Numerical Simulation of the Flow and Sound Field of

Numerical Simulation of the Flow and Sound Field of a Serrated Nozzle D. Eschricht∗, U. Michel† and F. Thiele‡ Berlin University of Technology, Berlin, Germany

M. Rose Rolls-Royce Germany Ltd & Co KG, Dahlewitz, Germany

Nowadays, turbine engines for commercial aircraft use high-bypass-ratio, dual-stream jets to limit the acoustic radiation. Even though a large noise reduction has been achieved since the middle of last century that depends heavily on the increased bypass ratio, additional reduction is sought by modifications to the initial turbulence field behind the nozzle exit. Such modification can be achieved for instance by micro jets, allowing active control, or by geometrical changes to the nozzle lip, i.e serrations. The present paper is concerned with the latter approach. A realistic, long-cowl nozzle configuration with a modified outer nozzle lip has been studied numerically using Detached-Eddy Simulation. The dual-stream configuration is of a high Reynolds and Mach number. For this configuration a noisereducing effect of the serrated nozzle lip was proven experimentally. The work presented here aims at reproducing the noise reduction numerically, and by analysing the numerical flow and noise field, to provide some insight into the physical mechanisms that lead to this noise reduction. The flow field of the configuration with a clean nozzle lip was simulated using the same methodology and a grid of equal resolution for this purpose. This provides the data used for comparison of the two configurations.

Nomenclature ϕ θ D ux ur h·i

Azimuthal angle Polar angle, zero along the positive x-axis Outer jet diameter Axial velocity component Radial velocity component time average

I.

Introduction

Jet noise is a major contributor to aircraft noise especially during take-off. The fact that civil air traffic is ever growing, has led to more restricting noise regulations in the past. Jet engine manufacturers are therefore seeking reliable methodologies that reduce the jet noise, while having only a minimal impact on nozzle thrust. The main concept of jet noise reduction has arised from the work of Lighthill 1 that connected the jet speed with the sound produced by the famous U 8 scaling law. Consequently jet noise can be reduced by reducing the jet exit speed. To maintain the level of thrust at the same time, the mass flux through the nozzle has to be increased. This has lead to the modern jet engines that rely on high bypass-ratio nozzles where the major thrust contribution is obtained by the cold, secondary stream. Although these modern nozzle are much quieter than their counterparts from the 1950s, additional noise reduction concepts are required as the size of the nozzles increases with the bypass ratio. At some point this concept can not be ∗ Research

engineer, [email protected] ISTA, [email protected]; CFD Software GmbH, Berlin, Germany, [email protected] ‡ Professor, ISTA, [email protected]; CFD Software GmbH, Berlin, Germany, [email protected] † Professor,

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driven any further, because of weight and fitting constraints. Other noise reduction concepts are therefore investigated that try to modify the shear layers directly to achieve a noise benefit with no or minimal thrust losses. This can either be achieved by passive means as geometrical modifications to the nozzle lip or by active methods such as microjet injections. Newer efforts to reduce the noise include bevelled nozzles.2 The idea to affect the shear layers by geometrical means is not new. The effects of such nozzle lip modifications on noise and thrust have been experimentally studied for instance by Westley&Lilley 3 in the 1950s. In more recent experiments Saiyed et al.4 studied the effects of serrations attached to the outer and/or inner nozzle lip for high-bypass-ratio engines and found that a noise reduction of about 2.5 EPNdB is possible with only small losses in thrust under cruise conditions. In Bridges&Brown5 experimental results for a short-cowl nozzle are reported where chevrons were placed between core and secondary stream. The chevrons were found to increase the turbulence intensity in the inner shear while reducing the turbulence further downstream where inner and outer shear layer interact. These findings support the explanation of the chevron physics, that chevrons enhance the turbulent mixing in the initial shear layer by increasing the turbulence levels. Due to the therefore increased shear layer thickness the turbulent production is decreased. This again lowers the turbulence further downstream and around the potential core were much of the lower frequency noise is produced. The increased turbulence in the initial shear layer produces more high freqency noise, while the lowered levels further downstream lead to a noise reduction at lower frequencies. This tradeoff between high-frequency penalty and low-frequency benefit makes the design of a chevron nozzle difficult as the overall noise benefit in EPNL depends on the specific design parameter. With the increase in computational power and the improvement of numerical methods in the last decade, the design process can be more and more aided by numerical predictions. Their are a number of approaches for the noise prediction of of jet flows. Methods based on the Reynolds-Averaged Navier-Stokes (RANS) equations require some modelling to cover the turbulence in the flow field and to recover the lost unsteady information for the broad-band noise prediction. Such a method was developed by Tam et al.6–8 and used for single and dual stream jets as well as for non-axisymmetric jets. Depending on the configuration, the agreement with the measured spectra is within 3 dB for the sideline angle θ = 90◦ . A similiar approach was used by Birch et al.9 , who applied an acoustic model to RANS computations of single-stream chevron nozzles that where experimentally investigated by Bridges&Brown 10 and the authors themselves. Although the method was found to work well for clean nozzles, the application to chevron nozzles showed some differences to the experiments at first. The comparison with the experimental data was much enhanced by adding an additional source term to the noise model that accounts for the longitudinal vortices introduced by the chevrons. If such a noise model be can ever be designed to generally work for all, new design concepts is questioned by the authors. A slightly different approach is developed by Ewert 11 called RPM. It also relies on a mean flow field by a RANS computation, but the unsteady noise sources are recovered using a stochasistic realisation of the Tam&Auriault 6 source model. This approach was extended to hot jets by Ewert et al.12 and its application to a nozzle with guide elements at the outer nozzle lip in Ewert&Neifeld 13 showed promising results. However, due to the dependence on a noise source model and a RANS mean flow field, the same arguments against a general applicability hold as before. The just mentioned approaches rely on RANS computations for the mean flow and turbulence field to provide the turbulent intensity and length scale as input for the noise model. If a RANS model can be derived that is generally applicable is another issue of ongoing research. A more promising approach to obtain the flow field information including the unsteadiness of the more complex nozzle design are resolving methods such as Direct-Numerical Simulation (DNS) or Large-Eddy Simulation (LES). While DNS is unfeasible for flows with Reynolds numbers of industrial interest, and will remain so for years to come, LES has already been successfully applied for all kind of jet flows including those with modified nozzle geometries. The first successful, resolved simulation of chevron effects was achieved by Shur et al.14, 15 . Due to limitations of the affordable grid size, the serrations were not explicitly represented in the simulation, their effect on the initial mean flow field was emulated. Yet, the effect on the sound field was captured by the approach. Later, other researchers included the nozzle geometrie in their simulation. Uzun&Hussaini16 studied the near field of a single-stream chevron nozzle of Bridges&Brown 10 using up to 100 million grid points. Similar nozzles were studied by Xia et al.17 using a hybrid RANS/LES approach. The results were further improved using a finer mesh of about 20 million cells in Xia&Tucker 18 . Both the turbulent intensities and the overall sound pressure levels predicted came to a very good agreement with the measurements. The aforementioned work show that LES or hybrid methods can be used to predict the unsteady flow and noise features not only of simple jets but also for more complex geometries. In this work, the effect of

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serrations placed at the outer nozzle lip is studied numerically using another hybrid RANS/LES approach. The Detached-Eddy Simulation (DES) developed by Spalart et al.19 , Shur et al.20 and Travin et al.21 combines grid-saving capabilities in the near wear wall region of the RANS with the unsteadiness of a LES which is to be paid in grid points. Thus allowing a trade-off between available computational resources and the need to get unsteady information for the noise prediction. I.A.

Flow Configuration

The long-cowl nozzles deployed are of a realistic design, including a cold secondary and a hot primary stream as well as a center body. The upstream section of the inner nozzle geometry follows the design used in the experiments. A sketch of the nozzle geometries examined in this work is given in figure 1. The two nozzles are of a similar shape, except at the outer nozzle lip where 20 serrations are attached in the second case (SR). At detailed view of these is given in figure 1(c). Both nozzles are simulated at the same model scale, at which the experiments were conducted, and the same total pressure and temperature parameter at the nozzle inflow are used. The general setup is equivalent to take-off conditions, including a flight stream Mach number of Mf = 0.26 and a flow speed of the secondary, cold stream about Mach number M = 0.93. The Reynolds number resulting from this reference flow speed and the outer nozzle diameter is about 4.6 million. The ratio of the inflow total temperature values is about 2.4.

(a) Clean nozzle (BS)

(b) Serrated nozzle (SR)

(c) Serration detail

Figure 1. Nozzle geometries

For the clean nozzle both PIV and acoustic data is available due to measurements provided by RollsRoyce Germany. For the serrated nozzle, the availabe experimental data is limited to acoustic spectra, which were also acquired by Rolls-Royce Germany and provided during a joint research projecta . The results of the acoustic measurements are shown in figure 2 where the sound field of the clean and serrated configuration are compared in terms of their power spectral densities (PSD) in 1/3-octave bands. This results show a noise reduction for all angles that covers a wide range of frequencies. The maximum reduction is about 2 dB and is most pronounced around the frequency of the peak value. While the frequency increases, the difference between the two configurations decreases until at about St = 5 both configurations reach similar levels. Beyond that frequency, the noise levels of the serrated configuration exceed those of the clean nozzle. This behaviour is attributed to the effect of the serrations on the turbulent shear layer downstream of the nozzle lip. Here, the serrations are thought to increase the small-scale turbulent content, which increases the highfrequency noise accordingly. An additional effect can be observed in the spectra at the low-angle θ = 36◦ in figure 2(a). The frequency of the peak value is about St = 0.28 for the clean nozzle. For the serrated nozzle this value is lower at about St = 0.22. For higher angles from the jet axis, some issues in the measurements can be noted. The spectra show an increase of the noise levels at low frequencies especially for larger angles from the jet axis. This behaviour is visible already at θ = 63◦ in figure 2(b) for the quieter serrated nozzle. At the more sideline position θ = 96◦ in figure 2(c), it can be observed for both configurations, being still more pronounced for the serrated configuration. The effect is explained by reflections from the walls of the anechoic chamber in which the measurements have been conducted. It is thought that for frequencies lower than St = 0.2, the walls can not be seen as being free of reflections.22 The acoustic data is therefore considered to be considerably disturbed by these reflections. a see

Acknowledgments

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Figure 2. Experimental noise spectra for clean (BS) and serrated nozzle (SR)

II. II.A.

Methodology

Flow solver

The flow solver elaN3D solves the Favre-averaged Navier-Stokes equations using the finite volume method. Though the simplicity of the method has drawbacks in terms of numerical accuracy (second order in space and time), the general stability of the method, its conservative nature, the possibility to use grids with local refinement and the lack of a stability-based, upper limit for the time step size, make it still an efficient tool for unsteady flow field predictions. The flow solver solves the unsteady Favre-averaged continuity, momentum and energy equations on structured, multiblock grids. The continuity equation is handled by a pressure correction algorithm (SIMPLE), where a close coupling between the convective velocity and the pressure is achieved by the Rhie and Chow interpolation method23 . Even though the set of equation is solved in its integral form to ensure conservativity, the solved Favre-averaged Navier-Stokes equations are given below in differential form for simplicity. ∂% ∂%uj + =0 ∂t ∂xj ∂%ui ∂%ui uj ∂p ∂σij ∂τij + =− + + ∂t ∂xj ∂xi ∂xj ∂xj   ∂%uj T ∂p ∂ q˙j ∂ui ∂%T ∂p + + uj − + (τij + σij ) + % cp = ∂t ∂xj ∂t ∂xj ∂xj ∂xj

(1) (2) (3)

Here, σij and τij denote the molecular and the Reynolds stress tensor, respectively, while cp is the specific, isobaric heat capacity. The temperature diffusive flux q˙j is modelled similar to Fick’s law containing a t) molecular and turbulent heat flux q˙j = cp (µ+µ PrT ∂T /∂xj . The two stress tensors are defined as    2  1 1  ∂uj ∂ui  1 + σij = 2µ Sij − Skk and τij = 2µt Sij − Skk − %kδij , with Sij = 3 3 3 2 ∂xi ∂xj

(4)

where the definition of the Reynolds stresses τij follows the ansatz of Boussinesq.24 To avoid reflections from the boundaries, non-reflective boundary conditions based on Bogey et al.25, 26 have been implemented. Near outflow boundaries an additional buffer zone following Freund27 is employed. II.B.

Turbulence modelling

For a complete system of equations, the turbulent kinetic energy k and the turbulent viscosity µt have to be modelled. The turbulence model used in the DES formulation used here is based on the Wilcox k-ω model,

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which writes   ∂ µt  ∂k ∂%k ∂%uj k + = µ+ + %Pk − cµ %kω ∂t ∂xj ∂xj σk ∂xj   ∂%ω ∂%uj ω ∂ µt  ∂k ω + = µ+ + cω1 % Pk − cω2 %ω 2 ∂t ∂xj ∂xj σω ∂xj k k µt = ρνt = % ω

(5) (6) (7)

p where the production term of the turbulent kinetic energy equation is defined as Pk = νt 2Sij Sij . The DES modifications of the model are applied to the last term of eq. (5) which is the dissipation term and to the equation for the turbulent viscosity eq. (7), where an associated length scale L = LRANS = k 1/2 /cµ ω is inserted. The modification of the turbulent viscosity equation was described by Yan et al28 and aims at reducing the grey area problem by accelerating the switch from RANS- to LES-mode. The modified equations become √ %k 3/2 (8) cµ %kω = Dk = and µt = %cµ L k . L So far no changes have been made to the model, the equations are still similar to the modelling equations used in RANS and URANS applications. To insert a dependency on the grid spacing that allows the model to discern between resolved and unresolved regions in the flow, the length scale L is made a function of the local grid spacing ∆. L = min(CDES ∆, LRANS ) (9) Note that in the originial DES formulation29 , the grid-dependend length scale L acts only on the dissipation term Dk in the turbulent, kinetic energy equation. The dissipation term is thus enlarged and the turbulent kinetic energy k reduced. Due to the relation of the viscosity µt and k, µt is reduced along with k. The speed of that reduction depends on the ratio of L and LRANS . The finer the grid, the smaller becomes L and the larger does the dissipation term become. This relation leads to grey area problem at the passage from RANS- to LES-mode region, because larger values of k may be convected into the LES region of the flow where its reduction takes some time along a stream line. Due to the yet large viscosity flowing in from upstream, the model is neither fully in LES- nor in full RANS-mode. In jet flows, this problem occurs in the vicinity of the nozzle lip, where part of the initial shear layer can remain in RANS-mode, due to a lack of grid resolution which would solve the problem. For jet flows, the problem is further enhanced by the lack of recirculation in this region. The reduced values of k further downstream do therefore not influence the upstream values, which is the case in blunt body flows. The additional insertion of L into the visocity equation reduces this problem, as the turbulent viscosity is now directly linked to the grid-dependend length scale via eq. (8). The passage to LES-mode is further accelerated by the fact that the production term of the k-equation is directly proportional to the turbulent viscosity. The grid-dependend length scale acts therefore not only on the dissipation but also on the production term of the k-equation. From the work of other researchers who do simulations of jet flow, one can draw the conclusion that a reduction of the modelled viscosity often improves the results. In LES simulations of a coaxial nozzle by Andersson et al30 , the definition of ∆ was reduced from ∆ = (∆x ∆y ∆z )1/3 to ∆ = min(∆x , ∆y , ∆z ). This showed an improving effect on the development of the initial shear layer. Bogey et al31 studied the effects of the subgrid scale model in simulations of round jets that where done with and without subgrid scale model. It was found that the subgrid scale model changed the effective Reynolds number in the simulation, and that therefore best results where achieved when only selective filtering was used. Similar observations were made by Shur et al.14, 32 This approaches, also known as implicit LES, is used by a number of researchers for the simulation of jet flows16, 18 . For DES as well as for LES, the most common definition of the grid scale ∆ is ∆ = max(∆x , ∆y , ∆z ). In this case the largest, local grid spacing defines what structure size is resolved by the mesh, and thus the length scale of the model. In cases of blunt body flows for which the DES has originally been developed, the hydrodynamic instability is much stronger and of a larger scale than in jet flows. Even the diffusivity of a full RANS-model is not able to suppress that instability. For such cases a fully converged RANS solution can seldomly been obtained at higher Reynolds numbers. Jet flows however are quite stable in such a RANS simulation even if the Reynolds numbers are high. From this one can conclude that the instability of the shear layer is easily suppressed by the additional viscous terms added by the RANS model. Inside the initial 5 of 14 American Institute of Aeronautics and Astronautics

shear layer this problem is especially important, as the development of the structures here affects their further development and the properties of the downstream turbulent shear layer. The initial shear layer is the location in the flow where the smallest structures in the simulation appear. Hence, the issue of to much damping becomes most apparent in this location, independent of the model used being LES, DES or implicit LES. In the present DES the original definition of Andersson et al 30 that was also used by Yan et al 33, 34 is therefore applied. ∆ = (∆x ∆y ∆z )1/3 (10) Even if its usage is questioned in both the LES and the DES community (as for instance noted by Spalart 35 ), it provides a means to reduce the modelled viscosity in the initial shear layer without having to use a zonal definition. In regions further downstream the jet where cell aspect ratios become lower, its value becomes close to the original max(. . . ) definition. II.C.

Numerical grid

The grid used for both simulations includes the inner nozzle and begins at x = −4D. Downstream of the nozzle it extends axially up to x = 65D and radially up to r = 18D. The numerical mesh of the near nozzle region is depicted in figure 3(a). Radial mesh lines are concentrated inside regions where they are needed to resolve the flow features, namely the near wall regions which become the shear layers once the flow gets of the nozzle. To resolve the wall boundary layers y + < 4 is ensured by the wall-normal grid spacing of the first cell. The axial grid spacing of the jet region begins at x = 0D with ∆x = 0.0024D and grows with a stretching ratio of 1.015 in the downstream direction up to x = 2.5D. From here on the axial spacing remains constant at ∆x = 0.04D up to x = 10D. A mild grid stretching is applied again in the downstream direction towards the outflow boundary, leading to a number of axial cells Nx = 538 in the jet-flow region. For the nozzle with serrations, 20 serrations are attached to the outer nozzle lip. In an earlier work36 a resolution of 16 cells per serration was found insufficient to deliver a good agreement with acoustic measurements. In this study the azimuthal resolution has therefore been increased to 32 cells per serration. To keep the overall number of cells for the simulations as low as possible, the high number of azimuthal cells Nϕ = 640 is only used in the outer shear layer up to x = 3D. In figure 3(a) regions of different azimuthal resolution are shown in different colours.

(a) Grid layout in the xr-plane, colours stand for different azimuthal resolution

(b) Wall and near nozzle grid

Figure 3. Grid structure

The full, 3D grid is obtained by rotation of a 2D grid in the xr-plane. To avoid highly deformed cells at the axis, the near-axis region of the rotated grid is replaced by a quadratic block. After adding the local, azimuthal refinement, the overall grid size is 52 million cells. The difference between clean and serrated nozzle in terms of the acoustic far-field spectra is about 2 dB at the maximum. To recover these small changes in the simulations, effects of the inevitable numerical error should be minimized. The grid for the serrated nozzle is therefore a copy of the clean-nozzle grid, except for small region near the nozzle lip, where the shape of the serration is introduced by a transformation algorithm. The actual number of cells remains thereby unchanged. A picture of the grid in this region is given in figure 3(b). It shows the mesh on the nozzle wall as well as in a xr-plane of the mesh. The xr-plane shown is one where the transformation algorithm creates the largest changes. Due to the serrations being relatively small compared to the nozzle diameter, no stronlgy deformed cells are created by the transformation algorithm. 6 of 14 American Institute of Aeronautics and Astronautics

II.D.

Far-field prediction

The unsteady flow-field data acquired during the simulation, was used to predict the far-field noise by means of the acoustic analogy of Ffowcs-Williams&Hawkings37 (FWH). The acoustic solver calculates the time series of the acoustic pressure at a given location xi by solving a solution to the FWH-equation which was given by Farassat38, 39 and is usually refered to as Formula 1A: # Z " %o (U˙ n + Un˙ ) %o Un (rM˙ r + co Mr − co M 2 ) dS + 4πp(xi , t) = r(1 − Mr ) r2 (1 − Mr )3 S ret # (11) Z "˙ 1 Lr + co r(Lr − LM ) Lr (rM˙ r + co Mr − co M 2 ) + + dS co S r(1 − Mr )2 r2 (1 − Mr )3 ret

using the notations Ui = vi + (%/%o )(ui − vi ) in the thickness noise term and Li = (pδij + %ui (uj − vj ))nj in the loading noise term. Here, %o denotes the reference density in the ambient field, vi is the velocity of the surface and Mi = co vi the surface Mach number based on the reference sound speed co . A subscript denotes a scalar product with either the surface outer normal, unit vector ni or the unit radiation direction vector rˆi . The acoustic analogy solver uses the source-time-dominant algorithm proposed by Brentner40 .

III.

Results

A first impression of the developing flow field in the two configurations is provided by figure 4. The vortex structures in the vicinity of the outer nozzle lip are visualised by iso-surfaces of the λ2 -vortex criterion41 at a value of λ2 = − 108 . The resulting iso-surfaces are coloured by the local, time-averaged ratio of the modelled, turbulent viscosity µt and the molecular viscosity µ. This value gives an idea of the turbulence model influence in the simulations. For both simulations presented here it is about two orders of magnitude lower than that of a RANS-simulation of the same configuration. This leaves the shear layer free to develop small scale turbulent content. Note that the use of the DDES keeps the near wall region in RANS mode and thus prohibits the development of turbulence inside the wall boundary layer. Furthermore, due the grid size used and the high Reynolds number of the flow, the development of such turbulence is not be expected independent of the model used. The initial shear layer has to become turbulent by itself as no forcing of the shear layer instability is used. This natural transition occurs rather quickly in case of the clean nozzle in the lower half of the figure. The flow develops wave-like structure very close to the nozzle. At x = 0.3D the flows is already turbulent. Note that in earlier simulations36, 42 of this configuration this intial region was dominated by ring-like structures. Especially the increased number of grid points in azimuthal direction which is more than five times higher than in this earlier works, allows such structures to develop. The flow behaves a little different for the serrated configuration. The serration points slightly into the secondary stream. The flow is therefore deflected radially inwards following the shape of the serration. Between each two of the serrations, a strong radial component develops that reaches about 11% of reference velocity as is shown in figure 5. Due to this, a forced axial vorticity component is developed which is absent in the clean nozzle flow field. Inside this zone of axial vorticity, vortex structures appear immediately at the serration. The existence of the axial vorticity in the mean flow can be further be observed in figure 5 where additional to the time-averaged, radial velocity contours, projected streamlines are displayed. Due to fact that the planes shown are axial planes, the streamlines have been calculated by omitting the axial velocity component. Thus showing a virtual flow inside these axial planes. These streamlines show the entrainment from the ambient as well as the formation of the axial vorticity regions. III.A. III.A.1.

Clean nozzle vs. experiment Flow field

For the clean nozzle PIV data exists, where axial and radial velocities in an xr-plane have been acquired. This data was provided by Rolls-Royce Germany. The simulation results for the clean nozzle configuration is compared to the PIV data in figures 6 and 7. The first figure shows radial profiles of the axial velocity component along with the PIV data at various positions along the jet axis. The agreement with the measurements is of a mixed type. The maximum velocities for primary and secondary stream agrees well with the measurements at all location. The same can be said about the outer shear layer where the profile is in 7 of 14 American Institute of Aeronautics and Astronautics

Figure 4. Instantaneous vortex structures near the nozzle lip (λ2 = −108 ), color by time-averaged ratio of modelled and molecular viscosity hµt /µi; black symbols mark every ∆x = 1/2 D

Figure 5. Contours of the time-averaged, radial velocity component in axial planes at x = 1/8D, x = 1/4D, x = 1/2D and x = 3/4D with projected streamlines

very good agreement with the measurements at x = 1D. The good agreement in the outer region remains for all the positions shown. A difference appears at the inner shear layer where the PIV data shows a much thicker shear layer than the DES. This difference remains until at about x = 4 − 5D inner and outer shear layer begin to interact. From here on the difference becomes the smaller as one moves downstream leading to a good agreement at x = 8D. 0.8

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Figure 6. Staggered, radial profiles of the time-averaged, axial velocity component for the clean nozzle in comparison with experimental data (PIV); for x = 1D – 9D with ∆x = 1D, staggering by 0.4 · (x/D − 1) · hux i/uref

Figure 7 shows components of the Reynolds stress tensor also in terms of staggered, radial profiles at different axial positions. As the simulation relies on a natural transition to turbulence in the shear layers, turbulent structures do not appear until x = 0.3D. The delay in transition results at first in augmented turbulence levels, which is visible in figure 7 for the leftmost lines (x = 1D) in the outer shear layer (r = 0.5D). This augmentation subsides quickly, and and the levels found further downstream for the outer shear layer agree well with the measurements for both hu0x u0x i and hu0x u0r i. The major differences between simulation and experiment appear again in the inner shear layer. Upstream of x = 4D nearly no turbulent content can be observed in the simulation. Beginning at x = 4D (fourth line from the left) an augmentation of the turbulence levels in the inner shear layer is observed. Due the relatively small thickness of this layer, the present grid does not provide sufficient resolution to resolve the turbulent structures upstream of that position properly. The thinness of the inner shear layer in the simulation may have an additional influence on this behaviour. Still, the augmentation subsides again, and after outer and inner shear layer have merged

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(b) hu0x u0r i Figure 7. Staggered, radial profiles of Reynolds stress components for different axial positions in comparison with experimental data (PIV); for x = 1D – 9D with ∆x = 1D, staggering by 0.02 · (x/D − 1) · hu0i u0j i/u2ref

at about x = 7D, the turbulence levels found in the simulation are in a fair agreement with the experiment. In the context of the Reynolds- or Favre-averaged momentum equation, the term hu0x u0r i accounts for the mixing of axial momentum in the radial direction. The good agreement of this term in the outer shear layer as shown figure 7(b) explaines to good agreement of the velocity profiles in this region. Yet, in the same time-averaged context the mean flow gradient appears in the production term of the turbulent, kinetic energy. Thus, one can not exist without the other. Similar arguments hold for the behaviour of the inner shear layer. The lack of turbulent mixing upstream of x = 4D accounts for this shear layer having a too small radial extent. Turbulent mixing in this region is neither provided by resolved turbulence nor by the underlying RANS model which considers the inner shear layer to be in LES mode. This seems to be a variant of the modeled-stress depletion, as it was named by Spalart et al.43 , where the grid is fine enough to affect the RANS/LES length scale exchange, while being to coarse to allow the accurate representation of small scale turbulence. However, between x = 5D and x = 7D the DES shows larger values for hu0x u0r i in the inner shear layer which makes the velocity profiles in this region to gain some of the missing thickness. III.A.2.

Far-field sound

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Figure 8. Comparison of the acoustic power spectral density from the DES/FWH approach for the clean nozzle with experiments, 1/3-octave bands

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Although there is a general agreement with the measurements, some difference must be noted. At the lower angle in figure 8(a), the lower frequencies lack some acoustic content of about 4 dB, while the higher frequencies show augmented levels if about 3 dB. This is attributed to the behaviour of the inner shear layer in the simulation. In fact we found a similar behaviour in an earlier simulation42 of that nozzle on a coarser mesh. Especially the augmentation at higher frequencies tends to be lowered and moved to higher frequencies with a refined mesh in the grid section 3D < x < 10D. Some under-prediction of noise levels at low frequencies is also present at higher angles. Though aforementioned issues seen in the measurements make an exact evaluation difficult. But we suspect that at least some part of the under-prediction at θ = 63◦ and θ = 91◦ is connected to the same reasons of noise missing at θ = 36◦ . The mid-range frequencies are in good agreement with the measurements. A sharp cut-off in the noise levels is observed at about St = 3 for the lower two angles. At the sideline angle it appears more gradual. Similar to other researcher we associate this with numerical dissipation by the grid spacing of the mesh. The sharper cut-off at the two lower angles supports this assumption as the axial grid spacing is much coarser than the radial. Sound waves traveling in the axial direction are therefore more affected by numerical dissipation than sound waves propagating radially. III.B.

Clean nozzle vs. serrated nozzle

III.B.1.

Flow field

Given that no experimental data for the flow field is available for serrated nozzle, the DES results can only be compared to the results obtained for the clean nozzle. As special care was taken to have very similar numerical meshes in terms of all grid spacings, a difference appearing between both simulations is therefore attributed to effects of the serrations on the flow. Figure 10 compares the correlation of the axial velocity component obtained for the two configurations. As the flow from the modified nozzle is no longer axisymmetric, the results differ between different aziumthal locations. To give a clearer picture of the behaviour of the serrated nozzle, radial profiles were extracted for notch and apex positions and named as depicted in figure 9. Similar to the azimuthal average procedure that was used for the far-field spectra, data is extracted for all twenty notches and apexes, and averaged to improve the statistics. 9. Position of raAt the location x = 1D, which is close to nozzle, the flow field is directly affected Figure dial profiles by the serrations. As mentioned earlier, an radially outwards directed flow develops behind notches, while the flow is directed inwards behind apexes. The radial position of the shear layer follows this redirection, as can be observed from the different radial positions of the peak values. Closer inspections reveals that radial the extent of the turbulent region is larger at both azimuthal positions than it is for the clean nozzle. The peak value behind the apex is slightly larger than that of the clean nozzle. Note, the levels at x = 1D of the clean nozzle simulation are larger than what the PIV data suggest.

0.8

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,

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/uref

(e) x = 8D

Figure 10. Comparison of radial profiles of hu0x u0x i from the DES of clean (BS) and serrated (SR) nozzle

The direct differences between apex and notch positions remain only visible for the first three diameters behind the nozzle. As figure 10(b) suggests, the turbulent mixing taking place along the way makes both

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positions overlap at x = 3D. The peak levels found at this position are considerably lower for the serrated configuration than observed for the clean nozzle. Similar observations are made at x = 5D. The effects of nozzle are limited to the outer shear layer for the first diameters. At about x = 4 − 5D inner and outer shear layer start to interact. As a consequence, the inner shear layer is affected by the lower turbulence levels found upstream in the outer shear layer. As shown in figures 10(d) and 10(e), the differences between the two simulations become weaker in the radially outer region, while differences in the inner region appear.

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(b) x = 3D

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Figure 11. Comparison of radial profiles of

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(d) x = 6D

(e) x = 8D

hu0r u0r i

0.01

from the DES of clean (BS) and serrated (SR) nozzle

From the correlation of the radial velocity component very similar observations can be made. Yet, the increase in the turbulence levels already observed close to the serrated nozzle is more pronounced than for axial velocity correlation. Apart from that, the decrease of the turbulence levels in the outer shear layer followed by an decrease extended to the inner layer is clearly observed. It must be noted that in the present simulation the ratio of u2r /u2x does not change in favour for ur in the interaction region of inner and outer shear layer. Such a behaviour was experimentally identified by Bridges&Wernet 5 . Even though in their experiment the inner nozzle lip instead of the outer one was modified by chevrons, one would not expect the interaction of an axisymmetric and a modified shear layer to become completely difference when these two are exchanged. Though it must be noted that in the present simulations the largest difference with respect to the experiments appear inside this interaction zone. III.B.2.

Far-field sound

The far-field results for the serrated nozzle are obtained using the same methodology as described earlier for the clean nozzle. The resulting power spectral densities are displayed in figure 12. For the differences at the lower angle θ 36 ◦ similar differences are observed as for the clean nozzle. The levels calulated at low frequencies show some lack of noise, while at higher frequencies an over-prediction occurs. With the same behaviour of the inner shear layer, a similar difference between simulation and experiments in the interaction region is expected, which leads to the similarly augmented sound field. Comparison with the experiments much improves for higher angles. Surprisingly, a good agreement with the measurements is observed up to St = 5. The cut-off following beyond, is just visible in figures 12(b) and 12(c). The disturbance in the measurements is more pronounced in this more silent case, which becomes visible by the noise levels going upwards for frequencies St < 0.2. For this configuration these issue in the measurements seems almost fully responsible for the difference between noise experiments and numerical prediction.

IV.

Summary and Conclusion

Even if differences between the present numerical prediction and the measurements exist, the comparison of these numerical predictions of clean and serrated nozzle in figure 13 shows that noise reducing effect of the serrations can be successfully predicted by the used methodology of coupled DES/FWH approach. The major differences between numerics and experiment in the noise field appears to be in the low frequency range at low angles. By comparison of the flow field with the PIV data available, the numerical represention of the inner shear layer and the interaction zone of outer and inner shear layer were idendified to be the origin of said difference. These issues will have to be adressed in future work by either refinement of the mesh in 11 of 14 American Institute of Aeronautics and Astronautics

0

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St

(a) θ = 36◦

Exp, SR DES/FWH, SR 1

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St

(b) θ = 63◦

(c) θ = 91◦

Figure 12. Comparison of the acoustic power spectral density from the DES/FWH approach for the clean nozzle with experiments, 1/3-octave bands

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the inner shear layer region or by zonally fixing the DES in RANS mode inside the nozzle at the inner shear layer. With this issues adressed, the difference between the two simulations will slighly increase to match the experimental noise reduction even better. Another feature of interest is high-frequency penalty observed in the experiments for frequencies St > 5. The present grid clearly can not capture this high frequencies. Yet, an augmentation of high frequencies is found in the simulated sound field of the serrated nozzle. The facts that it appears at a too low frequency compared to the measurements and that the noise levels beyond that frequency are lower than the experiments for the clean nozzle, point more on issues with the clean nozzle.

DES/FWH, BS DES/FWH, SR

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-50

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5

DES/FWH, BS DES/FWH, SR

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St

(b) θ = 63◦

1

5

St

(c) θ = 91◦

Figure 13. Comparison of acoustic power spectral density from the DES/FWH approach for both clean (BS) and serrated nozzle (SR), 1/3-octave bands

Acknowledgments This work was carried out in the project Optitheck funded by Rolls-Royce Germany and the German Federal Ministry of Economics and Technology. The simulation results have been achieved on the systems of the North-German Supercomputing Alliance (HLRN-II). The authors want to thank Rolls-Royce Germany for providing the PIV and the experimental, acoustic data as well as all members of the research group for the helpfull discussions on simulation results and experiments.

References 1 Lighthill, M., “On Sound Generated Aerodynamically, I: General Theory,” Proceedings of the Royal Society London, Vol. A221, 1952, pp. 564–587. 2 Viswanathan, K., Spalart, P., Czech, M., Garbaruk, A., and Shur, M., “Tailored Nozzles for Jet Plume Control and Noise Reduction,” AIAA Paper 2011-2788 , 2011. 3 Westley, R. and Lilley, G., “An investigation of the noise field from a small air jet and methods for its reduction,” Tech. Rep. 53, The College of Aeronautics, Cranfield, 1952. 4 Saiyed, N., Mikkelsen, K., and Bridges, J., “Acoustics and Thrust of Separate-Flow Exhaust Nozzles With Mixing Devices for High-Bypass-Ratio Engines,” Tech. Rep. TM-2000-209948, NASA, 2000. 5 Bridges, J. and Wernet, M., “Turbulence Measurements of Separate Flow Nozzles with Mixing Enhancement Features,” AIAA Paper 2002-2484 , 2002.

12 of 14 American Institute of Aeronautics and Astronautics

6 Tam,

C. and Auriault, L., “Jet Mixing Noise from Fine–Scale Turbulence,” AIAA Journal, Vol. 37, No. 2, 1999, pp. 145–

153. 7 Tam, C. and Pastouchenko, N., “Noise from Fine-Scale Turbulence of Nonaxisymmetric Jets,” AIAA Journal, Vol. 40, No. 3, 2002, pp. 456–464. 8 Tam, C. and Pastouchenko, N., “Fine Scale Turbulence from Dual Stream Jets,” AIAA Paper 2004-2871, 10th AIAA/CEAS Aeroacoustics Conference, Manchester, U.K., 2004. 9 Birch, S., Lyubimov, D., Maslov, V., and Secundov, A., “Noise prediction for chevron nozzle flows,” AIAA Paper 20062600 , 2006. 10 Briges, J. and Brown, C., “Parametric testing of chevrons on single flow hot jets,” AIAA Paper 2004-2824 , 2004. 11 Ewert, R., “RPM - the fast Random Particle-Mesh method to realize unsteady turbulent sound sources and velocity fields for CAA applications,” AIAA Paper 2007-3506 , 2007. 12 Ewert, R., Neifeld, A., and Wohlbrandt, A., “A three-parameter Langevin model for hot jet mixing noise prediction,” AIAA Paper 2012-2238 , 2012. 13 Ewert, R. and Neifeld, A., “On the Contribution of Higher Azimuthal Modes to the Near- and Far-Field of Jet Mixing Noise,” AIAA Paper 2012-2114 , 2012. 14 Shur, M., Spalart, P., and Strelets, M., “Noise prediction for increasingly complex jets. Part II: Applications,” International Journal of Aeroacoustics, Vol. 4, No. 3–4, 2005, pp. 247–266. 15 Shur, M. L., Spalart, P., Strelets, M., and Garbaruk, A., “Further steps in LES-based noise prediction for complex jets,” AIAA Paper 2006-485 , 2006. 16 Uzun, A. and Hussaini, M., “Simulation of Noise Generation in Near-Nozzle Region of a Chevron Nozzle Jet,” AIAA Journal, Vol. 47, No. 8, 2009, pp. 1793–1810. 17 Xia, H., Tucker, P., and Eastwood, S., “Large-eddy simulations of chevron jet flows with noise predictions,” International Journal of Heat and Fluid Flow , Vol. 30, No. 6, 2009, pp. 1067–1079. 18 Xia, H. and Tucker, P., “Numerical Simulation of Single-Stream Jets from a Serrated Nozzle,” Flow Turbulence Combust, Vol. 88, No. 1–2, 2012, pp. 3–18. 19 Spalart, P., Jou, W.-H., and Allmaras, S., “Comments on the feasibility of LES on wings and on a hybrid RANS/LES approach,” Advances in DNS/LES , edited by C. Liu and Z. Liu, Greyden Press, Proceedings of 1st AFOSR International Conference on DNS/LES, Ruston, LA, 4–8 August, 1997, pp. 137–147. 20 Shur, M., Spalart, P., Strelets, M., and Travin, A., “Detached-eddy simulation of an airfoil at high angle of attack,” Engineering Turbulence Modelling and Experiments 4 , edited by W. Rodi and D. Laurence, Elsevier, 1999, pp. 669–678. 21 Travin, A., Shur, M., Strelets, M., and Spalart, P., “Detached-Eddy Simulations Past a Circular Cylinder,” Flow, Turbulence and Combustion, Vol. 63, 2000, pp. 293–313. 22 B¨ ohning, P., private communications, 2011. 23 Rhie, C. and Chow, W., “Numerical study of the turbulent flow past an airfoil with trailing edge seperation,” AIAA Journal, Vol. 21, 1983, pp. 1525–1532. 24 Boussinesq, J., “Th´ ´ eorie de l’Ecoulement tourbillant,” Pr´ esent´ es par Divers Savants, Acad. Sci. Inst. Fr., Vol. 23, 1877, pp. 46–50. 25 Bogey, C. and Bailly, C., “Three-dimensional non-reflective boundary conditions for acoustic simulation: far field formulation and validation test cases,” Acta Acoustica, Vol. 88, 2002, pp. 463–471. 26 Bogey, C., Bailly, C., and Juve, D., “Noise Investigation of a High Subsonic Moderate Reynolds Number Jet Using a Compressible Large Eddy Simulation,” Theoret. Comput. Fluid Dynamics, Vol. 16, 2003, pp. 273–297. 27 Freund, J., “Proposed Inflow/Outflow Boundary Condition for Direct Computation of Aerodynamic Sound,” AIAA Journal, Vol. 35, No. 4, 1997, pp. 740–742. 28 Yan, J., Mockett, C., and Thiele, F., “Investigation of Alternative Length Scale Substitutions in Detached-Eddy Simulation,” Flow, Turbulence and Combustion, Vol. 74, 2005, pp. 85–102. 29 Travin, A., Shur, M., Strelets, M., and Spalart, P., “Physical and numerical upgrades in the Detached-Eddy Simulation of complex turbulent flows,” Advances in LES of complex flows, edited by R. Friedrich and W. Rodi, Kluwer Academic Publishers, 2002, pp. 239–254. 30 Andersson, N., Eriksson, L., and Davidson, L., “LES Prediction of Flow and Acoustic Field of a Coaxial Jet,” AIAA Paper 2005-2884, 11th AIAA/CEAS Aeroacoustics Conference, Monterey, CA, 2005. 31 Bogey, C. and Bailly, C., “Decrease of the Effective Reynolds Number with Eddy-Viscosity Subgrid-Scale Modeling,” AIAA Journal, Vol. 43, No. 2, 2005, pp. 437–439. 32 Shur, M., Spalart, P., and Strelets, M., “Noise prediction for increasingly complex jets. Part I: Methods and Tests,” International Journal of Aeroacoustics, Vol. 4, No. 3–4, 2005, pp. 213–246. 33 Yan, J., Tawackolian, K., Michel, U., and Thiele, F., “Computation of Jet Noise using a Hybrid Approach,” AIAA Paper 2007-3621, 13th AIAA/CEAS Aeroacoustics Conference, Rome, Italy, 2007. 34 Yan, J., Panek, L., and Thiele, F., “Simulation of jet noise from a long-cowl nozzle with serrations,” AIAA Paper 2007-3635, 13th AIAA/CEAS Aeroacoustics Conference, Rome, Italy, 2007. 35 Spalart, P., “Detached-Eddy Simulation,” Annu. Rev. Fluid Mech., Vol. 41, 2009, pp. 181–202. 36 Eschricht, D., Panek, L., Yan, J., Michel, U., and Thiele, F., “Jet Noise Prediction of a Serrated Nozzle,” AIAA Paper AIAA-2008-2971, 14th AIAA/CEAS Aeroacoustics Conference, Vancouver, Canada, 2008. 37 Ffowcs Williams, J. and Hawkings, D., “Sound Generated by Turbulence and Surfaces in Arbitrary Motion,” Philosophical Transactions of the Royal Society, Vol. A264, 1969, pp. 321–342. 38 Farassat, F., “The prediction of helicopter rotor discrete frequency noise,” Vertica, Vol. 7, No. 4, 1983, pp. 309–320. 39 Farassat, F., “Derivation of Formulations 1 and 1A of Farassat,” Tech. Rep. NASA TM–2007–214853, NASA Langley Research Center, Hampton, VA, USA, 2007.

13 of 14 American Institute of Aeronautics and Astronautics

40 Brentner,

K., “Numerical Algorithms for Acoustic Integrals - the Devil is in the Details,” AIAA Paper 96-1706 , 1996. J. and Hussain, F., “On the identifiction of a vortex,” J. Fluid Mech., Vol. 285, 1995, pp. 69–94. 42 Eschricht, D., Michel, U., and Thiele, F., “The Effect of Grid Refinement on Jet Noise Predictions Based on DetachedEddy Simulation,” Polish National Fluid Dynamic Conference, KKMP, Poznan, Poland, 2010. 43 Spalart, P., Deck, S., Shur, M., Squires, K., Strelets, M., and Travin, A., “A new version of detachededdy simulation, resistant to ambiguous grid densities,” Theor. Comp. Fluid Dyn., Vol. 20, 2006, pp. 181–195. 41 Jeong,

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