Thermal blob convection in spherical shells

Futterer, Birgit; Brucks, Antje; Hollerbach, Rainer; Egbers, Christoph

doi:10.1016/j.ijheatmasstransfer.2006.12.036

Cited by 15 publications

(8 citation statements)

References 17 publications

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“…When validated with numerical and experimental results of the concentric configuration, results suggested a power law correlation of the average N u number on the spherical boundaries with the Ra number and the aspect ratio, see equation (11), close to what has been proposed in previous work (see [15,16,6]). When simulating eccentric configurations, result suggested a transition from a conductive regime to a steady convective regime similar to that found in the concentric case.…”

Section: Discussionsupporting

confidence: 84%

Natural convection in eccentric spherical annuli

Gallegos

Málaga

2017

European Journal of Mechanics - B/Fluids

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A fluid between two spheres, concentric or not, at different temperatures will flow in the presence of a constant gravitational force. Although there is no possible hydrostatic state, energy transport is dominated by diffusion if temperature difference between the spheres is small enough. In this conductive regime the average Nusselt number remains approximately constant for all Rayleigh numbers below some critical value. Above the critical Rayleigh number, plumes appear and thermal convection takes place. We study this phenomenon, in particular the case where the inner sphere is displaced from the centre, using a two-component thermal lattice Boltzmann method to characterize the convective instability, the evolution of the flow patterns and the dependence of the Nusselt number on the Rayleigh number beyond the transition.

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Section: Discussionsupporting

confidence: 84%

Natural convection in eccentric spherical annuli

Gallegos

Málaga

2017

European Journal of Mechanics - B/Fluids

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“…In Futterer et al (2012) we present test cases of the Earth laboratory set-up, where the fluid-filled spherical shell is regarded as a heated inner sphere and cooled outer sphere corresponding to the fluid physics of natural convection in spherical enclosures (Futterer et al 2007;Scurtu, Futterer & Egbers 2010).…”

Section: Parametermentioning

confidence: 99%

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

et al. 2013

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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.

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“…However, a discrepancy between experimentally and numerically detected stability threshholds is found for a Pr = 100 fluid, which is discussed in more detail in [21].…”

Section: Primary Flowmentioning

confidence: 96%

“…Experimental studies with silicon oils as working fluids, and thus higher Prandtl numbers than water or air [3,32,37], were first performed by Egbers [19] and Böhm et al [5,6] starting with small radius ratios. Using a large diameter experimental cell (r 2 = 120 mm, η = 0.5, Pr = 100) Brucks was able to observe a third instability, the simultaneous existence of long stretched cells within the thermal boundary layer at the outer sphere and the time-dependent plumes descending from the cold inner sphere in distinct pulses [9,10,21]. Douglass et al [18] performed the first numerical linear stability analysis for radius ratios in the range of 0.35 ≤ η ≤ 0.95 and fluids corresponding with Prandtl numbers from Pr = 0 (idealisation of instantaneous communication of thermal perturbations throughout the fluid) to Pr = 100 [18].…”

Section: Introductionmentioning

confidence: 99%

Experimental investigation of natural convective flows in slowly rotating wide spherical shells

Brucks¹

2007

Arch Appl Mech

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Experimental results are presented on natural convection in a spherical shell of inner and outer radii r 1 = 14 mm and r 2 = 35 mm, with the inner sphere cooled and the outer sphere heated. The fluids filling the shell are two different silicon oils having Prandtl numbers 39 and 233. Both spheres are fixed together and can be rotated. In the studied regime, both Coriolis and centrifugal forces become significant. For sufficiently small Rayleigh numbers the resulting flow pattern is axisymmetric and steady, consisting of a plume descending from the south pole of the inner sphere, and returning in the equatorial regions. For greater Rayleigh numbers the flow becomes non-axisymmetric, with azimuthal modes m = 2 to 4 arising. We map out the critical Rayleigh number for the onset of these different modes, and consider how they vary with increasingly rapid overall rotation. Detailed flow measurements are done by converting a standard 2D particle image velocimetry system into a scanning quasi-3D PIV system.

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Thermal blob convection in spherical shells

Cited by 15 publications

References 17 publications

Natural convection in eccentric spherical annuli

Natural convection in eccentric spherical annuli

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

Experimental investigation of natural convective flows in slowly rotating wide spherical shells

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