Noise from Forced Mixers

Funded by the Indiana 21st Century Research and

Technology Fund

Correlating RANS Computed Mean Flow with Forced Mixed

Jets

C. Wright, G. Blaisdell, A. Lyrintzis

School of Aeronautics & AstronauticsPurdue University

Goals of Project

• The primary goal is to develop a greater understanding of the how noise from forced mixed jets may be correlated to the RANS calculated mean flow field.

• The ultimate goal is to develop quantitative correlations that could be used as input for a semi-empirical model

Approaches

• Careful selection of numerical tools such as the turbulence model and CFD code are very important. Validation should concentrate on a detailed comparison of flow contours rather than integrated quantities.

• Grid development and validation should likewise concentrate on the details of the flow.

• Qualitative trends and observations regarding the relationship between noise data and CFD results should be investigated before attempting to quantify the results.

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

1.7 million grid points 7 million grid points

Density

VorticityMagnitude

Spalart-Allmaras and and Menter SST at Nozzle Exit Plane

Spalart SST

Density

VorticityMagnitude

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

High Penetration Mixer Flowfield

• Case is for a high throttle setting at Mach 0.2

• Used Menter SST Turbulence Model

• Good overall agreement with experiment. TKE is a little low for X/D = 1.0 and X/D = 2.0. CFD results tend to be overly sharp and defined.

• CFD and experiment both show a substantial amount of interaction between the free shear layer and the streamwise vortices.

Medium Penetration Mixer Flowfield

• Case is for a high throttle setting at Mach 0.2

• Used Menter SST Turbulence Model

• The agreement between the CFD and the experiment is about the same as for the high penetration case.

• The free shear layer and the streamwise vortices exist as separate and distinct flow structures through at least X/D = 1.0.

Experimental Results (1/4 Scale Model)

Experimental Results (1/4 Scale Model)

Current State of Project

• Finishing up CFD runs. Using WIND and Menter SST turbulence model.

• Currently studying noise data along with RANS results and PIV experiments (including low penetration case not shown).

• Have identified some interesting trends, and are preparing more CFD runs to finalize these comparisons.

• Specifics of research is being published in a paper for the AIAA Reno conference (Jan. 2004).

Development of a Semi-Empirical Jet Noise Model for Forced Mixer

Noise Predictions

L. Garrison, Purdue University

W. Dalton, Rolls-Royce Indianapolis

A. Lyrintzis and G. Blaisdell

Purdue University

• Four-Source Model Comparisons– Four-Source method implementation– Predictions for the confluent mixer

• Two-Source Model– Formulation– Optimization procedure– Optimized results for the 12 lobe mixers– Optimized parameter correlations

Outline

Practical Configuration Geometry

Secondary Flow

Primary Flow

Flow Mixer

Nozzle Wall

Tail Cone(Bullet)

Final Nozzle Exit

Dual Flow Configurations• Four-Source method

developed for a coplanar, coaxial jet

• The configuration for the practical case has a buried primary flow in a convergent nozzle with a center body (tail cone or bullet)

• Based on an ‘Equivalent Coaxial Jet’– Approach developed by B. Tester and M. Fisher

• Define primary and secondary jets at the final nozzle exit plane

• Assumptions– Isentropic flow in the nozzle– Primary and secondary flows do not mix in the

nozzle– Static pressure of the two flows at the exit plane

are equal

Single Jet Property Calculation

Single Jet Property Calculation• Jet Areas at the Final Nozzle Exit

– Guess Ap

– Calculate As

– Calculate Mexit

– Calculate Pstatic

– Iterate until the primary and secondary static pressures are equal

pns AAA

12

1

22

1

22

1

1

1

cs

exit

exit

cs

cs

exit

M

M

M

M

A

A

12

2

11

exit

static

o MP

PJ

Four-Source Method Implementation• Primary and Secondary Jet Properties

– Calculated at the final nozzle exit

• Mixed Jet and Effective Jet Properties

λβδ1

λβ1TT

βδλ1

λβδ)λβ)(1(1DD

λβδ1

βδλ1VV

pm

2

1

2pm

2

pm

p

s

p

s

p

s

ρ

ρδ

A

Aβ

V

Vλ

pe

1/22pe

pe

TT

βλ1DD

VV

7dBe

Current Prediction Method Comparisons

• Four-Source / Single Jet / Experimental Data Comparisons– Confluent Mixer, Low Power Operating Point– ARP876C Method used for all single jet

noise predictions• Bass and Sutherland correction for atmospheric

attenuation

– Four-Source coaxial jet prediction• Based on equivalent coaxial jet properties

– Single jet prediction• Based on fully mixed flow at the final nozzle exit

Current Prediction Method Comparisons

Forced Mixer Experimental Data• Four Mixer Configurations

– Confluent Mixer (CFM)– Low Penetration 12 Lobe Mixer (12CL)– Mid Penetration 12 Lobe Mixer (12UM)– High Penetration 12 Lobe Mixer (12UH)

• Low Power Operating Point

H

Forced Mixer Experimental Data

• Objective:– Match the experimental data SPL spectrum at all

angles and all frequencies using two single stream jet sources.

• Formulation:s s s s 1 s0 USPL ( , ) SPL(V ,T ,D , , ) 10lo Bg ( dF , )cf ff f

Single Jet Prediction

Source Strength

Spectral Filter

Variable Parameters:

m m m m 1 m0 DSPL ( , ) SPL(V ,T ,D , , ) 10lo Bg ( dF , )cf ff f

s m

Spectral Filter Cut-off Frequency

, Source StrengtΔdB Δ hs )d BB (dcf

Two-Source Model

Two-Source Model

dB

dB

fc fc

• Variable Parameters

1/3 Octave Band Number 1/3 Octave Band Number

1/3

Oct

ave S

PL

[dB

]

1/3

Oct

ave S

PL

[dB

]

Effects of Variations in dB Effects of Variations in fc

• Optimization Procedure– For a given geometry and operating condition,

optimize the source strength parameters (dbs, dbm) for a range of cut-off frequencies

– Find the set of optimized parameters that minimize the prediction error for all operating conditions

– Correlate the final set of parameters to the changes in the mixer design

Two-Source Model Optimization

• Optimization Challenges– Optimum Criterion

• Maximum Error• Average Error• Weighted Error

– Solution Non-Uniqueness– Local Minima– Non-Linear Behavior

• Optimization Tools– Nonlinear Least Squares

• MATLAB: lsqnonlin (Levenberg–Marquadt Optimization Method )

Two-Source Model Optimization

Two-Source Model Optimization 15 Microphone locations (90 º to 160 º in 5º increments) 1 Sound Pressure Level (SPL) spectrum per microphone 27 Frequency Bands per spectrum (1/3 Octave Bands)

405 SPL values per data point

Microphone Locations

Jet 80observer

J

r

D

Two-Source Model Optimization• Optimum Criterion

– Based on a ‘OASPL type’ weighting– At each observer angle:

– Weighted error values:

exp exp max0.1 SPL , SPL ,

, 10i if f

w iE f

, , , ,w exp predError f E f SPL f SPL f

Two-Source Model Results• Test Case

– Low Penetration Mixer– Low Power Operating Point

• Two-Source Model– Upstream Source: Secondary Jet– Downstream Source: Mixed Jet

Prediction Method

Maximum Error [dB]

Average Error [dB]

Weighted Error [dB]

Four-Source 13.18 2.56 0.41

Single Jet 12.02 2.53 0.64

Two-Source 8.35 1.29 0.36

Optimized Two-Source Results

Optimized Two-Source Results

• Current jet noise predictions do not accurately model the noise from jets with internal forced mixers

• Forced mixer jet noise can be modeled by a combination of two single jet sources

• Optimized Two-Source model source strengths and cut-off Strouhal numbers appear to correlate linearly with the amount of lobe penetration

Summary

• Fisher, M.J., Preston, G.A., and Bryce, W.D., “A Modelling of the Noise from Simple Coaxial Jets Part I: With Unheated Primary Flow,” Journal of Sound and Vibration, 209(3):385-403, 1998

• Fisher, M.J., Preston, G.A., and Mead, C.J., “A Modelling of the Noise from Simple Coaxial Jets Part II: With Heated Primary Flow,” Journal of Sound and Vibration, 209(3):405-417, 1998

• “ARP87C: Gas Turbine Jet Exhaust Noise Prediction,” Society of Automotive Engineers, Inc., November, 1985.

• Bass, H.E., Sutherland, L.C., Zuckerwar, A.J., Blackstone, D.T., and Hester, D.M., “Atmospheric Absorption of Sound: Further Developments,” Journal of the Acoustical Society America, 97(1):680-683, 1995

References

Two-Source Model Optimization

SPLexp - SPLpredSPLexp – SPLexpmax