Isabelle Schmich
email: isabelle.schmich@cstb.fr

; Bruder

THE ACOUSTICAL IMPROVEMENT OF HISTORIC MONUMENTS SAINT JOSEPH CHAPEL -A CASE-STUDY PACS: 43.55.-n

The Saint Joseph chapel in the city of Caluire et Cuire, France is an historic monument built in 1885 by the architect Sainte Marie Perrin. CSTB has been asked to study the acoustics of the chapel. The aim is to create an acoustic environment that permits non-amplified performances such as chamber music with the goal of a reverberation time of 1.5s.

Characterizing acoustic measurements have been done in the chapel. The measurement results are presented. They show a reverberant acoustic which is too high for classical music.

After analysis of the acoustic measurements, CSTB was asked to propose modifications to improve the acoustics. These proposed modifications have to take into account the constraints due to the historical shape and architecture of the chapel.

Two different solutions are proposed. The first solution is based on greatly increasing the absorbing surfaces and comes close to the ideal acoustic for classical music. The second solution allows the improvement of the actual acoustic with less absorbing material. Some diffuse and mode breaking surfaces are added. This second solution also includes a proposal for adapted music in this architectural and acoustical framework.

INTRODUCTION

The Caluire et Cuire municipality would like to renovate the St Joseph Chapel, which was constructed in 1885, so that non-amplified performances can be given. The chapel is no longer used for worship services. The main objective of this renovation is to transform the volume of the chapel into a space that is adapted for musical concerts and, more specifically, for chamber music or instrumental recitals. To achieve this goal, it will be necessary to reduce the excessive reverberant acoustics to a reverberation time of 1.5 s at mid-range frequencies (see Table I) and at the same time to respect the architectural constraints of the historic building.

SAINT JOSEPH CHAPEL BEFORE RENOVATION

Characterizing measurements have been done before the start of the renovation.

Description

The chapel has a surface about 500 m² with an estimated volume of 8100 m 3 . Its roof has an average height of 15 m. The nave is 30.50 m long and 16.50 m wide including an aisle on each side. The choir is 5 m long and 9 m wide. The roof is covered with painted plaster and has several arches above the aisles. The chapel is ornately decorated with painted and sculptured motifs. Woodwork has been installed on the lower part of the side walls. The Stations of the Cross are composed of painted fabric which has been mounted on the walls (see Fig. 1 and2).

Measurement Results

The measurements have been done with a standard MLS-technique with the chapel being empty and without seats for 3 loudspeaker and 6 receiver positions. The measurement results are given in Table II. Some typical measured echograms are shown in Fig. 3. The reverberation time in the empty chapel is around 5.5 s at 500 Hz and, as originally suspected, much too high. This does not allow the performance of musical concerts in good acoustic conditions. The other criteria such as clarity and definition have typical values for acoustics with too much reverberation.

On the other hand, the echograms show smooth decay-curves which leads us to presume that the chapel has good acoustic qualities due to its architecture which is harmoniously composed of reflecting surfaces and diffuse elements including columns, capital, low-relief, high composed arches, and banisters. These qualities are hidden by the excess reverberation.

The seating capacity has been estimated to be 320 seats. Table III gives the estimated reverberation time for the chapel with 320 listeners. These values are still too high for classical music concerts and some architectural adjustments need to be made.

PROPOSED MODIFICATIONS

The main objective is to add absorbing surfaces to reduce the reverberation time in coherence with the architectural constraints of a historical building. First a list of possible absorbing surfaces has been established.

List of possible acoustic treated surfaces

The surfaces which could be possibly used for an absorbing acoustic treatment are the following:

• Floor (total surface of 432 m 2 ): It is possible to add a textile covering (fixed or detachable) on all or a part of the floor. The seating section would be about 160 m 2 . • Walls: approximately 350 m 2 could be treated with absorbing material like absorbing plaster or curtains (not counting the parts of the walls used by the frescoes or the woodwork). • Arches: in the same manner as the walls, 180 m 2 could be treated with absorbing plaster and additionally 9 m 2 could be treated with mineral wool placed behind the rosettes. • Doors: 70 m 2 of movable curtain could be placed before the sacristy and below the gallery.

To decrease the reverberation time to 1.5 s at mid-frequencies (with listeners), it would be necessary to increase the absorption over 500 m² of equivalent absorbing surfaces. To decrease the reverberation time to 2 s at mid-frequencies (with listeners), it would be necessary to increase the absorption over 300 m² of equivalent absorbing surfaces. Two solutions have been studied: With this proposed solution and a fully seated chapel, a reverberation time of 2.0 s at 500 Hz could be achieved (see. Table IV and Fig. 4). Despite large effort of adding sound absorbing material (even in technically difficult places) the goal of 1.5 s at 500 Hz cannot be reached. The acoutics obtained would be acceptable for some choral concerts, but not for chamber music.

nd solution: A reasonable amount of absorbing surfaces

The following proposed solution has in total about 180 m² of equivalent sound absorbing surfaces:

• Floor : carpeting below the seats and the side aisles • Walls (around the stained-glass windows): absorbing plaster or absorbing foam • Doors (before the sacristy and behind the husting): curtains • Arches: absorbing plaster or absorbing foam • Ceiling: Mineral wool behind rosettes • Diffuser: Add a maximum of large light fixtures or other diffusing elements With this proposed solution and a fully seated chapel, a reverberation time of 2.4 s at 500 Hz could be achieved (see. Table IV and Fig. 4). Even if the decrease of reverberation will be clearly audible, again the goal of 1.5 s at 500 Hz cannot be reached.

Average Reverberation Time

What next? Discussion

The first proposed solution takes into account all acoustically treatable surfaces (884 m²). Even if it does not achieve the ideal objective it corresponds to a clear improvement. Choral music would have excellent acoustic conditions. To apply this solution, some heavy construction work would be needed including the especially delicate work for the installation of mineral wool behind the painted fabric of the Stations of the Cross and the application of the mineral wool behind the woodwork. It does not seem reasonable in terms of cost-effectiveness, especially since the desired chamber music performances will still not have good conditions.

By applying the second proposed solution the most easily treatable surfaces (walls, floor and arches) are treated. This solution achieves a large decrease of the reverberation and, although not optimal, the improvement would be easily audible. The valuable historic architecture of the chapel would be preserved. This solution should be accompanied by a study of which musical repertoire would be most adequate for this acoustic (see Fig. 5).

Some other solutions may be possible but for all these solutions the 320 seats will need to be as absorptive as possible and the arches should always be treated with absorptive material, diffusers or mode breaking surfaces such as transparent small reflectors because of their focalizing shape. show an excessive reverberant acoustic in the chapel. Its acoustics can easily be improved by adding some absorptive surfaces. Despite the maximum proposed acoustically treated surfaces, the goal of an adequate acoustic for chamber music performances cannot be achieved. A research of adapted repertoire such as choral recitals has been suggested.

Figure 1 .

 1 Figure 1.-Front view of the chapel

Figure 3 .

 3 Figure 3.-Typical measured echogram (integrated 2.5ms) for the octave band 500 Hz and 1000 Hz

  : A maximum of absorptive surfaces The following proposed solution has in total about 270 m² of equivalent sound absorbing surfaces: • Floor : carpeting below the seats and the side aisles • Walls (woodwork): Mineral wool behind the grooved woodwork • Walls (Stations of the Cross): mineral wool behind the painted fabric • Walls (below the stained-glass windows): curtains or moving absorbing panels • Walls (around the stained-glass windows): absorbing plaster or absorbing foam • Doors (before the sacristy and behind the husting): curtains • Arches: absorbing plaster or absorbing foam • Ceiling: Mineral wool behind rosettes

Figure 4 .

 4 Figure 4.-Reverberation time of different proposed solutions for the chapel

Figure 5 .

 5 Figure 5.-Chorus recital in the chapel

Table I .

 I -Reverberation time objective for the seated chapel

	Frequency	125 Hz	250 Hz	500 Hz	1000 Hz	2000 Hz	4000 Hz
	RT	2.7 s	1.9 s	1.5 s	1.2 s	0.8 s	0.5 s

Table II .

 II -Measurement results for the empty chapel without seats

	Frequency	125 Hz	250 Hz	500 Hz	1000 Hz	2000 Hz	4000 Hz
	RT	5,6 s	5,2 s	5,5 s	5,4 s	3,7 s	2,3 s
	EDT	5.0 s	4.9 s	5.3 s	5.1 s	3.5 s	2.1 s
	C80	-4.4	-5.4	-7.3	-6.4	-1.8	0.3
	D50	21.2	16.1	9.2	13.2	31.8	40.8

Table III .

 III -Estimated reverberation time for the chapel with 320 listeners

	Frequency	125 Hz	250 Hz	500 Hz	1000 Hz	2000 Hz	4000 Hz
	RT	4.4 s	3.8 s	3.6 s	3.3 s	2.6 s	1.8 s

Table IV .

 IV -Estimated reverberation time for the two proposed solutions

	Frequency	125 Hz	250 Hz	500 Hz	1000 Hz	2000 Hz	4000 Hz
	RT (1 st solution)	3.3	2.4	2.0	1.8	1.4	1.1
	RT (2	nd solution)	3.6	2.8	2.4	2.2	1.7	1.3

Acknowledgement

Thanks to the Mairie de Caliure et Cuire, France


domain: spi phys

text:
Antoine Hajczak

Julien Christophe

Cansev Kucukosman

Christophe Schram

Numerical Parametric Investigation of Aeroacoustic Installation Effects in a Distributed Electric Propulsion System

.

This paper is the follow-up to this work and aims at investigating some remaining possibilities for the optimisation of the configuration main parameters, as for example the propeller position along the main wing chord, or the relative clocking angle in case of multi-propellers configurations, which are expected to induce a reduction of the noise footprint by acoustic shielding and destructive interferences, respectively. The present study proposes a parametric study for DEP configurations main parameters using fast low-order noise prediction methods in order to identify potential configurations leading to a substantial reduction of the noise radiated towards an observer located under the flightpath.

In this paper, three noise mechanisms are investigated using dedicated low-order methods, briefly described hereunder:

 for trailing-edge noise.

. Two configurations are proposed in the present study, that have been experimentally and numerically analysed within the scope of the H2020 EC project ARTEM. The model consists of a wing and up to three propellers positioned either in front of it (tractor configuration), or above it (pusher configuration). For these configurations, the two following parametric investigations are proposed:

• Variation of the propeller position relative to the main wing for a single propeller. This also includes separation distances that cannot be reached in the accompanying experiments for which the wake interaction noise might be dominant with respect to self noise only. • Variation of the clocking angle between two propellers to analyse its effect on the radiated tonal noise. This also includes the study of the possible acoustic benefit of changing the rotational direction of some propellers relative to the others (co-or contra-rotating pair of propellers).

Based on previous work conducted within the European H2020 project ARTEM, a series of parametric investigations has been performed by means of low order numerical simulations in order to establish some noise guidelines for the design of distributed propulsion systems. The physical phenomena investigated are tonal and broadband self noise from the propeller(s), as well as tonal noise due to the periodic impingement of a propeller wake on the wing leading-edge. In this work, the propeller and main wing geometries are prescribed while their relative positions are varied according to realistic propulsion configurations, referred to as pusher and tractor, respectively. For tonal self noise, the possible interferences that result from the superposition of two co-or contra-rotating propellers sound fields are also examined, as a function of the relative phase between both propellers, and in the possible presence of a neighbouring main wing. Some first conclusions about passive noise mitigation on distributed propulsion configurations are finally drawn. Noise shielding and appropriate phasing of the propellers are shown to yield beneficial effects, while scattering by the airfoil edges can be detrimental.

Nomenclature

I. Introduction

I n the recent years, much effort has been devoted toward the development of alternative aircraft propulsion concepts.

Distributed Electric Propulsion (DEP) is one of the most promising solutions contemplated thus far and has received considerable research attention, notably in terms of aerodynamics, emissions and costs. Regarding noise emissions, some acoustic prediction methodologies have been proposed in recent work from Rizzi et al. [START_REF] Rizzi | Annoyance to noise produced by a distributed electric propulsion high-lift system[END_REF], or Bernardini et al. [START_REF] Bernardini | Numerical Characterisation of the Aeroacoustic Signature of Propeller Arrays for Distributed Electric Propulsion[END_REF] for instance. In particular, a study conducted by the present authors within the European H2020 project ARTEM

II. Geometry and parameters investigated

The DEP configurations considered in the project are composed of a main wing body and from one to three propellers. The dimensions, described in Drofelnik et al. [START_REF] Drofelnik | Mid-fidelity aeroacoustic modelling and measurements of pusher and tractor generic Distributed Electric Propulsion systems[END_REF], and chosen so as to obtain a scale factor of about 1:3 with respect to a full scale configuration, are here briefly recalled. The airfoil is a PVS-DE(1)-261717 profile with a maximum thickness of 17%, relative to the chord length of 0.3 m. The incidence has been set to 5 • in the experiments. The airfoil span is taken equal to the width of the INCAS closed test section wind tunnel used for the experimental investigations, which is 2.5 m. The propeller selected in the experiments is a 3 bladed, 13 inches diameter Master Airscrew Clockwise model.

An extensive database has been constituted by varying the relative positions of the airfoil and propeller(s). Two categories of tests have been defined, corresponding to different propulsion architectures: one called «tractor», where the propellers were placed upstream of the wing leading-edge, and another called «pusher» where the propellers were placed above the wing. In the experiments, the min/max positions were 𝑑/𝑐 = 0.5 and 𝑑/𝑐 = 0.83 for the tractor configuration. In pusher, the propeller distance to the leading-edge was 𝑑/𝑐 = 0.6 for the most upstream position and 𝑑/𝑐 = 0.93 for the closest to the trailing-edge. When there were several propellers, their spacing was 𝐿/𝑐 = 1.23, and they were powered independently, so that no relative phase control was possible.

While the previous paper aimed at comparing experimental and numerical results, the aim of the present investigation is twofold:

1) explore parametric variations and corresponding noise results to give recommendations for the design of DEP systems; 2) avoid manufacturing constraints to augment the previous experimental database by studying configurations impossible in the experiments (e.g. short propeller-wing distance or imposed blade phase difference between two propellers). To do so, the following parameter variations have been considered:

• In pusher configuration, a single propeller has been translated in the chordwise direction from the trailing-edge to the leading-edge. A total of 11 computations have been carried out, thus covering the entire airfoil chord. • In tractor configuration, the propeller plane has been moved from about 0.0152 m from the airfoil leading-edge to 0.1652 m, thus spanning a distance of 0.15 m (half the airfoil chord). Here again, a total of 11 computations have been performed. • Finally, to study the effect of propellers relative phase on tonal noise interference, two propellers have been placed with a centre-to-centre separation distance of 0.4 m (𝐿/𝑐 = 1.33). The non-dimensional relative blade phase angle Δ𝜙 × 𝐵/2𝜋 has been varied from 0 to 1 by step of 0.1 (11 computations) in order to cover an entire blade-to-blade angular sector. These computations have been made both in free-field, and with the propeller pair at the airfoil mid-chord in pusher configuration. The acoustic pressure for all these cases has been computed on a far-field hemisphere of radius 𝑅 obs = 125 m (100 times the airfoil half-span) centered on the airfoil 1/4-chord line. Some extractions have been performed in the streamwise 𝑥𝑧 and spanwise 𝑦𝑧 planes.

A summary of these geometrical definitions is given in Fig. 1. Regarding the operating conditions, the propeller rotates at 10,000 RPM and the upstream Mach number is 0.09. In these conditions, the BPF is 500 Hz, and the corresponding chord-based Helmholtz number is 𝑘𝑐 = 2.77.

III. Tonal self noise

In this section, we study tonal self noise generated by the propeller at the BPF harmonics. Please note that no aerodynamic interactions (of potential or viscous nature) have been included in these computations. Therefore, the results presented here are restricted to steady loading and thickness noise.

A. Chordwise position variation for a pusher propeller

The first parameter investigated is the variation of the chordwise position for a propeller over the wing (ie in pusher configuration). A total of 11 positions evenly spaced between the trailing-edge and the leading-edge has been considered. For conciseness, the directivity of the far-field pressure has been presented in Fig. 2 for both the extreme positions and the intermediate one when the propeller is at mid-chord. Comparing the free-fied to the scattered noise levels, we see that the noise emitted by the propeller is partly attenuated by the presence of the wing, due to the specular reflection of acoustic waves on the suction side (shielding effect). However, the wing having a finite chord, some side-effects also take place. Those are particularly visible when the propeller is just above the trailing-edge, the latter behaving as a geometrical singularity that induces a scattering effect similar to what would be obtained when considering a semi-infinite flat plate, as already formally described by Roger [START_REF] Roger | On sound scattering by rigid edges and wedges in a flow, with applications to high-lift device aeroacoustics[END_REF] by using the half-plane Green's function. In that case, we see a significant increase of the noise levels toward upstream observers with respect to the free-field. Conversely, when the propeller is over the leading-edge, the scattered field does not exceed the free-field in the half-downstream part of the sphere, but is still increased with respect to the mid-chord position. These two opposite edge-effects are clearly visible in Fig. 3 where the SPL of the tone has been plotted for three different angles in the 𝑥𝑧 plane (see Fig. 1). Interestingly, at 90°, the noise level remains fairly constant, compared to the other directions that have been considered. The latter have been taken as ±30 • around the vertical and it appears clearly how the noise is increased toward upstream observers as the propeller gets closer to the trailing-edge, while the opposite behavior is found (although to a lesser extent) when the propeller gets closer to the leading-edge.

Some remarks can also be made in the 𝑦𝑧-plane. Looking at Fig. 2 (right column), one can see that the noise levels are not significantly altered toward horizonthal directions. However, when looking below the airfoil, we can see an asymmetry that results from the propeller sense of rotation. The most significant modification of the directivity occurs for azimuthal angles 90 • ≤ 𝜑 ≤ 180 • . This corresponds to the angular sector where the blade goes upward, from an upstream observer's point of view. In this angular sector, the noise reduction can reach almost 10 dB.

In terms of potential for noise reduction, the most favorable configuration seems to be the one where the propeller is at mid-chord. Indeed, as one would expect, this configuration is the one that maximizes specular reflection toward the sky while at the same time minimizing undesirable effects related to edge-scattering that tend to redistribute the noise radiation in the wing shadow region.

B. Streamwise position for a tractor propeller upstream of the wing

The second parameter investigated is the distance between the propeller and the wing leading-edge, when the propulsion system is in tractor configuration. Please note that in that case, aerodynamic interaction effects are expected under the form of viscous wake interaction noise, as well as unsteady loading variation on the blades due to the potential field of the wing. The intensity of these interactions is a priori expected to be directly related to the separation distance between the wing leading-edge and the propeller. This section is focused on the influence of the main wing presence, regardless of the aerodynamic interactions. The aerodynamic interaction between the propeller blades wakes and the wing leading-edge will be separately investigated in Sec. V. Thus, studying both contributions separately will allow to determine their relative importance as a function of the propeller distance.

To study this effect, 11 propeller / wing separation distances have been computed. The shortest separation distance is 0.015 m (𝑑/𝑐 = 0.05) and the longest is 0.165 m (𝑑/𝑐 = 0.55). In the corresponding experiments, the range of variations was between 0.15 m (𝑑/𝑐 = 0.5) and 0.25 m (𝑑/𝑐 = 0.83) [START_REF] Drofelnik | Mid-fidelity aeroacoustic modelling and measurements of pusher and tractor generic Distributed Electric Propulsion systems[END_REF]. The aim of the present investigation is to extend the experimental range in order to place the propeller closer to the main wing leading edge, which is expected to enhance the propeller-wing interactions. As in the previous paragraph, for clarity purpose, only the directivities corresponding to the shortest, the longest, and the intermediate distances have been presented in Fig. 4.

Looking first at the results for the shortest distance, we can see that the presence of the wing induces a very significant scattering effect, with a maximum noise level at an azimuthal angle 𝜑 > 90 • . As in the previous paragraph, this asymmetry results from the propeller rotational direction. Then, looking at the results for increasing separation distances, we see that the directivity of the noise emission gets closer to the free-field directivity as the propeller is displaced away from the wing, as expected. The present results seem to indicate that, even without considering the mutual aerodynamic interactions that can take place between the propeller and the wing (whether of potential or viscous nature), the presence of the wing can significantly amplify the propeller noise radiation. Considering the fact that a propeller radiates mostly in its rotation plane is a priori not in contradiction with this result. Indeed, the three-dimensional nature of the present case makes plausible the fact that some near-field component of the propeller sound field is scattered by the leading-edge with an increasing efficiency as the propeller gets closer to the wing.

C. Relative blades phase-angle

This paragraph is devoted to the case where two neighbouring propellers rotate in the same plane. In what follows, the separation between both propellers centre is fixed as 1.33𝑐 and their rotation velocity is equal to 10.000 rpm, making the computation of the total acoustic field possible by linear superposition of both individual complex pressure fields at common observer positions. First, the case where both propellers rotate in the same or opposite direction is studied in free-field with various blade azimuthal phase differences. Then, the main wing is added under the propeller pair to determine the noise reduction potential when combining both propeller synchronization and wing shielding effect. In that case, the propeller pair is placed at the mid-chord position, which has been identified as the most beneficial in terms of noise reduction in the paragraph III.A.

Two co-rotating propellers

The first case considered is when both propellers have the same sense of rotation. To assess the effect of propeller blade phase difference, the total field has been computed by linear superposition of the acoustic complex pressure field emitted by individual propellers, taking one of them as the reference and varying the intial azimuthal angle of the second to cover an entire blade-to-blade angular sector 2𝜋/𝐵.

The results obtained for propeller non-dimensional phase difference values Δ𝜙𝐵/2𝜋 of 0, 0.2, 0.5 and 0.7 are presented in Fig. 5. When both propellers are perfectly synchronized (Δ𝜙 = 0), all propeller blades are parallel from one propeller to the other at all times. In these conditions, we see some destructive interferences that occur around 𝜑 = 30 • and 𝜑 = 150 • , but also perfectly constructive interferences under the vertical (𝜃 = 𝜑 = 90 • ). In this particular direction, the sound waves coming from both propellers are perfectly in phase, resulting in an increase of the total field by 6 dB with respect to the value obtained for a single propeller (doubling the pressure amplitude of a given source results in an increase of 10log 10 (4) ≃ 6). Conversely, when the propeller non-dimensional phase difference Δ𝜙𝐵/2𝜋 is equal to 1/2, that is to say when the phase difference between both propellers is half a blade passage, we see that the total sound field is considerably reinforced everywhere but right under the propeller pair (𝜃 = 𝜑 = 90 • ) where it vanishes almost entirely. At intermediate phase differences, when Δ𝜙𝐵/2𝜋 is equal to 0.2 or 0.7 respectively, this direction of extinction is moved to the azimuths 𝜑 ≃ 120 • and 𝜑 ≃ 60 • , respectively. From the cases considered just above, the ones with zero and half blade passage phase difference have been considered with the wing placed such that the pair is at mid-chord, as presented in Fig. 6. In both cases, the acoustic shielding induced by the presence of the wing reduces the noise levels, except at the vertical when the propellers are rotating with half blade passage phase difference. In that case, the free-field result vanishes almost entirely in this particular direction, but the scattering by the wing body re-emits some secondary sound waves, leading to higher SPL values than in free-field. Nevertheless, even considering this phenomenon, the sound emitted toward the vertical direction remains significantly reduced with respect to the other directions, thus maintaining the benefit of this synchronization between propellers. The directivities associated to both relative phase angles between both propellers with the wing taken into account is presented in Fig. 7. The superposition of both results highlights the fact that the gain in flyover directions for half blade passage phase difference is considerably compensated by an over-emission toward sideline observers 0 ≤ 𝜑 ≤ 60 and 120 ≤ 𝜑 ≤ 180. To summarize, for a pair of propellers, constructive and destructive interferences occur between individual sound fields. These interferences are directly related to the phase angle between both propeller blades. In the case where both propellers are co-rotating, the two particular cases where both propellers are perfectly in phase and with half blade passage phase difference show complementary benefits over one another. While the former is preferable in sideline directions, the latter shows an extinction toward flyover observers. Thus, the determination of which configuration is the most desirable is not straightforward and would depend on the priority given, for instance, to cabin noise with respect to emissions toward the ground.

Two contra-rotating propellers

Now, we consider the case where the propellers rotate in opposite directions. The same phase differences than in the previous paragraph are considered, first in free-field, as presented in Figure 8.

When the propellers are perfectly synchronized, contrarily to the co-rotating case, destructive interferences occur under the vertical (𝜑 = 90 • ) while around 𝜑 = 30 • and 𝜑 = 150 • , constructive interferences lead to an increase of about 6 dB in the total field. Conversely, and again as opposed to the co-rotating case, constructive interferences occur at 𝜑 = 90 • when the blades nondimensional phase difference Δ𝜙𝐵/2𝜋 is equal to 1/2. For intermediate values of 0.2 and 0.7, the interference pattern is seen to "rotate" around the 𝑥-axis. Both particular cases where the relative phase angle between both propellers is zero and half a blade passage are considered with the inclusion of the wing inside the acoustic computation, the propeller pair being placed at mid-chord, as shown in Figure 9. Just like in the co-rotating case, the presence of the wing induces a general diminution of the noise levels, except at directions where wave cancellations occured in free-field, due to the wing secondary noise emission by scattering. Then, similarly to the co-rotating propeller pair, the cases with zero and half blade passage phase angle with inclusion of the wing effect are compared in Figure 10. While, in the co-rotating case, the best candidate depends on whether flyover or sideline observers are prioritized, here both sideline and flyover directions show lower noise levels when the propellers have zero relative phase difference.

IV. Broadband self noise

The methodology for predicting broadband trailing-edge noise briefly described in Sec. I relies on two-dimensional RANS computations performed at predefined iso-radii according to the adopted strip approach. The same Amiet-ATV methodology is applied for the present parametric study and includes the acoustic reflections of the propeller TE noise by the wing. In order to model the propeller noise source, 5 strips have been used, on which a corresponding RANS computation has been re-used from Drofelnik [START_REF] Drofelnik | Mid-fidelity aeroacoustic modelling and measurements of pusher and tractor generic Distributed Electric Propulsion systems[END_REF]. The Lee model [START_REF] Lee | Empirical Wall-Pressure Spectral Modeling for Zero and Adverse Pressure Gradient Flows[END_REF] is then used to compute the wall-pressure spectrum injected in the Amiet's theory in rotation [START_REF] Schlinker | Helicopted Rotor Trailing Edge Noise[END_REF]. The FEM mesh used to compute the ATV solution contains about 500,000 tetrahedral elements and the noise prediction is performed on the listener sphere shown in Fig. 1 using a Kirchhoff radiation condition applied to the outer surface of the FEM domain, as in Drofelnik [START_REF] Drofelnik | Mid-fidelity aeroacoustic modelling and measurements of pusher and tractor generic Distributed Electric Propulsion systems[END_REF].

A. Chordwise position variation for a pusher propeller

The parametric investigation of the propeller relative position compared to the wing is first made for the pusher configuration. The corresponding broadband trailing-edge noise radiated on the listener sphere is shown in Fig. 11, with bottom view representation and flight direction from the right to the left. Three frequencies are considered ( 𝑓 =100, 1000 and 5000 Hz, He=0.55, 5.5 and 33.3), the last corresponding to the maximum frequency that can be solved by the FEM mesh according to the six elements per wavelength criterion. The first column shows the noise radiation pattern of an isolated propeller with a zone of low noise emission in the propeller plane, due to the relatively low twist of the blades. This reference solution is compared to six different positions of the propeller over the wing ranging from the leading-edge to the trailing edge. It is first observed that for the trailing-edge position, the obtained radiated sound is similar to that of an isolated propeller, while the leading edge results are highly altered due to the presence of the wing. This is mainly attributed to the shape of the wing, where the round leading edge and sharp trailing edge have a different effect on the propeller noise scattering and regeneration on the opposite side of the wing. For the lowest frequency considered, corresponding to a Helmoltz number based on the wing chord lower than one, the directivity pattern remains close to the isolated propeller directivity. For that frequency, the wing can be considered as relatively compact and then transparent to the propeller noise emission. For the other frequencies, the sound directivities are strongly affected by the presence of the wing and the low sound emission plane of the isolated propeller is not observed anymore.

The radiated noise results are further analysed in Fig. 12 by intersecting the listener sphere by 𝑥𝑧 and 𝑦𝑧 planes, corresponding to streamwise and spanwise directions respectively. For the streamwise directivities of Fig. 12 column), the flight direction is from left to right, while for the spanwise directivities (right column), the configuration is seen from upstream, with the rotational direction from low to high 𝜑 angles. Looking to the streamwise directivity, the dipolar pattern observed for the isolated propeller is only slightly altered by about 2dB, mainly in the upstream direction. When increasing the frequency, the upstream part of the directivity remains similar to the isolated propeller case while an increase of the radiated sound towards the downstream direction is observed when the propeller is displaced from the leading edge to the trailing edge. Concerning the directivity in the spanwise direction, at low frequency, as the plane cut is performed in the propeller plane where no sound is radiated, the results are similar for all propellers positions over the wing. The small variations observed are attributed to the accuracy of the method, for which the results should be further consolidated in terms of mesh convergence of the FEM solution, effect of the finite span domain and number of integration points used over the propeller rotation. With increasing frequency, a directivity lobe appears on 𝜑 angles larger than 90 degrees, corresponding to positions where the blade is moving away from the wing in pusher configuration. This effect is amplified when the propeller is located at the leading edge, with up to 10 dB increase compared to the isolated configuration.

B. Streamwise position for a tractor propeller upstream of the wing

Similarly to the pusher configuration, the radiated noise in tractor configuration is first represented on the listener sphere in Fig. 13, with the isolated propeller in the first column and compared to a subset of computations with varying propeller-wing distances, similar to those investigated in Sec. III.A. For the 100 Hz frequency, the free-field noise radiation pattern remains for all positions of the propeller relative to the wing, with a low noise radiation observed in the propeller radiation plane. This pattern is attenuated when reaching positions close to the wing. With increasing frequency, this patterns gets highly altered. At 1000 Hz, a low emission zone is preserved below the propeller-wing geometry with an increase of the sound in the lower part of the sphere that corresponds to the side where the propeller blade is rotating towards the wing. This is explained mainly by the trailing-edge sound directivity that is oriented upstream of the blade segments and towards the propeller rotational direction. At 5000 Hz, more interferences are observed on the directivity with the similar increase on the lower part of the radiation sphere when decreasing the propeller-wing distance.

As for the pusher configuration, the radiated noise results are further analysed in Fig. 14 by intersecting the listener sphere by 𝑥𝑧 and 𝑦𝑧 planes, corresponding to streamwise and spanwise directions respectively. At 100 Hz, the dipolar directivity is preserved for all the investigated propeller-wing distances, with a small decrease of the maximum amplitude of about 2 dB when the propeller is installed. When the propeller is located at the closest position relative to the wing, the low noise emission observed in the propeller plane is smoothed, with an increase of about 5 dB at 𝜃 = 90 • . In the spanwise plane, at 100Hz, the cut is performed in the propeller plane where no sound is radiated, but also where the results might be corrupted by the numerical accuracy. Further investigations should be here performed in terms of mesh convergence of the FEM solution, effect of the finite span domain and number of integration point used over the propeller rotation. When increasing the frequency, the noise radiated upstream of the wing-propeller configuration is not influenced by the propeller position, the installed noise results being similar to the isolated one. When the propeller-wing distance is decreased, an increase of the sound is observed for the downstream angles with about 5 to 10dB, depending on the frequency and radiation angle. This increase toward the downstream angles is similar to the observations made in Sec. III.B for the propeller tonal self noise. In the propeller plane, the directivities being uniform over the angles for the isolated propeller are now presenting directivity lobes that are oriented to angles about 𝜑 = 150 • . As explained above, these angles correspond positions where the propeller blade is moving toward the wing and the corresponding radiated noise is amplified mainly due to the trailing-edge noise directivity.

• 135 • 90 • 45 • 0 • -90 -85 -80 -75 -70 SPL (dB) 180 • 135 • 90 • 45 • 0 • -55 -50 -45 -40 -35 SPL (dB) 1000 Hz 180 • 135 • 90 • 45 • 0 • -55 -50 -45 -40 -35 SPL (dB) 180 • 135 • 90 • 45 • 0 • -40 -30 -20 -10 SPL (dB) 5000 Hz 180 • 135 • 90 • 45 • 0 • -40 -30 -20 -10 SPL (dB)

V. Tonal wake interaction noise

The present tonal wake interaction noise study aims at quantifying the radiated noise levels and compare them to the tonal self-noise predictions made in Sec. III.A. Increasing the distance between the propeller and the main wing in the tractor configuration is supposed to result in decreasing amplitudes of the corresponding tonal wake interaction noise. The main objective here is then to determine if the tonal wake interaction noise is of importance compared to the tonal self-noise reported in Sec. III.A.

The methodology [START_REF] Grasso | Development of hybrid methods for the computation of tonal and broadband fan noise source and propagation[END_REF], based on RANS computations, is used to have a proper wake description at the main wing location. The methodology consists in cutting the different iso-radii 2D RANS computations at a particular distance from the propeller and to re-assemble them to obtain a wake velocity plane.

In the present case, the wake data from the RANS computations at 18 spanwise radius positions have been extracted at the same streamwise locations as used in Sec. III.A. In the interpolation process, the first 8 strip positions are disregarded as the RANS computations have not reached a fully converged solution. This is mainly due to the larger blade thickness at the root that leads to large structure oscillations around the profile, similar to the classical von Kármán vortex shedding observed around cylinders. The noise produced by the airfoil subjected to the wake interaction is also treated using a strip methodology. The total radiated sound is then the summation of the noise produced by the individual strips. A proper discretisation of the airfoil span is necessary to properly capture the wake variation along the airfoil span. The wing span is reduced to the extremity of the wake plane domain included in [-0.17, 0.17] m and is divided by 41 strips. The representation of the azimuthal wake velocity relative to the propeller reference frame is given in Fig. 15 (a) by representing in color dots the wing strips that are exposed to the propeller wake. The black dots represent the strips outside of the wake and are not considered for the noise computation. The corresponding upwash velocity component of the azimuthal velocity, which is the main contributor to the unsteady lift producing noise, is calculated for each wing strips which are exposed to the wake (shown in Fig. 15 (a) only for certain positions). Due to the counter clockwise rotation of the propeller, the wing strips which are on the left side of the propeller hub are exposed to an upwash component while the wing strips which are on the right side of the propeller hub are exposed to a downwash component along all the azimuthal angles. The wake velocity amplitude difference between the root and the tip of the blade is around maximum 24% with higher amplitudes at the blade root.

The Fourier coefficients of fluctuating lift at the harmonics of the blade passing frequency are calculated using an Amiet's theory framework [START_REF] Amiet | Noise due to Turbulent Flow past a Trailing Edge[END_REF][START_REF] Grasso | Development of hybrid methods for the computation of tonal and broadband fan noise source and propagation[END_REF]. Fig. 16 shows the five first harmonics of the lift fluctuations when the propeller is installed at 𝑑 = 0.25 𝑚 upstream of the main wing, corresponding to the largest distance used in the corresponding experiments [START_REF] Drofelnik | Mid-fidelity aeroacoustic modelling and measurements of pusher and tractor generic Distributed Electric Propulsion systems[END_REF]. The two first harmonics are largely dominant compared to the higher harmonics. Their amplitudes are decreasing with the increasing radius from hub to tip, that is directly related to the wake deficit amplitudes variations observed in Fig. 15 (b).

As for the other sound mechanisms investigated above, directivity plots of the sound radiated for the tonal wake interaction noise mechanism are shown in Fig. 17 for streamwise and spanwise cuts of the listeners sphere, for the three first BPFs. On the spanwise plane, quadrupolar directivities are observed due to the observed opposite phase of distributed dipoles on both sides of the mid-span plane. When the propeller-wing distance is large enough, the directivity is symmetrical with the mid-span plane resulting in similar amplitude on both sides with low amplitude sound radiation at 𝜑 = 90 • . With the decrease of the propeller-wing distance, a slight asymmetry is observed for the two first BPF, while a third lobe appears at the third BPF.

In terms of amplitude, the radiated sound increases with the propeller-wing distance reduction as expected, except for the first BPF. The reason for the different behaviour remains unclear at this stage, but may be linked to interferential effects related to the phases at which the different parts of the wake are interacting with the wing. This issue should be further verified by looking to variation of the wake deficit centerline over the blade span or to compare to 3D computations of the same blade. The amplitude of the tonal wake interaction noise remains lower than the tonal self noise at the first BPF, while the wake interaction noise mechanism is expected to dominate for small distances between the propeller and the wing. Again, the de-phasing of the acoustic sources on the main wing could result in the cancellation of constructive interferences.

Looking to the streamwise plane, dipolar directivities are observer for the 3 first BPF. Although this is a priori expected for the first BPF (He=2.77) [START_REF] Christophe | Application of hybrid methods to high frequency aeroacoustics[END_REF], the directivity of the airfoil response function resulting from Amiet's theory for leading-edge noise, on which the present model is based, is supposed to have an increased number of lobes with increasing Henumber. This behavior probably comes from the chord integration performed before the far field propagation, which limits the validity of the methodology for compact airfoils [START_REF] Grasso | Development of hybrid methods for the computation of tonal and broadband fan noise source and propagation[END_REF]. Finally, the large differences in amplitude observed in the streamwise plane with the propeller-wing distance that are mainly due to the location of the interference plane in the spanwise plane. Again, the effect of the 3D wake reconstruction from 2D-RANS computations should be further analysed to assess its influence on the phased dipole over the wing, and then the interference plane location that appears near the wing mid-span.

VI. Conclusion

The work presented in this paper is inscribed within the European research project ARTEM (Aircraft noise Reduction Technologies and related Environmental iMpact), dedicated to the development of innovative technologies for reducing aircraft noise at the source. In this context, one of the technologies considered is Distributed Electric Propulsion, which involves several propellers distributed on the aircraft wings to provide the required thrust. As a first step in this project, some numerical mid-fidelity methods have been proposed to be able to predict the noise generated by DEP configurations with sufficient accuracy and moderate computational cost. These methodologies have been confronted to noise measurements made specifically during the project, as presented in previous work [START_REF] Drofelnik | Mid-fidelity aeroacoustic modelling and measurements of pusher and tractor generic Distributed Electric Propulsion systems[END_REF]. Then, a second objective, tackled in this paper, was to use these prediction capabilities in order to determine the link between the propeller(s) / wing relative positions and the noise perceived by an observer on the ground.

To do so, these mid-fidelity methods have been used to perform parametric variations of pusher and tractor DEP configurations. In pusher, the chordwise position of a single propeller has been varied from the leading-edge to the trailing-edge, and the interferences resulting from the superposition of two coplanar propellers sound fields at the Blade Passing Frequency have been investigated, both in free-field and in the case where the pair was placed in pusher, at the airfoil mid-chord. In tractor configuration, the distance between a single propeller and the wing leading-edge has been increased, from very small distances to about half the airfoil chord. In all cases, the propeller self-noise (tonal and broadband) has been investigated, including the scattering effect induced by the presence of the wing. In tractor configuration, the tonal wake interaction noise resulting from the impact of the propeller blades viscous wakes on the airfoil has also been analysed and compared to tonal self-noise.

The analysis of the results can be presented for each noise source separately as follows: 1) For tonal self-noise, a beneficial effect can be expected at the considered Helmholtz number from noise shielding by the airfoil body, provided that the propeller is not placed too close to the airfoil edges. Indeed, in the latter case, our findings support previous observations according to which the propeller sound field is scattered by the edge and redistributed in the wing shadow region [START_REF] Roger | On sound scattering by rigid edges and wedges in a flow, with applications to high-lift device aeroacoustics[END_REF]. This shielding effect can be combined with an appropriate choice of the relative blade phase angle between two coplanar propellers to create destructive interferences in the desired direction. In some cases however, destructive interferences toward the ground also showed constructive inteferences in sideline directions, which would be detrimental to cabin noise for instance. In tractor configuration, no shielding can be expected, the directivity of propeller noise being concentrated in the rotation plane. On the contrary, while the directivity got closer to free-field radiation at the largest separation distances, the presence of the wing was shown to significantly enhance the propeller noise radiation by scattering.

2) For the broadband self noise, as for the tonal self noise, substantial noise shielding effect are expected for the pusher configuration. When placed close to the trailing-edge, the noise radiated has a directivity close to the isolated propeller. An increase of radiated noise is observed in the downstream and side regions when the propeller is moved toward the leading-edge, resulting in no particular shielding in the case of broadband noise mechanism. As for the tonal self-noise, no shielding was expected and the present study confirmed the increase of radiated noise due to the diffraction on the main wing, especially in the downstream and side region, as in the pusher configuration. 3) For the tonal wake interaction noise, the expected noise increase with the propeller-wing distance decrease only appeared from the first BPF. One possible explanation is the wake reconstruction methodology that is based on 2D RANS computations at iso-radii. As this methodology does not ensure a perfect synchronisation of the wake developments over the blade span, the corresponding resulting source dipoles on the main wing might suffer from phase inaccuracy when computed from the Amiet's theory framework, and would alter in turn the constructive or destructive interferences at the observer positions. The amplitudes at the first BPF remain lower than those observed for tonal self noise, while this was not expected for smaller propeller-wing distances, suggesting further investigations in future work.

  𝑥, 𝑦, 𝑧 = Cartesian coordinates 𝜃, 𝜑 = Polar and azimuthal observation angles Δ𝜙 = Relative phase angle between two propellers 𝑐 = Wing chord 𝑑 = Propeller plane -airfoil leading-edge distance 𝜆 = Acoustic wavelength He= 2𝜋𝑐/𝜆 = Helmholtz number 𝐵 = Number of propeller blades 𝐿 = Centre-to-centre distance between two propellers 𝑅 obs = Radius of the microphone half-sphere ì Ω = Propeller angular velocity vector

Fig. 1

 1 Fig. 1 Geometry and parameters investigated (microphone half-sphere not to scale).

Fig. 2

 2 Fig. 2 Sound Pressure Level of the far-field acoustic pressure at the BPF (He= 2.77) for observers located at the intersection between the hemisphere and the (left): 𝑥𝑧-plane, (right): 𝑦𝑧-plane. Propeller located at the (top-to-bottom): trailing-edge, mid-chord, leading-edge. (-): Scattered field, (-): Free-field.

Fig. 3

 3 Fig. 3 Sound Pressure Level of the far-field acoustic pressure at the BPF (He= 2.77) for three directions of observation.

Fig. 4

 4 Fig. 4 Sound Pressure Level of the far-field acoustic pressure at the BPF (He= 2.77) for observers located at the intersection between the hemisphere and the (left): 𝑥𝑧-plane, (right): 𝑦𝑧-plane. Propeller located at a distance from the leading-edge of (top-to-bottom): 0.015, 0.09, 0.165 m (d/c=0.05, 0.3, 0.55). (-): Scattered field, (-): Free-field.

Fig. 5

 5 Fig. 5 Free-field Sound Pressure Level of the far-field acoustic pressure at the BPF for observers located at the intersection between the hemisphere and the (left): 𝑥𝑧-plane, (right): 𝑦𝑧-plane. Two co-rotating propellers separated by a distance 𝐿/𝑐 = 1.33 with a relative phase angle Δ𝜙 × 𝐵/2𝜋 equal to (top-to-bottom): 0, 0.2, 0.5, 0.7.

Fig. 6

 6 Fig. 6 Sound Pressure Level of the far-field acoustic pressure at the BPF (He= 2.77) for observers located at the intersection between the hemisphere and the (left): 𝑥𝑧-plane, (right): 𝑦𝑧-plane. Two pusher co-rotating propellers separated by a distance 𝐿/𝑐 = 1.33 and positioned at the mid-chord of the main wing. Top: Δ𝜙 × 𝐵/2𝜋 = 0, bottom: Δ𝜙 × 𝐵/2𝜋 = 0.5. (-): Scattered field, (-): Free-field.

Fig. 7

 7 Fig. 7 Sound Pressure Level of the far-field scattered acoustic pressure at the BPF (He= 2.77) for observers located at the intersection between the hemisphere and the (left): 𝑥𝑧-plane, (right): 𝑦𝑧-plane. Two co-rotating propellers separated by a distance 𝐿/𝑐 = 1.33 with a relative phase angle Δ𝜙 × 𝐵/2𝜋 equal to (-): 0, (--): 0.5.

Fig. 8 Fig. 9

 89 Fig. 8 Free-field Sound Pressure Level of the far-field acoustic pressure at the BPF for observers located at the intersection between the hemisphere and the (left): 𝑥𝑧-plane, (right): 𝑦𝑧-plane. Two contra-rotating propellers separated by a distance 𝐿/𝑐 = 1.33 with a relative phase angle Δ𝜙 × 𝐵/2𝜋 equal to (top-to-bottom): 0, 0.2, 0.5, 0.7.

Fig. 10 SoundFig. 11

 1011 Fig. 10 Sound Pressure Level of the far-field scattered acoustic pressure at the BPF (He= 2.77) for observers located at the intersection between the hemisphere and the (left): 𝑥𝑧-plane, (right): 𝑦𝑧-plane. Two contra-rotating propellers separated by a distance 𝐿/𝑐 = 1.33 with a relative phase angle Δ𝜙 × 𝐵/2𝜋 equal to (-): 0, (--): 0.5.

Fig. 12 Sound

 12 Fig. 12 Sound Pressure Level of the far-field acoustic pressure resulting from the broadband propeller self-noise in pusher conditions for three selected frequencies (He= 0.55, 5.54 and 27.72) for observers located at the intersection between the hemisphere and the (left): 𝑥𝑧-plane, (right): 𝑦𝑧-plane. Propeller in free-field conditions (-), located at leading-edge (--), mid-chord (..) and trailing-edge (-.) above the wing.

Fig. 13

 13 Fig. 13 Sound pressure levels of the radiated sound on the listener sphere for the tractor configuration.

Fig. 14

 14 Fig. 14 Sound Pressure Level of the far-field acoustic pressure resulting from the broadband propeller self-noise in tractor conditions for three selected frequencies (He= 0.55, 5.54 and 27.72) for observers located at the intersection between the hemisphere and the (left): 𝑥𝑧-plane, (right): 𝑦𝑧-plane. Propeller in free-field conditions (-), located at a distance from the leading-edge of 0.015 (--), 0.09 (..), 0.165 m (-.) corresponding to d/c=0.05, 0.3, 0.55.

  Fig. 15 (a) Front representation of the wake data extracted at 𝑑 = 0.25 𝑚 downstream of the propeller and (b) the corresponding upwash velocity component over the azimuthal angle.

Fig. 16

 16 Fig. 16 Magnitude of the fluctuating lift harmonics for a propeller-wing distance of 𝑑 = 0.25 𝑚 on the (a) left and (b) right side of the origin.

Fig. 17

 17 Fig. 17 Sound Pressure Level of the far-field acoustic pressure resulting from wake interaction noise for the first three BPF harmonics (He= 2.77, 5.54 and 8.31) for observers located at the intersection between the hemisphere and the (left): 𝑥𝑧-plane, (right): 𝑦𝑧-plane. Propeller located at a distance from the leading-edge of 0.015 (-), 0.09 (--), 0.165 m (..) corresponding to d/c=0.05, 0.3, 0.55.

Acknowledgments

This project has received funding from the European Union's Horizon 2020 research and innovation program under grant agreement No 769350.


text:
Jeanne Methel
email: jeanne.methel@onera.fr

Fabien Méry
email: fabien.mery@onera.fr

Maxime Forte

Olivier Vermeersch

LAMINAR FLOW CONTROL ALONG THE ATTACHMENT LINE OF A SWEPT WING

Keywords: laminar-turbulent transition, attachment line contamination, wall suction

Reducing aircraft fuel consumption by maximising the extent of laminar flow on wings assumes that the initial flow, along the wing's attachment line, is laminar. However, if the wing is attached to a solid wall, the wing's attachment line can be contaminated by the turbulent boundary layer developing over the solid wall for flow conditions summarised in a critical Reynolds number (R) greater than 250. Since typical R values encountered in flight can be well above 400, techniques, such as wall suction along the wing's leading edge were developed to further delay the threshold R at which contamination occurs. The present paper presents the results from an experimental investigation performed on the ONERA DTP-A model fitted with leading edge suction capabilities. The experiment was performed in the ONERA F2 wind tunnel in the framework of the EU-funded Clean Sky 2 HLFC-WIN project (LPA-IADP platform), while the suction panels were manufactured by Aernnova, an aero-component manufacturing company. Hot film measurements and infra-red thermography showed that attachment line contamination could effectively be delayed up to threshold R values of 1000 for large suction flow rates. Although panels from different manufacturing processes and with different geometric characteristics were tested, no significant difference from these parameters were observed.

INTRODUCTION

Promoting laminar flow over the wings and empennage of an aircraft can result in a significant reduction in skin-friction drag, and consequently, fuel consumption. Although many techniques were successfully developed to maximise laminar flow, all work under the assumption that the initial starting flow, also known as the attachment line, is laminar. More precisely, the attachment line is defined at the streamline in the leading edge region across which flow separates between the upper and the lower surfaces, and where static pressure reaches a maximum.

Assuming laminar flow at the attachment line is not guaranteed, especially in the case where the wing section is attached to a solid wall (e.g., fuselage or wind tunnel wall). In this type of configuration, the turbulence that develops over the solid wall can propagate along the attachment line, resulting in attachment line contamination and turbulent flow over the entire wing. The contamination process is highly non-linear in that, once relevant flow conditions are reached, the attachment line as well as the entire wing become fully turbulent quasi-instantaneously.

Theoretical and experimental investigations by Pfenninger [START_REF] Pfenninger | Flow phenomena at the leading edge of swept wings. Recent development in boundary layer research[END_REF] and Poll [START_REF] Poll | Some aspects of the flow near a swept attachment line with particular reference to boundary layer transition[END_REF] enabled to define a criterion, critical Reynolds number R equal to 250, above which attachment line contamination (ALC) is most likely to occur. This Reynolds number is defined as:

R = W e η ν with η = ν dU e dx | x=0 , (1)
where W e is the spanwise component of velocity defined as W e = Q ∞ sin ϕ, Q ∞ the freestream velocity, ϕ the wing's sweep angle, ν the kinematic viscosity, and η a parameter related to the gradient of velocity in the curvilinear abscissa in the chordwise direction at the location of the attachment line, i.e., x = 0. The schematic representation of the contamination process shown in Figure 1 also illustrates the used nomenclature. Since R values encountered in flight by commercial aircraft are typically much greater than 400, avoiding ALC is therefore necessary to consider the implementation of laminar wings. One proven approach in preventing attachment line contamination is to use Laminar Flow Control (LFC) such as wall suction through micro-perforated panels at the leading edge of the wing. Direct numerical simulations performed by [START_REF] Spalart | Direct numerical study of leading-edge contamination. Fluid dynamics of three-dimensional turbulent shear flows and transition 1-5[END_REF] initially showed the ability of wall suction to delay contamination up to threshold R values of 400, while later experimental investigations by [START_REF] Arnal | Laminar Flow Control along the wing leading edge[END_REF], [START_REF] Méry | Laminar Flow control along the wing leading edge[END_REF] showed that this limit could be pushed even further, at approximately 650. In the present paper, references to the critical R always correspond to the range 250-280; while the threshold R is the value for which contamination occurs in the presence of active flow control, and is therefore generally greater than the critical R.

Once contamination is cancelled and if freestream turbulence is low, then natural transition in both the spanwise and chordwise (z -and x -, respectively) directions can occur. In both cases, transition can be modelled by linear stability theory, where the primary instabilities of the boundary layer evolve linearly up to a certain amplification threshold, past which secondary instabilities appear. At this stage, the first turbulent spot quickly occurs, heralding the beginning of the laminar-turbulent transition region and the breakdown to turbulence. For attachment line transition along the spanwise direction, the primary instabilities are known as Görtler-Hämmerlin. In the chordwise direction, the primary instabilities can take the form of either crossflow instabilities closer to the leading or Tollmien-Schlichting instabilities further downstream.

The present investigation aimed at testing the same model used in the experiments described in [START_REF] Arnal | Laminar Flow Control along the wing leading edge[END_REF], [START_REF] Méry | Laminar Flow control along the wing leading edge[END_REF] at higher R values to further test the limits of suction in delaying contamination. Another objective was to study the effect of the micro-perforated panels' geometric parameters on the effectiveness of wall suction. First, an overview of the experimental set-up will be provided, describing the wind tunnel facility, model and instrumentation. Next the experimental results will be discussed: first, by examining the pressure coefficient distribution at the leading edge and introducing the concept of the effective sweep angle; next by validating all tested configurations without wall suction against the Poll and Pfenninger criterion; and finally, by examining the evolution of the threshold R values where contamination occurs as a function of wall suction and the micro-perforated panel characteristics.

EXPERIMENTAL SET-UP

In this section, the experimental set-up is described, including the wind tunnel test facility and model used, the micro-perforated suction panels manufactured for this investigation, and the instrumentation available to transition or contamination monitoring.

Experimental facility and model

Experiments were performed in the ONERA F2 wind tunnel facility, a subsonic atmospheric closed-loop wind tunnel with a rectangular test section (1.8 m high x 1.4 m wide at the entrance). Over the 5 m length of the test section, the floor and ceiling diverge by 0.45°to account for the wall boundary layers. The freestream velocities achievable by the wind tunnel with the large model used for this experiment range from 5 m s -1 and 85 m s -1 . Turbulence levels are low enough to allow for natural laminar-turbulent transition experiments.

The DTP-A model used during this experimental was specifically designed to study attachment line transition and contamination. As shown on Figure 2a), the model consists of a semi-cylindrical leading edge with a radius of 200 mm extended by straight side panels forming a triangular cross-section. The total chord length, defined in the normal direction with respect to the leading edge, is 1200 mm. The model is mounted vertically (Figure 2b)) and is attached to the floor of the test section. In Figure 2c), the model is at a geometric sweep angle of 50°; subsequently, to reach higher Reynolds numbers R, the model was also set to ϕ equal to 60°. As a note, during the past experiments in [START_REF] Méry | Laminar Flow control along the wing leading edge[END_REF] performed during the winter 2018-2019, only the 50°s weep configuration was tested.

Micro-perforated suction panels

Along the leading edge of the model, three suction chambers sealed by a micro-perforated titanium panel can be seen on Figure 2. The panels were perforated and shaped to match the leading edge curvature by the manufacturer Aernnova, a company specialised in the design and manufacturing of aerostructures and components in the aerospace industry, and its affiliates. An overview of the panel geometries tested over the past two test campaigns in 2018 and 2022 is provided in Table 2.2. Only panel P1 was tested during both campaigns for repeatability validation between wind tunnel tests, and the present paper will focus on panels P4 and P5. In particular, panel P4 was designed to have almost equivalent geometry as panel P1, with a slight increase in hole diameter from 50 µm to 60 µm, to investigate the effect of manufacturing process between the two dates. Next, panel P5 was designed to study the effect of increasing porosity on suction performance, compared to panel P4. All panel perforations had a square pattern so that the geometric porosity, generally defined as the open area over the total area, is the area of the hole over the squared pitch distance. Additionally, geometric porosity is provided, as opposed to a more physical porosity related to the pressure loss across the panel. In particular, when comparing panels P1 and P4, which were designed to have the same geometric porosity, their pressure losses are different: for a suction mass flow rate of 10 g s -1 across each three suction chambers, panel P1 results in a 4500 Pa pressure loss, as opposed to P4 with a 11 000 Pa, as shown in Table 2.2 and Figure 3. This difference in pressure loss cannot solely be attributed to the slight change in hole diameter, but also to the difference in manufacturing process.

Inspection of the panel geometries using an Alicona Infinite Focus SL 3D optical surface measurements allowed to determine that both pitch and diameter dimensions were within ± 5 µm of specifications. Although such variation in the pitch only results in a ±0.02% variation in geometric porosity, the same variation in hole diameter results in a ±0.15% variation in porosity, which, relative to the low porosities under consideration, is significant. The geometric porosity should therefore be considered more as an ideal specification for manufacturing requirements, while the pressure loss across the panel for various suction flow rates should be considered the relevant parameter of interest.

As can be seen from Figure 3, although panels P1 and P5 have different hole pitch and diameter, their pressure loss across the different suction flow rates are comparable, as opposed to panel P4 that induces much greater pressure losses at high suction flow rates. Another suction parameter of interest that will be used subsequently in this paper is the ideal suction velocity, defined as:

V p = ṁ ρA panel (2)
with ṁ the suction mass flow rate, ρ the air density evaluated closest to the suction chamber, and A panel the suction panel total surface area. 3: Pressure loss (without freestream flow) as a function of suction mass flow rate for all three suction panels investigated in 2022. Each symbol corresponds to one of the suction chambers (cross: chamber 1, square: chamber 2, and circle: chamber 3.

Instrumentation

Four lines of static pressure ports, shown as the magenta lines on Figure 2b), are located at the junction between the different suction chambers (at the beginning of chamber C1, between C1 and C2, between C2 and C3, and at the end of C3), and spanning at least the entire width of the suction chambers. Since the model was set at a zero-lift angle of attack, the static pressure ports allowed to verify that flow symmetry was achieved. The pressure taps are orthogonal to the leading edge, i.e., aligned with the chordwise x-direction.

To monitor the attachment line contamination or natural transition in the leading edge region, hot films were also mounted on the model, as shown by the red circles on Figure 2b). Four of them were located along the attachment line: two upstream of the suction region, and closest to the junction with the test section floor, HF1 and HF2; one at the junction between chambers C2 and C3, HF5; one downstream of C3, HF7. Then, two hot films were placed downstream (in the x-direction) of each of the three suction chambers, as shown on Figure 2b) by the red labels, with "SB" (resp. "P") corresponding to the "starboard" (resp. "port") side. Hot films could not be placed over the perforated panels without blocking a portion of the suction area, and would have made changing the different panels more difficult. Additionally, since contamination is such an abrupt phenomenon involving the entire model quasi-instantaneously, the hot films' shifted location with respect to the attachment line should not be significant enough to affect the threshold R detection. Finally, by having two hot films on either side of each suction chamber, flow symmetry can also be further validated.

Infra-red (IR) thermography was also used to monitor contamination and transition. Since the leading edge, outside the suction chambers, consists of polyurethane, IR measurements could be performed directly on the model surface without the need for additional modifications or inserts. Two IR cameras (IRCAMERA IRC906 and FLIR SC7650) were mounted so as to be flush with the test section ceiling and to cover the entire span of the suction region down to the hot film second closest to the floor along the attachment line.

Finally the suction flow rate was set using an electric side channel vacuum pump and monitored using Brooks 5863S thermal mass flow meters. Manual valves were used to modify the flow rate during testing and were balanced to within 0.1 g s -1 of one another.

EXPERIMENTAL RESULTS

In this section the experimental results are first discussed in terms of the pressure coefficient distributions to allow the introduction of the notion of the effective sweep angle. Next the experimental set-up is validated for both configurations (at geometric sweep angles 50°and 60°) in the no suction case. Finally, the effect of wall suction in delaying the threshold R at which contamination occurs is compared for all three suction panels, as well as with previous experimental investigations performed in the same wind tunnel and on the same model.

Pressure coefficient distribution and effective sweep angle

Given its geometry and flow regime of investigation, the DTP-A model can be approximated as an infinite swept cylinder in inviscid flow. Under this assumption, the pressure coefficient C p around a swept cylinder of radius r can be expressed in terms of the azimuthal angle θ (related to the curvilinear abscissa in the chordwise direction x such that θ = x/r):

C p (θ) = cos 2 ϕ(1 -4 sin 2 θ) (3)
At the leading edge, where θ is zero, the C p value should be maximum. In order to match the C p in the inviscid flow solution at the leading edge with the measured C p , an effective sweep angle ϕ eff is introduced and defined such that:

ϕ eff = cos -1 max (C p,exp ) (4)
The measured pressure coefficient distributions along the different spanwise positions of the model are shown in Figure 4 for both sweep angle configurations at freestream velocity Q ∞ equal to 50 m s -1 . On Figure 4a), all C p,exp distribution overlap relatively well: the ϕ eff angle of 57°(shown as the dashed line) in this case is chosen as the mean value across all four maximum C p,exp . As an illustration, the theoretical pressure coefficient distributions calculated using equation 3 with both the geometric and effective sweep angles are shown as the dotted and dashed lines respectively.

However, in the case of the 60°geometric sweep angle configuration, a spanwise evolution of the C p,exp is observed. Based on flow visualisation performed using coloured viscous film showed no signs of significant recirculation regions on the DTP-A model. A numerical investigation is ongoing to provide further explanations for this phenomenon. Given the spanwise evolution of the C p,exp , a conservative approach to determine the ϕ eff was chosen. The static pressure line 1 was used to determine ϕ eff value of 70°and will be used in all subsequent calculations of R. iven the infinite sweep cylinder assumption and the use of ϕ eff , equation 1 for R can be further simplified to take the form of:

R = Q ∞ D 2ν sinϕ eff tanϕ eff 2 (5)
with D = 2r the diameter at the leading edge.

Validation of the contamination criteria without suction

The first step before investigating the effect of wall suction as an active anti-contamination device is to verify that the reference condition for both sweep configurations agree with the critical R= 250 criterion established by Pfenninger [START_REF] Pfenninger | Flow phenomena at the leading edge of swept wings. Recent development in boundary layer research[END_REF] and Poll [START_REF] Poll | Some aspects of the flow near a swept attachment line with particular reference to boundary layer transition[END_REF]. Based on equation 5, R is modified by varying the freestream velocity Q ∞ for a given sweep angle configuration.

Figure 5 shows the evolution of voltage fluctuations in terms of Root Mean Square (RMS) for all hot films as a function of R for both sweep configurations and without wall suction. The threshold contamination R value corresponds to the value at which fluctuations start to increase abruptly: no indication of the imminence of contamination can be detected before its occurrence. On Figure 5a), the first observation is that all hot films, except those identified as HF1 and H2, show an abrupt increase in voltage fluctuations at critical R equal to 275 ±15 and for all suction panels. These hot films signals therefore confirm that even though some of the hot films (HF3SB, HF3P, HF4SB, HF4P, HF6SB and HF6P) are slightly offset from the attachment line itself, their signal is still useful to identify the onset of contamination. Additionally, no effect from the suction panels without suction can be observed. The critical R value is within the range defined by Pfenninger and Poll, indicating that the experimental set-up is appropriate for the investigation of attachment line contamination.

The signals from HF1 and HF2 have greater RMS levels starting from the first R value, which corresponds to the minimum freestream velocity achievable by the wind tunnel facility. These hot films, located closest to the model/floor junction, are actually located inside the floor's turbulent boundary layer. Their signals therefore are not an indication of the attachment line boundary layer regime, and will not be used.

Figure 5b) shows the same measurements for the ϕ geom equal to 60°configuration. Combining the higher sweep angle and the minimum achievable freestream velocity, the minimum R value attained is equal to 300. However, considering the RMS levels as well as comparing the general trend with that of the ϕ geom equal to 50°configuration, contamination has occurred at a value close to or below 300, close to the reference empirical criterion. Both sweep angle configurations without wall suction therefore provide a sound reference, in agreement with the literature on contamination in low freestream turbulence. Since the two hot films HF1 and HF2, closest to the wall/model junction, are known to be always in the test section floor's boundary layer, their signal will not be used subsequently to determine the threshold R. On the other hand, since all other hot films seem to answer quasi-instantaneously, their signals will be used and compared with one another to check for any lag in the spanwise spread of contamination.

Anti-contamination using wall suction

Once the reference configurations are validated, wall suction along the model leading edge could then be applied to investigated the delay of contamination as a function of suction velocity.

Qualitatively, infra-red thermography images are shown on Figure 6 to illustrate the effect of applying wall suction at R values well above the contamination threshold without any control.

On Figure 6a), the DTP-A model at a geometric sweep angle of 50°and with a suction velocity V p of 21 cm s -1 over panel P5 (1.2%-2022) is shown at an R equal to 575, which corresponds to a freestream velocity Q ∞ of 40 m s -1 . As indicated in the figure caption, for this case, the laminar flow regions appear in light gray. The camera is fixed over the end of chamber C2 and the entire surface of C3, and the small bright spots followed by a dark gray turbulence cone correspond to the hot films located downstream of the suction chambers. With this suction flow rate, contamination is avoided and natural transition along the chordwise direction can take place, although its position is outside the camera's view.

Next, Figure 6b) shows the same view at a higher R equal to 610, which corresponds to Q ∞ equal to 50 m s -1 . In this case, although contamination is still cancelled, the natural transition front starts to appear. The visible sawtooth pattern, especially at the top of chamber C3 near the sides of the leading edge, is characteristic of the crossflow transition mechanism for swept wings. Finally, in Figure 6c), contamination is avoided at a still higher R value of 670, corresponding to Q ∞ equal to 55 m s -1 , while the crossflow transition front moves further upstream, closer to the leading edge, due to the greater freestream velocity. Next, a quantitative assessment of the effectiveness of leading edge wall suction using the hot films signals is provided in Figure 7. Similar to Figure 5, the voltage fluctuations in RMS are shown as a function of R (modified by changing the freestream velocity for each sweep configuration). For each suction velocity shown by a different colour, the signals from both hot films HF6SB and HF6P are shown: up to suction velocities of 30 cm s -1 , both hot films show an abrupt increase in their RMS values at the same R, indicating symmetric flow across the attachment line. On Figure 7b) however, the case with suction velocity 37 cm s -1 is not symmetric and the threshold R is different depending on the hot film.

Regardless of the sweep configuration, increasing suction flow velocity across panel P5 consistently delayed the threshold R. However, although a delay of 100 units of R was achieved by going from the no suction to the 3 cm s -1 case, the threshold R was only delay by 40 units when going from 21 cm s -1 to 24 cm s -1 . Increasing suction velocity therefore seems to become less effective at higher R. The same results were found for panels P1 and P4.

One noticeable trend for suction velocities above 12 cm s -1 is the gradual increase in RMS value preceding the abrupt boost, indicative of contamination. This initial intermediate increase is actually characteristic of the crossflow instabilities developing over the hot films, and should therefore not be interpreted as a phenomenon related contamination. A more concise representation to relate the delay in threshold R due to wall suction is to use the non-dimensional suction parameter K, defined as:

K = V p R Q ∞ sin ϕ . (6)
In this expression, V p is negative when applying suction, and therefore K will also be negative. Figure 8 shows the evolution of the threshold R detected using either HF6P or HF6SB as a function of K for all suction panels and sweep angle configurations. Overlaid with the experimental data, the dashed line is the empirical correlation R = 250 -150K established by Arnal et al. in [START_REF] Arnal | Laminar Flow Control along the wing leading edge[END_REF].

Regardless of suction panel or sweep angle configuration, all data points for both hot films agree well with the empirical correlation. The only main discrepancy between the two hot films is for suction velocity 37 cm s -1 , corresponding to K close to -7 for HF6P. This asymmetry was already identified in Figure 7. Overall though, increasing suction can effectively delay the threshold R up to values as high as 1000, relevant to commercial aircraft flight envelope.

CONCLUSIONS

Assuming laminar flow at the attachment line of a wing section attached to a solid wall or fuselage is not guaranteed and can completely cancel downstream strategies to maintain laminar flow. In particular, the incoming turbulent boundary layer from the solid wall can contaminate the wing section attachment line boundary layer and therefore the entire wing. The critical value of the Reynolds number R above which transition is likely to occur is between 250 and 280, while typical R values encountered in flight by commercial aircraft are significantly greater than 400. For this reason, strategies to delay the contamination threshold have to be adopted to consider the implementation of laminar wings in commercial aviation.

One effective strategy is by applying wall suction through micro-perforated panels located on the leading edge of the wing section. Although previous experiments confirmed that this method allowed to push the threshold R to 650, limitations inherent to previous experimental set-ups prevented verifying if greater threshold R values could be achieved. For this reason, the present paper focused on testing the DTP-A model at two sweep angle configurations in order to reach greater R values. Suction panels with varying geometries and from different manufacturing processes were tested. Both IR thermography and hot film anemometry were used to monitor the boundary layer in the leading edge region. Based on these measurements, wall suction was found to effectively delay the threshold R to value beyond 1000. The effect of panel geometry or manufacturing process was not significant in affecting suction effectiveness.

Future work on this topic within the HLFC-WIN project involves testing anti-contamination using suction in the compressible flow regime at the ONERA wind tunnel facility S1MA, again with suction panels manufactured by Aernnova. More generally, it will be necessary to investigate the feasibility of such high suction flow velocities using a practical suction system that could be mounted in a commercial aircraft wing or empennage.

Figure 1 :

 1 Figure 1: Schematic representation attachment line contamination with nomenclature.

Figure 2 :

 2 Figure 2: DTP-A model a) cross-section with key geometric features and dimensions, and b) front view of the model mounted inside the test section.

  mass flow rate m [g.s 1 ] chamber -Patm [Pa] P1 -0.8%-2018 P4 -0.8%-2022 P5 -1.2%-2022

Figure 4 :

 4 Figure 4: Pressure coefficient distribution on the different static pressure lines along the spanwise direction for Panel P5 with no suction at Q ∞ = 50 m s -1 . a) ϕ geom = 50°and b) ϕ geom = 60°G

Figure 5 :

 5 Figure 5: Voltage fluctuations of all hot films for all suction panels without wall suction. a) ϕ geom = 50°a nd b) ϕ geom = 60°.

Figure 6 :

 6 Figure 6: Infra-red thermography showing a cross-flow transition pattern of panel P5 (1.2%-2022) for configuration ϕ geom = 50°and ϕ eff = 57°with suction velocity 21 cm s -1 at a) R = 575, b) R = 610, and c) R = 670. Note that for figures a) through b), laminar regions are light gray whereas for c) laminar regions are dark gray due to a change in freestream flow temperature to recover thermal desequilibrium with the model and enhance IR visualisations.

Figure 7 :

 7 Figure 7: Voltage fluctuations of hot films HF6-SB (starboard) and HF6-P (port) for panel P5 1.2% -2022 for all tested suction velocities at a) ϕ geom = 50°and ϕ eff = 57°and b) ϕ geom = 60°and ϕ eff = 70°.

Figure 8 :

 8 Figure 8: Evolution of threshold R as a function of non-dimensional suction parameter K for all suction panels and sweep angle configurations evaluated at a) hot film HF6P and b) hot film HF6SB to check for symmetry.

Table 1 :

 1 Summary

				2022 test campaign
	P4	60	590	0.8	11000
	P5	60	485	1.2	4500
				2018 test campaign
	P1	50	500	0.8	4800
	P2	130	1820	0.4	7400
	P3	50	700	0.4	13500

of the micro-perforated suction panel geometry tested over the last two test campaigns. Panel P1 was tested during the 2022 campaign for repeatability validation. Panels P2 and P3 shown in italic were not tested in 2022. Hole Ø [µm] Pitch [µm] Geometric porosity [%] ∆P at ṁ=10 g s -1 [Pa]

Jeanne Methel, Fabien Méry, Maxime Forte, and Olivier Vermeersch

ACKNOWLEDGMENTS

The authors wish to thank the ONERA F2 wind tunnel testing team for their great flexibility and collaboration during this campaign. Additionally, the authors thank Aernnova for providing the suction panels.

This work was funded by the European Union within the frame of the HLFC-WIN project. This project is part of the Clean Sky 2 Joint Undertaking under the European Union's Horizon 2020 research and innovation programme, in the LPA-IADP platform (Grant agreement CS2-GAM-2020-LPA-AMD-945583-23).