N Dubary

C Bouvet

S Rivallant

L Ratsifandrihana

Damage tolerance of an impacted composite laminate

Keywords:

Composites are known to be vulnerable to out-of-plane loading such as impact. Investigating the residual properties of the laminate as a function of damage detection is the main purpose of impact damage tolerance design in aeronautics. As a good alternative to experimental campaigns, numerical approaches would lead to saving of time. The model developed in Institut Clément Ader over the last years enables representation of behavior of composite laminates subjected to low velocity/low energy impactincluding permanent indentation and Compression After Impact. Damage such as permanent indentation, fiber failures, matrix cracks and delamination are taken into consideration at each step thanks to a discrete ply modelling. The work presented here deals with the use of this model to make a composite laminate design optimization according to impact damage tolerance design. A method to improve optimization by reducing computation time is also proposed, based on a "best candidates" selection.

Introduction

Because of their high strength-to-weight ratio along with the will of using lighter structures, composites attract an increasing interest in many fields. However, their vulnerability to out-of-plane loading such as impacts leads to an over-dimensioning. Low velocity impacts can occur during manufacturing or operation on composite structures and can result in a significant reduction of the residual properties without visibly marking the surface. This external damage corresponding to the dent left by the impact event is called permanent indentation (PI). In aeronautics, requirements and design are based on the visibility of the damage (Fig. 1): under a certain level of detectability the structure should withstand ultimate loads; beyond this level the impacted structure should withstand limit loads without sudden failure until the detection of the damage during inspection. This level of detection is called "Barely Visible Impact Damage", or BVID [START_REF] Tropis | Certification of the composite outer wing of the ATR72[END_REF][START_REF] Huang | Analytical modeling of impact resistance and damage tolerance of laminated composite plates[END_REF][START_REF] Combes | Design for damage tolerance[END_REF], and is linked to the geometry, to the properties of the structure and to the impact energy. So even damaged and without detectability, the design should ensure that the structure bears in-service loads: this is the principle of damage tolerance. As a matter of fact, impact damage tolerance design of composite relies on two important parameters: residual strength and detectability of the impact given by the permanent indentation.

About modelling composites

From understanding to predictive work, many studies have been run on damage induced by Low-Velocity Impact (LVI) since 90's [START_REF] Huang | Analytical modeling of impact resistance and damage tolerance of laminated composite plates[END_REF][START_REF] Combes | Design for damage tolerance[END_REF][START_REF] Abrate | Impact on Composites Structures[END_REF][START_REF] Eve | Etude du comportement des structures composites endommagées par impact basse vitesse[END_REF][START_REF] Richardson | Review of low-velocity impact properties of composite materials[END_REF][START_REF] Cantwell | The impact resistance of composite materialsa review[END_REF][START_REF] Feraboli | Enhanced evaluation of the low-velocity impact response of composite plates[END_REF][START_REF] Pilchak | Low velocity impact response of small-angle laminated composites[END_REF]. Analytical, semi-analytical models and formulations are the first approaches for predicting induced damage during quasi-static response or LVI and for characterizing residual properties of the structure [START_REF] Huang | Analytical modeling of impact resistance and damage tolerance of laminated composite plates[END_REF][START_REF] Combes | Design for damage tolerance[END_REF][START_REF] Abrate | Impact on Composites Structures[END_REF][START_REF] Olsson | Analytical prediction of large mass impact damage in composite laminates[END_REF][START_REF] Zhou | The use of experimentally-determined impact force as damage measure in impact damage resistance and tolerance of composite structures[END_REF][START_REF] Suemasu | Compressive behavior of multiply delaminated composite laminates part 1: experiment and analytical development[END_REF][START_REF] Suemasu | Compressive behavior of multiply delaminated composite laminates part 2: finite element analysis[END_REF]. For instance, critical load could be analytically determined to predict delamination growth [START_REF] Olsson | Analytical prediction of large mass impact damage in composite laminates[END_REF]. Even if these approaches are quite efficient in certain domains, the complexity of the phenomena implies that numerical methodologies have to be developed. The FE method is a relevant approach to characterize the behavior of composite structures and to provide information on the impact damage phenomena. Reliable impact and Compression After Impact (CAI) simulations would be a valuable tool to replace tests and take place in the test pyramid [START_REF] Rouchon | Certification of Large Aircraft Composite Structures, Recent Progress and New Trends in Compliance Philosophy[END_REF][START_REF] Acar | Effects of structural tests on aircraft safety[END_REF]: this is the aim of virtual testing. The complexity of composites is that damage depend on the design of the laminate in terms of stacking sequence, ply thickness, nature of fibers, kind of re-inforcement… driving to a different repartition of stress in the laminate and so to a reduction or an increase in stress location.

In order to have a faithful and reliable behavior of the laminate during simulation, it is necessary to sufficiently represent the events occurring during loading and damage development. These damage could be classified into two parts: intralaminar damage developed inside the ply (matrix cracking, fiber breakage or fiber/matrix debonding) and interlaminar damage developed at the interface between two plies, namely delamination. To have a good accuracy, the main damage captured by a numerical low velocity impact simulation are matrix cracking, fiber breakage and delamination [16 18] driving to a "re levant physics of the impact process" from under BVID to perforation range of impact [START_REF] Lopes | Physically-sound simulation of low-velocity impact on fiber reinforced laminates[END_REF].

Important research has been done on understanding, capturing and modelling delamination with good results [19 27], on the effect of delamination on the residual strength [START_REF] Aslan | Buckling behaviour and compressive failure of composite laminates containing multiple large delaminations[END_REF][START_REF] Dang | A numerical study on impact and compression after impact behavior of variable angle tow laminates[END_REF] showing a reduction of the residual strength in presence of delamination. Since the introduc tion of the cohesive zone model (CZM) in the 60's [ 30 32], delamina tion in composites is nowadays commonly simulated using cohesive elements and interface elements. For instance, interface elements are integrated in the model [START_REF] Lopes | Low-Velocity impact damage on dispersed stacking sequence laminates. Part II: numerical simulations[END_REF][START_REF] Faggiani | Predicting low-velocity impact damage on a stiffened composite panel[END_REF][START_REF] Iarve | Mesh-independent matrix cracking and delamination modeling in laminated composites[END_REF], and used with contact algorithms and friction between delaminated plies. Turon et al. [START_REF] Turon | Accurate simulation of delamination growth under mixed-mode loading using cohesive elements: Definition of interlaminar strengths and elastic stiffness[END_REF] and Harper et al. [START_REF] Harper | A study on the influence of cohesive zone interface element strength parameters on mixed mode behavior[END_REF] studied influence of cohesive zone interface strength para meters on mixed mode behavior. For instance, Harper et al. conclude that one should pay attention to the length of the cohesive zone on what depends the accuracy of the interfacial stresses. Relatively short length of the cohesive zone enables better results. Other approaches exist with Li et al. [START_REF] Li | Modelling damage of multiple delaminations and transverse matrix cracking in laminated composites due to low velocity lateral impact[END_REF] who use fracture mechanics to simulate the delamination growth based on VCCT to evaluate the energy release rates. Or Menna et al. [START_REF] Menna | Numerical simulation of impact tests on GFRP composite laminates[END_REF] who choose a modelling of the bond between plies through distributed spring connections, each ply being modelled by three di mensional eight node finite elements. Delamination is modelled by the use of a surface to surface tiebreak contact algorithm based on the knowledge of interlaminar properties (normal and shear strengths).

Concerning intraply damage modelling, fiber breakage and matrix cracking can be approached by continuum damage mechanics model ling with three dimensional solid elements including internal damage variables and a degradation of material properties following the di rection as in [START_REF] Lopes | Low-Velocity impact damage on dispersed stacking sequence laminates. Part II: numerical simulations[END_REF][START_REF] Lopes | Physically-sound simulation of low-velocity impact on fiber reinforced laminates[END_REF][START_REF] Donadon | A progressive failure Model for composite laminates subjected to low velocity impact damage[END_REF]. All of these approaches are meso scale simu lation strategies.

Faggiani and Falzon [START_REF] Faggiani | Predicting low-velocity impact damage on a stiffened composite panel[END_REF] propose a continuum damage mechanics approach for fiber breakage and matrix failure, each in tensile and compressive failure mode, using continuum shell elements. Modelling of matrix cracking using extended finite element method is also con ducted by Iarve et al. [START_REF] Iarve | Mesh-independent matrix cracking and delamination modeling in laminated composites[END_REF]. This enables independence of the mesh orientation. Lopes et al. [START_REF] Lopes | Physically-sound simulation of low-velocity impact on fiber reinforced laminates[END_REF] also use cohesive elements in the ply between three dimensional elements in the material direction to cap ture matrix cracking. Likewise, de Moura and Gonçalves [START_REF] De Moura | Modelling the interaction between matrix cracking and delamination in carbon-epoxy laminates under low velocity impact[END_REF] place interface elements inside layers where matrix cracking is experimen tally observed, implying the need of a previous study.

The importance of coupling between interlaminar and intralaminar damage is also admitted in literature [18,22 27,29,34,38]. The use of cohesive elements inside the ply in the material direction to capture matrix cracking and get a good coupling with the delamination is an other point to obtain accurate damage predictions. It is admitted that matrix cracking has a precursory role on delamination.

Then to estimate the residual strength and evaluate the damage tolerance of the laminate, interest is focused on modelling Compression After Impact with, for instance, some quite accurate models developed by Gonzalez et al. [START_REF] Gonzalez | Simulation of dropweight impact and compression after impact tests on composite laminates[END_REF], Dang and Hallett [START_REF] Dang | A numerical study on impact and compression after impact behavior of variable angle tow laminates[END_REF], Tan et al. [START_REF] Tan | Predicting low velocity impact damage and Compression-After-Impact (CAI) behavior of composite laminates[END_REF] or re cently published by Panettieri et al. [START_REF] Panettieri | Delamination growth in compression after impact test simulations: Influence of cohesive elements parameters on numerical results[END_REF].

Gonzalez et al. [START_REF] Gonzalez | Simulation of dropweight impact and compression after impact tests on composite laminates[END_REF] agree that the predictions deteriorate with an increasing number of layers. Their predictions are close to the experi mental values, with a maximum relative error of 20% for the strength obtained during CAI.

Dang and Hallett [START_REF] Dang | A numerical study on impact and compression after impact behavior of variable angle tow laminates[END_REF] use a model that do not take into account fiber failure (impact are carried out at very low energy, and fiber fail ures do not occur or can be negligible in this case). During CAI, they link the compressive strength to the occurrence of significant delami nation events.

Tan et al. [START_REF] Tan | Predicting low velocity impact damage and Compression-After-Impact (CAI) behavior of composite laminates[END_REF] manage to capture both the qualitative and the quantitative aspects of intralaminar and interlaminar damage during impact and CAI. However they have little trouble to capture the good direction of delamination propagation, while having a good re presentation of the extended area.

Panettieri et al. [START_REF] Panettieri | Delamination growth in compression after impact test simulations: Influence of cohesive elements parameters on numerical results[END_REF] show the importance of the parameters of cohesive elements on the CAI result and on the computational cost. They point out that a compromise has to be made. They also admit than a reliable numerical approach could "not only lower the cost associated with the test but also enhance the design of composite structures".

Finally, related to the impact damage tolerance designing philo sophy, attention is given to permanent indentation as a predictive mark to evaluate the residual capabilities of the structure [START_REF] Wardle | On the use of dent depth as an impact damage metric for thin composite structures[END_REF]. This phe nomenon is not well controlled yet, because it depends on several parameters: plate geometry, material, stacking sequence, impact energy or impactor shape, etc… and its origin is complex: local fiber failure [START_REF] Chen | Failure mechanisms of laminated composites subjected to static indentation[END_REF], debris accumulation, local plasticity, etc. Some formulations exist to integrate dent during impact test simu lations: "plastic like" model included in the matrix behavior to take into account matrix cracking, plasticity and blocking debris [START_REF] Bouvet | Low velocity impact modeling in composite laminates capturing permanent indentation[END_REF], using anisotropic elasto plasticity theory [START_REF] He | Prediction of permanent indentation due to impact on laminated composites based on an elasto-plastic model incorporating fiber failure[END_REF], non linear shear of the in tralaminar damage model [START_REF] Shi | Modelling damage evolution in composite laminate subjected to low velocity impact[END_REF][START_REF] Tan | Predicting low velocity impact damage and Compression-After-Impact (CAI) behavior of composite laminates[END_REF] with combination of continuum theories of plasticity and continuum damage mechanics [START_REF] Donadon | A progressive failure Model for composite laminates subjected to low velocity impact damage[END_REF].

Objectives of this study

The Discrete Ply Model (DPM) developed at the Institut Clément Ader by Bouvet et al. makes possible to capture damage such as per manent indentation, delamination, fiber breakage and matrix cracks for are also set up. According to the ASTM D7137/D7137M standards [START_REF] Astm D ; M | Standard Test Method for Compressive Residual Strength Properties of Damaged Polymer Matrix Composite Plates[END_REF], they consist of two longitudinal stabilizing knives spaced 90 mm and two clamping blocks at the lower and upper sides of the plate spaced 130 mm (Fig. 3b).

Experimental validation

A previous validation of DPM capability to represent both impact and CAI has been done and presented in [START_REF] Hongkarnjanakul | Validation of low velocity impact modeling on different stacking sequences of CFRP laminates and influence of fibre failure[END_REF]. Validation was based on experimental/numerical comparisons of delamination (C scan), impact force/displacement curves and CAI strengths from various laminates with 0.5 mm thickness plies (0.5 mm plies in the numerical simulation, two 0.25 mm combined plies in the experiments).

During this study, new tests were done to validate the model with 0.25 mm thickness plies, in order to be able to simulate more realistic laminates. They consist in 25 J impact and CAI tests on 4 × 100 × 150 mm 3 laminates made of T700/M21 UD tapes. ASTM D7137/D7137M standards were used, and 6 specimens tested: 3 dif ferent stacking sequences, tested twice for repeatability.

A: [45/-45/90/0/90/0/45/-45] S K: [45/-45/0/45/-45/0/90 2 ] S O: [45/-45/45/-45/90/0/90/0] S Fig. 4 presents impact force/displacement curves for the three A, K and O specimens: two experimental curves for each specimen, and the associated simulation. A very good agreement was found for all three cases, both during loading and unloading phases.

To have more comparison data, C scan were also performed for one of each specimen type. The obtained delamination maps are also pre sented on Fig. 4, beside delamination coming from the numerical si mulation. Specimen A and K present good correlations, with very good numerical estimations of the delaminated interfaces, shapes and areas.

Finally, permanent indentations (Fig. 5a) were also measured 48 h after the end of impact tests, using digital image correlation. They are in accordance even if the numerical results are overestimated. One can explain this difference with the relaxation phenomena causing too high numerical permanent indentation value. Moreover, the evolutions of permanent indentation from one specimen to another are the same in experiments and simulations. At this level of modelling, it can be as sumed that the result is good.

Importance is finally given to the residual strength got during CAI on the three stacking sequences A, K and O. Fig. 5b shows that, even if, like for permanent indentation, the results are slightly overestimated (10 15%), the ranking in terms of performance is well represented. This means that the simulation is also able to give a hierarchy in terms of layups strength capacity, which is the most important in design when searching for the best laminate.

Numerical approach: Laminate design optimization with impact damage tolerance

Classical approach

Previous work and results presented first in this article show that the DPM model is advanced enough to propose an impact damage tolerance design approach. A classical numerical design approach would be to cover the laminate design space by changing stacking se quences, materials, number of plies, and calculate residual stress at BVID. As the concept of damage tolerance in composite is based on the visibility of the damage (residual strength is calculated at BVID), the optimization loop is based on an inner loop to determine the impact energy level to obtain a permanent indentation (PI) equal to BVID (Fig. 6). This inner loop does not necessitate the full impact and CAI calculation as the permanent indentation is calculated at the end of the impact energy and the CAI calculation is run only for the BVID energy Menna et al. talk about the mesh dependency of the result: "the composite material failure behavior is influenced by the element size affecting the absorbed energy which varies with the element length and converges for small element dimensions" [START_REF] Menna | Numerical simulation of impact tests on GFRP composite laminates[END_REF]. They use elements of approximatively 0.657 mm size. In our case, to obtain a good propa gation of the last interface delamination (at the non impacted face), the mesh is reduced to 0.833 mm size elements. It also has to be noticed that the thickness of elements is smaller than during previous validation of the model (0.25 mm against 0.5 mm) [START_REF] Hongkarnjanakul | Validation of low velocity impact modeling on different stacking sequences of CFRP laminates and influence of fibre failure[END_REF], and the number of in terfaces is increased causing a more complex model. It was observed that the result is more reliable when the element length is smaller. To avoid excessive time calculation, this size of 0.833 mm is the limit of the model to get a good delamination: beyond this size the propagation at the last interface does not occur.

E l t (GPa) E l c (GPa) E t (GPa) ν lt G lt (GPa) G tz (

Permanent indentation modelling

As previously seen, the permanent indentation is the mark left onto the surface after an impact event. It is defined as the difference in a direction normal to the face of the specimen between the lowest point in the dent and the surface that is undisturbed by the dent [START_REF] Astm /D ; M | Standard Test Method for Measuring the Damage Resistance of a fiber-reinforced polymer matrix composit to a drop-weight impact event[END_REF]. Its origin is not well controlled yet, but previous studies show that it is mainly linked to fiber breakage, matrix plasticity, or blocking debris [START_REF] Panettieri | Delamination growth in compression after impact test simulations: Influence of cohesive elements parameters on numerical results[END_REF]. In the model, it is represented thanks to a pseudo plastic non return law in intra ply interface elements.

The capability of DPM to represent permanent indentation is vali dated by the curves return during impact unload (in impact force dis placement curves). It is to be noticed that this model does not take into account the natural relaxation of the plate after impact: the permanent indentation value reduces during a couple of days following an impact event by elasticity behavior. For this reason, all measures of experi mental permanent indentation value are carried out at least 48 h after impact tests and could be smaller than the numerical ones measured at the end of impact simulation.

Material and boundary conditions

The model is so used to simulate experimental impact and CAI tests on 4 × 100 × 150 mm 3 rectangular laminate plates of T700/M21 UD carbon/epoxy composite. Properties used in the model are presented in Table 1. The number of plies is fixed at 16 plies of 0.25 mm thickness. Orientations in the stacking sequence are limited to 0°, ± 45° and 90°w ith the same fiber percentage for each direction. Considering sym metrical reasons, only a half plate is meshed. The boundary conditions are given by the contact between the plate and a fixed rigid body, re presenting experimental condition tests presented hereafter (Fig. 3).

For the impact test, the plate is supported by a 75 × 125 mm 2 window and is impacted at its center by a 2 kg hemispherical impactor of 16 mm diameter, numerically assumed non deformable (Fig. 3a). Following the impact, a relaxation step is simulated. This step put the plate in quasi static state by eliminating major vibrations and waves induced by the impact event. During this step CAI boundary conditions

Table 1

Material properties used in the model. important to put into perspectives the results of the optimization done with the DPM model. To the author's knowledge, the DPM is one of the most efficient models that can represent impact, impact induced damage (including PI), and CAI within the same model, with such a result quality: representativeness of mechanisms and values of impact force evolution, PI, CAI, etc. However, due to the great complexity of the phenomenon and of the model, one must not expect DPM model to give a very fine accuracy in the current state of virtual tools development. The model makes possible the ranking of laminates' residual strength (with a quite satisfactory accuracy). This is the most important point in the case of design optimization, to find the best structure. However, there is also a significant dispersion in experimental results that makes unnecessary the search for an extreme precision in the estimation of BVID energy level.

Anyway, nowadays, an experimental validation of the optimized laminate obtained by numerical design is still necessary.

Conclusion

Using the Discrete Ply Model, a numerical impact damage tolerance sizing is proposed. This work is possible thanks to the ability of the DPM in capturing main damage as fibre failure, matrix cracking and delamination from impact to CAI event. In the first part of the study, an experimental/numerical comparisons campaign was performed, showing quite accurate results in dent depth and residual strength prediction, two key parameters in this approach.

After this validation, the model was used to make a laminate design optimization with damage tolerance. In a first part, a reduced design space made of 19 laminates was proposed and full impact and CAI calculations were done at different impact energy level around the energy necessary to obtain a visible damage equal to BVID. Simple interpolations were then done to determine the best laminates in terms of damage tolerance strength, showing the ability of DPM to make a composite design optimization with damage tolerance. However, within the 19 samples studied, no clear rule or trend emerges to justify the impact damage tolerance of a given stacking sequence. This result again underlines the importance of numerical simulations development for composite damage prediction, as no practical rules can be established for an industrial use.

The principle of a classical optimization loop, more time-efficient, was also presented, but not applied here, the objective of the study being to study the evolution of CAI residual stress versus permanent indentation curves in order to propose an improved approach.

This approach is based on the knowledge of an approximate linear decrease of CAI stress when permanent indentation increases. It enables, from a single full impact and CAI calculation for all studied laminate, a rough estimation of the CAI strength. Thus, it is possible to define a reduced set of "best candidates" to perform a finer optimization. This enables reduction of computation time, which is a critical point in composite numerical simulations.

However, even with this reduction of the global number of simulations to perform during design optimization, the 36 h duration (on 20 CPUs) for a single impact and CAI simulation is still too high to be applied to more industrial design spaces made of hundreds or thousands laminates. An effort to drastically reduce models calculation time has to be done.

Fig. 1 .

 1 Fig. 1. Damage tolerance concept with detectable and undetectable damage.

Fig. 13 .

 13 Fig.13. "Best candidates" method: principle of CAI estimation at BVID.

Fig. 14 .

 14 Fig.14. "Best candidates" method applied to the 19 laminates, from 25 J energy.

Acknowledgments

Authors would like to gratefully acknowledge CALMIP (CALcul en Midi-Pyrénées) for access to the HPC resources under the allocation p1026.


M Nassouri

C Chauveau

F Halter

I Gökalp

Flame structure of ethanol-air premixed mixtures at high pressures in microgravity

Flame structure of ethanol-air premixed mixtures at high pressures in microgravity

Introduction

Towards the challenge concerning rarefaction of fossil energies, and in a durable developmental perspective, it is essential to very strongly invest in the control of energy consumption's and the emergence of new technologies making it possible to better exploit renewable energies. This study aims at looking further into knowledge on the phenomena concerned during the combustion of liquid fuels dispersed as aerosol. Twophase combustion is a widespread mechanism of energy conversion that is of practical importance in gas turbines, diesel and spark ignition engines, furnaces, and hazardous environments.

Recent studies showed that the flames being propagated through an aerosol/vapor mixture could show characteristics extremely different from their counterparts premixed gas (flame propagation velocity increased, inflammability limits extended). These characteristics can have advantages for certain applications (engines…) but also disadvantages for other cases such as those met in the context of the industrial risks. Thus, an understanding of the influence of the presence of liquid drops in a laminar aerosol flame is essential. Many studies were devoted under investigation of the flame propagation in a gas mixture, for various conditions of pressures and temperature, and for many fuels. Those devoted to the flame propagation in an aerosol/vapor mixture are sparser. Consequently, there are few experimental data of a fundamental nature which clearly shows the similarities and the differences for the laminar burning velocity between single and two phase combustion.

In this paper, spherical expanding flames are used to measure the differences in the structure of instabilities in laminar gaseous and aerosol flames. Aerosols of ethanol/air, in the droplet size range of 10 µm, are formed by the expansion of a gaseous pre-mixture to produce a homogeneous suspension of fuel droplets. The use of reduced gravity conditions, thanks to parabolic flights, made it possible to reduce the effects of the sedimentation of the droplets, and to be freed from the effects of the buoyancy on the propagation of the very slow flames.

Objectives

The first step of our work was to characterize experimentally the size of droplets composing the aerosol. This investigation was performed using a laser diffraction particle size analyzer. Aerosol mixtures are generated by the condensation by expansion cooling technique (Wilson cloud chamber technique), using ethanol as fuel. Under reduced gravity conditions larger droplet sizes are obtained together with more homogeneous and more mono-disperse aerosol mixtures [START_REF] Nassouri | Combustion of aerosols: droplet sizing study in microgravity[END_REF].

During the second step, studies of the propagation of the spherically expanding flames have been performed, for the previously characterized mixtures. Imaging is used to observe the propagation of the flame. Several initials conditions were varied such as pressure and the total equivalence ratio. Spherical flames were generated for both fuel droplet-vapor-air mixtures and premixed gas mixtures. The effects of droplet size distribution on the flame speed and structure have been investigated. The most recent similar studies were carried out by Lawes [START_REF] Lawes | [END_REF] using isooctane fuel in normal gravity condition and Nomura [3] using ethanol fuel in microgravity condition.

Experimental apparatus and procedure

Experiments were conducted in a dual-chamber pressure release type high-pressure combustion apparatus shown in Figure 1. The combustion chamber consists of a cylindrical vessel of 82.5 mm inner diameter, and 110 mm length. This inner vessel is located concentrically in an octagonal high pressure chamber able to sustain up to 12 MPa. This outer chamber is filled with nitrogen gas at same pressure as the inflammable mixture introduced in the inner vessel. Six specific pressure relief valves with 7 mm outlet diameter are located in the radial wall of the inner vessel symmetrically from the centre and angularly at 0, 120, and 240 degrees to allow for pressure release. The relief valves, equipped with calibrated compression spring, provide a seal between chambers for pressure differences between inner and outer chambers less than 0.5 atm. When the pressure difference exceed, the valves open allowing gases to flow from the inner to the outer chamber to maintain a nearly constant pressure. Since the inner vessel volume is 10 times smaller than that of the outer one, the total pressure increase after combustion is small, ensuring not only a nearly constant-pressure experiment, but operational safety for experiments conducted at high initial unburned gas pressures. Optical access is obtained through a pair of windows of 60 mm usable diameter, disposed face to face. The maximum allowed initial temperature of the inner vessel is 150 °C ensured jointly by heating cables, thermocouples and a PID regulator.

Fig. 1. Schematic representation of the combustion apparatus

Before filling a vacuum is created inside the chamber. The gases (air: inner, N 2 : outer) are introduced into the dual-chamber with thermal mass flow meters. The fuel is regulated thanks to a sample loop connected to the air injection. The use of a sampling and switching valve allows multiple injections of liquid with accuracy. The liquid fuel pushed by the air is then vaporized and mixed before being introduced into the combustion chamber. The mixture is ignited by two electrodes which form a spark in the centre of the combustion chamber. Although the capacitive discharge ignition system makes it possible to vary the deposited energy, the results presented in this paper are obtained with fixed adjustments of the ignition system.

A FrontDaq acquisition system is used to record the outputs of the system (pressure, temperature), whereas the whole control of the experiment, like specifying and monitoring the mixture preparation process, is ensured by a "Siemens Simatic" automation controller. A shadow photography system allows imaging of the flame front for a diameter up to 50 mm. Illumination is provided by a laser-driven light source (Energetiq); the parallel light beam is created by using two planoconvex lenses.

The evolution of the flame surface development is observed from shadowgraphy images recorded with a high speed CMOS Phantom v1210 camera operating at 15000 frames/s. The number of images considered in all experiments is higher than 200.

Results and Discussion

Ethanol-Air mixtures in microgravity

In normal gravity the droplets rapidly settle which increases the droplets number density N (droplets number/m 3 ) in the lower part of the combustion chamber and decreases it in the upper part. This produces an asymmetric structure of the flame and also disrupts its sphericity.

Figure 2 shows different behaviors of the flame in normal gravity and microgravity conditions. It was shown in the literature that the presence of droplets in a vapor-air mixture changes the flame structure, Hayashi [4] proposed that the presence of droplets produces heterogeneity in the unburned mixture, which should be responsible for the initiation process of such roughened cellular flame fronts and that the development of the roughness must be associated with the instability of the flame front. The pictures show that the roughness of the flame front increases as the flame ball grows.

Figure 2.A shows the effect of droplets on the flame structure at the same initial conditions in normal gravity and in microgravity. The effect of droplet sedimentation on the flame structure can be clearly observed as the cellular structure in normal gravity is concentrated in the lower part of the flame, whereas in the upper part which only includes a vapor-air mixture, no cellular structures are observed. Figure 3 shows various flames which were ignited at the same initial conditions of pressure, temperature and equivalence ratios, but at various moments after the end of the expansion. Droplet evaporation rates (which depends on the initial temperature and pressure as our previous study has showed [START_REF] Nassouri | Combustion of aerosols: droplet sizing study in microgravity[END_REF]) determine the duration of the aerosol lifetime before its complete vaporization. After the end of expansion time (which is 1.5s in our case) the droplet-vapor-air mixture is becoming more and more dilute with time passing, until the moment when the droplets are completely evaporated and then only a vapor-air-mixture exists. Figure 3 shows droplet sedimentation due to gravity. Experiences show that sedimentation starts 1sec after the end of the expansion and then a high concentration of small cells in the lower part of the flame is observed. The cells become larger in the upper part, until the moment when the cells disappear and the flame structure becomes that of a vapor-air mixture.

Flame structure and instability

During the investigation of spherical flames, two categories of instabilities are observed: unequal diffusion instability caused by unequal mass and thermal diffusion rates, and hydrodynamic instability caused by interactions between the flame and external disturbances. Many studies were devoted to the cells formation and the onset of instability in homogeneous vapor-air mixtures such as Bradley [5,6], Gu [7], Jomaas [8], Liu [9], Eisazadeh-Far [10,[START_REF] Eisazadeh-Far | Proceedings of the Combustion Institute[END_REF], and Marshall [START_REF] Marshall | [END_REF]. However, studies on cellular instabilities in droplet-vapor-air mixtures are scarcer. Pioneering works of Atzler [START_REF] Atzler | ICLASS 2006[END_REF] and Nomura [START_REF] Nomura | Proceedings of the Combustion Institute[END_REF] are references on the effects of the fine droplets on the laminar flame speed.

Figure 4 shows the evolution of instabilities at the same initial conditions of pressure, temperature and equivalence ratio, for vapor-air mixtures and dropletvapor-air mixtures. It can be noticed that until 5ms after flame initiation, there is no notable effect of droplets. However for later times, we dramatically note the droplet effect in droplet-vapor-air mixtures where we observe a significant multiplication of the cell number by scissiparity while the number of cells in vapor-air mixture remains sensibly the same. To better understand these differences, we studied the two types of mixture separately. a. Flame structure of Droplet-Vapor-Air mixtures Chiu [START_REF] Chiu | [END_REF] had already attempted to classify the different possible structures of droplet-vapor-air mixture flames, depending of the total number of droplets and the group combustion number G, which is mainly based on R e and P r numbers (Reynolds and Prandtl numbers respectively). Borghi [START_REF] Borghi | Lecture series -van Kareman Institute for fluid dynamics[END_REF] has also discussed the same problem by considering two non-dimensional parameters: d g /e L , the ratio of the mean initial droplet diameter to the characteristic thickness of a laminar flame, and n 1/3 .r F , where n is the droplet number density (droplets number / m 3 ), n 1/3 is the average distance which separates the droplets and r F is the radius of the diffusion flame that would be established around the mean droplet if it was alone in the oxidizing medium. Borghi [START_REF] Borghi | Lecture series -van Kareman Institute for fluid dynamics[END_REF] has shown that the flame structure will mainly depend on the droplets spacing parameter (n 1/3 .r F ).

When the flame zone approaches an aerosol in which droplets are sufficiently small or the propagation flame speed is sufficiently slow, these droplets may have enough time to fully vaporize. The value of this critical droplet diameter, below which droplets evaporate before the reacting zone, was defined by Hayashi [START_REF] Hayashi | [END_REF]. This critical diameter is above all sensitive to the propagation flame speed. For our cases we consider that the sizes of the fuel droplets are not necessarily identical, but they exhibit a near monosized distribution around a mean diameter value of 7µm; these values were measured during our previous work [START_REF] Nassouri | Combustion of aerosols: droplet sizing study in microgravity[END_REF]. We also consider that the medium is stagnant; the position of the fuel droplets is not regularly fixed, but is randomly and homogeneously distributed in microgravity. We shall add that the droplets spacing parameter n 1/3 .r F was calculated by considering that the initial quantity of condensed ethanol due to the expansion, is equal to the necessary quantity to achieve the saturated vapor pressure, which was calculated using Antoine equation [START_REF] Saat | AIP Conference Proceedings[END_REF]. However, if we increase the flame propagation speed by increasing equivalence ratio to (ɸ= 1.2) keeping the droplet spacing parameter at (n 1/3 .r F = 0.45), no significant change in the flame structure can be noticed. By increasing more the equivalence ratio, a different flame structure with larger cells can be observed. This flame structure was remarked for all rich droplet-vapor-air mixtures (above ɸ= 1.5), independently of the droplet spacing parameter value.

Figure 3 also shows the effect of droplets concentration on the flame structure. When the flame ignition is at 0.1 s after the expansion a dense cloud of droplets is obtained, which produces a dense cellular flame structure. However, when flame ignition takes place at 1.2 s and 1.4 s, droplet distributions become more dilute and the flame structure smoother.

b. Flame structure of Vapor-Air mixtures

The onset of flame instabilities of laminar ethanol vapor-air spherical premixed flames has been studied in the previously described apparatus, but without expansion. The initial pressures have been varied. Experimental results reveal that the pressure and the equivalence ratio are the most dominant parameters versus among all those studied. Ø = 0.84 Ø = 1 Ø = 1.2 Ø = 1.4 Fig. 6. Flame structure of ethanol vapor-air mixtures at 5 bars and 61°C

Figure 6 shows 4 vapor-air mixture flames, performed at 5 bars, 61°C and 4 different equivalence ratios. The effect of the equivalence ratio on the unequal diffusion instability can be clearly identified. The instabilities increase with the increasing equivalence ratio.

Fig.7. Effect of pressure and equivalence ratio on cell formation

For a better understanding of the observed phenomena, vapor-air mixture flames have been produced by varying the initial pressure from 1 up to 9 bars. For each pressure, the equivalence ratio was varied from 0.6 to 1.7. Figure 7 shows the experimental results obtained where both cellular and non-cellular zones can be identified. For initial pressures less than 3 bars, instabilities are not observed. Starting from 3 bars and Ø = 0.8 instabilities start to show up and become more intense with the increase of both pressure and equivalence ratio. This result is similar to those which have been described by Eisazadeh-Far [START_REF] Eisazadeh-Far | Proceedings of the Combustion Institute[END_REF] on the ethanol vapor-air mixture flames. They found that during the pressure increase throughout the flame propagation, cell formation is strongly dependent on the equivalence ratio, and for each equivalence ratios there is a specific range of pressure at which the flame becomes cellular.

Conclusions

The aim of the present work was to characterize the impact of fine droplets on the flame structure and cell formation in an aerosol mixture. Experiments in normal and microgravity conditions are conducted with ethanol as fuel. The effects of initial pressure and global equivalence ratio are investigated. Comparisons between the flame structures of vapor-air mixtures and droplets-vapor-air mixtures have been presented. Settling effects under normal gravity are clearly demonstrated. The use of microgravity conditions extends the experimental domain and allows examining more homogeneous and stable aerosol clouds. For the vapor-air mixtures, gravity does not disturb the flame behavior for an equivalence ratio less than ɸ= 1.5. Concerning the instabilities due to the presence of the droplets in an aerosol, we observe that the droplet spacing parameter (n 1/3 .r F ) is the main factor, except for rich mixtures. It is also highlighted that the increase of the pressure and equivalence ratio intensifies the onset of instability in vapor-air mixtures.

Fig. 2 .Figure 2 .

 22 Fig. 2. Images of ethanol droplet-vapor-air mixture flames

Fig. 3 .

 3 Fig. 3. Flame structures of ethanol-air mixtures at 60 °C, 4 bars and Ø=1.56 All pictures are taken at 1.1ms after the flame ignition.

Fig. 4 .

 4 Fig. 4. Flame structure of ethanol/air mixtures at 60 °C, 3.2 bars and Ø=1.52, both for gas and aerosol mixtures.

Fig. 5 .

 5 Fig. 5. Flame structure at 61°C, for droplet-vapor-air mixtures in microgravity.

Figure 5

 5 Figure 5 shows that at the same equivalence ratio (ɸ= 0.84) and three different droplet spacing parameters values, we have three different flame structures. The flame in the lean droplet-vapor-air mixtures with a very dilute aerosol (ɸ= 0.84, n 1/3 .r F = 0.27) is smoother and the flame front roughness increases with the increasing of droplets spacing parameter values.

Acknowledgements

The authors greatly acknowledge the continuous support of the CNES and the CNRS through the GDR MFA n°2799. M. Nassouri is supported by a joint grant from the CNES and the Conseil Régional Centre.