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核融合炉のMHD自由表面液体金属流の数値シミュレーション

ジャービル, サイフ, サイド, アル, サラーミー SAIF SAID AL SALAMI, JABIR 九州大学

2022.09.22

概要

Nuclear fusion is a promising alternative energy source, with the potential to provide the world with virtually unlimited energy without adverse climatic or environmental impacts. Despite these theoretical prospects, several significant technical challenges remain, putting into question the practicality and commercial viability of this technology. Most prominent among these technical challenges is the problem of designing plasma-facing components (PFCs) that can withstand the extreme heat and particle loads anticipated in reactors of practical scales. The PFC designs presently used in research reactors will not be adequate to handle the tremendous heat fluxes which are anticipated in future DEMO and commercial Tokamaks. At such extreme heat loads, solid components experience excessive melting and evaporation, compromising their structural integrity and adversely impacting plasma confinement. To address the shortcomings of solid PFC designs, several alternative concepts that utilize a flowing liquid metal surface have been proposed. Liquid metal PFCs, however, introduce several technical challenges. This is because the operation of such devices gives rise to complicated phenomena spanning multiple disciplines of physics, most notably the interaction of electromagnetic fields with electrically conductive fluids, or magnetohydrodynamics (MHD).

The complicated interactions and extreme physical parameters associated with the phenomena do not lend themselves well to theoretical analysis and experimental study. Numerical simulation is a powerful tool that enables researchers to study such complex phenomena and assess the viability of different designs. To date, most numerical studies of fusion-related liquid metal flows focused on internal magnetohydrodynamic flows in ducts. Free surface flows add a layer of complexity to such phenomena, requiring additional careful treatment. However, most previous numerical studies of such problems employed simplified, steady, or two-dimensional models that may overlook crucial features of the flow.

In this work, a fully 3-dimensional and transient numerical tool for the simulation of free surface, thermo-MHD phenomena is developed in the framework of the finite volume method and implemented using the OpenFOAM open-source toolkit. The goal of this development is to create a tool that aids in the design of liquid metal PFCs. In the developed solvers, the solution of the electromagnetic equations is carried out in a coupled manner, both in the fluid and solid domains. The MHD forces exerted on the flow are computed using the inductionless approximation that utilizes the electric potential as a solution variable. Furthermore, a solver that utilizes the magnetic vector potential is developed to include the effect of the induced magnetic field.

This thesis is organized in 3 parts, as follows:

1. Introduction:
Chapter 1, Introduction: the background of the problem that motivated this work is discussed, including a literature review of previous relevant experimental and numerical studies.

Chapter 2, Mathematical model: A detailed description of the mathematical model employed to describe magnetohydrodynamics, free surface flows and heat transfer is given, including a discussion of approximations used and boundary conditions.

2. Development and validation:
Chapter 3, Numerical method: The numerical solution methodology is discussed, including a description of implementation and domain coupling procedure.

Chapter 4, Validation: In this chapter, the developed solvers are validated for a number of relevant physical phenomena by comparing to analytical solutions and experimental measurements. This includes internal flows in ducts under the influence of strong uniform and variable magnetic fields. Validation is also carried out for internal, thermo-MHD flows, free surface flows with complicated free surface interactions and a first of its kind validation study of free surface MHD flows.

3. Applications:
Chapter 5: Applications: in this chapter, the developed set of tools are used to simulate practical problems related to the use of liquid metals in fusion reactors. This includes a numerical study of a scheme to decrease the pressure drop due to a magnetic field gradient. Furthermore, the behavior in the fast-flowing film divertor is simulated, revealing interesting features that cannot be produced by reduced-order models. Finally, the divertorlets liquid metal plasma-facing component concept, which utilizes a relatively slow flow is simulated. Simulations yield good matching with experimental observations and reveal the effect of the electrical conductivity of the boundaries on the device performance.

This thesis is concluded with a summary of findings and details regarding outlook and future work, including additional physics and numerical improvements.

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参考文献

[1] Mohamed A. Abdou. “Exploring novel high power density concepts for attractive fusion systems.” In: 45 (1999), pp. 145–167. DOI: 10 . 1016/s0920-3796(99)00018-6 (cit. on p. 11).

[2] Ciro Alberghi and Luigi Candido. “Verification and validation of COMSOL magnetohydrodynamic models for liquid metal breeding blankets technologies.” In: Fusion Engineering and Design April (2021) (cit. on p. 69).

[3] X. Albets-Chico, E.V. Votyakov, H. Radhakrishnan, and S. Kassinos. “Effects of the consistency of the fringing magnetic field on direct numerical simulations of liquid–metal flow.” In: Fusion Engineering and Design 86.1 (Jan. 2011), pp. 5–14. DOI: 10.1016/j.fusengdes. 2010.07.014 (cit. on p. 69).

[4] N.V. Antonov et al. “Experimental and calculated basis of the lithium capillary system as divertor material.” In: Journal of Nuclear Materials 241-243 (Feb. 1997), pp. 1190–1196. DOI: 10.1016/s0022-3115(97) 80219-x (cit. on pp. 13, 18).

[5] M.L. Apicella, G. Mazzitelli, V. Pericoli Ridolfini, V. Lazarev, A. Alek- seyev, A. Vertkov, and R. Zagórski. “First experiments with lithium limiter on FTU.” In: Journal of Nuclear Materials 363-365 (June 2007), pp. 1346–1351. DOI: 10.1016/j.jnucmat.2007.01.237 (cit. on p. 10).

[6] Marco Ariola and Alfredo Pironti. Magnetic Control of Tokamak Plasmas. 2016. DOI: 10.1007/978-3-319-29890-0 (cit. on pp. 5, 6).

[7] N. Asakura, K. Hoshino, Y. Homma, and Y. Sakamoto. “Simulation studies of divertor detachment and critical power exhaust parameters for Japanese DEMO design.” In: Nuclear Materials and Energy 26 (Mar. 2021), p. 100864. DOI: 10.1016/j.nme.2020.100864 (cit. on pp. 116,122, 128).

[8] N. Asakura et al. “Studies of power exhaust and divertor design for a 1.5 GW-level fusion power DEMO.” In: Nuclear Fusion 57.12 (Oct. 2017), p. 126050. DOI: 10.1088/1741-4326/aa867a (cit. on pp. 6, 128, 132).

[9] Guillaume Authié, Toshio Tagawa, and René Moreau. “Buoyant flow in long vertical enclosures in the presence of a strong horizontal magnetic field. Part 2. Finite enclosures.” In: European Journal of Mechanics, B/Fluids 22.3 (2003), pp. 203–220. DOI: 10.1016/S0997 -7546(03)00024-4 (cit. on p. 75).

[10] M. J. Baldwin and R. P. Doerner. “Helium induced nanoscopic mor- phology on tungsten under fusion relevant plasma conditions.” In: 48 (2008), p. 035001. DOI: 10.1088/0029-5515/48/3/035001 (cit. on p. 9).

[11] V Barabash, G Federici, M Rödig, L.L Snead, and C.H Wu. “Neutron irradiation effects on plasma facing materials.” In: Journal of Nuclear Materials 283-287 (Dec. 2000), pp. 138–146. DOI: 10 . 1016 / s0022 - 3115(00)00203-8 (cit. on p. 9).

[12] Timothy Barth and Dennis Jespersen. “The design and application of upwind schemes on unstructured meshes.” In: 27th Aerospace sciences meeting. 1989, p. 366 (cit. on p. 40).

[13] Pascal Beckstein, Vladimir Galindo, and Vuko Vukcˇevic´. “Efficient solution of 3D electromagnetic eddy-current problems within the finite volume framework of OpenFOAM.” In: Journal of Computational Physics 344 (2017), pp. 623–646. DOI: 10.1016/j.jcp.2017.05.005. arXiv: 1612.06580 (cit. on p. 31).

[14] M. G. Bell et al. “Plasma response to lithium-coated plasma-facing components in the National Spherical Torus Experiment.” In: 51 (2009), p. 124054. DOI: 10.1088/0741- 3335/51/12/124054 (cit. on p. 10).

[15] Artem Blishchik, Mike van der Lans, and Saša Kenjereš. “An ex- tensive numerical benchmark of the various magnetohydrodynamic flows.” In: International Journal of Heat and Fluid Flow 90 (Aug. 2021), p. 108800. DOI: 10.1016/j.ijheatfluidflow.2021.108800 (cit. on p. 18).

[16] Thomas Boeck, Dmitry Krasnov, and Egbert Zienicke. “Numerical study of turbulent magnetohydrodynamic channel flow.” In: Journal of Fluid Mechanics 572 (2007), pp. 179–188 (cit. on pp. 26, 27).

[17] C. M. Braams and P. E. Stott. “Nuclear Fusion: half a century of magnetic confinement research.” In: 44 (2002), pp. 1767–1767. DOI: 10.1088/0741-3335/44/8/701 (cit. on p. 5).

[18] Jeremiah U Brackbill, Douglas B Kothe, and Charles Zemach. “A continuum method for modeling surface tension.” In: Journal of com- putational physics 100.2 (1992), pp. 335–354 (cit. on pp. 25, 30).

[19] EC Brouillette and PS Lykoudis. “Magneto-Fluid-Mechanic Channel Flow. I. Experiment.” In: The physics of fluids 10.5 (1967), pp. 995–1001 (cit. on p. 26).

[20] L. Bühler. “A parametric study of 3D MHD flows in expansions of rectangular ducts.” In: Fusion Science and Technology 52.3 (2007), pp. 595–602. DOI: 10.13182/FST07-A1553 (cit. on pp. 101, 106).

[21] A. de Castro, C. Moynihan, S. Stemmley, M. Szott, and D. N. Ruzic. “Lithium, a path to make fusion energy affordable.” In: Physics of Plasmas 28.5 (May 2021), p. 050901. DOI: 10.1063/5.0042437 (cit. on p. 116).

[22] ANSYS CFX-Solver. “Theory guide.” In: Release ll (2006) (cit. on pp. 16, 28).

[23] Sergio Ciattaglia, Maria Carmen Falvo, Alessandro Lampasi, and Matteo Proietti Cosimi. “Energy Analysis for the Connection of the Nuclear Reactor DEMO to the European Electrical Grid.” In: Energies 13.9 (May 2020), p. 2157. DOI: 10.3390/en13092157 (cit. on p. 6).

[24] Stockholm COMSOL AB. Sweden. COMSOL multiphysics® v. 5.6 (cit. on p. 144).

[25] J. W. Connor, G. F. Counsell, S. K. Erents, S. J. Fielding, B. LaBombard, and K. Morel. “Comparison of theoretical models for scrape-off layer widths with data from COMPASS-D, JET and Alcator C-Mod.” In: 39 (1999), pp. 169–188. DOI: 10.1088/0029-5515/39/2/304 (cit. on p. 8).

[26] M. S. Darwish and F. Moukalled. “TVD schemes for unstructured grids.” In: 46 (2003), pp. 599–611. DOI: 10 . 1016 / s0017-9310(02 ) 00330-7 (cit. on pp. 43, 46).

[27] Peter Alan Davidson. An introduction to magnetohydrodynamics. 2002 (cit. on p. 21).

[28] Ethan Davis and Sidy Ndao. “On the Wetting States of Low Melting Point Metal Galinstan® on Silicon Microstructured Surfaces.” In: Advanced Engineering Materials 20.3 (Dec. 2017), p. 1700829. DOI: 10. 1002/adem.201700829 (cit. on p. 86).

[29] Suraj S Deshpande, Lakshman Anumolu, and Mario F Trujillo. “Eval- uating the performance of the two-phase flow solver interFoam.” In: Computational Science and Discovery 5.1 (Nov. 2012), p. 014016. DOI: 10.1088/1749-4699/5/1/014016 (cit. on pp. 25, 48).

[30] V.A Evtikhin, I.E Lyublinski, A.V Vertkov, N.I Yezhov, B.I Khripunov, S.M Sotnikov, S.V Mirnov, and V.B Petrov. “Energy removal and MHD performance of lithium capillary-pore systems for divertor target application.” In: Fusion Engineering and Design 49-50 (Nov. 2000), pp. 195–199. DOI: 10.1016/s0920-3796(00)00423-3 (cit. on pp. 13, 18).

[31] G. Federici, H. Wuerz, G. Janeschitz, and R. Tivey. “Erosion of plasma- facing components in ITER.” In: 61-62 (2002), pp. 81–94. DOI: 10.1016/ s0920-3796(02)00298-3 (cit. on p. 9).

[32] Ronald P. Fedkiw, Tariq Aslam, and Shaojie Xu. “The Ghost Fluid Method for Deflagration and Detonation Discontinuities.” In: 154 (1999), pp. 393–427. DOI: 10.1006/jcph.1999.6320 (cit. on p. 48).

[33] Jingchao Feng, Hongli Chen, Qingyun He, and Minyou Ye. “Further validation of liquid metal MHD code for unstructured grid based on OpenFOAM.” In: Fusion Engineering and Design 100 (2015), pp. 260–264. DOI: 10.1016/j.fusengdes.2015.06.059. URL: http://dx.doi. org/10.1016/j.fusengdes.2015.06.059 (cit. on pp. 18, 69).

[34] Richard C. Fernow. Principles of Magnetostatics. 2016. DOI: 10.1017/ cbo9781316676127 (cit. on p. 24).

[35] Joel H Ferziger, Milovan Peric´, and Robert L Street. Computational methods for fluid dynamics. Vol. 3. Springer, 2002 (cit. on pp. 37, 46).

[36] P Fiflis, L Kirsch, Daniel Andruczyk, Davide Curreli, and David N Ruzic. “Seebeck coefficient measurements on Li, Sn, Ta, Mo, and W.” In: Journal of nuclear materials 438.1-3 (2013), pp. 224–227 (cit. on p. 13).

[37] A. E. Fisher, M. G. Hvasta, and E. Kolemen. “Study of liquid metal surface wave damping in the presence of magnetic fields and elec- trical currents.” In: Nuclear Materials and Energy 19.February (2019), pp. 101–106. DOI: 10.1016/j.nme.2019.02.014. URL: https://doi. org/10.1016/j.nme.2019.02.014 (cit. on p. 83).

[38] A. E. Fisher, E. Kolemen, and M. G. Hvasta. “Experimental demon- stration of hydraulic jump control in liquid metal channel flow using Lorentz force.” In: Physics of Fluids 30.6 (2018). DOI: 10 . 1063 / 1 . 5026993. URL: http : / / dx . doi . org / 10 . 1063 / 1 . 5026993 (cit. on pp. 17, 83, 125).

[39] A. E. Fisher, Z. Sun, and E. Kolemen. “Liquid metal “divertorlets” concept for fusion reactors.” In: Nuclear Materials and Energy 25 (2020), p. 100855. DOI: 10.1016/j.nme.2020.100855. URL: https://doi.org/ 10.1016/j.nme.2020.100855 (cit. on pp. v, 13, 17, 143, 152).

[40] Adam Eli Fisher. “Free Surface Liquid Metal Flow for Fusion Reac- tors.” PhD thesis. Princeton University, 2020 (cit. on p. 12).

[41] Narendra Laxman Gajbhiye, Praveen Throvagunta, and Vinayak Eswaran. “Validation and verification of a robust 3-D MHD code.” In: Fusion Engineering and Design 128.March 2017 (2018), pp. 7–22. DOI: 10.1016/j.fusengdes.2018.01.017 (cit. on pp. 18, 69).

[42] D. Gao, N.B. Morley, and V. Dhir. “Numerical study of liquid metal film flows in a varying spanwise magnetic field.” In: Fusion Engineer- ing and Design 63-64 (Dec. 2002), pp. 369–374. DOI: 10.1016/s0920- 3796(02)00266-1 (cit. on pp. 14, 17, 125).

[43] D. Gerlach, G. Tomar, G. Biswas, and F. Durst. “Comparison of volume-of-fluid methods for surface tension-dominant two-phase flows.” In: 49 (2006), pp. 740–754. DOI: 10.1016/j.ijheatmasstransfer. 2005.07.045 (cit. on p. 52).

[44] M. R. Gilbert and J.-Ch. Sublet. “Neutron-induced transmutation effects in W and W-alloys in a fusion environment.” In: 51 (2011), p. 043005. DOI: 10.1088/0029-5515/51/4/043005 (cit. on p. 9).

[45] L.G. Golubchikov, V.A. Evtikhin, I.E. Lyublinski, V.I. Pistunovich, I.N. Potapov, and A.N. Chumanov. “Development of a liquid-metal fusion reactor divertor with a capillary-pore system.” In: Journal of Nuclear Materials 233-237 (Oct. 1996), pp. 667–672. DOI: 10 . 1016 / s0022 -3115(96)00010-4 (cit. on p. 13).

[46] Takuya Goto, Takeru Ohgo, and Junichi Miyazawa. “Experimental study on MHD effect of liquid metal sheath jet for the liquid metal divertor REVOLVER-D.” In: Plasma and Fusion Research 14 (2019), pp. 1405092–1405092 (cit. on p. 12).

[47] A. A. Harms, D. R. Kingdon, K. F. Schoepf, and G. H. Miley. Principles of Fusion Energy. An Introduction to Fusion Energy for Students of Science and Engineering. 2000. DOI: 10.1142/4447 (cit. on p. 4).

[48] D. J. E. Harvie, M. R. Davidson, and M. Rudman. “An analysis of parasitic current generation in volume of fluid simulations.” In: 46 (), p. 133. DOI: 10.21914/anziamj.v46i0.952 (cit. on p. 52).

[49] C. W. Hirt, A. A. Amsden, and J. L. Cook. “An arbitrary Lagrangian- Eulerian computing method for all flow speeds.” In: 14 (1974), pp. 227–253. DOI: 10.1016/0021-9991(74)90051-5 (cit. on p. 48).

[50] Tobias Holzmann. “Mathematics, numerics, derivations and Open- FOAM®.” In: Loeben, Germany: Holzmann CFD (2016) (cit. on p. 60).

[51] Heinrich Hora. “Developments in inertial fusion energy and beam fusion at magnetic confinement.” In: 22 (2004), pp. 439–449. DOI: 10.1017/s0263034604223242 (cit. on p. 5).

[52] Changhong Hu and Makoto Sueyoshi. “Numerical simulation and experiment on dam break problem.” In: Journal of Marine Science and Application 9.2 (2010), pp. 109–114 (cit. on p. 78).

[53] H.L Huang, A Ying, and M.A Abdou. “3D MHD free surface fluid flow simulation based on magnetic-field induction equations.” In: Fusion Engineering and Design 63-64 (Dec. 2002), pp. 361–368. DOI: 10.1016/s0920-3796(02)00261-2 (cit. on p. 14).

[54] Paul W Humrickhouse, Brad J Merrill, Su-Jong Yoon, and Lee C Cad- wallader. “The impacts of liquid metal plasma-facing components on fusion reactor safety and tritium management.” In: Fusion Science and Technology 75.8 (2019), pp. 973–1001 (cit. on p. 12).

[55] M. G. Hvasta, E. Kolemen, A. E. Fisher, and H. Ji. “Demonstrating electromagnetic control of free-surface, liquid-metal flows relevant to fusion reactors.” In: Nuclear Fusion 58.1 (2018), pp. 1–23. DOI: 10.1088/1741-4326/aa9344 (cit. on pp. 17, 83, 125).

[56] T Ihli et al. “Review of blanket designs for advanced fusion reactors.” In: Fusion Engineering and Design 83.7-9 (2008), pp. 912–919 (cit. on p. 10).

[57] Venkatesh Inguva, Andreas Schulz, and Eugeny Y Kenig. “On meth- ods to reduce spurious currents within VOF solver frameworks. Part 1: a review of the static bubble/droplet.” In: Chemical Product and Process Modeling (2020) (cit. on p. 52).

[58] Raad I Issa. “Solution of the implicitly discretised fluid flow equations by operator-splitting.” In: Journal of computational physics 62.1 (1986), pp. 40–65 (cit. on p. 45).

[59] Hrvoje Jasak, Aleksandar Jemcov, Zeljko Tukovic, et al. “OpenFOAM: A C++ library for complex physics simulations.” In: International workshop on coupled methods in numerical dynamics. Vol. 1000. IUC Dubrovnik Croatia. 2007, pp. 1–20 (cit. on pp. 18, 37, 60).

[60] R. Kaita et al. “Extremely low recycling and high power density han- dling in CDX-U lithium experiments.” In: 363-365 (2007), pp. 1231– 1235. DOI: 10.1016/j.jnucmat.2007.01.229 (cit. on p. 10).

[61] R. Kaita et al. “Low recycling and high power density handling physics in the Current Drive Experiment-Upgrade with lithium plasma-facing components.” In: 14 (2007), p. 056111. DOI: 10.1063/1. 2718509 (cit. on p. 10).

[62] Mohamed M. Kamra, Nik Mohd, Cheng Liu, Makoto Sueyoshi, and Changhong Hu. “Numerical and experimental investigation of three- dimensionality in the dam-break flow against a vertical wall.” In: 30 (2018), pp. 682–693. DOI: 10.1007/s42241-018-0074-x (cit. on p. 48).

[63] Weishan Kang, Zengyu Xu, and Chuanjie Pan. “MHD stabilities of liquid metal jet flows with gradient magnetic field.” In: Fusion Engineering and Design 81.8-14 (Feb. 2006), pp. 1019–1025. DOI: 10. 1016/j.fusengdes.2005.07.029 (cit. on p. 12).

[64] C. E. Kessel et al. “The Fusion Nuclear Science Facility, the Critical Step in the Pathway to Fusion Energy.” In: 68 (2015), pp. 225–236. DOI: 10.13182/fst14-953 (cit. on p. 17).

[65] CE Kessel et al. “Critical Exploration of Liquid Metal Plasma-Facing Components in a Fusion Nuclear Science Facility.” In: Fusion Science and Technology (2019), pp. 1–32 (cit. on pp. 8, 11–13).

[66] Andrei Khodak, Fan Yang, and Howard A. Stone. “Free-Surface Liquid Lithium Flow Modeling and Stability Analysis for Fusion Applications.” In: Journal of Fusion Energy 39.6 (2020), pp. 455–461. DOI: 10 . 1007 / s10894 - 020 - 00261 - 6. URL: https : / / doi . org / 10 . 1007/s10894-020-00261-6 (cit. on pp. 13, 28, 115).

[67] TM Kirshner. Modeling Multiphase Materials ProcessesFluid amplifier. 1966 (cit. on p. 127).

[68] KMT Kleefsman, G Fekken, AEP Veldman, B Iwanowski, and B Buchner. “A volume-of-fluid based simulation method for wave impact problems.” In: Journal of computational physics 206.1 (2005), pp. 363–393 (cit. on p. 48).

[69] E. Kolemen, M. Hvasta, R. Majeski, R. Maingi, A. Brooks, and T. Kozub. “Design of the Flowing LIquid Torus (FLIT).” In: Nuclear Materials and Energy 19.April (2019), pp. 524–530. DOI: 10.1016/j.nme. 2019.01.005. URL: https://doi.org/10.1016/j.nme.2019.01.005 (cit. on pp. 12, 123).

[70] DS Krasnov, Egbert Zienicke, Oleg Zikanov, Thomas Boeck, and Andre Thess. “Numerical study of the instability of the Hartmann layer.” In: Journal of Fluid Mechanics 504 (2004), pp. 183–211 (cit. on p. 26).

[71] Bruno Lafaurie, Carlo Nardone, Ruben Scardovelli, Stéphane Zaleski, and Gianluigi Zanetti. “Modelling Merging and Fragmentation in Multiphase Flows with SURFER.” In: 113 (1994), pp. 134–147. DOI: 10.1006/jcph.1994.1123 (cit. on p. 52).

[72] JD Lee. “Tritium breeding and energy generation in liquid lithium blankets.” In: Nuclear fusion reactors. Thomas Telford Publishing, 1970, pp. 471–482 (cit. on p. 10).

[73] Chenglong Li et al. “Evidence of vapor shielding effect on heat flux loaded on flowing liquid lithium limiter in EAST.” In: Plasma Science and Technology (Apr. 2022). DOI: 10.1088/2058-6272/ac6650 (cit. on pp. 10, 12).

[74] Zhiwei Li, Ji Li, Xingping Li, and Ming-Jiu Ni. “Free surface flow and heat transfer characteristics of liquid metal Galinstan at low flow velocity.” In: Experimental Thermal and Fluid Science 82 (2017), pp. 240–248. DOI: 10 . 1016 / j . expthermflusci . 2016 . 11 . 021. URL: http :/ / linkinghub . elsevier . com / retrieve / pii / S0894177716303375 (cit. on p. 86).

[75] Chungpin Liao and Mujid S. Kazimi. “On the design of liquid metal divertors.” In: Journal of Fusion Energy 13.1 (1994), pp. 33–38. DOI: 10.1007/BF02214046 (cit. on pp. 12, 115).

[76] RJ Lingwood and T Alboussiere. “On the stability of the Hartmann layer.” In: Physics of Fluids 11.8 (1999), pp. 2058–2068 (cit. on pp. 26, 27).

[77] Libor Lobovsky`, Elkin Botia-Vera, Filippo Castellana, Jordi Mas-Soler, and Antonio Souto-Iglesias. “Experimental investigation of dynamic pressure loads during dam break.” In: Journal of Fluids and Structures 48 (2014), pp. 407–434 (cit. on p. 78).

[78] Rainald Lohner, Chi Yang, and Eugenio Onate. On The Simulation Of Flows with Violent Free Surface Motion. 2006. DOI: 10.2514/6.2006-291 (cit. on p. 48).

[79] Kun Luo, Changxiao Shao, Min Chai, and Jianren Fan. “Level set method for atomization and evaporation simulations.” In: 73 (2019), pp. 65–94. DOI: 10.1016/j.pecs.2019.03.001 (cit. on p. 48).

[80] Yang Luo, Linlin Li, Yiping Wu, and Yuandong Huang. “Numerical investigation on the MHD flow characteristics of eutectic lead-lithium alloy in a U-turn duct with different aspect ratios of the connecting channel.” In: Fusion Engineering and Design 171 (Oct. 2021), p. 112647. DOI: 10.1016/j.fusengdes.2021.112647 (cit. on p. 118).

[81] Mikko Lyly, Juha Ruokolainen, and Esko Järvinen. “ELMER–a finite element solver for multiphysics.” In: CSC-report on scientific computing 2000 (1999), pp. 156–159 (cit. on p. 19).

[82] I Lyublinski, A Vertkov, S Mirnov, and V Lazarev. “Protection of tokamak plasma facing components by a capillary porous system with lithium.” In: Journal of Nuclear Materials 463 (2015), pp. 1156–1159 (cit. on p. 18).

[83] S Malang et al. “Self-cooled liquid-metal blanket concept.” In: Fusion Technol.;(United States) 14.3 (1988) (cit. on p. 10).

[84] D. K. Mansfield et al. “Enhancement of Tokamak Fusion Test Reactor performance by lithium conditioning.” In: Physics of Plasmas 3.5 (May 1996), pp. 1892–1897. DOI: 10.1063/1.871984 (cit. on p. 10).

[85] Emilie Marchandise, Jean-François Remacle, and Nicolas Chevaugeon. “A quadrature-free discontinuous Galerkin method for the level set equation.” In: 212 (2006), pp. 338–357. DOI: 10.1016/j.jcp.2005.07. 006 (cit. on p. 48).

[86] E Martelli et al. “Advancements in DEMO WCLL breeding blanket design and integration.” In: International Journal of Energy Research 42.1 (2018), pp. 27–52 (cit. on p. 10).

[87] G. Mazzitelli et al. “FTU results with a liquid lithium limiter.” In: 51 (2011), p. 073006. DOI: 10.1088/0029-5515/51/7/073006 (cit. on p. 10).

[88] Giuseppe Mazzone et al. “Choice of a low operating temperature for the DEMO EUROFER97 divertor cassette.” In: Fusion Engineering and Design 124 (Nov. 2017), pp. 655–658. DOI: 10.1016/j.fusengdes. 2017.02.013 (cit. on p. 115).

[89] FK McGinnis III and JP Holman. “Individual droplet heat-transfer rates for splattering on hot surfaces.” In: International Journal of heat and mass transfer 12.1 (1969), pp. 95–108 (cit. on p. 26).

[90] S V Mirnov, E A Azizov, V A Evtikhin, V B Lazarev, I E Lyublinski, A V Vertkov, and D Yu Prokhorov. “Experiments with lithium limiter on T-11M tokamak and applications of the lithium capillary-pore system in future fusion reactor devices.” In: Plasma Physics and Controlled Fusion 48.6 (May 2006), pp. 821–837. DOI: 10.1088/0741-3335/48/6/009 (cit. on pp. 10, 18).

[91] Chiara Mistrangelo and Leo Bühler. “Development of a Numerical Tool to Simulate Magnetohydrodynamic Interactions of Liquid Metals with Strong Applied Magnetic Fields.” In: Fusion Science and Tech- nology 60.2 (Aug. 2011), pp. 798–803. DOI: 10.13182/fst11-a12483 (cit. on p. 18).

[92] Keiji Miyazaki, Shoji Inoue, Nobuo Yamaoka, Tomomitsu Horiba, and Kazushige Yokomizo. “Magneto-Hydro-Dynamic Pressure Drop of Lithium Flow in Rectangular Ducts.” In: Fusion Technology 10.3 pt 2A (1986), pp. 830–836. DOI: 10.13182/fst10-830 (cit. on p. 102).

[93] S Molokov and CB Reed. Review of free-surface MHD experiments and modeling. Tech. rep. Argonne National Lab., IL (US), 2000 (cit. on p. 13).

[94] René Moreau, Sergey Smolentsev, and Sergio Cuevas. “MHD flow in an insulating rectangular duct under a non-uniform magnetic field.” In: PMC Physics B 3.1 (2010). DOI: 10.1186/1754-0429-3-3 (cit. on p. 103).

[95] Pablo Moresco and Thierry Alboussière. “Experimental study of the instability of the Hartmann layer.” In: Journal of Fluid Mechanics 504 (2004), pp. 167–181 (cit. on p. 27).

[96] N. B. Morley, S. Smolentsev, R. Munipalli, M.-J. Ni, D. Gao, and M. Abdou. “Progress on the modeling of liquid metal, free surface, MHD flows for fusion liquid walls.” In: 72 (2004), pp. 3–34. DOI: 10.1016/j.fusengdes.2004.07.013 (cit. on pp. iv, 12, 15).

[97] NB Morley, J Burris, LC Cadwallader, and MD Nornberg. “GaInSn usage in the research laboratory.” In: Review of Scientific Instruments 79.5 (2008), p. 056107 (cit. on pp. 83, 95).

[98] Neil B Morley. Numerical and experimental modeling of liquid metal thin film flows in a quasi-coplanar magentic field. Tech. rep. Oak Ridge Inst. for Science and Education, 1994 (cit. on pp. 12, 13).

[99] Fadl Moukalled, Luca Mangani, and Marwan Darwish. “The finite volume method.” In: The finite volume method in computational fluid dynamics. Springer, 2016, pp. 103–135 (cit. on pp. 37, 38, 40, 42, 46).

[100] Samir Muzaferija and David Gosman. “Finite-volume CFD procedure and adaptive error control strategy for grids of arbitrary topology.” In: Journal of computational physics 138.2 (1997), pp. 766–787 (cit. on p. 40).

[101] M Narula, M.A. Abdou, A Ying, N.B. Morley, M Ni, R Miraghaie, and J Burris. “Exploring liquid metal plasma facing component (PFC) concepts—Liquid metal film flow behavior under fusion relevant magnetic fields.” In: Fusion Engineering and Design 81.8-14 (Feb. 2006), pp. 1543–1548. DOI: 10.1016/j.fusengdes.2005.08.071. URL: https:/ / linkinghub . elsevier . com / retrieve / pii / S0920379605006964 (cit. on p. 16).

[102] M Narula, MA Abdou, A Ying, NB Morley, M Ni, R Miraghaie, and J Burris. “Exploring liquid metal plasma facing component (PFC) con- cepts—Liquid metal film flow behavior under fusion relevant mag- netic fields.” In: Fusion engineering and design 81.8-14 (2006), pp. 1543– 1548 (cit. on p. 16).

[103] M Narula, MA Abdou, AY Ying, T Sketchley, and J Burris. “Study of liquid metal film flow characteristics under fusion relevant magnetic field conditions.” In: 20th IEEE/NPSS Symposium onFusion Engineering, 2003. IEEE. 2003, pp. 2–5 (cit. on p. 16).

[104] M. Narula, A. Ying, and M. A. Abdou. “A study of liquid metal film flow, under fusion relevant magnetic fields.” In: Fusion Science and Technology 47.3 (2005), pp. 564–568. DOI: 10.13182/FST05-A745 (cit. on p. 16).

[105] Manmeet Singh Narula. Experiments and numerical modeling of fast flow- ing liquid metal thin films under spatially varying magnetic field conditions. University of California, Los Angeles, 2008 (cit. on p. 16).

[106] Ming Jiu Ni, Ramakanth Munipalli, Neil B. Morley, Peter Huang, and Mohamed A. Abdou. “A current density conservative scheme for in- compressible MHD flows at a low magnetic Reynolds number. Part I: On a rectangular collocated grid system.” In: Journal of Computational Physics 227.1 (2007), pp. 174–204. DOI: 10.1016/j.jcp.2007.07.025 (cit. on pp. 16, 53).

[107] Ming Jiu Ni, Ramakanth Munipalli, Neil B. Morley, Peter Huang, and Mohamed A. Abdou. “A current density conservative scheme for incompressible MHD flows at a low magnetic Reynolds number. Part II: On an arbitrary collocated mesh.” In: Journal of Computational Physics 227.1 (2007), pp. 174–204. DOI: 10.1016/j.jcp.2007.07.025 (cit. on pp. 16, 53, 65).

[108] Ming-Jiu Ni and Jun-Feng Li. “A consistent and conservative scheme for incompressible MHD flows at a low magnetic Reynolds number. Part III: On a staggered mesh.” In: Journal of Computational Physics 231.2 (2012), pp. 281–298 (cit. on pp. 16, 53).

[109] R. E. Nygren et al. “A fusion reactor design with a liquid first wall and divertor.” In: 72 (2004), pp. 181–221. DOI: 10.1016/j.fusengdes. 2004.07.007 (cit. on p. 11).

[110] Daniel Oliver O’Dea. “Power handling of liquid metal infused trenches in the EAST Tokamak.” PhD thesis. 2021 (cit. on p. 10).

[111] Roland W Ohse et al. Handbook of thermodynamic and transport proper- ties of alkali metals. Blackwell Oxford, 1985 (cit. on pp. 116, 118).

[112] Carl Ollivier-Gooch and Michael Van Altena. “A high-order-accurate unstructured mesh finite-volume scheme for the advection–diffusion equation.” In: Journal of Computational Physics 181.2 (2002), pp. 729– 752 (cit. on p. 40).

[113] Elin Olsson. “A Description of IsoAdvector–A Numerical Method for Improved Suface Sharpness in Two-Phase Flows.” In: Edited by Nilsson, H (2017) (cit. on pp. 50, 51).

[114] C F D Open. “Openfoam programmer’s guide.” In: OpenFOAM Foundation 2.June (2011) (cit. on pp. 18, 46).

[115] Edward Ott, Bertram Hui, and K. R. Chu. “Theory of electron cy- clotron resonance heating of tokamak plasmas.” In: 23 (1980), p. 1031. DOI: 10.1063/1.863085 (cit. on p. 6).

[116] Yuanjiang Pei, Sibendu Som, Eric Pomraning, Peter K. Senecal, Scott A. Skeen, Julien Manin, and Lyle M. Pickett. “Large eddy simulation of a reacting spray flame with multiple realizations under compres- sion ignition engine conditions.” In: 162 (2015), pp. 4442–4455. DOI: 10.1016/j.combustflame.2015.08.010 (cit. on p. 48).

[117] GJ Phillips and JJ Monaghan. “A numerical method for three-dimensional simulations of collapsing, isothermal, magnetic gas clouds.” In: Monthly Notices of the Royal Astronomical Society 216 (1985), pp. 883–895 (cit. on p. 9).

[118] B. F. Picologlou and C. B. Reed. “Experimental Investigation of 3-D MHD Flows at High Hartmann Number and Interaction Parameter.” In: Liquid Metal Magnetohydrodynamics. Springer Netherlands, 1989, pp. 71–77. DOI: 10.1007/978-94-009-0999-1_9 (cit. on p. 67).

[119] R. F. Post. Nuclear fusion by magnetic confinement. DOI: 10 . 2172 / 4605483 (cit. on p. 5).

[120] Munipalli Ramakanth, Shankar Vijaya, Chandler Carlos, Rowell Chris, Ni Mingjiu, Smolentsev Sergey, Morley Neil, Abdou Mohamed, and Hadid Ali. Development of a 3-D Incompressible Free Surface MHD Computational Environment for Arbitrary Geometries: HIMAG. Tech. rep. HyPerComp Inc., 2003 (cit. on p. 15).

[121] C. B. Reed, B. F. Piclolglou, T. Q. Hua, and J. S. Walker. “Alex Results - a Comparison of Measurements From a Round and a Rectangular Duct With 3-D Code Predictions.” In: (1987), pp. 1267–1270 (cit. on p. 67).

[122] Philip L Roe. “Some contributions to the modelling of discontinuous flows.” In: Large-scale computations in fluid mechanics (1985), pp. 163– 193 (cit. on p. 43).

[123] Johan Roenby, Henrik Bredmose, and Hrvoje Jasak. “A computational method for sharp interface advection.” In: Royal Society open science 3.11 (2016), p. 160405 (cit. on pp. 50, 51).

[124] Johan Roenby, Henrik Bredmose, and Hrvoje Jasak. “IsoAdvector: Geometric VOF on general meshes.” In: OpenFOAM®. Springer, 2019, pp. 281–296 (cit. on pp. 50, 51).

[125] DJ Rose. “Engineering feasibility of controlled fusion: A Review.” In: Nuclear Fusion 9.3 (1969), p. 183 (cit. on p. 10).

[126] Murray Rudman. “VOLUME-TRACKING METHODS FOR INTER- FACIAL FLOW CALCULATIONS.” In: 24 (1997), pp. 671–691. DOI: 10.1002/(sici)1097- 0363(19970415)24:7<671::aid- fld508> 3.0. co;2-9 (cit. on p. 48).

[127] D. N. Ruzic, W. Xu, D. Andruczyk, and M. A. Jaworski. “Lithium–metal infused trenches (LiMIT) for heat removal in fusion devices.” In: 51 (2011), p. 102002. DOI: 10.1088/0029- 5515/51/10/102002 (cit. on p. 13).

[128] D.N. Ruzic et al. “Flowing liquid lithium plasma-facing components – Physics, technology and system analysis of the LiMIT system.” In: Nuclear Materials and Energy 12 (Aug. 2017), pp. 1324–1329. DOI: 10.1016/j.nme.2017.06.001 (cit. on pp. 13, 18).

[129] F Saenz, Z Sun, A E Fisher, B Wynne, and E Kolemen. “Divertorlets concept for low-recycling fusion reactor divertor: experimental, ana- lytical and numerical verification.” In: Nuclear Fusion (Apr. 2022). DOI: 10.1088/1741-4326/ac6682 (cit. on pp. v, 13, 17, 143, 144, 152, 153).

[130] Nima Samkhaniani and Mohamad Reza Ansari. “The evaluation of the diffuse interface method for phase change simulations using OpenFOAM.” In: 46 (2017), pp. 1173–1203. DOI: 10.1002/htj.21268 (cit. on p. 52).

[131] Ruben Scardovelli and Stéphane Zaleski. “DIRECT NUMERICAL SIMULATION OF FREE-SURFACE AND INTERFACIAL FLOW.” In: 31 (1999), pp. 567–603. DOI: 10.1146/annurev.fluid.31.1.567 (cit. on p. 52).

[132] Herrmann Schlichting and Klaus Gersten. Boundary-layer theory. Springer Science & Business Media, 2003 (cit. on p. 26).

[133] Christian Schubert. “Evaluation numerischer Simulationsmethoden für die Untersuchung der Mehrphasenströmung im wechselstrombe- triebenen Elektroschlacke-Umschmelzverfahren mit rotierender Elek- trode; 1. Auflage.” de. PhD thesis. 2021, p. 2021. DOI: 10.18154/RWTH- 2022-00733 (cit. on p. 19).

[134] John Sheffield. “The physics of magnetic fusion reactors.” In: 66 (), pp. 1015–1103. DOI: 10.1103/revmodphys.66.1015 (cit. on p. 5).

[135] JA Shercliff. “Steady motion of conducting fluids in pipes under transverse magnetic fields.” In: Mathematical Proceedings of the Cam- bridge Philosophical Society. Vol. 49. 1. Cambridge University Press. 1953, pp. 136–144 (cit. on pp. 64, 65).

[136] M. Shimada. “A Possible Scheme for Mitigating grad-B MHD Drag.” In: 2nd US-Japan Workshop on Liquid Metal PFC (Mar. 8, 2022) (cit. on pp. v, 101).

[137] S Siriano, A Tassone, and G Caruso. “Numerical simulation of thin- film MHD flow for nonuniform conductivity walls.” In: Fusion Science and Technology 77.2 (2021), pp. 144–158 (cit. on p. iv).

[138] Vaclav Smil. Energy transitions: global and national perspectives. ABC- CLIO, 2016 (cit. on pp. 3, 4).

[139] S. Smolentsev and M. Abdou. “Open-surface MHD flow over a curved wall in the 3-D thin-shear-layer approximation.” In: Applied Mathematical Modelling 29.3 (Mar. 2005), pp. 215–234. DOI: 10.1016/j. apm.2004.07.002 (cit. on p. 15).

[140] S. Smolentsev and R. Moreau. “One-equation model for quasi-two- dimensional turbulent magnetohydrodynamic flows.” In: Physics of Fluids 19.7 (2007). DOI: 10.1063/1.2747234 (cit. on pp. 27, 102).

[141] S. Smolentsev, T. Rhodes, Y. Yan, A. Tassone, C. Mistrangelo, L. Bühler, and F. R. Urgorri. “Code-to-Code Comparison for a PbLi Mixed-Convection MHD Flow.” In: Fusion Science and Technology 76.5 (July 2020), pp. 653–669. DOI: 10.1080/15361055.2020.1751378 (cit. on p. 18).

[142] Sergey Smolentsev. “Design window for open-surface lithium diver- tor with helium-cooled substrate.” In: Fusion Engineering and Design 173.September (2021), p. 112930. DOI: 10.1016/j.fusengdes.2021. 112930. URL: https://doi.org/10.1016/j.fusengdes.2021.112930 (cit. on pp. 12, 17, 115, 116).

[143] Sergey Smolentsev, Charles E. Kessel, Jeremy D. Lore, Rajesh Maingi, Ranjit Singh, and Dennis L. Youchison. “Numerical Analysis of Liq- uid Metal MHD Flow and Heat Transfer for Open-Surface Li Divertor in FNSF.” In: (2022), pp. 1–6. DOI: 10.1109/tps.2022.3162141 (cit. on pp. iv, v, 17, 115, 135).

[144] Sergey Smolentsev, Thomas Rognlien, Mark Tillack, Lester Waganer, and Charles Kessel. “Integrated Liquid Metal Flowing First Wall and Open-Surface Divertor for Fusion Nuclear Science Facility: Concept, Design, and Analysis.” In: Fusion Science and Technology 75.8 (May 2019), pp. 939–958. DOI: 10.1080/15361055.2019.1610649 (cit. on p. 134).

[145] JoëL Sommeria and René Moreau. “Why, how, and when, MHD turbulence becomes two-dimensional.” In: Journal of Fluid Mechanics 118 (1982), pp. 507–518 (cit. on p. 27).

[146] P. C. Stangeby. The Plasma Boundary of Magnetic Fusion Devices. DOI: 10.1201/9780367801489 (cit. on p. 9).

[147] P.K. Swain, Pratik Koli, S. Ghorui, P. Mukherjee, and A.V. Deshpande. “Thermofluid MHD studies in a model of Indian LLCB TBM at high magnetic field relevant to ITER.” In: Fusion Engineering and Design 150 (Jan. 2020), p. 111374. DOI: 10.1016/j.fusengdes.2019.111374 (cit. on pp. 116, 118).

[148] P. K. Sweby. “High Resolution Schemes Using Flux Limiters for Hyperbolic Conservation Laws.” In: 21 (1984), pp. 995–1011. DOI: 10.1137/0721062 (cit. on p. 43).

[149] M. Szott and D.N. Ruzic. “2-D moving mesh modeling of lithium dryout in open surface liquid metal flow applications.” In: Fusion Engineering and Design 154 (May 2020), p. 111512. DOI: 10.1016/j. fusengdes.2020.111512 (cit. on p. 18).

[150] Matthew Michael Szott. “Advanced geometries for dryout mitigation in TEMHD-driven liquid lithium systems.” PhD thesis. University of Illinois at Urbana-Champaign, 2020 (cit. on p. 18).

[151] A. Tabasso, H. Maier, K. Krieger, J. Roth, and A.S.D.E.X. Upgrade Team. “Erosion of tungsten coated tiles on the central column of ASDEX Upgrade.” In: 40 (2000), pp. 1441–1444. DOI: 10.1088/0029-5515/40/8/101 (cit. on p. 9).

[152] T Tagawa. “Numerical simulation of two-phase flows in the presence of a magnetic field.” In: 72.4 (2006), pp. 212–219. DOI: 10.1016/j. matcom.2006.05.040 (cit. on p. 75).

[153] Dan Tong, David J. Farnham, Lei Duan, Qiang Zhang, Nathan S. Lewis, Ken Caldeira, and Steven J. Davis. “Geophysical constraints on the reliability of solar and wind power worldwide.” In: 12 (2021). DOI: 10.1038/s41467-021-26355-z (cit. on p. 3).

[154] Rachid Touzani and Jacques Rappaz. Mathematical Models for Eddy Currents and Magnetostatics. With Selected Applications. 2014. DOI: 10. 1007/978-94-007-0202-8 (cit. on p. 24).

[155] Yoshio UEDA. “Status of Plasma Facing Material Studies and Issues toward DEMO.” In: 5 (2010), S1009–S1009. DOI: 10.1585/pfr.5.s1009 (cit. on p. 9).

[156] Ya S Uflyand. Hartman problem for a circular tube. 1961 (cit. on p. 64).

[157] Bram Van Leer. “Towards the ultimate conservative difference scheme. II. Monotonicity and conservation combined in a second-order scheme.” In: Journal of computational physics 14.4 (1974), pp. 361–370 (cit. on pp. 43, 49).

[158] Juris Vencels, Andris Jakovics, Vadims Geza, and Mihails Scepanskis. “EOF Library: Open-Source Elmer and OpenFOAM Coupler for sim- ulation of MHD with free surface.” In: arXiv preprint arXiv:1707.04080 (2017) (cit. on p. 19).

[159] Henk Kaarle Versteeg and Weeratunge Malalasekera. An introduc- tion to computational fluid dynamics: the finite volume method. Pearson education, 2007 (cit. on pp. 37, 42, 46).

[160] H. G. Weller, G. Tabor, H. Jasak, and C. Fureby. “A tensorial ap- proach to computational continuum mechanics using object-oriented techniques.” In: Computers in Physics 12.6 (1998), p. 620. DOI: 10.1063/ 1.168744 (cit. on pp. 37, 60).

[161] D. G. Whyte, T. E. Evans, C. P. C. Wong, W. P. West, R. Bastasz, J. P. Allain, and J. N. Brooks. “Experimental observations of lithium as a plasma-facing surface in the DIII-D tokamak divertor.” In: 72 (2004), pp. 133–147. DOI: 10.1016/j.fusengdes.2004.07.014 (cit. on p. 10).

[162] John I. B. Wilson. “Tokamaks, 4th edn., by John Wesson. Scope: monograph. Level: postgraduate, advanced undergraduate, early career researcher, researcher, specialist, scientist, engineers.” In: 53 (2012), pp. 450–451. DOI: 10.1080/00107514.2012.720285 (cit. on pp. 4, 7, 8).

[163] Yican Wu, FDS Team, et al. “Conceptual design and testing strategy of a dual functional lithium–lead test blanket module in ITER and EAST.” In: Nuclear Fusion 47.11 (2007), p. 1533 (cit. on p. 10).

[164] Yican Wu, FDS Team, et al. “Overview of liquid lithium lead breeder blanket program in China.” In: Fusion Engineering and Design 86.9-11 (2011), pp. 2343–2346 (cit. on p. 10).

[165] Brian Wynne and Egemen Kolemen. “Magnetohydrodynamic Effects of a Gradient Magnetic Field on Liquid Metal Flows.” In: APS Division of Plasma Physics Meeting Abstracts. Vol. 2021. 2021, JP11–027 (cit. on p. 83).

[166] W Xu, D Curreli, D Andruczyk, T Mui, R Switts, and DN Ruzic. “Heat transfer of TEMHD driven lithium flow in stainless steel trenches.” In: Journal of Nuclear Materials 438 (2013), S422–S425 (cit. on p. 18).

[167] W Xu et al. “Vertical flow in the thermoelectric liquid metal plasma facing structures (TELS) facility at Illinois.” In: Journal of Nuclear Materials 463 (2015), pp. 1181–1185 (cit. on p. 18).

[168] J.-C. Yang, T.-Y. Qi, D.-W. Ren, M.-J. Ni, B.-Q. Liu, J.-S. Hu, and J.-G. Li. “Magnetohydrodynamic effects on liquid metal film flowing along an inclined plate relating to plasma facing components.” In: Nuclear Fusion 60.8 (July 2020), p. 086003. DOI: 10.1088/1741-4326/ab9257 (cit. on p. 16).

[169] Juan-Cheng Yang, Tian-Yu Qi, Dong-Wei Ren, Bai-Qi Liu, and Ming- Jiu Ni. “Rearrangement of liquid metal surface waves by a uniform transverse magnetic field.” In: Experiments in Fluids 59.11 (Oct. 2018). DOI: 10.1007/s00348-018-2617-x (cit. on p. 16).

[170] Wei Yang, Ming Jia, Kai Sun, and Tianyou Wang. “Influence of density ratio on the secondary atomization of liquid droplets under highly unstable conditions.” In: 174 (2016), pp. 25–35. DOI: 10.1016/j.fuel. 2016.01.078 (cit. on p. 48).

[171] AY Ying et al. “Exploratory studies of flowing liquid metal divertor options for fusion-relevant magnetic fields in the MTOR facility.” In: Fusion engineering and design 72.1-3 (2004), pp. 35–62 (cit. on pp. 12, 14).

[172] J.-H. You and I. Komarova. “Probabilistic failure analysis of a water- cooled tungsten divertor: Impact of embrittlement.” In: 375 (2008), pp. 283–289. DOI: 10.1016/j.jnucmat.2008.01.009 (cit. on p. 9).

[173] L.E. Zakharov, W. Blanchard, R. Kaita, H. Kugel, R. Majeski, and J. Timberlake. “Low recycling regime in ITER and the LiWall concept for its divertor.” In: Journal of Nuclear Materials 363-365 (June 2007), pp. 453–457. DOI: 10.1016/j.jnucmat.2007.01.230 (cit. on p. 115).

[174] Xiujie Zhang, Jie Mao, Yanjing Chen, Chuanjie Pan, and Zengyu Xu. “Investigations of liquid metal magnetohydrodynamic rectangular duct flows under inclined transversal magnetic fields.” In: Nuclear Fusion 59.5 (Apr. 2019), p. 056018. DOI: 10.1088/1741-4326/ab0b46 (cit. on p. 18).

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