Tesi di Laurea Magistrale in INGEGNERIA NUCLEARE
THERMAL - HYDRAULIC ANALYSIS OF THE ACTIVE CHANNEL OF THE HTHL FACILITY
Relatori
Dott. Ing. Nicola Forgione . . . . Prof. Ing. Walter Ambrosini . . . . Ing. Otakar Frybort . . . . Dott. Ing. Guido Mazzini . . . .
Candidato
Matteo Montella . . . .
Pisa — 14 April 2014 A.A. 2012/2013
The present work is focused on the thermal-hydraulics analysis of the active channel of the HTHL facility located in Research Center Rez in Czech Republic. The High Temperature Helium Loop (HTHL) facility is designed to offer, in laboratory conditions, analyses of materials under the combination of high temperature gas environment and γ irradiation effects. The introduction provides the general structures of the works and the overview of the facility in the framework of the Generation IV. Subsequently the description of the facility is reported with a particular emphasis of the active channel and its major compo-nents. Specific attention has been focused in studying the models used by RELAP5 code for implementing the helium as noncondensable gas. Furthermore, it has been evaluated an alternative solution in order to demonstrate the feasibility of the code for performing calculations with helium as main fluid. After simplified assessment of the capability of the code, the nodalization of the active channel was developed. Several calculations have been performed using the RELAP5/Mod3.3js version code owned by U.S. NRC. A preliminary analysis was conducted to obtain the steady state data of the active channel in both con-figurations (out of pile and in-pile). Subsequently, the results of the steady state have been used as starting conditions for the analyses of several scenarios. In particular, a set of transients representative of operational and accidental conditions, which are particular meaning to draw up the operational procedures of the HTHL facility and for future im-provements of the design, were performed. Nowadays, the facility is currently constructed for out of pile configuration and, at the end of September 2015, the in-pile configuration should be concluded with the insertion of the loop inside the research reactor LVR-15 hosted in Rez.
This thesis is the result of a six months work at Research Center Rez in Czech Republic. My first mention goes to Ing. Otakar Frybort: thank you for the opportunity you gave me to work on such an interesting topic.
Thanks to Francesco Venturi and Gianluca Barone for showing me the basics of the system code RELAP5.
Thanks to Dott.Ing Guido Mazzini and Ing. Ales Vojacek, who contributed to this work with their precious advices and experience.
Thanks to all the colleagues in Rez, with whom I had a great time during these six months. Thanks to my Italian and Czech friends, or whatever country you came from.
I had a great time with you and hope you are doing well wherever you are now. Thanks to Eluisa, for the patience she showed me these last months.
1 Introduction 1
1.1 Introduction . . . 1
2 Description of HTHL Facility 4 2.1 General Layout . . . 4
2.2 Active Channel . . . 6
2.2.1 Out of pile configuration . . . 8
2.2.2 In-pile configuration . . . 9
2.3 Major Components of Active Channel . . . 13
2.3.1 Compressor . . . 13
2.3.2 Heat Exchanger . . . 15
2.3.3 Electrical Heater . . . 17
2.3.4 Cooler . . . 19
2.4 Dosing and Helium Purification System . . . 21
2.5 Instrumentation Map . . . 23
3 Theory of Nuclear Thermal–Hydraulics Code 25 3.1 The System Code . . . 25
3.2 The RELAP5 Code . . . 27
3.3 Hydrodynamic model . . . 27
3.3.1 Mass Continuity . . . 29
3.3.4 Noncondensables in the Gas Phase . . . 33
3.4 Heat Structure . . . 35
4 Active Channel Model Development 38 4.1 Nodalization Scheme . . . 38 4.2 Model Assumption . . . 44 4.2.1 Compressor . . . 44 4.2.2 Downcomer . . . 44 4.2.3 Riser . . . 46 4.2.4 Heat Exchanger . . . 47 4.2.5 Electrical Heater . . . 48
4.2.6 Test material section . . . 49
4.2.7 Cooler . . . 50
5 Obtained Results 51 5.1 Introduction . . . 51
5.2 Steady State Analysis . . . 56
5.2.1 Test A . . . 56 5.2.2 Test B . . . 59 5.3 Transient Analysis . . . 62 5.3.1 Test C . . . 62 5.3.2 Test D . . . 64 5.3.3 Test E . . . 67 5.3.4 Test F . . . 68 5.3.5 Test G . . . 70 5.3.6 Test H . . . 72 5.3.7 Test I . . . 75 5.3.8 Test J . . . 77 5.3.9 Test K . . . 80 6 Conclusion 82 Appendices 87
A Thermophysical Properties of Matter 88
A.1 Thermophysical Properties of Helium . . . 88
A.2 Thermophysical Properties of Stainless Steel 304 . . . 94
A.3 Thermophysical Properties of Corundum . . . 96
A.4 Thermophysical Properties of Aluminum . . . 99
A.5 Thermophysical Properties of Air . . . 100
2.1 The High Temperature Helium Loop. . . 5
2.2 Cutaway active channel. . . 7
2.3 The active channel for out of pile configuration. . . 8
2.4 The active channel for in-pile configuration. . . 9
2.5 LVR-15 scheme. . . 10
2.6 LVR-15 core cartogram. . . 11
2.7 Circulatory compressor of the HTHL. . . 13
2.8 View of compressor. . . 14
2.9 Axonometric view of heat exchanger. . . 15
2.10 Cutaway heat exchanger. . . 16
2.11 View of heater section. . . 17
2.12 View of cross junction. . . 17
2.13 View of heater and test material channel. . . 18
2.14 Helical tube of the cooler. . . 19
2.15 Sketch of cooler assembly. . . 20
2.16 Main part of dosing and helium purification system . . . 22
2.17 Schematic view of instrumentation map. . . 24
3.1 General structure and key components of the numerical code. . . 26
3.2 Mesh point heat structure. . . 36
4.1 RELAP5/Mod3.3 nodalization. . . 43
5.1 Temperature downcomer. . . 55
5.2 Axial Temperature profile out of pile. . . 58
5.3 Axial Temperature profile in-pile. . . 60
5.4 Radial temperature on pressure tube, steady state. . . 61
5.5 Main temperatures for test C. . . 62
5.6 Temperatures downcomer different heights for test C . . . 63
5.7 Main temperatures for test D. . . 65
5.8 Temperatures downcomer different heights for test D . . . 66
5.9 Time dependent ∆Tmax on pressure tube for test D. . . 67
5.10 Maximum temperature in active channel and downcomer for test E. . . 68
5.11 Main temperatures for test F. . . 69
5.12 Time dependent ∆Tmax on pressure tube for test F. . . 69
5.13 Main temperatures for test G. . . 70
5.14 Time dependent ∆Tmax on pressure tube for test G. . . 71
5.15 Radial temperature on pressure tube at 4400 s for test G. . . 71
5.16 Main temperatures for test H. . . 73
5.17 Temperatures downcomer different heights for test H. . . 74
5.18 Time dependent ∆Tmax on pressure tube for test H. . . 74
5.19 Main temperatures for test I. . . 75
5.20 Time dependent ∆Tmax on pressure tube for test I. . . 76
5.21 Radial temperature on pressure tube at 4400 s for test I. . . 76
5.22 Main temperatures for test J. . . 77
5.23 Temperatures downcomer different heights for test J . . . 78
5.24 Time dependent ∆Tmax on pressure tube for test J. . . 79
5.25 Radial temperature on pressure tube at 3001 s for test J. . . 79
5.26 Main temperatures for test K. . . 80
5.27 Time dependent ∆Tmax on pressure tube for test K. . . 81
A.1 Viscosity of Helium at different Temperatures. . . 90
A.2 Thermal conductivity of Helium at different Temperatures. . . 90
A.3 Prandtl number of Helium. . . 91
A.6 VHC of AISI 304 at different Temperatures. . . 95
A.7 Thermal conductivity of corundum at different Temperatures. . . 97
A.8 VHC of corundum at different Temperatures. . . 97
B.1 Heat Transfer Phenomena . . . 101
B.2 Equivalent thermal circuit. . . 102
B.3 Convection current in a symmetric enclosure. . . 104
B.4 Thermal conductivity of air at different temperatures. . . 108
1.1 Support research facilities of ALLEGRO. . . 2
2.1 LVR-15 technical parameters. . . 12
4.1 Comparison of the helium properties at 226 kPa. . . 40
4.2 Comparison of the helium properties at 7.0 MPa. . . 41
5.1 Steady state calculations. . . 52
5.2 Transients calculations. . . 54
5.3 Results of test A. . . 56
5.4 Results of test B. . . 59
A.1 Thermodynamic Properties of Gas Helium at 7 MPa. . . 92
A.2 Thermal and structural properties of Corundum. . . 98
A.3 Thermal properties of Aluminum. . . 99
Chapter
1
Introduction
1.1
Introduction
A key challenge in the production of the electricity is reducing the CO2 emissions to the environment. Meanwhile, the world energy consumption is increasing as a necessity of de-veloping country and the industrialization process. Nuclear energy is not a CO2 emission energy source. The Fukushima accident in March 2011 has had an huge impact, around the world, with the public acceptance due to safety concerns. Nevertheless the nuclear power remain the only one economic alternative for the electricity generation rather than oil and natural gas.
The Next Generation Nuclear Plant (NGNP) will base on concepts of sustainability, eco-nomic competitiveness, safety, physical protection and nuclear proliferation resistance and is currently developed by the founding countries of Generation IV International Forum (GIF) which, in 2001, signed the founding document in order to develop nuclear systems [1]. Nowadays, the Sodium Fast Reactor (SFR) is still considered to be the reference technology since it has more substantial technological and reactor operations feed-back. The Lead(-bismuth) Fast Reactor technology has significantly extended its technological base and can be considered as the shorter-term alternative technology, whereas the Gas Fast Reactor technology has to be considered as a longer-term alternative option [2]. The main targets of the European Sustainable Nuclear Industry Initiative (ESNII), to achieve before the year 2025, is the design, the construction commission and put into operation of the Sodium Fast Prototype Reactor called ASTRID [3] and the flexible fast spectrum research reactor MYRRHA [4].
In parallel to the realization of those reactors, the Gas Fast Reactor technology should be continued, as a long term alternative to SFR. The intermediate step before to realize the GFR is the design and construction of a small demonstration reactor called ALLEGRO. The roles of ALLEGRO consists to the demonstration of specific safety systems of the GFR: the qualification of high temperature ceramic fuel at the full core level; the testing of the technologies of the GFR such as high temperature material; the spent fuel repro-cessing; the helium purification; the refueling; the test of heat process and regeneration. In order to build knowledge and facilities needed for nuclear energy systems development, the European Commission founded, in winter of 2010, the ADRIANA (ADvanced Reactor Initiative And Network Arrangement) project [5]. Several facilities have been identified with the aims to cover all technical areas necessary for ALLEGRO reactor. The following Table 1.1 reported the most high ranked facilities.
Table 1.1: Support research facilities of ALLEGRO. Accident analysis Fission Product Transport High Temp. Materials Graphite and Ceramics Fuel Czech Republic HTHL HTHL HTHL
France HELITE MERARG ENIGMA,
DEDIFAR HEDYT PLINIUS Germany ITHEX, HEBLO THAI HPLL GOLAB Italy HE-FUS3
The High Temperature Helium Loop (HTHL) facility located in the Research Center Rez in Czech Republic offers the opportunity to host separate effect tests carried out both out of pile and in-pile, hence offering the flexibility to address studies in which the combined effect of high-temperature gas environment and γ irradiation are of relevance, such as for instance on fission product transport or high-temperature materials or helium purification.
The purpose of this Master thesis in Nuclear Engineering is thermal-hydraulics analysis by system code with the targets to obtain technical information of the active channel of the HTHL facility and prepare new technical procedures as the primary step of the new experimental activities in in-pile configuration. The project was continuously accompanied with theoretical studies in order to analyze the code limitations during the calculations with helium fluid.
This thesis is divided into six chapters.
Chapter 2 presents the description of HTHL facility with a particular focus on the active channel. Two different configurations are reported and the main information of the re-search reactor LVR-15 are presents. The details and technical specifications of the main components of the active channel can be found in this chapter. An a section is dedicated to describe the dosing and helium purification system as part of the HTHL facility. This chapter is concluded with a brief section of the instrumentation located along the active channel.
Chapter 3 presents the theory at the base of the adopted nuclear thermal-hydraulics code, starting with an overview of the code structure and its main domains. In the following sections are reported details and information about RELAP5/Mod3.3 code with the main purpose to understand how the helium fluid is implemented into the code.
Chapter 4 presents the difficulties encountered with the modified version of RELAP5 and the main reasons of the change to the latest version js of the code. Subsequently is de-scribed its application for the active channel of the HTHL facility. Moreover the details and information of the model assumptions adopted in order to implementation the helium loop and the secondary water loop are reported.
Chapter 5 describes of the calculations performed during the thesis’s project. In parti-cular the steady state analyses and transient calculations for several initial events can be found in this chapter. For each tests are reported the salient parameters useful for future considerations.
Chapter 6 is a discussion of the major conclusions, as well as recommendations for future works.
Chapter
2
Description of HTHL Facility
2.1
General Layout
In December 2011, the Research Center Rez, a subsidiary of UJV a.s., became a promoter of the Sustainable Energy (SUSEN) project, financed from the structural funds of the European union under the ”Research and Development for Innovations” program, which is a part of the support provided by the European union focused on comparisons of the economic levels in individual regions (objective of the Convergence under the European Regional Development fund) [6].
The principal objective of the SUSEN project is to create a robust infrastructure for sustainable R&D activities in order to support the Czech participation on the European effort for safe and efficient energy generation in Europe in the 21st century. In particular the project focuses on the developments of Gen IV, nuclear fusion energy and on the safe operation of Gen III/III+ and Gen II. The structure of the SUSEN project is based on four different programs: study of nuclear fuel cycle (NFC); material research (MAT); structural and system diagnostic (SSD); technologies of experimental loop (TEO). The High Temperature Helium Loop (HTHL) facility is belong to the TEO program and it must follow the deadline of the SUSEN project. As previously described, the HTHL is one of the most interesting facility selected in the ADRIANA project with the intention to create a support to the research at the ALLEGRO gas cooled reactor.
The high flexibility of the facility guarantees to cover additional goals even outside at the GFR project. In fact, the feasibility to test materials under high temperature and/or γ
Nowadays the HTHL facility is already constructed for out of pile configuration, while the experimental buildings for in-pile arrangement are under construction. The conclusion of the work is expected at the end of September 2015. The SUSEN project should be concluded at the end of December 2020.
The following Figure 2.1 shows the scheme of the HTHL facility. The next sections are devoted to describe the active channel, with a particular focus on its main components and the possible configurations. Moreover, the last section of this chapter concerns the salient information of the dosing and the helium purification system, since it is an important part of the high temperature helium loop.
2.2
Active Channel
The active channel is the main part of the HTHL facility and it is designed to work in out of pile and in-pile configuration. The geometric parameters are the same for both configurations and they are reported in the Figure 2.2. The total length is 4790 mm and the outside diameter of pressure tube is 60 mm; inside the pressure tube it is present a system of coaxial tubes which provides the required flow, an heat exchanger, electrical heating, isolation and stabilizing elements. The helium coolant is at 7 MPa and it accomplishes two upward and two downward passages with a constant mass flow rate of 37.8 kg/h. The inlet temperature of the coolant is 210◦C and it flows enters the channel through the head and flow down around the inlet wall of pressure tube through the downcomer space. When the coolants reach the bottom of the downcomer, it turns around and flow upwards for the first passage before the heat exchanger. The heat loss in this region has been reduced by the introduction of a helium stagnation layer among the downcomer and the first upward channel with a thickness of 2 mm. The second downward passage proceeds on the shell side of the heat exchanger, where the helium heat up by the heat transfer from the primary side of heat exchanger. In this particular region there are two layers of helium stagnation in order to minimize the heat losses. After that the helium continues through the electrical heating area where the target parameters are achieved, then it enters the testing material zone. The maximum power provided by electrical heating is about 10.5 kW, otherwise it could be modified to supply different conditions and tests. The connection between the electrical heater and test material section is obtained by a particular cross junction, which consists of six small holes. More details are reported in the following paragraph.
After leaving the specimens zone, the helium coolant is turned around to complete the last passage in upward flow and it is led up to the heat exchanger. Here, it transfers the heat and it reduces its temperature before going to the cooler which consists in a helix tube with inside cold water. The coldest temperature of helium is achieved at the outlet section of the cooler and is the recommendation temperature in order to permit the correct behavior of the compressor. The loop is closed with the compressor line, which provides to the helium to start again a new cycle.
2.2.1 Out of pile configuration
Figure 2.3: The active channel for out of pile configuration. The HTHL facility for out of pile configuration is
already constructed and it is in the experimental building of Research Center Rez. In the Figure 2.3 it is possible to see the active channel.
The main purpose of this configuration is to prepare an intensive experimental campaign with a focus to assess the correct behavior of the chemical system and the main internals of active channel in order to have several fundamental information for the new activities of the HTHL facility inside of the LVR-15 core. The previous experimental campaign were concentrated on the dosing and helium purification system that is very important in order to prevent the presence of eventually impurity inside of the helium loop. More information about the chemical system are reported in the section 2.4. At this moment the HTHL in out of pile it is not available due to some technical problems probably regarding the purifica-tion of the helium coolant. As previous described, the active channel, from mechanical point of view, it is the same to the in-pile configuration; therefore the description, presented in the previous pages, it is still valid. Nevertheless the main change is the introduction of an insulator matrix that surround-ing the pressure tube with the purpose to minimize the heat loss from active channel to the environ-ment. The material is mineral wool webs that are quilted to a wire mesh and its thickness is such that the boundary condition of active channel could be represented as an adiabatic system.
2.2.2 In-pile configuration
At the end of September 2015, the active channel of the HTHL facility will be located inside the core of the LVR-15 nuclear research reactor. That arrangement is denominated in-pile and it will be possible to reach the maximum temperature of 900◦C due to the combination of electrical heating and γ irradiation. The reference sketch for in-pile configuration is reported in Figure 2.4. As it shown, the active channel will be immersed into the water reactor pool for a total length of 4.4 m, while only 0.4 m will be in air environment. In more details, the pressure tube will be situated inside an aluminum receiver with a width of 70 mm and thickness of 3 mm and an atmospheric air gap among them. This particular configuration is born with the intention to minimize the thermal stress on the pressure tube and to reduce the heat losses from the active channel. In fact, otherwise, the heat losses would have been very intensive if the water of the reactor pool, with a temperature of 50◦C, directly touches the outside wall surface of pressure tube.
Therefore, even if the thickness of air gap is only 3.5 mm, it is able to reduce the heat transfer from the pressure tube to the water pool and to guarantee the achievement of the prefixed targets without increasing the electrical power. The Appendix B is dedicated to study the heat transfer through the enclosure space air gap. In fact, due to the high different of the temperatures, among pressure tube surface and aluminum receiver, should be consider even the convection and radiation phenomena.
An other main different, respect the out of pile configuration, is regarding the effect of the LVR-15 reactor on the active channel. The LVR-15 is 10 MW pool-type LWR research reactor. It was built in 1989 through reconstruction of a VVR-S reactor, the reactor vessel was replaced (aluminum for stainless steel), as well as core components and reactor instrumentation. The reactor uses Russian IRT-4M fuel enriched to 19.75% U235 (level of enrichment under the limit of 20% imposed by the IAEA for classified low enriched uranium [7]); the fuel assemblies are sandwich-like type, with a uranium meat consisting of a UO2 dispersion and aluminum powder.
The assemblies are composed of tubes with a square cross-section, concentrically ar-ranged in six and eight-tube assemblies. The fuel assembly is sealed with aluminum caps on both ends. The fuel cladding is also aluminum. The fuel assembly is 800 mm long, with the active fuel length of 600 mm long. As a moderator and coolant the LVR-15 reactor used demineralised water while the reflector is composed of a water, or beryllium block, depending on the operation configuration. The Figure 2.6 reports the core map of the reactor. Other technical parameters of the LVR-15 reactor are reported in the Table 2.1.
Figure 2.6: LVR-15 core cartogram.
Nowadays the reactor is utilized for different project as basic and extended materi-als research; corrosion tests of primary circuit and internal structural materimateri-als of nuclear power plants in experimental loops and probes; development and production of new radio-pharmaceuticals; production of silicon through neutron doping for the electronic industry; irradiation services and boron neutron capture therapy (BNCT) [8].
Currently the correct position of the active channel is not already decided, but one probable position could be as shown from the previous Figure 2.6. Anyway, it is available the distribution of the maximum γ irradiation along the active channel. The total amount of the power provided by the core and applied on the stainless steel material structure is about 12.7 kW.
Table 2.1: LVR-15 technical parameters. Reactor Vessel
Diameter 2300 mm
Height 5760 mm
Wall thickness 15 mm
Bottom thickness 20 mm
Water volume in the vessel 22 m3 Weight (without water) 7900 kg
Operation Parameters
Max. thermal power 10 MW
Max. thermal neutron flux 1.0 · 1014 n/cm2s
Pressure atmospherics Max. temperature 56◦C Fuel Type IRT-4M Active length 600 mm Cladding Al
Fuel core U2O+Al
Enrichment 19.75% U235 Power control
N.control rods 12
2.3
Major Components of Active Channel
2.3.1 Compressor
In the high temperature helium loop, two compressors provides the correct mass flow rate of the helium at 7 MPa. In addition, due to relative high temperatures at the inlet of the downcomer, the compressor will operate at high temperature of about 200◦C with a mass flow of 0.0105 kg/s. The total length of the compressor component is 615 mm with a maximum width of 255 mm. The maximum pressure is 8 MPa and the nominal torque is 68 Nm. The total pressure drop across the active channel is nominally between 0.17 MPa and 0.19 MPa. In Figure 2.7 it is shown a view of compressor located in the experimental building of Cv-Rez Nuclear Research Center and assembled on the top of the active channel. The next Figure 2.8 reports a view of the helium compressor and its connection with the pressure tube.
2.3.2 Heat Exchanger
The heat exchanger is one of the most important integral component having the function to transfer the heat from the hot fluid to the cold fluid. A generic view of the heat exchanger is shown in Figure 2.9. It consists of 32 pipes in an hexagonal array with an internal diameter of 2.6 mm and with a total length of 3250 mm.
The tube bundle is surrounded by an hexagonal structure which, with the grid spacers, is necessary to maintain the correct rigidity of the structure. The number of the grids is sixteen and their thickness is 3 mm. Moreover, there are the baffles which are designed to support tube bundle. In addition three electricity cables go through the rod bundle to the electrical heater. These cables are used also to permit the access of the instrumentation probes, therefore they are not necessary to create new penetration inside of the active channel and to reduce the helium leakages. At the beginning of the hexagonal box, as shown in Figure 2.10, there are six small ”windows”, which are necessary to permit at helium to flow from raiser channel to shell side of heat exchanger.
2.3.3 Electrical Heater
The electrical heater is composed on five single modules with a total length of 240 mm. Each single module is reported in the Figure 2.11. As shown each modules is characterized by fourteen holes where inside of theme they are located the electrical wires carried by the the three cables described in the previous section. To these wires it is applied the three-phases electrical power and they can generated a maximum power of 10.5 kW. During the downward passage of the helium across the holes it is possible, at the end of the section, archived the maximum temperature 900◦C with the nominal mass flow rate and in in-pile condition. The material used for building the modules is corundum, a particular aluminum oxide mineral. More details about that material are reported in the Appendix A.3.
Figure 2.11: View of heater section.
The helium continue its downward passage and, before to entrance in the test material section, it across the particular cross junction as shown in the Figure 2.12. Its length is 25 mm while the diameter is 33.9 mm. Six small inclined channels, with an internal diameter of 5.0 mm, allow the helium coolant to flow inside the material channel and to heat up the specimen.
That component has the greater pressure drop inside of the active channel due to the combined effects among the particular mechanical geometry and the highest temperature of the helium. For that reason the outer surface is characterized by several fins, which have the purpose the increase the heat transfer surface.
The next Figure 2.13 reports the overview of the complex heater part and material section connected between them by the cross junction.
2.3.4 Cooler
Another integral component of the active channel is the cooler, which transfer the heat to the secondary circuit. The cooler is circumscribed by a relatively small space 42 mm in diameter. In order to achieve the outlet temperature of helium of 210◦C, the secondary circuit is constituted of a tube bent in a U shape and then twisted into a helix; the inner diameter is 5 mm and a wall thickness is 0.5 mm . The entire spiral, including inlet and outlet, is manufactured from one piece as shown in Figure 2.14.
Figure 2.14: Helical tube of the cooler.
The interior helium channel contains a metallic rod with a diameter 18 mm in order to prevent that the helium flow bypasses the cooler through the empty space inside it. The center rod also serves as a handling aid for the entire internal channel assembly. The space between is also used to run necessary measurement thermocouples and power conductors for electrical heating. A generic overview of the assembly helix plus rod is reported in the Figure 2.15.
The second loop is characterized by liquid water at 0.5 MPa with an temperature to the inner section of the cooler of 30◦C and the mass flow rate is 0.112 kg/s. The particular shape of the helix permits to remove the heat from the helium to the water by current and countercurrent flow. In fact, the first passage of the water is characterized by an opposite direction of flow respect to the helium, therefore the heat transfer is by countercurrent condition. Vice versa, during the upward passage of the water, it is relevant the current heat transfer mode. Therefore, with a short length, that cooler has an heat surface such that is able to reduce the helium temperature and to allow to the gas of flowing to the compressor line with the correct temperature of 210◦C. The outlet water temperature of the secondary loop is, during normal conditions, under the saturation point at 0.5 MPa which is 151.73◦C, therefore any boiling effect is avoided.
2.4
Dosing and Helium Purification System
In this section it is briefly described the main purpose of the dose and purification system. The helium purification system is also closely connected to proper dosing and measurement of impurities in the primary system [9]. The sources of impurities can be the following: residual content of impurities in helium and in structural materials from the manufacturing process, penetration of air, lubricants and other media from the secondary circuits, etc. Impurities may further react with one another and/or with the graphite core of the reactor, which can lead to the origin of other types of impurities.
The purification system is connected in parallel to the active channel and its main mass flow rate is about 3.6 kg/h.
The purification steps are arranged as follows:
• Helium is cooled from 210◦C (temperature at the outlet of the active channel) to 100◦C;
• Helium passes through two mechanical filters where particles larger than 5 µPa of corrosion products (including radioactive particles 60Co, 59Fe in case of in-pile op-eration) and dust are removed;
• Helium is heated by an electrical heater to 250◦C and it passes through a catalytic oxidizer with CuO where H2, tritium and CO are converted to water and CO2; • A mechanical filter is placed behind the oxidizer for capturing possible corrosion
products formed in the heater and the oxidizer;
• He is cooled in the cooler to 50◦C and passes through the molecular sieve where water and CO2 are removed;
• He enters the low temperature adsorber. The adsorber is cooled by a two-stage cooling system: down to −70◦C by a cooling compressor and from −70◦C to ap-proximately −160◦C by liquid nitrogen. Here, the system removes the remaining CH4, N2 and other impurities non-retained in the preceding steps.
• A heater is placed behind the low temperature adsorber where helium is heated to 20◦C. Helium passes then through a third mechanical filter and it is heated up to 130◦C in a regeneration exchanger before returning to the active channel.
The proper functions of the helium purification system shall be verified; the main operating parameters of interest are, e.g. the optimal size of adsorbers and filters, the optimal flow rate, and temperature and the type of a molecular sieve. CO4, O2, H2, H2O, N2and possibly other impurities shall be dosed through dosing valves and the dosing vessel into the helium circuit. Water is dosed by injecting a small amounts of liquid water into hot helium. The following pictures show some important components of chemical system.
(a) Low temperature absorber
(b) Molecular sieves
(c) Dispensers of impurities
2.5
Instrumentation Map
The instrumentation map of the facility is shown in Figure 2.17. As previously described, the electrical cables necessary for the heater section are used also for the thermocouples in order to reduce the penetration inside the active channel. For that reason, all temperature sensors are located in the same radial position but at different axial heights.
The following list report the map of the instrumentation installed in the active channel. √
Flow measurements:
• F1 = Mass flow in the dose and Purification system; • F4 = Mass flow bypass compressors;
• F5 = Mass flow through the compressors line; • F5 - F1 = Mass flow through the active channel. √
Pressure measurements:
• P1 = Pressure at the inlet section of the first compressor; • P2 = Pressure between the two compressors;
• P3 = Pressure at the outlet section of the first compressor; √
Thermocouples:
• T1 = Inlet temperature of the shell side of heat exchanger; • T2 = Outlet temperature of the shell side of heat exchanger; • T3 = Temperature at the beginning of test material section; • T4 = Inlet temperature of the pipe side heat exchanger; • T5 = Outlet temperature of the pipe side of heat exchanger; • T6 = Temperature at the of cooler section.
Chapter
3
Theory of Nuclear
Thermal–Hydraulics Code
3.1
The System Code
For over 40 years, the main area of research in the nuclear field has focused on nuclear power plants’ performance during accident conditions. In order to simulate the behavior of water cooled reactors, the nuclear engineering community developed several complex system thermal-hydraulic codes. Nowadays, the most important system codes are:
• ATHLET - Analysis of THermal-hydraulics of LEaks and Transients;
• CATHARE - Code for Analysis of THermal-hydraulics during an Accident of REactor;
• CATHENA - Canadian Algorithm for THermal-hydraulics Network Analysis; • TRACE - TRAC/RELAP Advanced Computational Engine;
• RELAP5 - Reactor Excursion and Leak Analysis Program.
Although many computational tools have been developed, their simplified structure can be described as is shown in Figure 3.1 [10].
Figure 3.1: General structure and key components of the numerical code.
The code is composed of three basic modules (or domains) for the calculation of the different phenomena:
1. Fluid domain; 2. Solid domain; 3. Core domain.
These domains are the main base of code and they are respectively used to solve the balance or conservation equations, the heat conduction or Fourier equation and the neu-tron kinetics as a simplified branch of current neuneu-tron physic. Additional domains are part of the structure and are necessary to extend the potential of the code to study par-ticular phenomena, which may occur in the nuclear power plant. In fact, as it is reported in Figure 3.1, there are modules for chemistry, mechanical, (nuclear) fuel, radiation heat transfer and transport of (non-condensable) gas and of solid (boron) particles. In general, several plant components (e.g. pressurizer, steam generators, pump, etc.) can be modelled
Simplified compact models for those components are also available as special packages. Moreover, another category with the name ”thermal-hydraulics” special model is pre-sented. This package includes the mathematical equations to describe some particular phenomena like countercurrent flow limitations (CCFL), two-phase critical flow (TPCF) etc. The models for state equations, materials properties and constitutive equations are available inside of structure code. After that the numerics and/or a suitable numerical solution algorithm is needed to solve the equations. The so called Control Volume plus Junction (CV + J) approach is adopted. The link among the user and the system code is the nodalization input data. In particular, the user shall translate the information characterizing a system into figures of merit (at the end digital values), which can be ”un-derstood” by the code. Additional information are the boundary and the initial conditions (BIC) and instrumentation and control (I & C) modules.
3.2
The RELAP5 Code
The RELAP5 computer code is a light water reactor transient analysis code developed for the U.S. Nuclear Regulatory Commission (NRC) for use in rulemaking, licensing audit calculations, evaluation of operator guidelines, and as a basis for a nuclear plant analyzer. Specific applications of this capability have included simulations of transients in LWR systems, such as loss of coolant, Anticipated Transients Without Scram (ATWS), and operational transients such as Loss of Feedwater, Loss Of Offsite Power (LOOP), Station Blackout (SBO), and turbine trip. RELAP5 is a highly generic code that, in addition to calculating the behavior of a reactor coolant system during a transient, can be used for simulation of a wide variety of hydraulic and thermal transients in both nuclear and nonnuclear systems involving mixtures of steam, water, noncondensable gas, and solute.
3.3
Hydrodynamic model
The hydrodynamic model and the associated numerical scheme are based on the use of fluid control volumes and junctions to represent the spatial character of the flow.
The control volumes can be viewed as stream tubes having inlet and outlet junctions. The control volume has a direction associated with it that is positive from the inlet to the outlet. Velocities are located at the junctions and are associated with mass and energy
flow between control volumes. Control volumes are connected in series, using junctions to represent a flow path. All internal flow paths, such as recirculation flows, must be explicitly modeled in this way since only single liquid and vapor velocities are represented at a junction. The hydrodynamics model of RELAP5 is mainly based on three balance equations, as follows :
• Mass Continuity
• Momentum Conservation • Energy Conservation
Therefore RELAP5 thermal-hydraulic model solves eight field equations for eight pri-mary dependent variables. The pripri-mary dependent variables are pressure (P ), phasic specific internal energies (Ug, Uf), vapor volume fraction (void fraction)(αg), phasic ve-locities (vg, vf), noncondensable quality (Xn), and boron density (ρb). The independent variables are time (t) and distance (x). Noncondensable quality is defined as the ratio of the noncondensable gas mass to the total gaseous phase mass, i.e., Xn =
Mn (Mn+ Ms) ,where Mn is the mass of noncondensable in the gaseous phase and Ms is the mass of the steam in the gaseous phase. The secondary dependent variables used in the equa-tions are phasic densities (ρg, ρf), phasic temperatures (Tg, Tf), saturation temperature ( Ts), and noncondensable mass fraction in noncondensable gas phase (Xni) for the i-th noncondensable species, i.e.,
Xni= Mni N X i=1 Mni = Mni Mn (3.1)
where Mni is the mass of the i-th noncondensable in the gaseous phase, Mnis the total mass of noncondensable gas in the gaseous phase, and N is the number of noncondensables. The basic two-fluid differential equations that form the basis for the hydrodynamic model are next presented. The differential form of the one-dimensional transient field equations is first presented for a onecomponent system (vapor/liquid system). The modifications necessary to consider noncondensables as a component of the gaseous phase is discussed in the section 3.3.4.
3.3.1 Mass Continuity
The phasic continuity equations are
∂ ∂t (αg ρg) + 1 A ∂ ∂x (αgρg vgA) = Γg (3.2) ∂ ∂t(αf ρf) + 1 A ∂ ∂x (αf ρf vf A) = Γf (3.3) Generally, the flow does not include mass sources or sinks, and overall continuity consideration yields the requirement that the liquid generation term be the negative of the vapor generation, that is,
Γf = −Γg (3.4)
The interfacial mass transfer model assumes that total mass transfer can be partitioned into mass transfer at the vapor/liquid interface in the bulk fluid Γig and mass transfer at the vapor/liquid interface in the boundary layer near the walls Γw, that is,
Γg = Γig+ Γw (3.5)
3.3.2 Momentum Conservation
The phasic conservation of momentum equations are used in an expanded form and in terms of momenta per unit volume using the phasic primitive velocity variables vg and vf. The spatial variation of momentum term is expressed in terms of v2g and vf2. This form has the desirable feature that the momentum equation reduces to Bernoulli’s equations for steady, incompressible, and frictionless flow.
A primary reason for use of the expanded form is that is it more convenient for development of the numerical scheme. The momentum equation for the vapor phase is
αg ρg A ∂vg ∂t + 1 2αg ρg A ∂vg2 ∂x = −αg A ∂P ∂x + αg ρgBxA − (αg ρgA) F W G(vg) + Γg A(vgI− vg) − (αg ρg A) F IG(vg− vf) − C αgαf ρmA ∂(vg− vf) ∂t + vf ∂vg ∂x − vg ∂vf ∂x (3.6)
and for the liquid phase is αf ρf A ∂vg ∂t + 1 2αf ρf A ∂v2 f ∂x = −αf A ∂P ∂x + αf ρf BxA − (αf ρf A) F W F (vf) − Γg A(vf I− vf) − (αf ρf A) F IF (vf− vg) − C αf αgρmA ∂(vf − vg) ∂t + vg ∂vf ∂x − vf ∂vg ∂x (3.7) These equations come from the one-dimensional phasic momentum equations with the following simplifications:
• Reynolds stresses are neglected; • phasic pressures are assumed equal;
• interfacial pressure is assumed equal to the phasic pressures (except for stratified flow);
• covariance terms are universally neglected (unity assumed for covariance multipliers); • interfacial momentum storage is neglected;
• phasic viscous stresses are neglected;
• interface force terms consist of both pressure and viscous stresses;
• normal wall forces are assumed adequately modeled by the variable area momentum flux formulation.
The phasic continuity equations are multiplied by the corresponding phasic velocity, and are subtracted from the momentum equations. The force terms on the right sides of Equation 3.6 and Equation 3.7 are, respectively, the pressure gradient, the body force (i.e., gravity and pump head), wall friction, momentum transfer due to interface mass transfer, interface frictional drag, and force due to virtual mass. The terms F W G and F W F are part of the wall frictional drag, which are linear in velocity, and are products of the friction coefficient, the frictional reference area per unit volume, and the magnitude of the fluid bulk velocity. The interfacial velocity in the interface momentum transfer term is the unit momentum with which phase appearance or disappearance occurs. The coefficients F IG
coefficient) are used for the interface friction drag, depending on the flow regime.
The coefficient of virtual mass is C, where the value depends on the flow regime. In the RELAP5/mod3 coding, however, this term is simplified. In particular, the spatial derivative portion of the term is neglected. The reason for this change is that inaccura-cies in approximating the spatial derivative portion of the term for the relatively coarse nodalizations used in system representations can lead to nonphysical characteristics in the numerical solution. The primary effect of the virtual mass term is on the mixture sound speed; thus, the simplified form is adequate, since critical flows are calculated in RELAP5 using an integral model in which the sound speed is based on an objective formulation for the added mass terms. Conservation of momentum at the interface requires that the force terms associated with interface mass and momentum exchange sum to zero, and is shown as: ΓgA vgI − (αg ρg A) F IG(vg− vf) − C αg αf ρm A ∂(vg− vf) ∂t + − Γg A vf I− (αf ρf A) F IF (vf − vg) − C αf αgρmA ∂(vf− vg) ∂t = 0 (3.8)
where the spatial derivatives have been eliminated as explained above. This particular form for interface momentum balance results from consideration of the momentum equa-tions in unexpanded form. The force terms associated with virtual mass acceleration in Equation 3.8 sum to zero identically as a result of the particular form chosen. In addition, it is usually assumed (although not required by any basic conservation principle) that the interface momentum transfer due to friction and due to mass transfer independently sum to zero, that is,
vgI = vf I = vI (3.9)
and
αg ρg F IG = αf ρf F IF = αg αf ρgρf F I (3.10) These conditions are sufficient to ensure that Equation 3.8 is satisfied.
3.3.3 Energy Conservation
The phasic thermal energy equations are
∂ ∂t (αg ρg Ug) + 1 A ∂ ∂x (αg ρgUgvg A) = −P ∂αg ∂t − P A ∂ ∂x (αg vg A) + Qwg+ Qig+ Γig h∗g+ Γwh 0 g+ DISSg (3.11) ∂ ∂t (αf ρf Uf) + 1 A ∂ ∂x (αf ρf Uf vf A) = −P ∂αf ∂t − P A ∂ ∂x (αf vf A) + Qwf + Qif + Γig h∗f + Γwh 0 f + DISSf (3.12) These equations has the following simplifications:
• Reynolds heat flux is neglected;
• covariance terms are universally neglected (unity assumed for covariance multipliers); • interfacial energy storage is neglected;
• internal phasic heat transfer is neglected.
In the phasic energy equations, Qwg and Qwf are the phasic wall heat transfer rates per unit volume. These phasic wall heat transfer rates satisfy the equation
Q = Qwg+ Qwf (3.13)
where Q is the total wall heat transfer rate to the fluid per unit volume.
The phasic enthalpies (h∗g, h∗f) associated with bulk interface mass transfer in Equation 3.11 and Equation 3.12 are defined in such a way that the interface energy jump conditions at the liquid-vapor interface are satisfied. In particular, the h∗g and h∗f are chosen to be hs
g and hf, respectively, for the case of vaporization and hg and hsg, respectively, for the case of condensation. The same is true for the phasic enthalpies (h0g, h0f) associated with wall (thermal boundary layer) interface mass transfer.
The vapor generation (or condensation) consists of two parts, vapor generation which results from energy exchange (Γig) and vapor generation due to wall heat transfer effects
Each of the vapor generation (or condensation) processes involves interface heat transfer effects. The interface heat transfer terms (Qig and Qif) appearing in Equation 3.11 and Equation 3.20 include heat transfer from the fluid states to the interface due to interface energy exchange in the bulk and in the thermal boundary layer near the wall. The vapor generation (or condensation) rates are established from energy balance considerations at the interface. The phasic energy dissipation terms, DISSg and DISSf, are the sums of wall friction and pump effects. The dissipation effects due to interface mass transfer, interface friction, and virtual mass are neglected. This is a reasonable assumption since these terms are small in magnitude in the energy equation. In the mass and momentum equations, interface mass transfer, interface friction, and virtual mass are important and are not neglected. The wall friction dissipations are defined as
DISS = DISSg+ DISSf (3.14)
where DISS is the energy dissipation.
3.3.4 Noncondensables in the Gas Phase
The basic, two-phase, single-component model just discussed can be extended to include a noncondensable component in the gas phase. The noncondensable component is assumed to move with the same velocity and have the same temperature as the vapor phase, so that
vn= vg (3.15)
and
Tn= Tg (3.16)
where the subscript, n, is used to designate the noncondensable component. The steam/non-condensable mixture conditions can still be nonhomogeneous and nonequilibrium com-pared to the liquid and saturation conditions.
The general approach for inclusion of the noncondensable component consists of assuming that all properties of the gas phase (subscript g) are mixture properties of the steam/non-condensable mixture. The quality, X, is likewise defined as the mass fraction based on the mass of the gas phase. Thus, the two basic continuity equations (Equation 3.2 and Equation 3.3) are unchanged.
However, it is necessary to add an additional mass conservation equation for the total noncondensable component, given by
∂ ∂t(αg ρg Xn) + 1 A ∂ ∂x (αg ρgXnvg A) = 0 (3.17) where Xn= N X i=1 Mni N X i=1 (Mni+ Ms) = Mn Mn+ Ms
Xn= total noncondensable mass fraction in the gas phase Mni = mass of i-th noncondensable gas
Mn = total mass of noncondensable gas in the gaseous phase Ms = mass of steam in the gas phase
N = number of noncondensables.
For each noncondensable specie, the mass conservation equation is
∂ ∂t(αg ρgXnXni) + 1 A ∂ ∂x (αg ρgXnXni vgA) = 0 (3.18)
where Xni is defined in Equation 3.1. Only N-1 of the noncondensable gas specie equations need to be solved since the mass fraction of the N-th specie can be found as the difference between the total noncondensable gas mass fraction and the sum of the N-1 noncondensable gas specie mass fractions. The energy equations are modified to include the sensible interface (direct) heating term Qgf. This term is necessary because the interfacial terms use saturation temperature based on the bulk steam partial pressure rather than saturation temperature based on the local (interface) steam partial pressure. This is another situation in which the assumption of no transverse gradients in the one-dimensional formulation of the conservation equations needs to be supplemented by a special model. The energy field equations have the form
∂ ∂t (αg ρg Ug) + 1 A ∂ ∂x (αg ρgUgvg A) = −P ∂αg ∂t − P A ∂ ∂x (αg vg A)
∂ ∂t (αf ρf Uf) + 1 A ∂ ∂x (αf ρf Uf vf A) = −P ∂αf ∂t − P A ∂ ∂x (αf vf A) + Qwf+ Qif + Γig h∗f+ Γw h 0 f + Qgf + DISSf (3.20) The term Qgf in Equation 3.19 and Equation 3.20 is the sensible heat transfer rate per unit volume. This is the heat transfer at the noncondensable gas-liquid interface, and it represents thermal energy exchange between the bulk fluid states themselves when noncondensable gas is present. This term is given by
Qgf =
(P − Ps
P ) P (Tg− Tf) = Pn
P Hgf (Tg− Tf) (3.21) where Hgf is the sensible (direct) heat transfer coefficient per unit volume. This makes use of Dalton’s law P = Ps− Pn, where Pn is the noncondensable gas partial pressure. The momentum field equations are unchanged when noncondensables are present. In all the equations, the vapor field properties are now evaluated for the steam/noncondensable mixture.
3.4
Heat Structure
Heat structures represent the selected, solid portions of the thermal-hydrodynamic system. Being solid, there is no flow, but the total system response depends on heat transferred between the structures and the fluid, and the temperature distributions in the structures are often important requirements of the simulation.
Modeling capabilities in RELAP5 of heat structures are general and include fuel pins or plates with nuclear or electrical heating, heat transfer across steam generator tubes, and heat transfer from pipe and vessel walls. Heat structures are assumed to be represented by one-dimensional heat conduction in rectangular, cylindrical, or spherical geometry. Surface multipliers are used to convert the unit surface of the one-dimensional calculation to the actual surface of the heat structure. Temperature dependent thermal conductivities and volumetric heat capacities are provided in tabular or functional form either from built-in or user-supplied data.
The integral form of the heat conduction equation is Z Z Z V ρ(T, ~x) ∂T (~x, t) ∂t dV = Z Z S κ(T, ~x) ~∇ T (~x, t) · d ~S + Z Z Z V S(~x, t) dV (3.22)
The boundary conditions applied to the exterior surface have the form
A(T )T (t) + B(T )∂T (t)
∂n = D(T, t) (3.23)
The relative one-dimensional heat conduction in cylindrical geometry is shown in the following Equation. It is assumed in one-dimensional heat conduction that the tempe-rature distribution in the axial or radial direction is the same throughout the structure being modeled and that the linear heat flow is negligible.
ρ Cp ∂T ∂t = 1 r ∂ ∂r r κ∂T ∂r + S(r, t) (3.24)
where T is the temperature, t is the time, r is the radius, S is the internal heat source, ρ Cp is the volumetric heat capacity, and κ is the thermal conductivity.
The Figure 3.2 illustrate placement of mesh points at which temperatures are computed. The mesh point spacing is taken in the positive direction from left to right. A composition is a material with associated thermal conductivity and volumetric heat capacity.
Heat structures can have an internal volumetric heat source that can be used to repre-sent nuclear, gamma, or electrical heating. The source S(r, t) is assumed to be a separable function of space and time.
S(r, t) = Pf Q(r) P (t) (3.25)
where
Pf = a scaling factor
Q(r) = a space distribution function P (t) = power
Chapter
4
Active Channel Model
Development
4.1
Nodalization Scheme
A preliminary study was undertaken to demonstrate the feasibility of the RELAP5/Mod3.3 thermal-hydraulic system code to perform the analysis with helium as primary fluid. Nowadays, as previously described, the helium was implemented inside the code as a noncondensable component in the gas phase. A relevant part of this thesis was to propose and to assess an alternative solution which guarantees the study of the active channel with the helium coolant. An initial approach was to consider the possibility in order to recompile the source file of RELAP5, called ”relap.s” and used in other occasions to the University of Pisa. In fact, the properties of lead, sodium, heavy water, potassium were implemented inside the code. The procedure to generate the modified RELAP5 was based on the implementation of the main properties of the fluid and the convection heat transfer correlations through the Fortran programming language. The code needs the data of thermodynamic properties and the equations, which describe the function of the transport properties (as thermal conductivity, surface tension and dynamic viscosity) at different temperatures. In particular, it was necessary to generate the file ”tpfhe” where were present the thermodynamic properties. Subsequently, previous implementation into the source file of the transport properties, it was necessary to generate the modified version that was called RELAP5 — UNIPI.
Thank to ENEA (Agenzia Nazionale per l’ Efficienza Energetica), it was possible to obtain directly the files of the thermo-physical properties as a function of the temperatures and pressures and the equations adopted for the helium’s transport properties. Therefore, the Fortran file was compiled generating the ”tpfhe” file, where it was present the specific volumes, internal energies, thermal expansion coefficients, isothermal compressibilities, specific heats, and entropies of helium at different temperatures and pressures of the helium. The procedure was concluded when the relap.s file was recompiled with the transport properties and the file ”tpfhe” as main helium data. In the Appendix A.1 are reported the properties of the helium. The next step was the assessment of the RELAP5 — UNIPI in order to understand if the code was able to perform calculations with the new changes. A simple circuit was modeled by one pipe, two time dependent volumes and one time dependent junction, which the mass flow rate it was imposed as a simulation of the compressor. Several analyses were performed by variation of the pressures and temperatures to the inlet section of the pipe, therefore was recorded the helium’s properties as thermal conductivity, dynamic viscosity and density by specific minor edits available in the code. The RELAP5 — UNIPI uses the correct helium properties for pressure less or equal to 226 kPa but the code is not able to give the right properties for higher pressures conditions. In particular the code uses the same properties, calculated at the initial temperature imposed by the time dependent volume, even if, subsequently, the temperatures conditions are changing. Therefore, the code is judged unsuitable to perform the calculations of the active channel at the nominal pressure of 7 MPa. The results of the assessment are reported in the Table 4.1 for the pressure of 226 kPa and in the Table 4.2 for the nominal pressure of the HTHL facility. At the last November 2013 Fall Code Applications and Maintenance Program (CAMP), Mr.Doug Barber presented the ”RELAP5 Status and User Problem Report” with the intention to explain the most recent developmental version 3.3js. In particular, he clarified that the RELAP5 patch 4 version 3.3js ”have been fixed several important bugs respect to the previous versions”, moreover in the code it has been added the ”pure noncondensable cases” [11].
An immediately analysis of the code with the previous analytic problems shows that is able to cover perfectly the helium’s properties at various boundary conditions.
4. Activ e Channel Mo del Dev elopmen t
RELAP5/mod3.3js RELAP5 — UNIPI Data from App. A.1
T ρ µ κ ρ µ κ ρ µ κ
(K) (kg/m3) (µPa · s) (W/m K) (kg/m3) (µPa · s) (W/m K) (kg/m3) (µPa · s) (W/m K)
300 0.366 20.042 0.149 0.362 20.125 0.150 0.362 20.125 0.150 350 0.314 22.324 0.166 0.310 22.411 0.167 0.310 22.410 0.167 400 0.274 24.454 0.182 0.272 25.533 0.184 0.273 25.533 0.185 450 0.244 26.423 0.198 0.241 26.515 0.200 0.241 26.515 0.200 500 0.219 28.332 0.214 0.217 28.387 0.215 0.217 28.387 0.215 550 0.199 30.007 0.229 0.197 30.152 0.230 0.197 30.153 0.230 600 0.183 31.759 0.243 0.181 31.824 0.245 0.180 31.824 0.245 650 0.169 33.373 0.258 0.167 33.445 0.259 0.167 33.445 0.259 700 0.157 34.917 0.272 0.155 34.967 0.273 0.155 34.967 0.275 750 0.146 36.404 0.285 0.144 36.455 0.287 0.144 36.455 0.287 800 0.137 37.844 0.299 0.136 37.863 0.300 0.136 37.862 0.300 850 0.129 39.238 0.312 0.128 39.237 0.313 0.128 39.237 0.313 900 0.122 40.560 0.325 0.120 40.568 0.326 0.120 40.568 0.326 1000 0.110 43.134 0.350 0.108 43.128 0.352 0.108 43.128 0.352 1300 0.084 50.177 0.422 0.083 49.959 0.423 0.083 49.959 0.423 40
4. Activ e Channel Mo del Dev elopmen t
RELAP5/mod3.3js RELAP5 — UNIPI Data from App. A.1
T ρ µ κ ρ µ κ ρ µ κ
(K) (kg/m3) (µPa · s) (W/m K) (kg/m3) (µPa · s) (W/m K) (kg/m3) (µPa · s) (W/m K) 300 11.233 20.126 0.1501 11.234 20.126 0.1501 11.234 20.126 0.150 350 9.6261 22.421 0.1675 9.629 20.126 0.1501 9.629 22.410 0.167 400 8.4291 24.529 0.184 8.426 20.126 0.1501 8.426 24.530 0.184 450 7.482 26.534 0.200 7.489 20.126 0.1501 7.489 26.522 0.200 500 6.745 28.368 0.215 6.741 20.126 0.1501 6.741 28.370 0.215 550 6.128 30.144 0.231 6.127 20.126 0.1501 6.127 30.145 0.231 600 5.616 31.827 0.245 5.617 20.126 0.1501 5.617 31.830 0.2453 650 5.185 33.43 0.261 5.106 20.126 0.1501 5.106 33.425 0.260 700 4.814 34.967 0.274 4.815 20.126 0.1501 4.815 34.967 0.274 750 4.495 36.442 0.287 4.494 20.126 0.1501 4.494 36.443 0.287 800 4.215 37.862 0.298 4.213 20.126 0.1501 4.213 37.860 0.300 850 3.964 39.247 0.313 3.370 20.126 0.1501 3.964 39.245 0.314 900 3.747 40.559 0.326 3.745 20.126 0.1501 3.745 40.570 0.327 1000 3.370 43.134 0.353 3.370 20.126 0.1501 3.370 43.128 0.352 1300 2.595 50.001 0.424 2.592 20.126 0.1501 2.592 50.002 0.424 41
Specific attention is taken in preparing the nodalization of the active channel of the HTHL facility, in particular, it is necessary to underline that the size of the channels of the helium loop is of the order of millimeters and, in some parts, the helium velocities and temperatures are very high. Moreover, the hydrodynamic volumes are set with a value of noncondensable fraction of helium gas equal to 100%, which flows at relative high mass flow rate in the gas phase.
Therefore, the nodalization of the active channel of the HTHL facility is prepared according to the criteria and the advice contained in the RELAP5/Mod3.3 user’s documentation [12]: 1. The length of volumes should be such that all have similar material Courant limits, i.e., flow length divided by velocity about the same. (Expected velocities during the transient must be considered);
2. The volumes should have L
D ≥ 1, expect for special cases such as the bottom of a pressurizer where a smaller L
D is desired to sharpen the emptying characteristic; 3. The total system cannot exceed the computer resources. RELAP5 dynamically
allocates memory based on the requirements of each problem, an most models require memory based on factors such as the number volumes, junction, number of heat structures and the number of mesh, and the number and length of various user input tables.
The scheme of the nodalization of the active channel of the HTHL facility is reported in the next Figure 4.1. As shown, the helium channel is represented through a close loop, which is thermally coupled with the open secondary water circuit through the cooler. In more details, the hydrodynamic part of the nodalization of the active channel is composed by: three time depend volumes, respectively TMDPVOL 101 at the inlet section of the helium loop and TMDPVOL 302 and 309 at the inlet and outlet section of the water circuit; two time dependent junctions, respectively TMDJUN 180, which is used as the helium compressor while the TMDJUN 303 that reproduced the water pump of the secondary circuit; fifteen pipes (PIPE) subdivided into 184 control volumes; fourteen single junctions, one branch (BRANCH) which is necessary to close the nodalization of active channel and fifteen heat structures with a total number of mesh points of 52.
4.2
Model Assumption
4.2.1 Compressor
The helium compressor is simulated by time depend junction and it is indicated with the acronym (TMDPJUN 180); through that hydrodinamic component it is possible to im-pose the phasic mass rate flow or phasic velocity as a function of time. Concerning the the steady state analysis, a constant mass flow rate is forced of 0.0105 kg/s.
In order to set the correct boundary condition needed for the TMDPJUN 180, it is neces-sary to impose an high value of local pressure drop at the junction of the time dependent volume 101 with the branch 203. In fact, this choice guarantees that the helium coolant goes directly from the outlet section of the pipe 095 to the compressor.
Regarding the behavior of time depend junction, it is necessary to emphasize that is not reflects the real behavior of the helium compressor. In fact, it is not able to perform the mechanical inertia of the shaft and the impeller. This aspect becomes very important when it is necessary to simulated specific transient analyses like switch off the compressor. For this reason, it is used an experimental curve which is obtained during previously tests for the out of pile configuration.
4.2.2 Downcomer
The downcomer is simulated with the pipe 001 and it is subdivided into 48 control volumes. The hydraulic diameters, flow areas, vertical angles, roughness and possible concentrate pressure drops are set as main parameters to apply the balance equations. In particular, the channel is characterized by hydraulic diameter of 2.0 mm, flow area of 2.0 mm2 and a roughness of 3.2 µm. The pipe 001 is connected with the riser channel across the single junction 117 where it is applied a factor of 0.75 as the local loss typical used in a bend. The corresponding heat structures is defined and connected to the hydrodynamic com-ponent. Concerning this aspect, it is useful distinguished the configurations of the active channel. In fact, it is used an adiabatic condition along the pressure tube for the out of pile arrangement, therefore any heat transfer phenomena to the environment is simulated. In relation to the the in-pile configuration, the heat structures of the downcomer are di-vided into three layers, respectively, the first of stainless steel with a thickness of 3.5 mm, the second of air with a thickness of 3.5 mm and the last aluminum thickness of 3.0 mm.
As previously described in the the section 3.4, the RELAP5/Mod3.3js code performs the radial conduction across the material; therefore specific attention is taken to study the second layer.
In fact, it is necessary to introduce the concept of thermal conductivity equivalent in order to implement the other heat transfer phenomena (convection and radiation). The theory at the base of this model assumption and its implementations by Matlab code it are re-ported in the Appendix B.
Defined the structure, the following step is decided the boundary condition adopted to sim-ulate the heat transfer to the environment. In particular, it is used a convective boundary condition as function of the heat transfer coefficient (HTC) with the surface temperature. At the beginning section of the downcomer is utilized an HTC from aluminum wall to air of 15 W/m2K with an air temperature of 30◦C, while, for the other parts, an HTC from aluminum wall to water of 18895 W/m2 K with the water temperatures of 50◦C. Into the heat structures of the in-pile configuration it is applied the γ power.
The Figure 4.2 shows the distribution of the relative γ irradiation along the active channel.
0 20 40 60 80 100 120 140 160 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 Height (cm) γrel
The profile of the γ irradiation starts from the bottom of pressure tube and it can be consider relevant for, at least, 1.2 m of height; furthermore the peak of the γ power is located at 30 cm and this height corresponds at the middle of the LVR-15 core. The local volumetric energy generation rate (Γ) is directly proportional to the density of the structural material (ρ), to the maximum specific energy deposited (γmax) and to the relative profile (γrel).
Γ(z) = γrel(z) · γmax· ρ
W m3
(4.1)
γmax= 3000 W/kg f or stainless steel ρ = 8000 kg/m3
The total of the γ power, which is applied at the downcomer channel, is around 7.15 kW, and it is equal to the 56.3% of the total amount of the irradiation power along the active channel.
4.2.3 Riser
The riser channel is modeled through the hydrodynamic pipe 028, which is composed in 46 control volumes. The corresponding hydraulic diameter is 2.0 mm, flow area of 128.8 mm2 and roughness of 3.2 µm. The pipe 028 is connected with the shell side of the heat exchanger across the single junction 129, where it is applied a factor of 0.75 as the local losses typical used in a bend. The riser is thermally coupled with the downcomer channel through the its heat structure. In particular, it is constituted of three materials collocated as a sandwich geometry. The first layer is in stainless steel, after a stagnation helium and the last again in stainless steel. The thickness are, respectively, 0.5 mm, 2.0 mm and 0.5 mm. As for the downcomer, also the heat structure of the rise channel is characterized of the γ heating. Although the size of the stainless steel is not relevant as for the pressure tube, the total of the γ power deposited along the riser channel is 1.6 kW.
4.2.4 Heat Exchanger
The heat exchanger is simulated by means of two pipes, respectively, 051, which represents the shell side, and 087 that is the pipe side. The shell side is characterized by free flow area of 0.43 mm2, while the hydraulic diameter is 3.77 mm. The procedure to calculate the hydrodynamic parameters of the pipe 051 is reported as follows.
• Free flow area shell side Af t = Aht− Np· π 4 · d 2 out = √ 3 2 · D 2 f t− Np· π 4· d 2 out= 0.43 mm2 • Hydraulic Diameter shell side
De= 4 · Af t Pw = 4 · Af t 2√3 · Df t+ Npπ · dout = 3.77 mm
Aht= Total area inside hexagon dout= Outside diameter of tube
Df t= Distance across flats of the hexagon Np= Number of pipes
Along the pipe 051 is applied an energy loss coefficient of the grids of 0.1. Moreover, the shell side is connected with the pipe 059 from the SNGLJUN 131. The energy loss coefficient of the junction is set to k = 1.652, in order to provide the correct local loss due to the change of the areas. Concerning the pipe side of the heat exchanger, it is constituted with 32 pipes with an hydraulic diameter of 2.6 mm, the total free flow area is of 169.8 mm2. The pipe 87 is connected with the cooler section from the junction 149 and with the previous pipe 084 through the junction 149. The energy loss coefficient is set to 0 for the first connection, while for the second connection the local loss is set equal to k = 0.409. The countercurrent heat exchanger is defined when the connection between the first control volume of the pipe side with the last control volume of the shell side in order to define the countercurrent condition is set. That sequence is applied for the all control volumes of the heat exchanger and it is defined for the heat structure of the pipe side. The thickness of the heat structure is 2 mm of stainless steel.
