# High-fidelity flow and noise simulations of double-stream jet installed in T-tail configuration

M. Huet, Fulvio Sartor, Thomas Renaud, F. Gand

► To cite this version:

M. Huet, Fulvio Sartor, Thomas Renaud, F. Gand. High-fidelity flow and noise simulations of double-stream jet installed in T-tail configuration. Journal of Sound and Vibration, 2026, 621, pp.119480. 10.1016/j.jsv.2025.119480. hal-05308075

HAL Id: hal-05308075

https://hal.science/hal-05308075v1

Submitted on 10 Oct 2025

HAL is a multi-disciplinary open access
archive for the deposit and dissemination of sci-
entific research documents, whether they are pub-
lished or not. The documents may come from
teaching and research institutions in France or
abroad, or from public or private research centers.

L'archive ouverte pluridisciplinaire HAL, est
destinée au dépôt et à la diffusion de documents
scientifiques de niveau recherche, publiés ou non,
émanant des établissements d'enseignement et de
recherche français ou étrangers, des laboratoires
publics ou privés.

<figure><img src="image_1.png" /></figure>
<figure><img src="image_2.png" /></figure>

ELSEVIER

Contents lists available at ScienceDirect

Journal of Sound and Vibration

journal homepage: www.elsevier.com/locate/jsvi

<figure><img src="image_3.png" /></figure>

# High-fidelity flow and noise simulations of double-stream jet installed in T-tail configuration

M. Huet<sup>a ID*</sup>, F. Sartor<sup>b</sup>, T. Renaud<sup>b</sup>, F. Gand<sup>b ID</sup>

<figure><img src="image_4.png" /></figure>

## ARTICLE INFO

### Keywords:

- Jet noise

- Simulation

- Installation

- Sonic fatigue

- Modelling

## ABSTRACT

The aerodynamic field and the acoustic signature of a mixed-stream cold coaxial jet, representative of a low-bypass ratio engine and installed on a T-tail configuration typical of business jets is investigated numerically. The nozzle diameter is 80 mm and the jet velocity is 280 m/s (M=0.9) for both streams, leading to a Reynolds number $Re_D = 1.5 \times 10^6$. The time-accurate flow fields are simulated with the Wall Modelled LES branch of the hybrid RANS/LES approach ZDES, namely ZDES mode 3, and are used to reconstruct radiated noise with the Ffowcs Williams and Hawkins integral formulation. The full T-tail region is included in the aerodynamic simulation to account for scattering effects. A very good match with the experimental flow and noise data is found but the important numerical dissipation that occurs during the propagation of the sound waves towards the tailplane restricts the prediction to low- and medium-frequencies in this direction. The jet is found to be far enough from the fuselage and horizontal tailplane not to be impacted by their presence; this property is used to model the acoustic radiation towards the tailplane from an isolated jet configuration that matches the wall pressure levels and spatial coherence up to the high frequencies.

## 1. Introduction

Jets are one of the most significant noise source of an aircraft at take-off [1]. The increasing number of airports and the restrictive regulations for acoustic pollution have focused the attention of many researchers on this topic. For this reason, studies on high-speed turbulent jets are becoming more and more popular due to the crucial implications for the aeronautical industry [2]. Since the pioneering work of Lighthill [3], the fundamental mechanisms underlying jet noise in academic configurations have been the subject of many experimental [4–7], theoretical [8–10] and numerical [11,12] investigations. However, less studies have focused on applied cases where the nozzle is installed on an aircraft. In these cases, the installation effects are of pivotal importance. First for noise sources, as they may be modified by the interaction of the flow with the solid bodies. Second for propagation, as the sound waves are scattered during propagation by the non-uniform mean flow and solid surfaces. In addition, sound waves induce vibrations of the aircraft structure, a phenomenon known as acoustic fatigue [13].

Fatigue in general causes damages in the aircraft structure that can lead to fatal accidents. The structural design required to sustain such damages entails additional weight and complexity, which eventually increases the aircraft footprint and operational costs. For that reason, it has long been a subject of study with the objective to propose low-order models that accurately predict service life [14]. Acoustic fatigue is caused by the dynamic response of the structure to unsteady pressure loading from aerodynamic

<footnote><sup>a</sup> DAAA, ONERA, Institut Polytechnique de Paris, Châtillon, 92320, France</footnote>

<footnote><sup>b</sup> DAAA, ONERA, Institut Polytechnique de Paris, Meudon, 92190, France</footnote>

<footnote>* Corresponding author.</footnote>

<footnote>E-mail address: maxime.huet@onera.fr (M. Huet).</footnote>

<footnote>https://doi.org/10.1016/j.jsv.2025.119480</footnote>

<footnote>Received 1 April 2025; Received in revised form 25 August 2025; Accepted 30 September 2025</footnote>

<footnote>Available online 8 October 2025</footnote>

<footnote>0022-460X/© 2025 The Author(s). Published by Elsevier Ltd. This is an open access article under the CC BY license</footnote>

<footnote>(http://creativecommons.org/licenses/by/4.0/).</footnote>
and engine acoustic sources [15] and its role in skin cracking or failure of internal support structure is known since the late 1950s [16]. The engine is a significant source of acoustic fatigue as jet and fan are very intense noise generators [17]; this is particularly true for jet noise which is very high for the low bypass ratio (BPR) engines that equipped the first civil aircraft. The increase of engine bypass ratio for more recent architectures significantly reduced pure jet noise but gave birth to jet-surface interaction noise. The concern also remains at least for 2 civil aircraft configurations where low BPR engines are used: supersonic aircraft [18] and business jet aircraft [19]. The complexity of the full process associated with fatigue, from the space-time excitation of the structure to the final mechanical failure, long remained too complex for theoretical and numerical analysis. This limitation tends to vanish with the improvement of the numerical capacities during the last decades (see for instance [20]) and the subject remains an open and active topic [21].

In order to accurately compute jet noise on installed configurations, the whole aircraft geometry must be taken into account. At the same time, reliable scale-resolving and unsteady approaches are needed to simulate the turbulent mechanisms which generate noise. Large Eddy Simulation has proven to be efficient in doing so [22], but this approach is challenging to implement in an industrial framework when dealing with complex geometries. Although some authors have shown encouraging results on complex configurations [23,24], it does not seem to be reasonable nor relevant to resolve the turbulence production mechanisms in all attached boundary layers for a complete aircraft as far as jet noise is concerned. Hybrid RANS/LES methods are suited to tackle this issue, thanks to their ability to model the attached boundary layers and resolve turbulence in free shear layers: while the RANS approach facilitates the modelling of complex geometry typical of industrial configuration, the high-fidelity approach adopted allows the resolution of the turbulence production mechanisms, which play a key role in the generation of noise. These methods have been successfully used for the simulation of installed configurations such as jet-wing interaction, either for academic configurations [25,26] or industrial-like geometries [27-29], and jet-pylon interaction [24]. Most of these applications remain however restricted to the strong coupling of the jet flow with a close solid body, and integration effects such as flow or noise interaction with the fuselage [30] or tailplane [19] are seldom computed.

The article focuses on a double-stream nozzle installed at the rear part of a business jet, in a T-tail configuration. The objectives of the numerical simulations are twofold. First, it is the evaluation of the noise radiated to the far-field and the impact of the aircraft structure on its azimuthal distribution. Second it is the reproduction of the spatio-temporal characteristics of the sound field on the T-tail, a prerequisite to the simulation of acoustic fatigue. The article is organized as follows: the numerical methodologies for the generation of initially turbulent jet flows and their noise radiation with integral methods are provided in Section 2; Section 3 details the geometry considered, the operating conditions, the numerical settings and the mesh while Section 4 presents the results of the Computational Fluid Dynamic (CFD) simulation; Section 5 is dedicated to far-field noise radiation and Section 6 to the radiation on the T-tail; finally, conclusions are provided in Section 7.

## 2. Computational methodology

The hybrid RANS/LES method used in this work is the Zonal Detached Eddy Simulation (ZDES) [31], developed at ONERA as an improvement to the Delayed Detached-Eddy Simulation (DDES) [32] derived from the original DES approach [33]. This approach has been used with success for different academic and industrial configurations [34,35], including simple jet flows [36,37], dual-stream nozzles [38,39] and installed configurations [40]. One of the advantages of the ZDES is that it covers several types of detached flows, which can be combined together. Modes 1 and 2 of ZDES belong to the so-called *natural Detached Eddy Simulation* approaches in which the attached boundary layers are treated in RANS while free shear flows are resolved in LES. Conversely, mode 3 of ZDES is a Wall Modelled LES (WMLES) approach in which the outer part of attached boundary layers is resolved in LES while the RANS-SA model is used as a wall model. An example of the combined use of the three modes of ZDES within the same computation can be found in [41]. The reader is referred to [31,35,42] for a detailed description of the ZDES equations. The present work combines ZDES mode 3 [43,44] to achieve a WMLES resolution in the fan outer boundary layer and ZDES mode 2 (2020) [45] to achieve a LES resolution in the jet and a RANS modelling everywhere else.

In order to perform WMLES simulations of fully turbulent boundary layers, resolved turbulence must be injected into the incoming flow to initiate the resolved turbulence development. Turbulence transition is triggered at the inlet of the ZDES mode 3 area with tripping dots, included in the computational domain using Immersed Boundary Conditions (IBC). The adopted approach has already shown accurate results in jet-flow aeroacoustic simulations [42] and has been improved via the use of unstructured meshes adapted to the jet flow topology [25,46]. Technical details are provided in Section 3.2.

To limit the computational cost of the simulation, the unsteady flow is resolved only in flow regions containing the noise sources and the propagation towards the T-tail. Time pressure histories on the microphones are reconstructed using the Ffowcs Williams and Hawkings (FWH) [47] porous surface formulation, considering a free-field Green's function. This integral formulation is common in aeroacoustics studies and has been used in many applications with success [48], including double-stream jets [49-51]. The formulation presently used is proposed by Rahier et al. [52] and includes additional flux terms that allow closing the porous surface at both extremities without producing significant spurious noise when it is crossed by turbulence. Such spurious noise is due to the fact that volume sources associated with the turbulence exiting the porous surface are not taken into account in the surface integration. The additional flux terms approximate the missing volume integral and strongly attenuate the spurious radiated pressure. The interested reader may refer to Rahier et al. [52] for a full description and validation of the formulation.
<figure><img src="image_5.png" /><figcaption>Fig. 1. Numerical model of nozzle installed under the T-Tail configuration.</figcaption></figure>

<figure><img src="image_6.png" /><figcaption>Fig. 2. Position of the experimental microphone arrays.</figcaption></figure>

## 3. Test case and simulation setup

### 3.1. *Installed jet configuration*

The test case, represented in Fig. 1, consists in an axi-symmetric nozzle with exhaust diameter *D* = 80 mm installed under the T-tail, hereafter called HTP (Horizontal Tail Plane). The model is starboard side and its coordinate system is set so that the nozzle axis corresponds to the *x* axis. The distance is approximately 1.5*D* between the nozzle and the fuselage and 6*D* between the nozzle and the HTP. The operating conditions correspond to the wind-tunnel off conditions (static jet) tested in the DLR/AWB facility during the DJINN project (funded by the European Union), where both streams have a total pressure of 1.69130 · *P*<sub>amb</sub> and a total temperature equal to the ambient temperature (cold jet). This yields a Mach number at the exit of *M* = 0.9 (velocity of 280 m/s), corresponding to a Reynolds number based on the exhaust diameter of *Re*<sub>D</sub> = 1.5 × 10<sup>6</sup>. All the results presented in the article have been normalized using the nozzle exit velocity *U*<sub>ref</sub> = 280 m/s and the nozzle diameter *D* as references. Where needed, the reference pressure and temperature are used to normalize, with the wind-tunnel values *P*<sub>ref</sub> = 101325.0 Pa and *T*<sub>ref</sub> = 288.15 K.

Steady aerodynamic measurements are only available for the isolated jet configuration, without fuselage and HTP. A rake equipped with 74 pressure probes and 1 temperature probe provides radial profiles of total pressure and static temperature on jet axis for 9 axial positions ranging from *x/D* = 0.25 to *x/D* = 10. The HTP is instrumented with 20 Kulite unsteady pressure transducers on its lower surface, aligned with the jet direction (*y* = 0, from *x/D* = 2.6 to 4.9) and normal to the jet (*x/D* = 4.1, from *y/D* = -2 to +1.6), as shown in Fig. 1.

Acoustics is captured with the 4 microphone arrays illustrated in Fig. 2. The arrays are parallel to the jet and located around 20*D* from its centreline. Their spherical coordinates (R, θ, φ) are set with the origin located at nozzle exit, with θ = 0° in the downstream direction. Arrays BS-CE and BS-SL are located below the aircraft at flyover (φ = 180°) and sideline (φ = 124°) azimuthal positions, respectively, while arrays BE-CE (φ = 0°) and BE-SL (φ = 54°) are positioned above the aircraft. Power spectral densities (PSDs) are provided by DLR. They are corrected from background noise and atmospheric absorption and normalized to a constant propagation distance of 1 meter, assuming a 1/r amplitude decrease with r the distance, and sources located at *x* = 7*D* on the jet axis.
<figure><img src="image_7.png" /><figcaption>**Fig. 3.** Schematic representation of the computational domain, including the storage surfaces and the boundary conditions for the far-field, the jet, and the triggering of the turbulence.</figcaption></figure>

<figure><img src="image_8.png" /><figcaption>**Fig. 4.** Illustration of the IBC trips to trigger turbulent transition inside the nozzle.</figcaption></figure>

## 3.2. Numerical settings

The unsteady flow simulation is performed with the elsA software (ONERA-SAFRAN property) [53]. The choice of the numerical settings is guided by best practices based on previous works and features available for unstructured grids. The spatial discretization is 2nd order accurate and relies on a 1-exact flux reconstruction at cell interfaces (formally 2nd order accurate on regular grids (almost cartesian), with a correction that ensures it remains at least 1st order accurate even on very irregular grids). The fluxes are computed with a 2nd order Roe scheme, while the gradients are computed with a Green-Gauss approach. The time integration is performed with a 2nd order accurate implicit backward differencing scheme with a time step of 1 µs (0.0035 convective time units, hereafter *D/U*) and 5 inner sub-iterations per time step to guarantee a decrease of at least 1 order of magnitude of the residuals during the sub-iteration process. This time step ensures the CFL criterion remains below 1 in the jet, except around the nozzle exit and inside the nozzle where it can rise locally to about 4. Recent improvements in code performance allowed for a significant reduction of the costs of the computation, allowing for a longer simulation of the exploitable time for the statistics and the acoustic analysis. Both the inviscid and viscous fluxes are approximated using the Roe scheme. For the conservative variables, 2nd order scheme without limiter is used with reconstruction at face centre. For the turbulent variables, the *minmod* limiter has to be used for stability reasons.

The computational domain is illustrated in Fig. 3, where the porous surfaces used for far-field noise radiation are represented in yellow. A focus on the nozzle region allows identifying the location of the turbulence-triggering devices needed for the ZDES mode 3, described in the next section. The domain size is composed of 100 nozzle diameters in the streamwise direction, 90 in the lateral and 60 in the vertical direction. Farfield conditions with a Mach number of 0.03 have been imposed both to improve the numerical stability of the simulation and to match experimental free-stream velocity.

The turbulence modelling approach used is the Zonal Detached Eddy Simulation (ZDES) [31]. The fan outer boundary layer is treated with ZDES mode 3 [43,44] to capture its turbulent dynamics with a Wall Modelled LES resolution and turbulence is generated with tripping dots modelled via Immersed Boundary Conditions (IBC), see Fig. 4. It is hypothesized that only the fan outer boundary layer requires resolution of unsteady turbulence to properly predict the jet acoustics, as the operating point considered produces a small wake between core and fan streams (see Fig. 8 later) and noise sources are expected mainly between fan and ambient flows. In addition, the sharp plug end ensures massive flow separation in that region without specific numerical treatment. The grid spacing inside the nozzle and the characteristics of the tripping dots (number, height and diameter) have been defined following the best practices from the literature [42,44]. They have been tuned via a preliminary study to ensure the 3D development of the
<figure><img src="image_9.png" /><figcaption>**Fig. 5.** Illustrations of the storage surfaces. For Figs. (c)–(d): — surfaces including the solid surfaces; – – surfaces excluding the solid surfaces; · endcap at $x/D = 24$.</figcaption></figure>

turbulence and no visible azimuthal impact on the mean flow at nozzle exit. This is discussed further in Section 4.2. The efficiency of this method to quickly develop three-dimensional turbulence without generating spurious noise (a common limitation of synthetic turbulence generators which can be used as an alternative to the present method) is demonstrated in [42,44]. In the present case, 45 tripping dots are placed on the outer secondary wall, whose height is equal to 0.6 times the local boundary layer thickness as suggested in the above-mentioned references. This is the only location where turbulence is tripped since the flow in this region will feed the mixing layer of the jet.

In the rest of the computational domain, the ZDES mode 2 (2020) [45] is adopted to achieve a LES resolution in the jet while the attached boundary layers on the remaining surfaces (where no significant noise sources are present) are automatically treated in RANS with the Spalart–Allmaras model.

In practice, a RANS simulation is conducted to initialize the flow field before the ZDES is first run for 220 $D/U$ to flush out the initial transient. Finally, the simulation is run for a total time of 480 $D/U$, where flow statistics are computed and on-the-fly data are extracted for the far-field noise post-processing with a time sampling of 8 µs (0.028 $D/U$). This translates to pressure time signals of ~ 450 $D/U$ on the sensors after the radiation step. The correct statistical convergence of the noise data is assessed using the isolated jet configuration (see Section 5.2). For this axisymmetric configuration, the comparison between the noise radiated on 12 microphone antennas equally distributed in azimuth and the azimuthally-averaged levels (not reproduced here) prove the duration of 450 $D/U$ is sufficient in the present case to reach uncertainty around ±1 dB and ±2 dB in the low- and high-frequency parts of the spectra respectively, and below 0.5 dB for the integrated levels.

Noise radiation is performed with the code KIM from ONERA [52,54]. The 3 porous storage surfaces used for the radiation are visible in Fig. 5. They are based on the results obtained for a single stream isolated jet [25]. The conical surfaces surrounding the jet are identical between both studies for $x/D > 10$ while the shape of the surfaces is adapted upstream to enclose a portion of the fuselage and HTP – Fig. 5(a) and solid lines in Figs. (c) and (d)–. That way, acoustic reflections occurring on these solid surfaces are accounted for in the CFD. The porous surfaces are closed in the downstream end with an endcap at $x/D = 27$. An additional endcap is placed at $x/D = 24$ (dash-dot lines). The presence of 3 conical surfaces and two endcaps ensures the noise radiated is not sensitive to the position of the surface considered (radiation from the different surfaces provide identical pressure signals, except for the maximum resolved, cut-off frequency which decreases as the surface is located farther away from the jet due to numerical dissipation) and only the results from the closest surface is shown in the article. It is worth recalling the use of additional flux terms in the FWH radiation process allows closing the porous surface with a downstream endcap without generation of spurious noise, even with the jet turbulence crossing the endcap [25,52]. Upstream, the endcap D1 is located at $x/D = -0.4$. Reflections occurring on the solid surfaces upstream of this position are therefore not accounted for in noise radiation. Such reflections are not the focus of the current study and are assumed to be weak. They could be captured by including the whole fuselage inside the storage surfaces (along with a refinement of the CFD grid) or by modelling the reflections on the fuselage during the acoustic radiation, at the price of an increased computational cost [25,55].

To investigate the impact of the fuselage on the generation and propagation of noise, additional surfaces, in dashed lines in Fig. 5, are defined in the upstream jet region – Fig. 5(b) and dashed lines in Figs. (c) and (d)– to enclose the jet flow only, with the exclusion of the solid surfaces.
<figure><img src="image_10.png" /><figcaption>Fig. 6. Grid spacing in various XY, XZ and YZ planes cutting the domain.</figcaption></figure>

<figure><img src="image_11.png" /><figcaption>Fig. 7. Instantaneous flow field, showing the superposition of an iso-surface of Q criterion (turbulent structures) and the density gradient (acoustic waves).</figcaption></figure>

### 3.3. Mesh

The mesh is generated with Pointwise and follows the methodology previously used for a single stream jet [25]. It is mainly composed of quadrilateral surface elements, extruded in the wall normal direction to account for boundary layers with hexahedra and prisms. The first wall cell height is located at $y^+ = 1$ according to usual RANS guidelines. Tetrahedra are used in the volume and a layer of pyramids allows for switching between one element and the other. Target cell sizes are prescribed following the guidelines given in [25] in the regions where noise generation (shear layer and jet plume) and propagation (near-field and towards the HTP) need to be accurately captured. Fig. 6 depicts the grid spacing at various locations, where the grid refinement for accurate flow and noise resolution is clearly visible in the jet region and between the nozzle and the HTP. In this figure, $\Delta$ corresponds to the diameter of the sphere inscribed in a regular tetrahedron and is related to the edge length of the tetrahedron $a$ with the relation $\Delta = a\sqrt{6}/6$. The limits of the noise propagation region are materialized by the boundaries of the storage surfaces in Fig. 5. They follow the topology given in [25] (Fig. 6) with the grid size of the mesh Uns-2, for which numerical dissipation was found to be negligible up to the cut-off Strouhal number $St_c = f_c D/U$ around 8 (with $f_c$ the grid cut-off frequency), corresponding to a resolution of about 8 elements per acoustic wavelength at least ($\lambda \ge 8\Delta$). A similar cut-off Strouhal number is expected in the present simulation. In total, the grid is composed of 300M cells, 100M points, and is split in 1152 blocks for parallel computation on the same number of cores.
<figure><img src="image_12.png" /><figcaption>Fig. 8. Velocity profiles of the boundary layer downstream of the turbulence-tripping devices inside the nozzle.</figcaption></figure>

# 4. Flow simulation

## 4.1. Flow visualizations

Fig. 7 left presents an instantaneous field of the iso-surface of Q criterion ($Q^* = QD^2/U_{ref}^2 = 1$), allowing for the visualization of the turbulent structures. The different flow behaviours in the boundary layers inside the nozzle, associated with the various modellings used for turbulence, are clearly visible. Internal walls, modelled with a RANS approach, have no resolved turbulence whereas the outer fan duct surface, treated with a WMLES approach, has a rich turbulent content generated by the tripping devices, enhanced in the mixing-layer region and convected downstream in the jet plume. The right side of the figure also shows the density gradient on a vertical plane in the jet axis and evidences the generation of the sound waves in the jet and their propagation towards the HTP.

## 4.2. Turbulence triggering and nozzle exit boundary layer

Time-averaged results are extracted inside the nozzle at various locations and averaged azimuthally to discuss the flow field on profiles normal to the wall. A specific azimuthal averaging procedure is first performed to analyse the impact of the turbulence-tripping devices, as presented in Fig. 8: 45 planes are extracted either on each tripping device, or in between them. The results, presented with $d/H_{trip}$ on the vertical axis, where d is the distance from the wall and $H_{trip}$ is the height of the tripping device, are plotted at various locations downstream after averaging over the 45 planes.

The first streamwise location, corresponding to $x/D = -1.5$ is just downstream the tripping device. A large separated zone is visible when considering the green dashed curve, extracted on the device, where negative velocity values are visible up to $H_{trip}$, corresponding to the height of the device. On the contrary, the red solid line – extracted in between two tripping devices – shows a typical boundary layer profile, indicating that the flow is not detached in this region. When moving downstream, the separation is growing: the green dashed line indicates that when considering a plane on the tripping device, negative velocity values can be seen even for $d > H_{trip}$, while the red solid line indicates that the velocity field between two plots is impacted. Moving further downstream, the flow is no longer separated already in $x/D = -1.375$, although the velocity profiles are still different when considering a plane on a tripping device or between two of them, indicating that the flow field is highly three-dimensional. Starting from $x/D = -1.25$ the 3D effects are less visible, with all the velocity profiles showing identical topologies. At $x/D = -1.00$, not only are the profiles identical, but their shape is similar to a typical boundary layer distribution. The right plot in Fig. 8 reproduces the velocity distribution in $x/D = -0.5$, which presents a typical boundary layer profile. This means that the boundary layer has recovered from the induced tripping before nozzle exit.

A boundary layer profile at the nozzle exit (corresponding to $x/D = 0$, highlighted by a red line in Fig. 8) is extracted and presented in Fig. 9, with the boundary layer thickness $\delta = 2.5$ mm. The left side reproduces the averaged velocity, compared with the RANS values. Although no experimental data are available, the results reproduce a velocity distribution typical of a boundary layer, indicating as discussed before that the recovery from the turbulence-tripping devices occurs before the nozzle exit. Similar conclusions can be drawn from the averaged pressure distribution. The ratio between the turbulent and molecular viscosities proves the ZDES mode 3 turbulence modelling is effective in this region, with only the inner part of the boundary layer being computed in RANS and the eddy viscosity collapsing rapidly in the outer part, solved in LES. The turbulence resolved in this region, already observed in Fig. 7, is associated with significant pressure and velocity fluctuations visible on the last 2 profiles of Fig. 9. In particular, velocity fluctuations rise to 4% of the reference velocity. This value is lower than the one observed for an initially turbulent jet issued from a straight nozzle [25,56] ($U_{rms}/U_{ref} \sim 10%$) but matches that of a convergent nozzle [57]. This difference in levels may come from the nozzle shape, as a convergent shape tends to relamínarize the flow. The fluctuations are however sufficient to reproduce a turbulent jet development, as will be observed in the next sections.
<figure><img src="image_13.png" /><figcaption>Fig. 9. Profiles normal to the wall at the nozzle exit (trailing edge of the nacelle). – RANS; —/— ZDES.</figcaption></figure>

<figure><img src="image_14.png" /><figcaption>Fig. 10. Velocity (left), total pressure (centre) and static temperature (right) profiles along the nozzle axis. – RANS (installed); — ZDES (installed); ■ experiment (isolated).</figcaption></figure>

<figure><img src="image_15.png" /><figcaption>Fig. 11. Radial velocity profiles at different streamwise locations. – RANS (installed); — ZDES (installed); ■ experiment (isolated).</figcaption></figure>

### 4.3. Time-averaged results

Fig. 10 reproduces the axial profiles of axial velocity, stagnation pressure and static temperature for the time-averaged ZDES flow, compared with the numerical data of the RANS simulation and the experimental data for the isolated jet. Simulated velocity is in good agreement with the experimental data, with a small underestimation in $x/D = 10$. The ZDES result (red solid line) presents a better agreement when compared with the RANS result (blue dashed line). This illustrates the limitations of RANS models to predict the jet flow development, while the LES resolution of the jet provided by the ZDES approach is well suited to reproduce the jet potential core length and mixing rate. This behaviour is also observed in the pressure distribution presented in the middle figure. On the right side, a small discrepancy on the jet temperature on both numerical results suggests there might be an issue when setting the total state in the boundary condition of the primary stream.

The radial velocity profiles along the Y direction ($Z=0$) are visible in Fig. 11. Here again, the ZDES results are in a better agreement with the experimental data than the RANS. Looking first outside of the jet plume ($y/D > 0.5$), a small discrepancy concerning the flow velocity can be noticed. Even if the jet is in static conditions, the external air is entrained by the jet, creating a flow that can reach up to 5% of the reference velocity in the experiments. This flow entrainment is slightly over predicted by the ZDES close to the nozzle exit (up to $x/D = 2$) but the comparison becomes favourable in the other locations. This small discrepancy may be attributed to the arbitrary value of the very slow coflow imposed outside the nozzle for numerical stability reasons, as usually done for static jet conditions [56,58,59], which has no impact on the jet flow development.

When focusing on the jet plume ($y/D < 0.5$), an overall good agreement can be observed between the ZDES result and the experimental data. In particular, the mixing layer between the primary and secondary streams, which has very low gradients since these two streams have the same characteristics, is well reproduced by the ZDES, despite the fact that in this region the turbulence has not been triggered as in the secondary stream. This is attributed to the correct behaviour of ZDES mode 2 which provides a
<figure><img src="image_16.png" /><figcaption>Fig. 12. Mean axial velocity on slices normal to the jet.</figcaption></figure>

<figure><img src="image_17.png" /><figcaption>Fig. 13. Pressure PSDs for the array BS-CE (installed configuration). — experiments, -- simulations.</figcaption></figure>

rapid switch to LES mode in the shear layer. Considering the first streamwise location available ($x/D = 0.25$), a small discrepancy is observed in the mixing layer between the secondary stream and the outer flow. In particular, a thicker boundary layer is observed on the nacelle in the experiments, even if the external velocity, as mentioned before, is lower than in the ZDES. Overall, the agreement on the velocity profiles remains satisfying, confirming that the ZDES is correctly reproducing the experimental results.

The very good agreement between the installed simulation and isolated experiment suggests the fuselage is far enough for the jet not to impact its development. The mean velocity maps normal to the jet illustrated in Fig. 12 for different axial positions prove the jet indeed develops in an axisymmetric way, which corroborates that observation.

# 5. Far-field noise

## 5.1. Assessment of the installed configuration

Following a noise radiation sensitivity study (not reproduced here for the sake of brevity), the surface closest to the jet with downstream endcap located at $x/D = 27$ is used to reconstruct the pressure signal at microphones location for all the results presented hereafter.

Figs. 13 and 14 reproduce the experimental and simulated PSDs for different observer positions of the arrays BS-CE and BS-SL, below the aircraft. For $\theta \ge 60^{\circ}$, simulated spectra match well with the experimental data up to the grid cut-off frequency which lies around $St_c \sim 8$. This value is close to the one observed in [25] using similar numerical parameters and computational methodology.
<figure><img src="image_18.png" /><figcaption>Fig. 14. Pressure PSDs for the array BS-SL (installed configuration). — experiments, - - simulations.</figcaption></figure>

<figure><img src="image_19.png" /><figcaption>Fig. 15. Pressure PSDs for the array BE-CE (installed configuration). — experiments, - - simulations.</figcaption></figure>

One may however notice a slight underestimation of the medium- and high-frequency noise levels at 40° (St = fD/U ≥ 1), as well as a hump around 90° for St ~ 4. For the first point, the large medium- and high-frequency noise underestimation at 40° visible for the array BS-SL might be explained by a bias in the measurements: at this observation angle, noise levels on the array BS-SL are found to be 1 dB higher compared to the array BS-CE even for the isolated configuration, where noise levels are not expected to depend on the azimuth of observation (a matter correctly recovered numerically). The variability of the experimental data is therefore assumed to be 1 dB. The second point is attributed to some reminiscent laminar/turbulent transition of the shear layer, despite the turbulence generation implemented for the outer fan duct boundary layer discussed in Section 4.2. Vortex pairings are indeed known to be efficient noise generators and were proved to radiate medium-frequency noise near the direction normal to the jet both in experiments [60–64] and simulations [65,66].
<figure><img src="image_20.png" /><figcaption>Fig. 16. Pressure PSDs for the array BE-SL (installed configuration). — experiments, - - simulations.</figcaption></figure>

<figure><img src="image_21.png" /><figcaption>Fig. 17. Experimental (symbols) and simulated (solid lines) integrated pressure levels for $St \in [0.05; 1.0]$ (installed configuration).</figcaption></figure>

Next, the PSDs for arrays BE-CE and BE-SL located above the aircraft are reproduced in Figs. 15 and 16. As in the arrays below the aircraft, a good reproduction of the experiments is observed numerically. The grid cut-off frequency is however lower; it lies below 1 for low observation angles and rises above 2 as the observation angle goes over 90°. This lower cut-off frequency is a consequence of the longer propagation of the acoustic waves in the CFD domain before they reach the porous surface, as visible in Fig. 5, which leads to higher numerical dissipation compared to radiation below the aircraft.

In addition to the PSDs, the integrated pressure levels are reproduced in Fig. 17 for the 4 arrays. For the sake of comparison between the different arrays, the levels are integrated on the range $St \in [0.05; 1.0]$ even if the cut-off frequency is larger for arrays BS-CE and BS-SL. Following the very good agreement observed for the PSDs, numerical integrated levels match with the experimental one with discrepancies below 1 dB. It outlines the simulation accurately captures the most energetic noise sources.
<figure><img src="image_22.png" /><figcaption>**Fig. 18.** Experimental PSDs for the isolated and installed configurations. Isolated configuration: — BS-SL. Installed configuration: - BS-CE; - BS-SL; - BE-CE; - BE-SL.</figcaption></figure>

## 5.2. Impact of the fuselage on noise

Fig. 18 compares the experimental PSDs of the installed configuration with those of the isolated case. The presence of the solid surfaces leads to a decrease of the medium- and high-frequency levels directly over the HTP with no significant change for the other azimuthal positions compared to the isolated jet. There are two possible causes for this change in levels: a modification of the noise sources by the presence of the surfaces, or acoustic shielding during the propagation of the sound waves. The contribution of these two causes is investigated in this section. To that end, acoustic pressure is radiated from the porous surface illustrated in Fig. 5(b), which only encloses the jet plume and excludes the fuselage and HTP surfaces. As the FWH method used assumes a free-field Green's function, the acoustic propagation is that of an isolated jet and comparison between simulated pressure levels and isolated jet experimental data directly evidences changes in noise sources caused by the presence of the solid walls. Therefore, this acoustic propagation simulation, although based on the same installed CFD data, is referred to as *isolated configuration* hereafter.

Simulated and experimental PSDs are reproduced in Fig. 19 for the array BE-CE. Observations are similar to those done previously for arrays BS-CE and BS-SL of installed configuration, with a medium frequency hump around 90° for $St \sim 4$ in the simulation. Except from that and low-frequency oscillations mostly caused by spurious reflections in the measurements, simulated pressure data match very well with the isolated experiment. It is worth mentioning the cut-off frequency, below which the numerical dissipation of the acoustic waves can be neglected, now lies around $St_c \sim 8$ for the 4 microphone arrays. This value is similar to the one observed for arrays BS-CE and BS-SL of the installed case, and much larger than the one observed for arrays BE-CE and BE-SL ($St_c \sim 1$) as numerical dissipation is now very limited due to the tight position of the porous surface for all azimuthal directions.

Numerical levels are also found to be independent of the azimuthal position and a similar agreement is observed for the other 3 arrays, as illustrated with the evolution of the integrated pressure levels in Fig. 20. This proves the solid surfaces are far enough from the jet not to impact the simulated noise sources, which are identical to those of the isolated jet. The changes in noise between isolated and installed configuration are therefore caused by the scattering of the acoustic waves on the fuselage and HTP solely.

# 6. Noise radiation on the HTP

A major objective of the present numerical simulations is the prediction of acoustic fatigue, caused by the intense noise radiation from the jet on the solid surfaces. On the one hand, without conjecturing the physics involved in the case under study, the most direct solution to evaluating simulated pressure fluctuations on the HTP is to include the acoustic propagation in the CFD. This is the first approach considered here, with the time pressure histories on the Kulite sensors shown in Fig. 1 directly obtained from the ZDES simulation. On the other hand, the results from the previous section proved the presence of the aircraft surfaces does not change the noise sources in the jet (they only have a scattering effect). Therefore, with appropriate modelling of sound scattering on solid surfaces such as the Boundary Element Method (BEM) [67,68], it is possible to correctly estimate the noise radiated on the HTP from the simulation of the isolated jet. This is the second approach considered, building on the *isolated jet* simulation (porous surface excluding the solid walls) and a simplified acoustic modelling detailed below.
<figure><img src="image_23.png" /><figcaption>Fig. 19. Pressure PSDs for the array BE-CE. — experiments, isolated configuration, - - simulations, isolated configuration, - - simulations, installed configuration.</figcaption></figure>

<figure><img src="image_24.png" /><figcaption>Fig. 20. Integrated pressure levels for $St \in [0.05; 10.0]$ (isolated configuration). ▲ BS-CE; ▶ BS-SL; ▼ BE-CE; ◁ BE-SL.</figcaption></figure>

As a first approximation, let us consider the noise obtained on the HTP is that directly radiated by the jet, without reflections from other solid surfaces (fuselage or Vertical Tail Plane – VTP), and the HTP is assimilated to a fully reflective infinite flat plate. The amplitude of the pressure wave reflected on the HTP is then identical to that of the incident wave, and the pressure radiated on the HTP can be approximated as twice the pressure radiated in the free field by the isolated jet at the position of the HTP, i.e.

$$p'_{HTP}(\vec{x}_0) = 2 \times p'_{ff}(\vec{x}_0) \qquad (1)$$

with $p'_{HTP}(\vec{x}_0)$ the pressure fluctuation at position $\vec{x}_0$ on the bottom surface of the HTP and $p'_{ff}(\vec{x}_0)$ the pressure radiated in the free field by the isolated jet at the same position $\vec{x}_0$.

## 6.1. Spectra

The pressure PSDs from the experiments, directly simulated from CFD (labelled simulation, installed jet) and modelled from the radiation of the isolated jet with Eq. (1) (labelled simulation, isolated jet + model) are reproduced in Fig. 21 for the 4 Kulite sensors evidenced in Fig. 1. These results are representative of those observed on the other sensors. Pressure signals directly computed from CFD are very close to the experiments up to $St \sim 0.7$. This frequency is lower than the cut-off frequency observed for far-field noise radiation on arrays BE-SL and BE-CE, outlining the very large numerical dissipation that occurs during propagation towards the HTP. The PSDs modelled from the isolated jet match those of the installed simulation from $St = 0.1$ to the cut-off frequency. In addition, these PSDs collapse with the experiments for larger frequencies, up to $St \sim 5$, thanks to the higher cut-off frequency for the isolated simulation. The discrepancies visible in the low-frequency range may be caused by the hypotheses of the modelling, not
<figure><img src="image_25.png" /><figcaption>Fig. 21. Pressure PSDs on the Kulite sensors. — experiments; - simulation, installed jet; - simulation, isolated jet + model.</figcaption></figure>

verified in these conditions: for such low frequencies, the acoustic wavelength is comparable to the size of the HTP which cannot be considered as an infinite surface, and the presence of the VTP might not be negligible anymore.

## 6.2. Coherence

Although noise levels on the HTP are correctly predicted by the numerical simulations, this is nevertheless not sufficient to predict acoustic fatigue because the excitation of the HTP also depends on the coherence of the pressure on the surface. The coherence $\gamma$ between 2 time signals $a(t)$ and $b(t)$ corresponds to the normalized cross spectral density of these 2 signals and writes

$$ \gamma = \sqrt{\frac{|P_{ab}|^2}{P_{aa}P_{bb}}} \qquad (2) $$

with $P_{ab}$ the cross spectral density. This coherence is plotted in Fig. 22 for different values of the Strouhal number along the Kulite sensors aligned with the jet. The direct simulation of the pressure signals from the CFD provides results close to the experiments at low frequencies. As the frequency increases, the agreement gets poorer and the simulation overpredicts the coherence. Similar conclusions are drawn for the signals modelled from the isolated jet, which provide coherence levels close to the ones directly obtained from CFD. It is worth noting the measurements of some Kulites are polluted by the power supply, which contaminates the low-frequency data. This is the case for the sensor at position $(x - x_{ref})/D = 0.7$ whose coherence for $St = 0.1$ and 0.2 should be disregarded.

The good agreement between the experiments and the simulations is observed also for the coherence in the direction orthogonal to the jet, reproduced in Fig. 23. Here most of the sensors, except for $(y - y_{ref})/D = 0$ and 2, are contaminated by the power supply with inaccurate coherence for $St = 0.1$ and 0.2 and should not be considered. Levels modelled from the isolated jet are comparable to those directly simulated from CFD, even if differences are observed for some frequencies: increase of coherence for $St = 0.5$ and decrease for $St = 5.0$, leading to a better match with the experiments for the latter.

## 7. Conclusion

The article presents a numerical investigation of the aerodynamic field and acoustic signature of a double-stream jet installed on a T-tail configuration, representative of business jets. The two streams are cold with a Mach number of 0.9 and the Reynolds number is $Re_D = 1.5 \times 10^6$. The turbulent boundary layer on the fan outer stream is successfully reproduced with the use of Zonal Detached Eddy Simulation (ZDES) mode 3, together with the inclusion of roughness elements in the computational domain to generate turbulence. The other boundary layers are treated in RANS and the turbulence model automatically switches to LES in free shear flows (ZDES mode 2). This high-fidelity hybrid RANS-LES simulation proves to be a reliable approach able to accurately capture the aerodynamic field over the considered configuration, with a good reproduction of the available experimental data.

Noise radiation to the microphones is achieved with the Fowcs Williams and Hawkings surface integral method. The storage surfaces enclose all the solid walls behind the engine to account for noise scattering directly in the flow simulation. The agreement
<figure><img src="image_26.png" /><figcaption>Fig. 22. Coherence values at different Strouhal numbers for the Kulites parallel to the jet axis (reference sensor is X1Y4). ▲— experiments; ■— simulation, installed jet; •— simulation, isolated jet + model.</figcaption></figure>

<figure><img src="image_27.png" /><figcaption>Fig. 23. Coherence values at different Strouhal numbers for the Kulites orthogonal to the jet axis (reference sensor is X11Y8). ▲— experiments; ■— simulation, installed jet; •— simulation, isolated jet + model.</figcaption></figure>

between the experimental and simulated data observed for the aerodynamics is recovered for the acoustics, which confirms the noise sources are globally well captured numerically despite a slight overestimation of the medium-frequency noise around 90°, associated with some reminiscent laminar-turbulent transition of the shear layer. The important numerical dissipation that occurs during the propagation of the sound waves in the CFD domain towards the HTP however restricts the prediction to low- and medium-frequencies in this direction.

An additional noise radiation performed from a porous surface surrounding only the jet and excluding the solid walls proves the aircraft fuselage is sufficiently far from the flow not to impact its development. The jet hence develops as an isolated jet. In practice, it means that one can reduce the numerical cost of the installation effect estimation by computing the isolated jet and using appropriate acoustic propagation and modelling tools to simulate installation effects. It also improves the reproduction of high-frequency noise levels as the propagation in the CFD domain is reduced.

A first application is illustrated for the evaluation of the sound pressure on the HTP. Noise directly predicted from the flow simulation matches the experimental levels and spatial coherence but numerical dissipation restricts the accuracy to the low part of the spectrum. A simplified model approaching the HTP with a flat plate is sufficient to recover the installed numerical results with an isolated jet simulation. In addition, it improves the maximum resolved frequency by a factor of 7. This approach provides a rapid and cost-effective solution to the parametric study of engine integration for the evaluation of acoustic fatigue on the tailplane.
CRediT authorship contribution statement

**M. Huet:** Writing – review & editing, Writing – original draft, Visualization, Validation, Software, Methodology, Investigation, Data curation, Conceptualization. **F. Sartor:** Writing – review & editing, Writing – original draft, Visualization, Validation, Software, Methodology, Investigation, Data curation, Conceptualization. **T. Renaud:** Writing – review & editing, Writing – original draft, Visualization, Validation, Software, Methodology, Investigation, Data curation, Conceptualization. **F. Gand:** Writing – review & editing, Writing – original draft, Visualization, Validation, Software, Methodology, Investigation, Funding acquisition, Data curation, Conceptualization.

Declaration of competing interest

The authors declare the following financial interests/personal relationships which may be considered as potential competing interests: Maxime Huet reports financial support was provided by European Commission. If there are other authors, they declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Acknowledgements

<figure><img src="image_28.png" /></figure>

This work benefited from fundings from the European Union's DJINN project and internal funding from ONERA. The EU DJINN (Decrease Jet Installation Noise) project received funding from the European Union's Horizon 2020 research and innovation programme under grant agreement No 861438. DJINN is a collaborative effort between CFD-Berlin (coordinator), Airbus SAS, Dassault Aviation, Safran Aircraft Engines, Rolls-Royce Deutschland, ONERA, DLR, University of Southampton, CERFACS, Imperial College London, von Karman Institute, CNRS, and Queen Mary University of London.

The authors are grateful to Dassault-Aviation and Rolls-Royce for providing the rear aircraft jet model and to Dr. Christian Jente from DLR for providing the experimental data.

Data availability

The authors do not have permission to share data.

References

[1] L. Leylekian, M. Lebrun, P. Lempereur, An overview of aircraft noise reduction technologies, AerospaceLab 7 (2014) 1–15.

[2] T. Castelain, M. Sunyach, D. Juvé, J.-C. Béra, Jet-noise reduction by impinging microjets: an acoustic investigation testing microjet parameters, AIAA J. 46 (2008) 1081–1087.

[3] M.J. Lighthill, On sound generated aerodynamically. I. General theory, Proc. R. Soc. Lond. Ser. A. Math. Phys. Sci. 211 (1952) 564–587.

[4] H.K. Tanna, P.D. Dean, M.J. Fisher, The influence of temperature on shock-free supersonic jet noise, J. Sound Vib. 39 (1975) 429–460.

[5] H.K. Tanna, An experimental study of jet noise. Part I: turbulent mixing noise, J. Sound Vib. 50 (1977) 405–428.

[6] C. Dahan, G. Elias, J. Maulard, M. Perulli, Coherent structures in the mixing zone of a subsonic hot free jet, J. Sound Vib. 59 (1978) 313–333.

[7] C.K.W. Tam, K. Viswanathan, K.K. Ahuja, J. Panda, The sources of jet noise: experimental evidence, J. Fluid Mech. 615 (2008) 253–292.

[8] O.M. Phillips, On the generation of sound by supersonic turbulent shear layers, J. Fluid Mech. 9 (1960) 1–28.

[9] A.P. Dowling, J.E. Ffowcs Williams, M.E. Goldstein, Sound production in a moving stream, Philos. Trans. R. Soc. Lond. Ser. A Math. Phys. Sci. 288 (1978) 321–349.

[10] C.K.W. Tam, L. Auriault, Jet mixing noise from fine-scale turbulence, AIAA J. 37 (1999) 145–153.

[11] C. Bogey, C. Bailly, Influence of nozzle-exit boundary-layer conditions on the flow and acoustic fields of initially laminar jets, J. Fluid Mech. 663 (2010) 507–538.

[12] C. Dreier, X. Vog, W. Schröder, M. Vorländer, Acoustic source characterization of simulated subsonic jet noise using spherical harmonics, J. Acoust. Soc. Am. 154 (2023) 167–178.

[13] J.S. Mixson, L.A. Roussos, Acoustic Fatigue: overview of Activities at NASA Langley, Tech. Rep. TM 89143, NASA, 1987.

[14] W. Schütz, Fatigue life prediction of aircraft structures – past, present and future, Eng. Fract. Mech. 6 (1974) 745–773.

[15] L.C. Chow, R.J. Cummins, Sonic fatigue study of an aircraft flap like structure, in: Proceedings of the 5th International Congress on Sound and Vibration, 1997.

[16] B.L. Clarkson, Review of Sonic Fatigue Technology, Tech. Rep. CR-4587, NASA, 1994.

[17] I. Holehouse, Sonic fatigue of aircraft structures due to jet engine fan noise, J. Sound Vib. 17 (1971) 287–298.

[18] T.H. Beier, P. Heaton, High Speed Research Program Sonic Fatigue - Summary Report, Tech. Rep. CR-2005-213742, NASA, 2005.

[19] F. Chalot, Z. Johan, M. Mallet, F. Billard, L. Martin, S. Barré, Extension of methods based on the stabilized finite element formulation for the solution of the Navier-Stokes equations and application to aerodynamic design, Comput. Methods Appl. Mech. Engrg. 417 (2023).

[20] J.J. Hollkamp, R.W. Gordon, S.M. Spottswood, Nonlinear modal models for sonic fatigue response prediction: a comparison of methods, J. Sound Vib. 284 (2005) 1145–1163.

[21] D. Drikakis, M. Spottswood, P. Tiso, Acoustic fatigue in aero structures [special issue], J. Sound Vib. 448 (2019).

[22] C. Bogey, O. Marsden, C. Bailly, Influence of initial turbulence level on the flow and sound fields of a subsonic jet at a diameter-based Reynolds number of $10^5$, J. Fluid Mech. 701 (2012) 352–385.
[23] J. Tyacke, M. Mahak, P. Tucker, LES of jet flow and noise with internal and external geometry features, in: Proceedings of the 53rd AIAA Aerospace Sciences Meeting, Paper 2015-0503, 2015.

[24] H. Xia, P.G. Tucker, S. Eastwood, M. Mahak, The influence of geometry on jet plume development, Prog. Aerosp. Sci. 52 (2012) 56-66.

[25] M. Huet, F. Gand, G. Rahier, Simulation of isolated and installed jet noise at mach=0.9: influence of numerical mesh and physical insights, Flow Turbul. Combust. 113 (2024) 623-665.

[26] Z.-N. Wang, A. Proença, J. Lawrence, P.G. Tucker, R. Self, Large-eddy-simulation prediction of an installed jet flow and noise with experimental validation, AIAA J. 58 (2020) 2494-2503.

[27] J.C. Tyacke, Z.-N. Wang, P.G. Tucker, LES-RANS of installed ultra-high-bypass-ratio coaxial jet aeroacoustics with flight stream, AIAA J. 57 (2019) 1215-1236.

[28] Z.-N. Wang, J.C. Tyacke, P.G. Tucker, LES-RANS study of serrated nozzle jet aeroacoustics for an installed ultra-high-bypass-ratio aeroengine, AIAA J. (2021).

[29] G. Pont, J. Huber, J.-P. Roméo, P. Brenner, Installed jet noise simulation in industrial framework, in: Proceedings of the 55th 3AF International Conference on Applied Aerodynamics, Paper FP46-AERO2020-PONT, 2020.

[30] A.P. Markesteijn, S.A. Karabasov, Large eddy simulation and acoustic modelling of an installed jet configuration of industrial complexity on graphics processing units, Appl. Acoust. 224 (2024).

[31] S. Deck, Recent improvements in the zonal detached eddy simulation (ZDES) formulation, Theor. Comput. Fluid Dyn. 26 (2012) 523-550.

[32] P.R. Spalart, S. Deck, M.L. Shur, K.D. Squires, M.K. Strelets, A. Travin, A new version of detached-eddy simulation, resistant to ambiguous grid densities, Theor. Comput. Fluid Dyn. 20 (2006) 181-195.

[33] P.R. Spalart, W.H. Jou, M. Strelets, S.R. Allmaras, Comments on the feasibility of LES for wings, and on a hybrid RANS/LES approach, in: Advances in DNS/LES: Direct Numerical Simulation and Large Eddy Simulation, 1997, pp. 137-148.

[34] F. Gand, Zonal detached eddy simulation of a civil aircraft with a deflected spoiler, AIAA J. 51 (2013) 697-706.

[35] S. Deck, F. Gand, V. Brunet, S.B. Khelil, High-fidelity simulations of unsteady civil aircraft aerodynamics: stakes and perspectives. Application of zonal detached eddy simulation, Philos. Trans. R. Soc. Lond. Ser. A Math. Phys. Sci. 372 (2014).

[36] N. Chauvet, S. Deck, L. Jacquin, Numerical study of mixing enhancement in a supersonic round jet, AIAA J. 45 (2007) 1675-1687.

[37] F. Gand, V. Brunet, G. Mancel, Zonal detached eddy simulation (ZDES) using turbulent inflow and high order schemes: application to jet flows, in: S. Girimaji, W. Haase, S.-H. Peng, D. Schwamborn (Eds.), Progress in Hybrid RANS-LES Modelling, Springer International Publishing, 2015, pp. 141-152.

[38] V. Brunet, S. Deck, Zonal-detached eddy simulation of a civil aircraft engine jet configuration, in: S.-H. Peng, P. Doerffer, W. Haase (Eds.), Progress in Hybrid RANS-LES Modelling, Springer Berlin Heidelberg, 2010, pp. 147-156.

[39] J. Verrière, F. Gand, S. Deck, Zonal detached-eddy simulations of a dual-stream jet, AIAA J. 54 (2016) 3176-3190.

[40] V. Brunet, Random turbulent flow generation coupled with ZDES for civil aircraft jet configurations, in: Proceedings of the 30th AIAA Applied Aerodynamics Conference, Paper 2012-2896, 2012.

[41] S. Deck, Numerical investigation of the flow dynamics past a three-element aerofoil, J. Fluid Mech. 732 (2013) 401-444.

[42] F. Gand, M. Huet, On the generation of turbulent inflow for hybrid RANS/LES jet flow simulations, Comput. Fluids 216 (2021).

[43] S. Deck, N. Renard, R. Laraufie, P. Sagaut, Zonal detached eddy simulation (ZDES) of a spatially developing flat plate turbulent boundary layer over the Reynolds number range 3 150 ≤ $Re_θ$ ≤ 14 000, Phys. Fluids 26 (2014).

[44] P.W. S. Deck, N. Renard, A rapid and low noise switch from RANS to WMLES on curvilinear grids with compressible flow solvers, J. Comput. Phys. 363 (2018) 231-255.

[45] S. Deck, N. Renard, Towards an enhanced protection of attached boundary layers in hybrid RANS/LES methods, J. Comput. Phys. 400 (2020).

[46] F. Gand, M. Huet, T. Renaud, F. Sartor, ZDES of jets aeroacoustics: recent progress with unstructured grids and challenges, in: Proceedings of the AIAA AVIATION 2023 Forum, Paper 2023-4484, 2023.

[47] J.E. Frowcs Williams, D.L. Hawkings, Sound generation by turbulence and surfaces in arbitrary motion, Philos. Trans. R. Soc. Lond. Ser. A Math. Phys. Sci. 264 (1969) 321-342.

[48] G. Rahier, J. Prieur, F. Vuillot, N. Lupoglazoff, A. Biancherin, Investigation of integral surface formulations for acoustic post-processing of unsteady aerodynamic jet simulations, Aerosp. Sci. Technol. 8 (2004) 453-467.

[49] B. Fayard, G. Rahier, F. Vuillot, F. Kerhervé, Flow field analysis for double stream nozzle: application to jet noise, in: Proceedings of the 14th AIAA/CEAS Aeroacoustics Conference, Paper 2008-2983, 2008.

[50] F. Vuillot, N. Lupoglazoff, M. Huet, Effect of chevrons on double stream jet noise from hybrid CAA computations, in: Proceedings of the 49th AIAA Aerospace Sciences Meeting, Paper 2011-1154, 2011.

[51] F. Gand, M. Huet, T. Le Garrec, F. Cléro, Jet noise of a UHBR nozzle using ZDES: external boundary layer thickness and installation effects, in: Proceedings of the 23rd AIAA/CEAS Aeroacoustics Conference, Paper 2017-3526, 2017.

[52] G. Rahier, M. Huet, J. Prieur, Additional terms for the use of fowows williams and hawkings surface integrals in turbulent flows, Comput. & Fluids 120 (2015) 158-172.

[53] L. Cambier, S. Heib, S. Plot, The ONERA elsA CFD software: input from research and feedback from industry, Mech. Ind. 14 (2013) 159-174.

[54] J. Prieur, G. Rahier, Aeroacoustic integral methods, formulation and efficient numerical implementation, Aerosp. Sci. Technol. 5 (2001) 457-468.

[55] G. Rahier, J. Prieur, Formulations and numerical techniques for computation of acoustic pressure and its gradient by integral method, J. Sound Vib. 597 (2025).

[56] G.A. Brès, P. Jordan, V. Jaunet, M. Le Rallic, A.V.G. Cavalieri, A. Towne, S.K. Lele, T. Colonius, O.T. Schmidt, Importance of the nozzle-exit boundary-layer state in subsonic turbulent jets, J. Fluid Mech. 851 (2018) 83-124.

[57] K.B.M.Q. Zaman, Exit Boundary Layer Data for a Round Convergent Nozzle in Support of Numerical Simulation Efforts, Tech. Rep. NASA/TM-2019-220242, 2019.

[58] G.-D. Stich, J.A. Housman, J.G. Kocheemoolayil, C.C. Kiris, J.E. Bridges, C.A. Brown, Hybrid RANS/LES simulation of jet surface interaction noise, in: Proceedings of the 25th AIAA/CEAS Aeroacoustics Conference, Paper 2019-2475, 2019.

[59] F. Gand, M. Huet, Improvement of jet flow simulations using ZDES mode 3 and silent turbulence generation, in: Proceedings of the 25th AIAA/CEAS Aeroacoustics Conference, Paper 2019-2687, 2019.

[60] K.B.M.Q. Zaman, Effect of initial condition on subsonic jet noise, AIAA J. 23 (1985) 1370-1373.

[61] K.B.M.Q. Zaman, Far-field noise of a subsonic jet under controlled excitation, J. Fluid Mech. 152 (1985) 83-111.

[62] K.B.M.Q. Zaman, Effect of initial boundary-layer state on subsonic jet noise, AIAA J. 50 (2012) 1784-1795.

[63] J.E. Bridges, A.K.M.F. Hussain, Roles of initial condition and vortex pairing in jet noise, J. Sound Vib. 117 (1987) 289-311.

[64] K. Viswanathan, Aeroacoustics of hot jets, J. Fluid Mech. 516 (2004) 39-82.

[65] C. Bogey, S. Barré, C. Bailly, Direct computation of the noise generated by subsonic jets originating from a straight pipe nozzle, Int. J. Aeroacoustics 7 (2008) 1-22.

[66] C. Bogey, O. Marsden, C. Bailly, Large-eddy simulation of the flow and acoustic fields of a Reynolds number 10⁵ subsonic jet with tripped exit boundary layers, Phys. Fluids 23 (2011).

[67] L. Sanders, D.-C. Mincu, P.L. Vitagliano, M. Minervino, J. Kennedy, G. Bennett, Prediction of the acoustic shielding by aircraft empennage for contrarotating open rotors, Int. J. Aeroacoustics 16 (2017) 626-648.

[68] D. Lindblad, M. Höchel, U. Michel, F. Thiele, H. Xia, Noise scattering using a regularized boundary element method coupled with the fowows-williams & hawkings method, in: Proceedings of the 30th AIAA/CEAS Aeroacoustics Conference, Paper 2024-3402, 2024.