Olivier Herbinet
email: herbinet@ensic.inpl-nancy.fr

Baptiste Sirjean

Frédérique Batin-Leclerc

René Fournet

Paul-Marie Marquaire

Thermal decomposition of norbornane (bicyclo[2.2.1]heptane) dissolved in benzene. Experimental study and mechanism investigation

Keywords: Pyrolysis, Norbornane, Bicyclo[2.2.1]heptane, Mechanism investigation, Low conversion, Diradical mechanism

The thermal decomposition of norbornane (dissolved in benzene) has been studied in a jet stirred reactor at temperatures between 873 and 973 K, at residence times ranging from 1 to 4 s and at atmospheric pressure, leading to conversions from 0.04 to 22.6%. 25 reaction products were identified and quantified by gas chromatography, amongst which the main ones are hydrogen, ethylene and 1,3-cyclopentadiene.

A mechanism investigation of the thermal decomposition of the norbornane -benzene binary mixture has been performed. Reactions involved in the mechanism have been reviewed: unimolecular initiations 1 by C-C bond scission of norbornane, fate of the generated diradicals, reactions of transfer and propagation of norbornyl radicals, reactions of benzene and cross-coupling reactions.

Introduction

While the thermal decomposition of cyclanes has been the subject of several papers, there are only few studies about the reactions of polycyclanes and the corresponding kinetic parameters are still very uncertain.

The geometry and the enthalpy of formation of norbornane or bicyclo[2.2.1]heptane (C 7 H 12 ), a bridged bicyclic alkane (Figure 1), have been previously studied in order to relate the structure of the molecule to its strain. 1,2 A ring strain energy of 17,2 kcal.mol -1 has been estimated for norbornane 2 (the ring strain energy is defined as the difference between the experimental gas phase enthalpy of formation and the gas phase enthalpy estimated using the group additivity method proposed by Benson 3 for the estimation of thermochemical data). Baldwin and al. [START_REF] Baldwin | [END_REF] studied the thermal isomerization of 3-butenyl-cyclopropane to norbornane. It was observed that 3-butenyl-cyclopropane lead to norbornane and many other hydrocarbons when heated at the temperature of 688 K. It was also established that the formation of norbornane occurs through the scission of the C2-C3 bond of 3-butenyl-cyclopropane and might involve the initial generation of a diradical (Figure 2).

Figure 1

Figure 2 O'Neal and Benson studied the kinetics of pyrolysis of some non-bridged bicyclic alkanes (e.g. bicyclo[2.2.0]hexane, bicyclo[3.2.0]heptane) from the point of view of diradical intermediates. 5 Diradical mechanism estimates were found to be consistent with experimental Arrhenius parameters for a large number of hydrocarbons. Reaction channels for the fate of diradicals were proposed by Tsang in the case of cyclopentane and cyclohexane. 6,7 Direct studies of trimethylene and tetramethylene diradicals have been performed by Pedersen and al. by using femtosecond laser techniques with mass spectrometry in a molecular beam. 8 More recently, Sirjean et al. performed quantum calculations about the gas phase unimolecular decomposition of cyclobutane, cyclopentane and cyclohexane by using a diradical mechanism. 9 The theoretical approach used for the calculation was validated by comparing calculated results with available experimental data. Several papers about the pyrolysis of tricyclo[5.2.1.0 2,6 ]decane, a tricyclic alkane, have been published. [10][11][12][START_REF] Davidson | 37th Joint Propulsion Conference[END_REF][START_REF] Herbinet | [END_REF] Indeed this hydrocarbon is a component of synthetic fuels used in aeronautics. A comprehensive primary mechanism of the pyrolysis of this species has been developed in our laboratory. [START_REF] Herbinet | [END_REF] The reactions of unimolecular initiation of this polycyclic compound have been detailed and the reactions of diradicals (decompositions by β-scission, internal disproportionnations) have been taken in account on a systematic way.

The first purpose of this article is to present new experimental results of the pyrolysis of norbornane (solid at room temperature) dissolved in benzene. In line with previous work on hydrocarbons, [START_REF] Herbinet | [END_REF][15][16][17] experiments have been performed in a jet stirred reactor which was operated at temperatures between 873 and 973 K, residence times between 1 and 4 s, at a pressure of 106 kPa and at high dilution. Conversions ranging from 0.04 to 22.6% have been obtained. The attention has been paid to the analysis of the products of the reaction. The formation of 25 major and minor products has been observed. The second objective of this paper is to describe the reactions involved in the mechanism of the pyrolysis of the norbornane -benzene binary mixture. These reactions include all the possible channels of unimolecular initiation of norbornane using a diradical approach as in the case of tricyclo[5.2.1.0 2,6 ]decane. [START_REF] Herbinet | [END_REF] Cross-coupling reactions due to the presence of benzene in the feed of the reactor have been also reviewed although it will be shown later in this paper that benzene is not very reactive under the operating conditions of this study.

Experimental Section

The apparatus (Figure 3) used for the experimental study of the thermal decomposition of norbornane (dissolved in benzene) has already been described in two papers about the pyrolysis of tricyclo[5.2.1.0 2,6 ]decane [START_REF] Herbinet | [END_REF] and n-dodecane, 15 respectively Its main features are reminded and specificities linked to the dissolution of norbornane in benzene are discussed below.

Figure 3

Experiments were performed in a continuous quartz jet stirred reactor operated at constant temperature (inner volume of about 90 cm 3 ). This reactor was designed to be perfectly stirred for residence times ranging from 0.5 to 5 s. 18,19 The heating of the reactor was achieved using Thermocoax heating resistors coiled around the vessel. Temperature inside the reactor was measured with a type K thermocouple which was located at the level of the injection cross at the center of the vessel. Before entering the reactor, reactants were preheated to the reaction temperature to avoid the formation of temperature gradients inside the gas phase due to the endothermal properties of the pyrolysis reaction.

The residence time of the reactants inside the annular preheater was very short, i.e. about 1% of the residence time inside the reactor. Pressure inside the reactor was set equal to 106 kPa and was controlled with a control valve set downstream the products analysis devices.

Unlike most hydrocarbons having close molecular weights, norbornane (C 7 H 12 ) is solid at room temperature. The melting point of pure norbornane at atmospheric pressure is 360 K 20 and its boiling point is 381 K. 21 In order to study the pyrolysis of norbornane with the same apparatus as that used for n-dodecane and tricyclo[5.2.1.0 2,6 ]decane, [START_REF] Herbinet | [END_REF]15 solid norbornane has been dissolved in a solvent.

Benzene was chosen since it is a good solvent for many hydrocarbons and because, as an aromatic compound, it is very unreactive at low temperature. Norbornane used for the experiments was provided by Aldrich (mass fraction purity greater than 0.98) and benzene was provided by Fluka (mass fraction purity greater than 0.99).

The liquid reactant (20 wt% norbornane, 80 wt% benzene) was stored in a pressurized glass vessel.

Before performing experiments nitrogen bubbling and vacuum pumping were performed in order to remove oxygen traces dissolved in the hydrocarbon mixture. The liquid reactant mass flow rate was controlled by a mass flow controller, mixed to the carrier gas (helium 99.995% pure) and evaporated in a single pass heat exchanger, the temperature of which was set above the boiling point of the diluted hydrocarbon mixture. The molar composition of the mixture at the inlet of the reactor was 0.7% norbornane, 3.6% benzene and 95.7% helium.

Products leaving the reactor have been analyzed by gas chromatography. Analyses were performed in two steps. Light species (which are gaseous at room temperature such as hydrogen and hydrocarbons containing less than 5 carbon atoms) were analyzed on-line by two gas chromatographs. The first chromatograph was fitted with a carbosphere packed column and both a flame ionization detector (FID) for the detection of methane and C2 hydrocarbons and a thermal conductivity detector (TCD) for the detection of hydrogen. Argon was chosen as carrier and reference gas in order to detect hydrogen with a better sensibility. A first analysis was performed with a constant oven temperature of 303 K to separate the hydrogen peak from the helium peak (experimental carrier gas). A second analysis was performed with a constant oven temperature of 473 K for the hydrocarbons separation. Retention times (in min) were: methane: 2.4, acetylene: 5.3, ethylene: 7.3 and ethane: 9.6. The second chromatograph used for light species analyses was equipped with a FID for the hydrocarbons detection and a Haysep D packed column. This column gave a good separation for hydrocarbons from methane to C 5 hydrocarbons. In particular the peaks corresponding to species like allene and propene or like 1-butene, 2-butene, 1,3butadiene and 1-butyne were well defined. Retention times (in min) for species whose formation was observed during the study were: methane: 2.6, ethane: 15.5, propene: 61.2, allene: 70.9, propyne: 73.5, 1-butene: 106.6, 1,3-butadiene: 107.7 and 1,3-cyclopentadiene: 147.8. Species identification and calibration were performed with gaseous standard mixtures provided by Air Liquide and Messer. Heavy species (hydrocarbons containing more than 5 carbon atoms which are liquid or solid at room temperature) were condensed in a trap connected at the outlet of the reactor and maintained at liquid nitrogen temperature during a determined period of time. After this time of accumulation, the trap was disconnected and solvent (acetone) and a known amount of internal standard (n-octane) were added.

When the temperature of the trap was back to a temperature close to 273 K the mixture was poured into a sampling bottle and then analyzed by gas chromatography. A first analysis was performed with a gas chromatograph fitted with a capillary HP-1 column and a FID for the separation and the detection of hydrocarbons. Oven temperature profile was set to: 313 K held 30 min, rate 5 K.min -1 , 453 K held 62 min in order to obtain a good separation of the products of the reaction. Retention times of main products of the reaction (in min) were: 1,3-cyclopentadiene: 3.7, benzene: 4.9, norbornane: 7.3, toluene: 7.9, styrene: 17.4, indene: 38.8, naphthalene: 46.3, biphenyl: 53.3. Calibration was performed with prepared solutions containing small amounts of quantified hydrocarbons and of n-octane (internal standard). A second analysis was performed for the identification of the products of the reaction with a gas chromatography-mass spectrometry system working in the same conditions than the gas chromatograph used for quantification (same column, same carrier gas, same carrier gas flow rate, same oven temperature profile). This procedure allowed us to obtain the same chromatograms with both chromatographs so that direct comparison of the peaks could be performed. Identification of the products separated by the HP-1 column was performed by comparison of the mass spectrum corresponding to the detected peaks with the numerous mass spectra included in the library NBS 75K which was provided by Agilent with the GC-MS apparatus.

The consistency between the different chromatographic analyses was verified from products which were present on two chromatograms (like 1,3-cyclopentadiene, methane and ethane). In each case the relative variation between the mole fractions corresponding to the different analyses was less than 5%.

The repeatability of experimental results has been studied. Calculated maximum uncertainties in the experimental mole fractions were ±5% for species analyzed on-line and ±8% for heavy species condensed in the trap. Carbon to hydrogen ratios (C/H ratios) in the products have been calculated. For this calculation all species have been taken in account except norbornane (this species has no influence on the value of the C/H ratio), benzene, toluene, styrene, naphthalene and biphenyl (these four last species mainly come from benzene). An average value of 0.60 (± 0.02) has been obtained. This value is slightly above the theoretical value (7/12=0.58) but it should be kept in mind that a rigorous distinction between products from the norbornane and from the benzene (C/H ratio of 1) is not possible.

Experimental Results

Norbornane -benzene binary mixture. The evolution of the conversion of norbornane with residence time is shown on Figure 4. Because the values of the difference between the mass flow rates of norbornane entering and leaving the reactor were not accurate enough for such low conversions, the values of conversion presented on this graph were deduced from the products of the reaction apart from aromatic and polyaromatic compounds (toluene, styrene, indene, naphthalene and biphenyl produced in very small quantities). Under the conditions of the study, these last products probably derived from benzene. At higher conversions aromatic and polyaromatic compounds could be formed through secondary reactions from small unsaturated hydrocarbons and from 1,3-cyclopentadiene. No evolution of the mass flow rate of benzene was observed between the inlet and the outlet of the reactor under the operating conditions of our study. Benzene appeared to be very stable corresponding to very low conversions.

Figure 4

Twenty five products of the thermal decomposition of the norbornane -benzene binary mixture have been analyzed. These products are (by increasing molecular weight): hydrogen, methane, acetylene, ethylene, ethane, allene, propyne, propene, 1-butene, 1,3-butadiene, 1,3-cyclopentadiene, 1,3cyclohexadiene, 1,4-cyclohexadiene, 5-methyl-1,3-cyclopentadiene, 1,3,5-hexatriene, toluene, 3-ethylcyclopentene, ethenyl-cyclopentane, 4-methyl-cyclohexene, methylene-cyclohexane, styrene, indene, naphthalene and biphenyl. An unidentified minor product (molecular weight of 94 g.mol -1 according to mass spectroscopy) has been detected between toluene and styrene.

It is worth noticing that the formation in small amounts of several species having the same molecular weight as norbornane has been observed: 3-ethyl-cyclopentene, ethenyl-cyclopentane, 4-methylcyclohexene and methylene-cyclohexane (Figure 5). The evolution of the mole fractions of these four products with residence time is shown on Figure 6. The possible channels of formation of these particular species which were observed even at very low conversion (less than 0.5%) will be discussed later in this paper. The formation of very small quantities of aromatic and polyaromatic compounds such as toluene, styrene, indene, naphthalene and biphenyl was also observed. These species probably come from reactions of benzene or from cross-coupling reactions of the norbornane -benzene binary mixture. The presence of benzene in the feed of the reactor masked the possible formation of small quantities of this species as specific product from norbornane. product is defined as the ratio of the mole fraction of the considered product and the sum of the mole fractions of all products) at a temperature of 973 K and a residence time of 1 s. This figure shows that the three main products of the reaction are hydrogen, ethylene and 1,3-cyclopentadiene which are formed in similar quantities. Figure 8 shows the evolution of the mole fraction with residence time of these three main products, as well as methane, propene, 1,3-butadiene, toluene and biphenyl.

Figure 7

Figure 8 The primary products of the reaction of the thermal decomposition of norbornane dissolved in benzene were determined from a study of the selectivity performed at a temperature of 953 K (corresponding to a maximum conversion of 15%). A species is probably a primary product if the extrapolation to origin of its selectivity versus residence time gives a value different from zero (corresponding to a non zero initial rate of production). According to this study 15 species seem to be primary products: hydrogen, methane, ethylene, ethane, propene, 1-butene, 1,3-butadiene, 1,3-cyclopentadiene, 1,3-cyclohexadiene, toluene, 3-ethyl-cyclopentene, 4-methyl-cyclohexene, methylene-cyclohexane, ethenyl-cyclopentane and biphenyl. The values of selectivities to origin of these products are given in Table 1. Species with the highest selectivities at origin are hydrogen (0.346), ethylene (0.314) and 1,3-cyclopentadiene (0.184). Unlike toluene and biphenyl (Figure 9a) other aromatic and polyaromatic compounds (styrene, indene and naphthalene) do not seem to be primary products (extrapolations to origin of their selectivities versus residence time are close to zero; Figure 9b). This can be explained by the fact that toluene and biphenyl can be obtained directly from phenyl radicals derived from benzene (by combination of phenyl radical and methyl radical for toluene, by selfcombination of phenyl radicals or by ipso addition of phenyl on benzene for biphenyl) whereas styrene, indene and naphthalene can not be directly formed from primary radicals generated by the decomposition of norbornane and benzene. Amongst species having the same molecular weight as norbornane 3-ethyl-cyclopentene has the largest selectivity to origin.

Table 1

Figure 9 Influence of the benzene on the kinetic of the reaction. A short study of the thermal decomposition of pure benzene was performed in order to determine if benzene plays a role in the kinetics of the reaction of pyrolysis of the norbornane -benzene binary mixture. Experiments were performed at temperatures between 913 and 973 K, at residence times ranging from 1 to 4 s and at a pressure of 106 kPa. The molar composition of the flow entering the reactor was 96.4% helium and 3.6% benzene (the mole fraction of benzene at the inlet of the reactor was fixed to the same value as in the case of the study of the binary mixture norbornane -benzene for direct comparison).

Figure 10 shows the evolution of the conversion of benzene with residence time at temperatures between 913 and 973 K (the conversion were deduced from the products of the reaction). Under these operating conditions benzene appeared to be very stable. A maximum conversion of benzene of 8×10-2 % was obtained at a temperature of 973 K and a residence time of 1 s. For comparison the conversion of norbornane (dissolved in benzene) was 9.7% under the same conditions.

Figure 10

The only product of the reaction which was detected was biphenyl. Hydrogen is probably another product of the reaction [22][23][24][25] but it was not detected (TCD is known for being a much less sensitive detector than the FID). The formation of toluene, styrene, indene and naphthalene was not observed. These species which were observed in the case of the norbornane -benzene binary mixture were probably formed from cross-coupling reactions or from specific reactions of norbornane.

Mole fractions of biphenyl which were obtained in both studies (pure benzene and norbornanebenzene binary mixture) have been compared. The two graphs of Figure 11 display the evolutions of the mole fractions of biphenyl with residence time (Figure 11a) and with temperature (Figure 11b). This figure shows that the mole fraction of biphenyl is always slightly larger in the case of the norbornanebenzene binary mixture than in the case of benzene (apart from the experiment leading to the lowest conversion and performed with a temperature of 913 K and a residence time of 1 s; Figure 11b). It can also be observed that the variation between the mole fractions obtained during the two studies increases with conversion.

While interactions between the two hydrocarbons do exist during the thermal decomposition of the norbornane dissolved in benzene, the conditions of our study (temperatures less than 973 K) are such that the presence of benzene has a negligible influence on the reactions of norbornane. In a recent paper 26 El Balkali et al. showed that in the case of the oxidation of an equimolar n-heptane -benzene binary mixture the presence of benzene had very little influence on the reactivity at low temperature.

Figure 11

Comparison with the reaction of pyrolysis of tricyclo[5.2.1.0 2,6 ]decane. Experimental results obtained during this study have been compared with previous ones obtained with tricyclo[5.2.1.0 2,6 ]decane, [START_REF] Herbinet | [END_REF] a tricyclic alkane the structure of which contains the structure of norbornane (Figure 12). This tricyclic alkane can be considered as a norbornane structure sharing two adjacent carbon atoms with a cyclopentane structure.

Figure 12

Figure 13 displays the evolution of the conversions of norbornane (dissolved in benzene) and tricyclo[5.2.1.02,6]decane obtained at temperatures ranging from 873 to 973 K, at a residence time of 1 s and at a pressure of 106 kPa. The mole percentages of norbornane and tricyclo[5.2.1.0 2,6 ]decane at the inlet of the reactor were set equal to 0.7%. This figure shows that the reactivities of the two polycyclic alkanes are very similar.

Figure 13

The thermal decomposition of tricyclo[5.2.1.0 2,6 ]decane leads to the formation of large amounts of hydrogen, ethylene, propene, 1,3-cyclopentadiene and cyclopentene. [START_REF] Herbinet | [END_REF] While hydrogen, ethylene and 1,3-cyclopentadiene were also amongst the main products of the thermal decomposition of norbornane, propene appeared to be a minor product and the formation of cyclopentene was not observed. An analysis of the kinetic model of the pyrolysis of tricyclo[5.2.1.0 2,6 ]decane [START_REF] Herbinet | [END_REF] shows that cyclopentene and allyl radicals (precursors of propene) mainly come from the cyclopentane part of the structure of tricyclo[5.2.1.0 2,6 ]decane. between the products and the reactants, and E -1 is the activation energy of the reverse reaction of closure of the diradical. If it is considered that the ring strain energy of norbornane 2 is equal to 17.2 kcal.mol -1 , that diradicals BR1 and BR2 have the same ring strain energy than cyclopentane (6,3 kcal.mol -1 ) and that BR3 has the same ring strain energy than cyclohexane (0 kcal.mol -1 ), the terms ∆E TC are equal to 10.9 kcal.mol -1 for BR1 and BR2 and to 17.2 kcal.mol -1 for BR3. If we approximate that the sum ∆H(C-C)+E -1 is equal to about 87 kcal.mol -1 (this was observed for cyclopropane, cyclobutane, cyclopentane and cyclohexane [START_REF] Herbinet | [END_REF] ) we obtain activation energies of 76.1 kcal.mol -1 for BR1 and BR2 and of 69.8 kcal.mol -1 for BR3.

Discussion

Figure 14

In previous studies of the pyrolysis of cyclanes and polycyclanes 6,7,9,14 it has been shown that diradicals could react through three ways:

(1) by combination to give back the initial (poly)cyclane; this reaction is the reverse step of an unimolecular initiation by C-C bond scission.

(2) by internal disproportionnation through a (poly)cyclic transition state intermediate; an unsaturated molecule is then obtained.

(3) by decomposition by β-scission; products of the reaction depend on the position of the two radical centers. In most cases, a smaller diradical and a molecule are obtained.

Figure 15

Kinetic parameters of these reactions have been estimated for cyclobutane, cyclopentane and cyclohexane by quantum calculation by Sirjean et al.. 9 This study showed that the easiest reaction is the reverse reaction by combination of the diradical formed by the unimolecular initiation (this is why cyclanes and polycyclanes present a greater stability than linear and branched alkanes). If we except this last reaction, the internal disproportionnation is largely easier than the decomposition by β-scission (apart from the particular case of cyclobutane in which the β-scission is easier because the broken C-C bond is in β position of the two radical centers). It is worth noticing that in the early stage of the reaction, (poly)cyclanes mainly lead to the formation of molecular species through diradicals and that they do not lead directly to the formation of free radicals. Thus at very low conversion the concentration of radicals is very low and the primary molecular initiation products from the reactant mainly react by unimolecular initiations to form new diradicals or free radicals. react by unimolecular initiations to form diradicals and/or free radicals.

13

During experiments the formation of small amounts of 3-ethyl-cyclopentene, ethenyl-cyclopentane, 4methyl-cyclohexene and methylene-cyclohexane (corresponding to MA4, MA2, MA6 and MA5 on the scheme of Figure 15) has been observed in the early stage of the reaction. These species can be obtained through internal disproportionnations of diradicals generated by the unimolecular initiations of norbornane and/or through metatheses of radicals involved in transfer and propagation reactions of the decomposition of the norbornyl radicals (but this last source of formation is in competition with more probable reactions of β-scission and isomerization). Thus 3-ethyl-cyclopentene, ethenyl-cyclopentane, 4-methyl-cyclohexene and methylene-cyclohexane likely come from the initiation step of norbornane (this is in accordance with the observation of the formation of these species at very low conversion).

The formation of 1-methylene,3-methyl-cyclopentane (MA1 on Figure 15) has not been observed under the conditions of our study. This is probably because the diradical BR1 is more likely to react by reaction of termination by combination to give back norbornane. Unlike 3-ethyl-cyclopentene and ethenyl-cyclopentane the formation of 4-ethyl-cyclopentene (MA3 on Figure 15) was not observed. This may be explained by the fact that the bicyclic structure of the transition state which connects diradical BR2 and MA3 is more strained than the transition states which connect BR2 with MA2 and MA4. Study of the selectivity of the products of the reaction showed that MA2, MA4, MA5 and MA6 seemed to be primary products (extrapolations of their selectivities to origin gave values different from zero). Among these four species MA4 (3-ethyl-cyclopentene) has the highest selectivity at origin (Table 1) which also means that it has the highest initial rate of formation. This let us suppose that the unimolecular initiation of norbornane to diradical BR2 followed by the internal disproportionnation to MA4 is the easiest path of the initiation step.

Possible unimolecular initiations of 3-ethenyl-cyclopentene (main initiation product from norbornane) are given as an example (Figure 16). The breaking of the two vinylic C-C bonds of MA4 are not written on the scheme of Figure 16 because the bond dissociation energy is much higher than those of alkylic and allylic C-C bonds.

Figure 16

Reactions of unimolecular initiation by breaking of C-H bonds can also be considered but these reactions are more difficult than reactions of unimolecular initiation by breaking of C-C bonds. These reactions can lead to the formation of the three norbornyl radicals shown on Figure 17; but this channel of formation is negligible compared to the reactions of metathesis of radicals from norbornane (see below).

Figure 17

Transfer and propagation reactions of norbornyl radicals. The molecule of norbornane owns three different carbon atoms. Reactions of metathesis of hydrogen atoms and radicals with norbornane lead to the formation of three norbornyl radicals (Figure 18).

The three norbornyl radicals can react by decompositions by β-scission to lead to the formation of six cyclic radicals (Figure 19). These six new radicals can then react by decompositions by β-scission, by isomerizations and by metatheses (H abstractions) with molecules. Figure 20 displays the reactions of β-scission, metathesis and isomerization of radical R6 from Figure 19. Only isomerizations involving allylic hydrogen atoms have been taken in account on this scheme. The metatheses of radical R6 with molecules lead to the formation of 3-ethenyl-cyclopentane (MA4) but these reactions are less probable that the reactions of β-scission and isomerization.

Estimations of activation energies of reactions of β-scission by opening of the ring of cyclopentyl and cyclohexyl radicals 9,27 showed that the values used for linear and branched alkyl radicals [28][29][30] cannot be used in a systematic way for cycloalkyl radicals. [START_REF] Herbinet | [END_REF] Norbornyl radicals have a more complex structure than cyclopentyl and cyclohexyl radicals and activation energies of their reactions of β-scission by opening of the ring are very uncertain. Moreover for some (poly)cyclic radicals (e.g. cyclopentyl radicals) the activation energy of the β-scission of C-C bonds may be much higher than the value used for linear and ramified alkanes [28][29][30] and the reactions of β-scission of C-H bonds may become competitive with the reactions of β-scission of C-C bonds.

Figure 20

Uncertainties on the kinetic parameters of reactions involved in the transfer and propagation steps of the norbornyl radicals make the discussion difficult at this stage of the study. Nevertheless it can be noticed that some radicals (like the radicals R6 and R7 of Figure 19) can lead to the formation of ethylene and cyclic C5 radicals which are precursors of 1,3-cyclopentadiene.

Figure 21

Reactions of benzene. Benzene is known for being a very stable hydrocarbon. At low temperature primary reactions of the pyrolysis of benzene are rather simple. 31 The only reaction of unimolecular initiation is the breaking of a C-H bond (bond energy of 110.9 kcal.mol -1 ). Breaking of a benzylic C-C bond of benzene is very difficult because of the high energy of this type of bond (120.8 kcal.mol -1 ).

Bimolecular initiation (reverse reaction of a termination by disproportionnation) consists in the transfer of an hydrogen atom from a molecule of benzene to another. This step leads to the formation of a phenyl radical and a 2,4-cyclohexadien-1-yl radical. Activation energy of this reaction of bimolecular initiation (close to the enthalpy of the reaction: 94.4 kcal.mol -1 ) is rather high. Under the conditions of our study, unimolecular and bimolecular initiations of benzene are probably negligible compared to unimolecular initiations of the norbornane which have lowest activation energies (part of the strain energy of norbornane is recovered during ring opening [START_REF] Benson | Thermochemical Kinetics[END_REF] ).

The initiation step mainly leads to the formation of hydrogen atoms and phenyl radicals (Figure 21).

Hydrogen atoms can reacts by reaction of metathesis with benzene to form an hydrogen molecule and a phenyl radical, by self combination to form hydrogen molecule (this trimolecular step is negligible) and by addition to benzene to lead to the 2,4-cyclohexadien-1-yl radical. Phenyl radicals can react by self combination or by addition to benzene (followed by the loss of an atom of hydrogen) to form biphenyl. Sivaramakrishnan et al. 32 observed the formation of acetylene and diacetylene from the decomposition by C-C bond β-scission of phenyl radical under extreme conditions (high temperature, high pressure benzene pyrolysis study behind reflected shock waves). 2,4-cyclohexadien-1-yl radical can react by C-H bond β-scission to give benzene, it can decompose by C-C bond β-scission to give 1,3,5-hexatrien-1-yl radicals and then acetylene and 1,3-butadien-1-yl radicals and can lead to 1,3-cyclohexadiene and 1,4-cyclohexadiene by metathesis on molecule. But under the conditions of the present study of benzene pyrolysis, i.e. at low temperature (below 973 K) and close to atmospheric pressure, decomposition of phenyl and 2,4-cyclohexadien-1-yl radicals does not occur and the formation of acetylene and unsaturated C4 hydrocarbons was not observed. This is in agreement with the observation of the formation of mainly hydrogen and biphenyl by Brooks and al. who studied the pyrolysis of benzene at temperatures between 873 and 1036 K in a static reactor. 25 According to Brioukov et al. 31 , which performed the analysis of the experimental results obtained by Brooks and al. 25 , the decomposition of benzene is dominated by the unimolecular initiation generating an hydrogen atom and a phenyl radical followed by the short propagation chain composed of the reaction of metathesis of an hydrogen atom with benzene and the reaction of ipso addition of a phenyl radical to benzene leading to biphenyl and an hydrogen atom.

Cross-coupling reactions of the benzene -norbornane binary mixture. Comparison between experimental results obtained during the study of the pyrolysis of pure benzene and that of norbornane dissolved in benzene showed that there are low interactions between the two hydrocarbons. There are very few possibilities of cross-coupling reactions (mainly reactions of metathesis and reactions of termination) because the primary mechanism of pyrolysis of benzene generates few species.

Bimolecular initiations involving norbornane and benzene molecules lead to the formation of the three norbornyl radicals and of 2,4-cyclohexadien-1-yl radical (Figure 22). Activation energies of these reactions (between 80.5 and 89.4 kcal.mol -1 according to the transferred hydrogen atom) are little higher than those of unimolecular initiation of norbornane but lower than the unimolecular initiation of benzene and than the bimolecular initiation of two molecules of benzene. Hydrogen atoms and radicals deriving from benzene (phenyl radicals and 2,4-cyclohexadien-1-yl radicals) can react by metatheses with norbornane to form the three norbornyl radicals (hydrogen, benzene, 1,3-cyclohexadiene and 1,4cyclohexadiene are obtained respectively). In the same way radicals deriving from norbornane (more numerous than in the case of benzene) can react by metatheses with benzene to lead to phenyl radicals (Figure 22). Reactions of termination between radicals deriving from the two hydrocarbons can explain the formation of some products like toluene: this last species can be obtained from the combination between a phenyl radical (deriving from benzene) and a methyl radical (deriving from norbornane and not from benzene at such low temperature).

Figure 22

Conclusions

New experimental results of the thermal decomposition of norbornane dissolved in benzene have been obtained in a jet stirred reactor. A great attention was paid to the identification and the quantification of the products of the reaction. The formation of 25 both major and minor species has been observed during the experiments. Main products were hydrogen, ethylene and 1,3-cyclopentadiene. The detection of minor species having the same molecular weight as norbornane gave interesting information about the reactions of unimolecular initiation of norbornane. The study of the selectivities of the products of the reaction showed that 15 species were probably primary products and values of extrapolations to origin of selectivities let us think that the easiest initiation of the norbornane leads to the formation of 3-ethenyl-cyclopentene. The use of benzene as solvent of norbornane appeared to be a good choice because benzene was very unreactive under the operating conditions of our study: firstly interactions between the two hydrocarbons remained low and the reactivity of norbornane was little affected by the presence of benzene; secondly unimolecular initiations of norbornane (most probable initiation steps)

were not masked by initiations involving benzene and the formation of molecular product from the diradicals generated through the initiations could be observed.

Reactions that occur during the pyrolysis of norbornane and during the pyrolysis of benzene have been reviewed and described. Cross coupling reactions in the case of the norbornane -benzene binary mixture are rather limited because the decomposition of benzene generates only few species at low temperature. The kinetics of the reactions of unimolecular initiation by breaking of the C-C bonds which are part of a ring structure, reactions of the diradicals (termination by combination, termination by disproportionnation and decomposition by β-scission) and reactions of decomposition by β-scission leading to the opening of a ring (e.g. reactions of β-scission of the norbornyl radicals) will require to be better investigated with reliable estimations of the kinetic parameters of these specific and sensitive reactions.

Figure 5 Figure 6

 56 Figure 5

Figure 7

 7 Figure 7 displays the distribution of the products in term of selectivity (here the selectivity of a

  Most of the reactions involved in the pyrolysis of polycyclanes are still badly known and the related kinetic parameters are still very uncertain. We describe here the reactions involved in the mechanism of the thermal decomposition of the norbornane -benzene binary mixture and the possible channels of formation of the products of the reaction are discussed Unimolecular initiations by bond scission of norbornane. Fate of diradicals. Unlike linear and branched alkanes for which two free radicals are directly obtained, unimolecular initiations of polycyclic alkanes by breaking of a C-C bond lead to the formation of diradicals (species with two radical centers). The molecule of norbornane (bicyclic alkane) has three different C-C bonds. The unimolecular initiations can lead to the formation of the three diradicals BR1, BR2 and BR3 shown on

Figure 14 .

 14 Figure 14. According to O'Neal and Benson 5 the activation energies of these reactions are given by the

Figure 15

 15 Figure 15 displays the possible internal disproportionnations and decompositions by β-scission of

Figure 2 .

 2 Figure 2. Isomerization of 3-butenyl-cyclopropane to norbornane through a diradical intermediate as proposed by Baldwin et al.. 4

Figure 4 .

 4 Figure 4. Evolution of the conversion of norbornane with residence time. ( 873 K, 893 K, 913

Figure 5 .

 5 Figure 5. Structure of products having the same molecular weight as norbornane. (a)

Figure 6 .

 6 Figure 6. Evolution of the mole fractions of products having the same molecular weight as norbornane.

Figure 7 .Figure 9 .

 79 Figure 7. Distribution of the products of the reaction at a temperature of 973 K and at a residence time

Figure 10 .

 10 Figure 10. Evolution of the conversion of benzene with residence time.

Figure 11 .

 11 Figure 11. Comparison of mole fractions of biphenyl obtained in the two studies. Evolution with

Figure 12 .Figure 14 .Figure 15 .Figure 16 .

 12141516 Figure 12. Structure of the tricyclo[5.2.1.0 2,6 ]decane.

Figure 17 .Figure 18 .Figure 19 .

 171819 Figure 17. Reactions of unimolecular initiation of norbornane by breaking of C-H bonds.

Table 1 .

 1 Values of selectivities at origin of primary products of the reaction of pyrolysis of norbornane in benzene at a temperature of 953 K. Structure of norbornane (bicyclo[2.2.1]heptane).

	Species

  Reactions of the radical R6 of Figure 19.Figure 21. Primary reactions of the pyrolysis of benzene.Figure 22. Cross-coupling reactions of norbornane and benzene.

	+		β-scission + H	+	R1 R2 R3	+ R15 (unimolecular initiation) (bimolecular initiation) C 2 H 4
	+		+		(bimolecular initiation)
	+ Rn	+ RnH			(metatheses of radicals deriving from
						norbornane with benzene)
	+ H + R6	+ H 2 isomerization R1 R2 +		(metathesis of H atoms with benzene) R17 (metathesis of phenyl R16 radical with norbornane)
	+ H	R3			(addition of H atoms to benzene)
	Rb + Rn	+	metathesis (+RH) products	MA4 + H (combination/disproportionnation of radicals (+R ) (addition of phenyl radicals to benzene) deriving from norbornane and benzene)
	H + H (+ M)	H 2 (+ M)			(combination of two H atoms)
		+				(combination of two phenyl radicals)

Figure 20.

ACKNOWLEDGMENT

This work was supported by MBDA-France and the CNRS. We are grateful to E. Daniau, M. Bouchez, and F. Falempin for helpful discussion.

kPa and with a mole percentage of reactant at the inlet of the reactor of 0.7%.


In the framework of Cleansky SFWA ITD, ONERA defined an experimental research program for the investigation of gust load in Wind Tunnel. Based on dedicated experimental set-up, three test campaigns were achieved in the ONERA S3Ch transonic facility. At first, the ability to produce a relevant and reproducible gust field was demonstrated. Then the second wind tunnel test was devoted to analyse gust effects on the aeroelastic behaviour on a 2D airfoil equipped with a control surface. Finally, gust load control based on closed loop approaches was investigated up to transonic flow and has demonstrated significant reductions of the model structural responses to gust. The experimental database and results have allowed to perform the calibration of numerical modelling capabilities of gust load as well as the assessment of advanced gust load alleviation functions.

INTRODUCTION

The mission of Clean Sky European research program is to develop breakthrough technologies to significantly increase the environmental performances of airplanes and air transport [START_REF]Clean Sky Website[END_REF]. In the framework of SFWA ITD (Smart Fixed Wing Aircraft Integrated Technology Demonstrator), one of the main improvements axes is the aircraft weight reduction through novel load control technologies in order to contribute to a step change in fuel consumption levels.

To achieve the investigation of the specific case of gust load, which is one of the most critical for strength design and fatigue loading source for transport type aircraft, ONERA has defined a dedicated experimental research program based on Wind Tunnel Tests (WTT).

In the literature, the experimental investigations of gust in wind tunnel have been mainly performed in low speed regime [2] [3] and there are few works conducted in the transonic regime [4] even less for load alleviation purpose [5].

In order to improve the understanding of fluidstructure interactions in presence of a gust perturbation, ONERA proposed to define a research tool for the investigation of gust load in Wind Tunnel (WT) tests conditions. The key objectives are :

• to improve the understanding of a large scope of physical phenomena induced by gust such as linear and non-linear aerodynamic in presence of gust, aeroelastic effects of an impact gust on a flexible model. • to dispose of comprehensive and relevant experimental databases for the validation of methodologies and tools of numerical simulation such as high fidelity tools of Computational Fluid Dynamic (CFD) and Computational Structure Mechanics (CSM). • to investigate gust load alleviation with control approaches based on closed-loop architecture.

THE EXPERIMENTAL SETUP

General considerations

The Gust Generator

The geometrical architecture of the gust generator is made of two identical NACA 0012 airfoils of c = 0.2m chord length placed at x = -0.63m, upstream of the entrance of the test section which corresponds to x = 0, and at h = +/-0.2m above and below the wind tunnel longitudinal axis. The airfoils span covers the entire width of the tunnel with a minimal gap between the wing tips and the WT walls. The dynamic actuation is performed by four servohydraulic jacks which synchronously rotate the two airfoils (i.e. pitch motions about the quarter chord point) with a frequency bandwidth of 100 Hz. The two airfoils are made of an optimized architecture that combines carbon reinforced skins and metallic parts to reduce inertia and allow high frequencies of actuation under heavy aerodynamic loads. An overview of this mount is shown in Fig 2.

The Aeroelastic Model

The aeroelastic airfoil is based on an ONERA supercritical profile (OAT15A [START_REF] Rodde | OAT15A Airfoil Data[END_REF]) with a 0.25 m chord length. The main components of the model part are composed of a steel spar and 2 upper and lower carbon reinforced skins. A specific manufacturing process was defined by Aviation Design in order to avoid any geometrical variations and to respect the aerodynamic shape of the airfoil (no cover, no access).

The boundary conditions of the model aim at providing the behaviour of a classical 2 dof aeroelastic model .i.e. a 2D model with a pitch and plunge stiffnesses. One of the most well-known in the literature is the Pitch And Plunge Apparatus (PAPA) developed at NASA [10] providing the two flexible dof needed for flutter test purpose. For the works presented in this paper, a novel concept has been studied for the design of a pitch-plunge device. The stiffness properties are driven by flexible beams with in addition an arrangement of bearings in order to better "constrain/prescribe" the "rigid body" motions of the wing. In the wind-tunnel test section, the mounting system is composed of 2 identical mountings parts located on each test section door as shown in Fig 3. For both dof, the geometrical parameters of stiffness beams have been numerically optimized through Finite Element Models (FEM) in order to satisfy static loads requirements and to tune dynamics properties in the frequency range of interest. The main advantage of this mount system is that pitch and plunge stiffnesses can be modified independently by adjusting the length of clamping condition of each "stiffness beam".

The model is equipped with a full span trailing edge control surface with a hinge axis located at 75% of the chord. On each side, the control surface is driven by a high torque -high speed actuator especially designed and manufactured for

Measurement devices

The goal of the first WTT was to estimate whether the gust generator was able to generate a relevant gust field and to qualify its characteristics. This campaign was performed for the case of an empty wind tunnel section.

Two measurement devices were used to qualify the flow :

• An unsteady clinometric probe especially designed and manufactured for these tests. This "gust sensor" is a fast-response 2 holes probe (equipped with 2 unsteady pressure sensors) and provides after calibration the unsteady flow angle.

• A two components phase averaged Particle Image Velocimetry (PIV) system composed of a double pulse laser and a high resolution camera. The laser was installed below the test section and delivered an (Oxz) measurement plan. The time resolution was obtained through phase averaging locked to the airfoil motion [START_REF] Brion | Generation of vertical gusts in a transonic wind tunnel[END_REF].

Typical results

Typical results are shown in Fig 5 presenting temporal evolutions of the unsteady clinometric probe for a harmonic oscillation of the gust generator. As expected, a sinusoidal command induced a sinusoidal dynamic motion of the 2 wings generating therefore a sinusoidal gust. For this example at Mach number 0.73, a dynamic actuation of the wings of +/2° in amplitude at f g = 40Hz induced a gust amplitude recorded by the probe of about +/-0.4° flow deviations. A frequency analysis is given in the lower part of Figure 5 and shows the principal component of the gust field is located on the command frequency. Higher harmonics could be identified but with a lower order of magnitude.

In addition to probe data, PIV measurements have allowed to qualify complementary the unsteady flow of the gust field. The influence of the walls and the effects of the wings wake (Z=+/-0.2m) are clearly emphasized with strong variations of the velocity longitudinal components while small scale disturbance are observed in central area (Z~0m). The vertical velocity field demonstrates clearly an alternating upward and downward flow, i.e. an alternating positive and negative flow angle, as function of time which exactly corresponds to the researched phenomenon. The analysis along the vertical axis indicates a variation of homogeneity which is still nevertheless moderated in the centre area.

Main outcomes of WTT1

The tests were performed following a parametric approach: the gust field properties were analysed depending on the aerodynamic conditions and the actuating conditions. Significant parameters have been investigated such as the amplitude  Actuation and the pulsation  of the dynamic actuation, the upstream flow velocity U  .

A complete synthesis of the gust generator performances is given in Moreover these data are in a good agreement with numerical predictions and analytical models developed in [START_REF] Brion | Generation of vertical gusts in a transonic wind tunnel[END_REF]. The reduced frequency and the dynamic pitch amplitude appear to be the dominant parameters with a positive effect on the gust generation. The Mach number has also a beneficial effect in lower order of magnitude by improving the airfoil performances.

The results and analyses of this first WTT demonstrated the ability to generate a cylindrical gust field in wind tunnel environment in a reproducible way with significant gust amplitudes.

OPEN-LOOP GUST LOAD TESTING

Aerodynamic behaviour in presence of gust

The first part of the second WTT was devoted to the study of the aerodynamic phenomena induced by gust on the airfoil. To reach this objective, the clamping conditions of the model were switched in "rigid configuration" (i.e. structural modes postponed at high frequency). Plunge Mode -f=24.7Hz -=2.3%

The plots shown in

Pitch Mode -f=40.6Hz -=1.9%

Figure 12: FRF between airfoil acceleration and gust perturbation

As presented in Fig 12, the tests demonstrated that it was unexpectedly impossible to excite the pitch mode (around 40 Hz). Although its behaviour was clearly linear and controlled during lab tests, the gust perturbations didn't allowed to obtain significant responses on this mode. Parametric analyses were performed to solve this issue and led to the conclusion of strong and unavoidable friction phenomena in a sealing area close to the walls-airfoil junction.

Open-loop behaviour for a control surface command

The

Closed-loop Control results

During the final WTT, the main objective was the demonstration in real time of gust load alleviation through the active control of the model aeroelastic response for a gust disturbance. For this first demonstration, the control laws were designed to act on the first plunge mode and to avoid any bad effect of the higher modes (e.g. amplification of the first bending). Practically, the control parameter (controller, gain and loop sign) were tuned at first in real time for a harmonic gust perturbation with a sinusoidal command locked on the plunge mode frequency. Although the prelaminar vibration tests have demonstrated the presence of structural nonlinearities, the robust control approach take into account the effect of the parameter variations and uncertainties ensuring a control efficiency.

Moreover, at the end of the final WTT, the controller robustness was also characterized through parametric tests. Typically, a controller designed from a given open-loop dataset was tested with variations of the Mach number, the angle of attack value or the static angle of the control surface. The results have demonstrated structural response reductions in a lesser extent but also the absence of instabilities.

Figure 2 :

 2 Figure 2: Overview of the gust generator installed upstream the S3 WTT section

Figure 3 :

 3 Figure 3: Overview of the 2D aeroelastic model installed in the S3 WTT section

  these tests and mainly composed of a rotative hydraulic actuator operating at 200 Bar and a fast response servo valve. As the actuation bandwidth is an important consideration for gust load alleviation law design and performance, position feedback control laws were precisely tuned to allow the dynamic deflection of the control surface up to 100 Hz.The instrumentation of the model is made of :• steady (31) and unsteady (44) pressure transducers arranged in two span stations. • accelerometers mounted (12) in three span stations to correctly handle the dynamic motions. • various strain gages bridges for monitoring purposes • an unsteady clinometric probe (see device described in section 3.1) mounted in the airfoil leading edge to estimate the gust field upstream the airfoil.An overview of the complete experimental set-up is shown in Fig 4.In the background, the gust generator device is located in final part on the convergent area of the wind tunnel while the wing part of the aeroelastic model is visible downstream in the test section equipped with the adaptive walls.

Figure 4 :

 4 Figure 4: Complete experimental setup for gust load investigation in the S3 WTT

  Fig 6 shows the spatiotemporal reconstructions of the longitudinal and vertical velocity components for the similar tests point presented in Fig 5. Each frame represents the flow variations over one wavelength of the gust.

Figure 5 -Figure 6 :

 56 Figure 5 -Signals obtained by the unsteady clinometric probe and associated spectra Normalised longitudinal velocity field (U/U)

  Fig 7 for the case of harmonic gust. The gust amplitude  Gust (i.e angular flow deviation in degrees) is normalised on the actuation amplitude and a correction factor =1/(1-M 2 ) 1/2 of the compressibility effects (according to the Prandtl-Glauert transformation). The resulting normalised gust angle is plotted versus the reduced frequency k=*c/U  , c being the chord of the gust generator wings.

Figure 7 :

 7 Figure 7: Synthesis of the performances of the Gust Generator The Fig 7 indicates clearly a good correlation between the probe and PIV measurements.Moreover these data are in a good agreement with numerical predictions and analytical models developed in[START_REF] Brion | Generation of vertical gusts in a transonic wind tunnel[END_REF]. The reduced frequency and the dynamic pitch amplitude appear to be the dominant parameters with a positive effect on the gust generation. The Mach number has also a beneficial effect in lower order of magnitude by improving the airfoil performances.

Fig 8 and

 8 Fig 9 present the typical results of a sinusoidal gust impacting the airfoil at a transonic Mach Number. In Fig 8, the grey surface covers all instantaneous pressure distribution recorded at high sampling rate while red and blue lines provided the time averaged data. As shown, the pressure levels fluctuations were significant in the supersonic plateau area and the shock location. The pressure signals were modulated at the Gust Generator frequency and for this case, the shock oscillated with a 8% chordwise amplitude between the extreme locations.

Figure 8 :

 8 Figure 8: Instantaneous (grey) and averaged (blue and red) pressure coefficient distributions The first harmonic pressure distribution in Fig 9 exhibited a classical shape. Contrary to subsonic case, pressure distribution is completely different between the suction and pressure sides. An important motion of the shock occurred on this upper side of this airfoil and a shift on the phase information.

Figure 9 :

 9 Figure 9: Distribution of First harmonic Pressure Distribution In order to estimate the global effects of impacting gusts on the aerodynamic behaviour of the airfoil, the unsteady lift force has been determined by integration of the unsteady pressure sensors, i.e. for each sample time. As shown in Fig 10, the lift coefficient signal is obviously dominated by the frequency of the gust generator command. For the presented example, the order of magnitude of the local lift coefficient fluctuation is Cl = +/-0.04 leading to a variation of the lift force of about +/-200N. This clearly demonstrates the ability of generating significant unsteady loads on the airfoil using the gust generator.

Figure 10 :

 10 Figure 10: Temporal evolution of the lift coefficient signal obtained by pressure integration

Figure 11 :

 11 Figure 11: First structural modes For the gust generation, sine sweep signals were used as input data which amplitude was modulated as function of the time to compensate the frequency effect described in Fig 7 and to generate a constant amplitude gust over the wide frequency bandwidth. On the Frequency Response Function (FRF) shown in Fig 12 between the structural acceleration and the gust perturbation, the contributions of the plunge and first bending modes are clearly visible.

  second WTT was also devoted to the characterisation of the gust model behaviour for a control surface input. Similarly to the gust load tests, a sweep sine command was generated over the frequency bandwidth [0-100] Hz. As presented in Fig 13, the three targeted modes (plunge, pitch and bending) are clearly visible on the command transfer function between the model acceleration and the control surface deflection command. In the view of achieving a closed-loop control, this point has guaranteed an a priori good controllability of these modes. The shape of the peak in the vicinity of the pitch frequency tends to indicate a nonlinear behaviour. This confirms the previous assumption of friction phenomena associated to this structural mode.

Figure 13 :

 13 Figure 13: FRF between airfoil acceleration and control surface command

Figure 14 :

 14 Figure 14: Block diagram of the robust control The synthetized controllers were implemented on a real time dSpace device with a dedicated real-time man/machine interface to monitor the signals and adjust control/command parameters. Several control architecture were tested and based on accelerometers data in a SISO configuration (i.e. Single Input Single Output) or MISO (i.e. Multi Input Single Output).

  An example of an accelerometer time history is given in Fig 15 and clearly demonstrates the control efficiency when the control is switched on. A quantitative evaluation for this test point pointed out a strong reduction of the model aeroelastic response up to -10 dB. The analysis of the control surface deflection indicated reasonable motions around one degree.

Figure 15 :

 15 Figure 15: Accelerometer time history for a sinusoidal gust perturbation at the plunge mode frequency Then the control efficiency was assessed for a wide band gust excitation driven by a sweep sine command. Depending on the controller type and the test case, some margin could have been considered on the main feedback gain to ensure stability of the closed-loop system over the wide frequency bandwidth. The open-loop data (i.e. without control) is superposed in Fig 16 with the closed-loop data (with active control). As expected, the control laws are very efficient in vicinity of the plunge mode and no amplification appears at higher frequency. Structural responses attenuations up 70% were observed on the plunge mode.

Figure 16 :

 16 Figure 16: Demonstration of the active gust load alleviation -FRF between accelerometer and gust driving signal

  According the experimental roadmap, three WTT have been achieved in the ONERA S3Ch facility. At first the analysis of the gust generator capabilities has demonstrated the ability to generate a cylindrical gust field in wind tunnel environment in a reproducible and controlled way. Then the aerodynamic and aeroelastic behaviours of a 2D model were investigated in presence of gust. The achieved open-loop tests have provided a comprehensive and consistent database used by the SFWA partners in a numerical restitution process to perform CFD/CSM simulations for gust cases[START_REF] Huvelin | High fidelity numerical simulations for gust response analysis[END_REF]. The users have pointed out the fact this database constitutes a first major step in the validation process of the simulation capacities of gust. Finally, active gust load alleviation was successfully demonstrated in real time up to transonic conditions. The control methodology was based on closed-loop architecture between accelerometers and the control surface command. Significant reductions of the model structural responses to gust were obtained with stability and robustness.

ACKNOWLEDGMENTS

This work has been undertaken within the Joint Technology Initiative "JTI CleanSky", Smart Fixed Wing Aircraft Integrated Technology Demonstrator "SFWA-ITD" project (contract N° CSJU-GAM-SFWA-2008-001) financed by the 7th Framework programme of the European Commission.


GREEN REGIONAL AIRCRAFT GUST RESPONSE

Keywords: aeroelasticity, fluid-structure coupling simulations, gust load alleviation, load control

This contribution deals with gust load alleviation due to control surfaces deflection time laws. In the framework of the JTI-GRA European project (Green Regional Aircraft), high-fidelity fluidstructure coupling numerical simulations have been performed in order to predict the GTF NLF aircraft gust response (Gear Turbo Fan -Non Laminar Flow).

The ZFW (Zero Fuel Weight) configuration of the GTF aircraft at Mach 0.48 and sea level has been handled and two one peak (1-cos) gusts have been considered. Control laws of the control surface have been provided by Alenia.

Significant load alleviation has been observed for both gust wavelengths when applying the aileron deflection laws.

INTRODUCTION

Dynamic fluid-structure coupling simulations have been performed using the high fidelity software elsA and its aeroelastic module Ael in order to assess the gust LC&A (Load Control & Alleviation) devices performances of the GTF-NLF (Gear Turbo Fan -Non Laminar Flow) aircraft [START_REF] Wing | Aeroelastic Design Optimised Wing Box -Preliminary Layout[END_REF]. The wing is equipped with an aileron which has been used to alleviate gust loads. "1-cos" single peak gusts, as defined in the certification documents [START_REF] Wing | Aeroelastic Design Optimised Wing Box -Preliminary Layout[END_REF], have been considered. Computations have been carried out for the ZFW (Zero Fuel Weight) mass configuration. Control laws have been provided by Alenia and result from a design process using low fidelity aerodynamic models [START_REF] Calvi | Final assessment of Load Control & Alleviation system for GTF A/C configuration[END_REF] for a Mach number of 0.48 at sea level. Two deflection laws have been provided for the ZFW configuration: one for a gust called "tuned gust" whose frequency of 3.41Hz is close to the aircraft 1 st eigen mode, and the second law for a gust called "Gust 25 chords" whose frequency is 1.74Hz. This paper presents the computations of the response to these two gusts using high fidelity numerical simulations.

The first part gives a brief description of the numerical methodology. The structural model, the gust characteristics and deflection laws of the control surface are specified in the second part. The third part is devoted to the analysis of the results of the numerical simulations.

NUMERICAL METHODOLOGY

CFD code elsA

Fluid-structure coupling computations are available in the CFD code elsA [START_REF] Cambier | The Onera elsA CFD software: input from research and feedback form industry[END_REF], using its optional "Ael" subsystem. The structure solver implemented in elsA-Ael is able to handle models built according to a modal approach or resulting from a condensation of the inverse of the finite element stiffness matrix (flexibility matrix). But only the modal approach can be used for dynamic simulations.

Gust models

The aeroelastic capabilities in elsA-Ael have been developed using an Arbitrary Lagrangian Eulerian formulation (ALE) of the fluid equations. The gust velocity depending on both space and time, has then been introduced as an additionnal grid deformation speed according to the Sitaraman field velocity approach [5].

Three models of discrete gust are available in elsA: the "sharped edge gust", the "one minus cosine" often used for certification, and "sine" which could be used for the simulation of harmonic gust response (Figure 2).

The coupling scheme involving the five operations represented in Figure 1 had been introduced within a time consistent scheme in order to be able to perform dynamic coupling simulations. Figure 3 shows an overview of the dynamic coupling scheme, that has been implemented in elsA. This scheme includes an external iteration loop driving the advance in the physical time. A second loop called "coupling loop" is aiming at getting a converged state of both the structure and the fluid within a physical time step. The five coupling operations are at last performed within this second loop: flow resolution, transfer from fluid to structure, structure resolution, transfer from structure to fluid, and aerodynamic mesh updating. The flow field is computed using a second order implicit dual time stepping algorithm allowing thus large physical time steps, and the structure displacement using a Newmark one. Furthermore, since dynamic aeroelasticity implies mostly low frequency phenomena and small enough amplitude vibrations so that the structure behavior remains linear, the structure is modelled using a modal approach, which simplifies the fluidstructure transfers and mesh updating operations.

The first N structural modes ( S  ) are indeed mapped to the aerodynamic surfaces (

i , A i , S     
), and N deformed aerodynamic grids are computed before starting the time iterations (

  m o d a l , 1, Ai iN X  
). The generalized aerodynamic forces that applies to the structure are deduced straight from the pressure distribution:

WdS dS n p gaf Wall i , A i       .
The generalized coordinates of the structure (   1,

n i iN q 
) are then computed by solving the structure modal equation. And the updated aerodynamic mesh is deduced from them by a simple linear combination of the "modal" aerodynamic meshes:

m o d a l , 1 N nn A i A i i X q X     
. The yellow boxes in Figure 3 have been added in order to be able to handle overlapping meshes using Chimera techniques.

MODEL DESCRIPTION

GTF-NLF configuration

The structural model used is the aeroelastic model of the wing box relevant to the Geared Turbofan (GTF) A/C [START_REF] Wing | Aeroelastic Design Optimised Wing Box -Preliminary Layout[END_REF].

The flexible wing box is delimited by the front and rear spars and by the upper and lower skins; it is fitted with 21 ribs, leading edge and LC&A devices (Figure 4). The leading edge is defined by means of lumped masses attached by Nastran rigid body RBE3 elements along the front spar; it has been fitted to the wing box model only to take account of its weight for dynamic and aeroelastic effects.

LC&A devices have been added on the wing box model to be taken into account by aeroelastic computations. The wing is thus equipped with 3 flaps, 2 ailerons (Figure 4) and a winglet. The total weight of the wing model (empty fuel) fitted with leading edge, winglet, LC&A devices and nonstructural mass is 2423 kg.

Gust characteristics and control laws

The gust corresponds to a "one minus cosine" single peak vertical gust whose speed U is defined with respect to space and time, according to the certification documents [START_REF] Wing | Aeroelastic Design Optimised Wing Box -Preliminary Layout[END_REF], as

        ) ( 2 cos 1 5 . 0 , t V x U t x U prop ds    
where U ds is the gust amplitude,  is the gust wavelength and V prop the wave propagation speed (equal here to the flight speed).

Control laws for the aileron deflection angle have been determined by Alenia from a design process using low fidelity aerodynamic models [START_REF] Calvi | Final assessment of Load Control & Alleviation system for GTF A/C configuration[END_REF] for a Mach number of 0.48 at sea level. Two deflection laws have been provided for the ZFW configuration and correspond respectively to:

a gust called "tuned" gust such that its frequency of 3.41Hz is close to the first eigen mode (3.92 Hz), its amplitude is U ds =12.33 m/s, and its wavelength is

=47.93m=12.75 chord,
a gust called "25-chords" gust whose frequency amplitude and wavelength are respectively 1.74Hz, U ds =14.36m/s, and =93.92m=25 chord.

Moreover, the initial instant of the time function of the gust speed has been determined to match the initial instant of the aileron deflection law and such that the gust wave reaches the fuselage nose at the instant t=0.1s. Time evolutions of both gusts and the corresponding deflection laws are given in Figure 5.

Numerical simulations

All gust responses have been computed for the aerodynamic conditions matching a flight at Mach number 0.48 and at sea level (zero altitude). Only the ZFW configuration (51356 kg according to the specifications given in [START_REF] Calvi | Final assessment of Load Control & Alleviation system for GTF A/C configuration[END_REF]) has been studied. This mass configuration matches a lift coefficient of C L =0.555 (1 g) which is reached with an angle of attack of 1.4°.

Numerical simulations have been performed with a structured mesh made of 78 blocks and about 2.5 million cells. This mesh has been built to model the half fuselage-wing configuration around the initial flight shape of the GTF wing (Figure 6). A static fluid-structure coupling simulation has first been carried out to get the flight shape of the wing for the above aerodynamic conditions. All further dynamic simulations will then be initialized with these static results. Five control surfaces are located on the wing, but the study has been focused on gust load alleviation resulting from the aileron deflection.

RESULTS

Aileron deflection effect on aerodynamic coefficients

Time simulations have been performed with and without aileron motion, and for both cases with 64 time steps per gust period. This corresponds to for the "tuned" gust and for the "25-chords" gust. Another simulation has been performed without any gust excitation, taking only into account the aileron motion. Figure 8 and Figure 9 show the resulting time evolutions of the lift, rolling and pitching moment coefficients for the "tuned" and "25-chords" gust respectively. The aileron motion induces an alleviation of the first peak (peak due to the gust passage) on lift (10.2% and 9.8% for the "tuned" and "25-chords" gust, respectively), and on the rolling moment (28% and 21.5% for the "tuned" and "25-chords" gust, respectively). But a slight increase of -4.5% of the pitching moment is observed for both gusts. In the case of the "25chords" gust (Figure 9), post gust oscillation of lower amplitude and higher damping than the case of the "tuned" gust is also noticed. 1st bending) for "tuned" and "25chords" gust.

Figure 8: Time evolutions of lift, rolling and pitching moment coefficients response to the "tuned gust" taking (blue curve) and not taking (red) into account the aileron deflection law

Aileron deflection effect on generalized coordinates

The application of the aileron deflection law induces a high decrease of the main peak of the first generalized coordinate (55.8% and 21.8% for the "tuned" and "25-chords" gusts, respectively). This bending mode coordinate shows opposite behaviors when the aircraft is excited by only a gust or by only an aileron motion (red and grey curves in Figure 10: it increases in the gust excitation case while decreasing in the only aileron excitation case. The combination of both excitations tends then to alleviate the main peak.

Especially in the case of the "tuned" gust, the amplitude of the main peak is then getting of the same order as the amplitude of the post gust oscillations. The latter are moreover strongly damped as soon as the aileron stops its deflection motion.

As regards the 4 th generalized coordinate which matches the first torsion mode (Figure 11), its time behavior is similar to the generalized coordinate of the imposed aileron motion. The pitch moment is indeed increasing with the upward deflection of the aileron. It also increases with the gust passage. The combined excitation of the gust and the aileron motion results then in a peak amplitude almost twice the one resulting from the simulation with only the gust and without any aileron motion (blue and red curves). Nevertheless, only aileron deflection is taken into account and not the horizontal tail plane deflection though the latter may have a strong impact on the moments. due to the gust passage. In order to get information from a more physical quantity about the wing deformation, time evolutions of the twist deformation of the wing section close to the wingtip (between the aileron and the winglet root) have been extracted from the simulations. They are very different from the 4 th generalized coordinates as can be seen in Figure 12 (positive values meaning an increase of the apparent incidence of the section). This shows that the wing twist is highly influenced by other modes than the first torsion one.

Furthermore, a significant alleviation of this twist deformation peak thanks to the aileron motion is noticeable ( Figure 13). Post gust oscillations are indeed in that case of greater amplitude than this first peak. Figure 13: Time evolutions of the twist angle variation of a section close to the wingtip ("tuned" gust).

Aileron deflection effect on integrated loads

At last, integrated loads have been computed with respect to time for both gust responses (with and without aileron motion) and for the aileron motion response (without gust) (Figure 14 and Figure 15). In the case of the "tuned" gust (Figure 14), similar time behavior can be noticed for both the shear force and bending moment. The aileron motion induces a significant alleviation of the peak due to the gust passage (11.9% for the shear force and 29.2% for the bending moment). From the torsion moment point of view, the aileron motion induces the peak removal, and resulting secondary oscillations are quickly damped as soon as the aileron motion stops (these oscillations vanish after 2s).

In the case of the "25-chords" gust (Figure 15), a load peak occurs during the gust passage but significant alleviations are obtained when enabling the aileron deflection movement (11.2% on the shear force and 21.6% on the bending moment). Only a slight decrease is observed on the torsion moment (3.7%). Furthermore, post gust oscillations vanish very quickly for this low frequency gust (1.74 Hz whereas the first structural natural frequency is equal to 3.92Hz).

CONCLUSIONS

Numerical simulations have been performed using high fidelity tools in order to assess gust load alleviation due to control surfaces deflection time law. The ZFW configuration of the GTF aircraft at Mach 0.48 and sea level has been handled and two single peak (1-cos) gusts have been considered: the "tuned" gust whose wave length has been defined to match the first structural natural frequency, and the "25 chords" gust whose wave length is equal to 25 times the mean chord.

Numerical simulations have been performed first with a fixed aileron and second taking into account the time deflection of the aileron, in order to assess the gust load alleviation due to the aileron motion.

The structure has been modeled using a modal approach and a reduction to 7 modes which have been selected for being the most contributing to the structure static behavior. Significant alleviations due to the aileron motions have indeed been noticed for both gust excitations and for several load quantities: aerodynamic lift coefficient, aerodynamic rolling moment coefficient, aerodynamic pitching moment coefficient, vertical displacement of the leading edge close to the wingtip, first generalized coordinate matching the 1 st bending mode of the structure, 4 th generalized coordinate corresponding to the 1 st torsion mode, shear force that applies at root, bending moment, and torsion moment (Table 1). Alleviation is of the same order for both gusts for quantities as lift coefficient, rolling moment coefficient, and shear force and bending moment at root, even if alleviation is slightly higher in the case of the tuned gust. But large discrepancies occur for the vertical displacement and the generalized coordinates. Since the first bending mode is one of the most contributing modes to the vertical displacement, resulting alleviation for those two quantities are similar for each gust excitation. But, a significantly higher alleviation has been noticed in the case of the tuned gust. On the other hand different behaviors of the twist and torsion related quantities [START_REF] Cambier | The Onera elsA CFD software: input from research and feedback form industry[END_REF] th generalized coordinate and torsion moment at root) have been observed. This may be partly explained by the fact that aileron upward deflections aiming at decreasing the lift peak due to gust tends to increase the pitching moment and then the torsion modal coordinate.

Although High fidelity numerical simulations have been performed taking into account only the aileron and neglecting the horizontal tail plane impact, gust load alleviations have been observed, alleviations that are of the same order as these computed using lower fidelity tools at the control law design stage and presented in [START_REF] Calvi | Final assessment of Load Control & Alleviation system for GTF A/C configuration[END_REF].

Table 1: Load alleviation due to the aileron deflection laws

ACKNOWLEDGEMENTS

This study was performed in the framework of the JTI-GRA European project. The authors would like to thank Alenia for their contribution.

Figure 1 :Figure 1

 11 Figure 1: Schematic overview of the methodology used in the Ael module of elsA

Figure 2 :

 2 Figure 2: Sharp edge (left) and one minus cosine (right) gust model implemented in elsA.

Figure 3 :

 3 Figure 3: Dynamic modal coupling diagram

Figure 4 :

 4 Figure 4: GTF wing box finite element model

Figure 5 :

 5 Figure 5: Time evolutions of the vertical gust velocity at the aircraft nose and the corresponding

Figure 6 :

 6 Figure 6: CAD model around the initial flight shape of the GTF-NLF wing. The aileron surface is highlighted in magenta.Fluid-structure coupling simulations require the building of a reduced order model of the structure. Most of time, dynamic simulations are carried out using a modal representation of the structure. A first step has thus consisted in computing the first eigen modes from the finite element model of the Geared Turbofan (GTF) A/C wing box[START_REF] Wing | Aeroelastic Design Optimised Wing Box -Preliminary Layout[END_REF] (Figure4). Based on static coupling results, 7 modes have been selected for having the most significant contribution to the structure behavior (Figure7): the first three bending modes, the first two torsion modes and 2 composite ones (mode number 1, 3, 5, 6, 7, 9, 10). Those modes have been obtained by applying clamping conditions in the symmetry plane in order to remove rigid modes. Those 7 modes, which have been computed from the finite element model, have been transferred to the

Figure 7 :

 7 Figure 7: Structural modes: visualisation of structural nodes (red square symbols), deformed mesh (orange) and undeformed mesh (grey).

Frequency

Figure 9 :

 9 Figure 9: Time evolutions of the aerodynamic coefficients (25 chords gust)

Figure 10 represents the time evolutions of the 1 st

 1 Figure 10 represents the time evolutions of the 1 st generalized coordinate (first bending mode) for both gusts.

Figure 10 :

 10 Figure 10: Time evolutions of the 1 st modal coordinate (1st bending) for "tuned" and "25chords" gust.

Figure 11 :

 11 Figure 11: Time evolutions of the 4 th generalized coordinate (1 st torsion) for "tuned" and "25 chords" gust.This 4 th generalized coordinate seems to be highly sensitive to the aileron motion, and the first upward deflection of the aileron tends to amplify the peak

Figure 12 :

 12 Figure 12: Time evolutions of the twist angle variation of a wingtip section and of the 4 th generalized coordinate in case of gust with aileron motion ("tuned" gust).

Figure 14 :

 14 Figure 14: Time evolution of the shear force, the bending and torsion moments at wing root for the "tuned" gust.

Figure 15 :

 15 Figure 15: Time evolution of the shear force, the bending and torsion moments at wing root for the "25-chords" gust.

5. Sitaraman J., Iyengar V. S., Baeder J.D. (2003)