holographic visualization of a low speed jet
TRANSCRIPT
Purdue UniversityPurdue e-Pubs
Publications of the Ray W. Herrick Laboratories School of Mechanical Engineering
10-23-2017
Holographic Visualization of a Low Speed JetMoohyung LeePurdue University
J Stuart BoltonPurdue University, [email protected]
Follow this and additional works at: http://docs.lib.purdue.edu/herrick
This document has been made available through Purdue e-Pubs, a service of the Purdue University Libraries. Please contact [email protected] foradditional information.
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
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
➢ 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
Herrick Labs, Purdue University 3
➢ 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
Herrick Labs, Purdue University 4
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
Herrick Labs, Purdue University 5
➢ 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
Herrick Labs, Purdue University 6
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
Herrick Labs, Purdue University 7
➢ 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.
Herrick Labs, Purdue University 8
➢ 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
Herrick Labs, Purdue University 9
➢ 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
Herrick Labs, Purdue University 10
➢ 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
Herrick Labs, Purdue University 11
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.
Herrick Labs, Purdue University 12
➢ 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
Herrick Labs, Purdue University 13
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
Herrick Labs, Purdue University 14
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
Herrick Labs, Purdue University 15
*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
Herrick Labs, Purdue University 16
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
Herrick Labs, Purdue University 17
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
Herrick Labs, Purdue University 18
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
Herrick Labs, Purdue University 19
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)
Herrick Labs, Purdue University 20
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)
Herrick Labs, Purdue University 21
➢ 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
Herrick Labs, Purdue University 22
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)
Herrick Labs, Purdue University 23
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
Axial Circumferential 0
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
Axial Circumferential 0
0.2
0.4
0.6
0.8
1
0 500 1000 1500 2000-20
0
20
40
60
80
Hz
dB
(rm
s)
Herrick Labs, Purdue University 24
PARTIAL FIELD (1)
< side view > < top view >
• Dipole-like component (the 1st partial field at 1 kHz)
Herrick Labs, Purdue University 25
PARTIAL FIELD (2)
< side view > < top view >
• Quadrupole-like component (the 2nd partial field at 1 kHz)
Herrick Labs, Purdue University 26
PARTIAL FIELD (3)
< side view > < top view >
• Quadrupole-like component (the 4th partial field at 1 kHz)
Herrick Labs, Purdue University 27
PARTIAL FIELD (4)
< side view > < top view >
• Octupole-like component (the 10th partial field at 1kHz)
Herrick Labs, Purdue University 28
ACOUSTIC INTENSITY (1)
< side view > < top view >
• Dipole-like component (the 1st partial field)
Herrick Labs, Purdue University 29
ACOUSTIC INTENSITY (2)
< side view > < top view >
• Quadrupole-like component (the 2nd partial field)
Herrick Labs, Purdue University 30
ACOUSTIC INTENSITY (3)
< side view > < top view >
• Quadrupole-like component (the 4th partial field)
Herrick Labs, Purdue University 31
ACOUSTIC INTENSITY (4)
< side view > < top view >
• Octupole-like component (the 10th partial field)
Herrick Labs, Purdue University 32
➢ 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
Herrick Labs, Purdue University 33
➢ 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
Herrick Labs, Purdue University 34
➢ 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
Herrick Labs, Purdue University 35
➢ 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
Herrick Labs, Purdue University 36
➢ 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
Herrick Labs, Purdue University 37
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
Herrick Labs, Purdue University 38
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
Herrick Labs, Purdue University 39