measurements in thermoacoustic oscillations: (i) pressure ...€¦ · measurements in...
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Measurements in thermoacousticoscillations:
(i) pressure and acoustic velocity uncertainty in practical systems
S. HochgrebUniversity of Cambridge
Tango WorkshopIIT Madras, 4-7 Feb, 2014
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Outline
2
• Introduction• Experimental issues in pressure measurements• Acoustic velocity calculations• Uncertainties in velocity calculations• Example: two-microphone vs. PIV
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The problem: how to make predictions for real injectors in real engines
3
0 200 400 600 800 1000 1200 1400
Frequency in Hz
Engine tests
Resulting spectrum: sum of interactions: - amplification of random fluctuations - system interaction with amplitude-
dependent heat release rate response
System characterization:- geometry - flows (including leaks)- acoustic boundary conditions- flame behaviour
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Background – Linearized Euler equations (1D)
4
• Inviscid flow• Small perturbations about mean flow
mass
momentum
thermodynamics
Couples p and
Couples u and p
Couples u and
How to measure?
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Background – Linearized Euler equations
5
Take div (momentum) + D/Dt (thermodyn)
Usual assumption:
So that:
heat release rate/volume
wave equation source term
Measuring pressure (at a surface): easyMeasuring heat release rate: hard!
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Network models
6
flame combustor nozzleplenum
Transfer function between boxesCoupling between state variables
Allows de-coupling between different elementsIndividual model for each sub-system
Largely most used and very successful model
experimentscalculations
geometryT, p, M
cooling
geometryT, p, M
geometryT, p, M
geometry of holesT, p, M
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Pressure measurements
7
Hardware• Accuracy• Location• Frequency resolution• Background• Vibration• Reflections• Losses
Signal processing• Simultaneity (multiplexing)• Frequency range• Frequency resolution• Phase resolution• Multiple frequencies• Unsteady frequency and phase
Assumptions• One-dimensionality• Losses across componen
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Pressure measurements
8
Hardware• Accuracy: differential / absolute; static / dynamic calibration• Location: positioning relative to flow/event• Frequency: response curve, Nyquist as a minimum; long
records; windowing• Background: vibration, changing thermal conditions• Vibration: particularly important during forcing• Reflections: flush or infinite loop used
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Pressure transducers
9
Type Principle Pros Cons Manufacturers
Capacitance Variable gap Sensitive, inexpensive
Fragile, sensitive to temperature
B&K,GRAS,others
Piezoelectric V from strain Sensitive, robust, high T, p
More expensive,sensitive to vibration
PCB, Vibrometer,, Kulite, Kistler, other
Quartz crystal
V from p, T Accurate,robust
High cost, T sensitive
PCB, GE, others
PCB 112A05315 C, 350 bar
B&K 4138-A-015100 C CP211
777 C, 350 bar
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Sensor response attributes
10
GRAS
Frequency response Linearity
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Sensor assembly
11
No reflections‘infinite’
Phasing: • zero lag/no multiplexing• flush or identical distances
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Close-coupled transducer on hot HP tube
12
FSN
Comp. Spring
N75 or Quartz
CP211 Rings
Siren Conical Duct
Choking Plane
Heatshield
Flow
CP211
Adapter Cooling air (Back-up)
1500 K
<800 KShort guideSame D as sensor
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Dynamic pressure measurements
13
Signal processing• Frequency range• Simultaneity (multiplexing)• Phase resolution• Multiple frequencies• Unsteady frequency and phase
Fouriertransform
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Fourier transform
14
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Fourier transform - windowed
15
Rules:- must sample at least two points per cycle (Nyquist criterion)
(higher frequencies will show up as harmonics – ‘aliasing’)- record length determines frequency resolution
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Acoustic velocity from pressure measurements: multiple microphone
16
Abom, M., H. Bodén, Error analysis of two-microphone measurements in ducts with flow, J. Acoust. Soc. Am. 83 (1988) 2429–2438.
Jang, S., J. Ih, On the multiple microphone method for measuring in-duct acoustic properties in the presence of meflow, 103 (1998) 1520–1526.
Li, L. PhD (2011): laminar excited jet
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Example: gas turbine injector non-reacting flow response
17
Separate turbulent signal from acoustic sign
Barker, a., J. Carrotte, P. Denman, Analysis of hot-wire anemometry data in an acoustically excited turbulent flow field, Exp. Fluids. 39 (2005) 1061–1070 doi:10.1007/s00348-005-0039-z.
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TMM vs PIV - CIPCF
Main Air
Exhaust
Water
Bypass
Needle valve
Pressure gauge
High pressure water (80 bar)
Cooling AirPlenum
screens
80o H water spray nozzle
Injector Flat quartz window
Quartz flame tube
PIV imaging
area
Siren
Flow restriction
nozzle
Pump
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Particle Image Velocimetry (PIV) set-up
Litron Nano PIV Laser120 mJ @ 532 nm
LaVision Imager Pro x 4M CCD camera
2048x2048 pixelsNikon AF
Micro Nikkor60 mm Lens
Laser sheet of 0.5 mm
thickness
Beam dump
Quartz Flame tube
Combustor
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Pressure data acquisition
p1 p2 p3
Kulitepressure sensor
P3
Quartz flame tube
Imaging area
Injector
• Dynamic pressures P1 and P2 at plenum section, P3 at injector sections are recorded for each test point
• From P1 and P2 data, phase and amplitude of acoustic velocity are calculated• Pressure P3 is used to synchronize the siren with PIV acquisition
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Cycle resolved PIV synchronization with Siren
Siren Pulse delay generator
Programmable Timing Unit
PIV Laser
PIV Camera
Data Acquisition
Board
Picoscope
P1
P2
P3
1/revExternal trigger
Cam
era
TTL
P3 signalDynamic pressures
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Instantaneous PIV image pair
X (mm)
Y (m
m)
X (mm)
One example of instantaneous PIV image pair (Δt = 4 µs)
2048
pix
el2048 pixel 61.1 mm
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PIV post processing
Reference flow field
No siren Mean flow field
PIV Image pre-processing• Subtracting a sliding background: 6 pixel scale length• Normalizing the particle intensity using min/max filter: 5
pixel scale length
PIV vector calculation• Multi-pass cross-correlation scheme
• Initial window size: 64X64 – one pass• Final window size: 32X32 – three passes
• Window overlap : 50%• Spatial resolution: 340 µm
PIV vector post-processing• Q-factor: 1.2 (ratio of highest to the second highest
peaks in the displacement correlation map)• Median filtering: 5X5 pixels
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PIV post processing
Reference flow field
No siren mean flow field
PIV Image pre-processing:• Subtracting a sliding background: 6 pixel scale length• Normalizing the particle intensity using min/max filter: 5
pixel scale length
PIV vector calculation:• Multi-pass cross-correlation scheme
• Initial window size: 64x64 – one pass• Final window size: 32x32 – three passes
• Window overlap : 50%• Spatial resolution: 340 µm
PIV vector post-processing:• Q-factor: 1.2 (ratio of highest to the second highest
peaks in the displacement correlation map)• Median filtering: 5x5 pixels
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Mean flow field: forcing frequency 82 Hz
Pha
se: m
1P
hase
: m2
Pha
se: p
Pha
se: t
m1
p
m2
t
P3 signal
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Mean flow field: forcing frequency 100 Hz
Pha
se: m
1P
hase
: m2
Pha
se: p
Pha
se: t
m1
p
m2
t
P3 signal
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Mean flow field: forcing frequency 200 Hz
Pha
se: m
1P
hase
: m2
Pha
se: p
Pha
se: t
m1
p
m2
t
P3 signal
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Mean flow field: forcing frequency 275 Hz
Pha
se: m
1P
hase
: m2
Pha
se: p
Pha
se: t
m1
p
m2
t
P3 signal
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Mean flow field: forcing frequency 350 Hz
Pha
se: m
1P
hase
: m2
Pha
se: p
Pha
se: t
m1
p
m2
t
P3 signal
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Mean flow field: forcing frequency 475 Hz
Pha
se: m
1P
hase
: m2
Pha
se: p
Pha
se: t
m1
p
m2
t
P3 signal
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PIV measurements: non-reacting
31
Fluctuation intensity decreasesPhase at peak changes
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TMM pressure data processing
32
DP1, DP2, DP3: Kulite
DP7, DP8: CP211
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Pressure fluctuations (pk-pk)
• very clean, noise-free response
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PIV data vs. TMM pre-injector
34
Non‐harmonic responseAmplitude decreases with f Assume no losses
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PIV data vs. TMM pre-injector
35
Very similar response
Comparison excluding recirculation zone
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Why such a large discrepancy?
• PIV region averaged• TMM: Uncertainties in pressure measurements
– Repeatability– Accuracy– Propagation of errors to velocity
• Direct• Area change
• Injector transmissivity
36
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PIV region averaged
37
0
0.05
0.1
0.15
0.2
0.25
0.3
0.35
0.4
0.45
0 100 200 300 400 500
Velocity fluctuation pk
‐pk u/U
Frequency (Hz)
R2
R3
R5
R1
R4
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Variable cross section
38
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Why such a large discrepancy?
• PIV region averaged• TMM: Uncertainties in pressure measurements
– Repeatability– Accuracy– Propagation of errors to velocity
• Area change• Direct
• Injector transmissivity
39
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Isothermal cases
40
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Repeatability: identical experiments on different dates
41
Date Burner Pin (bar) T30 (degC) T30 (K) m (kg/s) Cooling
% dP/P (%)
11.07.12 CD3b 2.5 20 293 0.39 20 7
18.07.12 CD3b 2.5 20 293 0.39 20 7
up to 14% variation from mean
DP1 DP2
Surprisingly good given that FS accuracy of Kulites is 0.5% p @ 10 bar
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Propagation of errors: repeatability of acoustic velocity
42
2.5 bar, 293-300 K
Good reproducibility
20% cooling
5.7 bar, 300 K
0% cooling
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Accuracy: CP211 in plenum: capped inlets
43
Unreliable(vibrations)
Hardly reliable (10-20% peak)
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Variable cross section
44
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45
Propagation of errors: effect of transducer error on acoustic velocity
Åbom, M., H. Bodén, Error analysis of two-microphone measurements in ducts with flow, J. Acoust. Soc. Am. 83 (1988) 2429–2438.
Seybert, A.F., B. Soenarko, Error analysis of spectral estimates with application to the measurement of acoustic parameters using random sound fields in ducts, J. Acoust. Soc. Am. 69 (1981) 1190–1199.
Small variance high coherence
Boden, H., Åbom, M. Influence of errors on the two-microphone method for measuring, J. Acoust. Soc. Am. 79 (1986) 541–549.
Not always possible over a wide range of frequencies
Multiple microphones essential
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Propagation of errors: sensitivity of u’ to p’ uncertainty
46
Propagation of 10% rmsGaussian error in DP1, DP2 into acoustic velocity at 75 Hz
Propagation of 10% rms Gaussian error in DP1, DP2 into acoustic velocity at inlet of injector
Small errors in pressure large deviation in velocity
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Orifice transmittance
47
DP1 DP2 DP7 DP8
DP3
CP211Kulites
Include area changeOrifice onlyNo losses
TMM: DP1+DP2S(x)
Output P: DP3Discrepancy: losses? accuracy?
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TMM velocity: forwards and backwards
48
DP1 DP2 DP7 DP8
DP3
CP211Kulites
Velocity@ downstream, S(x) Plenum vs. combustor TMM
Velocity @ downstream, TMM DP7-8
300 K
800 K
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Why such a large discrepancy?
• PIV region averaged• TMM: Uncertainties in pressure measurements
– Repeatability– Accuracy– Propagation of errors to velocity
• Area change• Direct
• Injector transmissivity
49
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Injector transmittance
50
injector
5.7 bar, 300 K, 20 % coolingCalculation with constant SVelocity upstream of injector
orifice
Velocity depends on injector transmittanceMeasured TMM velocity different from orifice
Measurements obtained from reflectionmeasurements atmospheric condition
Courtesy J. Carrotte, Loughborough
Frequency
Tran
smis
sivi
ty
injector
equivalent orifice
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Injector transmittance and reflectance
51
DP1 DP2 DP7 DP8
DP3
CP211Kulites
Directly measured in HP rig
Frequency
Tran
smis
sivi
tyinjector
equivalent orifice
Obtained from reflection in atmospheric rig
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Final comparison: PIV + TMM
52
Corrected for area and velocity changesCorrected using in situ measured transmissivity
OriginalNo area changeUpstream of injector
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Challenges for acoustic pressure and velocity measurements at high p,T
• Results on calculated acoustic velocity very dependent on accuracy of pressure transducers and their coherence: differential transducers required, not sensitive to vibration
• Area changes and transmissivity losses important, particularly for complex injectors: needs good measurements of non-reacting transfer functions, also dependent on M.
• Comparing apples and apples: PIV measurements for a window may not reflect effect over full flow
• Overall agreement is good, but not perfect: lack of symmetry, inaccuracies in pressure measurements, non-harmonic behavior of velocity and very high turbulent levels.
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