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Numerical Simulation of the Downstream Fan Noise of 3D Coaxial Engines

S. Redonnet *, E. Manoha.† ONERA (Office National d'Études et de Recherches Aérospatiales), Châtillon, France

and

O. Kenning‡ QinetiQ, Farnborough, Hampshire - GU14 0LX, United Kingdom

This paper presents an application of a Computational AeroAcoustics (CAA) hybrid process to the three-dimensional numerical prediction of the downstream fan noise of coaxial engines. This process may include the acoustic refraction effects resulting from the propagation through the highly inhomogeneous (subsonic hot) jet mean flow associated to the nozzle. The CAA hybrid methodology associates two different acoustic methods. Firstly, the near and mid field propagation through the (possibly inhomogeneous) mean flow is computed with an Euler, high order, finite differences solver. Then, the far field noise is calculated by use of a classical Kirchhoff integration. First computations are performed over a classical axi-symmetric coaxial nozzle in a fluid at rest, and are validated against BEM simulations. Then the simulations are performed including the jet viscous mean flow previously computed with a RANS solver. These computations show that the acoustic directivity pattern of fan noise is strongly modified when the jet mean flow is included in the simulation. Finally, a last computation is performed over a modified engine presenting a scarf of it secondary engine, this highlighting the abilities of the CAA process to handle full 3D problems, as well as underlining the potential shielding effect of such a structural modification of the nozzle.

Nomenclature x = axial direction y = sideline direction z = flyover direction f = fan noise frequency λ = acoustic wavelength k = wavenumber R = engine external radius Np = number of azimuthal grid planes r = distance from the origin, distance from the source location T = fan noise period t = physical time ∆t = calculation timestep

* Research Engineer, Computational Fluid Dynamics & Aeroacoustics Departement, stephane.redonnet@onera.fr † Research Engineer, Computational Fluid Dynamics & Aeroacoustics Departement, eric.manoha@onera.fr ‡ Propulsion Technologist, Aerospace Centre, okenning@QinetiQ.com Copyright ONERA 2005, except Figures 1 & 2 : Copyright QinetiQ 2005

11th AIAA/CEAS Aeroacoustics Conference (26th AIAA Aeroacoustics Conference)23 - 25 May 2005, Monterey, California

AIAA 2005-2816

Copyright © 2005 by ONERA. Published by the American Institute of Aeronautics and Astronautics, Inc., with permission.

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I. Introduction he noise generated by an aircraft in approach configuration has two main contributions, firstly the airframe noise resulting from turbulent flows over solid structures like wings, slats, flaps and landing gears and, secondly

the engine noise that results both from the jet noise and the fan noise, the latter propagating in both the upstream and the downstream directions.

For several years, ONERA has been developing sAbrinA (Solver for Acoustic BRoadband Interaction with Aerodynamics), a multi-purpose integrated CFD / CAA platform in order to perform general aeroacoustics simulations over complex geometries and flows.

The present paper addresses an application of sAbrinA to a problem relevant to the engine noise domain: the

simulation of the rear fan tone noise propagating in the downstream direction through the highly sheared mean flow of the hot subsonic jet characterizing a 3D coaxial engine.

A preliminary simulation conducted over the a classical axi-symmetric nozzle embedded in a medium at rest has permitted to validate both the employed method and solver by comparison with results obtained through the use of a BEM (Boundary Element Method) commercial code. In the same time, it has provided a reference solution where only the reflection / scattering effects due to the solid boundaries were presents.

Then, the computation has been performed over the same configuration, but including this time the RANS flow field, in order to highlight the refraction effects due to the non homogeneities of the mean flow.

Finally, the engine was modified into a scarfed nozzle and the computation was repeated (over the medium at rest) in order to underline the ability of the solver to handle full 3D geometries, this case providing too a first evaluation of the possible shielding effect that might be obtained form such a scarf.

The paper is organized as follows. Chapter II briefly reminds the CAA methodology and tools used for this

study. Chapter III recalls the preliminary CFD calculations performed over the classical geometry in order to provide its RANS mean flow, while Chapter IV presents the necessary derivation of a suitable CAA grid from the original CFD one. The following chapters describe successively the aeroacoustic simulations previously introduced, that is to say the rear fan noise computations conducted without (Chapter V) or with (Chapter VI) mean flow over the classical axi-symmetric engine, and finally performed without mean flow over the scarfed nozzle (Chapter VII) . Finally, Chapter VIII draws the main conclusions of this work, and lists the possible future engine CAA applications that could be attempted in a near future.

II. CAA Hybrid Methodology and Tools First it has to be noticed that the main objective of this work was to study the feasibility as well as the relevance

of the present numerical process to a realistic aeroacoustics applied problem. Following this process, several 2D problems of fan noise propagation over highly inhomogeneous mean flow were previously treated and fully validated 22. It has been considered here that, regarding to the full 3D applications effectively aimed at, it could be both an easier and an useful intermediate step to perform some 3D computations over an axi-symmetric configuration equivalent to the 2D one already used, which has been done first. Then, in a second time, this axi-symmetric exhaust was modified by analytical means into a scarfed nozzle, leading to a full 3D problem that was treated first over the medium at rest.

All this 3D acoustic computations combine two different methods applied successively; In the near field, acoustic waves (of spinning modes) generated by the fan have to correctly propagate through

the non-uniform highly sheared mean flow of the coaxial jet. In such a complex flow/geometry configuration, only the discretized Euler equations are able to simulate the acoustic convection, refraction and scattering effects. This first step was then achieved using sAbrinA, a multi-purpose integrated CFD/CAA platform that was developed at ONERA 1, 2, 3, 4, 5 and that has been widely used for the treatment of several CAA problems 6, 7, 8, 9. This code can solve steady / unsteady, Euler / Navier-Stokes equations on multidimensional and multiblock structured grids. In unsteady computations, the fluctuating variables can be complete or splitted into (i) a constant mean-flow and (ii) a fluctuating perturbation. Several time and space (finite differences / finite volumes) schemes are available.

In this first CAA calculation step, the acoustic propagation is performed over a steady viscous mean flow which is provided by a preliminary RANS computation. To perform such a propagation, the full Euler’s equations are solved by the help of high-order finite difference spatial and filter schemes, and a Runge-Kutta RK3 time scheme. Relatively to the surrounding free-field boundaries, a classical method of characteristics 10, 11 is coupled with a grid

T

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stretching over 8 rows of ghost points to let the perturbations leave properly the calculation domain (that is to say without generating any numerical reflection at the frontiers).

In a second time, the far field radiation has to be computed with the help of an integral method 12, 13 ; beyond a given radial distance from the jet axis (say about 2 nozzle radii) the mean flow can be considered as approximately uniform and the perturbed pressure field as purely acoustic. In this case, the free-field acoustic propagation can be exactly modeled by use of an adequate convected Green function implemented in a Kirchhoff integration. With this method, the radiated noise can be computed at any distance in the far field from the data (pressure and normal derivative of pressure) on a given surface enclosing all present sources. Due to the monochromatic nature of the acoustic excitations (fan BPF tone noise), it is much more straightforward to perform the Kirchhoff integration in the frequency domain than in the time domain; the convolution over retarded times is then simply replaced by multiplications of complex terms. Consequently, the far-field radiation step has been performed with the Kirch3D code, a three-dimensional and frequency Kirchhoff solver developed in the frame work of this study. The linking between the Euler propagation and the Kirchhoff radiation steps has required only a time Fourier transform of the pressure data collected over the integration frontier during the propagation process.

III. Preliminary CFD Computation In the frame work of a previous study 22, a 2,5D (axi-symmetric) RANS calculation was performed by QinetiQ

in order to provide the aerodynamic flow-field inside and outside a classical coaxial jet. The analysis was carried out using the commercially available unstructured Fluent v.5 CFD solver 15. This cell-centred finite volume code was run steady-state to solve the compressible Reynolds Averaged Navier-Stokes equations. Turbulence closure was achieved by implementing the standard k-ε model and wall functions were employed to resolve the near wall flow behavior. Figure 1 presents the geometry and mesh of the nozzle (symmetric part only).

This engine was of a ¾ cowl high bypass ratio coaxial jet design. The mesh, that was constructed using flow aligned structured blocks, extended 40 secondary diameters axially and 7 secondary diameters radially. This grid comprised 94,805 quadrilateral cells. Nozzle pressure and temperature ratios were chosen to represent an aircraft at a take-off flight condition, with a freestream Mach number of 0.25. The calculated mean flow was highly inhomogeneous and presented very high gradient both in density, velocity, pressure and temperature. The Figure 2 depicts the axial velocity profile obtained.

Figure 1. CFD grid. Close view of the nozzle geometry, and mesh detail. Copyright QinetiQ 2004

Figure 2. CFD computation. Axial velocity field. Copyright QinetiQ 2004

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IV. Acoustic Grid Derivation The original 2D-axisymmetric CFD grid

used for the RANS calculation presented a high refinement near the solid walls (for a correct simulation of the highly sheared flows in turbulent boundary layers and mixing layers), and - on the contrary - a coarse resolution over the mid and far field regions. It’s obvious that this aerodynamic grid was not suited for acoustic computations using Euler equations in perturbation form: such computations require homogeneous grids with an almost constant cell size driven by the shortest acoustic wavelength expected to be propagated on it. Consequently, a new specific “acoustic” grid has to be derived from the original “aerodynamic” one. This was done in two successive steps; first, in the 2D original plane, the grid multiblock topology was conserved, but each block was re-meshed following the requirement of constant cells with a size corresponding to one tenth of the typical wavelength of the fan blade passing frequency. Figure 3 shows a partial view of both the original aerodynamic grid and the intermediate (two-dimensional) acoustic one, which contains 64,408 elements.

Then, this last 2D grid was simply rotated and duplicated Np times around its symmetry axe, leading to a final 3D acoustic mesh of Np equi-spaced angular planes. Here, it is important to note that the choice of the number Np represents a compromise between the propagation capabilities of the grid (the greater Np is, the higher order spinning mode can be propagated) and the CPU price to pay for it (with a CPU memory - resp. time - requirement proportional to Np - resp. 2Np -). A part from that, it is necessary to deal with a minimum number of planes for pure “geometric” reasons, simply because the metrics errors are directly driven by the mesh lines regularity. Considering all those facts, and after several preliminary tests were performed, a number of 25 planes was finally chosen; this has led to a 1,606,000 elements 3D (axi-symmetric) mesh, which is partially showed on the Figure 4. In the radial direction, this grid remains homogeneous up to a region where the mean flow is assumed to be approximately uniform (r > 1.5R) while, in the axial direction, it extends up to x = 18.5 R in order to take into account the entire development of the jet mean flow. At all external boundaries, the grid is strongly stretched, a necessary requirement for a satisfying behaviour of the non-reflecting boundary condition.

Following some recent studies 20, which advice a minimum resolution of 12 point per (apparent) wavelength in the angular direction, this grid should allow the correct propagation of spinning modes of order up to 2. Consequently, only the two limit case modes, that is to say the mode m = 0 (plane wave) and the mode m = 2, were simulated; for that, a convenient pressure field was imposed at the upstream of the secondary exhaust (see Fig 5). We precise that no particular radial dependence was specified, and that a same normalized frequency kR = 2πR/λ of about 20 (corresponding to a typical 20-blade fan) was chosen.

It should be noticed also that, since both the geometry and the medium are axi-symmetric, no other modes than the one effectively simulated should appear during the simulation. It can be reminded too that the simulation of higher order modes would required no more effort than an increasing of the number of planes Np (and, consequently, of the CPU time / memory requirements).

Figure 3. Acoustic grid derivation. Partial views of the CFD (left side) and the CAA (right side) 2D grids.

Figure 4. Acoustic grid derivation Partial view of the 3D acoustic grid

Figure 5. Rear fan noise (left: mode 0, right: mode 2). Pressure field at the upstream of the secondary exhaust, in the beginning of a source cycle.

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V. Fan Noise Propagation of the Classical Nozzle, over the Medium at Rest The rear fan noise simulations have been firstly done with zero mean flow, for two reasons. The first reason is that one of the objectives of the present study is to highlight the influence of highly sheared

mean flow on the radiation of rear fan noise. In this context, the solution obtained without mean flow can be taken as a reference solution.

The second reason is that acoustic computations without mean flow only involve acoustic scattering effects on solid boundaries. For harmonic problems, this can be easily (and exactly) simulated by use of a Boundary Element Method, which solves the Helmoltz equation in the frequency domain and under rigid boundary conditions on solid walls. This method only requires meshing the solid boundaries, which is especially straightforward in 2D (and here in 2,5D) where solid walls are meshed using lineic elements. Since BEM can provide the pressure field at any observation point in the near field as in the far field, this method is a good tool for validating the hybrid Euler/Kirchhoff method used here.

A. Local Euler Perturbation Equation Simulation The time step was set to T/100, with T being the source period. The computation was conducted over 3,500

iterations and required almost 15,000 seconds of CPU on a NEC-SX5 (about 2.6 µs/∆t/cell).

Relatively to each of the two spinning modes, the top of the Figure 5 shows the instantaneous pressure field at the end of the computation (t = 70T); the scattering effects on the rigid walls generate directivity lobes as soon as the radiation starts. At t = 15 T the wave pattern has reached the stretched zone (r ≥ 2.46R, not visible in plots) where the radiation is mostly damped. It should be noticed that, at the end of the computation, the initial wave fronts have travelled over a distance of 70λ or about five times the radial extent of the domain, without significant reflections on the external boundaries. Both a closer view of the nozzle and a cut at x = constant are displayed on the bottom of the same Fig. 5. All these plots indicate that, as this could be expected, only the mode 0 provides a significant acoustic level along the nozzle axe, and that only the mode 2 has a real spinning motion.

B. Coupled Euler/Kirchhoff simulation For the Kichhoff integration purpose by use of the Kirch3D code, a control surface has been constituted from

the upstream boundary (x = -5R) to the downstream boundary (x = 20R), a surface involving all the grid cells located at a same distance (r ≈ 1.5R) from the nozzle. It should be noticed that this Kirchhoff envelop, on which the pressure fluctuations provided by sAbrinA were stored, was not closed in order to be used "as is" in computations involving the inhomogeneous mean flow; in that case, the non-acoustic pressure perturbations convected downstream would affect the Kirchhoff method which assumes that the perturbed pressure field is purely acoustic on the integration frontier. On another hand, this liberty could be taken especially since, due to the large extent of this frontier as well

as the r1 wave amplitude decay, the contribution of this closure to the far-field sound would be negligible. Another

point to note is that, due to the extreme sensitivity of the Kirchoff method to the geometric regularity of its integration surface, it was necessary to enhance this envelop with some intermediate angular lines on which the sAbrinA’s stored data were interpolated linearly.

Figure 6. Rear fan noise (left : mode 0, right : mode 2) in a medium at

rest. Instantaneous pressure field at t = 70T; full extent view (top), restricted view (bottom, left) and cut at x = constant (bottom, right)

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Figure 7 shows a local validation of the mono-chromatic Kirchhoff integration performed in the near field, and in the immediate vicinity of the control surface (which, here, follows the x-axis). The background of the plot is the instantaneous pressure field computed with sAbrinA at the beginning of a source cycle. The superimposed rectangle displays the real part of the complex pressure field computed via the Kirch3D code. The comparison shows a good continuity of both computations, even if some slight discrepancies appear, certainly due to the non closure of the control surface in the (upstream and downstream) axial directions.

Once this validation step checked, the Kirchhoff integration has been used to compute the pressure field along a circle of radius equal to 77R and centred on the plane origin (x = 0, y = 0, z = 0), in order to provide far-field directivity diagrams that are given below (see part V. D)

C. Validation by use of a Boundary Element Method (Sysnoise) In order to carry out a validation of the Euler/Kirchhoff results, a two-dimensional BEM model of the nozzle was

built with 904 lineic elements. As for Euler computations, an adequate pressure (same frequency, no radial dependence) was imposed at the upstream of the secondary nozzle. Then, relatively to each of the two considered modes, the pressure field was computed by use of the BEM commercial code Sysnoise (taken in its axi-symmertic version) either on a local midfield Cartesian domain, or along a circle of radius r = 77R centred on the plane origin for far-field directivity diagrams.

Figure 8 compares the R.M.S. (Root Mean Square) pressure fields obtained with the sAbrinA and Sysnoise codes; there is a very good agreement between both simulations. The validation is more explicitly provided on the Fig. 9 where the same quantity is plotted on several cuts taken along four radius located at different axial positions. Once again, despite of some little discrepancies, the sAbrina results match with the Sysnoise one all over the well resolved area (beyond which, because of the stretched zone, the Euler solution logically collapses).

Nevertheless, it has to be said that such comparisons were not straightforward since sources are of different nature in both computations: Sysnoise considers size-less Dirac monopoles whereas sAbrinA uses sources with spatial finite Gaussian distribution. The only correct method to quantitatively compare the results would have been to normalize amplitudes by the total acoustic power radiated in each configuration. In the present case, we simply adjusted the contour scales for both results in order to match the patterns.

Figure 7. Rear fan noise (left: mode 0, right: mode 2) in a medium at rest. sAbrinA (background) and Kirch3D (superimposed rectangle) results.

Figure 8. Rear fan noise (top : mode 0, bottom : mode 2) in a medium at rest. R.m.s. pressure field provided by sAbrinA (left) and by Sysnoise (right)..

Figure 9. Rear fan noise (left : mode 0, right : mode 2) in a medium at rest. R.m.s. pressure provided by sAbrinA (dotted lines) and by Sysnoise (solid lines); cut along four radius.

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D. Far-field directivity diagrams Figure 10 compares directivity

diagrams at r = 77R computed both by BEM and by Euler/Kirchhoff. The amplitudes (given in linear) have been arbitrarily normalized by their value in the direction α = 45°. Concerning the mode 0 results, it should be noticed that the lobe displayed at α = 0° in the Sysnoise directivity diagram is absent from the sAbrinA/Kirch3D computation : this lobe, that was well simulated and previously observed in the Euler results (see part V.B) has simply not been relayed by the Kirchhoff solver because of its (necessary) non closed control surface.

Despite of this expected difference, the sAbrinA/Kirch3D results agree very well to the Sysnoise one.

VI. Rear Fan Noise Propagation of the Classical Nozzle, over the Inhomogeneous Mean Flow The main interest of these computations is to underline the influence of highly inhomogeneous mean flow on the

studied acoustic sources. The previous computations have then been performed again but, this time, over the RANS mean flow obtained by the RANS preliminary calculation. The results are presented here. Obviously, in this case, there was no possible comparison with another acoustic method since BEM only handles acoustic scattering simulations without mean flow.

A. RANS mean-flow interpolation As it was seen in Chapter III, the steady flow-field was highly inhomogeneous, and presented very high

gradients of all quantities in the radial direction. Then, one necessary preliminary task was to correctly interpolate this flow field from the original aerodynamic grid to the new acoustic mesh. This process was not straightforward because both grids had completely different geometrical characteristics, especially regarding the cell size and distribution. This has been done by use of a barycentral bilinear technique already developed at ONERA in the framework of the Chimera method implementation in ONERA's elsA code. Figure 11 compares the xy-plane distribution of the density, plotted both on the aerodynamic grid (left) and on the acoustic mesh (center). It’s clear that the mean flow behaviour was exactly recovered from the original CFD grid, except obviously in the thin boundary layer regions that were no more meshed on the acoustic grid. A global view of the interpolated axial velocity field is plotted on the right of the same Fig 11.

B. Local Euler Perturbation Equation simulation

Figure 10. Rear fan noise (top: mode 0, bottom: mode 2) in a medium at rest. Directivity diagrams at r = 77R, provided by Sysnoise (in red) and sAbrina/Kirch3D (in green).

Figure 11. Inhomogeneous mean flow. RANS mean flow calculated on the original CFD grid

(density, left) and interpolated on the CAA grid (middle: density, right: axial velocity).

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Once this interpolation step was achieved, the same simulations of rear fan noise propagation have been performed, but this time over the RANS mean flow filed. Those computations were conducted exactly in the same way as previously, except that the sources were ramped up during their first periods by use of an adequate ramping function in order to avoid transient instabilities. It should be underlined that, regarding to the acoustic computations aimed at, the present highly inhomogeneous mean flow was a quiet severe one - with, in particular, a maximum Mach number of 0.9. Despite of that, the simulations did not generated unwanted pressure instabilities; the full Euler’s (perturbed) equations were used without requiring the suppression of any mean flow gradient terms in order to avoid unstable modes, as it seems to be necessary when linearized Euler equations are used to solve similar problems 16. Concerning the computational price to be paid, and dur to the logical increasing of the CFL number, such calculations required the double (30,000 sec. of CPU) than for the medium at rest cases.

Figure 12 shows the instantaneous pressure field obtained at the end of the computation (t = 70T). This plot has to be compared to the one relative to the same simulations performed in a medium at rest (Figure 6).

For both simulated modes, it is clear that the mean flow has a very strong influence on the sound waves propagation. More precisely, the mean flow tends to strongly deflect the sound propagation in the radial directions, whereas the propagation in the downstream axial direction is attenuated in a spectacular way. Anticipating far-field directivity diagrams, this last result shows that the mean flow has a critical influence on the overall directivity. Figure 13 displays the R.M.S. (Root Mean Square) pressure fields obtained for each of the two modes (we precise here that the x-axis discontinuity observed on the plots is purely graphical). Once again, the deflection effect due to the mean flow gradient is clearly visible. It should be noticed that such a deflection effect remains coherent with the well known law of acoustic refraction in shear layers 21; according to it, a wave propagating downstream the flow will be deflected toward the lower ambient speed regions

- which, here, are the extra-jet

Figure 12. Rear fan noise (left: mode 0, right: mode 2) over the inhomogeneous mean flow. Instantaneous pressure field at t = 70T; full extent view (top), restricted view (bottom, left) and cut at x = constant (bottom, right)

Figure 13. Rear fan noise (from left to right: mode 0, 1 and 2) over the inhomogeneous mean flow. Root Mean Square pressure field.

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core regions (see Fig. 2). The same analogy can be made with the phenomena of refraction in temperature gradients 21 for which, following the Snell’s law, the acoustic waves will be deflected toward the regions where the speed of sound (that is to say the temperature) is lower, regions that - here again - are located outside the jet core.

C. Coupled Euler/Kirchhoff simulation In the present case, the Kirchhoff method involves the

acoustic convected Green function, meaning that it can be used in a medium with non-zero mean flow as long as the latter can be assumed as uniform beyond the integration frontier. This hypothesis can reasonably be considered valid in the present configurations. However, in order to check it, the same local validations as displayed on Figure 7 have been conducted again for theses mean flow cases. The results are shown on Figure 14; again, the plots display a good continuity between Kirchhoff and Euler calculation domains. Here too, we can suppose that the slight error made on the phase of acoustic waves is due to the non closure of the integration frontier in the downstream direction, a non closure that - here - is necessary in order to avoid the possible pollution of the Kirchoff results by the non-acoustic pressure perturbations convected along the jet core.

D. Far-field directivity diagrams (Euler/Kirchhoff); evaluation of the mean flow effect on the overall radiation of each mode

Once the validation of the Kirch3D code was checked for these not quiescent medium cases, the Kirchhoff integration has been used to compute the pressure field along the same circle (0, 77R); Figure 15 provides the directivity diagrams calculated, and compares them to the previous one obtained in a medium at rest. Once again, it is clear that the mean flow gradients tend to both reinforce the directivity in the radial directions, and attenuate it in the axial direction. This confirms that the deflection effect occurred by the mean flow gradients on the near field acoustic propagation is recovered in the far field region.

This point may constitute an important conclusion for the context of installation effect studies; it would say that such studies have to be conducted with a convenient take into account of the mean flow, and that a “no flow” or an “uniform flow” hypothesis could be not sufficient enough to provide a good qualitative result.

However, this conclusion must be considered with reservations due to the source nature with respect to non-zero flow. It is known that one given sound pressure source may radiate different acoustic power depending on the ambient mean flow. This point has not been numerically verified and in the comparison presented above, amplitudes have not been corrected from the total radiated power.

VII. Rear Fan Noise Propagation of a Scarfed Nozzle, over the Medium at Rest In order to illustrate the ability of both the method and the tools to solve full 3D engine problems, a new

calculation over a non axi-symmetric geometry has been performed. Waiting for a new RANS computation that

Figure 14. Rear fan noise (left: mode 0, right: mode 2) over the inhomogeneous mean flow. sAbrinA (background) and Kirch3D (superimposed rectangle) results.

Figure 15. Rear fan noise (top: mode 0, bottom: mode 2) over the inhomogeneous mean flow. Directivity diagrams at r = 77R (solid lines), and comparison with the medium at rest results (dotted lines).

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could provide the mean flow field corresponding to this new geometry, the acoustic calculation was firstly conducted over the medium at rest.

The original axi-symmetric nozzle was modified into a new one, presenting a 10 degrees negative scarf of its secondary exhaust. Such a geometric trick is commonly used in the domain of engine intakes, because of the potential acoustic shielding effect that such a modification may occurs. The studies 23 conducted in this framework have shown that the noise attenuation experimentally observed was not only due to the acoustic reflections generated by the scarf, but was due too to the refraction effects driven by the (inevitable) modification of the flow. Obviously, because of the quiescent medium hypothesis firstly made, such effect can not be reproduced here.

A. Acoustic grid modification In order to obtain a scarf of the secondary

exhaust, the original grid CAA was modified by analytical means. Because it was more an illustration of the 3D abilities of the sAbrinA code than an effective prospecting of a new “Low Noise Engine”, no particular precaution were taken concerning the mean flow (and so on the engine) characteristics that such a scarfed nozzle could present. Nevertheless, a particular attention was paid to the preservation of the original secondary exhaust exit areas (and so on of its theoretical flood rate). The Figure 16 displays both two views of the modified engine and a comparison with the classical one, comparison that is given in the plane of maximum deformations (flyover or xz plane). As it can been seen only the shape of the secondary exhaust is modified, while the rest of the engine remains unchanged. It should be noticed too that the upstream of the secondary exhaust where the acoustic pressure sources are imposed is not affected by the modification, this ensuring that the acoustic input should have the same behaviour than the one of the classical engine case.

B. Local Euler Perturbation Equation simulation The acoustic propagation was computed in the same manner than before over this new geometry. For each

mode, Figure 17 displays the instantaneous pressure field at the end of the calculation (t = 70T), which is plotted on both the xz and the xy planes; the scarf seems to have only a few shielding effect on the mode 0 propagation, which presents quiet equivalent levels above and below the sideline plane (z = 0). On the contrary, it seems to affect more considerably the mode 2 propagation pattern; in particular, some noise reinforcement occurs in the upper part (z > 0) of the domain, while the overall sound emitted toward the ground (z > 0) seems to be attenuated.

Figure 16. Modified engine. Partial views of the CAA grid (left side, right side / top), and comparison with the original axi-symmetric nozzle (right side / bottom)

Figure 17. Rear fan noise of the scarfed engine (top: mode 0, bottom: mode 2), in medium at rest. Instantaneous pressure field at t = 70T: cuts in the xz (left) and xy (right) planes

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Those results are too deducible from the Figure 18 which provides same plane views of the R.M.S pressure; by comparing the overall acoustic levels above and below the sideline plane (z =0), it appears that only the mode 2 is noticeably affected by the scarf of the engine.

C. Far-field directivity diagrams (Euler/Kirchhoff); evaluation of the scarf effect on the overall radiation Another local validation of the Kirch3D step

(not shown here) has permitted to ensure that the re-enrichment of the Kirchhoff data between each pair of the 25 calculation planes was sufficient enough, regarding to the new acoustic patterns obtained with the sAbrinA computation. The same directivity diagrams on a flyover circle (0, z = 77R) have then been calculated; they are plotted (in red) on the Figure 19, which displays too the previous results obtained for the case of the classical engine in a medium at rest (in black). By comparing both the two results, it appears clearly that the scarfing effect on the mode 0 is not well drawn; the sound is attenuated or reinforced depending on the direction, even in the lower part of the domain (z < 0). Consequently, no overall shielding effect can be noticed in the ground direction.

On the contrary, concerning the mode 2, the sound is entirely both reinforced in the upper directions (z > 0) and attenuated in the lower directions (z < 0), leading to a consequent reduction of the overall noise level emitted toward the ground.

However, as it has been said before, these first quiescent medium computational cases did not included any of the mean flow refractions effects that could partially influence the overall scarfing efficiency. To investigate more this latest, it should be necessary now to run the computations again over the inhomogeneous mean flow corresponding to the new geometry, after obviously have computed it with a new RANS calculation. This should constitute the next step of this work.

Figure 18. Rear fan noise of the scarfed engine (top: mode 0, bottom: mode 2), in medium

at rest. Root Mean Square pressure field: cuts in the xz (left) and xy (right) planes

Figure 19. Rear fan noise of the scarfed engine (top: mode 0, bottom: mode 2), in medium at rest. Directivity diagrams at r = 77R (in red), compared with the classical engine one (in black).

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VIII. Conclusions and Undergoing Works The present study focused on the 3D numerical simulation of the rear fan noise downstream propagation

characterizing coaxial engines. This analysis has been done by a three-dimensional investigation of the acoustic near & mid-field propagation as

well as the far-field radiation of two spinning modes (modes 0 and 2) generated in the secondary exhaust of the nozzles.

A preliminary two-dimensional CFD calculation performed over a (classical) axi-symmetric engine considered under take-off conditions has provided the RANS mean flow characterizing its highly subsonic hot jet. Then, after a necessary 3D acoustic grid derivation step, CAA simulations were performed by use of a hybrid method combining (i) a high order finite difference Euler solver (sAbrinA) which simulated the acoustic propagation over the inhomogeneous mid-field and (ii) a Kirchhoff integration tool (Kirch3D) which calculated the noise radiation in the homogeneous far-field.

The calculation were conducted first over a quiescent medium, and validated by comparison with a commercial BEM solver. Then the inhomogeneous mean flow cases were ran, leading to a much more realistic result which taken into account the significant modification of the directivities by the mean flow gradients, with the direct consequence of a reinforcement of the far-field noise emitted toward the ground. This result is important because it suggests that, at least in this particular case of rear fan noise investigations, the prediction of installation effects under the no-flow (and possibly uniform flow) assumption may be erroneous.

In order to highlight the abilities of the solver to handle full 3D problems, as well as to initiate a qualitative study of possible acoustic benefits that could be obtained by scarfing effects, a last computation was conducted over a modified geometry; this geometry, presenting a scarfed secondary exhaust, was derived from the original one by analytical means. The computation conducted over a quiescent medium has led to the conclusion that a partially shielding effect could be effectively obtained by such a geometry modification, but that further investigations were necessary - in particular concerning the inhomogeneous mean flow refraction effects.

The next step of the present work will be to treat the case of the scarfed engine but, this time, including its non quiescent medium (which will have to be computed before). Some work will be done too concerning the ways how to simulate higher order spinning modes without increasing too much the computational effort.

Acknowledgements This work was partially co-funded by Airbus SAS and EREA (association of European Research Establishments in Aeronautics).

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