Geoflow: First Results from Geophysical Motivated

Experiments inside the Fluid Science Laboratory of

Columbus

Lothar Jehring∗ and Christoph Egbers†

Brandenburg University of Technology, Cottbus, D-03046, Germany

Philippe Beltrame‡

University of Augsburg, Augsburg, D-86159, Germany

Pascal Chossat§

University of Nice, Nice, F-06108, France

Frederik Feudel¶

University of Potsdam, Potsdam, D-14469, Germany

Rainer Hollerbach‖

University of Leeds, Leeds, LS2 9JT, U.K.

Innocent Mutabazi∗∗

University of Le Havre, Le Havre, F-76058, France

Laurette S. Tuckerman††

Ecole Superieure de Physique et de Chimie Industrielles, Paris, F-75231, France

Objective of GeoFlow experiment is to study thermally-driven rotating fluids, in order toinvestigate the stability, pattern formation, and transition to turbulence of viscous incom-pressible fluids contained between concentric, co-axially rotating spheres. These physicalmechanisms are important for a large number of astrophysical and geophysical problemsshowing flows in spherical geometry driven by rotation and convection: for example, toexplain the mantle convection of the Earth, or the flow in a planet’s interior.

The European microgravity experiment GeoFlow, which is executed in the Fluid ScienceLaboratory (FSL) of Columbus module on the International Space Station (ISS), is anexperiment investigating pattern formation and stability of thermal convection in rotatingspherical shells under the influence of an artificial central symmetric buoyancy field andeliminated gravity.

In this paper we present numerical preliminary studies of this spherical Rayleigh-Bnardproblem under a central dielectrophoretic force in microgravity environment and first ex-perimental results from ISS. Numerical simulations are done for a range of parametervalues for Rayleigh and Taylor number. For the experiment flow visualization is realisedusing the Wollaston-shearing method.

∗Senior Scientist, Dept. Aerodynamics and Fluid Mechanics, Siemens-Halske-Ring 14, Member†Head, Dept. Aerodynamics and Fluid Mechanics, Siemens-Halske-Ring 14‡Senior Scientist, Theoretical Physics, Universitatsstrasse 1§Senior Scientist, Laboratoire Jean Alexandre Dieudonne, 28 avenue Valrose¶Lecturer, Nonlinear Dynamics Group, Am Neuen Palais 10‖Senior Scientist, Department of Applied Mathematics, Woodhouse Lane∗∗Head, Laboratoire Mecanique, 53 rue Prony B.P. 540††Senior Scientist, Dept. Hydrodynamics and Mechanics, 10 rue Vauquelin

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47th AIAA Aerospace Sciences Meeting Including The New Horizons Forum and Aerospace Exposition5 - 8 January 2009, Orlando, Florida

AIAA 2009-960

Copyright © 2009 by the American Institute of Aeronautics and Astronautics, Inc. All rights reserved.

Nomenclature

c0 Variation of refractive index with temperatured = ro − ri Gap widther, eeq, ez Unit vector in radial, meridional and axial directionfphase Phase functionge Dielectrophoretic force fieldn Refractive indexp Pressure fieldPr Prandtl numberr RadiusRa Central RayleighRacentral Central Rayleigh numberRa Factor in eqn. (9)T Temperature fieldTa Taylor numberU = (u, v, w) Velocity fieldVrms High voltage

Greekα Cubic expansion coefficientβ = (ro − ri)/ri Aspect ratioγ Dielectric variability∆T Temperature differenceε Separation angleεr Dielectric constantη = ri/ro Radius ratioϑ Azimuthal angleκ Thermal diffusivityλ Thermal conductivity or Laser wavelengthν Kinematic viscosityρ Densityφ Meridional angleΩ Rotation rate

Subscripti innero outer

I. Introduction

The microgravity experiment GeoFlow is an European project, integrated in the Fluid Science Laboratory(FSL) in Columbus module of International Space Station (ISS). This experiment targets on the investigationof stability and pattern formation of thermal convection in a rotating spherical gap with an artificial centraldielectrophoretic force field by applying an alternating high voltage field on the inner sphere1–3 .

Focusing on main acting forces for example in the inner Earth, that is temperature gradients and rotation,and neglecting magnetic effects in order to stress thermal and rotating aspects of the theoretical formulationand experimental setup, that corresponds to research on stability and pattern formation of thermal convectionin a rotating spherical gap. If such phenomena are studied experimentally in an Earth lab, gravity acts axialto a spherical model, and not central, like in the Earth’s core. Such a central force field can be setup usingthe dielectrophoretic effect by applying a high voltage alternating field on the inner sphere which is thanacting as a spherical capacitor. Resulting artificial central acceleration equals approximately 10−2m/s2,showing that acceleration due to gravity with g = 10m/s2 will always be dominant in an Earth laboratory.Needed microgravity conditions for research due to thermal experiments especially requiring long-term onesare available at the International Space Station (ISS).

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A model of a spherical gap flow experiment should help to understand such phenomena as the zonalbands of Jupiter, the origin of extremely high winds in the tropics and subtropics of Jupiter, Saturn andNeptune, the persistent differential rotation of the Sun, the complex patterns of convection in the slowly-rotating mantle of the Earth, and the rapidly rotating flows in the Earth’s outer liquid core. In figure 1 aschematic cross section of the Earth is depicted. The convective motions of the liquid iron alloy in the outercore cause the main geomagnetic field.

Figure 1. Schematic cross section of the Earth - Ther-mal convective phenomena occur in the outer liquidcore, structural Earth’s composition from Kious4

Because thermal convective flows in sphericalshells represent an important topic in fluid dynam-ics, astrophysics and geophysics (Busse;5,6 Busseand Riahi;7 Cardin and Olsen;8–10 Carrigan andBusse;11 Cordero and Busse;12 Harder and Chris-tensen;13 Liu et al.;14 Roberts;15 Zhang16) this kindof fluid flow has been considered in various researchprograms. The observed modes of instability arestrongly dependent on parameters like rotation rate,temperature gradient, gap width, material functionsand others. Critical Rayleigh numbers were calcu-lated by Joseph and Carmi17 via linear and energystability analysis in the non-rotating case for differ-ent central force fields. Roberts15 calculated the flowand critical Rayleigh numbers in the limit of veryrapid rotation, and found that the critical Rayleighnumbers depends on the Taylor number accordingto Rac ∼ Ta2/3. Busse5 has also considered thiscase and predicted that the flow should take the shape of ”columnar cells”. Hart et al.18 considered thisproblem, too, using a hemispherical shell model and neglecting the centrifugal force.

Figure 2. Allocation of the GeoFlow Topical Team,industry partners and space agencies

In Yavorskaya19 the fluid flow analogy of spheri-cal gap flow model in atmospheric motion and con-vection in core regions of gaseous planets was dis-cussed theoretically. Research on convective flowstability under µ-gravity conditions in a sphericalshell system was realised by Hart et al. who per-formed experiments on board of NASA Space Shut-tle in 198518 and in a reflight campaign in 1995.20

The experiment consisted of a rotating hemispher-ical shell system with the possibility to apply ra-dial as well as latitudinal temperature gradient inequator-to-pole direction. Gravity was simulatedby an electrical field. The observed flow patternswere visualised with Schlieren technique and com-pared with 3D non-linear simulations. The use ofan artificial central buoyancy force field for simulat-ing gravity in geophysical analogy with respect tothe liquid outer core of Earth is discussed by Fruh21

and by Beltrame,3 who showed that the essentialbehavior of the flow is captured even if the powerlaw of the simulated artificial gravity for the cen-tral force field is not conform with the accelerationcaused by gravity on Earth.

For the preparation of the execution of the ex-periment on ISS a large number of preliminary in-vestigations were carried out using the EngineeringModel (EM) from the industry partner and the Sci-ence Reference Model (SRM) at BTU Cottbus. Inaddition to the experimental tests, a variety of numerical simulations were performed (Futterer et al.22 and

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Hollerbach23). These numerical studies were used for the preparation of the experimental design and com-plementary parameter variations as well as analysis of both - stable and time-dependent - flows that wasfound to exist in the parameter range of the GeoFlow experiment.

As optical measurement method Wollaston-shearing interferometry is used to determine the temperaturefields and corresponding flow pattern.

Here we present numerical preliminary studies which focus on dynamics of non-rotational and rotationalregimes. For the non-rotational case an approach combining numerical simulations with a spectral time-stepping code and path-following techniques allows the computation of both stable and unstable solutionbranches of stationary states. The transition from the stationary to the time-dependent regime is described.Direct numerical simulation of rotational regimes show bifurcations from basic via periodic and quasi-periodicstate into chaos. In the low rotation regime drift of time-dependent solutions is prograde while in the higherrotation regime drift is retrograde with rotation of the sphere.

Finally, we compare numerical predictions of different thermal flow states with first experimental datafrom ISS experiment. By comparing numerical and experimental results, it should be possible to determinethe dynamics of the observed flow patterns.

The GeoFlow Topical Team consists of science teams from BTU Cottbus (Germany) (PI), Univerity ofPotsdam (Germany), University of Leeds (U.K.), University of LeHavre (France), CIRM Marseille (France)and ESPCI Paris (France). GeoFlow is supported, in technical point of view by EADS Astrium Space Trans-portation GmbH Friedrichshafen (Germany), MARS Center Naples (Italy) and E-USOC Madrid (Spain).Financial and organisational support is given by the European Space Agency ESA in Noordwijk (The Nether-lands) and German Aerospace Center DLR (Germany).

II. The Experiment

Since 2002 the overall preparatory research program comprised work packages for the development ofhardware and software as well as preliminary numerical and experimental investigations. Experiments wereperformed in the laboratory at BTU Cottbus using the Science Reference Model (SRM), see fig. 3 (a) andalso in the laboratories of industrial partners who built and verified the experiment hardware using theEngineering Model (EM).

(a) Science reference model (SRM) in the laboratory at BTUCottbus

(b) Schematic cross section of GeoFlow experiment cell

Figure 3. Geoflow experiment

Numerical investigations and bifurcation analysis were performed by European research groups fromUnited Kingdom, France and Germany all being members of the GeoFlow Topical Team. These studies focuson preparation of the experiment design and on the observable parameter space by flow states simulationand on linear stability analysis and bifurcation analysis (Futterer;24 Travnikov;25 Gellert26).

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A. Experimental Setup

One major part of the European Columbus Orbital Facility of the ISS is the Fluid Science Laboratory (FSL).The FSL supports µ-gravity research in the field of fluid physics by means of a specific triggering and theobservation of phenomena inside of transparent and at the surface of opaque media. It is characterised by ahigh level of modularity on all experiment and facility (sub-)system levels.

Figure 4. Fluid Science Laboratoryintegrated into COLUMBUS (ImageSource: NASA)

For the scientific fluid physics research, the FSL provides differentmeasurement methods. While the Wollaston-Shearing Interferome-try (WSI) is primarily used for the GeoFlow experiment, also themeasurement methods Schlieren and Shadowgraphy can be applied.The FSL consists of two main parts, the Central Element Module(CEM) and the Optical Diagnostics Module (ODM), cf. figure 4.The CEM includes a manually accessible operational area which isdesigned to integrate the modular experiments integrated in Exper-iment Containers (EC).

The GeoFlow experiment hardware has been designed on thebasis of the geometrical data of the EC which is strongly limited tothe volume of 270× 280× 400 mm3.

The experimental core consists of an inner sphere, which is madeup of tungsten-carbide and two outer shells, made of BK7-glass (cf.fig. 3 (b)).

In the research cavity the temperature gradient is realised byuniformly heating the inner sphere and cooling the outer glass shellusing temperature controlled fluid circuits filled both with same sil-icone oil. The experiment cell is mounted on a rotating tray whichallows for solid body rotation. The central force field is generatedby applying a high voltage of Vrms = 10 kV between inner andouter sphere to generate the artificial central symmetric force fieldanalogous to the Earth’s gravity field.

A low viscous silicone oil (Bayer Baysilioner M5) is used as theworking fluid. Table 1 shows the properties of the working fluidmeasured at T = 25C, the average experiment environment tem-perature. In particular, in the expected environment temperaturerange which is approx. 20− 35C differences in physical propertiesfrom the given values are negligibly small. However, temperaturesof the in- and outflow of the cooling and heating loops are measuredpermanently and deviation of the parameters will be taken into ac-count in the data analysis. While the Coulomb force does not affectfluid due to high frequency alternation the dielectrophoretic effectresults in central force field and acts as ponderomotive force due tothe inhomogeneous electrical field.

The system is rotating with a constant rotational frequency N = Ω/(2π). The corresponding Taylornumber Ta is given by

Ta =(

2Ωd2

ν

)2

. (1)

In natural convection phenomena Rayleigh number Ra characterises the temperature difference:

Ra =α∆Tgd3

νκ. (2)

Additionally, we introduce a central Rayleigh number Racentral that is proportional not only to thetemperature gradient ∆T in the spherical gap but also takes into account the acceleration due to the centralforce field gE , i.e. Racentral ∼ (∆T · ge):

Racentral =γ∆Tged

3

νκ. (3)

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Here γ is the dielectric variability and ge the electric acceleration due to electrohydrodynamic forcemeasured in Vrms that is the high voltage alternating electrical field giving a central force

ge =2ε0εr

ρ· r2oβ2r5

· V 2rms. (4)

Because ge is proportional to V 2rms · r−5 it follows that Racentral ∼ ∆T · V 2

rms · r−5. While accelerationdue to gravity is approx. 10m/s2 on Earth’s surface the largest value of acceleration due to high voltagefield is less than 10−1m · s−2 at r = ro at Vrms = 10kV .

The Prandtl number Pr incorporates the physical properties of the working fluid:

Pr =ν

κ. (5)

Investigating convection in laboratory on Earth superimposed with artificial central force field, bothRayleigh numbers have to be considered. For the µ-gravity environment at ISS only Racentral is essential.

Geometric parameters

Inner radius ri 13.5 mm

Outer radius ro 27.0 mm

Gap width d = ro − ri 13.5 mm

Radius ratio η = ri/ro 0.5

Aspect ratio β = (ro − ri)/ri 1.0

Variable experiment parameter

Rotation rate Ω 0− 2 Hz

High voltage Vrms 0− 10 kV

Temperature difference ∆T 0− 10 K

Physical properties of the working fluid (T = 25C)

Type Silicone oil

Density ρ 920 kg ·m−3

Kinematic viscosity ν 5 · 10−6 m2 · s−1

Thermal conductivity λ 0.116 W ·K−1 ·m−1

Thermal diffusivity κ 7.735 · 10−8 m2 · s−1

Cubic exp. coeff. α 108 · 10−5 K−1

Dielectric constant εr 2.7

Therm. coeff. of εr 1.07 · 10−3 K−1

Dimensionless parameters

Taylor number Ta Ta ≤ 1.3 · 107

Central Rayleigh number Racentral Racentral ≤ 1.4 · 105

Prandtl number Pr Pr = 64.64

Table 1. Experiment parameters

B. Measurement Details

For the first GeoFlow on-orbit operations investigation of the flow field is performed using Wollaston-ShearingInterferometry (WSI). Schlieren technique and Shadowgraphy are implemented within FSL as well. Due toexperiment constraints measurement techniques are used in reflective mode. The inner sphere of the setupis prepared to act as a mirror. Figure 5 (a) shows a sketch of the WSI setup at BTU laboratory used forpreparatory experimental works. Because of the acceleration due to gravity the operation mode is parallelto the axis of the gravitational force g on Earth.

The Adaption Optics (AO) includes an optical lens tool which converts the planar waves emitted bythe Laser (Q) into spherical waves and the reflected waves vice versa. This is needed due to the spherical

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(a) Sketch of the WSI set-up at BTU Laboratory. Laser (Q),Lens (L), Beam Separation (ST), 90 mirror (US), AdaptionOptics (AO), Science Reference Model (EM), Wollaston prism(W), Polarisator (PO), CCD Camera (K), gravity (g) vector

(b) Natural Convection (Vrms = 0kV ). WSI images takenat constant Rayleigh number Ra = 4.31 · 106 and increasingTaylor numbers (from left to right and top to bottom: Ta = 0,Ta = 8.6 · 102, Ta = 1.3 · 105, Ta = 5.4 · 105, Ta = 1.1 · 107,Ta = 1.3 · 107)

Figure 5. Wollaston shearing (WSI) setup and interferograms from ground experiments

geometry of the experiment shell system. The 90 mirror (US) deflects the beams to the AO which focusesthe waves to the centre of the experiment cell (EM). The beam separation cube (ST) deflects the reflectedbeams coming from the AO to the Wollaston Prism (W) and the Polarisator (PO).

WSI method detects refractive index gradients of the working fluid and is therefore sensitive to densitygradients caused by temperature differences in the GeoFlow experiment. Optical path length variations resultin interference phenomena that are directly photographed by a CCD camera (K). Figure 5 (b) shows WSIimages from ground test sequences taken at different parameter points. Note the complicated interferogramstructures at large Taylor numbers. Rotating axis is located near to the middle bottom of images.

C. Data Transfer and Local Storage

Figure 6. GeoFlow data flow

The GeoFlow experiment is a fully automatedstand-alone experiment and could run with-out any crew time on ISS despite of start-ing up, shutting down, locking and unlocking.The specified Experiment Procedures (EP) areprogrammed by User Support and OperationsCentre in Madrid, Spain (E-USOC). The hard-ware support for the GeoFlow experiment isgiven by EADS Astrium in Friedrichshafen,Germany. The support for the Fluid Sci-ence Laboratory comes from MARS Centre inNaples, Italy. The data flow of the GeoFlowexperiment data is shown in figure 6.

The output of all planned experiment runsmainly consists of GBytes of images from WSIand telemetry data, i.e. information aboutall relevant experimental parameters belong-ing to each image. The downlink of image datais controlled by MARS Centre in Naples dis-tributing the data to the other centres. Thedata storage at BTU is capable to handle4000GB including backup, analysis and interpretation of data.

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III. Numerical Investigations

The non-dimensionalised equations governing thermal convection in the rotating spherical shell underthe influence of a dielectrophoretic force field for velocity field U and temperature field T are given by

∇ ·U = 0, (6)

Pr−1 ·[∂U∂t

+ (U · ∇)U]

(7)

= − ∇p+∇2U

+ RaT ez

+ Racentral T er +√Ta ez ×U

+ Ra T r sin θ eeq

∂T

∂t+ (U · ∇)T = ∇2T. (8)

The corresponding system of coordinates is given in fig. 7, respectively.

Figure 7. System of coordi-nates

Refer also to Bergemann27 for a more detailed description of scaling of thesystem of equations and the evolution of parameters.

GeoFlow experiment is characterised by Prandtl number Pr, equation (5)giving the material properties of the fluid and the Rayleigh number Ra formeasuring the imposed thermal forcing. Natural convection in spherical gapswith d = ro − ri for axial force field in an Earth laboratory is scaled by Ra,equation (2).

For the dielectrophoretic force field set-up parameter Racentral describes thecentral buoyancy thermal convection, equation (3).

Regarding convection in Earth laboratory superimposed with high voltagefield both Rayleigh numbers have to be considered. However, for microgravityenvironment at ISS only Racentral is essential.

Effects due to rotation are accounted for by Coriolis and centrifugal forces,described by Taylor number Ta in equation (1) and an additional factor Ra

Ra =α∆T

4Pr Ta. (9)

The boundary conditions associated with (7) and (8) are no-slip for velocity field U and the values atthe inner and outer shell for temperature T , respectively.

This system of equations and boundary conditions is solved using the numerical code developed byHollerbach23 where U and T are expanded in terms of Chebyshev polynomials in the radial direction r,and Legendre functions in the meridional θ and azimuthal direction ϕ. For the numerical simulation theparameter Racentral has to be used without taking into account the geometry of the problem. Thus, Rayleighnumber is defined now as

Racentral = (2 εr εr γ)/(ρ ν κ) ·∆TV 2rms. (10)

After reaching the final experiment temperature difference ∆T and high voltage value Vrms only thesetwo parameters power the convection.

Further input values for the calculations come along with experimental constraints. Working fluid fillingthe spherical gap is a silicone oil of GE Bayer Silicones having a Prandtl number Pr = 64.64. With innerradius ri = 27 mm and outer radius ro = 54 mm the ratio of radii is η = 0.5. Experimental runs are to beperformed by applying a constant voltage Vrms = 10 kV and varying ∆T up to 10 K resulting in a Rayleighnumber up to Racentral ≤ 1.4 · 105. Maximum rotation rate up to 2 Hz corresponds to a Taylor numbervalue of Tamax = 1.3 · 107.

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Figure 8. Overview of convective states in spherical shells of η = 0.5 for Pr = 64.64 depending onRacentral and Ta: Besides time-dependency of numerical solution diagram shows linear stability ofmost unstable modes m.

A. Thermal Convection

Main parts of parameter variation include setup of temperature gradient between inner and outer sphere(corresponding to Rayleigh number variation) and rotation of spherical system (corresponding to Taylornumber variation). Figure 8 shows this parameter regime and calculated convective states. Experimentruns follow this diagram with non-rotating cases by increasing Rayleigh number stepwise and rotating cases,where a distinct temperature difference is set up (Ra fixed) and then rotation rates are superimposed byincreasing Ta, starting with low rotation to intermediate to high rotation regime. In figure 9 these differentregions are described.

1. Non-Rotating Case

Increasing Rayleigh number corresponds to intensifying thermal impulse to the system. Transition from basicstate to steady and then direct to irregular time-dependent convective states are found (Fig. 8). Patterns ofsteady state convection depend on initial state. Increasing Rayleigh number stepwise leads to axisymmetricstates (Fig. 9 (a)-(b)), setting thermal impulse immediately from zero reveals more complex symmetries(Fig. 9 (c)-(d)). With methods of path following analysis the stability of patterns are validated in differentregimes. For experimental work on ISS different patterns will be observable due to different runs by changingthe initial states. Refer to Futterer et al.22 and Bergemann27 for more details on stability discussions. Forirregular flow tetrahedral patterns dominate flow structures.

2. Rotating Case

From low to intermediate to high rotation the experiment traverses stability lines belonging to most of theunstable modes (Fig. 8). The higher the rotation the higher the azimuthal mode of convective flow (Fig. 10).Furthermore a change of drift velocity occurs that was already predicted by stability analysis of Travnikov.28

Direct numerical simulation results show prograde drift for low rotation regime and retrograde drift forintermediate rotation regime. For low rotation patterns are just rotated but not distorted. For intermediate

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(a) axisymmetry atRacentral = 5000

(b) inverse axisymmetry atRacentral = 8000

(c) cubic symmetry atRacentral = 5000

(d) symmetry with az-imuthal wave number 5 atRacentral = 10000

Figure 9. Patterns of convective steady states for non-rotating case Ta = 0. Images show accumulated radialtemperature at northern hemisphere22,27

(a) m = 5 at Ta = 1 · 105,Racentral = 8000

(b) m = 6 at Ta = 2 · 105,Racentral = 10000

(c) m = 7 at Ta = 6 · 105,Racentral = 2000

(d) m = 8 at Ta = 1.5 · 106,Racentral = 50000

Figure 10. Patterns of convective steady states for rotating case Ta 6= 0. Images show radial temperature fieldin meridional cut.

rotation patterns start to align as tangential cylinders. Centrifugal effects become more important.Calculations for high rotation are still under progress. Additional time-series analysis for complex time

dependent behaviour is necessary as well. Final aim is to track the transition from basic via steady toperiodic and chaotic states for fixed Ta and increasing Ra as marked in diagram 8.

IV. Data Analysis

Figure 11 shows the way of data processing, evaluation and interpretation. On the left side forwardmodelling with simulation of 3D temperature field which is used for construction of numerical interferogramsis demonstrated. This allows comparison to the experimental interferograms. The small circle left bottomgives the actual observation area accessible in the experiment.

On the right side inverse modelling with calculation of the integrated temperature field is shown whichis based on experimental data. An example to demonstrate inverse modelling and to illustrate forwardmodelling is given next. This allows for comparison with numerically calculated temperature fields. Theobserved flow patterns can be analysed in detail by using this data flow in a useful manner and allows thecharacterization of the flow pattern. Also, numerical simulations can be verified with experimental data.

A. Image Processing

The temperature field T (ϑ, φ)

T (ϑ, φ) =∆ϑ λ2 d ε

·(dn

dT

)−1 ∫ ϑ1

ϑ0

fphase dϑ+ T0 (11)

is calculated in azimuthal and meridional deflection. Integration of the temperature field follows therequirements given by Immohr.29 Variable λ here is the wave length of the laser and fphase is a phasefunction that contains the derivative

∂T (ϑ, φ)∂ϑ

= fphase∆ϑ λ

2 d ε c0. (12)

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Figure 11. Verification of experimental data by analysis and comparison with numerical data.

Here dn/dT is the modification of the refractive index n due to change of temperature T , temperature T0

is used as an initial value for calculation.In figure 12 (a) a work flow for the evaluation of numerical data is shown namely the forward modelling.

The setup is for a heated inner sphere and cooled outer sphere here. The corresponding integrated temper-ature field is shown. The third picture visualises the variation of the optical path and on upper right sidethe simulated interferogram caused by this temperature field is illustrated. The numerical interferogram isneeded for the evaluation of experimental data. Figure 12 (b) shows the measured interferogram with atemperature difference of ∆T = 4 K, Ω = 0 Hz and Vrms = 0 kV on the top left. In the image down leftthere are the relevant extracted fringes for the consecutive flow analysis. A phase shift from the extractedfringe pattern is calculated for the flow analysis and afterwards integrated to the temperature field.30 Theimage on the right shows the phase function of the fringes and on the top right is the temperature field ofthis phase function demonstrated.

V. First Results from Orbit Experiments

First WSI results from COLUMBUS show a very good optical quality. Expected temperature gradientscould be achieved as well as central force field strength and rotation rates, i.e. Rayleigh and Taylor numbers.With end of 2008 10 scientific runs out of 36 will be completed. Some examples are presented in fig. 13 andfig. 14 without quantitative interpretation that is now under work.

In the upper half of the images a black line shows the position of north pole and rotation axis approxi-mately. Figures give 6 images for every 60, i.e. one revolution of the sphere.

For a low-rotation case at low Ra number, fig. 13 (a) an axisymmetric flow can be observed. IncreasingRa number, i.e. temperature difference, see fig. 13 (b), a more complicated flow pattern appears. A specialsymmetry can not recognised just from the interferograms, however, axial symmetry seems to be brokendefinitely.

Increasing Ta number while keeping constant Ra number, gives rise to an even more complex flow pattern,with increased influence of rotation rather than convection due to temperature gradient. However, these firstimages still have to be analysed in more detail and are intended only as demonstration of feasibility andquality of the first images from GeoFlow.

For every rotation the triggering gives 6 images with a small field of view near to north pole, which have

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(a) Forward modelling - numerical data (b) Inverse modelling - experimental data

Figure 12. Work flow for interferogram evaluation of numerical and experimental data

(a) ∆T = 0.28K, Ω = 0.2Hz, Vrms = 10kV, Ra = 4.01 ·103, Ta = 1.34 · 105

(b) ∆T = 6.2K, Ω = 0.2Hz, Vrms = 10kV, Ra = 8.87 ·104, Ta = 1.34 · 105

Figure 13. WSI interferograms for low-rotation cases at positions 0, 60, 120, 180, 240, 300, 360

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Figure 14. WSI interferograms for high-rotation case, images taken every 60: ∆T = 6.2K, Ω = 1.6Hz, Vrms =10kV, Ra = 8.87 · 104, Ta = 8.59 · 106

to be combined into one single image. An example is given in fig. 15. Images usually are overlapping eachother, so a defined mask (ROI) is applied over each image sequence giving 6 sectors. These sectors will becombined into 1 image showing the whole northern hemisphere fig. 15 (b).

(a) Masking: from sphere to plane (b) Combined image in plane view

Figure 15. Generation of a single image for northern hemisphere from 6 angular postions of sphere

After applying a azimuthal map projection the spherical view can be reconstructed for visualisation too,fig. 16.

(a) Combined image (b) Map projection (c) View on spherical surface

Figure 16. Map projection of plane image to sphere

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VI. Outlook

For further experimental data analysis the challenge is to implement image processing procedure forcomplex flow structures, concerning the the formation and position of the fringes. Additionally, the designof pattern recognition is necessary for an effective comparison and sorting of many images and other exper-imental data under specific criteria.While the first GeoFlow campaign is running now until July 2009, a re-flight campaign is under discussionalready (GeoFlow II). For this re-flight a fluid with strongly temperature-dependent viscosity will be usedto form a model for Earth mantle convection. The methods of scientific analysis will be comparable to thatfor GeoFlow I, but the convective behaviour is expected to be quite different compared to GeoFlow I.

Acknowledgements

The GeoFlow project is funded by ESA (grant no. AO-99-049) and by the German Aerospace CenterDLR (grant no. 50 WM 0122 and 50 WM 0822). The authors would also like to thank ESA for funding theGeoFlow Topical Team (grant no. 18950/05/NL/VJ). The scientists also thank the industry involved forsupport, namely Astrium GmbH, Friedrichshafen, Germany and the User Support Center MARS, Naples,Italy and E-USOC, Madrid, Spain.

References

1Futterer, B., Gellert, M., von Larcher, T., and Egbers, C., “Thermal Convection in rotating spherical shells: an experi-mental and numerical approach within GeoFlow,” Acta Astronautica, pp. 300-307 , 2008.

2von Larcher, T., Futterer, B., Egbers, C., Hollerbach, R., Chossat, P., Beltrame, P., Tuckerman, L., and Feudel, F.,“GeoFlow: European Microgravity Experiments on Thermal Convection in Rotating Spherical Shells under influence of CentralForce Field,” Proceedings of the 3rd International Symposium on Physical Sciences in Space (3rd ISPS 2007), 2007.

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