Tracer Particles and Seeding for PIV

Seeding particles for PIV

Proper tracer must be small enough to follow
(trace) fluid motion and should not alter fluid or flow properties.

Proper tracer must be large enough to be visible by the camera.

Uniform seeding is critical to the success of obtaining velocity field. No seed particles, no data.

The seeding source must be placed cleverly so that the particles mix with the flow well.

Particles with finite inertia are known to disperse nonuniformly in a turbulent flow, preferential concentration

Seeding particles for PIV (cont’d)

The tracing ability and the dispersion characteristics depends on the aerodynamical characteristics of particles and the continuous medium;

The visibility depends on the scattering characteristics of particles.

The choice of optimal diameter for seeding particles is a compromise between two aspects.

Scattering characteristics of particles

Laser sheet leads to a low energy density – particle scattering efficiency is important;

Light scattering capability - scattering cross section C s is defined as the ratio of the total scattered power P s
, to the laser intensity I
0 incident on the particle
C
P s s

I
0

Example of scattering cross section (1)
The scattering cross section as a function of the particle size (refractive index m =1.6).

Example of scattering cross section (2)
Diameter d p
Molecule
1  m
10  m
Scattering cross section C s
 10 -33 m 2
C s
 (d p
/  ) 4
C s
 ( d p
/  ) 2
 10 -12 m 2
 10 -9 m 2
Scattering cross section as a function of the particle size

Mie scattering of small particle (1)
Light Scattering by an oil particle in air when refractive index m ~ 1.4. Left: 1
 m diameter, right: 10
 m diameter

Mie scattering of small particle (2)
Light scattering by a 1
 m,
10
 m, and 30
 m glass particle in water.
Refractive index m = 1.52

Summary of particle light scattering for PIV

The ratio d p
/
I s90
/ I s0 decreases with increasing size parameter

, with values roughly in the range 10 -1 -10 -3 for scattering particles useful in PIV.

The resulting intensity of the scattered light for a given light sheet intensity will depend on the combined influences of C s and I s90
/ I s0
, which exhibit opposing tendencies with increasing particle size. In general, larger particles will still give stronger signals.

The ratio I s90
/ I s0 increases with increasing refractive index m . Hence particles in air gives stronger 90 o scattering than in water.

Tracking characteristics of particles

The tracking ability depends on

Particle shape – assumed spherical – aerodynamically equivalent diameter d p

Particle density
 p

Fluid density
 f and fluid dynamic viscosity
 or kinematic viscosity

=

/
 f

Newton’s Law governing the motion of a single particle:
 p
 d
6
3 p
 d U dt p   i

F i

General governing equation
 p
 d
3 p
6
 d U p  dt

3
 d p
V

  f
 d
3 p
6
 d U f dt

1
2
 f
 d
3 p
6 d V

 dt
3
2 d p
2
(
 f
)
1
2
 t
 t
0 d V
 d
 t d

 

Meaning of each term:
I.
Viscous drag according to the Stokes’ law
II.
Acceleration force
III. Force due to a pressure gradient in the vicinity of the particle
IV. Resistance of an inviscid fluid to the acceleration of the sphere (“added mass”)
V.
Basset history integral – resistance caused by the unsteadiness of the flow field.

Stokes’ drag law

The Stokes’ drag law is considered to apply when the particle Reynolds number Re p unity, where Re p is defined as is smaller than
 f
Vd p
Vd p
Re p
 
 

In a typical PIV experiment with 10
 m particles and 20 cm/s mean velocity,
Re p
=10x10 -6 x 0.2 / 1.46x10
-5 = 0.13 (air);
Re p
=10x10 -6 x 0.2/1.0x10
-6 = 2 (water).

Particle parameter
- the particle response time t p

Velocity lag of a particle in a continuously accelerating fluid:
2 if heavy particles (
 p
>>
(
 p
  f
) dU f
V

U p

U f
 d p
18
 dt 
The particle velocity response to the fluid velocity
 f
) in a continuously accelerating flow is:
U p
( t )

U f



1
 exp
 t t p









Particle response time: t p
 d
2 p
 p
18


Particle parameter
- the Stokes number St

Stokes number St as the ratio of the particle response time to the Kolmogorov time scale:
St
 t
/ p t k

St : the degree of coupling between the particle phase and the fluid.

St

0 the particles behave like tracers

St
 the particles are completely unresponsive to the fluid flow.

Particle parameter
- the characteristic frequency C

In the case of gas flow where
 p
>>
 f
, characteristic frequency of the particle motion
C

18
  p d p
2

Tracing ability in turbulence,
 c
=2
 f c u p
2 u f
2

( 1

1
 c
/ C )

Figure of characteristic frequency
The response of particles in turbulence flow. (From Haetig J,
Introductory on particle behavior ISL/AGRAD workshop on laser anemometry (Institute Saint Louis) report R 117/76, 1976)

Particle size vs. Turbulence scale

Seeding particles need to be smaller than the smallest turbulence scale if one wants to identify all the structures in the vicinity of the flow. The smallest fluid length scale is called the Kolmogorov length scale, and it is related to the size of the smallest eddy.

Additional Considerations

Particle seeding uniformity

Additional Considerations (cont’d)

Secure sufficient spatial detail in the flow field a higher concentration of particles is generally needed with PIV than with LDV, with which it is possible to wait indefinitely for the arrival of a scattering particle in the probe volume.

A uniform particle size is desirable in order to avoid excessive intensity from larger particles and background noise, decreasing the accuracy, from small particles.

Particles that naturally exist in the flow seldom meet the above requirements. Hence, in PIV applications, it is often necessary to seed the flow with a chosen tracer particle. The particles are either premixed with the whole fluid (e.g., stirred ) or released in situ by a seeding source .

Imaging of small particles

Relation between real particles and particle image recorded in the camera can be analyzed by the diffraction limited imaging of a small particle

For a given aperture diameter D a and wavelength the Airy spot size

,
I ( x )

0
I max
 d diff

2 .
44
 f / D a

Imaging of small particles (cont’s)

With an imaging lens, the diffraction-limited size: d diff

2 .
44 f # ( M

1 )


Estimate of the particle image diameter: d t

( Md p
)
2  2 d diff d p
: original particle diameter
1 z
0

1
Z
0

1 f
M
 z
Z
0
0

Seeding particles for PIV (liquid flow)
Type Material Mean diameter in
 m
Solid
Polystyrene
Aluminum
10-100
2 - 7
Liquid
Gaseous
Glass spheres 10-100
Granules for synthetic coatings 10-500
Different oils
Oxygen bubbles
50 - 500
50-1000

Seeding particles for PIV (gas)
Type
Solid
Smoke
Liquid
Material
Polystyrene
Aluminum
Magnesium
Glass micro-balloons
Mean diameter in
 m
0.5- 10
2 - 7
2 - 5
30-100
Granules for synthetic coatings 10-50
Dioctylphathalate 1-10
<1
Different oils 0.5 - 10

Commercial seeding particles - TSI
(http://www.tsi.com)

Silicon Carbide: Suitable for measurements in liquids and gases, silicon carbide particles have a narrow particle size distribution (mean diameter of 1.5
 m ). Their high refractive index is useful for obtaining good signals in water, even in backscatter operation. They can also be used in high temperature flows. Supplied as a dry powder, they can be mixed in liquid to form a suspension before dispersing.

Titanium Dioxide: Titanium dioxide particles (mean diameter of 0.2
 m ) are usually dispersed as a dry powder for gas flow measurement applications. The smaller particle size makes titanium dioxide attractive for high-speed flows.
It can also be used for high temperature flows.

Commercial seeding particles - TSI
( http://www.tsi.com
) (cont’d)

Polystyrene Latex : With an extremely narrow size distribution (nominal diameter of 1.0
 m), polystyrene latex
(PSL) particles are useful in many different measurements.
Supplied in water, they are not recommended for high temperature applications.

Metallic coated: Metallic coated particles (mean diameter of 9.0
 m ) are normally used to seed water flows for LDV measurements due to their lower density and higher reflectivity. They cannot be used where salt is present. Salt reacts with the metal coating, causing the particles to agglomerate and drop out of the flow.

Commercial seeding particles - TSI
( http://www.tsi.com
) (cont’d)
Particle
Type
Silicon carbide
Silicon dioxide
Nylon
PSL
Titanium dioxide
Metallic coated
Hollow glass spheres
Metallic coated,
Hollow glass spheres
Mean
Dia.
(µm)
Size
Range
(µm) Shape
1.5 Std. dev.= 1.4 Irregular
2.7 --- Irregular
4 Std. dev.= 1.5 Spherical
0.54 Std. dev.= 1.05 Spherical
3-5
9
---
4-12
Irregular
Spherical
8-12
10% < 3-5
90% < 14-17
Spherical
14
10% < 7
90% < 21
Spherical
Density
(g/cc)
3.2
2.3
1.14
1.05
4.2
2.6
1.05-1.15
Refractive
Index
(real)
Refractive
Index
(imag.)
2.65
1.47
1.53
1.55-1.6
2.6
0.21
---
---
---
---
---
2.62
1.5 ---
1.65 .21 2.62

Commercial seeding particles - Dantec
(http://www.dantecmt.com)

Polyamide seeding particles (PSP): These are produced by polymerisation processes and therefore have a round but not exactly spherical shape. They are microporous and strongly recommended for water flow applications.

Hollow glass spheres and silver-coated hollow glass spheres (HGS, S-
HGS): Intended primarily for liquid flow applications, these are borosilicate glass particles with a spherical shape and a smooth surface.
A thin silver coating further increases reflectivity.

Fluorescent polymer particles (FPP): These particles are based on melamine resin. Fluorescent dye (Rhodamine B:) is homogeneously distributed over the entire particle volume. In applications with a high background light level, fluorescent seeding particles can significantly improve the quality of vector maps from PIV and LDV measurements.
The receiving optics must be equipped with a filter cantered on the emission wavelength (excitation max.: 550 nm; emission max.: 590 nm).

Commercial seeding particles - Dantec
( http://www.dantecmt.com
) (cont’d)
PSP
Polyamide seeding particles
Mean particle size (µm)
Size distribution
Particle shape
5, 20, 50
1 - 10 µm
5 - 35 µm
30 - 70 µm non-spherical but round
Density (g/cm
3
)
Melting point (°C)
1.03
175
Refractive index
1.5
Material
Polyamide 12
HGS
Hollow glass spheres
10
2 - 20 µm spherical
1.1
740
1.52
S-HGS
Silver-coated hollow glass spheres
10
2 - 20 µm spherical
1.4
740
—
Borosilicate glass Borosilicate glass
FPP
Fluorescent polymer particles
10, 30, 75
1 - 20 µm
20 - 40 µm
50 - 100 µm spherical
1.5
250
1.68
Melamine resin based polymer

Particle generation

Liquid flow
 Simple, select proper powder then mix w/ liquid

Gas flow
 liquid droplets
 Atomization or Condensation
 solid particles

Atomization or Fluidization

Requirement for PIV

Nearly monodisperse size distribution

High production rate

Liquid droplets

Advantage

Steady production rate;

Inherently spherical shape;

Known refractive index

Problem

Form non-uniform liquid films on window

Generator

Laskin atomizer

Commercial atomizer (e.g., TSI)