Keywords

1 Introduction

Nuclear fusion energy is a kind of ideal new energy, and the reaction product is pollution-free and easy to emit, which is conducive to promoting a zero-carbon future. In 1985, the International Thermonuclear Experimental Reactor (ITER) project was established with the goal of building a thermonuclear fusion test reactor for self-sustaining combustion. The China Fusion Engineering Test Reactor (CFETR) is an independently designed fusion reactor in China and is a transition reactor from the ITER experimental reactor to the Demonstration Fusion Reactor (DEMO), designed to bridge the technology gap between the experimental reactor and the demonstration reactor. The devices in CFETR mainly consist of an external superconducting magnet system (containing toroidal field (TF) coils, central solenoid (CS) coils, and CS model coils), an internal vacuum vessel, and blankets in the vacuum vessel. The fusion reactor blanket is the focus of the CFETR design difficulties, which is divided into shielding blanket and breeder blanket. The shielding blanket is used to prevent neutron leakage, and the breeder blanket plays the roles of tritium breeding, neutron multiplier, and heat conversion. The study in this paper focuses on the breeder blankets.

Many feasible blanket concepts have been proposed in ITER projects, such as HCPB [1] and HCLL [2] in European Union (EU), SWCB [3] and WCCB [4] in Japan, HCSB [5] and HCCR [6] in Korea, HCCB [7] and DFLL [8] in China, etc., while for the CFETR project, three types of blankets are proposed, as: Helium Cooled Solid Breeder blanket (HCSB) [9], Water Cooled Ceramic Breeder blanket (WCCB) [10], and liquid lead-lithium blanket [11], and the design of these three types of blankets is currently being refined.

The development of fusion design requires a large number of material databases with mechanical, physical, and thermodynamic properties, and many countries have long established relatively well-developed material databases. For example, the Japanese Atomic Energy Agency (JAEA) has established the HFIR/ORR irradiated/non-irradiated experimental database [12], the Data-Free-Way database [13], the European Fusion Material properties database [14], the Fusion component failure rate database (FCFR-DB) [15], the EUROfusion RAFM steel database for EUROFER97 steel developed by the European Fusion Center [16], an international fusion materials database established by the International Energy Agency (IEA) [17], a database for nuclear materials management software (FUMDS) established by the FDS team at the Institute of Plasma Physics, Chinese Academy of Sciences (ASIPP) [18], the Nuclear Reactor Material Database (NRMD) [19] by the Chinese Academy of Sciences, and a database for fusion reactor tritium breeder material properties established by the Institute of Physics, Chinese Academy of Sciences.

The fusion reactor blanket is the carrier of the energy conversion function. In order for the coolant to heat the nucleus inside the blanket and transfer the heat to the outside of the blanket, it is necessary to perform flow heat exchange with various materials. The most basic of them is the thermal-hydraulic heat transfer model of coolant and structure, the distribution of neutron nuclear heat, etc. The special model involving thermal-hydraulic phenomena is also important to judge whether the blanket can operate safely during the transient conditions. Therefore, a thermo-hydraulic database was established to provide data and model support for the thermal hydraulic analysis of the CFETR blanket.

Compared with the previous databases for fusion, the thermo-physical property database and the thermo-hydraulic database for CFETR with both thermo-physical property of fusion materials and thermo-hydraulic models are not yet established. Besides, the above databases are not publicly available and the involved datasets are not targeted, so their data applicability does not cover the steady-state and transient conditions in the three types of blankets.

In this work, the thermo-physical property database of fusion material and the thermo-hydraulic database of blankets for CFETR were established as part of the development of the nuclear design and safety analysis code for the blanket system.

2 Introduction of Blankets

Several research teams in China have carried out corresponding blanket design and analysis work for CFETR based on ITER projects, and there are three main types of blanket concept schemes: helium-cooled solid breeder blanket, water-cooled ceramic breeder blanket, and liquid lithium-lead blanket. For CFETR phase I, University of Science and Technology of China (USTC) proposed the HCSB blanket [9], ASIPP proposed the HCCB blanket [20] and WCCB blanket [21, 22], and Southwestern Institute of Physics (SWIP) proposed the HCSB blanket. For the CFETR Phase II, which has much greater power and size than Phase I, SWIP updates the HCCB blanket and ASIPP proposes a new design for WCCB blanket [23]. In this subsection, the structure and coolant flow scheme will be introduced for the HCSB blanket from USTC, the WCCB blanket from ASIPP, and the DFLL blanket proposed by the Institute of Nuclear Energy Safety Technology (INEST-CAS) [24].

2.1 Helium Cooled Solid Breeder Blanket (HCSB)

The structural design of the HCSB blanket proposed by the University of Science and Technology of China is presented. The blanket, as a whole, is divided into 32 equal sectors along the annulus. The angle of each equal division is 11.25°. Each part has 15 groups of blanket modules along the toroidal direction, of which 7 modules from No. 1 to No. 7 are inner blanket modules and 8 modules from No. 8 to No. 15 are outer blanket modules. The radial-polar cross section of the inner blanket is rectangular, while the circumferential-radial cross section is trapezoidal. Due to the different locations, the neutron wall loads of different modules within the blanket vary greatly, and the maximum thermal load is calculated to appear on the inner side of the first wall of module No. 12, which is about 0.473 MW/m2. The structural schematic of this blanket module could refer to reference [9].

Fig. 1.
figure 1

Schematic of the typical blanket module[9] of HCSB

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This typical blanket module is rectangular in shape with the following main components along the radial direction from inside to outside: tungsten tile, first wall, stiffening plate, breeder unit backplate, breeder canister, partition plate, top and bottom caps, backplates, helium inlet and outlet, purge gas inlet and outlet, and four mechanical attachments. A 2 mm thick tungsten plate covers the first wall and protects the inner components from plasma heat flow. The outer backplate has four mechanical attachments to secure the module to the shield blanket and also has an inlet and an outlet for helium gas, an inlet and an outlet for purge gas. The outer backplate and the remaining five backplates, as well as the top and bottom caps and the first wall, enclose the three chambers for the distribution of helium and purge gas (He + 0.1% H2, 0.1 MPa) for tritium. The gas chambers are connected to the breeder zone, which has U-shaped breeder units packed with breeder pebbles of Li4SiO4 for tritium breeder and pebbles of Be for neutron multiplier. The pump pumps the cold helium into the inlet and then into the gas channels in FW. Afterwards, the helium absorbs part of the nuclear heat and enters the pipes in caps as well as the stiffening plates. After absorbing the internal heat of all the plates, it flows into the channels in the backplates, and finally all the helium is gathered and flows out through the outlet, which can take away most of the heat from the structural material.

2.2 Water Cooled Ceramic Breeder Blanket (WCCB)

ASIPP, in collaboration with European Nuclear Energy Agency (ENEA), has proposed a design for a water-cooled ceramic breeder blanket based on the latest design parameters of CFETR Phase II. Similar to the helium-cooled solid blanket, the WCCB can be divided into 16 toroidal sectors.

In each sector, modules from 1# to 6# are the outer blanket area, and modules from 7# to 11# are the inner blanket area. The inner blanket area has 2 identical sub-blankets along the toroidal, and the outer blanket area has 3 identical sub- blankets.

This section describes the structural design of blanket module 3# in WCCB for CFETR-2018 [23]. The outer shell of the blanket is a closed steel box with FW, top and bottom cover plates, and back plates. The first wall is fitted with tungsten tiles on the outside, and the interior is a U-shaped plate bent along the radial-annular direction. 95 square coolant channels are contained inside this plate, each with a cross-sectional area of 8 × 8 mm2 and a pitch of 22 mm between two adjacent channels. Each module contains three stiffening plates (SPs), which separate a blanket module into four sub-modules. Each SP contains 81 U-shaped channels inside, each with a cross-sectional area of 5 × 5 mm2. The cover plate contains 12 U-shaped channels with a square cross-section for removing heat from the module, and the upper and lower cover plates have a total of 16 purge gas channels for gas collection and gas distribution. Each module also has 23 cooling tube assemblies (CTAs) in the breeder zone for heat dissipation. Each assembly contains three coolant channels, toroidal and radial ribs, where the coolant flows and exits at the outlet. The ribs connect the cooling tubes to each other and fix the SPs to the sidewalls, which improves the structural stability and heat transfer performance of the module. The cooling system of the blanket could refer to reference [23]. It can be seen that three independent cooling systems are used in this blanket design scheme: cooling system 1 is mainly responsible for taking away the heat from the structural components such as the FW, CPs, and SPs, while cooling systems 2 and 3 mainly take away the heat from the pebble bed area of the blanket.

2.3 Dual-Functional Lithium-Lead (DFLL)

The dual-functional lithium-lead blanket (DFLL) is designed by the Institute of Nuclear Energy Safety Technology, Chinese Academy of Sciences, with helium and liquid Li-Pb as the coolant and liquid Li-Pb eutectic as the tritium breeder material. The whole blanket is divided into 16 sectors along the toroidal, the inner blanket module is divided into two sub-modules along the toroidal, and the outer blanket module can be divided into three sub-modules. A 2 mm thick tungsten protective layer is set on the surface of the blanket, followed by the first wall (FW), tritium breeder zone (TBZ), helium header (HH), back plate (BP), and shielding blanket (SB).

The structure design of the liquid lithium-lead blanket was shown in reference [24]. It is shaped like a rectangular box, consisting of the first wall (FW, U-shape, 15 mm in thickness), the upper and lower cover plates, and the back plate, with dimensions of 1280 mm (poloidal direction) × 1200 mm (radial direction) × 1300 mm (toroidal direction). Considering the structural stability and internal heat extraction, the toroidal-radial, radial-poloidal, toroidal-poloidal stiffening plates are welded together to form a U-shape and two sets of “7” shaped tritium breeder zones. Square-shaped helium coolant channels (cross-sectional area of 15 × 15 mm2, 20 mm in pitch) are uniformly arranged inside the CPs, the FW and the SPs, and several guide tubes (GTs) with 35 mm in diameter, 5 mm in thickness, 750 mm in length are arranged radially in the U-shaped breeder zones through the FWs and BPs. On the fourth backplate, there are several mechanical attachments, helium inlet and outlet pipes, and liquid Li-Pb inlet and outlet pipes, etc. The backplate is connected to the shielding blanket, which is connected by mechanical attachments, and the thickness of the shielding blanket is 250 mm.

The liquid Li-Pb enters the module at the inlet and is distributed among three sub-channels before flowing into the TBZs. Li-Pb enters the module, flows along the U-shaped channel, and then exits at outlet. At the same time, Li-Pb enters the ‘‘7’’ shaped TBZs from two sub-channels. In reference [24], the Li-Pb enters the module and flows upwards in two parts at the bottom, then converges at the same exit and exits the module at the outlet. The helium enters the first helium stage directly from the inlet tube, flows simultaneously into the FW and GTs, and exits through the FW helium outlet into the second helium stage. Afterwards, the helium flows simultaneously into the coolant channels of the radial-poloidal stiffening plates, the toroidal-poloidal stiffening plates, the toroidal-radial stiffening plates (rpSP, tpSP, trSP) and the cover plates. Finally, the helium is collected in the third stage helium manifold and flows out of the module through the outlet.

3 Databases

3.1 Thermo-Physical Property Database of Blanket Material

The thermo-physical properties for coolant and material are important elements of the fusion reactor database, and the various materials in the normal operating conditions of the blanket and in accident conditions need to be in a safe state, so before analyzing the safety of the blankets it is necessary to establish a material database that meets the temperature and pressure range in fusion reactor. In this section, we introduce the thermo-physical property database of materials under normal and transient conditions for CFETR blanket, mainly introducing the thermal properties of coolant materials, structural materials, breeder materials and PFM materials, as shown in the following Table 1.

Table 1. The materials in thermo-physical property database
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The coolant materials mainly involve H2O, He, and Li-Pb, and in some liquid metal blankets, Li and Flibe are used as coolant or breeder materials. Under special conditions, the first wall ruptures and causes the coolant water to be sprayed into the vacuum vessel, where the coolant reacts with hydrogen to become deuterated water (HTO) or tritium gas (T2), so it is also necessary to consider the thermal properties of HTO and T2. The thermal properties of coolant materials in the database involve density, specific heat capacity, thermal conductivity, kinematic viscosity, Prandtl number, specific enthalpy, latent heat of vaporization, specific entropy, surface tension, isothermal compressibility, etc.

The International Association for the Properties of Water and Steam (IAPWS) introduced the formula for the thermal properties of water and steam in 1997 [25], referred to as the IAWPS-IF97 formula. This formula can be calculated to obtain the thermal properties of water and steam in the range of pressure from 611.153 Pa to 100 MPa and temperature from 273.15 K to 1073.5 K. However, considering that the pressure in the vacuum vessel is close to 0 Pa, the thermal properties of water less than 611.153 Pa will be supplemented by referring to Gothic's theoretical manual [26], from which the thermal property data from 0 to 611.153 Pa can be obtained. Helium is a single phase within the blanket and does not undergo phase changes, and its physical properties are obtained from the National Institute of Standards and Technology (NIST), the International Atomic Energy Agency (IAEA) [27] and other journal supplemental data [28,29,30,31,32]. The current pressure range of helium is from 0 to 15 MPa and the temperature range is from 273.15 to 1273.15 K. The pressure in the liquid metal blanket is relatively low, with the thermal properties of Li-Pb ranging from 273.15K to 1473.15 K and 0 to 1 MPa [27, 33,34,35], and the thermal properties of Li ranging from 473.15 to 1673.15 K and 0.1 to 1 MPa [30, 36]. The melting point of Flibi is 732.15 K, so the current database contains its properties at a temperature greater than 732.15 K [30, 37]. The properties of water (H2O) and HTO are almost identical, and the thermal properties of water can be used directly in the calculations of HTO [38]. Tritium has properties similar to hydrogen except for density [39], and the hydrogen properties can be directly used in the calculations.

The structural material is the basis to ensure the structural stability of the blanket and efficient energy conversion. The structural material of FW in HCSB, WCCB, and DFLL is chosen from Reduced Activation Ferritic/Martensitic steel (RAFM). RAFM steel has higher thermal conductivity and smaller thermal expansion compared with other types of steel, and is the preferred steel type for fusion reactor structural materials in the prospect of better physical and mechanical properties. Among the RAFM steels [40], EUROFER97 steel, F82H steel, JLF1 steel, 9Cr-2WVTa steel and CLAM steel are currently well developed, among which CLAM steel and CLF-1 steel are researched and manufactured in China, while the rest of the steel types come from Europe, Japan and the United States. The current database contains the thermal properties of EUROFER97 [41], F82H [42], JLF-1 [42], CLF-1, and CLAM [43]. The oxygen-free copper wire as reinforcement material mainly serves to strengthen the mechanical properties of the sub-cable and increase the stability of the conductor. Due to their excellent thermal conductivity, the copper alloys are used as heat sinks in the high heat flow region of ITER. The CuCrZr-IG alloy has good thermal conductivity and is generally used as a structural and heat conduction material for divertors. Oxide dispersion-strengthened alloy (ODS) is a material formed on the basis of martensitic and ferritic steels that can withstand high neutron fluxes and has high temperature creep resistance. While conventional ferritic/martensitic steels can only reach a maximum working temperature of 550–600 ℃, ODS steels can increase the working temperature to 700 ℃ and are therefore one of the candidates for fusion blanket structure materials. The vacuum vessel design uses ultra-low carbon austenitic stainless steel 316L as the primary material. The database mainly contains the thermal property data of the above materials.

The fusion blanket is equipped with a breeder zone containing tritium breeder materials and neutron multiplier materials, which serve to maintain the fusion reaction by tritium breed and neutron multiplication [44,45,46]. The tritium breeder materials in the solid blanket are mainly Li2TiO3, LiAlO2, Li4SiO2, LiZrO3, and the required neutron multiplier is metallic lead or metallic beryllium, while the tritium breeder materials in liquid blankets are mainly Li, Li-Pb, molten salt, etc., and the required neutron multiplier is Pb. Among the three types of blankets, the breeder zone of HCSB is filled with Li4SiO4 and Be pebble beds, the breeder zone in WCCB is filled with Li2TiO3 and Be12Ti pebble beds, and the DFLL uses liquid Li-Pb eutectic as the breeder material only.

Tungsten is the material for the first wall protection layer facing the plasma in the current fusion blanket. The tungsten could protect the internal components from plasma heat flow and ensure the integrity of the blanket. The physical properties data can be referred to Structural Design Criteria for ITER In-vessel Components (SDC-IC).

Table 2. The models in thermo-hydraulic database
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3.2 Thermo-Hydraulic Database for Blankets

This chapter introduces thermal hydraulic models and special models for three types of blankets, which mainly deals with the models under steady state and transient accidents involved in HCSB, WCCB, and DFLL. The heat transfer models for the single phase of different coolants are presented first, followed by the two-phase boiling heat transfer models. The models in thermo-hydraulic database are listed briefly in Table 2.

Theoretical analysis of the full development of convective heat transfer by laminar flow in pipes is relatively well done and many results have been publicly available [47]. For forced convective heat transfer within a pipe, the longest and most commonly applied correlations are the D-B correlation and its modifications [48], the Gnielinski correlation [49], and the heat transfer formulas for liquid metals [36]. The steady-state conditions in fusion reactor mainly involve single-phase heat transfer, but in some special conditions the pressure in the channel changes, leading to the boiling of the liquid, when the phenomenon of boiling in the tube should be analyzed. Bergles and Rohsenow [50] derived a criterion for the onset of subcooled boiling based on experimental data obtained from several industrial smooth tubes. A more general model to determine the onset of subcooled boiling is Jens-Lottes formula [51], jointly with the single-phase forced convection equation. For nucleation boiling of different liquids, Rohsenow [52] proposed the correlations for calculation of heat flux or boiling temperature difference. Chen correlation [53], with a mechanism that considers both saturated boiling heat transfer and convective heat transfer, is applicable to the whole saturated boiling before DNB. In 1961, Kutateladze [54] proposed the calculation of the two-phase flow heat transfer coefficient for flow boiling by the asymptotic method, and another class of empirical correlations considers the total heat transfer coefficient as consisting of two components, such as the correlations used by Mattson [55]. Such correlations are applicable to both transition boiling and film boiling. There are also some empirical correlations with limited applicability, such as the McDonough correlation [56], the empirical correlations obtained by fitting experimental data of flow boiling proposed by Tran [57] and Lazarek-Black [58], etc. In particular,, for a single-sided heated pipe, Luan Zhenbo [59] proposed the heat transfer correlation for subcooled boiling.

The pressure drop of single-phase liquid between two sections can be calculated by the following equation:

$$ \Delta P = p_{1} - p_{2} = \Delta P_{el} + \Delta P_{a} + \Delta P_{f} + \Delta P_{c} $$
(1)

where, p is the static pressure of the fluid at the given cross-section. ΔPel is the elevation pressure drop caused by the change in height of fluid. ΔPa is the acceleration pressure drop caused by the change in fluid velocity. ΔPf is the pressure loss caused by frictional resistance. ΔPc is the local pressure drop, which should be calculated at the corner of the FW, bent pipe in CPs where the shape of the flow channel changes. The pressure drop model for two-phase flow is as follows:

$$ \Delta p = \Delta p_{E,TP} + \Delta p_{AD,TP} + {\Delta }p_{F,TP} $$
(2)

The terms on the right side are elevation pressure drop, acceleration pressure drop, and friction pressure drop, respectively.

For the two-fluid model of two-phase flow, there are interphase exchanges of mass, momentum, and energy in the boiling condition. In the six-equation model, the interphase mass transfer equation is the key, however, the equations are different in each flow pattern. The interphase heat exchange model in the database is from RELAP [60].

The transient conditions in the fusion blanket involve some special models. The critical flow model of coolant is involved in the break accident of a vacuum vessel, such as the single-phase critical flow model [61, 62] and the two-phase critical flow model [61, 62]. The calculation of the coolant leakage to the vacuum vessel is referred to the GETTHEM code [63]. The reaction rate of the oxidation reaction in the blanket cooling system, which involves the reaction between beryllium metal and water vapor and oxygen, and the oxidation reaction between tungsten metal and water vapor, can be calculated by the model [64,65,66]. The tritium extraction system (TES) is an auxiliary system whose function is to extract tritium from the blanket using the purge gas, and the exchange reaction of HT and HTO is considered as one of the important chemical reactions to obtain tritium from the purge gas, and the reaction rate constant can be calculated by [67, 68]. Flashing occurs at the break of the fusion blanket where the coolant flows from the high pressure region to the low pressure region. GETTHEM considers the special case of high pressure drop model for flashing phenomenon, which could refer to reference [63]. Cheng et al. [69] proposed an effective conduction coefficient model for flash evaporation of droplets by a diffusion-controlled evaporation model with convective heat transfer inside the droplet. Elias and Chambre [70] proposed a phenomenological model for predicting the flash evaporation of fluids during static or flow transients. Assuming that the water jet inside the vacuum vessel begins to evaporate in large quantities after contact with the FW and that the heat flux is distributed equally over the surface of the FW, the pressure of the vacuum vessel can be calculated using the equation [71].

4 The Testings of Database

The data presented above was organized into the database, which needs to be tested to ensure the accuracy of the data. The data or model will be calculated using a code written in Fortran language, and the results will be compared and analyzed with experimental or simulation results.

4.1 Testing of Material Database

Numerical simulations of convective heat transfer for uniform heating tubes were performed in the reference [72] to obtain the heat transfer coefficient of the wall. In this paper, the heat transfer coefficients at the same conditions are derived from the code with data in database, and compared with the reference.

Fig. 2.
figure 2

Comparison of calculated results and values in [72]

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The diameter of the circular tube is 11 mm, the wall is uniformly heated, the pressure is 10 MPa, and the inlet temperature of water is 373.15 K. The heat transfer coefficient between fluid and wall can be calculated for different flow velocities. The dimensions of the circular tube, pressure, and inlet temperature are written into the code, the thermal properties are read and the D-B correlation is selected as the heat transfer model for the calculation of the heat transfer coefficient. The obtained calculation results and results in reference are shown in Fig. 1, where the maximum error is within 6.2%.

4.2 Testing for Thermo-Hydraulic Database

In the reference [73], a thermal analysis of WCCB was carried out, and the RELAP5 code was applied to simplify the typical blanket and perform steady-state calculations to obtain the inlet and outlet temperatures, mass flow rate, and distributions of wall temperature. In this paper, based on the database data and the thermo-hydraulic models, a code was written in Fortran to perform steady-state calculations on the node diagram shown in Fig. 2, and the results were compared and analyzed with the results in reference [73].

The inlet and outlet temperatures of the flow channel, such as nodes 106, 207, 211, 215, 219, etc. in Fig. 3, are calculated by reading the thermal properties of fluid and structure based on the nuclear heat of each part and the fluid temperature at each location obtained from the neutronics analysis. Subsequently, the heat transfer coefficients are calculated based on the temperature distribution of the coolant along the axial height, the heat of the component, the size of the channel, and the mass flow rate, based on empirical correlations to obtain the wall temperature. The calculated results of temperatures on the left of the 2080 component and the left of the 2010 component are compared with the reference [73] as follows.

Fig. 3.
figure 3

The node diagram of WCCB [73]

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Fig. 4.
figure 4

Comparison of temperatures on the left of the 2080 component

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Fig. 5.
figure 5

Comparison of temperatures on the right of the 2010 component

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The comparison results are shown in Fig. 4 and Fig. 5. It can be seen that the overall data is relatively in good agreement, and the error may be caused by the heat flux of wall not being completely uniform.

5 Conclusions

The object of this paper is the three types of CFETR blanket: HCSB, WCCB, and DFLL. The thermal properties of coolant, structural materials, PFM materials, tritium breeder and neutron multiplier materials, the structural characteristics, and the coolant flow scheme in the three types of blanket are introduced, and the thermal hydraulic models and special models are summarized. Finally, based on the database, the data is tested and verified with different cases. The preliminary database has been built and briefly tested. However, the current data is not directly available to the system code without validation, and the data has not been integrated into the subroutines for code. For the thermo-hydraulic models, the applicability for CFETR blankets still needs to be further analyzed. In the future, we will use the system code and the physical property package of a database for testing as well as application evaluation for CFETR blankets.