The air -bubble plume induced by the steady release of air into water has been analyzed with an integral technique based on the equations for conservation of mass, momentum and buoyancy. This approach has been widely used to study the behavior of submerged turbulent jets and plumes. The case of air-bubble induced flow, however, includes additional features. In this study the compressibility of the air and the differential velocity between the rising air bubbles ,and the water are introduced as basic propertie s of the air -bubble plume in addition to a fundamental coefficient of entrainment and a turbulent Schmidt number characterizing the lateral spreading of the air bubbles.Theoretical solutions for two-and three-dimensional air-bubble systems in homogeneous, stagnant water are presented in both dimensional and normalized form and compared to existing experimental data. The further complication of a stratified environment is briefly discussed since this case is of great practical interest.
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Models are developed to describe the gross behavior of air-bubble plumes generated by point and line sources of air-bubbles released in stagnant water bodies of uniform density. The models predict plume width, velocities, and induced flow rates as a function of elevation above the source. The analysis is confined to the plume mechanics and does not include the horizontal flow created at the surface by the plume. An integral similarity approach, similar to that used for single-phase buoyant plumes, is employed. Governing equations are found by applying conservation of mass, momentum, and buoyancy. The compressibility of the air and the differential velocity between the rising air bubbles and water are introduced in the buoyancy flux equation. Generalized solutions to the normalized governing equations are presented for both point and line sources of air-bubbles. The results of the analyses are compared with existing large-scale experimental data. The comparisons indicate that the models predict the gross behavior of plumes well and yield estimates of the entrainment coefficients and lateral spreading ratios.
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