Impact of bubble size on turbulent statistics in bubble plumes in unstratified quiescent water

Abstract

We report an experimental investigation of turbulence in bubble plumes released in unstratified quiescent water. The focus is to study the detailed turbulent statistics and the budget terms in the equations of turbulent kinetic energy (TKE), particularly about their distributions in the radial direction of bubble plumes compared to those in the single-phase momentum jets and buoyant plumes. Two types of diffusers were used to generate plumes consisting of different bubble sizes and population at the same source gas discharge. The bubble plumes have different growth behaviors under different combination 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-to-mean 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 bubble slip velocity is validated for the TKE closure. We provide a diagram of TKE budget to illustrate the pathway of TKE terms in the radial direction, with the magnitude of each term influenced by bubble characteristics.