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Copyright © by Dr. Hui Hu @ Iowa State University. All Rights Reserved!
Dr. Hui Hu
Department of Aerospace Engineering
Iowa State University
Ames, Iowa 50011, U.S.A
Lecture # 12: Illumination, imaging, and particle image
velocimetry
AerE 344 Lecture Notes
Sources/ Further reading: Hecht, “Optics” 4th ed.
Raffel, Willert, Wereley, Kompenhans, “Particle image velocimetry: A practical guide” 2nd ed.
Copyright © by Dr. Hui Hu @ Iowa State University. All Rights Reserved!
The nature of light – as photons
Photon scattering:
• one finds experimentally that the frequency of the scattered wave is changed,
which does not come out of a wave picture of light. However, when the light is
viewed as a photon with energy proportional to the associated light wave,
excellent agreement with experiment is found.
The photoelectric effect:
• When light shines on a metal plate, electrons are ejected. These electrons are
accelerated to a nearby plate by an external potential difference, and a
photoelectric current is established, as below
• The photons hit an electron in the metal, giving up energy. If photon energy is
sufficient to free the electron, it is accelerated towards the other side; hence, a
flow of charges (current).
• The photoelectric current depends critically on the frequency of the light. This
is a feature of the energy that the electrons gain when struck by the light.
– in the wave description, the energy of the light depends on the
amplitude, and not on the frequency.
– however, in the photon description of light, the energy of the photon is
proportional to the frequency of the associated wave, which provides a
natural explanation of the frequency dependence of the photoelectric
current.
• The explanation was first given by Einstein and won him the Nobel Prize. JsconstPlanck
h3410624.6
Copyright © by Dr. Hui Hu @ Iowa State University. All Rights Reserved!
Light Scattering
• Scattering
– Scattering is a general physical process whereby
some forms of radiation, such as light, are forced
to deviate from a straight trajectory by one or
more localized non-uniformities in the medium
through which it passes.
• Elastic Scattering
– Excited electron or atoms emits a photo have
exact the same frequency as the incident one.
• Inelastic scattering
– Excited electron or atoms emits a photo have a
frequency different from the incident one.
Copyright © by Dr. Hui Hu @ Iowa State University. All Rights Reserved!
Elastic scattering
Rayleigh Scattering
–Light scattering from particles that are smaller than 1/15 of the incident light wavelength (d< /15).
–Efficiency of the scattering from a particle is expressed in terms of scattering cross section.
Mie Scattering
–Light scattering from a particles with its size close on bigger than the incident light wavelength (d > ).
–Conservation of polarization direction
–Angle dependent
• Forward scattering
• Back scattering
.
1065.6
)(
0
229
20
atomtheofwavelengthticcharateristheis
mT
TR
a. d=1μm b. d=10μm c. d=30μm
Copyright © by Dr. Hui Hu @ Iowa State University. All Rights Reserved!
Inelastic Scattering
Raman Scattering
– Inelastic scattering from molecules.
– Chance to occur is about 10-5 ~ 10-2 of times lower than the Rayleigh scattering
– Scattering cross section is several orders smaller than the Rayleigh scattering
– Stoke transition : the energy of the emitted photon is higher than the absorbed photo.
– Anti-stoke transition: the energy of the emitted photon is lower than the absorbed photo.
– Time between the absorption and emission: 10-14 s.
– Anti-stokes line will be stronger when the temperature is low.
Copyright © by Dr. Hui Hu @ Iowa State University. All Rights Reserved!
Fluorescence and phosphorescence
– Rayleigh and Raman scattering occurs essentially instantaneously. Not allowing other energy conversion phenomena to occur.
Fluorescence and phosphorescence
– Photoluminescence with time delay
Fluorescence
– Emission when the excited from singlet state to ground,
– lifetime is about 10-10 ~ 10-5 s.
Rhodamine B
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Fluorescence and phosphorescence
Phosphorescence
– Emission when the excited atom or molecule
from triplet state to ground,
– lifetime is about 10-4 ~ 10-5 s.
0
1000
2000
3000
4000
5000
200 300 400 500 600 700 800
T = 32.0oC
T= 25.4 o
CT= 19.7
oC
T= 14.5oC
T = 10.2oC
T= 3.40 oC
Wavelength (nm)
Rel
ativ
e in
tens
ity
Spectraphotometer Output vs Wavelength
fluorescence
Phosphorescence
MTV chemical: 1-BrNp•M-CD•ROH complex
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Absorption
Light is transmitted through a material, it will be
absorbed by the molecules of the material
Beer’s law:
• is the absorption or attenuation coefficient
•Lc=1/ is called penetration depth.
•When L=Lc, I/I0=1/e=37%, i.e., 63% energy was
absorbed
•Metals have very small Lc=1/.
– Copper, Lc=0.6nm for 100 nm UV light
– Copper, Lc=6.0nm for 1000 nm infrared light.
– 2nm copper plate as a low pass filter.
)exp(0 LII
L
I0
Copyright © by Dr. Hui Hu @ Iowa State University. All Rights Reserved!
Illumination
Light sources:
• Thermal source:
– Lamps: Continuous wave (CW)
– Flash lamps (Pulsed)
– Arc lamps
• Laser sources
– Continuous wave (CW)
– Pulsed laser
– Singe wavelength
• Point source:
• Plane source:
Copyright © by Dr. Hui Hu @ Iowa State University. All Rights Reserved!
Light source
• Thermal light source:
–Emit electromagnetic radiation as a result of being heated to
high-temperature
–Line sources:
–Continuum sources:
• Incandescent lamps: heated tungsten filament in a evacuated
glass container.
• Electric discharge lamps: fluorescent lamps. Filled with
mercury vapor at low pressure and utilize an electric discharge
through it to produce light in ultraviolet (UV) range. Through
fluorescent, it is convert to visible light.
• Flash lamps: tubes containing a noble gas such xenon,
krypton or argon. For their operation, high voltage stored in a
capacitor is discharged through the gas, producing a highly
luminous corona discharge. Light pulse is about 1s to1 ms.
• Sparks: produced by the electric breakdown of a gas (helium,
neo, argon or air) during an electric discharge between
electrodes. The choice of different electrodes produces sparks
of different shapes.
Copyright © by Dr. Hui Hu @ Iowa State University. All Rights Reserved!
Laser
• Laser: Light Amplification by Stimulated Emission of Radiation
(LASER)
• Advantages of laser light over thermal light source:
–Coherent light (with all light wave front in phase)
–Collimated and concentrated (parallel light with small cross
area)
–Monochromic (energy concentrated in a very narrow
wavelength band)
• How a laser works:
–Radiation energy is produced by an activated medium( can
be gas, crystal or semiconductor or liquid solution).
–The medium consists of particles (atom, ions or molecules).
–When a photo, having energy hv, approaching the particles,
the photo may be absorbed cause an electron or atoms to
be raised temporarily to high-energy level.
–When the excited electron or molecule to return ground
level, spontaneous emission or stimulated emission would
take place.
Copyright © by Dr. Hui Hu @ Iowa State University. All Rights Reserved!
Laser
–Spontaneous emission: emit a photo with the same
energy as that absorbed one, but in random direction.
–Stimulated emission: An electron or atom is already at a
higher energy level could become excited by an incident
photo, without absorb the photo, it will emission another
photo with identical energy (frequency), phase, and
direction as the incident photon.
–External power source is required to maintain the
population of the atoms in higher energy level in order to
make to stimulated emission taking place continuously.
–Optical cavity.
–Q-switch
Copyright © by Dr. Hui Hu @ Iowa State University. All Rights Reserved!
Commonly used Lasers
–Helium-neon (He-Ne) laser
• Active medium is helium neon atoms
• Continuous wave laser
• Power 0.3 ~15 mW
• =633nm (red)
–Argon-ion (Ar-ion) laser
• Active medium is argon atoms maintained at the ion
state.
• Continuous wave laser
• Power level: 100 mW ~10 W
• Have seven wavelengths
• =488n (blue)
• =514.5nm (green)
• LDV application
• LIF in liquid flows
Copyright © by Dr. Hui Hu @ Iowa State University. All Rights Reserved!
Commonly used Lasers
–Nd-YAG laser
• Solid-state laser
• Active medium: neodymium (Nd+3) as active medium
incorporated as an impurity into a crystal of Yattium-
Aluminium-Garnet (YAG) as a host
• Flash lamp is used as external source
• pulsed laser: 10 -400mJ/pulse or more
• Pulse duration: 100ps ~ 10ns
• Wavelenght of tube =1064nm (infrared)
• SHG: =532nm (green), THG: =355nm (UV), FHG:
=266nm (deepUV)
• PIV, MTV, PLIF
• Repetition rate can be as high as 30 Hz.
Copyright © by Dr. Hui Hu @ Iowa State University. All Rights Reserved!
Commonly used Lasers
–Copper Vapor laser
• Active medium: copper vapor
• Pulsed laser: 10mJ/pulse or more
• Pulse duration: 15 ~ 60ns
• =510.6nm (green), =578.2nm (yellow)
• Repetition rate can be as high as f=5,000~15,000 Hz.
• High-speed PIV, LIF and others
–Dye laser
• Active medium: complex multi-atomic organic molecules
• =200nm ~ 1500nm
–Excimer laser
• Gas laser KrF and Xecl
• High-energy
• UV wavelength
• Pulsed laser
• high repetition frequency
Copyright © by Dr. Hui Hu @ Iowa State University. All Rights Reserved!
Lenses
• Focal length: f
• f/# , “F-number”: defined as the
ratio of focal distance of the lens
and its clear aperture diameter.
• Depth of focus H = 2 ∙f/# ∙ c ∙ Z/f
Copyright © by Dr. Hui Hu @ Iowa State University. All Rights Reserved!
Photodetector
• Photo detector is a device to convert light to an electric
current through photo electric effect.
• Quantum efficiency:
• Noise:
– Shot noise: due to random fluctuation of the rate of
photon collection and back ground illumination
– Thermal noise: caused by amplification of current
inside the photo detector and by external amplifier.
• Dark current: the current produced by the photo detector
even in the absence of a desirable light source.
• Two kinds of photo detectors:
– Photomultiplier tubes (PMT)
– photodiodes (PD) or photo electric cells
electrons emitted ofNumber :
photons absorbed ofNumber :
p
e
p
eq
N
N
N
N
Copyright © by Dr. Hui Hu @ Iowa State University. All Rights Reserved!
Photodetector
• photodiodes (PD) or photo electric cells
– P-n junctions of semiconductors,
commonly silicon-silicon type.
– High quantum efficiency
– But not internal amplification
Copyright © by Dr. Hui Hu @ Iowa State University. All Rights Reserved!
Interlaced Cameras
The fastest response time of human being for images is about ~ 15Hz
Video format:
• PAL (Phase Alternating Line ) format with frame rate of f=25Hz (sometimes in 50Hz). Used by U.K., Germany, Spain, Portugal, Italy, China, India, most of Africa, and the Middle East
• NTSC format: established by National Television Standards Committee (NTSC) with frame rate of f=30Hz. Used by U.S., Canada, Mexico, some parts of Central and South America, Japan, Taiwan, and Korea.
Even field
(2,4,6…640)
Old field
(1,3,5…639)
Even field
Odd field
16.6ms 16.6ms
1 frame
F=30Hz
480 pixels by 640 pixels
Interlaced camera
time
Copyright © by Dr. Hui Hu @ Iowa State University. All Rights Reserved!
Progressive scan camera
• All image systems produce a clear
image of the background
• Jagged edges from motion with
interlaced scan
• Motion blur caused by the lack of
resolution in the 2CIF sample
• Only progressive scan makes it
possible to identify the driver
Copyright © by Dr. Hui Hu @ Iowa State University. All Rights Reserved!
Electronic shutter modes
• Rolling shutter: The sensor is exposed line by line. Each of the pixels integrate light for the
specified exposure time; however, not all pixels are exposing at the same time. The start time
for each pixel’s exposure is a function of sensor position. This mode is typical of large formate
sensors, such as digital SLR cameras.
• Global shutter: Each pixel integrates light for the specified exposure time simultaneously. This
method is preferred for capturing highly dynamic events. This mode is typical of high-speed
CMOS cameras which can operate at frame rates beyond 1 million frames per second.
Rolling shutter Gobal shutter
Point Grey Cameras Point Grey Cameras
Copyright © by Dr. Hui Hu @ Iowa State University. All Rights Reserved!
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
Copyright © by Dr. Hui Hu @ Iowa State University. All Rights Reserved!
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
Copyright © by Dr. Hui Hu @ Iowa State University. All Rights Reserved!
PIV System Setup
Illumination system
(Laser and optics)
camera
Synchronizer
seed flow with
tracer particles
Host computer
Particle tracers: track the fluid movement.
Illumination system: illuminate the flow field in the interest region.
Camera: capture the images of the particle tracers.
Synchronizer: control the timing of the laser illumination and camera acquisition.
Host computer: to store the particle images and conduct image processing.
Copyright © by Dr. Hui Hu @ Iowa State University. All Rights Reserved!
Tracer Particles for PIV
• Tracer particles should be neutrally buoyant and small enough to follow the flow perfectly.
• Tracer particles should be big enough to scatter the illumination lights efficiently .
• The scattering efficiency of trace particles also strongly depends on the ratio of the
refractive index of the particles to that of the fluid.
For example: the refractive index of water is considerably larger than that of air.
The scattering of particles in air is at least one order of magnitude more
efficient than particles of the same size in water.
h
Incident light Scattering light
a. d=1μm b. d=10μm c. d=30μm
Copyright © by Dr. Hui Hu @ Iowa State University. All Rights Reserved!
Tracer Particles for PIV
18
);exp(1()(
18
)(
2
2
p
ps
s
p
p
pPs
d
tUtU
gdUUU
U
gdUp
pg
18
)(2
PU
Copyright © by Dr. Hui Hu @ Iowa State University. All Rights Reserved!
• Tracers for PIV measurements in liquids (water):
• Polymer particles (d=10~100 m, density = 1.03 ~ 1.05 kg/cm3)
• Silver-covered hollow glass beams (d =1 ~10 m, density = 1.03 ~ 1.05 kg/cm3)
• Fluorescent particle for micro flow (d=200~1000 nm, density = 1.03 ~ 1.05 kg/cm3).
•Quantum dots (d= 2 ~ 10 nm)
• Tracers for PIV measurements in gaseous flows:
• Smoke …
• Droplets, mist, vapor…
• Condensations ….
• Hollow silica particles (0.5 ~ 2 μm in diameter and 0.2 g/cm3 in density for PIV
measurements in combustion applications.
•Nanoparticles of combustion products
Tracer Particles for PIV
Copyright © by Dr. Hui Hu @ Iowa State University. All Rights Reserved!
Illumination system
• The illumination system of PIV is always composed of light source and optics.
• Lasers: such as Argon-ion laser and Nd:YAG Laser, are widely used as light
source in PIV systems due to their ability to emit monochromatic light with high
energy density which can easily be bundled into thin light sheet for illuminating
and recording the tracer particles without chromatic aberrations.
• Optics: always consist of a set of cylindrical lenses and mirrors to shape the
light source into a planar sheet to illuminate the flow field.
laser optics
Laser beam
Laser sheet
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Double-pulsed Nd:Yag Laser for PIV
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Cameras
• Types of cameras for PIV:
• Photographic film-based cameras (old)
•Charged-coupled device (CCD) cameras
•High speed Complementary metal-oxide semiconductor (CMOS) cameras
•Advantages of digital cameras:
• It is fully digitized
• Various digital techniques can be implemented for PIV image processing.
• Conventional auto- or cross- correlation techniques combined with special
framing techniques can be used to measure higher velocities.
• Disadvantages of digital cameras:
• Low temporal resolution (defined by the video framing rate):
• Low spatial resolution:
Copyright © by Dr. Hui Hu @ Iowa State University. All Rights Reserved!
Synchronizer
• Function of Synchronizer:
• To control the timing of the laser illumination and camera acquisition
• “Frame straddling” strategy for two-frame single exposure recordings
1st
pulsed
2nd
pulsed
Timing of
pulsed laser
Timing of
CCD camera
time
1st frame exposure
2nd frame exposure
t
33.33ms
(30Hz)
To laser To camera
From computer
Synchronizer
Copyright © by Dr. Hui Hu @ Iowa State University. All Rights Reserved!
Host computer
• To send timing control parameter to synchronizer.
• To store the particle images and conduct image processing.
Host computer
To synchronizer
Image data from camera
Copyright © by Dr. Hui Hu @ Iowa State University. All Rights Reserved!
Single-frame technique
particle
Streak line
V L=V*t
single-pulse Multiple-pulse
Particle streak velocimetry
Copyright © by Dr. Hui Hu @ Iowa State University. All Rights Reserved!
Multi-frame technique
a. T=t0
b. T=t1
c. T=t2
a. T=t3
t=t0
t
LU
t= t0+t
L
Copyright © by Dr. Hui Hu @ Iowa State University. All Rights Reserved!
Example PIV raw data
In-plane
U
Δζ, Δz
Image: A B
Copyright © by Dr. Hui Hu @ Iowa State University. All Rights Reserved!
U
h
Through-plane In-plane Trefftz
plane
Example PIV raw data
Copyright © by Dr. Hui Hu @ Iowa State University. All Rights Reserved!
Image Processing for PIV
• To extract velocity information from particle images.
t=t0 t=t0+4ms
A typical PIV raw image pair
Y/D
X/D
-2 -1 0 1 2 31
1.5
2
2.5
3
3.5
4
4.5
5
1.1001.0501.0000.9500.9000.8500.8000.7500.7000.6500.6000.5500.5000.4500.4000.3500.3000.2500.2000.1500.100
Velocity U/Uin
Image processing
Copyright © by Dr. Hui Hu @ Iowa State University. All Rights Reserved!
Particle Tracking Velocimetry (PTV)
t=t0 t=t0+t
Low particle-image
density case
1. Find position of the particles at each
images
2. Find corresponding particle image pair
in the different image frame
3. Find the displacements between the
particle pairs.
4. Velocity of particle equates the
displacement divided by the time
interval between the frames.
Copyright © by Dr. Hui Hu @ Iowa State University. All Rights Reserved!
Particle Tracking Velocimetry (PTV)-2
Particle position of time step t=t1
Search region for
time step t=t4
Search region for time step t=t3
Search region for time step t=t2
Four-frame-particle
tracking algorithm
1. Find position of the particles at each
images
2. Find corresponding particle image pair
in the different image frame
3. Find the displacements between the
particle pairs.
4. Velocity of particle equates the
displacement divided by the time
interval between the frames.
PTV results
Copyright © by Dr. Hui Hu @ Iowa State University. All Rights Reserved!
Correlation-based PIV methods
high particle-image density
t=t0 t=t0+t
Corresponding flow
velocity field
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Correlation-based PIV methods
t=t0 t=t0+t
dvgyxgdvfyxf
dvgyxgfyxfqpR
22
)),(()),((
)),(()),((,
Correlation coefficient function:
Copyright © by Dr. Hui Hu @ Iowa State University. All Rights Reserved!
Cross Correlation Operation
Signal A:
Signal B:
dxuxgdxxf
dxuxgxfuR
])([*])([
)](*)([
22
Copyright © by Dr. Hui Hu @ Iowa State University. All Rights Reserved!
1 4 7 10 13 16 19 22 25 28 31S1
S10
S19
S280.7
0.75
0.8
0.85
0.9
0.95
1
Correlation coefficient distribution
dvgyxgdvfyxf
dvgyxgfyxfqpR
22
)),(()),((
)),(()),((,
R(p,q)
Peak location
Copyright © by Dr. Hui Hu @ Iowa State University. All Rights Reserved!
Comparison between PIV and PTV
• Particle Tracking Velocimetry:
• Tracking individual particle
• Limited to low particle image density case
• Velocity vector at random points where tracer particles exist.
• Spatial resolution of PTV results is usually limited by the
number of the tracer particles
• Correlation-based PIV:
• Tracking a group of particles
• Applicable to high particle image density case
• Spatial resolution of PIV results is usually limited by the size of
the interrogation window size
• Velocity vector can be at regular grid points.
PTV
t=t0+t
PIV
Y/D
X/D
-2 -1 0 1 2 31
1.5
2
2.5
3
3.5
4
4.5
5
1.1001.0501.0000.9500.9000.8500.8000.7500.7000.6500.6000.5500.5000.4500.4000.3500.3000.2500.2000.1500.100
Velocity U/Uin
Copyright © by Dr. Hui Hu @ Iowa State University. All Rights Reserved!
Estimation of differential quantities
X (mm)Y
(mm
)10 15 20 25 30 35
5
10
15
20
Copyright © by Dr. Hui Hu @ Iowa State University. All Rights Reserved!
Estimation of differential quantities
Copyright © by Dr. Hui Hu @ Iowa State University. All Rights Reserved!
Estimation of Vorticity distribution
y
U
x
Vz
Copyright © by Dr. Hui Hu @ Iowa State University. All Rights Reserved!
Estimation of Vorticity distribution
Stokes Theorem:
dA
AdldV
yx
z
C S
Copyright © by Dr. Hui Hu @ Iowa State University. All Rights Reserved!
Vorticity distribution Examples
-50 0 50 100 150 200 250 300-50
0
50
100
150
200
250
-25.00 -20.00 -15.00 -10.00 -5.00 0.00 5.00 10.00 15.00 20.00 25.00
Spanwise Vorticity ( Z-direction )
Re =6,700
Uin = 0.33 m/s
X mm
Ym
m
Uo
ut
water free surface
X (mm)
Y(m
m)
-20 0 20 40 60 80 100 120 140
-60
-40
-20
0
20
40
60 -3.2 -2.7 -2.2 -1.7 -1.2 -0.7 -0.2 0.3 0.8 1.3 1.8
10 m/sspanwisevorticity (1/s)
shadow region
GA(W)-1 airfoil
Copyright © by Dr. Hui Hu @ Iowa State University. All Rights Reserved!
Ensemble-averaged quantities
• Mean velocity components in x, y directions:
•Turbulent velocity fluctuations:
• Turbulent Kinetic energy distribution:
• Reynolds stress distribution:
NUuuN
i
i /)('1
2
N
i
i Vvv1
2)('
N
i
i NuU1
/
N
i
i NvV1
/
)''(2
1 22
vuTKE
N
i
ii
N
UvUuvu
1
))((''
Copyright © by Dr. Hui Hu @ Iowa State University. All Rights Reserved!
Ensemble-averaged quantities
X (mm)
Y(m
m)
-20 0 20 40 60 80 100 120 140
-60
-40
-20
0
20
40
60 U m/s: -1.0 1.0 3.0 5.0 7.0 9.0 11.0 13.0 15.0
10 m/s
shadow region
GA(W)-1 airfoil
X (mm)
Y(m
m)
-20 0 20 40 60 80 100 120 140
-60
-40
-20
0
20
40
60 vort: -3.0 -2.0 -1.0 0.0 1.0 2.0 3.0
10 m/s
shadow region
GA(W)-1 airfoil
X (mm)
Y(m
m)
-20 0 20 40 60 80 100 120 140
-60
-40
-20
0
20
40
60 -0.035 -0.025 -0.015 -0.005 0.005 0.015 0.025 0.035
shadow region
GA(W)-1 airfoil
NormalizedReynolds Stress
X (mm)
Y(m
m)
-20 0 20 40 60 80 100 120 140
-60
-40
-20
0
20
40
60 0.010 0.020 0.030 0.040 0.050 0.060 0.070 0.080 0.090 0.100
shadow region
GA(W)-1 airfoil
T.K.E
Copyright © by Dr. Hui Hu @ Iowa State University. All Rights Reserved!
Pressure field estimation
)(1
)(1
2
2
2
2
2
2
2
2
y
v
x
v
y
p
y
vv
x
vu
y
u
x
u
x
p
y
uv
x
uu
Copyright © by Dr. Hui Hu @ Iowa State University. All Rights Reserved!
Integral Force estimation
FVdfAdPAdVVVdVt
VCSCSCVC
........
~)(
X (mm)
Y(m
m)
-20 0 20 40 60 80 100 120 140
-60
-40
-20
0
20
40
60 U m/s: -1.0 1.0 3.0 5.0 7.0 9.0 11.0 13.0 15.0
10 m/s
shadow region
GA(W)-1 airfoil
Copyright © by Dr. Hui Hu @ Iowa State University. All Rights Reserved!
Tank with compressed air Test section
AerE344 Lab: Pressure Measurements in a de Laval Nozzle
Tap No. Distance downstream of throat (inches) Area (Sq. inches)
1 -4.00 0.8002 -1.50 0.5293 -0.30 0.4804 -0.18 0.4785 0.00 0.4766 0.15 0.4977 0.30 0.5188 0.45 0.5399 0.60 0.56010 0.75 0.58111 0.90 0.59912 1.05 0.61613 1.20 0.62714 1.35 0.63215 1.45 0.634
Copyright © by Dr. Hui Hu @ Iowa State University. All Rights Reserved!
1st, 2nd, and 3rd critical conditions
Under-
expanded
flow
Flow close to
3rd critical
Over-
expanded
flow
2nd critical – shock
is at nozzle exit
Over-expanded flow
with shock between
nozzle exit and
throat
1st critical – shock
is almost at the
nozzle throat.