Lecture # 05: Velocimetry Techniques and Instrumentationhuhui/teaching/2019-08Fx/AerE344x/class-no… · Laser Sheet 1 2 Z X Displacement vectors in left camera Displacement vectors

Copyright © by Dr. Hui Hu @ Iowa State University. All Rights Reserved!

Dr. Hui Hu

Dr. Rye Waldman

Department of Aerospace Engineering

Iowa State University

Ames, Iowa 50011, U.S.A

Lecture # 05: Velocimetry Techniques and

Instrumentation

AerE 344 Lecture Notes

Sources/ Further reading: Tropea, Yarin, & Foss, “Springer Handbook of Experimental Fluid Mechanics,” Part B Ch 5


Methods to Measure Local Flow Velocity - 1

• Mechanical methods: • Taking advantage of force and moments that a moving stream applies on immersed

objects.

• Vane anemometers

• Propeller anemometers

http://www.omega.com/ppt/pptsc.asp?ref=HHF803&nav=


Methods to Measure Local Flow Velocity -2

b. Flat plate

a. streamlined airfoil

Pressure difference methods: • Utilize relationship between the local velocity and

the static and total pressures (Bernoulli).

• Pitot-static tubes are instruments that measure both

static and stagnation pressures

• Static pressure taps are located circumferentially

around the probe stem and are connected to the

reference port of a differential manometer pstat

• Stagnation pressure tap at the probe tip senses p0

• The differential manometer measures the dynamic pressure, (p0 –pstat), which allows to the flow

velocity at the probe

/)(2

/)(2

)(,2

1

0

0

2

0

stat

stat

stat

ppCV

ppV

BernoulliVpp



• There are sources of error in the pressure

measurement, e.g., probe misalignment,

viscosity, compressibility, turbulence, shear,

and proximity to boundaries.

• Errors can be taken care of by an empirical

factor:

• Special arrangements of the pressure taps

(Three-hole, Five-hole, Seven-hole probes) in

conjunction with special calibrations are used

to measure all velocity components.

02( ) /statV C p p



• Thermal methods: (next week’s lecture) • Compute flow velocity from its relationship between local flow velocity and the

convective heat transfer from heated elements.

Hot wire anemometers Hot film anemometers


Particle-based 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 velocity

Vf

Particle velocity

Vp =

Measurement of

particle velocity



• Frequency-shift methods: • Based on the Doppler phenomenon: the frequency shift by moving objects

• Laser Doppler Velocimetry (LDV) or Laser Doppler Anemometry (LDA)

• Phase Doppler Anemometry (PDA)

• Planar Doppler Velocimetry (PDV)

Interference fringes


Doppler Shift

• The Doppler effect, named after Christian Doppler (an Austrian mathematician and

physicist), is the change in frequency and wavelength of a wave as perceived by an

observer moving relative to the source.

• Light from moving objects will appear to have different wavelengths depending on

the relative motion of the source and the observer.

• Observers looking at an object that is moving away from them see light that has a

longer wavelength than it had when it was emitted (a red shift), while observers

looking at an approaching source see light that is shifted to shorter wavelength (a

blue shift).


Doppler Shift

a. Stationary Sound Source b. Source moving with Vsource < Vsound

c. Source moving with Vsource = Vsound

( Mach 1 - breaking the sound barrier ) d. Source moving with Vsource > Vsound

(Mach 1.4 - supersonic)

http://www.kettering.edu/~drussell/Demos/doppler/bullet-3.gif


Fundamentals of LDV

• Take the coordinate system to be at rest with respect to the medium, whose speed of light wave is c. There is a source s moving with velocity Vs and emitting light waves with a frequency fs.

• There is a detector r moving with velocity Vr , and the unit vector from s to r is n i.e., .

• Then the frequency fr at the detector is found from

• If c >> Vs , then the change in frequency depends mostly on the relative velocity of the source and detector.

ˆ

2sin( )ˆ ˆ ˆ ˆ ˆ( ) 2

0

r s r s

s s

r i s r i

r s

f f V Vfn

f f c

Vn e e V e ef

V f c c


Fundamentals of LDV

• How to determine doppler shift? Optical heterodyne! Mix the response from two beams on the reciever:


Dual-Beam LDV

Fringe spacing: 2sin( / 2)

4Fringe number : ;

2 sin( / 2)

Frequency of the scattering light :

2sin( / 2)

Frequency shift according to Doppler shift theory:

2sin( / 2)

T

e

T T

DN

d

D f

Vf V

f V


• Dual-beam laser setup only can measure one

component of the velocity with its direction

normal to the fringe planes.

• Two-color LDV system can be used for 2-

components of flow velocity measurements.

• Ar-Ion Laser

• Blue (488nm)

• Yellow (514.5 nm)

2-component LDV systems

V

VT

2-component LDV


-2

1st order

refraction

-1

1

2

-2 -1 1 2

Incident ray

Reflection

2nd order

refraction

3rd order

4th order

5th order

6th order

7th order

8th order

np

nm

np > nm

• The intensity of the incident ray is

partly reflected and refracted.

• The intensity ratio is given by the

Fresnel coefficients and depends

on the incident angle, polarization

and relative refractive index.

• The scattering angle is given by

Snell’s law.

• The phase is given by the optical

path length of the ray.

• Most of the intensity is contained in

the first three scattering modes.

Phase Doppler Particle Analyzers/PDPA Systems


• Phase Doppler anemometers take

advantage that the phase difference

between burst signals observed at different

angles depends on particle size.

• A receiving lens at an off-axis angle

observes the Doppler burst signal with a

frequency proportional to the particle

velocity.

• The phase shift between the Doppler burst

signals from the different detectors is

proportional to the size of the spherical

particles.

Phase Doppler Particle Analyzers/PDPA Systems

PDPA system

-2

1st order

refraction

-1

1

2

-2 -1 1 2

Incident ray

Reflection

2nd order

refraction

3rd order

4th order

5th order

6th order

7th order

8th order

np

nm

np > nm


Particle-based techniques: Particle Image

Velocimetry (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 (L) of the tracer particles between known time

interval (t). The local velocity of fluid flow is calculated by U= L/t .

A. t=t0 B. t=t0+10 s C. Derived Velocity field

X (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 0.9

5.0 m/sspanwisevorticity (1/s)

shadow region

GA(W)-1 airfoil

t=t0 t

LU

t= t0+t L



• Marker tracing methods: • Trace the motion of suitable flow

makers, optically or by other means to

derive local flow velocity.

• Particle Imaging Velocimetry (PIV)

• Particle Tracking Velocimetry (PTV)

• Molecular Tagging Velocimetry (MTV)

t=t0 t=t0+4 ms

PIV image pair

MTV&T image pair

t=t0 t=t0+5ms

26.50

26.40

26.30

26.20

26.10

26.00

25.90

25.80

25.70

25.60

25.50

25.40

25.30

25.20

25.10

25.00

24.90

24.80

24.70

24.60

24.50

0.03 m/s

Temperature (OC)

Corresponding flow

velocity field


Stereoscopic PIV Measurements of a Wing-Tip Vortex

(Funded by AFOSR)

Camera 1 Camera 2

Laser Sheet

1

2

Z

X

Displacement vectors in left camera Displacement vectors in right camera

Stereo PIV technique

.deg0.5;000,52Re C

X/C =4.0

X pixel

Yp

ixe

l

0 500 1000 1500

0

200

400

600

800

1000

1200

X pixel

Yp

ixe

l

0 500 1000 1500

0

200

400

600

800

1000

1200

CFD simulation results

X/C=1.0

X/C=4.0


Flow Around a Circular Cylinder

uniform flow + a 2-D doublet = flow around a circular cylinder

Stagnation points

Pressure coefficient on the surface of cylinder

)1(sin

)1(cos

)1(cos

)1(sin

2

2

2

2

2

2

2

2

r

RVV

r

RVV

r

RrV

r

RrV

r

Lab#04 Measurements of Pressure Distributions around a

Circular Cylinder



Circular Cylinder

• At the surface of the cylinder,

• According to Bernoulli’s equation

• Pressure coefficient distribution on the surface of the circular cylinder will be:

sin2

0

VV

Var

r

2

2

2

22 1

2

12

1

2

1

V

V

V

PPVPVP

2

2

2

2

2

2

sin41)sin2(

11

2

1

V

V

V

V

V

PPCp

R

P

Incoming flow

X

Y

-3

-2

-1

0

1

0 100 200 300 400

Angle, Deg.

Cp


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 a Circular Cylinder



Circular Cylinder

R

P

Incoming flow

X

Y


Cp distributions over a circular cylinder

Cp distribution around a 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

-->

EFD

CFD

AFD


Circular Cylinder


Required Results for the Lab Report

Formal lab report format:

– Make a table showing all the time-averaged data you obtained for all

the cases you tested.

– Show all the calculation steps leading up to the final answer.

– Plot pressure coefficient (Cp) distributions on the cylinder from for all

the cases you tested.

– Comment on the characteristics of the pressure distribution compared

with the theoretical predictions.

– Calculate the drag coefficients (Cd ) of the circular cylinder for all the

cases you tested.

– Plot the drag coefficients (Cd ) of the circular cylinder as a function of at

the Reynolds numbers.

Lecture # 05: Velocimetry Techniques and Instrumentationhuhui/teaching/2019-08Fx/AerE344x/class-no… · Laser Sheet 1 2 Z X Displacement vectors in left camera Displacement vectors

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