Influence of boundary layers resolution on heated

19th AIAA/CEAS Aeroacoustics Conference May 27-29, 2013, Berlin, Germany

AIAA 2013-2141

Influence of boundary layers resolution on heated, subsonic, high Reynolds number jet flow and noise M. Huet∗

Downloaded by Maxime Huet on May 31, 2013 | http://arc.aiaa.org | DOI: 10.2514/6.2013-2141

Onera – The French Aerospace Lab, F-92322, Chˆ atillon, France

The noise generated by a hot single stream jet at Mach number Mj = 0.7 and diameterbased Reynolds number ReD = 400, 000 is investigated numerically. No artificial triggering of the flow is present and focus is given on the influence of internal and external boundary layers resolution on noise radiation for both static and take-off configurations. Simulations include the nozzle geometry and are performed for two distinct grids, the first one supporting the flow resolution near the wall whereas no boundary layers resolution is present for the second one. Uniform flow profiles are imposed at the inlet and the flow develops freely. All simulations exhibit low turbulence levels inside the nozzle at the throat, despite the transitional boundary layer observed with the resolution of the near-wall flow. Flow investigations downstream of the nozzle exit highlight the initially laminar development of the flow, especially without boundary layers resolution. The turbulent transition is fastened with boundary layers resolution in the presence of the external flow thanks to the turbulence developed on the external wall that triggers the flow. In the far field, both static simulations overestimate the radiated noise in the medium-frequency range especially because of the additional noise source coming from the initially laminar shear layer development. A similar overestimation is observed with the external flow when the boundary layers are not resolved. With the boundary layers resolution, this additional noise is suppressed and a good agreement is obtained with the experiments.

I.

Introduction

With the increase of the computational capacities in the last decades, it has now become possible to perform unsteady flow simulations to reproduce and investigate noise generation.1 If direct numerical simulations (DNS) are still limited to the description of low Reynolds number academic configurations,2, 3 the use of large-eddy simulations (LES) permits to compute higher Reynolds number turbulent flows4–8 more representative of the industrial concerns. A key issue of the success of such simulations is to provide boundary conditions representative of the anechoic facilities where jet noise experiments are performed. Non-reflective conditions are required at lateral and outflow boundaries to model the free-field conditions and to avoid spurious noise contamination of the physical sound field.9 Several formulations have been developed to provide non-reflective conditions, such as, amongst others, the characteristic wave decomposition of Thompson10, 11 and Poinsot & Lele,12 the asymptotic solutions suggested by Bayliss & Turkell,13 especially investigated by Tam & Webb14 and Tam & Dong15 and extended to 3-D geometries by Bogey & Bailly16 or the adding of a sponge zone, featuring either a grid stretching, a numerical damping or both to dissipate perturbations before they reach the boundary.17, 18 For a detailed review of available numerical boundary conditions for aeroacoustic simulations, the reader may refer to Tam.19 At the nozzle inflow it is furthermore necessary, in addition to the mean flow field, to reproduce turbulent quantities representative of the considered jet. This concern is especially important because jet development is strongly linked to the initial turbulent or laminar shear layer state, as observed by Zaman,20–22 the latter leading to additional noise. Several approaches have been developed to favour the turbulent transition of the jets. It is a difficult problem because the jet forcing must generate a minimum spurious noise, in order not to contaminate the acoustic field. Those methods can be divided in two categories, depending on the inclusion of the nozzle in the numerical domain or not. ∗ Research

scientist, CFD and aeroacoustics department, [email protected]

1 of 16 American Institute of Aeronautics and Astronautics Copyright © 2013 by Onera. Published by the American Institute of Aeronautics and Astronautics, Inc., with permission.


In the first category, the computational domain is restricted to the flow downstream of the nozzle exit. Jet inflow conditions are modelled by imposing mean flow profiles and disturbances are added to trigger the turbulence Some of the existing works are briefly described in the following. Freund2 and Labb´e et al.23 add velocity perturbations on the mean velocity profile at the nozzle inlet, using either fully random or modelled, space-time evolving and slowly varying, spatiotemporal disturbances. Bodony & Lele5 and Morris et al.24 choose to add pressure disturbances, corresponding to the summation of instability modes obtained from an inviscid modal analysis of the inflow profile. Bodony & Lele point out that, by construction, those instability modes are non-radiating. In an analogous way, Bogey et al.6, 25, 26 use velocity perturbations, located in the shear layer zone approximately half a diameter downstream of the inflow. These disturbances are obtained as a superimposition of ring vortices for different azimuthal modes with a random time evolution. They correspond to divergence-free perturbations to minimize the production of spurious acoustic waves. In the second category, the nozzle is included in the computational domain. Depending on the approach used by the authors, the upstream external flow can also be included in the simulation. If, as emphasised by Tam27 the importance of the nozzle has been clearly demonstrated in supersonic configurations where it plays a key role for the screech noise emission, its presence for subsonic jet simulations remains under discussion. The advantages of including the nozzle in the numerical domain are nevertheless manifold. First, it is expected that by removing the inflow boundary condition from a critical location, where instability waves must be allowed to develop freely, one would permit some kind of natural growth of instability waves to occur.28 Second, with the presence of the upstream external flow, the inclusion of the nozzle all the more permits to take into account the external nozzle shape and to simulate complex, realistic geometries such as short-cowl nozzles or/with the inclusion of a plug,8, 29 a pylon30 or chevrons29, 31, 32 for instance. The increased difficulty in mesh generation can be overtaken by using unstructured flow solver and grid generator. When dealing with a forcing of the jet, imposing perturbations upstream of the nozzle exhaust moreover permits to increase the amplitude of the disturbances compared to the excitation in the shear layer, because it is less exposed to spurious noise contamination. Finally, by letting the perturbations develop freely in the nozzle boundary layers, one can expect the turbulence to be more representative of that of a real jet with regard to arbitrary shaped disturbances imposed in the shear layer. With the presence of the nozzle, one can cite the simulations of Bogey et al.33, 34 who added small velocity disturbances random in space and time in the nozzle boundary layer, far upstream of the nozzle exhaust, to trigger the turbulence and of Uzun & Hussaini,31 featuring a turbulence rescaling-recycling procedure originally developed by Lund et al.35 Discussions on this recycling method can be found in Sagaut et al.36 Many authors also performed simulations without user-operated destabilization of the jet.4, 29, 37–40 In this latter case, the forcing is expected to rely mostly on numerical noise. To help simulate a fully-developed turbulent flow at the jet inlet with this approach, Bondarenko et al.39 attached a long pipe upstream of the nozzle to let the flow develop. As discussed by Vuillot et al.,28 if successful this approach may remove the dependence of flow and noise results from parameters external to the experimental configuration. Those simulations are classically run imposing uniform stagnation variables at the inlet; the boundary layer profile is thus not imposed and grows naturally in the computation. The above-mentioned simulations including the geometry focus on the turbulence development inside the nozzle. If one can expect this turbulence to be of prime importance for flow development and noise radiation, recent simulations nevertheless highlighted the influence of the external boundary layer on the jet evolution in the presence of an external flow.32 In the present study, the influence of the internal and external boundary layers resolution on jet flow development and noise radiation is investigated using LES combined with the Ffowcs Williams & Hawkings surface integral formulation41 to simulate the far-field noise. No turbulence seeding is made in the boundary layers. The jet main characteristics are its static temperature Tj = 830K, its Mach number Mj = Uj /c0 = 0.7 and its Reynolds number based on nozzle diameter ReD = Uj D/ν = 400, 000, where Uj stands for the jet exhaust velocity, c0 for the sound velocity in the medium at rest, D for the nozzle diameter and ν for the kinematic viscosity. The Reynolds number being high, the jet is expected to be initially turbulent. Simulations are performed for both take-off and static conditions, depending on the presence of an external flow or not. This jet has been the object of several experimental42, 43 and numerical investigations44–47 in the past. The paper is organized as follows. Details of the simulated configurations are given in section II, where the numerical parameters for flow and noise simulations and the computational grids are also described. Aerodynamic analyses are presented in section III. Mean flow and turbulence evolutions are especially


detailed upstream and downstream of the nozzle. Vorticity snapshots are also presented for all simulations. Far-field noise radiation is then presented in section IV and compared with the experimental data for both power spectral densities and integrated levels. To end, conclusions and perspectives are given in section V.

II. II.A.

Numerical procedure

Jet configurations


The geometry considered is a round nozzle with an exhaust diameter D of 80 mm. The jet static temperature is Tj = 830 K and its Mach number is Mj = 0.7, which corresponds to a jet velocity Uj of 410 m/s. The ambient pressure and temperature are p0 = 101325 Pa and T0 = 280 K, respectively. Both static and take-off (U0 = 90 m/s) operating conditions are considered. Aerodynamic43, 47 (static case only) and acoustic measurements, performed in the CEPRA19 anechoic facility of Onera,48 are available for comparisons between simulations and experiments.

(a) Global view

(b) Detailed view

Figure 1. Illustrations of the nozzle shape.

An illustration of the nozzle is given in Fig. 1. Inside the nozzle, the inflow condition is located 7 diameters upstream of the exhaust. A first contraction is present for −6 < x/D < −5.5, followed by a slowly converging shape up to the nozzle exit where a second contraction is visible for the last 13 mm (0.16 x/D). The nozzle fairing starts with a radius of 2.5 diameters at x/D = −18.5 and converges up to x/D = −13 with an angle of 4.3◦ and then up to x/D = −0.5 with an angle of 6.9◦ . These low angles may limit the risks of flow separation even with a flow at 90 m/s. At the exhaust, a convergence of 16.4◦ is visible. II.B.

Numerical methods and boundary conditions

Aerodynamic simulations are performed using the flow solver CEDRE developed at Onera. CEDRE is a multi-physics, reactive solver used by researchers and aeronautical industries for engine conception and optimisation, such as combustion,49, 50 turbine blade cooling51 and jet noise,40, 52 for instance. The resolution of the Navier-Stokes equations is made for the conservative variables and is based on a finite volume formulation using a second order upwind space discretization scheme for generalised polyhedral computational grids.53 Time integration is currently made with a first order implicit time scheme. Unsteady flow fields are computed using LES with a Smagorinsky subgrid-scale model.54 At the outflow boundary, static pressure is imposed. The grid is stretched on a distance of 75 D to damp turbulence and acoustic waves in order to avoid spurious noise reflections that could contaminate the numerical domain. A similar stretching is applied at upstream and lateral boundaries, where static temperature and velocity are imposed. Inside the nozzle, flow injection is made through uniform stagnation pressure and temperature values. The internal and external boundary layer profiles are thus not imposed and are expected to develop freely along the nozzle walls. Their thickness is expected to depend on the grid resolution and numerical schemes precision. Details of the near-wall regions grid sizing are given in section II.C. To end, no disturbances are added in the flow upstream of the nozzle exhaust; numerical noise is expected to destabilize the flow and to trigger the turbulence. Simulations are performed with a time step ∆t = 2 × 10−7 s which ensures a CFL criterion below 1 in almost all the numerical domain. After a transient period required to let the jet flow develop, the simulations are run for 300,000 iterations to perform mean flow averaging and far-field noise radiation. It corresponds to a physical time of 60 ms or to a non-physical time of 300 convective time units D/Uj . This duration is


thought to be long enough to ensure a sufficient statistical convergence of the flow fields and far-field pressure spectra. II.C.

Grids definition


Two different meshes are used for the simulations. They are both composed of 30 × 106 elements but their construction relies on different methodologies. The first grid, referred as jetBL in the following, is fully structured and is densified near the walls to resolve thickened boundary layers. As the numerical capacities are still insufficient to accurately resolve the physical boundary layers of a ReD = 400, 000 jet, it is decided for the second grid, jetNoBL, not to reproduce the near-wall flows in the grid and to preferably increase the flow resolution downstream of the nozzle. This grid is based on tetrahedra but includes a structured patch in the jet plume to increase turbulence and noise resolution. More details on this hybrid grid methodology can be found in Huet et al.40 Both grids include a O-type treatment on the jet axis to ensure that hexahedral cells have an homogeneous size in the core region.

(a) jetBL

(b) jetNoBL Figure 2. Grids detail at nozzle exit.

The jet boundary-layer thickness is estimated following the results of Zaman.21 For an isothermal jet with ReD = 400, 000, Zaman experimentally observed a boundary-layer momentum thickness of δθ /D ∼ 0.001. Because of computational restrictions, a larger value is usually used in the simulations, as done for instance by Bodony & Lele,5 Bogey et al.25 and Bodard et al.52 For the simulation of a ReD = 500, 000 jet with a laminar boundary layer, Bogey et al.33 imposed a shear-layer thickness δ/D = 0.064 corresponding to a momentum thickness δθ /D = 0.008. In the present simulations with the grid jetBL, a shear-layer thickness δ/D of 0.05 is chosen to be discretized with 20 cells, which corresponds to ∆r/D = 0.0025 at the wall. The same resolution is chosen to discretize the outer boundary layer. An illustration of the grid resolution at the nozzle exit is represented in Fig. 2, where the difference in the boundary layers discretization between the two grids is especially visible. The radial discretization in the hexahedral domain at the nozzle exit is represented in Fig. 3 for the two grids. The shear layer resolution is better for the grid JetBL (Fig. 3 (a)) because of the boundary layers resolution that imposes the same radial discretization (∆r/D = 0.0025) downstream of the nozzle lip, contrary to the grid JetNoBL, Fig. 3 (b), where the mesh sizing in the shear layer has been performed using 30 cells to reproduce a thickness estimated following an analytical expression (see Eq. 22 of Gavelle et al.46 and Huet et al.40 for further details) and leading to ∆r/D = 0.0052. The grids are radially stretched outside of this sheared-flow to limit the total mesh sizes. Downstream of the nozzle exit, the jet development area is refined in a volume corresponding to a truncated cone, with a length of 25D and a radius of 2D and 4D, for x/D = 0 and x/D = 25 respectively. Axial, radial and azimuthal discretizations in the axial direction along the nozzle lip are reproduced in Fig. 4 for the two grids. As these two grids are constructed with 120 cells on the azimuthal direction, they both have the same discretization along the nozzle lip (r = r0 ), r0 ∆θ/D = 0.026. A consequence of the boundary layers resolution with the grid jetBL is the lower amount of cells available for the flow resolution, that leads to a faster grid coarsening downstream of the nozzle exit. This coarsening is especially visible in the axial direction, where the elements reach their maximum size ∆x/D = 0.055 with a fast stretching 5 diameters after the nozzle exhaust, compared to the maximum value reached at x/D = 15 for the grid jetNoBL with 4 of 16 American Institute of Aeronautics and Astronautics

Copyright © 2013 by Onera. Published by the American Institute of Aeronautics and Astronautics, Inc., with permission.

(a) jetBL

(b) jetNoBL


Figure 3. Radial discretization in the radial direction at nozzle exit.

(a) jetBL

(b) jetNoBL

Figure 4. Grid discretization in the axial direction along the nozzle lip (r = r0 ). — ∆x/D, – – ∆r/D, • r0 ∆θ/D.

a lower stretching ratio. The radial resolution is nevertheless better with the grid jetBL, especially because of the smaller elements’ initial size at nozzle exit driven by the grid sizing for the boundary layers and shear layer resolution. II.D.

Noise radiation

The noise radiation is performed using the Ffowcs Williams & Hawkings (FW-H) porous surface formulation41 available in the code KIM developed at Onera.55 This formulation makes it possible to compute time pressure histories at any observer location by integration of the flow fields on a control surface surrounding the jet and containing all the noise sources. It is preferred to the Kirchhoff method that was shown by Rahier et al.55 to be more exposed to the generation of spurious noise, especially for hot jets. Following the results of Rahier et al., the control surface starts at the nozzle exit and extends downstream on a distance of 25D. The surface is kept open at both extremities to avoid the contamination of the pressure signals by spurious noise generated by the crossing of the surface by turbulent spots. Finally, far-field pressure spectra and integrated levels are averaged azimuthally on 36 microphones for each observer location. It has indeed been observed that radiated noise may vary up to 2 dB along the azimuthal position despite the axisymmetry of the configuration because of the short-time duration of the simulated signals.56 In practice, instantaneous flow fields are stored on several surfaces to ensure that the surfaces surround all the noise sources, are not contaminated by spurious noise and give only a negligible dissipation caused by the numerical schemes. In the present simulations, the storage is performed on 4 surfaces. Microphones are located 75D (6 meters) from the nozzle exit, as done experimentally. Results are given for one reference surface only, as it has been observed that radiated pressure does not depend on the position of the surface; numerical dissipation has moreover been shown to be negligible for frequencies below 10 kHz. 5 of 16 American Institute of Aeronautics and Astronautics

Copyright © 2013 by Onera. Published by the American Institute of Aeronautics and Astronautics, Inc., with permission.

III. III.A.

Flow analysis

Boundary layers mean flow and turbulence development


The mean axial velocity profiles in the radial direction inside the nozzle, 0.5D upstream of the exhaust, are represented in Fig. 5 for both grids. They correspond to the simulations of the static configuration. The external flow however does not modify the flow development inside the nozzle and identical results have been obtained for the take-off configuration. In this figure, rw corresponds to the distance from the wall and U0 to the velocity on the nozzle axis. The Blasius profile is given by a polynomial approximation (see Bogey et al.33 ) with a boundary layer thickness δ/D = 0.033.

Figure 5. Radial mean axial velocity profile in the nozzle, at x/D = −0.5. — jetBL, – – jetNoBL, ◦ Blasius profile.

The boundary layer profile is not imposed at the inflow in the simulations and therefore develops freely in the nozzle. With the coarse near-wall grid, jetNoBL, the velocity profile is almost constant on the whole section; as expected, no boundary layer profile is visible because of the insufficient grid resolution. With a near-wall flow resolution, a boundary layer profile of thickness 0.033D is observed. This value is 34% smaller than the estimation made during the grid construction; the boundary layer profile is thus discretized with 13 cells. Its momentum layer thickness is δθ /D = 0.00385, a value four times larger than the experimental observation of Zaman.21 The simulated velocity profile is sharper than the Blasius profile at the wall, which illustrates that the boundary layer is not laminar. This observation is confirmed by the shape factor H = δ? /δθ of 1.93, where δ? is the displacement thickness. This value stands between the asymptotic values for laminar (H = 2.59) and turbulent (H = 1.4) boundary layers20 and indicates that the boundary layer is transitional.

(a) Internal flow

(b) External flow

Figure 6. Maximum axial turbulent velocity evolution along the jet axis, upstream of the nozzle exit. Static configuration: — jetBL, – – jetNoBL. Take-off configuration: —2 jet BL, – –2 jet NoBL.

Despite the transitional boundary layer, turbulence levels are very low inside the nozzle, as illustrated in Fig. 6 (a), and do not exceed 0.25% of the jet exhaust velocity for all simulations. Zaman20 measured similar turbulence levels for an isothermal, untripped jet with a Reynolds number of 100,000. This result indicates



that the resolution of the boundary layer is not sufficient by itself to reproduce turbulence development in the nozzle and that the numerical noise is too low to trigger the flow turbulence. Turbulence levels of similar amplitude are observed close to the nozzle fairing for the static configuration simulations and for the take-off configuration without boundary layers resolution, see Fig. 6 (b). With the presence of an external flow and with the grid JetBL, a development of the turbulence is observed. Turbulence first grows linearly for −18.5 < x/D < −13, which corresponds to the first convergence of the fairing. The slope then increases with the higher convergence of the nozzle up to x/D = −10 where a saturation is observed with a level of 1.8% the jet exhaust velocity. The convergence of the nozzle is thus responsible of the turbulence growth in the external boundary layer.

Figure 7. Radial profile of axial turbulent velocity at nozzle exit. Static configuration: — jetBL, – – jetNoBL. Take-off configuration: —2 jetBL, – –2 jetNoBL.

The radial profiles of axial turbulence at nozzle exit are represented in Fig. 7. As pointed out previously, it is the resolution of the external boundary layer, with the converging nozzle fairing, that permits to provide turbulence with levels up to of 1.5% of the jet velocity at nozzle exhaust. III.B.

Nozzle exhaust vorticity snapshots

(a) Static, jetBL

(b) Static, jetNoBL

(c) Take-off, jetBL

(d) Take-off, jetNoBL

Figure 8. Vorticity snapshot in the shear layer downstream of the nozzle exit, in the (x,r) plane. 0 ≤ |ω|D/Uj ≤ 20, from white to black.

Grey scale is

Vorticity snapshots in the shear layer, just downstream of the nozzle exit, are represented in Fig. 8 for the 4 simulations. Coherent vortices typical of initially laminar shear layers are visible for all simulations. Vortex shedding is observed near x/D = 0.25 with the grid JetBL, for both configurations. Pairings seem to occur for x/D ∼ 0.7 for the static case and x/D ∼ 0.5 for the take-off case. Downstream, a breakdown of the structures is observed and the turbulence becomes chaotic. Turbulent transition hence appears to be more 7 of 16 American Institute of Aeronautics and Astronautics Copyright © 2013 by Onera. Published by the American Institute of Aeronautics and Astronautics, Inc., with permission.


rapid with the presence of the external flow, where coherent structures are less visible than for the static case, possibly thanks to the higher axial turbulent velocity levels observed at nozzle exit. The flow remains coherent for a longer distance with the grid JetNoBL, where vortex shedding is observed for x/D = 0.5 and pairings more downstream. With this latter grid, the flow remains well organized even at x/D = 1.5.

(a) Static, jetBL

(b) Static, jetNoBL

(c) Take-off, jetBL

(d) Take-off, jetNoBL

Figure 9. Vorticity snapshot in the shear layer downstream of the nozzle exit, in the (x,θ) plane. 0 ≤ |ω|D/Uj ≤ 20, from white to black.

Grey scale is

The azimuthal evolution of the vorticity in the shear layer downstream of the nozzle exhaust is visible in Fig. 9. With the grid JetBL, one can observe for both simulations that vortical structures strongly coherent in the azimuthal direction are visible just downstream of the nozzle exit, for x/D ∼ 0.25. This position corresponds to the location of the vortex shedding. Those structures start to decorrelate very fast for x/D = 0.4 and fine-scale, isotropic turbulence can be observed at x/D = 1. With the grid JetNoBL, tube-like structures are observed for x/D ∼ 0.5. Their azimuthal coherence is more important than with the grid JetBL. These structures remain strongly correlated while being convected by the flow especially for the take-off condition, see Fig. 9 (d), where vortical tubes are still observed 1 diameter after the nozzle exit. These different flow developments with the two grids cannot be attributed only to different turbulence levels at the nozzle exit. The static simulation with the grid JetBL indeed exhibits similar turbulence characteristics as observed with the grid JetNoBL; the radial shear layer resolution, higher for grid JetBL compared to grid JetNoBL, also seems to favour the transition of the shear layer from laminar to turbulent. To end, as the vortex pairings observed in the shear layer for all simulations are known to be efficient noise generators, one can expect to find their acoustic signature in the far field. This particular point will be discussed in section IV. III.C.

Jet mean and turbulent flow fields

The evolution of the shear-layer momentum thickness is reproduced in Fig. 10. The thickness evolution is qualitatively similar for all simulations. A very slow growth is observed in a first stage during the flow adjustment just downstream of the nozzle lip and ends when the first vortical structures are observed in the shear layer, where the growth strongly increases. In a third stage, a linear growth is finally visible. These observations are in agreement with those made experimentally by Hussain & Zedan57, 58 and Husain & Hussain59 and numerically by Bogey et al.33 and Bogey & Bailly60 for initially laminar shear layers and indicate that the simulations correspond to transitional jets. Moreover, as pointed out by Bogey & Bailly,60 the second stage of the shear-layer thickness growth takes place earlier with the smaller initial momentum thickness. This observation is coherent with the linear instability theory proposed by Michalke,61 who associates the highest rates of instability growth with the strongest velocity gradients. Turbulent transition therefore appears sooner in the jet with the grid JetBL than with grid JetNoBL. One must however keep in mind that the theory has been developed for inviscid and isothermal shear layers, two conditions that are not verified for the heated jet considered here.


(a) Static

(b) Take-off


Figure 10. Axial evolution of the simulated shear-layer momentum thickness. — JetBL, – – JetNoBL.

(a) Static

(b) Take-off

Figure 11. Evolution of the mean axial velocity along the jet axis. Simulations: — JetBL, – – JetNoBL. Experiments: Muller et al.43 (Tj /T0 = 2.96, Mj = 0.7), 4 Ahuja et al.62 (Tj /T0 = 2.7, Mj = 0.78), Bridges & Wernet63 (Tj /T0 = 2.7, Mj = 0.548), . Bridges & Wernet63 (Tj /T0 = 2.7, Mj = 0.904). The dotted line represents the potential core length limit.

From the momentum thickness evolutions illustrated in Fig. 10, one can expect the simulations without boundary layers resolution to give a shorter potential core length compared to the simulations with their resolution. In the present study, the potential core length xc is defined as the distance at which the axial velocity is 90% of the jet velocity: ux (x = xc ) = 0.9Uj . Mean axial velocity profiles are reproduced in Fig. 11, where the experimental data of Muller et al.43 for the same configuration and of other sources for similar test conditions are also reported. Following these data, simulations underestimate the potential core length of about 30% for the static case and 35% for the take-off configuration. This underestimation of the core length has been observed in several previous studies4, 33, 37, 44, 56 and is often associated with the more important mixing observed in the simulations compared to the experiments. It might be explained by the different initial state of the shear layer between simulations and experiments; Raman et al.64 indeed showed experimentally that jets with initially transitional shear layers develop with a shorter potential core length than initially turbulent jets. The higher momentum thickness in the simulations compared to the experiments may be another reason for this underprediction. Finally, the resolution of the shear layer also seems to play a role in the simulated core length value: a more important length is observed with the grid JetBL because the turbulent transition takes place sooner with this grid partially thanks to the better resolution of the radial velocity gradients. The turbulent axial velocity levels on the jet axis are reproduced in Fig. 12. The maximum turbulence level is shifted toward the nozzle exit in the simulations compared to the experiments, as a consequence of the shorter potential core length. A maximum rms level of 16% is obtained numerically for the static configuration. This value is in good agreement with the experimental data. The maximum level is decreased with the presence of the external flow, in agreement with the experimental observations of Ahuja et al.62 who concluded that an external forward velocity reduces the axial velocity decay rate and the turbulence


(a) Static

(b) Take-off


Figure 12. Evolution of the turbulent axial velocity along the jet axis. See Fig. 11 for the legend.

(a) Static

(b) Take-off

Figure 13. Axial evolution of the simulated peak turbulent axial velocity. — JetBL, – – JetNoBL.

intensity. To end this section, the axial evolution of the peak turbulent axial velocity is given in Fig. 13. The turbulence levels start from a vely low value at nozzle exit and grow very fast in the first diameters downstream of the nozzle exit, before decreasing with a lower rate. This turbulence evolution agrees well with the experimental observations of Husain & Hussain59 for an initially laminar jet and differs from that of an initially turbulent case which does not exhibit a strong peak just after the nozzle exit. This result confirms the transitional state of the shear layer in the simulations, as previously observed. The peak value is 21% for the static case, a value higher than the 18% level observed in the isothermal experiments of Husain & Hussain.59 This discrepancy might not be attributed to the jet temperature difference only, as a similar result has been obtained by Bogey et al.33 for an isothermal jet and was assumed to come from a thicker initial momentum thickness in the simulations in comparison with the experiments. In the presence of the external flow, this peak is reduced to 19% and 18%, respectively for grids JetBL and JetNoBL. This reduction can be explained by the weaker radial velocity gradients at nozzle exit. With the grid jetBL, the peak is observed 0.7D downstream of the nozzle exit. This value is slightly higher than in the experiments of Husain & Hussain59 (0.4D), possibly because of the thicker momentum thickness that drives the growth of the instabilities.61 With the grid JetNoBL, this peak is shifted to 1.2D for the static case and to 1.7D with the external flow because in theses cases the creation of the vortical structures is delayed compared to the simulations with the grid JetBL, as discussed previously concerning the evolution of the boundary-layer momentum thickness.


IV. IV.A.

Radiated noise

Static configuration


(a) 30◦

(b) 90◦

Figure 14. Power spectral densities at observer locations 75D (6 meters) from the nozzle exit. Static configuration. Simulations: — JetBL, – – JetNoBL. Experiments: .

Focus is now given on the pressure radiated to the far field. Simulated power spectral densities at 30◦ and 90 are visible in Fig. 14, where experimental data acquired in the CEPRA19 facility of Onera for the same configuration are also reproduced. At 30◦ the two computed spectra exhibit a similar shape, the levels being slightly higher for the grid JetNoBL especially for the medium and high frequencies. This difference can be associated with the more important mixing observed with the latter grid compared to jetBL, that leads to a shorter potential core length. A good agreement is observed between simulations and measurements at that angle. The frequency of maximum level, f = 800 Hz (StD = f D/Uj = 0.16), is especially well reproduced numerically. In the medium-frequency range, simulations slightly overestimate the experimental data with a maximum value of 2 and 4 dB, respectively for simulations with grids JetBL and JetNoBL. The underestimation of the low-frequency part of the simulated spectra is caused by the insufficient axial extent of the surface used for the radiation, kept open at the downstream end, which results in missing some contributions of the low-frequency noise sources for their radiation at fore angles. The better agreement between simulated and experimental low-frequency noise at 90◦ indeed indicates that those noise sources are well captured in the aerodynamic simulations. An improvement in the low-frequency part of the spectra could be achieved using a longer storage surface. To end with these spectra, one can notice that simulated levels collapse above 10 kHz; this value corresponds to the grid cut-off frequency. The higher levels observed for the grid JetNoBL with respect to the grid JetBL at 30◦ for the medium frequencies are also visible at 90◦ . An inversion of the two curves is noticed close to the grids cut-off frequency, for f = 8000 Hz, and can be attributed to the different radial grid resolution of the two meshes that leads to a faster numerical dissipation for the grid jetBL at high frequencies. For both simulations, medium-frequency levels overestimate the experimental data by up to 7 dB and the peak level is obtained for f = 2500 Hz (StD = 0.49), a value almost three times larger than in the experiments, f = 900 Hz (StD = 0.18). A similar increase of the medium-frequency noise has been observed experimentally by Zaman20 and Bridges & Hussain65 for untripped jets when compared to tripped jets, by Viswanathan66 for low Reynolds number jets (ReD < 400, 000) in opposition to high Reynolds number jets (ReD > 400, 000) and by Bogey et al.33, 67 who compared simulated transitional jets with experimental turbulent ones. Zaman20 experimentally observed that the peak frequency is obtained for Stθ ∼ 0.006, where Stθ = f δθ (0)/Uj is the Strouhal number based on the initial shear-layer momentum thickness δθ (0). Noticing that this frequency is half the value of the roll-up frequency,20, 68 he finally concluded that the first stage of pairing is the source of the additional noise. One can note that this roll-up frequency is close to the theoretical most unstable shear-layer frequency obtained with the linear stability theory,61, 69 Stθ = 0.017. In the present simulations, the initial shear-layer momentum thickness is δθ (0) ∼ 0.003D for both simulations. The simulated peak frequency is f = 2500 Hz and corresponds to Stθ = 0.0015, a value four times smaller than the predicted one. Two reasons at least can be envisaged to explain this discrepancy. First, ◦



the peak frequency obtained experimentally or from the instability theory has been determined for isothermal jets whereas the simulated jet is heated. Morris70 indeed reported that the most unstable frequency is decreased with increasing temperature. Second, the grid resolution in the initial development zone of the shear layer might not be sufficient to support the first instabilities, which finally grow after a thickening of the shear layer downstream of the nozzle exit. Considering a larger shear-layer thickness would increase the simulated non-dimensional peak frequency Stθ .

Figure 15. Overall sound pressure levels obtained 75D (6 meters) from the nozzle exit. Static configuration. Integration is performed for the frequency bandwidth [200 Hz; 20,000 Hz]. Simulations: — JetBL, – – JetNoBL. Experiments: .

The sound pressure levels obtained at 75D are reproduced in Fig. 15. Simulated levels with the grid JetNoBL are 1 dB higher than those with the grid JetBL for angles above 60◦ , as a consequence of the more important medium-frequency noise observed in the spectra. The opposite is observed for lower angles because of the weaker levels close to 1 kHz with the grid JetNoBL. The computed noise overestimation is 3 dB at 50◦ and decreases at fore angles because of the underestimation of the simulated low-frequency levels coming from the insufficient length of the storage surface, as discussed previously. It increases for larger angles and reaches 5 and 6 dB at 90◦ , respectively for grids JetBL and JetNoBL. These higher levels are the consequence of the medium-frequency additional noise observed in Fig. 14 (b), originating from the initial laminar state of the jet. These results are similar to those obtained by Bogey & Bailly33 for the simulation of an initially laminar jet. IV.B.

Take-off configuration

(a) 30◦

(b) 90◦

Figure 16. Power spectral densities at observer locations 75D (6 meters) from the nozzle exit. Take-off configuration. Simulations: — JetBL, – – JetNoBL. Experiments: .

Simulated power spectral densities obtained for the take-off configuration are reproduced in Fig. 16 for the angles of 30◦ and 90◦ and are compared with the experimental data. As previously observed for the static configuration, both computed spectra exhibit a similar shape at 30◦ , the medium-frequency levels being nevertheless about 2 dB higher with the grid JetNoBL. This difference can be explained by the more important mixing of the jet with this latter grid, as illustrated in Fig. 11 (b) with the shorter potential core 12 of 16 American Institute of Aeronautics and Astronautics Copyright © 2013 by Onera. Published by the American Institute of Aeronautics and Astronautics, Inc., with permission.


length and in Fig. 12 (b) with the higher maximum turbulence level on the jet axis. A good agreement is also observed between the two simulations and the experimental data, despite a slight overestimation of the computed medium and high frequencies. At 90◦ , more significant differences are observed between the two simulations. First, the mediumfrequency levels simulated with the grid JetNoBL are up to 5 dB higher than the ones obtained with the grid JetBL. Second, the frequency of maximum level is higher with the grid JetNoBL, f = 2000 Hz (StD = 0.39) compared to f = 1300 Hz (StD = 0.25) with the grid JetBL. When compared to the measurements, both simulations overestimate the experimental medium-frequency noise by a maximum of 4 dB and 8 dB, for the grids JetBL and JetNoBL respectively, and overpredict the experimental peak frequency, f = 800 Hz (StD = 0.16). As detailed previously for the static configuration, these discrepancies are caused by an additional medium-frequency noise, generated by the vortex pairings occurring in the shear layer of the simulated jets. The peak frequency being related to the initial shear-layer momentum thickness δθ (0), the faster growth of the momentum thickness in the jet with the grid JetBL, visible in Fig. 10, explains the lower peak frequency observed. This result is coherent with the experimental observations of Zaman20, 21 and the simulations of Bogey & Bailly60 for untripped jets. The overestimation of the experimental noise in the medium-frequency range is 4 dB lower with the grid JetBL than with the grid JetNoBL. This noise difference can be explained by the faster transition to turbulence with the resolution of the boundary layers, and thus the faster decorrelation of the coherent structures that develop in the shear layer, as evidenced in Fig. 8, and which are responsible of this additional noise.

Figure 17. Overall sound pressure levels obtained 75D (6 meters) from the nozzle exit. Take-off configuration. Integration is performed for the frequency bandwidth [200 Hz; 20,000 Hz]. Simulations: — JetBL, – – JetNoBL. Experiments: .

The sound pressure levels calculated at 75D with the two grids are illustrated in Fig. 17, where experimental data are also reproduced. For all angles, noise levels obtained with the grid JetNoBL are higher than the ones computed with the grid JetBL. The difference is 1.4 dB at 30◦ and 3 dB at 90◦ and comes from the higher medium-frequency levels observed in the power spectral densities without boundary layers resolution. This is especially visible for angles near 90◦ , where the higher contribution of the additional noise source for grid JetNoBL even leads to a bump in the directivity pattern. Both simulations overestimate the experimental levels above 30◦ . For angles closer to the jet axis or far upstream of the nozzle computed levels collapse because of the insufficient axial extent of the storage surface at the upstream and downstream ends; simulated levels will thus not be discussed for these positions. For the grid JetBL, the noise overestimation lies between 1.2 dB at 30◦ and 1.8 dB at 90◦ . The higher overestimation at the location normal to the jet is explained by the additional noise source. The overestimation of the experimental noise is of 2.7 dB at 30◦ for the grid JetNoBL and grows up to 4.8 dB at 90◦ because of the intense additional noise source originating from the vortex pairings. In the present simulations, the low amplitude perturbations that have grown on the outer fairing the nozzle have been sufficient to trigger the transition to turbulence and to drastically reduce the noise originating from the initially laminar jet development.



V.

Conclusion

In this paper, the influence of boundary layers resolution on the flow and noise of a heated, subsonic, high Reynolds number jet is investigated numerically. The flow is obtained with a large-eddy simulation solver and the noise is radiated to the far field with the Ffowcs Williams & Hawkings integral method. Two test conditions, corresponding to static and take-off configurations, are computed and all simulations are performed without artificial triggering of the flow. The influence of the boundary layers resolution is investigated with the use of two different computational grids; the first grid includes a fine resolution of the flow in the near-wall regions while a coarse mesh is used for the second grid on the inner and outer nozzle fairings. A first difference in the simulated flows between the two grids is observed inside the nozzle, where a transitional boundary layer profile is obtained with the fine resolution of the near-walls flow, compared to a flat profile with the coarse grid. The turbulence level nevertheless remains very low for all simulations and corresponds to initially laminar jet conditions. The early development in the simulated jets is thus dominated by processes of vortex roll-up and pairing, characteristic of such laminar flows. The turbulent transition occurs downstream and is especially favoured by the presence of turbulence at nozzle exit coming from the external boundary layers resolution with the external flow. The influence of the boundary layers resolution is also observed for the mean flow with for instance the improvement of the potential core length estimation In the far field, the vortex pairings lead to an additional noise source for the medium frequencies for angles around 90◦ , whose consequence is the overestimation of the experimental noise normal to the jet. Favouring the transition to turbulence thus decreases this additional noise source thanks to the faster decorrelation of the coherent structures in the shear layer. In the present simulations, the small turbulent perturbations obtained in the boundary layer of the outer fairing for the take-off condition are sufficient to drastically reduce this vortex-pairing noise and to recover the experimental sound pressure levels with an accuracy of less than 2 dB. In the light of these results, it appears that the resolution of the mean flow profiles in the internal and external boundary layers is required to numerically reproduce flow and noise representative of experimental turbulent jets. Indeed, the laminar or turbulent jet development is determined by the flow conditions at the nozzle exit and especially to the turbulence that grows in the boundary layers. The present simulations illustrate that, for take-off configuration, the external flow plays an important role in triggering the turbulence of an initially laminar jet and it can be expected that it also influences the flow development for initially turbulent jets. The simulations also indicate that the mean flow resolution in the boundary layers alone is not sufficient to properly reproduce experimentally turbulent jets, because the natural turbulence growth inside the nozzle is too weak to trigger itself the turbulent transition at nozzle exit. It thus appears to be necessary to seed turbulence inside the nozzle to numerically reproduce initially turbulent jets.

Acknowledgments The author is very grateful to the team of the CEPRA19 anechoic facility of Onera for the acoustic tests and especially to Jean-Marc Jourdan for processing the experimental data. Fruitful discussions with Renaud Davy about the exploitation of those data are also appreciated. Part of this work was granted access to the HPC resources of CINES under the allocation 2011-c2011026735 made by GENCI (Grand Equipement National de Calcul Intensif).

References 1 Wang, M., Freund, J. B., and Lele, S. K., “Computational prediction of flow-generated sound,” Annual Review of Fluid Mechanics, Vol. 38, 2006, pp. 483–512. 2 Freund, J. B., “Noise sources in a low-Reynolds-number turbulent jet at Mach 0.9,” Journal of Fluid Mechanics, Vol. 438, 2001, pp. 277–305. 3 Jiang, X., Avital, E. J., and Luo, K. H., “Sound generation by vortex pairing in subsonic axisymmetric jets,” AIAA Journal, Vol. 42, 2004, pp. 241–248. 4 Andersson, N., Eriksson, L.-E., and Davidson, L., “Large-eddy simulation of subsonic turbulent jets and their radiated sound,” AIAA Journal, Vol. 43, 2005, pp. 1899–1912. 5 Bodony, D. J. and Lele, S. K., “On using large-eddy simulation for the prediction of noise from cold and heated turbulent jets,” Physics Of Fluids, Vol. 17, 2005.



6 Bogey, C. and Bailly, C., “Computation of a high Reynolds number jet and its radiated noise using large eddy simulation based on explicit filtering,” Computers and Fluids, Vol. 35, 2006, pp. 1344–1358. 7 Koh, S. R., Schr¨ oder, W., and Meinke, M., “Turbulence and heat excited noise sources in single and coaxial jets,” Journal of Sound and Vibration, Vol. 329, 2010, pp. 786–803. 8 Vuillot, F., Lupoglazoff, N., and Rahier, G., “Double-stream nozzles flow and noise computations and comparisons to experiments,” Proceedings of the 46th AIAA Aerospace Sciences Meeting, No. AIAA 2008-9, 2008. 9 Tam, C. K. W., “Computational aeroacoustics: issues and methods,” AIAA Journal, Vol. 33, 1995, pp. 1788–1796. 10 Thompson, K. W., “Time dependent boundary conditions for hyperbolic systems, I,” Journal of Computational Physics, Vol. 68, 1987, pp. 1–24. 11 Thompson, K. W., “Time dependent boundary conditions for hyperbolic systems, II,” Journal of Computational Physics, Vol. 89, 1990, pp. 439–461. 12 Poinsot, T. J. and Lele, S. K., “Boundary conditions for direct simulations of compressible viscous flows,” Journal of Computational Physics, Vol. 101, 1992, pp. 104–129. 13 Bayliss, A. and Turkel, E., “Far field boundary conditions for compressible flows,” Journal of Computational Physics, Vol. 48, 1982, pp. 182–199. 14 Tam, C. K. W. and Webb, J. C., “Dispersion-Relation-Preserving finite difference schemes for computational acoustics,” Journal of Computational Physics, Vol. 107, 1993, pp. 262–281. 15 Tam, C. K. W. and Dong, Z., “Radiation and outflow boundary conditions for direct computation of acoustic and flow disturbances in a nonuniform mean flow,” Journal of Computational Acoustics, Vol. 4, 1996, pp. 175–201. 16 Bogey, C. and Bailly, C., “Three-dimensional non-reflective boundary conditions for acoustic simulations: far field formulation and validation test cases,” Acta Acustica United With Acustica, Vol. 88, 2002, pp. 463–471. 17 Colonius, T., Lele, S. K., and Moin, P., “Boundary conditions for direct computation of aerodynamic sound generation,” AIAA Journal, Vol. 31, 1993, pp. 1574–1582. 18 Bogey, C., Bailly, C., and Juv´ e, D., “Numerical simulation of sound generated by vortex pairing in a mixing layer,” AIAA Journal, Vol. 38, 2000, pp. 2210–2218. 19 Tam, C. K. W., “Advances in numerical boundary conditions for computational aeroacoustics,” Journal of Computational Acoustics, Vol. 6, 1998, pp. 377–402. 20 Zaman, K. B. M. Q., “Effect of initial condition on subsonic jet noise,” AIAA Journal, Vol. 23, 1985, pp. 1370–1373. 21 Zaman, K. B. M. Q., “Far-field noise of a subsonic jet under controlled excitation,” Journal of Fluid Mechanics, Vol. 152, 1985, pp. 83–111. 22 Zaman, K. B. M. Q., “Effect of initial boundary-layer state on subsonic jet noise,” AIAA Journal, Vol. 50, 2012, pp. 1784–1795. 23 Labb´ e, O., Peyret, C., Rahier, G., and Huet, M., “A hybrid LES/CAA method applied to jet noise prediction,” Proceedings of the 18th AIAA/CEAS Aeroacoustics Conference, No. AIAA 2012-2106, 2012. 24 Morris, P. J., Giridharan, M. G., and Lilley, G. M., “Turbulent mixing of compressible free shear layers,” Proceedings of the Royal Society of London, Series A, Vol. 431, 1990, pp. 219–243. 25 Bogey, C., Bailly, C., and Juv´ e, D., “Noise investigation of a high subsonic, moderate Reynolds number jet using a compressible large eddy simulation,” Theoretical and Computational Fluid Dynamics, Vol. 16, 2003, pp. 273–297. 26 Bogey, C. and Bailly, C., “Effects of inflow conditions and forcing on subsonic jet flows and noise,” AIAA Journal, Vol. 43, 2005, pp. 1000–1007. 27 Tam, C. K. W., “Supersonic jet noise,” Annual Review of Fluid Mechanics, Vol. 27, 1995, pp. 17–43. 28 Vuillot, F., Rahier, G., Lupoglazoff, N., Prieur, J., and Biancherin, A., “Comparative jet noise computations using a coupled CFD-acoustic solution,” 11th International Congress on Sound and Vibration, 2004. 29 Eastwood, S., Xia, H., and Tucker, P. G., “Large-eddy simulation of complex geometry jets,” Journal of Propulsion and Power , Vol. 28, 2012, pp. 235–245. 30 Vuillot, F., Lupoglazoff, N., and Huet, M., “Effect of a pylon on double stream jet noise from hybrid CAA computations,” Proceedings of the 16th AIAA/CEAS Aeroacoustics Conference, No. AIAA 2010-4029, 2010. 31 Uzun, A. and Hussaini, M. Y., “Simulation of noise generation in near-nozzle region of a chevron nozzle jet,” AIAA Journal, Vol. 47, 2009, pp. 1793–1810. 32 Vuillot, F., Lupoglazoff, N., and Huet, M., “Effect of chevrons on double stream jet noise from hybrid CAA computations,” Proceedings of the 49th AIAA Aerospace Sciences Meeting, No. AIAA 2011-1154, 2011. 33 Bogey, C., Barr´ e, S., and Bailly, C., “Direct computation of the noise generated by subsonic jets originating from a straight pipe nozzle,” International Journal of Aeroacoustics, Vol. 7, 2008, pp. 1–22. 34 Bogey, C., Barr´ e, S., Juv´ e, D., and Bailly, C., “Simulation of a hot coaxial jet: Direct noise prediction and flow-acoustics correlations,” Physics Of Fluids, Vol. 21, 2009. 35 Lund, T. S., Wu, X., and Squires, K. D., “Generation of turbulent inflow data for spatially-developing boundary layer simulations,” Journal of Computational Physics, Vol. 140, 1998, pp. 233–258. 36 Sagaut, P., Garnier, E., Tromeur, E., Larchevˆ eque, L., and Labourasse, E., “Turbulent inflow conditions for large-eddy simulation of compressible wall-bounded flows,” AIAA Journal, Vol. 42, 2004, pp. 469–477. 37 DeBonis, J. R. and Scott, J. N., “Large-eddy simulation of a turbulent compressible round jet,” AIAA Journal, Vol. 40, 2002, pp. 1346–1354. 38 Eschricht, D., Greschner, B., Thiele, F., and Jacob, M. C., “Numerical simulation of jet mixing noise associated with engine exhausts,” Notes on Numerical Fluid Mechanics and Multidisciplinary Design, Vol. 104, 2009, pp. 121–146. 39 Bondarenko, M., Hu, Z., and Zhang, X., “Large-eddy simulation of the interaction of a jet with a wing,” Proceedings of the 18th AIAA/CEAS Aeroacoustics Conference, No. AIAA 2012-2254, 2012.



40 Huet, M., Rahier, G., and Vuillot, F., “Simulation of flow control with microjets for subsonic jet noise reduction,” Applied Aerodynamics, edited by J. C. Lerner, chap. 5, Intech, 2012, pp. 79–106. 41 Ffowcs Williams, J. E. and Hawkings, D. L., “Sound generation by turbulence and surfaces in arbitrary motion,” Philosophical Transactions for the Royal Society of London, Vol. A264, No. 1151, 1969, pp. 321–342. 42 Dahan, C., Elias, G., Maulard, J., and Perulli, M., “Coherent structures in the mixing zone of a subsonic hot free jet,” Journal of Sound and Vibration, Vol. 59, 1978, pp. 313–333. 43 Muller, F., Vuillot, F., Rahier, G., Casalis, G., and Piot, E., “Experimental and numerical investigation of the near field pressure of a high subsonic hot jet,” Proceedings of the 12th AIAA/CEAS Aeroacoustics Conference, No. AIAA 2006-2535, 2006. 44 Lupoglazoff, N., Biancherin, A., Vuillot, F., and G.Rahier, “Comprehensive 3D unsteady simulations of subsonic and supersonic hot jet flow-fields. Part 1: aerodynamic analysis,” Proceedings of the 8th AIAA/CEAS Aeroacoustics Conference, No. AIAA 2002-2599, 2002. 45 Biancherin, A., Lupoglazoff, N., G.Rahier, and Vuillot, F., “Comprehensive 3D unsteady simulations of subsonic and supersonic hot jet flow-fields. Part 2: acoustic analysis,” Proceedings of the 8th AIAA/CEAS Aeroacoustics Conference, No. AIAA 2002-2600, 2002. 46 Gavelle, N., Mary, I., Elias, G., and Sagaut, P., “Large eddy simulation of a subsonic hot jet at high Reynolds number,” Proceedings of the 16th AIAA Computational Fluid Dynamics Conference, No. AIAA 2003-3556, 2003. 47 Muller, F., Vuillot, F., Rahier, G., and Casalis, G., “Modal analysis of a subsonic hot jet LES with comparison to the linear stability,” Proceedings of the 11th AIAA/CEAS Aeroacoustics Conference, No. AIAA 2005-2886, 2005. 48 Piccin, O., “CEPRA19: the ONERA large anechoic facility,” Proceedings of the 15th AIAA/CEAS Aeroacoustics Conference, No. AIAA 2009-3303, 2009. 49 Dorey, L.-H., Tess´ e, L., Bertier, N., and Dupoirieux, F., “A strategy for modeling soot formation and radiative transfer in turbulent flames,” Proceedings of the 14th International Heat Transfer Conference, No. IHTC 14-22819, 2010. 50 Dupoirieux, F. and Bertier, N., “The models of turbulent combustion in the CHARME Solver of CEDRE,” Aerospace Lab, Vol. 2, 2011, pp. 1–7. 51 Guillou, F. and Chedevergne, F., “Internal turbine blade cooling simulation: advanced models assessment on ribbed configurations,” Proceedings of the 8th Thermal Engineering Joint Conference, No. AJTEC 2011-44295, 2011. 52 Bodard, G., Bailly, C., and Vuillot, F., “Matched hybrid approaches to predict jet noise by using large-eddy simulation,” Proceedings of the 15th AIAA/CEAS Aeroacoustics Conference, No. AIAA 2009-3316, 2009. 53 Courbet, B., Benoit, C., Couaillier, V., Haider, F., Le Pape, M.-C., and P´ eron, S., “Space discretization methods,” Aerospace Lab, Vol. 2, 2011, pp. 1–14. 54 Smagorinsky, J., “General circulation experiments with the primitive equations,” Monthly Weather Review , Vol. 91, 1963, pp. 99–164. 55 Rahier, G., Prieur, J., Vuillot, F., Lupoglazoff, N., and Biancherin, A., “Investigation of integral surface formulations for acoustic post-processing of unsteady aerodynamic jet simulations,” Aerospace Science and Technology, Vol. 8, 2004, pp. 453–467. 56 Huet, M., Fayard, B., Rahier, G., and Vuillot, F., “Numerical investigation of the micro-jets efficiency for jet noise reduction,” Proceedings of the 15th AIAA/CEAS Aeroacoustics Conference, No. AIAA 2009-3127, 2009. 57 Hussain, A. K. M. F. and Zedan, M. F., “Effects of the initial condition on the axisymmetric free shear layer: Effects of the initial momentum thickness,” Physics Of Fluids, Vol. 21, 1978, pp. 1100–1112. 58 Hussain, A. K. M. F. and Zedan, M. F., “Effects of the initial condition on the axisymmetric free shear layer: Effect of the initial fluctuation level,” Physics Of Fluids, Vol. 21, 1978, pp. 1475–1481. 59 Husain, Z. D. and Hussain, A., “Axisymmetric mixing layer: influence of the initial and boundary conditions,” AIAA Journal, Vol. 17, 1979, pp. 48–55. 60 Bogey, C. and Bailly, C., “Influence of nozzle-exit boundary-layer conditions on the flow and acoustic fields of initially laminar jets,” Journal of Fluid Mechanics, Vol. 663, 2010, pp. 507–538. 61 Michalke, A., “Survey on jet instability theory,” Progress in Aerospace Sciences, Vol. 21, 1984, pp. 159–199. 62 Ahuja, K. K., Lepicovsky, J., Tam, C. K. W., Morris, P. J., and Burrin, R. H., “Tone-excited jet: theory and experiments,” Tech. rep., NASA CR-3538, 1982. 63 Bridges, J. and Wernet, M. P., “Establishing consensus turbulence statistics for hot subsonic jets,” Proceedings of the 16th AIAA/CEAS Aeroacoustics Conference, No. AIAA 2010-3751, 2010. 64 Raman, G., Rice, E. J., and Reshotko, E., “Mode spectra of natural disturbances in a circular jet and the effect of acoustic forcing,” Experiments In Fluids, Vol. 17, 1994, pp. 415–426. 65 Bridges, J. E. and Hussain, A. K. M. F., “Roles of initial condition and vortex pairing in jet noise,” Journal of Sound and Vibration, Vol. 117, 1987, pp. 289–311. 66 Viswanathan, K., “Aeroacoustics of hot jets,” Journal of Fluid Mechanics, Vol. 516, 2004, pp. 39–82. 67 Bogey, C., Marsden, O., and Bailly, C., “Large-eddy simulation of the flow and acoustic fields of a Reynolds number 105 subsonic jet with tripped exit boundary layers,” Physics Of Fluids, Vol. 23, 2011. 68 Zaman, K. B. M. Q. and Hussain, A. K. M. F., “Turbulence suppression in free shear flows by controlled excitation,” Journal of Fluid Mechanics, Vol. 103, 1981, pp. 133–159. 69 Gutmark, E. and Ho, C.-M., “Preferred modes and the spreading rates of jets,” Physics Of Fluids, Vol. 26, 1983, pp. 2932–2938. 70 Morris, P. J., “The instability of high speed jets,” International Journal of Aeroacoustics, Vol. 9, 2010, pp. 1–50.
