holographic visualization of a low speed jet

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10-23-2017

Holographic Visualization of a Low Speed JetMoohyung LeePurdue University

J Stuart BoltonPurdue University, [email protected]

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Lee, Moohyung and Bolton, J Stuart, "Holographic Visualization of a Low Speed Jet" (2017). Publications of the Ray W. HerrickLaboratories. Paper 162.http://docs.lib.purdue.edu/herrick/162

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HOLOGRAPHIC VISUALIZATION

OF A LOW SPEED JET

Moohyung Lee and J. Stuart Bolton

Ray W. Herrick Laboratories

Purdue University

Reference: M. Lee and J.S. Bolton, “Source characterization of a subsonic jet byusing near-field acoustical holography,” Journal of the Acoustical Society of America,Vol. 121, 967-977, 2007.

Go to: http://docs.lib.purdue.edu/herrick/ for related presentations (Herrick epubs)

LVA / UFSC / KTH Summer School in Aeroacoustics: 23 – 26 October 2017

http://www2.lib.purdue.edu:2149/WoS/CIW.cgi?SID=4DhMdgMNCEL@1en1iAk&Func=Abstract&doc=1/1

http://docs.lib.purdue.edu/herrick/

➢ Source imaging methods based on array measurement for jet

source localization

• One-dimensional array: acoustic mirror, acoustic telescope,

polar correlation technique

• Two-dimensional array based on beamforming theory

➢ Problem

• Farfield measurement

the spatial resolution with which a source can be visualized

is limited

• Model-based approach

The accuracy is dependent upon the way in which the

sources are modeled

PROBLEM DEFINITION

Herrick Labs, Purdue University 2

➢ Develop an alternative method for jet noise localization and visualization

• Identify source strength distributions

• Predict farfield radiation based on nearfield measurements

• Quantify the performance of noise control solutions

➢ NAH can provide more accurate results (with a higher spatial resolution) since no assumption is made as to the nature of sources

➢ Establish a strategy for designing measurement arrays

➢ Stabilize the inverse solutions

➢ Signal processing method to address the finite measurement effect

OBJECTIVES


➢ A three-dimensional sound field can be visualized based on

data measured on a two-dimensional surface (the hologram

surface)

➢ Many acoustical properties can be reconstructed based on

pressure measurements

• Sound pressure

• Particle velocity vector

• Acoustic intensity vector

• Sound power

BASIC CONCEPTS OF NAH

Predicted sound images

Inverse problem Forward problem


DFT-BASED NAH

Measured Pressure Temporal

FFT

Supersonic Intensity

),,,( tzrp h ),,,( zrp h

( , , )n zP r k

( , , )n zV r k

( , , , )r z

( , , , )p r z

Spatial IDFT

),,( zhn krP

ProjectionSpatial DFT

*1Re{ }

2p

( ) ( )*1Re{ }

2

s sp

Reconstructed PropertiesSound Power

Radiation Directivity

Acoustic Intensity

wave number domain


➢ In cylindrical coordinates

• Pressure on the reconstruction surface

• Radial particle velocity on the reconstruction surface

RADIAL PROJECTION OF THE SOUND FIELD

z

zki

hrn

rn

zhn

n

in kderkH

rkHkrPezrp z

)(

)(),(

2

1),,(

)1(

)1(

(1)

(1)

( )1( , , ) ( , )

2 ( )zik zin n rr

r n h z z

n n r h

H k rikr z e P r k e dk

ck H k r

pressure propagator

velocity propagator


MULTI-REFERENCE, SCAN-BASED NAH

The sound field is expressed in

terms of cross-spectral matrices as

H 1 H

pp rp rr rp rp rr rp

C C C C H C HHologram

surface

➢ Allows the visualization of sources comprising a number of uncorrelated

subsources and the separation of the total sound field into a corresponding

number of uncorrelated partial fields

➢ Scans the entire hologram surface over a number of patches in sequence

➢ The number of microphones required for measurements can be reduced

Fixed reference

microphone array

Roving field

microphone

array

where rprrrp CCH

1


➢ Requirement for holographic projection

- Spatially coherent sound field

➢ The composite sound field must be decomposed into coherent

partial fields

CONCEPT OF PARTIAL FIELD DECOMPOSITION

Total Sound Field

Engine Noise

Exhaust Noise

This work was done by Hyu-Sang Kwon.


➢ The number of references the number of incoherent sources

➢ Problem

• In the presence of noise, additional artificial sources are introduced

• The “position” as well as the number of references is important when sources are localized

➢ The use of a relatively large number of references

• A clearer separation between the source- and noise- related singular values

• Errors in both the singular values and vectors are reduced

• The number of partial fields required for sound field description approaches the actual number of subsources

THE NUMBER OF REFERENCE IN THE

CROSS-SPECTRAL MEASUREMENTS


➢ Virtual coherence function

where

➢ The sum of virtual coherence functions

• By finding the value of R that causes the sum of the virtual coherence functions to approach unity over the entire hologram surface:

• the number of virtual references required to describe the sound field

• the number of singular values to be discarded

SELECTION OF A CUT-OFF SINGULAR VALUE

2

:

1

1R

j i

i

for all 1,2, ,j M.

H

vp rpC U C

2

(scan)2

:

(scan) (scan)

i j

i i j j

v p

j i

v v p p

C

C C


➢ Requirement

• References should be placed in regions of low flow velocity

(i.e., rsr = 0 and psr = 0 )

• References should not sense any flow noise generated by

the interaction of the flow with the field microphones

(i.e., rsf = 0 )

➢ Restriction to the use of virtual coherence

• The diagonal components of (i.e., the auto-spectra

of field microphone self-noise) can not be removed.

This effect does not affect the accuracy of the partial field

decomposition, but causes the virtual coherence to drop

REMOVAL OF SELF-NOISE EFFECT

* TE sf sf p p


PATCH NAH

Conventional NAH

The measurement aperture should be

extended to the region in which the

sound level drops to a sufficiently low

level: complete scan of the sound field.

Patch NAH

Measurements are made over a

limited region of interest: partial scan

of the sound field.


➢ Difficult to measure the complete sound field when large scale-

structures are implemented

➢ Suffers from finite hologram effect

• Wrap-around error

Periodic replication of the data in the spatial domain

: easily dealt with by zero padding

• Windowing effect

A sharp transition at the edge of measurement aperture

introduces high wave number noise components

: degrades reconstruction results when projecting towards a

source due to the ill-posed nature of problem

CONSTRAINTS OF DFT-BASED NAH


PROCEDURE

Scan-based, Cross-

Spectral Measurement

Partial Field

Decomposition

Data Extrapolation

(Cylindrical Patch NAH)

Cylindrical NAH

• The use of a large number of references to minimize noise effects

• Careful design of a reference array

• Based on the use of the acoustic transfer matrix in conjunction with a regularization by using TSVD to correct for source nonstationarity

• Extension of the data measured in a finite region by iterative method

• Regularization: modified Tikhonov regularization used in conjunction with Mozorov discrepancy principle

• Pressure, particle velocity, acoustic intensity


APPLICATION TO AEROACOUSTIC SOURCES (1):

DUCTED AXIAL FAN*

• No. of references: 3

• No. of measurement points

: 8 by 8 (axial by circum.)

• Increment in the axial direction

: 39 cm

• Radius of the measurement

surface: 50 cm

• Frequency range: 0~400Hz

references

field

microphones


*Moohyung Lee, J. Stuart Bolton and Luc. Mongeau, “Application of cylindrical near-field acoustical holography to the

visualization of aeroacoustic sources,” Journal of the Acoustical Society of America, Vol. 114, 842-858, 2003.

➢ Configuration 1: Original form (without leakage)

➢ Configuration 2: With leakage

Configuration 2

upstream

(negative z-dir.)

TEST CONFIGURATIONS

holes


SINGULAR VALUES OF THE REFERENCE

CROSS-SPECTRA MATRICES

(a) without leakage (b) with leakage

• The three references used for the measurements were sufficient

to describe the sound field at both frequencies

50 100 150 200 250 300 350 400-20

-10

0

10

20

30

40

50

60

Frequency [Hz]

Sin

gu

lar

Valu

e [

dB

(rm

s)]

1st Singular value

2nd Singular value

3rd Singular value

50 100 150 200 250 300 350 400-20

-10

0

10

20

30

40

50

60

Frequency [Hz]

Sin

gu

lar

Valu

e [

dB

(rm

s)]

1st Singular value

2nd Singular value

3rd Singular value

Broadband

noise at 330 HzBlade passing

tone at 361 Hz


PARTIAL FIELDS (1)

(a) broadband noise (330 Hz) (b) blade passing tone (361 Hz)

The first partial fields for the first case (original)

• Dipole-like radiation at both frequencies


PARTIAL FIELDS (2)

The first partial fields for the second case (with leakage)

(a) broadband noise (330 Hz) (b) blade passing tone (361 Hz)

• Leakage has a larger influence on the blade passing tone


SOURCE DIRECTIVITIES FOR THE FIRST CASE

30

210

60

240

90

270

120

300

150

330

180 0

NAH

Theoretical

30

210

60

240

90

270

120

300

150

330

180 0

NAH

Theoretical

(a) 330 Hz (b) 361 Hz

(along with comparison to theoretical dipole directivity)

The total sound fields for the first case (original)


SOURCE DIRECTIVITIES FOR THE SECOND CASE

30

210

60

240

90

270

120

300

150

330

180 0

30

210

60

240

90

270

120

300

150

330

180 0

(a) 330 Hz (b) 361 Hz

The total sound fields for the second case (with leakage)


➢ Ma = 0.26 turbulent cold jet from a 0.8 cm diameter burner nozzle

➢ The number of references: 48 (6 linear arrays)

➢ Hologram radius: 30 cm

➢ The number of measurement points: 16 (circum.) by 36 (axial)

➢ Increment in the axial direction: 3 cm

APPLICATION TO AEROACOUSTIC SOURCES (2):

SUBSONIC FREE JET

reference

array

scanning

array

jet exit


EFFECT OF THE ARRAY CONFIGURATION (1)

array #2

array #3

array #1

array #4

array #5

array #6

0

Three array configurations

• Case 1: use 48 references

• Case 2: use 18 references (3 references from each array)

• Case 3: use 16 references (array #1 and #2)


EFFECT OF THE ARRAY CONFIGURATION (2)

< Singular values >

< Sum of the virtual coherence functions at 1 kHz >

0 500 1000 1500 2000-20

0

20

40

60

80

Hz

Sin

gu

lar

Va

lue

s [d

B]

0 500 1000 1500 2000-20

0

20

40

60

80

Hz

Sin

gu

lar

Va

lue

s [d

B]

1020

30

5

10

15

0

0.5

1

Axial Circumferential 0

0.2

0.4

0.6

0.8

1

1020

30

5

10

15

0

0.5

1


0.2

0.4

0.6

0.8

1

Case 1 Case 2 Case 3

Case 1 Case 2 Case 3

11 partial fields 18 partial fields 16 partial fields

10

2030

5

10

15

0

0.5

1


0.2

0.4

0.6

0.8

1

0 500 1000 1500 2000-20

0

20

40

60

80

Hz

dB

(rm

s)


PARTIAL FIELD (1)

< side view > < top view >

• Dipole-like component (the 1st partial field at 1 kHz)


PARTIAL FIELD (2)


• Quadrupole-like component (the 2nd partial field at 1 kHz)


PARTIAL FIELD (3)


• Quadrupole-like component (the 4th partial field at 1 kHz)


PARTIAL FIELD (4)


• Octupole-like component (the 10th partial field at 1kHz)


ACOUSTIC INTENSITY (1)


• Dipole-like component (the 1st partial field)




• Quadrupole-like component (the 2nd partial field)




• Quadrupole-like component (the 4th partial field)




• Octupole-like component (the 10th partial field)


➢ The sound field was constructed by using 11 partial fields

obtained when 48 references were used

➢ The comparison with the directly measured sound field was

made on the plane defined by

TOTAL SOUND FIELD

< reconstructed by NAH > < directly measured >

225


➢ The comparison with the directly measured directivity was made

on an arc 96 cm from the jet exit

FARFIELD DIRECTIVITY

< measurement array > < pressure at r = 96 cm >

0

-90 -60 -30 0 30 60 9020

25

30

35

40

45

50

Angle [degree]

Pre

ssu

re [d

B]

predicted by NAHdirectly measured

0


➢ Dipole-like: the 1st and 9th partial fields

➢ Quadrupole-like: partial fields from the 2nd to 8th

➢ Octupole-like: the 10th and 11th

SOUND POWER

Total Dipole Quadrupole Octupole0

10

20

30

40

50

Watt

ref

10

e(-

12

)

41.6 38.2 38.9 22.1

Dipole- and quadrupole-like components are the main contributors

to the sound radiation


➢ Cylindrical NAH procedure was applied to the visualization of

the sound field radiated by a subsonic jet

➢ Results reconstructed by using NAH were compared with

directly measured results, and good agreement was found

➢ Strategy for reference array design was described and its effect

was demonstrated

➢ It was found that the sound field generated by the turbulent jet

was naturally decomposed into dipole-, quadrupole-, and

octupole-like components

➢ I’d rather be on the inside looking out than the outside looking in!

SUMMARY


➢ NAH measurement on the conical hologram surface in

conjunction with either SVD-based NAH or SONAH to reduce

the finite measurement aperture effect

RECOMMENDATION

Jet Engine

jet flow

measurement aperture


See: Yong-thung Cho and J. Stuart Bolton, “Source visualization by using

statistically optimized nearfield acoustical holography in conical coordinates,”

Proceedings of INTER-NOISE 2012, 12 pages, 2012.

➢ Develop NAH formulation for simulating the sound field in a

take-off condition of flights: test-based prediction of farfield

radiation characteristics based on nearfield measurements

RECOMMENDATION

Directivity pattern changes due to the effect of a moving medium


See: Hyu-Sang Kwon, Yaying Niu and Yong-Joe Kim, “Planar Nearfield Acoustical Holography in moving fluid

medium with subsonic and uniform velocity,” Journal of the Acoustical Society of America, Vol. 128, No. 4, pp.

1823-1832, 2010.

➢ Test stand application: prediction of farfield radiation

characteristics based on nearfield measurements

➢ Visualization of Lighthill source terms

➢ Certification of various source terms to radiated source power

➢ Equivalent source method including higher order elemental

sources

RECOMMENDATION


holographic visualization of a low speed jet

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