Dottorato in ENERGIA E AMBIENTE

Titolo della tesi: Numerical simulation of MHD flows in breeding blanket and plasma-facing components

A fusion reactor is probably the most complex engineering challenge that humanity has attempted to overcome as it combines in its design disparate, and sometimes conflicting, requirements derived by several fields: neutronics, thermomechanics and thermohydraulics, electromechanics and applied superconductivity, magnetohydrodynamics (MHD) and radioprotection and safety. 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. Since 2014, the European R&D activities in nuclear fusion have been coordinated by the European Consortium for the Development of Fusion Energy (EUROfusion) to achieve the breakthrough goal of a operative demonstrative fusion power plant (DEMO) after 2050. One of the most promising blanket concepts is the Water Cooled Lithium Lead (WCLL), whose research activities are coordinate by the Brasimone Research Center of Italian National Agency for New Technologies,Energy and Sustainable Economic Development (ENEA), while 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 solutions both as working fluid in blankets and as “self-healing protection” in advanced divertor and Plasma Facing Components (PFCs) concepts, where the most promising candidates are, respectively, the lithium-lead eutectic alloy (PbLi) and lithium or thin. Unfortunately, due to the fact that they are electrically conductive, their motion is influenced by the magnetic field used in the reactor to confine the nuclear fuel, generating a complex phenomenology that is studied by the Liquid Metal Magnetohydrodynamics (LM-MHD), including the electromagnetic drag, turbulence suppression, modified heat and mass transport and electromagnetic coupling phenomena, that which must be considered in the design of the affected components. 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-Rm, laminar, incompressible and isothermal MHD flow for ducts with perfectly insulated or perfectly conductive walls. The solver was built by implementing the MHD equations in the formulation of the electric potential and adopts the numerical scheme proposed by Ni et al. [1] for the calculation of the current density in the cell centre has been implemented in a conservative way. phiFoam 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, 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 abrupt expansion and the distribution in three channels. The control parameters are the flow rate repartition between the channels and the three-dimensional pressure drop (∆p3D) due to the axial 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 Part III, the geometry and functioning of the PbLi co-axial manifold of WCLL is showed in detail and a prototypical co-axial channel model is presented in Chapter 6. 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, while in Chapter 8 the electromagnetic coupling between the external and internal channel of the co-axial geometry is studied as the intensity varies of the magnetic field and the flow rate repartition between the channels. For the uncoupled case, if the walls are perfectly insulated (cw = 0), 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 the 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. Changing the geometry of the channel by varying α and β, the fundamental characteristics of the flow remain unchanged as Ha and cw are constant, but the variation of the gap between the external and internal channel determines small variations that intensify when approaching cases in which the gap becomes very small. The electromagnetic coupling phenomena change considerably the flow features. Different flow repartition scenarios between the external and internal channel are investigated with ANSYS CFX 18.2 up to Ha = 2000. The external channel is greatly affected by the electromagnetic coupling phenomenon, which drastically changes the velocity distribution compared to the uncoupled case, already for small values of the internal flow rate. In particular, there is the formation of intense reverse jet in correspondence with the side wall shared with the internal channel and a progressive flattening of the speed 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. By fixing the flow rate in the two channels, as the Hartmann number increases the typical characteristics of that particular scenario are maintained and all effects are progressively intensified in accordance with the increase in Ha. It is important to note that the counter flow rate under WCLL operating conditions is estimated to be around 28 %. This 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. 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 Lithium Lead (DCLL), is analysed: double external feeding pipes, double intermediate feeding pipes and single central feeding pipe. The objective of the analysis is to assess the flow rate distribution to investigate what configuration is most desirable to minimize flow imbalance in the manifold (for the WCLL) or 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 merging of the channels. The total pressure loss is also estimated and its functional dependence on the collector configuration is discussed. In Part IV, a thin-film single-phase MHD flow, representative of the armour in a film-type divertor of PFCs, has been investigated with the ANSYS CFX 18.2code. The numerical model is validated up to Ha = 1000 for the case of insulated walls and 0.044 ≤ α ≤ 0.2. A good agreement is found with the theoretical solution presented by Shishko et al. [4]. 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, where 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 presence of a conductive backing plate with a conductive lateral wall has a great influence on the flow characteristics, greatly enhancing the free surface velocity and pressure drop. 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 lateral 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 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 at different rates of motion, 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, 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.