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Development of neutronic-thermal hydraulic-mechanic-coupled platform for WCCB blanket design for CFETR
Fusion Engineering and Design 137 (2018) 312–324
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Fusion Engineering and Design journal homepage: www.elsevier.com/locate/fusengdes
Development of neutronic-thermal hydraulic-mechanic-coupled platform for WCCB blanket design for CFETR
T
Kecheng Jianga,b, Weiqiang Dingc, Xiaokang Zhanga,b, Jia Lib, Xuebin Maa,b, Kai Huanga, ⁎ Yuetong Luoc, Songlin Liua, a
Institute of Plasma Physics, Chinese Academy of Sciences, Hefei, Anhui, 230031, China University of Science and Technology of China, Hefei, Anhui, 230027, China c Visualization & Cooperative Computing, Hefei University of Technology, Hefei, Anhui, 230009, China b
A R T I C LE I N FO
A B S T R A C T
Keywords: Coupled platform Neutronic–thermal hydraulic–mechanic Fusion blanket
In the conceptual design phase of a fusion blanket, many factors significantly affect the blanket performance, such as material selection, radial layout, coolant channels, neutron wall loading, and heat flux from plasma. The blanket should achieve multiple objectives under any conditions, such as ensuring that the materials temperature is within the allowable range, and the temperature of the breeder is beyond the limit for tritium release; realizing tritium self-sustainability; assuring the ability of the shielding neutrons; and maintaining structural integrity. This indicates that blanket design is an iterative process for obtaining an optimal structure, which involves numerous variables and restricted conditions. Apparently, it would be a challenge to analyze it manually if there is no comprehensive tool encapsulating this process. This work aims to develop an integrated platform that couples neutronics, thermal hydraulics, and mechanics calculation, and many necessary variables are covered. By defining the structure dimensions, materials, and operation conditions on the GUI, it can automatically build the model, create the mesh, apply boundary conditions, process the result data, and transfer them between different types of software. Under the requirements of nuclear–thermal design, the optimal radial layout is initially obtained using the methodology of “predict + verify” with the iterative adjustment of feedback. Then, the 3D structure of a symmetric breeder unit is constructed based on this radial layout. The stiffening components and coolant channels are added for the thermal–mechanical analysis. Finally, optimization of the water cooled ceramic breeder (WCCB) blanket is performed to demonstrate the technical procedure and high working efficiency of this platform.
1. Introduction As an essential in-vessel component in the fusion reactor, the blanket should satisfy a variety of design constrains owing to its harsh operating environment. To achieve continuous operation of the reactor, the blanket is required to breed tritium and collect it to refuel the reactor. In view of thermal hydraulics, the materials temperature should be within the allowable range. Thus, it is necessary to maintain the temperature of the breeder as high as possible to ensure easy release of the tritium for the solid breeder blanket [1]. The pressure drop of the coolant, which determines the efficiency of the thermoelectric conversion, should be controlled as low as possible. In addition, the structural integrity should be ensured under any operating conditions, and this requires maintaining the stress within the allowable range. Moreover, it needs sufficient shielding ability to protect the superconductor magnet
⁎
from neutron radiation. In the blanket conceptual design, there are various factors to consider. The material selection and ratio determine the performance of multiplying neutrons, breeding tritium, and converting neutron kinetic energy to power heat, etc. Nuclear power is the basis for thermal hydraulic analysis and it is mainly affected by the neutron wall loading (NWL), which varies significantly along the poloidal direction in a fusion reactor, and the radial–poloidal geometric dimensions of the blanket. The radial layout includes the thickness of different functional zones, cooling plate arrangement, and coolant operating conditions. It has a great effect on the tritium breeding ratio (TBR), temperature distribution, and capacity of shielding neutrons. Meanwhile, the blanket thermoelectric conversion efficiency is linked to the inlet and outlet coolant temperature, along with the pressure drop. In addition, the spacing of adjacent coolant channels can further affect the material
Corresponding author. E-mail address: [email protected] (S. Liu).
https://doi.org/10.1016/j.fusengdes.2018.10.013 Received 13 June 2018; Received in revised form 11 October 2018; Accepted 11 October 2018 0920-3796/ © 2018 Elsevier B.V. All rights reserved.
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Fig. 1. The WCCB blanket structure.
temperature. The structural stress, especially on the first wall, is closely related to the component design, temperature fields, coolant pressure, and the heat flux from plasma that remains uncertain according to recent studies [1]. Therefore, a large number of variables should be adjusted simultaneously to obtain an optimum design. This indicates that blanket design is an iterative process of multi-variables optimization for multi-objectives, and a reasonable methodology for optimization should be developed. In addition, manual operation of these iterative analyses is challenging, because it involves heavy and repetitive work, such as establishing a detailed 3D geometric model, writing the input file, creating the mesh, applying boundary conditions, and extracting and processing data. Moreover, the result data need to be transported between different codes. For example, neutronics analysis provides thermal hydraulics with the nuclear heating source, and further the mechanics needs the temperature fields, which are obtained from thermal hydraulics. However, data loss can appear easily if it is transported manually. Thus, a comprehensive automatic calculation tool that encapsulates all the variables and the advanced optimization approach is required to improve the efficiency in blanket design. To overcome the aforementioned shortcomings, various assistant codes have been developed with similar characteristics, such as parametric design or graphical user interface (GUI). Y. Gohar et al. developed the first wall/blanket/shield design and optimization system (BSDOS), which is incorporated with several typical geometric models of low dimension (1D and 2D) for pre-design of coupling neutronics and
thermal hydraulics [2]. A 2D nuclear–thermal coupled code named DOHEAT was created by Hiroyasu Utoh et al. [3]. It can deal with models of different blanket concepts and consider the effect of the coolant channel gap on temperature results. In addition, J.C. Jaboulay et al. performed a parametric analysis of the effects of geometry, materials selection, and shield thickness, among other factors, on the neutronics results, including TBR and nuclear heating, using the simplified 1D and 2D neutronics models [4]. This methodology is built into the system code for modelling Tokamak reactor (SYCOMORE), which is based on a modular approach. SYCOMORE includes the blanket design sub-module (the thermal hydraulic and thermo–mechanic pre-design tool) [5]. Besides, it is coupled with the URANIE platform for an optimization purpose [6,7]. Young-Seok Lee et al. developed a web-based simulator for neutronics analysis. In this code, the 3D model can be easily established by employing the point-and-click interface [8]. Moreover, Julien Aubert and P. A. Di Maio et al. developed the Python script file that covers the main geometric parameters of the first wall (FW). This tool can speed up the model creation for parametric thermal–mechanical analysis. Then, the data are transferred to the URANIE Platform for sensitivity analysis [9,10]. Y. Qiu developed an integrated coupling approach, which enables the conversion of CAD and mesh to Monte Carlo (MC) geometry, and the nuclear heating can be transferred to CFD and structural mechanic software [11]. Based on our original nuclear–thermal coupled code for the water cooled ceramic breeder (WCCB) blanket design [12,13], this work 313
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Fig. 3. Framework of this platform.
3. Description of the platform 3.1. General mathematical model of the ceramic blanket design Fig. 2. Work flow of the optimization of tritium breeder.
In the iterative calculation, it is difficult to use the 3D model owing to the complex modeling process. Therefore, a 1D or 2D model will be reasonable, especially given their higher efficiency [18]. In a typical layout, the blanket consists of functional materials generating nuclear power, such as the tritium breeder and neutron multiplier. These materials are divided into multiple zones by CPs that remove the heat. As the material selection and dimension of each zone have a great impact on the blanket performance, these should be adjusted intensively to obtain the optimal layout. Therefore, a design scheme can be expressed as the mathematical model described in Eq. (1).
improves the optimization method for a radial build and adds the function of 3D mechanical analysis while it enriches the GUI design, forming the neutronics–thermal hydraulics–mechanics coupled platform. It is specifically developed for optimizing the 2D radial layout of the WCCB blanket through a nuclear-thermal automatically iterative process, and for building the 3D model for structural analysis. This platform increases the working efficiency and ensures data transmission without losses, realizing the integration of multi-physics design tools.
⎧ B = (z1, z2, ⋅⋅⋅⋅,z n ) z i = (mi , x i , ci, ti ) ⎨ min max 1 n c ⎩ i = (x ⋅⋅⋅⋅⋅x , ti , ti )
2. Description of the WCCB blanket As a candidate blanket for the Chinese fusion engineering test reactor (CFETR) [14], the WCCB blanket is being comprehensively researched in the Institute of Plasma Physics of the Chinese Academy of Sciences (ASIPP) [15,16]. It adopts binary pebble beds of Li2TiO3 and Be12Ti as tritium breeder and primary neutron multiplier, respectively, and reduced activation ferritic–martensitic (RAFM) steel is the structural material [17]. The FW is coated with slight tungsten to protect it from plasma corrosion and erosion. In addition, a small quantity of beryllium (Be) pebble beds function as the secondary neutron multiplier. PWR conditions are applied for the coolant water, namely 15.5 MPa of pressure and inlet/outlet temperature of 285/325 ℃. The typical structure of the WCCB blanket at the equatorial plane is shown in Fig. 1. It mainly consists of FW, cooling plates (CPs), stiffening plates (SPs), side walls (SWs), manifold (M), and back plate (BP). The mixed tritium breeder and beryllium pebbles are filled in the space zones that are formed by the structural frame. The overall dimension is 1482 mm (poloidal) × 800 mm (radial) × 950 mm (toroidal). The FW is designed as a poloidal U-shaped structure. The cross area of the channel is 8 × 8 mm2 and the pitch is 22 mm. In the CPs, the cross area and pitch of the channel is 5 × 5 mm2 and 15 mm, respectively. As shown in Fig. 1 (d), each CP connects with the FW by the manifold and is bended along the poloidal and radial directions. Therefore, the coolant passage is such that it flows successively through the FW and CPs along the radial direction from the front to the back zone. Three SPs are inserted in the gap between the two adjacent CPs to divide the blanket into four spaces along the toroidal direction, and their main function is to enhance the structural strength. In each SP, there are 12 cooling channels internally built to remove the volumetric nuclear heat.
(1)
where z i is the zone; mi is the material type; x i is the dimension in m; ci is the design criteria; and ti is the temperature in ℃. Under the requirements of neutronics and thermal hydraulics, some boundary conditions (Eq. (2)) should be considered simultaneously: 1) The blanket should achieve tritium self-sufficiency, meaning TBR is greater than 1. 2) In each zone, the material temperature should be within the allowable range. Moreover, the temperature of the tritium breeders should be higher than the value that can release tritium to the purge gas system. 3) For a specific blanket, the sum of the sizes of all functional zones is fixed to length L when eliminating the structural components, such as FW and CPs. Thus, blanket design is a complicated multi-variable and multi-objective optimization process.
⎧TBR = f (x1, x2, ..., x n ) ⎪ n ∑ xi = L ⎨ i=1 ⎪timin ≤ ti (x1, x2, ..., x n ) ≤ timax ⎩
(2)
The optimization of the breeder layout is the primary issue, and it is quite difficult because of its multiple constrains regarding thermal hydraulics. Fortunately, the relationship between TBR and breeder temperature is positively related. It indicates that the larger the TBR is, the less CPs, and this will adversely increase the temperature. Therefore, the maximum TBR can be achieved by means of increasing the tritium breeder temperature as high as possible under the upper limits. In addition, because the breeder zones are cooled on both sides by the CPs, the temperature of one zone is little influenced by that in the other zones. This provides the inspiration for the optimization method: it starts inserting the CPs into the breeder zones one by one after the locations of FW and BPs are determined, as shown in Fig. 2. In particularly, for the type of blanket in which the breeder zones are arrayed along the radial direction, this optimization should be conducted 314
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Fig. 4. GUI arrangement.
Fig. 5. GUI edition in Part 2: (a) Materials. (b) Components.
following execution. 3) The methodology to obtain the optimal radial layout is included in the optimization module. 4) The simulation module activates the commercial software and delivers the calculation tasks to be carried out. 5) The data layer collects the data from the GUI, stores the results, and writes them into the file with an eligible format. The GUI windows are composed of eight main parts (Fig. 4). The function of each part is described as follows. Part 1) Before designing the blanket arrangement, the materials and components should be defined in detail. Each mixture contains one or more single materials with separate volume fractions. For example, the beryllium pebble bed is regarded as 80% elementary beryllium and 20% helium. Then, each
serially from the plasma side to the BP side, because the front zones near the plasma have a greater contribution to TBR.
3.2. Framework and GUI Using object-oriented programing in C++, this platform is developed on the VS2010 platform. As shown in Fig. 3, the framework mainly consists of five parts: 1) The GUI layer provides convenience for human–computer interaction, through which the geometry modeling and simulation can be done by simply clicking a button. 2) The project logical layer is used to recognize which features are ready for the 315
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Fig. 6. Flow chart of this platform.
Fig. 8. 2D thermal hydraulic model in the process of nuclear–thermal iterative analysis. Fig. 7. 1D cylinder model of neutronics.
calculation, and the results corresponding to that module will be stored. Part 3) Along the radial direction, each layer contains the thickness, material type, identification number, and composition. These parameters are encapsulated into different objects that can be created and modified. Part 4) In the process of arrangement, optimization, and calculation, the structure information, temperature, and TBR results will be displayed as a geometric figure. Part 5) There are two essential
component can be formed by mixtures with different thickness. For instance, the FW is constituted by 2 mm of elementary tungsten, 3 and 9 mm of RAFM, and 8 mm of a mixture of steel and water (Fig. 5). Part 2) In the CFETR, the blanket is divided in 10 modules that are arranged in a list, through which a specific module can be selected to perform the
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uniformly distributed temperature field can be obtained. Part 8) After the preliminary 2D radial building is optimized, the detailed 3D structure is designed for thermal–mechanical analysis (Fig. 6). The flow chart has two primary functions, as shown in Fig. 6. In Function 1, one specific blanket should be designed firstly, which includes the detailed radial building and 3D structure. Afterwards, the multi-physics analysis is performed continuously, without iteration. In Function 2, there is an optimization iteration on radial building, which just requires a preliminary general radial layout in advance. In the module of coupled nuclear–thermal iteration, the procedures of modeling, meshing, data extracting, processing, and transforming from MCNP to ANSYS are automatically executed based on the initial geometry and operating parameters. In each iterative cycle, the results are sent as feedback to the regulatory system, which adjusts the arrangement of CPs using effective strategies until the optimal layout is obtained. Then, according to this 2D layout, the integral 3D structure of one blanket unit is further built by adding the SPs and coolant channels, which are modeled in the APDL input file that performs the thermal–mechanical analysis. Afterwards, the results are used to determine whether it is necessary to readjust the radial layout and 3D structural building for further thermal–mechanical optimization.
Fig. 9. Linear relationship between temperature and thickness of tritium breeder. Table 1 Design parameters for the WCCB blanket. Design parameters Average NWL (MW/m2) Thermal hydraulics Coolant pressure (MPa) Inlet/outlet temp. (℃) HF from plasma (MW/m2)
0.454
4. Nuclear–thermal calculation 15.5 285/325 0.5
Materials
Composition
Temp. limits (℃)
Tungsten RAFM steel Breeder
100% 100% 14.4% Li2TiO3, 65.6% Be12Ti, and 20% Helium 80% beryllium
1300 550 900
Neutron multiplier Radial length (mm) Poloidal length (mm)
4.1. Modeling and methodology The 3D neutronics model, which contains the in-vacuum vessel components, geometry outline, and exact source distribution, is used to obtain the NWL on each blanket module surrounding the plasma. Instead of using the 3D models to continue performing the nuclear–thermal calculation for optimization, simplified models are adopted to increase the work efficiency. (1) In the neutronics model, the radial layout with homogeneous material in each layer is built in the 1D cylinder model (Fig. 7). It can effectively calculate the power heat, which is normalized to NWL in each cycle loop [18]. (2) In the thermal hydraulic model, the 2D model extended along the poloidal and radial directions is adopted. The coolant flowing scheme corresponds to the typical design of a 3D WCCB blanket, namely, it flows successively through the FW and CPs along the radial direction from the front to the back zone (Fig. 8). With respect to the thermal hydraulic conditions in the 2D model, (1) the heating source results are transferred from the 1D cylinder model to this model and applied in each corresponding radial layer; (2) the conditions of heat flux, velocity inlet, and pressure outlet are imposed as adjustable parameters in correspondence with the design principle. The other outer boundaries, such as the poloidal boundary, are assumed adiabatic.
600 802 1199
parameters, including the total radial length and BP length, that define the initial dimensions. Part 6) The operating conditions are quite different in the various blanket modules owing to the D-shape of the Tokamak reactor. Therefore, to make this platform more flexible and with wider application, the parameters of neutronics and thermal hydraulics are set as the variables that can be changed, including the plasma heat flux, NWL, inlet/outlet temperature, and coolant pressure. Part 7) After optimization with the automatic algorithm, the temperature of the back breeder zone may be too low. Through a slight manual adjustment, the
Fig. 10. Procedure of GUI operation for preliminary radial layout. 317
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Fig. 12. Variation of temperature along the radial direction at different iteration steps.
Table 2 Summary of the optimization results. Steps
1 2 3
Peak temp. (℃)
Thickness (mm)
BZ1
BZ2
BZ3
BZ4
BZ1
BZ2
BZ3
BZ4
899.46 897.95 898.85
4276 897.46 898.1
− 2143.64 900
− − 643.45
55 55 55
593 81 81
− 471 165
− − 295
Fig. 13. Variation of temperature along the poloidal direction at different iteration steps.
quickly by this function, and the corresponding (Xi* , Ti*) can be further calculated. 4) If the difference between Ti and Ti* is verified as small, then Xi* is the optimum thickness for this breeder zone; otherwise, re-fit the linear function by synthesizing the data of (Xi1 , Ti1), ....., (Xik , Tik ), (Xi* , Ti*) , and recycle the iteration until the requirement is achieved. Through this continuous prediction, verification, and function adjustment, the predicted (Xi* , Ti*) converges gradually to the ideal (Xi , Ti ) .
Fig. 11. Temperature field at different iteration steps. (a) Step 1. (b) Step 2. (c) Step 3.
The breeder is divided into multiple zones, and each zone is surrounded by CPs on both sides. After the materials are selected, the positions of the CPs have a profound influence on the temperature field and TBR. To find the optimum positions, there should be numerous iterative cycles between the neutronics and thermal hydraulic calculation. However, to adjust the CPs without effective rules would be an aimless and difficult endeavor. Fortunately, there is an almost linear relation between the thickness X and maximum temperature T for each breeder zone (Fig. 9). Therefore, the methodology of “predict + verify” is proposed to accelerate this process, as follows: 1) For each breeder zone i, firstly create the sample database with X and T, such as (Xi1 , Ti1), ....., (Xik , Tik ) . 2) Synthesize these data in the linear function T = f (X ) using Eq. (3).3) Under the ideal (Xi , Ti ) , Xi* can be predicted
T=
X − Xim Xn − X × Tin + ni × Tim n m Xi − Xim Xi − Xi
(3)
where (Xim , Tim), (Xin , Tin ) are the two results of the sample database (Xi1 , Ti1), ....., (Xik , Tik ) in breeder zone i, in which m ≠ n, 1 ≤ m , n ≤ k . 4.2. Application results and discussion A blanket optimization is performed to illustrate the application procedure of this platform. It is located on the mid equatorial plane. The design constrains are listed in Table 1. Fig. 10 shows the procedure of arranging the preliminary radial layout on the GUI. First, the initial 318
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Fig. 14. Results before the reverse correction. (a) Temperature. (b) Indexes of uniformity.
Fig. 15. Results after the reverse correction. (a) Temperature. (b) Indexes of uniformity.
0.17% and 0.1%. The temperature variation along the poloidal direction (located at the center of BZ1) is shown in Fig. 13. Because the breeder is cooled by coolant on both sides with an U-shaped passage and there is a small difference in water temperature between the two adjacent channels, the temperature increases along the poloidal direction and there is a maximum difference of only 6 ℃. This indicates that the optimized BZ at the front is unaffected by the change in the layout behind, which also verifies the reasonability of this “predict + verify” methodology. To maintain the temperature of the breeder at a high level with the decreasing nuclear power along the radial direction, the thickness of the breeder increases from the plasma side to the back side in the final layout, namely, 55, 81, 165, and 295 mm, respectively.
structural framework is assigned, which is based on the radial and poloidal length and FW, CPs, and BP dimensions. The structure framework holds the tritium breeder on two sides, as shown in Fig. 10 (a). Then, the CPs or Be pebble beds are inserted into the breeder by point and click. As the breeder is designed to separate from the Be, then the Be is placed next to the CPs on the right or left side, and this relative location can be defined. Furthermore, the thickness of each Be pebble bed and the design upper limits of breeder temperature are set up. In this illustration, there are two layers of Be located at the left side of the CPs. In the process of iteration, the temperature fields at different steps are presented in Fig. 11. The CPs are inserted into the BZ successively along the radial direction from the plasma side to the BP side. In the fluid domain, an elbow is established to connect the adjacent CPs. In step 2, two CPs bounded with Be pebble beds in the preliminary radial layout are arranged, but the temperature at BZ3 is still out of the allowable range. Therefore, another CP is adopted in step 3, in which the ultimate results satisfy the requirements. In each cycle loop, the mass flow rate is recalculated automatically based on the thermal balance in Eq. (4). To have a clear understanding of the temperature change during this process, Fig. 12 shows the variation in temperature along the radial direction. In step 1, a flat curve appears in the middle area of BZ2; this is because the temperature has exceeded the maximum identifiable limit of ANSYS. Compared with the breeder temperature, the slope of the temperature change tendency for Be is smaller; this is due to the larger thermal conductivity, which is advantageous for removing heat. Besides, the temperature curve of the same optimized BZ matches consistently with the different steps. For example, the peak temperatures of BZ1 in the three steps are 899.46, 897.95, and 898.85 ℃, respectively, as listed in Table 2, with relative deviations of only
Ptotal = mc ⋅cp⋅(Tin − Tout )
(4)
where Ptotal is the total heat, in W; mc is the mass flow rate, in kg/s; cp is the specific heat of the coolant, in J/(kg∙K); Tin is the coolant inlet temperature, in ℃; and Tout is the coolant outlet temperature, in ℃. The breeders occupy the largest volume fraction and are supported by structural components. Therefore, it is essential to distribute the temperature uniformly, to decrease the thermal stress and release the tritium. However, visual observation on the curve is not a practical method of judging this performance. Therefore, as shown in Eqs. (5)–(8), several mathematical indexes of the variable coefficient TBcv , weighted-variable coefficient TB wcv , maximum deviation TBdmax , and maximum deviation for a breeder TBdi are displayed on this GUI to reflect this uniformity in the final results. As shown in Fig. 14 (a), the peak temperature in the three front breeders reaches the design limit of 900 ℃ because of the design priority, but it is quite lower in BZ4 owing to the limited space left with smaller nuclear heat, which contributes more to the higher deviation of indexes in Fig. 14 (b). 319
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Fig. 16. 3D structural building. (a) Overall view. (b) Top view. (c) Channel arrangement. (d) SPs, SWs.
To overcome this shortcoming of the lower temperature in the back zone, the method of reverse correction is embedded into the algorithm. The temperature increment Δt in this zone is set as parameter for user input, and then the required extra thickness Δl is calculated by Eq. (9). As the total length of all breeders L remains unchanged when the reverse correction is performed (Eq. (10)), this extra thickness should only be contributed from the front breeder zones.
Table 3 Design parameters for this 3D model. Parameters
Values
Dtor (mm) SPs number FW DFW (mm) CP1–CP4 DCP (mm) SPs, SWs WU (mm) DU (mm)
900 3
Channel type (Square or Circle)
Square 25 Square
Δl = (Δt )/ a
18 50 50
n k=1
(6)
max ((t1 − Et ), (t2 − Et ), ..., (tn − Et )) Et
(7)
TBdi = max (ti − Et )/ Et where Et =
σt =
1 n
1 n
n ∑i = 1 ti
n (∑i = 1 li
(8)
is the average temperature of all points t , in ℃;
n
∑i = 1 (ti − Et )2 n ∑i = 1 li
is
the n ∑i = 1 li
standard
)2
k=1
(10)
where Δt is the increment in temperature in the back breeder zone, in ℃; Δl is the extra thickness required, in m; a is the slope of the function between peak temperature and thickness of the breeder, as described in Fig. 9; l′k and lk is the thickness of breeder number k before and after the reverse correction, respectively, in m; and L is the total length of all breeders, in m. There are two alternative strategies for this thickness assignment of the front breeders: a) equal division (see Eq. (11)); b) weighted division, in which the radial dimension of the different breeders is regarded as the weighted factor (see Eq. (12)). As shown in Fig. 15, the temperature of BZ4 is increased by 200–800 ℃ with an increment of 40 mm in thickness. It shows a more uniform distribution of temperature and lower indexes, when compared with Fig. 14.
(5)
σwt × 100% Ewt
TBdmax =
n
∑ l′k= ∑ lk=L
σ TBcv = t × 100% Et
TB wcv =
(9)
Square
deviation; n ∑i = 1 li
× (ti − Ei and σwt = are the Ewt = × ti ) weighted-average temperature and weighted-standard deviation, respectively; and li is the distance from each mesh point in the breeder to the plasma, in m.
Δl = Δl/(m − 1) 320
(11)
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Fig. 17. Temperature field with tungsten. (a) Breeder and Be pebble beds. (b) RAFM steel.
model is built through parametric input on the interface, and the 2D nuclear–thermal results are transferred into this model. This structure is a sliced symmetrical unit at the mid-poloidal location of the integral blanket module [19]. Compared with the 2D model, the SPs and SWs are added to enhance the structural integrity, and cooling channels are inserted to remove the heat. The coolant flow scheme is similar, as it serially passes through the FW, CPs, SPs, and SWs. In addition, the fixed boundary condition is imposed to the nodes lying on the extended back supporting structure (BSS) of 200 mm as mechanical constraints to simulate the real stress environment, as shown in Fig. 16. There are essential variables that are parameterized in the GUI (Table 3), including the toroidal length Dtor , distance of two adjacent channels of the FW and CPs, DFW , and DCPs , and channel number and type (square or circular), along with, inside the SPs and SWs, the width of the U-shaped channel WU and distance of two adjacent U-shaped channels DU . The coolant is assumed to be uniformly distributed in the channels of the same component, and the mass flow rate is calculated according to the total nuclear power. The mechanism of convective heat transfer is applied (Eq. (13)), in which the coolant temperature derives from the 2D results and the heat transfer coefficient is calculated by the widely used Dittus–Boelter function, as expressed in Eqs. (14)–(16). The thermal solid element SOLID70, which has eight nodes with a single degree of temperature freedom at each node, is used for the thermal analysis. Then, the element type is converted into the structural solid
Fig. 18. Comparison of temperature between 2D and 3D models.
Δlk =
lk × Δl m−1
∑k = 1 lk
(12)
where m is the total number of breeder zones; Δl and Δlk are the average assignments of thickness by strategies one and two, respectively, in m; and lk is the thickness of the front breeder k, in m. 5. Thermal–mechanical analysis Based on the optimized radial layout, a 3D thermal–mechanical
Fig. 19. Stress field with tungsten. 321
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Fig. 20. Temperature field without tungsten. (a) Breeder and Be pebble beds. (b) RAFM steel.
Fig. 21. Stress field without tungsten.
Fig. 22. Results of removing CP3. (a) Temperature field. (b) Stress field.
the thermal analysis of the blanket is applied as an imported mechanical load.
element SOLID185, which has eight nodes with three degrees of translations freedom at each node for the thermo-mechanical analysis [20]. The pressure of 15.5 MPa is imposed to the internal surfaces of the blanket cooling channels. The thermal deformation field obtained from
Q = hc⋅(tw − t f ) 322
(13)
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Fig. 23. Results of increasing the channel spacing in CP4. (a) Temperature field. (b) Stress field.
refers to 550 ℃). Fig. 20 shows the temperature field without tungsten. Because the thickness of tungsten is only 2 mm, the temperature of the breeder is almost not affected, but the temperature of the RAFM steel is increased by 20 ℃. The results of von Mises stress meet the requirements (Fig. 21). The peak value of 315 MPa occurs in the FW, and it is located at the junction corner between the FW, SPs and SWs. This is because the FW bears high heat flux from the plasma and coolant flows through the passages. In addition, the contact with the U-shaped channel inside the SPs and SWs further reduces the structural temperature. Thus, the temperature gradient is large in this site, and the stress of 300 MPa appears at the plasma-facing surface. Moreover, the stress of 196 MPa appears at the joint between the SPs and CPs owing to the interactive squeeze between the two components. In the CPs, the radial stress is quite nonuniform, owing to the larger temperature gradient. The maximum stress of the CPs is 174 MPa, and the stress at the corner of the channel is also greater owing to the square design. The following manufacturing design will add a fillet to avoid stress concentration. To increase the temperature of the back breeders, the following scheme is adopted. The former radial layout without CP3 is arranged on the GUI, along with the same channels in the 3D model building. Then, a nuclear–thermal–mechanical cycle loop is performed through Function 1 in Fig. 6. Afterwards, the channel spacing of CP4 is further increased from 18 to 65.8 mm. The 3 (radial) × 4 (toroidal) breeders present uniformly higher temperature distribution, except for the regions on both sides of the third row because of the smaller toroidal dimensions. As the temperature field is changed, the two schemes achieve the maximum stresses of 336 and 375 MPa, respectively, as shown in Figs. 22 and 23. They occur at the joint between CP2 and SWs owing to the interaction and temperature gradient. Removing the CP3 can effectively enlarge the temperature, and the three breeders almost achieve the same peak value of 800 ℃ (Fig. 24). This is beneficial for reducing the structural stress and releasing tritium. However, comparing cases 2 and 3, the increase in channel spacing can achieve only 5 ℃ of increment because the total mass flow rate remains unchanged, and the smaller number of channels inversely means a larger of heat transfer coefficient in each channel.
Fig. 24. Comparison of temperature results. Case 1: before adjustment. Case 2: removing CP3. Case 3: increasing the channel spacing in CP4.
Nu = 0.023⋅Re0.8⋅Pr 0.4
(14)
Re =
ρVDh u
(15)
hc =
Nu⋅λ Dh
(16)
where Q is the heat power transferred by the coolant, in W; hc is the coefficient of convective heat transfer between the coolant and channel wall; tw is the temperature of the channel wall, in ℃; t f is the average temperature of the coolant, in ℃; ρ is the density of the coolant, in kg/ m3; V is the coolant velocity, in m/s; 0.7 ≤ Pr ≤ 120, Re ≥ 104; Dh is the hydraulic diameter of the channel, in m; and λ is the thermal conductivity of the coolant, in W/(m∙K). There are 4 (radial) × 4 (toroidal) regions exhibiting hotspots (Fig. 17). The peak temperatures of the breeder, beryllium, and RAFM steel are 810.5, 550, and 422.5 ℃, respectively. They satisfy the thermal requirements. The temperatures of the two front rows of the breeder consistently match the 2D results. This demonstrates that the methodology of a simplified 2D model for preliminary nuclear–thermal iteration is reasonable. However, the deviation of 40.6% in the back zone is remarkable (Fig. 18). This divergence mainly results from the enhanced cooling performance of the SPs and SWs that have internal channels. As the difference in mechanical properties (such as thermal expansion) between RAFM steel and tungsten is quite large, the maximum von Mises stress of 1040 MPa occurs at the interface between the two materials (Fig. 19). According to the structural requirements of the SDC-IC code [21], it exceeds the upper limit of 3Sm = 351 MPa (which
6. Conclusion and follow up In this study, an integrated platform of neutronics–thermal hydraulics–mechanics is developed as an auxiliary tool to support the WCCB blanket design. The majority of essential variables that affect the blanket performance, such as geometry dimensions, materials, and operating conditions, are encapsulated within a friendly GUI. These variables can be flexibly adjusted to fulfil the requirements. In addition, 323
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by the Chinese National Natural Science Foundation under Grant Nos. 11775256.
the procedures of modeling, meshing, applying boundary conditions, calculating, data processing, and transferring are automatically executed. The tool improves the work efficiency and guarantees the integrity and cohesion of data with different types of software. In the module of nuclear–thermal iteration, simplified models of 1D + 2D are adopted. The optimal radial layout is obtained by an iterative process with the methodology of “predict + verify.” Besides, indexes of uniformity are embedded to mathematically judge whether the temperature is well distributed. Then, the scheme of reverse correction is further applied for this treatment. In the thermal–mechanical module, the parametric variables are designed on the GUI, including toroidal length, channel distance, and number and geometric dimensions of the SPs. Based on the optimal radial layout, a 3D model is built by adding SPs and SWs, along with channels. This model can calculate a more precise temperature field. The optimization is applied on a WCCB blanket to illustrate the operation procedures of this platform. All the nuclear-thermal and mechanical results satisfy the requirements. The temperature of the front breeders in the 3D sliced model consistently matches that of the 2D model, but a larger deviation of 40.6% occurred in the back zone. This is due to the effects of the SP and SW components. The peak temperature of 800 ℃ uniformly distributed in the different breeders is easily achieved through the GUI operation. The maximum stress occurs in the FW owing to the largest temperature gradient among the structural components. Owing to the large difference in mechanical properties (such as thermal expansion) between tungsten and RAFM steel, the peak stresses are 1040 MPa and 315 MPa for the designs with and without tungsten cover, respectively. The following work will be completed. 1) To find out the relationship of experimental results between the 2D and 3D models, and then apply this relationship as the forward adjusting factor in the process of nuclear–thermal iteration. Afterwards, the thermal hydraulic results of the 3D blanket structure can be predicted more precisely through the 2D model. 2) To design the 3D neutronics model that can calculate the NWL on each blanket module according to the geometry of the Tokamak reactor, and then apply it automatically for blanket optimization. 3) For more precise results, this platform should realize grid coupling for the data transferring between the neutronics transportation, CFD, and FEA. 4) For more flexibility, this platform should include other coolant flow schemes (such as parallel flow), rather than the current single serial flow along the radial direction.
References [1] Mohamed Abdou, Neil B. Morley, Sergey Smolentsev, et al., Blanket/first wall challenges and required R&D on the pathway to DEMO, Fusion Eng. Des. 100 (2015) 2–43. [2] Y. Gohar, et al., Fusion Blanket Design and Optimization Techniques, ANL/NE-1505, Argonne N.Lab., 2005. [3] Hiroyasu Utoh, Kenji Tobita, Youji Someya, et al., Development of a two-dimensional nuclear-thermal-coupled analysis code for conceptual blanket design of fusion reactors, Fusion Eng. Des. 86 (2011) 2378–2381. [4] J.-C. Jaboulay, A. Li Puma, J. Martínez, Neutronic predesign tool for fusion power reactors system assessment, Fusion Eng. Des. 88 (2013) 2336–2342. [5] A. Li-Puma, J. Jaboulay, B. Martinb, et al., Development of the breeding blanket and shield model for the fusionpower reactors system SYCOMORE, Fusion Eng. Des. 89 (2014) 1195–1200. [6] L. Di Gallo, C. Reux, F. Imbeaux, et al., Coupling between a multi-physics workflow engine and an optimization framework, Comput. Phys. Commun. 200 (2016) 76–86. [7] URANIE Platform. http://sourceforge.net/projects/uranie/. [8] Young-Seok Lee, Laurent Terzolo, Dong-Su Lee, A tool for blanket design and nuclear analysis based on MCNP code, IEEE Trans. Plasma Sci. 38 (March 3) (2010). [9] Julien Aubert, Giacomo Aiello, Christian Bachmann, et al., Optimization of the first wall for the DEMO water cooled lithium lead blanket, Fusion Eng. Des. 98–99 (2015) 1206–1210. [10] P.A. Di Maio, P. Arena, G. Bongiovì, et al., On the optimization of the first wall of the DEMO water-cooled lithium lead outboard breeding blanket equatorial module, Fusion Eng. Des. 98–99 (2015) 1206–1210. [11] Y. Qiu, L. Lu, U. fischer, et al., Integrated approach for fusion multi-physics coupled analyses based on hybrid CAD and mesh geometries, Fusion Eng. Des. 96-97 (2015) 159–164. [12] Jia Li, Kecheng Jiang, Xiaokang Zhang, et al., Nuclear-thermal-coupled optimization code for the fusion breeding blanket conceptual design, Fusion Eng. Des. 113 (2016) 37–42. [13] K. Jiang, J. Li, X. Zhang, et al., The development and application of one thermalhydraulic program based on ANSYS for design of ceramic breeder blanket of CFETR, J. Fusion Eng. 34 (5) (2015) 1088–1093. [14] Y. Wan, Jiangang Li, Yong Liu, et al., Overview of the present progress and activities on the CFETR, J. Nucl. Fusion 57 (2018) 10200. [15] Songlin Liu, et al., Conceptual design of a water cooled breeder blanket for CFETR, Fusion Eng. Des. 89 (7–8) (2014) 1380–1385. [16] S. Liu, X. Ma, K. Jiang, et al., Conceptual design of the water cooled ceramic breeder blanket for CFETR based on pressurized water cooled reactor technology, J. Fusion Eng. 124 (2017) 865–870. [17] L. Chen, X. Ma, X. Cheng, et al., Theoretical modeling of the effective thermal conductivity of the binary pebble beds for the CFETR-WCCB blanket, J. Fusion Eng. 101 (2015) 148–153. [18] K. Jiang, X. Zhang, Jia Li, et al., Using one hybrid 3D-1D-3D approach for the conceptual design of WCCB blanket for CFETR, J. Fusion Eng. 114 (2017) 57–71. [19] X. Ma, K. Jiang, S. Liu, et al., Thermo-mechanical analysis on the full module of water cooled ceramic breeder blanket for CFETR, J. Fusion Eng. 126 (2018) 116–123. [20] ANSYS 15.0 User’s Guide, November 2013. [21] F. Tavassoli, Fusion Demo Interim Structural Design Criteria (DISDC)/Appendix A Material Design Limit Data/A3.S18E Eurofer Steel, EFDA TASK TW4-TTMS-005D01. CEA Report DMN/DIR/NT/2004-02/A, December 2004.
Acknowledgements This work was supported by the National Magnetic Confinement Fusion Science Program of China under Grants No. 2014GB122000 and
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Fusion Engineering and Design journal homepage: www.elsevier.com/locate/fusengdes
Development of neutronic-thermal hydraulic-mechanic-coupled platform for WCCB blanket design for CFETR
T
Kecheng Jianga,b, Weiqiang Dingc, Xiaokang Zhanga,b, Jia Lib, Xuebin Maa,b, Kai Huanga, ⁎ Yuetong Luoc, Songlin Liua, a
Institute of Plasma Physics, Chinese Academy of Sciences, Hefei, Anhui, 230031, China University of Science and Technology of China, Hefei, Anhui, 230027, China c Visualization & Cooperative Computing, Hefei University of Technology, Hefei, Anhui, 230009, China b
A R T I C LE I N FO
A B S T R A C T
Keywords: Coupled platform Neutronic–thermal hydraulic–mechanic Fusion blanket
In the conceptual design phase of a fusion blanket, many factors significantly affect the blanket performance, such as material selection, radial layout, coolant channels, neutron wall loading, and heat flux from plasma. The blanket should achieve multiple objectives under any conditions, such as ensuring that the materials temperature is within the allowable range, and the temperature of the breeder is beyond the limit for tritium release; realizing tritium self-sustainability; assuring the ability of the shielding neutrons; and maintaining structural integrity. This indicates that blanket design is an iterative process for obtaining an optimal structure, which involves numerous variables and restricted conditions. Apparently, it would be a challenge to analyze it manually if there is no comprehensive tool encapsulating this process. This work aims to develop an integrated platform that couples neutronics, thermal hydraulics, and mechanics calculation, and many necessary variables are covered. By defining the structure dimensions, materials, and operation conditions on the GUI, it can automatically build the model, create the mesh, apply boundary conditions, process the result data, and transfer them between different types of software. Under the requirements of nuclear–thermal design, the optimal radial layout is initially obtained using the methodology of “predict + verify” with the iterative adjustment of feedback. Then, the 3D structure of a symmetric breeder unit is constructed based on this radial layout. The stiffening components and coolant channels are added for the thermal–mechanical analysis. Finally, optimization of the water cooled ceramic breeder (WCCB) blanket is performed to demonstrate the technical procedure and high working efficiency of this platform.
1. Introduction As an essential in-vessel component in the fusion reactor, the blanket should satisfy a variety of design constrains owing to its harsh operating environment. To achieve continuous operation of the reactor, the blanket is required to breed tritium and collect it to refuel the reactor. In view of thermal hydraulics, the materials temperature should be within the allowable range. Thus, it is necessary to maintain the temperature of the breeder as high as possible to ensure easy release of the tritium for the solid breeder blanket [1]. The pressure drop of the coolant, which determines the efficiency of the thermoelectric conversion, should be controlled as low as possible. In addition, the structural integrity should be ensured under any operating conditions, and this requires maintaining the stress within the allowable range. Moreover, it needs sufficient shielding ability to protect the superconductor magnet
⁎
from neutron radiation. In the blanket conceptual design, there are various factors to consider. The material selection and ratio determine the performance of multiplying neutrons, breeding tritium, and converting neutron kinetic energy to power heat, etc. Nuclear power is the basis for thermal hydraulic analysis and it is mainly affected by the neutron wall loading (NWL), which varies significantly along the poloidal direction in a fusion reactor, and the radial–poloidal geometric dimensions of the blanket. The radial layout includes the thickness of different functional zones, cooling plate arrangement, and coolant operating conditions. It has a great effect on the tritium breeding ratio (TBR), temperature distribution, and capacity of shielding neutrons. Meanwhile, the blanket thermoelectric conversion efficiency is linked to the inlet and outlet coolant temperature, along with the pressure drop. In addition, the spacing of adjacent coolant channels can further affect the material
Corresponding author. E-mail address: [email protected] (S. Liu).
https://doi.org/10.1016/j.fusengdes.2018.10.013 Received 13 June 2018; Received in revised form 11 October 2018; Accepted 11 October 2018 0920-3796/ © 2018 Elsevier B.V. All rights reserved.
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Fig. 1. The WCCB blanket structure.
temperature. The structural stress, especially on the first wall, is closely related to the component design, temperature fields, coolant pressure, and the heat flux from plasma that remains uncertain according to recent studies [1]. Therefore, a large number of variables should be adjusted simultaneously to obtain an optimum design. This indicates that blanket design is an iterative process of multi-variables optimization for multi-objectives, and a reasonable methodology for optimization should be developed. In addition, manual operation of these iterative analyses is challenging, because it involves heavy and repetitive work, such as establishing a detailed 3D geometric model, writing the input file, creating the mesh, applying boundary conditions, and extracting and processing data. Moreover, the result data need to be transported between different codes. For example, neutronics analysis provides thermal hydraulics with the nuclear heating source, and further the mechanics needs the temperature fields, which are obtained from thermal hydraulics. However, data loss can appear easily if it is transported manually. Thus, a comprehensive automatic calculation tool that encapsulates all the variables and the advanced optimization approach is required to improve the efficiency in blanket design. To overcome the aforementioned shortcomings, various assistant codes have been developed with similar characteristics, such as parametric design or graphical user interface (GUI). Y. Gohar et al. developed the first wall/blanket/shield design and optimization system (BSDOS), which is incorporated with several typical geometric models of low dimension (1D and 2D) for pre-design of coupling neutronics and
thermal hydraulics [2]. A 2D nuclear–thermal coupled code named DOHEAT was created by Hiroyasu Utoh et al. [3]. It can deal with models of different blanket concepts and consider the effect of the coolant channel gap on temperature results. In addition, J.C. Jaboulay et al. performed a parametric analysis of the effects of geometry, materials selection, and shield thickness, among other factors, on the neutronics results, including TBR and nuclear heating, using the simplified 1D and 2D neutronics models [4]. This methodology is built into the system code for modelling Tokamak reactor (SYCOMORE), which is based on a modular approach. SYCOMORE includes the blanket design sub-module (the thermal hydraulic and thermo–mechanic pre-design tool) [5]. Besides, it is coupled with the URANIE platform for an optimization purpose [6,7]. Young-Seok Lee et al. developed a web-based simulator for neutronics analysis. In this code, the 3D model can be easily established by employing the point-and-click interface [8]. Moreover, Julien Aubert and P. A. Di Maio et al. developed the Python script file that covers the main geometric parameters of the first wall (FW). This tool can speed up the model creation for parametric thermal–mechanical analysis. Then, the data are transferred to the URANIE Platform for sensitivity analysis [9,10]. Y. Qiu developed an integrated coupling approach, which enables the conversion of CAD and mesh to Monte Carlo (MC) geometry, and the nuclear heating can be transferred to CFD and structural mechanic software [11]. Based on our original nuclear–thermal coupled code for the water cooled ceramic breeder (WCCB) blanket design [12,13], this work 313
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Fig. 3. Framework of this platform.
3. Description of the platform 3.1. General mathematical model of the ceramic blanket design Fig. 2. Work flow of the optimization of tritium breeder.
In the iterative calculation, it is difficult to use the 3D model owing to the complex modeling process. Therefore, a 1D or 2D model will be reasonable, especially given their higher efficiency [18]. In a typical layout, the blanket consists of functional materials generating nuclear power, such as the tritium breeder and neutron multiplier. These materials are divided into multiple zones by CPs that remove the heat. As the material selection and dimension of each zone have a great impact on the blanket performance, these should be adjusted intensively to obtain the optimal layout. Therefore, a design scheme can be expressed as the mathematical model described in Eq. (1).
improves the optimization method for a radial build and adds the function of 3D mechanical analysis while it enriches the GUI design, forming the neutronics–thermal hydraulics–mechanics coupled platform. It is specifically developed for optimizing the 2D radial layout of the WCCB blanket through a nuclear-thermal automatically iterative process, and for building the 3D model for structural analysis. This platform increases the working efficiency and ensures data transmission without losses, realizing the integration of multi-physics design tools.
⎧ B = (z1, z2, ⋅⋅⋅⋅,z n ) z i = (mi , x i , ci, ti ) ⎨ min max 1 n c ⎩ i = (x ⋅⋅⋅⋅⋅x , ti , ti )
2. Description of the WCCB blanket As a candidate blanket for the Chinese fusion engineering test reactor (CFETR) [14], the WCCB blanket is being comprehensively researched in the Institute of Plasma Physics of the Chinese Academy of Sciences (ASIPP) [15,16]. It adopts binary pebble beds of Li2TiO3 and Be12Ti as tritium breeder and primary neutron multiplier, respectively, and reduced activation ferritic–martensitic (RAFM) steel is the structural material [17]. The FW is coated with slight tungsten to protect it from plasma corrosion and erosion. In addition, a small quantity of beryllium (Be) pebble beds function as the secondary neutron multiplier. PWR conditions are applied for the coolant water, namely 15.5 MPa of pressure and inlet/outlet temperature of 285/325 ℃. The typical structure of the WCCB blanket at the equatorial plane is shown in Fig. 1. It mainly consists of FW, cooling plates (CPs), stiffening plates (SPs), side walls (SWs), manifold (M), and back plate (BP). The mixed tritium breeder and beryllium pebbles are filled in the space zones that are formed by the structural frame. The overall dimension is 1482 mm (poloidal) × 800 mm (radial) × 950 mm (toroidal). The FW is designed as a poloidal U-shaped structure. The cross area of the channel is 8 × 8 mm2 and the pitch is 22 mm. In the CPs, the cross area and pitch of the channel is 5 × 5 mm2 and 15 mm, respectively. As shown in Fig. 1 (d), each CP connects with the FW by the manifold and is bended along the poloidal and radial directions. Therefore, the coolant passage is such that it flows successively through the FW and CPs along the radial direction from the front to the back zone. Three SPs are inserted in the gap between the two adjacent CPs to divide the blanket into four spaces along the toroidal direction, and their main function is to enhance the structural strength. In each SP, there are 12 cooling channels internally built to remove the volumetric nuclear heat.
(1)
where z i is the zone; mi is the material type; x i is the dimension in m; ci is the design criteria; and ti is the temperature in ℃. Under the requirements of neutronics and thermal hydraulics, some boundary conditions (Eq. (2)) should be considered simultaneously: 1) The blanket should achieve tritium self-sufficiency, meaning TBR is greater than 1. 2) In each zone, the material temperature should be within the allowable range. Moreover, the temperature of the tritium breeders should be higher than the value that can release tritium to the purge gas system. 3) For a specific blanket, the sum of the sizes of all functional zones is fixed to length L when eliminating the structural components, such as FW and CPs. Thus, blanket design is a complicated multi-variable and multi-objective optimization process.
⎧TBR = f (x1, x2, ..., x n ) ⎪ n ∑ xi = L ⎨ i=1 ⎪timin ≤ ti (x1, x2, ..., x n ) ≤ timax ⎩
(2)
The optimization of the breeder layout is the primary issue, and it is quite difficult because of its multiple constrains regarding thermal hydraulics. Fortunately, the relationship between TBR and breeder temperature is positively related. It indicates that the larger the TBR is, the less CPs, and this will adversely increase the temperature. Therefore, the maximum TBR can be achieved by means of increasing the tritium breeder temperature as high as possible under the upper limits. In addition, because the breeder zones are cooled on both sides by the CPs, the temperature of one zone is little influenced by that in the other zones. This provides the inspiration for the optimization method: it starts inserting the CPs into the breeder zones one by one after the locations of FW and BPs are determined, as shown in Fig. 2. In particularly, for the type of blanket in which the breeder zones are arrayed along the radial direction, this optimization should be conducted 314
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Fig. 4. GUI arrangement.
Fig. 5. GUI edition in Part 2: (a) Materials. (b) Components.
following execution. 3) The methodology to obtain the optimal radial layout is included in the optimization module. 4) The simulation module activates the commercial software and delivers the calculation tasks to be carried out. 5) The data layer collects the data from the GUI, stores the results, and writes them into the file with an eligible format. The GUI windows are composed of eight main parts (Fig. 4). The function of each part is described as follows. Part 1) Before designing the blanket arrangement, the materials and components should be defined in detail. Each mixture contains one or more single materials with separate volume fractions. For example, the beryllium pebble bed is regarded as 80% elementary beryllium and 20% helium. Then, each
serially from the plasma side to the BP side, because the front zones near the plasma have a greater contribution to TBR.
3.2. Framework and GUI Using object-oriented programing in C++, this platform is developed on the VS2010 platform. As shown in Fig. 3, the framework mainly consists of five parts: 1) The GUI layer provides convenience for human–computer interaction, through which the geometry modeling and simulation can be done by simply clicking a button. 2) The project logical layer is used to recognize which features are ready for the 315
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Fig. 6. Flow chart of this platform.
Fig. 8. 2D thermal hydraulic model in the process of nuclear–thermal iterative analysis. Fig. 7. 1D cylinder model of neutronics.
calculation, and the results corresponding to that module will be stored. Part 3) Along the radial direction, each layer contains the thickness, material type, identification number, and composition. These parameters are encapsulated into different objects that can be created and modified. Part 4) In the process of arrangement, optimization, and calculation, the structure information, temperature, and TBR results will be displayed as a geometric figure. Part 5) There are two essential
component can be formed by mixtures with different thickness. For instance, the FW is constituted by 2 mm of elementary tungsten, 3 and 9 mm of RAFM, and 8 mm of a mixture of steel and water (Fig. 5). Part 2) In the CFETR, the blanket is divided in 10 modules that are arranged in a list, through which a specific module can be selected to perform the
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uniformly distributed temperature field can be obtained. Part 8) After the preliminary 2D radial building is optimized, the detailed 3D structure is designed for thermal–mechanical analysis (Fig. 6). The flow chart has two primary functions, as shown in Fig. 6. In Function 1, one specific blanket should be designed firstly, which includes the detailed radial building and 3D structure. Afterwards, the multi-physics analysis is performed continuously, without iteration. In Function 2, there is an optimization iteration on radial building, which just requires a preliminary general radial layout in advance. In the module of coupled nuclear–thermal iteration, the procedures of modeling, meshing, data extracting, processing, and transforming from MCNP to ANSYS are automatically executed based on the initial geometry and operating parameters. In each iterative cycle, the results are sent as feedback to the regulatory system, which adjusts the arrangement of CPs using effective strategies until the optimal layout is obtained. Then, according to this 2D layout, the integral 3D structure of one blanket unit is further built by adding the SPs and coolant channels, which are modeled in the APDL input file that performs the thermal–mechanical analysis. Afterwards, the results are used to determine whether it is necessary to readjust the radial layout and 3D structural building for further thermal–mechanical optimization.
Fig. 9. Linear relationship between temperature and thickness of tritium breeder. Table 1 Design parameters for the WCCB blanket. Design parameters Average NWL (MW/m2) Thermal hydraulics Coolant pressure (MPa) Inlet/outlet temp. (℃) HF from plasma (MW/m2)
0.454
4. Nuclear–thermal calculation 15.5 285/325 0.5
Materials
Composition
Temp. limits (℃)
Tungsten RAFM steel Breeder
100% 100% 14.4% Li2TiO3, 65.6% Be12Ti, and 20% Helium 80% beryllium
1300 550 900
Neutron multiplier Radial length (mm) Poloidal length (mm)
4.1. Modeling and methodology The 3D neutronics model, which contains the in-vacuum vessel components, geometry outline, and exact source distribution, is used to obtain the NWL on each blanket module surrounding the plasma. Instead of using the 3D models to continue performing the nuclear–thermal calculation for optimization, simplified models are adopted to increase the work efficiency. (1) In the neutronics model, the radial layout with homogeneous material in each layer is built in the 1D cylinder model (Fig. 7). It can effectively calculate the power heat, which is normalized to NWL in each cycle loop [18]. (2) In the thermal hydraulic model, the 2D model extended along the poloidal and radial directions is adopted. The coolant flowing scheme corresponds to the typical design of a 3D WCCB blanket, namely, it flows successively through the FW and CPs along the radial direction from the front to the back zone (Fig. 8). With respect to the thermal hydraulic conditions in the 2D model, (1) the heating source results are transferred from the 1D cylinder model to this model and applied in each corresponding radial layer; (2) the conditions of heat flux, velocity inlet, and pressure outlet are imposed as adjustable parameters in correspondence with the design principle. The other outer boundaries, such as the poloidal boundary, are assumed adiabatic.
600 802 1199
parameters, including the total radial length and BP length, that define the initial dimensions. Part 6) The operating conditions are quite different in the various blanket modules owing to the D-shape of the Tokamak reactor. Therefore, to make this platform more flexible and with wider application, the parameters of neutronics and thermal hydraulics are set as the variables that can be changed, including the plasma heat flux, NWL, inlet/outlet temperature, and coolant pressure. Part 7) After optimization with the automatic algorithm, the temperature of the back breeder zone may be too low. Through a slight manual adjustment, the
Fig. 10. Procedure of GUI operation for preliminary radial layout. 317
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Fig. 12. Variation of temperature along the radial direction at different iteration steps.
Table 2 Summary of the optimization results. Steps
1 2 3
Peak temp. (℃)
Thickness (mm)
BZ1
BZ2
BZ3
BZ4
BZ1
BZ2
BZ3
BZ4
899.46 897.95 898.85
4276 897.46 898.1
− 2143.64 900
− − 643.45
55 55 55
593 81 81
− 471 165
− − 295
Fig. 13. Variation of temperature along the poloidal direction at different iteration steps.
quickly by this function, and the corresponding (Xi* , Ti*) can be further calculated. 4) If the difference between Ti and Ti* is verified as small, then Xi* is the optimum thickness for this breeder zone; otherwise, re-fit the linear function by synthesizing the data of (Xi1 , Ti1), ....., (Xik , Tik ), (Xi* , Ti*) , and recycle the iteration until the requirement is achieved. Through this continuous prediction, verification, and function adjustment, the predicted (Xi* , Ti*) converges gradually to the ideal (Xi , Ti ) .
Fig. 11. Temperature field at different iteration steps. (a) Step 1. (b) Step 2. (c) Step 3.
The breeder is divided into multiple zones, and each zone is surrounded by CPs on both sides. After the materials are selected, the positions of the CPs have a profound influence on the temperature field and TBR. To find the optimum positions, there should be numerous iterative cycles between the neutronics and thermal hydraulic calculation. However, to adjust the CPs without effective rules would be an aimless and difficult endeavor. Fortunately, there is an almost linear relation between the thickness X and maximum temperature T for each breeder zone (Fig. 9). Therefore, the methodology of “predict + verify” is proposed to accelerate this process, as follows: 1) For each breeder zone i, firstly create the sample database with X and T, such as (Xi1 , Ti1), ....., (Xik , Tik ) . 2) Synthesize these data in the linear function T = f (X ) using Eq. (3).3) Under the ideal (Xi , Ti ) , Xi* can be predicted
T=
X − Xim Xn − X × Tin + ni × Tim n m Xi − Xim Xi − Xi
(3)
where (Xim , Tim), (Xin , Tin ) are the two results of the sample database (Xi1 , Ti1), ....., (Xik , Tik ) in breeder zone i, in which m ≠ n, 1 ≤ m , n ≤ k . 4.2. Application results and discussion A blanket optimization is performed to illustrate the application procedure of this platform. It is located on the mid equatorial plane. The design constrains are listed in Table 1. Fig. 10 shows the procedure of arranging the preliminary radial layout on the GUI. First, the initial 318
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Fig. 14. Results before the reverse correction. (a) Temperature. (b) Indexes of uniformity.
Fig. 15. Results after the reverse correction. (a) Temperature. (b) Indexes of uniformity.
0.17% and 0.1%. The temperature variation along the poloidal direction (located at the center of BZ1) is shown in Fig. 13. Because the breeder is cooled by coolant on both sides with an U-shaped passage and there is a small difference in water temperature between the two adjacent channels, the temperature increases along the poloidal direction and there is a maximum difference of only 6 ℃. This indicates that the optimized BZ at the front is unaffected by the change in the layout behind, which also verifies the reasonability of this “predict + verify” methodology. To maintain the temperature of the breeder at a high level with the decreasing nuclear power along the radial direction, the thickness of the breeder increases from the plasma side to the back side in the final layout, namely, 55, 81, 165, and 295 mm, respectively.
structural framework is assigned, which is based on the radial and poloidal length and FW, CPs, and BP dimensions. The structure framework holds the tritium breeder on two sides, as shown in Fig. 10 (a). Then, the CPs or Be pebble beds are inserted into the breeder by point and click. As the breeder is designed to separate from the Be, then the Be is placed next to the CPs on the right or left side, and this relative location can be defined. Furthermore, the thickness of each Be pebble bed and the design upper limits of breeder temperature are set up. In this illustration, there are two layers of Be located at the left side of the CPs. In the process of iteration, the temperature fields at different steps are presented in Fig. 11. The CPs are inserted into the BZ successively along the radial direction from the plasma side to the BP side. In the fluid domain, an elbow is established to connect the adjacent CPs. In step 2, two CPs bounded with Be pebble beds in the preliminary radial layout are arranged, but the temperature at BZ3 is still out of the allowable range. Therefore, another CP is adopted in step 3, in which the ultimate results satisfy the requirements. In each cycle loop, the mass flow rate is recalculated automatically based on the thermal balance in Eq. (4). To have a clear understanding of the temperature change during this process, Fig. 12 shows the variation in temperature along the radial direction. In step 1, a flat curve appears in the middle area of BZ2; this is because the temperature has exceeded the maximum identifiable limit of ANSYS. Compared with the breeder temperature, the slope of the temperature change tendency for Be is smaller; this is due to the larger thermal conductivity, which is advantageous for removing heat. Besides, the temperature curve of the same optimized BZ matches consistently with the different steps. For example, the peak temperatures of BZ1 in the three steps are 899.46, 897.95, and 898.85 ℃, respectively, as listed in Table 2, with relative deviations of only
Ptotal = mc ⋅cp⋅(Tin − Tout )
(4)
where Ptotal is the total heat, in W; mc is the mass flow rate, in kg/s; cp is the specific heat of the coolant, in J/(kg∙K); Tin is the coolant inlet temperature, in ℃; and Tout is the coolant outlet temperature, in ℃. The breeders occupy the largest volume fraction and are supported by structural components. Therefore, it is essential to distribute the temperature uniformly, to decrease the thermal stress and release the tritium. However, visual observation on the curve is not a practical method of judging this performance. Therefore, as shown in Eqs. (5)–(8), several mathematical indexes of the variable coefficient TBcv , weighted-variable coefficient TB wcv , maximum deviation TBdmax , and maximum deviation for a breeder TBdi are displayed on this GUI to reflect this uniformity in the final results. As shown in Fig. 14 (a), the peak temperature in the three front breeders reaches the design limit of 900 ℃ because of the design priority, but it is quite lower in BZ4 owing to the limited space left with smaller nuclear heat, which contributes more to the higher deviation of indexes in Fig. 14 (b). 319
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Fig. 16. 3D structural building. (a) Overall view. (b) Top view. (c) Channel arrangement. (d) SPs, SWs.
To overcome this shortcoming of the lower temperature in the back zone, the method of reverse correction is embedded into the algorithm. The temperature increment Δt in this zone is set as parameter for user input, and then the required extra thickness Δl is calculated by Eq. (9). As the total length of all breeders L remains unchanged when the reverse correction is performed (Eq. (10)), this extra thickness should only be contributed from the front breeder zones.
Table 3 Design parameters for this 3D model. Parameters
Values
Dtor (mm) SPs number FW DFW (mm) CP1–CP4 DCP (mm) SPs, SWs WU (mm) DU (mm)
900 3
Channel type (Square or Circle)
Square 25 Square
Δl = (Δt )/ a
18 50 50
n k=1
(6)
max ((t1 − Et ), (t2 − Et ), ..., (tn − Et )) Et
(7)
TBdi = max (ti − Et )/ Et where Et =
σt =
1 n
1 n
n ∑i = 1 ti
n (∑i = 1 li
(8)
is the average temperature of all points t , in ℃;
n
∑i = 1 (ti − Et )2 n ∑i = 1 li
is
the n ∑i = 1 li
standard
)2
k=1
(10)
where Δt is the increment in temperature in the back breeder zone, in ℃; Δl is the extra thickness required, in m; a is the slope of the function between peak temperature and thickness of the breeder, as described in Fig. 9; l′k and lk is the thickness of breeder number k before and after the reverse correction, respectively, in m; and L is the total length of all breeders, in m. There are two alternative strategies for this thickness assignment of the front breeders: a) equal division (see Eq. (11)); b) weighted division, in which the radial dimension of the different breeders is regarded as the weighted factor (see Eq. (12)). As shown in Fig. 15, the temperature of BZ4 is increased by 200–800 ℃ with an increment of 40 mm in thickness. It shows a more uniform distribution of temperature and lower indexes, when compared with Fig. 14.
(5)
σwt × 100% Ewt
TBdmax =
n
∑ l′k= ∑ lk=L
σ TBcv = t × 100% Et
TB wcv =
(9)
Square
deviation; n ∑i = 1 li
× (ti − Ei and σwt = are the Ewt = × ti ) weighted-average temperature and weighted-standard deviation, respectively; and li is the distance from each mesh point in the breeder to the plasma, in m.
Δl = Δl/(m − 1) 320
(11)
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Fig. 17. Temperature field with tungsten. (a) Breeder and Be pebble beds. (b) RAFM steel.
model is built through parametric input on the interface, and the 2D nuclear–thermal results are transferred into this model. This structure is a sliced symmetrical unit at the mid-poloidal location of the integral blanket module [19]. Compared with the 2D model, the SPs and SWs are added to enhance the structural integrity, and cooling channels are inserted to remove the heat. The coolant flow scheme is similar, as it serially passes through the FW, CPs, SPs, and SWs. In addition, the fixed boundary condition is imposed to the nodes lying on the extended back supporting structure (BSS) of 200 mm as mechanical constraints to simulate the real stress environment, as shown in Fig. 16. There are essential variables that are parameterized in the GUI (Table 3), including the toroidal length Dtor , distance of two adjacent channels of the FW and CPs, DFW , and DCPs , and channel number and type (square or circular), along with, inside the SPs and SWs, the width of the U-shaped channel WU and distance of two adjacent U-shaped channels DU . The coolant is assumed to be uniformly distributed in the channels of the same component, and the mass flow rate is calculated according to the total nuclear power. The mechanism of convective heat transfer is applied (Eq. (13)), in which the coolant temperature derives from the 2D results and the heat transfer coefficient is calculated by the widely used Dittus–Boelter function, as expressed in Eqs. (14)–(16). The thermal solid element SOLID70, which has eight nodes with a single degree of temperature freedom at each node, is used for the thermal analysis. Then, the element type is converted into the structural solid
Fig. 18. Comparison of temperature between 2D and 3D models.
Δlk =
lk × Δl m−1
∑k = 1 lk
(12)
where m is the total number of breeder zones; Δl and Δlk are the average assignments of thickness by strategies one and two, respectively, in m; and lk is the thickness of the front breeder k, in m. 5. Thermal–mechanical analysis Based on the optimized radial layout, a 3D thermal–mechanical
Fig. 19. Stress field with tungsten. 321
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Fig. 20. Temperature field without tungsten. (a) Breeder and Be pebble beds. (b) RAFM steel.
Fig. 21. Stress field without tungsten.
Fig. 22. Results of removing CP3. (a) Temperature field. (b) Stress field.
the thermal analysis of the blanket is applied as an imported mechanical load.
element SOLID185, which has eight nodes with three degrees of translations freedom at each node for the thermo-mechanical analysis [20]. The pressure of 15.5 MPa is imposed to the internal surfaces of the blanket cooling channels. The thermal deformation field obtained from
Q = hc⋅(tw − t f ) 322
(13)
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Fig. 23. Results of increasing the channel spacing in CP4. (a) Temperature field. (b) Stress field.
refers to 550 ℃). Fig. 20 shows the temperature field without tungsten. Because the thickness of tungsten is only 2 mm, the temperature of the breeder is almost not affected, but the temperature of the RAFM steel is increased by 20 ℃. The results of von Mises stress meet the requirements (Fig. 21). The peak value of 315 MPa occurs in the FW, and it is located at the junction corner between the FW, SPs and SWs. This is because the FW bears high heat flux from the plasma and coolant flows through the passages. In addition, the contact with the U-shaped channel inside the SPs and SWs further reduces the structural temperature. Thus, the temperature gradient is large in this site, and the stress of 300 MPa appears at the plasma-facing surface. Moreover, the stress of 196 MPa appears at the joint between the SPs and CPs owing to the interactive squeeze between the two components. In the CPs, the radial stress is quite nonuniform, owing to the larger temperature gradient. The maximum stress of the CPs is 174 MPa, and the stress at the corner of the channel is also greater owing to the square design. The following manufacturing design will add a fillet to avoid stress concentration. To increase the temperature of the back breeders, the following scheme is adopted. The former radial layout without CP3 is arranged on the GUI, along with the same channels in the 3D model building. Then, a nuclear–thermal–mechanical cycle loop is performed through Function 1 in Fig. 6. Afterwards, the channel spacing of CP4 is further increased from 18 to 65.8 mm. The 3 (radial) × 4 (toroidal) breeders present uniformly higher temperature distribution, except for the regions on both sides of the third row because of the smaller toroidal dimensions. As the temperature field is changed, the two schemes achieve the maximum stresses of 336 and 375 MPa, respectively, as shown in Figs. 22 and 23. They occur at the joint between CP2 and SWs owing to the interaction and temperature gradient. Removing the CP3 can effectively enlarge the temperature, and the three breeders almost achieve the same peak value of 800 ℃ (Fig. 24). This is beneficial for reducing the structural stress and releasing tritium. However, comparing cases 2 and 3, the increase in channel spacing can achieve only 5 ℃ of increment because the total mass flow rate remains unchanged, and the smaller number of channels inversely means a larger of heat transfer coefficient in each channel.
Fig. 24. Comparison of temperature results. Case 1: before adjustment. Case 2: removing CP3. Case 3: increasing the channel spacing in CP4.
Nu = 0.023⋅Re0.8⋅Pr 0.4
(14)
Re =
ρVDh u
(15)
hc =
Nu⋅λ Dh
(16)
where Q is the heat power transferred by the coolant, in W; hc is the coefficient of convective heat transfer between the coolant and channel wall; tw is the temperature of the channel wall, in ℃; t f is the average temperature of the coolant, in ℃; ρ is the density of the coolant, in kg/ m3; V is the coolant velocity, in m/s; 0.7 ≤ Pr ≤ 120, Re ≥ 104; Dh is the hydraulic diameter of the channel, in m; and λ is the thermal conductivity of the coolant, in W/(m∙K). There are 4 (radial) × 4 (toroidal) regions exhibiting hotspots (Fig. 17). The peak temperatures of the breeder, beryllium, and RAFM steel are 810.5, 550, and 422.5 ℃, respectively. They satisfy the thermal requirements. The temperatures of the two front rows of the breeder consistently match the 2D results. This demonstrates that the methodology of a simplified 2D model for preliminary nuclear–thermal iteration is reasonable. However, the deviation of 40.6% in the back zone is remarkable (Fig. 18). This divergence mainly results from the enhanced cooling performance of the SPs and SWs that have internal channels. As the difference in mechanical properties (such as thermal expansion) between RAFM steel and tungsten is quite large, the maximum von Mises stress of 1040 MPa occurs at the interface between the two materials (Fig. 19). According to the structural requirements of the SDC-IC code [21], it exceeds the upper limit of 3Sm = 351 MPa (which
6. Conclusion and follow up In this study, an integrated platform of neutronics–thermal hydraulics–mechanics is developed as an auxiliary tool to support the WCCB blanket design. The majority of essential variables that affect the blanket performance, such as geometry dimensions, materials, and operating conditions, are encapsulated within a friendly GUI. These variables can be flexibly adjusted to fulfil the requirements. In addition, 323
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by the Chinese National Natural Science Foundation under Grant Nos. 11775256.
the procedures of modeling, meshing, applying boundary conditions, calculating, data processing, and transferring are automatically executed. The tool improves the work efficiency and guarantees the integrity and cohesion of data with different types of software. In the module of nuclear–thermal iteration, simplified models of 1D + 2D are adopted. The optimal radial layout is obtained by an iterative process with the methodology of “predict + verify.” Besides, indexes of uniformity are embedded to mathematically judge whether the temperature is well distributed. Then, the scheme of reverse correction is further applied for this treatment. In the thermal–mechanical module, the parametric variables are designed on the GUI, including toroidal length, channel distance, and number and geometric dimensions of the SPs. Based on the optimal radial layout, a 3D model is built by adding SPs and SWs, along with channels. This model can calculate a more precise temperature field. The optimization is applied on a WCCB blanket to illustrate the operation procedures of this platform. All the nuclear-thermal and mechanical results satisfy the requirements. The temperature of the front breeders in the 3D sliced model consistently matches that of the 2D model, but a larger deviation of 40.6% occurred in the back zone. This is due to the effects of the SP and SW components. The peak temperature of 800 ℃ uniformly distributed in the different breeders is easily achieved through the GUI operation. The maximum stress occurs in the FW owing to the largest temperature gradient among the structural components. Owing to the large difference in mechanical properties (such as thermal expansion) between tungsten and RAFM steel, the peak stresses are 1040 MPa and 315 MPa for the designs with and without tungsten cover, respectively. The following work will be completed. 1) To find out the relationship of experimental results between the 2D and 3D models, and then apply this relationship as the forward adjusting factor in the process of nuclear–thermal iteration. Afterwards, the thermal hydraulic results of the 3D blanket structure can be predicted more precisely through the 2D model. 2) To design the 3D neutronics model that can calculate the NWL on each blanket module according to the geometry of the Tokamak reactor, and then apply it automatically for blanket optimization. 3) For more precise results, this platform should realize grid coupling for the data transferring between the neutronics transportation, CFD, and FEA. 4) For more flexibility, this platform should include other coolant flow schemes (such as parallel flow), rather than the current single serial flow along the radial direction.
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Acknowledgements This work was supported by the National Magnetic Confinement Fusion Science Program of China under Grants No. 2014GB122000 and
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