Analysis of Air-Bubble Plumes

Abstract

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.

Bubble plume modeling for lake restoration

“…We assumed top hat distributions for all plume properties. Mathematically, the scaling involved here is nearly equivalent to that inherent in the horizontally integrated model, presented by Ditmars and Cederwall [1974]. It simplifies the model, but does not restrict its dynamic generality, as long as the profiles (of velocity and buoyancy) remain similar at all heights.…”

“…Previous work, which has been mainly concentrated on plumes in homogeneous water, has revealed various characteristics of the flow: the Gaussian radial distribution of plume velocity and bubbles, the similarity of the radial profiles at different distances from the source, and the entrainment of the surrounding water. Measurements have been carried out over a wide range of water depths from centimeters [Durst et al, 1986] to meters [Kobus, 1973;Ditmars and Cederwall, 1974;Goossens, 1979;Fannelop and Sjoen, 1980;Milgrarn and Van Houten, 1982] and up to tens of meters [Topham, 1975;Milgram, 1983] with airflow rates from 4 x 10 -7 N m 3 s -] (weak plume [Leitch and Baines, 1989]) to 0.66 N m 3 s -] (strong plume [Topham, 1975]).…”

“…Theoretical investigations followed the early work of Ditmars and Cederwall [1974], who applied the integral theory of a single-phase plume [Morton et al, 1956] to the two-phase bubble plume. The theory is based on the horizontally integrated equations of conservation of mass, momentum and buoyancy and on the entrainment hypothesis, which states that the volume of entrained water per unit height is proportional to both the local plume velocity and the plume circumference.…”

“…In this section, the integral plume theory will be extended to include not only bubble expansion [Ditmars and Cederwall, 1974], but also gas exchange (dissolution and stripping) for the dynamics of a buoyant plume. Previous investigators have not included the latter feature, which is important in deep lakes and for weak plumes.…”

Numerical simulations of turbulent thermal, bubble and hybrid plumes

“…While this has been circumvented by hydrostatic assumptions (Ditmars and Cederwall, 1974), even a constant slip velocity breaks self-similarity in the same way as a non-zero stratification. When w s /w 0 â 1, the gas phase contribution can be ignored as in Cardoso and McHugh (2009) (37)) the effect of bubbles on the turbulence is only accounted in the momentum Eq.…”