Fauske model, the full abrupt area change model
is activated with a discharge coefficient of 0.25, and the partial abrupt area change model
72
is activated with a discharge coefficient of 0.25. Even with a low discharge coefficient
value of 0.25, the HPC pressure quickly rises above the upper pressure setpoint of the
actual experiment to the pressure equalization trip which opens all of the ADS valves. It
is evident that merely adjusting the Henry-Fauske choked flow model inputs is not enough
to simulate the correct time to pressure equalization. Another attempt was made with the
Ransom-Trapp choked flow model. In Figure 4.17, the Ransom-Trapp model is activated
at the motor valve junction which represents PCS-106A along with the fulll abrupt area
change model per recommendations in INL (2005a) with the default discharge coefficient
for each flow regime of 1.0 and once with a value of 0.25 for all regimes. This figure also
illustrates that merely adjusting the rate at which mass enters the HPC is not enough to
properly model the transient and there is no reason other than trying to fit the data that
a discharge coefficient of 0.25 was chosen. Tuning discharge coefficients in this manner is
not a practice to emulate. However, this figure does suggest that the condensation rate
in the HPC is the dominant phenomenon. Also, the more recent addition to RELAP5,
the Henry-Fauske model, predicts essentially the same choked flow conditions regardless
of the user input options for the ADS blowdown.
4.2.4
Motor Valve Open/Close Rate
For the initial calculation, a closure rate of 1.0 s was used as an estimation for the
PCS-106A vent valve which is modeled with a motor valve in RELAP5-3D. Manufacturer
information was not available. A comparison of HPC pressure trends, Figure 4.18, during
the vent valve cycling shows that the RELAP5-3D model has a much higher peak pressure
which may be due to a poor approximation of the valve closure time.
This is easily
adjusted in RELAP5-3D and the motor valve component was adjusted to close in 0.5 s
and Figure 4.19 shows that the peak containment pressure compares better with the
experimental data.
73
2.0
1.8
1.6
Pressure (MPa)
1.4
1.2
1.0
0.8
0.6
0.4
R−01
R−02−04
R−02−05
0.2
0.0
0
1000
2000
3000
4000
5000
6000
Time (s)
FIGURE 4.15: Choked Flow Discharge Coefficients: HPC Pressure
3.0
R−02−05
R−02−06
R−02−07
R−02−08
2.5
Pressure (MPa)
2.0
1.5
1.0
0.5
0.0
0
500
1000
1500
2000
2500
3000
Time (s)
FIGURE 4.16: Henry-Fauske Study: HPC Pressure
3500
4000
74
5.0
R−02−09 HPC
R−02−10 HPC
R−02−09 RPV
R−02−10 RPV
4.5
4.0
Pressure (MPa)
3.5
3.0
2.5
2.0
1.5
1.0
0.5
0.0
0
500
1000
1500
2000
2500
3000
3500
4000
Time (s)
FIGURE 4.17: Ransom-Trapp Study: RPV/HPC Pressure
4.2.5
HPC Nodalization Sensitivity
An investigation into the influence of the user-defined HPC node sizes was also
undertaken. A finely noded and more coarsely noded high pressure containment were
developed from the starting point of the first calculation. However, several attempts were
made at developing a finer nodalization than that of the initial calculation, R-01, which
failed to finish their requested calculation time. In the end, a working HPC nodalization would have looked similar to the initial calculation, so only a coarser nodalization
is presented. The details can be found in Table 4.6. Some dimensions were unchanged
so similarity in ADS line connections was maintained between the separate set-ups. Figures 4.20 and 4.21 illustrate the differences in calculated HPC liquid level and primary
pressure respectively. It is apparent that steam condensed in containment at a considerably slower rate. The reason for the differences in the runs are connected to the transport
75
1.9
1.8
Pressure (MPa)
1.8
1.7
1.7
1.6
1.6
1.5
R−01
Exp
1.5
1.4
0
1000
2000
3000
4000
5000
6000
Time (s)
FIGURE 4.18: RPV Pressure, Motor Valve 1.0 s Closure Rate
1.9
1.8
Pressure (MPa)
1.8
1.7
1.7
1.6
1.6
1.5
R−02−11
Exp
1.5
1.4
0
1000
2000
3000
4000
5000
Time (s)
FIGURE 4.19: RPV Pressure, Motor Valve 0.5 s Closure Rate
6000
76
of air between the upper containment volumes and the direct link between the noncondensable volume mass fraction and the condensation heat transfer. The noncondensable
transport may have also led to the failure of the calculation with the finely noded HPC.
In Figure 4.22, the volume noncondensable (air) mass fractions for the upper containment
volumes in the R-01 (60701-60703) and R-02-12 (60501-60502) calculations are plotted.
Both of the uppermost volumes have considerably larger mass fractions. In Figure 4.23,
the effect of this can be seen through the heat fluxes in these volumes. The lower mass
fractions have much higher heat flux values and consequently, faster condensation rates.
The expectation is that the steam/air environment would be well mixed because the vent
lines exit into the containment via a sparger designed to disperse the steam. Also, the
similarities in heat transfer plate temperatures for the thermocouple banks exposed to the
air/steam environment suggest that the upper containment volume was well mixed and
that the concentration of noncondensable at the diffusion layer is similar. This is depicted
in Figure 4.24 with the three thermocouples located near the heat transfer plate in the
containment volume exposed to the air/steam environment. The time window starts from
a few hundred seconds into the transient after the plate has heated up. This thorough
mixing is not seen in the 1-D treatment of the HPC nodalization. Also, notice that the
temperatures are considerably lower than the saturation temperature of steam for the
pressures seen in containment. At 200 psig, the saturation temperature of water is 472 K
and rises to 482 K at 250 psig. The exact location of these thermocouples is not known,
but they are not embedded in the heat transfer plate though they are near its surface. It
does appear that these thermocouples show the affect that the collection of air near the
condensate film has on lowering the saturation temperature at the interface between the
condensate and high gas concentration/steam layer.
77
TABLE 4.6: High Pressure Containment Nodalization Study
Component # (Type)
#600 (Pipe)
1
2
#601 (Branch)
#602
1
2
3
4
5
6
7
8
#603
1
2
3
#604
1
#605
1
2
#606
1
#607
1
2
3
Length (m)
R-01
0.32123
0.32123
Length (m)
R-02-12
0.64246
—
0.1
0.1
0.33
0.33
0.33
0.33
0.308
0.25
0.29165
0.29166
0.6917
0.68
0.68
—
—
—
—
—
0.15951
0.25
0.276
0.53805
0.53805
—
0.51
0.51
0.23807
—
0.81434
0.55553
0.3382
—
0.2711
0.211
0.3115
—
—
—
(Pipe)
(Pipe)
(Pipe)
(Pipe)
(Pipe)
(Pipe)
78
4.5
R−01
R−02−12
HPC Level Increase (m)
4.0
3.5
3.0
2.5
0
1000
2000
3000
4000
5000
6000
Time (s)
FIGURE 4.20: HPC Nodalization Sensitivity: Containment Level
R−01
R−02−12
9.0
8.0
Pressure (MPa)
7.0
6.0
5.0
4.0
3.0
2.0
0
1000
2000
3000
4000
5000
6000
Time (s)
FIGURE 4.21: HPC Nodalization Sensitivity: Primary Pressure
79
60701
60702
60703
60501
60502
0.70
0.60
Volume Air Mass Fraction
0.50
0.40
0.30
0.20
0.10
0.00
0
1000
2000
3000
4000
5000
6000
Time (s)
FIGURE 4.22: HPC Nodalization Sensitivity: Noncondensable Transport
50000
45000
40000
Heat Flux (W/m2 )
35000
30000
25000
20000
15000
60701
60702
60703
60501
60502
10000
5000
0
0
1000
2000
3000
4000
5000
Time (s)
FIGURE 4.23: HPC Nodalization Sensitivity: Condensation Rate
6000
80
440.0
435.0
Temperature (K)
430.0
425.0
420.0
TF841
TF851
TF861
415.0
410.0
0
500
1000
1500
2000
2500
3000
3500
4000
Time (s)
FIGURE 4.24: Experimental Heat Transfer Plate Temperatures
4.2.6
Steady State Comparison
All of the previous calculations were performed as transient calculations in RELAP5-
3D without any calculational time devoted to problem initialization. The ADS blowdown
was started nearly instantaneously with the expectation that the thoroughness with which
the fluid volumes and heat structures were input initial conditions would be sufficient. This
included artificial stratifying the inputs across heat structure meshes and fluid temperatures between thermocouples A calculation was also performed where the experimental
core exit temperature, primary mass flow rate and pressure was taken to steady state and
then the transient was started after 4000 s of previous calculation time. After approximately 1200 s, steady temperatures and mass flow rates were seen in the primary vessel.
As shown in Figures 4.25 and 4.26, there is little difference in the two calculations and the
calculations should not be exactly the same because only the primary pressure, core exit
81
R−01
R−02−13
9.0
8.0
Pressure (MPa)
7.0
6.0
5.0
4.0
3.0
2.0
0
1000
2000
3000
4000
5000
6000
Time (s)
FIGURE 4.25: Steady State Initialization: Primary Pressure
temperature, and mass flow rate were matched, the rest of the primary side fluid temperatures are not matched exactly. This results in a slight difference in the primary side fluid
energy which needs to be dissipated in the HPC. Regardless, the close comparison between
the two calculations provides a greater level of confidence in this computational approach
which appears to be a consequence of the particular transient that was modeled. There
is a rapid loss of pressure once the ADS vent valve is opened and the fluid in the primary
vessel degrades to saturated conditions. Also because this is a loss of feedwater initiated
transient and the secondary side was not modeled, the important heat structure, the heat
transfer plate in containment, is cold at the beginning of the transient and requires no
initialization. This rapid change from the initial conditions combined with the cold heat
transfer plate seem to be the reason that the two calculations were similar.
82
4.5
R−01
R−02−13
HPC Level increase (m)
4.0
3.5
3.0
2.5
0
1000
2000
3000
4000
5000
6000
Time (s)
FIGURE 4.26: Steady State Initialization: Containment Level
4.3.
4.3.1
Third Calculation
Stand-alone Model
To determine the condensation rate during the single vent valve operation of the
blowdown transient, the level, pressure and temperature instrumentation in the HPC was
used along with the analysis method outlined in Todreas and Kazimi (1990). In the
discussion of containment pressurization thermodynamics in Todreas and Kazimi (1990),
the following ideal gas law treatment of the steam-air mixture in containment is presented
83
for determining the final containment pressure
p2 =
mw Rw T2 ma Ra T2
+
VT
VT
w = water
a = air
T2 = final equilibrium temperature
VT = final volume
R = individual gas constant
(4.3)
By assuming that the liquid volume in containment is incompressible, the final volume
may be determined from the level measurement in containment and the HPC dimensional data from Woods et al. (2010). The final pressure, p2 , is also known as well as
T2 . The unknown in the equation is the mass of water vapor that effectively pressurizes the containment vessel. However, the pressure in containment is high enough that
the ideal gas treatment may be insufficient without further modification. This is evident
from the literature review where Kim et al. (2009) noted that at 2.0 MPa, there was
a compressibility factor of 0.8852 for steam/gas mixtures. In Smith et al. (1996), the
generalized virial-coefficient correlation is used to develop compressibility factors for low
to moderate pressures. A compressibility factor for the water vapor present in the HPC
may be developed as follows. From the appendices of Smith et al. (1996), the following
values are provided for water: Tc /K = 647.1, Pc /bar = 220.55, ω = 0.345. These values
are used to compute reduced temperatures and pressures along with the instrumentation
measurements. This formulation will be used to determine a compressibility factor right
before upper ADS valve openings. This pressure is 200 psig or 14.8 bar and the resulting
84
mixture temperature is 199 ◦ C or 472 K.
472
= 0.729
647.1
14.8
= 0.0671
Pr =
220.55
Tr =
(4.4)
(4.5)
The following coefficients are then computed
0.422
= −0.616759
Tr1.6
0.172
B 1 = 0.139 − 4.2 = −0.509743
Tr
B 0 = 0.083 −
(4.6)
(4.7)
and then used with the acentric factor, ω
B 0 + ωB 1 = −0.616759 + (0.345)(−0.509743) = −0.792620
(4.8)
The final step is the computation of the compressibility factor
Z = 1 + (B 0 + ωB 1 )
Pr
0.0671
= 0.927
= 1 + (−0.792620)
Tr
0.729
(4.9)
In Perry et al. (1997), a tabulation of compressibility factors for air shows that at the
containment pressure of 14.8 bar and temperature of 472 K the ideal gas law is a reasonable approximation. No compressibility factor is necessary for the second addend of
Equation 4.3.
Unlike the several experiments mentioned in the literature review, the ADS blowdown transient ICSP is not designed to perform a condensation analysis. The steam input
to the containment is not strenuously regulated and the pressure in the HPC is also not
constant. Consequently, the data was analyzed to determine a portion of the single ADS
85
valve operation that was fairly constant to perform further computational and mathematical analysis. After a little over 1000 s into the transient, there are ten vent valve cycles
which have a recorded opening time of 8 s each with closure times between 74-77 s. During this period of the blowdown transient, one of the containment fluid thermocouples,
TF-831, becomes submerged as the containment level rises as a result of the condensation
of steam from the RPV. This will provide the means to approximate the temperature of
the newly condensed steam and then determine the mass of the liquid indicated by the
containment level measurement. With this calculation and the ideal gas law treatment of
the upper containment steam/air mixture, an increase in the containment mass can be
computed which will be used to approximate a mass flow rate through the ADS vent valve.
Right before the first valve opening in this sequence, the containment level instrument,
LDP-801, reading is 318.75 cm. The measurement that precedes the first valve opening
after this sequence reads 332.01 cm for a total difference of 13.26 cm. TF-831 becomes
submerged approximately 500 s into this 10 valve opening sequence. Starting from the
point once this thermocouple is submerged and extending the same length of time that the
studied sequence encompasses, the containment level rises 12.92 cm and during this time
the thermocouple registers an average temperature of 110.6 ◦ C with a maximum reading
of 114.07 ◦ C and minimum of 107.05 ◦ C. To determine the density of the condensed steam
that is added during this sequence, a temperature of 110.6 ◦ C will be assumed for the
added 13.26 cm water column which has a pressure of 200 psig or 14.8 bar. The density
is then 951.14 kg/m3 . The area of the lower containment is determined from Woods et al.
(2010) and resulting mass of the added liquid is then
13.26 cm ×
π · (27 cm − 2 · 0.419 cm)2
1 m3
kg
×
× 951.14 3 = 6.78 kg
3
3
4
100 cm
m
(4.10)
The difference in the steam content in the upper containment atmosphere is then computed
by first determining the initial amount of air in containment which remains constant
86
throughout the blowdown. The initial volume occupied by the air in containment is
computed as 0.3811 m3 from Woods et al. (2010) and the containment level measurement.
A density value of 1.1614 kg/m3 is taken from Incropera et al. (2006) which yields an air
mass of 0.44261 kg. The amount of steam present in the upper containment atmosphere
before the first valve opening is
0.44261 kg · 286 J/kg K · 472.08 K
0.3613 m3
0.3613 m3
×
= 2.351 kg
461.5 J/kg K · 472.08 K · 0.927
1479396.3 Pa −
(4.11)
and the amount of steam present in the upper containment atmosphere before the valve
opening of the next sequence is
0.44261 kg · 286 J/kg K · 472.26 K
0.3542 m3
0.3542 m3
×
= 2.299 kg
461.5 J/kg K · 472.26 K · 0.927
1480240.4 Pa −
(4.12)
The total mass added to containment during this proposed “steady state” sequence is 6.78
- (2.351-2.299) = 6.73 kg. A condensation study will be performed in RELAP5-3D with
this mass input for the eight valve openings.
average mass flow rate =
6.73 kg
= 0.084 kg/s
10 × 8 s
(4.13)
This data will be input into a time dependent junction. The quality will be assumed
equal to 1 and the temperature of the steam is set equal to the consensus from the fluid
thermocouples associated with the containment heaters which is approximately 391 ◦ F or
472.6 K. This will also be used to set the initial temperature for the steam/air mixture.
The heat transfer plate thermocouples were used to initialize the temperature of
87
the heat structure used to mimic the heat transfer between the HPC and CPV. The
three upper banks of thermocouples were used for the steam/mixture region and all have
similar values as evidenced in Table 4.7 with one exception. The recorded measurements
from TW-863 did not follow the trends of the other thermocouples or the laws of heat
conduction so the tabulated value in Table 4.7 is simply the average of the readings from
TW-862 and TW-864.
TABLE 4.7: Initial Heat Transfer Plate Wall Temperatures for Containment Simulation
Thermocouple
TW-842
TW-843
TW-844
TW-852
TW-853
TW-854
TW-862
TW-863
TW-864
Temperature (K)
411.7
384.5
349.8
413.2
382.7
351.5
413.8
382.5
351.3
Two equally spaced intervals (three mesh points) were utilized in the RELAP5-3D
heat structures representing the heat transfer plate to line up with the locations of the
heat transfer plate thermocouples. All of the liquid volume was assumed to be the value
of TF-831 as presented previously in determining the amount of mass injection or a few
kelvin less for the lower fluid volume (range of 315-320 K). The temperature of the liquid
volume should have little effect on the condensation heat transfer which is the aim of
this RELAP5-3D calculation. Heat structures were also used to model the ambient heat
loss for the containment vessel. The vessel initial temperature was assumed to be the
same as the injected steam since the transient was begun over 1000 s before this selected
experimental period. The vessel wall was not artificially stratified. The ambient air
88
temperature was recorded during the execution of the experimental testing. In Figure 4.27,
three containment pressure trends are plotted including the experimental data, a RELAP53D with code calculated condensation heat transfer (R-03-01), and a RELAP5-3D run with
an arbitrary heat flux boundary condition (R-03-02). A few items were discovered from
these calculations. First, the RELAP5-3D run with the built-in models used to determine
the heat flux through the heat transfer plate over-predicted the initial heat transfer as a
result of poor interface temperature treatment for the noncondensable condensation layer.
The experimental data was used to intialize the heat transfer plate mesh temperatures,
but once the calculation started, these temperatures rose substantially and the initial
temperature difference between the plate and the air-steam environment in containment
is the reason for the excess heat transfer. This is depicted in Figure 4.28. TW893 is
located on the insulated HPC vessel wall opposite the heat transfer plate thermocouple
bank of TF-85x offset by a few centimeters. Saturation temperature for water from 200250 psig is between 472-482 K and TW893 is in this temperature band. The heat transfer
plate thermocouple, TW852, was used to initialize the heat structure that mimics its
heat transfer in RELAP5-3D. From the figure, it is apparent that the RELAP5-3D mesh
point temperature quickly rises and approaches the gas temperature of the hydrodynamic
volume which is the left boundary of its heat structure. This temperature gradient is the
cause of the exaggerated heat transfer mentioned. To better approximate the experimental
trend, the heat flux out of the upper containment was manually increased with a user
imposed boundary condition (R-03-02).
Referring back to Figure 4.6, it is postulated that the initial high condensation
rate is due to poor interface temperature treatment which artificially creates a higher
temperature gradient between the cold surfaces of the heat transfer plate and the vessel
wall which are both simulated with heat structures. After the initial high condensation
89
rate, the heat transfer mode for the containment vessel wall heat structure quickly changes
to various convection heat transfer regimes which predict unnoticeable heat fluxes except
during a period where the single vent valve is open as seen in Figure 4.29. This shows
the heat flux out of the five uppermost HPC hydrodynamic volumes (negative value for
heat leaving the volume). Heat structure #60105 is associated with the uppermost HPC
containment volume on down to #60101 which is the volume below the ADS vent line
connection volume. Figure 4.30 shows the first 100 s of the calculation which are left out
of Figure 4.29 because of the disparity in values. This may be a cause of the subsequent
underprediction in condensation heat transfer that leads to a longer time to pressure
equalization because although the surface is insulated it is not perfectly adiabatic. The
reason that RELAP5-3D chooses convection as the mode of heat transfer is that the
vapor saturation temperature of the bulk fluid based upon the vapor partial pressure is
not greater than the wall temperature of the associated heat structure as described in
a flow chart in INL (2005c). As mentioned previously, the thermodynamic properties of
the insulating material were manually input into a RELAP5-3D table and the built-in
stainless steel properties of RELAP5-3D make up the thermal circuit that simulates the
containment ambient loss along with the actual ambient temperature. However, there is
not perfect contact between the insulation and the vessel on the facility and the treatment
in RELAP5-3D is understandably more idealized than actuality. There is no experimental
data for determining the heat loss through the containment vessel.
Another reason that the heat transfer in containment is underestimated is a direct
consequence of the initial high condensation rate. At the start of the transient, there are
3.0 m axially of the heat transfer plate which are not covered by liquid. 100 s into the
transient, RELAP5-3D predicts a liquid level increase in containment of 0.56 m which
is a 19% reduction in heat transfer area. The actual reduction after 100 s is only 7.2%.
90
2.3
Exp
R−03−01
R−03−02
2.2
2.1
Pressure (MPa)
2.0
1.9
1.8
1.7
1.6
1.5
1.4
1.3
0
100
200
300
400
500
600
700
800
900
Time (s)
FIGURE 4.27: Stand-alone Model: Containment Pressure
After 1000 s, RELAP5-3D predicts a 24% reduction in heat transfer area and there is
actually only a 13% reduction in heat transfer area. The difference between the times
to pressure equalization is more drastic than this value since RELAP5-3D required over
40% longer to predict the time to begin the long term cooling phase. This presents
a difficulty in determining where improvement may be made in the calculation of the
condensation in the presences of noncondensables. Because this was not a controlled,
steady-state condensation experiment, the information provided by the heat transfer plate
instrumentation can not be used to determine a heat flux through the conduction equation.
Judgement cannot be made on the applicability of the mass fraction adjusted condensation
heat transfer coefficient. However from Figures 4.28 and 4.24, it is apparent that RELAP53D predicts that the interface temperature is less affected by the high concentration of
noncondensables near the condensation surface. The heat structure that represents the
wall is allowed to heat up to a temperature closer to the bulk fluid.
91
500.0
490.0
480.0
Temperature (K)
470.0
460.0
450.0
Exp:TW893
Exp:TW852
R−03−01:TW893
R−03−01:TW852
440.0
430.0
420.0
410.0
400.0
0
100
200
300
400
500
600
700
800
900
Time (s)
FIGURE 4.28: Stand-alone Model: Containment Temperatures
5000.0
0.0
Heat Flux (W/m2 )
−5000.0
−10000.0
−15000.0
−20000.0
HS−60105
HS−60104
HS−60103
HS−60102
HS−60101
−25000.0
−30000.0
−35000.0
0
1000
2000
3000
4000
5000
6000
Time (s)
FIGURE 4.29: Initial Calculation: HPC Ambient Heat Loss - 100 − 6000 s
92
50000.0
0.0
−50000.0
−100000.0
Heat Flux (W/m2 )
HS−60105
HS−60104
HS−60103
HS−60102
HS−60101
−150000.0
−200000.0
−250000.0
−300000.0
−350000.0
−400000.0
0
10
20
30
40
50
60
70
80
90
Time (s)
FIGURE 4.30: Initial Calculation: HPC Ambient Heat Loss - 0 − 100 s
100
93
5.
CONCLUSIONS
A RELAP5-3D analysis of the ADS blowdown IAEA ICSP experiment conducted
at the MASLWR facility of OSU was performed to identify the strengths and weaknesses
of the best-estimate thermal-hydraulic code in predicting phenomena not present in commercial nuclear reactor designs. Coding calculations undertaken include full-time scale
calculations, sensitivity studies and investigations into built-in model options. Besides
graphical depictions of the coding and experimental results, the FFTBM was applied to
provide quantitative information. The qualitative and quantitative analysis has lead to
the following conclusions.
• The long term cooling phase of the transient was well simulated by RELAP5-3D.
• Better interface temperature treatment is necessary to properly model the temperature of the condensing surface.
• Adjusting the user inputs for the Henry-Fauske choked flow model activated at its
recommended location does not affect the calculational results for this experiment.
• Actual experimental heat losses for the containment vessel are required to ensure
a better prediction of the condensation heat transfer away from the heat transfer
plate.
• For this rapid loss of pressure transient, similar results were obtained with RELAP53D through a steady-state initialized calculation and a calculation with no coding
time allotted for initialization.
94
5.1.
Future Work
Because the experiment was not designed to focus on a specific phenomenon but
study a transient accident scenario, a few items were identified which need more clarification. Also, further RELAP5-3D investigations may be undertaken based upon additional
code options and additional instrumentation and testing if secured.
• A steady-state condensation experiment is needed to determine the efficacy of the
built-in RELAP5-3D condensation heat transfer correlations and iteration procedure
in the presence of noncondensables when applied to high pressure scenarios. Full
use of the heat transfer plate thermocouple information could then be applied.
• More instrumentation is needed to properly model the ADS lines. A mass flow
measurement device or pressure drop across the lines would be helpful especially in
adjusting the flow losses through the lower ADS lines once pressure equalization has
occurred.
• A study into the 2-D mixing capabilities of RELAP5-3D should be undertaken because the air/steam environment appears to be thoroughly mixed because of the
similarity of heat transfer plate temperatures for the upper containment. Using a
1-D model for the containment does not mix the air evenly through the containment
vessel.
95
BIBLIOGRAPHY
Relap5-3d code manual volume i: Code structure, system models and solution methods.
Technical Report INEEL-EXT-98-00834, Idaho National Laboratory, 2005a.
Relap5-3d code manual volume ii: Users guide and input requirements. Technical Report
INEEL-EXT-98-00834, Idaho National Laboratory, June 2005b.
Relap5-3d code manual volume iv: Models and correlations. Technical Report INEELEXT-98-00834, Idaho National Laboratory, 2005c.
Appendix a: Relap5-3d input requirements. Technical Report INEEL-EXT-98-00834-V2,
Idaho National Laboratory, 2005d.
S.N. Aksan, F. D’Auria, and H. Stdtke. User effects on the thermal-hydraulic transient
system code calculations. Nuclear Engineering and Design, 145(1-2):159 – 174, 1993.
ISSN 0029-5493.
W. Ambrosini, R. Bovalini, and F. D’Auria. Evaluation of accuracy of thermal-hydraulic
code calculations. Energia Nucleare, 7:5–16, 1990.
W. Ambrosini, N. Forgione, A. Manfredini, and F. Oriolo. On various forms of the heat
and mass transfer analogy: Discussion and application to condensation experiments.
Nuclear Engineering and Design, 236(9):1013 – 1027, 2006. ISSN 0029-5493.
Mark H. Anderson, Luis E. Herranz, and Michael L. Corradini. Experimental analysis
of heat transfer within the ap600 containment under postulated accident conditions.
Nuclear Engineering and Design, 185(2-3):153 – 172, 1998. ISSN 0029-5493.
ANS. Nuclear news. volume 54. April 2011a.
ANS. Nuclear news. volume 54. July 2011b.
96
ANS. Nuclear news. volume 54. June 2011c.
ANS. Nuclear news. volume 54. May 2011d.
H. J. H. Brouwers. Effect of fog formation on turbulent vapor condensation with noncondensable gases. Journal of Heat Transfer, 118:243–245, 1996.
A. P. Colburn and O. A. Housen. Design of cooler condensers for mixtures of vapors with
noncondensing gases. Industrial and Engineering Chemistry, 26:1178–1182, 1934.
M. L. Corradini. Turbulent condensation on a cold wall in the presence of a noncondensable
gas. Nuclear Technology, 64:186–195, February 1984.
CSNI. Csni loca standard problems. Technical Report 17, Committee on the Safety of
Nuclear Installations, Nuclear Energy Agency, OECD, August 1977.
Arijit Ganguli, A.G. Patel, N.K. Maheshwari, and A.B. Pandit. Theoretical modeling
of condensation of steam outside different vertical geometries (tube, flat plates) in the
presence of noncondensable gases like air and helium. Nuclear Engineering and Design,
238(9):2328 – 2340, 2008. ISSN 0029-5493.
S. M. Ghiaasiaan and D. A. Eghbali. On modeling of turbulent vapor condensation with
noncondensable gases. Journal of Heat Transfer, 119:373–376, 1997.
D. Grgic. Coupled relap5/gothic model for iris sbloca analysis. In 5th International
Conference on Nuclear Option in Countries with Small and Medium Electricity grids,
Dubrovnik, Croatia, May 16-20, 2004, 2004.
P.P. Groudev and M.P. Pavlova. Sensitivity calculations of prz water level during the
natural circulation test at unit 6 of kozloduy npp. Progress in Nuclear Energy, 49(2):
130 – 141, 2007. ISSN 0149-1970.
97
Y. A. Hassan and L. L. Raja. Analysis of experiments for steam condensation in the
presence of noncondensable gases using the relap5/mod3 code. Nuclear Technology,
104:76–87, 1993.
Y.A. Hassan and S. Banerjee. Implementation of a non-condensable model in relap5/mod3.
Nuclear Engineering and Design, 162(2-3):281 – 300, 1996. ISSN 0029-5493.
Luis E. Herranz, Mark H. Anderson, and Michael L. Corradini. A diffusion layer model for
steam condensation within the ap600 containment. Nuclear Engineering and Design,
183(1-2):133 – 150, 1998. ISSN 0029-5493.
Kevin Hogan, Yehong Liao, Bradley Beeny, Karen Vierow, Randall Cole Jr., Larry
Humphries, and Randall Gauntt. Implementation of a generalized diffusion layer model
for condensation into melcor. Nuclear Engineering and Design, 240(10):3202 – 3208,
2010. ISSN 0029-5493. 4th International Topical Meeting on High Temperature Reactor
Technology (HTR 2008), with Regular Papers.
F. P. Incropera, D. P. DeWitt, T. L. Bergman, and A. S. Lavine. Introduction to Heat
Transfer. John Wiley & Sons, 5th edition, 2006.
D. T. Ingersoll. Deliberately small reactors and the second nuclear era. Progress in Nuclear
Energy, 51:589–603, 2009.
Jong-Won Kim, Yeon-Gun Lee, Hyoung-Kyoun Ahn, and Goon-Cherl Park. Condensation
heat transfer characteristic in the presence of noncondensable gas on natural convection
at high pressure. Nuclear Engineering and Design, 239(4):688 – 698, 2009. ISSN 00295493.
Y. Liao and K. Vierow. A generalized diffusion layer model for condensation of vapor with
noncondensable gases. Journal of Heat Transfer, 129(8):988–994, 2007.
98
M. Misale, P. Ruffino, and M. Frogheri. The influence of the wall thermal capacity and
axial conduction over a single-phase natural circulation loop: 2-d numerical study. Heat
and Mass Transfer, 36:533–539, 2000. ISSN 0947-7411. 10.1007/s002310000120.
S. M. Modro, J. E. Fisher, K. D. Weaver, Jr. J. N. Reyes, J. T. Groome, P. Babka,
and T. M. Carlson. Multi-application small light water reactor final report. Technical
Report INEEL/EXT-04-01626, INEEL, December 2003.
Y. Mori and K. Hijikata. Free convection condensation heat transfer with noncondensable
gas on a vertical surface. International Journal of Heat and Mass Transfer, 16:2229–
2240, 1973.
Seyed Khalil Mousavian, Francesco D’Auria, and Mahmoud A. Salehi. Analysis of natural
circulation phenomena in vver-1000. Nuclear Engineering and Design, 229(1):25 – 46,
2004. ISSN 0029-5493.
N. Muellner, E. Seidelberger, A. Del Nevo, and F. D’Auria. Application of the fast fourier
transform based method to assist in the qualification process for the psb-vver1000 relap5
nodalisation. In Nuclear Energy for New Europe, September 2005.
A. Del Nevo, A. Manfredini, F. Oriolo, S. Paci, and L. Oriani. Integrated analysis for a
small break loca in the iris reactor using melcor and relap5 codes. 2004.
NRC.
Secy-10-0034 - potential policy, licensing, and key technical issues for
small modular nuclear reactor designs.
http://www.nrc.gov/reading-rm/doc-
collections/commission/secys/2010/secy2010-0034/2010-0034scy.html, March 2010.
L. Oriani, E. Conway, and D. Grgic. Small break loss of coolant accident analysis for the
international reactor innovative and secure (iris). In 5th International Conference on
Nuclear Option in Countries with Small and Medium Electricity Grids, May 2004.
99
Davide Papini, Davor Grgic, Antonio Cammi, and Marco E. Ricotti. Analysis of different
containment models for iris small break loca, using gothic and relap5 codes. Nuclear
Engineering and Design, In Press, Corrected Proof:–, 2010. ISSN 0029-5493.
R. H. Perry, D. W. Green, and J. O. Maloney, editors. Perry’s Chemical Engineers’
Handbook. McGraw-Hill, 1997.
P. F. Peterson, V. E. Schrock, and T. Kageyama. Diffusion layer theory for turbulent
vapor condensation with noncondensable gases. Journal of Heat Transfer, 115:998–
1003, November 1993.
Andrej Prosek, Francesco D’Auria, and Borut Mavko. Review of quantitative accuracy
assessments with fast fourier transform based method (fftbm). Nuclear Engineering and
Design, 217(1-2):179 – 206, 2002. ISSN 0029-5493.
J. D. Ramshaw and J. A. Trapp. Characteristics, stability, and short-wavelength phenomena in two-phase flow equation systems. Nuclear Science and Engineering, 66:93–102,
1978.
Jose N. Reyes and John King. Scaling analysis for the osu integral system test facility.
Technical report, Oregon State University, 2003.
Anis Bousbia Salah, Juswald Vedovi, Francesco D’Auria, Giorgio Galassi, and Kostadin
Ivanov.
Analysis of the vver1000 coolant trip benchmark using the coupled re-
lap5/parcs code. Progress in Nuclear Energy, 48(8):806 – 819, 2006. ISSN 0149-1970.
¡ce:title¿OECD/DOE/CEA V1000CT-1Benchmark¡/ce:title¿.
R. R. Schultz. Relap5-3d code manual volume v: User’s guidelines. Technical Report
INEEL-EXT-98-00834, Idaho National Laboratory, June 2005.
S. Shahedi, J. Jafari, M. Boroushaki, and F. D’Auria. Development of a qualified nodalization for small-break loca transient analysis in psb-vver integral test facility by re-
100
lap5 system code. Nuclear Engineering and Design, 240(10):3309 – 3320, 2010. ISSN
0029-5493. ¡ce:title¿4th International Topical Meeting on High Temperature Reactor
Technology (HTR 2008), with Regular Papers¡/ce:title¿.
J. M. Smith, H. C. Van Ness, and M. M. Abbott. Introduction to Chemical Engineering
Thermodynamics. McGraw-Hill, 5th edition, 1996.
N. E. Todreas and M. S. Kazimi. Nuclear Systems I: Thermal Hydraulic Fundamentals.
Taylor and Francis, 1990.
J. A. Trapp and V. H. Ransom. A choked-flow calculation criterion for nonhomogeneous,
nonequilibrium, two-phase flows. International Journal of Multiphase Flow, 8:669–681,
1982.
H. Uchida, A. Oyama, and Y. Togo. Evaluation of post-incident cooling systems of light
water power reactors. In Proceedings of the Third International Conference on the
Peaceful Uses of Atomic Energy, volume 13, pages 93–104, 1964.
Frank M. White. Fluid Mechanics. McGraw-Hill, 5th edition, 2003.
Brian G. Woods, Mark R. Galvin, and C. Jordan Bowser. Problem specification for the iaea
international collaborative standard problem on integral pwr design natural circulation
flow stability and thermo-hydraulic coupling of containment and primary system during
accidents [draft]. Technical Report OSU-ICSP-10001, Oregon State University, May
2010.