Lecture # 04: Velocimetry Techniques · Lecture # 04: Velocimetry Techniques ... Laser sheet with P-polarization direction Lobed nozzle 650mm 650mm 25 0 250 Synchronizer cylinder

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


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


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

−=

−=

+=


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



•• 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


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).


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)



•• 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


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


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


-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


Laser sheet withS-polarization direction

S-polarized laser beamP-polarized laser beam



Double-pulsed

Nd:YAG Laser set B


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)


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)


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.


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


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


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



•• 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



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

::


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


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


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

−−

−−

−=

+=


MultiMulti--sensor probessensor probes

•• Three sensor designThree sensor design

•• Four sensor design:Four sensor design:


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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Lecture # 04: Velocimetry Techniques · Lecture # 04: Velocimetry Techniques ... Laser sheet with P-polarization direction Lobed nozzle 650mm 650mm 25 0 250 Synchronizer cylinder