Characteristics of mean flow and turbulence in bubble plumes
Authors:   , Wu Huijie 
Published: March 2024

Bubble plumes are phenomenon when bubbles enter water continually and move through the water column, which is widely seen in both natural environment and industry. This dissertation investigates bubble plumes from different points of view, including integral quantities, turbulent kinetic energy (TKE) budget analysis, spectral analysis in the plume region, and the mean flow and turbulence characteristics in the surface region of the bubble plume. First, an experimental study to investigate the impact of bubble size on the behavior of bubble plumes was presented from the integral point of view. Two distinct types of bubble plume were generated under the same volumetric gas flow rate: many small bubbles using an air-stone diffuser and a few large bubbles using a single- orifice diffuser. The velocity fields in the plumes were measured via Particle Image Velocimetry (PIV), and the integral characteristics were derived for comparison, including the evolution of plume width, center-line velocity, volume flux, momentum flux, momentum amplification factor, and the entrainment coefficient. The measurement data show that the evolution of all the parameters in the plumes were influenced strongly by the different bubble sizes and population. The plumes with many small bubbles behave more similar to the single-phase coherent plumes, showing a linear growth of plume width and a decreasing center-line velocity. These characteristics were modified in the plumes with fewer but larger bubbles. With the same total initial buoyancy flux from the source, fewer but larger bubbles gave rise to weaker mean flow characteristics, i.e., smaller plume velocity and weaker fluxes of volume and momentum. This modification is attributed to the different mechanisms in fundamental transport of energy and momentum between mean and fluctuating components. In the single-orifice cases, the plumes were influenced by stronger but less frequent bubble wakes, compared to those more coherent bubble plumes in the air-stone cases. Higher momentum amplification factors were found in bubble plumes with fewer but larger bubbles, indicating a stronger ratio of turbulence kinetic energy to mean kinetic energy in these plumes. Despite the modification, all bubble plumes support a typical shear entrainment process within 40 cm height-of-rise. Hence, the integral model and the universal scaling using the plume length scale D(= gQg/4[pi][alpha]^2Ws^3 with g being gravitation acceleration, Qg being gas flow rate, [alpha] = 0.083 being a reference entrainment coefficient, Ws being bubble slip velocity) and the bubble slip velocity Ws were found to describe the integral behavior of bubble plumes generally well in the range of our experimental parameters, regardless of the different bubble sizes and population. Second, the detailed turbulent statistics and the budget terms in the equations of TKE were obtained, particularly about their distributions in the radial direction of bubble plumes compared to those in the single-phase momentum jets and buoyant plumes. The bubble plumes have different growth behaviors under different combinations of sizes and population: the plumes with many small bubbles show decreasing centerline velocities along the vertical direction; the plumes with larger but fewer bubbles have a tighter bubble core, a smaller spreading ratio, and almost constant centerline velocities. The ratio of turbulence kinetic energy-to-mean kinetic energy in momentum flux is strongly affected by bubble sizes and population, demonstrated in the profiles of normalized turbulent velocity correlations using mean flow parameterizations. Velocity fluctuations show a strong vertical-to-horizontal anisotropy in bubble plumes compared to those in single-phase jets and plumes. Strong vertical fluctuating velocity component contributes a significant role in re- shaping the radial profiles of turbulent stresses and transport terms when the bubble plume is composed of larger but fewer bubbles. Local balance cannot be established in the equation of TKE traditionally used for single-phase flows. A bubble-related source term in the governing equation is needed to close the budget. An empirical equation using drag force and Ws is validated for the TKE closure. A diagram of TKE budget is provided to illustrate the pathway of TKE terms in the radial direction, with the magnitude of each term influenced by bubble characteristics. In addition, a spectral analysis of the TKE budget in a bubble plume was conducted. Our findings confirmed the hypothesis of an inverse energy cascade in the bubble plume, where TKE is transferred from small to large eddies. This is attributed to direct injection of TKE by bubble passages across a wide range of scales, in contrast to canonical shear production of TKE in large scales. Turbulence dissipation was identified as the primary sink of the bubble produced TKE and occurred at all scales. The decomposition of velocities using the critical length scale of inter-scale energy transfer allowed us to distinguish between large- and small-scale motions in the bubble plume. The large-scale turbulent fluctuations exhibited a skewed distribution and were likely associated with the return flow after bubble passage and the velocities induced by the bubble wake. The small-scale turbulent fluctuations followed a Gaussian distribution relatively well. The large-scale motions contributed to over half of the Reynolds stresses, while there were significant small-scale contributions to the normal stresses near the plume center but not to the shear stress. The large-scale motions in the vorticity field induced a street of vertically elongated vortex pairs, while the small-scale vortices exhibited similar sizes in both horizontal and vertical directions. Finally, the surface region of the bubble plume, focusing on the mean flow and turbulent characteristics was also investigated using 2D2C PIV. It is a jet-like surface layer which flows mainly in the horizontal direction and starts from the radial location which is two times of plume radius. The depth of surface layer is obtained from the gaussian distribution of the vertical profile of mean flow. An existing theory was revised, based on the conservation of mass flux and momentum flux, to predict the mean velocity distribution. Reynolds stresses are mainly distributed within the depth of the surface layer. Large eddies associated with vertical motion are suppressed by the water surface whereas those large eddies associated with horizontal fluctuation are elongated. The distribution of dissipation shows an exponential decay in the vertical direction and peak value of the vertical profile of dissipation shows a gaussian decay in the horizontal direction. An empirical function is obtained to describe the two- dimensional distribution of dissipation. The normalized dissipation is highly influenced by the anisotropy of large-scale motion. But it remains constant when Taylor Reynolds number Re[lambda] is greater than 60 in the present study. Finally, a TKE budget is performed, and the pressure transport term is obtained as the closure term, which is predominant term near water surface. Overall, this dissertation discusses the influence of bubble size on mean flow and turbulence statistics in the zone of pure plume and surface region of bubble plume. The flow characteristics in the zone of pure plume would provide guidance to the use of bubble plume to prevent the spreading of pollutant, invasive fishes, as well as lake destratification. The characteristics in surface region can help to determine how the bubble plume will develop at water surface, this could help to the collection of oil plume.