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Particles:

The particles must be sufficiently bright to provide contrasted patterns (not a milky image), but they must be small enough to minimise inertia and sedimentation effects, as well as laser beam absorbsion. To avoid sedimentation, the density matching with the fluid is critical. In practice we use two kinds of particles.

In this case, we use pliolite particles (sold as an additive for painting by the company Goodyear). We select a particle size about 0.3 mm (the particles are grinded and sorted between sieves of mesh 0.25 mm and 0.40 mm). These particles have the advantage of being bright and available in large quantities with a well defined density, 1.0236 g/cm\( ^{3} \). Using salinity, we adjust the density of water to this value, in fact a little lower (1.023) as sedimentation in the bottom is preferable than accumulation at the free surface, which prevents visualisation. The particles sedimenting on the bottom (after a few hours) must be resuspended by moving a thin bar on the bottom. We can refill the upper part of the fluid layer by spraying with a perforated tube, slowly rotating above the surface. Both operations leave some residual turbulence, and a compromise must be found with particle rarefaction by sedimentation.

In stratified cases, we use expandable polystyrene particles of the same diameter (Gedexcel of the company HCC), which can be adjusted in density. These particles indeed swell by heating due to the formation of small pentane gas bubbles (this is used to make expended polystyrene). By heating in water at 70-80 \( ^{0}\)C, the density randomly decreases by a few percents from its initial value 1.05. After this heating, the particles are sorted by density in a vertical barrel filled with a stratified density. Particles with a given density range (3 10\( ^{-3} \)g/cm\( ^{3} \)) are stored in bottles (in a humid state). An equal quantity of particles from each density bin is introduced in a linearly stratified tank.

Note that in all cases, a tensio-active chemical, Ilfotol (used in photographic film processing), is mixed with water (concentration 2 10\( ^{-4} \)) to favour the wetting of particles and avoid agglomeration.

A sufficient number of particles (typically 0.05 per pixel) is essential to achieve good CIV results. For a field 1000x1000 pixels, we need therefore 50 000 particles. If the corresponding area is 2.5 x 2.5 m\( ^{2} \) and the laser sheet is 1 cm thick, the density of particles is therefore about 1.25 particle/cm\( ^{3} \). The mass of each particle, with radius a=0.2 mm, is 3.3x 10\( ^{-5} \) g, so the corresponding total particle mass for our full 100 m\( ^{3} \) tank is 4 kg (1.25 x 10\( ^{8} \) particles). The mass concentration is 3x 10\( ^{-5} \), which does not perturb the flow properties. Damping of laser light by scattering is however a serious drawback of excessive particle density. Taking a scattering cross section \( \pi a^{2} \)=0.0012 cm\( ^{2} \) for each particle, and the 100 particles found in a cm\( ^{2} \) beam section of length 100 cm have a total cross section 0.12 cm\( ^{2} \). The laser beam damping is therefore 12 % per meter, 40% reduction over the typical 4 m length of the laser sheet.

Note that the (maximum) power scattered by each particle is \( \pi a^{2}P(Wd)^{-1} \) , where \( P \) is the total power in the laser sheet, with width W and thickness d=1 cm. For W=250 cm and P=5 Watts; we get 2.4 10\( ^{-5} \)Watt. At a viewing distance 4 m, a lens 20 mm in diameter captures a solid angle 2 10\( ^{-6} \) rd\( ^{2} \), so that, assuming isotropic scattering (which is far from reality), a power 0.4 10\( ^{-10} \) Watts reaches the camera sensor. With 1/60 s exposure, this corresponds to 0.7 \( 10^{-12} \) J = 5 10\( ^{6} \) eV=2 10\( ^{6} \) photons. Another factor to consider is contrast: the luminosity of the particle must be compared to the background luminosity of the area corresponding to one pixel.

To get higher spatial resolution, with smaller fields of view, much higher particle density would be needed, for instance 16 times more for a 0.6 x 0.6 m\( ^{2} \) field. Then smaller particles must be used, 4 times smaller in diameter, to avoid laser sheet absorbsion. The viewing distance would be also 4 times smaller, with the same scattering power received in the camera.

Extension to larger fields of view (5x5 m\( ^{2} \)) with a higher resolution camera (2000x2000 pixels) would also require smaller particles (typically by a factor \( \sqrt{2} \) , to keep the same laser absorbsion over a twice longer length. As the viewing distance should be also increased (say by a factor \( \sqrt{2} \)), the captured scattered power drops by a factor of 4.


next up previous contents
Next: Laser illumination: Up: Physical conditions: Previous: Physical conditions:   Contents
Joel Sommeria 2003-02-14