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Turbulent mixing of oil droplets in a round water jet

Turbulent mixing of oil droplets in a round water jet

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taken into account. Also, a theoretical minimum level of peak-locking is shown.Figure B.2: Histogram of subpixel displacements of the axial velocity as calculated byPIVWare.This study shows peak-locking to integer displacements as expected. The level of peak-locking isthe same in case of the calculations by DaVis. The theoretical minimum peak-locking is calculatedassuming that the error level is proportional to the subpixel displacement in the range of 0 to 0.5pixels. The proportionality constant depends on the particle size. If the particle image diameteris equal to 2 pixels, leading to the most accurate determination of the subpixel displacement,the proportionality constant is around 0.1 [Westerweel, 2000]. From a normal distribution withthe mean equal to the subpixel displacement and the standard deviation equal to the error level,synthetic measured subpixel displacements are generated. This is done for every possible subpixeldisplacement within the range of 0 to 0.5. The total amount of generated displacements is equal tothe real number of measured displacements. As the normal distribution is wider for larger subpixeldisplacements, a bias towards smaller displacements results. In figure B.2, it is shown that theobserved peak-locking is not very much higher than the theoretical one. It must be remarked thatin this experiments, the droplet image diameter is probably around one pixel. As this results invery narrow correlation peaks, this is supposed to be the main cause of peak-locking.72

Appendix CComparison with PIVWareIn this appendix, the results of the velocity calculations in a two-phase jet at a measurementposition of z = 75 - 105 mm (see section 4.2) are compared with calculations that are done withthe non-commercial code PIVWare, developed by prof. Jerry Westerweel. A typical vector fieldcalculated by PIVWare is depicted in figure C.1. The displacements are calculated in two passes:the initial interrogation area is 64 x 64 pixels, the final interrogation area is 32 x 32 pixels. Outliersare not removed.10510095z [mm]90858075−30 −20 −10 0 10 20 30(x−x0) [mm]Figure C.1: A typical velocity vector field of an oil-water jet as calculated by PIVWare.The vector field corresponding to the same double image as calculated by DaVis is shown in figureC.2. Again, outliers are not removed. The difference field is depicted in figure C.3. Note, that thevectors in the difference field are stretched.It is remarkable that the number of spurious vectors in the PIVWare calculation is much largerthan in the DaVis calculation. In order to investigate whether mean variables are changed by thisdifference, the velocity fields of all the double images are calculated with PIVWare. To get rid ofspurious vectors, a median test is applied. If the vector components are 3 pixels larger than themedian of its neighbours it is marked as an outlier and replaced by the median of its neighbours.In figure C.4, the development of the 1/e width is shown for both PIVWare and DaVis. FigureC.5 pictures the centerline velocity.73

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