GEOFLOW II - Simulation of Geophysical Fluid Flows under Microgravity
Fluid Physics: Fluid and interface physics
ISS MagISStra - long duration mission
- (2010) ISS Increment 25-26
- (2011) ISS Increment 27-28
- (2011) ISS Increment 29-30 (PromISSe)
- (2012) ISS Increment 31-32
- (2012) ISS Increment 33-34
G. Egbers (1), B. Futterer (1), L. Jehring (1), P. Beltrame (2), P. Chossat (3), F. Feudel (4), R. Hollerbach (5), I. Mutabazi (6), L. Tuckerman (7)
|(1)||Department of Aerodynamics and Fluid Mechanics (LAS)|
Faculty of Mechanical, Electronic, and Industrial Engineering
Brandenburg University of Technology Cottbus
|Tel: ||+49 (0) 355 69 4868|
|Fax: ||+49 (0) 355 69 4891|
|(2)||Max-Planck-Insitut für Physik Komplexer Systeme|
Nöthnitzer Straße 38
|(3)||CIRM - Centre International Rencontres Mathematiques|
|(4)||Nonlinear Dynamic Group|
Institut für Physik und Astronomie
|(4)||Nonlinear Dynamic Group|
Institut für Physik und Astronomie
|(5)||Department of Applied Mathematics|
University of Leeds
|(6)||University of Le Havre|
|(7)||ESPCI - Ecole Supérieure de Physique et de Chimie Industrielles|
|||J.T. Ratcliff, P.J. Tackley, G. Schubert, A. Zebib, (1997), "Transitions in thermal convection with strongly variable viscosity", Search ResultsPhysics of the Earth and Planetary Interiors, 102, pp. 201-212.|
|||R. Trompert, U. Hansen, (1998), "Mantle convection simulations with rheologies that generate plate-like behaviour", Nature, 395, pp. 686-689.|
|||C. Egbers, W. Beyer, A. Bonhage, R. Hollerbach, P. Beltrame, (2003), "The GEOFLOW-experiment on ISS (part I): Experimental preparation and design", Advances in Space Research, 32, 2, pp. 171-180.|
|||V. Travnikov, C. Egbers, R. Hollerbach, (2003), "The Geoflow Experiment on ISS (Part II): Numerical Simulation", Advances in Space Research, 32, 2, pp. 181-189.|
|||P. Beltrame, C. Egbers, R. Hollerbach, (2003), "The GEOFLOW-experiment on ISS (part III): Bifurcation analysis", Advances in Space Research, 32, 2, pp. 191-197.|
|||M. Gellert, P. Beltrame, C. Egbers, (2005), "The GeoFlow experiment - spherical Rayleigh-Bénard convection under the influence of an artificial central force field", Journal of Physics: Conference Series 14, pp. 157-161.|
|||P. Beltrame, V. Travnikov, M. Gellert, C. Egbers, (2006), "GEOFLOW: Simulation of convection in a spherical gap under central force field", Nonlinear Processes in Geophysics, 13, pp. 1-11.|
|||B. Futterer, A. Brucks, R. Hollerbach, C. Egbers, (2007), "Thermal blob convection in sperical shells", International Journal of Heat and Mass Transfer, pp. 4079-4088.|
|||M. Ogawa, (2008), "Mantle convection: A review", Fluid Dynamics Research, 40, 6, pp. 379 - 398.|
|||(2008), "CRC Handbook of Chemistry and Physics", D.R. Ride, B&T.|
|||B. Futterer, R. Hollerbach, C. Egbers, (2008), "GeoFlow: 3D numerical simulation of supercritical thermal convective states", Journal of Physics: Conference Series 137 (2008) 012026 (5 pp).|
|||K. Bergemann, F. Feudel, L.S. Tuckerman, "GeoFlow: On symmetry-breaking bifurcations of heated spherical shell convection", Journal of Physics: Conference Series 137 (2008 ) 012027, 137, 1, pp. 4.|
|||N. Scurtu, B. Futterer, C. Egbers, (2008), "Three-dimensional natural Convection in spherical annuli", Journal of Physics: Conference Series. 137 (2008) 012017, pp. 9.|
|||T. von Larcher, B. Futterer, C. Egbers, R. Hollerbach, P. Chossat, P. Beltrame, L. Tuckerman, F. Feudel, (2008), "GeoFlow - European Microgravity Experiments on Thermal Convection in Rotating Spherical Shells under influence of Central Force Field", Journal of The Japan Society of Microgravity Application, 25, 3, pp. 297-302.|
|||B. Futterer, M. Gellert, T. von Larcher, C. Egbers, (2008), "Thermal convection in rotating spherical shells: An experimental and numerical approach within GeoFlow", Acta Astronautica, 62, 4, pp. 300-307.|
|||T. von Larcher, B. Futterer, C. Egbers, (2008), "The GeoFlow-Experiment on International Space Station (ISS): Research on Thermal Convective Flows in a Spherical Gap under influence of a Central Force Field", Sitzungsberichte der Leibniz-Sozietät der Wissenschaften zu Berlin e.V. "50 Jahre Weltraumforschung", Band 96, Leibniz-Sozietät der Wissenschaften zu Berlin e.V..|
|||T. von Larcher, B. Futterer, C. Egbers, (2008), "GeoFlow: On the status of experimental preparation of spherical gap flow experiments with central force field on International Space Station (ISS)", Journal of Physics: Conference Series 137 (2008 ) 012025, pp. 6.|
|||B. Futterer, C. Egbers, S. Koch, N. Dahley, L. Jehring, (2010), "First identification of sub- and supercritical convection patterns from GeoFlow, the geophysical flow simulation experiment integrated in Fluid Science Laboratory", Acta Astronautica, 66, pp. 193-200.|
|||N. Scurtu, B. Futterer, C. Egbers, (2010), "Pulsating and traveling wave modes in natural convection in spherical shells", Physics of Fluids, 22, 114108.|
|||F. Feudel, K. Bergemann, L. Tuckerman, C. Egbers, B. Futterer, M. Gellert, R. Hollerbach, (2010), "Symmetry-breaking bifurcations of central forced and heated convection in a spherical fluid shell", Physical Review E, in press.|
|||B. Futterer, N. Dahley, S. Koch, N. Scurtu, C. Egbers, (2011), "From GeoFlow I to II - fluid physics experiments on-board ISS for modeling convection phenomena in Earth's outer core and mantle", Acta Astronautica, submitted.|
FSL (Fluid Science Laboratory)
The main objective of this research activity is the experimental observation, by means of optical techniques, of convective instabilities that are of interest for geophysical research.
Experiment specific goals and detailed objectives
Experiment parameters are:
In all the experiment runs described in the present document, solid body rotation with varying rotation rate, fixed high voltage of 6 kV (or higher if available) and varying temperature difference and cold side temperature will be applied. For all the objectives, the flow pattern shall be observed by Wollaston Shearing Interferometry (WSI) and by an optional technique.
Thermal convection between non-rotating spherical shells, under a central force field. This objective shall include hysteresis effects investigation (i. e. sequence of experiment points with decreasing temperature difference across the spheres).
Thermal convection between rotating spherical shells, regime of low rotation (0.008 to 0.16 Hz), under a central force field.
Thermal convection between rotating spherical shells, regime of medium rotation (0.2 to 1 Hz), under a central force field.
Thermal convection between rotating spherical shells, regime of high rotation (1.2 to 2 Hz) where high centrifugal effects are expected (high Froude numbers), under a central force field.
Besides WSI, an additional optical diagnostic for each experimental point for a better analysis of the observed fluid flow state and its dynamic behaviour is considered. [see: F6-PR-BTU-0010, Scientific Justification of using Shadowgraphy in GeoFlow experiments, Issue 1, 15/3/2007].
The main feature of GeoFlow II is its geometry. That is, at variance with experiments that are performed in planar, cartesian geometries, GeoFlow II aims at observing flows in spherical geometries that are subjected to a central force field.
Such a condition, obviously impossible to reach on ground, is achieved by simulating buoyancy driven convection through a central dielectrophoretic field in reduced gravity conditions, providing a benchmark for a rich variety of numerical problems which are still a challenge for scientific research.
The present project forms a follow up of the first GeoFlow I experiment. For a detailed description of the experiment and an overview of the preparatory activities, see here and references. [Ref. 1- Ref. 11]. The activity here described is to be carried out in the same configuration (geometry, range of accessible Rayleigh numbers, temperature difference) but with a sample that displays a pronounced temperature dependent viscosity. This topic is of high interest in mantle convection studies, as temperature dependent viscosity is believed to play a fundamental role in mantle convection [Ref. 12]. The extremely high temperature difference across the mantle generates a variation of viscosity up to a factor 105 that deeply influences the properties of the flow in the entire domain. In particular, it affects the properties of the upper boundary layer that, being very viscous, takes the form of a so-called stagnant lid, where convection is heavily depressed and conduction becomes an important heat transport mechanism. Viscosity contrast generated stagnant lids are an essential feature of mantle convection and are at the basis of the still not fully explained formation of plate tectonics [Ref. 13].
Temperature dependent viscosity convection has been subjected to numerous numerical studies [see Ref. 14 and references therein] mainly carried out in Cartesian box geometries, that elucidate the transition to different convective regimes as viscosity contrast is increased. A current limitation of these studies is the lack of experimental evidence and the few results obtained in spherical geometry. Purpose of GeoFlow II is to observe the basic properties of the flow in the small viscosity contrast regime, by achieving the maximal viscosity variation allowed with the hardware limitation of the GeoFlow insert of the Fluid Science Laboratory. Even if the flow parameters are far from representing the actual ones found inside the mantle (a condition that poses an insurmountable experimental challenge), they are to be considered as the very first verification of present spherical numerical models. This will contribute to the extension of state of the art simulations to more realistic threedimensional spherical geometry, a clear trend of present research activities in the study of Earth mantle evolution [Ref. 14].
Experiments on thermal convection with a simulated central force field (similar to the gravity field acting on planets) are needed to understand large scale geophysical motions. Such a central symmetric force field can be produced by applying a high voltage potential between an inner and an outer sphere using the effect of dielectrophoretic force field. The simulated central gravity acceleration is of the order
of 10-1 g0 [Ref. 1], where g0 is the terrestrial gravity acceleration. Such kinds of experiments are therefore impossible to be carried out on ground, and require a reduced gravity environment where the uniaxial acceleration is order of magnitudes smaller than the central symmetric one.
Previous flight experiments (precursors)
– Drop tower: Egbers, C., Liu, M., Rath, H.J.: Microgravity sci. technol. 4 1993.
– Parabolic flights: Sitte, B., et. al., ZARM, University of Bremen, DLR parabolic flight campaign, Dec. 2000, (investigation of dielectrophoretic effect in microgravity).
– Sounding rockets: TCM-Wolna flown in 1995.
– ISS: GeoFlow I, 2008.
GeoFlow II was launched on board the ATV-2 "Johannes Kepler" on 16 February 2011. After docking on 24 February 2011 Geoflow II was unloaded and installed in the Fluid Science Laboratory (FSL) rack inside Columbus laboratory on 22 March 2011. Until early May 2012, a series of experiment runs could be performed. Because of promissing results, the science team submitted a request to perform additional runs during autumn/winter 2012.
At variance with GeoFlow I, where the convective pattern in spherical geometry was observed for the first time on a standard, model fluid (silicone oil), the purpose of GeoFlow II is to capture some essential feature of mantle convection, where the properties of the convecting fluid (Nonanol) are determined, among other factors, by the extremely high temperature and pressure variations. Keeping the current hardware limitations, it is proposed to utilize a sample with a more pronounced temperature dependence of viscosity, to capture the essential spatiotemporal features that are believed to be present in the mantle, even though without reaching its extreme temperature, pressure and viscosity conditions.
The choice of a suitable sample has been based on the following questions:
1. Which fluid is able to simulate mantle convection behaviour?
Mantle convection itself can be seen as a relatively simple convective fluid flow regarding the typical low velocities. Therefore rotational effects coming from Coriolis and centrifugal forces can be neglected. The challenge is the material that flows, i.e. the fluid itself. ”Rheology of mantle material is not simple Newtonian, and mantle materials are a multi-component system...” (Ogawa, 2008). Coming from geophysical/geological theory those aspects of viscous materials of the mantle are numerical modelled by the viscosity which depends on stress and temperature. By realising a first (!) comparable experiment in spherical shells one has to find an experimental fluid, which viscosity varies with temperature very strongly, herewith dropping aspects of stress dependency in this approach.
From fluid dynamics research, alkane fluids CnH2n+2 (formerly known as paraffines) as well as alkanole fluids show the relevant behaviour [Ref. 1]. Being highly viscous and changing their viscosity with temperature it seems that they can be used for modelling mantle dynamics (Figure 1).
2. Are the presented fluids able to be used in experimental environment of GeoFlow I, regarding dielectric properties?
Further relevant properties for the GeoFlow environment has to be considered, such as the dielectric properties for setting up the high voltage potential in order to set-up the central symmetry force field. The possibilities of experimental fluids from alkanes C12H26 up to C15H32, and from alkanoles the so called 1-Octanol C8H180 as well as the 1-Nonanol C9H200, assuming technical set-up of GeoFlow I have been discussed (also rapid rotation up to 2Hz resulting in very high Taylor number, which is not necessary for modelling mantle dynamics).
As a result the alkanes offer the better dielectric performance than the alkanoles.
They itself show a more significant percentage increase of temperature dependency of viscosity in the relevant thermal working regime. Dielectric performance is correlated with optical assessment of the fluid (refractive index correlates with dielectric properties by equation n2= εµ where µ can be dropped due to non-magnetic behaviour of the fluid and experiment itself. GeoFlow II will focus on temperature dependency of viscosity, therefore the following discussions are only for alkanoles 1-Octanol and 1-Nonanol, which are preferred for this scientific reasons. The dielectric constant of 1-Nonanol at 293.2 K is εr= 8.83 [Ref. 8]
3. Are the presented and chosen alkanole fluids able to be used in experimental environment of GeoFlow I, regarding optical performance?
The index of refraction of 1-Nonanol has been measured as a function of temperature. The results can be found in <Table for Figure 6 and 7> and in <Figures 6 and 7>. The test shows that 1-Nonanol generates appreciable temperature driven optical path differences inside GeoFlow experimental apparatus, similar to the ones now observed with the M5 silicon oil fluid.
The overall convective behaviour is expected to be very different from the results achievable by GeoFlow I, where a fluid with a negligible temperature dependent viscosity is used. Nevertheless for a scientific impact, scientific analyses are comparable to those for GeoFlow I, i.e.:
The stability of the basic states and its transitions will be studied for both the non-rotating and rotating situations;
The characteristics of the convection flows and in particular their symmetries will be determined;
The critical Rayleigh number which denotes linear stability and marks the onset of thermal convection should be detected;
The stability diagram for the different states should be measured and the occurrence of multistability will be investigated;
The energy transport from the inner sphere to the outer sphere should be estimated;
The characteristic wave numbers should be determined;
Time dependent up to chaotic behaviour will be detected; drift velocities and non-linear dynamics such as mode interactions will be analysed.
As a result, a detailed description of the transition to turbulence and the transition scenarios to chaos should be obtained. Numerical simulations and comparisons of the experiment with theoretical predictions for the flow pattern bifurcating from trivial state will be conducted, as well as a comparison with theoretical work on the flow in the Earth’s interior.
|Figure 1: Temperature dependency for different experiment fluids possible filling the spherical shell system of GeoFlow environment in comparison to experiment fluid of GeoFlow I, which is the silicone oil M5.|
|Figure 2: Experiment concept drawing|
|Figure 3: Experiment timeline|
|Figure 4: GeoFlow hardware|
|Figure 5: GeoFlow schematic drawing of hardware|
|Table for Figure 6_7 - Results of optical test on 1-Nonanol.|
|Figure 6_7 --- Figure 6: Temperature variability of 1-Nonanol as measured at BTU. The green line is the best fit with dn/dT = 3.69 x 10(power minus 4) K(power minus 1). Figure 7: Temperature variability of M3 fluid as presented at ELGRA meeting in 2005.|
|Figure 8: Principle of GeoFlow II Visual Data Analysis.|
Stefano Mazzoni (e-mail: email@example.com)