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Turbulent mixing of oil droplets in a round water jet

Turbulent mixing of oil droplets in a round water jet

1.5measured

1.5measured valuesfit1.41.31.2C c1.110.990 95 100 105 110 115 120 125z/dFigure 4.20: Variation of the centreline concentration along the axis at z = 75-105 mm.1measurementsGaussian fittheoretical profileAanen0.80.6C/C c0.40.20−0.4 −0.3 −0.2 −0.1 0 0.1 0.2 0.3 0.4(x−x0)/(z−z0c)Figure 4.21: Mean concentration profiles at z = 75-105 mm.46

0.50.45measurementspolynomial fitAanen0.40.350.3c rms/C c0.250.20.150.10.050−0.4 −0.3 −0.2 −0.1 0 0.1 0.2 0.3 0.4(x−x0)/(z−z0c)Figure 4.22: Concentration fluctuations at z = 75-105 mm.4.3.2 Counting dropletsInstead of smearing out the greyvalues in the image field, an algorithm is applied that counts theindividual droplets by searching for local maxima. The greyvalue of every pixel is compared to its8 neighbours. If the greyvalue is larger, a droplet is counted. To avoid counting maxima causedby noise, all greyvalues below a certain threshold are set to zero. If this threshold is chosen at twotimes the mean of the investigated greyvalue image, noise turns out to be removed sufficiently.Before the counting algorithm is applied on the measurements, it is tested on the reference images.The resulting droplet distribution over the light sheet is shown in figure 4.23.The development of the light sheet is still observed in this figure. The ratio of the maximum andminimum value is not very large though (around 1.2). Probably, the light sheet does not havethe same thickness everywhere. Therefore, it seems reasonable to scale the results of the dropletcounting by this reference. In figure 4.24, the resulting concentration field is given.It is clear that the concentration field is not spreading out homogeneously as it should. For a closerinspection of the concentration field, the development of the width and the centreline concentrationare shown in figures 4.25 and 4.26.The centreline concentration does not follow the self-similar curve at all. Also the development ofthe width shows a lot of deviation from the linear fit. If the concentration profiles are observed,it is also seen that they are not collapsing quite well when scaled by the centreline concentrationand plotted against the dimensionless variable (x − x0)/(z − z0c). This is shown in figure 4.27.There is a lot of spreading around the Gaussian fit curve and the values at the left outer region arehigher than in the right outer region. It must be concluded that this droplet counting algorithm isnot able to correct for the light sheet development, despite the scaling with the reference images.Apparently, the number of observed droplets increases if the concentration is larger. This confirmsthe hypothesis formulated in the previous section that the effective light sheet thickness increasesdue to multiple scattering.As the results are not improved with respect to the previous, the concentration determination as47

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