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 non-

uniformly 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

0IPC s

s

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

Molecule   10-33m2

1m Cs(dp/)4 10-12m2

10m 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: 1m diameter, right: 10m 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:

ii

ppp F

dt

Udd

6

3

General governing equation

Meaning of each term:I. Viscous drag according to the Stokes’ lawII. Acceleration forceIII. Force due to a pressure gradient in the vicinity of the

particleIV. 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.

t

tfpp

ffp

fppp

pt

d

d

Vdd

dt

Vdd

dt

UddVd

dt

Udd

0

21

)(2

3

62

1

63

62

333

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

In a typical PIV experiment with 10m 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).

ppf

p

VdVdRe

Particle parameter - the particle response time p

Velocity lag of a particle in a continuously accelerating fluid:

The particle velocity response to the fluid velocity if heavy particles (p>>f) in a continuously

accelerating flow is:

Particle response time:

dt

dUdUUV ffp

pfp

18

)(2

pfp

tUtU

exp1)(

18

2 ppp d

Particle parameter- the Stokes number St

Stokes number St as the ratio of the particle response time to the Kolmogorov time scale:

St: the degree of coupling between the particle phase and the fluid. St0 the particles behave like tracers

St the particles are completely unresponsive to the fluid flow.

kpSt /

Particle parameter- the characteristic frequency C

In the case of gas flow where p>>f,

characteristic frequency of the particle motion

Tracing ability in turbulence, c=2fc

218 ppdC

)/1(

12

2

Cu

u

cf

p

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

adiff DfdI

xI/44.20

)(

max

Imaging of small particles (cont’s)

With an imaging lens, the

diffraction-limited size:

Estimate of the particle image diameter:

22)( diffp dMdd

)1(#44.2 Mfddiff

fZz

111

00

0

0

Z

zM

dp: original particle diameter

Seeding particles for PIV (liquid flow)

Type Material Mean diameter in m Polystyrene 10-100 Aluminum 2 - 7 Glass spheres 10-100

Solid

Granules for synthetic coatings 10-500

Liquid Different oils 50 - 500 Gaseous Oxygen bubbles 50-1000

Seeding particles for PIV (gas)

Type Material Mean diameter in m Polystyrene 0.5- 10 Aluminum 2 - 7 Magnesium 2 - 5 Glass micro-balloons 30-100 Granules for synthetic coatings 10-50

Solid

Dioctylphathalate 1-10

Smoke <1 Liquid 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 1.5m). 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 0.2m) 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 1.0m), 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 9.0m) 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

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 ---

Nylon 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 ---

Metallic coated 9 4-12 Spherical 2.6 0.21 2.62

Hollow glass spheres

8-12 10% < 3-5

90% < 14-17 Spherical 1.05-1.15 1.5 ---

Metallic coated, Hollow glass spheres

14 10% < 7

90% < 21 Spherical 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

HGS

Hollow glass

spheres

S-HGS

Silver-coated

hollow glass

spheres

FPP

Fluorescent

polymer particles

Mean particle size (µm) 5, 20, 50 10 10 10, 30, 75

Size distribution 1 - 10 µm

5 - 35 µm

30 - 70 µm

2 - 20 µm 2 - 20 µm 1 - 20 µm

20 - 40 µm

50 - 100 µm

Particle shape non-spherical but

round

spherical spherical spherical

Density (g/cm3) 1.03 1.1 1.4 1.5

Melting point (°C) 175 740 740 250

Refractive index 1.5 1.52 — 1.68

Material Polyamide 12 Borosilicate glass Borosilicate glass 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)