Publikationen

The flow transformation and the generation of vortex structures by a strong magnetic dipole field in a liquid metal duct flow is studied by means of three-dimensional direct numerical simulations. The dipole is considered as the paradigm for a magnetic obstacle which will deviate the streamlines due to Lorentz forces acting on the fluid elements. The duct is of square cross-section. The dipole is located above the top wall and is centred in spanwise direction. Our model uses the quasistatic approximation which is applicable in the limit of small magnetic Reynolds numbers. The analysis covers the stationary flow regime at small hydrodynamic Reynolds numbers Re as well as the transitional time-dependent regime at higher values which may generate a turbulent flow in the wake of the magnetic obstacle. We present a systematic study of these two basic flow regimes and their dependence on Re and on the Hartmann number Ha, a measure of the strength of the magnetic dipole field. Furthermore, three orientations of the dipole are compared: streamwise-, spanwise- and wall-normaloriented dipole axes. The most efficient generation of turbulence at a fixed distance above the duct follows for the spanwise orientation, which is caused by a certain configuration of Hartmann layers and reversed flow at the top plate. The enstrophy in the turbulent wake grows linearly with Ha which is connected with a dominance of the wall-normal derivative of the streamwise velocity.

Free convection occuring during the drying of plane layers of polymer solutions may be due to various mechanisms, based on buoyancy or Marangoni effect, of thermal or solutal origin. This theoretical and numerical work provides all the required tools to analyze thoroughly the problem. In this transient flow, different methods (frozen time, non-normal, nonlinear methods) are proposed to predict critical times for convection onset and threshold values for convection. Nonlinear and non-normal methods give similar results, within the uncertainty inherent to any transient problem. It is shown that, when linear stability analysis indicates the presence of several instability mechanisms, it is necessary to invoke nonlinear arguments to establish the leading mechanism. The proposed methodology is then applied to experimental results from the literature for two polymer solutions (Polyisobutylene/toluene and Polystyrene/toluene).

Turbulent mixing and entrainment at the boundary of a cloud is studied by means of direct numerical simulations that couple the Eulerian description of the turbulent velocity and water vapor fields with a Lagrangian ensemble of cloud water droplets that can grow and shrink by condensation and evaporation, respectively. The focus is on detailed analysis of the relaxation process of the droplet ensemble during the entrainment of subsaturated air, in particular the dependence on turbulence timescales, droplet number density, initial droplet radius and particle inertia. We find that the droplet evolution during the entrainment process is captured best by a phase relaxation time that is based on the droplet number density with respect to the entire simulation domain and the initial droplet radius. Even under conditions favoring homogeneous mixing, the probability density function of supersaturation at droplet locations exhibits initially strong negative skewness, consistent with droplets near the cloud boundary being suddenly mixed into clear air, but rapidly approaches a narrower, symmetric shape. The droplet size distribution, which is initialized as perfectly monodisperse, broadens and also becomes somewhat negatively skewed. Particle inertia and gravitational settling lead to a more rapid initial evaporation, but ultimately only to slight depletion of both tails of the droplet size distribution. The Reynolds number dependence of the mixing process remained weak over the parameter range studied, most probably due to the fact that the inhomogeneous mixing regime could not be fully accessed when phase relaxation times based on global number density are considered.

We study distortion of laminar liquid metal flow by a magnetic point dipole in a straight square duct. This basic configuration is of fundamental interest for Lorentz force velocimetry, where the Lorentz force opposing the relative motion of conducting medium and magnetic field is measured to determine the flow velocity. The total force is highly dependent on the velocity profile, which changes its shape due to the acting Lorentz force itself. We are interested in the deflection of the flow and its dependence on magnitude and distribution of the magnetic field. To this end, we perform direct numerical simulations with an accurate finite-difference scheme in the limit of small magnetic Reynolds numbers. The hydrodynamic Reynolds number is choosen to be high enough to allow the generation of vortices and turbulent structures.