The behavior and scale-dependent dispersion of small air bubbles, and the rise of slightly buoyant oil droplets in water under isotropic turbulence conditions, are analyzed computationally. The flow field is simulated using a pseudo-spectral code, while the bubble dynamics are analyzed by integration of a Lagrangian equation of motion with buoyancy, virtual mass, pressure, drag and lift forces. Consistent with experimental data, bubble rise velocities are increasingly suppressed with increasing turbulence intensity. The role of the lift force in moving the bubbles to the down-flow side of turbulent eddies, and consequently retarding their rise, is observed. Analysis also reveals that the vertical bubble velocities are characterized by asymmetric probability density functions that are positive or negative-skewed dependent upon the non-dimensional turbulence intensity and the Taylor length scale. Lagrangian bubble trajectories are used to determine dispersion characteristics, following the theoretical development of Cushman and Moroni (2001). The dispersion of 40 μm bubbles exhibits transition to Fickian behavior, and the process is weakly affected by the turbulence level for the entire range considered. Larger, 400 μm bubbles are shown to be more sensitive to turbulence level, with transition to Fickian behavior delayed in low turbulence fields.
Computations are also performed to investigate the puzzling behavior observed by Friedman and Katz (2002), that the rise velocity of slightly buoyant droplets smaller than 800 μm in diameter is enhanced by turbulence whereas the rise of larger droplets is retarded. Using the quasi-steady, empirically-determined drag and lift coefficients, the observed experimental behavior could not be reproduced. Further, analysis of the effect of lift and history forces also indicates that, within a broad range of uncertainty, these forces do not account for the experimentally observed mean droplet rise. Guided by correlations obtained for the settling of heavy particles under high turbulence intensities, suppression of the drag and virtual mass coefficients for droplet diameters smaller than ten times the Kolmogorov lengthscale was postulated, with enhancement of the drag coefficient postulated for larger droplet diameters. Based on these postulates, the model is able to recover the observed preferential enhancement and retardation of the mean rise of small droplets.
|School:||The Johns Hopkins University|
|School Location:||United States -- Maryland|
|Source:||DAI-B 68/04, Dissertation Abstracts International|
|Subjects:||Mechanical engineering, Fluid dynamics, Gases|
|Keywords:||Bubbles, Droplets, Isotropic turbulence|
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