lecture # 13: particle image velocimetry techniquehuhui/teaching/2015sx/class-notes/aere344-… ·...

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 # 13: Particle Image Velocimetry Technique

AerE 344 Lecture Notes


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


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


PIV System Setup

Illumination system

(Laser and optics)

camera

Synchronizer

seed flow with

tracer particles

Host computer

Particle tracers: to track the fluid movement.

Illumination system: to illuminate the flow field in the interest region.

Camera: to capture the images of the particle tracers.

Synchronizer: to control the timing of the laser illumination and

camera acquisition.

Host computer: to store the particle images and conduct image processing.


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



18

);exp(1()(

18

)(

2

2

p

ps

s

p

p

pPs

d

tUtU

gdUUU

U

gdUp

pg

18

)(2

PU


• 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



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 consisted by a set of cylindrical lenses and mirrors to shape the

light source beam into a planar sheet to illuminate the flow field.

laser optics

Laser beam

Laser sheet


Optics for PIV


Cameras

• The widely used cameras for PIV:

• Photographic film-based cameras or Charged-Coupled Device (CCD) cameras.

•Advantages of CCD 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 CCD cameras:

• Low temporal resolution (defined by the video framing rate):

• Low spatial resolution:


Synchronizer

• Function of Synchronizer:

• To control the timing of the laser illumination and camera acquisition

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


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


Single-frame technique

particle

Streak line

V L=V*t

single-pulse Multiple-pulse

Particle streak velocimetry

http://www.pbase.com/andrej_z/weekly_assignment


Multi-frame technique a. T=t0

b. T=t1

c. T=t2

a. T=t3

t=t0

t

LU

t= t0+t

L


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


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.


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


Correlation-based PIV methods

high particle-image density

t=t0 t=t0+t

Corresponding flow

velocity field

Image: A B


Correlation-based PIV methods

t=t0 t=t0+t

dvgyxgdvfyxf

dvgyxgfyxfqpR

22

)),(()),((

)),(()),((,

Correlation coefficient

function


Cross Correlation Operation

Signal A:

Signal B:

dxuxgdxxf

dxuxgxfuR

])([*])([

)](*)([

22


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


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


Estimation of differential quantities

X (mm)Y

(mm

)10 15 20 25 30 35

5

10

15

20


Estimation of differential quantities


Estimation of Vorticity distribution

y

U

x

Vz


Estimation of Vorticity distribution

Stokes Theorem:

dA

AdldV

yx

z

C S


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


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

))((''


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


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


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


Example PIV experiments


X/D

Y/D

-0.5 0 0.5 1 1.5

-0.2

0

0.2

0.4

0.6 0.0 2.0 4.0 6.0 8.0 10.0 12.0 14.0 16.0 18.0 20.0 22.0 24.0 26.0

Wall

Velocity(m/s)

dimple

X

Y

-0.5 0 0.5 1 1.5

-0.2

0

0.2

0.4

0.60.0 2.0 4.0 6.0 8.0 10.0 12.0 14.0 16.0 18.0 20.0 22.0 24.0 26.0

Flat Plate

Velocity(m/s)

(a). Instantaneous velocity field over the dimpled (left) and flat (right) surfaces

X

Y

-0.5 0 0.5 1 1.5

-0.2

0

0.2

0.4

0.6 -5500 -4500 -3500 -2500 -1500 1500 2500 3500 4500 5500

Wall

SpanwsieVorticity (1/s)

dimple

X

Y

-0.5 0 0.5 1 1.5

-0.2

0

0.2

0.4

0.6 -5500 -4500 -3500 -2500 -1500 1500 2500 3500 4500 5500

Flat Plate

SpanwsieVorticity (1/s)

(b). Instantaneous vorticity distributions over the dimpled (left) and flat (right) surfaces

X/D

Y/D

-0.5 0 0.5 1 1.5

-0.2

0

0.2

0.4

0.6 0.00 0.10 0.20 0.30 0.40 0.50 0.60 0.70 0.80 0.90 1.00

Wall

U/U

Dimple

X/D

Y/D

-0.5 0 0.5 1 1.5

-0.2

0

0.2

0.4

0.6 0.00 0.10 0.20 0.30 0.40 0.50 0.60 0.70 0.80 0.90 1.00

Flat Plate

U/U

(c). Mean velocity field over the dimpled (left) and flat (right) surfaces

Turbulence quantities above dimple


X/D

Y/D

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0

-0.2

-0.1

0.0

0.1

0.2

0.3

0.0 2.0 4.0 6.0 8.0 10.0 12.0 14.0 16.0 18.0 20.0

Velocity(m/s)

Dimpled Surface

-4500

-3500

-3500

-3500

-3500

-3500

-2500

-2500

-25

00

-2500

-25

00

-2500

-150

0-150

0 -1500

-1500

-1500

-500

-500

-500

-500

-500

5005

00

500

500

500

500

1500

X/D

Y/D

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0

-0.2

-0.1

0.0

0.1

0.2

0.3

-6500 -5500 -4500 -3500 -2500 -1500 -500 500 1500 2500 3500

Vorticity(1/s)

Dimpled Surface

(a). Instantaneous velocity field (b). Instantaneous vorticity distribution

X/D

Y/D

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1-0.3

-0.2

-0.1

0

0.1

0.2

0.3

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 1.1 1.2(U

2+V

2)

1/2/U

Dimpled Surface

X/D

Y/D

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1-0.3

-0.2

-0.1

0

0.1

0.2

0.3

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 1.1 1.2(U

2+V

2)

1/2/U

Dimpled Surface

(c). Ensembles-averaged velocity field (d). Streamlines of the mean flow field

X/D

Y/D

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1-0.3

-0.2

-0.1

0

0.1

0.2

0.3

0.005 0.007 0.009 0.011 0.013 0.015 0.017 0.019 0.021 0.023 0.025

NormalizedIn-plane TKE

Dimpled Surface

X/D

Y/D

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1-0.3

-0.2

-0.1

0

0.1

0.2

0.3

-0.002 -0.001 0.001 0.003 0.004 0.005 0.007 0.009 0.010 0.012 0.013

NormalizedReynoldsStress

Dimpled Surface

(e). Normalized in-plane TKE distribution (f). Normalized Reynolds stress distribution

Fig. 8: PIV measurement results of the flow field inside the dimple at Re=36.7K.

Turbulence quantities inside dimple


Tank with compressed air Test section

AerE344 Lab#11: 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


1st, 2nd and 3rd critic 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.


Prediction of the Pressure Distribution within a De Laval Nozzle

by using Numerical Approach

atme PP

M<1 M>1

PT1 P1 PT

2

P2

M<1

Shock

AS

Ae

Throat

, A* or

At

atme PP

1

1

2

2

2

* 2

11

1

21

M

MA

A

• Using the area ratio, the Mach number at any

point up to the shock can be determined:

• After finding Mach number at front of shock,

calculate Mach number after shock using:

2

12

22

1

11

21

2

MM

M

• Then, calculate the A2*

1

122 2 2

2 2 2

2 11

1 2sA M A M

which allows us calculate the remaining Mach

number distribution

1

1

2

2

2

* 2

11

1

21

M

MA

A

2


Some Examples of Previous Student Lab Reports

Theoretical Data - Gauge Pressure vs. Position

-10

0

10

20

30

40

50

0 1 2 3 4 5

Position along Nozzle Axis, inches

Ga

ug

e P

res

su

re,

ps

i

3rd Critical 2nd Critical Normal Shock 1st Critical

Experimental Results - Pressure vs. Nozzle Location

-10

0

10

20

30

40

50

60

70

80

90

0 1 2 3 4 5

Nozzle location, inches

Gau

ge P

ressu

re,

psi

Under-Expanded Flow Approximately 2nd Critical Normal Shock

0

5

10

15

20

25

30

35

-5 -4 -3 -2 -1 0 1 2

Distance from Troat (in)

Pre

ssu

re (

PS

I)

Experimental

1-D Theory

Total Pressure = 34.336 PSI

lecture # 13: particle image velocimetry techniquehuhui/teaching/2015sx/class-notes/aere344-… ·...

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