Numerical simulation of MHD flows in breeding blanket and plasma-facing components

The construction of a nuclear fusion reactor is probably the most complex engineering challenge that humanity is trying to overcome as its design combines disparate, sometimes conflicting, requirements derived from different fields of technology: neutronics, thermomechanics and thermohydraulics, electromechanics and applied superconductivity, Magnetohydrodynamics (MHD), radioprotection and safety. The enormous benefits in the use of nuclear fusion as an energy source have led to a constant international commitment to the construction of the first nuclear fusion reactor, sanctioned by the decision to build an international experimental reactor (ITER) in 2006. Since 2014, the European research and development activities in nuclear fusion have been coordinated by the EUROfusion consortium to achieve the breakthrough goal of building a demonstration fusion power plant (DEMO) after 2050. Among the huge amount of components essential to the reactor operation, two of the key ones are certainly the Breeding Blanket (BB) and the divertor, which completely surround the plasma. The first has the task of ensuring the fuel self- sufficiency of the reactor, the extraction of the power generated by the nuclear reactions and shielding the other components and personnel from radiation. The second has the task of managing and extracting the power and particle exhaust. One of the most promising blanket concepts is the Water-Cooled Lead Lithium (WCLL), whose research activities are coordinate by the Brasimone research centre of the Italian National Agency for New Technologies, Energy and Sustainable Economic Development (ENEA). The most promising concept of divertor is the full-tungsten one that will be tested in ITER, but several advanced solutions are being studied that aim to bridge the gap in the requirements for power handling and component availability between ITER and DEMO. Liquid Metals (LM) are considered attractive solution both as working fluids in blankets and as “self-healing protection” in advanced divertor and Plasma Facing Components (PFCs) concepts, where the most promising candidates are the lead- lithium eutectic alloy (PbLi) for the blanket and lithium or tin for the PFCs. Unfortunately, due to the electrical conductivity of metals, their motion is influenced by the magnetic field used in the reactor to confine the plasma, generating a complex phenomenology which is studied by the Liquid Metal Magnetohydrodynamics (LM-MHD) and which must be considered in phase design. These phenomena include the electromagnetic drag, turbulence suppression, modified heat and mass transport and electromagnetic coupling phenomena. In this framework, intense studies and research activities are essential to provide high-quality experimental and numerical data and to develop accurate predictive numerical tools. The research activity presented in this PhD dissertation aims to contribute to the numerical modelling of MHD phenomena relevant for the BB and for advanced PFCs thought Computational Magnetohydrodynamics (CMHD) codes. In Part II, the state of the art of CMHD codes is briefly presented, with a particular focus on the codes used in this research: ANSYS CFX and OpenFOAM. Of the latter, the icoFoam solver is presented in detail, used as a basis for the implementation of the MHD model presented in Chapter 5. The solver, called phiFoam, is capable of simulating a low magnetic Reynolds number, laminar, incompressible and isothermal MHD flow for ducts with perfectly electrical insulated or perfectly conductive walls. The solver was built by implementing the MHD equations in the formulation of the electric potential and adopting the numerical scheme proposed by Ni et al. [1] for the calculation of the current density in the cell centre in a conservative way. The phiFoam solver was validated through a two-dimensional and a three- dimensional benchmark. The 2D benchmark is based on the comparison of the dimensionless flow rate for a square duct with perfectly insulated walls to the Shercliff analytical solution [2, 3]. For Ha = 500, where Ha is the Hartmann number and represents the intensity of the magnetic field, an error of ≃ 0.7 % was obtained, while for the case Ha = 5000 an error of ≃ 3 %. The 3D benchmark considers a manifold consisting of an inlet channel, an abrupt expansion and three distribution channels. The control parameters are the flow rate repartition between the channels and the three-dimensional pressure drop due to the axial electric currents that develop mainly due to expansion, that are predicted, respectively, with an error of ≃ 5 % and ≃ 9 %. Overall, phiFoam has been shown to be able to accurately predict the basic MHD phenomena for a laminar flow up to Ha = 5000. In Chapter 6, the geometry and functioning of the PbLi co-axial manifold of WCLL2018 is showed in detail and a prototypical co-axial, or annular, channel model is presented. In Chapter 7, the annular channel is characterized through numerical calculation by ANSYS CFX code by varying the intensity of the magnetic field, the geometric parameters and the conductivity of the wall, represented by the conductance ratio cw. In Chapter 8, the electromagnetic coupling between the external and internal channel of the co axial geometry is studied as the intensity of the magnetic field and the distribution of the flow rate between the external and internal channels vary. For the uncoupled case, if the walls are perfectly insulated, two outflow areas are formed in which the velocity is practically uniform, separated by an internal layer: a fast core located in the portion of the channel parallel to the magnetic field and a slow core situation in the normal portion. With electro- conductive walls (cw = 0.1), the fast core is substituted by two intensive jets close side walls. By increasing the wall conductivity, the flow features remain those described for the case cw = 0.1 up to cw = 1, after which the velocity tends to become uniform throughout the channel. As the geometry of the annular channel varies, with fixed Ha and cw, the fundamental characteristics of the flow practically unchanged until the gap between the external and internal channels becomes very small and the jets do not have the necessary space to develop completely. The electromagnetic coupling phenomena change considerably the flow features. Different flow repartition scenarios between the external and internal channel are investigated at Ha = 2000. The external channel is greatly affected by the electro- magnetic coupling phenomenon, which drastically changes the velocity distribution compared to the uncoupled case, already for small values of the internal flow rate. In particular, is observed the formation of an intense jet contrary to the main flow direction in correspondence with the side wall shared with the internal channel, and a progressive flattening of the velocity profile in the other areas. The internal channel, on the other hand, is much less interested by the coupling, having characteristics close to a uncoupled case even at a very reduced flow rate. As the Hartmann number increases, with a fixed flow rate repartition, all the typical characteristics of the particular scenario are maintained and all the effects are progressively intensified. It is important to note that the counter flow rate under WCLL operating conditions is estimated to be around 28 % and must be considered in studies related to the management of the tritium inventory, since fluid recirculation will inevitably lead to tritium accumulation, especially in the outflow manifold. The co-axial pressure gradient has been correlated with the pressure gradient of an equivalent channel for which exist an analytical solution, developing a correction factor between the configurations. This factor shows an asymptotic behaviour for Ha > 1000 and allows to estimate the pressure drop for a similar configuration at higher Hartmann numbers without performing a numerical simulation. These correction factors were used to estimate the pressure drop of the WCLL outboard PbLi spinal manifold that contribute for the 18.5 % of the total in-magnet PbLi loop pressure drop. In Chapter 9, the WCLL2018 bottom collector is discussed in detail and a prototypical collector model with three different feeding pipe configurations, similar to ones envisaged in the last iteration of the WCLL and Dual-Coolant Lead Lithium (DCLL) breeding blanket, are analysed through phiFoam solver. The aim of the study is to investigate which configuration minimizes the flow imbalance in the manifold for the WCLL or in the poloidal breeding zone channels for the DCLL. The distribution of the flow rate between the channels is strongly influenced by the position of the feeding pipes and by the development of the internal layer near the expansion which generates important jets close to the back plate and the upper one where the channels are attached. The channel aligned with the feeding pipe is the one carrying most of the flow, from 55 % to 82 %, while in the more distant one the flow is almost stagnant, carrying from 17 % to 6 % of the total flow rate. The total pressure loss is also estimated and its functional dependence on the collector configuration is discussed. In Chapter 10, a thin-film single-phase MHD flow, representative of the armour in a film-type divertor or PFCs, has been investigated with the ANSYS CFX code. The numerical model is validated through the theoretical solution presented by Shishko et al. [4] up to Ha = 1000 for an insulated chute with an aspect ratio from 0.044 to 0.2. Consequently, the flow in a chute with insulating, conductive and partially conductive walls has been investigated to highlight the effect of discontinuous wall conductivity on the backing plate and lateral walls. A partially conductive backing plate has a negligible effect on the flow, if also the lateral wall is insulated, consistent to the analogous bounded case, whereas the transition from insulating to conductive Hartmann wall causes larger pressure losses, higher free surface velocity, counter flow onset and structural change in the Hartmann boundary layer. The location of the conductive sections on the Hartmann wall influences the flow features, resulting in higher free surface velocity and pressure drop when these are close to the backing plate and free surface. The chute with both perfectly conductive backing plate and lateral walls is the one that experiences the greatest pressure drop and free surface velocity. These phenomena could be interesting for the PFCs applications, where increasing the free surface velocity with a contained pressure drop could be an attractive solution. In this case, the best compromise is to have a partially conductive lateral wall with the conductive portion placed in the middle/bottom part on the wall, instead of a totally conductive wall. In Chapter 11, is considered the rising of a bubble in a liquid metal under the action of a magnetic field. The multi-phase interIsoFoam solver present in the OpenFOAM distribution is validated in hydrodynamic conditions for a 2D stationary drop, 2D rising bubble, 3D rising bubble and for the coalescence of two bubbles. Then, it was tested for a high density ratio mixture, simulating the rising of a helium bubble in the PbLi with different diameters, showing the ability to correctly model different flow regimes. Overall, interIsoFoam has proven to be able to correctly simulate the basic characteristics of a flow with a high density ratio and therefore it is an excellent candidate for the future implementation of the MHD equations, for the study of the migration of helium bubbles in the blanket but also in the framework of the advanced PFCs.