[american institute of aeronautics and astronautics 15th aiaa/ceas aeroacoustics conference (30th...

American Institute of Aeronautics and Astronautics

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Computational AeroAcoustics of a Realistic Co-Axial Engine

in Subsonic and Supersonic Take-Off Conditions

Stéphane Redonnet1, Ciprian Mincu2, Eric Manoha3 ONERA (French Aerospace Centre), Department of CFD and Aeroacoustics, Châtillon, 92322, France

Aloïs Sengissen4 and Bastien Caruelle5 Airbus S.A.S., Department of Acoustic & Environment, Toulouse,31060, France

The present work is devoted to the numerical simulation of acoustic emissions characterizing turbojet engines, a subject that is relevant of the more general purpose of aircraft noise prevision and reduction. More precisely, we explore here the ability of a structured CAA (Computational AeroAcoustics) method/solver to address complicated problems of engine noise prediction. With that end, and by using the ONERA’s CAA solver sAbrinA.v0, we conduct realistic calculations of aft fan noise emission, which involve both a full-3D exhaust geometry (with its pylon / internal bifurcations) and typical fan noise modal contents (high azimuthal order / frequency). The results highlight how far the installation / refraction effects induced by the complex geometry / flow of an engine can affect its fan noise emission. Results also tend to demonstrate that both the here used CAA method and solver are mature enough to face out industrial-like engine noise problems.

Nomenclature BPF = blade passing frequency kR = reduced frequency (with respect to the outer radius of the engine secondary exhaust) Μ ∞ = steady mean-flow Mach number, at infinite Μ inj = steady mean-flow Mach number, at upstream plane of the secondary exhaust Μ max = steady mean-flow Mach number maximum value R = outer radius of the engine secondary exhaust f = acoustic source frequency m = acoustic source azimuthal order (spinning mode) c = sound speed

I. Introduction he noise environment around airport is a major cause of concern within the world, with many local communities exposed to high levels of aircraft noise; the effective reduction of such a ‘noise pollution’ represents both a

technical and a financial important challenge for the incoming years. The noise generated by an aircraft in approach or take-off configuration has two main contributions; firstly the

airframe noise resulting from the impinging of turbulent flows on solid structures (wings, slats, flaps and landing gears) and, secondly, the engine noise resulting from both the jet and the turbomachinery (fan, turbine, combustion) sound emissions. If the airframe and engine contributions to the overall aircraft noise are roughly equals at landing, the latter is largely dominant at take-off, due to the fact that the engine thrust is there at its maximum.

1 PhD, Research scientist, CFD and Aeroacoustics Department, ONERA - BP 72, 29 av Division Leclerc, F-92322. 2 PhD student, CFD and Aeroacoustics Department, ONERA - BP 72, 29 av Division Leclerc, F-92322. 3 PhD, Research scientist, CFD and Aeroacoustics Department, ONERA - BP 72, 29 av Division Leclerc, F-92322. 4 PhD, Research engineer, Department of Acoustic & Environment, Airbus S.A.S, BP M01 32/7, F-31060. 5 PhD, Research engineer, Department of Acoustic & Environment, Airbus S.A.S, BP M01 32/7, F-31060.

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15th AIAA/CEAS Aeroacoustics Conference (30th AIAA Aeroacoustics Conference)11 - 13 May 2009, Miami, Florida

AIAA 2009-3240

Copyright © 2009 by ONERA. Published by the American Institute of Aeronautics and Astronautics, Inc., with permission.


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One big challenge for both motorists and aircraft manufacturers is therefore to improve the acoustic discretion of the engines, as well as their integration within aircraft architectures. With this end, the development of capabilities offering both a deep understanding and an accurate prediction of the physics phenomena that underlie the propulsive noises generation and propagation processes has became a priority for the Aerospace applied research community.

In particular, coming in complement to the more traditional way that experimentation is, the numerical simulation constitutes an as powerful as cheap mean of investigation. More precisely, after a decade of continuous improvements, Computational AeroAcoustics (CAA) seems to be mature enough to face out industrial (i.e. complicated) engine noise problems.

II. Past Computational AeroAcoustics over Baseline Co-axial Engines Since 1998, ONERA has been developing the sAbrinA solver 1,2,6, a multi-purpose integrated CFD / CAA

platform allowing to perform general aeroacoustics simulations over non trivial geometries and flows. Concerning the propulsive noise problematic itself, the sAbrinA solver was used within the framework of several French national and European projects that aimed at characterizing both i) the aft fan noise radiation of co-axial engines 4, 5, 8, 9, and ii) its potential reduction through installation effects offered by innovative aircraft architectures 4,8,9. In particular, these studies implied different 2D or 3D engine exhausts, the latter being i) considered within isolated and/or installed configurations, ii) characterized by realistic ‘in-flight’ thermodynamic conditions, and iii) allotted with representative fan noise modal contents. Such computations were thus conducted with a constant concern for the correct taking into account of both the refraction effects (due to the jet mean flow heterogeneities) and the potential installation effects (due to the possible presence of airframe devices). As a reminder/illustration of such past works, Figure 0 displays the results obtained through two ‘aft fan noise’ CAA calculations that were conducted over a 3D exhaust, the latter being (i) affected of take-off flight conditions and (ii) considered within both an isolated and an installed (over an empennage airfoil) configurations.

III. Towards the Computational AeroAcoustics of Realistic Co-axial Engines These past studies have constituted an indirect but important assessment/validation campaign for both the sAbrinA method and solver, showing how far the latter were able to accurately simulate the (sometimes very complicated) acoustic patterns characterizing ‘in-flight’ and possibly installed co-axial engines. Nevertheless, for all these problems, and mainly for simplicity sake, only baseline engine geometries had been considered. In particular, although they could be of 3D nature 5, 8, 9, the exhausts were always taken as free of any additional devices that realistic engines generally comprise (such as the pylon, or the internal bifurcations). On that topic, one could have legitimately pointed out that such devices might strongly modify both the internal propagation of the emitted fan noise (through its possible modal content redistribution), as well as the external radiation of the latter (through possible additional installation effects). Consequently, a collaborative Airbus/ONERA project was initiated, aiming at CAA-characterizing the aft fan noise emission of a realistic full-3D exhaust, ‘realistic’ meaning here ‘with pylon and internal bifurcations’ (see Figure 1). This engine had to be allotted with i) typical in-flight thermodynamic conditions and/or ii) representative fan noise modal contents - both being provided/specified by the airliner (Airbus). The 14th AIAA/CEAS Aeroacoustics Conference was the occasion to present the preliminary outcomes of such project, through a dedicated

Figure 0. Past CAA computations of co-

axial engines. 3D baseline exhaust in take-off conditions, considered within isolated (up) / installed (over an empennage airfoil, right) configurations, and affected of realistic fan noise contents (up: mode (10,1) at 1 BPF,

right: mode (2,2) at ½ BPF)


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publication 10; highlighting the installation effects to which acoustic waves are submitted to, when propagating inside and outside an exhaust duct, these preliminary results shown how far the full-3D nature of a turbojet engine could strongly affect its noise emission. Such conclusion is of importance since it indirectly demonstrates the crude necessity of accounting for all the engine’s inter/outer devices when estimating the noise radiation emitted by an exhaust. Nevertheless, as pointed in conclusions of Reference 10, it was needed to qualify/quantify more precisely such acoustic installation effects; in particular, it was necessary to assess the respective contributions coming from both i) the reflexion/diffraction by the solid structure and ii) the refraction by the mean flow gradients, all that with respect to iii) the natural radiation behavior of the acoustic mode considered. In addition, these ‘3D exhaust calculations’ being particularly time / memory consuming when solved with a structured CAA method/solver, it was needed to asses how parallel computing features could relax the CPU/MEM constraints, so that ‘industrial-like’ engine noise problems can be handled in a still more flexible way. Finally, it was tempting to go further, by considering an exhaust allotted with stiff aerodynamics conditions, such as the ones provided by locally supersonic flows. Actually, the constantly growing of turbojets by-pass ratio (BPR) leads to a situation where commercial aircraft engines can be characterized with such supersonic flows, when pushed at full-thrust (for example, during take-off). From a physical point of view, it was thus interesting to assess how aft fan noise emissions could react to such locally supersonic regions that generally establish themselves at the outer of the secondary exhaust. On another hand, and from a more methodological point of view, there was a strong interest in addressing such ‘severe flow’ situations which CAA methods/solvers can be confronted to, at least in order to check/assess the effective robustness of the latter. Consequently, and coming in complement of the calculation initially presented in Reference 10, several additional and specific computations were recently conducted on the basis of the same ‘full-3D exhaust noise’ configuration; Firstly, two calculations were computed over a quiescent medium (i.e. without any background mean flow). These calculations were conducted for two representative aft fan noise modes, both pulsating at the Blade Passing Frequency (BPF), and being each one characterized by a given azimuthal order (m, respectively 13 and 26). These ‘no-flow’ calculations aimed at providing i) a validation of the CAA method/solver through comparison with BEM ones, and ii) a reference solution against which compare the ‘with flow’ cases, with respect to the ‘refraction effects’ question. Here, it can be noticed that computing two distinct fan noise modes instead of a single one was motivated by the necessity of ‘de-biasing’ this refraction effects analysis from the possible bias introduced by the natural behavior of the acoustic source to be considered (a behavior that can greatly differ from one to another mode).

Secondly, these two calculations were repeated but, this time, over a heterogeneous jet mean flow. Corresponding to typical take-off conditions, the latter was characterized by important velocity and temperature gradients, as well as a high subsonic region (with Mach numbers rising up to 0.9, in the outer section of secondary exhaust). Such calculations aimed at highlighting the pure refraction effects by mean flow gradients, through direct comparisons with the ‘quiescent medium’ cases previously evocated. Here again, the objective of computing two distinct fan noise modes was to assess the refraction effects with respect to the natural behavior of the noise source.

Finally, the ‘m = 13’ calculation was re-computed but, this time, with a jet mean flow corresponding to take-off conditions of stiffer nature, i.e. presenting a locally supersonic region (of Mmax = 1.1, located at the outer section of secondary exhaust). This last calculation mainly aimed at i) assessing the impact of locally supersonic regions onto the aft fan noise emission of high BPR engines, and ii) providing an indirect demonstration that the here-employed CAA method/solver was robust enough to handle such kind of severe mean flows. At the end, five inter-dependent calculations were thus conducted on the basis of the same “full-3D exhaust aft fan noise” configuration, each calculation differing from the other by both i) the azimuthal order of the fan noise mode to be simulated, and/or ii) the thermodynamic conditions to be accounted for (see Table 1). The present paper summarizes the main achievements and outcomes provided by such a calculation campaign.

Quiescent Medium Take-off / Subsonic (Mmax = 0.9) Take-off / Locally Supersonic (Mmax = 1.1)

Mode (13,1) M13Que M13Sub M13Sup Mode (26,1) M26Que M26Sub -

Table 1 : Calculation cases handled

Figure 1. Full-3D exhaust of a realistic engine, with pylon and internal bifurcations (with courtesy

of Airbus-France)


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IV. Computational AeroAcoustics of a Realistic Co-Axial Engine in Subsonic and Supersonic Take-Off conditions – Methodology

A. CAA Hybrid Methodology and Solver As for past studies conducted over baseline geometries5,8,9, the present realistic engine noise simulations were

conducted following the usual CAA hybrid process, where a preliminary aerodynamic computation provides a heterogeneous steady mean flow over which an acoustic calculation is then performed.

Concerning more precisely such acoustic calculations, use was made of the sAbrinA.v0 1,2 solver - which constitutes the CAA module of the wider ONERA’s CFD/CAA platform named sAbrinA. The sAbrinA.v0 code solves the full Euler equations, which are considered under a conservative / perturbed form (with a splitting of the complete variables into a ‘frozen’ mean flow quantity and a ‘fluctuating’ perturbed one). Such solving is classically conducted with the help of high-order finite differences (6th order spatial derivatives and 10th order filters), and a Runge-Kutta RK3 time marching scheme. The code deals with multidimensional / multiblocks structured grids, and it offers a wide set of boundary conditions (solid wall reflection, modal injection, free-field radiation, etc.). Here, one can precise that the modal injection is achieved via an explicit forcing of the perturbed field (over 6 rows of ghost point) 7,8,9, which enables to numerically generate any given duct mode on a particular boundary. One can also remind that the free-field radiation through peripheral boundaries is mimicked with the help of an as simple as efficient technique; originally proposed in 1,2 and accurately assessed/validated in 11, such technique is based on a progressive decreasing of the spatial derivatives / filters accuracy order (to be obtained via a reduction of the schemes’ stencil half-width). Coupled with a rapid grid stretching (over 6 peripheral rows of ghost points), this trick allows the perturbations to leave properly the calculation domain - that is to say without generating significant numerical reflections at the frontiers. Finally, it can be pointed out that sAbrinA.v0 solver had been recently parallelized (in a MPI – Message Passing Interface sense), which offered to run the present calculations in parallel (over 64 and 128 cores, depending of the considered configuration).

For more detailed information about the sAbrinA.v0 solver and its underlying methodology, we refer the reader to the references 1, 2, where both are fully described.

B. Preliminary CFD Computations In order to properly feed the

CAA solver with suitable stationary jet mean flows, two 3D RANS (Reynolds Averaged Navier-Stokes) computations were performed over the exhaust. The latter was allotted with thermodynamic conditions corresponding to a ‘take-off flight’, to be considered under both a subsonic and a locally supersonic regime. The Mach number characteristics were of M∞ = 0.26 at infinite, and Minj = 0.46 at the upstream section of the secondary exhaust (where the acoustic mode emission was to be forced). The RANS calculations were conducted by Airbus CFD team, with the help of ONERA’s CFD software named elsA (see http://elsa.onera.fr). Prior to that, the elsA solver being a structured code, a preliminary (though heavy) task of CFD-meshing was achieved (still by Airbus), providing a 3D grid of 416 blocks and 30 millions nodes. One can note that both the geometry and the aerodynamics (i.e. the problem) being symmetric, only one half of the configuration was meshed and computed (the results being here graphically duplicated).

Figure 2 : Steady jet mean flows. Mach number field, for take-off flight

conditions (top: subsonic, bottom: locally supersonic)


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As it can be seen on Figure 2, the resulting stationary jet mean flows are very complicated, presenting a highly heterogeneous nature both in velocity, temperature and pressure. One can remark that such mean flow field heterogeneities are due to both (i) the thermodynamic conditions (with strong shear layers developing naturally at the outer of the primary and secondary exhausts) and (ii) the full-3D nature of the geometry (with a clearly non axisymmetric general feature, reinforced by the pylon presence). Apart from that, for the locally supersonic case, one can notice the region located at the secondary exhaust ending, where Mach number values rise up to 1.1.

C. Acoustic Specifications Based on both the engine parameters (dimensions, rotor/stator blades number) and the secondary duct mean flow

characteristics, a dedicated study was conducted by Airbus acoustic team, in order to assess the fan noise emissions that were to be expected most. Among others, two particular acoustic modes were identified, and prescribed for being CAA-computed: the modes (13, 1) and (26, 1), both presenting a reduced frequency of kR = 28.17 (k being the acoustic wave number k=2πf/c, and R being the engine’s outer radius). Here, one can precise that such kR value could be commonly prescribed for all calculation cases, thanks to a proper frequency adjustment accounting for the Doppler effects associated with each thermodynamic condition. One can also note that such a kR value of 28.17 corresponds to one BPF (Blade Passing Frequency) of the engine at full thrust (as here, in take-off conditions).

Once all these modal contents had been identified, the most severe one (m = 26, kR = 28.17) was translated into precise meshing criteria, which then drove the CAA re-meshing task.

D. CAA Grid and Mean Flow Derivations For previous studies conducted over baseline geometries 5,8,9, the CAA grids and mean flows had been directly derived from the CFD ones, thanks to a dedicated 'in-house' code (ReMesh2D) specifically developed for this purpose. In the present case however, due to the CFD grid tricky nature, such tool could not be reasonably used as-is, nor easily improved. The present CFD → CAA re-meshing/interpolation task was thus achieved following a different strategy10, with the help of commercial software (Gambit, Tecplot). Although it was not straightforward at all, such an operation was successfully conducted, providing a generic CAA grid of about 12 millions cells (see Figure 3), with associated mean flows. This grid+flow material was compatible with acoustic modes of reduced frequency (kR) up to 30 (with a minimum value of 10 Points Per apparent Wavelength), and of azimuthal order up to 26 (with angular planes regularly spaced of approximately 1.25°).

As previously said, the two acoustic modes of interest differed only by their azimuthal order (m = 13 or 26). And, as fully detailed in references 5,8,9,10, for this kind of ‘3D-exhaust’ structured CAA calculations, it is precisely the ‘azimuthal order’ that weight more heavily onto the CPU & MEMory required for a proper calculation. Consequently, for obvious reasons of CPU savings, and although the latter could have been used ‘as is’ for computing the former, a specific ‘m = 13’ grid+flows material was derived from the generic ‘m = 26’ one. Such a thing was easily achieved through a ‘m = 26 → 13’ grid coarsening, which consisted simply in removing half of the ‘m = 26’ grid azimuthal planes. On this stage, it can be pointed out that, although both the geometry and the flows were symmetrical (this having allowed to CFD-compute only one half of the configuration), such aft fan noise propagation problems could not be considered as symmetric10. Indeed, except for the particular

mode (0, 1) that defines a plane wave, fan noise modes are all allotted of a spinning motion - which is sufficient to make any symmetry consideration vanish. On the same way, the engine geometry being symmetric but not

Figure 3. CAA structured mesh

Figure 4. CAA grid, with jet mean flow. Axial

velocity field (take-off / subsonic case)


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axisymmetric, such typical ‘rotating machine noise’ problems could not be considered as presenting particular corochronicity (or azimuthal periodicity) characteristics, which should have allowed to advantageously restrict the computational domain to a limited sector (as usually done when axisymmetric baseline engine geometries are considered 5,8,9). Consequently, the half-engine grid+flow materials were duplicated, so that they can be CAA-computed in an ‘entire engine’ sense (see Figure 4). On the contrary, mainly in order to save CPU time, and considering that high(er) azimuthal order modes (such as the ones considered here) radiate more radially than axially, some sub-domains located downstream the nozzle were suppressed. At the end, two types of CAA meshes were obtained, which comprised respectively 9.4 and 4.7 millions of cells.

Finally, all the calculations having to be run in parallel, the two previous sets of Grid+Flow material were properly pre-processed, being partitioned for a 64- or a 128-cores computation. Such an operation was automatically, rapidly and easily achieved with the help of a dedicated Parallel PreProcessing Toolbox (developed at ONERA, written in Python). As an illustration, Figure 5 provides the partitioned mesh associated with the 128-cores simulations.

V. Computational AeroAcoustics of a Realistic Co-Axial Engine in Subsonic and Supersonic Take-Off conditions – Results and discussion

According to their respective heaviness, both m = 13 and m = 26 calculations were computed over respectively 64 and 128 cores of the same parallel computer (an Itanium 64 bits platform that offers 932 calculation nodes, each node being composed of 4 dual-core processors).

Each calculation was run until a stationary state had established over the whole computational domain – which sometimes required a consequent simulation time. On that stage, one can remind that such a thing is intrinsically - and only - due to the configuration here investigated; as extensively shown in previous studies 5,8,9,10, for this kind of ‘3D exhaust’ structured CAA calculations, the overall CPU-time varies as four times the azimuthal order to be considered. When the latter exceeds 10, the computation can thus be particularly CPU-time consuming. In the present case, involving more than 9 millions cells and 37,500 iterations, the heaviest calculation (M26Sub case) required a total CPU time of 37 hours over 128 cores. If such calculation had been run over a single (mono-core vectorial) processor, it would have needed more than 500 CPU hours. Needless to say that such a fact clearly shows how far the parallel computing features can be a key solution for relaxing (not to say removing) the CPU/MEM constraints that constitute(d) the principal limitation of such aft fan noise structured calculations.

One can finally remark that, although their associated jet mean flows highly heterogeneous, the ‘in-flight’ calculations (M13Sub, M13Sup and M26sub cases) did not lead to any particular instability problem; the complete (full Euler’s perturbed) equations were here used without requiring the suppression of any mean flow gradient - as it seems to be sometimes necessary when the linearized Euler equations are used to solve similar problems.

In the next paragraphs, the results of the five calculation cases are displayed, their main outcomes being then discussed.

A. M13Sub case: Mode (13,1), within a Subsonic Jet Mean Flow Here, one can remind that such calculation had constituted the first successful attempt for CAA-computing a

“full-3D exhaust at take off” configuration. As detailed in 10, such calculation had provided meaningful insights, from both a physical and a methodological point of view. However, some additional works remained to be done, which were conducted here; firstly, compared to the initial calculation that had been computed in a sequential sense, the present case was run in parallel. Among other, this provided a direct validation of the sAbrinA.v0 parallel features, as well as a first assessment of the CPU/MEM gain that can be achieved thanks to the latter. Secondly, as mentioned in perspectives of Ref 10, this calculation was specifically post-treated in a ‘modal analysis’ sense, so that the modal redistribution possibly occurring within the secondary exhaust can be highlighted.

1. Results and discussion

Figure 6 displays two lateral views of the perturbed pressure field obtained at the end of the calculation. As it can be seen, such field exhibits very complicated patterns, both in terms of azimuthal and axial/radial characteristics. As widely investigated and explained in 5,8,9,10, such patterns can either result from i) the natural behaviour of the fan

Figure 5: CAA grid, for the parallel

computing (128-cores mesh)


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noise mode itself, as well as from its modification ii) by the internal/external engine devices (installation effects) or iii) by the primary/secondary jet mean flows (refraction effects).

Figure 6: M13Sub - Aft fan noise mode (13, 1) within a subsonic jet mean flow. Instantaneous perturbed

pressure field plotted over two lateral planes As an example, one can here remark the deflection of acoustic waves towards the radial direction - a thing that

characterizes more particularly ‘in-flight’ engines aft fan noise emissions 5,8,9,10. As pointed out in 10, there can be several causes to such a radial deflection of the emitted waves; firstly, the ‘high frequency and/or azimuthal order’ modes are generally characterized by a more radial directivity, once exiting a duct. Secondly, according to the general principle of acoustic propagation through velocity and temperature gradients 5,8,9, a wave propagating downstream a fluidic motion is deflected towards the regions of lower convection/sound speeds - which, here, correspond to the extra-jet core zone (see Figure 4). Finally, the external engine structure can also act as a radial deflector, reflecting any acoustic waves that impinge it (such as here, where a non negligible fraction of the emitted noise impacts the primary exhaust outer wall).

Obviously, such a ‘radial deflection’ is not the sole effect that the acoustic waves are presently submitted to. Indeed, a careful observation of numerous successive instantaneous snapshots (not provided here) shows that, once exiting the exhaust, these (originally ‘spinning’) acoustic waves propagate with no more azimuthal movement, being only characterized by axial / radial motions and / or rearrangements. As pointed in 10, such an ‘azimuthally frozen’ pattern seems to be inherited from what happens in the last section of the secondary exhaust, where - due to the internal pylon/bifurcation presence - the mode stops completely to rotate (see Figure 7). As shown in 10, such an internal modification of the emitted mode can be easily highlighted by a proper visualization of the acoustic field that establishes itself within the secondary exhaust; on Figure 8, the perturbed pressure field has been plotted over four successive (and equally spaced) vertical sections of the duct. The figure speaks by itself, exhibiting how the acoustic mode, once having been emitted at the upstream of the duct (Figure 8-a), progressively looses its initial azimuthal/radial features (Figure 8-b&c), for ending at the outer duct section with a totally different behaviour (Figure 8-d).

However, as pointed out in conclusions of 10, investigating further such an ‘in-duct modal rearrangement’ required specific post-treatments of the result, which were done and are presented in the next sub-section.

Figure 7: M13Sub - Aft fan noise mode (13, 1)

within a subsonic jet mean flow. Prints of the instantaneous perturbed pressure field, in the duct


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a) b) c) d)

Figure 8: M13Sub - Aft fan noise mode (13, 1) within a subsonic jet mean flow. Instantaneous perturbed pressure field plotted over four equally spaced lateral planes of the secondary exhaust.

2. Modal analysis

In order to asses the modal redistribution that could potentially occur within the secondary exhaust, a modal analysis of the acoustic field obtained in the duct was conducted. Here, it has to be said that such a ‘modal analysis’ is based on a ‘duct modes’ description of the acoustic field, which is legitimate only for ideal cases where i) the geometry is a pure cylindrical duct (axisymmetric, with no radius variation), and ii) the flow is uniform. Such hypothesis being clearly not fulfilled here, it had to be assumed that each x-axis section of the present configuration could be locally considered as a cylindrical duct, to be allotted with geometric and thermodynamics characteristics obtained by azimuthally- and/or radially- averaging the real ones. Under these (unavoidable) strong assumptions, a modal analysis of the acoustic field could then be performed; being conducted for each section of both the two half-exhausts, it provided the results displayed on Figure 9.

Figure 9: M13Sub - Aft fan noise mode (13, 1) within a subsonic jet mean flow. Modal analysis of the acoustic field within the secondary exhaust. Up: acoustic mode levels for each half-exhaust sides. Down: half-exhaust sides

Although the assumptions made impose to take them in a qualitative (not to say indicative) sense only, such

results deliver some meaningful insights, which seem to be coherent with the physics; in particular, one can observe that the mode (13,1) is partially redistributed over its immediate neighbours, i.e. the modes (14,1), (12,1) and (11,1). Moreover, when comparing directly the x-evolution of such modal contents to the (half-)exhaust shapes (see lower part of Figure 9), it turns out that there is an indubitable correlation between the modal redistribution, and the geometry modification (especially, at inflexion points). In particular, one can notice the progressive emergence of the mode (11,1), which evolution seems to directly follow the bifurcations’ shape slow variation. In addition to that,


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all modes which (negative) azimuthal order ranks from -21 to -12 seem to evolve just in the same way, though with much lower levels. It is clear that all these modal redistributions could be more or less driven by the continuous interaction of the emitted mode with the internal bifurcations. Apart form that, it is interesting to note that the prominence of modes (14,1) and (12,1) are inverted, depending on the half exhaust they propagate in. This certainly results from to the fact that, due to its spinning motion, the mode (13,1) does not impact on / interact with each side of the bifurcations in a equal manner. In addition, it can be noticed that these two particular modes (m = 14, m = 12) exhibit non negligible levels in the upper region of the secondary exhaust. Such a thing could indicate that such modes directly result from the impact of mode (13,1) with the beginning of the bifurcations; indeed, the acoustic reflection induced by this impact would then make the modally-redistributed contents (retro-)propagate also in the upstream direction. Another interesting thing to observe is that no mode of radial order strictly greater to one seems to emerge – which tends to demonstrate that no radial redistribution really occurs within the duct. Such a fact could indicate that the internal installation effects are here more azimuthally than radially effective. This seems logical, as one can expect a spinning mode to be much more affected by the presence of bifurcations it encounters, than by the progressive variation of the duct radii. One can also remark that all the ‘non-clearly emerging’ modes seem to constitute a kind of continuum background noise. Such an observation has nevertheless to be put in perspective, since part of such continuum (whose shape and level are not significant) could also have a numerical origin; indeed, both the CAA calculation and the modal analysis being discrete, they are not totally free of aliasing phenomena - which can rise whenever a continuous equation is solved in a discrete way. Finally, a last interesting thing to observe is the rapid and strong x-decay of the mode levels, in the very last part of the secondary exhaust; at the duct’s outer section, all modal contents end then with a quasi null value. First, one could think that such decay simply translates the apparent loss of acoustic energy that locally occurs in the downstream region of the duct, once the acoustic waves exit the latter (and adopt then a typical ‘free field’ 1/r decay in amplitude). But this could never lead to near-zero amplitudes of the acoustic field in the duct’s outer section – as it is confirmed by Figure 10, where the Root Mean Square (RMS) value of the perturbed pressure field is displayed. Such strong x-decay of the modal contents in the duct exit region could better indicate that the overall field cannot be longer considered (and, thus, ‘modal analysis’-detected) as a sum of elementary modal components. This would lead us to think that the internal installation effects not only result in a modal redistribution of the emitted noise, but end in a complete de-structuration of the associated modes.

On that stage, it has to be said that one cannot really state on what is the exact weight of such internal installation effects onto the overall acoustic emission. In other words, it is not obvious at all to identify in what proportion the external evolution of acoustic waves is due to the natural radiation of their internally modified patterns, or results from additional reflection / refraction effects (induced by the full 3D nature of external boundaries / flow). On the same way, still regarding the overall acoustic installation effects that characterize such engine geometry / flow, one cannot easily decide between reflection and refraction effects respective contributions. Investigating this question further requires a ‘quiescent medium’ computation, which has been conducted, and is presented at next paragraph.

B. M13Que case: Mode (13,1), within a Quiescent Medium In order to ‘de-bias’ the previous results from the refraction effects influence, the ‘quiescent medium’

counterpart of the M13Sub calculation was conducted. To do so, the computation was simply repeated, its mean flow material being simply disconnected from the simulation.

1. Results and discussion

On Figure 11 are displayed two views of the instantaneous perturbed pressure field obtained at the end of the calculation. Compared to its ‘subsonic’ counterpart of Figure 6 (→ M13Sub), this result exhibits a less important radial deflection of the acoustic waves exiting the exhaust. This indirectly confirms that pure refraction effects by mean flow gradients effectively play a non negligible role in such a radial deflection of engine aft fan noises.

Figure 10: M13Sub - Aft fan noise mode (13, 1)

within a subsonic jet mean flow. RMS perturbed pressure field (third lateral plane,

from right to left: duct’s outer section)


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Figure 11: M13Que - Aft fan noise mode (13, 1) within a quiescent medium. Instantaneous perturbed pressure

field plotted over two lateral planes

2. Modal analysis Here again, a modal analysis of the acoustic field obtained within the secondary exhaust was performed; as it

can be seen on Figure 12, the result is very close to its ‘subsonic’ counterpart (→ M13Sub, Figure 9). All the ‘modal redistribution’ features characterizing the M13Sub case are here recovered, except in one or two minor aspects; firstly, the axial evolution of all modal contents seem a little bit less smooth – which could be simply due to the fact that, here, there is no longer mean flow for x-stretching (by convection effects) their helicoïdal patterns. Secondly, if there is still an inverted prominence of redistributed modes m = 12 and m = 14 between both half-exhausts, it occurs only in their upper region. Finally, the mode (11,1) presents now non negligible levels in the upstream region – which let us think that it could also be created by the mode (13,1) initial impact onto the bifurcation.

Figure 12: M13Que - Aft fan noise mode (13, 1) within a quiescent medium. Modal analysis of the acoustic field

within the secondary exhaust. Up: acoustic mode levels for each half-exhaust. Down: half-exhausts

3. Confrontation / validation against BEM In addition to the assessment of refraction effects, such a ‘quiescent medium’ calculation case was also used for

confronting / validating the present CAA method / solver, through direct comparison with the Airbus’ Boundary Element Method solver ACTI3S. Figure 13 compares sAbrinA.v0 and ACTI3S results, both being plotted on a lateral


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section located downstream the secondary exhaust outer section; although a few discrepancies can be observed - which may result from an insufficient convergence of the CAA simulation, both results agree well. Such a confrontation / validation is thus more than satisfactory, especially if one considers the complexity of the present configuration, and the fact that the two solvers rely on completely different numerical methods, both regarding the modelling and the computing strategies.

Figure 13: M13Que - Aft fan noise mode (13, 1) within a quiescent medium. sAbrinA.v0 result (left side) against ACTIS3S one (right side); RMS perturbed pressure field, downstream the secondary exhaust outer section

C. M26Que case : Mode (26,1), within a Quiescent Medium Eliminating the refraction effects from the ‘m = 13 / in-flight’ case (→ M13Sub) by computing its ‘quiescent medium’ counterpart (→ M13Que) was not sufficient to assess completely the present acoustic installation effects. Indeed, as explained previously, each fan noise mode is characterized by a unique behaviour, which makes it react differently than another to the engine devices. In order to highlight such a fact, the previous ‘quiescent medium’ calculation was repeated but, this time, for the mode m = 26. 1. Results and discussion Figure 14 displays two snapshots of the resulting instantaneous perturbed pressure.

Figure 14: M26Que - Aft fan noise mode (26, 1) within in a quiescent medium. Instantaneous perturbed

pressure field plotted over two lateral planes


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By comparing this result with its ‘m= 13’ counterpart of Figure 11 (→ M13Que), one can easily note that the acoustic radiation is here characterized by i) a more complicated overall pattern (see the right-sided plot of Figure 14) and ii) a higher radial deflection (see the left-sided plot of same Figure 14). This last fact confirms that such radial deflection of acoustic waves is not due to the sole refraction effects by the mean flow, but is also strongly conditioned by the natural behaviour of the acoustic mode emitted by the fan.

2. Modal analysis

Here too, the acoustic field obtained within the secondary exhaust was submitted to a modal analysis, which result is displayed on Figure 15. As one can easily notice by comparing these plots to their ‘m = 13’ counterpart (→ M13Que, Figure 12), the main tendencies of the previous ‘quiescent medium’ modal redistribution are here recovered; in particular, again, such mode m (= 26) is partly redistributed on its immediate neighbours, which azimuthal order are given by m + 1 (= 27), m - 1(= 25), and m - 2 (= 24). Here again the respective prominence of redistributed modes m + 1 and m – 1 is inverted between both half-exhausts, but in their upstream region only. And here too, the m - 2 redistributed mode emerges as the bifurcation thickness increases.

Figure 15: M26Que - Aft fan noise mode (26, 1) within in a quiescent medium. Modal analysis of the acoustic field within the secondary exhaust. Up: acoustic mode levels for each half-exhaust. Down: half-exhausts

However, compared to their ‘m = 13’ counterpart (→ M13Que, Figure 12), these modal contents are

characterized by more complicated features. In particular, one can notice some strong oscillations, which might be due to a “stationary waves”-like pattern establishing itself in the upper part of the exhaust. Indeed, such mode (26, 1) being characterized by quick variations in the axial direction, the interference game of its incident and reflected waves could easily produce this kind of spatially oscillating field. Another important difference with the M13Que case is that, here, the x-decay of modal contents is much stronger. Considering that this mode (26,1) is also characterized by a stronger spinning motion, one could conclude that such x-decay is effectively due to a ‘modal de-structuration’ effect; indeed, impinging more importantly the bifurcations compared to its m = 13 counterpart, this mode m = 26 would then be de-structured sooner in its propagation path.

3. Confrontation / validation against BEM

Here too, thanks to the ‘quiescent’ character of the medium, the present calculation could be confronted to its BEM counterpart, which was also obtained with Airbus’ solver ACTI3S. Figure 16 compares both the sAbrinA.v0 and the ACTI3S results; once again, the two acoustic behaviours agree well and, although a few discrepancies can still be observed, their confrontation is very satisfactory – especially considering again the i) different nature of the computational methods and ii) the complexity of the present configuration.


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Figure 16: M26Que - Aft fan noise mode (26, 1) within in a quiescent medium. sAbrinA.v0 result (left side) against ACTIS3S one (right side); RMS perturbed pressure field, downstream the secondary exhaust outer section

D. M26Sub case: Mode (26,1), within a Subsonic Jet Mean Flow In the direct continuity of its ‘quiescent medium’ counterpart presented above (→ M26Que), the m = 26 calculation case was conducted again, but this time with the subsonic jet mean flow connected. 1. Results and discussion

Figure 17 displays two views of the instantaneous perturbed pressure field obtained at the end of the calculation. By comparing such result to its ‘quiescent medium’ counterpart (→ M26Que, Figure 14), one can clearly remark that the acoustic emission exhibits a more important radial deflection - which is obviously due to the refraction effects by mean flow gradients. On another hand, and by comparing this time both the ‘m = 26’ results (→ M26Sub, Figure 17 / → M26Que, Figure 14) to their ‘m = 13’ counterparts (→ M13Sub, Figure 6 / → M13Que, Figure 11), one can be convinced that the refraction effects do not affect all modes in a same relative way. Such a conclusion is of importance, since it indirectly demonstrates that the refraction effects cannot be investigated independently of the emitted noise content - which cannot be straightforward, if one considers that aft fan noises generally comprehend numerous acoustic modes of very different patterns.

Figure 17: M26Sub - Aft fan noise mode (26, 1) within a subsonic jet mean flow. Instantaneous perturbed

pressure field plotted over two lateral planes


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2. Modal analysis Here too, the acoustic field obtained within the secondary exhaust was modal-analyzed, providing the results displayed on Figure 18; as for the mode m = 13, such ‘subsonic flow’ results are very similar to their ‘quiescent medium’ counterpart (→ M26Que, Figure 15). One can nevertheless remark that, here, the third component on which the modal redistribution occurs is the m + 2 one (and no longer the m -2 one, as it was the case for all previous calculations). Apart form that, here again, the mean flow seems to smooth out all modal contents, this being also certainly due to the x-stretching its convection brings to the helicoïdal propagation paths.

Figure 18: M26Sub - Aft fan noise mode (26, 1) within a subsonic jet mean flow. Modal analysis of the acoustic

field within the secondary exhaust. Up: acoustic mode levels for each half-exhaust. Down: half-exhausts

E. M13Sup case : Mode (13,1), within a Locally Supersonic Jet Mean Flow Finally, as a first attempt of CAA-addressing more severe mean flows, the ‘m = 13 / take off’ calculation case

was conducted again, its ‘subsonic’ jet mean flow being then replaced with the ‘locally supersonic’ one.

1. Results and discussion The instantaneous perturbed pressure field obtained at the end of the simulation is plotted on Figure 20. By

comparing this result with its subsonic counterpart (→ M13Sub, Figure 6), it appears that both emissions patterns are roughly equals. Such an observation is more clearly visible on Figure 19, where the two results have been displayed; as it can be seen, both acoustic fields are very close one from the other, and no major differences can be observed between them. It turns out that the locally supersonic region seems to have only a little impact onto the aft fan noise emission - which invites us to put its effects into perspective. Apart from that, and from a more methodological point of view, it can be said again that, even with such a locally supersonic mean flow, no hydrodynamic instabilities occurred during the calculation - which tends to demonstrate that the CAA method/solver here-employed is robust enough to handle such kind of stiff thermodynamic conditions.

Figure 19: M13Sup - Aft fan noise mode (13, 1), within a locally supersonic jet mean flow. Instantaneous perturbed

pressure field plotted over the vertical central plane, for both the M13Sup (left side) and the M13Sub (right side) cases


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Figure 20: M13Sup - Aft fan noise mode (13, 1), within a locally supersonic jet mean flow. Instantaneous

perturbed pressure field plotted over two lateral planes

VI. Conclusion and perspectives In this study, the prediction of turbojet engine noise was numerically investigated. In particular, it was shown how the aft fan noise emissions characterizing realistic exhausts could be simulated via a structured CAA method/solver; after a brief description of both the methodology used and the pre-treatment tasks achieved, five typical ‘realistic engine aft fan noise’ calculations were presented, being then analyzed and discussed.

Firstly, from a pure physical point of view, the installation/refraction effects to which acoustic waves can be submitted whilst propagating inside and outside an exhaust duct were extensively discussed, highlighting how far the complex geometry and/or flow of a turbojet engine could strongly affect its expected noise emission. Such a conclusion is of importance since it demonstrates that a high fidelity to the reality is required when estimating the acoustic signature of a given engine.

Secondly, from a more methodological point of view, it was shown further how far the sAbrinA.v0 solver and its underlying structured CAA methodology were accurate / robust enough to offer both a high fidelity and a minimal flexibility when applied to realistic problems. In particular, it has been highlighted how the CPU time / MEMory constraints inherited from such a structured solving of exhaust problems could be relaxed (not to say removed) by adopting a parallel computing approach. The next step will now consist in investigating the ‘acoustic liner’ question, with respect to those realistic engine applications; taking place in a dedicated Airbus/ONERA framework, and relying on recent works achieved at ONERA12, such study shall assess how acoustic treatments could be properly CAA-simulated, for problems involving both non trivial geometries / flows and representative (broadband) fan noise contents.

Acknowledgments The authors acknowledge Airbus acoustic and aerodynamic teams, which have respectively achieved the

complete test case definition and the CFD meshing/computing tasks. In particular, the authors are grateful to Mr. Fabien Dettizer (who conducted the RANS calculations), to Dr. Yann Druon (who provided the acoustic specifications), and to Dr Céline Parzani (who achieved the BEM computations).

References

1Redonnet S., Manoha E. and Sagaut P. “Numerical Simulation of Propagation of Small Perturbations interacting with Flows and Solid Bodies”, AIAA Paper n° 2001-2223, 7th CEAS/AIAA Aeroacoustics Conference, Maastricht, The Netherlands, 28-30 May, 2001.

2Redonnet S., “Simulation de la propagation acoustique en présence d’écoulements quelconques et de structures solides, par résolution numérique des équations d’Euler”, PhD Thesis, Université Bordeaux I, Bordeaux, France, November 2001.

3Manoha E., Herrero C., Sagaut P. and Redonnet S. “Numerical Prediction of Airfoil Aerodynamic Noise”, AIAA Paper n°2002-2573, 8th CEAS/AIAA Aeroacoustics Conference, Breckenridge (Co), USA, 17-19 June, 2002.


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4Redonnet S., Manoha E. and Kenning O. “Numerical Simulation of the Downstream Fan Noise and Jet Noise of a Coaxial Jet with a Shielding Surface”, AIAA Paper n°2004-2991, 10th AIAA/CEAS Aeroacoustics Conference, Manchester, United Kingdom, 10-12 May, 2004.

5Redonnet S., Manoha E. and Kenning O., “Numerical Simulation of the Downstream Fan Noise of 3D Coaxial Engines”, AIAA Paper n°2005-2816, 11th AIAA/CEAS Aeroacoustics Conference, Monterey, USA, 23-25 May, 2005.

6Terracol M., Manoha E., Herrero C., Labourasse E., Redonnet S. and Sagaut P., “Hybrid Methods for Airframe Noise Numerical Prediction”, Theoretical and Computational Fluid Dynamics, vol. 19, n°3, Springer-Verlag, July 2005.

7C. Polacsek, S. Burguburu, S. Redonnet and M. Terracol, “Numerical Simulations of Fan Interaction Noise using a Hybrid Approach”, AIAA Journal Vol. 44, n°6, June 2006.

8S. Redonnet S., Desquesnes G. and E. Manoha E., “Numerical Study of Acoustic Installation Effects through a Chimera CAA Method”, AIAA Paper n°2007-3501, 13th AIAA/CEAS Aeroacoustics Conference, Roma, Italy, May 2007.

9Redonnet S., Parzani C., Manoha E. and D. Lizarazu D., “Numerical Study of 3D Acoustic Installation Effects through a Hybrid Euler/BEM method”, AIAA Paper n°2007-3500, 13th AIAA/CEAS Aeroacoustics Conference, Roma, Italy, May 2007.

10Redonnet S., Mincu C. and Manoha E., “Computational AeroAcoustics of Realistic Co-Axial Engines”, AIAA Paper n°2008-2826, 14th AIAA/CEAS Aeroacoustics Conference, Vancouver, Canada, May 2008.

11Guenanff R., Terracol M., Sagaut P. and Lewandoski R.,“Study of Stabilization Methods for CAA”, Reports of the French Academy of Sciences, T 333-9, 694 (2006).

12Delattre G., Sagaut P., Manoha E. and Redonnet S., “Time Domain Simulation of Sound Absorption on Curved Wall”, AIAA paper nº 2007-3493, 13th AIAA/CEAS Aeroacoustics Conference, Roma, Italy, May 2007.

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