Oulfat Amin
email: oulfat.aminali@gmail.com

Emmanuel Aragon
email: emmanuel.aragon@univ-tln.fr

Armand Fahs
email: armand.fahs@univ-tln.fr

Sylvain Davidson
email: sylvain.davidson@mio.osupytheas.fr

Bernard Ollivier
email: bernard.ollivier@mio.osupytheas.fr

Agnès Hirschler-Rea
email: agnes.hirschler-rea@mio.osupytheas.fr

Iron corrosion induced by the hyperthermophilic sulfate-reducing archaeon Archaeoglobus fulgidus at 70 • C

Keywords:

This work assessed the role of the hyperthermophilic sulfate-reducing archaeon, Archaeoglobus fulgidus in anaerobic iron corrosion, at 70 • C, in the presence and the absence of lactate as energy source. Experiments performed with A. fulgidus planktonic cells, displayed their capacity to form a biofilm on an iron coupon and exhibited their biocorrosive activity. A. fulgidus was shown to cause indirect corrosion by producing sulfide while oxidizing lactate. Furthermore, the archaeon could grow lithotrophically by using elemental iron as a mineral energy source. Under these latter conditions, A. fulgidus formed chimneys enhancing the direct corrosion process. Moreover, physiological modifications occurred under these conditions notably highlighting the probable use of CO 2 instead of sulfate as a terminal electron acceptor to produce acetate similarly to homoacetogens. All together, these results illustrate the metabolic versatility and hence the importance of this hyperthermophilic archaeon in microbial induced corrosion (MIC).

Introduction

Corrosion is commonly defined as natural oxidation with subsequent deterioration of metals and alloys (Perez, 2004;Videla and Herrera, 2005). As a metal, iron is very unstable in aqueous media. Therefore, it dissolves in water according to the following reaction: 4 Fe 0 ↔ 4 Fe 2+ + 8 e -; E 0 = -447 mV

(1)

The metallic surface works as an electrochemical cell combining an anodic site and a cathodic site where oxidation and reduction reactions occur, respectively, allowing an electron flow from anode to cathode [START_REF] Enning | Corrosion of iron by sulfate-reducing bacteria: new views of an old problem[END_REF][START_REF] Sherar | The effect of sulfide on the aerobic corrosion of carbon steel in near-neutral pH saline solutions[END_REF]. In oxic environments, electrons that result from Fe 0 oxidation reduce molecular oxygen and lead to rust or the formation of iron oxides. This aerobic corrosive process is mainly attributed to electrochemical reactions [START_REF] Enning | Corrosion of iron by sulfate-reducing bacteria: new views of an old problem[END_REF][START_REF] Sherar | The effect of sulfide on the aerobic corrosion of carbon steel in near-neutral pH saline solutions[END_REF][START_REF] Liengen | Understanding Biocorrosion[END_REF]. In anoxic conditions, electrons that result from Fe 0 oxidation reduce protons from dissociated water. However, this chemical iron oxidation coupled to proton reduction usually remains low [START_REF] Enning | Corrosion of iron by sulfate-reducing bacteria: new views of an old problem[END_REF]Enning et al., 2012;[START_REF] Kaesche | Corrosion of Metals: Physicochemical Principles and Current Problems[END_REF] in environments lacking oxygen or acid and metallic facilities [START_REF] Enning | Corrosion of iron by sulfate-reducing bacteria: new views of an old problem[END_REF]. Nevertheless, microorganisms drastically accelerate this phenomenon, and anaerobic corrosion mainly results from either microbial activity or the end products of their metabolism (Videla and Herrera, 2005;[START_REF] Cord-Ruwisch | Corroding iron as a hydrogen source for sulphate reduction in growing cultures of sulphate-reducing bacteria[END_REF][START_REF] Dinh | Iron corrosion by novel anaerobic microorganisms[END_REF][START_REF] Zhang | Electron mediators accelerate the microbiologically influenced corrosion of 304 stainless steel by the Desulfovibrio vulgaris biofilm[END_REF][START_REF] Liang | Anaerobic biodegradation of alternative fuels and associated biocorrosion of carbon steel in marine environments[END_REF]. More than 20% of all corrosion loss is recognized to be of microbial origin and is referred to as microbiologically influenced corrosion (MIC) [START_REF] Zhang | Electron mediators accelerate the microbiologically influenced corrosion of 304 stainless steel by the Desulfovibrio vulgaris biofilm[END_REF][START_REF] Hamilton | Microbially influenced corrosion as a model system for the study of metal microbe interactions: a unifying electron transfer hypothesis[END_REF][START_REF] Dang | Microbial surface colonization and biofilm development in marine environments[END_REF][START_REF] Beech | Biocorrosion: towards understanding interactions between biofilms and metals[END_REF]. Commonly, microorganisms adhere to metallic surfaces by forming a biofilm, which enables MIC through two mechanisms: (i) indirect corrosion by producing corrosive compounds such as sulfides, which provoke chemical attacks on iron, and (ii) direct corrosion by oxidizing Fe 0 and pulling electrons to reduce electron acceptors (Enning et al., 2012;[START_REF] Van Ommen Kloeke | Localization of cytochromes in the outer membrane of Desulfovibrio vulgaris (Hildenborough) and their role in anaerobic biocorrosion[END_REF][START_REF] Mehanna | Role of direct microbial electron transfer in corrosion of steels[END_REF][START_REF] Venzlaff | Accelerated cathodic reaction in microbial corrosion of iron due to direct electron uptake by sulfate-reducing bacteria[END_REF]. In direct corrosion, several theories were proposed among which the so called "cathodic depolarization" [START_REF] Wolzogen Kuehr | The Graphitization of cast iron as an electrobiochemical process in anaerobic soils[END_REF]. This theory suggests that H 2 resulting from the reduction of dissolved protons in water would builds-up a "hydrogen film" [START_REF] Venzlaff | Accelerated cathodic reaction in microbial corrosion of iron due to direct electron uptake by sulfate-reducing bacteria[END_REF]. In presence of hydrogenotrophic microorganisms, such as sulfate-reducing bacteria (SRB), it has been speculated that hydrogen formed on metallic surface can be scavenged by SRB thus facilitating the oxidative process [START_REF] Wolzogen Kuehr | The Graphitization of cast iron as an electrobiochemical process in anaerobic soils[END_REF]. However, this theory has been extensively questioned as it cannot affect or accelerate iron corrosion based on kinetics and thermodynamics perspectives [START_REF] Enning | Corrosion of iron by sulfate-reducing bacteria: new views of an old problem[END_REF][START_REF] Liang | Anaerobic biodegradation of alternative fuels and associated biocorrosion of carbon steel in marine environments[END_REF][START_REF] Costello | Cathodic depolarization by sulfate-reducing bacteria[END_REF][START_REF] Vigneron | Complementary microorganisms in highly corrosive biofilms from an offshore oil production facility[END_REF].

Many microbial groups such as acetogenic bacteria [START_REF] Enning | Corrosion of iron by sulfate-reducing bacteria: new views of an old problem[END_REF][START_REF] Kato | Isolation of acetogenic bacteria that induce biocorrosion by utilizing metallic iron as the sole electron donor[END_REF][START_REF] Mand | The role of acetogens in microbially influenced corrosion of steel[END_REF][START_REF] Mand | Microbial methane production associated with carbon steel corrosion in a nigerian oil field[END_REF], nitrate-reducing bacteria [START_REF] Enning | Corrosion of iron by sulfate-reducing bacteria: new views of an old problem[END_REF][START_REF] Hubert | Corrosion risk associated with microbial souring control using nitrate or nitrite[END_REF], sulfate and thiosulfate-reducing prokaryotes [START_REF] Enning | Corrosion of iron by sulfate-reducing bacteria: new views of an old problem[END_REF][START_REF] Liang | Anaerobic biodegradation of alternative fuels and associated biocorrosion of carbon steel in marine environments[END_REF][START_REF] Magot | Dethiosulfovibrio peptidovorans gen. Nov., sp. nov., a new anaerobic, slightly halophilic, thiosulfate-reducing bacterium from corroding offshore oil wells[END_REF] and methanogenic archaea [START_REF] Costello | Cathodic depolarization by sulfate-reducing bacteria[END_REF][START_REF] Vigneron | Complementary microorganisms in highly corrosive biofilms from an offshore oil production facility[END_REF][START_REF] Mand | Microbial methane production associated with carbon steel corrosion in a nigerian oil field[END_REF][START_REF] Davidova | Involvement of thermophilic archaea in the biocorrosion of oil pipelines[END_REF][START_REF] Liang | Roles of thermophilic thiosulfate-reducing bacteria and methanogenic archaea in the biocorrosion of oil pipelines[END_REF] have been identified as being involved in MIC. While MIC has been widely studied in sulfate-reducing bacteria (e.g., Desulfovibrio spp.) that are known to be widespread in natural environments [START_REF] Enning | Corrosion of iron by sulfate-reducing bacteria: new views of an old problem[END_REF][START_REF] Zhang | Electron mediators accelerate the microbiologically influenced corrosion of 304 stainless steel by the Desulfovibrio vulgaris biofilm[END_REF][START_REF] Hamilton | Microbially influenced corrosion as a model system for the study of metal microbe interactions: a unifying electron transfer hypothesis[END_REF][START_REF] Dang | Microbial surface colonization and biofilm development in marine environments[END_REF][START_REF] Beech | Biocorrosion: towards understanding interactions between biofilms and metals[END_REF][START_REF] Van Ommen Kloeke | Localization of cytochromes in the outer membrane of Desulfovibrio vulgaris (Hildenborough) and their role in anaerobic biocorrosion[END_REF], very few studies regarding sulfate-reducers belonging to the Archaea domain have been reported. Within the Archaea, sulfur-reducing, non-sulfate-reducing and sulfide-producing hyperthermophilic members of the order Thermococcales (e.g., Thermococcus spp.), which grow in co-culture with hydrogenotrophic methanogens, were demonstrated to be highly corrosive [START_REF] Davidova | Involvement of thermophilic archaea in the biocorrosion of oil pipelines[END_REF][START_REF] Liang | Roles of thermophilic thiosulfate-reducing bacteria and methanogenic archaea in the biocorrosion of oil pipelines[END_REF][START_REF] Duncan | Biocorrosive thermophilic microbial communities in Alaskan North slope oil facilities[END_REF]. They were also found to be biocorrosive in enrichment cultures in the presence of thiosulfate as a terminal electron acceptor [START_REF] Liang | Roles of thermophilic thiosulfate-reducing bacteria and methanogenic archaea in the biocorrosion of oil pipelines[END_REF]. In this respect, anaerobic hyperthermophilic Archaea representatives, and in particular sulfate-reducing archaea such as Archaeoglobus species, may be active contributors to corrosion at high temperature, notably in oilfield facilities and hot oil reservoirs where their presence has been demonstrated on several occasions [START_REF] Enning | Corrosion of iron by sulfate-reducing bacteria: new views of an old problem[END_REF][START_REF] Davidova | Involvement of thermophilic archaea in the biocorrosion of oil pipelines[END_REF][START_REF] Duncan | Biocorrosive thermophilic microbial communities in Alaskan North slope oil facilities[END_REF]Ollivier and Magot, 2005).

Archaeoglobus fulgidus is a hyperthermophilic sulfate-reducing archaeon that has been isolated from shallow submarine hot vents in the Mediterranean Sea [START_REF] Stetter | Archaeoglobus fulgidus gen. nov., sp. nov.: a new taxon of extremely thermophilic archaebacteria[END_REF], volcanic environments [START_REF] Zellner | Isolation and characterization of a thermophilic, sulfate-reducing archaebacterium, Archaeoglobus fulgidus strain[END_REF], various hot oil field waters in the North Sea [START_REF] Stetter | Hyperthermophilic archaea are thriving in deep North Sea and Alaskan oil reservoirs[END_REF][START_REF] Beeder | Archaeoglobus fulgidus isolated from hot North Sea oil field waters[END_REF], a continental reservoir [START_REF] L'haridon | Hot subterranean biosphere in a continental oil reservoir[END_REF] and a deep aquifer basin [START_REF] Fardeau | Archaeoglobus fulgidus and Thermotoga elfii, thermophilic isolates from deep geothermal water of the Paris basin[END_REF]. One of the most studied and well-characterized strain is A. fulgidus VC-16, which was the first sulfur-metabolizing archaeon whose genome was sequenced [START_REF] Klenk | The complete genome sequence of the hyperthermophilic, sulphate-reducing archaeon Archaeoglobus fulgidus[END_REF][START_REF] Henstra | Archaeoglobus fulgidus couples CO oxidation to sulfate reduction and acetogenesis with transient formate accumulation[END_REF][START_REF] Hocking | Identification of key components in the energy metabolism of the hyperthermophilic sulfate-reducing archaeon Archaeoglobus fulgidus by transcriptome analyses[END_REF]. It is an organotrophic and lithoautotrophic archaeon that grows on a variety of energy sources including lactate, hydrogen, and carbon monoxide [START_REF] Stetter | Archaeoglobus fulgidus gen. nov., sp. nov.: a new taxon of extremely thermophilic archaebacteria[END_REF][START_REF] Klenk | The complete genome sequence of the hyperthermophilic, sulphate-reducing archaeon Archaeoglobus fulgidus[END_REF][START_REF] Vornolt | Enzymes and coenzymes of the carbon monoxide dehydrogenase pathway for autotrophic CO2 fixation in Archaeoglobus lithotrophicus and the lack of carbon monoxide dehydrogenase in the heterotrophic A. profundus[END_REF] as well as aliphatic hydrocarbons [START_REF] Khelifi | Anaerobic oxidation of fatty acids and alkenes by the hyperthermophilic sulfate-reducing archaeon Archaeoglobus fulgidus[END_REF][START_REF] Khelifi | Anaerobic oxidation of long-chain n-alkanes by the hyperthermophilic sulfate-reducing archaeon, Archaeoglobus fulgidus[END_REF]. In addition to sulfate, thiosulfate and sulfite are also used as terminal electron acceptors [START_REF] Stetter | Archaeoglobus fulgidus gen. nov., sp. nov.: a new taxon of extremely thermophilic archaebacteria[END_REF]. Notably, hydrogen is only oxidized in the presence of thiosulfate [START_REF] Stetter | Archaeoglobus fulgidus gen. nov., sp. nov.: a new taxon of extremely thermophilic archaebacteria[END_REF][START_REF] Klenk | The complete genome sequence of the hyperthermophilic, sulphate-reducing archaeon Archaeoglobus fulgidus[END_REF]. Interestingly, the ability of A. fulgidus to form biofilms under stress conditions such as metal-enriched environment was demonstrated [START_REF] Lapaglia | Stress-induced production of biofilm in the hyperthermophile Archaeoglobus fulgidus[END_REF]. Therefore, A. fulgidus VC-16 represents a good candidate to study anaerobic biocorrosion processes at high temperature. Indeed, Islam & Karr had reported the corrosive ability of A. fulgidus by measuring weight loss [START_REF] Islam | Examination of metal corrosion by Desulfomicrobium thermophilum, Archaeoglobus fulgidus, and Methanothermobacter thermautotrophicus[END_REF]. Besides, [START_REF] Jia | Carbon steel biocorrosion at 80 • C by a thermophilic sulfate reducing archaeon biofilm provides evidence for its utilization of elemental iron as electron donor through extracellular electron transfer[END_REF], recently, performed a corrosion study with A. fulgidus. In their experiments, a robust biofilm initially developed on an iron coupon with organic matter in an enriched seawater medium. This mature biofilm was then exposed to different conditions of carbon starvation. They showed that the formed biofilm was very corrosive under organic carbon starvation and that the sulfate-reducing archaeon was able to use elemental iron as an electron donor [START_REF] Jia | Carbon steel biocorrosion at 80 • C by a thermophilic sulfate reducing archaeon biofilm provides evidence for its utilization of elemental iron as electron donor through extracellular electron transfer[END_REF].

In this work, planktonic cells of A. fulgidus were grown in a mineral culture medium containing a carbon steel coupon in presence and absence of an organic electron donor and with sulfate as terminal electron acceptor. The aim of the study is to deepen our understanding of the mechanisms of direct and/or indirect corrosion by A. fulgidus VC-16 and, specifically, under oligotrophic conditions, which are encountered, more particularly, in oilfield waters.

Materials and methods

Metal sample preparation

Coupons (Control 5, Mexico) made of SAE 1010 carbon steel (127 mm × 12.7 mm x 0.25 mm) served as the source of metallic iron. Beside Fe, their mass percentage composition is (wt %) C 0.10, Mn 0.45, P 0.04, S 0.05. These metallic coupons were mirror-polished by a specialized subcontractor (CHROMALU) and surface-activated for 2 min in diluted HCl (2 M) until the formation of a substantial amount of hydrogen bubbles. Each steel coupon was then rinsed immediately three times in distilled water for 10 s, sterilized by UV light for 20 min on each side and stocked in a drying chamber.

Growth of A. fulgidus VC-16

Archaeoglobus. fulgidus strain VC-16 (DSM 4304) was isolated from a marine hydrothermal vent [START_REF] Stetter | Archaeoglobus fulgidus gen. nov., sp. nov.: a new taxon of extremely thermophilic archaebacteria[END_REF]. It was provided by the Deutsche Sammlung von Mikrooganismen und Zellkulturen (Braunschweig, Germany). It was cultured in a defined culture medium [START_REF] Khelifi | Anaerobic oxidation of fatty acids and alkenes by the hyperthermophilic sulfate-reducing archaeon Archaeoglobus fulgidus[END_REF]

Electrochemical measurements and characterization

Experiments were carried out in a 1 L K0047 corrosion cell kit (AMETEK) that was sterilized with 96% ethanol prior to use. 0.8 L of sterile medium was added and purged by a stream of sterile N 2 -CO 2 (80:20) gas for 2-3 h prior to inoculation and first measurement. The corrosion cell was subsequently tightly closed and placed into a polyethylene glycol bath at 70 • C for approximately 40 min. The latter step allowed the culture medium to reach and maintain the growth temperature of A. fulgidus. A 1 cm 2 working electrode (iron coupon) was exposed to the culture medium (electrolyte), the reference electrode was a saturated calomel electrode (SCE) and a graphite rod served as a counter electrode. Electrochemical experiments were carried out using a potentiostat/galvanostat (BES EG®&R), and data were acquired using Softcorr III software. The free corrosion potential E corr was followed by connecting the working and reference electrodes of the electrochemical cell during their incubation in the electrolyte. After 8 days, E corr monitoring was stopped and followed by linear sweep voltammetry. The latter was performed over a range of ΔE = -600 mV-800 mV at a rate of 0.166 mV s -1 , starting 50 mV beneath the E corr . Electrochemical characterization was performed to compare the four conditions cited above (Cf. 2.3).

Statistical analyses

The significance of the results was examined by multifactor analysis of variance for concentration (ANOVA) followed by post hoc tests (Fisher's least significant difference tests). These analyses were performed using STATGRAPHICS Centurion XVI.II. P < 0.05 was considered statistically significant.

Results

To explore the initiation timeline of corrosion, A. fulgidus VC-16 was grown with lactate and/or an iron coupon as electron donor(s) and sulfate as a terminal electron acceptor at 70 • C for three weeks. These assays were compared to abiotic controls that contained an iron coupon and sulfate either in presence or in absence of lactate. Both assays and controls were incubated under the same experimental conditions. Experimental settings used in the whole study were optimized to avoid any biasness of the biological response to corrosion. For instance, oxygen scavenger or modulators of electrochemical measurements have been removed and replaced by neutral components (see material and methods).

Iron surface crust

After three weeks of incubation at 70 • C, iron surfaces were observed by SEM to assess development of A. fulgidus on the metallic coupon. Observations showed that precipitates had accumulated on the steel surface of abiotic controls (Fig. 1B) and A. fulgidus-inoculated assays (Fig. 1C andD). When compared to non-incubated metal reference (Fig. 1A), the iron coupon surface incubated in the culture medium was covered by a thick black crust (Fig. 1B). No difference was observed between the abiotic controls containing an iron coupon, sulfate, with or without lactate. Thus, only the abiotic control with lactate was represented. Aside from the crust produced on the abiotic control (Fig. 1B), tangled materials were observed on the coupons from the A. fulgidusinoculated assays in the presence of lactate (Fig. 1C). These tangled materials were less developed when lactate was lacking in the culture medium (Fig. 1D). Besides, particular chimney-like structures were observed, in the latter (Fig. 1D). Within 3 weeks, A. fulgidus grown on of the medium was adjusted to 7.0. The medium was prepared anoxically in penicillin bottles with a headspace of N 2 -CO 2 (4:1). Following sterilization, the medium was amended with sodium carbonate (2 g. L -1 ), sodium thioglycolate (0.2 g L -1 ), sodium ascorbate (0.2 g L -1 ), MgCl 2 ⋅6H 2 O (3.0 g L -1 ), 10 ml L -1 of a vitamin solution [START_REF] Wolin | Formation of methane by bacterial extracts[END_REF] and lactate (10 mM), except when stated.

The present medium was optimized to enable only biological response to corrosion process. Indeed, Na 2 S, and L-cysteine commonly used as oxygen scavengers were removed from the medium because they cause rapid chemical corrosion. They were replaced by sodium thioglycolate and sodium ascorbate, which are completely harmless on carbon steel. Moreover, since KH 2 PO 4 and K 2 HPO 4 distorted electrochemical signals, they were replaced by MOPS to buffer the culture medium. Actually, the medium was optimized to enable only biological response to corrosion process.

Precultures were inoculated at 10% (vol/vol) under anoxic conditions and incubated for 2 days at 70 • C.

Corrosion tests

Corrosion tests were performed in 25-ml Bellco tubes filled with A. fulgidus culture medium. A metallic coupon and/or lactate were added to the sterilized culture medium. A. fulgidus inoculum was washed once with substrate-free medium before being added at 10% v/v. The tubes were filled completely and incubated horizontally at 70 • C so the biofilm of A. fulgidus could develop on the larger surface of the metallic coupon in biological assays. The same inoculum was added to all assays. Corrosion test kinetics and analyses were carried out in one shot experiment where 4 conditions, in presence and absence of iron coupon, were performed: (i) abiotic, (ii) abiotic with lactate, (iii) A. fulgidus, (iv) A. fulgidus with lactate. Three tubes were sacrificed per condition for each time of monitoring.

Chemical measures and analyses

The sulfate concentration was quantified by ion chromatography (761 Compact IC Metrohm, Metrohm) using a Metrosep Anion Supp1 column (Metrohm). The lactate (electron donor) and acetate (endproduct of lactate oxidation) concentrations were determined by HPLC (Thermo Scientific) using an Aminex HPX-87H-300 x 7.8 column (Bio-Rad). The concentration of soluble Fe 2+ was measured using the colorimetric method described by Lovley et al. [START_REF] Lovley | Organic matter mineralization with reduction of ferric iron in anaerobic sediments[END_REF] after solubilization of the black precipitate for approximately 5 min with 0.35 M HCl.

Scanning electron microscopy and elemental identification

Iron coupons were incubated for 20 days in A. fulgidus-inoculated culture medium. A 1 cm 2 coupon surface was cut from each crustcovered specimen and fully dried before scanning electron microscopy (SEM). SEM was performed in secondary electron imaging mode (SE2) with acceleration voltage of 5 kV, using a Zeiss Supra 40 VP microscope, equipped with a GEMINI column and coupled with an X-max 20 mm 2 energy-dispersive X-ray analyzer (Oxford Instruments). To observe pits, the corrosion crusts were removed by immersion in a 6 M hexamethylenetetramine-HCl solution with 3 M NH 4 Cl for 5 min. After immersion, the iron specimens were rubbed with a toothbrush, rinsed with water and fully dried.

Atomic force microscopy

Topographic images of surface were recorded with an Atomic Force Microscopy (AFM) in intermittent contact mode. AFM experiments were performed in air using a Multimode AFM with Nanoscope V SPM controller. Silicon cantilever was used with a spring constant of 40 N m -1 and a resonant frequency of around 300 kHz. All images were iron coupon developed a microbial biofilm supported by the presence of tangled materials (Fig. 1C-D).

Iron surface deposits composition

Composition of materials and crusts deposited on iron surfaces (Fig. 1B-D) was analyzed by energy-dispersive X-ray spectroscopy (EDX). The tangled material in A. fulgidus containing lactate assays (Fig. 1C) revealed that high mass percent of Fe (42.4%), S (14.8%), O (14.1%) and C (12.5%) constituted these filamentous materials. Other elements such as Na (8%), Cl (4.5%), Si (2.7%) and Mg (1.3%) were also identified at lower concentrations (Table 1). The composition of crust in abiotic control (Fig. 1B) was quite different with very low concentrations of S (1.9%) and Si (0.4%) elements. In comparison, chimneys observed in lactate lacking assays (Fig. 1D) contained no Si and low S elements (1%). However, in these assays without lactate, Si and S were present but mainly in the filamentous tangled materials underneath the chimneys as revealed by SEM-EDX analyses (Fig. 2). Furthermore, theses analyses confirmed that the A. fulgidus chimneys were mainly composed of Fe, C, O, Na, and Mg (Fig. 2 and Table 1). Our data provide clear evidence that composition of deposits differs between the conditions studied.

Corrosion pits

The selective removal of the crust from iron coupons was performed to observe corrosion damages. SEM observations revealed clear changes of the metal surface aspect for treated iron coupons with different types of pits (Fig. 3). In addition, AFM images illustrated that these metallic coupons had rugged topographies, confirming the SEM observations (Fig. 3A-D). In the abiotic control (Fig. 3B), AFM analysis showed pits with depths of up to 700 nm and 1-2 μm widths. Although pits on the metal incubated with A. fulgidus had same depths to that of the abiotic control, they were two-fold wider (Fig. 3C). These pits were deeper and wider when organic electron donor was added to the culture medium (Fig. 3D).

Electrochemical activity of A. fulgidus on iron coupon

Effect of A. fulgidus on the free corrosion potential of iron

Electrochemical potential/time characterizations were carried out to assess deterioration of the metallic surface when it was immersed in A. fulgidus culture medium. Indeed, open circuit potential (E corr ) was monitored for 1 cm 2 immersed iron coupon in inoculated and abiotic culture medium in the presence or absence of lactate as an organic electron donor over 8 days (Fig. 4A). Under abiotic conditions (sterile electrolyte), the organic electron donor had no influence on the potential. Therefore, we chose to present only curve of controls in medium containing lactate (Fig. 4A). Within the first few hours, the E corr curves of all conditions decreased to more electronegative potentials and increased to more positive values after one day. In A. fulgidus-inoculated media with lactate, lowest E corr potentials were observed after one day of stabilization in comparison to other conditions. The abiotic control reached, approximately, -480 mV/SCE from day 3 and remained stable until day 5. It showed abrupt decrease to reach -600mV/SCE. However, it increased at day 6 to gain the initial level of -480 mV/SCE again. These abrupt decrease and increase corresponded to an artifact. A similar but smaller artifact was also observed few hours later in the A. fulgidus-inoculated assay without lactate; however, the artifact was not detected in the assay with lactate. In the absence of lactate as an electron donor, the E corr showed a slight increase compared to the abiotic condition before day 1. However, this increase does not last as E corr reached -550 mV/SCE at day 2 and remained stable without any variation. When lactate was added to the A. fulgidus-inoculated medium, E corr values were even more negative (-650 mV/SCE) compared to the A. fulgidus-inoculated medium lacking lactate (Fig. 4A). These data suggest that the presence of A. fulgidus leads to more electronegative potential and hence to electron uptake from the metal as it is corrosive.

A. fulgidus current-potential response to corrosion

After day 8 of culture in the corrosion cell, open circuit potential measurements (Fig. 4A) were stopped and followed by potentiodynamic characterization to assess corrosion rate (Fig. 4B). The potentiodynamic curves obtained allowed the extrapolation of Tafel's slopes from which the corrosion current densities were calculated (i corr ). Current densities of approximately 80, 105 and 500 μA/cm 2 were obtained for the abiotic control and assays without and with lactate, respectively (Fig. 4B). In the A. fulgidus-inoculated condition containing lactate, the corrosion current density was six times greater than that of the abiotic control and five times higher than that of A. fulgidus with iron coupon as the only electron donor. Besides, passivation phenomena were observed for the microbial assays that were greater in the medium lacking lactate (Fig. 4B). Thus, the presence of the archaeon increase corrosion rate.

A. fulgidus microbial activity

Lactate and sulfate consumption as well as the formation of Fe 2+ from Fe 0 oxidation were monitored over a month of incubation at 70 • C with the aim to evaluate Fe 0 oxidation and corrosion processes due to sulfide production. In these experimental settings, we added A. fulgidusinoculated controls without iron coupon, with sulfate and with or without lactate. In assays containing lactate and an iron coupon, the Fe 2+ concentration increased drastically up to four times than what detected in the abiotic control (Fig. 5A). The higher concentration was reached around day 4 and further increased until the end of the monitoring (Fig. 5A). In A. fulgidus-inoculated assays containing iron coupon only, the concentration of Fe 2+ slowly increased. Only after 4 days of incubation, it was different of that of the abiotic control and then became two times greater than that of the abiotic control (Fig. 5A). Interestingly, under these lithotrophic conditions, no sulfate consumption was detected (Fig. 5C) and small amounts of acetate were produced leading to the accumulation of about 0.9 mM acetate at the end of the experiment (Fig. 5D). Although, the culture medium contained 0.1 g.L -1 yeast extract, A. fulgidus was not able to grow and no acetate was produced in absence of an iron coupon (data not shown). All these results Table 1 Elements composition of crust deposits on metal surfaces by Energy-Dispersive X-ray spectroscopy analysis. Presentation of mass percent and Atomic percent of elements. nd: non detected.

Abiotic control

Elements

suggest that acetate production should result from lithotrophic growth on iron with CO 2 to be used as terminal electron acceptor. Under organotrophic conditions, kinetics of the lactate oxidized and the sulfate reduced were a little faster in A. fulgidus-inoculated controls without iron coupon than in assays with iron. Indeed, in the absence of iron, all the lactate was consumed after 5 days of incubation while small amounts remained even after 10 days in its presence (Fig. 5B). These results suggest that lactate oxidation is delayed in presence of iron. However, in both cases, the redox ratio was around 1.2 sulfate reduced per lactate oxidized (Fig. 5B andC). Interestingly, when A. fulgidus was grown with lactate and an iron coupon, acetate production occurred concomitantly to the consumption of lactate (Fig. 5D) from the 2nd day until the 6th day. Following this fast acetate production, the production continues with the kinetic tendency of the assay under lithotrophic growth condition. The acetate concentration reached a maximum of 1.45 mM at day 13 and then decreased slightly (1 mM remaining at day 32). Thus, acetate was first accumulated and slowly consumed afterwards when the medium became lactate deficient (after day 13). The increase of acetate concentration between day 6 and 13, seemed to follow the same tendency of the lithotrophic condition.

Discussion

While Lapaglia and Hartzel [START_REF] Lapaglia | Stress-induced production of biofilm in the hyperthermophile Archaeoglobus fulgidus[END_REF] demonstrated that A. fulgidus VC-16 was able to form different biofilm structures after 12-18 h under a high concentration of nickel, here we establish that when grown on iron coupon as a sole mineral energy source. This hyperthermophilic archaeon formed tangled materials (Fig. 1C-D) also corresponding to a microbial biofilm [START_REF] Motos | High rate copper and energy recovery in microbial fuel cells[END_REF][START_REF] Rastelli | Bacterial biofilms formed in arseniccontaining water: bacterial community characterization[END_REF]This biofilm was much more developed in the presence of lactate as an organic carbon and energy source.

Indeed, after crust removal, the pits observed on iron surface (Fig. 3) Abiotic control with iron steel; A. fulgidus with an iron coupon and lactate; A. fulgidus with lactate and without an iron coupon; A. fulgidus with an iron coupon and without lactate; and A. fulgidus without an iron coupon and without lactate. Statistical analyses were performed using a multifactor analysis of variance (ANOVA) followed by a Fisher's least significant difference (LSD) procedure to assess significant differences among the conditions. a, b, c, d, e Significant differences for the Fe 2+ , lactate and sulfate (p < 0.000) and acetate (p < 0.0001) concentrations. absence of sulfate. They also demonstrated that CO 2 may be used as a terminal electron acceptor by this microorganism to produce acetate [START_REF] Henstra | Archaeoglobus fulgidus couples CO oxidation to sulfate reduction and acetogenesis with transient formate accumulation[END_REF]. In this respect, under the above-mentioned culture conditions, we propose that A. fulgidus could oxidize iron by using CO 2 as terminal electron acceptor through the Wood-Ljungdahl metabolic pathway with acetate being an end-product of metabolism (homoacetogenesis), thus bypassing the reduction of SO 4 2-. The net reaction below (3) would therefore correspond to the combination of the two half-reactions (1) and ( 2):

2 HCO 3 -+ 9 H + + 8 e -↔ CH 3 COO -+ 4 H 2 O (2) 4 Fe 0 + 2 HCO 3 -+ 9 H + ↔ CH 3 COO -+ 4 Fe 2+ + 4 H 2 O (3)
Indeed, from day 13-32, the acetate concentration produced and Fe 2+ released (Fig. 5A-D) are in accordance with equation (3). In this respect, we could hypothesize that under our culture conditions, A. fulgidus could grow lithoautotrophically on iron steel using dissolved CO 2 as a terminal electron acceptor instead of sulfate. Such conclusion is reinforced by the fact that A. fulgidus is known to be able to use hydrogen, and consequently electrons delivered from hydrogen oxidation only when thiosulfate, but not sulfate served as terminal electron acceptor [START_REF] Hocking | Identification of key components in the energy metabolism of the hyperthermophilic sulfate-reducing archaeon Archaeoglobus fulgidus by transcriptome analyses[END_REF]. The absence of sulfate consumption in such culture conditions is also supported by the absence of FeS in the chimneys. Nevertheless, supplementary studies would be necessary to deepen this hypothesis.

In the presence of lactate, a more complex scenario was observed. The analysis of A. fulgidus-inoculated controls (no iron) shows that the ratio sulfate/lactate consumed was stable and was around 1.3 from early days. Thus, considering that a part of the lactate used is incorporated in the biomass as carbon source, the balance sheet is in accordance with a complete oxidation of lactate according to the following stoichiometric equation [START_REF] Stetter | Archaeoglobus fulgidus gen. nov., sp. nov.: a new taxon of extremely thermophilic archaebacteria[END_REF][START_REF] Möller-Zinkhan | Anaerobic lactate oxidation to 3 CO2 by Archaeoglobus fulgidus via the carbon monoxide dehydrogenase pathway: demonstration of the acetyl-CoA carbon-carbon cleavage reaction in cell extracts[END_REF], as already reported for A. fulgidus [START_REF] Stetter | Archaeoglobus fulgidus gen. nov., sp. nov.: a new taxon of extremely thermophilic archaebacteria[END_REF]:

CH 3 -CHOH-COO -+ 1.5 SO 4
2-→ 3 HCO 3 -+ 1.5 HS -+ 0.5 H + (4)

Nonetheless, in the assays containing both lactate and iron, acetate accumulated concomitantly to the oxidation of lactate (Fig. 5 B and D). Herein, we suggest that lactate oxidation was no more complete as in stoichiometric equation (4) because acetate accumulated even poorly. Hence, the ratio of sulfate/lactate (around 1.2) and the acetate produced (Fig. 5D) would approximately correspond to the stoichiometric equation below: CH 3 -CHOH-COO -+ 1.33 SO 4 2-→ 0.17 CH 3 COO -+ 1.33 HS -+ 2.66 HCO 3

- + 0.5 H + (5)
Moreover, acetate produced after the depletion of lactate (from day 6 to day 13) would result from homoacetogenesis with iron, corresponding to the reaction (3). This hypothesis is supported by the stabilization of the remaining sulfate concentration. The total acetate produced could be attributed, therefore, to direct corrosion process. Thus, we can suggest that direct corrosion may occur concomitantly to indirect corrosion in A. fulgidus-inoculated assays containing lactate when cells adhere to the metallic surface. A. fulgidus might use acetate as carbon and/or energy source, as already reported for Archaeoglobus veneficus [START_REF] Huber | Archaeoglobus veneficus sp. nov., a novel facultative chemolithoautotrophic hyperthermophilic sulfite reducer, isolated from Abyssal black smokers[END_REF] and Archaeoglobus profundus [START_REF] Burggraf | Archaeoglobus profundus sp. nov., represents a new species within the sulfate-reducing Archaebacteria[END_REF], respectively. Yet, these metabolic features have not been reported for A.fulgidus so far. Overall, iron presence slightly affects A. fulgidus metabolism leading to the incomplete oxidation of lactate.

We propose a schematic mechanism to illustrate electron flow from Fe 0 to A. fulgidus cells in the presence and absence of lactate (Fig. 6). In the presence of lactate (Fig. 6A), A. fulgidus enables indirect iron corrosion through the secretion of corrosive sulfide that chemically attacks the iron coupon. The archaeon may also oxidize iron directly as the metabolism is modified in the presence of an iron coupon. The latter possibility is not shown. In Fig. 6B, a schematic mechanism illustrates indicate the ability of A. fulgidus to corrode iron either in the presence or absence of lactate as an organic electron donor although pits were wider and deeper when lactate was added. These observations are supported by electrochemical analysis (Fig. 4). Actually, in terms of thermodynamic tendency, a more negative E corr indicates that the working electrode is more prone to donate electrons. Throughout the experiment, the most substantial electronegative potentials were observed for the A. fulgidus-inoculated assays and more importantly in assays with lactate (Fig. 4). These lower measured potentials of A. fulgidus-inoculated media correspond to an accelerated corrosion process [START_REF] Venzlaff | Accelerated cathodic reaction in microbial corrosion of iron due to direct electron uptake by sulfate-reducing bacteria[END_REF][START_REF] Wu | Microbiologically induced corrosion of X80 pipeline steel in a near-neutral pH soil solution[END_REF][START_REF] Raman | Evaluation of effective biocides for SRB to control microbiologically influenced corrosion[END_REF][START_REF] Cheng | Microbially influenced corrosion of stainless steel by marine bacterium Vibrio natriegens: (I) corrosion behavior[END_REF][START_REF] Alfaro-Cuevas-Villanueva | Microbiologically influenced corrosion of steels by thermophilic and mesophilic bacteria[END_REF], confirmed by our measured current densities. It could be related to intense microbial activity [START_REF] Cheng | Microbially influenced corrosion of stainless steel by marine bacterium Vibrio natriegens: (I) corrosion behavior[END_REF] and correlated to the SEM and AFM observations (Figs. 1C and3D). The evolution of the E corr to more cathodic potentials was a consequence of the biofilm formation, the development of associated corrosion products (Fig. 1B-D) and the passivation phenomena also observed on polarization curves (Fig. 4B). In addition to biofilm establishment, cell growth can lead to the production of corrosive metabolites such as sulfides [START_REF] Cheng | Microbially influenced corrosion of stainless steel by marine bacterium Vibrio natriegens: (I) corrosion behavior[END_REF]. In presence of lactate, passivation phenomena were weakened by the intense microbial activity. The passivation that developed in the absence of lactate could be due to a more stable layer of corrosion products. The anodic corrosion potentials (Fig. 4A) and current densities (Fig. 4B) supported all these results and confirmed an oxidation state of Fe 0 . Hence, corrosiveness could be related to indirect processes (e.g., sulfide production) and to direct mechanisms (e.g., metal oxidation).

In the absence of lactate, a thin microbial biofilm with chimneys developed on the iron coupon after 3 weeks of incubation (Fig. 1D). Recently, similar chimneys were also observed for the first time, in the absence of an organic electron donor with the mesophilic sulfatereducing bacterium, Desulfopila corrodens (Enning et al., 2012;[START_REF] Dinh | Iron corrosion by novel anaerobic microorganisms[END_REF]. The D. corrodens chimneys structures took 3 months to form at 28 • C and pH ≥ 9. They were considered to be ion conductive precipitates composed of FeS and FeCO 3 and were suggested to allow ion flow from the dissolving iron into the bacterial cells [START_REF] Enning | Corrosion of iron by sulfate-reducing bacteria: new views of an old problem[END_REF][START_REF] Venzlaff | Accelerated cathodic reaction in microbial corrosion of iron due to direct electron uptake by sulfate-reducing bacteria[END_REF]. The chimneys observed in the A. fulgidus VC-16 inoculated-assays were thinner than those of D. corrodens and formed within only 2-3 weeks at 70 • C. Moreover, those formed by A. fulgidus were observed in medium at pH 7. Therefore, the chimney formation rate of A. fulgidus may be linked to higher temperatures and/or differences in pH. The S and Si elements were specifically coupled to the microbial biofilm [START_REF] Alfaro-Cuevas-Villanueva | Microbiologically influenced corrosion of steels by thermophilic and mesophilic bacteria[END_REF] underneath the A. fulgidus chimneys. In contrast, S was found in the chimney composites formed by D. corrodens (Enning et al., 2012). All together, these results suggest that the chimneys formed by A. fulgidus differed slightly from those of D. corrodens since there is no FeS in the composition of the A. fulgidus VC-16 chimneys (Fig. 2). Chimney structures were not observed in the assays containing lactate (Fig. 1C). Under the latter condition, we can expect that chimneys did not form or the dense microbial biofilm or precipitates covered these chimneys. Nevertheless, it is clear from our experiments that these chemical structures result from microbial activity on iron coupons.

Besides the observation of biofilm and chimney formation, we demonstrate that A. fulgidus VC16 can use the iron coupon (Fe 0 ) as a sole electron donor oxidizing it to Fe 2+ similarly to other anaerobic microorganisms such as iron-oxidizing microorganisms and few sulfatereducing bacteria. Thus, our results confirm the previous study of Jia and coworkers (2018) who had established corrosive activity of A. fulgidus VC16 under carbon starvation [START_REF] Jia | Carbon steel biocorrosion at 80 • C by a thermophilic sulfate reducing archaeon biofilm provides evidence for its utilization of elemental iron as electron donor through extracellular electron transfer[END_REF]. Moreover, we showed that growth of A. fulgidus (e.g., biofilm formation) in iron-containing assays without lactate was not linked to sulfate reduction (Figs. 1D and5C). Interestingly, small amounts of acetate accumulated under these conditions (Fig. 5D). Previous studies by Henstra and coworkers (2007) revealed that A. fulgidus may perform homoacetogenesis using CO as an energy source either in the presence or how A. fulgidus VC-16 can act as a direct Fe 0 oxidizer. First, we must take into account the known key roles of hydrogenases and cytochromes in direct electron transfer [START_REF] Van Ommen Kloeke | Localization of cytochromes in the outer membrane of Desulfovibrio vulgaris (Hildenborough) and their role in anaerobic biocorrosion[END_REF][START_REF] Mehanna | Role of direct microbial electron transfer in corrosion of steels[END_REF][START_REF] Hernandez | Extracellular electron transfer[END_REF][START_REF] Deutzmann | Extracellular enzymes facilitate electron uptake in biocorrosion and bioelectrosynthesis[END_REF]. A. fulgidus has been recognized to possess several cytochromes [START_REF] Klenk | The complete genome sequence of the hyperthermophilic, sulphate-reducing archaeon Archaeoglobus fulgidus[END_REF] such as cytochrome-C 3 hydrogenase, which is known to be an excellent electron carrier [START_REF] Van Ommen Kloeke | Localization of cytochromes in the outer membrane of Desulfovibrio vulgaris (Hildenborough) and their role in anaerobic biocorrosion[END_REF][START_REF] Booth | Polarization studies of mild steel in cultures of sulphatereducing bacteria[END_REF], as well as two hydrogenases, one of which is periplasmic [START_REF] Hocking | Assessment of the carbon monoxide metabolism of the hyperthermophilic sulfate-reducing archaeon Archaeoglobus fulgidus VC-16 by comparative transcriptome analyses[END_REF]. The involvement of hydrogenase in direct electron uptake is not new. Indeed, microorganisms like Desulfovibrio vulgaris Hildenborough, for example, have already been shown to uptake electron directly from iron and transfer it to periplasmic hydrogenase [START_REF] Van Ommen Kloeke | Localization of cytochromes in the outer membrane of Desulfovibrio vulgaris (Hildenborough) and their role in anaerobic biocorrosion[END_REF]. In addition, chimneys formed by A. fulgidus may act as ion bridges to enable direct electron uptake from the iron coupon by the archaeal cells.

Conclusion

Our study provides evidence that A. fulgidus VC-16 possess the ability to corrode iron indirectly by producing sulfide while oxidizing lactate and directly by oxidizing iron steel. Throughout our study, we glimpse the many metabolic possibilities of A. fulgidus modulated by the presence of iron and also by the presence or absence of a suitable organic electron donor. Moreover, we provide evidence that A. fulgidus, which possibly thrives in hot oil reservoirs [START_REF] Davidova | Involvement of thermophilic archaea in the biocorrosion of oil pipelines[END_REF][START_REF] Duncan | Biocorrosive thermophilic microbial communities in Alaskan North slope oil facilities[END_REF][START_REF] Cord-Ruwisch | Sulfate-reducing bacteria and their activities in oil production[END_REF], may be a highly corrosive microbial agent possibly damaging oilfield facilities in terms of oil reservoir souring similarly to other sulfate-reducing bacteria. Further work is needed to clearly identify the economic losses in the oil industry that are due to its presence in deep hot petroleum reservoirs [START_REF] Davidova | Involvement of thermophilic archaea in the biocorrosion of oil pipelines[END_REF][START_REF] Duncan | Biocorrosive thermophilic microbial communities in Alaskan North slope oil facilities[END_REF].

Fig. 1 .

 1 Fig. 1. Scanning electron micrographs (SEM) of crusts on iron surfaces after incubation for 3 weeks. (A) non-incubated metal reference; (B) abiotic control; (C) A. fulgidus with lactate; and (D) A. fulgidus without lactate showing a chimney (bars, 10 μm).

Fig. 2 .

 2 Fig. 2. Scanning electron micrograph (SEM) and X-ray microanalysis (EDX maps) of a chimney observed after the exposure of an iron specimen to a culture of A. fulgidus for 3 weeks in the absence of lactate as an electron donor. (EHT = 5 kV, 4.00KX).

Fig. 3 .

 3 Fig. 3. Corrosion pits on iron steel SEM micrographs (left) and their corresponding 3D AFM images (right) obtained after 3 weeks of incubation. Corrosion crusts were removed before observation. (A) Unincubated metal reference; (B) abiotic control; (C) A. fulgidus without lactate and (D) A. fulgidus with lactate.

Fig. 4 .

 4 Fig. 4. Monitoring of the corrosion by electrochemical process. A) Kinetics of the open circuit potential vs. the saturated calomel electrode (SCE). B) Potentiodynamic curves performed vs. SCE (scan rate 0.166 mV s -1 ). Abiotic control; A. fulgidus without lactate; and A. fulgidus with lactate.

Fig. 5 .

 5 Fig. 5. Physiology of A. fulgidus in the presence and absence of an iron coupon. Fe 2+ released (A), remaining lactate (B) and sulfate (C), and acetate produced (D).Abiotic control with iron steel; A. fulgidus with an iron coupon and lactate; A. fulgidus with lactate and without an iron coupon; A. fulgidus

Acknowledgements

This work was partially supported by the French CNRS-INSU grant for the BIOHYDEX EC2CO-Microbien project. The laboratories of the MIO, Aix-Marseille University, where most of the experiments were performed, are in compliance with ISO9001-2015.

Declaration of competing interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Appendix A. Supplementary data

Supplementary data to this article can be found online at https://doi. org/10.1016/j.ibiod.2020.105056.


domain: spi chim info math phys

text:
Cyril Polacsek
email: cyril.polacsek@onera.fr

Majd Daroukh

Benjamin François

Raphael Barrier

Raphael Barrier Turbofan

TURBOFAN BROADBAND NOISE PREDICTIONS BASED ON A ZDES CALCULATION OF A FAN-OGV STAGE

published or not. The documents may come

INTRODUCTION

Turbofan broadband noise is nowadays a major topic of concern for aircraft engine manufacturers as its prediction and reduction are both challenging tasks. In the fan module, the main contribution of the broadband noise (BBN) more particularly at approach operation point, is the interaction of the turbulent structures generated in the fan wakes with the outlet guide vanes (OGV). The present work is done in the framework of TurboNoiseBB project and is devoted to the BBN prediction of rotorstator interaction (RSI) mechanism, based on an hybrid RANS/LES calculation applied to the ACAT1 turbofan model at approach conditions [START_REF] François | Zonal Detached Eddy Simulation of the Fan-OGV Stage of a Modern Turbofan Engine[END_REF]. The ACAT1 fan is equipped with 20 blades and 44 vanes and has been tested in AneCom facility (Fig. 1) [START_REF] Guérin | Noise prediction of the ACAT1 fan with a RANS-informed analytical method: success and challenge[END_REF]. A dedicated instrumentation including hot-wire probes and induct/outside microphone antenna has provided data set that are used here for main aerodynamic and acoustic validations. The CFD relies on a ZDES (Zonal Detached Eddy Simulation) that is detailed in a companion paper [START_REF] François | Zonal Detached Eddy Simulation of the Fan-OGV Stage of a Modern Turbofan Engine[END_REF], describing the numerical set-up and first aerodynamic results, while the present one focuses on turbulent wake analyzes and first acoustic predictions. The turbulent fan wakes need to be simulated either by a RANS calculation able to estimate its main averaged characteristics i.e., turbulent kinetic energy and integral length scale, either by a turbulence scale resolved approach to get the statistical and spectral quantities i.e., RMS velocities, power spectral density (PSD), and correlation length scales. The choice of the approach is a trade-off between physical accuracy and numerical cost. The more challenging aspect concerns the assessment of turbulent wall pressure over the vane surface. Although the vane response can be modeled by means of analytical models based on Amiet theory (requiring important simplifications of the turbulent flow and the geometry), the strategy adopted here aims to directly capture both the turbulent wakes and the turbulent sources at vane walls. Because of the high Reynolds number involved (around one million), turbulence-scale-resolved simulations of a fan stage require an important computational effort. For this reason, such BBN simulations remain scarce in the literature. The LBM approach has been successfully applied on the NASA Source Diagnostic Test (SDT) case with quite impressive results [START_REF] Casalino | Turbofan Broadband Noise Prediction Using the Lattice Boltzmann Method[END_REF]. For most current Navier-Stokes solvers, the use of a wall law (practically adopted in the LBM too) enables the reduction of the numerical effort, as done in wall-modeled LES (WMLES). WMLES technique has been recently performed in [START_REF] Arroyo | Large Eddy Simulation of a Scale-Model Turbofan for Fan Noise Source Diagnostic[END_REF] on the NASA SDT case. An alternative way is to resort to hybrid RANS/LES approaches in which the whole boundary layer is solved with a RANS modeling. Hence, their numerical cost is much less dependent on the Reynolds number. The use of ZDES technique remains quite new for such applications. This approach has already been used by Bonneau et al. [START_REF] Bonneau | Turbofan Broadband Noise Predictions using a 3-D ZDES Rotor Blade Approach[END_REF] for the prediction of turbofan broadband noise where only one fan blade was simulated. The present work is an extension of Ref. [START_REF] Bonneau | Turbofan Broadband Noise Predictions using a 3-D ZDES Rotor Blade Approach[END_REF] by accounting for the OGV in the computational domain. ZDES post-processed fields (turbulent wakes and turbulent pressure wall) are inputted in acoustic codes, briefly described in the paper, and respectively based on Amiet theory and Ffowcs-Williams and Hawkings (FWH) analogy. The present acoustic predictions are restricted to power spectrum densities (PSD) of sound power (PWL spectra) in the bypass duct, that are compared to RANS-based solutions also presented and discussed in a collaborative paper [START_REF] Guérin | ACAT1 Benchmark of RANS-informed Analytical Methods for Fan Broadband Noise Prediction: Part II -Influence of the Acoustic Models[END_REF], and to experiment. The paper is structured as follows:

• Section 2 briefly presents the CFD set-up with basic aerodynamics and data extraction for acoustics; • Section 3 is devoted to advanced turbulent wake analyses, by showing iso-contour maps and radial profile comparisons, looking to cyclo-stationnary and turbulent contributions, and addressing the spectral content of the turbulent velocity fields (PSD and correlation length scales); • Section 4 then gives a brief overview of the ONERA acoustic codes and their chaining to the ZDES, and first BBN predictions based on Amiet theory and FWH analogy are presented and compared to experiment; Finally, work status and some conclusions are suggested.

ZDES METHODOLOGY OVERVIEW AND DATA EXTRACTION FOR ACOUSTICS

CFD set-up

The configuration is studied at rig-scale (the outer radius of the fan is 0.42 m). The Inlet Guide Vanes (IGV) are not accounted for in the simulation because their contribution to the RSI noise is negligible compared to the fan-OGV contribution (the bypass ratio is around six). The configuration is studied at approach conditions (50% Nn, namely 3828.4 rpm) for which the RSI noise is dominant. The ZDES method developed by Deck [START_REF] Deck | Recent Improvements in the Zonal Detached Eddy Simulation (ZDES) Formulation[END_REF] and implemented in elsA ONERA code [START_REF] Cambier | The Onera elsA CFD Software: Input from Research and Feedback from Industry[END_REF] is used here. The DES mode 2 based on Spalart turbulence model adopted here is described in [START_REF] François | Zonal Detached Eddy Simulation of the Fan-OGV Stage of a Modern Turbofan Engine[END_REF][START_REF] Cambier | The Onera elsA CFD Software: Input from Research and Feedback from Industry[END_REF]. The convective flux discretization is treated with the AUSM (Advection Upstream Splitting Method) scheme with a third order limiter. The implicit time scheme is ruled by a second order scheme based on a Newton algorithm. Details about numerical parameters are given in Ref. [START_REF] François | Zonal Detached Eddy Simulation of the Fan-OGV Stage of a Modern Turbofan Engine[END_REF].

An illustration of the RANS/DES zones on single channel computational domain is shown in Fig. 2, top. The actual number of blades/vanes (20/44) is unfavorable to reduce the computational domain to a few inter-blade channels. For unsteady RANS simulations, classical phase-lagged boundary conditions allow the reduction of the domain to a single blade channel. Because they are based on the usual Fourier decomposition, they are unadapted for the convection of broadband structures. Consequently, a more favorable option is to change the vane number of the OGV to get a suitable divisor and to permit the use of periodic boundary conditions instead. Even if the periodicity is still questionable for the turbulence structures between adjacent channels, the spectral content and the cascade effects (with respect to the turbulent sources) are believed to be conserved through these boundary conditions. This strategy has already been used by several authors [START_REF] Arroyo | Large Eddy Simulation of a Scale-Model Turbofan for Fan Noise Source Diagnostic[END_REF]. For the present application, the number of vanes is thus reduced from 44 to 40. In order to keep the same flow pattern, the solidity is kept constant meaning that the chord is increased by 10%, the leading edge position being unchanged. This allows for the reduction of the computational domain to one fan channel and two OGV channels, with a negligible aerodynamic impact [START_REF] François | Zonal Detached Eddy Simulation of the Fan-OGV Stage of a Modern Turbofan Engine[END_REF]. A sliding mesh treatment is performed at the interface between the rotating fan and the fixed OGV domains.

Concerning the mesh, it is structured and multi-blocks. Two sets of criteria were used to build the present grids. The first relies on internal best practices concerning the use of the DES mode 2. The cell size must verify ∆x + , ∆y + , ∆z + < 200 in the free shear flow areas and first wall mesh size verifies ∆y + ≤ 1. The second criterion relies on the hydrodynamic wave length. A criterion of 20 points per wavelength leads to a mesh spacing requirement of 0.25 mm at 20 kHz, giving rise to a mesh of 3 billions cells. Practically, the selected cell size was 0.5 mm, ensuring a sampling of 20 points at 10 kHz and a total cell number restricted to 380 millions. A sectional view of ZDES mesh at mid-height (with duplicated blade channel) is shown in Fig. 2, bottom The complete grid (not shown) is extended 4 blade chords upstream and 3 vane chords downstream and is rapidly stretched in both directions (only visible upstream here) so that the last cell size reaches 3 cm and 2 cm respectively. Note that this stretching technique, aiming to increase the numerical dissipation, is currently used at ONERA for turbomachinery aeroacoustic applications in order to palliate the ineffective 1D characteristics-based nonreflecting boundary condition mostly implemented in CFD solvers (as in elsA) when using implicit schemes. The aerodynamic performances are quite well retrieved by the simulation as shown in Table 1. Small discrepancies on the secondary mass flow rate are due to the difficulty to monitor it with the DES solving. More details about convergence and basic aerodynamic analysis can be found in Ref. [START_REF] François | Zonal Detached Eddy Simulation of the Fan-OGV Stage of a Modern Turbofan Engine[END_REF].

Basic flow visualizations and aerodynamic performances

Data extraction for acoustics

The first objective of these advanced simulations is to accurately capture the flow unsteadiness and the main turbulent contents involved in the RSI mechanism. In order to check the flow properties issued from the ZDES by comparison with available HW measurements and to provide the required inputs to the acoustic postprocessing, data extractions over selected surfaces have been performed during the simulation [START_REF] François | Zonal Detached Eddy Simulation of the Fan-OGV Stage of a Modern Turbofan Engine[END_REF]. The main analyses are realised at HW1 plane (Fig. 1), located at axial position X = -2.685 m. The most useful extracted quantity here is the 3-component velocity field. Same data have been extracted along a curved plane closely aligned (5 mm upstream) to the OGV leading edge to feed the Amiet-based tool (in-house code TinA) as discussed in Sections 3 and 4. Skin surfaces over the blade/vane walls provide the required inputs (unsteady wall pressure) to the FWH-based solver (in-house code FanNoise). Additional extractions along slices upstream the rotor and downstream the stator will be used for future complementary analyses (not discussed here). All the data are extracted at a sampling frequency of 100 kHz, namely one time step over 30, and a maximum duration time of 2.8 revolutions (56 fan blade passages), allowing to perform PSD analyses averaged over 12 blocks with a frequency resolution equal to 273 Hz (without overlapping). Unfortunately, the simulation could not be performed on a longer duration time (as initially planned) for robustness reasons. Indeed, as discussed in Section 4, ZDES iterations had to be stopped at 2.8 revs. because of numerical instabilities generated at some radial stations of the sliding grid interface, revealed by the horizontal streaks visible in Fig. 3 (right), that could pollute the unsteady solution.

TURBULENT WAKE ANALYZES

Cyclo-stationnary fields

First flow analyses are devoted to cyclo-stationnary fields in terms of 2D contour maps (slices) at HW1 plane. Present results are focused on mean velocity and RMS turbulent velocity fields. Only one blade passage is solved in the ZDES (as the turbulent flow is assumed to be actually periodic from blade-to-blade), corresponding to a 2-vanes sector with the modified 40-vanes OGV adopted in the numerical set-up. 360° maps are simply obtained by duplicating the 1-blade-channel numerical solution over the 20 blades (Fig. 4, left), whereas the phase-locked HW measurements assess full 360° maps (Fig. 4, right) that can reveal significant blade-to-blade deviations (due to imperfect test conditions). Comparisons of phase-locked contour maps averaged and duplicated over 3-blade channels (Fig. 5) show a quite good agreement between ZDES and experiment for axial component (same trend is found for tangential and radial components). Similar analyses on turbulent velocity fields are shown in Fig. 6, highlighting blade-to-blade level deviations in the measurements (Fig. 6, top) probably due to non-identical blades (slight geometry defects) or non-perfectly axisymmetric turbulent inflow conditions. Results for other components (only discussed in section 3.2 for sake of conciseness) display almost the same patterns with close levels than those observed on axial component, which tends to confirm that isotropic assumption currently adopted (in the sense of energy) is roughly valid. However, the numerical predicted levels are found to be above the experiment arguing for an overestimation of the turbulent wake intensity by the ZDES.

Measurements

In fact, this level offset was recently attributed to the limited bandwidth of available HW probes (cut-off frequency around 7-8 kHz) giving rise to an underprediction of RMS values of about 1.5 factor. This point is more discussed in Sections 3.2 and 3.3.

Averaged radial profiles

Previous phase-locked results are circumferentially averaged to assess radial profiles. ZDES vs. experiment comparisons of mean velocity profiles are presented in Fig. 7, showing a very good agreement for axial and tangential components (same result for radial velocity). Similar analyses are proposed in Fig. 8 for RMS turbulent velocities by overplotting the experimental profiles obtained when applying the 1.5 factor correction (estimated from Parseval identity and integration of velocity PSD up to 8.5 kHz, as discussed in Section 3.3). A satisfactory matching is observed when adopting this correction, more particularly on the tangential component (Fig. 8, right). Turbulence intensity (TI) profiles provided by ZDES are compared to the so-corrected measurements in Fig. 9, in which a RANS-based solution (using k-ω Menter SST model) is also plotted. It is clearly observed that the ZDES-based solution better fits the experimental profile in the upper part of the vein up to the tip.

Velocity spectra and correlation length scales

Next results are devoted to PSD and correlation length scale analyzes. PSD are obtained using at least 10 averages with or without Welch method (50% overlapping) ensuring a frequency spacing of 273 Hz with the available signal duration. Comparisons to experiment at mid-height are proposed in Fig. 10, for axial (Fig. 10, left) and tangential (Fig. 10, right) turbulent velocity components (and using a Log axis scale limited to 20 kHz). Information about signal processing performed by DLR in AneCom tests can be found in [START_REF] Guérin | Noise prediction of the ACAT1 fan with a RANS-informed analytical method: success and challenge[END_REF]. One should note that tonal contribution (BPF harmonics) is included in the present measurement data set, whereas the cyclo-stationnary part was removed in the numerical solution. Theoretical PSD based on von-Karman (VK) spectrum model, with TI and turbulence length scale (TLS) values issued from RANS calculations (and adjusted to better fit the experiment), are addressed too. The ZDES spectrum is found to be in a good agreement with the experiment with respect to the maximum level "plateau", particularly for the tangential component, and is displaying a level attenuation slope not far from the VK one. However, although the ZDES slope is weaker, the experiment reveals a strong and questionable level attenuation slope beyond 7-8 kHz (see black dashed line), getting far away from expected VK -5/3 power law. This unphysical attenuation was recently attributed to an inappropriate cut-off frequency of hot wire probes (enlarged diameter justified by mechanical constraints and probe damages during AneCom tests). Consequently, RMS turbulence levels issued from the measurements are underpredicted by a factor that can be roughly set equal to 1.5 (estimated from theoretical -5/3 power law). The PSD shape issued from ZDES is a bit more flat compared to the theoretical VK slope achieved here by setting a TLS value around 5 mm. This discrepancy is more pronounced in the tip region, tending to show that the ZDES provides lower TLS values (closer to 2 mm) than the one issued from a VK spectrum adjusted to fit the measurements (up to the cut-off frequency) and more in the range of 5-6 mm. This trend seems to be confirmed by the correlation scale analyzes, for which an assessment of TLS issued from ZDES can be estimated using zero time-shift cross-correlation function (applied to the streamwise velocity component) and Taylor's assumption.

The radial profile of this length scale at HW1 position is plotted in Fig. 11 and compared to those issued from RANS (k-ω Menter SST) solution and deduced from current formula following Pope [START_REF] Pope | Turbulent Flows[END_REF] and Jaron [START_REF] Jaron | Impact of Turbulence Models on RANS-Informed Prediction of Fan Broadband Interaction Noise[END_REF] and detailed in Ref. [START_REF] Guérin | ACAT1 Benchmark of RANS-informed Analytical Methods for Fan Broadband Noise Prediction: Part II -Influence of the Acoustic Models[END_REF]. It can be observed that RANS-based TLS are increasing in the upper part of the duct and only decreasing near the casing wall, whereas ZDES solution predicts a significant decrease of TLS beyond r = 0.31 m up to the tip. This inverse trend is not easy to explain and more investigations should be done. As discussed in Section 4, a quite important quantity related to the turbulent wake trimming the RSI noise generation is the spanwise frequency-dependent correlation length scale (denoted l r here). It is obtained from the radial integration of the coherence function (root mean square), γ, applied to the upwash velocity component, u n , as follows [START_REF] Lynch | A Correlation Length Scale for the Prediction of Aeroacoustic Response[END_REF]:

; (1)
The coherence function is practically assessed by extracting a radial line at constant angular station and by splitting the field into 10 radial strips. Spanwise correlation length scales are shown in Fig. 12, for 3 radial stations (20% H, 50% H and 90% H), and compared to the theoretical expression related to VK spectrum and using TLS profile based on Pope (see Fig. 11, left):

(2) γ f , r 12

( ) = u n f , r 1 ( ) u n * f , r 2 ( ) S u n u n f , r 1 ( ) S u n u n f , r 2 ( ) ! " # $ 1/2  r f ( ) = γ f , r 12 ( ) 0 ∞ ∫ dr 12  y f ( ) = 8Λ 3 Γ 1 / 3 ( ) Γ 5 / 6 ( ) ⎛ ⎝ ⎜ ⎞ ⎠ ⎟ 2 k c / k e ( ) 2
3

+ 8 k c / k e ( ) 2
⎡ ⎣ ⎤ ⎦ 1 + k c / k e ( ) 2

BROADBAND NOISE PREDICTIONS

Acoustic codes overview

BBN predictions proposed in this work are obtained by chaining the CFD solutions to the two dedicated in-house acoustic codes currently used at ONERA for turbofan noise applications. TinA, is based on Amiet isolated airfoil formulation extended to annular cascade configurations by introducing a modal Green's function valid for semi-infinite annular duct and uniform flow, as proposed by Goldstein. 1D and 2D formulations implemented in TinA (respectively TinA1D and TinA2D versions) are detailed in [START_REF] Reboul | Ductedfan broadband noise simulations using unsteady or averaged data[END_REF]. TinA calculations are generally performed using RANS-based inputs [START_REF] Guérin | ACAT1 Benchmark of RANS-informed Analytical Methods for Fan Broadband Noise Prediction: Part II -Influence of the Acoustic Models[END_REF], but a modified version has been adapted to be chained with ZDES specific outputs. FanNoise [START_REF] Reboul | Ductedfan broadband noise simulations using unsteady or averaged data[END_REF][START_REF] Cader | Numerical prediction of rotor-stator interaction noise using 3D CAA with synthetic turbulence injection[END_REF], is a frequency domain code currently used to predict tonal and BBN spectra using a FWH analogy (restricted to the loading noise term) and adopting a modal Green's function too.

The required inputs are the unsteady pressure harmonics at the blade (rotor sources) or vane (stator sources) walls. BBN predictions related to RSI mechanism are practically obtained by using ZDES turbulent wall pressure extracted over the vane walls.

Amiet-based predictions using ZDES inputs

BBN predictions based on Amiet theory are first presented in this section. As explained previously, one of the objectives of using scale-resolved turbulence solutions is to evaluate current BBN predictions using isotropic turbulence spectrum models with main turbulence parameters (TI and TLS) deduced from RANS calculations, as done in [START_REF] Guérin | ACAT1 Benchmark of RANS-informed Analytical Methods for Fan Broadband Noise Prediction: Part II -Influence of the Acoustic Models[END_REF]. Indeed, turbulent wake spectral analyses presented in Section 3.3 have been used to directly feed the Amiet-based code TinA. Basically, the acoustic field is linked directly to the 2-wave number turbulence energy spectrum, φ unun , which can be related to the PSD of upwash velocity, S unun , and to the spanwise correlation length scale (l r ) as [START_REF] Bonneau | Turbofan Broadband Noise Predictions using a 3-D ZDES Rotor Blade Approach[END_REF][START_REF] Winkler | Airfoil trailing-edge blowing: broadband noise prediction from Large-Eddy Simulation[END_REF]:

φ u n u n k c , k r ( ) = U c π S u n u n f ( ) r f , k r ( ) (3)
 r f , k r ( ) = γ f , r 12 ( ) 0 ∞ ∫ cos k r r 12 ( )dr 12 (4)
These quantities can be directly obtained from the ZDES, as done here by restricting to the parallel gusts:

φ u n u n k c , 0 ( ) = U c π S u n u n f ( ) r f ( ) (5)
In order to get more reliable predictions, turbulent fields similar as those analysed in Section 3 at HW1 position have been extracted over a plane aligned the OGV leading edge (as done with the RANS inputs too). The corresponding BBN predictions in terms of PWL spectra in the bypass duct are presented in Fig. 13 (red curve). RANS-informed solutions obtained using conventional

Pope-based TLS and issued from TinA1D (blue dashed line) and TinA2D (blue thick line) are plotted too. As known from previous studies, RANS-informed solutions using TinA1D tend to overpredict the level in the low and medium frequency range whereas TinA2D predictions are expected to be more reliable. A first point to notice is that the peak level frequency is well captured when using the ZDES inputs whereas the one issued from RANS-based TinA1D solution is clearly shifted to a lower frequency. Moreover, PWL provided by ZDES-based predictions is surprisingly close to the RANS-based TinA2D solution, despite the fact that respective TI and TLS profiles were found to be significantly different. Some balancing effects might certainly explain this result. The ZDESbased solution seems to better fit the experiment in the low frequency range, but this is partly due to non-fully reliable numerical correlation length scales for which uncertainties are growing up at lowest frequencies (see Fig. 12). It would be quite interesting to check the effect of using Eq. ( 4) instead of Eq. ( 5) in the ZDES-based BBN predictions, but the numerical assessment of the complete 2-wavenumber turbulence energy spectrum using available ZDES data set is not so easy. Anyway, from these first acoustic results, it seems reasonable to say that isotropic assumptions and von-Karman turbulence spectrum models adopted in the current RANS-informed approaches are not invalidated by the present scale-resolved turbulence investigations.

FWH predictions using ZDES inputs

In this Section, the first BBN predictions obtained using the FWH analogy with direct source inputs are discussed.

ZDES data extracted at the vane wall are post-processed to feed the in-house code FanNoise, requiring to perform a Fourier transform of the turbulent pressure over the available signal duration. Practically, PSD are calculated from a single Fourier transform of the whole signal without statistical averaging, and a post frequency-band averaging is applied afterwards to reduce the level oscillations. RMS pressure fields over the vane surface are good indicators to check the convergence of the ZDES solution and to visualize the distribution of dominant sources, expected to be mainly located in the leading edge region. In Fig. 14, RMS wall pressure contour map over the vane suction side issued from ZDES post-processing (Fig. 14, right) is compared to a complementary numerical prediction (Fig. 14, left), obtained using a linearized Euler CAA solver with synthetic turbulence injection [START_REF] Cader | Numerical prediction of rotor-stator interaction noise using 3D CAA with synthetic turbulence injection[END_REF] (achieved in a dedicated task of TurboNoiseBB project). As expected, dominant sources are found to be concentrated in the leading-edge region with comparable levels (same scales are used). However, it can be noticed that the ZDES solution displays a source field spreading over the entire suction side with significant levels up to the trailing edge, whereas the CAA predicted levels are much more confined to the leading edge region (a similar observation has been made on the pressure side). Moreover, a few high-level spots are visible in the tip region for the ZDES solution. These additional sources are questionable here: they might be due to numerical noise generated at the sliding grid interface (as previously revealed by flow visualizations shown in Fig. 3, right). Another possible issue might be a numerical reflection at the exit boundary, although the ZDES grid cells are properly stretched in this region in order to increase the numerical dissipation (as explained in Section 2). Back-scattered incoming acoustic waves emitted from the exit boundary could pollute the turbulent wall pressure field. These two suspected causes of noise pollution are currently under investigation. PWL spectra in the bypass duct obtained with ZDES+FWH method are presented in Fig. 15 and compared to the experiment. The predicted levels are clearly over-estimated and reveal the presence undesirable tones with two high-level bumps (centred around 6500 Hz and 9200 Hz). A filtering of these tones combined with a 10-band averaging with a smoothing process is applied on the raw predictions, giving rise to the smoothed spectrum plotted in red line. Despite a drastic reduction of oscillating levels, the predicted levels are about 5-10 dB above the experimental ones, with deviations increasing with frequency. This result is quite disappointing and seems to confirm the presence of additional sources certainly due to numerical artefacts. In order to try to remove the contribution of these non-physical sources, the FWH surface integration is simply restricted to half a chord from the leading edge, as illustrated in Fig. 16, left. This 50% reduction is approximate, but it is a good way to evaluate the contribution of spurious sources (as noise generated by this truncated region should be low). The resulting solution is shown in Fig. 16 right, for raw and averaged/smoothed PWL spectra. A clear benefit can be observed, in particular for mid-frequency and highfrequency levels (beyond 3000 Hz), for which levels are significantly reduced and getting much closer to the expected ones. The frequency range of the spectrum in less impacted by this surface truncation, which is a good point since the initial levels were not so far from the measurements. It tends to show that the numerical noise contribution is quite important in this truncated region of the vane. Sensitivity to truncation extent has been studied by performing two additional calculations and applying 40% and 30% chord integration, with corresponding results plotted (for the three truncated cases) in Fig. 17, left. Shapes of the spectra are almost similar and levels are getting lower as reducing the integration surface (more particularly for 30% chord integration). Hence, it is actually not possible to ensure a fully reliable prediction and a reasonable compromise at 40% chord is retained in Fig. 17 (right), for comparisons with Amiet predictions using RANS-based and ZDES-based inputs, using a Log axis scale. A good agreement is observed at low frequencies with the RANS+Amiet solution, and all predictions are matching well in the mid-range. Although level oscillations are still present in the ZDES+FWH spectrum at higher frequencies, this solution seems to better capture the attenuation slope from experiment.

CONCLUSIONS

A ZDES approach has been conducted to simulate the turbulent flow and BBN power spectra of the ACAT1 fan-OGV stage, at approach conditions. Turbulent wake characteristics have been first analysed and compared to available HW measurements from AneCom test rig (focusing at mid-distance between fan and OGV). Radial profiles of turbulent velocity components are found quite close to the measurements when suited corrections (related to HW probes cut-off frequency around 8 kHz) are applied. The energy of turbulent wakes is shown to be roughly isotropic in the ZDES and in the experiment too. Turbulent velocity spectra show a reasonable agreement with the experiment (up to the HW cut-off frequency) and not far from usual isotropic turbulence von-Karman spectrum models when adjusting TI and TLS values.

Estimates and analyses of integral and spanwise correlation length scales have been discussed in order to provide relevant information aiming to feed in-house acoustic tools. Hence, first BBN predictions based on Amiet approach (using RANS-based and ZDES-based turbulent wake characteristics extracted just upstream the OGV) and FWH analogy with loading noise source terms (using turbulent wall pressure over the OGVs surface directly provided by ZDES) have been performed and discussed. Following comments can be pointed out:

-Numerical noise created at the sliding grid interface has been detected and is partly responsible for a pollution of turbulent pressure at the vane wall, also attributed to possible numerical reflections at the exit boundary of the CFD domain.

-Nevertheless, all the studied methods provide satisfactory estimations of PWL spectra in terms of shape and levels with overall deviations within 3 dB from each other and less than 5 dB from experiment.

-Despite a better capture of turbulent wake characteristics, the benefit of using direct ZDES inputs in Amiet-based predictions is not clearly addressed yet.

-ZDES+FWH direct method is certainly the most promising one, and its feasibility has been demonstrated, but the presence of additional spurious sources does not permit a fully reliable assessment of PWL spectra.

-RANS-informed solutions are still competitive and seem rather reliable regarding the present results, at least as long as scale-resolved turbulence methods are not getting more robust and not clearly addressing a much better accuracy in BBN predictions.

Figure 1 .

 1 Figure 1. Meridional view of the fan module in AneCom rig (top) and CFD domain with hot-wire probes at HW1 position (bottom).

Figure 2 .

 2 Figure 2. URANS and DES zones (top) and blade-toblade section mesh with 1 over 2 pts. shown (bottom).

Figure 3 (

 3 Figure 3 (top), presents a visualization of the instantaneous flow field around the fan blade: surfaces of iso-values of the Q-criterion colored by the axial momentum are displayed. It highlights the zonal solving (RANS flow in the primary region). Because the flow separates at the leading edge of the fan for this operating point, turbulent structures are generated from there and are convected downstream. The high grid density enables to capture small turbulent structures. A visualization of vorticity magnitude fields on an iso-radius surface and on a transverse slice upstream the OGV are shown in Fig.3(bottom), left and right, respectively. The thick black lines (left) depicts the areas in which the shielding function f d[START_REF] François | Zonal Detached Eddy Simulation of the Fan-OGV Stage of a Modern Turbofan Engine[END_REF] equals 0.95, thus defining the border between the RANS solving (in the boundary layer) and the LES solving (in the free shear flow areas). For both fan and OGV blades, the RANS solving is found able to encompass the whole boundary layer, and the turbulent wakes seem to convect correctly through the periodic boundaries up to the OGV domain.

Figure 3 .

 3 Figure 3. Iso-value surfaces of the Q-criterion around the fan blades (top) and of vorticity magnitude fields on an iso-radius slice (bottom, left) and on a transverse slice upstream the OGV (bottom, right).

Figure 4 .

 4 Figure 4. 360° maps of axial velocity: instantaneous ZDES solution (left) and phase-locked HW measurements (right).

Figure 5 .

 5 Figure 5. Phase-locked iso-contour maps of axial velocity issued from ZDES (left) and averaged experiment (right) duplicated over 3-blade channels.

Figure 6 .

 6 Figure 6. Comparison of RMS turbulent velocity fields (axial component): Phase-locked iso-contour maps issued from ZDES (left) and from 360° (top) and averaged (right) experiment.

Figure 7 .

 7 Figure 7. ZDES vs. experiment mean velocity profiles for axial (left) and tangential (right) components.

Figure 8 .

 8 Figure 8. ZDES vs. raw and corrected experiment of RMS turbulent velocity profiles: axial (top), radial (bottom, left) and tangential (bottom, right) components.

Figure 9 .

 9 Figure 9. Comparison of turbulence intensity profiles assessed by ZDES, RANS and corrected experiment.

Figure 10 .

 10 Figure 10. PSD (dB/Hz) of turbulent velocity (50% H) issued from ZDES, compared to VK and experimental spectra: axial (left) and tangential (right) components.

Figure 11 .

 11 Figure 11. TLS profile obtained from ZDES (in red) and compared to RANS-based solutions.

Figure 12 .

 12 Figure 12. PSD of spanwise correlation length scale obtained from ZDES and compared to RANS-based solutions (using VK model) at 3 height positions.

Figure 13 .

 13 Figure 13. PWL spectra (bypass) provided by TinA code using RANS and ZDES inputs extracted at OGV plane and compared to AneCom experiment.

Figure 14 .

 14 Figure 14. RMS wall pressure maps on vane suction side issued from CAA (left, from [15]) & ZDES (right).

Figure 15 .

 15 Figure 15. PWL spectra (bypass) issued from ZDES + FWH analogy (FanNoise) and compared to experiment

Figure 16 .

 16 Figure 16. Illustration of restricted FWH integration surface (left) and PWL spectra obtained with mid-chord integration and compared to experiment (right).

Figure 17 .

 17 Figure17. PWL spectra (dB/Hz) obtained from ZDES+FWH calculations using 50%, 40%, 30% chord integration (left), and compared (40% chord int.) to RANS-based solution and experiment (Log scale, right).

Table 1 .

 1 Comparison of aerodynamic performances.

ACKNOWLEDGEMENTS

The presented work was conducted in the frame of the project TurboNoiseBB, with funds from the European Union's Horizon 2020 research and innovation program under grant agreement No. 690714. Access to HPC resources was allocated by GENCI (French National Computing Center). The authors would like to thank DLR team for providing the experimental data set.