Download - Mechanical Engineering Lab. 2
Department of Mechanical Engineering
Mechanical Engineering Lab. 2
Velocity Measurements
Professor: Wontae Hwang ([email protected])T.A: Hoonsang Lee (880-7118, [email protected])
Museong Kim (880-7118, [email protected])
Department of Mechanical Engineering
Non-dimensional variables used in fluid mechanics
U : freestream velocity
L : characteristic length
ν : kinematic viscosity
ρ : density
A : frontal area
f : vortex shedding frequency
212
212
Re / /
/
/ ( )
/ ( )
D
L
UL UL
St fL U
C Drag U A
C Lift U A
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Strouhal number – Karman vortex shedding
Fv
t
Fv
0
T
U
- Van Dyke, “Album of fluid motion”
Force is oscillating by Karman vortex shedding,
which also has a specific frequency.
From measured data,
T : force oscillating period
f : force oscillating frequency
and,
Here,
L : Characteristic length
D : Diameter of cylinder
1f
T
fLSt
U
L D
https://en.wikipedia.org/wiki/Strouhal_number
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Resonance due to Karman vortex shedding – Tacoma bridge
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Flow Measurement (or Visualization)
Intrusive
Flow Measurement (Visualization)
Non-Intrusive
Quantitative QualitativeQuantitative
Shadowgraph
Schlieren
Dye Particle
LDV PIVPitot Tube Hot Wire
Anemometer
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Pitot tube
Hot-wire anemometer
Laser Doppler Velocimetry(LDV)
Particle Image Velocimetry(PIV)
Velocity Measurements
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Pitot tube
21
2
PV gz const
Pst : Stagnation pressure
Ps : Static pressure
γ : Specific weight (=ρ×g)
g : Gravitational acceleration
Pitot tube mounted on an airplane
V = 2g(Pst - Ps )
g
Can pitot tubes measure turbulent flow?
Yes, but only mean flow, not turbulence statistics (e.g. fluctuations)
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Hot-wire anemometer
Hot-wire Constant Temperature circuit
Wheat stone bridge system
Hot-wire probe
2
w
w
t
Heat generated byelectric resistor = Heat transfer byconvection
( )
I : hot wire current
R : hot wire resistor
T : hot wire temperature
T : temperature of fluid
h : convection coefficient
A : area
V : v
w w tI R hA T T
0 1
elocity
h C C V
The wheat stone bridge measures
the variation of resistance.
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Flow Measurement (or Visualization)
Intrusive
Flow Measurement (Visualization)
Non-Intrusive
Quantitative QualitativeQuantitative
Shadowgraph
Schlieren
Dye Particle
LDV PIVPitot Tube Hot Wire
Anemometer
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LDV (Laser Doppler Velocimetry)
LDV measures the velocity of gas or liquid by measuring the velocity of small (1
μm diameter) particles introduced into the flow as the particles cross pattern set up
by 2 intersecting laser beams.
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PIV (Particle Image Velocimetry)
PIV is the simultaneous measurement of particulate (which follows the
background flow faithfully) velocity vectors at many points, using optical
imaging techniques. The measurements are usually made in planar “slices”
of the flow field.
Particle + Image → Velocity
Re = 7000
4.80
4.39
3.98
3.57
3.16
2.76
2.35
1.94
1.53
1.12
0.71
0.31
-0.51
-0.92
-1.33
-1.73
-2.14
-2.55
-2.96
-3.37
-3.78
-4.18
-4.59
-5.00
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Flow characteristics around
a circular cylinder
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Karman Vortex (Shedding, Street)
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Example of Karman Vortex (Mt. Halla)
NASA, MODIS Rapid Response System
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Separation
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Bubble length
Re = 3900
Recirculation Bubble
(Formation region)
Length
Separation point
θ
Separation angle
Dividing streamline
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Flow characteristics around
a square cylinder
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Instantaneous vorticity contour
Re=10000
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Mean field
Re=10000
Recirculation Bubble
Length
Fixed separation point
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The effect of incidence angle
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The effect of incidence angle
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Introduction to PIV
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particle image velocimetry
Successive particle images Velocity vector field
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Experimental apparatus
Laser: High power LASER GAM-3000
-3W Green Laser
Camera: Motion Analysis Camera HHC X3
-Resolution : 800X600, Mono
-frame-rate : 1,000fps at full resolution
-exposure time : Min 1ms
High-speed
camera
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Seeding particle
Traceability
Small tracer particles must follow
closely the fluid movement
Flow
Water flow : 1 – 100 um solid particle
hollow glass, aluminum, polystyrene
Air flow : 1 – 5 um atomized liquid particle
olive oil, lubricant
2-3 pixel occupancy is optimal in image plane
cylinder
Laser sheet
High-speed
camera
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Raw images
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Raw images
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Getting velocity vectors
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Getting velocity vectors
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Getting velocity vectors
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Getting velocity vectors
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Getting velocity vectors
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Getting velocity vectors
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Getting velocity vectors
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Getting velocity vectors
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Getting velocity vectors
Interrogation Window (IW)
조사구간
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Getting velocity vectors
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Sample image
(800 pixels × 600 pixels)
Interrogation window
One pixel
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Sample image
(800 pixels × 600 pixels)
16 pixels
16 pixels
Interrogation window
(16 pixels × 16 pixels)
Interrogation window
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Sample image
(800 pixels × 600 pixels)
32 pixels
32 pixels
Interrogation window
(32 pixels × 32 pixels)
Interrogation window
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• For successful PIV processing,
DI, ∆t, Umax and Vmax should be chosen
to satisfy “the ¼ law”.
CCD camera
Laser
U
∆t
Field of view
Interrogation window
DI
PIV – The ¼ law
∆t : too large
∆t : too small
T+∆t
T+∆t T
T
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|Umax ∆t| < DI /4
|Vmax ∆t| < DI /4
• For successful PIV processing,
DI, ∆t, Umax and Vmax should be chosen
to satisfy “the ¼ law”.
CCD camera
Laser
U
∆t
Field of view
Interrogation window
DI
PIV – The ¼ law
“The ¼ law”
where
Umax, Vmax : the maximum velocity
∆t : time interval between two images
DI : the size of interrogation window
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Case 1 Case 2
PIV – The ¼ law
DI
1
2
1
2
Interrogation window (size: DI)
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Interrogation window (size: DI)
Case 1
|∆x1| < DI /4,
|∆y1| < DI /4
Case 2
|∆x2| > DI /4,
|∆y2| > DI /4
PIV – The ¼ law
DI
1
2
∆x1
∆y1
1
2∆x2
∆y2
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Interrogation window (size: DI)
“The ¼ law”
Case 1
|∆x1| < DI /4,
|∆y1| < DI /4
Case 2
|∆x2| > DI /4,
|∆y2| > DI /4
PIV – The ¼ law
DI
1
2
∆x1
∆y1
1
2∆x2
∆y2
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Vector Processing
i
j
i
j
T+∆t T
Interrogation window
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Vector Processing
i
j
i
j
0 1 2 3 4
0
1
2
3
4
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Vector Processing
IW i
j
0 1 2 3 4
0
1
2
3
4
1
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IW i
j
Vector Processing
0 1 2 3 4
0
1
2
3
4
1 1
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IW i
j
Vector Processing
0 1 2 3 4
0
1
2
3
4
1 1
2
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IW i
j
Vector Processing
0 1 2 3 4
0
1
2
3
4
1 1
20
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IW i
j
Vector Processing
0 1 2 3 4
0
1
2
3
4
1 1
20
1
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IW i
j
Vector Processing
0 1 2 3 4
0
1
2
3
4
1 1
20
1 1
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Displacement = (1,1)
IW i
j
Vector Processing
R(p,q)
p
q
0 1 2 3 4
0
1
2
3
4
1 1
21
1 1 0
1
1
The goal of vector processing is to find the most
matched points between the two interrogation windows!!
R p q IW i j SW i p j qi
M
j
N
( , ) ( , ) ( , )
0
1
0
1
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Purpose
• To understand the principle of Particle Image velocimetry
• To measure and analyze the velocity field around a circular cylinder
• To measure and analyze the velocity field around a square cylinder
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Procedures
Experiment A
• Fill water in the water tunnel.
• Turn on the power, laser and computer.
• Mix the particles with surfactant.
• Turn on the pump and increase the power of pump to flow water.
• Execute the camera program and observe the field of view.
• Execute the PIV program and get the velocity data.
• Repeat the above procedures with changing the power of pump.
• Velocity field data will be uploaded on the ‘maelab’ after experiments.
(http://maelab.snu.ac.kr/)
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Exp. A : Introduction to PIV
< Water tunnel, test-section > < Field of view >
800px, 47mm
60
0p
x, 3
4m
m
< Interrogation window>
We can get one velocity
vector from one
interrogation window • ¼ Law (rule) ?
“Particle displacement should not
exceed ¼ of the interrogation
window size”
: A rule of thumb
① Interrogation Window
② ¼ Law
Laser sheet DI = 32px
DI = 32px
• Real size of interrogation window
800px : 47mm = 32px: DI , DI = 47x32/800 =1.88mm
• Applying ¼ law
Dx £ 14 DI =1.88 / 4 = 0.47mm
Dx £ 14 DI
Assume U¥ = 40mm/s
40 ´ Dt £ 0.47, Dt £ 0.01s
Camera speed: 100 fps
Flow-vision: 10000ms
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Exp. A : Introduction to PIV
③ Pump calibration
Pump output vs Free-stream velocity (5, 10,15, 20)
Pump output
[Hz]5 10 15 20
④Averaging velocity field
• Picture 300 images
• Obtain 150 instantaneous velocity fields
…
img 1 img 2 img 3 img 4 img 299 img 300
• Calculate 1 averaged velocity field (Matlab)
How can we get free-stream velocity from PIV data?
U¥
[mm/s]
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Results and Discussions-Exp. A
<Report> -Recommended plotting software: Tecplot
1. Explain the experimental setup and the procedure of PIV technique.
2. Calculate and plot the time-averaged velocity field from vector
fields. (Use Matlab for the calculation.)
3. Plot the frequency of pump versus the measured velocity with PIV,
using the results from procedure 1 and obtain linear curve-fitted relation.
(The result will be also used for Experiments B and C.)
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Procedures
Experiment B
• Set up a 5mm circular cylinder.
• Fill water in the water tunnel.
• Turn on the power, laser and computer.
• Mix the particles with surfactant.
• Turn on the pump and increase the power of pump to flow water.
• Execute the camera program and observe the field of view.
• Execute the PIV program and get the velocity data.
• Drain the water.
• Repeat the above procedures with changing a circular cylinder from 5mm to 8.2mm.
• Copy the velocity data to your USB.
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Exp. B : Flow-field past a circular cylinder
① Experimental setup
• 2 circular cylinders
• Diameter (D) : 5mm, 8.2mm
•
• Using ¼ law & the results from Exp. A,
obtain ∆𝑡 and the pump output for given Re #
② Pre-requisites
• Streamline, streakline, pathline
• Vorticity
(3-D)
• Non-dimensionalization
(2-D)
U¥Re ,d
U D fDSt
U
1 1
2 2
i j k
vx y z
u v w
1
2z
v u
x x
, , , , ?x y u v
x y u vD D U U
D
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Exp. B : Flow-field past a circular cylinder
③ Instantaneous flow-field past a circular cylinder
ϴL
: Stagnation point: Separation point
ϴ: Separation angle
L : Recirculation length
③Averaged flow-field past a circular cylinder
Karman vortex sheddingf
f : vortex shedding frequency
U¥
U¥
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Exp. B : Flow-field past a circular cylinder
④ Boundary-layer separation (White, Ch. 7)
x,u
y,v
• By viscosity (no slip condition)
boundary layer occurs
• Du/dx=0, separation point
• Due to adverse pressure
gradient
“u profile”
0dp
dx 0
dp
dx
2
2
1
wall
u dp
y dx
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Results and Discussions - Exp. B
<Report> - plotting program: Matlab
1) Calculate and plot the time-averaged velocity field from vector fields.
2) Obtain the recirculation region and calculate the recirculation length using the
result from procedure 1.
3) Plot the time-averaged vorticity contours from the time-averaged velocity, and
compare them with the instantaneous fields.
4) Plot the time-averaged streamlines and compare them with the instantaneous
ones.
5) Calculate the Strouhal (St) number.
6) Calculate the turbulent kinetic energy of each experiments and plot the results.
Measure a transverse distance between the locations of peak points and a stream-
wise distance between the trailing edge of cylinder and peak point. Discuss this
results.
7) Repeat the above procedure 1~6 for the other cylinder. Compare the results of
two experiments, in terms of the dynamic similarity in fluid mechanics.
8) Determine whether the flows are turbulent or laminar. (Can they be
determined?) Provide your supporting arguments with the definition of turbulent
flow and laminar flow
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Procedures
Experiment C
• Set up a square cylinder
which incidence angle is 0 degree.
• Fill water in the water tunnel.
• Turn on the power, laser and computer.
• Mix the particles with surfactant.
• Turn on the pump and increase the power of pump to flow water.
• Execute the camera program and observe the field of view.
• Execute the PIV program and get the velocity data.
• Drain the water.
• Repeat the above procedures with changing the incident angle of rectangular cylinder.
• Copy the velocity data to your USB.
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① Square cylinder
• Characteristic length :
length of one side(square, triangle)
Exp. C: Flow-field past a square cylinder
ϴU¥
45
ϴ: Angle of attack
5 mm
0
U¥
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② Flow characteristics
Fixed separation point
Recirculation region
Exp. C: Flow-field past a square cylinder
<Instantaneous flow field>
<Time-averaged flow field>
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③ Drag coefficient (𝐶𝐷)
Square :
Triangle :
Exp. C: Flow-field past a square cylinder
0 45vs
0 60vs
2
2
1
2
C1
2
D
D
DragC
U A
Drag
U l
(3-D)
(2-D)
• Research papers and compare CD according to the angle of attack.
• Explain the difference of CD according to the angle of attack, based on the
PIV result.
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Results and Discussions-Exp. C
<Report> - plotting program: Matlab
1) Calculate and plot the time-averaged velocity field from vector fields
2) Obtain the recirculation region, recirculation length and separation point using
the result from procedure 1.
3) Plot the time-averaged vorticity contours from the time-averaged velocity, and
compare them with the instantaneous fields.
4) Plot the time-averaged streamlines and compare them with the instantaneous
ones.
5) Calculate the Strouhal (St) number.
6) Calculate the turbulent kinetic energy of each experiments and plot the results.
Measure a transverse distance between the locations of peak points and a stream-
wise distance between the trailing edge of cylinder and peak point. Discuss this
results.
7) Discuss the experimental results of two different incidence angles.
8) Which 𝐶𝐷 is bigger? (In order to obtain 𝐶𝐷 of the cylinders, refer to the relevant
papers including similar Re data.) Based on your experimental data and literature
survey, explain the reason why the drag of that cylinder is larger than the other?
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Scoring Standards
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Evaluation
Velocity experiment
Total score: 25
Report: 10 Quiz: 5 Attitude: 10
Exp. A, B, C Each 3 points
Preliminary report X
Result report (due a week)
At class time or 301-1215
Exp. A - 3 problems
Exp. B - 2 problems
Exp. C - 2 problems
Lateness -1 point
Absence -2 points
Two lateness = One absence