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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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from right to left in the measurement section caused by a lack of symmetry in the coflow field.The profile of Aanen is again scaled in the horizontal direction. The profile is also scaled in thevertical direction with a coflow correction. As the coflow is assumed to contribute about 10% tothe centerline velocity, used for normalisation, all profiles of Aanen are multiplied with 0.9.As a measure of the turbulence, the rms-values of the axial and radial velocities are depicted infigures A.5 and A.6.0.25measurementsAanen0.2U rms/U c0.150.10.050−0.3 −0.2 −0.1 0 0.1 0.2 0.3(x−x0)/(z−z0)Figure A.5: Turbulent intensity of the axial velocity fluctuations at z = 115-145 mm.The turbulence intensity shows a clear off-axis peak. This is also observed in previous experiments.This peak is associated with the local maximum of shear production of kinetic turbulent energy.The profile of the Reynolds shear stress is shown in figure A.7. The turbulent intensities are ofthe same order of magnitude as in the experiments of Aanen.Finally, the continuity equation (2.3) and the boundary-layer equation (2.7) are investigated. Infigure A.8, the gradient of the mean axial and radial velocities are plotted that should be in equilibriumto have conservation of momentum. In figure A.9, the average and turbulent terms in theboundary-layer equation are shown.As a consequence of the asymmetric radial velocity, both the continuity and boundary-layer equationare not perfectly fulfilled. However, the difference between the terms that should be inequilibrium are mostly of a small order of magnitude.A.2 Seeded jet and coflowNow, the same oil-water mixture is used for both jet and coflow. The jet is generated by a heightdifference between the jet water reservoir and the outlet of the measurement section, as describedin section 3.1.1. As a consequence, the Reynolds number is not known very accurately and themeasured velocities can differ from those of the experiment described above. The development ofthe 1/e width and the centerline velocity are shown in figures A.10 and A.11 respectively.The spreading rate, α, is equal to 0.080, and the virtual origin, z0, is located at -45d jet . The axial62

0.2measurementsAanen0.15V rms/U c0.10.050−0.3 −0.2 −0.1 0 0.1 0.2 0.3(x−x0)/(z−z0)Figure A.6: Turbulent intensity of the radial velocity fluctuations at z = 115-145 mm.0.02measurementstheoretical profileAanen0.01/U c20−0.01−0.02−0.3 −0.2 −0.1 0 0.1 0.2 0.3(x−x0)/(z−z0)Figure A.7: Reynolds shear stress at z = 115-145 mm.63

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