Development of Simulation Methodologies for Forced Mixers

Anastasios LyrintzisSchool of Aeronautics &

AstronauticsPurdue University

Acknowledgements

• Indiana 21st Century Research and Technology Fund

• Prof. Gregory Blaisdell • Rolls-Royce, Indianapolis (W. Dalton, Shaym

Neerarambam) • L. Garrison, C. Wright, A. Uzun, P-T. Lew

Motivation

• Airport noise regulations are becoming stricter.

• Jet exhaust noise is a major component of aircraft engine noise

• Lobe mixer geometry has an effect on the jet noise that needs to be investigated.

Methodology

• 3-D Large Eddy Simulation for Jet Aeroacoustics

• RANS for Forced Mixers• Coupling between LES and RANS

solutions• (Semi-empirical method)

3-D Large Eddy Simulation for Jet Aeroacoustics

Objective• Development and full validation of a

Computational Aeroacoustics (CAA) methodology for jet noise prediction using: A 3-D Large Eddy Simulation (LES) code

working on generalized curvilinear grids that provides time-accurate unsteady flow field data

A surface integral acoustics method using LES data for far-field noise computations

Numerical Methods for LES• 3-D Navier-Stokes equations• 6th-order accurate compact differencing scheme

for spatial derivatives• 6th-order spatial filtering for eliminating

instabilities from unresolved scales and mesh non-uniformities

• 4th-order Runge-Kutta time integration• Localized dynamic Smagorinsky subgrid-scale

(SGS) model for unresolved scales

Tam & Dong' s radiation boundary conditions

Tam & Dong' s radiation boundary conditions

Tam & Dong' soutflow boundaryconditions

Sponge zone

Tam &Dong' sradiationbcs

Vortex ring forcing

Computational Jet Noise Research• Some of the biggest jet noise computations:

Freund’s DNS for ReD = 3600, Mach 0.9 cold jet using 25.6 million grid points (1999)

Bogey and Bailly’s LES for ReD = 400,000, Mach 0.9 isothermal jets using 12.5 and 16.6 million grid points (2002, 2003)

• We studied a Mach 0.9 turbulent isothermal round jet at a Reynolds number of 100,000

• 12 million grid points used in our LES

Computation Details• Physical domain length of 60ro in streamwise

direction• Domain width and height are 40ro • 470x160x160 (12 million) grid points• Coarsest grid resolution: 170 times the local

Kolmogorov length scale• One month of run time on an IBM-SP using 160

processors to run 170,000 time steps• Can do the same simulation on the Compaq

Alphaserver Cluster at Pittsburgh Supercomputing Center in 10 days

x / ro

y/r

o

0 10 20 30 40 50 60 70-20

-10

0

10

20

30

40

z / ro

y/r

0

-20 -10 0 10 20-20

-15

-10

-5

0

5

10

15

20

x = 5ro

z / ro

y/r

0

-20 -10 0 10 20-20

-15

-10

-5

0

5

10

15

20

x = 15ro

z / ro

y/r

0

-20 -10 0 10 20-20

-15

-10

-5

0

5

10

15

20

x = 35ro

Mean Flow Results• Our mean flow results are compared with:

Experiments of Zaman for initially compressible jets (1998)

Experiment of Hussein et al. (1994) Incompressible round jet at ReD = 95,500 Experiment of Panchapakesan et al. (1993)

Incompressible round jet at ReD = 11,000

x / Dj

Uj/U

c(x)

0 10 20 300

0.5

1

1.5

2

2.5

3

3.5

4

4.5

5

slope = 0.161

From Zaman' sexperiments (1998):slope 0.155 for Mj = 0.9

Jet Mean Centerline Velocity Decay

x / Dj

Q(x

)/Q

e

10 15 20 25 304

5

6

7

8

9

10

11

slope = 0.267

From Zaman' sexperiments (1998):slope 0.26 for Mj = 0.9

Streamwise Mass Flux

slope = A = 0.092

experimental valuesof A : 0.086 - 0.096

x / ro

r 1/2(x

)/r o

0 5 10 15 20 25 30 35 40 45 50 55 600

0.5

1

1.5

2

2.5

3

3.5

4

4.5

5

5.5

6

Jet Half-Velocity Radius Growth

r / r1/2

u/U

c

0 0.5 1 1.5 2 2.50

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1x = 45rox = 50rox = 55roexp. data of Hussein et. al.exp. data of Panchapakesan et. al.

Mean Streamwise Velocity Profiles

r / r1/2

rx

0 0.5 1 1.5 2 2.50

0.005

0.01

0.015

0.02

0.025x = 45rox = 50rox = 55roexp. data of Hussein et. al.exp. data of Panchapakesan et. al.

rx = vx' vr' / Uc2

Reynolds Shear Stress Profiles

k1

E u(1)(k

1)

5 10 15 2010-7

10-6

10-5

10-4

10-3

10-2

10-1

100

k1-5/3

Grid cutoff

One-dimensional spectrum Eu(1) (k1) of vx'

at x = 20ro on the jet centerline

Jet Aeroacoustics• Noise sources located at the end of potential core• Far field noise is estimated by coupling near field

LES data with the Ffowcs Williams–Hawkings (FWH) method

• Overall sound pressure level values are computed along an arc located at 60ro from the jet nozzle

• Cut-off Strouhal number based on grid resolution is around 1.0

X

Y

Z

Control Surface

Control Surface

Jet Flow

x = 35 ro x = 45 ro x = 60 ro

30 ro

x / ro

y/r

o

0 10 20-5

0

5

10

15

R

• OASPL results are compared with: Experiment of Mollo-Christensen et al. (1964) Mach 0.9 round jet at ReD = 540,000 (cold jet) Experiment of Lush (1971)

Mach 0.88 round jet at ReD = 500,000 (cold jet) Experiment of Stromberg et al. (1980)

Mach 0.9 round jet at ReD =3,600 (cold jet) SAE ARP 876C database

Jet Aeroacoustics (continued)

(deg)

OAS

PL(d

B)

10 20 30 40 50 60 70 80 90 100 110 120100

102

104

106

108

110

112

114

116

118

120

LES + FWH (isothermal jet)SAE ARP 876C predictionexp. of Mollo-Christensen et al. (cold jet)exp. of Lush (cold jet)exp. of Stromberg et al. (cold jet)

St = f Dj / Uj

SPL

(dB

/St)

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 2.2 2.490

100

110

120

130

Our spectrum at x = 29ro and r = 12roBogey and Bailly' s spectrum at x = 29ro and r = 12ro

St = f Dj / Uj

SPL

(dB

/St)

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 2.2 2.490

100

110

120

130 Our spectrum at x = 11ro and r = 15roBogey and Bailly' s spectrum at x = 11ro and r = 15ro

Conclusions• Localized dynamic SGS model stable and

robust for the jet flows we are studying• Very good comparison of mean flow results

with experiments• Aeroacoustics results are encouraging• Valuable evidence towards the full

validation of our CAA methodology has been obtained

Near Future Work• Simulate Bogey and Bailly’s ReD = 400,000

jet test case using 16 million grid points 100,000 time steps to run About 150 hours of run time on the

Pittsburgh cluster using 200 processors• Compare results with those of Bogey and

Bailly to fully validate CAA methodology• Do a more detailed study of surface integral

acoustics methods

Can a realistic LES be done for ReD = 1,000,000 ?

• Assuming 50 million grid points provide sufficient resolution:

• 200,000 time steps to run• 30 days of computing time on the

Pittsburgh cluster using 256 processors• Only 3 days on a near-future computer that

is 10 times faster than the Pittsburgh cluster

Future Work

• Extend methodology to handle:– Noise from unresolved scales– Supersonic flow– Solid boundaries (lips)– Complicated (mixer) geometries

multi-block code

RANS for Forced Mixers

Objective

• Use RANS to study flow characteristics of various flow shapes

What is a Lobe Mixer?

Internally Forced Mixed Jet

Bypass Flow

Mixer

Core Flow

Nozzle

Tail Cone

Exhaust Flow

Exhaust / Ambient Mixing Layer

Lobed Mixer Mixing Layer

Forced Mixer

H

Lobe Penetration (Lobe Height)

H:

3-D Mesh

WIND Code options• 2nd order upwind scheme• 1.7 million/7 million grid points• 8-16 zones• 8-16 LINUX processors• Spalart-Allmaras/ SST turbulence model• Wall functions

Grid Dependence

Density Contours1.7 million grid points

Density Contours7 million grid points

Grid Dependence1.7 million grid points 7 million grid points

Density

VorticityMagnitude

Spalart-Allmaras and Menter SST Turbulence Models

Spalart-Allmaras

Menter SST

Spalart-Allmaras and and Menter SST at Nozzle Exit Plane

Spalart SST

Density

VorticityMagnitude

Mean Axial Velocity at x = 2.88”(High Penetration)

¼ Scale Spalartat x = 2.88/4”

experiment Spalart Allmaras

Mean Axial Velocity at x = 2.88”(High Penetration)

¼ Scale Menter SSTat x = 2.88/4”

experiment Menter SST

Spalart-Allmaras vs. Menter SST

• The Spalart-Allmaras model appears to be less dissipative. The vortex structure is sharper and the vorticity magnitude is higher at the nozzle exit.

• The Menter SST model appears to match experiments better, but the experimental grid is rather coarse and some of the finer flow structure may have been effectively filtered out.

• Still unclear which model is superior. No need to make a firm decision until several additional geometries are obtained.

Geometry at Mixer ExitLow Penetration Mid Penetration High Penetration

DENSITY CONTOURS (¼ Scale)

Low Penetration

Mid Penetration

Vorticity Magnitude at Nozzle Exit(¼ Scale Geometry)

Low Penetration Mid Penetration High Penetration

Turbulent Kinetic Energy at Nozzle Exit(¼ Scale Geometry)

Low Penetration Mid Penetration High Penetration

Preliminary Conclusions

• 1.7 million grid is adequate• Further work is needed comparing the

turbulence models and results for different penetration lengths

Future Work

• Analyze the flow fields and compare to experimental acoustic and flow-field data for additional mixer geometries.

• Further compare the two turbulence models.• If possible, develop qualitative relationship

between mean flow characteristics and acoustic performance.

Implementing RANS Inflow Boundary Conditions for 3-D

LES Jet Aeroacoustics 

Objectives• Implement RANS solution and onto

3-D LES inflow BCs as initial conditions.

• Investigate the effect of RANS inflow conditions on:– Reynolds Stresses– Far-field sound generated

Implementation Method

• RANS grid too fine for LES grid to match.

• Since RANS grid has high resolution, linear interpolation will be used.

LES

RANS

Issues and Challenges• Accurate resolution of outgoing

vortex with LES grid.• Accurate resolution of shear layer

near nozzle lip.• May need to use an intermediate

Reynolds number eg. Re = 400,000

Final Conclusion

• Methodologies (LES, RANS, coupling) are being developed to study noise from forced mixers