Modeling and scaling of aeration bubble plumes:: A two-phase flow analysis

In this paper, we focus on bubble plumes aimed at providing oxygen to, and at mixing unstratified water bodies. First, we discuss scaling relations obtained from a three-dimensional (3D) theoretical model for multi-component fluids. An expression for a length scale that represents a balance between inertia and buoyancy is derived, and it is used to scale vertical as well as horizontal (radial) distances. This length scale is then analyzed in terms of previous bubble-plume non-dimensional numbers. For the practical case in which the bubble diameter remains almost constant throughout the bubble plume, a one-dimensional theoretical model-which can be derived by integrating the 3D model in a horizontal plane-is used to show that the length scale (D) is well suited for defining zones in bubble plumes. These zones include a region near the diffuser where the size of the diffuser is important, an intermediate zone where the diffuser size and D determine the flow features, and an asymptotic region where plume variables approach a universal behavior. Procedures for scaling entire reservoirs and portions of reservoirs are developed. These procedures are evaluated with results from previous experiments and new observations in a large tank and a scaled physical model. Scaling of turbulence statistics in bubble plumes is also investigated.