Introduction to particle-based methods

Summer school on “Measuring techniques for turbulent open-channel flows”

Introduction to particle-based methods Key principles and hardware

Summer school on “Measuring techniques for turbulent open-channel flows” Lisboa, 28-30 July 2015

Rui M.L. Ferreira, Rui Aleixo

Instituto Superior Técnico, Universidade de Lisboa; GHT Photonics


Motivation

“Scientific observation is always a polemic observation […]. Naturally, passing from observation to experimentation, the polemic character of knowledge becomes clearer. It is necessary that the phenomenon is isolated, filtered, shaped by the instruments; it may be that instruments produce the phenomenon in the first place. And instruments are nothing but materialized theories. It results that phenomena bear the stamp of theory throughout”

Gaston Bachelard Le nouvel esprit scientifique, p. 12-13


Outline

- Basic ideas behind PIV and PTV (Eulerian/lagrangian flow descriptions)

- Particle-based methods

- Necessary hardware

- Basics of PIV

- Basics of PTV


basic ideas

Flow description

Particle Image Velocimetry (PIV) Particle Tracking Velocimetry (PTV)

Particle-based methods and optical methods

optical methods – particle-based, light scattering from tracers (as old as photography itself)

Percival Lowell – search for planet X Clyde Tombaugh – finding Pluto

Milton van Dyke – an album of fluid motion

Onera, 1974


How to measure fluid velocities?

Use tracers that follow the flow. Track the tracers with imaging techniques Determine tracers displacement (each tracer or its representative velocity in a small spatial domain) Determine tracers velocity

𝐯𝑝 = 𝐯𝑓

basic ideas

Flow description


basic ideas

Flow description

PIV – spatial (eulerian) flow description

PTV – material (lagrangian) flow description or spatial flow description


basic ideas

Flow description



Spatial (eulerian) description

1 2 3, , , ,jx t x x x t B B B


basic ideas

Flow description



Material (Lagrangean) formulation

1 2 3, , , ,jX t X X X t B B B

,0 ,0j jx XB B


basic ideas

Flow description

PIV – velocity is determined as a field variable; vector tangent to small displacements in any space location, concept of streamline

PTV – velocities of each parcel of continuum are determined by (lagrangian) by diferentiation of property position, concept of pathline

d 0 u l

D d

D djXt t t

B B B

Material derivative

jxB

d 0ijk i je u l

d

d

j

j

xu

t


basic ideas

Flow description

PIV – velocity is determined as a field variable; vector tangent to small displacements in any space location, concept of streamline

PTV – velocities of each parcel of continuum are determined by (lagrangian) by diferentiation of property position, concept of pathline

d 0 u l

Velocity estimate

d 0ijk i je u l

0 0

22

0

0 0 2

d d...

d 2!d

j j

j j

t t

x x t tx t x t t t

t t

0

0

0

0

d

d

j j j

t

x x t x tO t t

t t t

0

0

j j

j

x t x tu

t t


basic ideas

Flow description

Spatial and material flowlines are not the same in unsteady flows


basic ideas

Flow description

By definition, pathlines and streamlines are the same at origin


basic ideas

Flow description

By definition, pathlines and streamlines are the same at origin PTV can be used to determine an spatial (eulerian) velocity field (interpolation may be involved) what distinguishes really PTV from PIV is that PTV will originate a vector field associated to the motion of specific particles PIV will determine the characteristic motion of a small parcel of space density of tracers is a relevant parameter to choose one or the other


Questions:

Which tracers to use? How to see the tracers in the flow? How to determine the displacements?

basic ideas

Flow description


raw PIV image mean velocity field mean vorticity field and streamlines

the objective:

basic ideas

Flow description


Maxey-Riley equation

( ) ( ) ( )

( )

( ) ( )

( ) ( )

3 ( ) ( ) 2 2 3 ( )4 1 1 43 2 10 3

22 2

0

3 2

d d dd

d d d d

d 16 d

d 6

6

r r w

w

r w

r w

j j js w s

j

BA

t

j j

C

j j

D

u u ua a u a

t t t t

aa u u

t

au a u

( )

3 ( ) 3 ( ) ( )4 43 3

D

D

w

jw s w

j

GE

ua a g

t

particle-based methods

theory


( ) ( ) ( )

( )

( ) ( )

( ) ( )

3 ( ) ( ) 2 2 3 ( )4 1 1 43 2 10 3

22 2

0

3 2

d d dd

d d d d

d 16 d

d 6

6

r r w

w

r w

r w

j j js w s

j

BA

t

j j

C

j j

D

u u ua a u a

t t t t

aa u u

t

au a u

( )

3 ( ) 3 ( ) ( )4 43 3

D

D

w

jw s w

j

GE

ua a g

t

where ( ) ( ) ( )r s w

j j ju u u is the thj component of the relative tracer velocity, ( )s

ju and ( )w

ju are the thj 1

components of the velocity of tracers and fluid, respectively, ( )s and ( )w are the densities of the 2

tracer grains and of the fluid, respectively, a is the radius of the tracer grains (assumed to be 3

uniformly distributed), and are the viscosity and the kinematic viscosity of the fluid, 4

respectively and t stands for the independent variable time. The material derivatives d

dt and

D

Dt5

differ in the velocities used in the convective operator, ( )s

ju for the former and ( )w

ju for the latter. 6


added mass

Basset history term

viscous drag flow gradients buoyancy


theory


( ) ( ) ( )

( )

( ) ( )

( ) ( )

3 ( ) ( ) 2 2 3 ( )4 1 1 43 2 10 3

22 2

0

3 2

d d dd

d d d d

d 16 d

d 6

6

r r w

w

r w

r w

j j js w s

j

BA

t

j j

C

j j

D

u u ua a u a

t t t t

aa u u

t

au a u

( )

3 ( ) 3 ( ) ( )4 43 3

D

D

w

jw s w

j

GE

ua a g

t

where ( ) ( ) ( )r s w

j j ju u u is the thj component of the relative tracer velocity, ( )s

ju and ( )w

ju are the thj 1

components of the velocity of tracers and fluid, respectively, ( )s and ( )w are the densities of the 2

tracer grains and of the fluid, respectively, a is the radius of the tracer grains (assumed to be 3

uniformly distributed), and are the viscosity and the kinematic viscosity of the fluid, 4

respectively and t stands for the independent variable time. The material derivatives d

dt and

D

Dt5

differ in the velocities used in the convective operator, ( )s

ju for the former and ( )w

ju for the latter. 6



theory


Ferreira (2015) Principles of LDA instrumentation. In IAHR Monograph Experimetal techniques

modifyed Hjemfelt & Mockros (1966)

95% confidence

cut off frequency > 105 Hz

> LDA frequency (300 Hz)

122 2

1 21Ar

( ) ( )/s w

Ar u u

1 12 2

1 2 2

21 1 12 2 2

9 31

2

9 918

4

ff f

s s

f ff

s a s s

21 1 12 2 2

2 2 2

21 1 12 2 2

918 31

4 2

9 918

4

ff

s a s s

f ff

s a s s

silica powder ( 25.0a µm, 2.65s ). 1

air bubbles ( 0.5a µm, 0.0013s ) 1

titanium dioxide ( 0.5a µm, 4.20s ) 1

seeding requirements: solution of Maxey-Riley equation

key issue of particle-based methods


theory


seeding requirements

Example of tracer particles. Top: general view and micrographs of polyamide Dp= 50 μm, s = 1.03.

Bottom: micrograph (100x) of polyurethane beads; left: decosoft© 60 transparent beads (refractive index 1.5,

s = 1.05); right: decosoft© 60 white beads (refractive index 2.1, s = 1.3).


tracers

Should be chemical inert, non-toxic and cheap


Table 1. Common tracer particles for LDA. 1

Mean

diameter

µm

Refractive

index

Density

(g/cm3)

Shape

Titanium dioxide 0.1 - 50.0 2.60 4.3 Irregular

Silicon carbide 1.5 2.65 3.2 Irregular

Nylon 4.0 1.53 1.14 Spherical

Metallic coated hollow glass spheres 14.0 0.21+i2.62 1.65 Spherical

Polystyrene latex 0.5 1.6 1.05 Spherical

Zirconium Oxide 30.0 2.2 5.7 Irregular

Polyurethane beads 5.0-150.0 1.5-2.1 1.05-1.3 Irregular

Air bubbles 0.1-… 1.0 1.3x10–3

Spherical

2

Larger particles stronger scattering lower tracking ability and spatial resolution Lighter particles higher tracking ability more expensive More particles higher spatial/temporal resolution more expensive; intrusiveness/noise

seeding requirements


tracers


seeding: scattered light intensity

180 0

90

270

210

150

240

120

300

60

330

30

180 0

330210

240 300

270

150

120

90

60

30

180 0

210

150

240

120

270

9060

300

30

330

dp0.2 dp1.0 dp10

Mie’s polar plot of scattered light intensity versus scattering angle

scattered light intensity increases with

forward scattering would be a better option – impossible in PIV!

scattering is poor at 90º but this is normally the only practical option for PIV

increase number of particles

2

/pd


tracers



180 0

210

150

240

120

270

9060

300

30

330

dp10

forward scattering would be a better option – impossible in PIV!

2

/pd

forward scattering




tracers



180 0

210

150

240

120

270

9060

300

30

330

dp10



backward scattering would be another option – also difficult in PIV!

2

/pd

backward scattering


tracers



180 0

210

150

240

120

270

9060

300

30

330

dp10

90º scattering

scattering is poor at 90º but this is normally the only practical option for PIV

increase number of particles


tracers


PIV – pulse laser set up

How to see the tracers?

a PIV setup based on a pulsed laser

- laser head (laser production) - light sheet optics

digital camera (CCD, CMOS)

- frame grabber - timer control - acquisition software - preliminary data analysis

- timing unit (synchronization of laser and camera)

seeding particles

- power source

open “optical gates”

po

wer u

p la

se

r

power up laser user c

om

mands

op

en

sh

utte

r

store raw images processed data

external trigger


laser and light sheet optics

Laser (light amplification by stimulated emission of radiation)

- Laser material - pump source - resonator

Laser material - Helium-Neon, = 633 nm (red) (gas) – easy to produce, low power; - Argon-ion, = 514 nm (navy green) (gas) – difficult to pump, low efficiency, high power;

http://technology.niagarac.on.ca/people/mcsele/lasers/Lase

rsYag.htm

- Nd:YAG (neodymium-doped yttrium aluminium garnet), = 1064 nm (infrared), 532 nm (green) (solid state) – high power if operated with a “Quality switch” (Q-switch)







4 1E E E f Pump source pumping excites atoms to an upper energy level Laser light is produced by stimulated emission between two energy levels

pumping can be optical (white light for Nd:YAG), laser (diode lasers), or other electromagnetic







Resonator a resonator is achieved by mirror arrangement (the output mirror is partially reflecting)

the Q-switch (polarizer + Pokels cell) changes abruptly the resonance conditions; flash lamps operate and store energy but do not amplify light; that energy is released as a giant pulse when the Pokels cell removes polarization – an optical gate




timing

Lasing threshold, pockles ON

Flashlamp Output

Energy in Nd:YAG

Enable Q-switch,

Laser Output Energy

Lasing threshold, pockles OFF

Ken Krieger






typical configuration

-Nd:YAG , optical pumping -double pulsed – Q-switch operated; - production at infrared 1024 nm - phase matching (while converting infrared 1064 nm to green 532 nm) - cooling system!






laser beam - modes of resonance transverse electric mode TEM

TEM00 is standard for Nd:Yag lasers

http://www.rp-photonics.com/beam_profilers.html





Light sheet optics - telescope lenses; prismatic lenses;

- cylindrical lenses (production of laser sheet)

- mirrors, reflectors and -shutters




digital video camera

photoelectric effect

incoming photons

outgoing electrons

only sensitive to light intensity – ammount of energy, not wavelenght – no colour! (three cells per sensor to have colour, eg. RGB)

matrix of sensors (wells) with photosensitive cells

0

0

1 1eq V c

: electron charge, : stopping potential (volts); : Planck constant; : light velocity; :wave-length ; : threshold wavelength

(charge to voltage conversor)

eq0V

c

0





pixel size (and focal length) - typical values: 10 um - minimize the ratio arc/pixel

dynamic range - the ratio of the maximum possible signal (full well capacity in electrons) and the noise signal (in the dark, rms electrons); eg: 15000/8 = 1875 ; 3750 steps 212 - requires 12 bit pixel depth pixel depth - number of shades resolved by the charge to voltage converter noise - photon noise (background noise, unavoidable) - thermal noise: electrons released by temperature (avoidable) - read noise: property of the electric circuits (controllable)





CCD (charged-couple device) - every pixel's charge is transferred through the same output nodes - slow - susceptible to pixel burning due to well saturation

CMOS (complementary metal oxide semiconductor) - each pixel has its own charge-to-voltage conversion node - highly sensitive - fast (time resolving PIV) - noisy – high read noise (except sCMOS, wich is

slow) - susceptible to image deformation (it reads one line

at the time!)




a PIV setup based on a continuous laser

- laser head (laser production) - light sheet optics

digital fast camera (CCD, CMOS)

- frame grabber - timer control - acquisition software - preliminary data analysis

seeding particles

- power source

po

wer u

p la

se

r

power up laser user c

om

mands

store raw images processed data

Advantages: cheaper laser, simpler electronics, dt< ms

Laser is continuous. Camera shutter defines the dt. Time resolved description

PIV – continuous laser set up



a PIV/PTV setup without laser

Halogen projectors

LED projector

Mosaic of photos

PIV with no lasers





PIV basics



PIV principle

interrogation area

key issue: calculate

Δdthe characteristic displacement of each interrogation area

for each interrogation area evaluate the movement of the seeding particles between a small time lag (time-between-pulses)

PIV basics



PIV principle

correlation of image pairs

Δdhow to calculate

clear peak ambiguous peak (low signal-to-noise ratio)

PIV basics



PIV principle

Δdhow to calculate

Δd

it corresponds to the coordinates of the correlation peak in the referential of centre of the interrogation area

note that is not a mean displacement in the interrogation area! Δd

PIV basics



PIV principle

- type of correlation (cross-correlation, adaptative)

-(relative) size of interrogation area/size of seeding particles - time-between-pulses

- number of seeding particles -use of windows/filters

- subpixel interpolation

parameters that control the quality of the correlation

PIV basics



cross correlation

- cross-correlation of image pairs

- peak detection

PIV basics



type: cross-correlation/adaptive correlation

cross correlation


- peak detection

- offset based on centered differences

- peak detection

PIV basics



adaptive correlation


- peak detection


PIV basics





- peak detection

- reduce size of interrogation area


- peak detection

- … (repeat)


PIV basics





- peak detection

- reduce size of interrogation area


- peak detection

- … (repeat)


PIV basics



Finding through good correlations

ideal: several non-overlapping particles moving 25% of the size of the interrogation area

Δd

- seed appropriately (a lot… 5 per final interrogation area);

- adjust size of the interrogation area relatively to the size of the particles – particles should be about 9 px2;

- adjust the time between pulses and the size of the interrogation area to meet the above ideal displacement.

(issues concerning time-between-pulses, size of seeding particles and number of seeding particles)

PIV basics



Finding through good correlations Δd

be aware of out-of-plane loss of pairs (cause bias-to-zero) reduce time between pulses

in-plane loss of pairs consider windowing, consider offsetting

consider filtering to enhance peak width (may benefit subpixel

interpolation)

note that more than 50% movement causes aliasing! (Nyquist theorem) reduce time between pulses, increase interrogation area

PIV basics



mild problem, not enough noise - true peak dominates

Bias-to-zero due to loss of pairs

PIV basics



Noise dominates

severe problem - noise (uncorrelated) peak dominates -> Bias-to-zero

Bias-to-zero to loss of pairs

PIV basics



Noise dominates

do not consider outer rim for correlation - true peak retrieved!

Windowing

PIV basics



PTV basics

How to measure the tracers displacement?




Seeding concentration

http://www.piv.jp/data/01/piv01_1.bmp http://chemwiki.ucdavis.edu/@api/deki/f

iles/280/specklePattern.jpg

Laser Speckle PIV PTV

PTV basics



If low seeding concentration

Track individual particles between frames

PTV basics





PTV basics





PTV basics





PTV basics





Δd

PTV basics



High computational cost a) particle-by-particle operation

Track individual particles between frames Contrary to PIV (based on image correlation) PTV does not have a base scheme. Many algorithms for PTV are based on different algorithms: Least displacement, Cluster methods, Probabilistic, Genetic algorithms, etc.

PTV basics



be aware of / take in consideration that

Particle-based methods are not an non-intrusive measuring technique (can be extremely intrusive if Re is low and the fall velocity is large); PIV interrogation areas may smooth out small turbulent scales (be aware of anisotropy suppression); prone to noise (contrast, seeding, camera…) and to spikes (wrong correlation); data treatment is very time consuming.

Conclusions


be aware of / take in consideration that

PTV concentration is an issue many existing methods. detection of individual particles is critical data treatment is quite time consuming.

Conclusions


some references

[1] Wereley, S.T. & Meinhart, C.D. (2010). Recent Advances in Micro-Particle Image Velocimetry. Annual Review of Fluid Mechanics 42 (1): 557–576. doi:10.1146/annurev-fluid-121108-145427 [2] Raffel, M.; Willert, C.; Wereley, S. & Kompenhans, J. (2007) Particle Image Velocimetry, A Practical Guide, 2nd edn. Springer [3] Adrian, R.J. (2005). Twenty years of particle image velocimetry. Experiments in Fluids 39 (2): 159–169. doi:10.1007/s00348-005-0991-7 [4] Adrian, R. J. (1991) Particle imaging techniques for experimental fluid mechanics, Annual Review of Fluid Mechanics, vol.23, pp. 261-304. A lot more fundamental refs in [2]…

Conclusions


Yet another animation…

The end…

Thank you!

Documents

Introduction to particle-based methods