Sheet-like and plume-like thermal flow in a spherical convection experiment performed under microgravity

Abstract

We introduce, in spherical geometry, experiments on electro-hydrodynamic driven Rayleigh-Bénard convection that have been performed for both temperatureindependent ('GeoFlow I') and temperature-dependent fluid viscosity properties ('GeoFlow II') with a measured viscosity contrast up to 1.5. To set up a selfgravitating 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.

Thermal convection in a cylindrical annulus under a combined effect of the radial and vertical gravity

“…∂θ ∂t + u· ∇θ = 1 Pr θ (5) ∇· (1 − γ e θ) ∇φ = 0, E = − ∇φ (6) where Pr = ν/κ is the Prandtl number, Gr = α T Gd 3 /(ν 2 ) is the Grashof number (G = g in the gravity phase and G = 1.8 g in the hypergravity phase), T = T 1 − T 2 , γ a = α T is the thermal expansion parameter, γ e = T is the thermoelectric…”

“…The stability of the base state is performed by adding an infinitesimal perturbation (u , v , w , π , θ , φ ) into the flow equations (3), (4), (5), (6) and neglecting second and higher order terms in perturbations. The invariance in the axial and azimuthal directions allow for the development of the perturbations into normal modes of the form (û, v, ŵ, π, θ , φ ) e st+inϕ+ikz , where s is the complex growth rate, k is the axial wavenumber and n is the azimuthal mode number.…”

“…In particular, it was that the dielectrophoretic force can be used to increase the heat transport in cylindrical systems [3,4]. The generation of convective motions by the dielectrophoretic force has been successfully tested in the GEOFLOW experiments that were performed in the Fluid Science Laboratory of the International Space Station where thermal convection patterns have been observed in a differentially rotating spherical shell submitted to a dielectrophoretic force [5,6]. Preliminary observations of the dielectrophoretic force effects in the cylindrical annulus were performed in parabolic flight experiments [7,8] where non-axisymmetric patterns were identified.…”

Linear stability of a circular Couette flow under a radial thermoelectric body force

“…Realization of laboratory experiments with an artificial radial gravity is a key to advance the understanding of these flows. Some attempts have been made with the thermoelectric artificial gravity in annular geometry [20,22,23] and in spherical geometry [24][25][26][27][28]. An experiment with the thermomagnetic artificial gravity has also been reported in annular geometry [29].…”

Turbulent Rayleigh–Bénard convection in spherical shells

“…g ∼ 1/r 5 ). More recently, a similar experiment named "GeoFlow" was run on the International Space Station, where much longer flight times are possible (Futterer et al 2010;Futterer et al 2013). This later experiment was designed to mimic the physical conditions in the Earth mantle.…”