Transcript Tracer Particles and Seeding for PIV

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 Cs is defined as the ratio of the total
scattered power Ps, to the laser intensity I0
incident on the particle
Cs 
Ps
I0
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 dp
Scattering cross section Cs
10-33m2
Molecule
1m
Cs(dp/)4
10-12m2
10m
Cs( dp/)2
10-9m2
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 Is90/Is0 decreases with increasing size parameter


dp/, 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 Cs
and Is90/Is0, which exhibit opposing tendencies with
increasing particle size. In general, larger particles will still
give stronger signals.
The ratio Is90/Is0 increases with increasing refractive index
m. Hence particles in air gives stronger 90o scattering than in
water.
Tracking characteristics of particles
The tracking ability depends on
 Particle shape – assumed spherical –
aerodynamically equivalent diameter - dp
 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 3p dU p
6
dt

  Fi
i
General governing equation
p

d dU p

3
p
6
dt

  3d pV 
f

d dU f
3
p
6
dt

1
f
2

d 3p dV
6
dt

3 2
1
d p ( f ) 2 
2

t
t0

dV
d
d
t 
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 Rep is smaller than
unity, where Rep is defined as
 f Vd p Vd p
Re p 



 In a typical PIV experiment with 10m particles
and 20 cm/s mean velocity,
Rep=10x10-6 x 0.2 / 1.46x10-5 = 0.13 (air);
Rep=10x10-6 x 0.2/1.0x10-6 = 2 (water).
Particle parameter
- the particle response time tp
 Velocity lag of a particle in a continuously
accelerating fluid:
V  U p  U f  d p2
(  p   f ) dU f
18
dt
 The particle velocity response to the fluid velocity
if heavy particles (p>>f) in a continuously
accelerating flow is:

 t 
U p (t )  U f 1  exp  
 t 

 p 
 Particle response time:
t p  d p2
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
2
p
Tracing ability in turbulence, c=2fc
u p2
u
2
f

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 Da and wavelength ,
the Airy spot size
I ( x)
 0  d diff  2.44f / Da
I max
Imaging of small particles (cont’s)
 With an imaging lens, the
diffraction-limited size:
ddiff  2.44 f # (M 1)
 Estimate of the particle
image diameter:
1 1
1


z0 Z 0 f
dt  ( Md p )  d
M
2
2
diff
dp: original particle diameter
z0
Z0
Seeding particles for PIV (liquid flow)
Type
Solid
Liquid
Gaseous
Material
Polystyrene
Aluminum
Glass spheres
Granules for synthetic coatings
Different oils
Oxygen bubbles
Mean diameter in m
10-100
2-7
10-100
10-500
50 - 500
50-1000
Seeding particles for PIV (gas)
Type
Material
Polystyrene
Aluminum
Mean diameter in m
0.5- 10
2-7
Solid
Magnesium
Glass micro-balloons
Granules for synthetic coatings
Dioctylphathalate
2-5
Smoke
Liquid
Different oils
30-100
10-50
1-10
<1
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)
Mean
Dia.
(µm)
Size
Range
(µm)
Shape
Density
(g/cc)
Refractive
Index
(real)
Refractive
Index
(imag.)
Silicon carbide
1.5
Std. dev.= 1.4
Irregular
3.2
2.65
---
Silicon dioxide
2.7
---
Irregular
2.3
1.47
---
4
Std. dev.= 1.5
Spherical
1.14
1.53
---
PSL
0.54
Std. dev.= 1.05
Spherical
1.05
1.55-1.6
---
Titanium dioxide
3-5
---
Irregular
4.2
2.6
---
9
4-12
Spherical
2.6
0.21
2.62
8-12
10% < 3-5
90% < 14-17
Spherical
1.05-1.15
1.5
---
14
10% < 7
90% < 21
Spherical
1.65
.21
2.62
Particle
Type
Nylon
Metallic coated
Hollow glass
spheres
Metallic coated,
Hollow glass
spheres
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, SHGS): 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
HGS
Hollow glass
spheres
S-HGS
Silver-coated
hollow glass
spheres
FPP
Fluorescent
polymer particles
5, 20, 50
10
10
10, 30, 75
1 - 10 µm
5 - 35 µm
30 - 70 µm
2 - 20 µm
2 - 20 µm
1 - 20 µm
20 - 40 µm
50 - 100 µm
non-spherical but
round
spherical
spherical
spherical
Density (g/cm )
1.03
1.1
1.4
1.5
Melting point (°C)
175
740
740
250
Refractive index
1.5
1.52
—
1.68
Polyamide 12
Borosilicate glass
Borosilicate glass
Melamine resin
based polymer
Mean particle size (µm)
Size distribution
Particle shape
3
Material
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)