Laura Selliez

Christelle Briois

Nathalie Carrasco

Laurent Thirkell

Bertrand Gaubicher

Jean-Pierre Lebreton

Fabrice Colin

J.-P Lebreton

Analytical performances of the LAb-CosmOrbitrap mass spectrometer for astrobiology

A new generation of High Resolution Mass Spectrometers (HRMS) for space exploration is being developed for several years to augment significantly the analytical performances of these instruments in extraterrestrial environments. To this day, in-flight instruments have shown mass resolving powers up to 9,000 at Full Width at Half Maximum (FWHM) [START_REF] Balsiger | Rosina -Rosetta Orbiter Spectrometer for Ion and Neutral Analysis[END_REF]. Future instruments aim at reaching mass resolutions of a few tens of thousands to more than one hundred thousand in a mass range of a few thousands. In this frame, this paper presents results of the LAb-CosmOrbitrap, a high resolution mass spectrometer challenging to couple a laser ionization system with an Orbitrap TM cell. The mass analyzer called CosmOrbitrap is involved in a Technology Readiness Level (TRL) development. Tests have been conducted on three organic compounds to prove the relevance of this simple instrument configuration for astrobiology through a successful repeatability study in which a few tens to hundreds mass spectra have been analyzed. Mass resolving powers from 60,000 to more than 100,000 have been obtained in the mass range 136 to 431 u. The best result obtained shows a mass resolving power of 380,000 at m/z 136 (adenine) with a longer acquisition J o u r n a l P r e -p r o o f

I) Introduction

Astrobiology is a multidisciplinary science involving chemistry, biology, geology, physics and astronomy, among others. This field aims at understanding the emergence of life on Earth (ingredients, conditions, time scale) and its search beyond Earth, in the Solar System and further in the Universe. From a chemical point of view, these investigations are based on the study of the complex organic matter. Building blocks of life are composed by simple chemical elements such as Carbon, Hydrogen, Oxygen, Nitrogen, Phosphorous and Sulphur -so-called "CHNOPS" -which represent up to 97% of the mass in living cells [START_REF] J O U R N A L P R E -P R O O F Wackett | Microbial genomics and the periodic table[END_REF]. These simple elements form prebiotic compounds such as the amino acids constituting proteins and the nucleobases composing nucleic acids of DNA. Under certain conditions of temperature, availability of liquid water, organic compounds, energy source(s) and time, life is expected to appear. In the first stages of the emergence of life, we know that the simplest organic compounds come from inorganic matter and grow into complex organic blocks. These complex organic molecules are thus able to interact with each other and to initiate reaction chains. Some of these pathways are still not well understood. But building blocks of life such as CHNOPS molecules and prebiotic compounds are actively searched on other celestial bodies of the Solar System as a proof of a presence of life, past or emerging.

Several Solar System bodies are particularly targeted in the search of complex organic matter: Mars for the possible emergence of life during its early times; icy moons such as Jupiter's Europa and Saturn's Enceladus, based on the existence of subsurface oceans under their icy crusts; Titan, the biggest moon of Saturn, for the extremely rich organic chemistry detected from the surface to the ionosphere; and small bodies such as comets and asteroids, assumed to be sources of water and organic matter on Earth.

A large variety of analytical tools was used for decades to characterize extraterrestrial environments, to detect relevant compounds and to analyze chemical pathways leading to the growth of organic molecules involved in life. A powerful analytical tool used in space instrumentation for the study of J o u r n a l P r e -p r o o f chemical compounds is mass spectrometry. The identification of organic molecules leads to a good understanding of extraterrestrial environments and chemical pathways occurring at the surface or in the atmosphere. A reliable interpretation of the data obtained depends on the instrument performances.

A wide range of space mass spectrometers (MS) have been developed in the last 50 years. MS instruments have been flown since the beginning of space exploration (on Apollo 15, 16, 17 ;[START_REF] Hodges | The lunar atmosphere[END_REF] and later onboard the Mars Viking probes in 1976 [START_REF] Nier | Composition and Structure of the Martian Atmosphere: Preliminary Results from Viking 1[END_REF]Owen T. and Biemann K., 1976).

Both the INMS (Ion and Neutral Mass Spectrometer) instrument and GCMS (Gas Chromatography Mass Spectrometer) on the Cassini-Huygens mission has allowed identifications of many heavy organic compounds and showed the polymeric growth occurring in Titan upper atmosphere [START_REF] Vuitton | Ion chemistry and N-containing molecules in Titan's upper atmosphere[END_REF][START_REF] Westlake | The role of ion-molecule reactions in the growth of heavy ions in Titan's ionosphere[END_REF]. Our knowledge about the organic chemistry on Titan has been immensely improved with all the data recorded thanks to this space mission. However, it has also opened new scientific questions that can only be addressed by instruments with better (factor of 10 to 100) analytical performances. The INMS mass resolving power was 100 in the [1-100] m/z range allowing to distinguish chemical species with different nominal masses (but not isobars, for instance).

The most powerful MS to date that has flown on a space mission is the DFMS-ROSINA (Double Focusing Magnetic Mass Spectrometer-Rosetta Orbiter Spectrometer for Ion and Neutral Analysis) experiment on the Rosetta mission, with a mass resolving power of 9,000 at FWHM at m/z 28 [START_REF] Balsiger | Rosina -Rosetta Orbiter Spectrometer for Ion and Neutral Analysis[END_REF]. N 2 and O 2 have been detected in the environment of comet 67P/Churyumov-Guerasimenko and the glycine amino acid has been evidenced in situ for the first time in the coma of the comet (Altwegg Kathrin et al., 2016.;[START_REF] Bieler | Abundant molecular oxygen in the coma of comet 67P/Churyumov-Gerasimenko[END_REF][START_REF] Rubin | Molecular nitrogen in comet 67P/Churyumov-Gerasimenko indicates a low formation temperature[END_REF]. The available mass range, up to 150 mass units, limited the studies to low mass organic compounds.

The next generation of mass spectrometers for the future space missions need a mass resolution above 10,000 to make a difference, particularly in life detection. Indeed, such mass resolutions allow J o u r n a l P r e -p r o o f the unambiguous identification of the building blocks of life -the nucleobases of DNA but also proteins, peptides (among others heavy and complex organic compounds) and the understanding of their possible interactions with the non-organic matter. The complex matrix composed by organic compounds and mineral matter can be deciphered using High Resolution Mass Spectrometers This work presents the performances reached with a Laser ionization (Laser Ablation and Laser Desorption Ionization) Mass Spectrometer (LA/LDI-MS) based on the Orbitrap™ technology [START_REF] Makarov | Electrostatic Axially Harmonic Orbital Trapping: A High-Performance Technique of Mass Analysis[END_REF], an ion trap using a quadro-logarithmic electrostatic field for trapping the ions. The ionization source uses a 266 nm laser operating in a transitional regime between ablation and desorption ionization. The ability of this set-up to identify organic compounds has been demonstrated through a previous blind test [START_REF] Selliez | Identification of organic molecules with a laboratory prototype based on the Laser Ablation-CosmOrbitrap[END_REF]. Experiments conducted on metals [START_REF] Briois | Orbitrap mass analyser for in situ characterisation of planetary environments: Performance evaluation of a laboratory prototype[END_REF], aerosol analogs of Titan [START_REF] Selliez | High-resolution mass spectrometry for future space missions: Comparative analysis of complex organic matter with LAb-CosmOrbitrap and laser desorption/ionization Fourier transform ion cyclotron resonance[END_REF] and prebiotic compounds [START_REF] Arevalo | An Orbitrap-based laser desorption/ablation mass spectrometer designed for spaceflight[END_REF] have shown a mass resolving power up to 120,000 at m/z 136 and mass accuracies better than 3 ppm on this wide variety of samples. To go further, this paper addresses the reproducibility of the analytical performances obtained on organics samples, through the acquisition J o u r n a l P r e -p r o o f of a high number of mass spectra on organic compounds, and a preliminary study on the isotopic abundances.

J o u r n a l P r e -p r o o f

II) Methodology a) Instrument configuration

The laboratory device, LAb-CosmOrbitrap, used for the experiments has been fully described in previous papers [START_REF] Briois | Orbitrap mass analyser for in situ characterisation of planetary environments: Performance evaluation of a laboratory prototype[END_REF][START_REF] Arevalo | An Orbitrap-based laser desorption/ablation mass spectrometer designed for spaceflight[END_REF][START_REF] Selliez | Identification of organic molecules with a laboratory prototype based on the Laser Ablation-CosmOrbitrap[END_REF]. It is composed of the CosmOrbitrap mass analyzer [START_REF] Briois | Orbitrap mass analyser for in situ characterisation of planetary environments: Performance evaluation of a laboratory prototype[END_REF] directly coupled with a laser ionization system. The different elements are shown in Figure 1 (left).

Samples are ionized in a first vacuum chamber (10 -7 mbar). Ionization is made using a Nd-YAG laser emitting at 266 nm. This wavelength is optimal for organic compounds [START_REF] Goesmann | The Mars Organic Molecule Analyzer (MOMA) Instrument: Characterization of Organic Material in Martian Sediments[END_REF] 1 (right)) for future planetary missions dedicated, for instance, to the Europa exploration. This shows the relevance of the use of this wavelength for future spaceflight applications. In our set-up, fluence on the sample ranges from 2.9 to 12 J/cm 2 . We thus observe a transitional laser regime between pure ablation (> 10 J/cm 2 ) and laser desorption (< 1 J/cm 2 ) leading to the formation and detection of different kind of ions including thermo-desorbed and fragment ions (detailed in the result sections). Polymeric patterns specific to the aerosol analogs of Titan have demonstrated that ions extracted are representative of the sample [START_REF] Selliez | High-resolution mass spectrometry for future space missions: Comparative analysis of complex organic matter with LAb-CosmOrbitrap and laser desorption/ionization Fourier transform ion cyclotron resonance[END_REF].

Ions produced are injected, through a specifically-designed ion optics, into the Orbitrap TM analytical cell placed in a second vacuum chamber (10 -9 mbar). In this simple instrument configuration, all ions produced which enter the cell can be analyzed and there is neither C-trap nor ion selection. In the commercial instrument, ions selection and accumulation are made using a C-trap and stored ions enter the Orbitrap TM cell into very short pulsed packets [START_REF] Scigelova | Orbitrap Mass Analyzer -Overview and Applications in Proteomics[END_REF].

The High Voltage (HV) applied on the Orbitrap TM mass analyzer has two essential functions: to optimize the trapping of the injected ions and to maintain a stable oscillation frequency of these J o u r n a l P r e -p r o o f same ions. The trapping is coupled to the duration of the voltage switching at the time of ion injection. The stabilization of the oscillation frequency is proportional to the relative stability of the HV level applied during the measurement of the image current induced by the ions on the detection electrodes.

The Orbitrap TM cell has been modified to meet mechanical constraints as required for a space mission. Its current length is 81 mm for a diameter of 40 mm.

b) Samples

Three organic samples have been studied in this work. They are all nitrogenous and/or sulfurous compounds, covering masses from m/z 136 to m/z 431. One of them is the well-known adenine, nucleobase involved in DNA and thus, of primary interest to astrobiology. This compound has also been detected in Titan' aerosols analogues [START_REF] Hörst | Formation of Amino Acids and Nucleotide Bases in a Titan Atmosphere Simulation Experiment[END_REF]. Its chemical formula is C 5 H 5 N 5 , detected in this study under its positive ion and protonated form: C 5 H 5 N 5 +H + , at a theoretical m/z 136.0618. The two other compounds are named HOBt and BBOT standing for 1H-Benzotriazole,1hydroxy-and 2,5-Bis(5-tert-butyl-2-benzoxazolyl)thiophene. They have been identified through a blind test with the LAb-CosmOrbitrap [START_REF] Selliez | Identification of organic molecules with a laboratory prototype based on the Laser Ablation-CosmOrbitrap[END_REF]. These two compounds are good isotopic J o u r n a l P r e -p r o o f and elemental SIMS (Secondary Ion Mass Spectrometry) standards, mainly in meteorites analyses, and more specifically BBOT, an isotopic standard for NanoSIMS in cosmochemistry [START_REF] Ito | H, C, and N isotopic compositions of Hayabusa category 3 organic samples[END_REF]. defines the mass resolution power law of this device [START_REF] Makarov | Electrostatic Axially Harmonic Orbital Trapping: A High-Performance Technique of Mass Analysis[END_REF]:

Detected with the

( 𝑚 ∆𝑚 ) 50% = 𝑘 * ( 𝑚 𝑧 ) -1/2
(Eq 1) [START_REF] Briois | Orbitrap mass analyser for in situ characterisation of planetary environments: Performance evaluation of a laboratory prototype[END_REF] have previously shown that metallic species from 9 Be + to 206,207,208 Pb + follow this power law. In this work, we first validate the trend of organic ions as a function of this power law, by comparison to the metallic ions, then we have studied the effect of the acquisition time and the number of points included into the Fast Fourier Transform (FFT) algorithm.

The second analytical criterion studied is the mass accuracy. This parameter is the mass difference between the observed m/z ratio of a compound and its theoretical value:

∆ 𝑚𝑎𝑠𝑠 = ( 𝑜𝑏𝑠𝑒𝑟𝑣𝑒𝑑 𝑚 𝑧 -𝑡ℎ𝑒𝑜𝑟𝑒𝑡𝑖𝑐𝑎𝑙 𝑚 𝑧 𝑡ℎ𝑒𝑜𝑟𝑒𝑡𝑖𝑐𝑎𝑙 𝑚 𝑧
) * 10 6 (Eq 2)

This parameter (expressed in ppm) described any instrument bias and is improved by mass calibration. In this study, different kinds of mass calibration (single, double, on a target material species and on the organic studied) have been done and compared to each other, as described in the next section.

The third criterion considered here addresses the quantification of isotopic abundances in the studied sample. We calculate the error (%) on the observed abundances depending on the isotope considered from its natural value:

First, we calculate the intensity ratio between the parent ion and the isotopologue using the following formula:

𝑂𝑏𝑠𝑒𝑟𝑣𝑒𝑑 𝑟𝑎𝑡𝑖𝑜 = ( 𝐼𝑠𝑜𝑡𝑜𝑝𝑜𝑙𝑜𝑔𝑢𝑒 𝑖𝑛𝑡𝑒𝑛𝑠𝑖𝑡𝑦 𝑃𝑎𝑟𝑒𝑛𝑡 𝑖𝑛𝑡𝑒𝑛𝑠𝑖𝑡𝑦
) * 100 (Eq 3)

Then the error called ∆ isotopic error and expressed in %:

J o u r n a l P r e -p r o o f

∆ 𝑖𝑠𝑜𝑡𝑜𝑝𝑖𝑐 𝑒𝑟𝑟𝑜𝑟 = ( 𝑡ℎ𝑒𝑜𝑟𝑒𝑡𝑖𝑐𝑎𝑙 𝑟𝑎𝑡𝑖𝑜-𝑜𝑏𝑠𝑒𝑟𝑣𝑒𝑑 𝑟𝑎𝑡𝑖𝑜 𝑡ℎ𝑒𝑜𝑟𝑒𝑡𝑖𝑐𝑎𝑙 𝑟𝑎𝑡𝑖𝑜
) * 100 (Eq 4) The FFT algorithm is used to convert the time transient (the sum of sinusoid signals generated by each oscillating ions) into a frequency spectrum. Then, after a calibration, the frequency spectrum is converted into a mass spectrum. The FFT can be applied on the whole signal or on slices of it but we systematically remove the six first milliseconds, which are spoiled due to HV switching. This leads to a maximal transient duration of 832 ms and a FFT using at the most 4,164,305 points.

Data processing -A Hann window is applied on the data. Triple zero filling is used in order to increase the number of data points (three times in this case) in the frequency spectrum, hence in the mass spectrum, which allows to better define the peak shape because of a higher number of points. This technique aims at improving the mass accuracy. A single and a double method of mass calibration have been performed in this study. The single mass calibration method is the simplest acquisition that could be done in an extraterrestrial environment, if data processing would be done on board. In that mode, one calibration is done on the metallic species composing the sample-holder and another one on the parent protonated ion of our studied compound. The double mass calibration method on J o u r n a l P r e -p r o o f the ions (and also clusters of them) extracted from the metallic sample-holder has been tested to improve the mass accuracy at higher masses. There is no peak-fitting applied to compute the peak parameters (measured mass, mass resolution…) on top of zero-filling.

In order to quantify the improvement of the MRP with increasing the number of points used for the interpretation is depending on the MRP. As a m/∆m calculated at FWHM higher than 1,000 is sufficient to allow the separation of two nominal masses (m/z 136 and m/z 137 for instance), a value higher than 100,000 leads to the identification of isobaric species (at the same nominal mass).

In the transitional laser regime observed in our set-up -between laser ablation and laser desorption -different kind of ions are produced in the first vacuum chamber, at the laser beam-sample interface, before injection into the second vacuum chamber and then into the Orbitrap TM cell. The laser ablation regime, a hard ionization process, produces many fragment ions. The laser desorption regime, softer ionization process, allows (among other) the detection of the protonated and cluster ions. We first confirm that mass resolution calculated on the various organic ions detected are still J o u r n a l P r e -p r o o f aligned on the theoretical power law (described in the previous section, Eq 1). Figure 2 With the Fourier Transform mass spectrometers, such as the Orbitrap TM instruments, the mass resolution can be also degraded with the amount of ions inside the trap. In the case of our laboratory device, all the ions produced are directly injected inside the cell, with no accumulation and no selection of such m/z ranges. If the sample analyzed is easily ionized with the 266 nm wavelength used, the number of ions produced and injected inside the Orbitrap TM cell will depends on the energy applied for the ionization. The sampling of complex mixtures is thus possible, as any saturation observed on the signal recorded can be adjusted with the energy applied (from 50 to 500 µJ).

This first result shows the capability of the LAb-CosmOrbitrap to obtain similar mass resolution performances with organic molecules to those obtained with metals despite the fragmentation and the sample consumption due to the laser ablation ionization process. Metals present a homogeneous surface on the sample-holder, whereas organic samples are powders pressed onto a malleable J o u r n a l P r e -p r o o f metallic surface and consumed by the successive laser shots. This may induce a change of the surface conditions and thus a higher variability on the performances for organic samples (depending on the predominance of a signal coming from the metallic sample-holder ion for example).

In the context of an in situ space experiment, the sample collection will depend on the target studied and the mission architecture (lander, orbiter operating fly by…). A sample collection similar to the one used in our study (onto a metallic plate) can be foreseen. With the heritage of the COSIMA (Cometary Secondary Ion Mass Analyzer) instrument [START_REF] Kissel | Cosima -High Resolution Time-of-Flight Secondary Ion Mass Spectrometer for the Analysis of Cometary Dust Particles onboard Rosetta[END_REF] on the Rosetta space mission, one can imagine that a robotic arm (called TMU standing for Target Manipulator Unit, on the COSIMA instrument) would expose the metallic plate to a specific environment then to the mass spectrometer for the experiment.

An instrumental improvement in our case could be provided by the visualization of the sampleholder through a camera such as the optical microscope COSISCOPE [START_REF] Langevin | Typology of dust particles collected by the COSIMA mass spectrometer in the inner coma of 67P/Churyumov Gerasimenko[END_REF] still from the COSIMA mass spectrometer. This would help to focus the laser shots on the sample and to move on the sample-holder when the sample is totally consumed. It would also give important information about the sample typology, optical properties and laser shots characterization (spot size leading to the fluence calculations).

2) Effect of the FFT duration on the mass resolving power

The digital Picoscope® described in the methodology section is able to record signals of duration up to a few seconds. Our goal is to record transients longer than our reference duration (838 ms) to record more oscillations and with a higher number of points. Three sampling frequencies are used: On the left window, a shift of the MRP values of adenine from the theoretical curve is observed around 1,000 ms (red circle). These anomalies are due to the presence of double peaks not properly discriminated.

This experiment confirms the importance of the acquisition time and the number of points included into the FFT algorithm. Frequency resolution is proportional to the time transient duration, impacting the MRP. We show here the possibility to obtain a mass resolving power of 380,000 at a nominal m/z 136, on an organic ion, with a data acquisition about 3.3 s. The asymptotic trend of this improvement J o u r n a l P r e -p r o o f suggests that a limit exists mainly based on the ion stability inside the cell. With the HV sets in this study, a transient duration of 2.5 s is long-enough. This result has a crucial interest for a space mission as it shows the connection between experimental parameters, such as the HV and the acquisition time, and the analytical performances, like the MRP. Commercial instruments have reached MRP of 1,000,000 on the m/z range 300-400 with 3 seconds transient and specific tunings [START_REF] Denisov | Orbitrap Mass Spectrometry with Resolving Powers Above 1,000,000[END_REF]. For in situ astrobiology studies, this is relevant as some heavy organic ions are suspected and searched. One can note the positive and negative ions up to (respectively) a few hundreds and a few hundreds of thousands of mass units [START_REF] Waite | The Process of Tholin Formation in Titan's Upper Atmosphere[END_REF] in Titan's atmosphere by the CAPS (Cassini Plasma Spectrometer) instrument or the organic ions up to m/z 200 detected in the Enceladus plumes [START_REF] Waite | Liquid water on Enceladus from observations of ammonia and 40Ar in the plume[END_REF][START_REF] Postberg | Macromolecular organic compounds from the depths of Enceladus[END_REF] by the CDA (Cosmic Dust Analyzer) instrument. To increase the MRP can be particularly interesting in this case, as it decreases with the m/z. A mode with specific HV parameters coupled with a longer acquisition time would lead to deeper analyses of heavy organic ions and their isotopologues, at ultra-high mass resolution.

3) Mass accuracy improved with mass calibration

The previous section points out the importance of the MRP in the distinction of peaks with close masses on the mass spectrum. In addition, the mass calibration needs to be accurate in the m/z range studied at a level commensurate with the mass resolution.

We first simulate the case in which we don't know the compounds analyzed, like during an in situ space experiment. The mass calibration is made with the ions from the metallic target: Indium 115 In + in our case. This species is the only one to be known in the mass spectrum as it composes the surface of the sample-holder.

This experiment demonstrates the importance of a known species (for example, the target material)

for use as a calibrant. It allows to start the analysis with a relevant mass calibration to identify the main organic species composing the sample. In our study, this known species is present by design as J o u r n a l P r e -p r o o f it is a fundamental part of the experimental configuration: the metallic sample-holder. From this point of view, this species is not considered as a contamination but as the mass calibrant of the mass spectrum obtained.

Mass calibration on 115 In is done on the 150 mass spectra (as a reminder 75 on the HOBt analysis and 75 on BBOT). We note that the Δ m/z of HBOt with the indium ion is significantly smaller than the Δ m/z of BBOT with the indium ion: 21 mass units between indium and HOBt ions and 316 mass units between indium and BBOT ions.

About HOBt, the median of the mass accuracies is close to -3 ppm. About BBOT, this result is about -7

ppm. The mass difference between HOBt and BBOT with the indium ion clearly affects the mass accuracies calculated. The closer in mass with the calibrant, the better is the mass accuracy (the Figure SI-1 illustrates these results obtained using box plots).

To solve this deviation at higher masses, we look for a calibrant with a closer m/z from the BBOT m/z value in order to quantify the impact on the mass accuracy. Results are presented in the Figure 4. to help for the identification of some unknown compounds when the cluster is composed by one indium element added to an organic species [START_REF] Arevalo | An Orbitrap-based laser desorption/ablation mass spectrometer designed for spaceflight[END_REF][START_REF] Selliez | Identification of organic molecules with a laboratory prototype based on the Laser Ablation-CosmOrbitrap[END_REF]. The cluster can be also composed by two or more indium elements. In some other cases, they lead to the detection of very low masses organic species involved in Titan-like chemical pathways [START_REF] Selliez | High-resolution mass spectrometry for future space missions: Comparative analysis of complex organic matter with LAb-CosmOrbitrap and laser desorption/ionization Fourier transform ion cyclotron resonance[END_REF].

J o u r n a l P r e -p r o o f Moving the mass calibration from m/z 115 to m/z 230, we reduce by 115 mass units the mass difference between the calibration point and the mass of the organic species. The impact on the mass accuracy calculated is shown on Figure 4. We observe a shift of the median mass accuracy from -7 ppm (mass calibration on In + ) to -4 ppm (mass calibration on 2*In + ).

We then consider we know the analyzed sample. Using well-known specific peaks such as molecular, protonated and/or fragment ions, we are able to calibrate the whole mass spectrum in order to study, for instance, isotopic patterns and isotopologues. By definition, the observed m/z are equal to the theoretical m/z for the calibration peaks.

J o u r n a l P r e -p r o o f

Once the protonated ion of BBOT (m/z th 431.1782) has been well-identified thanks to the previous calibration step, we use this peak as a specific calibration point for the identification of BBOT isotopologues (first isotopologue at the nominal m/z 432, 12 C 25 13 C 1 H 26 N 2 O 2 S+H + , identifying the replacement of a carbon-12 atom by a carbon-13 atom). The mass difference between the protonated ion and its isotopologue is 1.0034 mass units. 88 mass spectra have been studied to show the relevance and reproducibility of results. The median of the mass accuracies obtained is comprised between 1 and 0 ppm. 50% of mass accuracies calculated are included between +2 and -1 ppm. Four outliers are observed on the 88 studied. This could be explained by an asymmetry of the protonated ion or an absence of the peak in the case the sample was totally consumed leading to a shift in the mass calibration. Results on the 88 mass spectra obtained with BBOT show the reproducibility of the mass accuracy on a high-mass organic species for a known-compound (the Figure SI-2 illustrates these results).

To conclude on the calibration methodology, a mass calibration on the metallic species composing the sample-holder, here 115 In, appears to be a relevant first step in the study of unknown compounds and/or mixtures. The capacity of indium to form clusters with itself allows mass calibrations at higher masses if the species of interest seems to be located at a few hundred mass units in the mass spectrum. Once the species to analyze are identified, another mass calibration on the parent ion leads to a thorough chemical analysis of the isotopologues and the isotopic patterns. In all cases, mass accuracies of a few ppm are obtained: -3 and -4 ppm with a target material mass calibration, +2

and -1 ppm with a specific mass calibration on organics. Reproducibility is demonstrated, as these results have been obtained with tens of mass spectra. This result highlights the interest of a mass calibration on the metallic sample-holder species. This is particularly relevant in the case of a space mission and an in situ experiment. First, this demonstrates which methodology can be applied to optimize the mass calibration of the mass spectra.

J o u r n a l P r e -p r o o f

In addition, it supports the simple sample preparation (described previously) as it allows the detection of cluster ions and some mixing of the organic studied and the metallic species used for the sample-holder. The choice of the metal composing the sample-holder depending on some physical properties will be evaluating in further studies.

5) Preliminary results on the isotope abundances

The aim of this preliminary study is to address if isotope abundances can be inferred from the CosmOrbitrap measurements. For this quantitative aspect, experiments have been conducted on the HOBt organic sample and calculations have been made on one typical mass spectrum in order to identify a trend. Composed by 6 carbon atoms and 3 nitrogen elements, the HOBt compound contains an isotopic doublet on its first isotopologue at the nominal m/z 137. We recall these two isotopologues (C 6 H 5 14 N 2 15 N 1 O+H + at m/z 137.0476 and 12 C 5 13 C 1 H 5 N 3 O+H + at m/z 137.0539) are separated from each other by 0.0064 mass unit.

The isotopologue corresponding to the carbon isotopic replacement should be observed, in terms of intensity, at 6.6% of the protonated (parent) ion. The other isotopologue of this doublet, corresponding to the nitrogen isotopic replacement, should have an intensity of 1.11%. All natural abundances and expected intensities depending on the molecule studied have been reminded in the Table SI-3.

First, as the two isotopologues composing the doublet at m/z 137 are very close, the MRP has to be high-enough in order to separate both of them. Red dots are the errors calculated on the isotopologue with a carbon replacement. Blue dots are the errors on the other isotopologue (nitrogen replacement). On the one hand, the shortest transient durations (from 100 to 200 ms) don't show results on the nitrogen replacement. The peak is not defined enough due to a low mass resolving power as shown in the Figure 5. On the other hand, with acquisition times longer than 300 ms, errors increased. The interesting window is therefore centered on 300 ms: errors calculated are more reproducible and closer to 0% between 250 to 400 ms (from -0.42 to 3.28% for the errors on the carbon replacement and from -1.49 to -5.67% for the errors about the nitrogen replacement). All results are reported in

V) Conclusion and perspectives

Results presented in this paper have been obtained through a repeatability study to show the relevance of the analytical performances of the LAb-CosmOrbitrap (CosmOrbitrap elements coupled with a laser ionization system at 266 nm). Tests have been performed on three organic molecules, as we aim to show the relevance of this simple instrument for astrobiology studies and future space missions (with the CORALS instrument for example). 92 mass spectra have been recorded on Adenine, 166 on HOBt and 271 on BBOT, three nitrogenous and sulfurous organic compounds covering a mass range from 136 to 431 mass units. Three analytical criteria have been studied: (i) the mass resolving power, (ii) the mass accuracy with a focus on the importance of the mass calibration and (iii) the isotopic abundances. The last one was not included in the repeatability study but is shown as a preliminary work opening new perspectives.

(i) Above m/z 100, mass resolving power higher than 100,000 have been obtained. Above m/z 400, mass resolving power is around 60,000. With an increase of the acquisition time, mass resolving power up to 380,000 have been shown on Adenine.

Adjustment of the HV with the acquisition time has shown that 2 seconds transients even allow to increase significantly the mass resolving power which could occasionally help on the study of heavy masses.

J o u r n a l P r e -p r o o f

(ii) Among the several mass calibrations tested, we highlight the use of the metallic sample holder with target material mass calibration on the indium ion 115 + and on clusters of indium to obtain accurate measurements at higher masses. With these calibrations, mass accuracies between -3 and -4 ppm have been obtained. With an internal mass calibration on the organic species of interest, we have shown mass accuracies comprised between +2 and -1 ppm on the isotopologues.

We conclude that the sample-holder metallic species provides a good known mass calibration allowing the identification of the main chemical species in the sample. A second mass calibration, on the compound of interest leads then to a deep chemical analysis of the isotopologues.

For these two first analytical criteria, the repeatability study has been successful despite the change of the surfaces conditions and sample consumption following a large number of laser shots. Some guidelines for the TRL development of CosmOrbitrap have also been evidenced. For example, a camera coupled to the sample-holder would be needed first to position efficiently the laser beam on the sample and then to derive some optical properties (before the ionization) and fluence calculations (after the ionization).

(iii) Finally, preliminary tests on isotopic abundances have demonstrated encouraging results on the FFT range 250 to 500 ms with errors calculated between -0.42 and 3.28% on carbon replacement and between -1.49 and -5.67% on nitrogen replacement, for the HOBt molecule. A consistent result has been obtained on the BBOT molecule, for the carbon replacement, with an error at 3% calculated with 100 ms FFT. On this compound, we also calculate an error at -2.7% on the sulfur replacement.

Consistent results on this last analytical criterion have been thus obtained on different isotopes (carbon, nitrogen and sulfur) for time transients comprises between 100 to 500 ms. This work has to be pursued, with an optimization of the HV on short acquisition time and with the record of more mass spectra, as it would lead to a deep chemical study of organic samples of a primary interest for astrobiology.

J o u r n a l P r e -p r o o f

This study supports the interest of using an Orbitrap TM cell, a powerful analytical mass analyzer with mass resolving powers never achieved in space mission to this day, inside a very simple instrument concept with a direct ionization ions injection leading to relevant analyses of heavy nitrogenous and sulfurous organic compounds, which are representative of molecules possibly involved in the life emergence. Heavy and complex organic compounds have been evidenced for instance on the Enceladus plumes thanks to the Cassini-Huygens mission [START_REF] Postberg | Macromolecular organic compounds from the depths of Enceladus[END_REF][START_REF] Waite | Liquid water on Enceladus from observations of ammonia and 40Ar in the plume[END_REF] with compounds at m/z higher than 200. Ocean worlds such as Enceladus or Europa, among other, are suspected to host building blocks of life evolving in a liquid water environment and this subsurface material may be ejected by plumes. Univocal identification of heavy organic compounds, organics mixed with ices, salts and minerals would be needed for the future exploration of these bodies as well as isotopic studies to characterize the primitive and prebiotic material detected on the surface of small bodies such as comets or asteroids in order to constrain their origin on Earth and giving clues about the Solar System formation.

The consistent characterization of organic samples would be provided by the new High Resolution Mass Spectrometers generation. These instruments will help to determine the chemical nature of these compounds and their biotic (or abiotic) source. Many mission projects are defined in the frame of the new programs and calls from Space Agencies. We cited the JAXA OKEANOS mission including the MULTUM instrument, with a mass resolving power of 30,000 at m/z 20 [START_REF] Ito | A Feasible Study of In-Situ Measurements of Light Isotopes and Organic Molecules with High Resolution Mass Spectrometer MULTUM on the OKEANOS Mission[END_REF], and the NASA Europa Clipper mission with the mass spectrometer MASPEX which will reach a mass resolving power of 50,000 (FWHM) (T. G. [START_REF] Brockwell | The mass spectrometer for planetary exploration (MASPEX)[END_REF]. Many missions concepts have been proposed

for the ESA call for the future M7 mission (such as the Castalia mission [START_REF] Snodgrass | The Castalia mission to Main Belt Comet 133P/Elst-Pizarro[END_REF] aiming at studying the MBC (Main Belt Comet) 133P/Elst-Pizarro). Enceladus is also supported by many mission concepts for several years [START_REF] Cable | The Case for a Return to Enceladus[END_REF][START_REF] Mitri | Exploration of Enceladus and Titan: investigating ocean worlds' evolution and habitability in the Saturn system[END_REF][START_REF] Mitri | Explorer of Enceladus and Titan (E2T): Investigating ocean worlds' evolution and habitability in the solar system[END_REF][START_REF] Reh | Enceladus Life Finder: The search for life in a habitable Moon[END_REF]). In the frame of the future space exploration of complex organic samples, the analytical performances of a simple and compact laser-CosmOrbitrap instrument for a spaceflight application J o u r n a l P r e -p r o o f appears as highly competitive and would bring a significant improvement for the in situ study of the bodies listed above and would help to answer key questions in astrobiology.

J o u r n a l P r e -p r o o f

  Analytical performances of the LAb-CosmOrbitrap mass spectrometer for astrobiology L. Selliez 1 (corresponding author) , C. Briois 1 , N. Carrasco 2 , L. Thirkell 1 , B. Gaubicher 1 , J.-P. Lebreton 1 , F. Colin 1 1-LPC2E, UMR CNRS 7328, Université d'Orléans, Cedex 2, France 2-Université Paris-Saclay, UVSQ, CNRS, LATMOS, 78280, Guyancourt, France ABSTRACT:

(

  HRMS). The development of the specific technologies required for the development of space instruments may take many years to reach a Technology Readiness Level (TRL) sufficient to be considered for selection by Space Agencies. A new generation of HRMS instruments based on different techniques is being developed: multi-bounce time of flight (MBTOF) for instance the MASPEX (MAss Spectrometer for Planetary Exploration) instrument (T. G. Brockwell et al., 2016) developed for the NASA Europa Clipper mission planned for launch in 2024; or the MULti-TUrn time-of-flight Mass spectrometer -MULTUM -instrument (Shimma et al., 2010) proposed for the OKEANOS (Oversize Kite-craft for Exploration and AstroNautics in the Outer Solar system) mission led by JAXA, planned for launch in 2030s and rendezvous with a Jupiter Trojan asteroid in 2040s (ITO et al., 2021).

Figure 1 :

 1 Figure 1 : (a) Schema of the LAb-CosmOrbitrap from Selliez et al., 2019 with the CosmOrbitrap mass analyzer currently under TRL development in red and (b) solid model of the CORALS instrument as described in the Europa Lander PIP document, from Willhite et al., 2021.

  LAb-CosmOrbitrap under their positive ion and protonated form, molecular formulae are C 6 H 5 N 3 O+H + (HOBt) and C 26 H 26 N 2 O 2 S+H + (BBOT) at, respectively m/z 136.0505 and m/z 431.1782. In the present study, they become relevant standard organic compounds for testing the capabilities of the LAb-CosmOrbitrap.The methodology of the sample preparation has been previously described in[START_REF] Selliez | Identification of organic molecules with a laboratory prototype based on the Laser Ablation-CosmOrbitrap[END_REF] Shortly, solid powder of each sample is pressed onto a metallic sample holder (indium). The malleability of indium allows the sample to be embedded in the sample holder. This technique leads to the formation of indium clusters such as [In+In] + and/or [In+organic] + observed in the mass spectra, and will be developed in the results section as clusters play a crucial role for the mass calibration. These experiments aim at studying the reproducibility of the results obtained on organic species with criteria defined in the next section. To this end, 92 mass spectra have been recorded on Adenine, 166 on HOBt and 271 on BBOT. The number of mass spectra recorded ensures good quantification of the performances of the LAb-CosmOrbitrap, despite the variability observed in the mass spectra. c) Analytical criteria Three main analytical criteria are considered here: (1) mass resolving power (MRP), (2) mass accuracy related to the mass calibration accuracy effect and (3) isotope abundance as a preliminary study. Formulae used and definition of each analytical criterion are detailed below. These three criteria have been chosen as they are critical for providing significant performance improvements from previous space instruments in order to be eligible for selection by Space Agencies.The MRP is defined as the capability of separating two close peaks. Named m/Δm and calculated at FWHM (or 50%), this value with the Orbitrap TM cell highest for the lowest m/z range is decreasing as a function of the mass on charge ratio (m/z) of the compound. Due to the physics inside the cell, the J o u r n a l P r e -p r o o f mass resolution is decreasing with the square root of the m/z ratio. The following equation (Eq 1)

  FFT algorithm (second results section), we have increased the acquisition time of a series of experiments performed on adenine. The data have been recorded with an analog/digital converter called Picoscope®. The longest transient duration was recorded during 3,352 ms with 16,777of the CosmOrbitrap performances with organic material The CosmOrbitrap time transient recorded represents the image current induced by the oscillations of the ion along the spindle-like central electrode of the Orbitrap TM cell. The mass resolution is a function of the transient duration (and number of oscillations recorded during this time) and data

  shows this comparison, using a transient duration of 832 ms. Data obtained in Briois et al., 2016 with metals have been added (red dots). Various organic ions resulting from the ionization of adenine, HOBt and BBOT are detected: molecular ions and fragment ions such as CNH 2 + at m/z 28.0182, C 6 H 5 N 3 + at m/z 119.0478, C 15 H 11 N 2 OS + at m/z 267.0585 and C 9 H 9 O + at m/z 133.0646. The mass resolving power of each organic compound is indicated as a function of the m/z ratio with the blue triangles.

Figure 2 :

 2 Figure 2 : The figure shows the MRP calculated at FWHM (Full Width at Half Maximum) as a function of the m/z of compounds studied. The red dots represent results on metals reported in Briois et al., 2016. Only one red dot is about an organic molecule: adenine at the nominal m/z 136. The blue triangles are protonated and fragments ions from organic compounds: HOBt+H (nominal m/z 136), adenine+H (nominal m/z 136) and BBOT+H (nominal m/z 431) and the main isotope ion of indium (nominal m/z 115) from the sample-holder. All these points are aligned on the power law fit function (black line). The theoretical power law specific to the Orbitrap TM cell is drawn as a green line, reduces by a factor 2 in order to simulate the application of a Hann window. A Hann window has been applied for each mass spectrum analyzed, from a time transient of 832 ms.

  5.2, 10.4 and 20.8 MHz. For each experiment, 5 mass spectra are recorded. The results of the analysis J o u r n a l P r e -p r o o f of the longest signal recorded is shown in Figure 3. It corresponds to a sampling frequency of 5.2 MHz; 16,777,216 points and a transient duration of 3,352 ms.

Figure 3 :

 3 Figure 3 : The left window shows the MRP (FWHM) of the organic sample adenine C 5 H 5 N 5 H + and potassium element K + depending on the FFT duration (until 3,352 ms). The transient has been processed in 16 time segments of 200 (black dots), 100 (blue dots) and 50 (red dots) from the beginning of the whole transient. The theoretical curves are drawn in violet. The top-right window shows the image of the VCE (Voltage Central Electrode) set to 3,500 V. The bottom-right window presents the peak amplitude of both species studied and the noise level (in brown). The sampling frequency is 5.2 MHz, with a record of 16,777,216 points during 3,352 ms.

  Mass calibration is done both (1) on the main ion of indium at the nominal m/z 115 (exact m/z 114.9033; lower part of the figure, blue) and (2) on the cluster of two indium ions at the nominal m/z 230 (exact m/z 229.8067; upper part of the figure, red). Indium clusters have indeed already been observed in previous CosmOrbitrap studies. They proved to be extremely useful, as they were shown

Figure 4 :

 4 Figure 4 : Box plots showing the mass accuracy of the protonated ion of BBOT at m/z 431. Mass accuracies have been calculated (1) with a mass calibration of the mass spectra on the main isotope of indium at nominal m/z 115 (vertical line, bottom of the figure, in blue), meaning with a Δ m/z of 316 (exact Δ m/z 316.2749) between the indium and the BBOT ions (boxplot to the left, indicated by the blue arrow) and (2) with a mass calibration of the mass spectra on the indium cluster ion (In+In + ) at nominal m/z 230 (vertical line, top of the figure, in red), presenting a Δ m/z of 201 (exact Δ m/z 201.3715) between the cluster and the BBOt ions (boxplot to the right, indicated by a red arrow). The mass calibration on the cluster ion of indium allows a mass calibration closer to the BBOT ion m/z than the indium ion. The effect is visible, as the right boxplot shows better mass accuracies, closer to 0 ppm. This comparison have been made on 20 mass spectra, selected to present both indium ion and cluster ion of indium.

  Figure 5 is part of a mass spectrum focused on the mass window m/z 137.042 to 137.067 in which both isotopologues can be observed. It shows the effect of the segment duration on which the FFT is applied on the isotopologues separation. The black line represents the longest one of 832 ms. Other color lines, from blue to red, show the decrease to the lowest one of 100 ms (red line). With this shortest segment duration, the first J o u r n a l P r e -p r o o f isotopologue cannot be readily detected but it visibly creates a clear asymmetry in the peak. For the second one (carbon replacement), a very large peak is detected. With 200 ms transient duration (brown line), the first isotopologue is still not observed but the second one is thinner. The yellow line shows the shortest time length (300 ms) allowing the distinction of these two isotopologues.

Figure 5 :

 5 Figure 5 : Mass spectrum showing the two first isotopologues of HOBt at the nominal m/z 137. Molecular formulae of the two ions are indicated. The color scale shows the mass spectrum obtained with different time transients, from 94 ms (FFT with 470,000 points) in red to 832 ms (FFT with 4,160,000 points) in black. The effect of the acquisition time on the mass resolving power is apparent. Shorter time transients until 200 ms are no long-enough to allow the distinction of the two isotopologues. The minimum required here is 300 ms (yellow curve) to observe both peaks.

Figure 6 :

 6 Figure 6 : Isotope abundances corresponding to the replacement of 12 C by 13 C and 14 N by 15 N in the HOBt molecule, at m/z 137.0539 and 137.0476 as a function of the transient duration (from 100 to 600 ms) on a typical mass spectrum. The black rectangle shows that the shorter time transients (between 250 to 400 ms) minimize the error on the isotopic abundance (errors comprised between 4 and -4%).

  IV)From laboratory to spaceflight applications Two laser-CosmOrbitrap based instruments are currently in development for future spaceflight applications. One of them, the CORALS instrument (Figure 1, right), is operating at 266 nm like the laboratory device LAb-CosmOrbitrap. The whole instrument (laser source, ion transfer optics and CosmOrbitrap mass analyzer) aims at being a versatile and low size (11,000 cm 2 ), weight (8 kg) and power (41 W peak) mass spectrometer (L. Willhite et al., 2021). Heritage of the MOMA laser, the CORALS laser provides three times more output energy than the latter with 450 µJ at 266 nm and a fluence about 20 J/cm 2 (M. Fahey et al., 2020). As shown on the Figure 1 (right), despite a different design the elements composing the LAb-CosmOrbitrap device and the CORALS prototype are similar J o u r n a l P r e -p r o o f as well as their working principle. The energy output and fluence of both configurations lead to the detection of the same kind of species, previously described. The similarities, in terms of constituents and working, allow us to compare and to extrapolate the results obtained with the LAb-CosmOrbitrap device with those expected with a laser-CosmOrbitrap based instrument such as the CORALS one. Another configuration named CRATER (Characterization of Regolith and Trace Economic Resources) and working at the 213 nm wavelength is currently in development as well.

Table SI -

 SI 3 summarizes the theoretical data and expected intensities of the isotopes studied with HOBt and BBOT.

d) Experimental parameters and data treatment Software -For these experiments, the data acquisition was performed by the Alyxan software (data acquisition board Acquitek CH-3160, 12-bit with different input gains). The maximum number of data points recorded is 4,194,304. In the standard operating mode, it corresponds to a transient duration of 838 milliseconds (ms) at a sampling frequency of 5 MHz. Other sampling frequencies (10 MHz, 20 MHz) lead to shorter transient durations (around respectively 400 and 200 ms).

  Table SI-3.Calculations have been made on the BBOT isotopologues as well. This time, there is no doublet at a same nominal m/z but two different isotopologues at two nominal m/z ratios: a carbon replacement at m/z 432.1821 and a sulfur replacement at m/z 433.1746. We observe here a high number of carbon atoms in the molecule (26 times) unlike sulfur atoms (only one). The strong difference of expected intensities leads us to consider two acquisition times because these two peaks don't need the same duration to reach a sufficient mass resolving power. On the same mass spectrum, we obtain errors at 3% with 100 ms on 12 C 25 13 C 1 H 26 N 2 O 2 S+H + and -2.7% with 500 ms on C 26 H 26 N 2 O 2 34 S+H + .Considering a short acquisition time of 300 ms, an error of 0.61% about the carbon isotopic abundance at the nominal m/z 137 is a very encouraging result. More studies are needed to improve this last analytical criterion with an optimization of the HV applied (regarding the first hundreds ms of the signal) and the record of many mass spectra to improve statistics and compensate the variability coming from the laser ionization. The high MRP and mass accuracies coupled with consistent isotopic abundances would give to this set-up a strong analytical power, particularly for the characterization of extraterrestrial environment. The improvement of results about isotope abundances will be thus thorough in the next studies.

	J o u r n a l P r e -p r o o f

Acknowledgements L. S. thanks the CNES (Centre National d'Etudes Spatiales) and the Région Centre-Val de Loire for the funding of her PhD. N.C. thanks the European Research Council for funding via the ERC PrimChem project (grant agreement No. 636829.) We gratefully acknowledged CNES for funding the instrumental development of the CosmOrbitrap, and Dr Titaina Gibert for lending us the Nd-Yag laser 266 nm used to perform all tests. J o u r n a l P r e -p r o o f


Thomas Schmitt
email: thomas.schmitt@centralesupelec.fr

David Marchal

Sébastien Ducruix

Bénédicte Cuenot

DOI: ADD DOINUMBER HERE REST HF-10 test case: Large-Eddy Simulations using the AVBP solver

The HF-10 test case, from the REST (Rocket Engine Stability Initiative) working group, is a typical injection element of LOX/CH4 liquid rocket engines. It is numerically studied with the AVBP solver from CERFACS, comparing two combustion models, either based on a beta-pdf equilibrium chemistry model or on reduced finite-rate chemistry. Both models lead to similar stable flame shapes, but locally higher temperatures and a shorter flame length are found with finite-rate chemistry. Phase-locked averages show that a pulsated inlet induces periodic oscillations of the heat release rate, which are however significant only at the lowest frequency.

Introduction

In the competitive sector of space launchers, methane is currently proposed to replace hydrogen in Liquid Rocket Engines (LRE) for operating cost reduction. Methane oxycombustion at high pressure and in subcritical or transcritical conditions raises however a number of questions that are not fully answered and require further investigation. [START_REF] Preuss | LOX/Methane Technology Efforts for Future Liquid Rocket Engines[END_REF] In particular, the slower oxidation chemistry of methane results in longer flames, which may also be more prone to instabilities. [START_REF] Li | Comparison of explosion characteristics between hydrogen/air and methane/air at the stoichiometric concentrations[END_REF] As the extreme conditions of LRE make experiments challenging, the use of numerical simulation is essential for the understanding of the physical mechanisms at play. Among the various modelling approaches, the Large Eddy Simulation (LES) has become a standard for the study of turbulent reacting flows, and has been successfully applied to LRE in stable or transient conditions. [START_REF] Lacaze | Large eddy simulation of laser ignition and compressible reacting flow in a rocket-like configuration[END_REF][START_REF] Schmitt | Large-eddy simulations of the mascotte test cases operating at supercritical pressure[END_REF][START_REF] Schmitt | Large-eddy simulation of oxygen/methane flames under transcritical conditions[END_REF][START_REF] Urbano | Study of flame response to transverse acoustic modes from the les of a 42-injector rocket engine[END_REF][START_REF] Urbano | Exploration of combustion instability triggering using large eddy simulation of a multiple injector liquid rocket engine[END_REF] The description of chemical kinetics may be based on the infinitely fast chemistry assumption, which is well suited for hydrogen oxycombustion. [START_REF] Ivancic | Time and length scales of mixing and combustion processes in high-pressure LOx/GH 2 rocket combustors[END_REF] However, to take into account finite-rate chemistry effects which may be important for methane flames, an accurate and cost-effective model must be included. Fully detailed mechanisms are available, but their very high number of species and reactions does not allow their use in 3D LES. On the other hand, one or two-steps global schemes do not reproduce sufficient details on the flame structure. An intermediate approach is to use reduced chemistry, which optimizes the tradeoff between accuracy and complexity. In the design of LREs, much efforts are devoted to the control of thermo-acoustic instabilities which may be very detrimental to the engine operation and even lead to its destruction. [START_REF] Culick | Overview of Combustion Instabilities in Liquid-Propellant Rocket Engines[END_REF] Although these phenomena have been extensively studied in hydrogen LREs, a different behavior is expected when methane is used. Numerical studies of flame-acoustic interaction using LES have been recently undertaken under various forced modulations [START_REF] Hakim | Large eddy simulations of multiple transcritical coaxial flames submitted to a high-frequency transverse acoustic modulation[END_REF][START_REF] Hakim | Dynamics of a transcritical coaxial flame under a high-frequency transverse acoustic forcing: Influence of the modulation frequency on the flame response[END_REF][START_REF] Nez | High-frequency combustion instabilities in liquid rocket engines driven by propellants flow rate oscillations[END_REF] showing large flame induced motions depending on the modulation characteristics.

In this paper, the HF10 test case defined by the REST (Rocket Engine Stability Initiative) working group as a typical injection element of LOX/CH4 liquid rocket engines, is numerically studied. The LES approach is used and two different chemistry descriptions, either based on infinitely fast or finite-rate chemistry for comparison purposes. Thermo-acoustics are then studied via the computation of the response of the flame to mass flow rate pulsation for various pulsating frequencies.

Governing equations, models and numerics

The compressible unstructured solver AVBP [START_REF] Moureau | High-order methods for DNS and LES of compressible multi-component reacting flows on fixed and moving grids[END_REF][START_REF] Schönfeld | Steady and unsteady flows simulations using the hybrid flow solver avbp[END_REF] developed by CERFACS is used for this study. Details about the numerical strategy and the thermodynamic modeling for real-gas flows can be found in Schmitt. [START_REF] Schmitt | Large-eddy simulations of the mascotte test cases operating at supercritical pressure[END_REF] It relies on a Taylor-Galerkin weighted residual central distribution scheme, called TTGC, third-order in time and space. [START_REF] Colin | Development of high-order Taylor-Galerkin schemes for unsteady calculations[END_REF] The subgrid-scale (SGS) stress tensor is computed with the WALE model. [START_REF] Nicoud | Subgrid-scale stress modelling based on the square of the velocity gradient[END_REF] Two strategies are considered in this study for the modeling of the chemical conversion. An infinitely fast chemistry model, [START_REF] Schmitt | Large-eddy simulations of the mascotte test cases operating at supercritical pressure[END_REF] referred as IFCM, is used for all the cases. This model accounts for the following species: CH4, O2 , H2O, OH, H2, CO2 and CO in order to properly calculate the burnt gas temperature. Equilibrium reference mass fractions are tabulated in terms of the mixture fraction and its variance, both computed via transport equations in the simulations. The species source terms are then computed following the method described in Schmitt. [START_REF] Schmitt | Large-eddy simulations of the mascotte test cases operating at supercritical pressure[END_REF] To investigate the impact of finite-rate chemistry, an Arrhenius-based chemical scheme is also considered for the calculation of the reference case, i.e., without inlet modulation. In this approach, all chemical species of the scheme are computed via their transport equation, including an Arrhenius chemical source term. To make the 3D LES affordable, the concept of Analytically Reduced Chemistry (ARC) [START_REF] Griffiths | Reduced kinetic models and their application to practical combustion systems[END_REF] is used to decrease the number of species and reactions, while keeping the required accuracy for selected target quantities. In addition, the Quasi Steady State Assumption (QSSA) [START_REF] Lu | Systematic approach to obtain analytic solutions of quasi steady state species in reduced mechanisms[END_REF] applied to the very fast species lowers the numerical stiffness of chemistry. A major advantage of ARC is to keep the most important reaction pathways, allowing to study detailed chemical effects. An ARC for methane oxycombustion at high pressure has been recently derived in [START_REF] Blanchard | Chemical modeling for methane oxy-combustion in liquid rocket engines[END_REF] and is used here. It contains 14 species, 4 QSS species, and 68 reactions, and has been validated in various one-dimensional stained diffusion flame cases.

Computational domain and simulated cases

The computational domain is shown in Fig. 1 and follows the guidelines of the REST HF-10 test case. It consists in a coaxial injector fed with liquid oxygen in the center and gaseous methane in the outer. Injection temperatures are set to 100 K for oxygen and 231 K for methane and mass flow rates are 0.46 kg/s for oxygen and 0.136 kg/s for methane. All the solid boundaries are treated as adiabatic walls. Wall-laws are used at the injector walls to properly represent the boundary layer. Oxygen and methane are injected using non-reflecting boundary conditions with mass flow rates and temperatures imposed, with an amount of 5% of turbulence, while pressure is imposed at outlet (100 bar). The mesh used for all the simulations comprises 2 million nodes and is discussed in Sec. The simulated cases are listed in Tab. 1. Two non-modulated cases (NM) are first considered. Case NM-IFCM assumes a fast chemistry coupled with a beta-pdf, [START_REF] Schmitt | Large-eddy simulations of the mascotte test cases operating at supercritical pressure[END_REF] while in case NM-ARC an ARC is directly resolved on the grid. Cases OM correspond to oxidizer-modulated cases, with an amplitude of modulation equal to 10% of the mass flow rate. Two modulation frequencies are considered : 1 kHz and 5 kHz. For the last case, referred as FM, the fuel stream is modulated, with an amplitude of 10% of the mass flow rate and a frequency of 5 kHz. All the cases are averaged over 10 ms, corresponding to 50 periods of modulation for cases OM-5kHz and FM-5kHz and 10 periods for case OM-1kHz. The computational cost for 10 ms of physical time is 50 kh for NM-IFCM and 150 kh for NM-ARC. 1: List of the simulated cases. "NM", "OM" and "FM" stand for Non-, Oxidizer-and Fuel-Modulated, respectively.

Case

Statistical convergence

The impact of the averaging time for case NM-IFCM is shown with longitudinal profiles of mean heat release rate per unit length and of cross-averaged temperature, oxygen mass fraction and axial velocity on Fig. 2 for two averaging times: 4 ms and 8 ms. The two curves are very close to each other, suggesting that statistical convergence has been reached for mean quantities. Similar results are obtained for the mean quantities of the modulated cases, but are not shown here for the sake of brevety. For a more quantitative comparison, radial profiles of mean temperature, heat release rate and axial velocity are plotted in Figs. 5 to 7. At z=0, mesh M0 strongly departs from the two other grids: the heat release rate, temperature and consequently axial velocity are overestimated. Further downstream, the three grids show close results. Meshes M1 and M2 are in good agreement at all locations and thus M1 will be used for the rest of the study.

Mean results

Mean results for all the simulated cases are presented in this section. First, cases NM-IFCM and NM-ARC are compared in Sec. 5.1. Mean results for cases NM-IFCM, FM and OM are then shown in Sec. 5.2.

Comparison between NM-IFCM and NM-ARC

Mean temperature and heat release rate for cases NM-IFCM et NM-ARC are compared using longitudinal slices in Fig. 8. The overall shape of the flame is similar in both cases, indicating a similar turbulent consumption rate. However the maximum average temperature and heat release rate are higher in case NM-ARC in the first part of the chamber. This is attributed to the filtering induced by the use of a beta-pdf in the IFCM approach, while the direct integration of ARC does not involve such filtering in the current implementation. Combining the direct integration of ARC with explicit filtering may improve these results and is an on-going work. The previous observations are in line with the longitudinal profiles shown in Fig. 9. Up to z=50mm, the temperature increases more quickly with ARC than with IFCM, then the slopes become closer until reaching a plateau around the same value. This impacts the axial velocity profile which stabillizes faster with ARC. The profiles of oxygen mass fraction also differ, showing a faster consumption with ARC in the first zone up to z=50mm and then a similar slope. Note that with ARC the oxygen mass fraction decreases below the exit equilibrium value before increasing again: this may be an effect of the semi-detailed ARC. Finally the heat release rate profiles are relatively similar, consistent with the similar flame shape.

Finally scatter plots of temperature and major species for the two simulations are provided in Fig. 10. The two scatter plots on the top are obtained from instantaneous solutions, whereas the two others are from averaged solutions. Not surprisingly, the structure of a diffusion flame is clearly recovered. As already observed from the mean fields, the IFCM results are more scattered in both the instantaneous and averaged solutions. The ARC instantaneous flame structure stays close to a strained laminar flame at a strain rate which does not strongly vary, whereas the beta-pdf introduces more variation in the IFCM case. The averaged solution shows more scattering in both cases, due to the turbulent flame motion at the resolved scale.

To evaluate the impact of the mesh on the direct integration of ARC, the NM-ARC case was also run on mesh M2. The high computational cost did not allow to reach convergence yet and only instantaneous temperature fields are shown in Fig. 11. It seems that the temperature field comes closer to the IFCM solution when the mesh is refined, as a consequence of the lower artificial thickening of the flame by the mesh.

Comparison between NM, OM and FM with IFCM

Longitudinal slices in the z-y plane are shown in Fig. 12 for the temperature and heat release rate fields. All the 4 cases show very close results, with negligible differences. This is confirmed with the longitudinal profiles of cross-averaged variables plotted in Fig. 13. The flame NM seems however slightly longer than the 3 others, but the difference remains very small and could be due to statistical limitations. Additional radial profiles of temperature and heat release rate are plotted in Figs. 14 and15. The larger departure is on the heat release rate, lower in the region 25 mm < z < 100 mm for case NM. In general, for the cases considered here, the modulation seems to have a negligible impact on the mean flame topology.

Phase-averaged results

The modulated simulations are now presented in terms of phase-averaged quantities. First, longitudinal slices are proposed in Sec. 6.1. Then, phase-averaged fluctuations fields are discussed in Sec. 6.2. Finally, the integrated flame response is given in Sec. 6.3.

Longitudinal slices (x-normal)

Slices of phase-averaged temperature and heat release rate are shown in Fig. 16 and 17 for ϕ = 0 and ϕ = π, ϕ being the phase of the modulation (equal to 0 when the modulated mass flow rate is minimum at inlets). All the cases show a corrugated inner jet, either directly provoked by the inner stream modulation or indirectly by the modulation of the annular jet. The wave length of the modulation roughly results from the central velocity and the modulation frequency.

The heat release rate is importantly modulated at the injector exit for all the cases and at the end of the flame for case OM-1kHz.

Phase-averaged fluctuations

To properly identify the fluctuations induced by the modulations, it is convenient to look at phase-averaged fluctuations.

For the heat release rate, it is defined as HRR'(ϕ)=HRR(ϕ)-<HRR>, <> indicating a temporal averaging procedure. Results are shown in Fig. 18 for all the modulated cases. Most heat release rate fluctuations induced by the inlet modulation are confined just at the injector exit for the two cases at 5 kHz. On the contrary, the case at 1kHz shows longer wave oscillations up to the middle of the domain. It is also interesting to notice that high frequency modulations produce a short wave length pattern of positive and negative contributions, which are expected to cancel each other once integrated over the flame length. the test case description: ϕ = 0 is defined at the minimum mass flow rate at inlet. The flame response is plotted in Fig. 19b. To ease the reading, the results are multiplied by 10 on the figure, roughly accounting for the modulation amplitude (i.e. 0.1) in order to mimic a gain. The two cases at 5 kHz, namely FM and OM-5kHz, show very small amplitude oscillations, with a gain lower than 0.03. On the contrary, a gain close to 0.25 is noticed for case OM-1kHz. This results should however be taken with care: a strong sensitivity to the averaging time is noticed and results with only 20 periods of modulation might not be properly converged. However, this result indicates that case OM-1kHz is a convenient case for solver comparison and an additional lower modulation frequency should be considered for case FM in order to produce an effective flame response.

a)

0 π/2 π 3π/2 2π
Phase [rad] 0.9 0.95

1 1.05 1.1 m'/m 0 [-] FM OM 1kHz OM 5kHz b) 0 π/2 π 3π/2 2π Phase [rad] 0 0.5 1 1.5 2 q'/q 0 x 10 [-] OM-1kHz OM-5kHz FM
Figure 19: a) Inlets mass flow rate (oxygen for OM cases and methane for FM case) over a period. b) Integrated heat release rate fluctuations q ′ normalized by the averaged value q 0 over a period. The amplitude is multiplied by 10 to account for the amplitude of modulation (0.1) and roughly represents a gain.

Conclusions

This work was realized in the framework of the REST (Rocket Engine Stability Initiative) working group on combustion instabilities in liquid rocket engines. The HF-10 test case is representative of a typical injection element from a liquid rocket engine, subject to pulsating mass flow rates at the inlet. The test comprises 3 sub-cases. In the first case, the outer flow (CH4) is pulsated at 5kHz. The second case consists in modulating the inner flow (O2) at 1kHz and in the third case the inner flow is pulsated at 5kHz. The HF-10 test case was simulated using the AVBP solver from CERFACS. The numerical approach relies on real-gas thermodynamics based on the SRK equation of state. Two combustion models are investigated: a beta-pdf based equilibrium chemistry model (IFCM) and an Arrhenius based finite-rate chemistry model, with an ARC scheme specifically derived for the present cases. The computed flame reaches about one third of the combustion chamber length for the isoline at 1500K. The flame expands quickly after the injection plane, and large scale intermittencies are observed. A mesh convergence is performed with the IFCM combustion model. It is found that after one iteration of localized refinement, the results do not show noticeable sensitivity to the grid resolution.

Comparison between IFCM and ARC chemical modeling indicates that the two chemical approaches lead to similar flame topologies. The finite-rate chemistry flame structure confirms that combustion occurs in a pure diffusion flame regime in this adiabatic configuration. However, in its current implementation, the direct integration of ARC requires a finer grid resolution in the flame front than the β-pdf model to better take into account the flame-turbulence interaction. As a consequence, for the grid resolution retained in this study, ARC produces a higher temperature field than IFCM.

Inlet pulsations do not significantly change the flame topology, both for OM and FM cases, when compared with the non-modulated case. However, phase-locked averages show induced periodic oscillations of the heat release rate along the flame. For the high-frequency cases at 5 kHz, these oscillations cancel along the flame length and the final contribution after integrating the heat release rate over the whole flame length is limited (the gain is lower than 0.03). On the contrary, the case OM at 1 kHz shows an important modulation of the flame heat release rate, close to a gain of 0.25. However, it is also found that with the number of modulation periods retained in this test case (10 in the recommendations -20 used in this work), the phase averaged flame response may not be properly converged with possible errors on both the gain and the phase. These results suggest that case OM 1kHz should be averaged over a longer physical time and that a lower frequency of modulation should be envisaged for case FM in the future HF-10 test case description.

Figure 1 :

 1 Figure 1: (a) Sketch of the full computational domain. (b) Coaxial injector.

Figure 2 :

 2 Figure 2: Longitudinal profiles for case NM-IFCM at t=4 ms and t=8 ms .

4 .

 4 Impact of the mesh resolution 4.1 MeshesThree different grid resolutions are compared for case NM-IFCM to assess the influence of the grid resolution of the simulation results. An adaptative mesh refinement technique is applied in this work. The grid is refined in regions where the flow is poorly resolved, using the Laplacian of the velocity, heat release rate and sound speed, computed from averaged solutions. Three meshes are considered. The reference one is M0. Meshes M1 and M2 correspond to one and two iterations of refinement, respectively. Longitudinal slices of the three grids in the near injector region are shown in Fig.3. The grids are strongly refined in the recessed region and immediately at the injector exit. Details on the meshes and their respective computational costs are given in Tab. 2.

Figure 3 :

 3 Figure 3: Longitudinal slices along the z axis with x-normal of the three meshes M0, M1 and M2.

4. 2 Figure 4 :

 24 Figure 4: Longitudinal slices (top half) of mean oxygen mass fraction, temperature and heat release rate for the 3 meshes M0 (top), M1 (middle) and M2 (bottom). The huge increase of heat release rate at the end of the domain are provoked by an exit sponge layer.

Figure 5 :Figure 6 :

 56 Figure 5: Radial profiles of temperature at different axial positions for meshes M0, M1 and M2.mean profiles, -rms profiles.

Figure 7 :

 7 Figure 7: Radial profiles of axial velocity at different axial positions for meshes M0, M1 and M2.mean profiles, -rms profiles.

TemperatureFigure 8 :Figure 9 :

 89 Figure 8: Longitudinal slices of mean temperature and heat release rate for cases NM-IFCM and NM-ARC.

Figure 10 :Figure 11 :

 1011 Figure 10: Scatter plots of temperature and species mass fractions in terms of the mixture fraction Z. Top: instantaneous solutions ; Bottom: average solutions.

Figure 12 :Figure 13 :Figure 14 :

 121314 Figure 12: Longitudinal slices of mean temperature and mean heat release rate for cases NM, FM and OM.

Figure 15 :

 15 Figure 15: Radial profiles of mean heat release rate (HRR) at different axial positions for cases NM, FM and OM.

Figure 16 :Figure 17 :Figure 18 :

 161718 Figure 16: Longitudinal slices of phase-averaged temperature (between 100 and 4000 K) for ϕ = 0 and ϕ = π.

Table 2 :

 2 Details of the 3 meshes used for the grid convergence study with NM-IFCM case. Simulations are performed using AMD Epyc processors @2,6 GHz.

	Mesh Nb of cells Nb of points CPU cost for 10 ms [kh]
	M0	3.7 10 6	0.7 10 6	7
	M1	11.5 10 6	2.0 10 6	50
	M2	48.1 10 6	8.3 10 6	450

Acknowledgements

This work was granted access to the HPC resources of TGCC (CEA), IDRIS and CINES made available by GENCI (Grand Equipement National de Calcul Intensif) under the allocation A0102B06176. A part of this work was performed using HPC resources from the mésocentre computing center of Ecole CentraleSupélec and Ecole Normale Supérieure Paris-Saclay supported by CNRS and Région Ile-de-France.


PUMP EROSION TEST : UN ÉRODIMÈTRE "LOW COST" DE TERRAIN

PUMP EROSION TEST : A LOW COST FIELD ERODIMETER

F. LARRARTE (1,2) , C. CHEVALIER (1) , C. MINATCHY (1) , H. CHOLLET (3) frederique.larrarte@univ-eiffel.fr; christophe.chevalier@univ-eiffel.fr; carlos.minatchy@univeiffel.fr; hugues.chollet@univ-eiffel.fr (1) Univ Gustave Eiffel, GERS-SRO, F-77454 Marne-la-Vallée, France (2) Laboratoire d'Hydraulique Saint Venant -6 quai Watier 78401 Chatou, France (3) Univ Gustave Eiffel, COSYS-GRETTIA, F-77454 Marne-la-Vallée, France

Résumé

Le PumpET (Pump Erosion Test) est un matériel de terrain dédié à la mesure de l'érodabilité de sédiments immergés. Après un rappel d'une partie des nombreux érodimètres existants, nous présenterons les principales étapes d'élaboration du prototype du PumpET et les résultats des premières campagnes expérimentales avant de conclure par les perspectives pour faire évoluer ce prototype.

Summary

The PumpET (Pump Erosion Test) is a field device dedicated to measuring the erodibility of submerged sediments. After a review of some of the many existing erodimeters, we will present the main steps in the development of the PumpET prototype and the results of the first experimental campaigns before concluding with the prospects for further development of this prototype.

.

I -Introduction

L'érosion par l'eau est un phénomène naturel qui peut avoir une forte influence sur la stabilité des structures de génie civil. De nombreuses tentatives ont été faites pour mesurer la sensibilité à l'érosion (l'« érodabilité ») au travers de grandeurs pouvant caractériser ces phénomènes notamment la contrainte de cisaillement et le taux d'érosion. L'objectif ici est de proposer un matériel de terrain « low cost » permettant de générer et caractériser l'érosion de sédiments présents sous quelques décimètres d'eau. Par « sédiments », nous entendons les matériaux constitutifs ou déposés au fond d'une rivière, d'un port, d'un canal et constitués d'éléments organiques ou minéraux, cohésifs ou non. Par « appareil de terrain », nous visons un matériel léger, autonome, aisé à transporter à la main le long d'un cours d'eau ou d'un estran, et sous l'appellation « low cost » : peu onéreux, facile à fabriquer et à réparer.

Le PumpET (Pump Erosion Test) vise à être un matériel de terrain dédié à la mesure de l'érodabilité, définie comme la capacité des sédiments fluviaux en place à pouvoir s'éroder sous différentes conditions hydrauliques. Son principe fondateur est l'aspiration d'eau en aval d'un canal d'essai immergé posé sur un lit sédimentaire. L'aspiration permet de générer à l'intérieur du canal un écoulement unidirectionnel contrôlé en vue d'éroder le sédiment. Le phénomène érosif se déclenche lorsque la contrainte critique de mise en mouvement des grains dans la zone d'essai est atteinte. Pour cela, l'évolution spatiale et temporelle de la déformée (en mm) de la surface de sédiment enclos dans la section de mesure sera suivie. Des mesures turbidimétriques pourraient être envisagées mais leur mise en place nécessite de prendre en compte la masse et l'encombrement dus aux capteurs. Au cours de l'essai d'érodabilité, les eaux de pompage pourront-être récupérées afin d'analyser en laboratoire la granularité et la fraction organique des sédiments érodés.

Après un rappel d'une partie des nombreux érodimètres existants, nous présenterons les principales étapes d'élaboration du prototype du PumpET, les difficultés surmontées, et les résultats des premières campagnes expérimentales.

II -Etat de l'art et aperçu des dispositif existant

L'érosion est communément entendue comme la mise en mouvement d'un solide sous l'effet de la contrainte de cisaillement que l'écoulement exerce sur l'interface sédiment-eau. Une contrainte de cisaillement minimale, également appelée contrainte de cisaillement critique c, est nécessaire pour éroder les sédiments.

Depuis [START_REF] Du | Le Rhône et les rivières à lit affouillable[END_REF], qui proposa une loi basée sur la pente du lit et la hauteur d'eau, de nombreux auteurs ont proposé des lois dont [START_REF] Jerez | Erosion measurement on immersed situations: a state of the art[END_REF] ont montré une comparaison graphique alors que [START_REF] Dey | Sediment threshold under steam flow : a state of the art review[END_REF][START_REF] Dey | Bed sediment entrainment by streamflow : state of the science[END_REF] faisaient des états de l'art des travaux sur le seuil d'érosion. Ces travaux montrent la difficulté à prévoir la résistance d'un sédiment donné à un phénomène érosif, ce qui n'est guère étonnant si l'on se réfère au panel de propriétés physico chimiques mises en jeu [START_REF] Grabowski | Erodibility of cohesive sediment: The importance of sediment properties[END_REF].

Abordant la question de la quantification de l'érosion ou du seuil d'érosion sous un autre angle, de nombreux collègues ont proposé des appareils pour des travaux soit de laboratoire soit de terrain [START_REF] Jerez | Erosion measurement on immersed situations: a state of the art[END_REF] et [START_REF] Regazzoni | Confrontation et analyse d'érodimètres et caractérisation de la sensibilité à 'érosion d'interface[END_REF] a montré que le seuil de contrainte de cisaillement est fortement dépendant de l'appareil utilisé. Plus récemment, [START_REF] Perez | A new method for mesuring sediment shear and erosion[END_REF] a proposé un appareil de terrain utilisant une hélice mais dont l'impact spatial est peu documenté alors que [START_REF] Grant | BEAST -A portable device for quantification of erosion in natural intact sediment cores[END_REF] proposait un appareil dit de terrain mais nécessitant un prélèvement au préalable, ce qui peut modifier les caractéristiques du sédiment. En parallèle de nos travaux, [9] a proposé un appareil mettant en oeuvre une chambre d'érosion qui est posée sur le sédiment.

III -Développement du prototype

Un bilan des précédents projets montre que les dispositifs expérimentaux de terrain étaient assez peu voir non transportables et d'un encombrement significatif. En revenant aux fondamentaux, le but est de disposer d'un appareil facilement portable, autonome et léger. Pour cela on a réduit la chambre d'observation à une veine de faible section, afin de réduire la puissance de la pompe nécessaire à atteindre les vitesses visées, mais aussi la taille de la batterie d'alimentation de cette pompe. Enfin, on a pris l'option d'un matériel à coût réduit en utilisant des composants aisément trouvables dans le commerce, par exemple nous utilisons de la tuyauterie PVC standard de 40 mm de diamètre se raccordant sur une veine de section en Altuglass.

Le PumpET est un dispositif compact, pesant moins de 3 kg, dont le coût est inférieur à 1000 euros (hors main d'oeuvre). Il convient de noter que quelques astuces initiales ont été mises en oeuvre pour améliorer la mesure :

 la chambre de mesure est de section variable (figure 1). L'entrée (80 x 30 mm ) est d'une section double de la sortie. L'évolution de la vitesse moyenne est pratiquement linéaire le long de la chambre, l'idée étant que le déclenchement devrait apparaître en aval où la vitesse est la plus importante, la position du seuil d'érosion le long de la chambre permettrait de déterminer une vitesse précise de déclenchement ;  une caméra sportcam filme la chambre pendant les phases de pompage, cela permet de déterminer la mise en mouvement des sédiments ;  deux plans laser inclinés de 45° sont projetés à travers la paroi supérieure transparente de la chambre de mesure. Leur déformation devrait permettre mesurer le creusement de la chambre (figure 2) ;  La pompe immergée est centrifuge (figure 3), elle permet d'assurer une vitesse moyenne de 0,7 m/s à la puissance maximale en 12V (c'est une 1100 GPH). Elle est pilotée en paliers de puissance (PWM) avec un micro-contrôleur ;

III -Tests préliminaires et calibration de la pompe

III -1 Calibration de la pompe

La puissance de la pompe se contrôle en PWM : Pulse Width Modulation. Ce paramètre numérique varie de 1 à 256. La calibration a été faire au laboratoire dans une cuve en eau calme. Nous avons fait varier la puissance de la pompe et mesuré le volume débité pendant 10 secondes pour chaque palier de puissance. Connaissant la section de la chambre, nous pouvons en déduire la vitesse (figure 4) de l'écoulement à l'endroit le plus étroit (aval de la chambre). Ces essais ont permis de confirmer que l'appareil peut être mis en oeuvre pour des vitesses d'écoulement jusqu'à 1 m/s. Au-delà, il est difficile pour l'expérimentateur d'assurer simultanément sa sécurité et de plaquer la chambre de mesure au fond. De plus, la jupe souple noire a alors tendance à se tordre sous l'effet du courant. La réflexion est en cours pour améliorer cela. Un individu à pieds peut sans difficulté utiliser l'appareil jusqu'à avoir de l'eau à la taille. Pour des hauteurs d'eau supérieures, nous envisageons une mise en oeuvre depuis un packraft.

Il convient enfin de noter que les essais sont destructifs au sens strict puisque le sédiment situé sous la chambre peut avoir été érodé. Cependant, comme l'emprise au sol est restreinte, il est possible de prélever du sédiment à l'extérieur immédiat de la chambre pour des analyses ultérieures au laboratoire (granulométrie mais également fraction organique).

IV -Détermination de l'érosion

Comme rappelé par [START_REF] Paphitis | Sand grain threshold, in relation to bed "stress history" : an experimental study[END_REF], la détermination du seuil a donné lieu à de nombreux travaux d'où il ressort que là encore le seuil dépend beaucoup de la manière de le déterminer mais également des phénomènes érosifs subis par les sédiments. Une autre famille d'approche peut être représentée par [START_REF] Chegini | Automated measurement of moving grains on bed deposits[END_REF] qui propose la détermination automatique de la mise en mouvement des grains en utilisant des images filmées au-dessus de la surface libre. Notre méthode est d'esprit semblable mais toujours avec choix délibéré de coût très maîtrisé, de légèreté et de matériel de terrain.

Pour le niveau de faisabilité, nous avons utilisé une méthode pas à pas. La scène filmée par la caméra a été divisée en 8 zones dans lesquelles nous avons quantifié le nombre de grains en mouvement (blanc si tous son immobiles, jaune si un grain bouge, orange si quelques grains bougent, rouge si le mouvement est généralisé). La figure 5 montre un exemple lors des tests de calibration en eau calme avec un sable d'Hostun homogène de granulométrie comprise entre 2 et 4 mm. Les images vidéo montrent clairement que, pour les faibles vitesses, seuls quelques grains sont mis en mouvement et que progressivement de plus en plus de grains bougent.

La figure 6 montre un exemple de résultats de terrain pour des mesures dans le Loiret avec une vitesse d'écoulement estimée à 0,2 m/s et une granulométrie inférieure à 1 mm. Il est de la même manière possible de quantifier la mise en mouvement des grains. Il convient de noter qu'une végétation non négligeable est présente et que donc de nombreuses particules en suspension circulent entre la caméra et la chambre de mesure. C'est un point qui sera à traiter pour une automatisation des traitements.

V -Conclusions et perspectives

Un prototype d'érodimètre, appelé PumpET, a été conçu et fabriqué avec une volonté délibérée de créer un appareil léger, peu couteux, facile à mettre en oeuvre par une équipe réduite. En ceci, la première étape du projet a été réalisée. Les tests effectués sur le terrain ont également permis de valider le concept puisqu'il est possible d'observer la mise en mouvement des particules du lit situé en partie inférieure de la chambre de mesure.

Divers projets d'amélioration sont déjà en réflexion comme la mise en place d'un compte tour, tel qu'un loch de voilier, visible dans le champ de la caméra et permettant de déterminer la vitesse de l'écoulement à proximité de la chambre de mesure ou l'adaptation d'un système de transport de la batterie permettant de travailler avec des hauteurs d'eau plus importantes, la mise en oeuvre depuis un engin permettant d'atteindre des hauteurs supérieures à 1 m d'eau.

Par ailleurs, des essais en laboratoire sont en préparation pour quantifier l'influence de la vitesse d'écoulement sur les résultats. Enfin, un travail de modélisation de l'écoulement à l'intérieur et autour de la chambre a été confié à des étudiants de Master 2 de l'Institut Francilien de Sciences Appliquées.

Figure 1 -

 1 Figure 1 -Schéma de principe de la chambre de mesure

Figure 2 :Figure 3 :

 23 Figure 2 : Une des têtes de plan laser dans son tube de montage usiné à 45° Figure 3 : Pompe et son positionnement à la verticale

Figure 4 :

 4 Figure 4 : courbe d'étalonnage

Figure 4a :

 4a Figure 4a : Transport avant mesure Figure 4b : Mise en oeuvre pour une mesure de terrain