Scaling Analysis for the Direct Reactor Auxiliary Cooling System for AHTRs
THESIS
Presented in Partial Fulfillment of the Requirements for the Degree Master of Science in the Graduate School of The Ohio State University
By
Qiuping Lv, B.S.
Graduate Program in Nuclear Engineering
The Ohio State University
2013
Master's Examination Committee:
Prof. Xiaodong Sun, Advisor
Prof. Thomas E. Blue
Prof. Richard N. Christensen
Copyright by
Qiuping Lv
2012
Abstract
The Advanced High Temperature Reactor (AHTR) or Fluoride Salt Cooled High
Temperature Reactor (FHR) is one of the advanced rector concepts that have been proposed for Gen IV reactors. The AHTR combines four main proven nuclear technologies, namely, the liquid salt of molten salt reactors, the coated particle fuel
(TRISO particle) of high-temperature gas-cooled reactors, the pool configuration and passive safety system of sodium-cooled fast reactors, and the Brayton power cycle technology. The AHTR is capable of providing very high temperature (750 to 1,000ºC) heat for various industrial processing needs, hydrogen production, and electricity generation.
The Direct Reactor Auxiliary Cooling System (DRACS) is a passive heat removal system that was derived from the Experimental Breeder Rector-II (EBR-II), and then improved in later fast reactor designs. The DRACS has been proposed for AHTR as the passive decay heat removal system. The DRACS features three coupled natural circulation/convection loops relying completely on buoyancy as the driving force. In the
DRACS, two heat exchangers, namely, the DRACS Heat Exchanger (DHX) and the
Natural Draft Heat Exchanger (NDHX) are used to couple these natural circulation/convection loops. In addition, a fluidic diode is employed to restrict parasitic flow during normal operation of the reactor and to activate the DRACS in accidents.
ii
While the DRACS concept has been proposed, there are no actual prototypic
DRACS systems for AHTRs built and tested in the literature. In this report, a detailed modular design of the DRACS for a 20-MWth FHR is first developed. As a starting point, the DRACS is designed to remove 1% of the nominal power, i.e., the decay power being 200 kW. The design process for the prototypic DRACS involves selection of the salts, identification of the reactor core, design of the DHX and NDHX, design of the fluidic diode, design of the air chimney, selection of the loop pipes, and finally determination of the loop height based on pressure drop analysis. FLiBe with high enrichment in Li-7 and FLiNaK have been selected as the primary and secondary salts, respectively. A 16-MWth pebble bed core proposed by University of California at
Berkeley (UCB) is adopted in the design. Shell-and-tube heat exchangers have been designed based on Delaware Method for the DHX and NDHX. A vortex diode that has been tested with water in the literature is adopted in the present design. Finally, pipes with inner diameter of 15 cm are selected for both the primary and secondary loops of the
DRACS. The final DRACS design features a total height less than 13 m. The design presented here has the potential to be used in the planned small-scale FHR test reactor and will also benefit and guide the DRACS design for a commercial AHTR.
Following the prototypic DRACS design is the detailed scaling analysis for the
DRACS, which will provide guidance for the design of scaled-down DRACS test facilities. Based on the Boussinesq assumption and one-dimensional formulation, the governing equations, i.e., the continuity, integral momentum, and energy equations are non-dimensionalized by introducing appropriate dimensionless parameters, including the
iii dimensionless length, temperature, velocity, etc. The key dimensionless numbers, i.e., the
Richardson, friction, Stanton, time ratio, Biot, and heat source numbers that characterize the DRACS system, are obtained from the non-dimensional governing equations. Based on the dimensionless numbers and non-dimensional governing equations, similarity laws are proposed. In addition, a scaling methodology has also been developed, which consists of the core scaling and loop scaling. Due to the importance of the core heat transfer in establishing the DRACS steady state, core scaling is started with, from which the convection time ratio is obtained. The loop scaling is accomplished by utilizing the convection time ratio obtained from the core scaling and by making two assumptions that are related to the power and loop height of the test facility. The consistence between the core and the loop scaling is examined through the reference volume ratio that can be obtained from both scaling processes. The scaling methodology and similarity laws have been applied to obtain a scaled-down low-temperature DRACS test facility (LTDF) and a scaled-down high-temperature DRACS test facility (HTDF).
iv
Dedication
This document is dedicated to my family.
v
Acknowledgments
There are many people I want to thank.
First and foremost, I must give my deepest gratitude to my advisor, Prof. Xiaodong
Sun, for his guidance, supervision, attention and support throughout my study and research.
In addition, I sincerely thank Prof. Richard Christensen and Prof. Thomas Blue for their constructive comments and suggestions during all the research meetings.
Helps from Dr. Xia Wang, Dr. Grady Yoder and Dr. Dane Wilson (ORNL), and Dr.
Piyush Sabharwall (INL) are greatly appreciated.
I also would like to thank my friends and the colleagues in the Ohio State University
Nuclear Engineering Program. They have been helpful in improving my English.
Special thanks to my wife and my parents for always being understanding and supportive.
Finally, the support from the U.S. Department of Energy for our DRACS project is gratefully acknowledged.
vi
Vita
2009...... B.S. in Physics, Nanjing University, China 2009-2010 ...... Teaching Assistant, Physics Department, Iowa State University 2010-2011 ...... Graduate Fellow, Nuclear Engineering Program, The Ohio State University 2011 to present ...... Graduate Research Associate, Nuclear Engineering Program, The Ohio State University
Publications
1. X. Wang, Q. Lv, X. Sun, R.N. Christensen, T.E. Blue, G. Yoder, D. Wilson, and P. Sabharwall, “A Modular Design of a Direct Reactor Auxiliary Cooling System for AHTRs,” Transaction of the American Nuclear Society, Vol. 104, 2011 American Nuclear Society Annual Meeting, June 26-30, 2011, Hollywood, FL, pp. 1077-1080.
2. X. Wang, Q. Lv, X. Sun, R.N. Christensen, T.E. Blue, G. Yoder, D. Wilson, and P. Sabharwall, “Scaling Analysis for the Direct Reactor Auxiliary Cooling System for AHTRs,” Transaction of the American Nuclear Society, Vol. 105, 2011 American Nuclear Society Winter Meeting, October 30 – November 3, 2011, Washington, DC, pp. 1027-1030.
3. X. Wang, Q. Lv, X. Sun, R.N. Christensen, T.E. Blue, G. Yoder, D. Wilson, and P. Sabharwall, “Design of a Scaled-down DRACS Test Facility for an AHTR,” Transaction of the American Nuclear Society, Vol. 105, 2011 American Nuclear Society Winter Meeting, October 30 – November 3, 2011, Washington, DC, pp. 1031-1034.
vii
4. Q. Lv, X. Wang, I. Adams, X. Sun, R.N. Christensen, T.E. Blue, G. Yoder, D. Wilson, and P. Sabharwall, “Design of a Scaled-down Low-temperature DRACS Test Facility for an AHTR,” Transactions of the American Nuclear Society, Vol. 106, 2012 American Nuclear Society Annual Meeting, June 24-28, 2012, Chicago, IL, pp. 1071-1074.
5. Q. Lv, I. Adams, X. Wang, X. Sun, R.N. Christensen, T.E. Blue, G. Yoder, D. Wilson, and P. Sabharwall, “A MATLAB Code for Thermal Performance Evaluation of a Low- Temperature DRACS Test Facility”, Transaction of the American Nuclear Society, Vol. 107, 2012 American Nuclear Society Winter Meeting, November 11-15, 2012, San Diego, CA, pp. 1374-1377.
Fields of Study
Major Field: Nuclear Engineering
viii
Table of Contents
Abstract ...... ii
Dedication ...... v
Acknowledgments...... vi
Vita ...... vii
Table of Contents ...... ix
List of Tables ...... xii
List of Figures ...... xiv
Nomenclature ...... xvi
Chapter 1: Introduction ...... 1
1.1 Gen IV Reactors ...... 1
1.2 Molten Salt Reactor (MSR) ...... 3
1.3 Advanced High Temperature Reactor (AHTR) ...... 5
1.3.1 The Pebble Bed AHTR (PB-AHTR) by UCB ...... 6
1.3.2 The Advanced High Temperature Reactor (AHTR) by ORNL ...... 10
1.3.3 The Small Modular AHTR (SmAHTR) by ORNL ...... 14
ix
Chapter 2: Direct Reactor Auxiliary Cooling System for AHTRs ...... 18
2.1 Introduction to the Direct Reactor Auxiliary Cooling System (DRACS) ...... 18
2.2 Scope of Present Study ...... 21
2.3 DRACS Prototypic Design...... 22
2.3.1 Selection of Salts ...... 23
2.3.2 Selection of Core Design and its Pressure Drop Calculation ...... 25
2.3.3 Selection of Fluidic Diode and its Pressure Drop Calculation ...... 29
2.3.4 Heat Exchanger Design ...... 32
2.3.5 Selection of Loop Pipes ...... 48
2.3.6 Summary of Prototypic Design ...... 49
Chapter 3: Scaling Analysis for the DRACS ...... 51
3.1 Governing Equations ...... 51
3.2 Scaling Similarity Criteria ...... 55
3.3 Scaling Methodology ...... 57
3.4 Core Scaling Analysis ...... 60
3.4.1 Scaling Results for Low-Temperature DRACS Test Facility (LTDF)...... 68
3.4.2 Scaling Results for High-Temperature DRACS Test Facility (HTDF) ...... 73
Chapter 4: Conclusion...... 82
References: ...... 84
x
Appendix A: Input Parameters for the Design/Rating of the Shell-and-Tube Heat
Exchanger ...... 89
xi
List of Tables
Table 1. Features of the PB-AHTR design by UCB, the AHTR and SmAHTR designs by
ORNL ...... 10
Table 2. Summary of properties of FLiBe and FLiNaK (T in Kelvin) ...... 25
Table 3. Pressure drop in the core ...... 29
Table 4. Parameters of the vortex diode ...... 31
Table 5. Empirical coefficients for calculation of ji [26] ...... 36
Table 6. Empirical coefficients for calculation of fi [26] ...... 39
Table 7. Thermal conductivities of Hastelloy N [27] ...... 40
Table 8. Design results of the DHX ...... 43
Table 9. Design results of the NDHX ...... 47
Table 10. Temperatures and mass flow rates of working fluids ...... 50
Table 11. Pressure losses and heights of the primary and secondary loops ...... 50
Table 12. Reference values and dimensionless parameters ...... 53
Table 13. Design parameters in the prototype and model ...... 57
Table 14. Dimensions of the fuel pebble and the TRISO particle [31] ...... 64
Table 15. Properties of the structure materials of a pebble...... 67
Table 16. Dimensions of the core design in LTDF ...... 70
Table 17. Thermal properties of YTZP at room temperature [41] ...... 70
xii
Table 18. Core and loop scaling results for LTDF ...... 71
Table 19. DHX and NDHX scaling results for LTDF ...... 72
Table 20. Design results summary for LTDF ...... 73
Table 21. Summary of properties of FLiNaK and KF-ZrF4 (T in Kelvin)...... 77
Table 22. Dimensions of the core design in HTDF ...... 78
Table 23. Core and loop scaling results for HTDF ...... 79
Table 24. DHX and NDHX scaling results for HTDF...... 80
Table 25. Design results summary for HTDF ...... 81
xiii
List of Figures
Figure 1. Evolution of nuclear power systems [1] ...... 2
Figure 2. Scheme of the Molten Salt Reactor (MSR) [1] ...... 4
Figure 3. Schematic drawing of the PB-AHTR system [10] ...... 7
Figure 4. 3-D drawing of the PB-AHTR primary loop, intermediate loop, and power conversion system [10] ...... 8
Figure 5. AHTR heat transport path overview [14] ...... 11
Figure 6. Overview of AHTR core, vessel, heat transfer, and refueling components ...... 12
Figure 7. SmAHTR integral primary system [17] ...... 15
Figure 8. Schematic drawing of the DRACS with the primary heat transport system [5] 21
Figure 9. The pebble bed reactor core used in FHR-16 [10] and simplified sketch of the reactor core...... 26
Figure 10. Reverse and forward directions in a vortex diode ...... 30
Figure 11. The adopted vortex diode [25] ...... 31
Figure 12. Relation between the Reynolds number and resistance coefficient (forward flow) [25] ...... 32
Figure 13. Pressure drop composition for the shell side [26] ...... 37
Figure 14. Relation between the tube length and tube side inlet temperature ...... 42
Figure 15. Relation between the primary loop height and tube side inlet temperature .... 42
xiv
Figure 16. Air chimney with the NDHX at the bottom ...... 44
Figure 17. Relation between the chimney height and the air exit temperature, with 50 tubes/row ...... 45
Figure 18. Relation between the secondary loop height and the air exit temperature, with
50 tubes/row ...... 46
Figure 19. Relation between the chimney height and the air exit temperature, with 2 rows
...... 46
Figure 20. Relation between the tube length and the air outlet temperature, with 2 rows 47
Figure 21. Pressure drop per length versus pipe diameter in both primary and secondary loops ...... 48
Figure 22. Prototypic design of the DRACS ...... 50
Figure 23. Flowchart for the core scaling ...... 58
Figure 24. Flowchart for the primary loop scaling ...... 59
Figure 25. Relations between the transition Reynolds number and Grashof number ...... 62
Figure 26. The structure of a fuel pebble and TRISO particle [10] ...... 63
Figure 27. Fractional change of thermal conductivity of matrix graphite with fluence at
1123-1213 K [36] ...... 65
Figure 28. Temperatures variation during the LOFC transient [31] ...... 66
Figure 29. Core design in the experiment ...... 69
Figure 30. The FHR-16 pebble bed core [10] and SmAHTR core [17] ...... 75
Figure 31. Layout of the DRACS secondary loop ...... 76
Figure 32. The core design in the high-temperature test facility ...... 78
xv
Nomenclature
a Flow area
as Cross-sectional area of structure
A Cross-sectional area of reactor core (Equation 2)
Non-dimensional flow area (Equation 34)
Ai Total heat transfer area based on tube inner diameter
Ao Total heat transfer area based on tube outer diameter
Bi Biot number
cp Specific heat capacity of fluid
cps, Specific heat capacity of shell-side fluid
cps Specific heat capacity of structure d Diameter of diode axial nozzle (Equation 6)
Hydraulic diameter (Equation 30)
Inner diameter of tube (Equation 51)
dp Pebble diameter
D Heater rod diameter (Table 16)
Pipe diameter (Table 20)
xvi
Dh Hydraulic diameter
Dt Tube outer diameter
DOSIS Neutron fluence
Dti Tube inner diameter
Dw Equivalent hydraulic diameter in baffle window f Friction factor
fi Friction factor
ft Friction factor for tube-side flow
F Mean temperature difference correction factor
F Friction number g Gravity
G Mass flux
Gr Grasholf number
Gs Shell-side fluid mass flux h Heat transfer coefficient
haverage Average heat transfer coefficient for heater buddle
hi Heat transfer coefficient for ideal cross flow over tube banks
hs Shell-side heat transfer coefficient
ht Tube-side heat transfer coefficient
H Loop height
xvii ji Heat transfer factor
Jb Correction factor for bypass flow
Jc Correction factor for baffle cut
Jl Correction factor for leakage flow
J r Correction factor for adverse temperature gradient
J s Correction factor for unequal baffle spacing
kcoating Thermal conductivity of fuel pebble coating
ks Thermal conductivity of structure
kpebble Thermal conductivity of fuel pebble
kshell Thermal conductivity of fuel pebble shell
kt Thermal conductivity of tube-side fluid
ktw Thermal conductivity of tube wall
K Form loss coefficient l Length
L Height of reactor core
L Non-dimensional length
Lbc Baffle central spacing
LMTD Logarithmic mean temperature difference
Lti Tube length
xviii
Ltp Tube pitch
Ltw Tube wall thickness m Mass flow rate
ms Mass flow rate of shell-side fluid
mw Mass flow rate of shell-side fluid in baffle window
Nb Number of baffles
Ntcc Number of tubes in baffle compartment
Ntcw Number of tubes in baffle window
Nu Nusselt number
P Decay power (Equation 4)
Heater rod pitch (Table 16)
Po Reactor nominal power
Pr Prandtl number
Prs Prandtl number of shell-side fluid
Prt Prandtl number of tube-side fluid
qs Power density in structure
Q Decay power
Qact Actual heat removal rate of heat exchanger
Qs Heat source number for structure
R Richardson number xix
Rb Correction factor for bypass flow
Rl Correction factor for leakage flow
Rs Correction factor for unequal baffle spacing
Re Reynolds number
Res Reynolds number of shell-side fluid
Ret Reynolds number of tube-side fluid
Rfo, Fouling on shell side
Rfi, Fouling on tube side
St Stanton number
t Time (Equation 30)
Wall thickness of tube (Equation 51)
T Temperature of fluid
Tin, cold Cold side inlet temperature
Tin, hot Hot side inlet temperature
Tout, cold Cold side outlet temperature
Tout, hot Hot side outlet temperature
Ts Temperature of structure
T Time ratio number
u Velocity of fluid
ur Representative velocity
xx
U Non-dimensional fluid velocity
Uo Overall heat transfer coefficient based on tube outer diameter
U r Non-dimensional representative velocity
vt Flow velocity of tube-side fluid
V Fluid velocity at diode axial nozzle
Vr Reference velocity
Vshell Volume of fuel pebble shell
Vcoating Volume of fuel pebble coating
W Wall distance
y Transverse coordinate
Y Non-dimensional transverse coordinate
z Axial coordinate
Z Non-dimensional axial coordinate
s Thermal diffusivity of structure
Thermal expansion coefficient of fluid
Conduction depth
Δp Pressure drop
pbi Pressure drop for ideal cross flow over tube banks
pc Cross-flow pressure drop over baffle compartments
pe End-zone pressure drop
xxi
pt Pressure drop for tube side
pw Pressure drop over baffle windows
Δρ Density difference
T Temperature difference
T1 Temperature difference between hot side inlet and cold side outlet
T2 Temperature difference between hot side outlet and cold side inlet
R Total thermal resistance based no tube outer diameter o
Volume fraction of fluid (Equation 2)
Resistance coefficient of diode (Equation 7)
Non-dimensional temperature for fluid
th s Non-dimensional temperature for structure in i section
Dynamic viscosity of fluid
s Dynamic viscosity of shell-side fluid
sw, Dynamic viscosity of shell-side fluid based on wall temperature
t Dynamic viscosity of tube-side fluid
tw, Dynamic viscosity of tube-side fluid based on wall temperature
Kinetic viscosity of fluid
Wetted perimeter
Density of fluid
s Density of shell-side fluid (Equation 20) xxii
s Density of structure (Equation 32)
t Density of tube-side fluid
Time after reactor startup (Equation 4)
Non-dimensional time (Equation 35)
s Reactor operating time
Subscripts i ith section (scaling analysis)
0 Reference valve s structure
R Model-to-prototype ratio i Ideal cross flow (heat exchanger design) i Inner o Outer in Inlet out Outlet s Shell side t Tube side w Tube wall w Baffle window
xxiii
Chapter 1: Introduction
1.1 Gen IV Reactors
As the global population grow, so will the demand for energy to ensure standards of living, health and life expectancy, literacy and opportunity, etc. To cope with this energy demand, nuclear energy, which is believed to be sustainable, clean and safe, has been extensively advocated. To enhance the future role of nuclear energy systems, a generation of innovative nuclear energy systems, known as Generation IV, has been proposed to replace the current Gen II/III reactors and Gen III+ reactors that will be deployed in near future, as shown in Figure 1. Under the support of Gen IV International
Forum (GIF), a technology roadmap has been developed, which defines the technological goals of Gen IV reactors as [1]:
Sustainability: Gen IV nuclear reactors will provide sustainable and clean energy
that promotes long-term availability of systems and effective fuel utilization for
global energy production. In addition, Gen IV reactors will improve protection for
the public health and the environment by notably minimizing the nuclear waste
and reducing the long-term stewardship burden.
Economics: Gen IV nuclear reactors will have a clear life-cycle cost advantage
over other energy sources, as well as a level of financial risk that is comparable to
other energy projects.
1
Safety and Reliability: Gen IV nuclear reactors will be prominent in safety and
reliability, in terms of a very low likelihood and degree of reactor core damage,
and the elimination of the need for offsite emergency response.
Proliferation Resistance and Physical Protection: Gen IV nuclear reactors will be
very unattractive and the least desirable route for diversion or theft of weapon-
grade nuclear materials. Furthermore, Gen IV reactors will be capable of
providing increased physical protection against acts of terrorism.
Figure 1. Evolution of nuclear power systems [1]
GIF followed an evaluation and selection methodology to select the nuclear systems to be developed as Gen IV, based on which the selected systems should advance any of the aforementioned technological goals as they are equally important. Six Gen IV nuclear reactor concepts with great potential were selected, which are Gas-Cooled Fast
2
Reactor System (GFR), Lead-Cooled Fast Reactor System (LFR), Molten Salt Reactor
System (MSR), Sodium-Cooled Fast Reactor System (SFR), Supercritical-Water-Cooled
Reactor System (SCWR), and Very-High-Temperature Reactor System (VHTR). With these six systems, the important missions of electricity generation, hydrogen and process heat production, and actinide management will be adequately addressed. The selected systems will also provide some overlapping coverage of capabilities since not all of the systems may ultimately be viable or attain their performance objectives and attract commercial deployment.
1.2 Molten Salt Reactor (MSR)
Molten Salt Reactor (MSR) is a category of nuclear fission reactors, which use molten salts dissolved with liquid fuel as the primary coolant. The scheme of a typical molten salt reactor is illustrated in Figure 2. The molten salt reactors have some unique characteristics, including good neutron economy, high-temperature operation and correspondingly high thermal efficiency, low operation pressure, inherent safety by fail- safe drainage and passive cooling, and online refueling and management of fuel salt [1].
Extensive research into molten salt reactors was dated back to 1954, when the
Aircraft Reactor Experiment (ARE) was initiated in Oak Ridge National Laboratory
(ORNL) in support of the U.S. Aircraft Nuclear Propulsion (ANP) program. The ARE adopted a 2.5-MWth reactor core designed to obtain sufficient high power density for use as an aircraft engine. The ARE was fueled with NaF-ZrF4-UF4 (53-41-6 mol%), and moderated by beryllium oxide (BeO). During its operation for 100 MW-hours in 1954, peak temperature of 860ºC was reached [2, 3]. The ARE for the first time established 3 benchmarks in performance for a circulating fluoride molten salt system.
Figure 2. Scheme of the Molten Salt Reactor (MSR) [1]
Following the ARE, effort in the research of molten salt reactors was carried out by ORNL in terms of the Molten-Salt Reactor Experiment (MSRE). The MSRE featured a 7.4-MWth core, which was completed by 1964, and first reached critical in 1965. The
MSRE utilized salt mixture of LiF-BeF2-ZrF4-UF4 (65-29-5-1, mol%) as the fuel, and pyrolytic graphite as the moderator. A Ni-based alloy, Hastelloy-N was used and proved to be compatible with fluoride salts in the MSRE. The MSRE was operated for 4 years, with an equivalent full power operation of around 1.5 years, and reached a peak 4 temperature of 650ºC [4]. The MSRE has demonstrated many features, including a lithium/beryllium fluoride salt, graphite moderator, use of different fuels, off-gas systems, and stable performance.
During the 1970s, ORNL has been continuously striving to promote a development program that would culminate in the construction and operation of a demonstration reactor called the Molten Salt Breeder Reactor (MSBR). In spite of the efforts that ORNL had made, in 1976, ORNL had to terminate all the molten salt reactor development work due to budgetary reasons [5].
1.3 Advanced High Temperature Reactor (AHTR)
As the Molten Salt Reactor was selected as one of the Gen IV nuclear reactors, there had been a recent resurgence in the research of the MSR. In 2003, Forsberg,
Peterson, and Pickard proposed a new reactor concept called Advanced High
Temperature Reactor (AHTR), which combined four main proven nuclear technologies, namely, the liquid salt of molten salt reactors, the coated particle fuel (TRISO particle) of high-temperature gas-cooled reactors, the pool configuration and passive safety system of sodium-cooled fast reactors, and the Brayton power cycle technology [6, 7]. Due to the fact that liquid fluoride salts that have been proven in the MSRE are exclusively proposed for the AHTR, it is now also referred to as Fluoride-Salt-Cooled High-Temperature
Reactor (FHR). The liquid fluoride salts feature high boiling temperature of ~ 1,400ºC , which enables the AHTR to be operated at low pressure or near atmospheric pressure.
This helps to reduce the capital cost of the AHTR significantly. In addition, with the excellent heat transfer properties of liquid fluoride salts, the AHTR possesses several 5 potential benefits, including the increased design margins, high temperatures, high core power density, and improved decay heat removal. The AHTR is capable of providing very high temperature (750 to 1,000ºC ) heat for various industrial processing needs, hydrogen production, and electricity generation [8].
There have been recently three main pre-conceptual AHTR designs developed, which are the pebble bed AHTR (PB-AHTR) by University of California at Berkeley
(UCB), the AHTR and the small modular AHTR (SmAHTR) by ORNL. These three designs employ different core geometries, namely, pebble bed fuel, plate fuel, and prismatic fuel, which are all considered as potential designs for a future commercial
AHTR power plant. With these three AHTR designs, typical characteristics of the future commercial AHTRs can be demonstrated.
1.3.1 The Pebble Bed AHTR (PB-AHTR) by UCB
UCB had developed a modular pebble bed AHTR design with a nominal thermal power output of 900 MWth and electrical output of 410 MWe, which was the outcome from their NE 170 senior design class. This design has been selected as the baseline design for a potential commercial FHR, which is being investigated jointly by the
Massachusetts Institute of Technology (MIT), UCB, and University of Wisconsin (UW)
[9]. Re-examination of the PB-AHTR design is being performed. The schematic drawing of the PB-AHTR system is shown in Figure 3, along with a 3-D drawing shown in Figure
4. The entire PB-AHTR system includes four primary salt loops, four intermediate salt loops, and a power conversion system (PCS). Heat generated in the core is transferred from the primary loops to the intermediate loops through four intermediate heat 6 exchangers (IHXs). Two primary and intermediate pumps are installed in the primary and intermediate loops, respectively. Each primary pump and intermediate pump provides
7 forced flow to two of the four IHXs. For the baseline design, FLiBe ( LiF-BeF2, 66-34 in mol%) and FLiNaK (LiF-NaF-KF, 46.5-11.5-42 in mol%) have been selected as the primary and intermediate salts, respectively [10].
Figure 3. Schematic drawing of the PB-AHTR system [10]
7
Figure 4. 3-D drawing of the PB-AHTR primary loop, intermediate loop, and power conversion system [10]
The PB-AHTR adopts an annular core design, with an internal and an external graphite reflector. The pebbles are radially zoned, with the fuel pebbles sandwiched between two layers of blanket pebbles which are simply graphite pebbles to provide neutron moderation. To maintain the pebbles radially zoned, the core employs a diverging inlet and a converging outlet. The fuel pebbles are made of TRISO particles dispersed in the graphite matrix. To enhance heat transfer, the pebbles have been reduced in diameter to 3 cm, in contrast to the 6 cm diameter for conventional pebbles. The overall density of a pebble is smaller than that of the salt FLiBe, which will make the 8 pebbles float in the salt and make online refueling possible. The entire core sits in the
FLiBe pool, which provides a heat sink when the reactor is shut down. A buffer salt is injected between the reactor vessel and the guard vessel, which further increases the thermal inertia of the system. For the baseline design, the core inlet and outlet temperatures are set to 600 and 704ºC , respectively [7, 11].
The four IHXs used in the PB-AHTR were derived from the heat exchanger design in the molten salt breeder reactor (MSBR) program in ORNL. These heat exchangers are shell-and-tube type, with one tube pass, and disk and doughnut baffles.
UCB proposed three candidate designs that were slightly different in the dimensions. The selected baseline design uses 9,465 8.54-m long tubes, yielding a total length of approximately 7.94 m (the tubes are bent by 90 degree at the inlet and outlet which is why the total tube length is longer than that of the IHX) and a diameter of 2.16 m for the
IHX. The primary salt flows in the tubes, with inlet and outlet temperature of 704 and
600ºC , respectively, while the intermediate salt circulates around the tubes, with inlet and outlet temperature of 545 and 690ºC , respectively. To cope with the corrosion problem,
Incoloy 800H tubes with Hastelloy N cladding have been proposed [12].
The adopted primary and intermediate pumps were of the same type, canteliever sump pump, which were also derived from designs originally developed for the MSBR program. The pump motor is isolated from the slat intake and discharger by the long shaft which is 3 m long for the primary pump. The intermediate pump adopts the same motor as in the primary pump, however, shaft is slightly shorter due to spacing constraints [13].
The PB-AHTR adopts a multiple-reheat Brayton cycle for the power conversion
9 system (PCS), which uses helium as the working fluid. The PCS consists of three identical power conversion units, which are similar to the PCS designs developed by
Mitsubishi Heavy Industries for the Pebble Bed Modular Reactor (PBMR). The PCS adopted in the PB-AHTR features a power conversion efficiency of 46% due to the use of a closed Brayton cycle [13].
Some features of the UCB PB-AHTR have been summarized in Table 1, along with the features of the other two AHTR designs proposed by ORNL for comparison. It should be noted that, the PB-AHTR design features a passive safety system, DRACS.
However, a detailed design of the DRACS for the baseline 900-MWth PB-AHTR has not been developed yet.
Table 1. Features of the PB-AHTR design by UCB, the AHTR and SmAHTR designs by
ORNL
PB-AHTR AHTR SmAHTR
(UCB) (ORNL) (ORNL) Thermal Output (MWth) 900 3,400 125 Electric output (MWe) 410 1,500 50 Primary Salt FLiBe FLiBe FLiBe Intermediate Salt FLiNaK KF-ZrF4 FLiNaK Primary Salt Temperature (ºC) 706/600 700/650 700/650 Intermediate Salt Temperature 690/545 670/600 690/600 (ºC)
1.3.2 The Advanced High Temperature Reactor (AHTR) by ORNL
ORNL is now investigating an AHTR design for the U.S. Department of energy,
Office of Nuclear Energy’s Advanced Reactor Concepts program, which has a nominal
10 thermal power of 3,400 MWth and an electric output of 1,500 MWe. The principal goal of developing the AHTR is to demonstrate the viability of FHRs as low-cost, large-size power producers while retaining the characteristic of passive safety. Figure 5 and Figure
6 show the overview of the AHTR heat transport path, and the representation of the entire
AHTR system. Three intermediate loops couple the three primary loops with the two power conversion loops. The AHTR design adopts an advanced supercritical-water power cycle and a cooling tower as the ultimate heat sink, which is believed to be the highly efficient and the most technologically mature large-scale power cycle at typical
FHR output temperatures. FLiBe is selected as the primary salt, the same as in PB-AHTR, while a different salt, KF-ZrF4 (42-58, mol%) is identified as the intermediate salt. The selected intermediate salt does not contain any lithium, which will not dilute the enrichment of the lithium in the primary salt if any leak happens [14].
Figure 5. AHTR heat transport path overview [14] 11
Figure 6. Overview of AHTR core, vessel, heat transfer, and refueling components
The AHTR design employs a pool design, in which the FLiBe circulates through the downcomer at the periphery of the reactor vessel to the core at a nominal temperature of 650ºC . The primary salt is heated to 700ºC in the core by 252 hexagonal fuel assemblies, each containing 18 fuel plates. Each plate contains 40% volumetric fraction of AGR-2 coated particle fuel grain (TRISO). The use of plate fuel assemblies helps to reduce the pressure drop across the core, which will facilitate the natural circulation flow through the core during any loss-of-forced coolant accidents. The entire core is refueled with a 6-month interval, using a conventional, less-complex, offline refueling process that 12 draws upon the design of recent liquid-metal-cooled reactors [15, 16].
Intermediate heat exchangers are located in the cold legs of the primary loops, and are in the vicinity of the reactor vessel to reduce the inventory of the expensive primary salt. Shell-and-tube heat exchangers are being investigated by ORNL, which are required to limit the flow velocity to 3 m/s for both the shell and tube side. A baseline design assumes the primary salt to be on the tube side, with inlet and outlet temperature of 700 and 650ºC , respectively, while the intermediate salt on the shell side, with inlet and outlet temperature of 600 and 675ºC , respectively. The resulted shell body length is around 12 m, if U-tubes are used [15, 16].
Two supercritical water power cycles are employed in the AHTR design, each containing a supercritical water generator (SCWG) and a reheater. The supercritical water generator and reheater is a single shell-and-tube heat exchanger with intermediate salt on the shell side and two independent sets of parallel tubes containing the high pressure water. The supercritical water generated in one set of tubes passes through the high pressure turbine (HPT) and is then returned to the reheater tubes, in which low pressure steam will be generated. The low pressure steam will further pass through the intermediate pressure turbine (IPT) and the low pressure turbine (LPT) consecutively.
The supercritical water outlet temperature is rated to 650ºC , which will yield a net thermal efficiency of 45% for the power conversion system [14].
The AHTR design employs three DRACSs to deal with the decay heat removal.
Each DRACS is assumed to be capable of removing 0.25% of the total power (8.5 MWth) at 700ºC mean primary salt temperature. The DRACS heat exchangers (DHX) will be
13 submerged in 3 of the 7 downcomer compartments. The DRACS system for the present
AHTR design is still under investigation.
1.3.3 The Small Modular AHTR (SmAHTR) by ORNL
SmAHTR is a 125-MWth integral FHR primary system developed by ORNL, with the design goals of delivering safe, affordable and reliable high-temperature process heat and electricity from a small modular plant that is easy to transport and assemble at remotes sites. An overview of the SmAHTR system is illustrated in Figure 7. All the components involved in the primary salt loop are integrated in a single reactor vessel.
The SmAHTR can be operated in three modes, namely, process heat production, electricity generation, and combined cogeneration. Multiple SmAHTRs can be clustered to meet energy needs greater than 125 MWth. The SmAHTR is based on the two-out-of- three design philosophy, and employs three main circulating loops (MCL), each containing an in-vessel primary heat exchanger (PHX) and a main circulating pump
(MCP). Three passive DRACS systems are also employed based on the same design philosophy. An innovative energy storage system called salt vault has also been employed, which provides three benefits: (1) the potential to combine multiple
SmAHTRs to meet higher energy demands; (2) large thermal inertia; and (3) ability to buffer multi-reactor module installations from upsets in one single reactor [17].
14
Figure 7. SmAHTR integral primary system [17]
The SmAHTR fuel adopts an annular fuel pin design, with inner and outer diameter of 2.2 and 6.5 cm, respectively. However, a plank-type fuel assembly in a
“cartridge core” configuration that can provide many operational advantages is now being investigated. 15 fuel pins with length of 80 cm, and 4 graphite pins of the same length form a hexagonal block. 19 such fuel blocks are assembled in one layer, and 5 layers are stacked to form the core, resulting in a total core height of 4 m and effective diameter of 2.2 m. The annular design has the advantage of improved thermal coupling between the fuel and coolant, and correspondingly decreased fuel peak operating temperature. In addition, the annular fuel also enables the use of a C-C composite mounting rod to hold shorter fuel segments. For the baseline design, the core inlet and
15 outlet temperature has been set to 650 and 700ºC , respectively.
The SmAHTR employs three in-vessel PHXs and corresponding MCPs. Each
PHX is designed to remove 50% of the nominal reactor power (62.5 MWth). During nominal operation, all three PHXs will be in operation, and removes 33% of the total power. The PHX is a shell-and-tube type heat exchanger, with 354 horizontal tubes. The primary salt, FLiBe flows on the shell side with inlet and outlet temperature of 700 and
650ºC , respectively. For the selection of the secondary salt, it will depend on what mode the reactor is operated at. In process heat production mode, the secondary salt transfers heat from the primary slat through the PHX to a secondary heat exchanger (SHX), which connects to the specific application process. The secondary salt should be fluoride salts with thermal properties to match the application temperatures. In electricity production mode, the PHXs will be connected to the power conversion systems through the intermediate circulating loop (ICL). In this mode, the secondary salt on the tube side has been selected to be FLiNaK, with inlet and outlet temperature of 600 and 690ºC , respectively.
ORNL has investigated different power conversion system options, among which the particularly attractive option is high-efficiency closed-cycle supercritical carbon dioxide (S-CO2) power conversion system. The S-CO2 system can potentially provide a combination of small system components and high operating efficiency even at modest operating temperatures. S-CO2 system could be configured in numerous ways, and the recompression cycle was adopted. The S-CO2 recompression Brayton system for
SmAHTR incorporates a salt-to-gas heat exchanger, high-temperature and low-
16 temperature recuperators, a waste heat rejection heat exchanger, and a single turbine and two compressors on a common shaft. With the limited number of components, the cycle efficiency can achieve 40% at temperature above 450ºC , yielding an electric output of
500 MWe for the SmAHTR.
Three DRACS systems have been employed in the SmAHTR, each capable of removing 0.33% of the total thermal power (0.42 MWth). Therefore, when all three
DRACS systems are functional, 1% of the total power can be removed. Each DRACS employs a shell-and-tube heat exchanger with vertical tubes for the DHX, which is also submerged in the salt pool. The natural draft heat exchanger (NDHX) in the cooling tower is also a shell-and-tube design with finned tubes to enhance the air-side heat transfer. The total height of the cooling tower is 12 m, which will provide enough driving head for the air flow.
17
Chapter 2: Direct Reactor Auxiliary Cooling System for AHTRs
2.1 Introduction to the Direct Reactor Auxiliary Cooling System (DRACS)
Passive safety system requires no activation component, which is essential to simplifying the reactor design, as well as achieving economic competitiveness. The
Direct Reactor Auxiliary Cooling System (DRACS) is a passive decay heat removal system, completely relying on natural convection of the coolants and air. The concept of
DRACS originated from Experimental Breeder Reactor-II (EBR-II), and had been improved and refined in following designs, e.g., PRISM, ALMR [18]. The feasibility of
DRACS concept was demonstrated with two representative tests carried out in EBR-II in
1986. In the first test, loss of flow was initiated without scram from the full power. The second test was a loss of heat sink without scram from the full power. Both tests demonstrated that natural process such as natural convection of the primary coolant was able to keep the core cooled without causing any failure [19].
The DRACS was proposed as the passive safety system, responsible of decay heat removal, when the AHTR concept was developed. Figure 8 shows a schematic drawing of one proposed DRACS design for a planned Fluoride Salt-Cooled High-Temperature
Test Scale Reactor [5]. There are three natural circulation/convection loops during the functioning of the DRACS:
Loop 1: The primary coolant (liquid fluoride salt) flows from the reactor core to
18
the in-vessel DRACS Heat Exchanger (DHX), to the fluidic diode, and then back
to the core through piping. During this process, the decay heat from the core is
carried by the primary coolant and transferred to the secondary salt in the DHX;
Loop 2: The secondary coolant (liquid fluoride salt) flows from the DHX to the
Natural Draft Heat Exchanger (NDHX), and then back to the DHX through piping.
In the NDHX, the energy carried by the secondary salt is dissipated to the
surrounding air;
Loop 3: The surrounding airflow circulates between the NDHX and the
environment regulated by a louver system.
It is noted that the performance of each of the three loops/subsystems is not only dependent on itself, but also upon the other two. The close coupling among these subsystems results in a major difficulty in designing and evaluating a DRACS system.
During normal operation of the reactor core, most of the primary salt circulates toward the intermediate heat exchanger, exchanging heat to the intermediate salt.
However, there is still a parasitic flow through the DHX, losing some heat to the DRACS secondary loop. To avoid excessive energy loss to the DRACS during normal operation of the core, a fluidic diode has been introduced beneath the DHX, with upward direction being the high flow resistance direction. The residual flow through the fluidic diode and
DHX should be scaled properly to keep the secondary salt in the secondary loop from freezing.
Two important components in the DRACS are the DRACS heat exchanger (DHX) and natural draft heat exchanger (NDHX), which provide the couplings among the three
19 natural circulation/convection loops. Shell-and-tube heat exchanger which exhibits low pressure drops and has relatively mature technology has been proposed for the DHX. The primary salt flows on the shell side, while the secondary salt flows inside the tubes. The
NDHX also adopts a shell-and-tube design, however, with no physical shell. The inferior heat transfer on the air side of NDHX may affect the capability of the entire DRACS, in which case finned tubes are usually recommended to enhance the air-side heat transfer.
The NDHX sits near the bottom of an air chimney, made from reinforced concrete. The air intake is located near the top of the chimney, and air flows down an annulus around insulated inner duct in which the heated air flows up. A passive louver system, coupled directly to the primary salt pump(s), is installed at the air intake to regulate the DRACS heat removal capability [5].
The DRACS can be modularized in that multiple DRACS systems can be clustered to meet specific heat removal requirement. The modular and passive feature of
DRACS, enabled by the excellent natural circulation cooling provided by liquid fluoride salts, allows FHRs to be developed at almost any scale while maintaining full passive safety.
20
Figure 8. Schematic drawing of the DRACS with the primary heat transport system [5]
2.2 Scope of Present Study
AHTRs (or FHRs) are an emerging class of advanced reactors that combine existing nuclear technologies. Although these technologies have been proven in different preceding reactors, no complete AHTR class-design has yet been developed. It can be envisioned that the first AHTR will necessarily be a test-scale reactor to validate the system attributes before proceeding to larger and commercial systems. Recently, an
Integral Research Project (IRP) that focuses on the development of FHR technology has been initiated jointly by the MIT, UCB, and UW, in which MIT is responsible of developing a test-scale FHR design that can be deployed in the near future [9]. This test- scale FHR features a thermal power smaller than 20 MWth. In the present study, a modular DRACS design for a 20-MWth FHR has been developed. In addition, detailed 21 scaling analysis for the DRACS has been performed to identify the key dimensionless numbers that characterize the system. A scaling methodology consisting of the core scaling and loop scaling has also been developed. Following the scaling methodology, scaling analysis for a low-temperature DRACS test facility (LTDF) and a high- temperature DRACS test facility (HTDF) has been carried out, with the results listed in subsequent discussion. The scaling results will provide the guidance for the design of the two test facilities.
2.3 DRACS Prototypic Design
In the current study, a detailed modular design of the DRACS for a 20-MWth
FHR is developed. As a starting point, the DRACS is designed to remove 1% of the nominal power, i.e., the decay power being 200 kW. The design presented here has the potential to be used in the planned small-scale FHR test reactor and will also benefit and guide the DRACS design for a commercial AHTR.
The design process for the prototypic DRACS involves selection of the salts, identification of the reactor core, design of the DHX and NDHX, design of the fluidic diode, design of the air chimney, selection of the loop pipes, and finally determination of the loop height based on pressure drop analysis. The working temperatures for the salts have been determined based on the analysis of bulk temperature increase in the core during the transient, the optimization of the two heat exchanger designs, as well as the loop heights. The loop height is obtained by balancing the total pressure drop in the loop with the available driving force. The driving force overcoming the total pressure loss
( p ) is generated from the density variation due to temperature difference of the salt or 22 air and vertical distance as:
Δp ΔρgH, (1) where is the vertical distance between the thermal centers of the DHX and reactor core in the primary loop, or that between the NDHX and DHX thermal centers in the secondary loop, or the louver height in the third loop. Here, is the density difference between the hot salt (or air) and cold salt (or air) in a certain loop and is the gravitational acceleration. Contributions to the total pressure loss in the primary loop are due to the flow through the reactor core, shell side of the DHX, fluidic diode, and connecting pipes, including elbows. In the secondary loop, the pressure drops take place on the tube side of the DHX, tube bundles in the NDHX, connecting pipes, and all elbows. In the third loop, the pressure loss is mainly due to the air flow across the tube bundles of the NDHX, and frictional pressure drop along the chimney, as well as the form loss.
2.3.1 Selection of Salts
Compared to other available heat transfer fluids, liquid fluoride salt coolants show several advantages at high temperature, such as the excellent heat transfer capability, high boiling temperature that enables the reactor to be operated at low pressure, and low chemical reactivity in air. A number of studies on physical properties, nuclear properties, and chemical factors of fluoride salts have been performed in the literature; in addition, considerable experience was obtained with the fluoride salts from the Molten Salt
Reactor (MSR) program in ORNL. Grimes [20, 21] established a set of criteria for
23 selecting candidates of primary and secondary salt coolants in molten salt reactor applications. Some of the criteria remain applicable for determining the primary salt coolant in the current design and are listed as follows:
1. has a small thermal neutron capture cross section (<1 barn),
2. exhibits chemical stability at T > 800ºC,
3. is stable under intense radiation,
4. melts at useful temperatures (<525ºC) and is not volatile,
5. is compatible with high-temperature alloys and graphite.
When the secondary salt coolant for the secondary loop is considered, criteria 1 and 3 may be relaxed. In addition, it is safer to adjust the freezing temperature requirement in criterion 4 to an even lower value.
Different types of fluoride salts have been investigated, including alkali fluorides
(such as LiF-KF, LiF-RbF, LiF-NaF-KF), ZrF4 salts (such as LiF-ZrF4, NaF- ZrF4), and
BeF2 salts (such as LiF-BeF2, LiF-NaF-BeF2). As suggested by Williams et al. [22],
7 FLiBe ( LiF-BeF2, 66-34 in mol%) that has superior heat transfer performance under different conditions including forced convection and natural convection, low vapor pressure, and low corrosivity serves as a good candidate of primary salt. The lithium is enriched with more than 99.995% 7Li, providing a large moderating ratio and small coolant parasitic capture probability. In addition, FLiBe has been selected as the baseline primary salt for all the AHTR designs that are under investigation. Therefore, FLiBe with the enriched lithium is chosen as the primary salt in the current study. FLiNaK (LiF-NaF-
KF, 46.5-11.5-42 in mol%) is chosen as the secondary salt due to its good heat transfer
24 capability, low melting point and low cost. Table 2 summarizes the thermophysical properties of the liquid fluoride salts used in this design, i.e., FLiBe and FLiNaK.
Table 2. Summary of properties of FLiBe and FLiNaK (T in Kelvin)
Specific Melting Thermal Density heat Viscosity point conductivity (kg/m3) (J/Kg- (cP) (oC) (W/m-K) K) 2280-0.4884(T- 0.0005T+32/33- FLiBe 458 2380 273) 0.116exp(3755/T) 0.34 0.0005T+32/41.3- FLiNaK 454 2530-0.73(T-273) 1883 0.04exp(4170/T) 0.34
2.3.2 Selection of Core Design and its Pressure Drop Calculation
Several core designs have been proposed in the literature for AHTRs, including the PB-AHTR by UCB, the AHTR and the SmAHTR by ORNL as introduced earlier.
However, all of these AHTR designs have thermal power much larger than 20 MWth.
Despite of MIT’s current effort in developing a test-scale FHR design, there has been so far only one preliminary test-scale FHR core design proposed by the UCB, the FHR-16 pebble bed core design [10]. This core design features a thermal output of 16 MWth, and the detailed dimensions of the core are available as shown in Figure 9. To estimate the pressure loss through the core, the core was conceptually divided into 6 sections from bottom to top, with a diverging entrance region and a converging exit region, as shown in
Figure 9.
25
Figure 9. The pebble bed reactor core used in FHR-16 [10] and simplified sketch of the reactor core
The pressure drop over each section can be calculated using the Ergun equation for packed pebble bed [23]:
2 1 A L m p 170 (1 ) 1.75 . (2) 3 mdpp d A
Here, and denote the volume fraction, dynamic viscosity, density, and mass flow rate of the fluid (FLiBe in the current analysis), respectively; L and A are the height and cross sectional area of the reactor core; is the pebble OD.
26
The mass flow rate ( m ) of the primary salt in the core can be calculated as:
Q m , (3) cTp where is the decay heat rate. and T are the average specific heat at constant pressure of the salt and the temperature difference between the hot and cold state of the primary salt. The mass flow rate of the secondary salt and the air can be evaluated in the similar way. As can be seen, in order to determine the mass flow rate, we have to first determine the temperature increase in the core, or in other words the hot and cold temperatures of the primary salt.
The bulk temperature increase of FLiBe (the primary salt) in the core when the decay power is balanced by the DRACS heat removal capability was first examined. Due to lack of the information on the decay power curve for the core design shown in Figure
9, the decay power equation for the light water reactors (LWRs) was employed, given as
[24]:
P 0.2 0.2 7 0.2 7 0.2 0.1 (ss 10) ( 10) 0.87( 2 10 ) 0.87( 2 10 ) (4) Po where P , , , and are the decay power, reactor power, time after reactor startup, and reactor operating time, respectively. The unit of time is second. It was found that the reactor power decreases to 1% after about 2.08×104 seconds (5.8 hours) and the increase in the bulk temperature of FLiBe is around 70oC. The temperatures of FLiBe when it enters and exits the core under normal operation are designed to be 600 and 704oC, respectively [10]. Therefore, the bulk temperature of the primary salt in the core will be
27 around 722oC at the quasi steady state of the DRACS (when the decay power decreases to 1%). To be conservative, the core inlet temperature at quasi steady state of the DRACS was assumed to be close to the core outlet temperature when the core is in normal operation, i.e., 704oC. We therefore assumed that 705 and 750oC are respectively the temperatures of FLiBe at the inlet and outlet of the core when the DRACS is capable of removing 200 kW decay heat in accidents. The primary salt mass flow rate was then found to be 1.84 kg/s.
With the hot and cold temperatures of the primary salt determined, its properties can be evaluated using Table 2. Also, the pebbles used in the FHR-16 design have a diameter of 3 cm, in contrast to the 6 cm for conventional pebbles. There are totally
34,000 pebbles in the core [5], which leads to a volume fraction of 41% for the salt. The pressure drops in each section of the core were then calculated, with the results summarized in Table 3. It should be noted that, the form loss has also been taken into account, which can be estimated using:
1 p K V 2, (5) 2 r
where K is 1 for expansion and 0.5 for contraction. The velocity Vr is always based on the area of the smaller section. As seen, the form loss is negligible in contributing to the total pressure drop in the core.
When the DRACS functions (i.e., the reactor is scrammed), the velocity of FLiBe decreases rapidly to less than 1 mm/s in the main region of the core. It results in a calculated pressure drop in the core, including the form loss, being 13 Pa, which is
28 significantly smaller than that at the normal operating condition. It is noteworthy that the power provided in this core design (16 MWth) is lower than our proposed power level
(20 MWth). This issue will be discussed later.
Table 3. Pressure drop in the core
Pressure Drop (Pa) Section 1 2.2 Section 2 1.4 Section 3 1.3 Section 4 0.6 Section 5 1.8 Section 6 5.3 Form loss 0.001 Total 13
2.3.3 Selection of Fluidic Diode and its Pressure Drop Calculation
An important component in the DRACS system is the fluidic diode, which is a passive flow control device with low flow resistance in one direction (downward in
Figure 8) and high flow resistance in the opposite direction. Under normal conditions, the fluidic diode rejects most of the primary salt, which flows in the reverse direction of the fluidic diode with a significant pressure drop, in order to prevent the DRACS from parasitical heat removal. In the meanwhile, a small amount of primary coolant inevitably passes through the fluidic diode and transfers its energy at the DHX, which is helpful to prevent the secondary salt from freezing. In the event of loss of forced flow coupled with loss of shutdown cooling, the primary coolant inside the reactor core is heated to a high temperature. The difference in temperature results in the difference in density of the salt
29 due to its large thermal expansion, promoting the natural circulation in the forward direction of the fluidic direction, which is essentially Loop 1.
There have been different fluidic diode designs proposed, including the floating ball type fluidic diode, the guide blade fluidic diode, and the vortex fluidic diode [5], of which the vortex diode is utilized in this report due to its relatively mature technology.
The basic design of a vortex diode consists of a disc-shaped chamber with cylindrical axis and tangential ports. As shown in Figure 10, flow entering the device through the tangential port sets up a vortex, which induces a large pressure drop in the flow path; while flow entering through the axial port creates a predominantly radial flow distribution over the chamber cross section, which develops only a modest pressure drop.
Figure 10. Reverse and forward directions in a vortex diode
The performance of the fluidic diode greatly depends on the specific design parameters, and can be evaluated by CFD simulation or experimental test. In our design, a classic vortex diode that has been tested with water by Chikazawa et al. [25] was adopted, as shown in Figure 11. The design parameters of this vortex diode are summarized in Table 4. The pressure loss (in forward flow direction of the diode) is 30 calculated based on the relation between the Reynolds number and resistance coefficient obtained by Chikazawa et al. [25] from experiments, as plotted in Figure 12. Here, the
Reynolds number ( Re ) and resistance coefficient ( ) are respectively defined as:
Figure 11. The adopted vortex diode [25]
Table 4. Parameters of the vortex diode
Diameter of vortex room (mm) 326.7 Height of vortex room (mm) 130.7 Diameter of vertical nozzle (mm) 36.0 Tangential nozzle height (mm) 131.0 Tangential nozzle width (mm) 12.8
(6)
(7) where V, d, , and are the flow velocity at the upper vertical nozzle at the vortex chamber ceiling, diameter of the upper vertical nozzle, kinetic viscosity and density of 31 the fluid, respectively. When the capability of the DRACS is 200 kW, corresponding to the highest and lowest FLiBe temperatures of 750 and 705oC, respectively, the Reynolds number of FLiBe evaluated at the average temperature of is 1.21×104, which is beyond the points shown in Figure 12. However, it may be appropriate to assume that the resistance coefficient does not change dramatically when the Reynolds number changes from 1.0×105 to 1.21×104 after we examined the trend in Figure 12. Therefore, the resistance coefficient could be taken between 0.3 and 0.35 when Reynolds number is around 1.21×104. It results in a pressure drop ranging from 288 to 330 Pa including the form loss in our study. The pressure loss can be further reduced by increasing the dimensions of the fluidic diode if needed.
Figure 12. Relation between the Reynolds number and resistance coefficient (forward flow) [25]
2.3.4 Heat Exchanger Design
Shell-and-tube heat exchanger has been proposed for the DHX and NDHX due to its low pressure drop and mature technology. Although commercial codes are available 32 for the design of shell-and-tube heat exchangers, we developed our own heat exchanger design code which would be used in another code for the thermal performance evaluation of the DRACS. This design code is based on the well-developed Delaware Method [26], and is implemented in MATLAB. In the following section, the Delaware Method will be first introduced, followed by the designs of the DHX and NDHX.
Delaware Method for Shell-and-Tube Heat Exchanger Design
The design of a shell-and-tube heat exchanger is the process of determining all the essential constructional dimensions to fulfill a given heat duty and respect limitations on shell-side and tube-side pressure drops. In order to determine the constructional dimensions, the steady-state conditions at which the heat exchanger will work must be specified. However, even if with the working conditions and allowed pressure drops specified, the design of the heat exchanger is still an underdetermined problem.
Conventionally, one will choose a set of possibly optimal dimensions for the heat exchanger based on existing experimental data, and then rate it. Some necessary modifications will be made until the desired performance is achieved.
The set of input parameters that are required to finalize or rate a shell-and-tube heat exchanger are summarized in Appendix A. Detailed explanations of these parameters, as well as how to determine them are too lengthy to be included here. For more details, readers can refer to the Heat Exchanger Design Handbook [26].
The two flows on the shell and tube side can be arranged as either cocurrent or countercurrent, the latter of which is more efficient and is usually selected. The main
33 work of the rating process is to evaluate the actual heat removal rate of the heat exchanger using:
QAacto U o LMTD() . F (8)
In above equation, A is the total heat transfer area of the heat exchanger based on the o outer diameter of the tubes. LMTD is the logarithmic mean temperature difference, which is defined as:
TT 12for T T ln(TT / ) 12 LMTD 12 , (9) TT 12for T T 2 12 where the two temperature differences are defined as:
TTTTTT1 in , hot out , cold,. 2 out , hot in , cold (10)
F is the mean temperature difference (MTD) correction factor, and is 1 for countercurrent flow. The overall heat transfer coefficient U (based on A ) is the reciprocal of the total o o thermal resistance R , which consists of: o
11AAL 103 RRR o o tw , (11) o f,, o f i hs h t A i A i k tw
where hs and ht are the heat transfer coefficients for the shell and tube side, respectively;
Rfo, and Rfi, denote the fouling on the shell and tube side, respectively; Ltw is the tube
wall thickness, and ktw is the thermal conductivity of the tube material.
The most important part of the design or rating process is the calculation of the heat transfer coefficients, especially for the shell side. The shell-side heat transfer
34 coefficient is based on that for ideal cross flow over tube banks, and then corrected by a series of correction factors as following:
hsi h c(), l J b J r J s J J (12) where Jc, Jl, Jb, Jr, and Js are the correction factors for the effect of baffle cut, leakage flow, bypass flow, adverse temperature gradient associated with laminar flow, and unequal baffle spacing. These correction factors depend on the heat exchanger geometry and the flow regime (Jr), and are detailed in the Heat Exchanger Design Handbook [26]. hi is the heat transfer coefficient for ideal cross flow over tube banks:
(13)
where cp,s, Gs, Prs, and μs are the heat capacity, mass flux, Prandtl number, and viscosity of the shell-side fluid, respectively. The tube wall effect is accounted for by considering
μs,w, which is the viscosity of the shell-side fluid at the tube wall temperature. The heat transfer factor ji is obtained as follows:
(14)
(15)
where Ltp and Dt are the tube pitch and outer diameter, respectively. The values of a1 , a2 ,
a3 , and a4 corresponding to different Reynolds number Re are listed in Table 5 [26].
35
Table 5. Empirical coefficients for calculation of ji [26]
Re a1 a2 a3 a4 105 - 104 0.321 -0.388 104 - 103 0.321 -0.388 103 - 102 0.593 -0.477 1.450 0.519 102 - 10 1.360 -0.657 < 10 1.400 -0.667
The calculation of the heat transfer coefficient for the tube-side is much more straightforward than the shell-side. For laminar flow (Re < 2000), Hausen correlation is suggested:
(16)
where kt, μt, Ret, and Prt are the thermal conductivity, viscosity, Reynolds number, and
Prandtl number of the tube-side fluid, respectively; μt,w is the viscosity of the tube-side fluid estimated at the tube wall temperature; Dti and Lti are the tube inner diameter and length, respectively. Sieder-Tate correlation can be used for the turbulent flow (Re >
10000):
(17)
For transition flow, the heat transfer coefficient is obtained by the linear interpolation between the above two correlations.
The shell-side and tube-side fouling factors are related to the specific applications and processing fluids. Empirical data exists for most of the cases. However, for most of
36 the time, as long as the processing fluids are clean enough and will not cause significant deposits on the tubes, fouling factors can be neglected. With the total thermal resistance determined, the actual heat removal rate in the heat exchanger can be evaluated, which should be compared with the heat duty that has been specified as one of the input parameters. If the two do not match, the heat exchanger geometry, usually the tube length and the number of tubes, should be varied until agreement is achieved. In the meanwhile, pressure drops for both the shell and tube side should be checked to see if they are within the specified limits.
For the shell side, the total pressure drop is composed of three distinct parts:
pressure drop in pure cross flow, pc ; pressure drop in the baffle window, pw ; and
pressure drop in the end zone (first and last baffle spacing), pe . The regions covered by these three pressure components are illustrated in Figure 13.
Figure 13. Pressure drop composition for the shell side [26] 37
Both the pressure drop in the cross flow and that in the end zones are based on the
pressure drop for ideal cross flow over tube banks, pbi . The cross-flow pressure over
(1)N baffle compartments is obtained as: b
ppcbi NR bb(1).R l (18)
The end-zone pressure drop is calculated as:
Ntcw pebib s pR R1, (19) Ntcc
where Rb , Rs , and Rl are the correction factors for bypass flow, unequal baffle spacing,
and leakage flow. These correction factors are detailed in the design handbook. Ntcw and
Ntcc is the number of tubes in the baffle window and baffle compartment, respectively.
The ideal tube bank-based pressure (Pa), by definition, is:
2 0.14 m p2, f N s s (20) bi i tcc s s, w where the friction factor is empirically correlated as:
b 1.33 b fb Re2 , (21) is1 LDtp/ t
b b 3 . (22) b4 1 0.14 Res
Here, Ltp and Dt are the tube pitch and tube outer diameter, respectively. The correlational coefficients, b’s, are summarized in Table 6 for different Reynolds number.
38
Table 6. Empirical coefficients for calculation of fi [26]
Re b1 b2 b3 b4 105 - 104 0.372 -0.123 104 - 103 0.486 -0.152 103 - 102 4.570 -0.476 7.00 0.500 102 - 10 45.100 -0.973 < 10 48.000 -1.000
The pressure drop over the N baffle widows for turbulent flow ( Re100 ) is b s calculated as:
m 2 p NNR2 0.6. w (23) w btcwl 2 s
The factor 2 in above equation accounts for the velocity heads due to the window
turnaround and 0.6 accounts for the frictional effects. For laminar flow ( ), pw is expressed as:
2 mw s N tcw L bc mw pw NR bl 262 , (24) LDD ( )2 2 s tp t w s
where Dw is the equivalent hydraulic diameter of a baffle window. The first two terms in above equation refer to the cross flow and longitudinal flow friction, respectively. The last term represents the two velocity heads associated with the flow turnaround in the baffle window.
The main pressure drop on the tube side comes from the friction inside the tubes, which is defined as:
39
0.14 L p0.5 f v2 ti t , (25) t t t t Dti t, w
where Lti and Dti are the baffled tube length and tube inner diameter, respectively. The friction factor f for laminar flow ( Re2100 ) is simply: t t
64 ft . (26) Ret
For the transition and turbulent flow regimes ( Re2100t ), Karman-Nikuradse equation is suggested for the calculation of the friction factor:
1 0.8 0.87ln Re.ttf (27) ft
Design of DHX
A MATLAB code based on the aforementioned Delaware Method has been developed. Hastelloy N, a nickel-base alloy, was selected as the structure material for both the DHX and NDHX as it has good oxidation resistance to liquid fluoride salts at high temperatures up to 871oC (1,600oF). The thermal conductivity of Hastelloy N at different temperature is provided in Table 7.
Table 7. Thermal conductivityof Hastelloy N [27]
Temperature (oC) 200 300 400 500 600 700 Thermal conductivity 13.1 14.4 16.5 18.0 20.3 23.6 (W/m-K)
A one-pass shell and one-pass tube type heat exchanger was designed for the
40
DHX, where FLiBe (hot fluid) and FLiNaK (cold fluid) were on the shell and tube side of the DHX, respectively. As aforementioned, the highest and lowest temperatures of FLiBe are 750 and 705oC, respectively when the capability of the DRACS is 200 kW. In addition, we assumed that the tube side (FLiNaK) outlet temperature is 680oC based on the consideration of the DHX effectiveness, as well as leaving a sufficient margin above the melting point of FLiNaK. Actually, a closer look at the definition of the LMTD reveals that it will decrease with the increase of the tube side (cold side) outlet temperature. The tube side inlet temperature (FLiNaK) was considered as a variable, and was determined based on optimization of the DHX, as well as the loop height.
The standard BWG 18 tubes with outer diameter (OD) of 15.875 mm and tube thickness of 1.245 mm were selected. They were arranged in a triangular pattern, with a pitch-to-diameter ratio of 1.4. Four baffles with a cut of 25% were used to increase the heat transfer capability. Figure 14 and Figure 15 show the variations of the tube length and primary loop height with the tube side inlet temperature for three different tube numbers, i.e., 141, 196, and 261. As can be seen, with more tubes used, although the tube length is smaller, larger loop height will be resulted in. Also, the tube side inlet temperature seems to have opposite effects on the tube length and the primary loop height.
A tradeoff among the tube number, tube length and primary loop height calls for the design with 196 tubes and tube inlet temperature of 630oC, leading to a tube length of
1.21 m and shell inner diameter of 350 mm for the design. The design results of the selected DHX design are summarized in Table 8.
41
Figure 14. Relation between the tube length and tube side inlet temperature
Figure 15. Relation between the primary loop height and tube side inlet temperature
42
Table 8. Design results of the DHX
Capability (kW) 200 Material Hastelloy N Shell side fluid FLiBe Tube side fluid FLiNaK Shell side temperature (oC) 750/705 Tube side temperature (oC) 680/630 Shell side mass flow rate (kg/s) 1.84 Tube side mass flow rate (kg/s) 2.12 Tube OD (mm) 15.875 Tube thickness (mm) 1.245 Tube number 196 Pitch to diameter ratio (Triangular 1.4 pattern) Tube length (m) 1.21 Shell ID (mm) 350 Baffles 4 Baffle cut 25% Shell side pressure drop (Pa) 122 Tube side pressure drop (Pa) 28
Design of NDHX and Air Chimney
A similar MATLB code to the one for DHX design has also been developed for the design of the NDHX. The secondary salt (FLiNaK) flows inside the straight tube bundles of the NDHX while air flows across the tube bundles, as illustrated in Figure 16.
For the NDHX design, we used the same dimensions for the tubes as those in the DHX design and arranged them in a triangular pattern with a pitch-to-diameter ratio of 2. The
NDHX was placed at the bottom of the air chimney with 4 louvers near the top, as shown in Figure 16. Clearance between the tube bundle and the inner surface of the chimney will be blocked to confine the air flow through the tubes. The cross-sectional area of the chimney annulus was set to be the same as that of the NDHX to reduce the form loss
43 associated with the turnaround of air flow at the bottom of the chimney. The louvers were assumed half open in the calculations to ensure that the louver would have enough controlling capability on the DRACS performance.
Figure 16. Air chimney with the NDHX at the bottom
Designs with different number of rows, different number of tubes per row, and different air exit temperature were examined. It was found that with increase in the number of tube rows, both the chimney height and the secondary loop height increase significantly, especially the chimney height, as seen in Figure 17 and Figure 18.
Therefore, only two rows of tubes were used in our design. The air inlet temperature was selected to be 40oC to be conservative. The air outlet temperature was determined by investigating its influence on the chimney height and tube length. It was found that the air outlet temperature should be higher than 90oC if we want the chimney height to be below
44 a reasonable height (~ 10 m), as can be seen in Figure 19. On the other hand, higher air outlet temperature demands longer tubes for all the cases with different number of tubes per row, as shown in Figure 20. Using more tubes per row helps to reduce the tube length, but the width of each row is also increased correspondingly. We finally decided to employ 50 tubes per row, which yielded a tube length closer to the row width. With all above considerations, the air outlet temperature was chosen to be 100oC, leading to the tube length of 1.93 m and air chimney height of 10.43 m. The design results of the
NDHX are summarized in Table 9.
Figure 17. Relation between the chimney height and the air exit temperature, with 50 tubes/row
45
Figure 18. Relation between the secondary loop height and the air exit temperature, with
50 tubes/row
Figure 19. Relation between the chimney height and the air exit temperature, with 2 rows 46
Figure 20. Relation between the tube length and the air outlet temperature, with 2 rows
Table 9. Design results of the NDHX
Capability (kW) 200 Material Hastelloy N Shell side fluid Air Tube side fluid FLiNaK Shell side temperature (oC) 100/40 Tube side temperature (oC) 680/630 Shell side mass flow rate (kg/s) 3.31 Tube side mass flow rate (kg/s) 2.12 Tube OD (mm) 15.875 Tube thickness (mm) 1.245 Tube number 100 (2 rows with 50 tubes per row) Pitch to diameter ratio (Triangular 2 pattern) Tube length (m) 1.93 Shell side pressure drop (Pa) 96 Tube side pressure drop (Pa) 2.03
47
2.3.5 Selection of Loop Pipes
Selection of the loop pipe is based on the friction pressure drop in it. The variation of the friction pressure drop per unit pipe length with the pipe diameter for both the primary and secondary loops are shown in Figure 21. As can be seen, when the pipe diameter is larger than 15 cm, the pressure loss per unit length of pipe will be less than 1
Pa/m in both the primary and secondary loops, which seems acceptable. Therefore, pipes with inner diameter of 15 cm have been selected for both the primary and secondary loops.
Figure 21. Pressure drop per length versus pipe diameter in both primary and secondary loops 48
2.3.6 Summary of Prototypic Design
Based on the aforementioned studies, the total pressure loss in the core of the
UCB FHR-16 design is about 13 Pa, which is considerably small compared with the values due to other components in the primary loop such as the DHX (~ 122 Pa) and fluidic diode (~ 330 Pa). Therefore, the pressure loss in the core region plays a minor role in the total pressure loss in the primary loop. This confirms that the use of the core dimensions from the UCB FHR-16 design to estimate the pressure loss in the reactor core is reasonable.
In summary, a modular design of the DRACS for a 20-MWth FHR, capable of removing 200 kW decay heat has been accomplished, as shown in Figure 22. The vertical thermal center-to-center distance from the DHX to the core is approximately 2.28 m. The total pressure drop in the secondary loop is about 150 Pa, which mainly comes from the tube side of the DHX (96 Pa). It requires a 0.42-m thermal center-to-center distance from the NDHX to DHX and a 10.43-m high air chimney. This design limits the total height of the DRACS to about 13 m. It is also feasible to use several such modules to satisfy the heat removal requirement for a larger scale reactor. The design results are summarized in
Table 10 and Table 11.
49
Figure 22. Prototypic design of the DRACS
Table 10. Temperatures and mass flow rates of working fluids
FLiBe FLiNaK Air (oC) 750 680 100 (oC) 705 630 40 (kg/s) 1.84 2.12 3.31
Table 11. Pressure losses and heights of the primary and secondary loops
Primary Loop Pressure Drop (Pa) Height DHX Fluidic Piping + Core Total (m) shell side diode connections 13 122 330 ~ 16 ~ 491 2.28 Secondary Loop Pressure Drop (Pa) Height DHX tube NDHX tube Piping + Total (m) side side connections 28 96 ~ 26 ~ 150 0.42
50
Chapter 3: Scaling Analysis for the DRACS
As seen from the DRACS prototypic design, shown in Figure 22, the total height of the system is around 13 m, which is too tall to be accommodated in our laboratory. In addition, real-scale experiment is usually costly, which forces us to scale down the
DRACS system. In order to be able to model the prototypic DRACS system with the scaled-down DRACS facility, similarity laws are necessary. We thus conducted a scaling analysis, trying to figure out the key dimensionless numbers that characterize the performance of the DRACS system at both transient and steady-state conditions. Based on these dimensionless numbers, similarity laws have been proposed. In addition, a scaling methodology consisting of the core scaling and loop scaling has also been developed. The scaling methodology was then applied to a low-temperature DRACS test facility (LTDF) that would use water as the surrogate coolants, and a high-temperature
DRACS test facility (HTDF) that would use liquid fluoride salts as the coolants. The scaling results will provide guidelines for the designs of the two test facilities.
3.1 Governing Equations
The principle of the scaling analysis is to non-dimensionaIize the governing equations of the DRACS by introducing appropriate dimensionless parameters. In the similarity analysis, we applied Boussinesq approximation, which states that the fluid is
51 incompressible except in the buoyancy term in the momentum equation. The density is therefore given as
(28) where subscript 0 stands for the reference constant value; , , and T are the density, thermal expansion coefficient, and temperature of the coolant.
With this assumption, the one-dimensional governing equations were obtained as
[28, 29]:
Continuity equation:
(29)
Integral momentum equation:
(30)
Fluid energy equation for ith section:
(31)
Solid energy equation for ith section:
(32)
Boundary condition between fluid and structure for ith section:
(33)
52
Here, subscripts i, r, and s are the ith component, representative variable, and solid structure, respectively. In addition, t, u, a, l, g, f, K, d, cp, h, k, and are the time, velocity, flow area, axial length, gravitational acceleration, friction factor, form loss factor, hydraulic diameter, heat capacity, heat transfer coefficient, conductivity, and volumetric heat generation, respectively. y and z denote the transverse and axial coordinates, respectively. The steady-state values in each loop were selected as reference values, and the dimensionless parameters were defined, as summarized in Table 12. Here, the hydraulic diameter d and conduction depth are respectively defined as and , where is the wetted perimeter.
Table 12. Reference values and dimensionless parameters
Dimensionless Reference values parameters : steady-state fluid velocity in the pipe (in Velocity primary or secondary loop) : vertical distance between thermal centers of DHX & core in primary loop or that between thermal centers of NDHX & DHX in secondary Length loop
: conduction depth
: cross-sectional area of the pipe (in primary or Area secondary loop) Time : temperature difference of primary salt in Temperature primary loop or that of secondary salt in secondary loop in steady state
53
The aforementioned governing equations were non-dimensionalized by plugging in the previously discussed dimensionless parameters. We then obtained the non- dimensional conservation equations as:
(34)
(35)
(36)
(37)
(38)
From these non-dimensional conservation equations, the dimensionless numbers were obtained. The dimensionless numbers are defined as follows:
Richardson number:
Friction number:
Stanton number:
Time ratio number:
54
Heat source number:
Biot number:
There are specific physical meanings associated with above dimensionless numbers. The Richardson number denotes the ratio of the driving force to the inertia force, which is directly related to the successful operation of a loop. The Friction number is the ratio of the flow resistance to the inertia force. It characterizes the pressure drop in a specific component. The Stanton number denotes the ratio of the radial convection to the axial convection, and the Biot number is the ratio of wall convection to wall conduction at the liquid-solid interface. These two numbers are related to simulation of the interfacial temperature, due to the dependence on the heat transfer coefficient [28].
The time ratio number denotes how fast the convection is, compared with the conduction in the structure. The heat source number denotes the ratio of the heat generation rate to the heat removal rate.
3.2 Scaling Similarity Criteria
The similarity criteria between the prototype and model were established based on the aforementioned non-dimensional governing equations and dimensionless numbers.
These criteria are summarized as follows:
(39)
55
(40)
(41)
(42)
(43)
(44)
(45)
(46)
Here, the subscript R denotes the ratio between the model and the prototype. Equations
(39) - (41) are the requirements concerning the entire primary/secondary loop, while the rest are applied to each component in the primary/secondary loop. It is noted that the summations in Eqs. (39) and (40) provide weaker restrictions. A more restrictive relation applied to an individual component in the loop can be provided. For instance, Eq. (39) can be replaced by considering the axial geometrical similarity, given as:
(47)
Considering the steady-state momentum and energy conservations of the entire primary/secondary loop, we got the ratios for the reference velocity and temperature difference as following:
56
(48)
(49)
The requirement of the Richardson number is satisfied automatically if Eqs. (48) and (49) are fulfilled.
Table 13 summarizes the design parameters in the prototype and model
(experiment), as well as some constraints in our experiment.
Table 13. Design parameters in the prototype and model
Parameters Value in prototype Value in experiment Ratio Q 200 kW 2 ~ 50 kW 0.01 ~ 0.25 l Primary loop 2.28 m < 2 m < 0.88 0 Secondary loop 0.42 m If the same height 1.0 u Primary loop 0.0541 m/s 0 Secondary loop 0.0586 m/s If real time simulation: Primary loop 42.2 s 1.0 l /u 42.2 s 0 0 If real time simulation: Secondary loop 7.2 s 1.0 7.2 s ΔT Primary loop 45C Measurable > 10C > 0.22 0 Secondary loop 50C Measurable > 10C > 0.20
3.3 Scaling Methodology
For the primary loop scaling, we had two equations, i.e. Eqs. (48) and (49), but 5 unknowns, , , , , and . To close the equation system, three assumptions had to be made. Due to the power and space that would be accessible in our 57 experiment, we started with some assumptions on the power and loop height ratios, as listed in the last column of Table 1.3.2. So far, the only component that has been fixed in the prototypic design is the pebble bed reactor core while designs of other components are relatively flexible. Therefore, it is reasonable to provide the third assumption by performing core scaling analysis.
According to the time ratio scale in Eq. (45), the convection time ratio is formulated as:
(50)
We determined the convection time ratio in the primary loop based on the information on the structure material of the heat source and heat transfer coefficient, both in the prototype and experiment. This enables us to complete the core and primary loop scaling, as illustrated in Figure 23 and Figure 24. The product of the loop height ratio and pipe area ratio (which is the volume ratio) can be calculated either by using Eq. (46) with specified core geometry or from the loop scaling analysis. The heat source number matches if the evaluated values of this product from the two approaches are the same.
Time scale from h ratio in core, Eq. (50)
Conduction depth Hydraulic diameter Loop height times pipe area ratio, Eq. (45) ratio, Eq. (43) ratio, Eq. (46)
Figure 23. Flowchart for the core scaling
58
Time ratio from h ratio in core, Eq. (50) The loop height ratio is assumed Pipe flow velocity ratio
Temperature difference ratio, Eq. (41) The power ratio is assumed
Pipe area ratio, Eq. (48) or (49)
Loop height ratio times pipe area ratio
Figure 24. Flowchart for the primary loop scaling
For the secondary loop scaling, the same set of equations were applied, but the number of unknowns was reduced to 3 instead of 5 compared to the primary loop scaling.
The reason is that one unknown, , which is the heat removed by the secondary loop, is the same as that removed by the primary loop if the heat loss is negligible. In addition, the primary and secondary loops are the coupled through the DHX. Starting with the definition of the conduction depth, the convection time ratio in the primary loop is related to that in the secondary loop as:
l0 2 u0 d R_1 Loop , (51) l0 dt2 R u 0 R_2 Loop where d and t are the tube inner diameter and tube wall thickness , respectively. As seen,
59 the time ratio for the two loops will be the same if the thickness of the tubes of the DHX is considerably small compared to the tube diameter, which means that there is little storage energy in the structure. As a result, only loop height ratio was assumed for the secondary loop scaling. The process for the primary loop scaling (Figure 23 and Figure
24) can then be applied to the secondary loop as well.
As the heat transfer and pressure losses inside the DHX and NDHX are important,
Eqs. (43) - (45), as well as the requirement of the friction number, are applied to DHX and NDHX, respectively. The fluidic diode in the primary loop exhibits negligible heat loss, but experiences significant pressure drop, which indicates that only the requirement of the friction number needs to be enforced on the fluidic diode. Upon the completion of the component scaling, Eqs. (39) and (40) should be examined for the entire primary and secondary loops, respectively. If these requirements are not met, some compromise will need to be made in the scaling of some components.
3.4 Core Scaling Analysis
As discussed earlier, the scaling process started with the core scaling, more specifically the convection time ratio in the primary loop, which is related to the convective heat transfer coefficient in the reactor core and the properties of the reactor fuel.
Extensive literature review of the heat transfer correlations in pebble bed has been performed. However, it was found out that most of the correlations were valid for high
Reynolds number cases. Only one study related to the heat transfer in pebble bed with small flows was identified, which was carried out by Karabales et al. [30]. Virtually, the 60 correlations proposed in their study were for mass transfer. However, they also pointed out that analogy could be made to heat transfer by analogising the Sherwood number to the Nusselt number and the Schmidt number to the Prandtl number. We therefore employed their correlations in the heat transfer analysis. Based on their study, the heat transfer in the pebble bed could be natural, mixed, or forced convection, depending on its
Reynolds number and Grashof number, which are respectively defined as:
dG Re, p (52)
g Td 3 Gr. p (53) 2
Here, dp, , G, and are the pebble diameter, temperature increase, mass flux, dynamic viscosity, and kinematic viscosity of the fluid, respectively. The heat transfer correlations for different flow regimes were given by Karabales et al. as [30]:
Mixed convection:
1/6 6 6 Laminar : Nu= 0.46 GrPr1/4 + 4.58Re1/3 Pr 1/3 , (54) 1/2 2 2 Turbulent: Nu= 0.112 GrPr1/3 + 2.39Re0.56 Pr 1/3 ,
Forced convection:
(55)
By a close inspection of above correlations, it can be seen that the first term in the mixed convection correlations denotes the contribution of pure natural convection, while the second term denotes the contribution of pure forced convection. To find the proper 61 correlation to use, the flow regime in the prototypic core needs to be identified. The transition line from the mixed convection to forced convection can be obtained by equating the corresponding heat transfer correlations, with the result shown in Figure 25, which provides the relations between the transition Reynolds number and the transition
Grashof number. Above this transition line it is considered as forced convection, while below this line it is considered as mixed or natural convection. The Reynolds number and
Grashof number when the capability of the DRACS is 200 kW are 3.9 and 4.6E5, respectively, leading to a mixed laminar condition. The Nusselt number is 22.1 based on
Eq. (54), and the heat transfer coefficient is 832 W/m2-K with FLiBe used as the primary coolant.
Figure 25. Relations between the transition Reynolds number and Grashof number
Figure 26 shows the annular fuel pebble that has been used in the prototypic core design proposed by Peterson [10]. This fuel pebble is smaller in size compared to 62 conventional fuel pebble (3 cm vs. 6 cm in diameter) to enhance the heat transfer and thus lower the pebble center temperature. TRISO particles are embedded in the spherical shell with high-density graphite as the binder. The low-density graphite enclosed in the center of the pebble can adjust the overall density. The fuel pebbles will be floated in the primary salt so that online refuelling is enabled. The detailed dimensions of the pebble and the TRISO particle are summarized in Table 14.
Figure 26. The structure of a fuel pebble and TRISO particle [10]
The TRISO particle has been well studied, and the material properties are readily available. The properties of different materials constructing a TRISO particle were summarized by Gougar et al. [32]. It is found that, the physical properties, such as specific heat capacity, density, and thermal conductivity, highly depend on the temperature. The thermal conductivity is also a function of the received neutron fluence.
However, there have been limited studies on the matrix graphite, namely, the high-
63 density graphite coating and the filling graphite in the fuel spherical shell. In the current study, we assumed the matrix graphite to be the same as used in High Temperature Gas-
Cooled Reactors (HTGRs).
Table 14. Dimensions of the fuel pebble and the TRISO particle [31]
Fuel pebble Graphite Fuel zone Coating Total number Volumetric fraction of kernel outer radius thickness of TRISO TRISO radius 0.992 cm 1.25 cm 0.25 cm 2144 20% TRISO particle Porous Layer Fuel kernel Pyrocarbon SiC Pyrocarbon carbon Radius 0.25 0.34 0.38 0.42 0.46 (mm)
Two HTGR concepts have been developed: one is the pebble bed design adopted by Germany, China, and South Africa, and the other is the prismatic design adopted by the USA and Japan. Different fabricating processes of the fuel elements have be illustrated and compared by Barrachin et al. [33]. Despite the difference in the fabrication technology, the matrix graphite in the fuel pebble or the prismatic compact has the same composition, namely, 64% natural graphite, 16% synthetic graphite, and 20% thermosetting resin. We therefore assumed that the matrix graphite has the same properties despite its fabrication process. The properties of the matrix graphite depend on the temperature. The thermal conductivity of the matrix graphite also decreases with the increased neutron fluence that has been irradiated. The un-irradiated matrix graphite has thermal conductivity of 62 W/m-K at the room temperature [34] and 35 W/m-K at
64
1,000oC [35]. The thermal conductivity of the un-irradiated matrix graphite at an arbitrary temperature between 25 and 1,000oC is obtained by linear interpolation. The change of the thermal conductivity with the received neutron fluence for the matrix graphite was obtained by Ahlf et al. [36], as shown in Figure 27.
Figure 27. Fractional change of thermal conductivity of matrix graphite with fluence at
1123-1213 K [36]
The temperature information was based on the simulations performed by Griveau
[31], who modelled the temperature evolution inside the pebble bed reactor during the loss of forced coolant accident (LOFC) transient. From Figure 28, an average temperature of 750oC (1023 K) inside the fuel was assumed in our analysis. The properties of every structure material at 750oC are given in Table 15 under different fluence conditions. In what follows, we will discuss how to evaluate the effective properties of the entire pebble.
65
Figure 28. Temperatures variation during the LOFC transient [31]
We used volumetric average to evaluate the effective density, and mass-weighted average to evaluate the effective specific heat capacity. The determination of the effective thermal conductivity was a little complicated and consisted of two steps. First of all, we used the empirical German relationship [37] for the homogeneous fuel spherical shell:
(56) where is the effective thermal conductivity of the fuel spherical shell in W/cm-K; T is the temperature in oC; DOSIS is the neutron fluence in E25 n/m2. Secondly, a volume- based harmonic average was made over the fuel spherical shell and the high-density graphite coating by considering that the two layers are in series and the total thermal resistance should be the summation of the individual ones. The effective thermal
66 conductivity of the entire pebble, , was thus calculated as:
VVshell coating kpebble . (57) Vshell// k shell V coating k coating
The effective properties of the entire pebble are also provided in Table 15.
Table 15. Properties of the structure materials of a pebble
Fluence (E25 n/m2) 0 0.1 0.2 0.5 1 3--8 UO2 3.26 3.26 3.26 3.26 3.26 3.26 Porous carbon 1.44 1.38 1.32 1.19 1.04 0.64 k Pyrocarbon 4.42 4.24 4.07 3.66 3.18 1.97 (W/m- SiC 19.48 19.23 19.00 18.28 17.15 10.15 K) Matrix graphite 41.9 40.0 38.2 33.9 30.1 27.6 Effective 36.5 33.1 30.8 26.7 23.7 21.0 UO2 289 Porous carbon 645 c p Pyrocarbon 2175 (J/kg- SiC 1200 K) Matrix graphite 1772 Effective 1635 UO2 10750 Porous carbon 970 ρ Pyrocarbon 1900 (kg/m3) SiC 4210
Matrix graphite 1740 Effective 1894
The next step is to determine the core and coolants for the experiment. With the core and coolants specified, we can apply similar analysis to above to obtain the heat transfer coefficient and properties of the structure material of the heater rods in the experiment, based on which, the convection time ratio can be obtained from Eq. (50). The
67 scaling strategy in form of the flow chart shown in Figure 23 and Figure 24 enables us to complete the scaling of the entire system.
3.4.1 Scaling Results for Low-Temperature DRACS Test Facility (LTDF)
The LTDF will be built using water as the surrogate coolants. The low- temperature facility will provide us with some insights into the couplings among the three natural circulation/convection loops, which are critical to the integral performance of the
DRACS system. The scaling results for the low-temperature facility will be presented in following discussion.
Figure 29 shows the core design that has been proposed for the LTDF. It is composed of three electric heaters fitted into a circular vessel. Literature review of heat transfer study in such a core geometry has been performed. A number of studies of the heat transfer coefficient in a different 7-rod geometry have been identified, such as those by Mohanty and Sahoo [38], Sahoo and Mohanty [39], and those by Todreas and Kazimi
[40]. However, no exact study for a 3-rod geometry has been found. By noticing that the main difference between the 3-rod and the 7-rod geometry is only the angle θ embraced by the type II wall sub-channel (150o vs. 120o), we assumed that the heat transfer correlations for the 7-rod geometry also apply to the 3-rod case.
68
Figure 29. Core design in the experiment
Different core geometries (by varying the heater diameter D, the pitch P, and the wall distance W), and different sheath materials for the heaters (ranging from ceramics to alloys) have been examined. It is found that the loop scaling results may vary significantly with the core geometry and sheath material selections. The trend of the variation is that, with more compact core design and less thermally conductive material for the sheath, the core and loop scaling results will be better. A speculation reveals that the prismatic core design used in the experiment is inferior to the prototypic pebble bed core in heat transfer. Thus the core in experiment needs to be more compact to increase the heat transfer. Also, due to the deteriorated heat transfer in the experiment, the convection process becomes less effective. Correspondingly, the conduction process in the heat source should also be inhibited, which calls for the use of less thermally conductive material as the sheath. Out of the extensively examined cases, one attractive 69 case (not necessarily the best) dictates the core design as summarized in Table 16. The area-based average heat transfer coefficient is found to be 267 W/m2-K. The sheath for this case consists of two layers of different materials, namely, the YTZP ceramic and the
SS 304. YTZP is one kind of Zirconia ceramic that features low thermal conductivity as shown in Table 17.
Table 16. Dimensions of the core design in LTDF
P/D 1.6 W/D 1.4 Vessel diameter (cm) 3.47 Heater diameter (cm/inch) 0.95/0.375 Heated length (m) 1 h (type II) (W/m2-K) 229 h (type I) (W/m2-K) 461 h (W/m2-K) average 267
Table 17. Thermal properties of YTZP at room temperature [41]
Thermal Conductivity (W/m- Density (kg/m3) Specific Heat (J/Kg-K) K) YTZP 6070 400 2.2
The core and loop scaling results, as well as that for the DHX and NDHX are summarized in Table 18 and Table 19. SS 304 has been assumed as the construction material for the DHX and NDHX. The results corresponding to the case with highest neutron fluence received by the prototypic core are the best, as highlighted. When the heat transfer coefficient in the core was determined, the core geometry must be specified, which would give a value for the hydraulic diameter ratio. In the meanwhile another
70 hydraulic diameter ratio in the core can be obtained from the core scaling. As can be seen, the two values for the hydraulic diameter ratio in the core do not match very well, which will cause distortion in the Stanton number, and correspondingly the interfacial temperature simulation. Also, the heat source number ratio is much larger than 1, which will probably cause higher peak temperature in the core in the experiment.
Table 18. Core and loop scaling results for LTDF
Fluence (1025 n/m2) 0 0.1 0.2 0.5 1 3--8 Power (kW) 2.05 Power ratio, % 1.03 Time ratio 0.65 0.72 0.77 0.89 1.00 1.14 Length ratio 0.75 0.75 0.75 0.75 0.75 0.75 D From h 0.24 0.26 0.28 0.32 0.36 0.41 ratio Scaling From in 1.10 Primary Core Design loop δ ratio in core 0.25 0.28 0.30 0.34 0.39 0.44 Velocity ratio 1.15 1.04 0.97 0.84 0.74 0.66 Area ratio 0.011 0.015 0.019 0.029 0.042 0.061 ΔT ratio 0.87 0.72 0.62 0.47 0.37 0.29 Heat source 59 79 99 151 216 313 number ratio Time ratio 0.65 0.72 0.77 0.89 1.00 1.14 Length ratio 1 1 1 1 1 1 Secondary Velocity ratio 1.54 1.39 1.29 1.12 1.00 0.88 0.017 loop Area ratio 0.0034 0.0045 0.0056 0.0086 0.0123 9 T ratio 1.85 1.52 1.31 0.99 0.78 0.61
For the DHX and NDHX scaling, most of the ratios are close to one as seen from
Table 19. Therefore the designs of the DHX and NDHX in the LTDF should have dimensions similar to those in the prototypic design.
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Table 19. DHX and NDHX scaling results for LTDF
Fluence 0 0.1 0.2 0.5 1 3--8 (E25 n/m2) ratio 0.75 0.78 0.81 0.87 0.93 0.98 DHX Shell side D ratio h 0.66 0.69 0.72 0.77 0.82 0.87 h ratio 0.90 0.85 0.82 0.77 0.72 0.68 ratio 0.77 0.81 0.84 0.90 0.95 0.98 DHX Tube side D ratio h 0.56 0.58 0.61 0.65 0.69 0.72 h ratio 0.92 0.87 0.84 0.78 0.74 0.68 ratio 0.77 0.81 0.84 0.90 0.95 1.01 NDHX D ratio h 0.56 0.58 0.61 0.65 0.69 0.74 h ratio 0.92 0.87 0.84 0.78 0.74 0.69
No awkward results have been encountered in the loop scaling, as can be seen from Table 20, which ensures the successful running of the circulation loops. It should be noted that, the scaling results presented here just gives a reference paper design. The core based on the core scaling results seems feasible. However, there might be engineering difficulties with the fabrication of the core, e.g. the ceramic cladding for the heaters, and fitting tiny heaters into small vessel. If the difficulties cannot be resolved, and the core design has to be modified, the convection time ratio obtained here should be retained, since it yields good heat exchanger and loop scaling results which are more important in determining the successful running of the circulation loops, and the integral performance of the system. The resulted issues will be more deterioration in core scaling.
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Table 20. Design results summary for LTDF
Parameters Value for Value for Ratio Prototype Experiment Q 200 kW 2.0 kW 0.01 Primary Loop 2.28 m 1.71 m 0.75 lo Secondary Loop 0.42 m 0.42 m 1 Primary Loop 0.054 m/s 0.036 m/s 0.66 uo Secondary Loop 0.059 m/s 0.052 m/s 0.88 Primary Loop 42.2 s 48.1 s 1.14 lo/ uo Secondary Loop 7.2 s 8.2 s 1.14 Primary Loop 45oC 12.9oC 0.29 To Secondary Loop 50oC 30.1oC 0.61
D : pipe Primary Loop 150 mm 37.0 mm 0.25 diameter Secondary Loop 150 mm 20.0 mm 0.13
Primary Loop 1.84 kg/s 0.038 kg/s 0.021 m Secondary Loop 2.12 kg/s 0.016 kg/s 0.008
3.4.2 Scaling Results for High-Temperature DRACS Test Facility (HTDF)
Under the present DRACS project, a high-temperature DRACS test facility
(HTDF) is also planned, which will use liquid fluoride salts as the coolants. This facility will be operated at temperatures similar to those in the prototypic DRACS design. With this high-temperature facility, critical phenomena in a prototypic DRACS system can be reproduced. Also, the extensive experimental data from this facility will be beneficial to the benchmark of the liquid fluoride salt heat transfer and pressure drop models, as well as the related DRACS design and analysis codes.
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Updates to Prototypic Design
As seen from previous calculations, a height of 0.42 m (vertical distance between the thermal centers of the DHX and NDHX) is sufficient to overcome the pressure drops along the secondary loop. However, this height calculation did not take into account of the physical layout of the reactor, especially the reactor pool, which might impose some other constraints on the loop height due to the fact that the DHX would be submerged in the pool. To date, there has not been any test FHR built yet. The only known effort in designing and building a test-scale FHR is due to the Massachusetts Institute of
Technology (MIT) under an Integrated University Project [9]. Before they accomplish the final design of the test FHR, the pebble bed reactor core adopted in our previous DRACS prototype will be retained. This pebble bed core, as shown in Figure 9, was the yield from a nuclear engineering design class at UC Berkeley. The detailed dimensions of the core were given, which were utilized in the calculation of the pressure drop over the core.
However, a complete pool design for this pebble bed core, which would affect the layout and height of the DRACS secondary loop, was never accomplished. Due to this, we have referred to the SmAHTR design [17] by ORNL to reach a relatively more realistic layout for the DRACS secondary loop. The SmAHTR design features a total thermal power of
125 MWth, which is much larger than that of the pebble bed core. However, the physical size of the SmAHTR core, as seen from the comparison in Figure 30, is comparable to that of the pebble bed core. Referring to the SmAHTR pool design will provide us some idea of the layout for the DRACS secondary loop.
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Figure 30. The FHR-16 pebble bed core [10] and SmAHTR core [17]
By referring to the SmAHTR pool design, the layout of the DRACS secondary loop has been proposed as illustrated in Figure 31. The DHX will be submerged in the pool salt by 0.5 m, above which will be 0.5-m clearance for an inert gas. After exiting the DHX, the piping is routed in a zigzag shape to avoid interference with any equipment above the reactor. The NDHX is elevated from the chimney bottom by 0.5 m to enable the air flow to turn around by 180 degree. With such a loop layout, the height of the secondary loop has been intentionally increased from 0.42 to 2.3 m, including half of the
DHX length. The high and low temperatures in the DRACS secondary loop have been selected based on the optimization of the DHX and NDHX designs, which will be maintained. With the total power fixed, the flow and pressure drops along the secondary 75 loop will be the same as before. Due to the increased loop height, however, there will be an extra buoyancy of approximately 630 Pa induced in the secondary loop, which should be accommodated by adding extra throttling.
In conclusion, the DRACS secondary loop height has been increased to 2.3 m, considering the constraints imposed by the physical layout of the reactor. The designs of the DHX and NDHX stay the same as before. A throttling of 630 Pa will be necessary to account for the increase in the loop height.
Figure 31. Layout of the DRACS secondary loop
Scaling Results for HTDF
The same scaling process as applied to the low-temperature test facility has been followed to obtain a reference design for the high-temperature test facility, based on which an engineering design can be developed. 76
Before starting the scaling analysis, the coolants must be identified. Based on previous experience with the scaling analysis of the low-temperature test facility, a fluoride salt with high thermal conductivity is preferred as the primary salt. In this regard,
FLiNaK (LiF-NaF-KF, 46.5-11.5-42 in mol%) was selected as the primary salt. For the secondary salt, there is more concern with the potential issue of salt freezing caused by overcooling; accordingly, KF-ZrF4 (58-42 in mol%) with low melting point has been chosen. The physical properties of FLiNaK and KF-ZrF4 are summarized in Table 21.
Table 21. Summary of properties of FLiNaK and KF-ZrF4 (T in Kelvin)
Specific Melting Thermal Density heat Viscosity point conductivity (kg/m3) (J/Kg- (cP) (oC) (W/m-K) K) 2530- 0.0005T+32/41.3- FLiNaK 454 1883 0.73(T-273) 0.04exp(4170/T) 0.34 KF- 3416- 0.0005T+32/103.9- 390 1046 0.159exp(3179/T) ZrF4 0.887(T-273) 0.34
In the high-temperature facility, seven electric heaters in a triangular pattern are used to simulate the core. The cross-sectional view of the core is shown in Figure 32.
Extensive cases with different core geometries and heater sheath materials have been studied, of which one of the best promising cases yields a core design as summarized in
Table 22. This design results an average heat transfer coefficient of 251 W/m2-K for the core, and calls for heater sheath of 0.8-mm YTZP cladded with 0.4-mm Hastelloy N.
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Figure 32. The core design in the high-temperature test facility
Table 22. Dimensions of the core design in HTDF
P/D 1.6 W/D 1.4 Vessel diameter (cm) 9.53 Heater diameter (cm/inch) 1.91/0.75 Heated length (m) 0.8 h (type II) (W/m2-K) 200 h (type I) (W/m2-K) 320 h (W/m2-K) average 251
The scaling results are summarized in Table 23, Table 24, and Table 25. Inconel
600, which is a nickel-based high temperature alloy [42], has been assumed as the construction material for the DHX and NDHX. The results corresponding to a fresh prototypic core are the best, and have been highlighted. As can be seen, the same problems as in the scaling for low-temperature facility are encountered, i.e., the Stanton 78 number and the heat source number are not matched well. Distortion in interfacial temperature scaling and higher structure peak temperature will be caused.
Table 23. Core and loop scaling results for HTDF
Fluence (1025 n/m2) 0 0.1 0.2 0.5 1 3--8 Power (kW) 10.03 Power ratio, % 5.02 Time ratio 1.04 1.14 1.23 1.42 1.60 1.81 Length ratio 0.6 0.6 0.6 0.6 0.6 0.6 D From h 0.38 0.42 0.45 0.52 0.59 0.67 ratio Scaling From in 2.14 Primary Core Design loop δ ratio in core 0.29 0.32 0.34 0.39 0.44 0.50 Velocity ratio 0.58 0.52 0.49 0.42 0.38 0.33 Area ratio 0.27 0.36 0.45 0.69 0.99 1.43 ΔT ratio 0.39 0.32 0.28 0.21 0.16 0.13 Heat source 104 140 174 267 381 552 number ratio Time ratio 1.04 1.14 1.23 1.42 1.60 1.81 Length ratio 0.6 0.6 0.6 0.6 0.6 0.6 Secondary Velocity ratio 0.58 0.52 0.49 0.42 0.38 0.33 loop Area ratio 0.17 0.23 0.29 0.45 0.64 0.93 T ratio 0.64 0.53 0.46 0.34 0.27 0.21
For the DHX and NDHX scaling, most of the ratios are close to one as seen from
Table 24. This signifies that the heat exchangers in the prototypic design can be used as the starting point for the heat exchanger design in HTDF, which will ease the design process significantly.
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Table 24. DHX and NDHX scaling results for HTDF
Fluence (E25 n/m2) 0 0.1 0.2 0.5 1 3--8 ratio 1.11 1.16 1.20 1.29 1.37 1.46 DHX Shell side D ratio h 1.25 1.31 1.36 1.46 1.55 1.65 h ratio 0.98 0.94 0.90 0.84 0.79 0.75 ratio 1.11 1.16 1.20 1.29 1.37 1.46 DHX Tube side D ratio h 1.32 1.38 1.44 1.54 1.64 1.74 h ratio 0.98 0.94 0.90 0.84 0.79 0.75 ratio 1.13 1.19 1.23 1.32 1.40 1.49 NDHX D ratio h 1.31 1.37 1.42 1.53 1.62 1.73 h ratio 0.98 0.93 0.90 0.84 0.79 0.74
It seems a good reference design for the HTDF has been achieved based on the results shown in Table 25. However, as can be imagined, many engineering issues will be encountered mainly due to the high temperature and corrosion issue associated with the
HTDF. The core, including the heaters, and the DHX and NDHX cannot exactly follow the reference design presented here. It should be remembered that, no matter what changes have to be made to the core, DHX or NDHX design, good loop scaling results should always be aimed at. Since the convection time ration used here gives rise to satisfactory loop scaling results, it is highly recommended to be retained.
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Table 25. Design results summary for HTDF
Value for Value for Parameters Ratio Prototype Experiment Q 200 kW 10.0kW 0.05 Primary Loop 2.28 m 1.37 m 0.6 lo Secondary Loop 2.3 m 1.38 m 0.6 Primary Loop 0.054 m/s 0.031 m/s 0.58 uo Secondary Loop 0.059 m/s 0.034 m/s 0.58 Primary Loop 42.2 s 43.9 s 1.04 lo/ uo Secondary Loop 7.2 s 7.5 s 1.04 Primary Loop 45oC 17.6oC 0.39 To Secondary Loop 50oC 32.1oC 0.64
D : pipe Primary Loop 150 mm 78.0 mm 0.52 diameter Secondary Loop 150 mm 62.7 mm 0.42
Primary Loop 1.84 kg/s 0.302 kg/s 0.16 m Secondary Loop 2.12 kg/s 0.299 kg/s 0.14
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Chapter 4: Conclusion
In the present study, a detailed modular design of the DRACS for a 20-MWth
FHR is first developed. As a starting point, the DRACS is designed to remove 1% of the nominal power, i.e., 200 kW. FLiBe with high enrichment in Li-7, and FLiNaK have been selected as the primary and secondary salts, respectively, due to their superior thermal properties. A 16-MWth pebble bed core proposed by the UCB is adopted in the design. Shell-and-tube heat exchangers have been designed for the DHX and NDHX with a MATLAB code based on the Delaware Method. A vortex diode that has been tested with water is adopted in the present design. Finally, pipes with inner diameter of 15 cm are selected for both the primary and secondary loops. The final DRACS design features a total height less than 13 m. The design presented here has the potential to be used in the planned small-scale FHR test reactor and will also benefit and guide the DRACS design for a commercial AHTR.
Detailed scaling analysis for the DRACS has also been performed, which will provide guidance for the design of scaled-down DRACS test facilities. Based on the
Boussinesq assumption and one-dimensional formulation, the governing equations are non-dimensionalized by introducing the appropriate dimensionless parameters. The key dimensionless numbers that characterize the performance of the DRACS system are obtained from the non-dimensional governing equations, which include the Richardson,
82 friction, Stanton, time ratio, Biot, and heat source number. Based on the dimensionless numbers and non-dimensional governing equations, similarity laws are proposed. In addition, a scaling methodology has also been developed, which consists of the core scaling and loop scaling. The scaling methodology and similarity laws have been applied to obtain a scaled-down low-temperature DRACS test facility (LTDF), and a scaled- down high-temperature DRACS test facility (HTDF).
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Appendix A: Input Parameters for the Design/Rating of the Shell-and-Tube Heat
Exchanger
Item Symbol Units Description Shell-side geometry data Tube and tube layout
1 Ds mm Inside shell diameter
2 Dt mm Tube outside diameter
3 Ltw mm Tube wall thickness
4 Dti mm Inside tube diameter Tube wall material thermal 5 k W/m-K tw conductivity
6 Ltp mm Tube layout pitch
7 tp deg Tube layout characteristic angle Tube length
8 Lto mm Overall nominal tube length
9 Lti mm Baffled tube length Effective tube length for heat transfer 10 L mm ta area Baffle geometry
11 Bc % Baffle cut as percent of
12 Lbc mm Central baffle spacing
13a Lbi mm Inlet baffle spacing (optional)
13b Lbo mm Outlet baffle spacing (optional) Nozzle Shell-side nozzle, impingement 14 CN code protection, annular distributor Tube bundle geometry Total number of tubes or holes in 15 N tt tubesheet for U tubes 89
16 Ntp Number of tube passes
17 Nss Number of sealing strips (pairs) Tube bundle type (FX, UT, SRFH, 18 CB code PFH, PTFH) Tube OD ( D )-to-baffle hole 19 L mm t tb clearance (diametrical) Inside shell-to-baffle clearance 20 L mm sb (diametrical) Inside shell-to-tube bundle bypass 21 L mm bb clearance (diametrical) Temperatures
22 Tsi ˚C Shell-side temperature inlet
23 Tso ˚C Shell-side temperature outlet
24 Tti ˚C Tube-side temperature inlet
25 Tto ˚C Tube-side temperature outlet Shell-side process information
26 M s kg/s Shell fluid mass flow rate At shell fluid mean temperature 3 27 s kg/m Density
28 ks W/m-K Thermal conductivity
29 ()cps J/kg-K Specific heat
30 s cP = mPa-s Dynamic viscosity Shell-side fouling resistance (referred 31 ()R m-K/W fo to shell-side surface) Tube-side process information
32 M t kg/s Tube fluid mass flow rate At tube fluid mean temperature 3 33 t kg/m Density
34 kt W/m-K Thermal conductivity
35 ()cpt J/kg-K Specific heat
36 t cP = mPa-s Dynamic viscosity Tube-side fouling resistance (referred 37 ()R m-K/W fi to tube-side surface) Special information Shell-side heat transfer coefficient 38 h W/m2-K s (specified or estimated) 2 39 ht W/m -K Tube-side heat transfer coefficient 90
(specified or estimated) Maximum permissible pressure drop, 40 ()p kPa s max shell side Maximum permissible pressure drop, 41 ()p kPa t max tube side
91