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Thermal-hydraulic analysis on the whole module of water cooled ceramic breeder blanket for CFETR
Fusion Engineering and Design 112 (2016) 81–88
Contents lists available at ScienceDirect
Fusion Engineering and Design journal homepage: www.elsevier.com/locate/fusengdes
Thermal-hydraulic analysis on the whole module of water cooled ceramic breeder blanket for CFETR Kecheng Jiang a,b , Xuebin Ma a,b , Xiaoman Cheng a , Shuang Lin b , Kai Huang a , Songlin Liu a,b,∗ a b
Institute of Plasma Physics, Chinese Academy of Sciences, Hefei, Anhui, 230031, China University of Science and Technology of China, Hefei, Anhui, 230027, China
h i g h l i g h t s • • • •
The 3D thermal hydraulic analysis on the whole module of WCCB is performed by CFD method. Temperature field and mass flow distribution have been obtained. The design of WCCB is reasonable from the perspective of thermal-hydraulics. The scheme for further optimization has been proposed.
a r t i c l e
i n f o
Article history: Received 7 April 2016 Received in revised form 31 July 2016 Accepted 31 July 2016 Keywords: Thermal hydraulic WCCB blanket CFETR
a b s t r a c t The Water Cooled Ceramic Breeder blanket (WCCB) is being researched for Chinese Fusion Engineering Test Reactor (CFETR). The thermal-hydraulic analysis is essential because the blanket should remove the high heat flux from the plasma and the volumetric heat generated by neutrons. In this paper, the detailed three dimensional (3D) thermal hydraulic analysis on the whole module of WCCB blanket has been performed by Computational Fluid Dynamics (CFD) method, which is capable of solving conjugate heat transfer between solid structure and fluid. The main results, including temperature field, distribution of mass flow rate and coolant pressure drop, have been calculated simultaneously. These provides beneficial guidance data for the further structural optimization and for the design arrangement of primary and secondary circuit. Under the total heat source of 1.23 MW, the coolant mass flow rate of 5.457 kg/s is required to make coolant water corresponding to the Pressurized Water Reactor (PWR) condition (15.5 MPa, 285 ◦ C–325 ◦ C), generating the total coolant pressure drop (P) of 0.467 MPa. The results show that the present structural design can make all the materials effectively cooled to the allowable temperature range, except for a few small modifications on the both sides of FW. The main components, including the first wall (FW), cooling plates (CPs), side wall (SWs)&stiffening plates (SPs) and the manifold(1–4), dominate 4.7%/41.7%/13%/40.6% of the total pressure drop, respectively. Additionally, the mass flow rate of each channel has been obtained, showing the peak relative deviation of 3.4% and 2% from the average for the paratactic channels and components separately. Generally, the results indicate that the present design of WCCB blanket can meet the requirements of thermal hydraulics. © 2016 Elsevier B.V. All rights reserved.
1. Introduction Among all of the technical objectives of Chinese Fusion Engineering Test Reactor (CFETR) [1], one major mission is to design one promising blanket, which can achieve the goals of tritium
∗ Corresponding author at: Institute of Plasma Physics, Chinese Academy of Sciences, Hefei, Anhui, 230031, China. E-mail address: [email protected] (S. Liu). http://dx.doi.org/10.1016/j.fusengdes.2016.07.027 0920-3796/© 2016 Elsevier B.V. All rights reserved.
self-sufficiency as well as high heat extraction for generating electricity. Therefore, three kinds of conceptual blanket design are being researched simultaneously, including the Helium Cooled Ceramic Breeder Blanket (HCCB), Dual Coolant Lithium Lead (DCLL) and Water Cooled Ceramic Breeder blanket (WCCB). This paper mainly concentrates on WCCB [2]. In this conceptual design, the mixed pebble bed of Li2TiO3/Be12Ti [3,4] functions both as the tritium breeder and primary neutron multiplier. Besides, there is additional independent pebble bed of beryllium served as supplement of multiplying neutrons. The structural material consists of
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Reduced Activation Ferritic-Martensitic (RAFM) steel. The tungsten armor is coated on the FW to protect it from plasma erosion and corrosion. The operating conditions of coolant water correspond to Pressurized Water Reactor (PWR), namely 15.5 MPa pressure and inlet\outlet temperature of 285 ◦ C\325 ◦ C,which is widely and maturely applied in the commercial fission reactor. Table 1 lists the adopted materials and the corresponding temperature limits. The blanket operates in the harsh environment, because it should withstand the high heat flux directly radiated from plasma and the nuclear heat deposited in the materials [5]. These heat should be removed by coolant availably to ensure that the temperature of materials is cooled effectively to the allowable range. In addition, it is necessary to calculate the total coolant pressure drop, which determines the selection of pump in the design arrangement of primary coolant circuit. For each component in the blanket module, the proportion of total pressure drop should be obtained as accurately as possible. This can provide useful guidance data for the further structural optimization to reduce pressure drop accompanied with increasing thermoelectric conversion efficiency. Furthermore, there are lots of parallel cooling channels in the blanket due to its limited space and high power heat. In order to ensure the materials cooled uniformly, it is essential to evaluate whether the larger non-uniform flow distribution among the designed parallel channels occurs or not, and makes a guidance for the further optimization of structure design. Therefore, the thermal hydraulic analysis, which can provide essential parameters, plays an essential role in the process of blanket design. Previously, the researchers [6–12] conducted the thermal hydraulic analysis based on the 2D or simplified sliced 3D numerical calculation model. Usually the components of blanket are all analyzed independently with assumed boundary conditions, such as adiabatic and symmetric conditions. Apparently, this method can increase computational efficiency with less computing resources. However, the calculation model is different from the real geometrical model, and this causes the detailed parameters as mentioned above cannot be calculated much more accurately. In this study, based on the structural design and heat source of outboard WCCB blanket located on the equatorial plane, the computational model has been extended to the whole blanket module for 3D thermal hydraulic analysis using Fluent code. This commercial software adopts the Finite Volume Method (FVM) which is capable of solving the coupling heat transfer between solid and fluid. Thus, the main thermal hydraulic parameters of solid and fluid can be calculated simultaneously, including temperature field of all materials, mass flow rate of each channel and total coolant pressure drop of the cooling system.
2. Structure design and cooling scheme Fig. 1 shows the typical structure design of the WCCB blanket which mainly consists of FW, CPs, SPs&SWs, Manifold (M) and Back plate (BP). The mixed tritium breeder and beryllium pebbles are filled in the empty zones which are separated by the frame structure. The overall dimension is 1482 mm in poloidal, 800 mm in radial and 950 mm in toroidal direction, respectively. The FW is designed as poloidal U-shaped structure that is built with 42 internal cooling passages. The cross-sectional area of these channels is 8 × 8 mm2 and the pitch of channel is 22 mm. There are four CPs and each of them has 15 internal cooling channels with cross-sectional area of 5 × 5 mm2 and pitch of 15 mm. The CPs are bended along the coolant flowing direction to divide the blanket into four empty zones along the radial direction, ensuring that the coolant can flows in series and temperature of functional materials can be below the upper limits. In the three gaps between two adjacent CPs, the SPs are inserted to split the blanket into four empty zones along the
Table 1 Summary of the materials adopted in WCCB blanket. Items
Components
Temperature limits/(◦ C)
Tritium breeder
14.4% Li2 TiO3 , 65.6% Be12 Ti and 20% He 80% 6 Li enrichment 80% Be and 20% He 100% RAFM steel 100% tungsten
900
Neutron multiplier Structural materials First wall armor
600 550 1300
toroidal direction. Its main function is to enhance the structural strength. In each SP, there are 12 cooling channels internally built to remove the volumetric nuclear heat away. The main components are connected by the manifolds. Fig. 1(c–d) shows the coolant flowing scheme as the following: (1) coolant water is pumped into M1 from outer pipe, and then M1 distributes it to cool the FW; (2) the M2 collects the coolant and allocates it to cool the CPs; (3) the coolant is gathered in the M2 again and then flows into M3; (4) the SPs&SWs are cooled by coolant from M3; (5) the coolant is collected in M4 and transported to M1 which connects with the outlet pipe. 3. Numerical calculation procedure 3.1. Modeling Under the hypothesis of steady state operating conditions, the 3D thermal hydraulic analysis is conducted by using Fluent code, which is able to solve the coupled heat transfer between solid and fluid. Therefore, the temperature field and flowing distribution of the computational model can be calculated simultaneously. In this analysis, the whole blanket module is considered as the numerical calculation model without any simplification on the geometric. The mechanism of fluid flowing involves with the conservations of mass, momentum and energy. In this calculation, these conservation equations are dispersed by finite volume method using the commercial software Fluent. Considering that the state of coolant is in turbulence, the k- turbulent model is selected to close the Reynolds stress term in the conservation equation of momentum. The SIMPLE algorithm is employed to couple the pressure and velocity. The second order upwind scheme is used to model the quantities including temperature, momentum, pressure, turbulent kinetic energy and turbulent dissipation rate terms. In order to make it easier for computing convergence, the structured mesh is generated for all components of blanket. The standard wall function is adopted for near-wall treatment. The mesh near channel wall is carefully arranged dense enough to ensure the first node from wall is located in the law area, namely Y+ is in the range of 30–100 [13] over the entire fluid zone. The total number of nodes for this whole blanket module is 37574900 which is solved by 24-core server with parallel computing. 3.2. Thermal hydraulic conditions The parameters for thermal hydraulic calculation is listed in Table 2. The blanket located on the equatorial plane endures the neutron wall loading of 0.454 MW/m2 corresponding to 200 MW fusion power, and this generates the total nuclear heat power of 0.6 MW on the components. Besides, the heat flux from plasma of 0.5 MW/m2 is implemented as the FW boundary condition, and the adiabatic condition is imposed on the other surfaces of blanket. Under the total thermal power of 1.23 MW, the coolant mass flow rate of 5.457 kg/s with inlet temperature of 285 ◦ C is required to match with the outlet condition of PWR according to the law of thermal equilibrium. The thermal physical properties parameters of all materials [3,14–18] adopted are shown in Formulas (1)–(8).
K. Jiang et al. / Fusion Engineering and Design 112 (2016) 81–88
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Fig. 1. The WCCB blanket structure.
Table 2 Thermal hydraulic parameters. Parameters
Value
Neutron wall loading FW heat fluxNuclear power Total thermal power Coolant Operating pressure Mass flow rate Inlet/outlet temperature
0.454 MW/m2 0.5 MW/m2 0.53 MW 1.23 MW 15.5 MPa 5.457 kg/s 285 ◦ C/325 ◦ C
The variation of nuclear heat along the radial direction is shown in Fig. 2. Mixed pebble −7
×10
[3]
= 1.68215 + 0.0013(T + 273) − 1.894
(T + 273)2
(1) Fig. 2. Variation of nuclear heat along the radial direction.
Tungsten
[14]
= 207.98 − 0.136(T + 273) + 5.649(T + 273)2
−7.835 × 10−9 (T + 273)3
Beryllium pebble
[15,16]
= 10.897 + 0.0016(T + 273) − 5.265
×10−6 (T + 273)2
RAFM
(2)
(3)
[17]
= 32.5
(4)
[18]
= 1.587 − 0.0018(T + 273)
(5)
Water
Water [18] = 1902.14 − 2.054(T + 273)
(6)
cpWater [18] = −7733 + 23(T + 273)
(7)
Water [18] = 0.000314706 − 3.95055 × 10−7 (T + 273)
(8)
Where is the thermal conductivity, w/(m k); is the density, kg/m3 ; cp is the specific heat capacity, j/(kg k); is the dynamic viscosity, Pa·s; T is the temperature, ◦ C.
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Fig. 3. Temperature field of the whole blanket module.
Fig. 5. Temperature distribution along the assigned direction.
Fig. 4. Temperature field on the toroidal and poloidal cross-section.
4. Results and analysis 4.1. Temperature field Fig. 3 shows the temperature field of this entire blanket module. There are many cooling channels surrounding the blanket. This makes the temperature on external surface of blanket structure wall is rather lower, and the internal breeder zone presents the maximum value of 807 ◦ C. Owing to the high plasma heat flux, the apparent higher temperature occurs on FW. For a further investigation on the internal temperature distribution, the temperature fields on the cross-section of toroidal and poloidal are acquired, as shown in Fig. 4. On the toroidal cross section, the SPs&CPs divide the blanket into 16 cavities of 4 (radial) × 4 (poloidal) that are packed with pebbles of breeder and multiplier. Thus there is temperature concentration happened in these areas. Fig. 5 shows the temperature distribution along the assigned direction. For the radial direction through point A, the parabolic
tendency is appeared in the variation curve, because the large nuclear heat is contained in the breeder zones which are cooled by the CPs on both sides. At the center located in the four breeder zones, the peak temperature of 768 ◦ C/803 ◦ C/725 ◦ C/509 ◦ C is achieved, respectively. Additionally, the temperature of tritium breeder decreases much more sharply than beryllium. This is because the beryllium has much higher thermal conductivity, which is beneficial for heat transferring and flattening temperature distribution. The nuclear heat in the blanket decreases exponentially from FW to BP. Considering the goal of releasing tritium easily, the temperature of breeder zone should be maintained as high as possible and below the allowable upper limits. Therefore, the thickness of the breeder zones is designed to be increasing along the radial direction, namely 53 mm/77 mm/139 mm/327 mm. For the poloidal direction through point B, the temperature remains the constant value of 800 ◦ C at the range of 0.2 m–1.1 m. This is because no channels are arranged passing through the breeder zone. However, the temperature decreases rapidly approaching to 300 ◦ C at the both ends where the effects of FW&CP dominate. The temperature field of each component is shown in Fig. 6. The peak temperature of armor, RAFM steel, mixed breeder pebble bed and independent beryllium multiplier is calculated to be 579 ◦ C/569 ◦ C/807 ◦ C/546 ◦ C, respectively. The mixed breeder contacts with the cooling plates, and this makes the outer surface has the relatively lower temperature, while the sliced profile shows the higher temperature concentration inside the breeder. Clearly it can be seen that the temperature of breeder is kept at the higher level, making it easier for releasing tritium. The maximum temperature of armor and FW both appears in area on both sides. Especially
K. Jiang et al. / Fusion Engineering and Design 112 (2016) 81–88
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Fig. 6. Temperature field of each component.
the peak value of 569 ◦ C for FW has already slightly exceeded the upper limit of RAFM steel, namely 550 ◦ C. Because there is no cooling channels arranged in this area that has the thickness of 23 mm and faces the high heat flux. In the following structure optimization, it is suggested that either the width of cooling channel on both sides is increased or two new channels are rearranged. The cooling plates likewise achieve the peak temperature of 358 ◦ C on
the corner of CP1&CP4, and it is within the acceptable temperature range. Obviously the elliptical distribution is presented for the temperature field of beryllium owing to the effects of cooling channels around. In the front areas between the two U-shaped internal cooling channels, the obvious temperature concentration with the greatest value of 412 ◦ C appears in one column along the poloidal direction for each side wall. Because these areas are close to plasma,
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Table 3 Summary of the temperature results. Materials Solid (max/min temperature) Breeder Beryllium Tungsten RAFM steel Coolant Inlet/outlet temperature
Results(max/min)(◦ C) 807/291 546/298 579/371 569/285 285/325
enduring higher nuclear heat and heat flux. Unlike the side wall, there are three columns showing clear larger temperature field for each stiffening plate. The reason is that this component is located in the middle of two breeders, causing difficulties for heat transferring. The temperature decreases from forward to the backward corresponding to the nuclear heat variation. The temperature of all fluid domains is shown in Fig. 6(h). The peak temperature of 336 ◦ C occurs in the FW channels which faces the high heat flux directly. The saturation temperature of water at 15.5 MPa pressure is 345 ◦ C, therefore, the margin of 9 ◦ C is kept in this cooling system. In general, the present design of WCCB blanket cooling system can make all components effectively meet the thermal requirements, unless the small modifications in the area on the sides of FW need to be considered. Table 3 summarizes the maximum and minimum temperature of all materials. 4.2. Flow distribution Fig. 7(a) shows the 3D structure design scheme of flowing distribution for CPs. The four CPs connects with M2 in parallel. The coolant from the FW is gathered in the first cavity of M2, then flows into CPs. To enhance the structural strength, the outlet cavity of M2 is divided into four cavities by the structural rib along the toroidal direction, as shown in Fig. 7(b). The mass flow rate in each channel of CPs is shown in Fig. 8. The x axis means the channels along the arrow direction. The four CPs presents the same variation tendency. The channels on both sides have the higher value than the channels in the middle positions, showing the U-shaped curve. This is because the coolant flowing located on the both sides is accelerated due to the blocking effects of structural rib. Among all the sixty channels, the maximum and minimum value are 0.093 kg/s and 0.089 kg/s, respectively, corresponding to the relative deviation of 2.2% and −2.2% from average value of 0.091 kg/s. The 3D structure design scheme of flowing distribution for SPs&SWs is shown in Fig. 9. Each SPs&SWs owns one M3 and another M4. The manifold 3 (1–5) is designed as one-side opening connected with M2. It is in charge of collecting coolant from M2 and providing SPs&SWs with coolant. The manifold 4 (1–5) similarly contacts with M1 by the one-side opening. Its main functions are to collect coolant from SPs&SWs and transfer it to M1. There are 12 internal channels arranged along the poloidal direction for each SPs&SWs. The inlet and outlet communicates with M3 and M4, respectively. Fig. 10 depicts the distribution of mass flow rate in all channels of SPs&SWs. The x axis represents the channels. For each SPs&SWs, the channel arrangement along the positive direction of x axis is identical with the negative poloidal direction on the geometrical component. Unlike CPs, the effect of gravity causes the variation tendency more irregularly. The averaged mass flow rate of the channels is 0.091 kg/s. The maximum and minimum value are 0.094 kg/s and 0.088 kg/s, respectively, matching with the relative deviation of 3.3% and −3.4% to the average. To have a better understanding of the flow distribution in all of the components, the total mass flow rate of each component is summarized in Table 4. Apparently the paratactic CPs acquire much more uniform distribution. Each CP occupies about the equal 25%
Fig. 7. Structure design of flow distribution for CPs.
Fig. 8. The distribution of mass flow rate for CPs.
K. Jiang et al. / Fusion Engineering and Design 112 (2016) 81–88
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Fig. 9. Structure design of flow distribution for SPs&SWs.
Fig. 10. The distribution of Mass flow rate for SPs&SWs.
Table 4 Total mass flow rate of each component. Components
Mass flow rate/(kg/s)
Percentage/(%)
FW CP1 CP2 CP3 CP4 Total
5.457 1.372 1.357 1.361 1.367 5.457
100 25.1 24.9 24.9 25.1 100
SW1 SP1 SP2 SP3 SW2 Total
1.077 1.07 1.1 1.1 1.11 5.457
19.7 19.6 20.2 20.2 20.3 100
of the total value. The average mass flow rate is 1.364 kg/s, and the largest deviation value from the average is 1.372 kg/s, corresponding to the largest relative deviation of 0.56%. The peak relative difference of 2% from the average occurs for the SPs&SWs, and each component dominates about 20% of the total mass flow rate. In addition, the calculated results show that the FW, CPs and SPs&SWs all have the identical total mass flow rate of 5.457 kg/s. This further
Fig. 11. The pressure of the inlet and outlet of each channel in each component.
verifies that the convergence is achieved when the conservation equation of mass is numerically calculated in this study. 4.3. Coolant pressure drop The coolant pressure of inlet and outlet of each channel in each component is given, as shown in Fig. 11. The pressure of inlet pipe is 0.5 MPa. After experiencing the M1, visibly there appears V-shaped variation of pressure for the inlet channels of FW. The greatest relative difference between the maximum and minimum value is 5.1%. This is because the flowing near inlet pipe is very disordered, and this causes larger pressure loss. As shown in Fig. 12 for the streamline on the poloidal cross-section of M1. The coolant comes into contact with the wall directly at high velocity, then flows separately to the both sides. The details of back flow, vortex, and secondary flow are revealed. Before entering into CPs, the coolant undergoes the backflow in M2, as shown in Fig. 7(a). This buffering makes the inlet pressure of all CPs channels slightly varied. This is beneficial
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Fig. 12. Flow streamline on the poloidal cross-section of M1. Table 5 Summary of the total coolant pressure drop for each component. Components
Coolant pressure drop/(MPa)
Percentage/(%)
M1 FW M2 CPs M3 + M4 SPs&SWs Total
0.138 0.022 0.016 0.195 0.035 0.061 0.467
29.5 4.7 3.5 41.7 7.6 13 100
for the blanket safety operation, ensuring the uniformity of mass flow distribution. Similarly to the variation curve of flow distribution, the effect of gravity makes the pressure varies complicatedly for SPs&SWs. The total coolant pressure drop of each component is summarized in Table 5. Among all the components, the CPs dominate the largest proportion of 41.7% to the total pressure drop of 0.467 MPa, namely 0.195 MPa. This is because the CPs has the longest channel length that contributes to the pressure drop largely. Although the SPs&SWs has the equal channel number with CPs, it only owns the percentage of 13% due to the relative shorter channel length. The M1 occupies the larger portion of 29.5% owing to the complicated flowing stream. The calculation results provide useful guidance for the further structural optimization, like the flowing space of M1 should be expanded to reduce flowing resistance. 5. Conclusions The three dimensional thermal hydraulic analyses are conducted on the whole WCCB blanket module. The essential results, including temperature field of all components, mass flow rate of all channels and coolant pressure in the whole cooling system, are numerically calculated simultaneously. Under the total heat source of 1.23 MW, the mass flow rate of 5.457 kg/s with inlet temperature of 285 ◦ C is needed to match with PWR condition. For the temperature results, unless the temperature on both sides of FW has slightly exceeded the upper limits, the other components can be all availably cooled to the allowable temperature range. For the further structure optimization of FW, it is recommended that either increasing the width of cooling channel or rearranging new channels on the edges. Besides, the temperature of mixed breeder pebble bed is maintained properly at the higher level to make the tritium released easily. The largest relative deviation from the averaged mass flow rate for the parallel channels and components is only 3.4% and 2%, respectively. The total coolant pressure drop of the whole cooling system is calculated as 0.467 MPa, of which the CPs dominates the largest percentage of 41.7% owing to
the longest channel length. Additionally, the M1 also occupies the larger percentage of 29.5% because of the disordered flowing stream increasing flowing resistance in this limited fluid space. The corresponding measures, such as expanding the flowing regions, will be adopted in the further optimization design to reduce pressure drop. On the whole, the present structural design of WCCB blanket can meets the requirements of thermal hydraulics. However, in the further work, it is necessary to make small structural modifications on the FW and Manifold. Acknowledgements This work was supported by the National Magnetic Confinement Fusion Science Program of China under Grants No. 2013GB108004, No. 2015GB108002 and No. 2014GB122000. References [1] Y. Wan, Design and strategy for the Chinese fusion engineering testing reactor (CFETR), in: Presented in SOFE 2013, San Francisco, USA 10–14 June, 2013. [2] Songlin Liu, et al. Conceptual design of a water cooled breeder blanket for CFETR, Fusion Engineering and Design, 89(2014), 1380–1385. [3] Y. Someya, et al., A feasible DEMO blanket concept based on water cooled solid breeder, 24th IAEA Fusion Energy Conf. FTP/P7-33 (2012). [4] Lei Chen, Xuebin Ma, Xiaoman Cheng, et al., Theoretical modeling of the effective thermal conductivity of the binary pebble beds for the CFETR-WCCB blanket, Fusion Eng. Des. 101 (2015) 148–153. [5] Abdou Mohamed, B. Neil, 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. [6] J. Cheng, et al., Neutronics and thermal-hydraulic design of supercritical-water cooled solid breeder TBM, Fusion Eng. Des. 92 (2015) 52–58. [7] M. Enoeda, Y. Kosaku, T. Hatano, et al., Design and technology development of solid breeder blanket cooled by supercritical water in Japan, Nucl. Fusion 43 (2003) 1837–1844. [8] Yoshihiko YANAGI, Satoshi SATO, Mikio ENOEDA, et al. Nuclear and thermal analysis of supercritical water cooled solid breeder blanket for fusion DEMO reactor, Journal of Nuclear Science and Technology, 38(11), 1014–1018. [9] Mu-Young Ahn, Duck Young Ku, Seungyon Cho, et al., Pre-conceptual design study on K-DEMO ceramic breeder blanket, Fusion Eng. Des. 100 (2015) 159–165. [10] Mu-Young Ahn, Duck Young Ku, Seungyon Cho, et al., Thermal hydraulic and thermal-mechanical analysis of Korean helium cooled solid breeder TBM, Fusion Eng. Des. 85 (2010) 1664–1669. [11] Mu-Young Ahn, Duck Young Ku, Seungyon Cho, et al., Thermal hydraulic analysis on Korean helium cooled solid breeder TBM with updated back manifolds design, Fusion Eng. Des. 86 (2011) 2289–2292. [12] P.A. Di Maio, P. Arena, J. Aubert, et al., Analysis of the thermal-mechanical behaviour of the DEMO Water-Cooled Lithium Lead breeding blanket module under normal operation steady state conditions, Fusion Eng. Des. 98 (2015) 1737–1740. [13] ANSYS Fluent-12 User Manual, ANSYS-Fluent, 2009. [14] Anon et al. Report on the Mechanical and Thermal Properties of Tungsten and TZM Sheet Produced in the Refractory Metal Sheet Rolling Program. Southern Research Institute Report 7563-1479-XII to the U.S. Bureau of Naval Weapons, August 31, 1966 (638631 CE). [15] J. Reimann, G. Piazza, Z. Xu, et al., Measurements of the Thermal Conductivity of Compressed Beryllium Pebble Beds: EFDA Reference: TW2-TTBB-007a D4, Wissenschaftliche Berichte FZKA, 2005, pp. 7096. [16] J. Reimann, G. Piazza, H. Harsch, Thermal conductivity of compressed beryllium pebble beds, Fusion Eng. Des. 81 (2006) 449–454. [17] Takanori Hirose, Takashi Nozawa, R.E. Stoller, et al., Physical properties of F82H for fusion blanket design, Fusion Eng. Des. 89 (2014) 1595–1599. [18] Jialu Yan, Xiaofu Yu, Yongqing Wang, Thermodynamic Property Tables and Diagram For Water and Steam[M], Beijing: Higher Education Press, 2006 (In Chinese).
Contents lists available at ScienceDirect
Fusion Engineering and Design journal homepage: www.elsevier.com/locate/fusengdes
Thermal-hydraulic analysis on the whole module of water cooled ceramic breeder blanket for CFETR Kecheng Jiang a,b , Xuebin Ma a,b , Xiaoman Cheng a , Shuang Lin b , Kai Huang a , Songlin Liu a,b,∗ a b
Institute of Plasma Physics, Chinese Academy of Sciences, Hefei, Anhui, 230031, China University of Science and Technology of China, Hefei, Anhui, 230027, China
h i g h l i g h t s • • • •
The 3D thermal hydraulic analysis on the whole module of WCCB is performed by CFD method. Temperature field and mass flow distribution have been obtained. The design of WCCB is reasonable from the perspective of thermal-hydraulics. The scheme for further optimization has been proposed.
a r t i c l e
i n f o
Article history: Received 7 April 2016 Received in revised form 31 July 2016 Accepted 31 July 2016 Keywords: Thermal hydraulic WCCB blanket CFETR
a b s t r a c t The Water Cooled Ceramic Breeder blanket (WCCB) is being researched for Chinese Fusion Engineering Test Reactor (CFETR). The thermal-hydraulic analysis is essential because the blanket should remove the high heat flux from the plasma and the volumetric heat generated by neutrons. In this paper, the detailed three dimensional (3D) thermal hydraulic analysis on the whole module of WCCB blanket has been performed by Computational Fluid Dynamics (CFD) method, which is capable of solving conjugate heat transfer between solid structure and fluid. The main results, including temperature field, distribution of mass flow rate and coolant pressure drop, have been calculated simultaneously. These provides beneficial guidance data for the further structural optimization and for the design arrangement of primary and secondary circuit. Under the total heat source of 1.23 MW, the coolant mass flow rate of 5.457 kg/s is required to make coolant water corresponding to the Pressurized Water Reactor (PWR) condition (15.5 MPa, 285 ◦ C–325 ◦ C), generating the total coolant pressure drop (P) of 0.467 MPa. The results show that the present structural design can make all the materials effectively cooled to the allowable temperature range, except for a few small modifications on the both sides of FW. The main components, including the first wall (FW), cooling plates (CPs), side wall (SWs)&stiffening plates (SPs) and the manifold(1–4), dominate 4.7%/41.7%/13%/40.6% of the total pressure drop, respectively. Additionally, the mass flow rate of each channel has been obtained, showing the peak relative deviation of 3.4% and 2% from the average for the paratactic channels and components separately. Generally, the results indicate that the present design of WCCB blanket can meet the requirements of thermal hydraulics. © 2016 Elsevier B.V. All rights reserved.
1. Introduction Among all of the technical objectives of Chinese Fusion Engineering Test Reactor (CFETR) [1], one major mission is to design one promising blanket, which can achieve the goals of tritium
∗ Corresponding author at: Institute of Plasma Physics, Chinese Academy of Sciences, Hefei, Anhui, 230031, China. E-mail address: [email protected] (S. Liu). http://dx.doi.org/10.1016/j.fusengdes.2016.07.027 0920-3796/© 2016 Elsevier B.V. All rights reserved.
self-sufficiency as well as high heat extraction for generating electricity. Therefore, three kinds of conceptual blanket design are being researched simultaneously, including the Helium Cooled Ceramic Breeder Blanket (HCCB), Dual Coolant Lithium Lead (DCLL) and Water Cooled Ceramic Breeder blanket (WCCB). This paper mainly concentrates on WCCB [2]. In this conceptual design, the mixed pebble bed of Li2TiO3/Be12Ti [3,4] functions both as the tritium breeder and primary neutron multiplier. Besides, there is additional independent pebble bed of beryllium served as supplement of multiplying neutrons. The structural material consists of
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Reduced Activation Ferritic-Martensitic (RAFM) steel. The tungsten armor is coated on the FW to protect it from plasma erosion and corrosion. The operating conditions of coolant water correspond to Pressurized Water Reactor (PWR), namely 15.5 MPa pressure and inlet\outlet temperature of 285 ◦ C\325 ◦ C,which is widely and maturely applied in the commercial fission reactor. Table 1 lists the adopted materials and the corresponding temperature limits. The blanket operates in the harsh environment, because it should withstand the high heat flux directly radiated from plasma and the nuclear heat deposited in the materials [5]. These heat should be removed by coolant availably to ensure that the temperature of materials is cooled effectively to the allowable range. In addition, it is necessary to calculate the total coolant pressure drop, which determines the selection of pump in the design arrangement of primary coolant circuit. For each component in the blanket module, the proportion of total pressure drop should be obtained as accurately as possible. This can provide useful guidance data for the further structural optimization to reduce pressure drop accompanied with increasing thermoelectric conversion efficiency. Furthermore, there are lots of parallel cooling channels in the blanket due to its limited space and high power heat. In order to ensure the materials cooled uniformly, it is essential to evaluate whether the larger non-uniform flow distribution among the designed parallel channels occurs or not, and makes a guidance for the further optimization of structure design. Therefore, the thermal hydraulic analysis, which can provide essential parameters, plays an essential role in the process of blanket design. Previously, the researchers [6–12] conducted the thermal hydraulic analysis based on the 2D or simplified sliced 3D numerical calculation model. Usually the components of blanket are all analyzed independently with assumed boundary conditions, such as adiabatic and symmetric conditions. Apparently, this method can increase computational efficiency with less computing resources. However, the calculation model is different from the real geometrical model, and this causes the detailed parameters as mentioned above cannot be calculated much more accurately. In this study, based on the structural design and heat source of outboard WCCB blanket located on the equatorial plane, the computational model has been extended to the whole blanket module for 3D thermal hydraulic analysis using Fluent code. This commercial software adopts the Finite Volume Method (FVM) which is capable of solving the coupling heat transfer between solid and fluid. Thus, the main thermal hydraulic parameters of solid and fluid can be calculated simultaneously, including temperature field of all materials, mass flow rate of each channel and total coolant pressure drop of the cooling system.
2. Structure design and cooling scheme Fig. 1 shows the typical structure design of the WCCB blanket which mainly consists of FW, CPs, SPs&SWs, Manifold (M) and Back plate (BP). The mixed tritium breeder and beryllium pebbles are filled in the empty zones which are separated by the frame structure. The overall dimension is 1482 mm in poloidal, 800 mm in radial and 950 mm in toroidal direction, respectively. The FW is designed as poloidal U-shaped structure that is built with 42 internal cooling passages. The cross-sectional area of these channels is 8 × 8 mm2 and the pitch of channel is 22 mm. There are four CPs and each of them has 15 internal cooling channels with cross-sectional area of 5 × 5 mm2 and pitch of 15 mm. The CPs are bended along the coolant flowing direction to divide the blanket into four empty zones along the radial direction, ensuring that the coolant can flows in series and temperature of functional materials can be below the upper limits. In the three gaps between two adjacent CPs, the SPs are inserted to split the blanket into four empty zones along the
Table 1 Summary of the materials adopted in WCCB blanket. Items
Components
Temperature limits/(◦ C)
Tritium breeder
14.4% Li2 TiO3 , 65.6% Be12 Ti and 20% He 80% 6 Li enrichment 80% Be and 20% He 100% RAFM steel 100% tungsten
900
Neutron multiplier Structural materials First wall armor
600 550 1300
toroidal direction. Its main function is to enhance the structural strength. In each SP, there are 12 cooling channels internally built to remove the volumetric nuclear heat away. The main components are connected by the manifolds. Fig. 1(c–d) shows the coolant flowing scheme as the following: (1) coolant water is pumped into M1 from outer pipe, and then M1 distributes it to cool the FW; (2) the M2 collects the coolant and allocates it to cool the CPs; (3) the coolant is gathered in the M2 again and then flows into M3; (4) the SPs&SWs are cooled by coolant from M3; (5) the coolant is collected in M4 and transported to M1 which connects with the outlet pipe. 3. Numerical calculation procedure 3.1. Modeling Under the hypothesis of steady state operating conditions, the 3D thermal hydraulic analysis is conducted by using Fluent code, which is able to solve the coupled heat transfer between solid and fluid. Therefore, the temperature field and flowing distribution of the computational model can be calculated simultaneously. In this analysis, the whole blanket module is considered as the numerical calculation model without any simplification on the geometric. The mechanism of fluid flowing involves with the conservations of mass, momentum and energy. In this calculation, these conservation equations are dispersed by finite volume method using the commercial software Fluent. Considering that the state of coolant is in turbulence, the k-
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Fig. 1. The WCCB blanket structure.
Table 2 Thermal hydraulic parameters. Parameters
Value
Neutron wall loading FW heat fluxNuclear power Total thermal power Coolant Operating pressure Mass flow rate Inlet/outlet temperature
0.454 MW/m2 0.5 MW/m2 0.53 MW 1.23 MW 15.5 MPa 5.457 kg/s 285 ◦ C/325 ◦ C
The variation of nuclear heat along the radial direction is shown in Fig. 2. Mixed pebble −7
×10
[3]
= 1.68215 + 0.0013(T + 273) − 1.894
(T + 273)2
(1) Fig. 2. Variation of nuclear heat along the radial direction.
Tungsten
[14]
= 207.98 − 0.136(T + 273) + 5.649(T + 273)2
−7.835 × 10−9 (T + 273)3
Beryllium pebble
[15,16]
= 10.897 + 0.0016(T + 273) − 5.265
×10−6 (T + 273)2
RAFM
(2)
(3)
[17]
= 32.5
(4)
[18]
= 1.587 − 0.0018(T + 273)
(5)
Water
Water [18] = 1902.14 − 2.054(T + 273)
(6)
cpWater [18] = −7733 + 23(T + 273)
(7)
Water [18] = 0.000314706 − 3.95055 × 10−7 (T + 273)
(8)
Where is the thermal conductivity, w/(m k); is the density, kg/m3 ; cp is the specific heat capacity, j/(kg k); is the dynamic viscosity, Pa·s; T is the temperature, ◦ C.
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Fig. 3. Temperature field of the whole blanket module.
Fig. 5. Temperature distribution along the assigned direction.
Fig. 4. Temperature field on the toroidal and poloidal cross-section.
4. Results and analysis 4.1. Temperature field Fig. 3 shows the temperature field of this entire blanket module. There are many cooling channels surrounding the blanket. This makes the temperature on external surface of blanket structure wall is rather lower, and the internal breeder zone presents the maximum value of 807 ◦ C. Owing to the high plasma heat flux, the apparent higher temperature occurs on FW. For a further investigation on the internal temperature distribution, the temperature fields on the cross-section of toroidal and poloidal are acquired, as shown in Fig. 4. On the toroidal cross section, the SPs&CPs divide the blanket into 16 cavities of 4 (radial) × 4 (poloidal) that are packed with pebbles of breeder and multiplier. Thus there is temperature concentration happened in these areas. Fig. 5 shows the temperature distribution along the assigned direction. For the radial direction through point A, the parabolic
tendency is appeared in the variation curve, because the large nuclear heat is contained in the breeder zones which are cooled by the CPs on both sides. At the center located in the four breeder zones, the peak temperature of 768 ◦ C/803 ◦ C/725 ◦ C/509 ◦ C is achieved, respectively. Additionally, the temperature of tritium breeder decreases much more sharply than beryllium. This is because the beryllium has much higher thermal conductivity, which is beneficial for heat transferring and flattening temperature distribution. The nuclear heat in the blanket decreases exponentially from FW to BP. Considering the goal of releasing tritium easily, the temperature of breeder zone should be maintained as high as possible and below the allowable upper limits. Therefore, the thickness of the breeder zones is designed to be increasing along the radial direction, namely 53 mm/77 mm/139 mm/327 mm. For the poloidal direction through point B, the temperature remains the constant value of 800 ◦ C at the range of 0.2 m–1.1 m. This is because no channels are arranged passing through the breeder zone. However, the temperature decreases rapidly approaching to 300 ◦ C at the both ends where the effects of FW&CP dominate. The temperature field of each component is shown in Fig. 6. The peak temperature of armor, RAFM steel, mixed breeder pebble bed and independent beryllium multiplier is calculated to be 579 ◦ C/569 ◦ C/807 ◦ C/546 ◦ C, respectively. The mixed breeder contacts with the cooling plates, and this makes the outer surface has the relatively lower temperature, while the sliced profile shows the higher temperature concentration inside the breeder. Clearly it can be seen that the temperature of breeder is kept at the higher level, making it easier for releasing tritium. The maximum temperature of armor and FW both appears in area on both sides. Especially
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Fig. 6. Temperature field of each component.
the peak value of 569 ◦ C for FW has already slightly exceeded the upper limit of RAFM steel, namely 550 ◦ C. Because there is no cooling channels arranged in this area that has the thickness of 23 mm and faces the high heat flux. In the following structure optimization, it is suggested that either the width of cooling channel on both sides is increased or two new channels are rearranged. The cooling plates likewise achieve the peak temperature of 358 ◦ C on
the corner of CP1&CP4, and it is within the acceptable temperature range. Obviously the elliptical distribution is presented for the temperature field of beryllium owing to the effects of cooling channels around. In the front areas between the two U-shaped internal cooling channels, the obvious temperature concentration with the greatest value of 412 ◦ C appears in one column along the poloidal direction for each side wall. Because these areas are close to plasma,
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Table 3 Summary of the temperature results. Materials Solid (max/min temperature) Breeder Beryllium Tungsten RAFM steel Coolant Inlet/outlet temperature
Results(max/min)(◦ C) 807/291 546/298 579/371 569/285 285/325
enduring higher nuclear heat and heat flux. Unlike the side wall, there are three columns showing clear larger temperature field for each stiffening plate. The reason is that this component is located in the middle of two breeders, causing difficulties for heat transferring. The temperature decreases from forward to the backward corresponding to the nuclear heat variation. The temperature of all fluid domains is shown in Fig. 6(h). The peak temperature of 336 ◦ C occurs in the FW channels which faces the high heat flux directly. The saturation temperature of water at 15.5 MPa pressure is 345 ◦ C, therefore, the margin of 9 ◦ C is kept in this cooling system. In general, the present design of WCCB blanket cooling system can make all components effectively meet the thermal requirements, unless the small modifications in the area on the sides of FW need to be considered. Table 3 summarizes the maximum and minimum temperature of all materials. 4.2. Flow distribution Fig. 7(a) shows the 3D structure design scheme of flowing distribution for CPs. The four CPs connects with M2 in parallel. The coolant from the FW is gathered in the first cavity of M2, then flows into CPs. To enhance the structural strength, the outlet cavity of M2 is divided into four cavities by the structural rib along the toroidal direction, as shown in Fig. 7(b). The mass flow rate in each channel of CPs is shown in Fig. 8. The x axis means the channels along the arrow direction. The four CPs presents the same variation tendency. The channels on both sides have the higher value than the channels in the middle positions, showing the U-shaped curve. This is because the coolant flowing located on the both sides is accelerated due to the blocking effects of structural rib. Among all the sixty channels, the maximum and minimum value are 0.093 kg/s and 0.089 kg/s, respectively, corresponding to the relative deviation of 2.2% and −2.2% from average value of 0.091 kg/s. The 3D structure design scheme of flowing distribution for SPs&SWs is shown in Fig. 9. Each SPs&SWs owns one M3 and another M4. The manifold 3 (1–5) is designed as one-side opening connected with M2. It is in charge of collecting coolant from M2 and providing SPs&SWs with coolant. The manifold 4 (1–5) similarly contacts with M1 by the one-side opening. Its main functions are to collect coolant from SPs&SWs and transfer it to M1. There are 12 internal channels arranged along the poloidal direction for each SPs&SWs. The inlet and outlet communicates with M3 and M4, respectively. Fig. 10 depicts the distribution of mass flow rate in all channels of SPs&SWs. The x axis represents the channels. For each SPs&SWs, the channel arrangement along the positive direction of x axis is identical with the negative poloidal direction on the geometrical component. Unlike CPs, the effect of gravity causes the variation tendency more irregularly. The averaged mass flow rate of the channels is 0.091 kg/s. The maximum and minimum value are 0.094 kg/s and 0.088 kg/s, respectively, matching with the relative deviation of 3.3% and −3.4% to the average. To have a better understanding of the flow distribution in all of the components, the total mass flow rate of each component is summarized in Table 4. Apparently the paratactic CPs acquire much more uniform distribution. Each CP occupies about the equal 25%
Fig. 7. Structure design of flow distribution for CPs.
Fig. 8. The distribution of mass flow rate for CPs.
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Fig. 9. Structure design of flow distribution for SPs&SWs.
Fig. 10. The distribution of Mass flow rate for SPs&SWs.
Table 4 Total mass flow rate of each component. Components
Mass flow rate/(kg/s)
Percentage/(%)
FW CP1 CP2 CP3 CP4 Total
5.457 1.372 1.357 1.361 1.367 5.457
100 25.1 24.9 24.9 25.1 100
SW1 SP1 SP2 SP3 SW2 Total
1.077 1.07 1.1 1.1 1.11 5.457
19.7 19.6 20.2 20.2 20.3 100
of the total value. The average mass flow rate is 1.364 kg/s, and the largest deviation value from the average is 1.372 kg/s, corresponding to the largest relative deviation of 0.56%. The peak relative difference of 2% from the average occurs for the SPs&SWs, and each component dominates about 20% of the total mass flow rate. In addition, the calculated results show that the FW, CPs and SPs&SWs all have the identical total mass flow rate of 5.457 kg/s. This further
Fig. 11. The pressure of the inlet and outlet of each channel in each component.
verifies that the convergence is achieved when the conservation equation of mass is numerically calculated in this study. 4.3. Coolant pressure drop The coolant pressure of inlet and outlet of each channel in each component is given, as shown in Fig. 11. The pressure of inlet pipe is 0.5 MPa. After experiencing the M1, visibly there appears V-shaped variation of pressure for the inlet channels of FW. The greatest relative difference between the maximum and minimum value is 5.1%. This is because the flowing near inlet pipe is very disordered, and this causes larger pressure loss. As shown in Fig. 12 for the streamline on the poloidal cross-section of M1. The coolant comes into contact with the wall directly at high velocity, then flows separately to the both sides. The details of back flow, vortex, and secondary flow are revealed. Before entering into CPs, the coolant undergoes the backflow in M2, as shown in Fig. 7(a). This buffering makes the inlet pressure of all CPs channels slightly varied. This is beneficial
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Fig. 12. Flow streamline on the poloidal cross-section of M1. Table 5 Summary of the total coolant pressure drop for each component. Components
Coolant pressure drop/(MPa)
Percentage/(%)
M1 FW M2 CPs M3 + M4 SPs&SWs Total
0.138 0.022 0.016 0.195 0.035 0.061 0.467
29.5 4.7 3.5 41.7 7.6 13 100
for the blanket safety operation, ensuring the uniformity of mass flow distribution. Similarly to the variation curve of flow distribution, the effect of gravity makes the pressure varies complicatedly for SPs&SWs. The total coolant pressure drop of each component is summarized in Table 5. Among all the components, the CPs dominate the largest proportion of 41.7% to the total pressure drop of 0.467 MPa, namely 0.195 MPa. This is because the CPs has the longest channel length that contributes to the pressure drop largely. Although the SPs&SWs has the equal channel number with CPs, it only owns the percentage of 13% due to the relative shorter channel length. The M1 occupies the larger portion of 29.5% owing to the complicated flowing stream. The calculation results provide useful guidance for the further structural optimization, like the flowing space of M1 should be expanded to reduce flowing resistance. 5. Conclusions The three dimensional thermal hydraulic analyses are conducted on the whole WCCB blanket module. The essential results, including temperature field of all components, mass flow rate of all channels and coolant pressure in the whole cooling system, are numerically calculated simultaneously. Under the total heat source of 1.23 MW, the mass flow rate of 5.457 kg/s with inlet temperature of 285 ◦ C is needed to match with PWR condition. For the temperature results, unless the temperature on both sides of FW has slightly exceeded the upper limits, the other components can be all availably cooled to the allowable temperature range. For the further structure optimization of FW, it is recommended that either increasing the width of cooling channel or rearranging new channels on the edges. Besides, the temperature of mixed breeder pebble bed is maintained properly at the higher level to make the tritium released easily. The largest relative deviation from the averaged mass flow rate for the parallel channels and components is only 3.4% and 2%, respectively. The total coolant pressure drop of the whole cooling system is calculated as 0.467 MPa, of which the CPs dominates the largest percentage of 41.7% owing to
the longest channel length. Additionally, the M1 also occupies the larger percentage of 29.5% because of the disordered flowing stream increasing flowing resistance in this limited fluid space. The corresponding measures, such as expanding the flowing regions, will be adopted in the further optimization design to reduce pressure drop. On the whole, the present structural design of WCCB blanket can meets the requirements of thermal hydraulics. However, in the further work, it is necessary to make small structural modifications on the FW and Manifold. Acknowledgements This work was supported by the National Magnetic Confinement Fusion Science Program of China under Grants No. 2013GB108004, No. 2015GB108002 and No. 2014GB122000. References [1] Y. Wan, Design and strategy for the Chinese fusion engineering testing reactor (CFETR), in: Presented in SOFE 2013, San Francisco, USA 10–14 June, 2013. [2] Songlin Liu, et al. Conceptual design of a water cooled breeder blanket for CFETR, Fusion Engineering and Design, 89(2014), 1380–1385. [3] Y. Someya, et al., A feasible DEMO blanket concept based on water cooled solid breeder, 24th IAEA Fusion Energy Conf. FTP/P7-33 (2012). [4] Lei Chen, Xuebin Ma, Xiaoman Cheng, et al., Theoretical modeling of the effective thermal conductivity of the binary pebble beds for the CFETR-WCCB blanket, Fusion Eng. Des. 101 (2015) 148–153. [5] Abdou Mohamed, B. Neil, 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. [6] J. Cheng, et al., Neutronics and thermal-hydraulic design of supercritical-water cooled solid breeder TBM, Fusion Eng. Des. 92 (2015) 52–58. [7] M. Enoeda, Y. Kosaku, T. Hatano, et al., Design and technology development of solid breeder blanket cooled by supercritical water in Japan, Nucl. Fusion 43 (2003) 1837–1844. [8] Yoshihiko YANAGI, Satoshi SATO, Mikio ENOEDA, et al. Nuclear and thermal analysis of supercritical water cooled solid breeder blanket for fusion DEMO reactor, Journal of Nuclear Science and Technology, 38(11), 1014–1018. [9] Mu-Young Ahn, Duck Young Ku, Seungyon Cho, et al., Pre-conceptual design study on K-DEMO ceramic breeder blanket, Fusion Eng. Des. 100 (2015) 159–165. [10] Mu-Young Ahn, Duck Young Ku, Seungyon Cho, et al., Thermal hydraulic and thermal-mechanical analysis of Korean helium cooled solid breeder TBM, Fusion Eng. Des. 85 (2010) 1664–1669. [11] Mu-Young Ahn, Duck Young Ku, Seungyon Cho, et al., Thermal hydraulic analysis on Korean helium cooled solid breeder TBM with updated back manifolds design, Fusion Eng. Des. 86 (2011) 2289–2292. [12] P.A. Di Maio, P. Arena, J. Aubert, et al., Analysis of the thermal-mechanical behaviour of the DEMO Water-Cooled Lithium Lead breeding blanket module under normal operation steady state conditions, Fusion Eng. Des. 98 (2015) 1737–1740. [13] ANSYS Fluent-12 User Manual, ANSYS-Fluent, 2009. [14] Anon et al. Report on the Mechanical and Thermal Properties of Tungsten and TZM Sheet Produced in the Refractory Metal Sheet Rolling Program. Southern Research Institute Report 7563-1479-XII to the U.S. Bureau of Naval Weapons, August 31, 1966 (638631 CE). [15] J. Reimann, G. Piazza, Z. Xu, et al., Measurements of the Thermal Conductivity of Compressed Beryllium Pebble Beds: EFDA Reference: TW2-TTBB-007a D4, Wissenschaftliche Berichte FZKA, 2005, pp. 7096. [16] J. Reimann, G. Piazza, H. Harsch, Thermal conductivity of compressed beryllium pebble beds, Fusion Eng. Des. 81 (2006) 449–454. [17] Takanori Hirose, Takashi Nozawa, R.E. Stoller, et al., Physical properties of F82H for fusion blanket design, Fusion Eng. Des. 89 (2014) 1595–1599. [18] Jialu Yan, Xiaofu Yu, Yongqing Wang, Thermodynamic Property Tables and Diagram For Water and Steam[M], Beijing: Higher Education Press, 2006 (In Chinese).