Experimental and Numerical Investigation of the Near

Field Pressure of a High Subsonic Hot Jet

F. Muller∗ and F. Vuillot† and G. Rahier‡

ONERA, Chatillon, France

G. Casalis§ and E. Piot¶

ONERA, Toulouse, France

The near field of a hot subsonic jet is explored through a modal decomposition of thepressure. This modal analysis is performed from pressure fields obtained both experimen-tally and numerically. Experimentally, an azimuthal array of twenty microphones is usedto measure the near field pressure of the jet. The numerical part of the study consistsof the azimuthal decomposition of the near field pressure of a Large Eddy Simulation. Alinear stability analysis based on the so called PSE (Parabolized Stability Equations) is alsoperformed to compute the pressure modes in the near field of the jet.

The shape of the spectra obtained by the LES in the near field for axial positions non-dimensionalized by the potential core length is in good agreement with the experimentalones (with a constant overestimation of about 8 dB/Hz). In the same manner, the axialevolution of the pressure modes from the LES is similar to the one obtained experimentally.

The study based on the PSE also shows a good agreement with the modal analysis ofthe LES except in the region where the perturbation is spatially damped. This is believedto be due to important non linear interactions between modes.

Nomenclature

cj sound velocity inside the jet flow at the nozzle exitco ambient sound speedDj jet diameterLc potential core lengthM Mach number based on the ambient speed of soundm azimuthal mode numberMj local Mach number at the nozzle exitRe Reynolds number based on the jet diameter and the jet velocity at the nozzle exitSt Strouhal number based on the jet diameter and jet velocity at the nozzle exitTj jet static temperature at the nozzle exitUj jet velocity at the nozzle exit

I. Introduction

Large Eddy Simulation seems to be a very promising tool to compute jet noise with the growing compu-tational power available, but most of the LES conducted for high Reynolds number jets (see Shur et al.,1,2

Andersson et al.3,4) jets have difficulties to recover absolute far field noise levels. For instance the numericalprocedure used for the present study has been shown to systematically overestimate the noise levels in thefar field by about 5 − 7dB.5,6, 7 Although this methodology does not catch the absolute levels, one canlegitimately wonder if the physic contained in the simulation is realistic or not, and if one can use thesesimulations to gain insight into jet noise generation mechanisms. This is what is suggested in the present

∗PhD Student, Department DSNA, frederic.muller@onera.fr†Deputy head, Department DSNA, Francois.Vuillot@onera.fr‡Research Engineer, Department DSNA, Gilles.Rahier@onera.fr§Research Engineer, Department DMAE, Gregoire.Casalis@onecert.fr¶PhD Student, Department DMAE, Estelle.Piot@onera.fr

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12th AIAA/CEAS Aeroacoustics Conference (27th AIAA Aeroacoustics Conference)8 - 10 May 2006, Cambridge, Massachusetts

AIAA 2006-2535

Copyright © 2006 by the American Institute of Aeronautics and Astronautics, Inc. All rights reserved.

study. Particularly, the modal structure of the computed jet is explored in order to determine if it is realisticenough.

Dj [m] 0.08 Re 400,000Mj = Uj/cj 0.7 c∞[m/s] 335.M = Uj/c∞ 1.2 u∞[m/s] 0.0

uj [m/s] 410 p∞[Pa] 101325Tj [K] 830 Tj/T∞ 2.96

Table 1. Jet characteristics

This paper deals with a high Reynolds subsonic hot jet (see table 1). Note that, although the jet is locallysubsonic (Mj = Uj/cj = 0.7) due to the high temperature at the nozzle exit, it is supersonic compared tothe ambient sound speed (M = Uj/c∞ = 1.2), therefore a Mach wave radiation mechanism is expected.The nozzle is included in the simulation but it is important to notice that no attempt was made to resolvethe nozzle boundary layer (it would be far too expensive). The reason for including the nozzle into thesimulation is only to avoid special treatment at the inlet boundary condition such as external forcing (moredetails about the numerical procedure can be found in Lupoglazoff et al.,5 Biancherin et al.8,9 and Mulleret al.10).

This study is based on three different approaches for determining the modal structure of the near fieldpressure:

• decomposition of the experimental near field pressure by applying a double Fourier transform in fre-quency and into the azimuthal direction,

• decomposition of the pressure field computed by the LES by applying the same procedure,

• use of the PSE (Parabolized Stability Equations) based on the mean flow provided by the LES tocompute the pressure modes in the linear approach.

The results of the first (experimental) approach is taken as a reference to validate the two others. Thesecond approach was performed by the first author and presented in more details in Muller et al.10 Thethird approach was developed and applied on this jet by E. Piot from the DMAE department of ONERAToulouse and will be described in more details in a paper submitted for the present conference in Piot etal.11

II. Experimental procedure

Both acoustic (near and far field) and aerodynamic fields were explored during the experimental campaign.Aerodynamic field measurements were performed using a five holes probe for eight axial locations (see figure2). Some measurements have been conducted very close to the nozzle (at x/D = 0.1) where it is interesting tonotice the second inflection point in the velocity profile, which confirms the second inflection point observedin the numerical simulation profile (see figure 3). For a more detailed analysis of the second inflection pointand his influence on the local instability waves see Muller et al.10

Sixteen microphones placed at 75D from the exit were used to measure the far field acoustic pressure.The microphones are positioned at angles between 20 and 140 degrees.

Measurements of the near pressure field of the jet were performed using a twenty microphones azimuthalarray (see figure 4) for eight axial positions and five radial positions (see figure 5). Free-field 1/4-inch micro-phones (type 4939) with Bruel & Kjaer preamplifiers (type 2670) were used for the near field measurements.These measurements have been conducted in the anechoic wind tunnel of ONERA Cepra19 by the firstauthor. This experimental campaign was supported by ONERA internal funding and was carried out withthe help of Cepra19 and DSNA technical staff. Similar circular arrays have been used to compute theazimuthal structure of the near field of the jet by Jordan et al.12 for a lower Mach number (M = 0.3)subsonic jet and by Kopiev et al.13 with a six microphones array for a high supersonic jet (M = 2.0). In asimilar way, the near field pressure measured with a conical microphone array (with six microphones in the

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Figure 1. Description of the methodology used to study the modal structure of the jet near field

azimuthal direction) for different operating conditions are compared in Reba et al.14 in order to constitutean analytical source model.

The pressure signals are stored for a time duration of 10 s with sampling frequency fe = 125, 000 Hz.A high-pass filter was employed with a filter value of 200 Hz. Twenty microphones are used except for theradial location r/D = 1.5 where only ten microphones are used to avoid interferences and ensure that themicrophones are not too close to each others.

x/D

y/D

0 1 2 3 4 5 6-1.5

-1

-0.5

0

0.5

1

1.5<U(x/D=0.1)>/ Uj<U(x/D=0.25)>/Uj<U(x/D=0.5)>/Uj<U(x/D=1)>/Uj<U(x/D=2)>/Uj<U(x/D=3)>/Uj<U(x/D=4)>/Uj<U(x/D=5)>/Uj

Figure 2. Mean velocity radial profiles measured in the jet flow

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<U> (m/s)

r/D

0 100 200 300 400-1

-0.5

0

0.5

1x/D=0.1

LES

EXPE

<U> (m/s)

r/D

0 100 200 300 400-1

-0.5

0

0.5

1x/D=0.25

LES

EXPE

Figure 3. Radial profile of the axial component of the mean velocity at x/D = 0.1 and x/D = 0.25

Figure 4. Microphone array used to measure the near field pressure of the jet. ONERA Cepra19 anechoicwind tunnel

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Figure 5. Positions of the microphones in the near field. Region treated by the LES and PSE respectively inpurple and inside the area delimited by the yellow line.

III. Large Eddy Simulation

A. Numerical procedure

1. Governing equations

The compressible Navier-Stokes equations are solved in their conservative form, with a perfect gas assump-tion. The filtered conservation equations of mass, momentum and total energy per unit volume (hereafterdenoted ρE) read,

∂ρ

∂t+∇ · (ρu) = 0 (1)

∂ρu

∂t+∇ ·

(ρu⊗ u + pI − τ

)= 0 (2)

∂ρE

∂t+∇ ·

((ρE + p)u− τ · u + ϕ

h

)= 0, (3)

where the total energy E per unit mass is the sum of internal energy e(T ) and kinetic energy 12u · u, so the

filtered total energy per unit volume read, ρE = ρe(T ) + 12ρu · u and pressure p is related to density ρ and

temperature T through the state equation, p = RρT .In these filtered Navier-Stokes equations, the dissipative fluxes τ and ϕ

hinclude subgrid modelization.

If S0 is the deviatoric (trace-free) part of the strain-rate tensor S,

S0 =12(∇u +t ∇u)− 1

3∇ · uI, (4)

the expression for τ and ϕh

are (neglecting some terms in the development of the filtered quantities),

τ = 2(µ + µs)S0 (5)

ϕh

= −(κ + κs)∇T . (6)

The type of modelization depends on the expressions used to compute µs and κs:

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• The simplest approach is the Monotonically Integrated Large Eddy Simulation (MILES),15 where theonly subgrid dissipation comes from the numerical scheme,

µs = 0 , κs = 0 (7)

• In the classical Smagorinsky16 model, the expressions for µs and κs are,

µs = ρ(Cs∆)2√

2S : S (8)

κs = µscp/Prt (9)

where S = 12 (∇u+t∇u) is the strain-rate tensor, Cs is the Smagorinsky constant (which is often taken

with the value Cs = 0.18) and Prt is the turbulent Prandtl (with the value Prt = 0.9).

These two modelizations have been tested and have been shown to give very similar results for this jet(with the relative coarse grid and the present numerical scheme). So, the MILES approach was retained forthe present study.

B. Modal Fourier decomposition of the LES pressure field

A double Fourier transform in time and in the azimuthal direction is applied on the pressure field:

• first, the Fourier transform in the azimuthal coordinate is taken,

Pm(x, r, t) =∫ 2π

0

p(x, r, θ, t)e−jmθdθ , (10)

• second, the Fourier transform in time is taken,

Pm,ω(x, r) =∫ T

0

Pm(x, r, t)e−jωtdt , (11)

with ω = 2πf and m the azimuthal wave number. The temporal FFT is performed on a time duration of72ms divided into four non-overlapping blocks. The time resolution of the stored data is ∆t = 45× 10−6 swhich corresponds to a sampling frequency of fe ≈ 22 kHz and a frequency resolution of ∆f = 55 Hz (theStrouhal number bandwidth is ∆St ≈ 0.01).

C. Mean flow

On figure 6, the mean velocity profile along the jet axis is printed versus the axial distance non-dimensionalizedwith the jet diameter (figure 6a)) and versus the axial distance non-dimensionalized with the jet potentialcore length (figure 6b)) . Though the potential core length is underestimated by the simulation, a goodagreement is observed with the experiments when the axial distance is scaled with the potential core length.

The same observation can be made for the jet mixing layer half-width (see figure 7), which is overestimatedby the simulation when the comparison is performed directly (see figure 7a)), but exhibits a better agreementwith the measurements when the axial distance is non-dimensionalized by the potential core length.

This difference between the potential core length of the simulated jet and the measured one must beconsidered when proceeding to comparisons in the near or far field of the jet.

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x/Dj

<U

>/U

j

0 5 10 15 200

0.2

0.4

0.6

0.8

1

1.2

LES

CEPRA19

A17

3.3 6

x/Lc

<U

>/U

j

0 1 2 3 40

0.2

0.4

0.6

0.8

1

1.2

LES

CEPRA19

A17

a) b)

Figure 6. Mean velocity profile along the axis : a) versus the axial length scaled with the jet diameter; b)versus the axial length scaled with the jet core length. The red curve corresponds to the LES and the twoothers are the experimental references.

x/D

b/D

0 1 2 3 4 50

0.2

0.4

0.6

0.8

LES

EXPE

x/Lc

b/D

0 0.2 0.4 0.6 0.8 10

0.2

0.4

0.6

0.8

LES

EXPE

a) b)

Figure 7. Comparison of the jet mixing layer half-width between the LES (MSD) and the measure (CEPRA19)

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D. Acoustic far field

An integral formulation of Ffowcs Williams & Hawkings is employed to compute the radiated pressure inthe far field (see Rahier et al.7). Assuming that the sources are negligible outside the surface containing theflow field and integrating with the Green function G, the surface integral formulation of Ffowcs Williams &Hawkings can be written as follows,

ρ′(x, t) =∫ ∫

FFWH(y, τ)G(x, t|y, τ)d2ydτ (12)

with,

FFWH(y, τ) =(p′un + ρun(un − vn)) · (x− y)

c20|x− y|

+∂

∂τ

((p′un + ρun(un − vn)) · (x− y)

c30|x− y|

)+

∂

∂τ(

1c20

(ρ0vn + ρ(un − vn))) (13)

In practice, the control surfaces are fixed (vn = 0).The surface used is open to avoid spurious contribution of the vortical and entropic components that

cross the surface situated in the flow field.

IV. Use of the PSE

A linear stability analysis is performed based on the mean flow provided by the LES. The mean flowis assumed to be steady and axisymmetric (independent of the azimuthal angle θ). In addition the meanpressure is assumed to be constant everywhere. Consequently the mean flow is characterized by two nonzero velocity components : (Ur(r, x), 0, Ux(r, x)), and by the mass flux ρ(r, x) (or similarly the temperatureT (r, x) thanks to the equation of state), each quantity being a function of the radius and the axial coordinatesonly. The upper bar refers thus to basic flow quantities. A small perturbation is then superimposed to thisbasic flow and the resulting flow quantities are introduced into the governing equations. In the presentstudy, the equations are the usual ones written for an inviscid perfect gas. In addition, the specific heatscapacities Cp and Cv are assumed to be constant. Focusing on the linear regime, which remains valid as longas the fluctuating quantities amplitudes are small in comparison with the corresponding basic flow values,the equations are linearized. The steady basic flow equations are subtracted from these linearized equations,and thus the final system writes as :

∂ρ

∂t+ U · ∇ρ +∇ρ · u + ρ∇ · U + ρ∇ · u = 0

∂u

∂t+∇U · u +∇U · U = −1

ρ∇p

∂s

∂t+∇s · U +∇S · u = 0

(14)

with s the entropy fluctuation and S = Cv ln Pργ , using the perfect gas assumption.

The idea of the parabolized stability equations (PSE) approach, initially developed by Herbert & Bertolotti,17

is to take into account the non-parallelism of the flow by decomposing the x-dependent terms of the distur-bance quantities into a slowly varying shape (amplitude) function and a rapidly wave-like part to obtain,

q(r, θ, x, t) = q(r, x) exp(

i

∫α(ξ)

)exp(i(mθ − ωt)) (15)

generalizing the normal mode form. The azimuthal wave number m and the circular frequency ω remainconstant and are real numbers, whereas the complex streamwise wavenumber k is explicitly written asan (unknown) function. An analysis of (15) reveals that the streamwise change of the fluctuation can beabsorbed into either the amplitude function or the exponential term containing the streamwise wavenumber.This sharing is obviously ambiguous. A normalization is thus introduced to eliminate that problem and

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simultaneously to force the fluctuation to be as close as possible to the normal mode form. Most of thewaviness and growth of the fluctuation are absorbed into the exponential term, making the amplitudefunction q(r, x) slowly varying in x. For instance the normalization :∫ +∞

0

(u∗r

∂ur

∂x+ u∗θ

∂uθ

∂x+ u∗x

∂ux

∂x

)(16)

based on the kinetic energy of the amplitude functions can be used : it will force the amplitude functions tobe only weakly dependent on x.

Introducing the form (15) into the linearized system (14) leads to a system of partial differential equations(PDE system) with respect to x and r. In the present case, this system is parabolic in x, as it can readilybe checked using the characteristics method. Indeed, the PSE system is derived from the Euler equations,and thus, unlike the previous PSE studies based on the Navier-Stokes equations, none of its terms have tobe neglected to obtain parabolicity. Then the system is solved numerically with a marching procedure in xstarting with an initial value at x = x0 and, for each value of x, the same boundary conditions as the onesused in the parallel theory.

V. First comparisons between LES, PSE and experiments

Figure 8 shows the axial evolution of the axisymmetric mode at r/D = 1.5 for three different values ofthe Strouhal number and for the three approaches described in the introduction. The levels of the LES arerescaled in order to fit with the experimental data by subtracting 8 dB/Hz and the comparisons are performedversus the dimensionless axial position x/Lc where Lc is the potential core length. The agreement betweenthe three methods is relatively good for x/Lc < 1 (before the end of the potential core). Downstream of thepotential core (x/Lc > 1), there is only one experimental point so there is no more experimental reference tocompare to the two other methods. In this region the results from the PSE diverge from the LES probablydue to the non linear effects that are important there. More generally the difference between the LES andthe PSE can be linked to regions where the perturbations are damped, with the PSE exhibiting a largerdamping than the LES.

x/Lc

dB/H

z

0 0.5 1 1.5 2

90

100

110

120

LES

PSE

EXPE

m=0 , St =0.2 , r/D=1.5

x/Lc

dB/H

z

0 0.5 1 1.5 280

90

100

110

120 m=0 , St=0.3 , r/D=1.5

LES

EXPE

PSE

x/Lc

dB

/Hz

0 0.5 1 1.5 2

75

80

85

90

95

100

105 m=0 , St=0.6 , r/D=1.5

LES

PSE

EXPE

Figure 8. Axial evolution of the axisymmetric mode PSD along the r/D = 1.5 line. The results from the LESare shifted by − 8 dB/Hz to match the experimental ones.

The PSD of the axisymmetric mode are presented on figure 9 for six different axial positions betweenx/Lc = 1/6 and x/Lc = 1. The blue line corresponding to the LES (shifted by − 8 dB/Hz) has the sameglobal shape as the red curve describing the experimental results, except for x/Lc = 1/6. This is consistentwith the mean flow characteristics: at x/Lc = 1/6, the jet mixing layer half-width of the simulation is thinnerthan the measured one (see figure 7) but, for x/Lc ≥ 1/3, the agreement between the simulation and theexperiments is relatively good.

A better agreement is observed when the axial distance is increased, which means that the sound radiateddownstream (dominated by the large-scale structure noise) is captured more accurately than the sidelineradiated noise (mostly due to fine-scale turbulence). This is not surprising that the numerical methodsemployed are more suitable for capturing the large-scale dynamic, than the fine scale turbulence whichwould require a finer grid resolution.

Figure 10 shows the power spectral density of the first eight modes for a location situated in the near

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St

SPL(dB/Hz)

0.5 1 1.5260

70

80

90

100

110

120 m = 0 ; x/Lc=1/6 ; r/D=1.5

LES - 8 dB/Hz

EXPE

St

SPL(dB/Hz)

0.5 1 1.5260

70

80

90

100

110

120 m = 0 ; x/Lc=1/3 ; r/D=1.5

LES - 8 dB/Hz

EXPE

St

SPL(dB/Hz)

0.5 1 1.5260

70

80

90

100

110

120 m = 0 ; x/Lc=1/2 ; r/D=1.5

LES - 8 dB/Hz

EXPE

St

SPL(dB/Hz)

0.5 1 1.5260

70

80

90

100

110

120 m = 0 ; x/Lc=2/3 ; r/D=1.5

LES - 8 dB/Hz

EXPE

St

SPL(dB/Hz)

0.5 1 1.5260

70

80

90

100

110

120 m = 0 ; x/Lc=5/6 ; r/D=1.5

LES - 8 dB/Hz

EXPE

St

SPL(dB/Hz)

0.5 1 1.5260

70

80

90

100

110

120 m = 0 ; x/Lc=1 ; r/D=1.5

LES - 8 dB/Hz

EXPE

Figure 9. PSD of the axisymmetric mode for six different positions. The red curve corresponds to theexperiments and the blue one to the LES shifted by − 8dB/Hz

field (r/D = 2), downstream of the potential core (x/Lc = 7/6). As we can see, by subtracting 8 dB/Hz,the spectral shapes of the first eight modes are relatively well recovered by the LES. It is very interesting tonotice that although the jet simulated has not exactly the same aerodynamic field, the spectral shape for axiallocations non dimensionalized by the potential core length is nearly the same in relative levels. Especiallythe modal repartition of the modes is recovered at least for the first eight modes. The underestimation ofthe pressure levels for the high frequencies (St > 1) being due to the resolution limitation of the relativelycoarse grid used for the LES calculations.

These results leads to wonder wether taking the potential core length into account could give improvedrelative (not absolute) directivity in the far field. Figure 11 shows the sound pressure levels in the far field(75D) obtained by recomputing the angles of the microphones by taking into account the difference betweenthe two potential core lengths.

A description of the procedure used to compute the new positions of the microphones taking into accountthe potential core length difference between the LES and the experiments is presented on figure 12. Let xEXP

be the axial coordinate of the experimental microphone in a frame of reference centered at the end of thepotential core. Assuming that the aerodynamic field of the simulated jet is a space contraction along theaxial coordinate of the experimental aerodynamic field, the equivalent axial position in the simulation frameof reference centered at the end of the numerical potential core is defined as follows,

xLES = xEXP × LLES/LEXP . (17)

Let φLES be the angle defining the position of the microphone in a frame of reference centered at the end ofthe numerical potential core,

φLES = arctan(

y

xLES

)= arctan

(y

xEXP

LEXP

LLES

). (18)

Thus, new microphones positions for the simulation can be computed knowing the simulation and experi-mental potential core lengths and the experimental microphones positions.

As we can see, with the new microphones positions, we have a good estimation of the directivity for theangles below 90 degrees (but an overestimation of the levels approximately equal to 20× log(LEXP /LLES).So it rises the question of the scaling of the far field sound pressure levels by the potential core length. Is

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St

SP

L(d

B/H

z)

0.5 1 1.5250

60

70

80

90

100

110 m = 0 ; x/Lc = 7/6

LES - 8 dB/Hz

EXPE

St

SP

L(d

B/H

z)

0.5 1 1.5250

60

70

80

90

100

110 m = 1 ; x/Lc = 7/6

LES - 8 dB/Hz

EXPE

St

SP

L(d

B/H

z)

0.5 1 1.5250

60

70

80

90

100

110 m = 2 ; x/Lc = 7/6

LES - 8 dB/Hz

EXPE

St

SP

L(d

B/H

z)0.5 1 1.5250

60

70

80

90

100

110 m = 3 ; x/Lc = 7/6

LES - 8 dB/Hz

EXPE

St

SP

L(d

B/H

z)

0.5 1 1.5250

60

70

80

90

100

110 m = 4 ; x/Lc = 7/6

LES - 8 dB/Hz

EXPE

St

SP

L(d

B/H

z)

0.5 1 1.5250

60

70

80

90

100

110 m = 5 ; x/Lc = 7/6

LES - 8 dB/Hz

EXPE

St

SP

L(d

B/H

z)

0.5 1 1.5250

60

70

80

90

100

110 m = 6 ; x/Lc = 7/6

LES - 8 dB/Hz

EXPE

St

SP

L(d

B/H

z)

0.5 1 1.5250

60

70

80

90

100

110 m = 7 ; x/Lc = 7/6

LES - 8 dB/Hz

EXPE

Figure 10. PSD of the first eight azimuthal modes at x/Lc = 7/6 and r/D = 2. The red curve corresponds tothe experiments and the blue one to the LES shifted by − 8dB/Hz

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there a linear relation between these two components? Is it possible to have a predictive simulation of jetnoise by scaling the results on the potential core length?

The overestimation for angles greater than 90 degrees is probably attributable to the not accuratelyresolved turbulent fine scales. It seems that the fine scale contribution to the noise spectrum is not reachablewithout increasing the spatial resolution of the grid.

a)Angle (deg.)

OA

SP

L(d

B)

20 40 60 80 100 120 14090

95

100

105

110

115

120

Expe CEPRA19

FW-H

b)Angle (deg.)

OASPL

(dB)

20 40 60 80 100 120 14090

95

100

105

110

115

120

Expe CEPRA19

FWH Micros Recentrés-20Log(Lexp/LLES)=-5dB

FW-H Recentered Microphones

Figure 11. Overall far field (at 75D from the jet exit) sound pressure levels obtained a) without taking intoaccount the difference between the potential core length of the experimental and simulated jet; b) by takinginto account the potential core length for determining the position of the microphones that is comparable withthe measures.

VI. Conclusion

The present work presents comparisons between the modal structure of the near field pressure computedfrom three different approaches: Large Eddy Simulation, Parabolized Stability Equations based on the meanflow provided by the LES, and the experimental measurements. It is shown that, by taking into account thedifference between experimental and computed potential core lengths, the spectral shape of the computednear field pressure is in good agreement with the experimental ones (with an constant overestimation of about8 dB/Hz). The axial evolution of the jet near field pressure is also well recovered by the three approachesbefore the end of the potential core (x/Lc = 1). In the region where the perturbations are damped the nearfield computed with the PSE differs from the LES one. This is consistent with the assumption (see Bertolotti& Colonius18) that the acoustic field computed from the PSE is not accurate near and after the end of thepotential core where non linear effects are believed to be important.

It is clear that the LES calculations used for the present study need to be improved to resolve accuratelythe mean flow and predict the fine scale turbulence noise and we cannot escape for this task, but the presentpaper only attends to address the issue of what can (and cannot) be captured with a low cost large eddysimulation with only 1.5 million cells compared to high resolution simulations that can be found in theliterature.

It seems that the methodology (third order scheme in space, second order implicit time scheme andrelatively coarse grid) employed is able to capture the low frequency part of the noise radiated by the largescale structures of the jet flow. This is the dominant part of the noise radiated downstream (angles < 90◦).However, capturing accurately the noise radiated for large angles ( ≥ 90◦) will necessitate a finer gridresolution.

Acknowledgments

The authors are greatly indebted to O. Piccin from Cepra19, as well as DSNA and Cepra19 technicalstaffs for their efforts to make the experiments possible. It is a pleasure to thank G. Elias for providingscientific advice and for sharing his knowledge about jet noise, and H. Gounet for her active participation to

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Figure 12. Description of the procedure used to compute the new microphones positions accounting for thedifference of potential core length between the simulation and the experiments.

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the experiments.

References

1M.L. Shur, P.R. Spalart, and M. Kh. Strelets. Noise prediction for increasingly complex jets. Part I: Methods andtests. International Journal of Aeroacoustics, 4(3-4):213–246, 2005.

2M.L. Shur, P.R. Spalart, and M. Kh. Strelets. Noise prediction for increasingly complex jets. Part II: Applications.International Journal of Aeroacoustics, 4(3-4):247–266, 2005.

3N. Andersson. A Study of Mach 0.75 Jets and Their Radiated Sound Using Large-Eddy Simulation. PhD thesis,Chalmers University of Technology, 2003.

4N. Andersson, E. Eriksson, and L. Davidson. Large-eddy simulation of a mach 0.75 jet. In AIAA Paper 2003-3312,2003.

5N. Lupoglazoff, A. Biancherin, F. Vuillot, and G. Rahier. Comprehensive 3D unsteady simulations of subsonic andsupersonic hot jet flow-fields. Part 1 : Aerodynamic analysis. In AIAA Paper 2002-2599, 2002.

6F. Vuillot, G. Rahier, N. Lupoglazoff, J. Prieur, and A. Biancherin. Comparative jet noise computations using acoupled CFD-acoustic solution. In 11th Int. Cong. on Sound and Vibrations, Saint Petersbourg, 2004.

7G. Rahier, J. Prieur, F. Vuillot, N. Lupoglazoff, and A. Biancherin. Investigation of integral surface formulationsfor acoustic post-processing of unsteady aerodynamic jet simulations. Aerospace Science and Technology, 8(6):453–467, 2004.

8A. Biancherin, N. Lupoglazoff, F. Vuillot, and G. Rahier. Comprehensive 3D unsteady simulations of subsonic andsupersonic hot jet flow-fields. Part 2 : Acoustic analysis. In AIAA Paper 2002-2600, 2002.

9A. Biancherin. Simulation aeroacoustique d’un jet chaud subsonique. PhD thesis, Universite Paris VI, 2003.10F. Muller, F. Vuillot, G. Rahier, and Casalis G. Modal analysis of a subsonic hot jet LES with comparison to the

linear stability analysis. In AIAA Paper 2005-2886, 2005.11E. Piot, G. Casalis, and F. Muller. A comparative use of the PSE and LES approaches for jet noise predictions. In

AIAA Paper (submitted), 2006.12Jordan P., C.E. Tinney, J. Delville, F. Coiffet, M. Glauser, and A. Hall. Low-dimensional signatures of the sound

production mechanisms in subsonic jets : Toward their identification and control. In AIAA Paper 2005-4647, 2005.13V. Kopiev, M. Zaitsev, and R. Karavosov. On azimuthal structure of supersonic jet noise. In Tenth International

Congress on Sound and Vibration, 2003.14R. Reba, S. Narayanan, T. Colonius, and T. Suzuki. Modeling jet noise from organized structures using near-field

hydrodynamic pressure. In AIAA Paper 2005-3093, 2005.15J.P. Boris, F.F. Grinstein, E.S. Oran, and R.L. Kolbe. New insights into large-eddy simulation. Fluid Dyn. Res.,

10:199–228, 1992.16J. Smagorinsky. General circulation experiments with the primitive equations. Monthly Weather Review, 91(3), 1963.17T. Herbert and F.P. Bertolotti. Stability analysis of non-parallel boundary layers. Bull. Am. Phys. Soc., 32, 1987.18F. P. Bertolotti and T. Colonius. A low-dimensional description of the compressible axisymmetric shear layer. In

AIAA Paper 2003-1062, 2003.

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