domain: info phys spi

text:
Benjamin Franc
email: benjamin.francois@onera.fr

Cyril Polacsek

Rapha Ël Barrier

Zonal Detached Eddy Simulation of the Fan-OGV Stage of a Turbofan Engine: Part I -Methodology, Numerical Setup and Aerodynamic Analysis

The present article deals with the Zonal Detached Eddy Simulation of the fan module of a modern turbofan engine for the prediction of the broadband noise due to the interaction of the fan turbulent wakes with the stationary outlet guide vanes. The simulation relies on a hybrid RANS/LES approach with a zonal strategy: the core airflow is treated in RANS while the bypass airflow is solved with the hybrid approach. The simulation was performed during four revolutions and statistical convergence was reached. Inspections of the flow-fields

INTRODUCTION

Because of the significant reduction of tonal noise in modern turbofans, the broadband component of the overall perceived noise has become a growing contribution and is nowadays a major topic of concern for aircraft engine manufacturers [START_REF] Peake | Modern Challenges Facing Turbomachinery Aeroacoustics[END_REF]. The present work adresses a hybrid RANS/LES methodology to predict this noise contribution on a fan module of a civil modern turbofan at approach conditions. Only the aerodynamic simulation and the associated results are presented here, the broadband noise analyzes are discussed in a complementary (Part II) paper [START_REF] Polacsek | Zonal Detached Eddy Simulation of the Fan-OGV Stage of a Turbofan Engine: PartII -Broadband Noise Predictions[END_REF].

In the fan module, a major contribution of the broadband noise is the interaction of the turbulent structures generated in the fan wakes with the outlet guide vanes (OGV) located downstream [START_REF] Moreau | Ranking of Fan Broadband Noise Sources based on an Experimental Parametric Study[END_REF].

The turbulent structures are scattered by these vanes which generate radiating acoustic waves in the upstream and downstream directions.

Because of the high Reynolds number involved (around one million), turbulence scale resolved simulations of a fan blade or a fan stage of a turbofan engine require a significant computational effort. For this reason, such simulations remain scarce in the literature. Indeed, the high Reynolds number implies tremendous mesh refinement in the boundary layer for Wall-Resolved Large Eddy TURBO-21-1140 -Franc ¸ois 2

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Journal of Turbomachinery Simulations (WRLES). In Wall-Modeled LES (WMLES), the use of wall law enables to reduce the computational effort compared to WRLES but the mesh requirement still strongly increases with the Reynolds number. An alternative way is to resort to hybrid RANS/LES approaches in which the whole boundary layer is solved with a RANS modeling. Hence, their numerical cost is much less dependent on the Reynolds number. This simulation strategy is followed here and relies on the Zonal Detached Eddy Simulation from Deck et al. [START_REF] Deck | Recent Improvements in the Zonal Detached Eddy Simulation (ZDES) Formulation[END_REF]. This approach has already been used by Bonneau et al. [START_REF] Bonneau | Turbofan Broadband Noise Predictions using a 3-D ZDES Rotor Blade Approach[END_REF] on a turbofan for the prediction of broadband noise in which only a fan blade was simulated. Aerodynamic features of the wake were extracted (wake width, velocity deficit, turbulent kinetic energy) to feed an Amiet-like code to compute the noise radiating by the OGV.

Franc ¸ois et al. [START_REF] Franc ¸ois | Zonal Detached Eddy Simulation of the Fan-OGV Stage of a Modern Turbofan Engine[END_REF] extended the work of Bonneau et al. by performing simulations of the fan blade with the outlet guide vanes, giving access to the unsteady pressure fluctuations on the vanes.

The acoustic predictions of these simulations were presented in a dedicated conference paper by Polacsek et al. [START_REF] Polacsek | Turbofan Broadband Noise Predictions Based on a ZDES Calculation of a Fan-OGV Stage[END_REF].

To the authors' knowledge, previous works relying on turbulence scale resolved simulations for aeroacoustic of turbofans were performed mainly on the NASA Source Diagnostic Test (SDT) configuration with different numerical approaches: WRLES (Kholodov et al. [START_REF] Kholodov | Wall-Resolved Large Eddy Simulation of a Realistic Turbofan Rotor for Noise Prediction[END_REF]), WMLES (Leonard et al. [START_REF] Leonard | Large Eddy Simulation of a Scale-Model Turbofan for Fan Noise Source Diagnostic[END_REF], Arroyo et al. [START_REF] Arroyo | Large Eddy Simulation of a Scale-Model Turbofan for Fan Noise Source Diagnostic[END_REF], Hah and Romeo [START_REF] Hah | LES Investigation of Wake Development in a Transonic Fan Stage for Aeroacoustic Analysis[END_REF]), hybrid RANS/LES (Shur et al. [START_REF] Shur | Unsteady simulations of a fan/outlet-guide-vane system: Aerodynamics and turbulence[END_REF], Suzuki et al. [START_REF] Suzuki | Unsteady simulations of a fan/outlet-guide-vane system: broadband-noise computation[END_REF]) and Lattice Bolzmann method (Casalino et al. [START_REF] Casalino | Turbofan Broadband Noise Prediction using the Lattice Boltzmann Method[END_REF]). The present turbofan configuration (ACAT1 fan stage) treated in this paper is quite new in the literature [START_REF] Meyer | Instantaneous Flow Field Measurements in the Interstage Section between a Fan and the Outlet Guiding Vanes at Different Axial Positions[END_REF][START_REF] Kissner | ACAT1 Benchmark of RANS-Informed Analytical Methods for Fan Broadband Noise Prediction-Part I-Influence of the RANS Simulation[END_REF][START_REF] Gu Érin | ACAT1 Benchmark of RANS-Informed Analytical Methods for Fan Broadband Noise Prediction: Part II-Influence of the Acoustic Models[END_REF] and only a few partners from the associated project performed turbulence scale resolved simulations (Lewis et al. [START_REF] Lewis | ACAT1 Fan Stage Broadband Noise Prediction Using Large-Eddy Simulation and Analytical Models[END_REF],

Tucker and Wang [START_REF] Tucker | Eddy Resolving Strategies in Turbomachinery and Peripheral Components[END_REF]).

The present paper is the continuation of the work from Franc ¸ois et al., Polacsek et al. [START_REF] Franc ¸ois | Zonal Detached Eddy Simulation of the Fan-OGV Stage of a Modern Turbofan Engine[END_REF][START_REF] Polacsek | Turbofan Broadband Noise Predictions Based on a ZDES Calculation of a Fan-OGV Stage[END_REF]:

a new Zonal Detached Eddy Simulation was performed accounting for a more realistic boundary layer upstream of the fan, the turbulence scale-resolved area was slightly extended and the outlet pressure in the bypass airflow was adjusted to reduce the massflow rate discrepancy with the measurement. Also, a large dataset of measurements including the final calibrations and the uncertainties, not present in the conference papers, are presented and compared to the numerical results. RANS results are also included in the comparison. The paper is organized as follows.

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First, the paper presents the main features of the fan geometry and operating point. Then, several aspects of the CFD strategy such as the methodology, the mesh critera, the boundary conditions and the numerical parameters are discussed. Third, analysis of the convergence of the simulation are addressed. Fourth, three-dimensional analysis of the flow inspecting the consistency of the ZDES solution are carried out. Finally, comparisons with hot-wire measurements performed in AneCom test falicity [START_REF] Meyer | Instantaneous Flow Field Measurements in the Interstage Section between a Fan and the Outlet Guiding Vanes at Different Axial Positions[END_REF] are discussed.

PRESENTATION OF THE CONFIGURATION

METHODOLOGY

Zonal Detached Eddy Simulation

The Zonal Detached Eddy Simulation (ZDES) developped by Deck [START_REF] Deck | Recent Improvements in the Zonal Detached Eddy Simulation (ZDES) Formulation[END_REF] and implemented in the elsA code [START_REF] Cambier | The Onera elsA CFD Software: Input from Research and Feedback from Industry[END_REF] is used here. This formulation offers the possibility to treat different parts of the computational domain with a specific ZDES formulation or a full URANS solving. This approach has already been used on aircraft, space launchers, jet flows and turbomachinery [START_REF] Bonneau | Turbofan Broadband Noise Predictions using a 3-D ZDES Rotor Blade Approach[END_REF][START_REF] Deck | High-Fidelity Simulations of Unsteady Civil Aircraft Aerodynamics: Stakes and Perspectives. Application of Zonal Detached Eddy Simulation[END_REF][START_REF] Ri Éra | Zonal Detached-Eddy Simulation applied to the Tip-Clearance Flow in an Axial Compressor[END_REF]. The zonal aspect enables to alleviate the computational cost compared to other DES techniques with areas treated with a RANS solving, requiring a reduced mesh density. Also, such approach offers a large flexibility for the user to choose the most suitable ZDES formulation with respect to the flow physics to deal with. The present paper only describes the ZDES mode 2 (refering to Deck et al. [START_REF] Deck | Recent Improvements in the Zonal Detached Eddy Simulation (ZDES) Formulation[END_REF]) used in the simulation and the reader can refer to the aforementioned paper for further information.

The ZDES mode 2 allows the boundary layer to be solved with an URANS treatment, the remaining part being treated by a LES solving with an automatic detection of both areas. To know whether the computed cell is in the attached boundary layer or not, a shielding function f d , inherited from the Delayed Detached Eddy Simulations (DDES) from Spalart et al. [START_REF] Spalart | A New Version of Detached-Eddy Simulation, Resistant to Ambiguous Grid Densities[END_REF], is evaluated. It reads:

r d = ν + ν U i,j U j,i κ 2 d 2 w , f d = 1 -tanh (8r d ) 3
where ν is the eddy viscosity solved in the equation of the Spalart-Allmaras turbulence model [START_REF] Spalart | A One-Equation Turbulence Model for Aerodynamic Flows[END_REF] 2 , ν the molecular viscosity, U i,j the velocity gradient, κ the Karman constant, d w is the distance to the wall. The parameter r d is equal to one in the logarithmic area of the boundary layer and vanishes at the edge of the boundary layer. Consequently, the function f d equals zero in the boundary layer and activates the URANS mode. Outside the boundary layer, it equals one and allows the switch 2 In the classic DDES from Spalart et al. [START_REF] Spalart | A New Version of Detached-Eddy Simulation, Resistant to Ambiguous Grid Densities[END_REF], the variable νt is used. TURBO-21-1140 -Franc ¸ois 5

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Journal of Turbomachinery to the LES mode. The ZDES mode 2 from Deck et al. presents similarities with the DDES from Spalart et al. [START_REF] Spalart | A New Version of Detached-Eddy Simulation, Resistant to Ambiguous Grid Densities[END_REF]. The main difference concerns the choice of the characteristic mesh length. In DDES, it is based on the largest cell size such as ∆ = max(∆x, ∆y, ∆z) while in ZDES, it reads:

∆ =      ∆ max = max(∆x, ∆y, ∆z) if f d < f d0 ∆ vol = (∆x∆y∆z) 1/3 if f d > f d0
where f d0 is a constant equal to 0.8. Deck et al. made comparisons between the DDES and the ZDES mode 2 on various applications (mixing layer, backward facing step, airfoil). They highlight that ZDES keeps the strong assets of DDES such as the treatment of the attached boundary layer while improving other aspects such as reducing the delay in the formation of the instabilities.

Flow Domains

Repartition of RANS and ZDES zones

The objective being the simulation of the interaction between the fan wake with the OGV in the bypass airflow, the core airflow can be solved with an URANS solving, reducing the mesh requirements in this area. Also, the upstream turbulence rate measured in the experimental facility upstream of the fan is very low (around 0.3%) [START_REF] Meyer | Instantaneous Flow Field Measurements in the Interstage Section between a Fan and the Outlet Guiding Vanes at Different Axial Positions[END_REF]. Hence, the noise associated with the impingement of the infinite inflow turbulence on the fan is negligible compared to the RSI noise. Thus, an URANS modeling is sufficient upstream of the fan. All the remaining areas of the computational domains are treated with the ZDES formulation described in section 3.1. The border between the URANS domain and the ZDES mode 2 domain must be chosen with care at the separation between the primary and the bypass airflow. Indeed, the ZDES mode 2 domain needs to be large enough to ensure that the flowpaths nearby the fan blade, going then into the bypass airflow and generating wakes, are well treated in ZDES mode 2. Otherwise, part of the fan wakes interacting with the OGV will be solved in RANS and they will remain RANS-like in the bypass airflow domain.

An illustration of the RANS/DES zones on single channel computational domain is given in Fig. 2.

TURBO-21-1140 -Franc ¸ois 6 Consequently, a more favorable option is to change the blade number of the OGV to get a suitable divisor and allow the use of periodic boundary conditions instead. Even if the periodicity is still questionnable for the turbulence structures between adjacent channels, the spectral content is believed to be conserved through these periodic boundary conditions. This strategy has already been justified and used by several authors on the NASA SDT for broadband noise predictions [START_REF] Leonard | Large Eddy Simulation of a Scale-Model Turbofan for Fan Noise Source Diagnostic[END_REF][START_REF] Arroyo | Large Eddy Simulation of a Scale-Model Turbofan for Fan Noise Source Diagnostic[END_REF][START_REF] Hah | LES Investigation of Wake Development in a Transonic Fan Stage for Aeroacoustic Analysis[END_REF]. The same strategy was followed on the ACAT1 configuration by Lewis et al. [START_REF] Lewis | ACAT1 Fan Stage Broadband Noise Prediction Using Large-Eddy Simulation and Analytical Models[END_REF] for WMLES.

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OGV Rescaling and aerodynamic impact

The number of the OGV is thus reduced from 44 to 40. To keep the same flow pattern, the solidity is kept constant meaning that the chord is increased by 10%, the leading-edge position is unchanged. Such a blade number modification allows to reduce the computational domain to one fan channel and two OGV channels. The unchanged geometrical parameters are the solidity, the leading-edge position, its sweep and lean angles, the thickness-to-chord and angles law along the streamwise variable and inner and outer duct walls.

The modified parameters with respect to the original geometry are the number of blades (44 to 40), the chord (+10%), the aspect ratio and the thickness.

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Journal of Turbomachinery RANS simulations of the fan-OGV configuration with the nominal number of OGV and with the modified number of rescaled OGV were performed at the same massflow by Franc ¸ois et al. [START_REF] Franc ¸ois | Zonal Detached Eddy Simulation of the Fan-OGV Stage of a Modern Turbofan Engine[END_REF].

Inspection of the absolute flow angles, absolute Mach number at position upstream and downstream of the OGV show identical radial evolution. Same conclusions were drawn regarding the pressure maps distribution on the walls. The conservation of the solidity is a key aspect in the OGV modification. First, it enables to get a similar mean velocity field to convect the fan wake through the vanes. Second, a modification of solidity can affect the vane aeroacoustic response due to wake interaction, as shown by Posson et al. [START_REF] Posson | Parametric Study of Gust Scattering and Sound Transmission through a Blade Row[END_REF].

Computational domain

The computational domain is composed of one fan and two OGV inter-blade channels. The fan and the OGV domains are solved in their respective frame of reference. The inlet of the computational domain is located at four fan chords upstream of the fan leading-edge while the outlet is located at three vane chords downstream of the vane trailing-edge.

Boundary Conditions

The modification of the OGV geometry mentioned in the previous section enables to get the same azimuthal periodicity with one fan blade and two vanes. As a consequence, periodic boundary conditions can be used for the azimuthal border of the computational domain for the unsteady simulation. At the interface between the rotating domain of the fan and the fixed domain of the vanes, a sliding mesh treatment is performed. It relies on interpolation of the state vector of a donor grid on a receive grid and then on a half-sum between the donor and the receiver cells from both domain on the conservative variables. Errors of interpolation on a few cells between the moving grids were detected by Polacsek et al. [START_REF] Polacsek | Turbofan Broadband Noise Predictions Based on a ZDES Calculation of a Fan-OGV Stage[END_REF], generating spurious noise sources. Corrections were brought in the elsA flow solver in the moving grid BC treatment and these interpolations errors have now fully disappeared in the ZDES simulation presented in this paper and the companion paper dedicated to the acoustic analysis.

At the inlet of the computational domain, stagnation pressure, stagnation enthalpy and absolute velocity directions are imposed. For the outlet of the core and the bypass airflow, a radial TURBO-21-1140 -Franc ¸ois 8

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Journal of Turbomachinery equilibrium is imposed with a user-prescribed pressure at the lower wall. The inlet and outlet BC are combined with sponge layer to limit spurious reflections (see further details in Sec. 3.4.2).

Compared to the ZDES performed by Franc ¸ois et al. [START_REF] Franc ¸ois | Zonal Detached Eddy Simulation of the Fan-OGV Stage of a Modern Turbofan Engine[END_REF], two modifications were brought in the simulation to better match the experimental conditions:

-A radial heterogeneous profile of stagnation pressure (instead of an uniform one) is imposed at the inlet of the present simulation to match the hot-wire measurements upstream of the fan (see Fig. 3-a). The shroud boundary layer impinging the fan has a significant effect on the tip gap flow. With this radial profile, the present ZDES is thus more realistic than the previous one.

Axial velocity profile (Fig. 3-b) highlights a quite good agreement with the measurements, with discrepancies lower than 2 m/s.

-The user-prescribed pressure at the bypass lower wall was slightly increased to better match the measured massflow rate. Discrepancies between measured and simulated massflow rates reduce from +1% to -0.25%. Because the operating point is close to surge, these differences may have a significant influence on the shape of the wakes and tip gap flows impinging the OGV. Furthermore, flow separation are observed on both fan and OGV, with significant effects on acoustic radiation, as discussed in the companion paper [START_REF] Polacsek | Zonal Detached Eddy Simulation of the Fan-OGV Stage of a Turbofan Engine: PartII -Broadband Noise Predictions[END_REF].

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Mesh

Mesh criterion

Two sets of criteria were used to build the present mesh. The first relies on internal best practices concerning the use of the ZDES mode 2. The cell size verifies ∆x + , ∆y + , ∆z + < 200 in the free shear flow areas, namely a cell size lower than 0.6 mm for the present mesh. The first wall mesh size verifies ∆y + ≤ 1.

The second criterion relies on the aeroacoustic mechanism at stake. The impinging turbulent wake from the fan blade can be modelled by a set of hydrodynamic waves. The impingement of each hydrodynamic wave, also called gust, on the vane generates acoustic waves with the same frequency. Among the different waves at stake and given the Mach number of the considered flow, the gust wavelength is here the most stringent. Its expression reads λ h = U c f -1 where U c is the local convection speed and f is the frequency. Preliminary RANS simulations show that in the interstage area, the absolute velocity ranges from 100 m/s and 140 m/s. Accounting for the smallest velocity value and sampling the wavelength by 20 points leads to a mesh size of 0.25 mm at 20 kHz, (human ear upper limit frequency). Such cell size would imply for the intended computational domain a mesh of 3 billions cells. An acceptable trade-off between cost and accuracy is to select a cell size of 0.5 mm, leading to a mesh of 1/8 of this grid size (e.g. 400 million cells) while ensure a sampling of 20 points at 10 kHz.

Mesh characteristics

Repartition of points Build following the criteria mentionned above, the mesh has a total cell number equal to 380 millions. The mesh used is structured and multi-blocks. Its first mesh size is three micrometers and corresponds to y + values equal to 1 at the cell center. Its main characteristics are gathered in Fig. 4 and sectional views are given in Fig. 5. centimeters downstream of the OGV.

Buffer areas

Flow Solver and Numerical Parameters

The flow solver is the elsA software [START_REF] Cambier | The Onera elsA CFD Software: Input from Research and Feedback from Industry[END_REF], developed at ONERA. This compressible flow solver is based on a cell centered finite volume technique and structured multiblock meshes. The time scheme is achieved by an implicit second order scheme based on a Newton algorithm. The timestep has been set to 3.2 × 10 -7 s. The choice was mainly driven by acoustic CFL 3 number considerations and computational cost (the selected timestep is small enough to capture the turbulent structures at stake). It corresponds to a convective CFL number around 36 in the smallest cells in the boundary layer and of 0.35 for cells the length of which is 0.5 mm. This timestep samples the fan blade passing periods by 2400 and the revolution by 48000. 5 sub-iterations are used in the inner-loop of the time scheme and the residuals decrease by one order of magnitude.

3 Courant Friedrichs Lewy TURBO-21-1140 -Franc ¸ois 11

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The convective flux discretization is treated with the AUSM (Advection Upstream Splitting Method) scheme with a third order limiter. The turbulence model used is the Spalart-Allmaras model [START_REF] Spalart | A One-Equation Turbulence Model for Aerodynamic Flows[END_REF].

The simulation was performed on the supercomputers from CINES 4 . The simulation is done on 28 nodes and 672 cores, the total computational time is 2 million of CPU hours. Nearly four full revolutions were simulated.

Time Convergence

Initialization setup and Numerical transient

To reduce the numerical transient in the ZDES, a preliminary set of RANS and then URANS simulations were performed. The URANS simulation was run until the massflow rate was converged, namely two complete revolutions.

The time-length of the numerical transient is here determined by the convergence of the timeaveraged quantities (over a large time-width with respect to the blade period) of the flow quantities either global (massflow) or local (axial momentum on a numerical probes).

Statistical convergence

For the convergence of the statistics, the numerical transient of the signal is removed from the complete signal. Only the portion from t = 40 FBP to t = 76 FBP is used to perform the statistics.

Because the flow quantities exhibits strong deterministic signatures due to fan-OGV interaction in both the fan and the OGV computational domain, a cyclostationnary (or phase-averaged) decomposition of the signal is used. Inspired by the pioneer idea of Hussain and Reynolds [START_REF] Hussain | The Mechanics of an Organized Wave in Turbulent Shear Flow[END_REF],

the signal is split into a deterministic and a stochastic part u(x, t) = u cyclo (x, t) + u stoc (x, t) where u cyclo (x, t) contains the deterministic variation of the signal and its time averaging and u stoc (x, t)

the remaining part of the turbulent signal. The cyclostationnary signal u cyclo (x, t) is calculated with the number of fan blade passages equal to

N (t) = E T -1 BP (t -t 0 )
where E is the floor function,

T BP is the period of one blade passage and t 0 is the duration in time of the numerical transient.

This relation enables to see the progressive convergence of the cyclostationnary signal. The last period of the cyclostationnary signal is then used to compute the fluctuating part. In the fan domain, the OGV blade passage period is used while in the OGV domain, the fan blade passage period is used.

A direct application is performed on the axial momentum signal on the numerical probe located at 90% of channel height near the OGV leading-edge. during six FBP and the cyclostationnary signal. In the cyclostationnary signal, the stochastic part of the signal is filtered. The identical shape of this signal between the successive fan blade periods indicates that the signal is phase-averaged. Accurate repeatability of the phase-averaged FBP signatures is a good indicator of the convergence of the periodic contributions to be assessed in view of cyclostationnary analyses. In contrast, the instantaneous signal exhibits different velocity deficits for each fan blade period due to the stochastic nature of turbulence.

The phase-averaged property of the signal indicates that the time signal (without the numerical transient) is long enough to get converged cyclostationnary averages and thus reliable informations for the acoustic prediction presented in the companion paper. The turbulent signature used for broadband noise analyzes is assessed by subtracting the cyclostationnary part to the instantaneous signal. The convergence of this part of the signal is studied in Fig. 7-b : the Root Mean Square (RMS) is calculated over several numbers of FBP and deviations with the RMS evaluation are evaluated. It shows that for this numerical probe within the tip gap flow, the RMS estimation is converged with an accuracy of 5%. Lower RMS convergence levels (2%) are found on other numerical probes at mid-height, not shown here for conciseness.

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VERIFICATION OF ZDES

This section focuses on the analysis of the aerodynamics flow-field and on the consistency of the flow solution obtained with the ZDES approach. separates at the leading-edge of the fan for this operating point, turbulent structures are generated there and are convected downstream. Figure 8 illustrates also a benefit of the ZDES approach:

thanks to the reduced mesh effort in the boundary layers, a high grid density (cell width of 0.5 mm) could be used in the free-shear areas allowing the capture of very small turbulent structures.

Such mesh density in these areas would require a larger number of cells in the whole mesh with a WMLES approach.

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Convection of the fan wakes through the OGV

The main source of broadband noise is the interaction of the turbulent structures from the fan wake with the OGV walls. An important key point in this simulation is to ensure that the turbulence is properly convected from the fan through the OGV. (in the free shear flow areas). For both fan and OGV blades, this RANS solving is consistent and seems qualitatively to encompass the whole boundary layer. A noticeable point is the rapid switch from RANS to LES at the trailing-edge of the blade (visible in the zoom in Fig. 9). The RANS boundary layer velocity profile degenerates into turbulent eddies due to a good detection of a free-shear flow area and the specific features of the ZDES described in the work of Deck et al. [START_REF] Deck | Recent Improvements in the Zonal Detached Eddy Simulation (ZDES) Formulation[END_REF]. Similar conclusions with the same approach were drawn by Gand on a flow separation on a spoiler [START_REF] Gand | Zonal Detached Eddy Simulation of a Civil Aircraft with a Deflected Spoiler[END_REF] and Verri ère et al. on a jet flow [START_REF] Verri Ère | Zonal Detached-Eddy Simulations of a Dual-Stream Jet[END_REF].

A second noticeable point concerns the shielding function shape around the OGV walls: the interaction of the turbulent structures from the fan wake with the OGV do not (qualitatively) degrade the shielding of the boundary layer (zooms in Fig. 9). Complementary analysis on the shieding function in the tip gap flow on the same configuration are shown by Franc ¸ois et al. [START_REF] Franc ¸ois | Zonal Detached Eddy Simulation of the Fan-OGV Stage of a Modern Turbofan Engine[END_REF]. They all demonstrate a good robustness and maturity of the approach for turbomachinery flows.

VALIDATION AGAINST MEASUREMENTS

Measurements were performed on the selected fan configuration at the studied operating point.

Hot-wire measurements in between the fan and the OGV for the three directions of velocity are available. The reader can refer to the paper of Meyer et al. [START_REF] Meyer | Instantaneous Flow Field Measurements in the Interstage Section between a Fan and the Outlet Guiding Vanes at Different Axial Positions[END_REF] for further information.

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Aerodynamic performances

Measurements Present ZDES Previous ZDES [START_REF] Franc ¸ois | Zonal Detached Eddy Simulation of the Fan-OGV Stage of a Modern Turbofan Engine[END_REF] Core massflow [kg/s] 1 highlights that the aerodynamic performances are retrieved by the present ZDES with a maximum discrepancy lower than 0.4% whereas the previous ZDES [START_REF] Franc ¸ois | Zonal Detached Eddy Simulation of the Fan-OGV Stage of a Modern Turbofan Engine[END_REF] exhibits a massflow difference of 1% with the measurements.

Two-dimensional map visualizations

The ZDES solution has been extracted over a cross-section at HW1 position in order to perform mean flow and wake analyses, by splitting periodic and fully turbulent contributions, and to make comparisons with the latest available measurements. Cyclostationnary axial and tangential velocities are compared between the measurements and the simulation in Fig. 10. A close agreement is obtained on both levels and shape: wakes and tip gap flows are also well retrieved. The mechanisms generating this background turbulence are not understood yet. In the simulation, no background turbulence is predicted. Same observations was made by all the partners performing numerical simulations (RANS or LES) in the EU project (see Lewis et al. [START_REF] Lewis | ACAT1 Fan Stage Broadband Noise Prediction Using Large-Eddy Simulation and Analytical Models[END_REF] for instance). the velocity deficit is over-estimated for the relative radii at 50% and at 75% of the duct height by 10 -15%. RANS results predict also quite well the wake features at 50% and 75% channel height with the same velocity deficit as ZDES but with a smaller width. At 97%, the tip gap flow is visible on the azimuthal profiles with a secondary dip or peak. The main dip/peak and the secondary ones are quite well captured by the ZDES with a slightly lower intensity for the latter one compared to the measurements. Globally, the shape and the levels of the velocity variation over the azimuthal extent are quite consistent between ZDES and measurements. For RANS results, both models tend to overestimate the main dip/peak by factor two. As a consequence, the intensity of the secondary dip/peak is not correct either despite their positions are consistent with TURBO-21-1140 -Franc ¸ois 22

Radial Profiles

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Journal of Turbomachinery solving areas) and a correct convection of the broadband turbulent structures to the OGV. The overall analysis of the aerodynamics flow underlines a consistent behavior of the RANS/LES approach applied to a complex turbomachinery flow. The key aerodynamic phenomena responsible for the generation of broadband noise such as the wake interaction in the secondary airflow are qualitatively well captured.

A comparison between the numerical results and a large dataset of hot-wire measurements in between the fan and the OGV using the final calibrations of the project was presented. Global performances (massflow, compression ratio) are better retrieved. Two-dimensional flow maps are well reproduced both in shape and levels by the simulation. Analysis of the radial profiles highlights an excellent agreeement of the RMS quantities between ZDES results and measurements, particularly in the tip gap flow area, while RANS results do not predict consistent radial and azimuthal profiles. Finally, azimuthal profiles comparisons, enabling the inspection of wake thickness and deficit, reveals quite consistent ZDES results with the measurements. These results demonstrate a good maturity of the ZDES approach for complex turbomachinery flows.

The present paper focused only on aerodynamic aspects whereas broadband noise assessment is detailed in the companion paper [START_REF] Polacsek | Zonal Detached Eddy Simulation of the Fan-OGV Stage of a Turbofan Engine: PartII -Broadband Noise Predictions[END_REF]. This involves complementary turbulent flow analyzes, and sound radiation through dedicated processing methods respectively based on extended Amiet's theory and FWH analogy.

Fig. 1 .

 1 Fig. 1. Sketch of the rig set-up at AneCom's UFFA (reprint with TurboNoiseBB Consortium permission) with the hot-wire probes.

Fig. 2 .

 2 Fig. 2. Repartition of the RANS and ZDES mode 2 areas in the computational domain. The border between URANS and ZDES mode2 area from the former simulation [6] is indicated. The borders of the present simulation are shown with blue and red colors.

3. 2 . 2

 22 Modification of the geometry Motivation To reduce the numerical cost, only a few interblade channels are simulated. The current number of blades (20 for the fan, 44 for the OGV) is unfavorable to reduce the computational domain to a few inter-blades channels. For unsteady RANS simulations, classic phaselag boundary conditions allows the reduction to one channel. Because they are currently based on the usual Fourier decomposition, they are unadapted for the convection of broadband structures.

Fig. 3 .

 3 Fig. 3. Comparison of the absolute stagnation pressure (a) and the axial velocity (b) between the hot-wire measurements and the simulation upstream of the fan (position 0)

10 A c c e p t e d M a n u s c r i p t N o t C o p y e d i t e dFig. 4 .Fig. 5 .

 1045 Fig. 4. Repartition of points of the mesh

Figure 6

 6 gives an illustration by showing the evolution of the bypass air mass flow non-dimensioned by its final value 5 at t = 76 FBP6 . Both the instantaneous signal and the time-averaged one over ten FBP are shown. The abscissa axis is given in fan blade passage (20 equals a complete revolution). From the URANS simulation, the massflow shifts slighly because of the flow solution is quite different between the RANS and the ZDES in the flow separated areas. The massflow curve shows that the massflow is stabilized after two revolutions (variations of the time-averaged quantity on ten fan blade passages are lower than 0.2%). Flow quantities such as the axial momentum and the static pressure on numerical probes (not shown here for conciseness) meet the same requirement. The conjoint analysis of different time-averaged flow quantities indicates that the numerical transient lasts two revolutions.4 French National Computing Center 5 This nondimensionalization gives direct access to the time-variation of the signal in percent. 6 FBP:Fan Blade Passage TURBO-21-1140 -Franc ¸ois 12

Fig. 6 .

 6 Fig. 6. Convergence of the bypass air massflow rate at the outlet of the computational domain, nondimensioned by the massflow rate at t=76 FBP (Fan Blade Passage).

Figure 7

 7 presents the instantaneous signal TURBO-21-1140 -Franc ¸ois 13

A c c e p t e d M a n u s c r i p t N o t C o p y e d i t e dFig. 7 .

 7 Fig. 7. (a) Instantaneous and cyclostationnary signals of the axial momentum on a numerical probe at 90% of channel height, near the OGV leading-edge. Wake and part of the tip gap flow can be seen respectively large and small axial momentum dips, (b) Deviation of the RMS evaluation of the stochastic part of the same probe signal over a given number of FBP with respect to the RMS value of the full signal.

Fig. 8 .

 8 Fig. 8. Illustration of the zonal solving with ZDES by the visualisation of iso-value surfaces of the Q criterion (Q=10 with Q=Q×t 2 adim and t adim =2.915 ms) around the fan blades (a) and around the OGV blades (b). The color indicates the non-dimensioned axial momentum (ρ adim =1.185 kg/m 3 and V adim =343.0 m/s).

Figure 8

 8 Figure 8 presents a visualization of the instantaneous flow-field around the fan blade: surfaces of iso-values of the Q criterion colored by the axial momentum are displayed. It illustrates the zonal solving with the ZDES. The core airflow is treated in URANS and only very large turbulence structure are present such as an horseshoe vortex at the intersection of the fan blade and the hub. The bypass airflow is treated with the ZDES mode 2 (see Section 3.1). Because the flow

Figure 9

 9 presents fields of vorticity magnitude on a developed blade-to-blade surface. The vorticity fields are consistent: the fan wakes are convected without noticeable attenuation or numerical artefact through the stage interface and the periodic boundary conditions. Fig. 8-b gives a hub-to-shroud view of the fan wakes interacting with the OGV, supporting the previous statement.

Figure 9

 9 Figure 9 depicts in thick black lines the areas in which the shielding function f d equals 0.95, defining thus the border between the RANS solving (in the boundary layer) and the LES solving

Fig. 9 .

 9 Fig. 9. Visualisation of non-dimensioned vorticity magnitude fields (t adim =2.915 ms) on a developed blade-to-blade surface at 50% of the OGV span. The black lines denote f d =0.95.

  depth of the velocity deficit is slightly over-estimated by the simulation. The comparison of the TURBO-21-1140 -Franc ¸ois 17

A c c e p t e d M a n u s c r i p t N o t C o p y e d i t e d Journal of TurbomachineryFig. 10 .Fig. 11 .

 1011 Fig. 10. Maps of velocity flow fields at HW1 plane with ZDES (a-c) and measurements (b-d) -Cyclostationary quantities are shown: axial velocity (a-b) -tangential velocity (c-d). Three blade channels are displayed.)

Fig. 12 . 19 A c c e p t e d M a n u s c r i p t N o t C o p y e d i t e dFig. 14 .

 121914 Fig. 12. ZDES and experimental radial profiles at the HW1 location: axial (a), tangential (b) and radial (c) mean velocity

  Journal of Turbomachinery made by GENCI (French National Computing Center). The authors are grateful to S ébastien Deck and Nicolas Renard from the Advanced Modeling Turbululence Simulation team in ONERA for the fruitful discussion and their help on the ZDES. Shielding function in the ZDES APPENDIX: POSTPROCESSING OF THE EXPERIMENTAL DATA Meyer et al. [15] describes the post-processing of the hot-wire data. Two sets of hot-wire probes allows the measurements of the three components of the velocity at the HW1 plane. A trigger signal from the rotor shaft was recorded with the hot-wire signals. This ensured an exact allocation of each wake to the corresponding blade of the phase downstream of the rotor, allowing to calculate 360 • phase-averaged flow velocity maps. These flow velocity maps exhibits difference from one channel to an other. Split into 20 subzones (as many as the number of channels), they are averaged and used for comparison with the numerical results (see Fig. 10-b and 10-d ). The TURBO-21-1140 -Franc ¸ois

Table 1 .

 1 Comparison of aerodynamic performancesTable

		6.41	6.43	6.44
	Bypass massflow [kg/s]	48.76	48.60	49.26
	Bypass pressure ratio	1.108	1.105	1.106

Journal of Turbomachinery. Received July 06, 2021; Accepted manuscript posted May 04, 2022. doi:10.1115/1.4054528 Copyright © 2022 by ASME Downloaded from http://asmedigitalcollection.asme.org/turbomachinery/article-pdf/doi/10.1115/1.4054528/6878708/turbo-21-1140.pdf by ONERA user on 05 July 2022

In the EU project, the same calibration was used by others partners for RMS comparison such as Lewis et al.[START_REF] Lewis | ACAT1 Fan Stage Broadband Noise Prediction Using Large-Eddy Simulation and Analytical Models[END_REF] for instance.

ACKNOWLEDGEMENTS

The presented work was conducted in the frame of the project TurboNoiseBB, which has received funding from the European Union's Horizon 2020 research and innovation programme under grant agreement No. 690714. The authors want to thank the members of the TurboNoiseBB

Journal of Turbomachinery

The above 2D fields have been circumferentially averaged in order to perform more quantitative radial profile comparisons. Axial, tangential and radial components of mean velocity provided by ZDES and experiment are plotted in Fig. 12 from left to right, respectively. Measurement data for the same gemeotry with a long-gap between fan and OGV (EXP LG) is also added. The grey area illustrates the uncertainties associated with the measurements between the different interchannels blades. Indeed, the measured flow is different between adjacent channels. This was observed and referenced in the literature by Meyer et al. [START_REF] Meyer | Instantaneous Flow Field Measurements in the Interstage Section between a Fan and the Outlet Guiding Vanes at Different Axial Positions[END_REF]. According to the authors, the most probable reason are slight geometrical discrepancies between adjacent blades. This is amplified by the aerodynamic flow conditions: for the selected operating point, flow detachment is present on both the fan and the OGV and very small change of stagger angle between adjacent blades may cause these significant differences. Details on the calculation of the error bar are given in the appendix.

Analysis of Fig. 12 shows that mean axial and tangential velocity profile are well retrieved both in shape and levels, the mean axial and tangential velocity being over-estimated by the simulation by less than 3%. The casing boundary layer is not correctly reproduced but the prediction is improved compared to the ZDES from Franc ¸ois et al. [START_REF] Franc ¸ois | Zonal Detached Eddy Simulation of the Fan-OGV Stage of a Modern Turbofan Engine[END_REF] in which the boundary layer was too thin.

Concerning the radial velocity, the predicted levels overestimates significantly the measurements (+5 -10 m/s). For this flow variable, numerical results of partners in the EU project shows the same trends as the present ZDES results (see Lewis et al. [18]). For this reason, measurements on the same fan configuration with a long gap (LG) distance between the fan and the OGV are plotted on the same figure. The ZDES results (such as other numerical results from EU partners of the project) are more consistent with this set of measurements. The difference of measurements between short gap and long gap configurations for this velocity component remain unexplained yet. RANS results using the Menter Shear Stress Transport k -ω and the Smith k -l models [START_REF] Menter | Two-Equation Eddy-Viscosity Turbulence Models for Engineering Appli-TURBO-21-1140 -Franc ¸ois 30[END_REF]31] are shown on the same figure for comparison using a mesh with five million cells (one rotor and one stator channel). Results are close to the ZDES results for the tangential and the radial velocities but discrepancies are visible on the axial velocity profile (+6 -7%). This is attributed to an overestimation of the tip gap flow area at the HW1 position.

TURBO-21-1140 -Franc ¸ois 20

A c c e p t e d M a n u s c r i p t N o t C o p y e d i t e d

Journal of Turbomachinery Similar comparisons of radial profiles have been realized for the three RMS components (axial, tangential, radial) of the velocity and the turbulent kinetic energy plotted in Fig. 13. Only the radial section concerning the secondary airflow (ZDES mode 2 solving) is shown. The grey area denotes the uncertainties due to the measurements as mentioned in the previous paragraph, larger for RMS quantities than for mean quantities. For the three components, a sufficiently good agreement is obtained between the measurements and the ZDES results, in particular in the tip gap flow area. In terms of levels, the discrepancies remains within the range of the uncertainties due to the measurements and the shapes of the curves are well reproduced. RANS results, obtained by a reconstruction of the Reynolds tensor with the Boussinesq relation, present larger discrepancies with the measurements than the ZDES results, particularly in the tip gap. The shape of the radial profile is also different from the measurements in this area for the two models.

Azimuthal Profiles

Comparison of the azimuthal profiles for the cyclostationary velocity is shown in Fig. 14 at 50% and 75% of the duct height to analyse the velocity deficit caused by the wake and at 97%

for the tip gap flow. Depth of the velocity deficit 8 and width of the velocity deficit (commonly named wake thickness) are two key parameters in the rotor-stator interaction noise generation for the axial and azimuthal velocity components but they induce a change of incidence on the stator and thus of aerodynamic loading. For these velocity components, the wake thickness is well reproduced by the ZDES simulation compared to the measurements whereas the depth of RMS velocity component azimuthal profiles depict the repartition of the turbulence energy in the wake and over the three velocity components. This distribution is an important parameter for the broadband rotor-stator interaction noise. Same pattern as Fig. 14 is shown in Fig. 15 for the RMS quantities. At channel height of 50% and 75%, measurements show that the wake exhibits a main peak with an asymmetrical shape or with a secondary peak caused by the flow separation at the fan leading-edge. These features are globally reproduced by the ZDES results except for TURBO-21-1140 -Franc ¸ois 23

A c c e p t e d M a n u s c r i p t N o t C o p y e d i t e d

Journal of Turbomachinery some plots with small secondary peaks present in the simulation but absent in the measurements.

The width of the wake is very consistent with the measurement while the height of the RMS peak is globally overestimated by 15% in average (from 3% to 25% depending on the plot). The RANS results show always wakes narrower than ZDES and measurements while the height of the RMS peak is quite close to the ZDES results. However, the shape of the RMS profile from RANS results remains often quite symmetrical. For RANS and ZDES, the azimuthal profiles exhibit an absence of turbulence outside the wakes while this turbulence is noticeable in the experiments (mentioned in the analysis of the flow maps in section 5.2). In the tip gap flow, the turbulence is present in the whole inter-blade channel and captured by the simulation (because the tip gap flow fills the whole channel). The variation of the RMS quantities is more complex than at channel height of 50% and 75%: two peaks of similar amplitude are visible. With less accuracy than at mid-height, the shape and the levels of the azimuthal profile are globally reproduced by ZDES : secondary dips/peaks are captured but their positions are shifted and their heights are different compared to the measurements. RANS results show that only a main peak is predicted and RMS levels are overestimated compared to the experimental data.

CONCLUSIONS

A Zonal Detached Eddy Simulation approach has been applied to a turbofan stage to simulate the interaction of the turbulent fan wakes with the OGV. The final goal of this simulation is the prediction of the associated broadband noise. Extending the work from Franc ¸ois et al. [START_REF] Franc ¸ois | Zonal Detached Eddy Simulation of the Fan-OGV Stage of a Modern Turbofan Engine[END_REF], the ZDES presented here accounts for a more realistic boundary layer impinging the fan, the simulated massflow rate is closer to the measurements, a better space repartition between the RANS and ZDES mode 2 zones was chosen. To limit the numerical efforts, the number of the OGV blades has been modified to allow a significant reduction of computed inter-blade channels while preserving the main aerodynamic performances.

The ZDES was performed on four revolutions and convergence of the cyclostationnary values (thanks to analysis of numerical controller probes) was achieved. Inspection of the flow field highlights a very consistent behaviour of the shielding function (border between RANS and LES TURBO-21-1140 -Franc ¸ois 24

A c c e p t e d M a n u s c r i p t N o t C o p y e d i t e d

consortium for providing the raw experimental data and for fruitful discussions throughout the Experimental uncertainties are quite significant in RMS radial profiles comparison (Fig. 13) and azimuthal profiles comparison (Fig. [START_REF] Casalino | Turbofan Broadband Noise Prediction using the Lattice Boltzmann Method[END_REF][START_REF] Meyer | Instantaneous Flow Field Measurements in the Interstage Section between a Fan and the Outlet Guiding Vanes at Different Axial Positions[END_REF]. The methodology to calculate these uncertainties is detailled here. First of all, noticeable heterogeneity in the 360 • flow measurements for the velocity components between the differents fan channels in the HW1 plane are visible [START_REF] Polacsek | Turbofan Broadband Noise Predictions Based on a ZDES Calculation of a Fan-OGV Stage[END_REF][START_REF] Meyer | Instantaneous Flow Field Measurements in the Interstage Section between a Fan and the Outlet Guiding Vanes at Different Axial Positions[END_REF]. The reason for this heterogeneity is not well understood yet and thus the authors can only make assumptions.

Slight fan blade geometry differences (pitch angle, geometry itself) might exist between the adjacent blades. Because the studied operating point in this paper implies a flow separation on the fan leading-edge, small differences of geometry/pitch angle may cause a strong heterogeneity on the appearance/disappearance of flow separation cell in all the blades, on the flow separation cell sizes. This would affect the cyclostationnary flow velocity field downstream of the fan blade at the HW1 measurement plane (Fig. 13) and the turbulence generated in the flow separation cell and then convected, merged with the wake, increasing the variability of the RMS quantities between adjacent channels (Fig. [START_REF] Casalino | Turbofan Broadband Noise Prediction using the Lattice Boltzmann Method[END_REF][START_REF] Meyer | Instantaneous Flow Field Measurements in the Interstage Section between a Fan and the Outlet Guiding Vanes at Different Axial Positions[END_REF].

Only this contribution is accounted for in the estimation of the measurement uncertainty presented in aforementionned figures. This estimation proceeds as follows:

1. The 360 • flow measurements map of velocity is split into 20 subzones, This section will be created when tables are included with a caption.

TURBO-21-1140 -Franc ¸ois 34


S Smiy
email: sabsmiy@gmail.com

M Bejar

E Dhahri

T Fiorido

K Aguir

M Bendahan

Preparation of double-doping 𝑳𝒂𝑭𝒆𝑶 𝟑 thin film for ethanol sensing application

Keywords: 𝐿𝑎 0.8 𝐶𝑎 0.1 𝑃𝑏 0.1 𝐹𝑒𝑂 3, films, sensors, ethanol, response, 5 𝑝𝑝𝑚

Recently, perovskite-based nanomaterials are used in diverse applications. Many perovskite nanoparticle-based devices have been demonstrated with extraordinary sensing performances to various chemical species in both solid and solution states. In this context, a new ethanol gas sensor 𝐿𝑎 0.8 𝐶𝑎 0.1 𝑃𝑏 0.1 𝐹𝑒𝑂 3 has been developed. 𝐿𝑎 0.8 𝐶𝑎 0.1 𝑃𝑏 0.1 𝐹𝑒𝑂 3 film has been prepared using the drop coating method onto 𝑆𝑖𝑂 2 /𝑆𝑖 transducers with platinum interdigited electrodes based on the use of nanopowders which are prepared by sol-gel method. X-ray diffraction (XRD) showed that our sample was still perovskite phase with orthorhombic structure with 𝑃𝑛𝑚𝑎 space group. The electrical properties showed the P-type semiconductor behavior of our sensor and the ethanol sensing measurements revealed his good sensitivity towards 𝐶 2 𝐻 5 𝑂𝐻-gas. The response (𝑆 = 𝑅 𝑔 /𝑅 𝑎 ) was found to increase from 2.040 to 3.250 when concentration increased from 5 𝑝𝑝𝑚 to 30 𝑝𝑝𝑚 at the operating temperature of 250°𝐶.

I. Introduction :

Perovskite materials (𝐴𝐵𝑂 3 ), where 𝐴 is a rare earth and 𝐵 is a transition metal, are very used as gas sensors materials due to their thermal stability at higher temperature [1-4].

One of these functional materials is 𝐿𝑎𝐹𝑒𝑂 3 which is P-type semi-conductor material in air [START_REF] Murade | Preparation and ac electrical conductivity of nanocrystalline 𝐿𝑎𝐹𝑒𝑂 3[END_REF][START_REF] Sun | Structure and electrical properties of nanocrystalline 𝐿𝑎 1-𝑥 𝐵𝑎 𝑥 𝐹𝑒𝑂 3 for gas sensing application[END_REF]. In the surface of this sensor, oxygen adsorption enhances the conductivity of these materials on account of the increase of holes concentration, which are the main charge carrier species in P-type semiconductor [START_REF] Chen | Ethanol-sensing properties of 𝑆𝑚𝐹𝑒 1-𝑥 𝑁𝑖 𝑥 𝑂 3 perovskite oxides[END_REF]. For this reason, the resistance of these materials increases by applying reducing gases like ethanol [START_REF] Cao | The influence of nonstoichiometry on electrical transport and ethanol sensing characteristics for nanocrystalline 𝐿𝑎𝐹𝑒 𝑥 𝑂 3- sensors[END_REF]. In literatures, many studies have reported that LaFeO 3 is characterized by higher resistance which present a disadvantage in the gas sensing application and the partial substitution of 𝐿𝑎 by lower valent cation elements, such as 𝑃𝑏 [9]and 𝐶𝑎 [10] could reduce the resistance of the mother compound. Besides, and using Kroger-Vink defect notations, its charge carries are holes 𝒉 . , which are produced by the ionization of 𝐿𝑎 3+ ions vacancy defect [𝑽 𝑳𝒂 𝒙 ] and the ionization reaction is (𝑽 𝑳𝒂 𝒙 → 𝑽 𝑳𝒂 ,,, + 𝟑𝒉 . ). When 𝐿𝑎 3+ ion is substituted by 𝑃𝑏 2+ one, the ionization reaction of this element is (𝑷𝒃 𝑳𝒂 𝒙 → 𝑷𝒃 𝑳𝒂 , + 𝒉 . ) (where 𝑷𝒃 𝑳𝒂 𝒙 is related to the point defect which is formed when 𝑳𝒂 𝟑+ is replaced by 𝑷𝒃 𝟐+ in the crystal and (𝒉 . ) are the generated holes). As a result of propanol has been prepared and ultrasonicated for 10 𝑚𝑖𝑛 at 40 °C in order to ensure a good homogenization for the mixture. Subsequently, the deposition of thin films has been assured by coating the substrate drop by drop. Films thickness is found to be equal to 300 𝑛𝑚 and it was measured using a DEKTAK6𝑀 mechanical profilometer. This method is completed by annealing our films at 500°𝐶.

II.2. Gas sensing measurements:

The electrical and gas sensing measurements were measured using a test chamber with a volume of 2L which allowing the control of the operating temperature and the gas concentration. Dry air was used as reference gas and voltage has been fixed to 0.05 𝑉. The resistance measurements of La 0.8 Pb 0.1 Ca 0.1 𝐹𝑒O 3 sensor were carried out in dry air and in presence of ethanol gas at various working temperatures from 200 °C to 280 °C.

Ethanol concentrations were obtained by diluted the saturated-ethanol with different amount of dry air in order to provide a final ethanol concentration between 5 and 30 𝑝𝑝𝑚.

The sensing response was defined as 𝑆 = 𝑅 𝑔 /𝑅 𝑎 , where 𝑅 𝑎 defines the resistance in air and 𝑅 𝑔 is the resistance in presence of ethanol gas. Where:  defines the Bragg diffraction angle, 𝛽 demonstrates the effective strain, 𝑘 is the shape factor and the 𝐷 𝑊-𝐻 presents the average crystallizes size.

III. Results and

Habitually, sensor materials with a smaller crystallite size are characterized by higher activity, which facilitates the chemisorption of oxygen species leading to an increase of the response of materials used for gas sensing application

III.2. Gas sensing properties:

In the following part, we investigate the response of La 0.8 Pb 0.1 Ca 0.1 𝐹𝑒O 3 sensor in presence of ethanol gas with different concentrations 5, 10, 20 and 30 𝑝𝑝𝑚.

In order to ensure the adsorption of our La 0.8 Pb 0.1 Ca 0.1 𝐹𝑒O 3 nanopowders over the 𝑆𝑖𝑂 2 𝑆𝑖 ⁄ substrate, a view using the optical microscope, will takes place with a magnification of 1.25 to see the surface [14] (𝐅𝐢𝐠𝐮𝐫𝐞 . 𝟓).

Operating temperature is one of crucial parameter to consider for the potential practicality application of gas sensors and sensing process, such as gas adsorption and desorption phenomena on sensors surface are subject to the sensors operating In the one hand, 𝐵𝑎𝑆𝑛𝑂 3 is a perovskite sensor which presents a higher response in presence of ethanol gas. Then, response is found to be equal to 5 at the operating temperature which is equal to 300 𝑝𝑝𝑚 for a concentration equal to 50 𝑝𝑝𝑚 [START_REF] Kumar | Tunning operating temperature of BaSnO3 gas sensor for reducing and oxidizing gases[END_REF]. In the other hand, our sensor presents a response equal to 2.040 in presence of very low concentration (5 𝑝𝑝𝑚) of ethanol gas (𝐓𝐚𝐛𝐥𝐞 . 𝟐). In addition, the mother compound

𝐿𝑎𝐹𝑒𝑂

Conclusion:

A new perovskite La 0.8 Pb 0.1 Ca 0.1 𝐹𝑒O 3 thin film has been prepared using drop-coating method for 𝐶 2 𝐻 5 𝑂𝐻-gas sensing application. The morphology and microstructure proved that our sensor can be usable for ethanol sensing application. The XRD pattern revealed that our sample crystallized in the orthorhombic phase with Pnma space group. The gas sensing properties of the double doped sensor LaFeO3 by Ca and Pb showed that this captor could be a promising candidate for the detection of ethanol gas because of the detection of very low concentration equal to 5 ppm at 250°C. Then, 250°C corresponds to the best value of sensitivity that we have a maximum of chemisorbed oxygen at the surface.

Discussion : III. 1 .

 1 XRD and Morphological studies: The phase of La 0.8 Pb 0.1 Ca 0.1 𝐹𝑒O 3 nanopowder was performed by means of X-ray diffraction with 𝐶𝑢𝐾  radiation ( = 1.5406 Å) using the FULLPROF program. 𝑭𝒊𝒈𝒖𝒓𝒆. 𝟏 demonstrates that our sample crystallizes in the orthorhombic structure with the 𝑃𝑛𝑚𝑎 space group and we notice the existence of the 𝐹𝑒 3 𝑂 4 secondary phase. The lattice refined parameters 𝑎, 𝑏 , 𝑐 and the volume 𝑉 are gathered in 𝑻𝒂𝒃𝒍𝒆. 𝟏. Based on the use of the Williamson-Hall's equation (𝑊 -𝐻) [12] (𝑬𝒒. 𝟏), we estimated the average crystallite size 𝐷 𝑊-𝐻 which is found to be equal to 83.023 𝑛𝑚 (𝑭𝒊𝒈𝒖𝒓𝒆. 𝟐. ) 𝜷𝒄𝒐𝒔() = 𝒌 𝑫 𝑾-𝑯 ⁄ + 𝟒 𝐬𝐢𝐧( 𝜽) (𝑬𝒒. 𝟏)

temperature [ 15 ]. 6 .

 156 General diagram of measurements setup used to characterize ethanol microsensors is presented in figure La 0.8 Pb 0.1 Ca 0.1 FeO 3 sensor response 𝑆 = 𝑅 𝑔 /𝑅 𝑎 as a function of time (𝑇 = 220°𝐶, 𝑇 = 240°𝐶, 𝑇 = 250°𝐶 and 𝑇 = 270°𝐶) , in presence of 30 ppm of ethanol reducing gas for an exposure time equal to 1 min, are presented in 𝑭𝒊𝒈𝒖𝒓𝒆. 𝟕. We can see that for temperatures equal to 𝑇 = 220 °𝐶 and 𝑇 = 270 °𝐶 the 𝑅(𝑡) curves doesn't return to the baseline. This variation depends on the amount of oxygen adsorbed on the surface because the electron trapped by the oxygen at the surface from the semiconductor increases the resistance by decreasing the major charge carrier (hole) concentration [16]. However, for a temperature equal to 𝑇 = 240 °𝐶 or 𝑇 = 250 °𝐶, we observe the presence of a reversibility of 𝑅(𝑡) curves. Our captor has been exposed at different temperatures in order to identify the optimal operating one. From 𝑭𝒊𝒈𝒖𝒓𝒆 . 𝟖 some observations can be selected: ❖ The 𝐶 2 𝐻 5 𝑂𝐻-gas response increases and reaches a maximum value at an optimum operating temperature equal to 250 °𝐶. ❖ The La 0.8 Pb 0.1 Ca 0.1 FeO 3 sensor demonstrates a p-type semiconducting properties because the resistance increases when reducing gas is introduced [17]. A typical La 0.8 Pb 0.1 Ca 0.1 FeO 3 sensor response to small ethanol concentrations is shown in 𝑭𝒊𝒈𝒖𝒓𝒆. 𝟗. The variation of 𝑅(𝑡) demonstrates a good reversibility in presence of different amount of 𝐶 2 𝐻 5 𝑂𝐻-gas at the operating temperature of our sensor. In addition, the sensitivity indicates the ability of a material to respond to low ethanol concentrations of 5 𝑝𝑝𝑚 compared to others perovskite materials [18, 19]. The response of La 0.8 Pb 0.1 Ca 0.1 𝐹𝑒O 3 sensor at the operating temperature vs. 𝐶 2 𝐻 5 𝑂𝐻 concentrations is depicted in 𝑭𝒊𝒈𝒖𝒓𝒆. 𝟏𝟎. From this figure we can conclude that the intensity of the response peak increases monotonically with increasing gas concentration and consequently increasing the response (𝑅 𝑔 𝑅 𝑎 ⁄ ).As is well-accepted, the gas sensing mechanism of others materials such as metal oxide semiconductors involves an adsorption -desorption phenomena in which chemisorbed oxygen plays a crucial role[START_REF] Alagh | CVD growth of self-assembled 2D and 1D WS2 nanomaterials for the ultrasensitive detection of NO2[END_REF]. In our case -case of perovskite materials-these two phenomena are ensured because La 0.8 Pb 0.1 Ca 0.1 FeO 3 sensor shows a good return to the base line at the operating temperature which is equal to 250°C in presence of reducing gas. Reactions between adsorbed ionized oxygen species on the surface:𝑂 2 , 𝑂 2 -, 𝑂 -and 𝑂 2-are expressed as follows Eq(2When ethanol gas was introduced, recombination phenomena between electrons and holes are produced, inducing consequently a decrease in the density of holes-number in the La 0.8 Pb 0.1 Ca 0.1 𝐹𝑒O 3 sensor. This phenomena leads to an increase in the electrical resistance of the compound during adsorption of the reducing gas [21]. Reactions that occur between 𝐶 2 𝐻 5 𝑂𝐻 gas and oxygen chemisorbed ions adsorbed in the surface are [22, 23]and the mechanism of the reaction is comparable to that mentioned by T. Tharsika et 𝑎𝑙. [24]: 𝐶 2 𝐻 5 𝑂𝐻 (𝑣𝑎𝑝) + 6𝑂 (𝑎𝑑𝑠) -→ 2𝐶𝑂 2(𝑔𝑎𝑧) + 6é -+ 3𝐻 2 𝑂 (𝑣𝑎𝑝) (𝐄𝐪 . 𝟔) 𝐶 2 𝐻 5 𝑂𝐻 (𝑣𝑎𝑝) → 𝐶 2 𝐻 5 𝑂 (𝑠𝑢𝑟𝑓𝑎𝑐𝑒) + 𝐻 (𝐄𝐪 . 𝟕) 𝐶 2 𝐻 5 𝑂𝐻 (𝑣𝑎𝑝) + 𝑂 (𝑎𝑑𝑠) -↔ 𝐶𝐻 3 𝐶𝐻𝑂 (𝑎𝑑𝑠) + 𝐻 2 𝑂 (𝑣𝑎𝑝) + 𝑒 - (𝐄𝐪 . 𝟖) Our La 0.8 Pb 0.1 Ca 0.1 𝐹𝑒O 3 sensor response (𝑆 = 𝑅 𝑔 /𝑅 𝑎 ) confirms their use for ethanol sensing application. Indeed, La 0.8 Pb 0.1 Ca 0.1 FeO 3 has been used on this application but in pellets forms by A. Benali et al. In addition, authors are used a very large amount of ethanol gas (250, 500 and 1000 ppm), but in this research paper we try to detect a small amount of ethanol reducing gas (5 𝑝𝑝𝑚). Added to that the deposition of La 0.8 Pb 0.1 Ca 0.1 𝐹𝑒O 3 in thin films forms leads to a decrease in the operating temperature from 280 °𝐶 [2] to 250 °𝐶 in case of our sample.

°)Figure. 1 :

 1 Figure. 1: Observed (red), Calculated (black solid line), their difference patterns (blue) and the Bragg positions (green) of 𝐿𝑎 0.8 𝑃𝑏 0.1 𝐶𝑎 0.1 𝐹𝑒𝑂 3 sensor and the secondary phase which is attached to the 𝐹𝑒 3 𝑂 4 impurity.

Figure. 2 :

 2 Figure. 2: Williamson-Hall plot of 𝐿𝑎 0.8 𝑃𝑏 0.1 𝐶𝑎 0.1 𝐹𝑒𝑂 3 compound prepared by the sol-gel method.

Figure. 3 :

 3 Figure.3: EDS-micrograph of chemical elements of 𝐿𝑎 0.8 𝑃𝑏 0.1 𝐶𝑎 0.1 𝐹𝑒𝑂 3 compound prepared by the sol-gel method.

Figure. 4 :

 4 Figure. 4: EDS-mapping of chemical elements in 𝐿𝑎 0.8 𝑃𝑏 0.1 𝐶𝑎 0.1 𝐹𝑒𝑂 3 sample prepared by the sol-gel method.

Figure. 5 :

 5 Figure.5: Optical view after drop coating of La 0.8 Pb 0.1 Ca 0.1 FeO 3 sensor.

Figure 6 :

 6 Figure 6: General diagram of measurements setup used to characterize ethanol microsensors.

Figure. 7 :

 7 Figure. 7: Ethanol gas response of La 0.8 Pb 0.1 Ca 0.1 FeO 3 sensor as a function of time at several temperatures (𝑇 = 220°𝐶, 𝑇 = 240°𝐶, 𝑇 = 250°𝐶 and 𝑇 = 270°𝐶).

Figure. 8 :

 8 Figure.8: The relationship between response (𝑆 = 𝑅 𝑎 𝑅 𝑔 ⁄ ) vs. temperature (𝑇) of La 0.8 Pb 0.1 Ca 0.1 𝐹𝑒O 3 based sensor during ozone exposing time of 1 𝑚𝑖𝑛 for a concentration equal to 30 𝑝𝑝𝑚.

Figure. 9 :

 9 Figure.9: L a 0.8 Pb 0.1 Ca 0.1 𝐹𝑒O 3 sensor response (𝑆) to different concentrations (5,10, 20 𝑎𝑛𝑑 30𝑝𝑝𝑚) of ethanol gas (𝐶 2 𝐻 5 𝑂𝐻) at 𝑇 𝑂𝑝 = 250°𝐶 and for an exposure time equal to 4 𝑚𝑖𝑛.

Figure. 10 :

 10 Figure. 10: Response (𝑆 = 𝑅 𝑎 /𝑅 𝑔 ) vs. ethanol-concentrations (5, 10, 20 and 30𝑝𝑝𝑚) at the working temperature (𝑇 𝑜𝑝 = 250°𝐶).

  3 presents a response equal to 3.8 in the existence of a concentration equal to Other important performance which is influenced by quantities of chemisorbed oxygen species is response time. Response time is defined as the time required to reach 90 % of the electrical resistance [27]. Response time values are gathered in Table 2, we can note that La 0.8 Pb 0.1 Ca 0.1 𝐹𝑒O 3 sensor shows low response time compared to other materials which are used for ethanol sensing application [28].

Table 1 :

 1 The Rietveld refinement results of X-Ray diffraction (𝑋𝑅𝐷) data of La 0.8 Pb 0.1 Ca 0.1 𝐹𝑒O 3 compound.

		Space group	𝑎(Å)	𝑏 (Å)	𝑐(Å)	𝑉 (Å 3 ) DW-H (nm)
	La 0.8 Pb 0.1 Ca 0.1 𝐹𝑒O 3	Pnma	5.5493	7.8488	5.5394	241.24	83.023
	𝐹𝑒 3 𝑂 4	Pbcm	11.868	11.851	16.752	589.03	_

Table 2 :

 2 Response time of La 0.8 Pb 0.1 Ca 0.1 𝐹𝑒O 3 sensor at 250°C compared to WO3 sensor

	[28].
	C (ppm)	5	10	20	30
	S (Rg/Ra)	2.040	2.370	2.835	3.250
	Response time (s) (PW)	200	190	183	146
	Response time (s) (WO3) [28]	580	-	-	-