[en] The two questions of main interest for the design of a fusion blanket are whether the heat transfer to the coolant is high enough that the temperature of the plasma facing wall does not exceed a critical value and whether the corrosion rate is below a certain limit. Both processes are governed by convective - diffusive transport mechanisms. A numerical code for the 3D-solution of these equations in the laminar flow regime is discussed. It is assumed that tthe flow is fully developed when entering the heated section of a blanket element. The interaction of the strong magnetic field with the electrically conducting fluid is taken into account by an asymptotic analysis valid for fully developed MHD flows in ducts with arbitrary shape of cross section. Heat transfer conditions are discussed for circular pipes and square ducts. The influence of the main parameters on wall temperature is analyzed in detail and summarized by an empirical correlation. As an example for an extended use of the heat transfer code the full numerical solution of fully developed MHD flows in circular and rectangular ducts is presented. (orig.)

[en] A simple model for elastic properties in packed beds of granular material is described. It is assumed that the packing is initially dense but with small gaps between some potential contact points. These gaps close during elastic loading and increase progressively the stiffness of the packing. The hysteresis during uniaxial compression cycles can be partly related to wall friction. Results are applied for Li₂SiO₄ pebbles and compared to some experimental data. (orig.)

[en] An asymptotic analysis for magnetohydrodynamic flows between perfectly conducting concentric cylindrical shells has been performed. The flow in the model geometry exhibits all features which had been discovered in the past for the case of differentially rotating spherical shells considered in the context of geophysical analyses. For strong magnetic fields the flow region splits into distinct subregions and exhibits two different types of cores which are separated from each other by a tangent shear layer. The fluid in one core flows similar to a solid-body rotation and the outer core is entirely stagnant. For stronger magnetic fields the shear layer becomes thinner and since the flow rate carried by the layer asymptotes to a finite value the velocity in the layer increases as the layer thickness decreases. Moreover, the flux carried by the layer rotates in the opposite direction compared with the rotation of the body. It is shown that the rotating jet is driven by the electric potential difference between the edges of the inner and the outer core. The considered tangent layer is very similar to the internal layers observed in pressure driven 3D MHD flows through ducts with sharp expansions. Such flows received attention in nuclear fusion engineering as e.g. described in Buehler (2003), technical report, Forschungszentrum Karlsruhe, FZKA 6904. While in the case of 3D duct flows the core solutions have to be determined numerically, in the present example of a rotating flow, the core solutions are known analytically. For that reason the rotating layer served as a test example for the derivation of the more complex flows described in the latter reference. (orig.)

[en] The major part of the magnetohydrodynamic pressure drop in the European water cooled concept for a fusion blanket arises in the circular pipes which distribute the liquid metal breeder among the poloidal containers. These channels are surrounded by a very massive structure of electrically conducting ferromagnetic material. The present work highlights the key problems which concern pressure drop and flow distribution in circular pipes with thick conducting walls. The point which has not been investigated in the past is the influence of ferromagnetic wall material. The wall acts like a magnetic shielding for moderate external magnetic fields. The field inside the pipe is strongly reduced and as a result also the magnetohydrodynamic pressure drop. For conditions relevant for applications in fusion blankets the magnetic shielding is not as perfect since the wall material reaches magnetic saturation at the very strong external fields required for the magnetic confinement of the fusion plasma. Therefore the reduction of pressure drop is small for magnetic fields which are much larger than the saturation field of the wall material. The most interesting regime exists near the magnetic saturation where curvilinear field lines inside the pipe are observed. They result in velocity profiles which differ from the well known classical solutions. (orig.)

[en] The prediction of three-dimensional MHD flows for applications in fusion engineering, where magnetic fields confining the plasma are very high, is still a challenging task since, up to the present day, numerical simulations for such conditions are beyond the capabilities of modern CFD tools. Also experimentally, on laboratory scales, these values of parameters are hard to reach. Asymptotic analyses instead are able to cover such regimes in which inertia and viscous forces play only a minor role in comparison with the strong electromagnetic forces. However, especially for geometries with sudden changes of cross section, inertia effects may still be present in thin viscous parallel layers, where relatively high values of velocity can occur. For such cases only numerical simulations and/or experiments can give the proper insight into the physics involved. Those methods are therefore applied to determine the relevant scaling laws for strong fields, which allow a physically meaningful extrapolation of data to the desired parameters for engineering applications. As an example the 3D MHD flow through a sudden expansion of rectangular ducts is considered; results have been obtained by asymptotic theory for strong magnetic fields, by numerical simulations up to moderate magnetic fields and they are compared with experimental data. It is possible to derive the relevant scaling laws for pressure drop, as a function of the Hartmann number Ha and the interaction parameter N. Results obtained by asymptotic analysis and numerical simulations show quite good agreement with experiments for the investigated parameters. Moreover, the numerical simulations allow analyzing the interesting 3D transitions and changes in the flow topology, occurring in the parameter range between the hydrodynamic case with Ha = 0 and the strong field case where Ha >> 1, N >> 1. (orig.)

[en] In the EVOLVE concept for a fusion blanket a boiling scenario is proposed where a number of permanent vertical vapor channels are formed in a horizontal layer of liquid lithium. The present analysis focuses on the flow of the electrically conducting liquid phase in the presence of a strong uniform horizontal magnetic field. The cross section of vapor channels is circular if surface tension dominates magnetic forces. In the other case a stretching of the liquid-vapor interface along magnetic field lines is observed and contours become possible where a major part of the interface is straight and aligned with the field. For strong magnetic fields the liquid flow exhibits several distinct subregions. Most of the liquid domain is occupied by inviscid cores. These are separated from each other by parallel layers that spread along the field lines which are tangential to the vapor channel. In the core between two parallel layers the flow direction is preferentially oriented along magnetic field lines, while outside these layers the flow is perpendicular to the field. The magnetohydrodynamic pressure drop in the liquid phase is relatively small. (orig.)

[en] Inductionless, incompressible MHD flows in expansions of rectangular ducts are investigated by asymptotic techniques for strong, uniform, externally applied magnetic fields. The geometries considered are closely related to applications in nuclear fusion reactors, where liquid alloys are used as breeding materials. The liquid metal velocities are very small so that inertia is negligible in comparison with the electromagnetic forces. The major balance of forces establishes in the core between pressure and Lorentz forces while viscous forces are confined to very thin boundary layers along the duct walls. Near the expansion one can observe an intense exchange of flow between the upstream and downstream cores with the corresponding side layers. This effect becomes more pronounced with decreasing length of the expansion region. For the limiting case of infinitesimally expansion length, i.e. for a sudden expansion an internal layer develops along magnetic field lines. This expansion layer matches the solutions in both rectangular ducts. Depending on the electric conductivity of the duct walls this layer is able to carry a significant amount of the total flow. The three-dimensional flow near the expansion drives additional electric currents which are responsible for higher pressure drop compared with fully developed conditions. An an example, the detailed flow structure in the expansion layer is analyzed and discussed for an expansion ratio of 4:1. (orig.)

[en] Inductionless magnetohydrodynamic (MHD) flows at high Hartmann numbers are calculated by splitting the whole flow region into an inviscid core and into very thin boundary layers near channel walls. The momentum equations are linearized for high interaction parameters by neglecting inertial terms. These assumptions allow considerable simplifications of the governing equations in all subregions. In the core the general 3D equations are reduced to 2D equations by an analytical integration. The boundary conditions at channel walls are satisfied by the solution of boundary layer equations, leading to 2D equations for charge conservation in the layer. The interior of every arbitrary shaped channel is mapped by a coordinate transformation to a standard volume. The coupled 2D equations are solved numerically on the surface of this standard volume. (orig.)

[en] The magnetohydrodynamic flow in the improved Dual Coolant Blanket is analyzed with focus on velocity distribution and pressure drop for a fully developed flow in the long poloidal rectangular channels. The fluid in the channels is insulated from the electrically conducting walls by means of ceramic flow channel inserts for pressure drop reduction. It is found that the pressure drop for the poloidal flow is low even if the insulation provided by the insert is not perfect. The distribution of velocity in a laminar regime is not optimal for heat transfer if the electric conductivity of the insert is too high. Then most of the fluid is carried along the side walls in jets with high velocity. Such flows tend to develop instabilities associated with intense mixing. Three-dimensional effects near expansions and contractions cause a major fraction of the total pressure drop. Results for flows in these geometric elements have been obtained by using empirical correlations which had been derived for different geometries. More detailed analysis would require 3D inertial computations which are foreseen in future. For validation experiments are recommended. (orig.)

[en] If liquid-metall is used as coolant in fusion-applications, the magnetic field confining the plasma exerts a strong electrodynamic interaction on the motion of the electrically conducting fluid. In the first part of the present report the MHD-flow in ducts with varying cross-section is investigated numerically. In the second part the code is extended to the calculation of the temperature distribution in the fluid. This enables the calculation of heat-transport in arbitrary three-dimensional geometries for blanket-relevant MHD-flows. (orig.)