Two-dimensional numerical study of ELMs-induced erosion of tungsten divertor target tiles with different edge shapes
Introduction
Tungsten (W) has chosen to be the material for the divertor armor of ITER due to its high thermal conductivity, high melting point, low tritium inventory, etc. During the ITER operation, W-based PFMs are foreseen to face severe heat loads generated by transient events such as plasma disruption, edge localized modes (ELMs), and vertical displacement events (VDEs) [1]. The high heat loads during these intense transient events will lead to the surface cracking of bulk W armor, which will be a major disadvantage for W [2], [3]. To mitigate the surface cracking, the divertor armor in ITER will be manufactured by splitting them into small-size tiles. However, this configuration of castellated tiles will result in the uneven distribution of energy flux on the divertor tiles; therefore, it is necessary to evaluate the thermal performance of the edge region of plasma-facing diverter tiles with considering the effect of the castellated tile configuration. The issue of material melting under transient heat fluxes is the most outstanding open question associated with the use of W divertor targets on ITER [4], [5].
The high-confinement mode (H-mode) in company with type-I ELMs is considered as the reference operating scenario for ITER [6]. A characteristic feature of this regime is periodically expelling impurities and energy from core plasma by multiple ELMs. However, heat loads brought by large ELMs may damage the target plates and thus significantly reduce the lifetime of divertor tiles and subsequently lead to the contamination of core plasma, and even resulting in the disruption [7]. The lifetime of the divertor against ELMs is of great concern in the design of a tokamak fusion reactor.
A typical feature of the type-I ELMs is that its frequency increases with the heating power. ASDEX-U and DIII-D experiments showed the plasma energy loss ratio induced by the type-I ELMs was nearly constant [8]. In future tokamak ITER, which will operate mainly on the elmy H mode, the ELMs are foreseen about 1–3 MJ/m2 with duration 0.1–1 ms, and inter-ELMs thermal loads are expected 5–20 MW/m2 [9], [10], [11], [12]. Recently, the values of heat fluxes to the castellated divertor tiles were evaluated by a 2d3v PIC-MCC model [13]. This simulation work showed that the lateral and top sides of a divertor tile facing the plasma received a higher energy flux, especially, the area near the plasma-wetted edge formed by top and lateral surfaces received the highest energy load but the energy flux fell dramatically along either lateral side down to the gap, and that the energy flux tended to be a constant on the plate surface away from the edge.
The edge shape of plasma-wetted divertor plates is very important in determining their lifetime. Therefore great efforts have been put into related studies. For example, many experiments [14], [15], [16], [17] were carried out for ELM-like heat loads demonstrated a significant erosion of frontal and lateral divertor tile edges; Bazylev et al. [18], [19] evaluated the thermal erosion of the W divertor tile under type-I ELMs by using the code MEMOS. Based on the latter work, we further include in a somehow self-consistent way the recent new finding [13], [20], [21]-the geometrical effects of castellated divertor on the energy flux distribution received by the tile-for more realistic assessment of the thermal erosion of the W divertor tile under type-I ELMs.
In this paper we extend the previous work [22] from a one-dimensional domain to a two-dimensional domain to quantitatively evaluate the thermal erosion to the castellated W divertor tiles with three edge shapes (rectangular edge, slanted edge, and rounded edge) during the afore-mentioned type-I ELMs under a set of plasma parameters similar to those of ITER.
Section snippets
Model description
In this work, the whole model consists of two parts: the first part is a PIC-MCC model, which is used to evaluate the position-dependent distribution of incoming energy flux to the tile plate; the second part is a heat conduction model, which is used to assess the thermal erosion of the tile during the irradiation with the energy flux distribution obtained from the former model as input. Regarding to the PIC/MCC model, there are seminar books and reviews available (e.g., [23], [24]) for
Results and discussion
Before carrying out our study, we first checked our model with comparing with a previous work [28], in which the temperature variation of a W target plate exposed to a heat flux 23 MW/m2 with a duration of 1.5 s had been monitored experimentally and also simulated. We took the same simulation parameters and boundary conditions with those used in this reference and employed the present model to do the same calculations. Fig. 2 presents the temperature evolution for the surface and the back
Summary
A two-dimensional heat conductivity equation has been employed in this work to assess the thermal response and erosion of the divertor W target tiles with different edge shapes during a typical type-I ELM for ITER. To make the assessment adequately, the heat flux to each side of the divertor tile evaluated first by a two-dimension-in-space and three-dimension-in-velocity particle-in-cell plus Monte Carlo Collisions code was used as input for the heat conductivity model. The simulation results
Acknowledgments
This work was supported by National Magnetic Confinement Fusion Science of China under Contract Nos. 2013GB109001 and 2013GB107003, National Natural Science Foundation of China under Grant No. 11275042, and the Fundamental Research Funds for the Central Universities No. DUT13ZD102.
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