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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 # 04: Lecture # 04: VelocimetryVelocimetry TechniquesTechniques
AerEAerE 311L & AerE343L Lecture Notes311L & AerE343L Lecture 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
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 --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
−=
−=
+=
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 --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
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 -- 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
Copyright Copyright ©© by Dr. Hui Hu @ Iowa State University. All Rights Reserved!by Dr. Hui Hu @ Iowa State University. All Rights Reserved!
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).
Copyright Copyright ©© by Dr. Hui Hu @ Iowa State University. All Rights Reserved!by Dr. Hui Hu @ Iowa State University. All Rights Reserved!
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)
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 -- 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
Copyright Copyright ©© by Dr. Hui Hu @ Iowa State University. All Rights Reserved!by Dr. Hui Hu @ Iowa State University. All Rights Reserved!
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
Copyright Copyright ©© by Dr. Hui Hu @ Iowa State University. All Rights Reserved!by Dr. Hui Hu @ Iowa State University. All Rights Reserved!
Stereoscopic Particle Image Stereoscopic Particle Image VelocimetryVelocimetry (SPIV) Technique(SPIV) Technique
•• Use 2 cameras viewing from different Use 2 cameras viewing from different perspectives.perspectives.
•• Each camera is processed using a planar Each camera is processed using a planar techniquetechnique
•• Information from the 2 cameras is Information from the 2 cameras is combined to reconstruction three combined to reconstruction three components of velocity vectorscomponents of velocity vectors
Camera 1 Camera 2
Laser Sheet
α1
α2
Z
X
X PIXEL
YP
IXE
L
0 500 10000
100
200
300
400
500
600
700
800
900
1000
X PIXEL
YP
IXE
L
0 500 10000
100
200
300
400
500
600
700
800
900
1000
Displacement vectors in left camera Displacement vectors in right camera
-30-20
-100
1020
30X mm
-30
-20
-10
0
10
20
30
Ym
m
X
Y
Z W m/s20.0019.0018.0017.0016.0015.0014.0013.0012.0011.0010.00
9.008.007.006.005.004.003.00
20 m/s
Copyright Copyright ©© by Dr. Hui Hu @ Iowa State University. All Rights Reserved!by Dr. Hui Hu @ Iowa State University. All Rights Reserved!
-11.0
-7.0
-7.0
-5.0
-5.0
-3.0
-3.0-3.0
-3.0
-1.0
-1. 0
-1.0
-1.0
-1.0
-1.0
-1.0
1.0
1.0
1.01.0
1.0
1.0
3.0
3.0
3.0
3.0
3.0
3.0
3.0
3.0
5.0
5.0
5.0
5.05.0
5.0
5.0
7.0
7.0 7.0
7.09.011.0
X mm
Ym
m
-40 -20 0 20 40
-30
-20
-10
0
10
20
30
40
11.009.007.005.003.001.00
-1.00-3.00-5.00-7.00-9.00
-11.00
Vorticity distribution(X-component)
a. Xa. X--component of Vorticitycomponent of Vorticity
-11.
0
-11.0
-11.0
-11.0
-9.0
-9.0-9.0
-9.0
-7.0
-7.0-7.0
-7.0
-7.0
-7.0
-5.0
-5.0
-5.0
-5.0
-5.0
-3.0
-3.0
-3.0 -3.0
-3.0
-3.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
1.0
1.0
1.0
1.0
1.0
1.0
3.0
3.0
3.0
3.0
3.0
5.0
5.0
5.0
5.0
7.0
7.0
7.0
7.0
7.0
9.0
9.0
9.0
9.0
9.0
11.0
11.0
11.0
11.0
11.0
X mm
Ym
m
-40 -20 0 20 40
-30
-20
-10
0
10
20
30
40
11.009.007.005.003.001.00
-1.00-3.00-5.00-7.00-9.00
-11.00
Vorticity distribution(Y-component)
b. Yb. Y--component of Vorticitycomponent of Vorticity
-4.5
-4.5
-3.5
-2.5
-2.5
-2.5 -2.5
-1.5
-1.5
-1.5
-0.5-0.5
-0.5
-0.5
-0.5
-0.5
-0.5
-0.5
0.5
0.50.5
0.5
0.5
1.5
1.5
1.5
1.5
2.53.5
4.5
X mmY
mm
-40 -20 0 20 40
-30
-20
-10
0
10
20
30
40
4.503.502.501.500.50
-0.50-1.50-2.50-3.50-4.50
Vorticity distribution(Z-component)
c. Zc. Z--component of Vorticitycomponent of Vorticity
Lobed nozzle/mixerLobed nozzle/mixerEnsembleEnsemble--averaged averaged velocity vectorsvelocity vectors
-30-20
-100
1020
30X mm
-30
-20
-10
0
10
20
30
Ym
m
X
Y
Z W m/s20.0019.0018.0017.0016.0015.0014.0013.0012.0011.0010.009.008.007.006.005.004.003.00
20 m/s
All three components of All three components of velocity vectorsvelocity vectors
DualDual--plane Stereoscopic Particle Imaging plane Stereoscopic Particle Imaging VelocimetryVelocimetry
Measurement region80mm by 80mm
Laser sheet with P-polarization direction
Lobed nozzle
650mm
650mm
25 0
25 0
Synchronizer
cylinder lens Host computer
high-resolution CCD camera 3
Double-pulsed
Nd:YAG Laser set A
Polarizer cube
Polarizing beam splitter cubes
Mirror #3
Mirror #4
Half wave (λ/2) plateMirror #1
Mirror #2
high-resolution CCD camera 1
Laser sheet withS-polarization direction
S-polarized laser beamP-polarized laser beam
high-resolution CCD camera 2
high-resolution CCD camera 4
Double-pulsed
Nd:YAG Laser set B
Copyright Copyright ©© by Dr. Hui Hu @ Iowa State University. All Rights Reserved!by Dr. Hui Hu @ Iowa State University. All Rights Reserved!
Molecular Tagging Velocimetry (MTV) techniqueMolecular Tagging Velocimetry (MTV) technique(line(line--typed tagging for onetyped tagging for one--componentcomponent velocityvelocity measurement)measurement)
first image (right after laser firing)
second image (14 ms later)•• Tagged lines are imaged twice with knownTagged lines are imaged twice with known time delaytime delay
•• Intensity profile for each row Intensity profile for each row --> line center locations > line center locations •• Difference between the line centers gives displacementDifference between the line centers gives displacement•• Velocity = displacement / delay timeVelocity = displacement / delay time
Flow visualization of the vortex shedding from the trailing edge of an oscillating airfoil (Bohl et al. 2002)
Copyright Copyright ©© by Dr. Hui Hu @ Iowa State University. All Rights Reserved!by Dr. Hui Hu @ Iowa State University. All Rights Reserved!
First image(right after the laser pulse)
Second image(imaged 3.5 ms later)
•• Create a 2Create a 2--D grids with multiple laser beams.D grids with multiple laser beams.•• Take two images with known time delay.Take two images with known time delay.
•• Find the displacement vectors of the grids through a image proceFind the displacement vectors of the grids through a image processing procedure. ssing procedure.
•• Local velocity = displacement/time delay.Local velocity = displacement/time delay.
The velocity field derived usinga spatial correlation procedure (Bohl et al. 2002)
Molecular Tagging Velocimetry (MTV) Molecular Tagging Velocimetry (MTV) (Grid(Grid--typed tagging for twotyped tagging for two--componentcomponent velocityvelocity measurement)measurement)
Copyright Copyright ©© by Dr. Hui Hu @ Iowa State University. All Rights Reserved!by Dr. Hui Hu @ Iowa State University. All Rights Reserved!
Applications: MTV Measurements of the Vortex Applications: MTV Measurements of the Vortex Shedding from an Oscillating AirfoilShedding from an Oscillating Airfoil
Strong concentrated vortices are formed immediately at the trailing edge.Note the location and sign of the vortices formed at the trailing edge.(Courtesy of Bohl et al., 2002)
Using the grid tagging method, the in-plane velocity components and the vorticity field are mapped. Data below are for k = 11.5.
Copyright Copyright ©© by Dr. Hui Hu @ Iowa State University. All Rights Reserved!by Dr. Hui Hu @ Iowa State University. All Rights Reserved!
Simultaneous Velocity & Temperature FieldsSimultaneous Velocity & Temperature Fields
first image (1ms after laser pulse ) first image (1ms after laser pulse )
TTfluidfluid = 24.0 = 24.0 °°C , C , TTcylindercylinder = 35.0 = 35.0 °°CC, U, Uinin=0.026m/s=0.026m/s
Re=130,Re=130, Gr=3300, Gr=3300, Ri=0.19,Ri=0.19, St=0.157St=0.157
second image (6ms after laser pulse ) second image (6ms after laser pulse ) Y/D
X/D
-5 -4 -3 -2 -1 0 1 2 3 4 5 6 7
-1
0
1
2
3
4
5
6
7
8
9
10
11
26.00025.92525.85025.77525.70025.62525.55025.47525.40025.32525.25025.17525.10025.02524.95024.87524.80024.72524.65024.57524.500
Temperature ( OC )
0.026 m/s
Copyright Copyright ©© by Dr. Hui Hu @ Iowa State University. All Rights Reserved!by Dr. Hui Hu @ Iowa State University. All Rights Reserved!
Technical Fundamentals Technical Fundamentals --11
•• Thermal anemometers:Thermal anemometers:•• Measure the local flow velocity through its relationship to the Measure the local flow velocity through its relationship to the convective cooling of electrically convective cooling of electrically
heated metallic sensors.heated metallic sensors.
•• Hot wire anemometersHot wire anemometers: : •• for clean air or other gas flowsfor clean air or other gas flows
•• Hot film anemometers:Hot film anemometers:•• for liquid or some gas flowsfor liquid or some gas flows
Copyright Copyright ©© by Dr. Hui Hu @ Iowa State University. All Rights Reserved!by Dr. Hui Hu @ Iowa State University. All Rights Reserved!
How a Hot wire Sensor WorksHow a Hot wire Sensor Works
Electric current, i, Electric current, i, through wirethrough wire
The electric current (i) flowing through the wire The electric current (i) flowing through the wire generates heat (igenerates heat (i22RRww))
In equilibrium, this must In equilibrium, this must be balanced by heat lost be balanced by heat lost (primarily convective) to (primarily convective) to the surroundings.the surroundings.
Flow FieldFlow FieldVV
Copyright Copyright ©© by Dr. Hui Hu @ Iowa State University. All Rights Reserved!by Dr. Hui Hu @ Iowa State University. All Rights Reserved!
Technical Fundamentals Technical Fundamentals --22
•• Heat transfer characteristics:Heat transfer characteristics:•• Convection (nature convection, forced convection Convection (nature convection, forced convection
or mixed convection depending on Richardson or mixed convection depending on Richardson numbers)numbers)
•• Conduction to the supporting prongConduction to the supporting prong•• Radiation: <0.1%, is negligible.Radiation: <0.1%, is negligible.
θ
TTw >
TV ,r
wT
prongs
Hot wireHot wire
Fluid flowFluid flow
),/,,,,Pr,(Re,)(
θπ
dlaKnMGrNuTTlk
qNu
T
w
=−
=&
TTTa
Mccd
Kn
cVMdTTgGr
Ud
wT
vp
w
−=
==
=−
=
==
Re/
21
;)(
Pr;Re
2
3
πλν
αγν
μρ
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Technical Fundamentals Technical Fundamentals --33
44Re02.0,)211)(Re48.0
140Re44,)211)(Re56.024.0(
17.051.0
17.045.0
<<+=
<<++=
foraNu
foraNu
T
T
n
w
BVATT
E+=
−
)](1[ TTaRR wrrw −+=
According to Collis and According to Collis and WillamsWillams (1959):(1959):
For a given sensor and fixed overheat ratio, The above equation For a given sensor and fixed overheat ratio, The above equation can transfer as the relationship can transfer as the relationship between the voltage output, E, of the hotbetween the voltage output, E, of the hot--wire operation circuit and the flow velocity wire operation circuit and the flow velocity
Following KingFollowing King’’s Law (1915),s Law (1915),m
Tn aBANu )
211)(Re( ++=
Wire temperature cannot be measured directly, but can be estimatWire temperature cannot be measured directly, but can be estimated from its relationship to the ed from its relationship to the wire resistance, wire resistance, RRww, directly measured by the operating bridge., directly measured by the operating bridge.For metallic wires:For metallic wires:
temepaturereferenceTtcoefficienyresistivitthermala
r
r
::
Copyright Copyright ©© by Dr. Hui Hu @ Iowa State University. All Rights Reserved!by Dr. Hui Hu @ Iowa State University. All Rights Reserved!
Technical Fundamentals Technical Fundamentals -- 44
Flow Field
Current flow through wire
The rate of which heat is removed from the sensor is directly related to the velocity of the fluid flowing over the sensor
The hot wire is electrically heated.
If velocity changes for a unsteady flow, convective heat transfer changes, wire temperature will change and eventually reach a new equilibrium.V
Copyright Copyright ©© by Dr. Hui Hu @ Iowa State University. All Rights Reserved!by Dr. Hui Hu @ Iowa State University. All Rights Reserved!
Technical Fundamentals Technical Fundamentals -- 55
•• For a sensor placed in a unsteady flow, the unsteady energy equaFor a sensor placed in a unsteady flow, the unsteady energy equation will tion will become:become:
),(2ww
w TVqRidt
dTmc &−=
),(:::
wTVqqfluxheatconvectiveqsensortheofheatspecifichc
sensortheofmassthem
&&& =
The above equation has three unknowns: i, The above equation has three unknowns: i, TTww (or (or RRww) and V) and V
To render this equation solvable, one must keep with the electriTo render this equation solvable, one must keep with the electric current, i, or the c current, i, or the sensor temperature (sensor temperature (TTww) constant, which can be achieved with the use of suitable ) constant, which can be achieved with the use of suitable electric circuits.electric circuits.
The corresponding methods are known as: The corresponding methods are known as: (1). Constant(1). Constant--current anemometrycurrent anemometry(2). Constant(2). Constant--temperature anemometrytemperature anemometry
Copyright Copyright ©© by Dr. Hui Hu @ Iowa State University. All Rights Reserved!by Dr. Hui Hu @ Iowa State University. All Rights Reserved!
MultiMulti--sensor probessensor probes
•• CrossCross--wire (Xwire (X--wire) design:wire) design:
VV22
VV11
VV22
VV11
VV22
VV11
Vr
VVeffeff--AA
VVeffeff--BB
)(22
)(22
21
21
VVV
VVV
Beff
Aeff
−=
+=
−
−
)(22
)(22
2
1
BeffAeff
BeffAeff
VVV
VVV
−−
−−
−=
+=
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MultiMulti--sensor probessensor probes
•• Three sensor designThree sensor design
•• Four sensor design:Four sensor design:
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Diameter of hot wires Diameter of hot wires
•• L = 0.8 ~ 1.5 mmL = 0.8 ~ 1.5 mm•• D = ~ 5 D = ~ 5 μμm for conventional applicationsm for conventional applications•• D = ~ 10 D = ~ 10 μμm for highm for high--speed applicationsspeed applications•• D = ~ 2 D = ~ 2 μμm for low speed applicationsm for low speed applications•• Prongs: usually tapered to be dProngs: usually tapered to be d≤≤ 1mm1mm
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