Thomas Livebardon
email: livebard@cerfacs.fr

Stéphane Moreau

Laurent Gicquel

Thierry Poinsot

Eric Bouty

Combining LES of combustion chamber and an actuator disk theory to predict combustion noise in a helicopter engine

Keywords:

A method to predict combustion noise in real aero-engines using Large Eddy Simulations (LES) of the combustion chamber coupled with an analytical approach to model the acoustic transmission of acoustic and entropy noise through the turbine stages is described. The proposed strategy is tested by comparing predictions of the computed noise with experimental results obtained for a full helicopter engine with high frequency pressure sensors located in the chamber and in all turbine stages. First, an extensive experimental database is used to localize the acoustic sources responsible for the "core-noise" by a three-sensor technique constituting the reference data against which predictions will be assessed. Second, LES of the combustion chamber for two representative operating points are achieved and discussed. The waves leaving the combustion chamber are extracted from these simulations at the outlet of the chamber, and an analytical method based on actuator disk theory and compact assumptions gives noise levels at the various turbine stages using the waves amplitudes at the chamber outlet. Excellent agreement is found at low frequencies between simulations and engine measurements. These results also confirm the importance of indirect combustion noise (due to entropy waves) generated in a helicopter turboshaft engine for the first time.

Introduction

Dwindling oil reserves and ACARE 2050 targets on noise and pollution challenge aerospace industry to design increasingly efficient and silent aero-engines. To meet such new challenges, turbulent and lean partially premixed combustion has emerged in recent aeronautical engine combustion chambers but it triggers unwanted effects such as thermo-acoustic instabilities and noise generation. For several decades, combustion noise has been known as a major contributor to the broadband noise generated by aircraft engines also called "core noise". Current understanding decomposes combustion noise into two main noise sources:

• Direct combustion noise corresponds to the generation of acoustic waves by turbulent combustion within the chamber.

• Indirect noise is the generation of downstream and upstream acoustic waves due to the acceleration of temperature inhomogeneities propagating through the turbine stages.

Indirect noise mechanisms were first described in [START_REF] Candel | Acoustic transmission and reflection by a shear discontinuity separating hot and cold regions[END_REF][START_REF] Marble | Acoustic disturbances from gas nonuniformities convected through a nozzle[END_REF][START_REF] Marble | The coherent flame model for turbulent chemical reactions[END_REF], where one way coupling mechanisms between entropy spots and acoustic waves due to a velocity gradient in a quasi-one-dimensional nozzle was established. Using a compact assumption (characteristic length of the nozzle being negligible compared with the wavelength of the low-frequency combustion noise), linearized jump relations linking entropy and acoustic fluctuations are written through the nozzle. More recently, different analytical methods have been developed to remove the compact assumption in a quasi-one-dimensional case [START_REF] Morgans | Model-based control of combustion instabilities in annular combustors[END_REF][START_REF] Giauque | Analytical analysis of indirect combustion noise in subcritical nozzles[END_REF][START_REF] Duran | Numerical simulation of acoustic and entropy waves propagating through turbine blades[END_REF], taking into account arbitrary nozzle shapes [START_REF] Moase | The forced response of choked nozzles and supersonic diffusers[END_REF] or shock waves. In the same manner, modeling of combustion-generated noise through turbine stages was addressed by Cumpsty and Marble [START_REF] Cumpsty | The interaction of entropy fluctuations with turbine blade rows; a mechanism of turbojet engine noise[END_REF] or Pickett [START_REF] Pickett | Core engine noise due to temperature fluctuations convecting through turbine blade rows[END_REF], using the compact assumption and conservation laws between downstream and upstream sections of a turbine row. The low-frequency nature of combustion noise allowed considering only two-dimensional waves with no radial component. Thanks to this two-dimensional description, azimuthal modes, as well as flow deviation, could be considered. In practice, all these analytical methods and models must be validated using either numerical simulations or experimental databases. In realistic aeronautical engines, measurements of core-noise are a challenge because of the harsh conditions found in combustion chambers and turbines stages. In this context, analytical models for acoustic generation-transmission in turbines were primarily based on a database provided by NASA [START_REF] Doyle | Attenuation of upstream-generated low frequency noise by gas turbines[END_REF]. Recently, in the Seventh European Framework of Programme for research, the Turboshaft Engine Exhaust Noise Identification (TEENI) project was dedicated to the location of acoustic sources in a realistic helicopter engine covering the entire downstream section of a real engine from the combustion chamber to the exhaust with an identification of sources in a radiated acoustic field issued by real operating conditions. To this end, TEENI partners developed sets of sensors for measuring and analyzing unsteady quantities in a fullscale engine.

Nomenclature

Currently, numerical simulations are potential alternatives to real test cases. Large-Eddy Simulation (LES) techniques, coupled with the increase of computing power, are mature methods to provide accurate compressible simulations of complex reacting turbulent flows. They have been successfully validated on academic and realistic burners, to retrieve mean statistical features, but also unsteady flow characteristics [START_REF] Gicquel | Large eddy simulations of gaseous flames in gas turbine combustion chambers[END_REF][START_REF] Moin | Large-eddy simulation of realistic gas turbine combustors[END_REF][START_REF] Mahesh | Large eddy simulation of reacting turbulent flows in complex geometries[END_REF][START_REF] Fureby | LES of a multi-burner annular gas turbine combustor[END_REF][START_REF] Kuenne | LES modeling of premixed combustion using a thickened flame approach coupled with FGM tabulated chemistry[END_REF]. More precisely, LES is able to capture the strong interactions between turbulent structures and flames, which lead to acoustic wave generation. As such, it was used to study combustion instabilities within industrial and academic burners [START_REF] Roux | Influence of outlet boundary condition for large eddy simulation of combustion instabilities in gas turbine[END_REF][START_REF] Wolf | Massively parallel LES of azimuthal thermo-acoustic instabilities in annular gas turbines[END_REF], demonstrating the efficiency of LES for combustion-generated noise. With such tools, Leyko [START_REF] Leyko | Waves transmission and generation in turbine stages in a combustion-noise framework[END_REF] used an actuator disk theory [START_REF] Cumpsty | The interaction of entropy fluctuations with turbine blade rows; a mechanism of turbojet engine noise[END_REF] coupled with a LES of a turbulent reactive flow in an aero-engine to compute core-noise induced by a combustion chamber. Using also numerical simulations of a twodimensional turbine stage, Leyko proved the ability of this analytical method to predict indirect combustion noise generated by entropy fluctuations, the direct combustion noise generated through a stator [START_REF] Leyko | Waves transmission and generation in turbine stages in a combustion-noise framework[END_REF] or a rotor [START_REF] Duran | Study of the attenuation of waves propagating through fixed and rotating turbine blades[END_REF] and through a complete turbine stage [START_REF] Duran | Numerical simulation of acoustic and entropy waves propagating through turbine blades[END_REF]. In the same way, this actuator disk theory is investigated by comparing two-dimensional numerical simulations of a subsonic stator with an injection of entropy spots against analytical predictions [START_REF] Mishra | Evaluation of actuator disk theory for predicting indirect combustion noise[END_REF] showing the validity of this theory for low-frequency cut-on acoustic modes. Indirect noise has been thoroughly studied by DLR in an experiment called Entropy Wave Generator [START_REF] Bake | Experimental investigation of the entropy noise mechanism in aero-engines[END_REF][START_REF] Bake | The entropy wave generator (EWG): a reference case on entropy noise[END_REF] which has also been computed by many groups [START_REF] Muhlbauer | Numerical investigation of the fundamental mechanism for entropy noise generation in aero-engines[END_REF][START_REF] Giauque | Analytical analysis of indirect combustion noise in subcritical nozzles[END_REF][START_REF] Leyko | Numerical and analytical investigation of the indirect noise in a nozzle[END_REF]. This experiment, however, is a single nozzle and misses many features of real engines so that, to date no actual industrial configuration has been tackled numerically or theoretically to assess the importance of combustion noise. In a first attempt to fill in this gap, the current study presents the TEENI data and a numerical tool to predict noise generated by a real helicopter engine. A complete description of the TEENI experimental setup and main results are presented in Section 2. Section 3 describes the hybrid method called CONOCHAIN coupling LES and analytical approach. LES results are detailed in Section 4.1. Finally, Section 4.2 discusses the validation of the CONOCHAIN tool by comparing predictions with full-scale test results.

TEENI: a full-scale experimental test

Experimental setup

The experimental system is a fully instrumented helicopter engine shown in Fig. 1. The harsh conditions, in terms of temperature and pressure especially in the combustion chamber, required dedicated original probe designs, developed by DLR (Berlin). Each pressure probe is a flush-mounted pin-hole apparatus with a remote microphone put perpendicular to a semi-infinite tube to limit standing wave effects [START_REF] Perennes | Aerodynamic noise of a two-dimensional wing with high-lift devices[END_REF]. To protect the microphone from hot combustion products, a cooling system injects a controlled air flow rate through the tube [START_REF] Bake | Investigation of entropy noise in aero-engine combustors[END_REF]. Temperature sensors are based on a twin thermocouple designed to be able to detect fluctuations up to 700 Hz.

To measure pressure and temperature fluctuations in each module of the engine from the combustor to the exhaust, several probes are mounted at different circumferential locations (Fig. 2):

• 2 pressure probes and 4 twin thermocouples are located in the combustion chamber (position A in Fig. 2 ).

• 2 pressure probes and 2 twin thermocouples are placed between the high-pressure turbine (HPT) and the power turbine (position B in Fig. 2).

• 2 pressure probes located between the first and the second turbine stages of the power turbine (position C in Fig. 2).

• 30 pressure probes are present in an extended nozzle: 2 planes with 3 probes and 2 planes with 12 probes (position D in Fig. 2).

For proper calibration, a complex transfer function is computed at ambient conditions for each remote pressure probe up to 4000 Hz [START_REF] Perennes | Aerodynamic noise of a two-dimensional wing with high-lift devices[END_REF]. The in-situ calibration has been achieved with a B&K Type-4228 pistonphone for each pressure probe without any cross-flow present but with the cooling tubes attached. Pressure fluctuations in the engine are recorded with a sampling frequency of 25.6 kHz whereas unsteady temperatures are recorded with a sampling frequency of 102.4 kHz. Unfortunately, the twin thermocouples failed to provide reliable temperature fluctuations within the combustion chamber and the high-pressurized turbine. Data acquisition is performed at 7 different operating points from the lowest power setting encountered in flight conditions to take-off power. Measurements are performed at stabilized operating points after a transitional phase to reach the engine thermal equilibrium.

In this paper, only results relative to two operating points, at the lowest and highest powers, are presented. The combustion chamber parameters are detailed in Table 1. The dimensionless parameters are referenced to the high-power settings.

Signal processing and experimental data exploitation 2.2.1. Power spectral density of pressure fluctuations

Power spectral densities (PSD) of pressure fluctuations at each location within the engine (Fig. 2) are given in Fig. 3 for low and high power. In the combustion chamber, the acoustic activity is very similar for both power settings, exhibiting narrowband ( f = 140 Hz) as well as broadband ( f = 1200 Hz) modulations (Fig. 3(a)). Both modulation patterns were identified: they correspond to acoustic resonances within the sensors, where the kinematic viscosity decreases with pressure and leads to weak acoustic damping. As the combustion chamber pressure is the highest within the engine, these resonances in the PSD of pressure fluctuations are mostly seen at station A (Fig. 3(a)). Details of an acoustic modeling of the pressure probes used in the experiment are provided in the appendix.

Figure 3 (b) focuses on the high pressure turbine PSD levels. A difference of 5 dB is noted over the whole spectra obtained for the two operating points with a broadband hump up to 1500 Hz. Similarly to the combustion chamber, acoustic resonances are also visible in this section of the engine. Tonal peaks generated by the rotating shafts are also present in both plots (although more pronounced in the HPT Fig. 3(b), the frequency shift between peaks being induced by the difference in rotating shaft speeds of the two operating conditions. These peaks are also visible in the power turbine PSD in Fig 3(c), the difference between the two operating conditions being in the order of 2 dB. The PSD at the exhaust in Fig 3(d), shows a 5 dB difference from 500 Hz to 4000 Hz, identical acoustic levels being recorded below 500 Hz.

Three-sensor technique

Due to the broadband nature of combustion noise, characterization of its contribution in the core noise requires broadband-noise breakdown techniques. Indeed, each signal X results from a signal emitted by a source S through a linear transfer function H and an added uncorrelated noise N. In frequency domain, X is equal to H • S + N. In the scope of combustion noise, the aim is to identify the acoustic power produced within the engine correlated with the acoustic power radiated at the outlet. The first way is to compute coherence spectra between any pressure probe signal in the engine and an exhaust sensor signal. Yet, this method does not yield significant coherence levels, the correlation being lost because of the high uncorrelated turbulent levels at the exhaust. To enhance the signal-to-noise ratio, a technique based on averaged cross-spectra between three sensors is applied [START_REF] Chung | Rejection of flow noise using a coherence function method[END_REF][START_REF] Krejsa | Combustion noise from gas turbine aircraft engines measurement of far-field levels[END_REF][START_REF] Shivashankara | Gas turbine core noise source isolation by internal-to-farfield correlations[END_REF][START_REF] Wirsching | Random vibrations: theory and practice[END_REF]. Its objective is to obtain the coherent power emitted by an acoustic source S within the engine without contributions of uncorrelated noise and radiated at the exhaust. From the combustion chamber to the power turbines at each location defined in Fig. 2, the two pressure probes (noted with the subscripts 1 and 2, respectively) are combined with a reference probe at the exhaust (noted with the subscript 3). Averaged cross-spectra between these signals are

G 12 = H 1 • H * 2 • S • S * , (1)
G 23 = H 2 • H * 3 • S • S * , (2)
G 31 = H 3 • H * 1 • S • S * . (3)
Note that these cross-spectra are not impacted by power provided by uncorrelated noise. The coherent power of the source S can thus be recovered and follows for the exhaust probe

G S3 = G 23 • G 31 G 12 = H 3 • H * 3 • S • S * . (4)
Finally, applying the three-sensor technique between an exhaust pressure probe and each pair of probes located either in the combustion chamber or in the high pressure turbine or in the power turbine, localization of broadband noise generation radiated in the exhaust is available. Using this method for probes located in the combustion chamber yields a narrow-band coherent PSD close to 200 Hz as evidenced in Fig. 4 for both operating points. On the contrary, this technique shows a global increase of coherent PSD in the range [200 Hz, 1000 Hz] in Fig. 5, which is emphasized at the high power setting. Furthermore, no change is detected in the generation of added coherent PSD in [0 Hz, 4000 Hz] in the power turbine compared with the high pressure turbine as seen in Fig. 6. However, cross-correlations between pressure fluctuations at any location in the whole engine or unsteady temperature measured by twin-thermocouples in the combustion chamber and the highpressure turbine did not provide any noticeable results to directly conclude on acoustic waves generated by entropy spots. In summary, the three-sensor technique reveals a significant narrow direct combustion noise component around 200 Hz generated in the combustion chamber, and a broadband hump up to 1500 Hz attributed to broadband noise generated by the HPT which could be indirect combustion noise.

Combustion noise prediction: CONOCHAIN methodology

The full simulation of core noise and its propagation through the turbine stages is currently out of reach in terms of computational cost. However, in order to predict combustion noise generation, LES is a necessary tool to correctly predict entropy, vorticity and acoustic waves generated by the turbulent combustion process. This step is highlighted in Section 3.1. As combustion noise is low frequency and therefore corresponds to wavelengths much larger than the blade chords and heights, acoustic generation and propagation through turbine stages can be described with a twodimensional compact actuator disk theory dealt with Section 3.2. This analytical method is termed CHORUS. The combination of LES simulations and CHORUS is the CONOCHAIN methodology (Fig. 7). Flow variables are extracted from LES at several planes perpendicular to the engine axis at the exit of the combustion chamber (planes P in Fig. 7). They yield the primitive dimensionless fluctuating variables used in Cumpsty and Marble's model [START_REF] Cumpsty | The interaction of entropy fluctuations with turbine blade rows; a mechanism of turbojet engine noise[END_REF]: By assuming time harmonic fluctuations, these primitive variables are combined to build upstream and downstream propagating acoustic waves (w + and w -), entropy waves (w s ) and vorticity waves (w v ). Thus, each wave is written as follows:

• entropy (s ′ /C p ) • velocity magnitude (w ′ /c) • pressure (p ′ /γ p) • flow angle (θ ′ ).
w = |w| exp iω t - 1 c K(cos ν + sin ν) (5)
where K is a dimensionless wave number magnitude and ν the wave front angle with respect to the engine axis. The whole process can be summarized by the following steps [START_REF] Duran | Numerical simulation of acoustic and entropy waves propagating through turbine blades[END_REF][START_REF] Leyko | Waves transmission and generation in turbine stages in a combustion-noise framework[END_REF][START_REF] Duran | Study of the attenuation of waves propagating through fixed and rotating turbine blades[END_REF]]:

• Instantaneous LES solutions are interpolated over planes at the outlet of the combustion chamber (typically 500 to 1000 snapshots) as shown in Fig. 7. Primitive variables denoted by f ′ are radially averaged and decomposed using temporal Fourier transform, namely

f ′ (R, α, t ) → f ′ (α, t )
Radial average [START_REF] Duran | Numerical simulation of acoustic and entropy waves propagating through turbine blades[END_REF] and

F ′ (α, ω) = 1 t LES t LES 0 f ′ (α, t )e -iωt dt
Temporal Fourier trans f orm [START_REF] Moase | The forced response of choked nozzles and supersonic diffusers[END_REF] where t LES is the duration of the productive simulation and F ′ is the primitive variable f ′ in the frequency domain. Radial averaging is used to extract the zeroth radial mode from the unsteady fields at the chamber exit. This mode is the only one which can be handled by the two-dimensional actuator disk theory.

F ′ (m, ω) = 1 α max -α min αmax α min F ′ (α, ω)e -imα dα.
Azimuthal Fourier trans f orm [START_REF] Cumpsty | The interaction of entropy fluctuations with turbine blade rows; a mechanism of turbojet engine noise[END_REF] Using Eq. ( 8) and the energy conservation in terms of signal power ensured by Parseval's theorem, the relative contribution of the azimuthal mode F ′ (m, ω) is evaluated with

F ′ (m, ω) 2 1 αmax-α min αmax α min F ′ (α, ω) 2 dα . (9)
• Dispersion relations, derived from two-dimensional linearized Euler equations, allow building primitive variables in a waveform

   s ′ /C p w ′ /c p ′ /γ p θ ′    = [K]    w s w v w + w -    (10)
where the matrix K is defined as follows:

    1 0 0 0 0 -i sin(υv-θ ) Kv K+cos(θ -υ+ ) 1-K+Mcos(υ+-θ ) K-cos(θ -υ-) 1-K-Mcos(υ--θ ) 0 0 1 1 0 i cos(υv-θ ) KvM K+sin(υ+-θ ) 1-K+Mcos(υ+-θ ) K-sin(υ--θ ) 1-K-Mcos(υ--θ )     . (11)
• The waves w are filtered at the exit of the combustion chamber using the set of N planes interpolating planes to extract the propagating components [START_REF] Kopitz | Characteristics-based filter for identification of planar acoustic waves in numerical simulation of turbulent compressible flow[END_REF], namely

ŵ = 1 N planes N planes i=1 w i exp (-iKx i ). ( 12
)
• Using this wave decomposition and an extension of the actuator disk theory [START_REF] Cumpsty | The interaction of entropy fluctuations with turbine blade rows; a mechanism of turbojet engine noise[END_REF], CHORUS propagates these waves through turbine stages and computes acoustic power attributed to direct and indirect combustion noise at several locations in a real turbine (Fig. 8).

LES solver

Two LES have been performed using the AVBP solver [START_REF] Avbp | [END_REF]. AVBP runs on massively parallel schemes to solve the compressible reacting Navier-Stokes equations. To limit the computational cost, only one sector is simulated. AVBP uses unstructured grids with the TTG scheme that has a third order spatial and temporal accuracy [START_REF] Colin | Development of high-order Taylor-Galerkin schemes for unsteady calculations[END_REF]. Subgrid scale stresses are described by the Smagorinksy model [START_REF] Smagorinsky | General circulation experiments with the primitive equations. 1. The basic experiment[END_REF] while the dynamic thickened flame model is used to model the flame/turbulence interactions [START_REF] Colin | A thickened flame model for large eddy simulations of turbulent premixed combustion[END_REF][START_REF] Selle | Compressible large-eddy simulation of turbulent combustion in complex geometry on unstructured meshes[END_REF][START_REF] Poinsot | Theoretical and numerical combustion[END_REF]. Kerosene/air chemistry is modeled using a synthetic surrogate coupled with a reduced mechanism involving 6 species and 2 reactions [START_REF] Franzelli | A two-step chemical scheme for large-eddy simulation of kerosene-air flames[END_REF]. Reaction rates are modeled by Arrhenius laws [START_REF] Poinsot | Theoretical and numerical combustion[END_REF], where the preexponential constants are fitted in rich regimes to recover proper laminar flame speeds. The unstructured mesh considered in this study contains 12 million tetrahedral elements, the primary zone of the combustor being described with mesh element sizes close to 0.5 mm. Previous numerical simulations of this combustion chamber were performed to investigate the acoustic coupling between the unsteady flame and the system acoustic eigenmodes [START_REF] Wolf | Massively parallel LES of azimuthal thermo-acoustic instabilities in annular gas turbines[END_REF] based on a similar methodology. Since the objective is to compute waves leaving the chamber to enter the turbine, boundary conditions require specific treatments to handle the unsteady flow features. In AVBP, the Navier Stokes Characteristic Boundary Conditions (NSCBC) method is implemented [START_REF] Poinsot | Boundary conditions for direct simulations of compressible viscous flows[END_REF][START_REF] Selle | The actual impedance of non-reflecting boundary conditions: implications for the computation of resonators[END_REF] decomposing each variation of the flow variables on the boundaries into ingoing and outgoing waves. In these computations, the NSCBC treatment is only applied at the inlet where the mass flow rate and the flow temperature are known, while wall-law adiabatic conditions are imposed at all walls of the chamber. To mimic the choked stator of the high pressure turbine, a nozzle is added at the chamber outlet to keep the curvilinear variation of normal surface through the row. The throat section of the nozzle matches the section of the real HPT stator used experimentally. Since the throat is choked, no additional boundary condition is needed at the chamber outlet.

CHORUS: an analytical model of acoustic propagation and generation of core-noise in a turbine

CHORUS computes the acoustic propagation and generation of indirect combustion noise induced by non-homogeneous flows through turbine blades based on the actuator disk theory [START_REF] Cumpsty | The interaction of entropy fluctuations with turbine blade rows; a mechanism of turbojet engine noise[END_REF] recently revisited by Moreau and co-workers [START_REF] Duran | Numerical simulation of acoustic and entropy waves propagating through turbine blades[END_REF][START_REF] Duran | Study of the attenuation of waves propagating through fixed and rotating turbine blades[END_REF][START_REF] Duran | Computing combustion noise by combining large eddy simulations with analytical models for the propagation of waves through turbine blades[END_REF][START_REF] Duran | Computing combustion noise by combining large eddy simulations with analytical models for the propagation of waves through turbine blades[END_REF][START_REF] Leyko | Simulation and modelling of the waves transmission and generation in a stator blade row in a combustion-noise framework[END_REF]. The flow can be considered two-dimensional, inviscid and isentropic in a blade-to-blade plane (blades heights are assumed small). Fluctuations of flow variables are assumed to be small compared with mean values: the conservation equations of mass, entropy and stagnation temperature through a stator. In the case of a rotor, stagnation temperature conservation is replaced by the rothalpy conservation. A last relation is given by Kutta's condition at the trailing edge of the blades. The set of resulting equations used in

CHORUS reads ṁ′ ṁ u = ṁ′ ṁ d (13) s ′ c p u = s ′ c p d (14) T ′ t T t u = T ′ t T t d (15) θ ′ u = β θ ′ d ( 16
)
for a stator and

ṁ′ ṁ u = ṁ′ ṁ d ( 17
)
s ′ c p u = s ′ c p d ( 18
)
I ′ t I t u = I ′ t I t d (19) θ ′ u = β θ ′ d ( 20
)
for a rotor. These jump conditions can be written in terms of the fluctuations of the primitive variables:

ṁ′ ṁ = p ′ γ p + 1 M w ′ c -θ ′ tan θ (21)
T ′ t T t = 1 1 + (γ -1) 2 M 2 (γ -1) p ′ γ p + s ′ c p + (γ -1)M w ′ c ( 22
)
I ′ t I t = 1 1 -ζ T ′ t T t -ζ 1 M w ′ c + θ ′ tan θ (23)
where ζ = Uv h t . Thus, these equations can be written in a matrix form. For a row i: [START_REF] Giauque | Analytical analysis of indirect combustion noise in subcritical nozzles[END_REF] where [ǫ i ] is

ǫ i u    s ′ /C p w ′ /c p ′ /γ p θ ′    i u = ǫ i d    s ′ /C p w ′ /c p ′ /γ p θ ′    i d
ǫ i =    1 0 0 0 -1 1 M i 1 -tan θ i µ i γ -1 µ i M i µ i 0 0 0 0 β i    , µ i = 1 + γ -1 2 M 2 i and M i = w i c i ( 25
)
Using the matrix K i defined in Eq. ( 10), the matrix product, Eq. ( 24), becomes

ǫ i u K i u    w s w v w + w -    i u = ǫ i d K i d    w s w v w + w -    i d , (26)
T i u W i u = T i d W i d with T i = ǫ i K i and W i =    w s w v w + w -    i ( 27
)
Note finally that to take into account the fact that wave propagation occurs between the rows of the turbine, phase shifts based on the wave travel times between rows are computed. Even though stators and rotors are assumed to be compact, these travel times between rotors and stators make the formulation frequency dependent. The combination of consecutive blade rows leads to matrix product giving a transfer function for each computed wave. For the case of multiple blade rows, the phase-shift of the waves through the blade-row spacing is taken into account. This is done using the matrix [S], in which the diagonal terms are the phase-shift of the waves, namely

S i =    exp(-ik s x L i ) 0 0 0 0 exp(-ik v x L i ) 0 0 0 0 exp(-ik + x L i ) 0 0 0 0 exp(-ik - x L i )    . (28)
The downstream waves vector W i d is related to the following blade row through

W i+1 u = S i W i d .
Combining the successive stages of the turbine, a relation between the inlet and the outlet waves of the turbine can be written in a matrix form, giving

Ns-1 i=1 T i+1 u S i T i d T 1 u .W 1 u = T Ns d W Ns d . (29)
As a result, CHORUS allows discriminating noise generated by entropy, vorticity as well as acoustic waves propagated through any number of turbine stages. Finally, Welsh's periodogram is used to compute the power spectral density of the acoustic pressure at the outlet of any turbine stage that takes into account the convective terms [START_REF] Bretherton | Wavetrains in inhomogeneous moving media[END_REF].

CHORUS was validated on canonical test cases: twodimensional LES were first performed to mimic acoustic generation in a stator [START_REF] Leyko | Waves transmission and generation in turbine stages in a combustion-noise framework[END_REF][START_REF] Leyko | Simulation and modelling of the waves transmission and generation in a stator blade row in a combustion-noise framework[END_REF] by plane entropy waves, and compared with the CHORUS method. Good agreement was found between analytical and computed acoustic transfer functions. Entropy to acoustic transfer functions was found to depend on the scattering of the normal entropy wave to higher-order modes through the stator because of a non-uniform convective velocity through the blade rows. Indeed, turbulence mixing induced by the turbine blades generates a planar wave distortion and a damping of entropy waves through the first stages and no more indirect noise generation in the last stages. To take into account this low-pass filter behavior of the turbine stages, a scaling function was implemented based on the characteristic pitch of a blade row. The impact of this transfer function on numerical predictions will be discussed in Section 4.2. Validations of acoustic and entropy transfer functions through a rotor and a stator-rotor configuration were addressed in [START_REF] Duran | Study of the attenuation of waves propagating through fixed and rotating turbine blades[END_REF][START_REF] Duran | Computing combustion noise by combining large eddy simulations with analytical models for the propagation of waves through turbine blades[END_REF]. Under the compact assumption, all these studies show the ability of the analytical method to predict acoustic generation through a complete turbine stage at low frequency. Comparisons with the present experimental database (Section 2) are provided in the following sections.

CONOCHAIN results and discussion

CONOCHAIN is applied here to the TEENI engine. Combustion LES results are first presented in Section 4.1, before describing CHORUS results for noise in Section 4.2.

Combustion chamber LES results

Mean flow predictions

The computed combustion chamber is shown in Fig. 9. Pressurized air is injected from the compressor through the air inlet in Tadiab-Tinlet with an isoline of stoichiometric mixture fraction in plane 1 (Fig. 9).

Fig. 11. Mean dimensionless velocity magnitude u

Uinlet with white contours of mean heat release (W/m 3 ) in plane 1 (Fig. 9). the casing. In a real engine, liquid fuel is injected through injectors where it is atomized and vaporized. In these simulations, fuel is injected in gaseous phase close to the vaporizing zone at the lips of the injector. Taking into account the liquid spray of kerosene can impact the thermo-acoustic activity in Rich Quench Lean burners where evaporation and atomization characteristic times can modify the acoustic flame response [START_REF] Gajan | Investigation of spray behavior downstream of an aeroengine injector with acoustic excitation[END_REF][START_REF] De La Cruz | Investigations on the selfexcited oscillations in a kerosene spray flame[END_REF]. Nevertheless, for these regimes, the atomization and the vaporization zones of the injected liquid fuel are very small and gaseous computations are sufficient to capture acoustic behavior of this combustion chamber [START_REF] Wolf | Massively parallel LES of azimuthal thermo-acoustic instabilities in annular gas turbines[END_REF]. Dilution holes ensure homogenization of burnt gases and a reduced mean temperature at the outlet of the combustion chamber. To ensure thermal wall protection, multi-perforated plates are positioned near the primary zone to generate local effusion cooling. Contrary to the dilution holes which are resolved, multi-perforated Fig. 12. Streamlines of the mean velocity vectors projected over the plane 1 (Fig. 9).

Fig. 13. Instantaneous dimensionless temperature field T -Tinlet

Tadiab-Tinlet at high power in plane 1 (Fig. 9). plates are modeled using a homogenized model that takes into account the mass flow rate across the plate [START_REF] Mendez | Acoustic modeling of perforated plates with bias flow for large-eddy simulations[END_REF]. Figure 10 shows the dimensionless mean temperature field (according to the inlet temperature in the combustion chamber and the stoichiometric adiabatic flame temperature at these regimes) for the two operating points (Table 1) in the meridional plane 1 (Fig. 9), with an isoline of stoichiometric fuel concentration. The variation of fuel-to-air ratio between these two simulations explains the difference of fuel and mean temperature distributions in the combustion chamber.

Figure 11 displays mean velocity fields (magnitude) for the low and high power cases: the mean velocity magnitudes are normalized by the mean inlet velocities which are identical in both cases. The flame (visualized by white isolines of heat release) is stabilized at the swirler outlet in a low velocity recirculation zone induced by the swirling flow close to the lips of the swirler as well as by the dilution jet flows. The upper jet flow feeds the largest recirculation zone (Fig. 12) which leads to the slight asymmetry (with respect to injector axis) in the stoichiometric fuel fraction and the mean heat release. Spatial distributions of mean heat release in Fig. 11 show two main combustion regions, near the lips of the injector separator and close to the dilution holes. As expected, a larger and more spread-out heat release distribution is observed for the high power condition similarly to the isoline of stoichiometric fuel fraction.

Unsteady activity in the combustor

Combustion noise is due to the the acoustic waves generated by the unsteady heat release within the combustor (direct noise) and is also linked to the generation of entropy spots as well as vorticity waves (indirect noise). An unsteady analysis of LES results is therefore required before applying CHORUS.

Instantaneous dimensionless temperature fields are shown in Figs. [START_REF] Mahesh | Large eddy simulation of reacting turbulent flows in complex geometries[END_REF] and 14 in a meridional plane 1 and a cylindrical plane 2 respectively. Both show significant temperature fluctuations generated by the turbulent combustion process and a strong stratification after the dilution holes with the formation of entropy spots. The largest temperature fluctuations occur in the second half of the flame tube where the dilution jets impact the gases leaving the primary zone. More quantitative results are obtained by the PSD of numerical temperature fluctuations over several planes defined in Fig. 13. The first plane is placed between the end of recirculation zone, the injector and the dilution holes while the second plane is located just after the dilution holes. Finally, a last plane is located before the flame tube starts turning. Fig. 10 showed that the mean Fig. 17. Coherence signals between unsteady global heat release and a pressure probe at the outlet of the combustion chamber (plane P in Fig. 7) -low power (---) and high power (

).

temperature decreases from the combustion zone to the exit of the flame tube. However, the PSD levels of the temperature fluctuations increase from the plane 1 to 2 more importantly for the high power case. Furthermore, RMS temperature levels show that temperature spots are mainly generated by the dilution and cooling devices of the combustion chamber, confirming the fields shown in Figs. 13 and14. PSD levels found in plane 3 in both cases show that the amplitude of temperature fluctuations do not depend on the operating point for which the mean velocity field is not modified (Fig. 15). PSD of numerical and experimental pressure fluctuations at location A in Fig. 9 are plotted in Fig. 16. The levels are well-predicted by the simulation for both power settings not only Fig. 18. Normalized modal PSD of pressure at the outlet of the combustion chamber (plane P in Fig. 7) using Eq. ( 9). Fig. 19. Normalized modal PSD of entropy at the outlet of the combustion chamber (plane P in Fig. 7) using Eq. ( 9). in magnitude but also in shape. The experimental oscillations are again caused by the response of the remote microphone probe as explained in the appendix. Note that there are very few examples of LES applied to real engine data and that Fig. 16 is one of the first quantitative demonstrations of LES capacities to predict noise within a real engine chamber.

Based on these LES, the dependence of the unsteady heat release on the combustor pressure fluctuations is highlighted by coherence spectra in Fig. 17 for the two operating conditions: as expected, wall pressure fluctuations are coupled with the global heat release in the chamber. Direct noise is dominant in the chamber.

Combustion noise evaluation

The CONOCHAIN method presented in Section 3.2 is now applied to the LES fields for the low and high power cases.

CHORUS post-processing in the combustion chamber

Low-frequency properties of combustion noise require LES to be computed for a long duration (80 ms) as well as numerous instantaneous solutions to ensure an appropriate sampling frequency. For the CHORUS analysis, instantaneous flow solutions are extracted at a 50 kHz sample rate to extract primitive variables over several outlet planes P (Fig. 7). A modal decomposition of the pressure or entropy fields over one plane (most downstream plane P in Fig. 7) at the outlet of the combustor is shown in Figs. 18 and19, respectively.

As only one sector is computed, the first plane wave is sufficient to describe the pressure field. In contrast, the entropy field is a composition of several modes even if only the first planar mode will be considered in the following results. Indeed, the analytical model CHORUS is based on a mode-matching technique and the acoustic modes generated by the higher entropy modes cannot be propagated through the turbine stages because the first circumferential mode corresponds to the first multiple of the number of sector with a cut-off frequency out of the frequency range of interest. The difference of level close to 500 Hz between the energy carried by entropy modes 1 and -1 is found to be caused by the mean azimuthal velocity at the outlet of the combustion chamber, itself induced by the multi-perforated plates and the swirling flow motion in the flame tube.

The remaining part of this section deals with the PSD of acoustic pressure computed by the analytical method CHORUS at each experimental probe location and compared with experimental PSD. ) in the HPT position B in Fig. 2).

(a) Low power (b) High power As indicated in Section 3.2, the attenuation of the entropy wave induced by the different turbine stages is taken into account with the transfer functions computed with the thermodynamic conditions encountered in the TEENI turbine and plotted in Fig. 20. Turbine rows are similar to low-pass filters and the increase of turbine stages leads to an important loss of entropy signal above 2000 Hz. Indeed, the attenuation of plane entropy wave is a scattering process of energy into higher modes that it is not included in the disk actuator theory. Finally, scaling of each transfer function is based on a reference case corresponding to entropy wave propagation through a turbine stage [START_REF] Duran | Numerical simulation of acoustic and entropy waves propagating through turbine blades[END_REF][START_REF] Duran | Study of the attenuation of waves propagating through fixed and rotating turbine blades[END_REF] at a given operating point based on the upstream mean velocity for each turbine row. For all these reasons, the large variations of thermodynamic conditions encountered in a real turbine can lead to slight differences between real attenuation transfer functions and the ones used in these computations.

High pressure turbine

Figure 21 shows the contribution of direct noise compared with the PSD levels of pressure fluctuations measured in the HPT (see Fig. 2). The compact assumption limits the comparison below 3000 Hz in the acoustic case (λ > 10l c which corresponds to a reduced frequency = lc λ < 0.1). Figure 21 confirms that the direct noise contribution to the overall noise in the turbine is small. A weak contribution of vorticity waves to the indirect noise is found and consequently, only indirect noise induced by entropy waves is considered.

Figure 22 shows that the indirect noise generated by entropy waves going through the HPT stage is larger than direct noise even when an attenuation factor is used for entropy waves. Furthermore, the large experimental hump in PSD spectra at low frequency is correctly predicted both in terms of magnitude and pattern. Propagation of entropy waves through only two turbine rows did not show an important impact of the attenuation transfer function below 1000 Hz as suggested by the attenuation-transfer function plotted in Fig. 20. The predicted indirect noise humps are centered around 500 Hz where the entropy plane mode induced by the combustion chamber topology contribute the most (Fig. 19). Indirect noise is a major contributor to the total engine-radiated noise for this case. Furthermore, the low-frequency activity measured experimentally is correctly predicted both in terms of magnitude and pattern by CONOCHAIN.

Power turbine

As in the HPT, the direct noise predicted by CONOCHAIN is lower than the pressure fluctuations measured in the power turbine (Fig. 23). Computed indirect combustion is over-predicted by 6 dB in both cases (Fig. 24) below 1000 Hz. Resonances between successive turbine rows can occur and yield these low-frequency humps. Above 1000 Hz, the larger impact of the transfer function of entropy attenuation on the computed PSD should be noted induced by the succession of turbine rows increases the scattering of the entropy planar mode.

Exhaust

At the exhaust, direct noise is definitely not an important contributor to the radiated total noise of the engine. The predicted magnitudes for direct noise in Fig. 25 are 5-10 dB lower than experimentally measured pressure fluctuations. The narrow-band experimental component found in the experiment at 200 Hz and attributed to the direct combustion noise is not present in the LES. By computing only a single sector of the annular combustion chamber, the acoustic field obtained with the LES is truncated which can explain the low levels of predicted direct combustion noise levels. Computed indirect noise with the entropy conservation through turbine stages is impacted by acoustic longitudinal resonances between the turbine rows in both cases (Fig. 26). At low power, computed indirect noise with the attenuation function matches the experimental PSD in the exhaust below 2000 Hz whereas computed indirect noise with the entropy wave conservation is 10 dB over-estimated. For the high power operating point, a slight difference occurs between computed indirect noise with the attenuation function and the experimental PSD below 1000 Hz. As mentioned in the previous paragraph, this difference can be attributed to acoustic resonances within the turbine or an underpredicted attenuation of the entropy planar mode at very lowfrequency. For instance, the tone at 1100 Hz comes from turbines rotating shafts. Above 1500 Hz, numerical results do not lie on the experimental values.

Ratio of indirect noise to direct noise

The ratios of indirect-to-direct noise in Fig. 27 emphasizes the importance of indirect noise in the overall radiated core-noise. For both power settings, the patterns are very similar. Indirect-todirect noise ratios below 2000 Hz is close to 10 in the HPT and the power turbine (Fig. 27(a) and (c)) and grows up to 100 in the exhaust. The slight difference in the exhaust (Fig. 27(c)) is mainly caused by different mean thermodynamic conditions in the turbine stages between the two operating points inducing different entropy planar mode scatterings.

Conclusions

The core-noise produced by a turboshaft engine has been investigated both experimentally and numerically within the European Project Framework TEENI.

Measurements in an actual turboshaft engine show for the first time that direct noise, generated by the acoustic activity within the combustion chamber and propagated through the turbine stages, corresponds to a narrowband peak close to 200 Hz in the overall radiated noise. Indirect core noise, induced by the acceleration of entropy and vorticity waves through the turbine stages, is mainly generated by the high-pressure turbine and characterized by a broadband hump up to 1500 Hz.

In parallel, the CONOCHAIN methodology is applied to the actual experimental configuration to evaluate its ability to predict the combustion noise generated by a helicopter engine. Mechanisms responsible for combustion noise generation have been identified using full-gaseous reactive and turbulent LES of a single-sector of the annular combustion chamber. On the one hand, unsteady combustion due to flame oscillations in the first section of the combustion chamber is found to be the main source of pressure fluctuations in the combustor that are correctly predict by LES. It yields the direct combustion noise. On the other hand, entropy spots are mainly generated by dilution devices located further downstream the chamber primary zone without much acceleration. Nevertheless, computing only a single-sector of a combustion chamber can impact the acoustic activity where the acoustic longitudinal modes are dominant and the spatial decomposition of the flow variables at the combustor exit to feed the actuator disk theory for which only planar modes are considered.

The analytical model mimicking the combustion-noise generation within turbine stages and proposed by Cumpsty and Marble [START_REF] Cumpsty | The interaction of entropy fluctuations with turbine blade rows; a mechanism of turbojet engine noise[END_REF], further developed by Leyko in a stator vane [START_REF] Leyko | Simulation and modelling of the waves transmission and generation in a stator blade row in a combustion-noise framework[END_REF] and numerically validated by Duran in a full turbine-stage cascade [START_REF] Duran | Computing combustion noise by combining large eddy simulations with analytical models for the propagation of waves through turbine blades[END_REF] is also applied to this actual engine and directly compared with experimental pressure fluctuations spectra for two operating points.

This coupled LES computation of the combustion chamber in the CONOCHAIN hybrid method shows the dominant role of indirect combustion noise in a turboshaft engine for the first time. Narrow-band contribution attributed to direct noise at 200 Hz in the experiment was not captured by LES in which predicted direct noise levels are found to be very low. Experimental broadband noise generation in the high-pressurized turbine can be related to entropy noise in the light of CONOCHAIN results. More generally, CONOCHAIN tool provides a reasonable estimation of broadband noise in the turbine stages below 1500 Hz. The results also show the importance of entropy wave dispersion caused by turbine stages on the indirect combustion noise magnitude. Even if the transfer function applied to the entropy wave level to mimic this mechanism might not be well-adapted for the whole turbine, the conservation of entropy fluctuation through a row as proposed by Cumpsty and Marble [START_REF] Cumpsty | The interaction of entropy fluctuations with turbine blade rows; a mechanism of turbojet engine noise[END_REF] is not an acceptable assumption when several turbine stages are considered and yields significant overprediction of the indirect-to-direct noise ratio. A model for entropy waves attenuation is required. Finally, indirect noise induced by entropy waves is identified as a major contributor to the radiated core-noise below 1500 Hz contrary to direct noise which is found negligible.

A.2. Acoustic modeling

No mean flow is considered in the sensor because the outlet 3 is closed. Mean temperature and mean pressure are assumed to be equal to the inlet combustion chamber values. Acoustic perturbations are supposed one-dimensional and harmonic. Thus, acoustic pressure fluctuation p ′ is written as p ′ (x, t ) = p + e i(ωt-k + x) + p -e i(ωt+k -x) with k = ω c 0 [START_REF] Shivashankara | Gas turbine core noise source isolation by internal-to-farfield correlations[END_REF] and the associated acoustic velocity fluctuation u ′ is

u ′ (x, t ) = 1 ρ 0 c
p + e i(ωt-k + x) -p -e i(ωt+k -x) (

The analytical transfer function is computed between the acoustic pressure in 4 and the acoustic pressure in 1. Closed ends are considered in 3 and 4 to set infinite acoustic impedances. In 2, a compact T-junction gives pressure and velocity jump conditions using mass and pressure conservation. These conditions provide a set of six equations p ′ I (0, t ) = p ′ II [START_REF] Kopitz | Characteristics-based filter for identification of planar acoustic waves in numerical simulation of turbulent compressible flow[END_REF] p ′ I (0, t ) = p ′ III [START_REF] Avbp | [END_REF] u ′ I (0, t ).S I + u ′ II (0, t ).S II + u ′ III (0, t ).S III = 0 (34)

p ′ I (l I , t ) = 1 (35) p ′ II (l II , t ) = Z 3 u ′ II (l II , t ) (36)
p ′ III (l III , t ) = Z 4 u ′ III (l III , t ).

(

) 37
Using the plane wave formulation in Eqs. [START_REF] Shivashankara | Gas turbine core noise source isolation by internal-to-farfield correlations[END_REF], and (31)), the set of Eqs. ( 32)-( 37) is expressed only with downstream and upstream acoustic waves. So, the system can be written in matrix form: MX = B

Solving the system of equations gives directly the acoustic pressure fluctuation recorded by the microphone. However, this modeling is not sufficient to explain the acoustic resonance visible in the PSD of pressure fluctuations in Fig. 16(b) and (a) because the effect of kinematic viscosity, responsible for the ability of the probe to absorb standing waves within the sensor, is not taken into account. To do this, a modified wave number k m k m = 1 4

(1 -i)

L p A 2ν 0 ω k 1 + (γ -1) 1 √ Pr + k (41)
is used to introduce an imaginary part able to mimic damping effect of the kinematic viscosity, as proposed in [START_REF] Rienstra | An introduction to acoustics No[END_REF] to consider acoustic damping within boundary layers. Note that the modified wave number defined in [START_REF] Selle | The actual impedance of non-reflecting boundary conditions: implications for the computation of resonators[END_REF] tends to k when the kinematic viscosity tends to zero. Finally, several acoustic transfer functions are plotted in Fig. 29 for pressure probe mounted in the combustion chamber (position A in Fig. 2) and in the power turbine (position C in Fig. 2). Note that the mean pressure is higher in the combustion chamber for both power settings. Thus, damping effect in the sensors decreases with increasing pressure. Finally, the multiple peaks correspond to the maxima observed in the PSD of pressure in the combustion chamber (Fig. 3(a)), suggesting that the modulation observed on all experimental PSD is due to the transfer function of the pressure probes.

  Luft-und Raumfahrt LES Large Eddy Simulations NASA National Aeronautics and Space Administration PSD power spectral density

Fig. 1 .

 1 Fig. 1. Schematic of the real TEENI turboshaft engine.

Fig. 2 .

 2 Fig. 2. Sketch of TEENI experimental setup and location of unsteady pressure and temperature probes.

Fig. 3 .

 3 Fig. 3. PSD of pressure fluctuations at maximum power () and minimum power measured (---) in different locations within the engine.

Fig. 4 .

 4 Fig. 4. PSD of the three-sensor technique applied between the combustion chamber and the exhaust (---) and PSD of pressure fluctuations of the reference probe ().

Fig. 5 .Fig. 6 .

 56 Fig. 5. PSD of the three-sensor technique applied between the HPT and the exhaust (---) and PSD of pressure fluctuations of the reference probe ().

Fig. 7 .

 7 Fig. 7. Sketch of the CONOCHAIN methodology.

Fig. 8 .

 8 Fig. 8. Sketch of the actuator disk theory applied on turbine stage.

Fig. 9 .

 9 Fig. 9. Numerical domain for the LES and cutting planes locations over an axial section of the combustion chamber.

Fig. 10 .

 10 Fig. 10. Mean dimensionless temperature Tmean -TinletTadiab-Tinlet with an isoline of stoichiometric mixture fraction in plane 1 (Fig.9).

Fig. 14 .

 14 Fig. 14. Instantaneous dimensionless temperature fluctuation field T -Tmean max(T -Tmean ) at high power in plane 2 (Fig. 9).

Fig. 15 .

 15 Fig. 15. Power spectral densities of unsteady temperature (K 2 /Hz) in flame tube -plane 1 ( ), plane 2 (•) and plane 3 (+) in Fig. 13.

Fig. 16 .

 16 Fig. 16. spectral densities of pressure fluctuations (position A in Fig. 7) -LES (-• -) Experiment ().

Fig. 20 .

 20 Fig. 20. Attenuation transfer function applied on entropy wave through the turbine at high power -position B (), position C ( ), and position D (•) in Fig. 2.

Fig. 21 .

 21 Fig. 21. Computed direct noise (•) and experimental PSD of pressure fluctuations () in the HPT position B in Fig.2).

Fig. 22 .

 22 Fig. 22. Computed indirect noise with entropy conservation ( ) through the stage and without the attenuation function (•) and experimental PSD of pressure fluctuations () in the HPT (position B in Fig.2).

Fig. 23 .

 23 Fig. 23. Computed direct noise (•) and experimental PSD of pressure fluctuations () in the power turbine (position C in Fig.2).

Fig. 24 .

 24 Fig. 24. Computed indirect noise with entropy conservation ( ) through the stage and without the attenuation function (•) and experimental PSD of pressure fluctuations () in the power turbine (position C in Fig.2).

Fig. 25 .

 25 Fig. 25. Computed direct noise (•) and experimental PSD of pressure fluctuations () in the exhaust (position D in Fig.2).

Fig. 26 .

 26 Fig. 26. Computed indirect noise with entropy conservation ( ) through the stage and without the attenuation function (•) and experimental PSD of pressure fluctuations () in the exhaust (position D in Fig.2).

Fig. 27 .

 27 Fig. 27. Indirect to direct noise ratios η at maximum power (

Fig. 28 .

 28 Fig. 28. Sketch of a pressure probe.

Fig. 29 .

 29 Fig. 29. PSD of pressure fluctuations in the combustion chamber and the power turbine (positions A and C in Fig. 2 respectively) () and analytical transfer functions (---).

Table 1

 1 Dimensionless combustion parameters at low and high powers.

	Dimensionless combustion parameters	Operating points
		Low	High
	Engine power	310 kW	900 kW
	Stagnation temperature	0.8	1
	Stagnation pressure	0.66	1
	Fuel-air ratio	0.78	1
	Mass flow rate	2.20 kg/s	3.25 kg/s

Acknowledgments

The authors would like to thank Karsten Knobloch and Benjamin Pardowitz from the DLR for providing the TEENI internal data, GENCI (Grand Equipement National de Calcul Intensif) and IDRIS (Institut du Developpement et des Ressources en Informatique Scientifique) for providing part of the computing power necessary for these simulations. The support of ANRT/CIFRE is also acknowledged. This work was funded by Turbomeca.

Appendix A. Analytical transfer function of experimental pressure probe in harsh conditions

An analytical model to mimic the acoustic response of the experimental pressure probe used in the TEENI experiment is presented (Fig. 28). It is based on one-dimensional propagation in junction tubes [START_REF] Rienstra | An introduction to acoustics No[END_REF] and is similar to what has been used for remote microphone probes in [START_REF] Perennes | Aerodynamic noise of a two-dimensional wing with high-lift devices[END_REF][START_REF] Moreau | Effect of airfoil aerodynamic loading on trailing edge noise sources[END_REF][START_REF] Chauvin | Experimental and numerical investigation on noise induced by a butterfly valve[END_REF].

A.1. Sketch of the sensor

The remote microphone is cooled by a controlled air flow injected from 3. The mass flow rate is set to ensure an efficient cooling and avoid noise generation. Along each pipe an x-coordinate with a positive direction outwards from 2 is defined.


Denis Lafage
email: lafage.denis@gmail.com

Julien Pétillon

Relative importance of management and natural flooding on spider, carabid and plant assemblages in extensively used grasslands along the Loire

Keywords: Coleoptera Carabidae, Araneae, stochastic disturbance, cutting-date, fertilizers

In Europe, agri-environment schemes (AES) have been implemented to counteract the effects of agricultural intensification. Studies investigating the role of management improvement induced by AES are quite numerous, but rarely take into account the effect of natural perturbations such as flooding, although severe disturbances are well known to shape community structure. Here we investigated the relative importance of management improvement and flooding to explain community parameters of two dominant arthropod groups and vegetation in alluvial meadows.

Sampling took place in 2013, using suction samplers for arthropods and phytosociological relevés for vegetation, in 83 meadows distributed along 200 km of the Loire Valley (France). Pair-matched approach (by R-ANOVA) was used to assess overall effects of AES whereas a gradient analysis (GLM) was carried out to assess the impact of AES prescriptions (fertilisation and cutting-date) together with indirect (long-term) and direct (short-term) effects of flooding.

No significant effect of AES was found on arthropod and plant assemblages, abundance/productivity or diversity (both and ), but the number of rare plant species was higher in sites under AES. Prescriptions had little impact on most response variables considered; the only significant impact being the positive effect of high-amounts of fertilisers on spider -anddiversities. Conversely, systematic long-term effects of flooding were found on all response variables of spiders, carabids and plants, underlining the key role of this factor in alluvial meadows.

Our study demonstrates that maintaining or enhancing hydrological functioning of ecosystems is even more important than regulating both the cutting-dates and the low input of fertilisers for conservation purposes in flooded, already naturally nutrient rich, meadows.

Running title: Efficiency of AES in flooded meadows

Word count: 5124

A c c e p t e d M a n u s c r i p t Introduction Over the last decades, agricultural intensification has accelerated adverse effects on wildlife (Millennium Ecosystem Assessment 2005). In Europe, agri-environment schemes (AES) have been implemented to counteract these effects by providing financial incentive for farmers to adopt extensive agricultural practices. Farmers involved in AES preferentially engage fields which are less suitable for intensive farming [START_REF] Kleijn | The conservation effects of meadow bird agreements on farmland in Zeeland, the Netherlands, in the period 1989-1995[END_REF], explaining why semi-natural grasslands are especially targeted by AES.

Investments in AES were substantial, with for example 34.9 billion Euros provided for [2007][2008][2009][2010][2011][2012][2013] programmes (COM, 2008). They currently cover 21% of all farmlands in the 27 EU countries.

Despite these high financial inputs, AES seem to have contrasting successes [START_REF] Kleijn | Mixed biodiversity benefits of agri-environment schemes in five European countries[END_REF], depending on the AES type and the model studied. For example, AES are recognised to have positive effects on birds in the UK [START_REF] Brereton | The changing status of the Chalkhill Blue butterfly Polyommatus coridon in the UK: the impacts of conservation policies and environmental factors[END_REF] and on pollinators in Switzerland [START_REF] Albrecht | The Swiss agri-environment scheme enhances pollinator diversity and plant reproductive success in nearby intensively managed farmland[END_REF]. However, AES also prove damaging when poorly designed or when targeting single taxon [START_REF] Konvicka | How too much care kills species: Grassland reserves, agri-environmental schemes and extinction of Colias myrmidone (Lepidoptera: Pieridae) from its former stronghold[END_REF]. Results on plant diversity are usually reported to be positive (e.g., [START_REF] Kleijn | Agri-environment schemes do not effectively protect biodiversity in Dutch agricultural landscapes[END_REF][START_REF] Critchley | The contribution of English agri-environment schemes to botanical diversity in arable field margins[END_REF]. Monitoring and evaluating these schemes is imperative to improve their efficiency and maximize the conservation outcomes.

Evaluation of AES impact has usually focused on birds [START_REF] Kleijn | Agri-environment schemes do not effectively protect biodiversity in Dutch agricultural landscapes[END_REF], Kleijn et al., 2006;Marshall, West, & Kleijn, 2006) and vegetation [START_REF] Critchley | The contribution of English agri-environment schemes to botanical diversity in arable field margins[END_REF] mainly because they are the main targets of AES as arthropods are often neglected in biodiversity conservation policies (e.g., [START_REF] Cardoso | The seven impediments in invertebrate conservation and how to overcome them[END_REF]. Nevertheless, some studies also dealt with arthropods-mainly bees and grasshoppers [START_REF] Kleijn | Agri-environment schemes do not effectively protect biodiversity in Dutch agricultural landscapes[END_REF][START_REF] Knop | Effectiveness of the Swiss agri-environment scheme in promoting biodiversity[END_REF], and found positive effects of AES. Despite Flooding is a key driver of intertidal and riparian ecosystems, and particularly of arthropod communities [START_REF] Desender | Diversity and conservation of terrestrial arthropods in tidal marshes along the River Schelde: a gradient analysis[END_REF] and vegetation [START_REF] Violle | Plant functional traits capture species richness variations along a flooding gradient[END_REF]. Arthropod communities of European rivers are likely to use a 'risk strategy' to survive in this naturally disturbed habitat. The strategy consists of a suite of life history traits such as high productivity ('rstrategy'), high capacity for dispersion, and active recolonisation from areas that have been sheltered from flooding [START_REF] Zulka | Carabids in a Central Europe floodplain: species distribution and survival during inundations[END_REF]. Vertical emigration to uplands or higher vegetation is also expected to increase recolonisation success [START_REF] Adis | Terrestrial invertebrates inhabiting lowland river floodplains of Central Amazonia and Central Europe: a review[END_REF]. A few terrestrial species also withstand short to prolonged (up to several weeks) periods of submersion (e.g., insects [START_REF] Hoback | Insects in hypoxia[END_REF], spiders: Pétillon et al., 2009). Conversely, flood events can be seen as a way to colonise new habitats and exchange individuals between distant populations [START_REF] Lambeets | Spatial genetic variation of a riparian wolf spider Pardosa agricola (Thorell, 1856) on lowland river banks: The importance of functional connectivity in linear spatial systems[END_REF], possibly enhancing among-site diversity in the long term. In the short-term, flood events strongly reduce local diversity. Floodplains are generally characterized by a low percentage of stenotopic species [START_REF] Lafage | Short term recolonisation by arthropod after a spring flood, with a focus on spiders and carabids[END_REF]. Specialist species with adaptations to flooding are found in more regularly flooded habitats like gravel banks [START_REF] Lambeets | Understanding the impact of flooding on trait-displacements and shifts in assemblage structure of predatory arthropods on river banks[END_REF] or salt marshes [START_REF] Pétillon | Evaluating the success of managed realignment for the restoration of salt marshes: lessons from invertebrate communities[END_REF].

No study has assessed the relative effects of AES vs. stochastic disturbances induced by flooding in such ecosystems, yet their expected effects on biodiversity are potentially opposite. Consequently, no or few effects of AES in shaping arthropod and plant assemblages are expected in floodplains.

To test this hypothesis, we evaluated the role of AES and flooding in explaining and diversities, abundances (biomass for plants), species rarity and assemblage composition of two non-target groups (spiders and carabids) and vegetation in the flooded meadows of the Loire River (France).

For spiders and carabids, analyses of rarity were not performed because of the lack of proper A c c e p t e d M a n u s c r i p t 6 national or regional statuses of rarity (the English classification cannot be applied here: [START_REF] Pétillon | First assessment of spider rarity in Western France[END_REF], and also because the number of stenotopic and/or rare species is low in these habitats [START_REF] Lafage | Short term recolonisation by arthropod after a spring flood, with a focus on spiders and carabids[END_REF].

Material and methods

Study area and sampling design

The study area covered 200 km of the Loire Valley (France: Fig. 1). Land is mainly covered by hay meadows with an extensive hedgerow network. Meadows are usually cut in early or mid-summer with second-crop grazing. The amount of fertilisers is generally low as regular winter and spring floods bring a large amount of organic matter into the system. Pesticides are seldom used. Thus, the management intensity is rather low. The study site included four AES zones with various prescriptions regarding cutting-dates and fertilizers. Cutting-dates were between June 5th to July 20th, within four defined classes: free (not under AES), before June 20th, between June 20th and July 1st, after July 1st. Fertiliser prescriptions were 0, 30 or 60 N unit/ha. A 'free' class was added for sites not under AES. Almost all meadows are flooded during winter for about 3 months, but in 2012 and 2013, the study sites were also flooded during spring for 5 to 22 days. Spring-flood had not occurred since 2004 in the Loire Valley.

Carabids, spiders and plants were sampled in 83 hay meadows. To reduce the variance between fields, a paired-matched approach was used to test the impact of AES (see statistical analysis section). Paired sites (with and without AES contract) were chosen with same vegetation types and flooding regime. Distance between sites belonging to a pair was inferior to 1 km. Table 1 summarizes the number of sites per treatment and moisture level. Site size ranged from 1.3 ha to 265.3 ha (mean = 34.7 ± 50.3 SD ha).

A c c e p t e d M a n u s c r i p t 7 Carabids and spiders were sampled using suction sampling (a standard technique providing quantitative data, i.e. abundance of individuals, on arthropods: [START_REF] Brook | Experimental verification of suction sampler capture efficiency in grasslands of differing vegetation height and structure[END_REF]. Each site was sampled once during June 2015 before the first cutting date-given the strong impact of cutting on spiders and carabids (e.g., Lafage & Pétillon 2014). Suction sampling was realised using a 12.5 cm diameter intake placed on the ground. At each sampling site, 5 samples (10 x 15 s suctions) were taken (total area: 0.12 m²/sample). Samples were stored in 70% alcohol and taken to the laboratory for sorting and identification to species level.

At each site, plants were sampled once during spring 2013 (from June 1 st 2013 to July 10 th 2013, before the first cutting date). Sampling followed the Braun-Blanquet (1928) method. One phytosociological relevé per sampling site was made in a 16 m² plot. Vegetation biomass was approximated using a vegetation index derived from MODIS satellite imagery: the Enhanced Vegetation Index (EVI: Lafage, Secondi, Georges, Bouzillé, & Pétillon, 2014) measured during 16 days by LP DAAC (product MOD13Q1).

Statistical analysis

Spatial autocorrelation, tested using Moran's I, was low enough (see Appendix A, table 1) to be neglected [START_REF] Gerisch | Community resilience following extreme disturbances: the response of ground beetles to a severe summer flood in a central European lowland stream[END_REF]. Spatial patterns in response variables were also researched using Moran's eigenvector maps (MEM) following [START_REF] Borcard | Numerical ecology with R[END_REF], but they were not significant (see Appendix A, table 2). Arthropod -diversities were estimated for each sampling site using the average of four nonparametric estimators based on species incidence: Chao1, Jacknife1, Jacknife2 and Bootstrap [START_REF] Carvalho | Determinants of spider species richness in coastal dunes along a gradient of mediterraneity[END_REF]). -diversity was estimated through a dissimilarity matrix (corresponding to Sørensen pair-wise dissimilarity) partitioned into its two components -species turnover ( t) and nestedness ( n)-following [START_REF] Baselga | Partitioning the turnover and nestedness components of beta diversity[END_REF] ). Vegetation diversity was estimated by the classical Shannon index. Plant rarity was estimated using the number of plants red-listed at either national or regional scale per sample. As no red list exists for spiders and carabids in France, analyses on arthropod rarity were not performed.

A paired-sample approach (with or without AES) was used to test the overall AES effect on abundance/productivity, -diversity, -diversity and rarity (plants) of arthropods and plants.

Repeated analyses of variance (R-ANOVA) with site as the within-subjects factor (e.g., [START_REF] Varet | Age-dependent colonisation of urban habitats : a diachronic approach using carabid beetles and spiders[END_REF] and AES presence/absence as a fixed factor were performed between paired sites presenting similar abiotic conditions (see similar designs in previous studies on AES efficiency: [START_REF] Knop | Effectiveness of the Swiss agri-environment scheme in promoting biodiversity[END_REF][START_REF] Kleijn | Mixed biodiversity benefits of agri-environment schemes in five European countries[END_REF][START_REF] Scheper | Environmental factors driving the effectiveness of European agri-environmental measures in mitigating pollinator loss -a meta-analysis[END_REF].

To test for differences in spider, carabid and plant assemblages between sites under AES and sites not under AES, analyses of variance (ANOSIM) were performed.

To test for differences in -diversities among groups (i.e., between sites under AES and not under AES), multiple-site dissimilarity matrices were computed using the betapart package for R [START_REF] Baselga | betapart: an R package for the study of beta diversity[END_REF] and the Simpson dissimilarity index. We then performed a re-sampling procedure in the -diversity matrix (50 pairs of sites were randomly sampled 50 times) to perform multiple comparison tests.

To investigate arthropod and plant responses to management and flooding, drivers of species assemblages were investigated using constrained analysis. The choice between redundancy analysis (RDA) and constrained correspondence analysis (CCA) was made according to the axis length of a detrended correspondence analysis (DCA). Abundances of all species (for arthropods) and Braun-Blanquet coefficients of abundance (for plants) were the response variables. The cutting-date (four classes), fertiliser input (three levels), a variable describing whether or not the site had been flooded during spring 2013 (i.e., binary variable for short-term effects of flooding), and a moisture gradient (i.e., discrete variable for long-term effects of flooding) were predictors. Five moisture classes were A c c e p t e d M a n u s c r i p t 9 defined from low (1) to very high (5) according to the mean Ellenberg indicator value [START_REF] Ellenberg | Zeigerwerte von Pflanzen in Mitteleuropa, 2nd ed[END_REF] of each vegetation type (defined by a Two-Way Indicator Species Analysis). Class 1 corresponded to sites with mean Ellenberg value lower the 5 (mean=4.6), class 2 to sites with 5<Ellenberg value< 6 (mean=5.4), class 3 to sites with 6<Ellenberg value<7 (mean=6.4), class 4 to sites with 7<Ellenberg value<8 (mean=7.5) and class 5 to sites with Ellenberg value higher than 8 (mean=8.3). Monte Carlo tests with 999 permutations were carried out to test the significance of the selected environmental factors and constrained analyses axes.

Responses of arthropod and plant -diversities, and abundances and vegetation productivity to both the cutting-date (four classes) and fertiliser input (three levels) were tested using Generalised Linear Models (GLMs) with gaussian distribution and a stepwise model selection by AIC [START_REF] Akaike | A new look at the statistical model identification[END_REF].

Flooding (i.e., binary variable for short-term effects of flooding) and moisture (five classes) variables were also included. As flooding was expected to influence both the effects of the cuttingdate and of fertiliser amounts, interactions between those variables were also included. The same GLM were applied to explain plant rarity. Pairwise-t-test were relalised to compare means of response variables depending on significant factors by GLM.

To identify the variables significantly influencing arthropod and plant -diversities, similarity matrices corresponding to species turnover were regressed against environmental variables using the Canonical Analysis of Principal Coordinates (CAP) implemented in the vegan package for R [START_REF] Oksanen | vegan: Community Ecology Package[END_REF]. The model included the same explanatory variables as previous GLMs.

Statistical analyses were performed using R software (R Development Core team 2013) with vegan [START_REF] Oksanen | vegan: Community Ecology Package[END_REF], MASS [START_REF] Venables | Modern Applied Statistics with S, Fourth[END_REF] and PCNM packages [START_REF] Legendre | PCNM: MEM spatial eigenfunction and principal coordinate analyses[END_REF].

A c c e p t e d M a n u s c r i p t

Results

A total of 6,036 spiders belonging to 97 species (see Appendix A, Table 3 for a detailed list of species), 383 carabids (see Appendix A, Table 4 for a detailed list of species) belonging to 43 species, and 150 plant species (see Appendix A, Table 5 for a detailed list of species), 3 of them being red-listed, were sampled. Spider and carabid assemblages were dominated by small aerial dispersers: 78% of spiders were Linyphiidae and 78% of carabids were small winged species.

Spider assemblages were dominated by six linyphiid species Tenuiphantes tenuis (29.4% of individuals), Meioneta rurestris (7.0%), Erigone dentipalplis (4.8%), Bathyphantes gracilis (4.8%), Oedothorax fuscus (4.4%) and Meioneta mollis (4.2%). Carabid assemblages were dominated by two harpaline species (Acupalpus exiguus: 51.0% and Syntomus obscuroguttatus: 15.4%) and one bembidiine species (Bembidion biguttatus: 7.8%). Plant assemblages were more balanced with ten species cumulatively covering 35%, with a frequency ranging from 6.1% (Lolium perenne) to 2.3% (Plantago lanceolata).

Spider -diversity was 0.97, corresponding to t = 0.95 and n = 0.02. Carabid -diversity was 0.95, corresponding to t = 0.92 and n = 0.03. Plant -diversity was 0.96, corresponding to t = 0.95 n = 0.01. n of the three groups was thus considered negligible and was not included in further analyses. Repeated ANOVAs revealed no significant effect of AES, site, or of the interaction between AES and site on estimated -diversity and abundance of spiders and carabids, or on plant productivity and -diversity (Table 2). A significant difference was found for plant rarity (Table 2), the number of rare plants being higher in sites under AES. No significant difference was found between assemblages of sites under AES vs. sites not under AES for spiders (R=0.011, P=0.365), carabids (R=0.008, P=0,347) or plants (R=-0.039, P=0,879). No significant difference was found between - CCA on spider assemblages was significant (F=1.61, P=0.048) and explained 55.5% of the total variance, with the first three axes of the CCA being significant (respectively P=0.005; P=0.020 and P=0.020). Axis 1 and 3 were associated with moisture index and axis 2 with cutting date but the only variable significantly explaining spider species composition was moisture (F=1.67, P=0.050) (Fig. 2).

RDA on carabid assemblages was not significant (F=0.98, P=0.430). RDA on plant assemblages was significant (F=1.58, P=0.005) and explained 66.3% of the total variance, with the first three axes of the RDA being significant (respectively P=0.005; P=0.015 and P=0.005). Cutting-date, occurrence of a spring flood in 2013 and moisture were the three variables significantly explaining species assemblages (respectively F=1.99, P=0.010; F=1.64, P=0.010; F=2.89, P=0.010).

In the GLMs performed on spider, carabid and plant and -diversities, abundance, and rarity, no interaction between flooding and prescriptions (i.e., fertiliser amount and cutting-date) were found, indicating that the impact of prescriptions, if any, was not influenced by flooding (Table 3).

Spider estimated -diversity was significantly influenced by fertiliser amount and moisture (Table 3). Sites under AES with 60 kg/ha nitrogen had higher estimated spider species richness (Fig. 3A).

Sites with low moisture level (classes 1 and 3, i.e. with less frequent floods) presented higher estimated spider species richness than sites with very high moisture level (class 5) (Fig. 3B). Spider abundance was significantly affected by fertilisation but post-hoc tests were not significant (Table 3 and Fig. 3C).

Spider -diversity was significantly influenced by fertiliser amount and cutting-date (Table 3 and Fig. 3D and3E). Spider mean -diversity increased with increasing fertiliser amount, with the mean -diversity being maximal with 60 kg/ha and free fertilisation. An opposite response was A c c e p t e d M a n u s c r i p t 12 found for the cutting-date: mean -diversity was lower with later cutting dates and was maximal in fields not under AES.

Carabid estimated -diversity was not influenced by predictive variables. Carabid abundance was significantly influenced by moisture (Table 3), with higher carabid abundances in sites presenting very high moisture level (class 5) (Fig. 3F).

Carabid -diversity was significantly influenced by the occurrence of a flooding in spring 2013, with the mean -diversity being higher in fields that were not flooded during spring 2013 (Fig. 3G).

Plant -diversity was significantly influenced by moisture (Table 3). Plant -diversity of sites with a high moisture level (Class 5) was significantly lower than those with a lower moisture level (class 1: Fig. 3H). Plant biomass (EVI) was significantly and positively impacted by moisture. Higher EVI was found in moister sites, although differences among means were not significant. Fertiliser amount, cutting-date, flooding, and moisture all had a significant effect on plant -diversity (Table 3) but no significant effect of fertiliser amount and cutting-date were found when comparing mean -diversity between classes (Fig. 3I,3J). Plant rarity was significantly impacted by moisture, with a higher number of rare plants in moister sites (Table 3 and Fig. 3K).

Discussion

Overall, our results demonstrated no significant impact of AES on -diversity, -diversity, abundance / biomass and assemblages of the three groups studied in flooded meadows. A positive effect was still found on rare plants. The absence of differences between meadows with vs. meadows without AES is in accordance with some previous studies in non-flooded habitats that focussed on spiders [START_REF] Knop | Effectiveness of the Swiss agri-environment scheme in promoting biodiversity[END_REF]Marshall, West, & Kleijn, 2006), carabids (Marshall, West, & Kleijn, 2006) and plants [START_REF] Kleijn | Agri-environment schemes do not effectively protect biodiversity in Dutch agricultural landscapes[END_REF] A c c e p t e d M a n u s c r i p t 13 Marshall, West, & Kleijn, 2006). However, the existence of different levels in AES prescriptions could potentially lower the impact of the most binding AES. Furthermore, meadows not under AES remain rather extensively managed. It is thus possible that AES prescriptions do not constitute a sufficient change in practices to have a detectable impact. The positive impact of AES contractualisation on protected plants might not be a consequence of a change in farmers' practices.

Indeed, farmers preferentially engage in AES fields which are less suitable for intensive farming [START_REF] Kleijn | The conservation effects of meadow bird agreements on farmland in Zeeland, the Netherlands, in the period 1989-1995[END_REF]. In our case, fields with higher moisture levels are preferentially engaged because soil bearing does not allow early cutting-dates. In the Loire Valley, most of the protected plants are hygrophilous and are thus located in the engaged fields. In a large-scale study, [START_REF] Kleijn | Mixed biodiversity benefits of agri-environment schemes in five European countries[END_REF] found no impact of AES on rare arthropods and plants, except for a positive one on plant rarity in two countries. Our results are partly in opposition but, like in [START_REF] Kleijn | Mixed biodiversity benefits of agri-environment schemes in five European countries[END_REF], the low number of rare species encountered prevents reliable estimates of AES impacts.

Spider assemblages and -diversity were significantly influenced by moisture which is in accordance with [START_REF] Desender | Diversity and conservation of terrestrial arthropods in tidal marshes along the River Schelde: a gradient analysis[END_REF], [START_REF] Pétillon | Influence of abiotic factors on spider and ground beetles communities in different salt-marsh systems[END_REF] and [START_REF] Lafage | Disentangling the influence of local and landscape factors on alpha and beta diversities: opposite response of plants and ground-dwelling arthropods in wet meadows[END_REF]. Cutting-date only influenced spider -diversity. Cutting-date has recently been shown to have little impact on spider -diversity and abundance, but a significant impact on traits (Lafage & Pétillon 2014), suggesting a potential impact on -diversity in accordance with our results.

We found spider -diversity to decrease when cutting-dates were delayed. That could be explained by the fact that the engaged farmers have to cut their fields in a very narrow time-frame in order to maximise the nutritional value of hays (that decreases over time: [START_REF] Nocera | Compatibility of delayed cutting regime with bird breeding and hay nutritional quality[END_REF]. In fields not under AES, the diversity of cutting dates would oppositely increase the -diversity of spiders.

As opposed to the biodiversity-productivity theory [START_REF] Grime | Control of species density in herbaceous vegetation[END_REF], sites fertilised with 60 kg/ha nitrogen supported highest spider -diversity. Sites not under AES were also not different from sites A c c e p t e d M a n u s c r i p t 14 with medium or low nitrogen inputs. This is in accordance with studies suggesting a "bottom-up" control of arthropod diversity [START_REF] Siemann | Experimental tests of effects of plant productivity and diversity on grassland arthropod diversity[END_REF][START_REF] Patrick | Brown" World Invertebrates Contradict "Green" World Biodiversity Theory[END_REF] mediated by plant and consumer biomass [START_REF] Borer | Plant diversity controls arthropod biomass and temporal stability[END_REF]. Nevertheless, these findings are still being discussed as, for example, Haddad, Haarstad, and Tilman (2000) found insect diversity to be negatively influenced by long-term fertiliser input. The lack of fertilisation effects on spider and carabid abundances could be explained by a threshold effect. Fertiliser inputs remained low, even in fields not under AES contract, compared to the large quantities of organic matter introduced in the system by winter floods [START_REF] Junk | The flood pulse concept: new aspects, approaches and applications -an update[END_REF]. Consequently, the fertiliser levels might remain too low to initiate a trophic cascade which is confirmed by the absence of impact of fertilisers on plant biomass and -diversity (see below).

As expected, carabids were only influenced by spring floods and moisture, for -diversity and abundance respectively. Carabids have been shown to recover less rapidly than spiders after spring floods [START_REF] Lafage | Short term recolonisation by arthropod after a spring flood, with a focus on spiders and carabids[END_REF], especially regarding species composition, which could explain the impact of spring floods on carabid -diversity. [START_REF] Gerisch | Community resilience following extreme disturbances: the response of ground beetles to a severe summer flood in a central European lowland stream[END_REF] demonstrated that carabid -diversity remains high after important flooding events, indicating persistent shifts in species assemblages. [START_REF] Gerisch | Community resilience following extreme disturbances: the response of ground beetles to a severe summer flood in a central European lowland stream[END_REF] and [START_REF] Lafage | Short term recolonisation by arthropod after a spring flood, with a focus on spiders and carabids[END_REF] finally show massive decreases in carabid abundance after spring floods. This dominance of small species could first be attributed to a sampling effect, although suction sampling is usually recommended to quickly obtain a representative sample of epigeic arthropod communities (e.g. [START_REF] Duffey | Comparative sampling methods for grassland spiders[END_REF]). In fact, [START_REF] Mommertz | A comparison of D-Vac suction, fenced and unfenced pitfall trap sampling of epigeal arthropods in agro-ecosystems[END_REF] considered it an inefficient way to sample large arthropods (such as Carabidae and Lycosidae). However, [START_REF] Brook | Experimental verification of suction sampler capture efficiency in grasslands of differing vegetation height and structure[END_REF] considered suction sampling an efficient technique to sample arthropods, including Carabidae, pending a sufficient sampling effort. Here we performed sampling duration and replication higher than recommanded by [START_REF] Brook | Experimental verification of suction sampler capture efficiency in grasslands of differing vegetation height and structure[END_REF] for spiders (16x2s recommanded vs 5x10x15s performed)

A c c e p t e d M a n u s c r i p t 15 and slightly inferior than recommanded by [START_REF] Brook | Experimental verification of suction sampler capture efficiency in grasslands of differing vegetation height and structure[END_REF] for beetles (54,8x15,6s recommended vs 5x10x15s performed) with similar sampling area. We can thus consider that our results were not biased by the sampling technique, and that the dominance of small aerial dispersers was a consequence of an environmental filter, here the stochasticity due to flooding [START_REF] Zulka | Carabids in a Central Europe floodplain: species distribution and survival during inundations[END_REF].

Plant -diversity, -diversity, biomass and assemblages were systematically influenced by flooding (i.e., moisture and occurrence of spring floods) because of both its large spatial extent (including both AES and non-AES meadows) and its duration (here several months). These results are in accordance with previous studies. The central role of moisture in shaping plant communities has indeed been demonstrated by many authors (e.g., [START_REF] Dwire | Plant biomass and species composition along an environmental gradient in montane riparian meadows[END_REF][START_REF] Wassen | Patterns in vegetation, hydrology and nutrient availability in an undisturbed river floodplain in Poland[END_REF][START_REF] Zelnik | Distribution of plant communities, ecological strategy types and diversity along a moisture gradient[END_REF]. Moisture's role on plant diversity has also been demonstrated. For example, [START_REF] Zelnik | Distribution of plant communities, ecological strategy types and diversity along a moisture gradient[END_REF] found plant and -diversities to be strongly and negatively influenced by moisture in wetlands. Plant rarity was also positively affected by moisture, which is not surprising as most plant species protected in the area are hygrophilous or meso-hydrophilous species.

Regarding AES prescriptions, cutting-date significantly influenced -diversity and plant assemblages. Late cutting dates are indeed well known to induce vegetation modifications by favouring annual plant species; maximum plant -diversity being usually observed for late cuttingdates (mid-June to mid-July) in European grasslands (e.g. [START_REF] Critchley | The contribution of English agri-environment schemes to botanical diversity in arable field margins[END_REF].

Fertilisation level had a significant impact only on plant -diversity, which is in accordance with [START_REF] Klimek | Additive partitioning of plant diversity with respect to grassland management regime, fertilisation and abiotic factors[END_REF] who found plant species -diversity being influenced, at a local scale, by fertilisation input. A significant reduction of -diversity and a biomass increase are usually observed even for low levels of fertilizers (e.g., [START_REF] Plantureux | Biodiversity in intensive grasslands: Effect of management, improvement and challenges[END_REF]. Nevertheless, in flooded grasslands, no effect of fertilisation on plant diversity was reported under 90 kg/ha/yr A c c e p t e d M a n u s c r i p t 16 [START_REF] Bonis | Fertilisation et qualité de l'eau en prairies naturelles humides (marais de l'Ouest)[END_REF]. Thus, the fertilisation level permitted in sites under AES and effectively used in sites not under AES, may be too low to allow a detection of their impact.

Our results suggest that flooding might be a stronger driver of vegetation and arthropod assemblages than differences in cutting dates or low fertilizer inputs. The impact of flooding and management practices seems to vary with organism mobility [START_REF] Adis | Terrestrial invertebrates inhabiting lowland river floodplains of Central Amazonia and Central Europe: a review[END_REF]. Indeed, we found plants to be the organisms that are the most sensitive to perturbations induced by flooding, and also to variations in management practices. Conversely, carabid assemblages, mainly composed of highly mobile small species, were only influenced by flooding.

Our results further suggest that the regulation of cutting dates and low input fertilisers of grasslands has few, if any, effects on arthropods and plants compared to those induced by a prolonged flooding.

Conservation actions in such ecosystems might have to focus on maintaining and/or enhancing hydrological functioning in order to rewild those ecosystems [START_REF] Merckx | Reshaping agri-environmental subsidies: From marginal farming to large-scale rewilging[END_REF].

Nevertheless, because natural meadows are in constant regression by conversion to intensive agriculture (Millennium Ecosystem Assessment 2005), AES can yet be considered an efficient way of maintaining an endangered habitat, despite their limited efficiency in flooded systems.

  value in agricultural landscapes, predator arthropods like spiders and carabid beetles remain relatively less studied in the context of AES compared to other taxa.

  and using the betapart R package(Baselga & Orme

  under vs. not under AES for spiders ( ²=49, P=0.473), carabids ( ²=45.60, P=0.555) or plants ( ²=46.74, P=0.625).

Fig. 1 .

 1 Figure caption

Fig. 2 .

 2 Fig. 2. CCA on spider species. Sites under AES are represented by triangles and sites not under

Fig. 3 .

 3 Fig. 3. Variations in mean response variables depending on significant factors by GLM (different

Figure 1 .

 1 Figure 1. Lafage and Pétillon, 2015

  Figure 2 : Lafage and Pétillion, 2015 576

Table 3 .

 3 GLM selected by stepwise procedure for spider, carabid and plant abundance / biomass (approximated by EVI index), estimated richness ( -diversity), -diversity, and rarity (for plants only).

	Group Response	Variables kept	F	P
		Estimated species richness
	Spiders	( -diversity)	Fertilisers	4.28	0.008
			Moisture	4.45	0.003
			F x VT	1.92	0.101
		Abundance	Fertilisers	3.33	0.024
			Moisture	1.75	0.150
			F x VT	1.99	0.090
		-diversity	Fertilisers	1.59	0.020
			Cutting date	1.69	0.020
	Carabids Estimated species richness
		( -diversity)	-	-	-
		Abundance	Fertilisers	1.16	0.330
			Moisture	2.89	0.028
			F x VT	2.11	0.074
		-diversity	Flooding	1.03	0.010

Acknowledgements

We would like to thank the CORELA for its support, Charlotte Papin and Thomas Joubin for field and laboratory assistance, Arnaud Horellou for his help in identifying problematic carabids, and Aldyth Nys and Len Gambla for editing the English. Two anonymous referees provided very useful

 2. Per site means ± s.e. of response variables for fields under AES or not (Free), with F and P values for fixed factor (contract), within-subject factor (site) and their interaction (R-ANOVA).

Abundance: total number of individuals per 0.12m². Estimated species richness: average of four non-parametric estimators based on species incidence: Chao1, Jacknife1, Jacknife2 and Bootstrap.

AES