Development of Simulation Methodologies for Forced Mixers

Anastasios Lyrintzis

School of Aeronautics & Astronautics

Purdue 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

1

x = 45ro

x = 50ro

x = 55ro

exp. 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

0.025

x = 45ro

x = 50ro

x = 55ro

exp. data of Hussein et. al.exp. data of Panchapakesan et. al.

rx = vx' vr' / Uc2

Reynolds Shear Stress Profiles

k1

Eu(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)

OA

SPL

(dB

)

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 = 12ro

Bogey 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 = 15ro

Bogey 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 Dependence

1.7 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