[american institute of aeronautics and astronautics 17th aiaa/ceas aeroacoustics conference (32nd...

American Institute of Aeronautics and Astronautics

1

Large-Eddy Simulation of High-Subsonic Jet flow

with Microjet Injection

Shunji ENOMOTO1 and Kazuomi YAMAMOTO

2

Japan Aerospace Exploration Agency, Chofu, Tokyo, JAPAN

Kenshi YAMASHITA3

Advanced Science & Intelligence Research Institute Corp., Chiyoda-ku, Tokyo, JAPAN

and

Nozomi TANAKA, Yoshinori OBA and Tsutomu OISHI4

IHI Corporation, Nishitama-gun, Tokyo, JAPAN

Large-Eddy Simulation of high subsonic jet with microjet injection was performed

using UPACS-LES code which is developed in JAXA. Large scale (476M grid point)

simulation was executed on JAXA Supercomputer System using 980 processors. The

result shows good agreement with the experimental data in terms of velocity fluctuation

and far-field noise level. Far-field noise prediction using FW-H method from the LES

results show that the LES successfully predict noise reduction by microjets for lower

frequency component emitted in 30 deg. observation angle, while it still has difficulty in

predicting reduction of higher frequency noise emitted in 90 deg. observation angle.

Nomenclature

a = speed of sound in the ambient

D = diameter of main nozzle

Ma = acoustic Mach number = Uj / a

r = radial coordinate

R = distance from the center of nozzle exit to observation point of far-field noise

St = Strouhal number = (frequency D) / Uj

U = axial velocity (time averaged)

u’ = axial turbulent velocity

Uj = main jet velocity

X = axial coordinate

Y or Z = transverse coordinate

θ = observation angle of far-field noise from the downstream jet axis

I. Introduction

One of the main noise sources of airplane is jet noise. Jet noise reduction method, such as microjet injection,

is widely investigated. Experimental investigation1 of microjet effects on subsonic M=0.9 unheated jet showed

that microjet injection reduced turbulent intensities up to 20% and far field noise reduction was about 0.5 – 2 dB.

Alkislar examined the effect of streamwise vortex generated by microjets2, and he measured the flow field of the

Chevron-Microjet combination concept in detail3. Gutmark et al.4 applied microjets to double stream

configuration. Zaman5 showed that the smaller diameter microjet ports with higher driving pressure can produce

better noise reduction. Castelain et al.6 made detail measurements of flow field and far field noise on microjets,

and studied the noise reduction as a function of the mass flux of microjet injection.

Numerical simulation of jet flow and jet noise is expected to be utilized as a design tool for those jet nozzles.

Several studies of jet noise simulation have been carried out using large-eddy simulation (LES), and some of

1 Associate Senior Researcher, Aerospace Research and Development Directorate, 7-44-1 Jindaiji-Higashi,

Chofu, Tokyo 182-8522, JAPAN, AIAA member 2 Senior Researcher, AIAA senior member

3 Engineer, Science Engineering Division, 1-18-14 Uchi-Kanda, Chiyoda-ku, Tokyo 101-0047, JAPAN

4 Aero-Engines & Space Operations, 229 Tonogaya, Nishitama-gun, Tokyo 190-1297, JAPAN

17th AIAA/CEAS Aeroacoustics Conference (32nd AIAA Aeroacoustics Conference)05 - 08 June 2011, Portland, Oregon

AIAA 2011-2883

Copyright © 2011 by the author(s). Published by the American Institute of Aeronautics and Astronautics, Inc., with permission.


2

them showed good accuracy. Bodony and Lele7 performed LES of subsonic and supersonic circular jet. Mach

numbers were from 0.5 to 1.5, Reynolds numbers were 105-10

6. Sixth order compact scheme were used for

radial and axial direction, and spectral method for circumferential direction. They used a dynamic Smagorinsky

model for the calculation. Bogey and Bailly8 used high-cut filter instead of SGS model for their LES of subsonic

jet Ma = 0.9. They investigated the influence of inflow condition and inlet disturbance. Uzun and Lyrintzis9

performed LES of subsonic jet (Ma = 0.9, ReD = 105) using dynamic Smagorinsky model and 6

th order compact

scheme. Shur et al.10

uses 5th order upwind scheme for LES simulation without subgrid scale model. PC clusters

were used for their calculation and LES of practical nozzles, such as chevron nozzles and slanted nozzles, were

carried out.

Numerical simulations are also applied to microjet flow. Huet et al.11

numerically investigated the efficiency

of microjets. Their LES showed that the microjets led to a reduction of the turbulence in the shear layer and a

decrease of the far field noise. LES of Shur et al.12

successfully predicted the difference between baseline jet

noise and noise reduction by microjets, and showed that the microjets concept might not effective in flight

conditions.

UPACS is a CFD code developed in JAXA13

. It is a multi-block structured grid solver for general curvilinear

grids. Third order MUSCL and Roe method are used for spatial discretization. UPACS-LES is a modified

version of UPACS. Sixth-order compact scheme are used for spatial discretization. Imamura et al.14,15

uses this

code for vortical flows around high lift device, such as a flap and a slat.

We have been trying to simulate jet flow with microjet injection using UPACS-LES. Previous computation16

was not fully satisfactory to simulate details of flow phenomena, and it's reason seemed to be insufficient grid

resolution. In the present study, we had an opportunity to use large number of CPUs, so we used denser grid to

simulate jet flow.

II. Numerical Method

UPCAS-LES is an unsteady three dimensional filtered compressible Navier-Stokes solver based on finite

volume method using multi-block structured grids. The convection term is discretized by high-order compact

scheme for finite volume method, and a low storage four-stage Runge-Kutta method is implemented for the time

integration. Smagorinsky model is used for the subgrid scale stress model of LES.

Symbols in this section are not included in nomenclature.

Governing equations used in UPACS-LES are spatial filtered Navier-Stokes equations17

,

(( ) )

( )

where the overbar ( ) denotes a filter operation, tilde denotes Favre filter operation ( ⁄ ). Here, f is an

arbitrary variable.

(

)

(

)

For the subgrid scale stress model of LES, Smagorinsky model are used.

( )


3

| | | |

The convection term was discretized by Kobayashi’s compact scheme for finite volume method18

. In the

compact scheme for finite volume method, cell-face quantities are reconstructed from cell-averaged quantities,

and the fluxes on the cell-face are calculated from the reconstructed quantities:

where on the left hand side denotes interpolated value at cell faces, and on the right hand side denotes

cell-averaged value. Sixth order is achieved when the coefficients are:

Since this equation uses interpolated values at the adjacent cell faces implicitly, a tri-diagonal matrix has to

be solved. The scheme maintains 6th order only when the computational grid is equally spacing orthogonal grid.

On the general curvilinear grid, it maintains 3rd order.

At the interface between each block, 4th order explicit scheme is used in order to avoid accessing the

variables of adjacent blocks:

To prevent numerical odd-even oscillation, a compact filter, whose order of accuracy is up to 14, was used:

∑

on the right hand side denotes original value, and on the left hand side denotes filtered value. The

coefficients α and aj are shown in Reference [19]. The essentials of the filter are the same as the method of

Gaitonde et al.20

, but it does not use one-sided filter near the boundaries, instead, it use lower order central filter

near the boundaries in order to avoid phase error.

III. Numerical Simulation

As the verification data for our computational method for jet flow with microjet injection, we referred to the

experiment of Castelain et al. 6,21,22

. In their experiment, the diameter of the main jet nozzle was D = 50mm, the

air was heated to maintain the temperature of the expanded jet close to the ambient temperature, Mach number

based on the jet velocity Uj and the ambient speed of sound a is Ma= Uj / a = 0.9, and the Reynolds number ReD

= 106. Eighteen microjet nozzles were placed around the main jet nozzle. The diameter of microjet nozzle was

1mm each, and injection angle was 45 degree. The mass flow rates of each microjet to main jet are shown in

Table 1. There are seven test points in the experiment of Castelain et al21

and we selected two test points, rm(3)

and rm(7)

from them, because noise reduction levels were relatively large comparing to the other test points. The

baseline jet (without microjet) is also computed and referred as rm(0)

.

Table 1 Microjet condition

test point rm(0)

rm(3)

rm(7)

microjet mass flow ratio 0 3.36 8.86 (×10-4

)

Figure 1 shows computational grids. Figure 1a is a side view of the grid. The physical part of computational

region extends −0.1 ≤ X/D ≤ 20. The sponge zone, where grid spacing is extended gradually, is extended outside.

Freund method23

is applied in the sponge zone to attenuate outgoing waves. Table 2 shows the specification of

the computational grids. “fine” is the present case. “coarse” is our previous computation16

which is shown here

as a reference. Nozzle exit region is shown in Fig. 1b. The main nozzle is straight pipe and it does not represent

the nozzle profile of the experiment. The main nozzle exit position is X/D = 0, and it extends upstream to X/D =

−1. Grid is almost equally spaced for all direction near nozzle exit region. Detail of microjet injection region is

shown in Fig. 1c, where grid lines are tilted 45°. Microjet flow is specified as an inflow boundary condition, and


4

is represented by 4x4cells, which are shown as red line in Fig. 1c. Figure 1d is bird's-eye view of the grid near

main nozzle exit.

Table 2 Specification of computational grids

Case Grid points Grid spacing Grid spacing for

microjet

fine (present) 476M 0.005D 4x4

coarse (reference) 28M 0.013D 2x2

Inflow velocity profile is constant velocity Uj. For laboratory jets, inflow boundary layer thickness is very

thin. Our grid is not clustered to nozzle wall and is spaced about 0.005D, so physical boundary layer thickness is

less than one grid spacing. Hence, we did not specify any boundary layer profile at inflow boundary of jet

nozzle.

In LES of jet flow, it is necessary to impose inflow disturbance for laminar-turbulent transition in very early

stage of the shear layer. Present simulation used an inflow forcing based on Bogey’s method24

. Inflow forcing

was added near the nozzle wall (X/D = −0.2 and r/D=0.48) in order to simulate the turbulence in the boundary

layer of nozzle inside wall. The amount of disturbance should be greater enough to make the shear layer

turbulent, and should be as small as possible so that noise emitted from the disturbance does not affect far-field

SPL estimation.

For each simulation, we ran 200,000 time steps for initial transients, which is 200 non-dimensional time

based on speed of sound in the ambient a and diameter of the main nozzle D. Then we collected the flow

statistics over 150,000 time steps (150 non-dimentional time).

The computation was executed on JAXA Supercomputer System (JSS). The system has total 3008 nodes,

and 4 cores are in one node. MPI and openMP are used for the parallel computation. Three cases are computed

(rm(0)

, rm(3)

, and rm(7)

), and 980 nodes (3920 cores) × 12 days were used for each case.

IV. Results and discussion

A. Baseline jet without microjet injection

First, we compared the baseline jet result (rm(0)

) with existing data in order to verify the accuracy of the code.

In Fig. 2, axial mean and turbulent velocities on the centerline and on the lipline of the LES are compared

with experimental data of Bridges & Wernet25

and Lau et al26

. The data of Bridges do not include isothermal

condition. Hence, cold jet of Ma = 0.9 (set point 7) is used instead. The data of Lau are isothermal jet of Ma = 0.9.

LES result is indicated as “fine” and “coarse”, “fine” is present result and “coarse” is our previous16

result with

coarser grid. Figure 2a shows centerline axial mean velocity. “coarse” exhibit an earlier potential core collapse

than the experiment. On the other hand, the potential core of “fine” is longer than the experiment. The mean

velocity decay rate of “fine” is close to Bridges data. Lipline axial mean velocity is shown in Fig .2b. “fine”

exhibits good agreement with the experiment. “coarse” shows lower lipline velocity. In “coarse” simulation,

thick boundary layer profile was set at the nozzle inflow boundary, so lipline does not correspond to the center

of the shear layer. Figure 2c is centerline axial turbulent velocity. “coarse” exhibits low turbulence level. “fine”

has very similar profile to Bridges data, but it shifts downstream about X/D=1 compared to the data. Bridges

data exhibits u’/Uj=0.015 at the beginning of jet, but LES result exhibits lower value of 0.05. Inflow disturbance

of LESs were added near the nozzle wall, but no disturbance were added to whole jet. To simulate centerline

turbulence correctly, adding small inflow disturbance to whole jet might be needed. Figure 2d shows lipline

axial turbulent velocity. “fine” exhibits a little higher level than the Bridges data. Figure 2e shows centerline

transverse turbulent velocity. “fine” exhibits similar peak value to Lau’s data except for the location of the peaks.

Figure 3 is axial mean and turbulent velocity profiles at X/D = 4, 8, 12, and 16. Axial mean velocities are

shown on the left column, Fig. 3a, 3c, 3e, and 3g. “fine” exhibits good agreement with Bridges, but it’s shear

layer expands slower than the experiment. The profiles of “coarse” are wider and the peak value is lower than

the experiment. For axial turbulent velocity profiles, shown on the right column of Fig. 3b, 3d, 3f, and 3h, “fine”

shows very good agreement with Bridges.

The above results shows that the LES result of “fine” grid exhibits good agreement with the experiment,

especially with Bridges25

, and “coarse” does not. So further discussion in this paper will be made with “fine”

data.

Next, far-field sound pressure level (SPL) is compared with an experiment. The porous Ffowcs Williams-

Hawkings (FW-H) method28,29

is used to study the far-field noise of our LES result. The FW-H integral surface

does not include downstream jet exit region. Far-field noise level of LES are computed at R/D = 40. Figure 4

shows sound pressure levels from LES and the experiment of Tanna27

. The experimental data have been scaled

to the same observation distance of R/D = 40. Overall SPL of the LES exhibits 2dB lower than the experiment

(see Fig. 4a). Figure 4b and 4c show the 1/3 octave band sound pressure levels at observation angles θ =30° and


5

90°. At θ = 30°, the profile of LES agrees well with the experiment, but peak level at St = 0.2 is 3dB lower than

the experiment. At θ = 90°, the profile of LES is about 5dB lower than the experiment, and peak frequency is

higher. These results are not very accurate as Shur et al.12

, especially for θ = 90°, but the differences between

LES and the experiment are not very large. Hence, the simulation code seems to be eligible for an evaluation

tool for microjet effects.

For both angles, higher frequency of St > 4 show lower SPL, that means the cut-off frequency of the

prediction is St = 4.

B. Flow field with microjets

From Fig. 5 to Fig. 7 compare the computational results with microjet injection with the experimental data

by Castelain22

. Figure 5 shows u-velocity fluctuation at X/D=1 cross section. Left column, Fig. 5a, 5c and 5e are

LES results, and right column, Figs.5b, 5d, and 5f, are PIV data of Castelain22

. These figures for the experiment

are the same data shown in Castelain22

. The color map is adjusted to be the same between the experiment and

the LES. We can see deformation of shear layer and increase of fluctuation caused by microjet injection from

these figures. The shear layer of rm(0)

is thicker than the experiment. But shear layer thickness and the

deformation of the shear layer of rm(3)

and rm(7)

are closer to the experiment. The peak locations of the turbulence

are between microjet injection points in the experiment, and the fact is the same in the LES results (Fig. 5c and

5e).

Figure 6 shows axial velocity fluctuation at X/D=3. In this section, the deformation caused by microjet

injection is not clearly seen. But it is apparent that microjet decreases turbulence level in the experiment, and the

LES results also shows the same trend. LES shows lower turbulence level for rm(0)

(Fig. 6a) than the experiment

in this section, and microjet have a little effect to decrease turbulence (Fig. 6c and 6e). The shear layer

thicknesses for all cases have good agreement with the experiment.

Figure 7 shows the Reynolds stress like component at X/D=1 defined in Ref.[22]. It represents turbulent

mixing in the jet shear-layer in radial direction. Again, shear layer width of the LES results is wider than that of

the experiment, but the shape of the shear layer and the level of Reynolds stress agree with the experiment.

Figure 8 is the Reynolds stress at X/D=3. Overall value of the LES is less than the experiment, but there can be

seen that microjets make the Reynolds stress lower in LES as well as the experiment. From these comparisons,

it is shown that the LES successfully captures the flow physics of shear layer deformation due to the microjet

injections in detail, which enhances the mixing in the jet shear-layer then reduces turbulence level in

downstream region.

Figure 9 shows turbulent kinetic energy along X-Y plane which is not obtained in the experiment. Despite

the difference in Fig. 5 to Fig. 7, the LES result for rm(3)

does not show much difference with this global view. In

contrast, TKE for rm(7)

clearly shows the effect of microjet injection; TKE increases near the nozzle exit in

X/D<1, then decreases in 2≤X/D≤4. Further downstream beyond X/D=4, the LES results show little difference

among them.

In Fig. 10, three cross sections X/D=0.12, 0.2, and 0.6 are shown to observe process that the microjet

injection generates shear-layer deformation and turbulence which is difficult to measure in experiments. The left

column is rm(3)

and the right column is rm(7)

. In each figure, axial velocity (U) is shown on the left, and turbulent

kinetic energy (TKE) is shown on the right. At X/D=0.12 (Fig. 10a), microjets impingement make “concave

regions” on the shear layer between main jet and the ambient air, and higher TKE region appears at the bottom

of the concave regions. Note that microjets impinge at around X/D=0.06 to the shear layer, and they merge into

the main jet after the impingement. Figure 11 shows closer view of the Z=0 section near microjet injections.

This result clearly shows that the turbulence is not generated by the microjet impingement itself but generated in

the strong shear in outer side of the shear-layer downstream of the impingement. In Fig. 10b, the regions of

higher TKE develops along concave shaped shear-layer. At a downstream location of X/D=0.6 (Fig. 10c), high

TKE regions extend circumferentially and connect with each other. For rm(7)

, on the other hand, microjets

deform the shear layer deeper, but not wider like rm(3)

at X/D=0.12 (Fig. 10d). In Fig. 10e, the shear layer

deforms and shows omega (Ω) shape, and TKE exhibits high value along the shear layer. In Fig. 10f the higher

TKE region spreads along the shear-layer between the microjet locations. It is interesting that in the rm(3)

case

TKE spreads almost uniformly along the deformed shear-layer. On the other hand, in the rm(7)

case, it spreads

outer side of the shear-layer after the omega shape deformation due to strong microjet injection. To enhance the

turbulent mixing in the shear-layer, it is preferred that the TKE spreads along the middle in the shear-layer

thickness like rm(3)

results. Therefore, injection for rm(7)

may be too much to obtain optimal efficient condition

that realizes noise reduction with less mass flow injection. Actually, the experimental results in Castelain22

shows rm(3)

obtained a comparable level of noise reduction to rm(7)

which mass flow rate is more than twice as

much.


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C. Sound Pressure Level

Figure 12 compares frequency weighted power spectral density (Pa2) of far-field sound pressure level

obtained at R/D=40 between the experiment6 and the LES. Figure 12a is observation angle of θ = 30° from the

downstream jet axis. Low frequency component is dominant for this angle. The experiment shows 30%

reduction with microjet (both for rm(3)

and rm

(7)) at the peak frequency of 1.5kHz. The LES result shows half

value of the experiment at the peak, while peak frequency is close to the experiment. Although in the spectra for

rm(3)

, LES fails to obtain noise reduction, for rm(7)

it successfully shows noise reduction. Absolute level of spectra

is different but ratio of noise level between microjet on and off is close to the experiment. For θ = 90° (Fig. 12b),

the SPL of the experiment exhibits peak frequency of 5kHz, and about 40% of noise reduction are achieved with

both rm(3)

and rm(7)

. Slight increase of SPL of the experiment are seen at 20k-40kHz of rm(7)

, and this is caused by

strong interaction between the microjets and the jet-mixing layer6. On the other hand, the LES results show peak

frequency at 10k-20kHz, and they do not show noise reduction distinctly with the microjet injection. Excessive

peak are seen at 30kHz on rm(7)

, and this may be also caused by the interaction between microjets and the mixing

layer. This over-prediction might also be related to the imposed inflow disturbance. It is still under investigation.

The 1/3 octave band SPL of the LES result is shown in Fig. 13. For the observation angle θ = 30° (Fig. 13a),

noise reduction is 1.5dB at the peak frequency (St = 0.2) for rm(7)

, but noise reduction is not clearly seen for rm(3)

.

High frequency noise, St > 2, is increased for both cases. For the observation angle θ = 90° (Fig. 13b), 0.5-1dB

noise reduction is seen for rm(7)

, and no noise reduction is seen for rm(3)

. Again, high frequency noises are

increased. Directivity of overall sound pressure level (OASPL) is shown in Fig. 14. For rm(7)

, sound pressure

level decreases at low observation angle θ < 55°, and increases at high observation angle θ > 55°. No noise

reduction is seen for rm(3)

.

V. Conclusion

Large-Eddy Simulations of jet flow with microjet injection were executed using 476 million grid points on

980 nodes of JAXA Supercomputer System (JSS). Flow field and far-field noise prediction of the baseline jet

(without microjet) was within 2-5dB accuracy compared with the experimental data. Two test points of microjet

injection, rm(3)

and rm

(7) were numerically simulated. Shear layer deformation and turbulent velocity change

caused by microjet injection were simulated satisfactory. The detail figures of microjets injection suggest how

microjets increase turbulence kinetic energy.

Far-field noise prediction using FW-H method from the LES results show that the LES successfully predict

noise reduction by microjets for lower frequency component emitted in 30 deg. observation angle, while it still

has difficulty in predicting reduction of higher frequency noise emitted in 90 deg. observation angle.

Acknowledgments

We are indebted to many people for this research. First of all, we would like to thank Prof. Castelain of Univ.

of Lyon and Prof. Bogey of Ecole Centrale de Lyon for detail discussion about microjet experiment and

simulation, allowing us to use experimental data in this paper to compare with the LES result. We also would

like to thank Mr. M. Huet and Dr. F. Vuillot of ONERA for the discussion on the computational method for

microjet. Our colleagues in JAXA, Dr. Imamura and Dr. Amemiya helped us with the FW-H code for the far-

field noise calculation.

The computational resource was provided by "Strategic Large-Scale Simulation scheme" of JAXA Super-

computer System (JSS).

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vol.490, pp.75-98, 2003 2 M. B. Alkislar, et al., “The effect of streamwise vortices on the aeroacoustics of a Mach 0.9 jet”, J. Fluid Mech.

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AIAA 2009-851 4 S. M. Harrison et al., “Jet Noise Reduction by Fluidic Injection On a Separate Flow Exhaust System”, AIAA 2007-

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7

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2864 15 Imamura et al., “Designing of Slat Cove Filler as a Noise Reduction Device for Leading-edge Slat”, AIAA 2007-

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analysis”, Ph.D. thesis, ECL-No.2006-33 23 J. B. Freund, “Proposed In-flow/Outflow Boundary Condition for Direct Computation of Aerodynamic Sound”,

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3751 26 J. C. Lau, P. J. Morris and M. J. Fisher, “Measurements in subsonic and supersonic free jets using a laser

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(Acoustic) far-field", Inter. J. Aeroacoustics, Vol. 2, No. 2, 2003, pp.95-128.


8

(a) conputational grid (every 16

th grid line is shown)

(b) nozzle exit region (every 4

th grid line is shown)

(c) microjet injection region

(d) Main nozzle exit and microjet injection (bird’s view)

Figure 1 Computational Grid

X/D

Y/D

0 10 20

-4

-2

0

2

4

X/D

Y/D

-1 -0.5 0 0.5 1 1.5 2-1.5

-1

-0.5

0

0.5

1

1.5

X/D

Y/D

-0.1 0 0.1 0.2

0.4

0.5

0.6


9

(a) Centerline axial mean velocity (r/D=0.0)

(b) Lipline axial mean velocity (r/D=0.5)

(c) Centerline axial turbulent velocity (r/D=0.0)

(d) Lipline axial turbulent velocity (r/D=0.5)

(e) Centerline transverse turbulent velocity (r/D=0.0)

Figure 2 Comparison with the experimental data: axial profiles. Axial mean and turbulent velocities on the centerline and on the lipline are compared with the experimental data

of Bridges25

and Lau26

X/D

U/U

j

5 10 15 200

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

coarse

fine

Bridges

Lau

X/D

U/U

j

0 5 10 15 20 250

0.2

0.4

0.6

0.8

coarse

fine

Bridges

X/D

u'/U

j

0 5 10 15 20 250

0.02

0.04

0.06

0.08

0.1

0.12

0.14

0.16coarsefineBridgesLau

X/D

u'/U

j

0 5 10 15 20 250

0.05

0.1

0.15

0.2

0.25

coarse

fine

Bridges

X/D

v'/U

j

0 5 10 15 20 250

0.02

0.04

0.06

0.08

0.1

0.12

0.14

0.16

coarse

fine

Lau


10

(a) Axial mean velocity, X/D = 4

(b) Axial turbulent velocity, X/D = 4

(c) Axial mean velocity, X/D = 8

(d) Axial turbulent velocity, X/D = 8

Figure 3 Comparison with the experimental data: radial profiles.

Axial mean and turbulent velocities at X/D = 4, 8, 12 and 16 are compared

with the experimental data of Bridges25

and Lau26

Y/D

U/U

j

-1 -0.5 0 0.5 1

0.2

0.4

0.6

0.8

1coarsefineBridgesLau

Y/D

u'/U

j

-1.5 -1 -0.5 0 0.5 1 1.5-0.02

0

0.02

0.04

0.06

0.08

0.1

0.12

0.14

0.16

0.18


Y/D

U/U

j

-1 -0.5 0 0.5 1

0.2

0.4

0.6

0.8


Y/D

u'/U

j

-1.5 -1 -0.5 0 0.5 1 1.5-0.02

0

0.02

0.04

0.06

0.08

0.1

0.12

0.14

0.16

0.18

0.2

coarsefineBridgesLau


11

(e) Axial mean velocity, X/D = 12

(f) Axial turbulent velocity, X/D = 12

(g) Axial mean velocity, X/D = 16

(h) Axial turbulent velocity, X/D = 16

Figure 3 Comparison with the experimental data: radial profiles. (cont’d) Axial mean and turbulent velocities at X/D = 4, 8, 12 and 16 are compared

with the experimental data of Bridges25

and Lau26

Y/D

U/U

j

-1 -0.5 0 0.5 1

0.2

0.4

0.6

0.8


Y/D

u'/U

j

-1.5 -1 -0.5 0 0.5 1 1.5-0.02

0

0.02

0.04

0.06

0.08

0.1

0.12

0.14

0.16

0.18


Y/D

U/U

j

-1 -0.5 0 0.5 1

0.2

0.4

0.6

0.8


Y/D

u'/U

j

-1.5 -1 -0.5 0 0.5 1 1.5-0.02

0

0.02

0.04

0.06

0.08

0.1

0.12

0.14

0.16

0.18

0.2

coarsefineBridgesLau


12

(a) Overall SPL(dB)

(b) 1/3 octave SPL, θ = 90°

(c) 1/3 octave SPL, θ =30°

Figure 4 Comparison with the experimental data : Far-fleld noise level

angle

OA

SP

L

40608010012098

100

102

104

106

108

110

112

114

LES

Tanna

St

SP

L(d

B)

10-1

100

101

70

75

80

85

90

95

100

105

110

LES

Tanna

St

SP

L(d

B)

10-1

100

10170

75

80

85

90

95

100

105

110

LES

Tanna

observation angle θ


13

(a) LES, baseline (rm

(0))

(b) Experiment, baseline (rm

(0))

(c) LES, rm

(3)

(d) Experiment, rm

(3)

(e) LES, rm

(7)

(f) Experiment, rm

(7)

Figure 5 Axial turbulent velocity with microjets, X/D=1 left: present LES, right: experiment of Castelain

22


14


(0))


(0))

(c) LES, rm

(3)

(d) Experiment, rm

(3)

(e) LES, rm

(7)

(f) Experiment, rm

(7)

Figure 6 Axial turbulent velocity with microjets, X/D=3 left: present LES, right: experiment of Castelain

22


15


(0))


(0))

(c) LES, rm

(3)

(d) Experiment, rm

(3)

(e) LES, rm

(7)

(f) Experiment, rm

(7)

Figure 7 Reynolds stress (√ ), X/D=1

left: present LES, right: experiment of Castelain22


16


(0))


(0))

(c) LES, rm

(3)

(d) Experiment, rm

(3)

(e) LES, rm

(7)

(f) Experiment, rm

(7)

Figure 8 Reynolds stress (√ ), X/D=3

left: present LES, right: experiment of Castelain22

3

3

3


17

(a) baseline (rm

(0))

(b) rm

(3)

(c) rm

(7)

Figure 9 Turbulent Kinetic Energy, Z=0


18

(a) rm

(3), X/D=0.12

(d) rm

(7), X/D=0.12

(b) rm

(3), X/D=0.2

(e) rm

(7), X/D=0.2

(c) rm

(3), X/D=0.6

(f) rm

(7), X/D=0.6

Figure 10 Axial velocity and turbulent kinetic energy distribution


19

(a) rm

(3)

(b) rm

(7)

Figure 11 Velocity magnitude (color) and TKE (line) Closer view of the Z=0 section near microjet injections.

0.01

0.01

0.02

0.02

0.030.04

0.04

X/D

Y/D

0 0.1 0.2 0.3

0.4

0.45

0.5

0.55

0.6

Vmag

0.85

0.75

0.65

0.55

0.45

0.35

0.25

0.15

0.05

rm3

0.01

0.01

0.01

0.01

0.02

0.02

0.02

0.02

0.03

0.03

0.03

0.04

0.04

X/D

Y/D

0 0.1 0.2 0.3

0.4

0.45

0.5

0.55

0.6

Vmag

0.85

0.75

0.65

0.55

0.45

0.35

0.25

0.15

0.05

rm7


20

(a) θ = 30°

(b) θ = 90°

Figure 12 Far-field Sound Pressure Level (Frequency weighted PSD)

LES and the experiment7

Freq. (Hz)

St

Fre

q.w

eig

hte

dP

SD

(Pa

2)

103

104

10-1

100

0

5

10

15

20

25

30

35

40

45

50

Exp-rm0

Exp-rm3

Exp-rm7

LES-rm0

LES-rm3

LES-rm7

Exp. : Castelain et al.,AIAA J. Vol46, No.5, 2008

Freq. (Hz)

St

Fre

q.w

eig

hte

dP

SD

(Pa

2)

103

104

10-1

100

0

0.5

1

1.5

2

2.5

3

Exp-rm0

Exp-rm3

Exp-rm7

LES-rm0

LES-rm3

LES-rm7

Exp. : Castelain et al.,AIAA J. Vol46, No.5, 2008


21

(a) θ = 30°

(b) θ = 90°

Figure 13 Far-field Sount Pressure Level, 1/3 octave band SPL

St

SP

L(d

B)

10-1

100

10170

75

80

85

90

95

100

105

110

LES(rm0)

LES(rm3)

LES(rm7)

St

SP

L(d

B)

10-1

100

101

70

75

80

85

90

95

100

105

110

LES(rm0)

LES(rm3)

LES(rm7)


22

Figure 14 Far-field Sound Pressure Level, overall SPL

angle

OA

SP

L

40608010012098

100

102

104

106

108

110

112

114

LES(rm0)

LES(rm3)

LES(rm7)

observation angle θ

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