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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
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Copyright © by Dr. Hui Hu @ Iowa State University. All Rights Reserved!
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
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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
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Methods to Measure Local Flow Velocity -2
• 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
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Copyright © by Dr. Hui Hu @ Iowa State University. All Rights Reserved!
Methods to Measure Local Flow Velocity -3
• 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
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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
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Methods to Measure Local Flow Velocity - 4
• 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
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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).
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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)
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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
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Fundamentals of LDV
• How to determine doppler shift? Optical heterodyne! Mix the response from two beams on the reciever:
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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
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• 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
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-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
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• 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
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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
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Methods to Measure Local Flow Velocity - 5
• 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
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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
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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
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Lab#04 Measurements of Pressure Distributions around a
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
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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 a Circular Cylinder
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Lab#04 Measurements of Pressure Distributions around a
Circular Cylinder
R
P
Incoming flow
X
Y
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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
Lab#04 Measurements of Pressure Distributions around a
Circular Cylinder
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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.