lecture # 05: velocimetry techniques and instrumentationhuhui/teaching/2014fx/class...title:...
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Copyright Copyright ©© by Dr. Hui Hu @ Iowa State University. All Rights Reserved!by Dr. Hui Hu @ Iowa State University. All Rights Reserved!
Dr. HDr. Hui Huui Hu
Department of Aerospace EngineeringDepartment of Aerospace EngineeringIowa State University Iowa State University
Ames, Iowa 50011, U.S.AAmes, Iowa 50011, U.S.A
Lecture # 05: Velocimetry Techniques and Instrumentation
AerEAerE 3344 44 Lecture NotesLecture Notes
Copyright Copyright ©© by Dr. Hui Hu @ Iowa State University. All Rights Reserved!by Dr. Hui Hu @ Iowa State University. All Rights Reserved!
Methods to Measure Local Flow Velocity Methods to Measure Local Flow Velocity -- 11
•• Mechanical methods:Mechanical methods:•• Taking advantage of force and moments that a moving stream appliTaking advantage of force and moments that a moving stream applies on immersed objects.es on immersed objects.•• Vane anemometersVane anemometers•• Propeller anemometersPropeller anemometers
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Methods to Measure Local Flow Velocity Methods to Measure Local Flow Velocity --22
b. Flat plateb. Flat plate
a. streamlined airfoila. streamlined airfoil
•• Pressure difference methods:Pressure difference methods:•• Utilize analytical relationship between the local Utilize analytical relationship between the local
velocity and the static and total pressuresvelocity and the static and total pressures• The tubes sensing static and stagnation pressures are
usually combined into one instrument known as Pitot-static tube.
• Pressure taps sensing static pressure (also the reference pressure for this measurement) are placed radially on the probe stem and then combined into one tube leading to the differential manometer (pstat).
• The pressure tap located at the probe tip senses the stagnation pressure (p0).
• Use of the two measured pressures in the Bernoulli equation allows to determine one component of the flow velocity at the probe location.
• Special arrangements of the pressure taps (Three-hole, Five-hole, seven-hole Pitot) in conjunction with special calibrations are used two measure all velocity components.
• It is difficult to measure stagnation pressure in real, due to friction. The measured stagnation pressure is always less than the actual one. This is taken care of by an empirical factor C.
ρ
ρ
ρ
/)(2
/)(2
)(,21
0
0
20
stat
stat
stat
ppCV
ppV
BernoulliVpp
−=
−=
+=
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Methods to Measure Local Flow Velocity Methods to Measure Local Flow Velocity --33
•• Thermal methods:Thermal methods:•• Compute flow velocity from its relationship between local flow vCompute flow velocity from its relationship between local flow velocity and the convective heat elocity and the convective heat
transfer from heated elements.transfer from heated elements.
Hot wire anemometersHot wire anemometers Hot film anemometersHot film anemometers
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ParticleParticle--based Flow Diagnostic Techniquesbased Flow Diagnostic Techniques
• Seeded the flow with small particles (~ µm in size)
• Assumption: the particle tracers move with the same velocity as local flow velocity!
Flow velocityFlow velocityVVff
Particle velocityParticle velocityVVpp
=
Measurement of particle velocity
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Methods to Measure Local Flow Velocity Methods to Measure Local Flow Velocity -- 44
•• FrequencyFrequency--shift methods:shift methods:•• Based on the Doppler phenomenon, namely the shift of the frequenBased on the Doppler phenomenon, namely the shift of the frequency of waves scattered by moving cy of waves scattered by moving
particles. particles. •• Laser Doppler Laser Doppler Velocimetry(LDVVelocimetry(LDV) or Laser Doppler Anemometry (LDV)) or Laser Doppler Anemometry (LDV)•• Planar Doppler Planar Doppler VelocimetryVelocimetry (PDV) or Planar Doppler Anemometry(PDV) or Planar Doppler Anemometry (PDA)
Interference fringesInterference fringes
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Doppler ShiftDoppler Shift•• The Doppler effect, named after The Doppler effect, named after Christian Doppler (an Austrian mathematician and Christian Doppler (an Austrian mathematician and
physicist )physicist ),, is the change in frequency and wavelength of a wave that is peris the change in frequency and wavelength of a wave that is perceived by an ceived by an observer moving relative to the source of the waves.observer moving relative to the source of the waves.
•• Light from moving objects will appear to have different wavelengLight from moving objects will appear to have different wavelengths depending on the ths depending on the relative motion of the source and the observer.relative motion of the source and the observer.
•• Observers looking at an object that is moving away from them seeObservers looking at an object that is moving away from them see light that has a longer light that has a longer wavelength than it had when it was emitted (a red shift), while wavelength than it had when it was emitted (a red shift), while observers looking at an observers looking at an approaching source see light that is shifted to shorter wavelengapproaching source see light that is shifted to shorter wavelength (a blue shift).th (a blue shift).
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Doppler ShiftDoppler Shift
a. Stationary Sound Source a. Stationary Sound Source b. Source moving with b. Source moving with VsourceVsource < < VsoundVsound
c. Source moving with c. Source moving with VsourceVsource = = VsoundVsound( Mach 1 ( Mach 1 -- breaking the sound barrier ) breaking the sound barrier )
d. Source moving with d. Source moving with VsourceVsource > > VsoundVsound(Mach 1.4 (Mach 1.4 -- supersonic) supersonic)
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Fundamentals of LDVFundamentals of LDV•• Take the coordinate system to be at rest with respect to Take the coordinate system to be at rest with respect to
the medium, whose speed of light wave is c. There is a the medium, whose speed of light wave is c. There is a source s moving with velocity Vsource s moving with velocity Vss and emitting light and emitting light waves with a frequency waves with a frequency ffss. .
•• There is a detector r moving with velocity There is a detector r moving with velocity VVrr , and the , and the unit vector from s to r is n i.e. . unit vector from s to r is n i.e. .
•• Then the frequency Then the frequency ffrr at the detector is found from at the detector is found from
•• If c>>VIf c>>Vs s , then the change in frequency depends mostly , then the change in frequency depends mostly on the relative velocity of the source and detector.on the relative velocity of the source and detector.
λ
φ
λ
φ
φ
φφ
φ
)2
sin(2)2
sin(2
)2
sin(2)ˆˆ(0
ˆˆˆ
ˆ
⋅=
⋅=Δ⇒
⋅=
−⋅=
Δ⇒
⎭⎬⎫
=−=
−⋅−=
−=
Δ
V
f
fVf
c
V
ceeV
ff
Veen
cVVn
fff
ff
irs
sr
ir
sr
s
sr
s
r
rr
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DualDual--Beam LDVBeam LDV
⊥
⊥⊥
=
==
=
=
=
Vf
VVf
fDdDN
TT
e
T
λθ
λθ
δ
θπ
θλδ
)2/sin(2
:ryshift theoDoppler toaccordingshift Frequency
)2/sin(2
:light scattering theofFrequency
)2/sin(2
;4 :number Fring
)2/sin(2 :spacing Fring
⊥V
VT
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•• DualDual--beam laser setup only can measure one beam laser setup only can measure one component of the velocity with its direction component of the velocity with its direction normal to the fringe planes.normal to the fringe planes.
•• TwoTwo--color LDV system can be used for 2color LDV system can be used for 2--components of flow velocity measurements.components of flow velocity measurements.
•• ArAr--ion Laser beamsion Laser beams•• Blue (488nm)Blue (488nm)•• Yellow (514.5 nm)Yellow (514.5 nm)
22--component LDV systemscomponent LDV systems
⊥V
VT
22--component LDVcomponent LDV
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•• As particles pass through the probe volume, they As particles pass through the probe volume, they scatter light from the beams and create an scatter light from the beams and create an interference fringe pattern. interference fringe pattern.
•• A receiving lens at an offA receiving lens at an off--axis collection angle axis collection angle projects part of this fringe pattern onto detectors, projects part of this fringe pattern onto detectors, which produce a Doppler burst signal with a which produce a Doppler burst signal with a frequency proportional to the particle velocity.frequency proportional to the particle velocity.
•• The phase shift between the Doppler burst The phase shift between the Doppler burst signals from the different detectors is signals from the different detectors is proportional to the size of the spherical particles.proportional to the size of the spherical particles.
Phase Doppler Particle Analyzers/PDPA SystemsPhase Doppler Particle Analyzers/PDPA Systems
PDPA systemPDPA system
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ParticleParticle--based techniques: Particle Image based techniques: Particle Image VelocimetryVelocimetry (PIV)(PIV)
• To seed fluid flows with small tracer particles (~µm), and assume the tracer particles moving with the same velocity as the low fluid flows.
• To measure the displacements (ΔL) of the tracer particles between known time interval (Δt). The local velocity of fluid flow is calculated by U= Δ L/Δt .
A. t=tA. t=t00 B. t=tB. t=t00+10 +10 μμssClassic 2Classic 2--D PIV measurementD PIV measurement
C. Derived Velocity fieldC. Derived Velocity fieldX (mm)
Y(m
m)
-50 0 50 100 150
-60
-40
-20
0
20
40
60
80
100
-0.9 -0.7 -0.5 -0.3 -0.1 0.1 0.3 0.5 0.7 0.95.0 m/sspanwise
vorticity (1/s)
shadow region
GA(W)-1 airfoil
t=tt=t00 tLUΔΔ
=
t= tt= t00++ΔΔttΔΔLL
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Methods to Measure Local Flow Velocity Methods to Measure Local Flow Velocity -- 55
•• Marker tracing methods:Marker tracing methods:•• Trace the motion of suitable flow makers, Trace the motion of suitable flow makers,
optically or by other means to derive local optically or by other means to derive local flow velocity. flow velocity.
•• Particle Imaging Particle Imaging VelocimetryVelocimetry (PIV)(PIV)•• Particle Tracking Particle Tracking VelocimetryVelocimetry (PTV)(PTV)•• Molecular Tagging Molecular Tagging VelocimetryVelocimetry (MTV)(MTV)
t=t0 t=t0+4 ms
PIV image pairPIV image pair
MTV&T image pairMTV&T image pairt=t0 t=t0+5ms
26.5026.4026.3026.2026.1026.0025.9025.8025.7025.6025.5025.4025.3025.2025.1025.0024.9024.8024.7024.6024.50
0.03 m/s
Temperature (OC)
Corresponding flow velocity field
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Stereoscopic PIV MeasurementsStereoscopic PIV Measurements
Camera 1Camera 1 Camera 2Camera 2
Laser SheetLaser Sheet
αα11
αα22
ZZ
XX
Displacement vectors in left camera Displacement vectors in left camera Displacement vectors in right camera Displacement vectors in right camera
Stereo PIV techniqueStereo PIV technique
.deg0.5;000,52Re == αC
X/C =4.0
X pixel
Ypi
xel
0 500 1000 1500
0
200
400
600
800
1000
1200
X pixel
Ypi
xel
0 500 1000 1500
0
200
400
600
800
1000
1200
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Flow Around a Circular CylinderFlow Around a Circular Cylinder
uniform flow +uniform flow + a 2a 2--D doublet = flow around a circular D doublet = flow around a circular cylindercylinder
Stagnation pointsStagnation points
Pressure coefficient on the surface of cylinderPressure coefficient on the surface of cylinder
)1(sin
)1(cos
)1(cos
)1(sin
2
2
2
2
2
2
2
2
rRVV
rRVV
rRrV
rRrV
r
+−=
−=
+=
−=
∞
∞
∞
∞
θ
θ
θφ
θψ
θ
Lab#04 Measurements of Pressure Distributions around a CircularLab#04 Measurements of Pressure Distributions around a Circular CylinderCylinder
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Lab#04 Measurements of Pressure Distributions around a CircularLab#04 Measurements of Pressure Distributions around a Circular CylinderCylinder
•• At the surface of the cylinder, At the surface of the cylinder,
•• According to BernoulliAccording to Bernoulli’’s equation s equation
•• Pressure coefficient distribution on the surface of the circularPressure coefficient distribution on the surface of the circular cylinder will be:cylinder will be:
⎩⎨⎧
−==
⇒=∞ θθ sin2
0VV
Var r
2
2
2
22 1
212
121
∞∞
∞∞∞ −=
−⇒+=+
V
V
V
PPVPVPρ
ρρ
θθ
ρ
22
2
2
2
2sin41)sin2(11
21 −=
−−=−=
−=
∞
∞
∞∞
∞
VV
VV
V
PPCp
Rθ
P
Incoming flow
X
Y
-3
-2
-1
0
1
0 100 200 300 400
Angle, Deg.
Cp
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Numerical results for the velocity magnitude and pressure distributions over a circular cylinder using FlowLab(Vh=35.8 m/s, Re=1.89E+05)
Pressure Distribution around Pressure Distribution around a Circular Cylindera Circular Cylinder
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Lab#04 Measurements of Pressure Distributions around a CircularLab#04 Measurements of Pressure Distributions around a Circular CylinderCylinder
Rθ
P
Incoming flow
X
Y
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Cp distributions over a circular cylinder
-3.5
-3
-2.5
-2
-1.5
-1
-0.5
0
0.5
1
1.5
0 1 2 3 4 5 6 7
theta (rad ) -->
cp --
>
EFDCFDAFD
Lab#04 Measurements of Pressure Distributions around a CircularLab#04 Measurements of Pressure Distributions around a Circular CylinderCylinder
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Required Required ResultsResults for for the the Lab ReportLab Report
–– To make a table showing all the timeTo make a table showing all the time--averaged data you obtained averaged data you obtained for all the cases you tested.for all the cases you tested.
–– To show all the calculation steps leading up to the final answerTo show all the calculation steps leading up to the final answer..
–– To plot pressure coefficient (To plot pressure coefficient (CCpp) distributions on the cylinder from ) distributions on the cylinder from for all the cases you tested.for all the cases you tested.
–– To make comments on the characteristics of the pressure To make comments on the characteristics of the pressure distribution compared with the theoretic predictions.distribution compared with the theoretic predictions.
–– To calculate the drag coefficients (To calculate the drag coefficients (CCdd ) of the circular cylinder for ) of the circular cylinder for all the cases you tested.all the cases you tested.
–– To plot the drag coefficients (To plot the drag coefficients (CCdd ) of the circular cylinder as a ) of the circular cylinder as a function of at the Reynolds numbers.function of at the Reynolds numbers.