The divertor is the most solicited one of the plasma facing components (PFCs), which are the components of a nuclear fusion reactor that constitute the boundary between the fusion plasma and the rest of the device. To withstand the extreme heat loads incoming from the plasma, liquid metals (LM) are considered as armor in some PFCs concepts either as a flowing film, a curtain of droplets (liquid wall), or imbibed in a porous medium. LM breeders are also considered in the design of the breeding blanket (BB), where neutron capture reactions generate tritium, fuel for the machine, and helium as byproduct. The necessity to account for the interaction between the electrically conductive LM and the magnetic field employed to confine the plasma, the magnetohydrodynamic phenomena (MHD), is one of the most challenging engineering issues in the LM application for fusion. Computational fluid dynamics (CFD) is a valid alternative to experimental analysis for complex and expensive systems such as PFCs and BBs. Among the CFD codes, OpenFOAM is a very promising opensource code as it allows a deep customization of the models, providing an ideal and almost indispensable environment for computational MHD (CMHD). The aim of this project is the development of an OpenFOAM MHD solver capable of simulating a multi-phase mixture with a high-density ratio between the phases, a numerically challenging task even for an ordinary mixture. Such a solver would allow a detailed analysis of multiphase flow in LM PFCs and BBs that are currently under development in the framework of the roadmap towards fusion electricity proposed by EUROfusion, the European consortium for the development of nuclear fusion, and will ultimately be tested in the ITER and DEMO reactors.
This project aims to contribute to the numerical modelling of multiphase MHD flows in conditions of fusion interest using the open-source code OpenFoam. It has been recognized for at least thirty years that computational science constitutes a third and independent branch of science on equal footing with theoretical and experimental sciences. However, over the past years, the quality of open-source software has significantly grown, largely aided by the move to object-oriented programming and online version-control repositories [1].
The development of a tool based on a highly customizable open-source code is ideal for tackling a non-ordinary problem such as a flow composed of a liquid metal and a gas phase in the presence of a magnetic field. The numerical simulation of such a flux is not trivial even in the absence of a magnetic field given the extreme density ratio present between the phases which can lead to the generation of fictitious velocity and is fundamental, above all, in the dynamics of bubbles. To the best of our knowledge, in the literature there are analyses of air bubbles in ordinary liquids which have maximum density ratios of the order of 10^3 [2,3], against a density ratio of 10^5 for a mixture of LiPb-He under the temperature and pressure conditions typical of a breeding blanket in a fusion reactor (600 K, 1-30 bar). In itself, to demonstrate the capability of OF to perform realistic multi-phase simulations in such extreme conditions will be a novel and significant achievement.
Looking at MHD multi-phase numerical models, the state-of-the-art seems to be represented by the 2014 article by Zhang et al. [4], in which it is shown an approach for direct simulation of the MHD multi-phase flow at high density ratio based on the VOF method with the AMR technique used to solve the interface and boundary layer. The authors tested this approach on unspecified code with mixture of Ar-GaInSn and N2-Hg under the influence of small magnetic fields intensity (Hartmann number, Ha up to 100), therefore a significant milestone will be achieved once it would be clear the limits in terms of density ratio and Ha accessible with this approach. The mixtures considered by Zhang et al. have a lower density ratio than the reference mixture for fusion He-LiPb and the intensity of magnetic field is much lower than in a fusion reactor (Ha up to 9000).
This project aims to develop an OF solver capable of simulating MHD multi-phase mixture with high density ratio and fusion relevant magnetic field intensity, bringing a state-of-the-art advancement in simulating extremely important systems for fusion technology i.e. the PFCs and BB. Examples of possible applications of the abovementioned solver are the simulation of the drift and coalescence of helium bubbles in a liquid metal breeder blanket and the motion of a curtain of droplets forming a liquid first wall. The former phenomenon affects the blanket performance through the effects of the gas phase on the temperature and velocity distribution of the liquid phase and the surrounding structural materials. Estimating the bubble path is also necessary to design an efficient purging system. In the latter case, the droplets interact both with the magnetic field and the plasma wind thus the stability of the curtain and the efficiency of the protection offered to the solid substrate must be estimated accounting for MHD effects. The successful development of this tool will pose the Sapienza Nuclear Engineering group at the forefront of the research on multi-phase MHD tools and the only one in Europe; a strategic position that is likely to increase our involvement in the EUROfusion and Fusion 4 Energy consortia.
Bibliography:
[1] G. Chen, Q. Xiong, P.J. Morris, E.G. Paterson, A. Sergeev, Y.-C. Wang, OpenFOAM for Computational Fluid Dynamics, Not. Am. Math. Soc. 61 (2014) 354. https://doi.org/10.1090/noti1095.
[2] S. Hysing, S. Turek, D. Kuzmin, N. Parolini, E. Burman, S. Ganesan, L. Tobiska, Quantitative benchmark computations of two-dimensional bubble dynamics, Int. J. Numer. Methods Fluids. 60 (2009) 1259¿1288. https://doi.org/10.1002/fld.1934.
[3] D.M. Sharaf, A.R. Premlata, M.K. Tripathi, B. Karri, K.C. Sahu, Shapes and paths of an air bubble rising in quiescent liquids, Phys. Fluids. 29 (2017) 122104. https://doi.org/10.1063/1.5006726.
[4] J. Zhang, M.J. Ni, Direct simulation of multi-phase MHD flows on an unstructured Cartesian adaptive system, J. Comput. Phys. 270 (2014) 345¿365. https://doi.org/10.1016/j.jcp.2014.03.030.