experimental studies on the burning of coated and uncoated micro and nano-sized aluminium particles

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Aerospace Science and Technology 11 (2007) 33–38 www.elsevier.com/locate/aescte Experimental studies on the burning of coated and uncoated micro and nano-sized aluminium particles P. Escot Bocanegra, C. Chauveau, I. Gökalp Laboratoire de Combustion et Systèmes Réactifs, Centre National de la Recherche Scientifique, 1C, avenue de la Recherche Scientifique, 45071 Orléans cedex 2, France Received 8 February 2006; received in revised form 18 October 2006; accepted 20 October 2006 Available online 6 December 2006 Abstract Two different approaches are used in this work to reduce the burning times of aluminium particles with the ultimate goal to improve the performances of solid propellants. One method is to coat the micro-sized particles by nickel, and the second is to decrease the particle sizes to nano-metric scales. A thin coating of Ni on the surface of Al particles can prevent their agglomeration and at the same time facilitates their ignition, thus increasing the efficiency of aluminized propellants. In this work, ignition and burning of single Ni-coated Al particles are investigated using an electrodynamic levitation setup and laser heating of the particles. The levitation experiments are used to measure the particle ignition delay time and burning time at different Ni contents in the particles. Decreasing the size of Al particles increases their specific surface, and hence decreases the burning time of the same mass of particles. In this investigation, a cloud of Al nano-particles formed in a combustion tube is ignited by an electric spark. The cloud experiments are used to measure comparative flame front propagation velocities for different Al particle sizes with and without organic coating. The results and their analysis show that both methods reduce the Al burning time. Ni coating reduces significantly the ignition time of micro- sized Al particles and hence the total burning time compared to non-coated particles. Nano-sized particle clouds burn faster than micro-sized Al particle clouds. © 2006 Elsevier Masson SAS. All rights reserved. Résumé Deux approches sont étudiées pour diminuer le temps de combustion des particules d’aluminium dans le but d’améliorer les performances des propergols solides. Il s’agit d’une part d’enrober les particules de tailles micrométriques dans une fine couche de nickel, et d’autre part, d’utiliser des particules d’aluminium de taille nanométrique. Une mince couche de nickel couvrant les particules d’Al permet d’empêcher leur agglomération et facilite leur allumage. Dans ce travail, l’allumage et la combustion des particules isolées d’Al enrobées dans du Nickel sont étudiés à l’aide du lévitateur électrodynamique du LCSR équipé d’un dispositif d’allumage par laser. Ce dispositif permet de déterminer les temps d’allumage et de combustion des particules en fonction de la composition du milieu gazeux environnant, la pression et le contenu en Nickel de la particule. Les expériences sont conduites notamment dans de l’air et le CO 2 jusqu’à 40 bars et des pourcentages en Nickel de la particule de 0 à 15% en masse. Diminuer la taille des particules à des échelles nanométriques augmente leur surface spécifique et par conséquent diminue le temps de com- bustion d’une même masse d’Al. Dans cette étude, un nuage de nano particules d’Al est formé dans un tube de combustion et allumé par des électrodes. Ces expériences permettent de déterminer les vitesses comparatives de propagation du front de flamme en fonction de la taille des particules et de la nature de leur enrobage (alumine ou des matériaux organiques). Les résultats préliminaires et leurs analyses montrent que les deux méthodes permetent de réduire d’une façon significative les temps de combustion des particules de’aluminium. © 2006 Elsevier Masson SAS. All rights reserved. Keywords: Aluminized propellants; Aluminium particles; Combustion; Nano-particles; Particle coating * Corresponding author. Tel.: +33 238 25 54 63; fax: +33 238 25 78 75. E-mail address: [email protected] (I. Gökalp). 1270-9638/$ – see front matter © 2006 Elsevier Masson SAS. All rights reserved. doi:10.1016/j.ast.2006.10.005

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Aerospace Science and Technology 11 (2007) 33–38

www.elsevier.com/locate/aescte

Experimental studies on the burning of coated anduncoated micro and nano-sized aluminium particles

P. Escot Bocanegra, C. Chauveau, I. Gökalp ∗

Laboratoire de Combustion et Systèmes Réactifs, Centre National de la Recherche Scientifique, 1C, avenue de la Recherche Scientifique,45071 Orléans cedex 2, France

Received 8 February 2006; received in revised form 18 October 2006; accepted 20 October 2006

Available online 6 December 2006

Abstract

Two different approaches are used in this work to reduce the burning times of aluminium particles with the ultimate goal to improve theperformances of solid propellants. One method is to coat the micro-sized particles by nickel, and the second is to decrease the particle sizes tonano-metric scales.

A thin coating of Ni on the surface of Al particles can prevent their agglomeration and at the same time facilitates their ignition, thus increasingthe efficiency of aluminized propellants. In this work, ignition and burning of single Ni-coated Al particles are investigated using an electrodynamiclevitation setup and laser heating of the particles. The levitation experiments are used to measure the particle ignition delay time and burning timeat different Ni contents in the particles.

Decreasing the size of Al particles increases their specific surface, and hence decreases the burning time of the same mass of particles. In thisinvestigation, a cloud of Al nano-particles formed in a combustion tube is ignited by an electric spark. The cloud experiments are used to measurecomparative flame front propagation velocities for different Al particle sizes with and without organic coating.

The results and their analysis show that both methods reduce the Al burning time. Ni coating reduces significantly the ignition time of micro-sized Al particles and hence the total burning time compared to non-coated particles. Nano-sized particle clouds burn faster than micro-sized Alparticle clouds.© 2006 Elsevier Masson SAS. All rights reserved.

Résumé

Deux approches sont étudiées pour diminuer le temps de combustion des particules d’aluminium dans le but d’améliorer les performances despropergols solides. Il s’agit d’une part d’enrober les particules de tailles micrométriques dans une fine couche de nickel, et d’autre part, d’utiliserdes particules d’aluminium de taille nanométrique.

Une mince couche de nickel couvrant les particules d’Al permet d’empêcher leur agglomération et facilite leur allumage. Dans ce travail,l’allumage et la combustion des particules isolées d’Al enrobées dans du Nickel sont étudiés à l’aide du lévitateur électrodynamique du LCSRéquipé d’un dispositif d’allumage par laser. Ce dispositif permet de déterminer les temps d’allumage et de combustion des particules en fonctionde la composition du milieu gazeux environnant, la pression et le contenu en Nickel de la particule. Les expériences sont conduites notammentdans de l’air et le CO2 jusqu’à 40 bars et des pourcentages en Nickel de la particule de 0 à 15% en masse.

Diminuer la taille des particules à des échelles nanométriques augmente leur surface spécifique et par conséquent diminue le temps de com-bustion d’une même masse d’Al. Dans cette étude, un nuage de nano particules d’Al est formé dans un tube de combustion et allumé par desélectrodes. Ces expériences permettent de déterminer les vitesses comparatives de propagation du front de flamme en fonction de la taille desparticules et de la nature de leur enrobage (alumine ou des matériaux organiques).

Les résultats préliminaires et leurs analyses montrent que les deux méthodes permetent de réduire d’une façon significative les temps decombustion des particules de’aluminium.© 2006 Elsevier Masson SAS. All rights reserved.

Keywords: Aluminized propellants; Aluminium particles; Combustion; Nano-particles; Particle coating

* Corresponding author. Tel.: +33 238 25 54 63; fax: +33 238 25 78 75.E-mail address: [email protected] (I. Gökalp).

1270-9638/$ – see front matter © 2006 Elsevier Masson SAS. All rights reserved.doi:10.1016/j.ast.2006.10.005

34 P. Escot Bocanegra et al. / Aerospace Science and Technology 11 (2007) 33–38

1. Introduction

Previous studies have shown that the use of Ni-coated Alparticles may improve combustion performances of aluminizedpropellants. For example, coating Al particles with a thin (10–100 nm) film of Ni reduces particle agglomeration [1,2]. Thiseffect is explained by the fact that the melting point of Ni(1728 K) is much higher than that of Al (933 K). The solid Nilayer on the surface of Al droplets prevents their coalescenceand agglomeration on the surface of the burning propellant orin the gas phase. At the same time, there are some indicationsthat Ni-coated Al particles ignite easier than original Al par-ticles. In addition, studies on flame propagation in clouds ofNi-coated Al particles in air revealed an increase in the flamefront velocity by a factor of 4 as compared with uncoated Alparticle clouds [11]. The authors explained this effect by the re-duction of the ignition delay time of the particles due to thermalstress cracking and peeling of solid Ni shell followed by easyignition of the bare Al core. Note, however, that the exothermicchemical reactions between Al and Ni [10] may also promoteignition.

Combustion of single Ni-coated Al particles (36–63 µm,51 wt% Ni) in pure gases such as air, O2, CO2, and Ar wasstudied previously [9]. The particles were levitated in an elec-trodynamic chamber at room temperature and ignited by a CO2laser. A number of interesting results related to the influenceof Ni coating were obtained, such as two-stage burning in air.The ignition delay times were nearly identical in all oxidisingatmospheres.

The available literature also shows that Al nano-powdercan significantly improve the performances of some energeticmaterials, especially for propulsion applications. Solid propel-lants containing Alex nano-scale powders exhibit burning ratesmuch higher (in some cases as much as 5 to 20 times higher)than the propellant formulations containing regular Al pow-der [3]. Further, in a hybrid rocket, HTPB-based solid-fuelformulations containing Alex or other nano-powders demon-strated mass burning rates in a hybrid rocket up to 50% higherthan the baseline formulations with regular Al [7]. These su-perior performances of energetic compositions containing Alnano-particles compared to conventional micro-size particlesare related to the higher specific area and reactivity of nano-scale powders.

In the present work, combustion of levitated and laser-ignited Ni-coated Al particles is studied over a wide range ofNi mass fractions, from 0 to 14 wt% and in air and in CO2 up to0.6 MPa. Note that only particles with relatively small contentof Ni are of interest for propulsion applications. The emphasisis put in this work on the measurements of the ignition delaytime and of the combustion time for particles with different Nimass fractions and on comparison with the original (naturallycoated by alumina) Al particles.

The second part of the investigation is related to combustionstudies of Al nano-particles injected into a tube and ignited byan electric spark after the formation of a cloud. The nano-Alparticles can also be coated with different materials to pre-vent agglomeration. The cloud experiments are used to measure

flame front propagation velocities for different sizes and coat-ings of the Al particles.

2. Experimental techniques

Experiments on the combustion of single Ni-coated Al par-ticles in air and CO2, under room temperature and pressuresbetween 0.1 and 0.6 MPa, were conducted using the electrody-namic levitation facility of the LCSR-CNRS (Fig. 1). The ex-perimental procedure and main parts of the apparatus were de-scribed previously [4–6]. Briefly, the electrodynamic levitatorallows freely suspending single metal particles of initial diame-ters in the range of 15–150 µm. The levitator is placed inside ahermetic chamber equipped with a particle injection system, al-lowing experiments in different atmospheres and pressures. Thesingle levitating particle is ignited by using a 50 W CO2 laser(Synrad 48) with the beam split in two beams and focused ontoopposite sides of the particle. The focusing is accomplishedwith two ZnSe lenses. Micro-metric measurements show thatthe beam diameter in the centre of the levitator is ∼340 µm.Prior to ignition, a video camera and a long-distance micro-scope (Questar QM100) are used to adjust the position of thelevitated particle at the focal point of the laser. The laser is in-terrupted at particle ignition automatically using a threshold forthe light emission intensity. This allows insuring self sustainedparticle burning. A photomultiplier measures the light emissionintensity of the burning particle, variation of which allows de-termination of the ignition delay and burning times.

Fig. 2 shows the experimental set up used for studying thecombustion of nano-particle clouds in air under normal condi-tions of pressure and temperature. The combustion chamber isessentially a quartz tube (inner diameter 14 mm, height 170 mmgiving an inner volume of 26 cm3), the bottom end of which is

Fig. 1. Schematic diagram of the experimental setup for studies on combustionof levitated particles; the bottom image shows the design of the levitator.

P. Escot Bocanegra et al. / Aerospace Science and Technology 11 (2007) 33–38 35

Fig. 2. Experimental set up for studies on the burning of nano-particle clouds.

Table 1Ni mass fraction and coating thickness in the used Ni-coated Al particles

Ni, wt% 0.93 1.87 3.11 4.33 9.10 14.4

Thickness, nm 17 35 58 81 180 301Particle size, µm 32–40 32–40 32–40 32–40 32–40 32–40

closed by a porous metal plate, and the top end is closed by athin cellulose film. For the present reactor volume, the stoichio-metric conditions in air correspond to 13 mg of Al mass. Thepresent experiments were performed for rich conditions corre-sponding to a global Al concentration of 1150 gm−3.

The powder sample is placed in the bottom of the tube. In-jection of particles and formation of the cloud inside the tubeis achieved using an electrical valve which creates a pulsed airflow to carry and disperse the particles in the tube. The injectionpressure and duration are adjusted to achieve optimum distrib-ution of the powder inside the tube. After suspension, the cloudis stationary due to low sedimentation velocities of Al nano-particles, in the range of 10−5–10−3 cm/s. The particle cloudis ignited by a spark placed on the axis at 60 mm above the bot-tom section of the tube. In these preliminary experiments, thisignition section was selected as providing the optimum ignitionprobability for all the combinations between the injected pow-der quantity, the injection time and pressure.

A high-speed video camera (Phantom V5.0 with 1000 fps atmaximum resolution 1024 × 1024 pixels2, or higher frequencyby reducing the resolution) is used for flame front observationsand propagation velocity measurements. The propagation ve-locity of the burning cloud is determined for different Al nano-powder samples by image analysis.

For the levitation experiments, the Al powder 32–40 µm insize, from The Metal Powder Company Ltd. (Madurai, India)was coated by Ni at Technion – Israel Institute of Technol-ogy [8]. Six powder lots with different Ni loadings, i.e. withdifferent thicknesses of Ni coating, were produced. Table 1summarises the data on the mass fraction of Ni in the pow-der lots determined with atomic absorption spectroscopy andon the coating thickness calculated for the mean diameter withthe assumption that the particles are ideal spheres with uniformNi coating. In addition, the coating thickness for the particleswith 4.33 wt% Ni was measured using Auger electron spec-troscopy (AES) in Technion. The value of 56 nm obtained withthe standard assumption that the Ni layer depth corresponds tohalf of the maximum Ni concentration, is in reasonable agree-

(a)

(b)

Fig. 3. Light emission during ignition and combustion in CO2 of levitated par-ticles. The dashed line shows the laser monitoring sequence (0 = off, 1 = on).(a) Al particles; (b) Al/Ni (14.4 wt% Ni) particles.

ment with the estimates. Further, AES analysis of the initial Alparticles clearly shows that the thickness of oxide film on theirsurface is about 10 nm.

For cloud burning experiments, three different nano-powdersof mean particle size 150 nm were used: Alex type powdersproduced at Tomsk State University by A. Vorozhtsov (TSU,Tomsk, Russia); Al nano-powders produced at the Institute ofHigh Current Electronics by V. Sedoy (IHCE, Siberian Branchof the Russian Academy of Sciences, Tomsk, Russia); Al nano-powders produced by the Gen-Miller method and coated by2-trimethylsilyl at the Institute for Energy Problems of Chem-ical Physics by M. Larichev (INEPCP, Russian Academy ofSciences, Moscow, Russia) and a micro-scale Al powder (6 µm)provided by SNPE Matériaux Énergétiques.

3. Experimental results

Figs. 3 show typical time variations of the light emission in-tensity measured during ignition and combustion of Al (Fig. 3a)and Al/Ni (Fig. 3b) particles in CO2 and at 0.4 MPa. The laseris interrupted automatically when the light emission intensityfrom the particle burning reaches a threshold, which is fixed thesame for all experiments. The time from starting the laser to itsinterruption is defined as the ignition delay time. The time fromthe interruption of the laser to its automatic relight at the end ofthe autonomous burning process is defined as the burning time.The total combustion time is the sum of the ignition delay timeand the burning time.

36 P. Escot Bocanegra et al. / Aerospace Science and Technology 11 (2007) 33–38

Fig. 4. Ignition delay time, combustion time and total combustion time ofNi-coated Al particles in air as a function of Ni mass fraction.

(a) (b)

Fig. 5. SEM visualisations of the investigated nickel coated Al particles.(a) 2 wt% Ni coating; (b) 10 wt% Ni coating.

Fig. 4 shows the measured ignition delay time, the burn-ing time and the total combustion time of Al particles withdifferent contents of Ni in air at atmospheric pressure. Eachdata point was obtained by statistical analysis of 20–40 exper-iments. It is observed that the ignition delay time significantlydecreases with increasing the Ni mass fraction from 0 to 3%and changes only slightly with further increasing the Ni content.The data for low coatings, particles with 0.93 and 1.87 wt% Ni,are characterised by a large scattering of their ignition delay.This implies that these powders contain particles with partiallycoated surfaces which is clearly shown on Fig. 5 where SEMvisualisations of nickel coated particles are displayed. Becauseof the difficulty to reach a high coating quality for low contentsof the coating material, the particle surface is not totally coatedand parts of the surface are covered by alumina. With increas-ing Ni mass fraction, coating of the Al particle becomes moreefficient, as observed both by the decrease of the ignition timeand less scattered experimental values. However, the data ob-tained allow clear identification of two characteristic values ofthe ignition delay time: one for the original Al particles, andthe second, much shorter, for Al particles with Ni coating at3–14 wt% Ni. The data for the burning time show that it in-creases with increasing the Ni mass fraction from 0 to 5%.After 5%, the combustion time decreases up to about the samevalue of 0% wt Ni.

Fig. 6 shows two successive images of Al micro-sized parti-cles cloud flame propagation obtained by the high speed videocamera and the same images after image analysis. The timevariation between the two images is 322 µs. The variation be-tween the two flame front positions divided by the time be-tween two images gives the spatial flame propagation velocity.

(a) (b)

Fig. 6. Al particles (6 µm) cloud burning images. (a) Two successive images ofthe propagating flame. (b) The same images after numerical analysis. Note thatthe space scales are different for the two axes.

The flame front propagation velocity is calculated using simi-lar successive images corrected by the thermal expansion factorbetween hot and cold gases. The calculated adiabatic flame tem-perature for stoichiometric gaseous Al-air mixture at 300 K isfound equal to 3600 K and the thermal expansion ratio to 9.48.

Figs. 7 show the flame front velocities for different initialconditions (Figs. 7a, 7b) and for different samples (Figs. 7c,7d); they are discussed below.

4. Discussion

Fig. 4 represents the ignition delay time, combustion timeand total combustion time of Ni-coated Al particles in air as afunction of Ni mass fraction. The ignition delay time was stud-ied before [8] and it was shown that the ignition delay time ofsingle Ni-coated Al particles in air is significantly shorter thanfor original Al particles, obviously due to the lower ignitiontemperature. Fig. 4 shows not only the ignition delay time butalso the combustion time in air of single Ni-coated Al particlesand the total combustion time. The total combustion time is thesum of the ignition delay time and the combustion time. Thistime is constant for the four first coating values and then de-creases for the highest coating value; the total combustion timeis divided by two for Ni mass fraction of 15% in comparisonwith the classical particles without coating. This behaviour canbe explained referring to the combustion time of the particles,which also first increases and then decreases. Detailed micro-scopic examinations of the sample particles have shown thatthe coating is not always homogeneous on the surface of theparticle. For low coating values, the Ni coating is in the formof small grains all around the particle which is not fully cov-ered (Fig. 5a). For higher coating values, a homogeneous filmcoating is achieved (Fig. 5b). Two conclusions can be there-fore drawn. First, as the coating is not homogeneous for lowcoating values, the observed decrease of the ignition time canbe readily attributed to inter-metallic reactions. Second, as thecombustion time only decreases for a homogeneous coating, itcan be assumed that the cracking of the Ni shell after the fullliquefaction of the encapsulated Al gives rise to a more ener-getic burning after ignition.

Figs. 7 present the cloud propagation velocities for the nano-aluminium particles. In the present preliminary study, the com-bustion front propagates both downwards and upwards alongthe tube axis. The downwards propagation ends quickly be-

P. Escot Bocanegra et al. / Aerospace Science and Technology 11 (2007) 33–38 37

(a) (b)

(c) (d)

Fig. 7. (a) Upward flame propagation velocities of nano-aluminium particles cloud. Influence of the particle injection duration. (b) Upward flame propagationvelocities of nano-aluminium particles cloud. Influence of the particle injection pressure. (c) Upward flame propagation velocities of nano-aluminium particlescloud. Comparison between nano-metric and micro-metric particles with the same injection parameters. (d) Upward flame propagation velocity of nano-aluminiumparticles cloud. Comparison between coated and uncoated nano-metric particles.

cause of the limited volume below the ignition source. Theupwards propagation is aided by the expansion of the hot prod-ucts resulting from downwards propagation. These high tem-perature gases heat the unburned particles in the upper part ofthe tube at a quicker rate. Consequently, the upward propaga-tion velocities are much higher in this configuration comparedto additional experiments conducted with the same apparatusbut when the cloud is ignited in the upper part of the tube andthe flame propagates downwards. In this last configuration, theparticle heating and ignition occur at a weaker rate than pre-viously. These additional results will be published separately.In the present experiments, the higher cloud flame propagationvelocities are representative of particle cloud burning wherethe particles are injected in a hot gaseous environment. There-fore, it is clear that the present measurements do not representthe fundamental cloud flame propagation velocities. It is note-worthy however that the ranking of burning velocities in thepresent experiments with respect to particle sizes (micro ornano) or particle nature (coated or uncoated) is similar to theone obtained with experiments when the cloud is ignited inthe upper part of the tube and when the cloud flame propaga-tion occurs downwards that is towards non-preheated two-phaseflow.

In Figs. 7, only the propagation velocities for upwards prop-agating flames are shown. The global shape of the curves is thesame for all conditions as they all show first an increase of thepropagation velocity with distance from the ignition locationand then a decrease. Several factors can be invoked to explainthis observation. First, the cloud can have close to the ignitionsection (located at the lower one-third of the tube) a residualvelocity due to the particles injection pulse. Second, this behav-

iour can be due to a non-homogeneous particle concentration inthe tube. The particle concentration can be too strong or tooweak at the beginning and at the end of the tube, but can be inoptimum (stoechiometric) proportions in the middle portion ofthe tube. A third explanation possibility can be related to pres-sure oscillations in the tube due to spark ignition.

Figs. 7a and 7b present the effects of the modification ofthe cloud formation parameters such as the injection pressureand injection duration. The curves demonstrate that the flamepropagation velocity increases with the injection pressure anddecreases with injection duration. A plausible explanation ofthis behaviour is related to particle agglomeration. Indeed, forlow injection pressures and long injection times, agglomera-tion of particles is favoured by increased contact probabilitybetween each other. For agglomerated particles (or for largeragglomerates), the melting and vaporisation times are longerand the consequence is lower flame propagation velocities.

Figs. 7c and 7d illustrate the comparison of cloud propaga-tion velocities for different particles but with the same cloudformation parameters. The particle size affects strongly the par-ticle cloud flame propagation velocity. As shown on Fig. 7c,the propagation velocity of the cloud of nano-particles is aboutthree times higher than that of the cloud of micro-particles. Theexplanation resides in the larger specific surface area of nano-particles and their shorter ignition and burning times.

On Fig. 7d, the two samples have the same size distributionbut one of them is composed of particles of nano-aluminiumcoated by 2-trimethylsilyl and the other is composed of nano-particles of Al naturally coated by alumina. The artificial coat-ing prevents the agglomeration of the nano-particles in thecloud, so the particles burn easier and quicker, giving propaga-

38 P. Escot Bocanegra et al. / Aerospace Science and Technology 11 (2007) 33–38

tion velocities about seven times higher compared to naturallycoated particles.

5. Conclusions

This work demonstrates the feasibility of two different meth-ods of reducing the time of combustion of Al particles. Onemethod is to coat by Ni the Al particles and the second is to re-duce their size. In the first method, the particle ignition times arestrongly reduced due to energetic inter-metallic reactions be-tween the liquid Al core and the solid shell of Ni. Reducing thesize of particles from micro-scale to nano-scales also reducesthe ignition and burning times significantly and increases theparticle cloud flame propagation velocity. By combining bothsize reduction and coating, an even larger cloud flame propaga-tion velocity is obtained. In the next phases of this work, moreexperimental data will be obtained under better controlled con-ditions to validate the preliminary observations and explanatoryhypotheses outlined in this paper. For the nickel-coated mi-cron size aluminium particle experiments, high pressure effectswill be systematically investigated. For nano-aluminium cloudburning experiments, downward propagating flames will be in-vestigated in detail in order to obtain the fundamental cloudflame propagation velocities to be compared to numerical mod-elling results that are also progressing in our group.

Acknowledgements

This research is supported by CNES, ESA, SME and theConseil Régional Centre. Also, the joint support by INTAS and

ESA (project 99-0138) is gratefully acknowledged. This pa-per has benefited from continuous discussions with Dr. DmitryDavidenko, research engineer at the LCSR-CNRS.

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