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Turbulent mixing of oil droplets in a round water jet

Turbulent mixing of oil droplets in a round water jet

List of

List of Figures2.1 A turbulent jet, visualised with fluorescein . . . . . . . . . . . . . . . . . . . . . . . 32.2 Schematic drawing of a self-similar jet . . . . . . . . . . . . . . . . . . . . . . . . . 62.3 Theoretical profile of the axial velocity . . . . . . . . . . . . . . . . . . . . . . . . . 92.4 Theoretical profile of the radial velocity . . . . . . . . . . . . . . . . . . . . . . . . 92.5 Theoretical profile of the Reynolds shear stress . . . . . . . . . . . . . . . . . . . . 102.6 Map of flow regimes in turbulent particle-laden flows . . . . . . . . . . . . . . . . . 132.7 Theoretical profile of the concentration (a) and radial turbulent flux (b) . . . . . . 183.1 Experimental set-up . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 203.2 Working principle of the LIGA micromixer . . . . . . . . . . . . . . . . . . . . . . 213.3 SEM images of a mixing element consisting of 2 x 15 interdigitated microchannelswith corrugated walls . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 213.4 Number density distribution of a 1:1 silicon oil in water emulsion as a function ofthe volume flow rate using a 40 µm LIGA mixing element . . . . . . . . . . . . . . 213.5 Light scattering by a 10 µm glass particle in water with incident light of λ = 532 nm 233.6 Composition of peaks in the cross-correlation function . . . . . . . . . . . . . . . . 244.1 Visualisation of a jet with fluorescein at Re jet = 800 . . . . . . . . . . . . . . . . . 314.2 Visualisation of a jet with fluorescein at Re jet = 1000 . . . . . . . . . . . . . . . . 324.3 The mean coflow field over 200 images at z = 75 - 105 mm . . . . . . . . . . . . . 344.4 A typical greyvalue image of an oil-water jet as recorded with CamWare . . . . . . 354.5 A typical velocity vector field of an oil-water jet as calculated by DaVis . . . . . . 354.6 The mean axial velocity field at z = 75-105 mm . . . . . . . . . . . . . . . . . . . . 364.7 Development of the 1/e width for the velocity field at z = 75-105 mm . . . . . . . 374.8 Variation of the centreline velocity along the axis at z = 75-105 mm . . . . . . . . 384.9 Axial velocity profile at z = 75-105 mm . . . . . . . . . . . . . . . . . . . . . . . . 384.10 Radial velocity profile at z = 75-105 mm . . . . . . . . . . . . . . . . . . . . . . . . 394.11 Turbulent intensity of the axial velocity fluctuations at z = 75-105 mm . . . . . . . 394.12 Turbulent intensity of the radial velocity fluctuations at z = 75-105 mm . . . . . . 404.13 Reynolds shear stress at z = 75-105 mm . . . . . . . . . . . . . . . . . . . . . . . . 414.14 Different terms in the continuity equation . . . . . . . . . . . . . . . . . . . . . . . 414.15 Different terms in the boundary-layer equation . . . . . . . . . . . . . . . . . . . . 424.16 Development of the light intensity over the light sheet at z = 75-105 mm . . . . . . 434.17 Mean oil concentration in the image field . . . . . . . . . . . . . . . . . . . . . . . 444.18 The mean concentration field at z = 75-105 mm . . . . . . . . . . . . . . . . . . . . 454.19 Development of the 1/e width of the concentration field at z = 75-105 mm . . . . . 454.20 Variation of the centreline concentration along the axis at z = 75-105 mm . . . . . 464.21 Mean concentration profiles at z = 75-105 mm . . . . . . . . . . . . . . . . . . . . 464.22 Concentration fluctuations at z = 75-105 mm . . . . . . . . . . . . . . . . . . . . . 474.23 Droplet distribution over the light sheet at z = 75-105 mm . . . . . . . . . . . . . 484.24 The mean concentration field at z = 75-105 mm (droplet counting) . . . . . . . . . 484.25 Development of the 1/e width of the concentration field at z = 75-105 mm. Dropletsare counted . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4980

4.26 Variation of the centreline concentration along the axis at z = 75-105 mm. Dropletsare counted . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 504.27 Mean concentration profiles at z = 75-105 mm. Droplets are counted . . . . . . . . 514.28 Axial turbulent flux u ′ c ′ at z = 75-105 mm . . . . . . . . . . . . . . . . . . . . . . 514.29 Radial turbulent flux v ′ c ′ at z = 75-105 mm . . . . . . . . . . . . . . . . . . . . . . 524.30 Mean advection terms in the transport equation of a passive mixed quantity . . . . 524.31 Turbulent terms in the transport equation of a passive mixed quantity . . . . . . . 534.32 Mean advection and turbulent transport terms in the transport equation of a passivemixed quantity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53A.1 Development of the 1/e width for the velocity field at z = 115-145 mm. . . . . . . 60A.2 Centerline mean velocity variation at z = 115-145 mm . . . . . . . . . . . . . . . . 60A.3 Axial velocity profile at z = 115-145 mm . . . . . . . . . . . . . . . . . . . . . . . . 61A.4 Radial velocity profile at z = 115-145 mm . . . . . . . . . . . . . . . . . . . . . . . 61A.5 Turbulent intensity of the axial velocity fluctuations at z = 115-145 mm . . . . . . 62A.6 Turbulent intensity of the radial velocity fluctuations at z = 115-145 mm . . . . . 63A.7 Reynolds shear stress at z = 115-145 mm . . . . . . . . . . . . . . . . . . . . . . . 63A.8 Different terms in the continuity equation . . . . . . . . . . . . . . . . . . . . . . . 64A.9 Different terms in the boundary-layer equation at z = 115-145 mm . . . . . . . . . 64A.10 Development of the 1/e width for the velocity field at z = 115-145 mm . . . . . . . 65A.11 Centerline mean velocity variation at z = 115-145 mm . . . . . . . . . . . . . . . . 65A.12 Axial velocity profile at z = 115-145 mm . . . . . . . . . . . . . . . . . . . . . . . . 66A.13 Radial velocity profile at z = 115-145 mm . . . . . . . . . . . . . . . . . . . . . . . 67A.14 Turbulent intensity of the axial velocity fluctuations at z = 115-145 mm . . . . . . 67A.15 Turbulent intensity of the radial velocity fluctuations at z = 115-145 mm . . . . . 68A.16 Reynolds shear stress at z = 115-145 mm . . . . . . . . . . . . . . . . . . . . . . . 68A.17 Different terms in the continuity equation . . . . . . . . . . . . . . . . . . . . . . . 69A.18 Different terms in the boundary-layer equation . . . . . . . . . . . . . . . . . . . . 69B.1 Histogram of subpixel displacements of the axial velocity as calculated by DaVis . 71B.2 Histogram of subpixel displacements of the axial velocity as calculated by PIVWare 72C.1 A typical velocity vector field of an oil-water jet as calculated by PIVWare . . . . 73C.2 A typical velocity vector field of an oil-water jet as calculated by DaVis . . . . . . 74C.3 Difference of velocity vector field of an oil-water jet between PIVWare and DaVis . 74C.4 Development of the 1/e width for the velocity field (PIVWare and DaVis) . . . . . 75C.5 Variation of the centerline velocity along the axis (PIVWare and DaVis) . . . . . . 76C.6 Axial velocity profile (PIVWare and DaVis) . . . . . . . . . . . . . . . . . . . . . . 76C.7 Radial velocity profile (PIVWare and DaVis) . . . . . . . . . . . . . . . . . . . . . 77C.8 Turbulent intensity of the axial velocity fluctuations (PIVWare and DaVis) . . . . 77C.9 Turbulent intensity of the radial velocity fluctuations (PIVWare and DaVis) . . . . 78C.10 Reynolds shear stress (PIVWare and DaVis) . . . . . . . . . . . . . . . . . . . . . . 78C.11 Residue of terms in the continuity equation (PIVWare and DaVis) . . . . . . . . . 79C.12 Residue of terms in the boundary layer equation (PIVWare and DaVis) . . . . . . 7981

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