Sascha Heitkam

Elastic properties of solid material with various arrangements of spherical voids

Abstract In this work the linear elastic properties of materials containing spherical voids are calculated and compared using finite element simulations. The focus is on homogeneous solid materials with spherical, empty voids of equal size. The voids are arranged on crystalline lattices (SC, BCC, FCC and HCP structure) or randomly, and may overlap in order to produce connected voids. In that way, the entire range of void fraction between 0.00 and 0.95 is covered, including closed-cell and open-cell structures. For each arrangement of voids and for different void fractions the full stiffness tensor is computed. From this, the Youngs modulus and Poisson ratios are derived for different orientations. Special care is taken of assessing and reducing the numerical uncertainty of the method. In that way, a reliable quantitative comparison of different void structures is carried out. Among other things, this work shows that the Youngs modulus of FCC in the (1 1 1) plane differs from HCP in the (0 0 0 1) plane, even though these structures are very similar. For a given void fraction SC offers the highest and the lowest Youngs modulus depending on the direction. For BCC at a critical void fraction a switch of the elastic behaviour is found, as regards the direction in which the Youngs modulus is maximised. For certain crystalline void arrangements and certain directions Poisson ratios between 0 and 1 were found, including values that exceed the bounds for isotropic materials. For subsequent investigations the full stiffness tensor for a range of void arrangements and void fractions are provided in the supplemental material.

A simple collision model for small bubbles

In this work, a model for the interaction force between a small bubble and a wall or another bubble is presented. The formulation is especially designed for Lagrangian calculations of bubble or soft sphere trajectories, with or without resolution of the continuous fluid. The force only relies on position and velocity of the bubble. The model does not include any empirical parameter that would have to be calibrated. Therefore, this force model is easy to implement. The formulation of the force is explicit, which means low computational effort. The collision of a small bubble with an inclined top wall is investigated numerically and experimentally. The computational results achieved with the new collision model show good agreement with the experiment.

Using Lorentz forces to control the distribution of bubbles in a vertical tube filled with liquid metal

In this work, a method to increase the residence time of bubbles in tubes or pipes filled with liquid metal is investigated. Imposing a horizontal electric current and a perpendicular horizontal magnetic field generates an upward-directed Lorentz force. This force can counteract gravity and cause floating of bubbles. Even with homogeneous electric fields these float in the mean but fluctuate randomly within the swarm due to mutual interactions. In the present case the cylindrical shape of the container furthermore creates inhomogeneous electric currents and an inhomogeneous force distribution resulting in a macroscopic convection pattern stirring the bubbles and further homogenising the spatial distribution of the bubbles.