Recent studies on thermo-electro-hydrodynamic (TEHD) convection are reviewed with focus on investigations motivated by the analogy with natural convection. TEHD convection originates in the action of the dielectrophoretic force generated by an alternating electric voltage applied to a dielectric fluid with a temperature gradient. This electrohydrodynamic force is analogous to Archimedean thermal buoyancy and can be regarded as a thermal buoyancy force in electric effective gravity. The review is concerned with TEHD convection in plane, cylindrical, and spherical capacitors under microgravity conditions, where the electric gravity can induce convection without any complexities arising from geometry or the buoyancy force due to the Earth's gravity. We will highlight the convection in spherical geometry, comparing developed theories and numerical simulations with the GEOFLOW experiments performed on board the International Space Station (ISS).

We consider a fluid-filled cylindrical enclosure with an inner heated cylinder of radius ri maintained at temperature Ti and an outer cooled cylinder of radius ro maintained at temperature To. This vertical annulus is of height H with adiabatic top and bottom boundaries. The temperature difference ΔT=To-Ti induces natural convection in the gap width d=ro-ri at small values of ΔT. This base flow experiences transition to instabilities depending on the radius ratio η=ri/ro, aspect ratio Γ=H/(ro-ri), physical properties of the fluids (weighted with the Prandtl number) and on the driving force (weighted with the Rayleigh number). In this work, we study experimentally the heat transfer enhancement by the dielectrophoretic force induced by the application of an alternating (a.c.) electric field superposing natural convection in the vertical annulus. This procedure allows to introduce an electric Rayleigh number for the system. We will show a clear distortion of the base flow via flow visualization, and we quantify heat transfer by measurements of the Nusselt number for the inner cylinder. For low values of the electric Rayleigh number the superposed electric field damps the heat transfer, whereas for large values we observe a clear increase via an increase of the Nusselt number.

Thermal convection within fluids is ubiquitous in nature and engineering. It plays a major role in heat transfer and is a main driver for geophysical and atmospheric structures. This thermally driven convection is conjoined with Archimedean buoyancy force due to the variation of the density with the temperature T in the gravitational field https://www.w3.org/1998/Math/MathML"> g → https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9781003338277/96e4c35b-543f-4f9f-ac76-b28d51ed1948/content/eq23.tif" xmlns:xlink="https://www.w3.org/1999/xlink"/> . In most of the fluids, the density decreases with the temperature and its behavior can be modeled by a linear relation for a small temperature variation: ρ(T) = ρ 0[1 – α(T – Tref )], where ρ 0 = ρ (Tref ), Tref is the reference temperature, and a is the volume thermal expansion coefficient. The Archimedean buoyancy force reads (9.1) https://www.w3.org/1998/Math/MathML"> F → = − ρ 0 α ( T − T r e f ) g → https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9781003338277/96e4c35b-543f-4f9f-ac76-b28d51ed1948/content/eq24.tif" xmlns:xlink="https://www.w3.org/1999/xlink"/>

AbstractGeoFlow ist ein Schwerelosigkeitsexperiment zur bildhaften Untersuchung von Strömungen im flüssigen Erdkern oder im zähflüssigen Erdmantel. Es erfasst vereinfacht die wichtigsten Antriebsmechanismen im Erdinneren, wie Temperaturunterschiede, Rotation und Materialeigenschaften. Gleichzeitig lassen sich mit den Ergebnissen Computermodelle überprüfen.

AbstractWe introduce, in spherical geometry, experiments on electro-hydrodynamic driven Rayleigh–Bénard convection that have been performed for both temperature-independent (‘GeoFlow I’) and temperature-dependent fluid viscosity properties (‘GeoFlow II’) with a measured viscosity contrast up to 1.5. To set up a self-gravitating force field, we use a high-voltage potential between the inner and outer boundaries and a dielectric insulating liquid; the experiments were performed under microgravity conditions on the International Space Station. We further run numerical simulations in three-dimensional spherical geometry to reproduce the results obtained in the ‘GeoFlow’ experiments. We use Wollaston prism shearing interferometry for flow visualization – an optical method producing fringe pattern images. The flow patterns differ between our two experiments. In ‘GeoFlow I’, we see a sheet-like thermal flow. In this case convection patterns have been successfully reproduced by three-dimensional numerical simulations using two different and independently developed codes. In contrast, in ‘GeoFlow II’, we obtain plume-like structures. Interestingly, numerical simulations do not yield this type of solution for the low viscosity contrast realized in the experiment. However, using a viscosity contrast of two orders of magnitude or higher, we can reproduce the patterns obtained in the ‘GeoFlow II’ experiment, from which we conclude that nonlinear effects shift the effective viscosity ratio.

We introduce our spherical experiments on electro-hydrodynamical driven Rayleigh-Benard convection that have been performed either with temperature-independent properties of the fluid, called ‘GeoFlow I’, or with temperature-dependent properties, called ‘GeoFlow II’. To set up a self-gravitating force field with radial directed buoyancy, we use a high voltage potential between the inner and outer boundaries and a dielectric insulating liquid and perform the experiment in the microgravity conditions of the ISS [1, 2]. We further run numerical simulations in a 3D spherical geometry to reproduce the results obtained in the GeoFlow experiments.

enard convection in spherical geometry plays an important role in geophysical and astrophysical research. However, laboratory experiments with a central symmetry buoyancy field are hardly to realize, since the microgravity condition is not fulfilled on earth. The GeoFlowII experiment, which is mounted in the ISS, is set-up by means of a high voltage potential in microgravity conditions. We are using the working fluid 1-Nonanol to investigate the influence of temperature dependent viscosity on the fluid flow and the temperature field. During the experiment two routes are traced, i.e. the Rayleigh number is varied in two different regimes of higher and lower viscosity respectively. The achieved viscosity ratio remains below two. Nevertheless, single spots of plumelike upwelling are observed. The temporal characteristics is highly chaotic, already for lower Rayleigh number. This is in contrast to the isoviscous spherical convection patterns of GeoFlowI, which are large-scaled upwellings. Additionally to the experimentally performed parameters of the experiment, numerical simulations based on a pseudo spectral method have been performed. The full experimental parameter space is covered in terms of various Rayleigh numbers and viscosity ratios. The numerical output as artificial interferogram is compared with the experimental outcome. In both cases we reproduce a highly chaotic flow structure even for small viscosity ratios, which is not observed in the iso-viscous experiment.

Thermal convection in vertical concentric cylinders under the influence of different buoyancy force fields is the focus of the experimental project ’CiC’ (Convection in Cylinders). The objectives are to investigate thermal convective flow in natural gravity with axial buoyancy and in micro-gravity environment of a parabolic flight with radial buoyancy, and additionally also the superposition of both buoyancy force fields. The radial buoyancy is forced by the dielectrophoretic effect due to applying a high-voltage potential Vapp between the two cylinders. The experiment contains two separately fully automated experiment cells, which differ only in their radius ratio η = b/a. The convective flow is observed with tracer particles and laser light sheet illumination. For the case of natural convection, there exists a stable single convective cell over the whole Rayleigh number domain with Ra ∼ ∆T with increasing the temperature difference between the inner and outer cylindrical boundaries. For the case of a pure dielectrophoretic driven convection in micro-gravity environment, stratification effects are described with RaE ∼ Vapp with increasing the high voltage potential. The superposition of both buoyancy forces indicates the disturbance of the single convective cell and therewith the onset of instabilities at very low Ra for the smaller η. The presented results demonstrate that the dielectrophoretic effect can be used for flow control and enhancement of heat transfer applications in space as well as on Earth.

Within the project "Convection in a Cylinder" (CiC) heat transfer enhancement is studied for the case of two concentric, vertically aligned cylinders. The cylindrical gap is filled with a dielectric liquid, which viscosity is just few times higher than that of water. The inner cylinder is heated and the outer one is cooled. This setup in a gravitational buoyancy field leads to a fluid movement in a single convective cell with hot fluid rising at the inner boundary and cold fluid sinking at the outer boundary. The top and bottom part of the system shows horizontal movement, again in boundary layers. The strengthening of temperature gradient induces instabilities of that convective motion. If we vary the buoyancy force by means of electro-hydrodynamic effects, the patterns of convection differ from those instabilities rising only from variation of the temperature gradient.

The numerical solution of the Navier-Stokes equations in the spherical annulus is of fundamental interest for geophysical and astrophysical applications. The highly non-linear nature of the equations needs therefore special treatment. Consequently the full problem has to be calculated with numerical simulations. Due to the special geometry of the problem the class of spectral methods has become an appropriate tool to solve the equations in Boussinesq approximation. The presented method has been implemented into the numerical code developed by R. Hollerbach [1]. This code follows a spectral method, where the radial components are discretised on Chebyshev grid points. The toroidal-azimuthal components are further expanded as spherical harmonics. In a typical manner the boundaries are either stress-free or no-slip at the inner and outer sphere. The viscous components are solved with an operator splitting method. In the rst step the isoviscous, linear terms are calculated in spectral space implicitly, which guarantees high numerical stability. The temperature dependent non-linear variations are transformed in real space, followed by a real-space calculation of the tensor elements and transformed back into spectral space. Viscosity contrasts of up to T = 2 can be calculated with comparable iso-viscous numerical resolutions. The reference values are Pr=185 and Ra=20000, which correspond to the working uid 1-nonanol at 20 C and a temperature dierence

The spherical shell convection in the lower rotational regime is discussed with numerical simulation by the use of a pseudo-spectral code and experimental observation by the use of a microgravity experiment in self-gravitating force field. While a low Coriolis force produces traveling waves of cubic, five-fold and frozen tetrahedral symmetry with a prograde drift, in the transition zone to chaos an axisymmetric flow is visible. The chaotic fluid flow does neither show a specific drift nor a dominating pattern of convection. Numerical and experimental data are in a good agreement.

Symmetry-breaking bifurcations have been studied for convection in a nonrotating spherical shell whose outer radius is twice the inner radius, under the influence of an externally applied central force field with a radial dependence proportional to 1/r(5). This work is motivated by the GeoFlow experiment, which is performed under microgravity condition at the International Space Station where this particular central force can be generated. In order to predict the observable patterns, simulations together with path-following techniques and stability computations have been applied. Branches of axisymmetric, octahedral, and seven-cell solutions have been traced. The bifurcations producing them have been identified and their stability ranges determined. At higher Rayleigh numbers, time-periodic states with a complex spatiotemporal symmetry are found, which we call breathing patterns.

With the hydrodynamic experiment ‘GeoFlow’ (Geophysical Flow Simulation) instability and transition of convection between two spherical shells are traced. The flow is driven by a central-symmetry buoyancy force field in microgravity conditions. We performed experiments for a wide range of rotation regimes, within the limits between non- and rapid-rotation. Here we focus on the non-rotational convection in an isoviscous experimental fluid as in ‘GeoFlow I’ and the preparation of ‘GeoFlow II’, that uses a temperature-dependent viscous fluid. Theoretical predictions on thermal, dielectric and optical performance of the fluid suggest the use of an alkanole, i.e. 1-Nonanol as working fluid for ‘GeoFlow II’. Initial ground based experiments demonstrate the influence of the viscosity contrast on fluid flow patterns. Specific results from the ‘GeoFlow I’ experiment, i.e. steady-state convection above a threshold and transition to chaos, are used as a reference.