- Email: [email protected]
Evaluation of implantation-driven tritium transport in the first wall of the WCCB blanket for CFETR
Fusion Engineering and Design 152 (2020) 111430
Contents lists available at ScienceDirect
Fusion Engineering and Design journal homepage: www.elsevier.com/locate/fusengdes
Evaluation of implantation-driven tritium transport in the first wall of the WCCB blanket for CFETR
T
Kai Huang*, Xueli Zhao, Bo Lyu, Songlin Liu Institute of Plasma Physics, Chinese Academy of Sciences, Hefei, Anhui, 230031, China
A R T I C LE I N FO
A B S T R A C T
Keywords: Tritium transport Implantation First wall WCCB blanket CFETR
Tritium is the fuel for the future magnetic-confined fusion devices that requires accurate simulation investigation. A generic multi-physics model is implemented in this work to analyze the tritium transport behaviors in the fusion reactor components. The model is applied to evaluate plasma-induced tritium permeation and retention in the first wall (FW) of the water-cooled ceramics breeder blanket under typical operational conditions for the China Fusion Engineering Test Reactor. The total amount of tritium retention and permeation due to ion-implantation is obtained for different reactor power levels. The impact on the tritium transport behaviors from the Soret effect is also analyzed. Simulation results suggest that the tungsten armor can be a dominating source of mobile tritium retention in comparison to the steel structure in the FW; and that the Soret effect would impact the amount of tritium permeated into the coolant, in a favorable way.
1. Introduction Tritium induced by high-energy ionic bombardment coming from the plasma chamber side represents one of the major tritium sources for the breeder blankets of future magnetic-confined fusion devices. Implanted tritium would penetrate the surface of the plasma facing components (PFCs) and migrate around in the materials owing to its high mobility. Therefore, accurate assessment of tritium permeation and inventory in the blanket first wall (FW) caused by implantation is crucial to the design of a safe and efficient tritium generating-circulating system. It is conventionally believed that experimental data from direct instrumental readings be more convincing than simulation results. Plasma-driven tritium implantation, however, can scarcely be studied experimentally at component and device levels due to lack of full-scale experimental facilities. Nor could the data obtained from small, millimeter-sized samples be readily extrapolated to meter scales with high fidelity. Thus, the numerical simulation approach is often visited as an alternative resort. Such efforts have been vast in literature, with simulation objects ranging from the laboratory material sample scale to fusion device component scales [1–12]. The essence of these reported work is to first construct and then solve the set of governing equations that describe the transport behavior of hydrogen isotopes under the coexisting physical gradient fields mainly involving temperature and concentration. The credibility of the simulation results relies largely on:
⁎
1) the strictness of the governing equations; 2) the appropriateness of the boundary conditions; 3) the preciseness of the transport parameters; and 4) the effectiveness of the solver. The tritium transport behavior in materials and on the surface generally complies with the classical chemical diffusion theory, thus a unified set of governing equations must be reached, should all the transport phenomena be taken into account. Yet the parameters such as diffusivity are by no means easily available, especially when solving a temperature dependent problem. Interpolation, often extrapolation, has to be resorted to based on a group of discrete experimental data. This brings additional uncertainty to the final simulation results. The solver, however, has a wide spectrum of choices, among which the standard finite element method can provide a handy option because of its convenience to treat complex geometries present ubiquitously in a future fusion machine such as the China Fusion Engineering Test Reactor (CFETR). The CFETR (see Fig. 1) has been depicted as the next targeting device in the official road-map for the Chinese fusion energy development program since 2015 [13]. The latest CFETR design specifications updated in the year of 2018 require that operation modes of the fusion machine be adapted to stepped power levels, that is, fusion power of 200 MW, 500 MW, 1 G W, and 1.5 G W [14]. Among the key missions of the CFETR project stands the demonstration of reliable tritium selfsustainability using breeding blankets. Featured by the regular PWR coolant thermal conditions, the water-cooled ceramic breeder (WCCB) blanket (see Fig. 2) being developed at the Institute of Plasma Physics,
Corresponding author. E-mail address: [email protected] (K. Huang).
https://doi.org/10.1016/j.fusengdes.2019.111430 Received 9 August 2019; Received in revised form 10 November 2019; Accepted 6 December 2019 0920-3796/ © 2019 Elsevier B.V. All rights reserved.
Fusion Engineering and Design 152 (2020) 111430
K. Huang, et al.
Chinese Academy of Sciences is listed as one of the candidate blankets for the CFETR. Previous work has been conducted to analyze the overall hydrogen isotopes transport behavior in this water-cooled blanket working at the CFETR low power mode of 200 MW [15]. The current work, however, presents the implementation of a two-dimensional finite element model to specifically analyze the plasma-induced tritium permeation through the FW of the new WCCB blanket design released in 2018 [16], under the operational conditions of elevated power levels. The total amount of tritium permeation and retention in the FW of the WCCB blanket is calculated and reported for different power scenarios. The impact to the tritium concentration distribution from the Soret effect is also analyzed. 2. Calculation method 2.1. Equations The time-dependent tritium transport equation is
∂ (Csol (x , t ) + Ctrap (x , t )) = (1 − r ) I0 φimp (x ) − ∇⋅Jsol (x , t ) ∂t
(1)
where Csol is the solute tritium concentration, Ctrap the trapped tritium concentration, Jsol the diffusive flux, r the reflection coefficient, I0 the implanted tritium ion flux, and φimp the tritium implantation profile. Eq. (1) states that the changing rate of the total tritium concentration (including the solute and trapped tritium) in any infinitesimal volume be equal to the sum of tritium diffusion inflow rate and the implantation source within this volume. The first term on the right-hand side (RHS) of Eq. (1) refers to implantation. A portion of the implanted particles, controlled using parameter r, are directly reflected off the first wall and back into the plasma chamber. The injected particles would reach a depth of nanometers beneath the plasma-wall interface and build a Gaussian concentration profile in the vicinity as
Fig. 1. Sketch of the CFETR layout.
φimp (x ) = A exp(−(x − Rp)2 /(2ε 2))
(2)
where A is the normalization constant, Rp is the mean implantation depth, and ε is the variance. The normalization constant can be obtained by L
A = 1/
∫ exp(−(x − Rp)2/(2ε 2))dx 0
Fig. 2. Design of the WCCB blanket modules for CFETR.
(3)
The second term on Eq. (1)'s RHS represents diffusion. The concentration gradient driven diffusive flux should comply with the Fick's law given by (4)
Jsol (x , t ) = −D∇Csol (x , t )
where D is the tritium diffusion coefficient in a certain material. D can be expressed as
D = D0 exp(
−Ea ) kB T
(5)
where D0 is the pre-exponential factor, Ea is the diffusion activation energy, kB is Boltzmann constant, and T is the temperature. An adjustment to Eq. (4) can be made to take into account the impact from the co-existence of a temperature gradient, namely, the Ludwig-Soret effect:
Jsol (x , t ) = −D (∇Csol (x , t ) +
Q Csol (x , t ) ∇T ) RT 2
(6)
where Q is the heat of transport, and R is the gas constant. From Eq. (4), the temperature-dependent characteristic of the diffusion coefficient naturally requires that the tritium concentration field given by Eq. (1) be coupled with the energy equation
Fig. 3. The 2D geometric model of the FW. 2
Fusion Engineering and Design 152 (2020) 111430
K. Huang, et al.
Table 1 Tritium transport properties. RAFM Steel (F82 H)
Tungsten
−7
2
Diffusion coefficient (m /s) Recombination coefficient (m4/mol/s) Solubility (mol/m3/Pa0.5)
1.07 × 10 exp(-0.144/kT) [20] NA×9.4 × 10−26exp(-0.12/kT) [10] (6.21 × 1023/NA)exp(-0.28/kT) [10]
4.1 × 10−7exp(-0.39/kT) [11] NA×(3 × 10−25/T0.5)exp(2.06/kT) [21] (1.83 × 1024/NA)exp(-1.04/kT) [10]
k is the Boltzmann constant; NA is the Avogadro constant; T represents temperature.
two tritium atoms are recombined and desorbed. Hence the recombination boundary conditions are imposed, given by
Table 2 Thermo-physical properties of tungsten. Property
Unit
Value 3
Density Conductivity Heat capacity
2 Jsol (x , t ) = −2Kr Csol (x , t )
19000 175 132
kg/m W/m/K J/kg/K
and
Kr = Kr0 exp(−Er / kT )
3
Density (kg/m ) Heat capacity (J/kg/K) Conductivity (W/m/K)
200
300
400
500
600
700
7819 510 32.9
7786 544 33.4
7752 586 33.0
7715 644 32.7
7676 728 32.3
N/A 866 31.9
(10)
where Kr is the recombination coefficient, Kr0 is the pre-exponential factor, and Er is the recombination energy. Moreover, the stiff-spring method is applied to define the boundary condition at the interfaces across different materials [8].
Table 3 Thermo-physical properties of RAFMs [22,23]. Temperature (℃)
(9)
3. Modeling 3.1. Geometric model of the WCCB blanket FW
ρCp
∂T − ∇⋅(k∇T ) = q + h (Text − T ) ∂t
The FW as the inner-most plasma facing component of a fusion reactor defines the tangible boundary of the burning plasma confined in the vacuum chamber. It constantly keeps receiving mass (ions and neutrons) and heat flux from inside the fusion core. Until recently, cladding the FW with a tungsten layer has become a common practice and been widely applied in the blanket design around the international fusion engineering community. The benefits from this fashion are twofold: 1) the enhancement of the surface durability under the high-energy ion bombardments, especially for the plasma disruption condition, and 2) the reinforcement of the tritium blocking ability of the FW. According to Ref. [16], the FW of the latest CFETR-WCCB blanket design comprises a layer of tungsten armor with a thickness of 2 mm, and a substructure with a thickness of 20 mm that is made of RAFM steel embedded by 8 mm × 8 mm square coolant channels (see Fig. 3). The distance between the tungsten-steel interface and the left boundary of the coolant channel is 3 mm. The central distance of adjacent coolant channels is 13 mm, considerably smaller compared with the 22 mm of that in the previous design [17]. The shrinkage of the center-to-center spacing of adjacent channels is due to the larger number of coolant
(7)
where ρ is the material density, Cp is the heat capacity, k is the thermal conductivity, q is the volumetric nuclear heating source, h is the convective heat transfer coefficient, and Text is the exterior temperature. The trapped tritium concentration in Eq. (1) complies with the following balance equation [8]
∂ 2 2 Ctrap (x , t ) = DaW (x , t ) Csol (x , t ) − DaCtrap (x , t ) Csol (x , t ) ∂t 3 3 −Eb 8D − 2 Ctrap (x , t )exp( ) a kB T
(8)
where: a is the metal lattice constant, W(x,t) is the trap density function, and Eb is the binding energy of tritium with traps. 2.2. Boundary conditions Tritium will migrate to the material surface through dynamic diffusion and permeation, followed by the recombination process in which
Fig. 4. Steady-state isothermal distribution in the FW at 1.5 G W fusion power (The right legend represents the temperature with unit K). 3
Fusion Engineering and Design 152 (2020) 111430
K. Huang, et al.
Fig. 5. Steady-state tritium concentration (T/m3) distribution in the FW (The left legend is for the tungsten armor, and the right is for RAFM steel). Table 4 Steady-state tritium inventory and permeation in the FW under different power levels. 200 MW T retention in tungsten (g) T retention in RAFM steel (g) T permeation rate to the coolant (g/s) T consumption rate (g/s)
500 MW
−2
−1
1.67 × 10 1.72 × 10−2 1.12 × 10−5 8.86 × 10−4
6.85 × 10 8.62 × 10−3 4.08 × 10−6 3.54 × 10−4
1 GW
1.5 GW −1
3.32 × 10 3.03 × 10−2 2.35 × 10−5 1.77 × 10−3
5.14 × 10−1 4.39 × 10−2 3.65 × 10−5 2.66 × 10−3
Fig. 6. Steady-state tritium concentration (T/m3) distribution in the FW with the Soret effect at 200 MW fusion power (The left legend is for the tungsten armor, and the right is for RAFM steel).
channels arranged in the updated blanket design, allowing a greater heat removal capability for the high-power mode of 1.5 G W [16].
3.2. Parameters The parameters involved in this work can generally be categorized into two classesthe diffusive transport parameters and the thermal parameters. Listed in Table 1 are the tritium transport properties 4
Fusion Engineering and Design 152 (2020) 111430
K. Huang, et al.
Fig. 7. Steady-state tritium concentration (T/m3) distribution in the FW without the Soret effect at 200 MW fusion power (The left legend is for the tungsten armor, and the right is for RAFM steel).
Fig. 10. Variation of average tritium permeation rate into the coolant with and without the Soret effect (200 MW).
Fig. 8. Variation of average tritium concentration in the tungsten armor with and without the Soret effect (200 MW).
structural material [16,18]; however, the tritium transport properties for these materials are not yet sufficient. Hence the available data set of the F82H steel is used instead. The thermo-physical properties of tungsten are given in Table 2, in accordance with the material specification of ITER [19]. The same set of properties for the RAFM steel are given in Table 3. It should be noted that the temperature-dependence of the thermal properties for the RAFM steel is taken into account, while this dependence is neglected for tungsten due to the unavailability of material data varying with temperatures. Moreover, the average temperature of the water coolant is 593 K. The implantation flux from the plasma chamber side is chosen as 1.5 × 1021 T/m2/s [10] for the 200 MW case, and assumed to be varying linearly with the total fusion power.
4. Results and discussion The set of governing equations described in Section 2 are solved using the finite element method. Four reactor power levels—200 MW, 500 MW, 1 G W and 1.5 G W—are investigated. As the present work focuses on the implantation-induced tritium permeation and retention, the tritium flux from the breeding zone is excluded in the simulation. Fig. 4 shows representatively the steady-state isothermal distribution for the 1.5 G W fusion power case, in which a sharp temperature
Fig. 9. Variation of average tritium concentration in RAFM steel with and without the Soret effect (200 MW).
including the effective diffusion coefficient, the recombination coefficient and the solubility for tungsten and steel. Attention has to be paid that the WCCB blanket design employs the CLF-1 or CLAM steel as the 5
Fusion Engineering and Design 152 (2020) 111430
K. Huang, et al.
Table 5 Steady-state tritium retention and permeation in the FW under different conditions.
T retention in tungsten (g) T retention in RAFM steel (g) T permeation rate to the coolant (g/s)
200 MW (with the Soret effect)
200 MW (without the Soret effect)
1.5 G W (with the Soret effect)
1.5 G W (without the Soret effect)
7.25 × 10−2 8.26 × 10−3 3.03 × 10−6
6.85 × 10−2 8.62 × 10−3 4.08 × 10−6
5.45 × 10−1 4.21 × 10−2 2.85 × 10−5
5.14 × 10−1 4.39 × 10−2 3.65 × 10−5
steady-state values for the cases with and without accounting the Soret effect (2.62 × 1014 T/m2/s versus 3.53 × 1014 T/m2/s) implies that this effect can help reduce the amount of tritium permeated into the coolant by as much as 25.8 %. Table 5 reports the total amount of plasma-induced tritium retention and permeation in the FW of the CFETR. Results for two power levels are given for comparison purposes. It is found that for both the 200 MW and 1.5 G W cases, when the Soret effect is imposed, the tritium retention amount increases in tungsten while decreases in steel, and the permeation rate is reduced. These are in consistent with the observations made from Figs. 8–10.
gradient can be observed across the tungsten/steel interface. Fig. 5 shows the steady-state distribution of tritium concentration in the FW for all the four power levels studied. It can be seen that the majority of the implanted tritium either resides in the materials to the left of the coolant channel, or gets permeated into the coolant, leaving only a tiny portion diffused beyond the position of coolant channels in the radial direction. This implies that the ion-implantation imposed on the plasma-facing components has a relatively strong feature of locality. Table 4 summarizes the total amount of tritium retention and permeation in the FW of CFETR under different power levels. It can be found that for each and every case, the amount of tritium retention in the tungsten armor is about one order of magnitude larger in the tungsten armor than in the RAFM steel, indicating that the former can be a dominating source of the retained tritium in the FW. The saturated tritium retention in the FW due to plasma-implantation is 6.85 × 10−2g at 200 MW, and monotonically increases with the fusion power. This value reaches 5.14 × 10-1g at 1.5 G W. The similar trend can be spotted for the tritium retained in the steel structure as well. A straight-forward observation can be made that the amount of tritium retention will be considerably larger for a higher reactor power, which should be brought into attention in the development of maintenance strategies of the fusion reactor PFCs when working under an elevated power level. The rate of tritium permeation into the water coolant channels in the FW of CFETR is also evaluated. Likewise, the rate increases with power as well. The value of the permeation rate is found to be almost one order of magnitude higher in the 1.5 G W case than the initial power of 200 MW. Given in addition in table 4 are tritium consumption rate corresponding to different fusion power levels, to better illustrate the magnitude of tritium permeation rate into the FW coolant channels due to implantation. Simulation results reported above are obtained assuming that the diffusion flux of tritium complies with the Fick’s law in the primitive form, as given in Eq. (4). Nevertheless, the co-existence of a temperature field in the blanket FW in addition to the concentration gradient may have a profound impact on the mass diffusion process. Therefore, the modified diffusion rule Eq. (6) is used to study the influence of the Soret effect on tritium retention and permeation behaviors. The heat of transport Q for the RAFM steel is taken from Ref. [24]. Figs. 6 and 7 demonstrate the steady-state tritium concentration distribution with and without the Soret effect at 200 MW, respectively. It can be seen that the concentration gradient is less steep in the case without considering the temperature effect and the implanted tritium can generally get diffused more deeply in the bulk of the material. As a contrast, the region of high tritium concentration right to the W-steel interface is significantly compressed in the case with the Soret effect accounted, indicating that the negative heat of transport value of the RAFM steel leads to retarding the diffusion process of the hydrogen isotope from the upstream tungsten armor side in the radial direction considerably. Comparisons of the time evolution for average tritium concentration with and without the Soret effect at 200 MW are plotted for tungsten and steel in Figs. 8 and 9, respectively. It is observed that the impediment of the diffusion process resulted from the temperature effect leads to an increased tritium inventory in the tungsten armor, yet a reduced amount in the RAFM steel area. The time-dependent variation of the tritium permeation rate into the coolant is shown in Fig. 10. The significant discrepancy of the
5. Summary A generic multi-physics model is implemented and applied to evaluate transport behaviors of the implantation-induced tritium in the FW of the WCCB blanket for CFETR. The total amount of tritium retention and permeation is reported for different reactor power levels. For each case studied, the tritium inventory is about one order of magnitude larger in tungsten than in the RAFM steel, indicating that the former can be a dominating source of the retained tritium. The saturated tritium retention in the FW materials increases monotonically with the fusion power, and becomes considerably larger at the high reactor power ends. The similar trend is also found for the tritium permeated into the coolant. When taking the Soret effect into account, the diffusion process from the tungsten armor side will be considerably hindered, leading to a steeper tritium concentration gradient and narrower region of high tritium concentration right next to the W-steel interface. Regardless of the fusion power, the tritium inventory would increase in tungsten while decrease in steel due to the Soret effect, which can help reduce the amount of tritium permeated into the coolant as well. CRediT authorship contribution statement Kai Huang: Conceptualization, Writing - original draft. Xueli Zhao: Formal analysis, Visualization. Bo Lyu: Writing - review & editing. Songlin Liu: Funding acquisition. Declaration of Competing Interest 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 National Key R&D Program of China [No. 2017YFE0300502] and the National Natural Science Foundation of China [Grant No. 11775256]. References [1] A. Ying, et al., Breeding blanket system design implications on tritium transport and permeation with high tritium ion implantation: a MATLAB/Simulink, COMSOL integrated dynamic tritium transport model for HCCR TBS, Fusion Eng. Des. 136 (Part B, November) (2018) 1153–1160.
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[14] Y. Wan, J. Li, et al., Present progresses and activities on the Chinese fusion engineering test reactor, Presented in the SOFT 2018 Conference (2018). [15] X. Zhao, B. Zhang, L. Chen, K. Huang, S. Liu, Tritium transport analysis for WCCB blanket of CFETR based on COMSOL, Fusion Eng. Des. 140 (March) (2019) 1–10. [16] S. Liu, X. Li, X. Ma, et al., Updated design of water-cooled breeder blanket for CFETR, Fusion Eng. Des. 124 (2018). [17] S. Liu, X. Ma, X.K. Jiang, et al., Conceptual design of the water-cooled ceramic breeder blanket for CFETR based on pressurized water cooled reactor technology, Fusion Eng. Des. (2017). [18] P. Wang, J. Chen, H. Fu, et al., Effect of N on the precipitation behaviors of the reduced activation ferritic/martensitic steel CLF-1 after thermal ageing, J. Nucl. Mater. 442 (1–3) (2013) S9–S12. [19] ITER Material Specification for the Supply of Tungsten Plates for the ITER Divertor, (2009). [20] E. Serra, A. Perujo, G. Benamati, Influence of traps on the deuterium behavior in the low activation martensitic steels F82H and Batman, J. Nucl. Mater. 245 (2) (1997) 108–114. [21] M.A. Pick, K. Sonnenberg, A model for atomic hydrogen-metal interactions — application to recycling, recombination and permeation, J. Nucl. Mater. 131 (2–3) (1985) 208–220. [22] F. Tavassoli, Fusion demo interim structural design criteria (DISDC)/appendix A:material design limit data/A3. S18E eurofer steel, EFDA TASK TW4-TTMS-005D01. CEA Report DMN/DIR/NT/2004-02/A (2007). [23] T. Hirose, T. Nozawa, R.E. Stoller, et al., Physical properties of F82H for fusion blanket design, Fusion Eng. Des. 89 (7-8) (2014) 1595–1599. [24] G.R. Longhurst, The soret effect and its implications for fusion reactors, J. Nucl. Mater. 131 (1985) 61–69.
[2] L. Candido, R. Testoni, M. Utili, et al., Tritium transport model at the minimal functional unit level for HCLL and WCLL breeding blankets of DEMO, Fusion Eng. Des. (2018). [3] E. Carella, C. Moreno, F.R. Urgorri, et al., Tritium modeling in HCPB breeder blanket at a system level, Fusion Eng. Des. (2017). [4] A. Ying, H. Zhang, B.J. Merrill, et al., Advancement in tritium transport simulations for solid breeding blanket system, Fusion Eng. Des. 109-111 (2016) 1511–1516. [5] L. Candido, M. Utili, I. Nicolotti, et al., Tritium transport in HCLL and WCLL DEMO blankets, Fusion Eng. Des. 109-111 (A) (2016) 248–254. [6] A. Ying, H. Zhang, M.Y. Anh, et al., Tritium transport evolutions in HCCR TBM under ITER inductive operations, Fusion Sci. Technol. 68 (2) (2015) 346–352. [7] A. Santucci, S. Tosti, S.F. Franza, Model improvements for tritium transport in DEMO fuel cycle, Fusion Eng. Des. 98-99 (2015) 1880–1884. [8] A. Ying, H. Liu, M. Abdou, Analysis of Tritium/Deuterium retention and permeation in FW/Divertor including geometric and temperature operating features, Fusion Sci. Technol. 64 (2) (2013) 303–308. [9] F. Franza, L.V. Boccaccini, A. Ciampichetti, et al., Tritium transport analysis in HCPB DEMO blanket with the FUS-TPC code, Fusion Eng. Des. 88 (9-10) (2013) 2444–2447. [10] H. Nakamura, S. Sakurai, S. Suzuki, et al., Case study on tritium inventory in the fusion DEMO plant at JAERI, Fusion Eng. Des. 81 (8) (2006) 1339–1345. [11] O.V. Ogorodnikova, J. Roth, M. Mayer, Deuterium retention in tungsten in dependence of the surface conditions, J. Nucl. Mater. s313–316 (2) (2003) 469–477. [12] O.V. Ogorodnikova, X. Raepsaet, M.A. Futterer, Tritium permeation through the first wall of the EU-HCPB blanket, Fusion Eng. Des. 49-50 (2000) 921–926. [13] Y. Wan, J. Li, Y. Liu, et al., Overview of the present progress and activities on the CFETR, Nucl. Fusion 57 (10) (2017) 102009.
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Contents lists available at ScienceDirect
Fusion Engineering and Design journal homepage: www.elsevier.com/locate/fusengdes
Evaluation of implantation-driven tritium transport in the first wall of the WCCB blanket for CFETR
T
Kai Huang*, Xueli Zhao, Bo Lyu, Songlin Liu Institute of Plasma Physics, Chinese Academy of Sciences, Hefei, Anhui, 230031, China
A R T I C LE I N FO
A B S T R A C T
Keywords: Tritium transport Implantation First wall WCCB blanket CFETR
Tritium is the fuel for the future magnetic-confined fusion devices that requires accurate simulation investigation. A generic multi-physics model is implemented in this work to analyze the tritium transport behaviors in the fusion reactor components. The model is applied to evaluate plasma-induced tritium permeation and retention in the first wall (FW) of the water-cooled ceramics breeder blanket under typical operational conditions for the China Fusion Engineering Test Reactor. The total amount of tritium retention and permeation due to ion-implantation is obtained for different reactor power levels. The impact on the tritium transport behaviors from the Soret effect is also analyzed. Simulation results suggest that the tungsten armor can be a dominating source of mobile tritium retention in comparison to the steel structure in the FW; and that the Soret effect would impact the amount of tritium permeated into the coolant, in a favorable way.
1. Introduction Tritium induced by high-energy ionic bombardment coming from the plasma chamber side represents one of the major tritium sources for the breeder blankets of future magnetic-confined fusion devices. Implanted tritium would penetrate the surface of the plasma facing components (PFCs) and migrate around in the materials owing to its high mobility. Therefore, accurate assessment of tritium permeation and inventory in the blanket first wall (FW) caused by implantation is crucial to the design of a safe and efficient tritium generating-circulating system. It is conventionally believed that experimental data from direct instrumental readings be more convincing than simulation results. Plasma-driven tritium implantation, however, can scarcely be studied experimentally at component and device levels due to lack of full-scale experimental facilities. Nor could the data obtained from small, millimeter-sized samples be readily extrapolated to meter scales with high fidelity. Thus, the numerical simulation approach is often visited as an alternative resort. Such efforts have been vast in literature, with simulation objects ranging from the laboratory material sample scale to fusion device component scales [1–12]. The essence of these reported work is to first construct and then solve the set of governing equations that describe the transport behavior of hydrogen isotopes under the coexisting physical gradient fields mainly involving temperature and concentration. The credibility of the simulation results relies largely on:
⁎
1) the strictness of the governing equations; 2) the appropriateness of the boundary conditions; 3) the preciseness of the transport parameters; and 4) the effectiveness of the solver. The tritium transport behavior in materials and on the surface generally complies with the classical chemical diffusion theory, thus a unified set of governing equations must be reached, should all the transport phenomena be taken into account. Yet the parameters such as diffusivity are by no means easily available, especially when solving a temperature dependent problem. Interpolation, often extrapolation, has to be resorted to based on a group of discrete experimental data. This brings additional uncertainty to the final simulation results. The solver, however, has a wide spectrum of choices, among which the standard finite element method can provide a handy option because of its convenience to treat complex geometries present ubiquitously in a future fusion machine such as the China Fusion Engineering Test Reactor (CFETR). The CFETR (see Fig. 1) has been depicted as the next targeting device in the official road-map for the Chinese fusion energy development program since 2015 [13]. The latest CFETR design specifications updated in the year of 2018 require that operation modes of the fusion machine be adapted to stepped power levels, that is, fusion power of 200 MW, 500 MW, 1 G W, and 1.5 G W [14]. Among the key missions of the CFETR project stands the demonstration of reliable tritium selfsustainability using breeding blankets. Featured by the regular PWR coolant thermal conditions, the water-cooled ceramic breeder (WCCB) blanket (see Fig. 2) being developed at the Institute of Plasma Physics,
Corresponding author. E-mail address: [email protected] (K. Huang).
https://doi.org/10.1016/j.fusengdes.2019.111430 Received 9 August 2019; Received in revised form 10 November 2019; Accepted 6 December 2019 0920-3796/ © 2019 Elsevier B.V. All rights reserved.
Fusion Engineering and Design 152 (2020) 111430
K. Huang, et al.
Chinese Academy of Sciences is listed as one of the candidate blankets for the CFETR. Previous work has been conducted to analyze the overall hydrogen isotopes transport behavior in this water-cooled blanket working at the CFETR low power mode of 200 MW [15]. The current work, however, presents the implementation of a two-dimensional finite element model to specifically analyze the plasma-induced tritium permeation through the FW of the new WCCB blanket design released in 2018 [16], under the operational conditions of elevated power levels. The total amount of tritium permeation and retention in the FW of the WCCB blanket is calculated and reported for different power scenarios. The impact to the tritium concentration distribution from the Soret effect is also analyzed. 2. Calculation method 2.1. Equations The time-dependent tritium transport equation is
∂ (Csol (x , t ) + Ctrap (x , t )) = (1 − r ) I0 φimp (x ) − ∇⋅Jsol (x , t ) ∂t
(1)
where Csol is the solute tritium concentration, Ctrap the trapped tritium concentration, Jsol the diffusive flux, r the reflection coefficient, I0 the implanted tritium ion flux, and φimp the tritium implantation profile. Eq. (1) states that the changing rate of the total tritium concentration (including the solute and trapped tritium) in any infinitesimal volume be equal to the sum of tritium diffusion inflow rate and the implantation source within this volume. The first term on the right-hand side (RHS) of Eq. (1) refers to implantation. A portion of the implanted particles, controlled using parameter r, are directly reflected off the first wall and back into the plasma chamber. The injected particles would reach a depth of nanometers beneath the plasma-wall interface and build a Gaussian concentration profile in the vicinity as
Fig. 1. Sketch of the CFETR layout.
φimp (x ) = A exp(−(x − Rp)2 /(2ε 2))
(2)
where A is the normalization constant, Rp is the mean implantation depth, and ε is the variance. The normalization constant can be obtained by L
A = 1/
∫ exp(−(x − Rp)2/(2ε 2))dx 0
Fig. 2. Design of the WCCB blanket modules for CFETR.
(3)
The second term on Eq. (1)'s RHS represents diffusion. The concentration gradient driven diffusive flux should comply with the Fick's law given by (4)
Jsol (x , t ) = −D∇Csol (x , t )
where D is the tritium diffusion coefficient in a certain material. D can be expressed as
D = D0 exp(
−Ea ) kB T
(5)
where D0 is the pre-exponential factor, Ea is the diffusion activation energy, kB is Boltzmann constant, and T is the temperature. An adjustment to Eq. (4) can be made to take into account the impact from the co-existence of a temperature gradient, namely, the Ludwig-Soret effect:
Jsol (x , t ) = −D (∇Csol (x , t ) +
Q Csol (x , t ) ∇T ) RT 2
(6)
where Q is the heat of transport, and R is the gas constant. From Eq. (4), the temperature-dependent characteristic of the diffusion coefficient naturally requires that the tritium concentration field given by Eq. (1) be coupled with the energy equation
Fig. 3. The 2D geometric model of the FW. 2
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Table 1 Tritium transport properties. RAFM Steel (F82 H)
Tungsten
−7
2
Diffusion coefficient (m /s) Recombination coefficient (m4/mol/s) Solubility (mol/m3/Pa0.5)
1.07 × 10 exp(-0.144/kT) [20] NA×9.4 × 10−26exp(-0.12/kT) [10] (6.21 × 1023/NA)exp(-0.28/kT) [10]
4.1 × 10−7exp(-0.39/kT) [11] NA×(3 × 10−25/T0.5)exp(2.06/kT) [21] (1.83 × 1024/NA)exp(-1.04/kT) [10]
k is the Boltzmann constant; NA is the Avogadro constant; T represents temperature.
two tritium atoms are recombined and desorbed. Hence the recombination boundary conditions are imposed, given by
Table 2 Thermo-physical properties of tungsten. Property
Unit
Value 3
Density Conductivity Heat capacity
2 Jsol (x , t ) = −2Kr Csol (x , t )
19000 175 132
kg/m W/m/K J/kg/K
and
Kr = Kr0 exp(−Er / kT )
3
Density (kg/m ) Heat capacity (J/kg/K) Conductivity (W/m/K)
200
300
400
500
600
700
7819 510 32.9
7786 544 33.4
7752 586 33.0
7715 644 32.7
7676 728 32.3
N/A 866 31.9
(10)
where Kr is the recombination coefficient, Kr0 is the pre-exponential factor, and Er is the recombination energy. Moreover, the stiff-spring method is applied to define the boundary condition at the interfaces across different materials [8].
Table 3 Thermo-physical properties of RAFMs [22,23]. Temperature (℃)
(9)
3. Modeling 3.1. Geometric model of the WCCB blanket FW
ρCp
∂T − ∇⋅(k∇T ) = q + h (Text − T ) ∂t
The FW as the inner-most plasma facing component of a fusion reactor defines the tangible boundary of the burning plasma confined in the vacuum chamber. It constantly keeps receiving mass (ions and neutrons) and heat flux from inside the fusion core. Until recently, cladding the FW with a tungsten layer has become a common practice and been widely applied in the blanket design around the international fusion engineering community. The benefits from this fashion are twofold: 1) the enhancement of the surface durability under the high-energy ion bombardments, especially for the plasma disruption condition, and 2) the reinforcement of the tritium blocking ability of the FW. According to Ref. [16], the FW of the latest CFETR-WCCB blanket design comprises a layer of tungsten armor with a thickness of 2 mm, and a substructure with a thickness of 20 mm that is made of RAFM steel embedded by 8 mm × 8 mm square coolant channels (see Fig. 3). The distance between the tungsten-steel interface and the left boundary of the coolant channel is 3 mm. The central distance of adjacent coolant channels is 13 mm, considerably smaller compared with the 22 mm of that in the previous design [17]. The shrinkage of the center-to-center spacing of adjacent channels is due to the larger number of coolant
(7)
where ρ is the material density, Cp is the heat capacity, k is the thermal conductivity, q is the volumetric nuclear heating source, h is the convective heat transfer coefficient, and Text is the exterior temperature. The trapped tritium concentration in Eq. (1) complies with the following balance equation [8]
∂ 2 2 Ctrap (x , t ) = DaW (x , t ) Csol (x , t ) − DaCtrap (x , t ) Csol (x , t ) ∂t 3 3 −Eb 8D − 2 Ctrap (x , t )exp( ) a kB T
(8)
where: a is the metal lattice constant, W(x,t) is the trap density function, and Eb is the binding energy of tritium with traps. 2.2. Boundary conditions Tritium will migrate to the material surface through dynamic diffusion and permeation, followed by the recombination process in which
Fig. 4. Steady-state isothermal distribution in the FW at 1.5 G W fusion power (The right legend represents the temperature with unit K). 3
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Fig. 5. Steady-state tritium concentration (T/m3) distribution in the FW (The left legend is for the tungsten armor, and the right is for RAFM steel). Table 4 Steady-state tritium inventory and permeation in the FW under different power levels. 200 MW T retention in tungsten (g) T retention in RAFM steel (g) T permeation rate to the coolant (g/s) T consumption rate (g/s)
500 MW
−2
−1
1.67 × 10 1.72 × 10−2 1.12 × 10−5 8.86 × 10−4
6.85 × 10 8.62 × 10−3 4.08 × 10−6 3.54 × 10−4
1 GW
1.5 GW −1
3.32 × 10 3.03 × 10−2 2.35 × 10−5 1.77 × 10−3
5.14 × 10−1 4.39 × 10−2 3.65 × 10−5 2.66 × 10−3
Fig. 6. Steady-state tritium concentration (T/m3) distribution in the FW with the Soret effect at 200 MW fusion power (The left legend is for the tungsten armor, and the right is for RAFM steel).
channels arranged in the updated blanket design, allowing a greater heat removal capability for the high-power mode of 1.5 G W [16].
3.2. Parameters The parameters involved in this work can generally be categorized into two classesthe diffusive transport parameters and the thermal parameters. Listed in Table 1 are the tritium transport properties 4
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Fig. 7. Steady-state tritium concentration (T/m3) distribution in the FW without the Soret effect at 200 MW fusion power (The left legend is for the tungsten armor, and the right is for RAFM steel).
Fig. 10. Variation of average tritium permeation rate into the coolant with and without the Soret effect (200 MW).
Fig. 8. Variation of average tritium concentration in the tungsten armor with and without the Soret effect (200 MW).
structural material [16,18]; however, the tritium transport properties for these materials are not yet sufficient. Hence the available data set of the F82H steel is used instead. The thermo-physical properties of tungsten are given in Table 2, in accordance with the material specification of ITER [19]. The same set of properties for the RAFM steel are given in Table 3. It should be noted that the temperature-dependence of the thermal properties for the RAFM steel is taken into account, while this dependence is neglected for tungsten due to the unavailability of material data varying with temperatures. Moreover, the average temperature of the water coolant is 593 K. The implantation flux from the plasma chamber side is chosen as 1.5 × 1021 T/m2/s [10] for the 200 MW case, and assumed to be varying linearly with the total fusion power.
4. Results and discussion The set of governing equations described in Section 2 are solved using the finite element method. Four reactor power levels—200 MW, 500 MW, 1 G W and 1.5 G W—are investigated. As the present work focuses on the implantation-induced tritium permeation and retention, the tritium flux from the breeding zone is excluded in the simulation. Fig. 4 shows representatively the steady-state isothermal distribution for the 1.5 G W fusion power case, in which a sharp temperature
Fig. 9. Variation of average tritium concentration in RAFM steel with and without the Soret effect (200 MW).
including the effective diffusion coefficient, the recombination coefficient and the solubility for tungsten and steel. Attention has to be paid that the WCCB blanket design employs the CLF-1 or CLAM steel as the 5
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Table 5 Steady-state tritium retention and permeation in the FW under different conditions.
T retention in tungsten (g) T retention in RAFM steel (g) T permeation rate to the coolant (g/s)
200 MW (with the Soret effect)
200 MW (without the Soret effect)
1.5 G W (with the Soret effect)
1.5 G W (without the Soret effect)
7.25 × 10−2 8.26 × 10−3 3.03 × 10−6
6.85 × 10−2 8.62 × 10−3 4.08 × 10−6
5.45 × 10−1 4.21 × 10−2 2.85 × 10−5
5.14 × 10−1 4.39 × 10−2 3.65 × 10−5
steady-state values for the cases with and without accounting the Soret effect (2.62 × 1014 T/m2/s versus 3.53 × 1014 T/m2/s) implies that this effect can help reduce the amount of tritium permeated into the coolant by as much as 25.8 %. Table 5 reports the total amount of plasma-induced tritium retention and permeation in the FW of the CFETR. Results for two power levels are given for comparison purposes. It is found that for both the 200 MW and 1.5 G W cases, when the Soret effect is imposed, the tritium retention amount increases in tungsten while decreases in steel, and the permeation rate is reduced. These are in consistent with the observations made from Figs. 8–10.
gradient can be observed across the tungsten/steel interface. Fig. 5 shows the steady-state distribution of tritium concentration in the FW for all the four power levels studied. It can be seen that the majority of the implanted tritium either resides in the materials to the left of the coolant channel, or gets permeated into the coolant, leaving only a tiny portion diffused beyond the position of coolant channels in the radial direction. This implies that the ion-implantation imposed on the plasma-facing components has a relatively strong feature of locality. Table 4 summarizes the total amount of tritium retention and permeation in the FW of CFETR under different power levels. It can be found that for each and every case, the amount of tritium retention in the tungsten armor is about one order of magnitude larger in the tungsten armor than in the RAFM steel, indicating that the former can be a dominating source of the retained tritium in the FW. The saturated tritium retention in the FW due to plasma-implantation is 6.85 × 10−2g at 200 MW, and monotonically increases with the fusion power. This value reaches 5.14 × 10-1g at 1.5 G W. The similar trend can be spotted for the tritium retained in the steel structure as well. A straight-forward observation can be made that the amount of tritium retention will be considerably larger for a higher reactor power, which should be brought into attention in the development of maintenance strategies of the fusion reactor PFCs when working under an elevated power level. The rate of tritium permeation into the water coolant channels in the FW of CFETR is also evaluated. Likewise, the rate increases with power as well. The value of the permeation rate is found to be almost one order of magnitude higher in the 1.5 G W case than the initial power of 200 MW. Given in addition in table 4 are tritium consumption rate corresponding to different fusion power levels, to better illustrate the magnitude of tritium permeation rate into the FW coolant channels due to implantation. Simulation results reported above are obtained assuming that the diffusion flux of tritium complies with the Fick’s law in the primitive form, as given in Eq. (4). Nevertheless, the co-existence of a temperature field in the blanket FW in addition to the concentration gradient may have a profound impact on the mass diffusion process. Therefore, the modified diffusion rule Eq. (6) is used to study the influence of the Soret effect on tritium retention and permeation behaviors. The heat of transport Q for the RAFM steel is taken from Ref. [24]. Figs. 6 and 7 demonstrate the steady-state tritium concentration distribution with and without the Soret effect at 200 MW, respectively. It can be seen that the concentration gradient is less steep in the case without considering the temperature effect and the implanted tritium can generally get diffused more deeply in the bulk of the material. As a contrast, the region of high tritium concentration right to the W-steel interface is significantly compressed in the case with the Soret effect accounted, indicating that the negative heat of transport value of the RAFM steel leads to retarding the diffusion process of the hydrogen isotope from the upstream tungsten armor side in the radial direction considerably. Comparisons of the time evolution for average tritium concentration with and without the Soret effect at 200 MW are plotted for tungsten and steel in Figs. 8 and 9, respectively. It is observed that the impediment of the diffusion process resulted from the temperature effect leads to an increased tritium inventory in the tungsten armor, yet a reduced amount in the RAFM steel area. The time-dependent variation of the tritium permeation rate into the coolant is shown in Fig. 10. The significant discrepancy of the
5. Summary A generic multi-physics model is implemented and applied to evaluate transport behaviors of the implantation-induced tritium in the FW of the WCCB blanket for CFETR. The total amount of tritium retention and permeation is reported for different reactor power levels. For each case studied, the tritium inventory is about one order of magnitude larger in tungsten than in the RAFM steel, indicating that the former can be a dominating source of the retained tritium. The saturated tritium retention in the FW materials increases monotonically with the fusion power, and becomes considerably larger at the high reactor power ends. The similar trend is also found for the tritium permeated into the coolant. When taking the Soret effect into account, the diffusion process from the tungsten armor side will be considerably hindered, leading to a steeper tritium concentration gradient and narrower region of high tritium concentration right next to the W-steel interface. Regardless of the fusion power, the tritium inventory would increase in tungsten while decrease in steel due to the Soret effect, which can help reduce the amount of tritium permeated into the coolant as well. CRediT authorship contribution statement Kai Huang: Conceptualization, Writing - original draft. Xueli Zhao: Formal analysis, Visualization. Bo Lyu: Writing - review & editing. Songlin Liu: Funding acquisition. Declaration of Competing Interest 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 National Key R&D Program of China [No. 2017YFE0300502] and the National Natural Science Foundation of China [Grant No. 11775256]. References [1] A. Ying, et al., Breeding blanket system design implications on tritium transport and permeation with high tritium ion implantation: a MATLAB/Simulink, COMSOL integrated dynamic tritium transport model for HCCR TBS, Fusion Eng. Des. 136 (Part B, November) (2018) 1153–1160.
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