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Numerical research of magnetohydrodynamics buoyant flow in dual functional lead lithium fusion blanket
Fusion Engineering and Design xxx (xxxx) xxxx
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Numerical research of magnetohydrodynamics buoyant flow in dual functional lead lithium fusion blanket Shichao Zhanga,b, Lin Chena,b, Zi Menga,⁎, Zhang Guangyua a b
Key Laboratory of Neutronics and Radiation Safety, Institute of Nuclear Energy Safety Technology, Chinese Academy of Sciences, Hefei, Anhui 230031, China University of Science and Technology of China, Hefei, Anhui 230027, China
ARTICLE INFO
ABSTRACT
Keywords: MHD Buoyant flow Liquid metal blanket
Blanket is key component of fusion reactor, which functions as tritium breeder, energy conversion component and radiation shield. Liquid metal fusion blanket is a promising candidate of future fusion power plants for its high temperature operating characteristics and efficient thermoelectric conversion. However, motion of liquid metal under fusion reactor high magnetic field (∼4 T) causes serious magnetohydrodynamics (MHD) effect, and extreme non-uniform volumetric heat deposited by fusion neutrons produces strong buoyancy effect. Both effects greatly change flow field and heat transfer characteristics of liquid metal blanket, which are key issues for thermal-hydraulic design of liquid metal blankets. In this paper, MHD buoyant flow of Dual Functional Lead Lithium blanket (DFLL) under typical fusion magnetic field and non-uniform volumetric nuclear heating were studied. Buoyancy force induced drastic natural convection in LL1 (the 1st Lead Lithium channel) channel of blanket and increased the heat leaked to Helium coolant and reduced the outlet temperature. FCI (flow channel insert) material with heat conductivity < 1W/m K was required to achieve high outlet temperature (700 K). Reversed direction of original flow in DFLL blanket would smooth the flow and reduce heat leakage of PbLi, which formed the idea of improvement. At the extreme condition of duct with steel wall, Lorentz force completely suppressed buoyancy. According to the founding above, we analyzed the MHD buoyant flow in an upsidedown DFLL blanket and temperature distribution and heat leakage were significantly improved. This finding would be valuable for liquid blanket thermal hydraulic design.
1. Introduction
structure, whose kinetic energy transforms to deposited heat. Because of penetration characteristic of neutrons, the FW structure and LL1 channel are mostly heated. The neutron heat deposited in the liquid metal zone presents great heterogeneity, which forms drastic gradient of deposited neutron heat and causes temperature gradient and buoyant flow in liquid blanket [11]. For DFLL blanket under ITER TBM (test blanket module) condition, the ∼4 T magnetic field and 0.78 MW/m2 neutron wall loading induce huge Lorentz force and buoyancy force. The Hartmann number (ratio of electromagnetic force to viscous force) reaches 1.0 × 10 4 and the Grashof number (ratio of buoyancy force to viscous force) is 4.4 × 109 , where the liquid metal flow is greatly altered by Lorentz force and buoyancy force and forms MHD buoyant flow. The MHD buoyant flow formed by the coupled effect of Lorentz force and buoyancy force is different from the general buoyant flow. The Lorentz force is very sensitive to magnetic fields, electric conductivity of wall and liquid flow, while buoyancy is sensitive to gradient of deposited neutron heat, heat conductivity of wall and liquid flow, direction of flow channel, liquid metal density and so on. So MHD buoyant flow will be
Blankets [1,2] are key components of fusion reactor, which transfer fusion energy to heat, breed tritium and shield neutrons. According to state of breeder form, fusion blankets can be classified as liquid breeder blanket [2–4] and solid breeder blanket [5–7]. For liquid blanket, the tritium breeder PbLi is also neutron multiplier, while for solid blanket, additional neutron multiplier such as Be is added among the tritium breeder. FDS team developed conceptual design of the China fusion power plant FDS-II [8], where the blanket DFLL adopted the liquid leadlithium as coolant [9]. Liquid metal blanket has the advantage of high temperature operation and high thermal efficiency, which is a promising candidate for future fusion power plant. However, in most fusion reactors fusion plasma is constrained by strong magnetic fields and blankets operate under the influence of magnetic fields. The flowing liquid metal under strong magnetic fields would induce Lorentz force which is equal to or even larger than driven force, forming MHD flow [10]. In liquid metal blankets, fusion neutrons are absorbed by liquid metal breeder and
⁎
Corresponding author. E-mail address: [email protected] (Z. Meng).
https://doi.org/10.1016/j.fusengdes.2019.111331 Received 25 February 2019; Received in revised form 26 July 2019; Accepted 20 September 2019 0920-3796/ © 2019 Published by Elsevier B.V.
Please cite this article as: Shichao Zhang, et al., Fusion Engineering and Design, https://doi.org/10.1016/j.fusengdes.2019.111331
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Nomenclature Re Ha Gr Snuclear heat e x p
v f J B
Gravity Temperature Average temperature Specific heat of fluid Electric conductivity of fluid Heat conductivity of fluid Buoyancy force
g T T0 cp
Reynold number, ratio of inertial force to viscous force Hartmann number, ratio of electromagnetic force to viscous force Grashof number, ratio of buoyancy force to viscous force Source of deposited neutron heat Natural constant Distance from first wall of blanket Pressure Density Velocity vector Buoyancy force Induced electric current density Magnetic field Dynamic viscosity
f
Abbreviations MHD DFLL PbLi LL1, LL2, FCI Re
closely related to magnetic fields, electric conductivity, heat conductivity and flow direction. For simple vertical infinite plate MHD buoyant flow [12], theory results showed that magnetic field would suppress buoyant flow. L. Bühler [13,14] investigated MHD buoyant flow in blanket-related channel, and found that the flow jet location was deeply related to magnetic field direction and heat flux direction. Ozoe [15] numerical investigated natural convection in cavity under different magnetic field direction and found that the magnetic field parallel to heat flux suppressed buoyancy significantly, while magnetic field perpendicular to heat flux suppressed buoyancy weakly. Smolentsev [16] developed a code for fully developed MHD flow of a liquid metal blanket using insulation techniques and compared the flow rate in the central channel with and without FCI (flow channel insert). Khodak [17] investigated the preliminary design of the DCLL TBM, including complex helium flow channels, lead-lithium flow channels with FCIs and structural materials and improved the design, which can lead to significant reduction of the pressure drop and improvement in temperature uniformity. Kharicha [18] analyzed MHD buoyant flow in single duct of HCLL blanket. For horizontal duct, MHD buoyant convection had a weak influence on temperature. But for vertical duct, temperature was greatly changed by buoyant convection. Okada [19] carried out an MHD buoyant
magnetohydrodynamics Dual Functional Lead Lithium blanket Lead-lithium eutectic alloy LL3 First, second and third vertical flow channel flow channel insert Reynold number
flow experiment, where liquid metal Ga was filled into a cavity with heat flux and magnetic fields and validated the relation of magnetic field direction with MHD suppression on buoyancy. Meng [21] carried out simulation of this experiments and found the same results. From these theories and experimental investigation, we can predict that in actual liquid blanket channels, the influence of electric conductivity, heat conductivity of wall and flow direction on MHD buoyant flow is non-negligible. This paper aimed to analyze MHD buoyant flow behavior in PbLi blanket DFLL with code MTC, which has been validated according to for the magnetohydrodynamic flow at high Hartmann number [20,21]. Typical fusion condition of ITER TBM [22] were adopted as basic physical condition. The influence of heat conductivity and electric conductivity of wall, direction of flow field on MHD buoyant flow were analyzed. The MHD buoyant effect on temperature distribution in DFLL blanket was evaluated and optimization design was proposed to improve the thermal-hydraulic performance of DFLL blanket. 2. Influence factor analysis for MHD buoyant flow 2.1. Blanket related channel model and mathematical formulation DFLL blanket was a box-shaped structure, which composes of first
Fig. 1. Isolated LL1 channel near first wall of DFLL blanket. 2
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wall (FW) directly facing neutron bombardment, cover plate, separate plates, back plate and PbLi channels. Radial-poloidal separate plate and toroidal-poloidal separate plate form flow channel of liquid PbLi, with He coolant flowing inside plate with fine channel like blood vessel to remove heat. The magnetic field of the fusion reactor is along the toroidal direction, which will significantly affect PbLi flow in blanket. As shown in Fig. 1, liquid PbLi channels were composed of 3 vertical flow channels: LL1, LL2, and LL3, with LL1 closest to the first wall, and physically connected to LL2 and LL3, the latter being the farthest from the first wall, both accepting liquid metal flow from LL1. The vertical flow channel LL1 was isolated for MHD buoyant flow analysis, where most of the neutron heat deposited and buoyancy effect was most significant, and. The purpose of this simplification is to get a basic understanding of the effects of the FCI thermal conductivity, the FCI electric conductivity, and liquid metal flow direction on MHD buoyant flow. Based on these understandings, suggestions to improve the thermal-hydraulic performance of DFLL blanket might be deduced. For liquid metal blankets, to reach high temperature and reduce MHD pressure drop, FCI [22] with low heat conductivity and electric conductivity was inserted in liquid metal channels. The real FCI structure was complex, where 5 mm PbLi interlay existed between FCI and steel wall, and pressure equalization slots existed in FCI. Due to the SiC materials with low electric (0.1–10 S/m) and thermal conductivity (∼ 3 W/(m K)), the gap flow between steel wall and FCI has little influence on the temperature of bulk flow and electric conductivity of FCI as the boundary condition of bulk flow. In this model, steel wall and gap flow of PbLi were ignored and the boundary wall of LL1 bulk flow were simplified to be insulted FCI (as shown in Fig. 2). As shown in Table 1, the thickness of FCI wall was 5 mm and the temperature of FCI wall was set as the average of inlet and outlet helium coolant temperature, and the size of LL1 channel was 0.11 m (radial) × 0.207 m (toroidal) × 1.5 m (poloidal). The magnetic field was set as 4 T for ITER TBM and deposited neutron heat power distribution satisfied the following formula [23]:
Snuclear heat = 0.6798 e (drad
0.2463)/0.1023
+ 0.0595(MW / m3)
+ 1.3939 × 10
8
×e (drad
blanket under strong magnetic fields. Momentum equation:
v + (v t
)v
=
p+
2v
+f + J ×B
(2)
Where v , B , , , p are velocity, magnetic field, kinematic viscosity, density and pressure separately. J stands for electric current density, B stands for magnetic field and J × B is Lorentz force, f stands for (T T0)) , which is modelled by buoyancy force and f = g (1 Boussinesq buoyancy model as in [14]:
(
0)
g =
0
(T
(3)
T0 ) g
Where T, are temperature and density of flow, T0, 0 are reference temperature, reference density of flow , is the thermal expansion coefficient. According to the PbLi density function of temperature [26]:
= 10450
(4)
1.682 T
The density of PbLi changes only about 7% with temperature increasing from 573 K to 973 K, so Boussinesq buoyancy model is suitable for this case. Validation of this model for MHD buoyant flow has been done [21] by comparing MTC simulation results with experimental data of natural convection of molten gallium suppressed under an external magnetic field in either the X, Y, or Z direction [15]. Liquid PbLi can be regarded as an incompressible fluid, so the continuity is: (5)
v =0 Energy equation:
T + (v t
cp
)T =
( T) +
1
J 2 + Snuclear heat
(6)
Where cp is specific heat, , are electric conductivity and heat con1 ductivity of fluid. J 2 is Joule heat in MHD flow and Snuclear heat is the deposited neutron heat define in Eq. (1). Ohm's law:
0.2463)/0.0073
J =
(1)
(
+ v ×B)
(7)
Conservation of charge:
Snuclear heat is the source of deposited neutron heat, and e is natural constant and dtor is the radial distance from first wall of DFLL blanket. The governing equations for MHD buoyant flow in fusion blankets combine Navier-Stokes equations for hydrodynamics, electric potential equations and energy equation. Considering the low magnetic Reynolds number (Rm = 0.01∼0.1) in fusion liquid metal blankets, the inductionless approximation [12] was adopted, where the magnetic fields induced by currents in the fluid is negligible compared to the externally applied field B. Mingjiu Ni’s current density conservative scheme [25] for incompressible MHD flows at a low magnetic Reynolds number was adopted in our code MTC [20] to simulate the liquid metal flow of DFLL
J =0
(8)
The factors influencing MHD buoyant flow were flow direction, heat conductivity and electric conductivity of FCI. In the following sections all these factors were analyzed independently for LL1 channel of DFLL blankets under ITER TBM condition using MHD code MTC [21]. 2.2. Influence of heat conductivity of FCI on MHD buoyant flow FCI was key component of high temperature PbLi blankets such as DFLL and DCLL [11], which acted as heat-insulting material to achieve
Fig. 2. Simplification of the cross-section view of LL1 channel with FCI. 3
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Table 1 Parameters of LL1 channel.
FCI Wall
Fluid
Material
SiC
Thickness (mm) Density (kg/m³) Specific heat(J/kg K) Heat conductivity (W/m K) Electric conductivity (S/m) Temperature of wall near FW Temperature of radial-poloidal wall Temperature of toroidal-poloidal wall
5 2500 600 sensitive parameter sensitive parameter (THe inlet + THe outlet)/2 = (613+668)/2 K= 640.5 K (THe inlet + THe outlet)/2 = (668+675)/2 K= 671.5 K (THe inlet + THe outlet)/2 = (668+685)/2 K = 676.5 K
Material
PbLi
Inlet temperature (K) Inlet velocity (m/s) Outlet condition Density (kg/m³) Specific heat (J/kg K) Heat conductivity (W/m·K) Electric conductivity (S/m) Kinetic viscosity (Pa-s) Magnetic field Reynold number
753 0.014 Pressure-outlet set as 0.5 MPa 9184 188 16.71 0.744e6 0.0012 4T, toroidal 1.1 × 10 4
Hartmann number
1.0 × 10 4
Stuart number
9.2 × 103
Grashof number
4.4 × 109
high temperature. The designed heat conductivity of FCI was between 1∼5 W/m K. In real operating condition under neutron irradiation and high temperature, heat conductivity of FCI usually degenerates to ∼15 W/m K. In this section, the influence of FCIs with different heat conductivity of 1 W/m K, 5 W/m K and 15 W/m K on MHD buoyant flow were analyzed. The flow was designed downward in LL1 channel. As shown in Fig. 3, under the buoyancy force, the core flow near first wall with highest neutron heat power flowed upward, and the flow far from first
wall flowed downward, which formed natural convection in LL1 channel. If we observe the velocity carefully in Fig. 4, we found that there was no downward flow even near the cooled boundary in the case with heat conductivity 1 W/m K. While for heat conductivity 5 W/m K and 15 W/m K, significant downward boundary flow appeared near wall which is cooled by helium coolant. The temperature distribution of LL1 channel is shown in Fig. 5. The reverse buoyant flow drove heated fluid back to the cold inlet area, forming heat-mixing area with temperature difference ∼200 K. As
Fig. 3. MHD buoyant flow distribution in LL1 channel with different FCI heat conductivity. 4
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Fig. 4. Velocity distribution in LL1 channel cross section with different FCI heat conductivity (Unit: s/m).
Fig. 5. Temperature distribution in LL1 channel with different FCI heat conductivity (Unit: K).
can’t reach high temperature. Leakage from FW accounted for more than half of the total leakage. We can conclude that the design requirement of heat conductivity of FCI should be much lower, for example, 0.1 W/m K to get high outlet temperature.
Table 2 Volumetric nuclear heat leakage rate in LL1 channel. FCI (W/ m K)
Heat leakage rate
Leakage from FW and cover plate
Leakage from R-T plate
Leakage from R-P plate
1 5 15
52.34% 102% 125%
23.9% 53.1% 70.6%
13.3% 26.9% 33.2%
15.2% 22.5% 21.2%
2.3. Influence of flow direction on MHD buoyant flow For vertical flow, flow direction is important relative to gravity direction. In LL1 channel of DFLL blanket, PbLi was design to flow downward, while in LL1 channel of US DCLL blanket, PbLi was design to flow upward. If buoyancy was not considered, both flow directions had no difference. But for buoyant flow, the direction of buoyancy force and driven force would make a significant difference.
shown in Table 2, the heat leakage of PbLi volumetric nuclear heat in LL1 channel to helium was calculated. More than 50% heat leaked from FCI of 1 W/m K. For FCI > 5 W/ m K, all deposited neutron heat was leaked, which means that the outlet 5
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Fig. 6. Flow distribution in LL1 channel under different driven direction.
Fig. 7. Velocity distribution in LL1 channel cross section under different driven direction (Unit: s/m).
MHD buoyant flows in LL1 channel with upward and downward directions were analyzed and compared. From the streamline pattern in Fig. 6, we found that the upward driven flow was in accordance with the buoyant flow near first wall, and natural convection almost disappeared. Core fluid flowed upward as shown in Fig. 6(b), only small area of downward boundary flow appeared. The buoyancy force increased the upward velocity near first wall, as shown in Fig. 7(b). Relative to the drastic natural convection flow in downward driven flow case, the upward driven flow did not conflict with buoyant flow and took away volumetric nuclear heat smoothly, which eliminated heat
mix area near inlet and decreased volumetric nuclear heat leakage. The upward flow significantly increased outlet PbLi temperature, which would improve the original design as shown in Fig. 8. 2.4. Influence of electric conductivity of FCI on MHD buoyant flow FCI was usually made of low electric conductivity material SiC, which aimed to reduce MHD effects. Design requirement of electric conductivity of FCI was between 1∼10 S/m. Under high temperature condition, electric conductivity of material SiC would increase to ∼20 6
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Fig. 8. Temperature distribution in LL1 channel cross section under different driven direction (Unit: K).
Fig. 9. MHD buoyant flow distribution in LL1 channel with different FCI electric conductivity.
S/m. In this section, the influence of FCI with different electric conductivity of 1 S/m, 50 S/m and purely steel wall on MHD buoyant flow was analyzed and compared. To keep the natural convection strength, the design flow was set downward. When electric conductivity of FCI was low (1∼50 S/m), obvious reverse flow near first wall appeared and natural convection formed in channel, as shown in Figs. 9(a), (b) and 10 (a), (b). Little difference was found between the condition of 1 S/m and 50 S/m. But when FCI was replaced by steel with high electric conductivity 1.023E6 S/m, MHD Lorentz force greatly surpassed buoyancy force and completely suppressed buoyant flow. No reverse flow appeared and the MHD buoyant flow was almost the same with MHD Hunt [24] flow with typical jet near side wall. As shown in Fig. 11(c), the electric current path was very similar to that of MHD Hunt case. We analyzed the electric
current density and found that electric current density in the core area under insulated wall condition was 0∼200 A/m2, while for steel wall the electric current density was 1700∼2000 A/m2. The huge Lorentz force J × B dominated the flow characteristic in channel with steel wall. 3. MHD buoyant flow analysis of DFLL blanket 3.1. Model of DFLL blanket In this section, MHD buoyant flow in DFLL blanket under ITER TBM condition was analyzed. The wall of channel was simplified to 5 mm FCI with electric conductivity 5 S/m. According to the analysis in Section 2.2, the heat conductivity of FCI was assumed to be 0.1 W/m·K to get high outlet temperature. The
7
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Fig. 10. Velocity distribution in LL1 channel cross section with different FCI electric conductivity (Unit: s/m).
Fig. 11. Electric current distribution in LL1 channel cross section with different FCI electric conductivity.
detailed parameters of this model were shown in Table 3. To clarify the influence of buoyancy with Grashof number 4.4 × 109 , firstly we compared thermal-hydraulic phenomena of DFLL blanket under buoyant condition with non-buoyant condition. Then according to the improvement suggestion of Section 2.3, we analyzed the MHD buoyant flow in the upside-down DFLL blanket.
condition in Figs. 12(a), 13 (a), reverse flow appeared in LL1 and LL2 channel. Local natural convection existed in LL1 channel and global natural circulation formed between LL2 and LL3 channel, which made the flow in LL3 channel completely reversed. In LL1 channel, buoyant convection with peak upper velocity of 0.0887 m/s and peak downward velocity of 0.315 m/s which greatly surpassed the driven velocity 0.014 m/s. While in LL2 and LL3 channels, the difference of volumetric nuclear power deposited in the two connected channels formed natural circulation between the two channels. The peak upward velocity in LL2 reached 0.06 m/ s, which also surpassed the driven velocity. As shown in Fig. 14(b), when no buoyancy existed, temperature distribution was in accordance with the design except the local high
3.2. Thermal-hydraulic analysis As shown in Figs. 12(b), 13 (b), when no buoyancy existed, PbLi flowed smoothly through LL1 channel and distributed to LL2 and LL3 channels. No reverse flow or convection flow formed. But under buoyant
8
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temperature at corner of LL1 channel. The inlet cold PbLi flowed smoothly, gradually accumulating volumetric nuclear heat. There was stagnant zone in the LL1 corner, which reduced the convection heat transfer and formed local high temperature. This situation could be simply solved by chamfering the corner. For buoyant condition in Fig. 14(a), the temperature distribution was disordered. The highest temperature located at upper corner near inlet of LL1 channel, where hot reverse flow mixed with cold inlet flow. From both analysis we can conclude that smooth flow without stagnant and reverse flow is important for reaching high outlet temperature. Disordered flow would form local high temperature area and lead to additional volumetric nuclear heat leakage, also increasing the thermal stress of structure.
Table 3 Parameters of DFLL blanket.
Wall
Fluid
Material
SiC
Thickness (mm) Density (kg/m³) Specific heat(J/kg K) Heat conductivity (W/m K) Electric conductivity (S/m)
5 2500 600 0.1 5
Material
PbLi
Inlet temperature (K) Inlet velocity (m/s) Outlet condition Density (kg/m³) Specific heat (J/kg K) Heat conductivity (W/m K) Electric conductivity (S/m) Kinetic viscosity(Pa-s) Magnetic field
753 0.014 Pressure-outlet set as 0.5 MPa 9184 188 16.71 0.744e6 0.0012 4T, toroidal
3.3. Improvement of DFLL blanket In Section 2.2 we found that when PbLi in LL1 flowed upward, no reverse flow appeared and heat was smoothly taken away. In this section we reversed the vertical direction of DFLL blanket and made the LL1 flow upward, as shown in Fig. 15(a). From Fig. 15(b) we found that
Fig. 12. Flow distribution of DFLL blanket.
Fig. 13. Velocity distribution in channel cross section of DFLL blanket (Unit: s/m).
9
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Fig. 14. Temperature distribution of DFLL blanket (Unit: K).
Fig. 15. Improved model of DFLL blanket.
PbLi flowed smoothly in LL1 channel and no reverse flow existed here. In LL2 and LL3 channels, global natural circulation formed and reversed flow in LL2 increased its temperature. By comparing temperature distribution of Fig. 16(a) with (b), this peak temperature decreased 100 K. The location of peak temperature was middle part of LL2 channel, which was formed by reverse flow there. The improved temperature distribution was in accordance with design goal, where high temperature existed near outlet and low temperature existed near inlet.
factors analysis, and optimization suggestions of blanket design were concluded according to the detailed analysis. The buoyancy induced natural convection in the duct, which increased the heat leaked to Helium coolant and reduced the outlet temperature. To achieve high temperature (973 K) at outlet of PbLi duct, heat conductivity of FCI material was suggested to be < 1 W/m·K to reduce the heat leaked to Helium coolant. Reversed direction of original flow in DFLL blanket would be helpful to reduce heat leakage of PbLi volumetric nuclear heat and get high temperature at outlet. The Lorentz force induced by moving PbLi under magnetic field suppressed buoyancy strength. At the extreme condition of duct with steel wall, buoyancy was completely suppressed by Lorentz force, and no buoyant flow exists. According to the founding above, we analyzed the MHD buoyant flow in an upside-down DFLL blanket. The temperature distribution in the improved model was in accordance with design goal, where high temperature existed near outlet and low temperature existed near inlet.
4. Conclusion In this paper, MHD buoyant flow of Dual Functional Lead Lithium blanket (DFLL) under typical fusion magnetic field and non-uniform volumetric nuclear heating were studied. PbLi duct LL1 near first wall of DFLL blanket with the most significant buoyancy effect was chosen for influence
10
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Fig. 16. Temperature distribution of original and improved DFLL blanket (Unit: k).
Declaration of Competing Interest
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The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper. Acknowledgements This work was supported by the National Magnetic Confinement Fusion Science Program of China (2015GB116000B), the National Natural Science Foundation of China (51606206), the informatization Project of Chinese Academy of Sciences (XXH13506-104), the National R&D Infrastructure and Facility Development Program of ChinaFundamental Science Data Sharing Platform (DKA2017-12-02-17), the Special Project of Youth Innovation Association of Chinese Academy of Sciences and the Industrialization Fund. In addition, the authors would like to show their great appreciation to other members of the FDS Team for supports to this research. References [1] D. Maisonnier, I. Cook, P. Sardain, et al., A Conceptual Study of Commercial Fusion Power Plants-Final Report of the European Fusion Power Plant Conceptual Study (PPCS), EFDA, Switzerland, 2005. [2] Y.C. Wu, FDS Team, Conceptual design of the China fusion power plant FDS-II, Fusion Eng. Des. 83 (10–12) (2008) 1683–1689. [3] Y. Poitevin, L.B. Boccaccini, A. Cardella, L. Giancarli, R. Meyder, E. Diegele, et al., The European breeding blankets development and the test strategy in ITER, Fusion Eng. Des. 75–79 (2005) 741–749. [4] M.S. Tillack, X.R. Wang, J. Pulsifer, et al., ARIES-ST breeding blanket design and analysis, Fusion Eng. Des. 49 (2000) 689–695. [5] F. Cismondi, S. Kecskés, M. Ilic, et al., Design update, thermal and fluid dynamic analyses of the EU-HCPB TBM in vertical arrangement, Fusion Eng. Des. 84 (2) (2009) 607–612. [6] Feng, Yongjin Feng, et al., Current status of the fabrication of Li4SiO4 and beryllium pebbles for CN HCCB TBM in SWIP, Plasma Sci. Technol. 15 (3) (2013) 291–294. [7] M. Enoeda, H. Tanigawa, T. Hirose, et al., R&D status on water cooled ceramic breeder blanket technology, Fusion Eng. Des. 89 (7-8) (2014) 1131–1136. [8] Y.C. Wu, Conceptual design of the China fusion power plant FDS-II, Fusion Eng.
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Fusion Engineering and Design journal homepage: www.elsevier.com/locate/fusengdes
Numerical research of magnetohydrodynamics buoyant flow in dual functional lead lithium fusion blanket Shichao Zhanga,b, Lin Chena,b, Zi Menga,⁎, Zhang Guangyua a b
Key Laboratory of Neutronics and Radiation Safety, Institute of Nuclear Energy Safety Technology, Chinese Academy of Sciences, Hefei, Anhui 230031, China University of Science and Technology of China, Hefei, Anhui 230027, China
ARTICLE INFO
ABSTRACT
Keywords: MHD Buoyant flow Liquid metal blanket
Blanket is key component of fusion reactor, which functions as tritium breeder, energy conversion component and radiation shield. Liquid metal fusion blanket is a promising candidate of future fusion power plants for its high temperature operating characteristics and efficient thermoelectric conversion. However, motion of liquid metal under fusion reactor high magnetic field (∼4 T) causes serious magnetohydrodynamics (MHD) effect, and extreme non-uniform volumetric heat deposited by fusion neutrons produces strong buoyancy effect. Both effects greatly change flow field and heat transfer characteristics of liquid metal blanket, which are key issues for thermal-hydraulic design of liquid metal blankets. In this paper, MHD buoyant flow of Dual Functional Lead Lithium blanket (DFLL) under typical fusion magnetic field and non-uniform volumetric nuclear heating were studied. Buoyancy force induced drastic natural convection in LL1 (the 1st Lead Lithium channel) channel of blanket and increased the heat leaked to Helium coolant and reduced the outlet temperature. FCI (flow channel insert) material with heat conductivity < 1W/m K was required to achieve high outlet temperature (700 K). Reversed direction of original flow in DFLL blanket would smooth the flow and reduce heat leakage of PbLi, which formed the idea of improvement. At the extreme condition of duct with steel wall, Lorentz force completely suppressed buoyancy. According to the founding above, we analyzed the MHD buoyant flow in an upsidedown DFLL blanket and temperature distribution and heat leakage were significantly improved. This finding would be valuable for liquid blanket thermal hydraulic design.
1. Introduction
structure, whose kinetic energy transforms to deposited heat. Because of penetration characteristic of neutrons, the FW structure and LL1 channel are mostly heated. The neutron heat deposited in the liquid metal zone presents great heterogeneity, which forms drastic gradient of deposited neutron heat and causes temperature gradient and buoyant flow in liquid blanket [11]. For DFLL blanket under ITER TBM (test blanket module) condition, the ∼4 T magnetic field and 0.78 MW/m2 neutron wall loading induce huge Lorentz force and buoyancy force. The Hartmann number (ratio of electromagnetic force to viscous force) reaches 1.0 × 10 4 and the Grashof number (ratio of buoyancy force to viscous force) is 4.4 × 109 , where the liquid metal flow is greatly altered by Lorentz force and buoyancy force and forms MHD buoyant flow. The MHD buoyant flow formed by the coupled effect of Lorentz force and buoyancy force is different from the general buoyant flow. The Lorentz force is very sensitive to magnetic fields, electric conductivity of wall and liquid flow, while buoyancy is sensitive to gradient of deposited neutron heat, heat conductivity of wall and liquid flow, direction of flow channel, liquid metal density and so on. So MHD buoyant flow will be
Blankets [1,2] are key components of fusion reactor, which transfer fusion energy to heat, breed tritium and shield neutrons. According to state of breeder form, fusion blankets can be classified as liquid breeder blanket [2–4] and solid breeder blanket [5–7]. For liquid blanket, the tritium breeder PbLi is also neutron multiplier, while for solid blanket, additional neutron multiplier such as Be is added among the tritium breeder. FDS team developed conceptual design of the China fusion power plant FDS-II [8], where the blanket DFLL adopted the liquid leadlithium as coolant [9]. Liquid metal blanket has the advantage of high temperature operation and high thermal efficiency, which is a promising candidate for future fusion power plant. However, in most fusion reactors fusion plasma is constrained by strong magnetic fields and blankets operate under the influence of magnetic fields. The flowing liquid metal under strong magnetic fields would induce Lorentz force which is equal to or even larger than driven force, forming MHD flow [10]. In liquid metal blankets, fusion neutrons are absorbed by liquid metal breeder and
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Corresponding author. E-mail address: [email protected] (Z. Meng).
https://doi.org/10.1016/j.fusengdes.2019.111331 Received 25 February 2019; Received in revised form 26 July 2019; Accepted 20 September 2019 0920-3796/ © 2019 Published by Elsevier B.V.
Please cite this article as: Shichao Zhang, et al., Fusion Engineering and Design, https://doi.org/10.1016/j.fusengdes.2019.111331
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Nomenclature Re Ha Gr Snuclear heat e x p
v f J B
Gravity Temperature Average temperature Specific heat of fluid Electric conductivity of fluid Heat conductivity of fluid Buoyancy force
g T T0 cp
Reynold number, ratio of inertial force to viscous force Hartmann number, ratio of electromagnetic force to viscous force Grashof number, ratio of buoyancy force to viscous force Source of deposited neutron heat Natural constant Distance from first wall of blanket Pressure Density Velocity vector Buoyancy force Induced electric current density Magnetic field Dynamic viscosity
f
Abbreviations MHD DFLL PbLi LL1, LL2, FCI Re
closely related to magnetic fields, electric conductivity, heat conductivity and flow direction. For simple vertical infinite plate MHD buoyant flow [12], theory results showed that magnetic field would suppress buoyant flow. L. Bühler [13,14] investigated MHD buoyant flow in blanket-related channel, and found that the flow jet location was deeply related to magnetic field direction and heat flux direction. Ozoe [15] numerical investigated natural convection in cavity under different magnetic field direction and found that the magnetic field parallel to heat flux suppressed buoyancy significantly, while magnetic field perpendicular to heat flux suppressed buoyancy weakly. Smolentsev [16] developed a code for fully developed MHD flow of a liquid metal blanket using insulation techniques and compared the flow rate in the central channel with and without FCI (flow channel insert). Khodak [17] investigated the preliminary design of the DCLL TBM, including complex helium flow channels, lead-lithium flow channels with FCIs and structural materials and improved the design, which can lead to significant reduction of the pressure drop and improvement in temperature uniformity. Kharicha [18] analyzed MHD buoyant flow in single duct of HCLL blanket. For horizontal duct, MHD buoyant convection had a weak influence on temperature. But for vertical duct, temperature was greatly changed by buoyant convection. Okada [19] carried out an MHD buoyant
magnetohydrodynamics Dual Functional Lead Lithium blanket Lead-lithium eutectic alloy LL3 First, second and third vertical flow channel flow channel insert Reynold number
flow experiment, where liquid metal Ga was filled into a cavity with heat flux and magnetic fields and validated the relation of magnetic field direction with MHD suppression on buoyancy. Meng [21] carried out simulation of this experiments and found the same results. From these theories and experimental investigation, we can predict that in actual liquid blanket channels, the influence of electric conductivity, heat conductivity of wall and flow direction on MHD buoyant flow is non-negligible. This paper aimed to analyze MHD buoyant flow behavior in PbLi blanket DFLL with code MTC, which has been validated according to for the magnetohydrodynamic flow at high Hartmann number [20,21]. Typical fusion condition of ITER TBM [22] were adopted as basic physical condition. The influence of heat conductivity and electric conductivity of wall, direction of flow field on MHD buoyant flow were analyzed. The MHD buoyant effect on temperature distribution in DFLL blanket was evaluated and optimization design was proposed to improve the thermal-hydraulic performance of DFLL blanket. 2. Influence factor analysis for MHD buoyant flow 2.1. Blanket related channel model and mathematical formulation DFLL blanket was a box-shaped structure, which composes of first
Fig. 1. Isolated LL1 channel near first wall of DFLL blanket. 2
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wall (FW) directly facing neutron bombardment, cover plate, separate plates, back plate and PbLi channels. Radial-poloidal separate plate and toroidal-poloidal separate plate form flow channel of liquid PbLi, with He coolant flowing inside plate with fine channel like blood vessel to remove heat. The magnetic field of the fusion reactor is along the toroidal direction, which will significantly affect PbLi flow in blanket. As shown in Fig. 1, liquid PbLi channels were composed of 3 vertical flow channels: LL1, LL2, and LL3, with LL1 closest to the first wall, and physically connected to LL2 and LL3, the latter being the farthest from the first wall, both accepting liquid metal flow from LL1. The vertical flow channel LL1 was isolated for MHD buoyant flow analysis, where most of the neutron heat deposited and buoyancy effect was most significant, and. The purpose of this simplification is to get a basic understanding of the effects of the FCI thermal conductivity, the FCI electric conductivity, and liquid metal flow direction on MHD buoyant flow. Based on these understandings, suggestions to improve the thermal-hydraulic performance of DFLL blanket might be deduced. For liquid metal blankets, to reach high temperature and reduce MHD pressure drop, FCI [22] with low heat conductivity and electric conductivity was inserted in liquid metal channels. The real FCI structure was complex, where 5 mm PbLi interlay existed between FCI and steel wall, and pressure equalization slots existed in FCI. Due to the SiC materials with low electric (0.1–10 S/m) and thermal conductivity (∼ 3 W/(m K)), the gap flow between steel wall and FCI has little influence on the temperature of bulk flow and electric conductivity of FCI as the boundary condition of bulk flow. In this model, steel wall and gap flow of PbLi were ignored and the boundary wall of LL1 bulk flow were simplified to be insulted FCI (as shown in Fig. 2). As shown in Table 1, the thickness of FCI wall was 5 mm and the temperature of FCI wall was set as the average of inlet and outlet helium coolant temperature, and the size of LL1 channel was 0.11 m (radial) × 0.207 m (toroidal) × 1.5 m (poloidal). The magnetic field was set as 4 T for ITER TBM and deposited neutron heat power distribution satisfied the following formula [23]:
Snuclear heat = 0.6798 e (drad
0.2463)/0.1023
+ 0.0595(MW / m3)
+ 1.3939 × 10
8
×e (drad
blanket under strong magnetic fields. Momentum equation:
v + (v t
)v
=
p+
2v
+f + J ×B
(2)
Where v , B , , , p are velocity, magnetic field, kinematic viscosity, density and pressure separately. J stands for electric current density, B stands for magnetic field and J × B is Lorentz force, f stands for (T T0)) , which is modelled by buoyancy force and f = g (1 Boussinesq buoyancy model as in [14]:
(
0)
g =
0
(T
(3)
T0 ) g
Where T, are temperature and density of flow, T0, 0 are reference temperature, reference density of flow , is the thermal expansion coefficient. According to the PbLi density function of temperature [26]:
= 10450
(4)
1.682 T
The density of PbLi changes only about 7% with temperature increasing from 573 K to 973 K, so Boussinesq buoyancy model is suitable for this case. Validation of this model for MHD buoyant flow has been done [21] by comparing MTC simulation results with experimental data of natural convection of molten gallium suppressed under an external magnetic field in either the X, Y, or Z direction [15]. Liquid PbLi can be regarded as an incompressible fluid, so the continuity is: (5)
v =0 Energy equation:
T + (v t
cp
)T =
( T) +
1
J 2 + Snuclear heat
(6)
Where cp is specific heat, , are electric conductivity and heat con1 ductivity of fluid. J 2 is Joule heat in MHD flow and Snuclear heat is the deposited neutron heat define in Eq. (1). Ohm's law:
0.2463)/0.0073
J =
(1)
(
+ v ×B)
(7)
Conservation of charge:
Snuclear heat is the source of deposited neutron heat, and e is natural constant and dtor is the radial distance from first wall of DFLL blanket. The governing equations for MHD buoyant flow in fusion blankets combine Navier-Stokes equations for hydrodynamics, electric potential equations and energy equation. Considering the low magnetic Reynolds number (Rm = 0.01∼0.1) in fusion liquid metal blankets, the inductionless approximation [12] was adopted, where the magnetic fields induced by currents in the fluid is negligible compared to the externally applied field B. Mingjiu Ni’s current density conservative scheme [25] for incompressible MHD flows at a low magnetic Reynolds number was adopted in our code MTC [20] to simulate the liquid metal flow of DFLL
J =0
(8)
The factors influencing MHD buoyant flow were flow direction, heat conductivity and electric conductivity of FCI. In the following sections all these factors were analyzed independently for LL1 channel of DFLL blankets under ITER TBM condition using MHD code MTC [21]. 2.2. Influence of heat conductivity of FCI on MHD buoyant flow FCI was key component of high temperature PbLi blankets such as DFLL and DCLL [11], which acted as heat-insulting material to achieve
Fig. 2. Simplification of the cross-section view of LL1 channel with FCI. 3
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Table 1 Parameters of LL1 channel.
FCI Wall
Fluid
Material
SiC
Thickness (mm) Density (kg/m³) Specific heat(J/kg K) Heat conductivity (W/m K) Electric conductivity (S/m) Temperature of wall near FW Temperature of radial-poloidal wall Temperature of toroidal-poloidal wall
5 2500 600 sensitive parameter sensitive parameter (THe inlet + THe outlet)/2 = (613+668)/2 K= 640.5 K (THe inlet + THe outlet)/2 = (668+675)/2 K= 671.5 K (THe inlet + THe outlet)/2 = (668+685)/2 K = 676.5 K
Material
PbLi
Inlet temperature (K) Inlet velocity (m/s) Outlet condition Density (kg/m³) Specific heat (J/kg K) Heat conductivity (W/m·K) Electric conductivity (S/m) Kinetic viscosity (Pa-s) Magnetic field Reynold number
753 0.014 Pressure-outlet set as 0.5 MPa 9184 188 16.71 0.744e6 0.0012 4T, toroidal 1.1 × 10 4
Hartmann number
1.0 × 10 4
Stuart number
9.2 × 103
Grashof number
4.4 × 109
high temperature. The designed heat conductivity of FCI was between 1∼5 W/m K. In real operating condition under neutron irradiation and high temperature, heat conductivity of FCI usually degenerates to ∼15 W/m K. In this section, the influence of FCIs with different heat conductivity of 1 W/m K, 5 W/m K and 15 W/m K on MHD buoyant flow were analyzed. The flow was designed downward in LL1 channel. As shown in Fig. 3, under the buoyancy force, the core flow near first wall with highest neutron heat power flowed upward, and the flow far from first
wall flowed downward, which formed natural convection in LL1 channel. If we observe the velocity carefully in Fig. 4, we found that there was no downward flow even near the cooled boundary in the case with heat conductivity 1 W/m K. While for heat conductivity 5 W/m K and 15 W/m K, significant downward boundary flow appeared near wall which is cooled by helium coolant. The temperature distribution of LL1 channel is shown in Fig. 5. The reverse buoyant flow drove heated fluid back to the cold inlet area, forming heat-mixing area with temperature difference ∼200 K. As
Fig. 3. MHD buoyant flow distribution in LL1 channel with different FCI heat conductivity. 4
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Fig. 4. Velocity distribution in LL1 channel cross section with different FCI heat conductivity (Unit: s/m).
Fig. 5. Temperature distribution in LL1 channel with different FCI heat conductivity (Unit: K).
can’t reach high temperature. Leakage from FW accounted for more than half of the total leakage. We can conclude that the design requirement of heat conductivity of FCI should be much lower, for example, 0.1 W/m K to get high outlet temperature.
Table 2 Volumetric nuclear heat leakage rate in LL1 channel. FCI (W/ m K)
Heat leakage rate
Leakage from FW and cover plate
Leakage from R-T plate
Leakage from R-P plate
1 5 15
52.34% 102% 125%
23.9% 53.1% 70.6%
13.3% 26.9% 33.2%
15.2% 22.5% 21.2%
2.3. Influence of flow direction on MHD buoyant flow For vertical flow, flow direction is important relative to gravity direction. In LL1 channel of DFLL blanket, PbLi was design to flow downward, while in LL1 channel of US DCLL blanket, PbLi was design to flow upward. If buoyancy was not considered, both flow directions had no difference. But for buoyant flow, the direction of buoyancy force and driven force would make a significant difference.
shown in Table 2, the heat leakage of PbLi volumetric nuclear heat in LL1 channel to helium was calculated. More than 50% heat leaked from FCI of 1 W/m K. For FCI > 5 W/ m K, all deposited neutron heat was leaked, which means that the outlet 5
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Fig. 6. Flow distribution in LL1 channel under different driven direction.
Fig. 7. Velocity distribution in LL1 channel cross section under different driven direction (Unit: s/m).
MHD buoyant flows in LL1 channel with upward and downward directions were analyzed and compared. From the streamline pattern in Fig. 6, we found that the upward driven flow was in accordance with the buoyant flow near first wall, and natural convection almost disappeared. Core fluid flowed upward as shown in Fig. 6(b), only small area of downward boundary flow appeared. The buoyancy force increased the upward velocity near first wall, as shown in Fig. 7(b). Relative to the drastic natural convection flow in downward driven flow case, the upward driven flow did not conflict with buoyant flow and took away volumetric nuclear heat smoothly, which eliminated heat
mix area near inlet and decreased volumetric nuclear heat leakage. The upward flow significantly increased outlet PbLi temperature, which would improve the original design as shown in Fig. 8. 2.4. Influence of electric conductivity of FCI on MHD buoyant flow FCI was usually made of low electric conductivity material SiC, which aimed to reduce MHD effects. Design requirement of electric conductivity of FCI was between 1∼10 S/m. Under high temperature condition, electric conductivity of material SiC would increase to ∼20 6
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Fig. 8. Temperature distribution in LL1 channel cross section under different driven direction (Unit: K).
Fig. 9. MHD buoyant flow distribution in LL1 channel with different FCI electric conductivity.
S/m. In this section, the influence of FCI with different electric conductivity of 1 S/m, 50 S/m and purely steel wall on MHD buoyant flow was analyzed and compared. To keep the natural convection strength, the design flow was set downward. When electric conductivity of FCI was low (1∼50 S/m), obvious reverse flow near first wall appeared and natural convection formed in channel, as shown in Figs. 9(a), (b) and 10 (a), (b). Little difference was found between the condition of 1 S/m and 50 S/m. But when FCI was replaced by steel with high electric conductivity 1.023E6 S/m, MHD Lorentz force greatly surpassed buoyancy force and completely suppressed buoyant flow. No reverse flow appeared and the MHD buoyant flow was almost the same with MHD Hunt [24] flow with typical jet near side wall. As shown in Fig. 11(c), the electric current path was very similar to that of MHD Hunt case. We analyzed the electric
current density and found that electric current density in the core area under insulated wall condition was 0∼200 A/m2, while for steel wall the electric current density was 1700∼2000 A/m2. The huge Lorentz force J × B dominated the flow characteristic in channel with steel wall. 3. MHD buoyant flow analysis of DFLL blanket 3.1. Model of DFLL blanket In this section, MHD buoyant flow in DFLL blanket under ITER TBM condition was analyzed. The wall of channel was simplified to 5 mm FCI with electric conductivity 5 S/m. According to the analysis in Section 2.2, the heat conductivity of FCI was assumed to be 0.1 W/m·K to get high outlet temperature. The
7
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Fig. 10. Velocity distribution in LL1 channel cross section with different FCI electric conductivity (Unit: s/m).
Fig. 11. Electric current distribution in LL1 channel cross section with different FCI electric conductivity.
detailed parameters of this model were shown in Table 3. To clarify the influence of buoyancy with Grashof number 4.4 × 109 , firstly we compared thermal-hydraulic phenomena of DFLL blanket under buoyant condition with non-buoyant condition. Then according to the improvement suggestion of Section 2.3, we analyzed the MHD buoyant flow in the upside-down DFLL blanket.
condition in Figs. 12(a), 13 (a), reverse flow appeared in LL1 and LL2 channel. Local natural convection existed in LL1 channel and global natural circulation formed between LL2 and LL3 channel, which made the flow in LL3 channel completely reversed. In LL1 channel, buoyant convection with peak upper velocity of 0.0887 m/s and peak downward velocity of 0.315 m/s which greatly surpassed the driven velocity 0.014 m/s. While in LL2 and LL3 channels, the difference of volumetric nuclear power deposited in the two connected channels formed natural circulation between the two channels. The peak upward velocity in LL2 reached 0.06 m/ s, which also surpassed the driven velocity. As shown in Fig. 14(b), when no buoyancy existed, temperature distribution was in accordance with the design except the local high
3.2. Thermal-hydraulic analysis As shown in Figs. 12(b), 13 (b), when no buoyancy existed, PbLi flowed smoothly through LL1 channel and distributed to LL2 and LL3 channels. No reverse flow or convection flow formed. But under buoyant
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temperature at corner of LL1 channel. The inlet cold PbLi flowed smoothly, gradually accumulating volumetric nuclear heat. There was stagnant zone in the LL1 corner, which reduced the convection heat transfer and formed local high temperature. This situation could be simply solved by chamfering the corner. For buoyant condition in Fig. 14(a), the temperature distribution was disordered. The highest temperature located at upper corner near inlet of LL1 channel, where hot reverse flow mixed with cold inlet flow. From both analysis we can conclude that smooth flow without stagnant and reverse flow is important for reaching high outlet temperature. Disordered flow would form local high temperature area and lead to additional volumetric nuclear heat leakage, also increasing the thermal stress of structure.
Table 3 Parameters of DFLL blanket.
Wall
Fluid
Material
SiC
Thickness (mm) Density (kg/m³) Specific heat(J/kg K) Heat conductivity (W/m K) Electric conductivity (S/m)
5 2500 600 0.1 5
Material
PbLi
Inlet temperature (K) Inlet velocity (m/s) Outlet condition Density (kg/m³) Specific heat (J/kg K) Heat conductivity (W/m K) Electric conductivity (S/m) Kinetic viscosity(Pa-s) Magnetic field
753 0.014 Pressure-outlet set as 0.5 MPa 9184 188 16.71 0.744e6 0.0012 4T, toroidal
3.3. Improvement of DFLL blanket In Section 2.2 we found that when PbLi in LL1 flowed upward, no reverse flow appeared and heat was smoothly taken away. In this section we reversed the vertical direction of DFLL blanket and made the LL1 flow upward, as shown in Fig. 15(a). From Fig. 15(b) we found that
Fig. 12. Flow distribution of DFLL blanket.
Fig. 13. Velocity distribution in channel cross section of DFLL blanket (Unit: s/m).
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Fig. 14. Temperature distribution of DFLL blanket (Unit: K).
Fig. 15. Improved model of DFLL blanket.
PbLi flowed smoothly in LL1 channel and no reverse flow existed here. In LL2 and LL3 channels, global natural circulation formed and reversed flow in LL2 increased its temperature. By comparing temperature distribution of Fig. 16(a) with (b), this peak temperature decreased 100 K. The location of peak temperature was middle part of LL2 channel, which was formed by reverse flow there. The improved temperature distribution was in accordance with design goal, where high temperature existed near outlet and low temperature existed near inlet.
factors analysis, and optimization suggestions of blanket design were concluded according to the detailed analysis. The buoyancy induced natural convection in the duct, which increased the heat leaked to Helium coolant and reduced the outlet temperature. To achieve high temperature (973 K) at outlet of PbLi duct, heat conductivity of FCI material was suggested to be < 1 W/m·K to reduce the heat leaked to Helium coolant. Reversed direction of original flow in DFLL blanket would be helpful to reduce heat leakage of PbLi volumetric nuclear heat and get high temperature at outlet. The Lorentz force induced by moving PbLi under magnetic field suppressed buoyancy strength. At the extreme condition of duct with steel wall, buoyancy was completely suppressed by Lorentz force, and no buoyant flow exists. According to the founding above, we analyzed the MHD buoyant flow in an upside-down DFLL blanket. The temperature distribution in the improved model was in accordance with design goal, where high temperature existed near outlet and low temperature existed near inlet.
4. Conclusion In this paper, MHD buoyant flow of Dual Functional Lead Lithium blanket (DFLL) under typical fusion magnetic field and non-uniform volumetric nuclear heating were studied. PbLi duct LL1 near first wall of DFLL blanket with the most significant buoyancy effect was chosen for influence
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Fig. 16. Temperature distribution of original and improved DFLL blanket (Unit: k).
Declaration of Competing Interest
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The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper. Acknowledgements This work was supported by the National Magnetic Confinement Fusion Science Program of China (2015GB116000B), the National Natural Science Foundation of China (51606206), the informatization Project of Chinese Academy of Sciences (XXH13506-104), the National R&D Infrastructure and Facility Development Program of ChinaFundamental Science Data Sharing Platform (DKA2017-12-02-17), the Special Project of Youth Innovation Association of Chinese Academy of Sciences and the Industrialization Fund. In addition, the authors would like to show their great appreciation to other members of the FDS Team for supports to this research. References [1] D. Maisonnier, I. Cook, P. Sardain, et al., A Conceptual Study of Commercial Fusion Power Plants-Final Report of the European Fusion Power Plant Conceptual Study (PPCS), EFDA, Switzerland, 2005. [2] Y.C. Wu, FDS Team, Conceptual design of the China fusion power plant FDS-II, Fusion Eng. Des. 83 (10–12) (2008) 1683–1689. [3] Y. Poitevin, L.B. Boccaccini, A. Cardella, L. Giancarli, R. Meyder, E. Diegele, et al., The European breeding blankets development and the test strategy in ITER, Fusion Eng. Des. 75–79 (2005) 741–749. [4] M.S. Tillack, X.R. Wang, J. Pulsifer, et al., ARIES-ST breeding blanket design and analysis, Fusion Eng. Des. 49 (2000) 689–695. [5] F. Cismondi, S. Kecskés, M. Ilic, et al., Design update, thermal and fluid dynamic analyses of the EU-HCPB TBM in vertical arrangement, Fusion Eng. Des. 84 (2) (2009) 607–612. [6] Feng, Yongjin Feng, et al., Current status of the fabrication of Li4SiO4 and beryllium pebbles for CN HCCB TBM in SWIP, Plasma Sci. Technol. 15 (3) (2013) 291–294. [7] M. Enoeda, H. Tanigawa, T. Hirose, et al., R&D status on water cooled ceramic breeder blanket technology, Fusion Eng. Des. 89 (7-8) (2014) 1131–1136. [8] Y.C. Wu, Conceptual design of the China fusion power plant FDS-II, Fusion Eng.
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