Modeling and simulation of thermo-electro hydrodynamics

The GeoFlow (Geophysical Flow) experiment on the International Space Station (ISS) and the AtmoFlow (Atmospherical Flow) experiment are designed to study convective processes under microgravity conditions in the spherical gap geometry. By applying a high voltage field between two concentric spherical shells and utilizing a dielectric working fluid it is possible to maintain an artificial radial force field that is comparable to a planetary gravitational field. This makes it possible to study convection such as known from the Earth's outer core, the Earth's mantle, or planetary atmospheres. The radial force field is based on the dielectrophoretic effect and is described by thermo-electro hydrodynamics (TEHD). This habilitation thesis presents a comprehensive view on modeling TEHD and the numerical simulation of the governing equations with a focus on GeoFlow and AtmoFlow. The GeoFlow experiment investigated thermal convection with and without dielectric (internal) heating under long-time micro-gravity conditions on the ISS. This unique experimental setup consisted of a bottom heated and top cooled spherical gap, filled with the silicon oil M5 or 1-Nonanol. Rotation, varying voltage, and temperature differences across the gap could be applied, to spread the experimental parameter space. The main focus of GeoFlow was the investigation of flow properties such as the convective onset, the transition from laminar to turbulent flows, and the influence of rotation on convection. Experimental outcomes were compared with theoretical and numerical results via advanced post-processing techniques. This includes pattern recognition algorithms and statistical evaluation of the numerical simulations. The TEHD model was validated on the onset of convection through linear stability analysis, on properties of columnar cells and global convective structures such as regular laminar flows. It is shown that TEHD based convection is comparable with Rayleigh-Benard convection and that is can be described by the quasi-normal approximation. For rotating cases and low super-criticalities the Proudman-Taylor theorem dominated the fluid flow which resulted in global columnar cells. In summary, the presented TEHD model is able to explain certain aspects of convective flows observed in GeoFlow. It is the first validation for such a model at all stages. The AtmoFlow experiment is based on GeoFlow but is designed to investigate global cells and planetary waves which are known from planetary atmospheres. Its unique feature are the atmospheric-like boundary conditions. Understanding the interaction between atmospheric circulation and a planet's climate, be it Earth, Mars, Jupiter, or a distant exoplanet, contributes to various fields of research such as astrophysics, geophysics, fluid physics, and climatology. AtmoFlow is currently under construction and is planned for operation on the ISS in 2024.