domain: spi phys

text:
Mathieu Lorteau
email: mathieu.lorteau@onera.fr

Thomas Le Garrec
email: thomas.le_garrec@onera.fr

Majd Daroukh
email: majd.daroukh@onera.fr

Cyril Polacsek
email: cyril.polacsek@onera.fr

Acoustic Assessment of BLI Effects on Airbus Nautilius Engine Integration Concept -Part II: Noise Radiation

This work is performed within the scope of the the European Union's Horizon 2020 research project ARTEM (Aircraft noise Reduction Technologies and related Environmental iMpact) which addresses the technology challenges on "Reducing aviation noise". The present study deals with the acoustic assessment of the Airbus Nautilius engine integration concept implemented on NOVA (New Generation Onera Versatile Aircraft). In the first part of this study, the noise sources associated to the tonal fan noise are computed by a numerical methodology based on steady and unsteady CFD simulations performed with the elsA solver. The second part of this study makes use of an immersed boundary approach developed in previous work in the CAA solver sAbrinA_v0 to evaluate the propagation in the near field of acoustic waves generated by analytic modes associated to fan noise injected in the nacelle duct, in the presence of a realistic aircraft geometry and a realistic non uniform mean flow obtained with the CFD solver elsA. The aircraft geometry is partially taken into account with CAA due to the mesh extent limitations. The duct modes amplitudes injected in the CAA simulations are provided directly from the first part of the study. The propagation in the far field which accounts for the whole aircraft geometry (reflection and diffraction effects) is then performed with a Boundary Element Method solver based on the CAA near field pressure fluctuations data.

The Nautilius concept integrated on the NOVA aircraft is compared to a reference podded NOVA configuration in terms of acoustic levels of the fan tonal noise at BPF1 and BPF2 in the near field as well as in the far field. The comparisons highlight the great impacts that the mean flow distortion and the integration effects have on the acoustic radiation.

I. Introduction

For many years, aircraft noise reduction has been the subject of research studies and continuous improvements were achieved through an enhanced understanding of the noise generation mechanisms. However, due to ever more restrictive noise regulations around airports, new aircraft noise reduction strategies are mandatory. One strategy consists in studying new aircraft architecture in particular for the engine integration. In this context, the engine integration concept based on the boundary layer ingestion (BLI) appears as a disruptive solution and has been studied for some years, in particular on NOVA (New Generation Onera Versatile Aircraft) for the aerodynamic performances [START_REF] Wiart | Development of NOVA Aircraft Configurations for Large Engine Integration Studies[END_REF]. The Airbus Nautilius engine integration concept [START_REF] Rogero | Ensemble pour aéronef comprenant des moteurs à propulsion par ingestion de la couche limite[END_REF][START_REF] Negulescu | Assembly for aircraft comprising engines with boundary layer propulsion by injection[END_REF] presents an even more significant ingestion of the boundary layer compared to other versions of the BLI concept. While recent studies of this concept applied on NOVA (see for instance Wiart & Negulescu [START_REF] Wiart | Exploration of the Airbus "Nautilius" engine integration concept[END_REF]) show a promising power saving estimate, the acoustic assessment has not been performed yet. This is the main objective of the present study.

Here, the Immersed Boundary Method (IBM) workflow implemented in the CAA solver sAbrinA_v0 [START_REF] Terracol | Hybrid method for airframe noise numerical prediction[END_REF][START_REF] Polacsek | An equivalent-source model for simulating noise generation in turbofan engines[END_REF][START_REF] Redonnet | Numerical study of acoustic installation effects with computational aeroacoustics method[END_REF][START_REF] Reboul | Towards Numerical Simulation of Fan Broadband Noise Aft Radiation from Aero-engines[END_REF][START_REF] Redonnet | Computational Aeroacoustics of Realistic Co-Axial Engines[END_REF] as well as the BEM solver BEMUSE [START_REF] Juvigny | A fast algebraic boundary integral solver[END_REF] are used to study the propagation of the acoustic waves emitted by a turbofan integrated as in the Airbus Nautilius concept and more precisely those associated to the rotor-stator stage of the turbofan, with a realistic aircraft geometry in the presence of a non uniform mean flow at a Mach number 𝑀 ∼ 0.25 with an angle of attack (AoA) of 8°corresponding to take-off flight conditions. These flow characteristics lead to quite strong distortion effects occurring at the nacelle intake which are taken into account in the present simulations. To this aim, the radiated acoustic field from the Nautilius concept on the NOVA aircraft is compared to the SFN configuration (Side Fulselage Nacelle) which corresponds to the same turbofan in a reference podded configuration of the NOVA aircraft. Firstly, the acoustic duct modes associated to the intake noise sources computed in the first part of this study (see Daroukh et al. [START_REF] Daroukh | Acoustic assessment of BLI effects on Airbus Nautilius engine integration conceptpart I: noise generation[END_REF]) are injected inside the duct and propagated in the near field in the CAA computation which accounts for a part of the geometry as well as the mean flow. Secondly, these near field pressure fluctuating data are used as inputs for the BEM computations which give access to the pressure levels in the far field while considering the whole aircraft geometry.

This paper is organized as follows. In section II, the methodology used in this paper to evaluate the acoustic installation effects is briefly presented, some details are given on the CAA and the BEM computations. Then, section III gives some details on the simulation parameters used in this work: the configurations of interest as well as the acoustic meshes. In section IV, near and farfield acoustics are illustrated and compared. Finally, some conclusions and perspectives are given in section V.

II. Numerical methodology

In order to estimate the noise radiation of the Nautilius engine integration concept applied to the NOVA aircraft, we intend to compute the noise propagation of the acoustic sources generated in the nacelle in [START_REF] Daroukh | Acoustic assessment of BLI effects on Airbus Nautilius engine integration conceptpart I: noise generation[END_REF] by means of CAA and BEM for the Nautilius configuration as well as the SFN one. The full IBM methodology developed for CAA and detailed in Mincu et al. [START_REF] Mincu | Immersed boundary conditions for high order CAA solvers-Aeroacoustics installation effects assessment[END_REF] and Lorteau et al. [START_REF] Lorteau | Numerical study, with experimental validation, of fan noise installation effects in Over-Wing Nacelle configuration using the Immersed Boundary Method[END_REF] is applied in a first step. This IBM methodology has been recently successfully applied in Lorteau & Le Garrec [START_REF] Lorteau | Numerical assessment of fan noise confinement effects in a closed wind-tunnel[END_REF] for the evaluation of acoustic confinement effects of turbofan noise in a closed wind-tunnel.

For the CAA computations, the geometry of interest is taken into account with the IBM approach, which thus greatly simplifies the CAA mesh design process for such a geometry, the mesh simply consisting in a single 3D Cartesian grid. The heterogeneous mean flow issued from the elsA calculations from [START_REF] Daroukh | Acoustic assessment of BLI effects on Airbus Nautilius engine integration conceptpart I: noise generation[END_REF] is interpolated from the CFD grid to the CAA grid by the use of the in-house Cassiopée tool [START_REF] Benoit | Cassiopee: A CFD pre-and post-processing tool[END_REF]. The CAA computation is then performed in the temporal domain, and thus including all the considered frequencies in a single computation, to propagate dominant angular modes on the mean flow from inside the nacelle to the outside up to the fuselage in the nacelle's vicinity where the mean flow is highly non uniform. The modal amplitudes specified in the source model are directly provided by the unsteady CFD simulation performed in part I. Besides a great simplification of the mesh generation process, the IBM approach also allows to maximize the time step (as a polar mesh is not needed inside the nacelle) and thus minimize the computational time. More information on the solvers used for the CFD and CAA steps are provided in the next sections.

In a following step, the near-field pressure fluctuations obtained from the CAA and stored on a selected control surface are Fourier-transformed to feed a Kirchhoff integral method written in the frequency domain [START_REF] Pilon | Integral methods for computational aeroacoustics[END_REF][START_REF] Polacsek | Numerical simulation of a fan interaction noise using a hybrid approach[END_REF], requiring the calculation of the pressure as well as its gradient normal to the control surface. The direct harmonic pressure field is coupled to an in-house BEM solver BEMUSE [START_REF] Juvigny | A fast algebraic boundary integral solver[END_REF] in order to evaluate the acoustic installation effects (i.e. scattering effects) considering the whole aircraft geometry (fuselage and wings). The total pressure, which is obtained by adding the direct and scattered sound fields, is then evaluated on a 100 m radius sphere centred on the aircraft barycentre.

III. Numerical parameters A. NOVA aircraft geometries and operating conditions

The two studied geometries issued from the NOVA aircraft [START_REF] Wiart | Development of NOVA Aircraft Configurations for Large Engine Integration Studies[END_REF] are illustrated in figure 1. The podded version, also called SFN, will serve as a reference in the following compared to the Nautilius version of the NOVA aircraft [START_REF] Wiart | Exploration of the Airbus "Nautilius" engine integration concept[END_REF] which is the subject of the present study. In the following, the Nautilius configuration will be referred as NOVA-Nautilius and the SFN configuration as NOVA-SFN.

The engine of the present aircrafts accounts for 𝐵 = 18 fan blades and 𝑉 = 40 stator vanes (OGVs). For this study, a non uniform mean flow at 𝑀 ∞ = 0.25 has been considered with an angle of attack of 8°. These parameters are representative of take-off flight conditions.

B. Mean flow computation

The mean flow field around the aircraft and inside the nacelle has been computed in the first part of this study [START_REF] Daroukh | Acoustic assessment of BLI effects on Airbus Nautilius engine integration conceptpart I: noise generation[END_REF]. Only a brief summary is given here. The mean flow is computed using ONERA's solver elsA [START_REF] Cambier | The Onera elsA CFD software: input from research and feedback from industry[END_REF] with a RANS approach on several Cartesian grids by means of the chimera technique. The turbulence modelling is handled by the Spalart-Allmaras model [START_REF] Spalart | A one-equation turbulence model for aerodynamic flows[END_REF]. The fan stage is modelled through a body-force approach.

C. CAA computations

The CAA calculations are conducted with ONERA's sAbrinA_v0 structured CAA solver [START_REF] Terracol | Hybrid method for airframe noise numerical prediction[END_REF][START_REF] Polacsek | An equivalent-source model for simulating noise generation in turbofan engines[END_REF][START_REF] Redonnet | Numerical study of acoustic installation effects with computational aeroacoustics method[END_REF][START_REF] Reboul | Towards Numerical Simulation of Fan Broadband Noise Aft Radiation from Aero-engines[END_REF][START_REF] Redonnet | Computational Aeroacoustics of Realistic Co-Axial Engines[END_REF] that solves either the full or the linear Euler equations, in a conservative and perturbed form. The sAbrinA_v0 solver employs high-order, finite difference operators, involving 6th-order spatial derivatives and 10th-order filters, as well as a 3rd-order, compact, Runge-Kutta explicit time-marching scheme. More detailed information about the sAbrinA_v0 solver and its underlying methodology can be found in [START_REF] Redonnet | Numerical simulation of propagation of small perturbations interacting with flows and solid bodies[END_REF][START_REF] Redonnet | Simulation de la propagation acoustique en présence d'écoulements quelconques et de structures solides, par résolution numérique des équations d'Euler[END_REF].

Acoustic sources

In both CAA simulations, an acoustic source representative of an interaction mode associated to the fan stage with the inflow distortion effects has been considered at BPF1 and BPF2. Distortion effects arise for both configurations due to the incidence of the aircraft (AoA = 8°) and is strongly increased for the BLI concept (i.e. NOVA-Nautilius). While the overall geometry is considered, only one turbofan source is enforced in the left-hand side nacelle of the aircraft. The azimuthal mode is chosen following the well-known theory of Tyler & Sofrin [START_REF] Tyler | Axial flow compressor noise studies[END_REF]: 𝑚 𝜃 = 𝑛.𝐵 -𝑘.𝑉 ± 𝑘 𝑑𝑖𝑠𝑡 , where 𝑘 𝑑𝑖𝑠𝑡 is the harmonic order of angular-Fourier transform of the inflow distortion (see figure 9 of part I [START_REF] Daroukh | Acoustic assessment of BLI effects on Airbus Nautilius engine integration conceptpart I: noise generation[END_REF]). Without any distortion effects, rotor locked mode 𝑚 = 18 at BPF1 is expected to be cut-off in the intake whereas the BPF1 tone is cut-on with distortion (see [START_REF] Daroukh | Acoustic assessment of BLI effects on Airbus Nautilius engine integration conceptpart I: noise generation[END_REF]). In this part II, acoustic calculations are focused on BPF1 and BPF2 for mesh size considerations (see section III.C.2), and only the dominant modes (see figure 14 of part I [START_REF] Daroukh | Acoustic assessment of BLI effects on Airbus Nautilius engine integration conceptpart I: noise generation[END_REF]) are considered.

The acoustic modes can be injected in sAbrinA_v0 by means of an equivalent source model introduced by Polacsek et al. [START_REF] Polacsek | An equivalent-source model for simulating noise generation in turbofan engines[END_REF] and generalized by Reboul & Polacsek [START_REF] Reboul | Towards Numerical Simulation of Fan Broadband Noise Aft Radiation from Aero-engines[END_REF]. It can be also injected using the NRI technique [START_REF] Redonnet | The non-reflective interface: an innovative forcing technique for computational acoustic hybrid methods[END_REF], recently adapted for suitability with the IBM approach. Combined with an additional sponge zone, the NRI technique offers the possibility to easily manage the upstream/downstream direction of the source propagation, so that one can study separately the fan sources, propagating in the intake and radiated by the inlet, and the OGV sources, propagating in the bypass duct and radiated by the exhaust, by either focusing on modes shown in figures 13 or 14, respectively, of part I [START_REF] Daroukh | Acoustic assessment of BLI effects on Airbus Nautilius engine integration conceptpart I: noise generation[END_REF]. Here, the fan sources are injected using the NRI technique in the upstream direction. The azimuthal modes of the injected source modes and their amplitudes at the carter's surface are summarized in table 1, for these modes only the first radial mode is cut-on. The pressure fluctuations computed by the CAA solver for the modes generated by the fan sources at BPF1 and BPF2 and injected in the fan plane is illustrated in figure 2(a) in the source plane. A section view of the axial mean velocity in the upstream fan plane is plotted in figure 2(b). A sponge zone has been added at the outlet to damp the acoustic waves propagating in the downstream direction which are associated to the reflections at the inlet inside of the duct. Previous studies showed indeed that, without a specific treatment, upstream and downstream radiations could merge and produce interference patterns and cannot be separated anymore.

Acoustic meshes

As previously mentioned, in the CAA computations, the geometry of interest is taken into account with the IBM approach, which thus greatly simplifies the CAA mesh design process for such a geometry. The mesh consists in a single 3D Cartesian grid. A refined mesh zone was defined around the nacelle by setting a maximum mesh size chosen to resolve the acoustic waves. Outside of the refined mesh zone, a grid stretching is applied with a geometrical ratio equal to 𝑟 = 1.05 in all three directions to increase by a factor 20 the refined mesh size to the exit boundary conditions. Note that for the Nautilius configuration, because of their proximity, both nacelles are encompassed in the refined mesh zone whereas for the SFN configuration, only the nacelle with the acoustic source is included as they are well separated by the fuselage. The maximum cell size inside the refined mesh zone was calibrated from the target frequency associated to BPF2. 15 points per acoustic wavelength are considered for the latter frequency in the upstream and downstream directions, the source injection plane being the reference. The mesh size Δ𝑥, associated to the apparent wavelength due to the convection effects, is then Δ𝑥 = 𝜆.(1 ± 𝑀)/15 with 𝜆 the wavelength at rest and 𝑀 the Mach number. This gives a total number of points of 735 × 10 6 and 530 × 10 6 for the NOVA-Nautilius and NOVA-SFN cases, respectively. The figures 3 and 4 depict both the computational domain and a mesh cut for the two configurations.

Numerical parameters

The time step Δ𝑡 was chosen to get a maximum CFL number of about 0.75. Results and statistics are acquired over 2𝑇 once the convergence is reached (where T is the period associated to the frequency BPF2) after a numerical transient time of 50𝑇 for both simulations. The NOVA-SFN simulation required about 18.3 × 10 3 CPU hours (on 336 parallel cores) whereas the NOVA-Nautilius simulation required about 23.5 × 10 3 CPU hours (on 672 parallel cores). These computational times are rather inexpensive compared to computations with curvilinear and body-fitted meshes thanks to the IBM which enables to maximize the time step and thus to minimize the number of iterations for one period of the source, here: Δ𝑡 = 𝑇/100. Furthermore, the IBM preprocessing was performed in less than 1% of the overall computational time.

D. BEM computation

The BEM computations are performed with ONERA's BEM solver BEMUSE [START_REF] Juvigny | A fast algebraic boundary integral solver[END_REF] that solves the Helmholtz equation at rest in the frequency domain with the Brakhage-Werner formulation [START_REF] Brakhage | Über das Dirichletsche aussrenraumproblem für die Helmholtzsche schwingungsgleichung problems[END_REF] on an unstructured surface mesh of the aircraft geometry with a criterion of Δ𝑥 ≈ 𝜆/6 for the cell size. It should be noted that no mean flow is considered in these BEM computations as it is not possible in the current version of the solver. However, the acoustic direct field, which serves as input of the BEM computation, has been obtained from the radiation of the CAA near field into the far field via a Kirchhoff integral method considering a uniform mean flow at 𝑀 = 0.25 with an angle of attack of 8°. The linear system obtained for the problem is solved with the GMRES iterative method. The matrix of the linear system is compressed with the Hierarchical Matrix approach [START_REF] Bedendorf | Approximation of boundary element matrices[END_REF] completed by the Adaptive Cross Approximation method. The solver is parallelized with an hybrid MPI/OpenMP approach. For the SFN configuration the computational time was about 80 elapsed hours on a 0.3 × 10 6 nodes mesh at BPF1 and about 1500 elapsed hours on a 10 6 nodes mesh at BPF2 (on 224 parallel cores with a ratio 7 to 1 between the OpenMP threads and the MPI process).

IV. Acoustic results

In this section, the acoustic results are presented. First, effects of the non uniform mean flow on the near acoustic field as well as the close proximity of the fuselage to the nacelle are illustrated by the direct outputs of the CAA computations for the two configurations. Then, the installation effects of the whole fuselage on the acoustic field are quantified by means of BEM computations issued from the near pressure field data. Finally, the acoustic power levels for the two configurations are estimated.

A. Near field acoustics

The acoustic field associated to each BPF can be easily obtained by simply taking the Fourier transform of the temporal pressure field at the selected frequency. The real part of the Fourier transform of the fluctuating pressure associated to BPF1 and BPF2 is presented in figures 5 and 6 for both cases. For rendering purposes, different colour scales [-𝑃 𝑚𝑎𝑥 ; +𝑃 𝑚𝑎𝑥 ] have been considered for each group of figures. The colour scales maximum values 𝑃 𝑚𝑎𝑥 are provided in table 2. For figures 5 and 6, the pressure field has been restricted to the refined mesh zone (see section III.C.2) as it has been checked that the pressure waves amplitudes are rapidly dissipated due to the grid stretching. For the NOVA-Nautilius, in figure 5, a complex pattern can be observed in the upstream direction and is mainly related to the specular reflection of the acoustic waves by the fuselage, especially at the frequency BPF1 for which several azimuthal mode orders have been injected (see table 1).

In the downstream direction, practically no waves are emitted at the jet exit compared to the upstream radiation, as expected from the combined effect of the sponge zone and the prescribed source direction (intake propagation). It is rather representative for the fan sources of a real engine since sound propagation in the bypass is partly blocked by the stator screen effects and obstructed by the internal deviations which connect the hub to the nacelle.

Another observation of interest is the small radiation originating from the opposite nacelle (see figures 5(c) and (d)). This latter radiation comes from the excitation of a duct mode inside the opposite nacelle by the acoustic field radiated from the first nacelle which produces acoustic interferences, particularly visible in figures 5(e) and (f). Moreover at BPF2, as can be seen in figure 5(f), the radiated waves appear to be more energetic in the right-hand side of the aircraft (i.e. the Y+ half plane, the opposite side of the acoustic source) and especially in the ground direction. This is related to the empty space between the rear end of the fuselage and the inlet of the nacelles (see for instance figure 5(c)).

For the NOVA-SFN, see figure 6, similar observations can be made for the upstream radiation, in particular for the acoustical interferences between the direct and the reflected waves on the fuselage. However, no acoustic coupling between the two nacelles can be observed as the refined mesh zone has not been extended to the opposite nacelle for the NOVA-SFN mesh because of the greater distance between the two nacelles than for the NOVA-Nautilius and the presence of the fuselage between the two nacelles which produces a stronger shielding effect.

However, as can be illustrated in figures 6(a) and (b), the NOVA-SFN tends to radiate more in the ceiling direction than in the ground direction, contrary to the NOVA-Nautilius. This could be related to complex interferences pattern between the acoustic waves directly radiated from the inlet and those reflected by the fuselage. The pressure maps presented in figure 7 might give another possible explanation. In this figure, the real part of the fluctuating pressure field is shown at BPF2 for the NOVA-Nautilius and the NOVA-SFN configurations around the nacelle inlet and at a constant radial position 𝑟/𝑅 𝑚𝑎𝑥 ≈ 0.95. For the NOVA-SFN, a supersonic pocket (delimited by the thick solid black line on the map in figure 7) is detected on more than half the perimeter of the nacelle for 150°< 𝜃 < 360°, so basically on all the lower part of the nacelle. This supersonic pocket seems responsible for a blockage of the sound waves. For the NOVA-Nautilius, the supersonic pocket presents a smaller azimuthal extent on the nacelle inlet and thus may give rise to a smaller blockage effect. Furthermore, the above-mentioned empty space between the rear end of the fuselage and the inlet of the nacelles, located at angles around 𝜃 = 0, allows acoustic waves to radiate in the ground direction. Similar observations apply for the frequency BPF1. A more detailed analysis is required to better evidence and confirm this blockage phenomenon especially for the NOVA-SFN by focusing on the isolated nacelle in order to remove all the installation effects and focus on this supersonic pocket.

B. Farfield acoustic installation effects

As explained in section II, the Fourier transform of the pressure data extracted from the refined mesh zone boundaries of the CAA computations (see section III.C.2) are used as inputs for the Kirchhoff integral to compute the incident field required for the BEM computations. The CAA computation is restricted to an area close to the nacelle accounting only for the first reflections of the acoustic waves on the fuselage (i.e. the main part of the reflected waves), due to computational cost considerations, whereas the BEM computations give access to the propagation of the acoustic waves accounting for the whole aircraft geometry. The acoustic waves including installation effects are computed on a 100 m radius sphere of microphones centred on the aircraft barycentre. The BEM computations parameters are given in section III.D. It should be noted that, similarly to the CAA computations the pressure fields have not been duplicated with a symmetry hypothesis in addition to a incoherent or coherent summation. to mimic a two engines configuration. Then, the results presented in this section correspond a one-sided engine aircraft.

The figures 8 and 9 depict the pressure levels estimated on the aforementioned sphere of microphones by the BEM computations for the two aircraft configurations. Similarly to the figures 5 and 6, different color scales [0; +𝑃 𝑚𝑎𝑥 ] have been considered for each group of figures, for rendering purposes. The colour scales maximum values 𝑃 𝑚𝑎𝑥 are given in table 2.

For the NOVA-Nautilius, the pressure levels are greater at the right-hand side of the plane (i.e. on the opposite side of the acoustic source), this phenomenom is more pronounced for the frequency BPF2. This result is coherent with the previous observation on the near radiated field (see figure 5(e) and (f)). This preferred direction of radiation is related to the fact that the engine is located further at the rear end of the aircraft with a very small part of the fuselage that could participate in the shielding of the acoustic waves.

A more classical level distribution is recovered for NOVA-SFN, where the acoustic shielding by the fuselage is the dominant installation effect. Diffraction effects are very limited or missing, since almost no edges nor sharp surfaces are crossed along ray paths, the only one being the main wing which is expected to modify acoustic directivity mainly in the upstream direction. As a consequence, most of the acoustic radiation occurs in the left-hand side of the aircraft.

Based on all these observations, the NOVA-SFN configuration is more suitable to minimize acoustic installation effects. The reader has to keep in mind that the sources levels are quite different with the NOVA-Nautilius ones. For the NOVA-Nautilius, the distortion effects are enhanced by the maximized BLI effect in comparison to the NOVA-SFN, leading to the apparition of highly energetic acoustic modes. The BLI concept may increase the aerodynamic performance, but is less favorable for acoustics than classical architecture as the NOVA-SFN.

C. Acoustic power levels

Finally, the acoustic power levels are computed from the total pressure levels obtained from the BEM computations on the 100 m radius microphones sphere presented in the previous section. Considering the distance from the sources (larger than 200 wavelengths at BPF1), the power levels have been computed with a plane wave approximation formula and a no flow assumption to be coherent with the BEM computations. Values are reported in figure 10. The NOVA-Nautilius produces acoustic levels around 15 dB higher than the NOVA-SFN for the two frequencies, with the power levels at BPF2 around 12 dB higher than those at BPF1. These results agree with those obtained at BPF1 in the part I paper of the study [START_REF] Daroukh | Acoustic assessment of BLI effects on Airbus Nautilius engine integration conceptpart I: noise generation[END_REF] (see figure 10(b)). However, at BPF2 the results differ: the two configurations have equivalent acoustic power levels unlike the present study. As explained by the authors, the power levels are assessed by adopting the Goldstein's analogy which assumes an infinite and constant annular duct and a uniform flow. Therefore, no duct geometry variations nor three-dimensional flow effects have been taken into account unlike the present CAA simulations.

The strong influence of the non-uniform mean flow is corroborated by the results presented in figure 7(b) where the supersonic pocket is responsible for a blockage of the sound waves near the tip region or an acoustic reflection since most of the mode energy is located at the carter (concentrated sound energy associated to the first radial mode).

V. Conclusion

Acoustic simulations taking into account the complex aircraft geometries as well as non uniform mean flows have been successfully performed for the Nautilius and SFN configurations of the NOVA aircraft at take-off condition with an angle of attack equal to 8°. These simulations considered dominant acoustic duct modes, at BPF1 and BPF2, representing interaction modes associated to distortion effects due to the angle of attack and the considered engine architectures. The source amplitudes are directly taken from the noise generation solutions based on unsteady CFD performed in the first part of this study [START_REF] Daroukh | Acoustic assessment of BLI effects on Airbus Nautilius engine integration conceptpart I: noise generation[END_REF].

The near field results demonstrated that the Nautilius configuration is producing radiated sound fields poorly impacted by the scattering effects on the fuselage and has no noticeable benefit from possible shielding by the wings with respect to the ground direction. This is due to the location of the engines at the rear end of the aircraft, contrary to the SFN configuration. This explains the differences in the main directions of radiation in the far field (NOVA-Nautilius: bottom right-hand side; NOVA-SFN: top left-hand side) for the take-off configuration.

The far field results taking into account the whole aircraft geometry (obtained with BEM computations) confirm the near field conclusions and the acoustic power levels in the far field confirm that the NOVA-Nautilius configuration radiates higher noise levels than the NOVA-SFN configuration. Moreover, the NOVA-Nautilius radiates mainly in the ground direction, contrary to the NOVA-SFN configuration, which is even more detrimental. This study case at take-off condition is particularly critical and difficult to simulate. It has been shown that the mean flow field has a great influence on the acoustic radiation. The conclusions would be different for other operating points for which the distortion effects would be less pronounced and certainly with no supersonic pocket at the nacelle inlet.

Currently, this study is limited to frequencies up to BPF2, higher frequencies have not been yet considered (from part I paper CFD computations, source inputs are available up to BPF5) for computational resources considerations and will be considered in a near future to deepen this analysis. The main limitation not only arises from the frequency (and the apparent wavelength related to the propagation in the upstream direction) but also from the azimuthal mode order to be injected. Cartesian grids are less suitable than polar meshes to discretize azimuthal directions.

Besides, as previously mentioned, the present CAA methodology based on an adapted NRI technique will offer the possibility to investigate practical installation effects focusing on the sound radiation from the inlet or the exhaust, by splitting the injected sources from the fan upstream plane (rotor sources contribution) and the OGV downstream plane (stator sources contribution) which could give access to a more complete view of the acoustic radiation of this innovative engine integration concept.

Fig. 1

 1 Fig. 1 Views of (a) the NOVA-Nautilius and (b) the NOVA-SFN configurations without empennage nor lifting devices.

Fig. 2

 2 Fig. 2 Views of (a) the instantaneous pressure field generated in the source plane and (b) the axial mean velocity field in the intake plane for the NOVA-SFN.

Fig. 3 Fig. 4

 34 Fig. 3 NOVA-Nautilius: views of (a) the CAA computational domain and (b) a cut of the mesh in the nacelle midsection plane (one in three points are plotted); with the refined mesh zone delimited in red.

Table 2

 2 Min/max values ±𝑃 𝑚𝑎𝑥 of the colour scales for the results in the near field (figures 5 and 6) and in the far field (figures 8 and 9). The values have been normalized by the 𝑃 𝑚𝑎𝑥 value used at BPF1 in the far field for the NOVA-SFN.

Fig. 5

 5 Fig. 5 Real part of the fluctuating pressure field associated to (top) BPF1 and (bottom) BPF2 in (a,d) vertical longitudinal XZ plane, (b,e) a horizontal longitudinal XY plane and (c,f) in a crosswise YZ plane upstream of the nacelle for the NOVA-Nautilius.

Fig. 6

 6 Fig. 6 Real part of the fluctuating pressure field associated to (top) BPF1 and (bottom) BPF2 in (a,d) vertical longitudinal XZ plane, (b,e) a horizontal longitudinal XY plane and (c,f) in a crosswise YZ plane upstream of the nacelle for the NOVA-SFN.

Fig. 7

 7 Fig. 7 Real part of the fluctuating pressure field associated to BPF2 on a radial slice corresponding to 95% of the nacelle inner radius for (a) the NOVA-Nautilius and (b) the NOVA-SFN. The thick solid black line corresponds to the limit of a supersonic mean flow zone in the vicinity the nacelle inlet.

Fig. 8 NOVA

 8 Fig. 8 NOVA-Nautilius: magnitude of the total pressure (incident+scattered fields) at (top) BPF1 and (bottom) BPF2 on a 100 m radius sphere around the aircraft (a,c) below the aircraft (i.e. 𝑍 < 0) and (b,d) on the left-hand side of the aircraft (the side with the acoustic source, i.e. 𝑌 < 0). The black lines corresponds to the vertical and horizontal middle lines of the sphere. The aircraft is represented with an angle of 8°corresponding to AoA.

Fig. 9 Fig. 10 PWL

 910 Fig. 9 NOVA-SFN: magnitude of the total pressure (incident+scattered fields) at (top) BPF1 and (bottom) BPF2 on a 100 m radius sphere around the aircraft (a) below the aircraft (i.e. 𝑍 < 0) and (b) on the left-hand side of the aircraft (the side with the acoustic source, i.e. 𝑌 < 0). The black lines corresponds to the vertical and horizontal middle lines of the sphere. The aircraft is represented with an angle of 8°corresponding to the AoA.

Table 1 Azimuthal orders of the

 1

	BPF1	BPF2

Acknowledgments

This project is supported by the project ARTEM (Aircraft noise Reduction Technologies and related Environmental iMpact) which has received funding from the European Union's Horizon 2020 research and innovation programme under grant No. 769350. The authors would further like to thank Marco Carini and Olivier Atinault for their valuable help on the NOVA configurations.