Juan Milanesio

Pablo Hegel

Yaocihuatl Medina-Gonzalez

Séverine Camy

Jean-Stéphane Condoret
email: jeanstephane.condoret@ensiacet.fr

Extraction of lipids from Yarrowia Lipolytica t

Keywords: lipid extraction, lipid solubility, Yarrowia lipolytica, supercritical extraction, yeast pretreatments

BACKGROUND: Microorganisms have often been considered for the production of oils and fats as an alternative to agricultural and animal resources. Extraction experiments were performed using a strain of the yeast Yarrowia lipolytica (Y. lipolytica), a high-lipid-content yeast. Three different methods were tested: Soxhlet extraction, accelerated solvent extraction (ASE) and supercritical carbon dioxide (SCCO 2 ) extraction using ethanol as a co-solvent. Also, high pressure solubility measurements in the systems 'CO 2 + yeast oil' and 'CO 2 + ethanol + yeast oil' were carried out. RESULTS: The solubility experiments determined that, at the conditions of the supercritical extractor (40 °C and 20 MPa), a maximum concentration of 10 mg of yeast oil per g of solvent can be expected in pure CO 2 • 10% w/w of ethanol in the solvent mixture increased this value to almost 15 mg of yeast oil per g of solvent. Different pretreatments were necessary to obtain satisfactory yields in the extraction experiments. The Soxhlet and the ASE method were not able to complete the lipid extraction. The 'SCCO 2 + ethanol' extraction curves revealed the influence of the different pretreatments on the extraction mechanism. CONCLUSION: Evaluating the effectiveness of a given pretreatment, ASE reduced the amount of material and solvent used compared with Soxhlet. ln all three cases, the best total extraction performance was obtained for the ethanol-macerated yeast (EtM). Addition of ethanol to the solvent mixture enhanced the oil solubility. Oil can be extracted from Y. lipolytica in two different steps: a non-selective ethanol extraction followed by TAG-selective SCCO 2 purification.

INTRODUCTION

Microorganisms have often been considered for the production of oils and fats as an alternative to agricultural and animal resources. 1 Single-cell oil (SCO)from yeasts has gained commercial importance mainly due to its similarity in properties to vegetable oils and fats. 2 Oleaginous yeasts have been reported to grow and accumulate very significant amounts of lipids (60 to 70% w/w of dry mass). 2 However, even under propitious conditions, only a small fraction of yeast biomass is in the form of lipids. For example, Saccharomyces cerevisiae (S. cerevisiae) has between 5 and 10% of lipids w/w of dry mass. The main lipidic components of this yeast are triacylglycerols (TAGs) and steryl esters (SEs), but phospholipids (PLs) and free fatty acids are also present. 3 Microorganisms may also contain other lipids, like sphingolipids or glycolipids. 2 These are usually found within special organelles called lipid particles or lipid bodies (LB), which are surrounded by a PL monolayer with embedded proteins.

The yeast Yarrowia lipolytica (Y. lipolytica) is a high-lipid-content yeast. Several technologies, including various fermentation con figurations, have already been used for SCO production by strains of Y. lipolytica grown on various agro-industrial by-products or wastes. 5 The potential applications of these processes include the production of reserve lipids with particular structures (e.g. oils en riched in essential polyunsaturated fatty acids) and the production of non-specific oils for use as renewable starting materials for the synthesis of bio-fuels. 6 The extraction of lipids from yeasts with various conventional organic solvents, such as chloroform and methanol, hexane and/or petroleum ether, and their application, even at industrial scale, has already been reported in the literature. 2 According to the Principles of Green Chemistry, the organic solvents used at pilot and industrial scale have to be replaced in the near future by non-flammable, less toxic and more benign solvents in order to obtain sustainable processes. [START_REF] Anastas | Origins, current status, and future challenges of green chemistryt[END_REF] Carbon dioxide (CO 2 ) is an inert, inexpensive, easily available, odorless, tasteless, environment friendly, ideally suitable for thermally labile natural products and generally regarded as safe (GRAS) solvent. 8 ln addition, its solvent power and selectivity can be adapted according to the operating conditions.

Extraction of lipids from yeast using SCC0 2 is rarely considered in the literature. To palliate this scarcity of knowledge, an analysis of the data published on oil extraction from seeds could be an interesting starting point. The use of SCC0 2 and co-solvents for the selective extraction of triglycerides has been studied, for example, in the case of canola, soybean lecithin and sunflower oil. 9 -13 To estimate the maximum oil concentration in the solvent that can be expected in the output effluent of a supercritical extractor, oil solubility measurements (phase boundaries) are very helpful. Cocero and Calvo [START_REF] Cocero | Supercritical fluid extraction of sunflower seed oil with C0 2 -ethanol mixtures[END_REF] have shown that, in the case of sunflower oil, the solubility is increased with increasing pressure at a given temperature and is reduced with increasing temperature at constant pressure. Also, the authors showed that the addition of ethanol to the solvent mixture increased the oil solubility at a given temperature and pressure.

The aim of this work is to compare the performance of three different techniques for lipid extraction from a specific yeast material and to estimate, from solubility measurements, the maximum oil concentration that can be expected at the output of the supercritical extractor. The raw material used in this work was a strain of Y. lipo/ytica with high lipid content. lt was provided by a major European industrial yeast producer. Different pretreatments were applied in order to increase the yield.

EXPERIMENTAL

Materials

Yeast materials

The yeast Y. lipolytica was provided by Lesaffre Group®, after harvesting and preconditioning. The yeast was received in three different forms (raw materials):

1. Compressed yeast (block).

Yeast cream (water suspension). 3. Yeast dried by atomization (powder).

The water content of the compressed yeast blocks was 60% w/w. The yeast cream was always centrifuged before the extraction experiments (20 min at 10 000 rpm). The water content of the centrifuged yeasts was 70% w/w. According to the provider, the Y. lipolytica had a TAG fraction of 17.7% w/w of the dry mass. The original raw materials were subjected to different pretreatments as described below:

1. The compressed yeast blocks were dried for 15 h at 60 °C and then milled and sieved (mesh = 1 mm).

2. The yeast cream was centrifuged (20 min at 10 000 rpm), dried for 15 h at 60 °C and then milled and sieved (mesh = 1 mm). 3. The yeast cream was centrifuged (20 min at 10 000 rpm). Then the centrifuged yeast was disrupted by rapid decompression after exposure to SCC0 2 (6 h at 20 MPa and 40 °C) following the procedure of Lin et a/. [START_REF] Lin | An improved method for disruption of microbial cells with pressurized carbon dioxide[END_REF] After that, the yeast was dried at 60 °C for 15 h, milled and sieved (mesh = 1 mm). 4. The yeast cream was centrifuged (20 min at 10 000 rpm). Then the centrifuged yeast was macerated in ethanol for 20 h (one part of yeast and nine parts of ethanol by weight), dried at 60 °c for 15 h and milled (mesh = 1 mm).

5. The yeast cream was centrifuged (20 min at 10 000 rpm). Then the centrifuged yeast was macerated in methanol for 2 h (one part of yeast and nine parts of methanol by weight), dried at 60 °c for 20 h and milled (mesh = 1 mm).

The milling process was done using a laboratory knife grinder (IKA, Model A 11 Basic). The size classification used a sieve EtMSCD yeast (view Table 1 ). Case B: WEtMSCD yeast (view Table 1 ). EtOH: ethanol and SC: supercritical.

Al Yeastcream

B[

Yeastcream

with a maximum particle diameter of 1 mm. Also, some of the pretreatments described above were combined to improve the extraction efficiency:

1. The compressed yeast blocks were dried for 15 h at 60 °C and then milled and sieved (mesh = 1 mm). This was followed by an ethanol maceration step (20 h at ambient temperature) and a filtration process. Then, the yeasts were disrupted by rapid decompression after exposure to SCC0 2 (2 h at 20 MPa and 40 °C) following the procedure of Lin et a/. [START_REF] Lin | An improved method for disruption of microbial cells with pressurized carbon dioxide[END_REF] 2. Ethanol maceration for 20 h at ambient temperature followed by centrifugation (only for the yeast cream). The yeasts were then milled and disrupted by rapid decompression after exposure to SCC0 2 (2 h at 20 MPa and 40 °C).

The flow diagrams of Fig. 1 show the different steps for the combined pretreatments described above. The materials used for the extractions and their corresponding acronyms are listed in Table 1.

Sa/vents

The C0 2 used for the phase equilibrium measurements and for the supercritical extractions was provided by L'Air Liquide with 99.9% purity. The ethanol used for the solubility measurements was absolute ethanol provided by Sigma Aldrich with a minimum purity of 99% by volume. The ethanol used for the supercritical extractions was supplied by Sigma Aldrich with a purity of 96% by volume. The methanol and chloroform used for the Soxhlet extractions and the ASE were of analytical grade. The solvents were supplied by Sigma Aldrich with a minimum purity of 99.9%. The acetone (analytical grade) used to purify the TAG fraction was provided by Scharlau with a minimum purity of 99.5% obtained by GC.

Experimental procedures

So/ubility measurements

To estimate the maximum oil concentration in the solvent that can be expected in the output effluent of a supercritical extractor, oil solubility measurements (phase boundaries) were performed. The experimental determination of the phase equilibrium for the 'yeast oil+ C0 2 ' binary system and the 'yeast oil+ C0 2 + ethanol' ternary system was carried out in a high-pressure variable-volume equilibrium cell (Top Industries S.A., France). The variable-volume windowed equilibrium cell could operate at pressures up to 50 MPa. The variable volume of the cell (13 ml maximum volume) made it possible to independently contrai pressure and temperature (in a constant volume cell, when temperature is increased, the pressure increase is correlated with it). This set up was based on the so-called 'synthetic method.' 15 ln this simple experimental method, the phase transitions, resulting from pressure variations, are observed by direct visualization.

To determine the solubility of oil in the solvent, a gravimetrically determined amount of yeast oil (TAGs fraction of yeast lipids) was placed inside the cell. Then, a given amount of C0 2 was loaded into the cell using a syringe pump (Teledyne Iseo, Madel 260D). For the ternary system, after the oil had been loaded and before loading the C0 2 , a gravimetrically determined a mou nt of absolute ethanol was placed inside the cell. At the end of the loading process, there was a mixture of known composition inside the cell. Next, the system was set under conditions of temperature and pressure such that a homogenous fluid could be observed through the cell window. Then, the pressure was slowly reduced, at constant temperature, until the fluid system became opalescent. This characteristic opalescence corresponded to the formation of a new dense phase. The variable volume equilibrium cell is similar to devices described earlier in the literature. 1 6 • [START_REF] Mchugh | the reacting mixture in the dimethyl carbonate synthesis from supercritical CO2[END_REF] The main elements of the experimental set-up are schematically represented in Fig. 2 and are fully described elsewhere. 18 The temperature was measured with an accuracy of ± 0.2 K and the pressure measurement was accurate to ± 0.02 MPa. Each experimental data point was repeated at least three times and each curve was measured twice. The uncertainties in the oil solubility values were estimated through a very conservative propagation of error analysis, for ail systems studied in this work. Overpressures were prevented by a rupture disk.

Soxhlet extractions and characterization of Soxhlet extracted lipids

Soxhlet extraction is a widely used and suitable method for determining the lipid content of a wide variety of solid matrices. However, it is a time-consuming technique which requires large volumes of organic solvents. For instance, using a solvent mixture of chloroform and methanol (2: 1 by volume), good results were obtained for a number of food products. Soxhlet extractions were carried out for 8 h with a chloroform: methanol solvent mixture (2: 1 by volume). After the extraction, the solvents were recovered in a rota-evaporator, which was operated with a vacuum pump.

The crude lipidic extract obtained from the Soxhlet extractor contained carbohydrates, proteins, and other unwanted materials, which were separated by a method based on the work of Hubbard eta/. [START_REF] Hubbard | Com parison of various methods for the extraction of total lipids, fatty acids, cholesterol, and other sterols from food products[END_REF] The first step of the method consisted in re-dissolving the crude lipidic extract in 50 ml of the original solvent mixture used for the Soxhlet extraction (chloroform: methanol, 2: 1 by volume) and then adding 12 ml of a solution of sodium chloride (NaCI) in distilled water (1% w/w). A separating funnel was used to decant the two-phase mixture for 2 h. The chloroform-rich heavy phase contained a mixture of TAGs and Pls. The chloroform was separated from the lipids using a rota-evaporator. ln the lipid mixture, the PL fraction was separated from the TAGs and quantified by adding cold acetone, which dissolves neutral lipids only. The acetone mixture was decanted into a separate beaker. This method is employed to enrich the PL content in commercial soybean lecithin [START_REF] Vandana | A simple method to enrich phospholipid content in commercial soybean lecithin[END_REF] and for oil recovery and lecithin production using water degumming sludge of crude soybean oils. 21 The lipid fraction that was insoluble in acetone was assumed to be the PL fraction. Lipids that were soluble in acetone were assumed to be TAGs and free fatty acids. The extraction and the purification processes were repeated at least twice. The experimental error caused by the presence of ethanol remaining in the total extract or acetone in the TAG fraction was considered negligible. Each extraction yield was noted as the mean value ± standard deviation.

Pump valve

Nit.rogen

Extraction rell

Callec: tion 11ial 2. Each run was repeated three times. The method was found to be very reproducible. Each extraction yield was noted as the mean value± standard deviation.

Acce/erated Sa/vent Extractions

Supercritica/ extractions

Supercritical CO 2 has been successfully used to extract lipids from oil seeds. This has been one of the most important and most-studied applications of this technology sin ce the pioneering works on this tapie were published. [START_REF] King | Supercritical fluid technology[END_REF] • 25 Supercritical studies More studies can be found for SCCO 2 lipid extraction from algae material 28 but few references 1 • 29 can be found in the literature about the detailed extraction of lipids from yeasts with CO 2 and co-solvents, especially taking into account the yeast pretreatment, which has a marked influence on the extraction efficiency.

Supercritical extractions were carried out in the pilot plant (Separex Chimie Fine Madel SF 300, France) represented in Fig. 4. Supercritical 'CO 2 + ethanol' extraction conditions were selected according to previous works 9 • 30 in order to obtain selectivitytowardsTAGs. The pilot plant has two cyclone separators downstream of the extractor. The maximum CO 2 flow rate was 1.6 x 10-3 kg s-1 • Ali the experiments were performed using a 54 ml tray to hold the yeast sample. The yeast was placed inside the tray, which had an upper and a lower stainless steel frit to allow the solvent to flow through the yeast sample. Subcooled liquid CO 2 was pumped by a volumetric membrane pump (Dosapro Milton Roy, Madel MB), then heated to the desired temperature and continuously introduced into the extractor. The maximum operating pressure was 30 MPa and the maximum temperature a round 60 °C. The experimental procedure has been described in previous publications. 11 • 31 Briefly, the heating system was set at the desired temperature and the extraction cylinder was filled with a given amount of yeast and placed inside the extractor vessel. Once the high pressure extractor vessel was closed, CO 2 was pumped into the extractor until the operating pressure was reached. A co-solvent was used to increase the solvent power of CO 2 and to facilitate the mechanical recovery of the extract in the separators. A given flow-rate of ethanol was pumped into the vessel to obtain the desired solvent mixture. Eight minutes were necessary to stabilize the process conditions. The extractor and the separator pressures were maintained using three back pressure regulators (BPRs).

Lipids + ethanol samples were taken from the separators every 5 or 10 min du ring the total extraction time (120-180 min). They were collected from the bottom of the separators in 100 ml glass flasks. Then the ethanol was separated from the lipids in a rota-evaporator at 60 °C operated with a vacuum pump. For each sample, the amount of extracted lipids was quantified gravimetrically after the separation. Each extraction curve was repeated twice. The mean extraction yield was noted.

The mass of yeast loaded was usually a round 20 g. The operating conditions were: 20 MPa in the extractor, 6 MPa in the first separator and 2 MPa in the second separator, a temperature of 40 °C for the extractor and the separators, a flow-rate of 30 ± 2 g min-1 of CO 2 and a flow rate of 3 ± 0.2 g min-1 of ethanol. The experiments were carried out for 120-180 min,

RESULTS

Solubility results

ln order to determine the maximum amount of oil that can be dissolved by the pure C0 2 or 'C0 2 + ethanol' mixture, the yeast oil solubility was measured as a function of pressure, at three different temperatures. Here the term 'yeast oil' corresponds to the extract obtained from the Soxhlet apparatus, then purified by acetone (i.e. it corresponds to the TAG and free fatty acid fraction).

Figure 5 shows the solubility data obtained in the present work as a function of pressure for the system 'yeast oil+ C0 2 ' at 40, 50 and 60 °C. The dashed lines in Fig. 5 correspond to smoothed data and have been added to facilitate the visualization of the trends. The results in Fig. 5 show that the solubility increased with the increase of pressure at a given temperature. On the other hand, the solubility decreased with the increase of temperature at constant pressure. This phenomenon is called 'retrograde solubility' and has often been reported in the literature. 32 Also, Fig. 5 shows that 10.35 ± 0.09 mg of yeast oil per g of pure C0 2 can be dissolved at 40 °C and 20.52 MPa. Raw experimental data for this system are reported in Table 3. 6 displays the experimental solubility data for the 'yeast oil + C0 2 + ethanol' system using a solvent mixture with 10% w/w of ethanol. The dashed lines in Fig. 6 correspond to smoothed data and have been added to facilitate visualization. The trends are similar to those presented for the 'yeast oil + C0 2 ' system. The solubility increased with increasing pressure at a given temperature and decreased with increasing temperature at constant pressure. The addition of ethanol to the solvent mixture increased the amount of oil that could be dissolved. According to Fig. 6, 12.55 ± 0.1 mg of yeast oil per g of solvent can be dissolved at 16.09 MPa and 40 °C. This value implies that, at 20 MPa and 40 °C, more than 12.55 ± 0.1 mg of yeast oil per g of solvent can be dissolved (around 15 mg of yeast oil per g of solvent, following the tendencies of Fig. 6). Cocero and Calvo 9 measured solubility data for the 'sunflower oil + C0 2 + ethanol' using a solvent mixture with 10% w/w of ethanol and the results obtained in the present work are consistent with theirs regarding the effect of pressure and temperature on the total a mou nt of oil dissolved. Raw experimental data for this system are reported in Table 3.

ln their study of S. cerevi si ae SCCO 2 extraction, using the same experimental set-up, Hegel etai. [START_REF] Hegel | Influence of pretreatments for extraction of lipids from yeast by using supercritical carbon dioxide and ethanol as cosolvent[END_REF] reported that, with this flow configuration, the maximum lipid concentration in the output fluid phase was about 4.5 mg of yeast oil per g of CO 2 • The maximum oil concentration in the CO 2 -rich fluid phase was significantly lower than the solubility observed in the present phase equilibrium results. This result shows that saturation of the solvent mixture was not reached in this case, probably because of hydrodynamic or mass transfer limitations in the extraction cylinder since channeling, entrance and exit flow perturbations and/or free convection effects cou Id be occur there.

Extraction results

Soxhlet extracti ons

Table 4 shows the results in terms of total extract, PL and TAG fractions after the Soxhlet extractions for the different yeast samples. These results were obtained after the separation procedure described above. The maximum amount of TAGs extracted was obtained for the ethanol-macerated (EtM) yeast. Also, the total extract shows a maximum for this pretreatment, reaching 29.7±2.So/ow/w ofdry mass. The unexpectedly high mass of total extract found in this case could be associated with a high water-content in the matrix, due to an incomplete drying process. For the methanol-macerated (MeM) yeast, the dried and milled (DM) yeast and the supercritical disrupted (SCD) yeast, similar results were obtained for the TAG fraction (between 7.4 ± 0.6 and 8.4±0. 7%w/w of dry mass). The worst extraction performance was obtained with the atomized (ATOM) yeast. Figures 7 and8 display the total extract yields and the TAG fraction yields respectively.

The TAG fraction given by the provider was never obtained, as can be seen in Table 4. The procedure used by the provider involved much longer extraction times (24 h) and successive changes of the solvent mixture. The results obtained in this work by the Soxhlet procedure show that a strong lipid-matrix interaction is present. The different pretreated materials gave different extraction results. As was shown by Hegel etai. [START_REF] Hegel | Influence of pretreatments for extraction of lipids from yeast by using supercritical carbon dioxide and ethanol as cosolvent[END_REF] for S. cerevisi ae, the key step for yeast oil extraction is the pretreatment Experimental TAG fraction yields for the Soxhlet method (in % w/w of dry mass). The bars correspond to the different pretreated yeast materials (Table 1). Dried and milled yeast (DM); atomized yeast (ATOM}; methanol macerated yeast (MeM); ethanol macerated yeast (EtM); supercritical disrupted yeast (SCD}. The results in Fig. 10 show that the best performance at the end of the extraction run was obtained for the EtM yeast. ln this case, the solute concentration in the fluid phase reached a value of 4.3 mg of lipids per g of solvent in the first part of the extraction curve. The total extraction yield at the end of the extraction was 10.8% w/w of dry mass. For the ATOM yeast, the total extract yield reached almost 8% w/w of dry mass but the shape of the extraction curve is markedly different. The initial solute concentration is very low (0.25 mg of lipids per g of solvent) and increases during the Experimental total extract yields for the ASE method (in % w/w of dry mass}. The bars correspond to the different pretreated yeast materials (Table 1). Dried and milled yeast (DM}; atomized yeast (ATOM}; methanol macerated yeast (MeM}; ethanol macerated yeast (EtM}; supercritical disrupted yeast (SCD).

--. ---+-- extraction. The highest concentration observed along the curve is around 0.5 mg of lipids per g of solvent. ln the final part of the extraction curve, the solute concentration in the fluid phase decreases again. For the SCD yeast, the initial slope is 2.4 mg of lipids per g of solvent. ln the second period of the extraction curve, a relatively high oil concentration, compared with the other curves (0.25 mg of lipids per g of solvent), is observed for this extraction stage. This relatively high slope is evidence of incomplete solute extraction caused by a strong matrix-lipid interaction. The yield at the end of the extraction reaches a value of 6.4% w/w of dry mass. The MeM yeast and the DM yeast show low initial concentrations, less than 2 mg of lipids per g of solvent, and also low total extract yield at the end of the extraction, less than 5% w/w of dry mass.

To improve the extraction yields, two combinations of different pretreatments were used (described in Fig. 1 ). A maceration step was combined with a drying and milling process and a supercritical disruption in different sequences. ln case Aof Fig. 1, the centrifuged cream yeast was subjected to a drying process (15 h at 60 °C) followed by a milling step (mesh = 1 mm). The dried material was macerated with ethanol for 20 hours at ambient temperature. Finally, the material was filtered and placed in the extractor. Then a supercritical disruption (2 h at 40 °c and 20 MPa and suddenly decompressed) was performed before the extraction.

To quantify the amount of lipids extracted by the ethanol in the maceration step, the solute was separated from the solvent in a rota-evaporator, operated with a vacuum pump. ln Table 1, the acronym used for this pretreated material is EtMSCD. ln case B of Fig. 1, the centrifuged cream yeast was not dried before maceration with ethanol. The wet yeast was left in contact with for 20 h at ambient temperature and then centrifuged again. The amount of lipids extracted by the ethanol in the maceration step was quantified, separating the solute from the solvent in the ethanol rich liquid phase using the same rota-evaporator described above. The yeast gel obtained after maceration was milled and placed in the extractor. A supercritical disruption (2 h at 40 °C and 20 MPa and suddenly decompressed) was performed before the extraction. The advantage of this combination of pretreatments is that it can be done in situ in an industrial extractor, because no drying step is involved. ln Table 1, the acronym used for this pretreated material is WEtMSCD.

The extraction results for these combined methods are shown in Table 6. The corresponding extraction curves are presented in Fig. 11. The EtMSCD pretreated material exhibited low yield (7.4 ± 0.3% w/w of dry mass). lt is very likely that part of the lipids was extracted by ethanol during the maceration step because, in this case, ethanol was separated from the solid by filtration, entraining the dissolved lipids. Regarding this result, the ethanol maceration step not only modified the matrix, allowing the extraction of bonded lipids, but it constituted a pre-extraction step. More than 50% of the total extract was obtained from the maceration step (determined by evaporation of the filtrate). The last experimental points of the extraction curve for this material show a solute concentration in the fluid phase (i.e. the slope of the extraction curve) of 0.12 mg of lipids per g of solvent. This value of concentration demonstrates that solute extraction was not complete at the end of the experiment and that there is a strong interaction between the solute and the matrix.

For the WEtMSCD pretreated material, similar behavior was observed but with an increase in the yield. The total extraction yield reached 25.4± 1.0% w/w of dry mass. ln Fig. 11 EtMSCD yeast (see Table 1). Grey squares: WEtMSCD yeast (see Table 1).

The retention time was the same for all the experiments. yield corresponding to the ethanol maceration is higher than 85%.

As was shown for the EtMSCD yeast, the maceration constituted a pre-extraction step. Nevertheless, the TAG fraction in the ethanol soluble extract was 30%. The ethanol-maceration pre-extraction step is not selective towards TAGs.

These results indicate that oil can be extracted from yeast in two different stages, non-selective ethanol extraction followed by TAGs-selective SCCO 2 purification.

DISCUSSION

The results shown above with the different extraction techniques indicate that the key step for complete lipid extraction is pretreatment of the matrix to weaken the interaction between lipids and biopolymers present in the membranes.

Drying is a thermal pretreatment usually applied in the edible oil industry in order to coagulate proteins, to decrease oil affinity for solid surfaces and to agglomerate the oil into larger droplets. 33 The extraction curve for the DM pretreated material (Fig. 10) showed that soluble lipids still have a strong interaction with the matrix at the start of the extraction process. The output fluid phase concentration in the first extraction period was less than 2 mg of lipids per g of solvent. This value is lower than the initial output fluid phase concentration obtained in previous work by Hegel et a!. [START_REF] Hegel | Influence of pretreatments for extraction of lipids from yeast by using supercritical carbon dioxide and ethanol as cosolvent[END_REF] for the extraction of TAGs from 5. cerevisiae with the same operating conditions in the same extractor, using oil impregnated glass beads. Also, this value is much lower than the thermodynamic solubility, which was experimentally determined in our high pressure cell. This low yield cou Id be attributed to the coagulation and agglomeration of proteins, which encapsulate the lipids to be extracted. These phenomena are caused by exposure to high temperature. Also, the incomplete drying of the material cou Id lower the extraction efficiency due to hydrophilic hindrance of the lipids to be extracted. However, the ethanol presence cou Id help to dehydrate the material.

The hypothesis for the low yield attributed to the coagulation of proteins in the drying process at 60 °C can be confirmed by looking at the results for the ATOM yeast. ln this case, the drying of the material was produced by rapid pulverization in heated air. According to the cumulative extraction curve, we can see that, at the end of the process, a larger amount of solute could be extracted from the ATOM yeast than the DM yeast. Nevertheless, the extraction curve of this material shows an unexpected shape, with a low solute concentration obtained in the first period of the extraction. This peculiar behavior is still not explained.

The SCD yeast was prepared following the procedure described by Lin etal. [START_REF] Lin | An improved method for disruption of microbial cells with pressurized carbon dioxide[END_REF] According to these authors, the pressurized C0 2 penetrates into the cells and breaks the cell walls during the releasing process. However, SCF disruption of the yeasts barely improved the results, when compared with the other pretreatments. The TAG fraction of extracted lipids was also found to be similar to our previous results.

Maceration in polar solvents, like alcohols, makes it possible to disrupt the interaction between lipids and other biopolymer molecules containing hydrogen bonds (COOH, NH 3 , and polar functional groups of proteins). The extraction yields from this material revealed the noteworthy impact of the pretreatment. The fraction of non-bonded lipids in the membrane was significantly increased after this pretreatment. The initial output fluid phase concentration was 4.3 mg of lipids per g of solvent. This increase in the concentration of the output extract indicates the presence of larger amounts of free-oil, compared with other pretreatments.

The combined pretreatment EtMSCD demonstrates that the drying process at 60 °C can coagulate the yeast proteins, leading to a decrease in the total extract yield. Without the drying process, as can be seen for the WEtMSCD pretreated yeast, the ethanol maceration pre-extraction step yields a large amount of extract. This combined pretreatment also demonstrates that the yeast lipids are soluble in ethanol and that the SCC0 2 extraction step can be useful for a TAG purification process.

CONCLUSION

Extraction of lipids from a non-conventional matrix, the yeast Y. lipolytica, has been carried out using three different extraction techniques: (i) Soxhlet extraction, (ii) ASE, and (iii) SCC0 2 + ethanol high pressure extraction. ln order to determine the maximum possible solute content at the output of the supercritical extractor, yeast oil solubility in pure C0 2 and in 'C0 2 +ethanol' was measured in a high pressure cell. ln both cases, the oil solubility increased with increasing pressure at a given temperature. Also, a retrograde solubility phenomenon was observed in the range of pressures tested. Roughly, at the conditions of the supercritical extractor (4 0 °c and 20 MPa), a maximum concentration of 10 mg of yeast oil per g of solvent can be expected in pure C0 2 • The addition of ethanol increases this value to almost 15 mg of yeast oil per g of solvent.

The Soxhlet extraction using a chloroform : methanol (2: 1 by volume) solvent mixture showed different yields depending on the type of pretreatment. The maximum TAG fraction and total extract were obtained for the EtM yeast. At the conditions tested in this work (8 h), this technique was unable to complete the lipid extraction in all the cases studied. The ASE results were similar to those obtained for the Soxhlet extraction. The highest yield was obtained for the EtM yeast with a total extract yield of almost 27 .7±0.3% w/w of dry mass. ASE reduced the time and the mate rial needed to evaluate the effectiveness of the different pretreatments compared with Soxhlet. 'SCC0 2 + ethanol' supercritical extraction curves revealed the extraction mechanism. ln the first part of the extraction curves, generally, the solute is not bound with other biomolecules and its concentration in the fluid phase has the highest value of the entire extraction curve. The second part of the extraction curves corresponds to a diffusion-controlled extraction stage, where the solute concentration in the fluid phase decreases significantly. The best total extraction performance was obtained f o r the EtM yeast. ln all cases studied a strong solute-matrix interaction was observed and the performance of the extraction was markedly dependent on the pretreatment of the material. Combined pretreatments revealed that the alcohol maceration constituted a pre-extraction step not selective toward TAGs. Oil can be extracted from Y. lipolytica in two different steps: a non selective ethanol extraction followed by TAG-selective SCC0 2 purification.

CentrifugationFigure 1 .

 1 Figure 1. Flow diagrams for the combined yeast pretreatments. Case A: EtMSCD yeast (view Table 1 ). Case B: WEtMSCD yeast (view Table 1 ). EtOH: ethanol and SC: supercritical.

19

 19

2 Figure 2 .

 22 Figure 2. Schematic experimental setup of the high pressure phase equilibrium cell: 1. magnetic stirrer, 2. sapphire windows, 3. pressure valve, 4. pressure transducer, S. thermometer, 6. thermostatic bath, 7. screw pump.

Figure 3 .

 3 Figure 3. Schematic for experimental setup of the accelerated solvent extractor.

A

  recently developed method to determine lipid content is accelerated solvent extraction (ASE ® ), a technique registered by Dionex, Germany.[START_REF] Richter | Accelerated solvent extraction: a technique for sample pre paration[END_REF] This technique uses liquid solvents at high temperatures and pressures. The solvents are those normally used for standard liquid extraction techniques such as Soxhlet. The ASE technique reduces the volume of solvent required and shortens the sample extraction time compared with Soxhlet. ASE yields are comparable with those obtained with the Soxhlet method.[START_REF] Schafer | Accelerated solvent extraction of lipids for determining the fatty acid composition of biological material[END_REF] Nevertheless, there is evidence that ASE efficiencies depend on specific lipid-matrix interactions.23 Yeast lipid extraction was performed by the ASE technique 22 with a chloroform: methanol solvent mixture (1 : 1 by volume, using the same solvents as for the Soxhlet extractions). High pressure and temperature operation accelerated the extraction kinetics. ASE can be used to replace Soxhlet extraction for the determination of oil content in conventional matrices, such as oil seeds. An automated extraction system for accelerated solvent extraction (Dionex Madel ASE 200, Germany) was used to perform the extractions. The ASE system (Fig. 3) consists of a stainless steel sample cell with electronically controlled heaters and pumps to maintain extraction parameters (pressure, temperature, volume of solvent, extraction time) at the programmed set points. The upper temperature limit at the extraction system is 200 °c. To begin the extraction,a 2 g yeast sample was placed in an 11 mlstainless steel cell and then the cell was filled with the extraction solvent mixture. A static extraction cycle began at high temperature (80 °C) and pressure (10 MPa). The different yeast samples were subjected to five static extraction cycles of 8 min each. The extract was filtered with a cellulose filter and a stainless steel frit at the outlet, and finally collected in a 40 ml glass vial. The extraction conditions for the yeast samples are shown in Table

Fi g ure 4 .

 4 Simplified flow sheet of the pilot plant for the supercritical extraction experiments: B, CO 2 cylinder; E, extraction vessel; 5, separators; P, pump; G, cooling and heating group; D, back pressure regulator valves; C, co-solvent; VE, venting system.

22 24

 22 Fi g ure S. Experimental solubility values as a function of pressure for the ystem 'yeast oil + CO/ at three different temperatures. Filled triangles: 40 °C; empty circles: 50 °C; grey squares: 60 °C. Triangles, circles and quares: raw experimental data (this work). Dashed lines: smoothed data.

2 : 20 Figure 6 .

 2206 Figure 6. Experimental solubility values as a function of pressure for the system 'yeast oil + CO 2 + ethanol' with a solvent mixture of 90% w/w of CO 2 and 10% w/w of ethanol at three different temperatures. Filled triangles: 40 °C; empty circles: 50 °C; grey squares: 60 °C. Triangles, circles and squares: raw experimental data (this work). Dashed lines: smoothed data.

Figure 7 .

 7 Figure 7. Experimental total extract yields for the Soxhlet method (in % w/w of dry mass). The bars correspond to the different pretreated yeast materials (Table1). Dried and milled yeast (DM); atomized yeast (ATOM); methanol macerated yeast (MeM); ethanol macerated yeast (EtM); supercritical disrupted yeast (SCD).

Figure 10

 10 Figure 10 shows the results of the extraction for the different pretreated yeasts. The residence time of the solvent was kept constant in all the experiments. The comparative results of the 'SCC0 2 + ethanol' extractions are shown in Fig. 1 O. The dashed lines in Fig. 10 correspond to smoothed data and have been added to facilitate visualization of the trends. ln the first part of the extraction curves the solute concentration in the fluid phase is generally high, as can be seen from the high slopes of the curves. The different pretreatments can affect the interactions between the lipids and other biomolecules. ln the first extraction period, the accessible free solute can easily be removed by the solvent. The amount of free solute depends on the efficiency of the pretreatment. High lipid concentration in the output fluid phase can be found in this extraction step. ln the second period of the extraction curves, the solute concentration in the output fluid phase decreases significantly. This is a diffusion-controlled extraction stage characterized by a strong solute-matrix interaction.The results in Fig.10show that the best performance at the end of the extraction run was obtained for the EtM yeast. ln this case, the solute concentration in the fluid phase reached a value of 4.3 mg of lipids per g of solvent in the first part of the extraction curve. The total extraction yield at the end of the extraction was 10.8% w/w of dry mass. For the ATOM yeast, the total extract yield reached almost 8% w/w of dry mass but the shape of the extraction curve is markedly different. The initial solute concentration is very low (0.25 mg of lipids per g of solvent) and increases during the

  0 =..;.;__....._ ____________ ....._ __ ___,J 0 •free yeast (9'g) , Fi g ure 1 O. SCC0 2 + cosolvent experimental extraction curves for differ ent pretreated Y. lipolytica yeast samples. Extraction conditions: 30 g C0 2 min-1 , 3 g EtOH/min, 40 °c and 20 MPa in the extractor. Dashed lines: smoothed data. Filled squares: dried and milled yeast (DM}; X: methanol macerated yeast (MeM); empty circles: supercritical disrupted yeast (SCD}; grey rhombuses: atomized yeast (ATOM}; black triangles: ethanol macer ated yeast (EtM}. The retention time was the same for all the experiments.

  , the extraction curve for this material shows asymptotic behavior. The slope of the curve at the end of the experiment is almost zero, showing that solute extraction was complete. The fraction of the total extraction 40

Figure 11 .

 11 Figure 11. SCCO 2 + cosolvent experimental extraction curves for the different combinated pretreatments in Y. lipolytica yeast samples. Extraction conditions: 30 g CO 2 min-1 , 3 g ethanol min-1 , 40 °C and 20 MPa in the extractor. Dashed lines: smoothed data. Empty circles:EtMSCD yeast (see Table1). Grey squares: WEtMSCD yeast (see Table1). The retention time was the same for all the experiments.

Table 1 .

 1 Acronyms for the different pretreated materials. The grey filled cells represent the combination of a raw material (in rows) with a given pretreatment (in columns) Raw materials are listed in rows and the different pretreatments in columns. When a given raw material was subjected to a given pretreatment, the corresponding box is shaded gray. The last column shows the acronyms used in this work to identify the extraction materials.

	Pretreatment		Dried	Milled		MeOH	EtOH
	Raw material	Centrifugation	(60 C)	(mesh = 1 mm)	SC disruption	maceration	maceration	Acronym
	Compressed yeast block							DM
	Atomized							ATOM
	Yeast cream (water suspension)							DM
								SCD
								MeM
								EtM
								EtMSCD
								WEtMSCD

Table 2 .

 2 Extraction conditions for the ASE techniquehave been reported for the extraction of high added-value products from yeast, such as astaxanthin and squalene. 1 , 26 ,[START_REF] Lim | Separation of astaxanthin from red yeast Phaffia rhodozyma by supercritical carbon dioxide extraction[END_REF]

	Cell volume [ml]	11
	Mass of yeast loaded [g]	"'2
	Pressure [MPa]	10
	Temperature [ ° C]	80
	Static extraction time [min]	8
	Number of cycles	5
	Chloroform-methanol volume ratio	1 :1
	Amou nt of solvent renewed on each cycle [%]	100

Table 3 .

 3 Experimental phase equilibrium data for the systems 'CO 2 + yeast oil' and 'CO 2 + ethanol + yeast oil' (this work) CO 2 + yeast oil T = 40 °C

	Pressure [MPa]	Solubility [mg oil g-1 solvent]
	13.76	2.3 ± 0.1
	14.9	3.9±0.1
	17.31	6.98 ± 0.1
	20.52	10.35 ± 0.09
	T = 50 °C
	16.48	2.3 ± 0.1
	17.44	3.9±0.1
	20.16	6.98 ± 0.1
	22.23	10.35 ± 0.09
	T = 60 °C
	16.83	1.93±0.1
	19.71	3.9±0.1
	21.68	6.98 ± 0.1
	23.57	10.35 ± 0.09
	T = 40 °C
	10.18	1.99 ± 0.1
	13.26	4.44 ± 0.1
	13.73	6.70 ± 0.1
	16.09	12.55 ± 0.1
	T = 50 °C
	12.32	1.99 ± 0.1
	14.40	4.44 ± 0.1
	15.05	6.70 ± 0.1
	17.31	12.55 ± 0.1
	T = 60 °C
	14.41	1.99 ± 0.1
	16.43	4.44 ± 0.1
	16.82	6.70 ± 0.1
	18.12	12.55 ± 0.1
	Figure

CO 2 (90% w/w) + ethanol (10% w/w) + yeast oil

Table 4 .

 4 Soxhlet lipid extraction results using 2 chloroform:1 methanol (by volume) mixture as solvent

	DM
	ATOM
	MeM
	EtM
	SCD
	35

Table 1

 1

	Acce/erated sa/vent extracti ons
	ln the present work, the aim of the ASE experiments was to assess
	the influence of the different pretreatments and not to perform
	complete lipid extraction. For each extraction, 40 min and less
	than 40 ml of solvent mixture were used. The experimental results
	obtained are shown in Table S. Figure 9 displays a bar graph with
	the total extractyield. Due to the small amounts of extract obtained
	in each ASE run, it was not possible to differentiate the lipid
	composition (TAGs, PLs) in the total extract (following Hubbard et a/.'s purification procedure 19 ). Here also, the pretreatments have
	a remarkable effect. The highest yield was obtained for the EtM
	yeast. The total extraction yield reached 27.7 ± 0.3% w/w of dry
	mass. This result is consistent with the one obtained for the Soxhlet
	extraction. The unexpectedly high mass of total extract cou Id be
	associated with an incomplete drying process. The MeM yeast and
	the ATOM yeast showed similar results with a total extraction yield
	of 16.2 ± 0.3% w/w of dry mass and 15.6 ± 0.3% w/w of dry mass,

). Dried and milled yeast (DM); atomized yeast (ATOM); methanol macerated yeast (MeM); ethanol macerated yeast (EtM); supercritical disrupted yeast (SCD).

of the matrix. The Soxhlet technique was unable to complete the lipid extraction in almost ail the cases studied. respectively. The lowest total extraction yields were obtained for the SCD yeast and the DM yeast with values of 11.5 ± 0.3% w/w of dry mass and 11.6 ± 0.3% w/w of dry mass respectively. According to these results, ASE extraction performance is comparable with that of Soxhlet extraction but saving time and materials.

Table 5 .

 5 ASE

results. The extraction conditions are listed in Table 1 Total extract yield [% w/w of dry mass] DM ATOM MeM EtM SCD Supercritica/ extractions 11.6 ± 0.3 15.6 ± 0.3 16.2 ± 0.3 27.7 ± 0.3 11.5 ± 0.3

Table 6 .

 6 Extraction results for the combined pretreatments listed in Table1

		EtMSCD total	WEtMSCD total
		extract yield	extract yield
		[% w/w of dry mass]	[% w/w of dry mass]
	Pre-extraction	4.1 ±0.2	22.2 ± 1.0
	(maceration)
	with ethanol
	SC extraction	3.3 ± 0.2	3.2 ± 0.2
	Total	7.4 ± 0.3	25.4±1.0

ACKNOWLEDGEMENTS

The authors would like to thank the Agence Nationale de la Recherche (ANR) for its financial support to this research through the LIPICAERO project, and one of the partners, the Lesaffre Group, for providing the samples of Y. /ipo/ytica used in this work.


Carole Michel

Sylvie Salvatico

Haouaria Belkhelfa

Laïla Haddioui

C Roques
email: ch.roques@wanadoo.fr

Activity of Drill ® lozenges on the main microorganisms responsible for upper respiratory tract infections

Keywords: Sore throat, Chlorhexidine, H1 N1 virus, Upper respiratory tract infections

Activity of Drill® lozenges on the main microorganisms responsible for upper respiratory tract infections

Open Archive TOULOUSE Archive Ouverte (OATAO)

OATAO is an open access repository that collects the work of Toulouse researchers and makes it freely available over the web where possible. , Head and Neck Diseases, vol. 130 (n° 4). pp. 189-193. ISSN 1879-7296 Any correspondance concerning this service should be sent to the repository administrator: staff-oatao@listes-diff.inp-toulouse.fr

To cite this version :

  This is an author-deposited version published in : http://oatao.univ-toulouse.fr/ Eprints ID : 9760 To link to this article : DOI:10.1016/j.anorl.2012.09.009 URL : http://dx.doi.org/10.1016/j.anorl.2012.09.009 Michel, Carole and Salvatico, Sylvie and Belkhelfa, Haouaria and Haddioui, Laila and Roques, Christine. Activity of Drill® lozenges on the main microorganisms responsible for upper respiratory tract infections. (2013) European Annals of Otorhinolaryngology


Emmanuel Motheau
email: emmanuel.motheau@cerfacs.fr

Yoann Mery
email: yoann.mery@snecma.fr

Franck Nicoud
email: franck.nicoud@univ-montp2.fr

Thierry Poinsot
email: thierry.poinsot@cerfacs.fr

Analysis and Modelling of Entropy Modes in a Realistic Aeronautical Gas Turbine

A combustion instability in a combustor typical of aero-engines is analyzed and modeled thanks to a low order Helmholtz solver. A Dynamic Mode Decomposition (DMD) is first applied to the Large Eddy Simulation (LES) database. The mode with the highest amplitude shares the same frequency of oscillation as the experiment (approx. 350 Hz) and it shows the presence of large entropy spots generated within the combustion chamber and convected down to the exit nozzle. The lowest purely acoustic mode being in the range 650-700 Hz, it is postulated that the instability observed around 350 Hz stems from a mixed entropy/acoustic mode where the acoustic generation associated with the entropy spots being convected throughout the choked nozzle plays a key role. A Delayed Entropy Coupled Boundary Condition is then derived in order to account for this interaction in the framework of a Helmholtz solver where the baseline flow is assumed at rest. When fed with appropriate transfer functions to model the entropy generation and convection from the flame to the exit, the Helmholtz solver proves able to predict the presence of an * Address all correspondence to this author.

G Gain of the transfer function Z Impedance Z p,u Impedance defined with state variables p and û Z J,m Impedance defined with state variables Ĵ and m Z 0 Impedance imposed at the edge of the zero Mach number domain Z M Impedance computed at the edge of the LEE domain

unstable mode around 350 Hz, in agreement with both the LES and the experiments. This finding supports the idea that the instability observed in the combustor is indeed driven by the entropy/acoustic coupling.

Introduction

It has been long known that combustion instabilities in industrial systems can lead to high amplitude oscillations of all physical quantities (pressure, velocities, temperature, etc.). A classical mechanism for combustion instability is a constructive coupling between acoustic waves and the unsteady combustion that arises when pressure and heat release fluctuations are in phase [START_REF] Rayleigh | The explanation of certain acoustic phenomena[END_REF][START_REF] Lieuwen | Combustion instabilities in gas turbine engines. operational experience, fundamental mechanisms and modeling[END_REF]. Another mechanism that may also support self-sustained instabilities relies on the acoustic perturbations induced by entropy spots (temperature and/or mixture heterogeneities say) being generated in the flame region and evacuated through the downstream nozzle [START_REF] Culick | Unsteady Motions in Combustion Chambers for Propulsion Systems[END_REF][START_REF] Hield | Thermoacoustic limit cycles in a premixed laboratory combustor with open and choked exits[END_REF]. This latter mechanism is particularly relevant to (high speed) reacting flows where the flow through time is small and turbulent mixing cannot significantly reduce the amplitude of the entropy spots being convected from the flame region to combustor exit.

Several recent studies have shown that the Large Eddy Simulation (LES) approach is a powerful tool for studying the dynamics of turbulent flames and their interactions with the acoustic waves [START_REF] Huang | Bifurcation of flame structure in a lean premixed swirl-stabilized combustor: Transition from stable to unstable flame[END_REF][START_REF] Schmitt | Large-eddy simulation and experimental study of heat transfer, nitric oxide emissions and combustion instability in a swirled turbulent high-pressure burner[END_REF]. However, these simulations are very CPU demanding and faster tools are required in the design process of new burners. A natural approach is to characterize the stable/unstable modes in the frequency domain. An approximate linear wave equation for the amplitude p(x) of the pressure perturbations p(x,t) = p(x)exp(-jωt) in reacting flows may be derived from the Navier-Stokes equations [START_REF] Poinsot | Theoretical and Numerical Combustion[END_REF] and reads:

∇ • c 2 0 ∇ p + ω 2 p = jω(γ -1) q (1)
where q(x) is the amplitude of the unsteady heat release q(x,t) = q(x)exp(-jωt), c 0 is the speed of sound, and ω is the complex angular frequency. In order to close the problem, the flame is often modeled as a purely acoustic element thanks to a nτ type of model [START_REF] Crocco | Aspects of combustion instability in liquid propellant rocket motors. part II[END_REF] which essentially relates the unsteady heat release to acoustic quantities at reference locations; Eq. ( 1) then corresponds to a non-linear eigenvalue problem which can be solved by using appropriate algorithms [9]. Eq. ( 1) relies on the so-called zero Mach number assumption stating that the mean velocity is very small compared to the speed of sound. A recent study suggests that the domain of validity of the zero mean flow assumption might be rather small [START_REF] Nicoud | About the zero mach number assumption in the calculation of thermoacoustic instabilities[END_REF]. One reason for this is that Eq. ( 1) does not support entropy waves. Thus the acoustic generation due to the entropy spot being accelerated in the nozzle/turbine located downstream of the combustion chamber is not accounted for. Since the production of sound by acceleration of entropy fluctuations is a key phenomenon when dealing with combustion noise [START_REF] Marble | Acoustic disturbances from gas nonuniformities convected through a nozzle[END_REF][START_REF] Leyko | Comparison of direct and indirect combustion noise mechanisms in a model combustor[END_REF], neglecting this acoustic source when studying thermoacoustic instabilities is highly questionable. Note also that mixed modes may exist that rely on a convective path and acoustic feedback when the baseline flow is not at rest [START_REF] Culick | Unsteady Motions in Combustion Chambers for Propulsion Systems[END_REF], and that cannot be captured when using Eq. ( 1).

Nevertheless, this somewhat restrictive assumption is necessary to derive a wave equation for the thermoacoustic perturbations superimposed to a non isentropic baseline flow, the alternative being to use the complete set of Linearized Euler Equations (LEE) [START_REF] Nicoud | About the zero mach number assumption in the calculation of thermoacoustic instabilities[END_REF]. Unfortunately, this would make the computational effort needed to compute the thermoacoustic modes significantly larger (five coupled equations being solved for) than what is required when dealing with Eq. ( 1). Being able to partly account for the non zero Mach number effects without relying on the LEEs is therefore highly desirable. The objectives of this paper are then as follows:

• analyze fully nonlinear large-eddy simulation data to test for the presence of mixed modes in a realistic combustion chamber; • develop and validate a methodology to mimic the mean flow effects within the zero Mach number framework (Eq. 1); • apply the method to a 3D industrial combustor where entropy-acoustic coupling is included in the Helmholtz solver framework.

First, the industrial configuration and associated instability are presented in Section 1; a Dynamic Mode Decomposition (DMD) is applied to the LES results in order to investigate the presence of an entropy-acoustic coupling. A proper formalism is then introduced in Section 2 in order to account for the entropy-acoustic coupling within the zero Mach number framework. The underlying Delayed Entropy Coupled Boundary Condition (DECBC) is also validated in this section by considering an academic quasi-1D combustor mounted on a nozzle. Finally, results from a zero Mach number Helmholtz solver with and without the DECBC approach are presented in Section 3 to illustrate the benefit of the method.

Description of the combustor and analysis 1.Geometry

The case considered in this study is a combustor developed by the SAFRAN Group for aero-engine applications. The main parts are displayed in Figure 1 which shows the combustion chamber and the casing with primary and dilution holes. The air inlet connected to the upstream compressor is also displayed. Note that the downstream high pressure distributor which connects the combustor to the turbine is modelled by a chocked nozzle with equivalent cross section area. For chocked conditions, this ensures that the chamber sees an acoustic environment close to the actual one. The fuel line is also visible, as well as a cut of the swirled injector used to mix fuel and air and to generate the recirculation zone which stabilizes the flame. In the actual situation, several injectors are mounted all around the azimuthal combustion chamber although only one sector with one injector is displayed in the figure. For confidentiality concerns, some parts of the geometry are not displayed in Figures 1, 2, 3 and 6.

DMD analysis of the LES data

Experiments were performed by SAFRAN on the configuration described in section 1.1. Under certain operating conditions, the configuration becomes unstable at approximately 350 Hz. To analyze this instability, large eddy simulations (LES) were performed at CERFACS and SAFRAN. For this purpose, the general AVBP [START_REF]AVBP Handbook[END_REF] code developed at CERFACS and IFP Energies Nouvelles was used. It is based on a cell-vertex formulation and embeds a set of finite element / finite volume schemes for unstructured meshes. In the present study an implementation of the Lax-Wendroff scheme (2 nd order in time and space) was retained. Two regimes were computed by LES, corresponding to the two operating conditions investigated experimentally at SAFRAN: one which contains an instability at 350 Hz and one which shows no instability. Although not discussed in this paper, the LES was able to distinguish these two regimes very nicely, displaying a stable turbulent flame for the latter regime and an unstable mode close to 330 Hz for the former. These flows were computed over a 4.5 million elements mesh with the static Smagorinsky subgrid scale model whereas turbulent combustion was represented with the Dynamic Thickened Flame Model [START_REF] Colin | A thickened flame model for large eddy simulations of turbulent premixed combustion[END_REF]. A simple two-step kinetic scheme was used to represent the kerosene-air flame in the combustor [START_REF] Franzelli | A two-step chemical scheme for Large-Eddy Simulation of kerosene-air flames[END_REF]. The boundary conditions are imposed through the NSCBC formulation [START_REF] Poinsot | Boundary conditions for direct simulations of compressible viscous flows[END_REF] so as to prevent spurious acoustic reflections. Note that as the nozzle is chocked, the physics inside the combustion chamber depends only upon the sonic throat which imposes the effective outlet state. Figure 2 displays a typical snapshot of the LES where the complex 3D flame structure can be seen on top of the temperature field. A pressure signal at a probe within the combustion chamber demonstrates the presence of a thermoacoustic instability at approx. 350 Hz. The amplitude of the limit cycle is quite large and may be explained by the fact that some acoustic dampers such as perforated liners were not included in the computations. However, this result is in the range of pressure fluctuations amplitudes measured in the experiments (∼ 8.10 4 Pa peak to peak). Note also the the amplitude was found robust to the shape of the nozzle used to mimic the high pressure distributor. Dynamic Mode Decomposition (DMD) was applied to the LES data in order to better understand the nature of the instability illustrated in Figure 2. For this purpose, 250 snapshots were recorded over a time range corresponding to approx. 13 cycles characteristics of the instability phenomena, thus leading to a sampling of 20 snapshots by period. This amount of data is sufficient for the DMD to breakdown the reactive turbulent flow into dynamically relevant structures with periodic evolution over time [START_REF] Schmid | Dynamic mode decomposition of numerical and experimental data[END_REF]. Note that the input vectors for the DMD algorithm were built from the nodal values of pressure, static temperature and reaction rate at each grid point of the mesh used for the LES. The fluctuating pressure and temperature fields reconstructed from the DMD mode with the highest amplitude are displayed in Figure 3. Note that this mode oscillates at 331 Hz, in good agreement with the experimental data. The four phases displayed in Figure 3 support the idea that the unstable mode of interest relies, at least partly, on an entropy-acoustic coupling. At phase 0, the pressure is low everywhere within the combustion chamber and a pocket of cold gas is present downstream of the primary reaction zone, roughly at the middle of the combustion chamber. At phase π/2, this pocket is convected downstream and the unsteady pressure in the chamber is approximately zero. At phase π, this cold pocket interacts with the exit nozzle and a new pocket of hot gas is generated downstream of the primary zone, while the fluctuating pressure within the chamber is now positive. At phase 3π/2, the pocket of hot gas is convected by the mean flow and the pressure within the chamber decreases. Note that each interaction between hot or cold pocket of gas and the nozzle generates acoustics [START_REF] Marble | Acoustic disturbances from gas nonuniformities convected through a nozzle[END_REF] which may propagate downstream (generating what is known as indirect noise) or upstream (generating another perturbation of the flame region and promoting the creation of a new entropy spot).

The idea that the unstable mode close to 350 Hz involves a coupling between entropy and acoustics is further supported by the numerical Helmholtz analysis of the combustor, which shows that the smallest thermoacoustic frequency mode is close to 670 Hz, very far from the observed 350 Hz (see Section 3 for a longer discussion). Although not shown in this paper, the DMD analysis also capture a weaker mode at 680 Hz which only exhibit small pressure fluctuations (∼ 1.10 3 Pa) and no significant temperature fluctuations (∼ 60 K), suggesting that this mode is purely of acoustic nature, which is consistent with the Helmholtz analysis. In the next two sections, we introduce an acoustic-entropy coupling strategy into the Helmholtz framework to investigate whether such a coupling can predict the 350 Hz mode.

2 Introducing entropy-acoustic coupling in the Helmholtz framework Since Eq. ( 1) assumes no mean flow, it is necessary to restrict the study of thermo-acoustic instabilities to only the combustion chamber (where the Mach number is always small). It is then crucial to take into account the proper acoustic environment of the combustor, as for example the presence of a compressor or a turbine; this is illustrated in Figure 4 where Z 0 up stands for the proper acoustic impedances that must be imposed at the edges of the Helmholtz domain in order to account for the acoustic waves transmission/reflection due to the compressor and turbine.

Acoustic boundary conditions

The acoustic impedance of a non zero Mach number flow element can be assessed analytically under the compact assumption [START_REF] Marble | Acoustic disturbances from gas nonuniformities convected through a nozzle[END_REF]. This acoustic impedance gives rise to a relationship between the inlet acoustic velocity entering the element and the acoustic pressure as follows:

ρ 0 c 0 Z M up û -p = 0 or alternatively c 0 ρ 0 Z M mJ m -Ĵ = 0 (2)
where m and Ĵ are the (complex amplitude of the) mass flow rate and total enthalpy respectively and Z M up and Z M mJ are the impedances associated with variables ( û, p) and ( m, Ĵ) respectively. Moreover, the superscript M denotes the fact that the choked compact nozzle. This quantity can then be used as a proper acoustic boundary condition at the edge of the Helmholtz domain; one obtains

Z 0 up = 1 M 1 + (γ -1)M 2 /2 1 + (γ -1)/2 (6)
which is different from the classical nozzle impedance Z M up = 2/(γ -1)M derived from Eq. (4).

Delayed entropy coupled boundary conditions

Imposing the acoustic impedance, Eq. ( 6), means neglecting the entropy-acoustics coupling and the subsequent sound being generated by the entropy spots flowing through the exit nozzle or turbine. This coupling is contained in the boundary condition Eq. ( 4) or [START_REF] Huang | Bifurcation of flame structure in a lean premixed swirl-stabilized combustor: Transition from stable to unstable flame[END_REF]. Note however that ŝ is not available in the Helmholtz domain. Thus the entropy fluctuation at the edge of the combustion chamber must be modeled before Eq. ( 4) or ( 5) can be applied. Assuming that the entropy fluctuations flowing through the exit have first been generated in the flame region before being convected by the mean flow, one obtains ŝ = ŝ f exp( jωτ c ) where ŝ f is the amount of entropy generated by the flame and τ c is the convection time from the flame to the exit. Consistently with the Helmholtz framework, it is then useful to relate the generated entropy ŝ to some acoustic quantity. It is done here in a way similar to the nτ model [START_REF] Crocco | Aspects of combustion instability in liquid propellant rocket motors. part II[END_REF] for unsteady heat release, connecting the entropy fluctuation to the acoustic velocity taken at a reference point located upstream of the flame region :

ŝ f = G us e jωτ us ûref (7)
where G us and τ us are, respectively, the gain and the time delay of the entropy generation from an acoustic perturbation ûref . These quantities can be assessed analytically in the simple case of a 1D premixed flame [START_REF] Motheau | Using boundary conditions to account for mean flow effects in a zero mach number acoustic solver[END_REF]19] and read:

G us = - ρ u (γ -1)(T b -T u )C 2 p ρ b u b c 2 b ; τ us = 0 ( 8
)
where the subscripts u and b denote the unburnt and burnt gas respectively. Note that τ us = 0 because the referential velocity is considered at the flame location. Eventually, for the simple case of a 1D premixed flame in a duct, the proper boundary condition at the downstream edge of the Helmholtz domain is (assuming that burnt gas are present at this boundary and C p is constant):

c b Z 0 up û -p/ρ b -G us e jωτ c c 2 b (1 -M 2 b ) C p (γ + 1) ûref = 0 (9)
Note that (ρ b û, p/ρ b ) replace ( m, Ĵ) in Eq. ( 5) as appropriate in a zero Mach number flow domain. Note also that under the zero Mach number assumption, the momentum equation for the fluctuations reduces to jρω û = d p/dx so that Eq. ( 9) is indeed a boundary condition for the acoustic pressure that can be used when solving the Helmholtz equation. As a validation case, the Delayed Entropy Coupled Boundary Condition (DECBC) for 1D compact flames, Eq. ( 9), was used together with the Helmholtz equation to analyze an academic 1D combustor mounted on a compact nozzle (see [START_REF] Motheau | Using boundary conditions to account for mean flow effects in a zero mach number acoustic solver[END_REF] for the details of the geometry and physical parameters). As illustrated in Figure 5, the proposed coupled boundary condition provides a good prediction of the first acoustic mode in the combustor over the entire range of Mach numbers considered. The first low frequency mode is an entropic mode, also referred to as rumble, which involves the convection of entropy spots from the flame to the exit nozzle; consistently, its frequency of oscillation increases linearly with the Mach number, in contrast to the first acoustic mode whose frequency is virtually constant. Interestingly enough, this low frequency mode is also recovered by the zero Mach number approach completed by the DECBC, demonstrating that the proposed approach properly accounts for the entropy-acoustic coupling in thermoacoustic systems. Of course, when the Helmholtz equation is solved with Eq. ( 6) as a boundary condition, the entropic mode is not found. Furthermore, the first acoustic mode is not captured as accurately as when the entropy coupling is modeled at the exit boundary. Even if the comparison is not as good regarding the growth rate of the different modes, the DECBC approach allows a significant improvement of the results from the Helmholtz equation.

Helmholtz analysis of the SAFRAN combustor

In this section, Helmholtz analysis of the industrial combustor described in Section 1 is performed. Recall that this configuration exhibits a low frequency mode of oscillation at a frequency significantly smaller than any acoustic mode; it is thus natural to investigate whether the DECBC approach described in Section 2 recovers this low frequency mode.

Name DECBC Active Flame Frequency (Hz) Growth/decay rate (s Contrary to the simple case considered in Section 2.2, the flame in the SAFRAN combustor is neither 1D nor premixed. Thus, the simple analytical model Eq. ( 8), used to derived the boundary condition Eq. ( 9), is not relevant for the 3D case of interest. Instead, the transfer function between the acoustic velocity upstream of the flame and the entropy generated downstream of the primary zone was assessed by post-processing the LES. More precisely, this entropy transfer function was defined as

G LES us e jωτ LES us = < ŝ f > ûref • n ref (10)
where n ref is a unitary vector of reference aligned with the main axis of the combustor, ûref is the acoustic velocity at the reference point depicted in Figure 6 and < ŝ f > is the entropy fluctuation averaged over a small volume located downstream of the primary combustion zone, in agreement with the mode structure observed from the DMD analysis of Section 1.2 (see also Figure 3). Obtaining the acoustic velocity fluctuations ûref is a difficulty because the reference point is located inside the swirler where hydrodynamics fluctuations occurs. However, as the present study focuses on a low-frequency instability, the hydrodynamic component is considered negligible. Note that this transfer function is similar to but different from the classical flame transfer function which relates the upstream acoustic velocity to the unsteady heat release thanks to a nτ type of model [START_REF] Crocco | Aspects of combustion instability in liquid propellant rocket motors. part II[END_REF]9]. Following the rationale developed in section 2.2, the LES data were also used to measure the convection time τ LES c from the flame region to the end of the combustion chamber (see Figure 6). Note that because the entropy spots decay during their convection through the chamber exit (because of the turbulent mixing and dissipation), the time delay τ LES c must be completed by a gain G LES c (smaller than unity) to relate the entropy in the flame region to the entropy at the exit :

ŝ = G LES c e jωτ LES c < ŝ f > (11)
Finally, the entropy fluctuations in Eq. ( 5) can be modeled as :

ŝ = G LES us G LES c e jω(τ LES us +τ LES c ) ûref • n ref ( 12
)
The DECBC condition for the 3D SAFRAN combustor is obtained by injecting Eqs. ( 6) and ( 12) into (5) and reads:

c b Z 0 up û • n BC -p/ρ b - G LES us G LES c e jω(τ LES us +τ LES c ) c 2 b (1 -M 2 b ) C p (γ + 1) ûref • n ref = 0 ( 13
)
where n BC is the unitary outward vector normal to the boundary and (ρ b û • n BC , p/ρ b ) replace ( m, Ĵ) in Eq. ( 5) as appropriate in a 3D zero Mach number flow domain. The following typical values were obtained from LES and used for the subsequent acoustic analysis: G LES us ≈ 160 m/s/K; G LES c ≈ 0.25; τ LES us ≈ 0.79 ms; τ LES c ≈ 2.98 ms. Note that these values were obtained from the first DMD mode at 331 Hz and were supposed independent on frequency.

Several Helmholtz computations were performed by using the AVSP solver developed at CERFACS [9]. In all the cases, a coarse mesh (approx. 10 5 nodes) was generated from the LES grid in order to represent the geometry properly. Additionally, a zero acoustic velocity condition was imposed over all the boundaries except a) over the chamber exit where a compact nozzle condition, with or without the DECBC contribution, was imposed and b) over the air inlet where the reduced impedance measured with the help of the resulting pressure and velocity fluctuations taken from the DMD mode at 331 Hz was imposed, Z LES ≈ -2.2 -1.6i (inward). Also, the local speed of sound was deduced from the time averaged LES data and extrapolated on the coarse acoustic mesh.

The main properties of the runs performed are gathered in Table 1 where the frequency of the first mode is also reported. The Active Flame column reports whether or not the flame-acoustic coupling (the RHS term of Eq. ( 1)) is included; if yes, Fig. 6. Computational domain for the Helmholtz analysis. The point of reference and the zone of averaging used for the entropy generation modeling (Eq. 10) are displayed as well as the exit section where the entropy-acoustic boundary condition (Eq. 5) is applied.

the corresponding gain and time delay are computed from the LES in the same way as the entropy-acoustic transfer function. The DECBC column reports the use of the boundary condition (Eq. ( 13)) developed in this paper. Run A is a classical acoustic computation with variable speed of sound.

As already stated in section 1, the first acoustic mode oscillates at around 670 Hz, very far from the 330 -350 Hz instability observed in the LES and experiment; this acoustic mode is slightly damped (decay rate -7 s -1 ) due to the acoustic loss at the inlet/outlet. Run B shows that the coupling with the flame does not shift the frequency of oscillation. Introducing the DECBC approach without the flame coupling (Eq. ( 13) with G LES us assessed from LES), Run C produces a mode in the expected frequency range at 320 Hz. This is notably due to the convection delay τ LES c in Eq. ( 13) which introduces a longer time scale to the problem. Note however that this mode is damped (decay rate -68 s -1 ), which is not consistent with this mode being detected in the experiment and LES. Introducing the flame-acoustic coupling together with the DECBC approach corrects this behavior, since Run D gives an unstable mode (growth rate 26 s -1 ) oscillating at 320 Hz, in fair agreement with the LES and experiment. Note that the frequency of oscillation obtained (320 Hz) is rather close to the first DMD mode (331 Hz), thus justifying a posteriori the fact that the transfer function gain and delay were supposed independent on frequency when performing the Helmholtz computations of Table 1.

A limitation of the proposed approach is that the Helmholtz/DECBC solver must be fed by data coming from LES results. This may appear as a strong limitation since the cost of a LES must be paid before the DECBC methodology can be applied. Still, the Helmholtz/DECBC approach remains useful in situations where the same upstream velocity-exit entropy transfer function can be reused for multiple test conditions. Another potential field of application is the study of annular combustors; in this case, one can imagine that a simple one sector LES (containing only one burner) could be performed to feed a Helmholtz/DECBC computation of the whole annular combustor with several identical burners, thus avoiding the extremely CPU demanding LES of the full combustor. This strategy is justified if the flames behave independently and was already used for accounting for the flame response in annular combustors [START_REF] Wolf | Acoustic and large eddy simulation studies of azimuthal modes in annular combustion chambers[END_REF][START_REF] Sensiau | A tool to study azimuthal and spinning modes in annular combustors[END_REF].

A Delayed Entropy Coupled Boundary Condition was developed as a means to recover some of the convective effects when representing a thermo-acoustic system under the zero Mach number formalism. In this view, a simple model was first used in order to assess the entropy fluctuations at the exit of the combustion chamber. This modeling consists of two steps, one for the entropy generation in the flame region, a second one for the convection/dissipation of the entropy spots through the combustion chamber. This results in a transfer function which relates a reference acoustic velocity in the burner and entropy at the exit of the chamber and which was assessed by post-processing LES data. The acoustics generated by the convection of the entropy spots through the exit nozzle are then treated by applying a proper boundary condition which couples entropy and acoustic quantities. The latter was deduced from the theory of compact nozzles in the present paper. The computation of a SAFRAN combustor which exhibits a low frequency instability demonstrates the potential of the method.

Nomenclaturep

  Static pressure c Sound speed ω Angular frequency γ Ratio of the specific heats q Heat release rate per unit volume ĝ fluctuating part of quantity g LES Large Eddy Simulations LEE Linearized Euler Equations DMD Dynamic Mode Decomposition DECBC Delayed Entropy Coupled Boundary Condition T res Flow-through time ρ Density J Total stagnation enthalpy m Mass-flow rate u Fluid velocity M Mach number k Wave number g 0 Subscript for mean quantity of g s Entropy C p Heat capacity per mass unit at fixed pressure τ Convection time delay n re f Unitary reference vector u re f Velocity at reference point

Fig. 1 .

 1 Fig. 1. Description of the configuration of interest. One sector of the azimuthal SAFRAN combustor is represented.

Fig. 2 .

 2 Fig. 2. Typical snapshot from the LES of the SAFRAN combustor and time evolution of pressure within the chamber.

Fig. 3 .

 3 Fig. 3. Fluctuating pressure (left) and temperature (right) from the DMD mode at 331 Hz. From top to bottom, the four rows correspond to phases 0, π/2, π and 3π/2.

Fig. 5 .

 5 Fig. 5. Frequency of oscillation (upper graph) and growth rate (bottom graph) corresponding to a 1D combustor mounted on a compact choked nozzle. Solid line ( ): analytical result at finite Mach number [19]. Symbols: Helmholtz equation at zero Mach number and Eq. (9)as boundary condition, without ( + , G us = 0) or with (×, G us from Eq. (8)) entropy coupling.

Table 1 .

 1 Main properties and results of the Helmholtz computations.

	-1 )

Acknowledgments

E. Motheau gratefully acknowledges support from SNECMA. The authors also thank T. Jaravel and J. Richard (CER-FACS) for their technical support for the DMD analysis as well as Y. Méry (SNECMA) for providing the data. Part of this study has been performed during the Summer Program 2012 of the Center for Turbulence Research, Stanford University.

impedances in Eqs. ( 2) are relevant to acoustic elements where the mean flow is not at rest (as in a compressor or turbine, Figure 4). Of course, the impedances Z M up and Z M mJ are two different complex valued numbers although they represent the same physical element (compressor or turbine). For example, a perfect tube end where the acoustic pressure p is zero would correspond to Z M up = 0 but Z M mJ = M = u 0 /c 0 because Ĵ = p/ρ 0 + u 0 û and m = ρ 0 û + u 0 p/c 2 0 . More generally, these impedances are related by the following relation:

Now, since the Helmholtz equation is solved for in the combustion chamber where the mean flow is assumed at rest, a boundary impedance Z 0 up should be imposed in order to account for the effects of the compressor/turbine on the acoustics. Even if p is the primary variable (see Eq. ( 1)) in the combustion chamber, the proper impedance to impose at the edge of the chamber is not necessarily Z M up . The reason is that the Mach number is zero in the chamber but not when computing Z M up . A careful analysis of the acoustic flux through the interface between the combustion chamber and the outer acoustic elements [START_REF] Motheau | Using boundary conditions to account for mean flow effects in a zero mach number acoustic solver[END_REF] shows that a proper choice for Z 0 up is Z M mJ instead of Z M up . For example, if a choked feeding line is located upstream of the combustion chamber, the mass flux is constant ( m = 0, Z M mJ = ∞) and the proper boundary condition for the Helmholtz domain is simply Z 0 up = ∞. Similarly, if the feeding line imposes the velocity instead of the mass flux ( û = 0, Z M mJ = 1/M, Z M up = ∞), the proper boundary impedance is Z 0 up = 1/M and not ∞. When the LEEs are solved for everywhere (including the combustion chamber and surrounding elements), entropy fluctuations can be convected to the exit nozzle or turbine where the mean flow is accelerated. These accelerated entropy spots may interact with the acoustics so that the complete boundary condition describing the nozzle or turbine may involve ŝ, û and p. For example, the relationship derived by [START_REF] Marble | Acoustic disturbances from gas nonuniformities convected through a nozzle[END_REF] for a compact choked nozzle reads:

or, using the ( m, Ĵ) variables:

The third term is usually neglected when assuming zero Mach number in the combustion chamber (because no entropy spot can reach the exit if the convection by the mean flow is neglected) and Eq. ( 5) allows calculating the impedance Z M mJ of a