Guillaume Lecocq
email: guillaume.lecocq@ineris.fr

Jérôme Daubech

Emmanuel Leprette

Experimental and numerical study of the fuel effect on flame propagation in long open tubes

Keywords: premixed gaseous flame propagation, hydrogen, methane, pipes, CFD

Previous works (Daubech, Lecocq, 2019) were dedicated to gaseous flame acceleration along long pipes with a set of cases studied both experimentally and numerically. In these cases, the flammable mixture was initially quiescent and homogenously distributed. The impact of the tube diameter and material were studied trough both approaches for rather slow flames, the fuel being methane. While main features of the real flame were recovered by the chosen CFD method, some limits remained.

A new experimental dataset is detailed and analyzed with a quicker flame, the fuel being hydrogen and the same experimental set-up as the one used for measuring slow flames. Thus, the fuel effect on the flame dynamics can be directly highlighted.

A simple CFD approach is tested for recovering two distinct flame behaviors: a deflagration flame and another undergoing deflagration-to-detonation transition. Furthermore, the modelling results are used to propose elements of interpretation for flame acceleration.

Introduction

Scenarios of formation of gaseous flammable clouds in long ducts can be identified during risk analyses of industrial processes. If an ignition occurs, a flame can propagate in such flammable cloud and undergo an acceleration which is specific to this confined and elongated geometry.

If the flammable cloud formation and the ignition cannot be avoided, it is key to assess the flame acceleration process and the generated pressure effects associated to the explosion scenario. These latter should be compared to the mechanical resistance properties of the pipe in which the explosion could be triggered. To do so, the flame acceleration process has to be understood with the specificities of the explosion scenario (tube material and diameter, flammable cloud length, spatial distribution of the fuel in this cloud, …).

Previous experimental and numerical works were detailed for 24 m long pipes made of PMMA or steel, with varying diameters (150 or 250 mm), the fuel being methane (Daubech, Lecocq, 2019). The pipes were open at one end and closed at the other where ignition was triggered. The tests showed the impact of the pipe material and diameter.

In the current work, new experimental data are presented. They correspond to the case of a 150 mm wide steel tube in which a homogenous hydrogen/air cloud with a volume fraction of 20 % is ignited. They are compared to another experimental point for which the flammable cloud is made of a stochiometric methane/air cloud.

A CFD approach is proposed and tested, in order to assess its predictive capacities and study if elements could be extracted from computations for helping to interpret experiments.

Experimental set-up and results

The current work is dedicated to flames propagating in a straight, 24-m long steel pipe, open at one end and closed at the other. It is filled with a quiescent stoichiometric methane/air mixture. Ignition is performed on the middle of the closed end with an electrical spark whose energy is about 100 mJ.

Two flammable mixtures are studied:

-A stoichiometric methane/air mixture, -A lean hydrogen/air mixture, with a hydrogen volume fraction in air of 20 %.

Figure 1 shows the pipe in which flame propagation is measured. For the methane/air flame, while the flame speed keeps on increasing, its maximum value remains about 140 m/s. Two main peaks can be seen for each pressure signal.

The first one can be explained with flame elongation that follows ignition, which leads to an increase of the burnt gases volume variation per time unit. When this variation becomes weaker, because a maximum in flame surface is reached, the pressure decays. The flame continues to accelerate, eventually with a change in flame shape, and the volume production of burnt gases creates the second peak which is limited by the amount of flammable mixture in the tube. A maximum overpressure about 400 mbar is reached. The time needed to burn all the flammable mixture is between 0.25 s and 0.3 s.

For the hydrogen/air flame also, a continuous flame acceleration can be noticed. A maximum flame speed higher than 2000 m/s is measured. This value can be compared to the Chapman-Jouguet velocity, about 1710 m/s. In this case, a transition from a deflagration regime to a detonation one (DDT) is observed.

At the pressure probe located 5.5 m away from ignition point, a first peak similar to the first peak identified for the methane/air flame appears. A slight pressure decay then occurs and is followed by a continuous pressure increase until a maximum overpressure of 3 bar. 15.5 m away from ignition point, a shock wave appears with a peak about 20 bar. This value is higher than the Chapman-Jouguet pressure (13 bar), which, additionally to what was said for flame velocity, indicates an overdriven detonation.

Phenomenology related to explosions in pipes and CFD modelling

Phenomenology

Cicarelli et al. (2008) proposed a review article dedicated to flame acceleration in pipes. With ignition, a burnt gases kernel is created, which leads to the formation of a premixed laminar flame. It is first wrinkled due to Darrieus-Landau instability, which is promoted or counteracted by thermo-diffusive effects, respectively if the Lewis number is lower or higher than 1. In the same time, the fresh gases are pushed ahead of the flame front due to thermal expansion effects. The flame front then reaches the lateral wall of the tube, leading to slight deceleration of the burnt gases production, the flame surface being reduced. It can be also promoted by heat losses, depending on the tube material. After this initial stage, the flame keeps on propagating with a shape that can sequentially change from an elongated flame to a tulip-shape flame, still pushing the fresh gases. The flame acceleration mechanism in this phase remains discussed.

With his pioneer works, [START_REF] Shchelkin | Influence of the wall roughness on initiation and propagation of detonation in gases[END_REF][START_REF] Shchelkin | Gas dynamics of combustion[END_REF] explained flame self-acceleration in tubes with flame/turbulence interaction, turbulence being produced in the fresh gases after generation of a boundary layer on the walls. This explanation highlights the importance of the wall roughness on the flame dynamics. Experiments (Daubech, 2019) carried out for methane/air flames propagating in long open tubes with different materials (ie PMMA for a smooth tube and steel for a rough tube) indeed led to different flame dynamics provided the tube diameter was small enough. The same set of experiments also showed the wall turbulence remained limited at the walls for the widest tubes while flame acceleration was noticed.

According to [START_REF] Cicarelli | Flame acceleration and transition to detonation in ducts[END_REF], a detonation can be first initiated after a shock reflection or a shock focusing. The shock is strong enough to auto-ignite fresh gases and trigger detonation. It can also be due to more subtle mechanisms involving instabilities and mixing processes. These phenomena were first explained by [START_REF] Yab | On the development of detonation in a non-uniformy preheated gas[END_REF] and [START_REF] Lee | Photochemical initiation and gaseous detonations[END_REF]: if an induction time gradient is formed, due to local inhomogeneities (temperature and/or concentration). The related spontaneous flame would release heat and create a shock wave. If the heat release strengthens the shock wave sufficiently, a detonation can occur. More recent works [START_REF] Ivanov | Flame acceleration and DDT of hydrogen-oxygen gaseous mixtures in channels with no-slip walls[END_REF] called into question this mechanism. According to the authors, DDT occurs when the flame is so fast that formed shock waves sit on the flame front and a coupling mechanism leads to a sufficient increase of flame speed and pressure peak.

Modelling approaches available in the literature

CFD approaches available in the literature for flame acceleration in tubes rely either on a highly detailed description of the flow [START_REF] Oran | Origins of the deflagration-to-detonation transition in gas-phase combustion[END_REF] or "under resolved" modelling that are built with numerous sub-models, each one accounting for a physical feature [START_REF] Wieland | Efficient simulation of flame acceleration and deflagration-to-detonation transition in smooth pipes[END_REF].

With such models, the chemical source term which pilots the propagation speed of the flame front is simply closed as the product of the gradient of the progress variable (𝑐), the volume mass of the fresh gases (𝜌 ) and a characteristic flame speed: 𝜌̅ 𝜔 ̇ = 𝜌 S |∇𝑐|. The flame speed S then writes: Ξ. S where Ξ is a wrinkling factor. This latter is explained as the product of characteristic wrinkling factors, each one accounting for a phenomenon accelerating the flame speed: thermo-diffusive and Darrieus-Landau instabilities, pressure effects, … Some authors [START_REF] Wieland | Efficient simulation of flame acceleration and deflagration-to-detonation transition in smooth pipes[END_REF][START_REF] Bradley | Autoignitions and detonations in engines and ducts[END_REF] describe detonation as the coupling of auto-ignition of fresh gases coupled to the propagation of a shock wave. Chemical source terms can be built from two contributions [START_REF] Lecocq | A new LES model coupling flame surface density and tabulated kinetics approaches to investigate knock and pre-ignition in piston engines[END_REF][START_REF] Wieland | Efficient simulation of flame acceleration and deflagration-to-detonation transition in smooth pipes[END_REF]: one modelling a premixed flame, the other autoignition, in order to account for the transition between the deflagration and the detonation.

Approach retained

The computations presented in the current work are based on a modelling strategy close to the one of [START_REF] Wieland | Efficient simulation of flame acceleration and deflagration-to-detonation transition in smooth pipes[END_REF] for modelling deflagrations. The transport equations are solved for momentum, pressure, a progress variable and energy with a pressure-based solver of the CFD code OpenFoam v2106 [START_REF] Weller | A tensorial approach to computational continuum mechanics using object-oriented techniques[END_REF]. Turbulence is also modelled with a k-𝜔 SST model [START_REF] Menter | Ten years of industrial experience with the SST turbulence model[END_REF].

Concerning the methane/air flame the pressure effects remain moderate. A constant laminar flame speed of 0.4 m/s was used. The pressure effects are well higher for the hydrogen/air flame and they have to be included for the estimation of the fresh gases volume mass 𝜌 and the laminar flame speed S . 𝜌 is simply quantified under the assumption of an adiabatic compression, thanks to the pressure field. Correlations can be found in the literature for the laminar flame speed of hydrogen. Nevertheless, it is not clear according to bibliography if laminar flame speed should increase or decrease with pressure [START_REF] Bougrine | Numerical study of laminar flame properties of diluted methane-hydrogenair flames at high pressure and temperature using detailed chemistry[END_REF][START_REF] Salzano | Explosion behavior of hydrogen-methane/air mixtures[END_REF]. Then, for the sake of simplicity, a constant laminar flame speed value of 0.9 m/s is used for the hydrogen flame.

The wrinkling factor Ξ is closed as: Ξ = Ξ . Ξ where Ξ represent flame wrinkling induced by flame/turbulence interaction and is closed with the turbulent flame speed correlation proposed by [START_REF] Gülder | Turbulent premixed flame propagation models for different combustion regimes[END_REF]. The wrinkling factor Ξ represents the effects of instabilities. The commonly made assumption of a unitary Lewis number for methane/air flames is kept and Ξ is set to 1.0 in this case.

Concerning the hydrogen/air flame, its Lewis number, about 0.6, is smaller than 1.0 and instabilities at the flame front are expected. A value for Ξ remains hard to predict. An ad hoc way was to tune it in order to recover a proper flame trajectory with time. A constant value of 3.3 was identified.

The computational domain is limited to the part of the pipe filled by the flammable mixture. At walls, velocity is zero and turbulent viscosity is modelled with a wall law. At the outlet plane, the pressure is set to the atmospheric pressure and the velocity gradient is set to 0.

The walls are assumed to be adiabatic (temperature gradient set to 0). The steel roughness is assumed to be around 150 μm which corresponds to a weakly rusted steel. This characteristic is used in the wall laws.

The mesh is made of 2.5 million hexahedra. The maximum characteristic cell width is about 6 mm. The cells are refined at the walls.

Results

According to Figure 2, the computation enabled to recover a qualitative agreement for the evolution of the flame front position with time. The increase in flame velocity is satisfying from t=0s to t=0.05 s and from t=0.15 s to t=0.25 s but is overpredicted from t=0.05 s to t=0.15 s.

Figure 3 shows the main features of the pressure signals are predicted. At 5.5 m and 10.5 m, there is a first pressure peak, followed by a pressure decay and one or several peaks. The amplitude of the first pressure peak is about 200 mbar and the second is about 400 mbar. The overestimation of the first peak by the modelling is about 25 % while the second one ranges from 25 to 50 %.

It is interesting to go a little bit further in the computation post-processing as several quantities can explain pressure effects. Indeed, these latter are related to the volume rate at which burnt gases are produced by flame propagation, the tube acoustics and the effect of the opening.

The total flame surface captured by the mesh is quantified as: 𝑆 = ∫ |∇𝑐| 𝑑𝑉. A resolved wrinkling, Ξ , can be defined as the ratio of this surface to the tube section. The turbulent wrinkling averaged on the flame surface, < Ξ > is also computed. The evolution of these quantities with time is plotted in Figure 4. < Ξ > mainly increases with time, starting from t=0.05 s. The final value reached is about 15. Ξ does not follow the same evolution: there are two cycles of increase/decrease and a constant value is observed for the final propagation phase. The maximum value is about 8. According to the Figure 5, the maximum values, reached for example at t=0.05 s and t=0.15 s correspond to elongated flames.

The lowest values at the end of flame propagation are obtained for quasi-flat flames.

It is notably interesting to note that:

-the first pressure peak at 0.07 s seems to be mainly explained by flame elongation and very weak flame/turbulence interaction, -the pressure decay that follows is related to the change of the flame shape (from an elongated shape to a tulip shape), -the pressure peak at 0.15 s is obtained when the product < Ξ > . Ξ is the highest. Figure 6 shows the experimental and predicted flame trajectory. It should be recalled here that the parameter Ξ was adjusted to recover a satisfying flame trajectory.

Figure 7 highlights the main trends of the pressure signals were recovered. At 5.5 m, the computed pressure signal is characterized with three peaks, with an overall pressure increase. The amplitude of the pressure is closed to the measured one. 15.5 m away from ignition point, the measured shock wave is predicted, nevertheless with a peak overestimation of 75 %. This proves a pressure-based solver is able to deal with shocks. Other authors choose to change their solver when the flame velocity exceeds a critical value [START_REF] Wieland | Efficient simulation of flame acceleration and deflagration-to-detonation transition in smooth pipes[END_REF].

The characteristic wrinkling factors are also plot for the hydrogen flame (Figure 8). < Ξ > mainly increases, starting from 0.01 s to 0.06 s and then decreases. The peak value is very high (85 ie about 6 times the peak value observed for the methane/air flame). As for the methane/air flame, Ξ sequentially increases and decreases. The peak values of lower than those obtained for the methane/air flame.

The first pressure peak seems to be explained by an increased flame surface as well as flame instabilities. A pressure decay is observed, related to a rapid change of the flame shape which is not compensated by flame instabilities and flame/turbulence interaction. After this phase, while the flame shape and surface evolve (Figure 9), the flame acceleration is mainly promoted by flame/turbulence interaction, until the end of the flame propagation in the tube.

Here DDT was approached through a continuous turbulent flame acceleration until the flame front reaches the preceding shock wave. This point of view is closed to the Shchelkin one but it may be too much simple compared to realistic mechanisms. It is indeed possible that the CFD model should predict flame extinction instead of flame acceleration.

Conclusions

Experimental results were first shown for a 24 m long steel pipe in which initially quiescent flammable mixtures were ignited, one being a stoichiometric methane/air mixture, the other a lean hydrogen/air mixture. Two distinct flame behaviours were observed: the maximum propagation speed of the methane/air flame was about 140 m/s while DDT occurred for the hydrogen/air flame.

A simple CFD model was used to recover features of both cases. An agreement was found for flame position with time and pressure effects.

The raw CFD results were post-processed to give pieces of interpretation for what was observed. One interest of CFD here is to give access to more quantities than the measured ones. Thus, it was possible to study the effect of turbulence, instabilities and flame shape changes on the pressure effects.

Nevertheless, the current CFD model should be completed with other sub-models (extinction, autoignition sub-models, …) as it is possible that the acceleration for the hydrogen flame, numerically explained by flame/turbulence interaction is not as large as predicted.

Fig. 1 .

 1 Fig. 1. View of the experimental set-up. Steel pipe, with a 150-mm inner diameter.

Fig. 2 .

 2 Fig. 2. Experimental and computed flame trajectory on the axis for the methane/air flame.

Fig. 3 .

 3 Fig. 3. Experimental and computed pressure signals at 5.5 m (left) and 15.5 m (right) from ignition point for the methane/air flame.

Fig. 4 .

 4 Fig. 4. Evolution of characteristic wrinkling factors for the methane/air flame with time (left) and of the products of all wrinkling factors (right)

Fig. 5 .

 5 Fig. 5. Evolution with time of the flame (left) and of the pressure field (right) for the computed methane/air flame. Units for pressure are mbar.

Fig. 6 .

 6 Fig. 6. Experimental and computed flame trajectory on the axis for the hydrogen/air flame

Fig. 8 .

 8 Fig. 8. Evolution of characteristic wrinkling factors for the hydrogen/air flame with time (left) and of the products of all wrinkling factors (right)


Guillaume Lecocq
email: guillaume.lecocq@ineris.fr

Jérôme Daubech

Emmanuel Leprette

CFD modelling of vented explosions for chambers of two different scales

Keywords: vented explosion, scale effect, hydrogen, CFD

. Different mixture compositions are considered as well as several initial turbulent intensities. This step enables a first assessment of the CFD model. Another set of computations is performed for a 37 m 3 chamber, also free of obstacle, with multiple vents in order to study the robustness of the model predictions when changing the flammable cloud length scale as well as the venting method. The limits of the modelling are finally discussed.

Introduction

Hydrogen is more and more used in the industrial processes in order to contribute to their decarbonization. In practice, hydrogen-based processes are often packaged in sea containers.

A representative but simplified configuration could be an electrolyser installed inside a container, surrounded with numerous pipes for conveying water and the separated gases, eventually large capacity storage vessels and a power supply network, all these elements occupying about at least 30 % of the container inner volume. Doors enable to access the technical zones of the container.

A risk analysis dedicated to this equipment could identify a scenario of a large flammable volume formation inside the container in case of hydrogen leak in the process. If an ignition occurs, a flame will be generated and propagate inside the container with a pressure rise leading to doors or vents opening, if these latter are present. At this stage, if the fresh gases are not totally burned, they can be ejected outside the container where a secondary explosion occurs due to flame propagation in the ejected flammable volume.

The pressure effects of such explosion have to be quantified for the safety study related to the equipment. Computational Fluid Dynamics (CFD) is an attractive tool for addressing an explosion in a container as numerous geometrical effects are at stake. Accounting for them could theoretically bring more accuracy in the results when compared to another approach involving approximations in the problem description. Nevertheless, performing a CFD modelling is not straightforward as it requires skills in numerical methods, knowledge of the explosion physics and of the capacities of the physical sub-models (turbulence, flame / turbulence interaction, …). Numerous CFD approaches were provided in the literature for modelling vented explosions for empty boxes, notably by [START_REF] Duclos | Développement de modèles phénoménologiques et de maitrise des risques d'explosion pour la filière émergente hydrogène-énergie[END_REF][START_REF] Molkov | Fundamentals of Hydrogen Safety Engineering, parts I & II. Free download ebook[END_REF] and [START_REF] Tolias | An improved CFD model for vented deflagration simulations -Analysis of a medium-scale hydrogen experiment[END_REF]. Roughly, they are built in a similar manner but with different sub-models, which is notably explained by the different points of view of the authors concerning numerical models, explosion physics and modelling.

The current paper aims at contributing to the reflexion around the CFD modelling of vented explosion, this one being limited to free of obstacle enclosures. To meet this objective, two configurations are considered:

-A 4 m 3 enclosure with a 0.7 m x 0.7 m vent in which homogenous hydrogen/air mixtures can be ignited. The mixture can be turbulent before ignition or quiescent. Three hydrogen volume fractions are considered. -A 37 m 3 vessel on which are mounted several vents, the total surface being conserved. The dimensions of this vessel are close to those of a 20 ft ISO container. A single equivalence ratio is studied.

CFD computations are performed for each geometry with an approach similar to the one published by Tolias in order to 1) assess if the choice of a set of sub-models can be used for modelling vented explosions with variations of the initial turbulence, hydrogen volume fraction and geometry and 2) evaluate whether the physics of the external explosion can be identified with such modelling or not.

Experimental set-ups

Numerous explosion tests were carried out by [START_REF] Duclos | Développement de modèles phénoménologiques et de maitrise des risques d'explosion pour la filière émergente hydrogène-énergie[END_REF] with an enclosure whose length, width and height are respectively 2 m, 2 m and 1 m. Homogenous flammable H 2 /air mixtures were generated in the box. The parameters of interest were the initial hydrogen volume fraction and the initial turbulence intensity. The mixture is ignited at the centre of a 2 m x 1 m face and the 0.7 m x 0.7 m vent is located on the opposite face. This vent is a plastic sheet that weakly resists to pressure effects.

Figure 1 shows the location of the pressure sensors. Tests that will be studied in the paper are listed in the Table below. Note the turbulence was experimentally characterized with a turbulent length scale and a fluctuating velocity. [START_REF] Daubech | Influence of vent distribution on the violence of a gas explosion[END_REF] supply results of another experimental campaign with explosions in a larger scale enclosure. It is indeed 2.5 m wide and high and 6 m long. H 2 / air homogenous mixtures were formed in the box and the one considered in the current paper, with a hydrogen volume fraction of 15.5 %, was ignited on the small face. The mixture was quiescent before ignition. Venting was ensured by four 0.3 m x 0.4 m vents with an opening pressure of 50 mbar. Two configurations are regarded for the opening surface distribution: either they are grouped on the face opposite to the ignition location or they are split on two faces of the enclosure (Figure 2). The location of the pressure sensors can be seen in Figure 3.

Phenomenology

If the mixture is initially quiescent, after the ignition phase the flame front is expected to selfaccelerate due to Darrieus-Landau and thermo-diffusive instabilities as it was previously observed for spherical lean hydrogen flames [START_REF] Bauwens | Experimental investigation of spherical-flame acceleration in lean hydrogen-air mixtures[END_REF]. If there is an initial turbulence, the flame front acceleration is due to both intrinsic flame instabilities and flame / turbulence interaction. According to lab-scale tests, the flame front wrinkling for a given wave number can be dominantly by one phenomenon or the other depending both on the ratio of the fluctuating velocity, u', and the laminar flame speed S L and on the Karlovitz number [START_REF] Yang | Role of Darrieus-Landau instability in propagation in expanding turbulent flames[END_REF].

When moving, the flame pushes the fresh gases that flow out of the enclosure once a vent is open. Depending on the propagation history of the flame inside the enclosure, the outer flow of fresh gases might differ when the flame exits the enclosure. Roughly, if the flame comes out of the box shortly after fresh gases ejection, the flame will propagate in a vortex, if it exits the enclosure later, propagation will occur in a jet. According to a numerical study, in the first case, turbulence is localized to the shear layer surrounding the jet that pushes the vortex [START_REF] Daubech | Rayleigh-Taylor instability: Modelling and effect on coherent deflagrations[END_REF]. In the second case, it is possible to encounter on a more extended area a more intense turbulence. According to [START_REF] Tolias | An improved CFD model for vented deflagration simulations -Analysis of a medium-scale hydrogen experiment[END_REF], it seems that the external explosion effects can be explained mostly by a flame / turbulence interaction. Other authors like [START_REF] Duclos | Développement de modèles phénoménologiques et de maitrise des risques d'explosion pour la filière émergente hydrogène-énergie[END_REF] and Keenan (2014) estimate the Rayleigh-Taylor instability, related to a sudden acceleration of the flame front when it exits the enclosure, plays a significant role in the pressure effects generation in the external explosion.

Available approaches in the literature

CFD approaches available in the literature for vented explosions mostly rely on Large Eddy Simulation (LES) for turbulence modeling. Nevertheless, applying this method is very expensive in terms of computational resources as the non-resolved kinetic energy should remain below 20 % [START_REF] Pope | Ten questions regarding the large-eddy simulation of turbulent flows[END_REF]. A RANS framework is then preferred in the current paper.

Among the available models for CFD modeling of vented explosions, the one of [START_REF] Tolias | An improved CFD model for vented deflagration simulations -Analysis of a medium-scale hydrogen experiment[END_REF] relies on a RANS framework.

Tolias et al. approach is based on the k-𝜖 model including the modification of Kato-Launder for turbulent correlation closures.

The chemical source term which pilots the propagation speed of the flame front is simply closed as the product of the gradient of the progress variable (𝑐), the volume mass of the fresh gases (𝜌 𝑢 ) and a characteristic flame speed: 𝜌 𝜔 𝑐 = 𝜌 𝑢 S F |∇𝑐|. The flame speed S F then writes: Ξ.S L where Ξ is a wrinkling factor. As evocated previously, the lean hydrogen flames are prone to thermo-diffusive instabilities. The choice of closure for the chemical source term implicitly assumes that differential diffusion effects, responsible of these instabilities, are not accounted for by the diffusion operator in the transport equations. Furthermore, a proper modelling of instabilities might need a sufficient resolution of the flame front thickness by the mesh, which is not encountered in RANS modeling.

The wrinkling factor Ξ has to account for all physical phenomena that locally impact the flame speed.

In the work of Tolias et al., the wrinkling factor is decomposed in a product of wrinkling factors representing independently the effect of a single phenomenon (turbulence, instabilities, flamegenerated turbulence) on the flame front velocity: Ξ = Ξ t Ξ 𝑘 Ξ 𝑙𝑝 . Most of CFD approaches that deal with under-resolved modeling of explosions rely on a similar approach [START_REF] Molkov | Fundamentals of Hydrogen Safety Engineering, parts I & II. Free download ebook[END_REF][START_REF] Duclos | Développement de modèles phénoménologiques et de maitrise des risques d'explosion pour la filière émergente hydrogène-énergie[END_REF]. Recently, [START_REF] Lapenna | Subgrid modeling of intrinsic instabilities in premixed flame propagation[END_REF] proposed a similar sub-grid scale modeling from DNS studies of small-scale premixed flames.

Ξ t models the flame / turbulence interaction. It is closed with the model of [START_REF] Schmid | A model for calculating heat release in premixed turbulent flames[END_REF] that can be applied in all turbulent combustion regimes.

Ξ 𝑡 = 1 + 𝑢′/𝑆 𝐿 (1 + 𝐷𝑎 -2 ) -1/4
where Da is the Damköhler number. Ξ 𝑘 accounts for the effect of flame-generated turbulence, a phenomenon drive by hydrodynamic instability and Ξ 𝑙𝑝 enables to integrate the effect of differential diffusion on the flame speed. Both models were originally proposed by [START_REF] Molkov | Fundamentals of Hydrogen Safety Engineering, parts I & II. Free download ebook[END_REF]. They integrate a progressive increase of the corresponding wrinkling factor with the flame radius (𝑅) towards a maximum value. Thus, Ξ 𝑘 = 1 + (𝜓Ξ 𝑘,𝑚𝑎𝑥 -1)(1 -exp(𝑅/𝑅 0𝑘 )) with Ξ 𝑘,𝑚𝑎𝑥 = (𝜏 -1)/√3, 𝜏 being the thermal expansion rate and Ξ 𝑙𝑝 = Ξ 𝑚𝑎𝑥 𝑙𝑝 /2(1 + tanh((𝑅 -𝑅 0𝑙𝑝 )/0.01)). [START_REF] Molkov | Fundamentals of Hydrogen Safety Engineering, parts I & II. Free download ebook[END_REF] proposed values for the remaining parameters that depend on the hydrogen volume fraction of the hydrogen / air mixture. According to their formulation, the models for Ξ 𝑘 and Ξ 𝑙𝑝 seem to be designed for flames with an hemispherical or spherical shape.

Approaches retained

The computations presented in the current work are based on a modelling strategy close to the one of Tolias. The transport equations are solved for momentum, pressure, a progress variable and energy with a pressure-based solver of the CFD code OpenFoam [START_REF] Weller | A tensorial approach to computational continuum mechanics using object-oriented techniques[END_REF]. Nevertheless, turbulence is modelled with a standard k-𝜖 model and while the chemical source term closure of Tolias et al. was kept, the reference radius 𝑅 0𝑘 appearing in the expressions of Ξ 𝑘 was adjusted to the computed configurations in order to get a predicted pressure peak inside the enclosure at the same time as the measured one. Furthermore, for a volume fraction of 16 %, the value of Ξ 𝑚𝑎𝑥 𝑘 was increased of 50 %, in order to recover the internal peak pressure. Table 2 shows the parameters values retained. For the explosion in the 4m 3 chamber, the computational domain was 22 m long, 20 m wide and 11 m high. It was composed of 5 million hexahedra with a cell size of 4 cm on the flame path. The mesh for the largest chamber, covering a 14 m x 20 m x 12 m domain was made of 5 million hexahedra, the smallest being 4 cm wide. It can be noted here that modelling an experiment with numerous pressure probes is more challenging but brings a safer assessment basis: the L2 signal shows the qualitative agreement of the predicted explosion with the measured one is not fully representative.

Case of the 4 m 3 chamber

Comparison of numerical prediction and measurements for a hydrogen volume fraction of 21 % (Figure 4) shows a P2 pressure peak approached and a large overestimation (about 100 %) for pressure peak L1. The time agreement for pressure peak occurrence inside the box for measurement and prediction seems to lead to a time agreement for the pressure peak occurrence outside of the enclosure. The observations made for the 21 % hydrogen volume fraction case can be kept for the 25 % hydrogen volume fraction case (Figure 5). Finally, a case for which the velocity field inside the enclosure is turbulent before ignition is considered. For this one the hydrogen volume fraction is 21 % and turbulence is characterized by a fluctuating speed of 5 m/s and an integral length scale of 7 cm. With a Karlovitz number of 70, the combustion regime is, according to the combustion diagram [START_REF] Peters | Turbulent combustion[END_REF], a thickened-wrinkled reaction sheet. The model that was used for the quiescent case is kept, the impact of initial turbulence being accounted for in the initialization of the scalar 𝑘 and 𝜖. This modelling (not shown) led to significant overestimation of all pressure peaks. It was chosen to multiply the chemical source term with a damping factor in order to retrieve the pressure signal inside the enclosure. A value of 0.27 has to be taken. It can be seen as a correction for the prediction of instabilities effects when turbulence exists before ignition.

Introducing this correction factor, the pressure signal P2 is recovered (Figure 6), but the pressure peak outside of the box close to the vent, measured in L1, is overestimated (about 100 %).

For other turbulent cases with hydrogen volume fraction of 16 % or 25 %, in the same way a damping coefficient lower than 0.5 should be applied to the chemical source term to recover the pressure signal in P2 (Table 2). If the mixture is initially turbulent, the chemical source term has to be damped by a coefficient which ranges from 0.3 to 0.5, depending on the hydrogen volume fraction. This shows a limit to the generic character of the model which should be applied only for initially quiescent mixtures.

The predicted pressure peak in L1 is either equal or well higher than the measured one. It is possible that the 𝑘 -𝜖 model produces too much turbulence outside the enclosure and/or the assumption of an equilibrium turbulent speed reached instantaneously during flame / turbulence interaction is too conservative.

A secondary peak is predicted for the L2 signal. This one is not existing in reality or is largely overestimated. It is explained by a sudden acceleration on the flame axis when approaching the tip of the flammable cloud. The causes of this can be similar the ones mentioned above for L1 signal.

Case of the 37 m 3 chamber

The CFD model is, in this section, applied to the case of the explosion of a quiescent and homogenous hydrogen / air mixture with a hydrogen volume fraction of 15.5 % in the 37 m 3 chamber. In the computation, the progressive opening of the vent was not modelled. Each vent was replaced with a permanent opening.

The CFD modelling proposed for a 16 % flammable volume in the 4 m 3 chamber was retained. The computation led to an overestimation of the inner pressure peak. In order to retrieve the final pressure peak, the parameter Ξ 𝑚𝑎𝑥 𝑘 was divided by 2.

Figure 7 compares the measured and computed inner pressure signals for configuration 1 and 2. The effect of the vent at the beginning of the signal is not retrieved., nevertheless, in both cases the order of magnitude of the pressure peak is recovered. The external pressure signals outside the chamber can be seen in Figure 8 and 9 for configurations 1 and 2. For configuration 1, the measured pressure peak at L1 is about 50 mbar while the CFD model predicts a peak of 280 mbar. For configuration 2, the measured peak is 25 mbar and the predicted one is 20 mbar.

At the pressure probe L2, the maximum measured pressure is 25 mbar for configuration 1 and 7 mbar for configuration 2 and the respective predicted values are 20 and 14 mbar. The orders of magnitude are recovered. Once more, it appears that the modeling of instabilities in the CFD model is not generic and that the model used should also depend to the geometry. The section of the combustion chamber is a square whereas it was rectangular in the smallest chamber. This may explain that Ξ 𝑚𝑎𝑥 𝑘 had to be adjusted.

The global sequence of the explosion related to configuration 1 first appears similar to the explosion in the small combustion chamber. Nevertheless, the outer flammable cloud is different when the flame exits the enclosure. The outer flammable cloud appears as a jet while in the case of the 4 m 3 chamber took the shape of a large vortex. The overestimation of the prediction of the pressure peak in L1 can be explained by an exaggerated production of turbulence by the 𝑘 -𝜖 model, by an equilibrium assumption for the flame speed and maybe by missing a physical feature. Local extinction phenomena could be encountered.

Conclusions

Computations were performed for vented explosions with varying parameters (hydrogen volume fraction, initial turbulence and geometry). They aimed at verifying if a CFD model similar to these encountered in the literature could predict all these cases.

It appeared that the model for the effects of instabilities in the enclosure had to be modified for certain hydrogen volume fraction and geometries for recovering inner pressure peaks. If initial turbulence was present in the enclosure, a damping factor has to be introduced whose value is difficult to quantify a priori.

The peak pressure of most of the external explosions was overpredicted. It can be due to an overestimation of the turbulence production outside of the box, the assumption of a turbulent flame speed reaching instantaneously its equilibrium value or a part of physics which is missing, like maybe local extinction.

Going deeper in that work is needed to propose a generic way to model the effects of the instabilities on the flame inside the enclosure.

Concerning the external explosion, the pressure effects can be explained by a flame / turbulence interaction. Nevertheless, the outer fresh gases flow should be studied in detail in order to identify the reason the CFD approach of the paper overestimates the pressure effects of the external explosion.

Fig. 1 .

 1 Fig. 1. Locations of the pressure sensors for the 4 m 3 enclosure. View from the top.

Fig. 2 .

 2 Fig. 2. View of the 37 m 3 enclosure and of the possible locations of the vents (in red). Left: configuration 1, right: configuration 2. Panels in blue are safety vents which should not open during the explosion.

Fig. 3 .

 3 Fig. 3. Location of the ignition source and pressure sensors for the 37 m 3 confined explosions (P1, P2: inside pressure -Lent1, Lent2: outside pressure

Figure 3

 3 Figure 3 highlights, for an initially quiescent mixture with a hydrogen volume fraction of 16 %, the pressure signals measured inside the enclosure at two locations, P1 and P2, and outside the box on the axis of the vent. It appears that signals P1 and P2 are distinct whereas identical signals could be expected inside the enclosure for all tests carried out on this enclosure. The reason for this specificity is not known to date. All CFD computations predict same signals for P1 and P2.

Fig. 3 .

 3 Fig. 3. Case of the initially quiescent mixture with a hydrogen volume fraction of 16 %. Comparison of the computed and measured pressure signals inside (left) ou outside (right) the 4 m 3 enclosure.

Fig. 4 .

 4 Fig. 4. Case of the initially quiescent mixture with a hydrogen volume fraction of 21 %. Comparison of the computed and measured pressure signals inside ou outside the 4 m 3 enclosure.

Fig. 5 .

 5 Fig. 5. Case of the initially quiescent mixture with a hydrogen volume fraction of 25 %. Comparison of the computed and measured pressure signals inside ou outside the 4 m 3 enclosure.

Fig. 6 .

 6 Fig. 6. Case of the initially turbulent mixture with a hydrogen volume fraction of 21 %. Comparison of the computed and measured pressure signals inside (left) and outside (right) the 4 m 3 enclosure.

Fig. 7 .

 7 Fig. 7. Comparison of the measured and computed pressure signals inside the 37 m 3 enclosure for the two configurations.

Fig. 8 .

 8 Fig. 8. Comparison of the measured and computed pressure signals at the pressure probe L1 outside the 37 m 3 enclosure for the two configurations.

Fig. 9 .

 9 Fig. 9. Comparison of the measured (left) and computed (right) pressure signals at the pressure probe L2 outside the 37 m 3 enclosure for the two configurations.

Table 1 :

 1 Retained parameters values for modeling the 4m 3 vented explosions. Bold values correspond to adjustments of the original values supplied by[START_REF] Molkov | Fundamentals of Hydrogen Safety Engineering, parts I & II. Free download ebook[END_REF]

	Test

Hydrogen volume fraction Regime before ignition Damköhler number (in initial conditions) Karlovitz number (in initial conditions)

	4 and 36	16 %	Laminar	Undefined	Undefined
	24 and 25	16 %	Turbulent (𝑢 ′ = 2,3 m/s,	20	30
			𝐿 𝑡 = 3,2 cm)
	-	21 %	Laminar	Undefined	Undefined
	23	21 %	Turbulent (𝑢 ′ = 5 m/s, 𝐿 𝑡	35	70
			= 7 cm)
	26	25 %	Laminar	Undefined	Undefined
	28	25 %	Turbulent (𝑢 ′ = 4,5 m/s,	70	60
			𝐿 𝑡 = 7 cm)

Table 2 :

 2 Retained parameters values for modeling the 4m 3 vented explosions. Bold values correspond to adjustments of the original values supplied by[START_REF] Molkov | Fundamentals of Hydrogen Safety Engineering, parts I & II. Free download ebook[END_REF]

	Hydrogen	𝑺 𝑳 (m/s) 𝝉 (-) 𝑹 𝟎𝒍𝒑	𝚵 𝒎𝒂𝒙 𝒍𝒑	(-) 𝚵 𝒎𝒂𝒙 𝒌	(-)	𝑹 𝟎𝒌	𝝍 (-) Reduction
	volume			(m)				(m)		factors for
	fraction									turbulent cases
	16 %	0.505	4.5	0.01	2	3		0.5	1	0.5
	21 %	0.9	5.75		2	(𝜏 -1)/ √3=2,75	0.2	1	0.27
	25 %	1.5	6.45		1,7	(𝜏 -1)/ √3=3,15	0.8	0.8	0.37

Acknowledgements

This work was granted access to the HPC resources of TGCC under the allocation 2021-A0102B11482 made by GENCI (Grand Equipement National de Calcul Intensif)


Charles W Scheel

Hal Wylie

Claire-Heureuse in 'Compère Général Soleil' to Edwidge Danticat's 'Claire of the Sea Light': What Fate for Haitian Marvelous Realism?

de niveau recherche, publiés ou non, émanant des établissements d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

Such echoes make it irresistible to approach Danticat's new book from the angle of "marvelous realism," a notion promoted by Jacques Stephen Alexis in the wake of the "marvelous real," which the Cuban writer Alejo Carpentier had presented in the famous prolog of his novel The Kingdom of this World (1949). A year only after publishing his first novel, Compère, with Gallimard in Paris, Alexis read (in French) his "Prolegomena to a Manifesto of Haitian Marvelous Realism" at the watershed event of the First International Congress of Black Writers and Artists at the Sorbonne in 1956. Alexis's essay formalized a specifically Haitian aesthetic, blending -at times somewhat awkwardly-a synthesis of African and Caribbean cultural inheritances with the dictates of socialist realism. His first novel illustrated such an aesthetic rather convincingly by centering on the destiny of Hilarius Hilarion, a proletarian protagonist, between his imprisonment in Port-au-Prince for stealing a wallet while desperately hungry, and his tragic death during the infamous 1937 mass-slaughter of Haitian cane workers by Dominican armed forces along the aptly named Massacre River bordering the two nations. 2 Between the two events, Hilarius had been enlightened about Haitian society by mixing with communist and union leaders, and also become the common-law husband of a young and pretty woman, Claire-Heureuse, who survived the massacre alone: the couple's new-born baby, Désiré, was killed by Dominican police dogs during the family's flight back to Haiti. Alexis' intense and substantial novel has been likened to a large social fresco of Haiti in the 1930s, and the author's commitment to both his country and the class struggle is expressed in a way -often highly poetic and/or impetuously didactic-that illustrates what Alexis meant by Haitian marvelous realism, in a distinctly epic manner, one he will not resort to in his three later works of fiction. In fact, it is often Alexis's second novel, Les Arbres musiciens (1957, still not translated in English), which foregrounds the "magical" elements in the beliefs of a main protagonist living in the wilderness and of rural communities heavily involved novelists deal respectively, in English, with the legacies of infamous dictators Trujillo and Duvalier, which have weighed heavily on Haitian or Dominican survivors and their offspring to this day. Yet these books, although produced on the basis of a similar history, are very different in tone or style and are likely to strike different chords depending on the reader's familiarity with the French-Haitian and/or Spanish-Dominican literary backgrounds of these young diaspora authors living in the USA. The famous aesthetic notion of "the American marvelous real," which the Cuban writer Alejo Carpentier started promoting in the 1940s, furnished an interesting angle of attack for a study of Diaz's postmodern and postcolonial novel [START_REF] Scheel | Magical Versus Marvelous Realism in French Fiction[END_REF].

with voodoo practices, that is associated with "marvelous realism" or "magical realism," seen as forms of popular cultural resistance to economic and religious oppression by Haiti's political elite and its accomplices: the Catholic church and American capital. Because Alexis's underlying Marxist rhetoric is far more discreet in that second novel, it is easier to see in it an illustration of Carpentier's "marvelous real," understood as a worldview still imbued with a strong faith in ancestral powers, whether of African or pre-Colombian American origin, deemed superior to a Western culture which is considered to have lost its soul in the cult of reason and technological progress.

Marvelous realism versus the marvelous real in the North-American champ littéraire

At this point it should be underlined that, while comparatists in 20 th-century world fiction, familiar with the literary fields of Europe and the Americas, might be aware of the subtle links and distinctions between Carpentier's "marvelous real" and Alexis's "marvelous realism" (and their common or respective historical links with the far more popular notions of "surrealism" and "magical realism"), the two notions are often fused together or mixed up. Also, their receptions in an Anglophone country like the USA, are hardly comparable in quantitative terms. If we play with keywords on various databases (starting with the MLA's), references to Carpentier and the "marvelous real" are usually ten to twenty times more numerous than the ones to Alexis and "marvelous realism." This discrepancy in popularity is the result of two phenomena: firstly, the resonance of Carpentier's publications in Spanish within the huge Latin-American world and the international attention gained as of the 1960s by its "Boom" writers ("for whom Carpentier prepared the ground," as formulated by Kramer 2014); secondly, the fact that English translations of Carpentier's works started appearing in New York as early as 1957 (The Kingdom of this World), over forty years before the first Alexis novel appeared in the States. Within the Americas, the potential public of francophone Caribbean literature (from Haiti and the French départements of Martinique, Guadeloupe and Guyane) was limited from its start in the 1950s to a literate elite of about 3 to 10% of the populations in those small territories, and to the Québec readership (itself only starting to develop on a large scale in the 1960s). And while readers of fiction in Spanish had access to translations of Compère as early as the 1970s, scholars of Caribbean literatures had to wait till 2008 for the Spanish translation of Alexis's 1956 Manifesto -almost a halfcentury after its publication in French and English, and exactly 60 years after the original publication of Carpentier's famous "Prólogo."

In light of these considerations, it is hardly surprising that except for the groundbreaking Canadian publications in English, by [START_REF] Dash | Toronto: Black Images[END_REF][START_REF] Dash | Toronto: Black Images[END_REF] on both Alexis and his manifesto "Of the Marvelous Realism of the Haitians," the reception of Alexis's works in American academia was de facto limited to departments teaching francophone literature in French 3 or to Quebec. 4 In this context, the publication in the USA of an English translation of Alexis's masterwork of Haitian literature in 1999 appears almost miraculous and has rekindled interest in Alexis, as witnessed by a recent article in an American publication [START_REF] Kramer | Marvelous Realism in the Caribbean: A Second Look at J. S. Alexis and Alejo Carpentier[END_REF]. Surely 1955 was not a good moment for an American editor to even think of publishing a book so glowingly and explicitly committed to communism as Compère, but it strikes one as odd that it was not done at the latest in the seventies. Whatever be the reasons for such a tardy publication, one cannot but admire the translation offered by Carrol F. Coates and the beautiful editorial and printing job of this Caraf Book by the University Press of Virginia. 5

Coates's General Sun, My Brother and marvelous realism

So late in the season, Coates's good work might not allow Alexis to "catch up" with Carpentier's reputation in Anglophone (not to mention Hispanic) academia, but the Caraf edition is bound to become the main reference for readers of the novel in English and both the translation and Coate's introduction to Alexis's novel need to be assessed critically. Thus while the blurb on the book, offered on the University of Virginia Press web page,6 mentions that Alexis's first novel "has brought comparisons to the work of Emile Zola, André Malraux, Richard Wright, and Ernest Hemingway," it seems to me that John Steinbeck would constitute a more suitable reference than Hemingway, as it should become clear further down. The blurb also states that "a militant Marxist himself, Alexis championed a form of the 'marvelous realism' developed by the Cuban novelist 3 This is how this (French) reader discovered Compère in a graduate course on Black Francophone literature at UT-Austin in the late 1980s, given by Hal Wylie, who also published one of the few studies on Alexis in English (1989) and saluted the novel's long-awaited translation (2000). 4 Thus, one of the most interesting studies of Alexis's marvelous realism in French was produced in Québec in 1987 by Maximilien Laroche, an Haiti-born connoisseur of Haiti literature and culture, unfortunately published in a Laval University research journal that was not easily accessible from abroad (in the same year, the same research group also published a study by Cecilia Ponte, "Le Réalisme merveilleux dans Les Arbres musiciens de J. S. Alexis").

5

Even if the choice of a slick and elegant page layout may translate into vexing readability issues, signaled by various reviewers, including Hal Wylie, for whom "the only problematic aspect is the way Coates handles the Creole sprinkled through the work. He insists upon the new 'standard' or 'American' spelling of Kreyòl, distancing it from the old orthography which made clear its relation to French. He even puts proverbs in French in the original into Kreyòl. And when Alexis placed a note at the bottom of the page, Coates sends us to the glossary in the back of the book." (Wylie 2000.) Alejo Carpentier, who called for a vision of historical reality from the standpoint of slaves for whom the supernatural was as much a part of everyday experience as were social and other existential realities." Both halves of this statement strike me as problematic because, as previously emphasized, Carpentier offered not a marvelous realism but a marvelous real. 7 Nor should Carpentier's "marvelous real" be reduced to its illustration in The Kingdom of this World, in which some of the narrative is, indeed, focalized by an illiterate and yet astute slave, Ti Noelbut only some.

Just what Alexis's marvelous realism was cannot be summarized easily, and although Coates's 24-page introduction to his translation is quite balanced on the whole and extremely informative for readers with little knowledge of Haitian literary and political history, the two paragraphs dedicated to the question of marvelous realism and its origins are as problematic as their further reduction on the book's back cover. While Coates does well to mention the stimulating visits in Haiti by Nicolás Guíllen (1942), Alejo Carpentier (1943) and André Breton (1945-46), and the original impact of Césaire's négritude in those years (p. x), he does not make clear that by 1955-1956, Alexis had long rejected both Breton's surrealism (because while in Paris he felt much closer to the ex-surrealist but then communist Louis Aragon) and négritude (because he wanted to stress the various facets of Haiti's cultural makeup and not reduce it to only its African roots -a point finely analyzed as early as 1978 by Claude Souffrant in Une Négritude socialiste). Even more problematic is the paragraph on Carpentier in which Coates equates the latter's alleged idea of the "marvelous American realism" with "magical realism" (x). Such a confusion is common, often unexplained, sometimes willful, 8 and not restricted to comments about Carpentier.9 When referring to Carpentier, we need to remember that Carpentier had adamantly distinguished his "marvelous American real" from both surrealism and magical realism, which he considered as flawed by their European origin and alleged artificiality. In the same paragraph, Coates wants to illustrate Carpentier's "marvelous realism [sic]" by mentioning "stereoscopic vision" (with reference to 7 This very common confusion is also apparent in Marco Katz's 2012 article on Carpentier and "Marvelous Realism and a New Place for America." 8 Attempts at differentiating between the two notions exist too. Thus Margaret Heady, who had published in French on "Le merveilleux et la conscience marxiste dans Les arbres musiciens de Jacques-Stephen Alexis" in 2002, offered an interesting comparative study in English (2005) about "double consciousness" in Alexis and Simone Schwarz-Bart novels. But this reader fails to understand the theoretic underpinnings of what she calls a Caribbean "discourse of the marvelous" on the one hand, and "the narrative technique of magical realism" on the other. Laroche 1987, 8). Unfortunately that particular notion is a good example of the alleged European artificiality that Carpentier denounced.10 A short but excellent critical analysis of the history of these different aesthetic movements was provided in Haiti by philosopher Jacques Gourgue in his introduction to an anthology of texts under the title "Du Surréalisme au Réalisme Merveilleux" (1992,(6)(7)(8)(9). Gourgue opined that, in a country like Haiti, where popular imagination expresses itself in an "ordinary delirium" both surrealism and Carpentier's marvelous real were "conservative theories" (7), and that "the aporias of the aesthetics of both Carpentier and Alexis [these Siamese twins that are so easily mistaken] stem from their desire to seize art as if it were perfectly circumscribed […] when they refer to images and not to things" (9, my translation).

Coates devotes another paragraph specifically to Alexis's 1956 Paris lecture "Of the Marvelous Realism of the Haitians," from which he quotes a sentence about the various cultural sources of Haitian art and the inclusion, in marvelous realism, of the mysterious, of dreams, of beauty and even of ugliness. He then notes that Alexis had also claimed recognition for Kreyòl "as a language and not simply a patois" (xii). This is true but very incomplete. Considering the importance of the notion of Marvelous Realism in the history of Haitian literature and with regard to Compère especially, it is regrettable that Coates should not have quoted more precisely the four point-summary that Alexis gave at the end of his clearly programmatic manifesto: 1) sing the beauties of the Haitian fatherland, its greatness as well as its misery […]; 2) reject art without any real or social content; 3) look for expressive words suitable for its people […]; 4) have a clear awareness of the precise, concrete and current problems and real dramas that the masses are confronting, in order to touch them, and to lead the people in its struggles. (Alexis 1956, 268) It seems rather clear that, whatever cultural concessions Alexis makes in points 1 and 3 about the "specifically Haitian beauties" and the "suitable words" to express them, points 2 and 4 mean that Haitian artists were expected to harness themselves to a program that corresponded to the agenda of socialist realism. Alexis's essay paid barely lip service to any artistic freedom. If we bear this in mind, it is hard to ignore that Compère is overall a precise illustration of points 1, 2 and 4 of this program (point 3 needs to be bracketed out, since the vast majority of Haitians could not have understood -and certainly not read-Alexis' lofty French prose). Further down in his introduction, Coates explains how the five years (1955)(1956)(1957)(1958)(1959)(1960)) of Alexis's amazingly rich literary production as a fiction writer, run parallel to his growing political involvement with unionism and communism, from the Haitian to an increasingly international scene, culminating in his fateful choice "to put down the pen and pick up the gun to become a guerillero"11 and fight with his own hands the newly-risen dictator in his country. Towards the end of his analysis of the novel's structure, Coates does state that Alexis wrote "of course, a 'Communist' novel," with a realistic presentation of misery, political corruption, a deleterious U.S. involvement, and a people that kept faith in spite of all that (xxii). It is therefore puzzling that his concluding lines about the novel's French title, Compère Général Soleil, are these:

Referring to Hilarion's role as a kanzo, I would propose that General Sun/Legba is, in fact, the guardian spirit, the sustainer of life, and the leader of the true nèg, the Toma d'Ayiti. Thus, this novel, rejected by some readers as 'communist,' is not simply a 'proletarian novel' but a novel of Haitian common men and women, steeped in Haitian traditions and initiated into Haitian religion, believing profoundly in the value of human existence and love, and following the spirits of his ancestors, most notably, Brother General Sun/Legba. It should be indisputable that the hero in General Sun's army here is "comrade" or "brother" Paco Torres, the Dominican worker who lost his job for being a union leader and who died for having the courage to call for a strike among the cane-cutters, thus prompting Trujillo to restore discipline and make for a whiter population in the D.R. by ordering the slaughter of thousands of Haitian workers. Even if Alexis did portray the amazing feats that could be performed by participants in voodoo services when overcome by the spirit, or the human solidarity shown by a Christian Dominican shepherd like Cocozumba, the narrator of Compère leaves no doubt about his skepticism where religions are concerned, voodoo included: "It is frightening how Africa weighs on these poor people" (102). In the chapter devoted to the voodoo service held in Hilarion's hometown Leogane, the narrator tells that the "damned lieutenant had to be paid [….] so that the forbidden rites could take place" (106), because voodoo and Protestantism had been fought by the Catholic Church in Haiti since 1835. But the whole endeavor initiated by Hilarion's mother to pacify the allegedly angry voodoo gods is described by the narrator in internal focalization on Hilarion, and he observes that the poor people in the country "have to sacrifice their last pennies for masses and requiems and then they pray to the deaf old gods of Africa […] but nothing works. As Jean-Michel says, it's time to stop praying, for God's sake, and to rebel!" (90). The reunion (only "tolerated" by the local police officer) ends in a disaster that forces Hilarion's cousin Josaphat to flee to the D.R. after he killed the officer who tried to rape his young sister. In any case, it was not to reinstate voodoo (that was done gradually by François Duvalier as of 1957), that Alexis came back from Cuba to Haiti in 1961, but to launch a communist party and lead the Haitian army of workers to victory against exploitation -and not back to the spirit of the African ancestors.

It has been observed by many commentators that the literary treatment of voodoo by Alexis (and by Roumain) is ambiguous, but anybody doubting Alexis's priorities in "the struggle" should read his little known but wonderfully clever and erudite open letter to Father Salgado (1958), in answer to the latter's dismissive review of Les Arbres musiciens, Alexis's second novel, which he had dedicated to "his friends among the new generation of Catholic Haitian priests." 12The most telling statements in this letter, in the midst of many pages of a passionate apology of Haiti's popular religion as a means of survival and cultural resistance to shameless exploitation by a corrupt government and shameless repression by the Catholic church, are the ones in which Alexis claims that, although not a Catholic himself, he concedes "that the adoption of Catholicism by great masses of Haitians would mean that our people has finally gotten over the semi-tribal, semi-feudal stage in order to enter the indispensable passage to capitalism and modern technique" (Souffrant 219, my translation).

Ever since Michel Seonnet's rather poetic, and lavishly illustrated, biography of J.S. Alexis, 13 it seems to me that there has been a tendency to water down Alexis's commitment to communism while stressing his blackness and his alleged endorsement of voodoo as the authentic Haitian cultural trait. I believe that where Compère is concerned (and Les Arbres musiciens too), such readings stretch the texts. Very recent studies stress again Alexis's decidedly political targets. 14 Also, in a detailed comparative analysis of Carpentier and Alexis's respective theories and literary works, Nicholas Kramer argues convincingly that: the absence of the mention of Carpentier in Alexis's writing is due not so much to a desire to erase the strong influence the Cuban had exerted upon him, but rather to the fundamentally divergent theory of Haitian identity that Alexis had established. Alexis draws upon Carpentier's theory of marvelous realism [sic] not as a model to imitate, but as a paradigm against which to define his own more politically engaged and Haiti-specific writing. ( 232)

To go back to Coates's introduction to Compère, as Coates observes, "the novel personifies the sun as the ally, brother, and leader of the peasants." Just like Roumain's hero Manuel taught the peasant masters of the dew to organize their work as a cooperative, or a "koumbite," Alexis has Hilarion express his own final message of the necessity of communist action, in a grandly epic style rather typical of so-called "social realism," and reminiscent of Bigger Thomas's sudden articulateness at the end of Richard Wright's Native Son (1940), or of the highly symbolic final images of John Steinbeck's Grapes of Wrath (1939). Alexis's Compère clearly ties up with such proletarian or social novels of the 1930s, rather 13 A book which revealed a lot about the inner turmoil of a man constantly torn between several facets of his personality, a book much read by the new young militants, which has been labeled as "weird," "shaggy," "inspirational," and as "mixing the creative with the scholarly" (Wylie 1989, 32). 14 Thus Pierre Schallum concludes his interdisciplinary dissertation (2013) by hoping that Alexis's marvelous realism, which he calls "a neo-humanism," will inspire future studies that "will enrich the kind of thinking that Edouard Glissant calls, not without reason, le Tout-Monde" (312, my translation). In his discussion of Alexis's exchange with Father Salgado, Schallum underlines what had been pointed out by others before him, that even if Alexis defended the right of people to choose voodoo as their religion (or cultural practice), Alexis (and Roumain) considered religion as an opium and that its promotion by the Haitian Griots and ethnologists "was more propaganda for an alleged 'African soul' than science" (257).

than with later works more concerned with cultural identity and the search of roots. To conclude any presentation of Compère, I feel it should be pointed out that beyond its undeniable engagé and social realist aspect, Alexis managed to paint a large fresco of contemporary Haiti in a decidedly poeticized narrative couched in impeccable, stylistically varied, often sophisticated or even erudite French, a novel of much wider scope than Roumain's previous masterpiece of a peasant novel written in creolized French, an artistic masterpiece in a new aesthetic theorized by its very creator. To a large extent and in fascinating formal variations, the combined qualities of a poetic narration and an undeniable political involvement,15 evident in Compère and theorized in "Le réalisme merveilleux des Haïtiens" also inform the next works published by Alexis, as Elisabeth Mudimbe-Boyi indicated in the very apt title of her 1992 study, L'oeuvre romanesque de Jacques-Stephen Alexis, une écriture poétique, un engagement politique.16

From Claire-Heureuse to the female characters in Claire of the Sea Light What is Claire-Heureuse's part in General Sun, My Brother? Her original encounter with Hilarion, as a young and pretty girl swimming naked in the sea, provided an idyllic love scene, and her honesty, strength of character, intelligence, and hard work made her the ideal companion and supporter of an Hilarion equally willing to learn and do well. But her decision to follow Hilarion, while pregnant, to work in the Dominican cane-fields to make a living, after their economic situation in Port-au-Prince became unbearable, added to the final tragedy. The dying Hilarion urges her "to remarry and to continue to work for a Haiti where people can live in dignity and peace." 17 Then Claire is left alone in a remote area, totally exhausted by days of flight and heartbroken over the death of the baby and of her companion. She is truly "mal-heureuse." Not only left "alone" (the final word of the novel) but much worse-off than Annaïse, the female protagonist in Masters of the Dew, who, in the end, lost her man but carried hope in her belly ("la vie nouvelle") and can count on the support of Manuel's parents to raise her and Manuel's child in his hometown. Assuming Claire-Heureuse makes it back to Port-au-Prince to convey Hilarion's message to Jean-Michel, the communist doctor, and tell him that he was right in his commitment to the cause, it is hard for the reader to imagine how she will have a life, apart from getting some support perhaps from her Godmother, to go back to her street-vending activities. Her part in the novel, just like the ones of the few other strong women who helped her during her stay in Macoris (Conception, who rented them a room, and Domenica, the painter, who hid them from the militia after Paco was killed, and found them a guide to lead them back to the border), was only supportive. It was Claire and the baby who gave Hilarion the incentive to move on and fight for a better job and the kind of instruction dealt by unionists, before he was forced out of town to work in the cane fields. But Claire herself was not instructed in the class struggle.

Edwidge Danticat may have been living in the States for several decades by now but her involvement with her country of birth and with Haitian literature in particular has been ongoing. It is therefore hardly surprising that her very positive review of the English translation of "Jacques Stephen Alexis' masterpiece Compère Général Soleil, [...] this brave and timeless narrative [by a] most committed and enormously talented writer" should feature prominently in the description of the Caraf edition. 18Danticat's most recent novel is completely set in Haiti -a fairly contemporary one-and its heroine is another Claire, not "Happy-Claire," but "Claire of the Sea Light." It may be stated from the start that there is nothing comparable, in Danticat's sober prose, to Alexis's poetic flights (starting with the striking modernism of the Prolog of Compère that tells of sordid events in a highly aestheticized manner, and several other lengthy passages of a descriptive and lyrical rather than narrative nature) or to Alexis's political rants (expressed by the narrator or various characters) about the country's history, the fate of the Haitian worker, and the glory of unionist commitment. Thus we may note from the start that a main ingredient of Alexis's marvelous realism, the exhortation to the class struggle, is missing. Yet Danticat's novel, although not constituting nearly as large a social fresco as Compère, also depicts various facets of current Haitian society in a small town 19 while developing a plot that includes several tragic events -often linked to stark class differences and a corrupt political system. Certain things, like poverty and acts of violence, do not appear very different from what Alexis knew in the 1930s, even if the scale of horrors may not be anymore what they were under the Stenio Vincent and Duvalier regimes. If there is a political "hero" in Danticat's book, it is probably the local radio hostess Louise George, who allows people to unveil personal and often controversial stories, one of which leading to the suicide of a young and rich rapist, ten years after the facts. But her kind of committed journalism centers on feminist issues rather than on the class struggle.

So in spite of a title, Claire of the Sea Light, that is as poetically phrased as Alexis's General Sun, My Brother, Danticat's themes and her discourse strike one at first as far removed from Alexis's committed marvelous realism, both in its poetic and political sense. What Danticat has been doing in her books is pushing the frontiers of her linguistic, social, and literary consciousness into the Haitian Diaspora in the USA, thus expanding the awareness of Haitian reality in directions that Alexis could not have foreseen when he wrote in the 1950s as a male, French-educated doctor, writer and political activist.

What kind of Haitian marvelous realism could be left in a novel in which the heroine, Claire "Limyè Lanmè" -as her name would be in her Creolespeaking world-on her emotion-laden seventh birthday, runs down from the Ville Rose lighthouse to leave her poor fisherman father's shack and become the adopted daughter of the widowed bourgeoise, Madame Gaëlle?

"In this stunning novel about intertwined lives, Edwidge Danticat crafts a tightly woven, breathtaking tapestry that explores the mysterious bonds we share -with the natural world and with one another" says the synopsis of the book by Random House on the back cover, and "intertwining" is indeed -and again-the key word in Danticat's discourse. The plot centers on Claire and the unusual events on her seventh birthday, but it also explores the lives of about a dozen characters which intersect during some fifteen years in the fictive small town of Ville Rose in contemporary Haiti. The book is divided in two parts of four chapters each and framed by chapters entitled respectively "Claire of the Sea Light" and "Claire de Lune" -the latter consisting of a pretty pun on the French expression "clair de lune" or moonlight. Here Claire, named after her mother and the "light of the sea" (two words which happen to have the same pronunciation both in French -la mer/mère-and in Creole -lanmè), exits the novel under the moonlight and with an adoptive mother.

Within the book, the proximity of birth and death is heavily thematized: life appears as fragile and permanently threatened by nature's or mankind's outbursts. At dawn on Claire's seventh birthday, the sea, in the guise of a freak wave, takes away an old fisherman -and would have taken Claire's father away too, had he not been running a bit late on that day; that same night the sea brings back the body of a drowned young man, who might be resuscitated or not. Claire observes all this from the seaside, while her own life is about to change drastically: she is to leave her father's shack and be adopted by a rich widow who had lost her own daughter, Rose, in a street accident on Claire's fourth birthday.

The book's composition underlines a paradoxical sense of both randomness and circularity -even a certain fatalism. Such a feature does not square with the mainly socialistic and nationalistic thrust or the "dialectical materialism" of Alexis's conception of marvelous realism: Hilarion was killed for a reason and by an enemy, not by accident. At the end of Compère, Claire-Heureuse, although half-dead with exhaustion and half-demented by grief, is still supposed to help with the class struggle. At the end of Claire, we can only hope that Claire's accepted new life with rich Madame Gaelle will be better than with her poor but loving father. In the final section of Compère, the narration is almost exclusively left to an (unlikely) heroic first-person discourse held by the dying Hilarion, which leaves Claire in a silent witness position. In Claire, Claire hardly speaks because she is shy and mostly alone, but the narration is focalized internally on her and we learn that after her bewildered run to the lighthouse (which was her way of expressing her own will), she is now intent on going back one more time to her father's place before moving on towards a very open future.

What also changes quite a bit from Compère is the portrayal of characters, especially the female ones. Claire Narcisse, Claire's mother, was a simple person but also loving and wise in the handling of corpses because of her job in a funeral parlor, and perhaps also wise in foreseeing her early death in childbirth: she had established a tie with Mme Gaelle during the latter's pregnancy and thus paved the ground for Claire's later adoption, when her father decided it was time for him to find a better job -presumably in the D.R., which is still a potential reservoir of employment for destitute Haitians, in spite of the historical massacres at the border and a rampant anti-Haitian racism. Mme Gaelle is not a proletarian figure but a wealthy business woman, financially and sexually independent after her husband's accidental death in a gang war on the very day she had given birth to their daughter.

Even more "modern" in Claire is Jessamine, a young Haitian-American woman from Miami, who visits Haiti for the first time and accompanies Max Ardin Junior on his return home after ten years in the States. She is only Max's friend, since the latter is gay, and she finds out via a radio program, that Max had raped his family's teenaged housemaid when he was nineteen, and that a boy was born of that single sexual contact. The most radical character in the book is Flore Voltaire, that former Ardin housemaid turned manager of a beauty parlor who, for revenge, not only comes in order to coldly introduce her ten-year-old son to the boy's father, but invites herself to a radio-show in which she tells the sordid tale of her rape for all the town to hear. While Max's father is merely annoyed by the revelation, his son is so affected that he attempts suicide by wading into the sea in his red shirt.

Most intriguing, perhaps, among the female protagonists of the novel, is Louise George, a single woman, independent radio journalist, and occasional lover of Max Ardin Senior, the respected owner of the town's reputed private school. Louise accepted to interview Flore Voltaire in her challenging "Tell me" program, because she wanted to get back at Max Ardin who had let a student's mother slap her in his office, in retaliation for having herself slapped the boy for unruly behavior in a class. Flore also told on the radio program how Max Senior offered her money to make up for her rape, while sending his son to his mother in Miami, so that he need not deal personally with the consequences of his action.

Conclusion

These are a few examples of how in many distinct scenes, often quite innocuous seeming, Danticat's narrative exposes the various threads that interconnect several personal lives, thus furnishing a fairly rich and realistic but also a thrilling picture of contemporary life in a Haitian small town, without ever taking sides or promoting a political attitude. If some of the characters experience some nice moments, there is no insistence on any "marvelous" quality of Haiti's nature or society: people are varied, no character is idealized, and life is insecure or unpredictable for most people, especially the poor. Young as she is, Claire of the Sea Light seems to be aware of all that and ready to take the plunge, away from her father's familiar presence and on to the mysterious world of Mme Gaelle, who wears a slick wig, lives in a villa and drives a Mercedes.

What is marvelous in the book is the quiet and methodic way in which its rich and realistic social tapestry is woven. As a story, it is also greatly successful because of its subtle and intriguing composition. But the novel's style and mood are as far removed from Alexis's aesthetic of marvelous realism as from the "hip neo-baroquism" and the "postmodernist magical realism" of Junot Diaz's Oscar Wao, 20 or from the egotistic, erotic, and macho playfulness of a Dany Laferrière. More than the political and cultural line that still separates today Creole-speaking Haiti from the Spanish-speaking Dominican Republic on the Hispaniola map, could it be that, where the contemporary literary aesthetics of the writers of the Haitian and Dominican diasporas are concerned -all the way from the Caribbean, up to New York and Montreal, via Miami-the divide, both marvelous and realistic, be ultimately a matter of gender? 21 20 See Scheel 2014. 21 A stark contrast of that nature was already underlined by Marie Dominique Le Rumeur in her study "Apogée ou déclin du réalisme merveilleux des Haïtiens ?" which she concludes thusly: "The marvelous does not show up in the extraordinary anymore but in the poetics of reality and in the details of daily life. / When claiming the word, women hardly feel like theorizing.

[…] Surely Haitian women [writers] are still talking about the marvelous but their perspective is different.

[…] Far removed from clichés, their breath symbolizes hope, the will to face adversity, and the permanent struggle to attain love. Just it is the case with Danticat, the marvelous in Lahens or Jan J. Dominique finds refuge in the unremarkable, in the daily

  (xxxiii) Brother General Sun = Legba? How could that be, when towards the end of the novel, Coates translated the following sentences in Hilarion's impassioned death speech to Claire-Heureuse: I thought my illness[epilepsy] was caused by an evil spell cast by Brother Sun. And yet, General Sun is a great man -he has always been the friend of poor black men[…]. The great truth is that the sun of Haiti shows us what we have to do. Pierre Roumel, Jean-Michel, Paco, and all the others finally understood that. I didn't want to become a soldier in General Sun's army as they did. I have always been a hardheaded man, a bad man, one who follows his own way! […] You must give birth to another Hilarion, other Désirés, and only you can create them. […] Tell Jean-Michel that I saw the light the day when a great red sun lit the chest of a worker named Paco Torres. Tell him he has to follow that sun! (289-290, italics mine)

See http://books.upress.virginia.edu.

In a recent, substantial publication on Haitian Exile literature, Martin Munro mentions "Alexis's magical realism"(2007, 61, 87) when I suspect he meant his "marvelous realism."

"Stereoscopic vision" was claimed by writers like Ernst Jünger and Massimo Bontempelli who had given a futuristic and/or mystical twist to Franz Roh's original 1925 coining of the phrase "magical realism" as a new, post-expressionist aesthetic in European painting[START_REF] Scheel | Magical Versus Marvelous Realism in French Fiction[END_REF].

As Souffrant put it (193, my translation).

Salgado's review and Alexis's answer to it were appendixed in Souffrant 1978; I am not aware of a published English translation.

This combination lies at the core of a redefinition of marvelous realism as a narrative mode[START_REF] Scheel | Magical Versus Marvelous Realism in French Fiction[END_REF] 2005).

A similar approach had already been chosen in French academia by a comparatist from Venezuela, Marina Boadas, in her 1987 dissertation on "Le réalisme merveilleux dans l'oeuvre de Jacques Stephen Alexis."

According to the Caraf description of the novel. Actually, Claire and Hilarion were not married, for such an institution is presented as bourgeois in the novel; what Hilarion tells Claire is that "she needs to have a life and other babies."

Quoted in the pre-title pages of General Sun, My Brother. Nor is it surprising that her expertise led her to function as co-translator, with Coates, for the English translation of Alexis's last novel, L'Espace d'un cillement (1959), published in the Caraf collection under the title In the Flicker of an Eyelid in 2001.

It may not be mere coincidence that the novel, set in a town called Ville Rose, is dedicated to Danticat's mother, Rose, and to her own daughters, and that in the acknowledgments she thanks her "family in Leogane for introducing and reintroducing [her] to the sea."


Cheikh T Bop

Kamel Hammami

Arame Ndeye

Nejmeddine Diago

Jaidane

Ndeye A B Faye

N Jaïdane

Excitation ro-vibrationnelle du fluorure de césium (CsF) induite par collision avec He

come

Introduction

L'étude du transfert d'énergie ro-vibrationnelle induit par collision a attiré une attention particulière ces quatre dernières décennies. Cela a été motivé par ses applications innombrables dans divers domaines tels que l'astrophysique, la physique du plasma et la chimie des molécules froides. Dans ce travail, pour une meilleure interprétation de l'expérience de Borkenhagen et al., nous avons étudié l'excitation ro-vibrationnelle du système collisionnel CsF-He.

Méthodes

Ce travail est effectué au moyen des calculs ab initio en deux étapes:

La 3D-SEP du système CsF-He a été calculée avec la méthode de clusters couplés standard incluant un traitement perturbatif de la triple excitation (CCSD(T)) implémentée dans le logiciel MOLPRO 2010 (Werner et al.). Les atomes F et He ont été décrits avec la base aVQZ et le césium avec le pseudo potentiel relativiste à 9 électrons de valence ECP46MDF. A ces bases, ont été ajoutées des fonctions de liaison placées à mi-distance entre le centre de masse de CsF et He. L'erreur de superposition des bases à été corrigée avec la procédure du contre poids.

En utilisant cette 3D-SEP, nous avons calculé les sections efficaces ro-vibrationnelles de CsF induites par collision avec He avec la méthode close-coupling implémentée dans le programme MOLSCAT (Hutson & Green) pour des énergies thermiques allant jusqu'à 500 cm -1 . Des tests de convergence ont été effectués pour fixer les paramètres de MOLSCAT à savoir R max , R min , STEP et j max .

Résultats et Discussions

La Fig. 1 présente une coupe bidimensionnelle de la SEP, on note une forte anisotropie de l'interaction entre 0 • (approche de He du coté de F) et 180 • (approche de He du coté de Cs). Cette SEP présente deux puits de potentiel, le plus profond est localisé à θ =∼ 75 • et R = 6.5 a 0 avec une profondeur de ∼ 60 cm -1 . Les coefficient radiaux de la 3D-SEP (qui seront utilisés dans les calculs dynamiques) sont représentés à la Fig. 2. Pour λ > 0 le terme V 001 est dominant. La Fig. 3 montre des courbes de sections efficaces rotationnelles pour des transitions 0 -→ j (panneau gauche) et ∆j = 1 (panneau droit). Des résonances apparaissent aux faibles énergies cinétiques. Ce comportement provient du fait que l'hélium soit temporairement piégé autour du puits de potentiel où le complexe CsF-He forme des états quasi-liés. A partir du panel gauche, on observe une règle de sélection en faveur des transitions vers des valeurs de j impaires ce qui provient de la dominance du terme V 001 . Les sections efficaces ro-vibrationnelles obtenues dans ce travail ont été comparées avec les résultats expérimentaux de Borkenhagen et al. aux Tab. 1 et 2, un bon accord est observé.

Fig. 1 :Fig. 3 :

 13 Fig. 1: Contours de la surface d'énergie poten-Fig. 2: Expansion des coefficients radiaux V 00λ tielle bidimensionnelle du système CsF -He (pour λ = 0, 1, 2, 3) du système CsF -He en en fonction de R et θ. fonction de R.CsF-He-XS-0--j

Remerciements

Nous remercions l'ICTP qui a financé ce travail à travers le programme NET 45.


Dr Gabriel Morin Geap

Keywords:

New paradigm in leadership theories:

-leader & leadership as 2 distinct attributes; -their potential development in the individual is key.

Introduction

Cross-cultural leadership (Gelfand et al., 2007;Kirkman et al., 2006;Leung et al., 2005;House et al., 2004;Hofstede, 2001)

Lancaster

Military leadership & semantics: B: many examples of definition given by the officers interviewed

-"imposing your will and persuading other people to do things they might not actually want to do and get them want to do it for you";

-"vision, conviction, courage, communication and compassion. Conviction is passion in work, in individuals, in teams. For courage it is physical, moral and still emotional. Compassion is something nice and empathetic, it is a mixture of the two, something that says you have to be human, as a leader, you can be very hard and sometimes it is necessary, because you have to send people into important dangers, sometimes you have to accompany them";

-"passion, perspective, patience, inquisitiveness and warmth.";

-"a blend of trust and loyalty that go up and down and sideways."

F: absence (of word in the French language and no definition given by the officers interviewed)

Results: military leadership both near & far

How military leadership is made: two distinct paths that meet heterogeneous objectives

-Time & content are different; -F: embrace the entire military career, transforming a 20 year-old student into a future military leader capable of developing a vision; -B: make a high school graduate a platoon commander as quickly as possible; -Motto: Saint-Cyr "They study to vanquish" vs Sandhurst "Serve to lead"; -4 years vs 10 months.

How military leadership is made: institutionalization of leadership in the

House treaties ( 2

 2 , intercultural awareness, political awareness, self, empathy) General skills (communication, persuasion, confidence, physical courage, charisma, influence, change catalyst, networking) Managerial skills (attraction & retention of talents, team orientation, conflict management, moral courage, development of individuals) Leadership (social/relational capital) Leader (human/individual capital) retention of talents, team orientation, conflict management, moral courage, development of individuals) Leadership (social/relational capital) Leader (human/individual capital) the use of case study -Primary data: 25 officers interviewed + participating observation led in each army; -Secondary data: internal HR documents, official military guides published by each army, reviews of military strategy thinking and research, military books and press articles published in military journals; -Triangulation of the data. Sample: grounded theory (Glaser & Strauss,1967) -Average age: 43 years; -Average grade: colonel; -All have experienced the military leadership of the other army in at least 2 experiences. Data processing and analysis: grounded theory (Glaser & Strauss,1967) -Full transcription of the interviews (50 days); -Use of a software analysis date (NVivo); -Interview: average duration 52min, 154 pages of transcription, 112 409 words.

  British Army, essentially empirical in the French Army -Selection method: Leadership potential vs academic; -Training: fighting spirit (rugby, boxing), bayonet & Lieut. Col. Herbert Jones vs the place of the officer (front scene vs background), the vision & the "effet majeur" (major effect); -Victory vs "beau geste" (beautiful gesture): "the British have the cult of victory, I am not saying that we are not interested in victory but a beautiful defeat suits us too." the need for space in leadership development -"I was given some good advice once which I try to follow when it comes to delegate responsibility you should delegate so much that you feel uncomfortable. The moment you feel uncomfortable that's probably when you're about right. I think for the French that would be seen as 'we don't do that'. We give more freedom, more space, and more room to move to officers."

	Discussion: French military leader vs British military leadership
	How F and B military leadership differ
	1. The making of military leadership: leader (human capital) F vs leadership
	(social capital) B,
	2. Military leadership & space: How F & B military leadership look like
	1. Military leadership & semantics: leadership serving command, means vs end
	2. Military leadership & time: culture, authority & leadership
	-"Culture and leadership are two sides of the same coin" (Schein, 2004): the Suez
	Expedition (1956);
	-Why leadership became so mandatory: collapse of tradition & authority (Arendt,
	1972).

 -"We try to develop a theory from the reality not the contrary as the French do"; -Grandes Ecoles (mainly based on written & academic skills) vs the culture of leadership (from primary school to Sandhurst).

Military leadership & time: history

-Rupture (revolution) vs continuity (tradition); -Current situation: highly committed army F vs no major commitment B; -Deep mutual respect for the culture & history; -Same understanding of leadership evolution in a VUCA world ("in society today it is easier to say 'no' than it used to be").