Bubble plume modeling for lake restoration

Abstract

A steady bubble plume model is developed to describe a weak air (or oxygen) bubble injection system used for the restoration of deep stratified lakes. Since the model is designed for two modes of operation, i.e., oxygenation and artificial mixing, gas exchange between water and bubbles has to be included. The integral model is based on the entrainment hypothesis and a variable buoyancy flux determined by the local plume properties and the ambient water column. Fluxes of eight properties are described by nonlinear differential equations which can be numerically integrated. In addition, five equations of state are used. The model leaves open two initial conditions, plume radius and plume velocity. Model calculations with real lake water profiles demonstrate the range of applicability for both modes of operation. The model agrees reasonably well with field data and with laboratory experiments conducted by various investigators.into the lower end of the inner tube, in which the water rises, then sinks back through the outer tube and leaves the system through outlets placed at the appropriate depth.In this article a different approach is described. The system "Tanytarsus," designed by the two Swiss engineers, E. Jungo and U. Schaffner, is presently in operation in several deep Swiss lakes [Imboden, !985; Stadelmann, 1988; St6ckli and Schmid, 1987]. The system uses the same lake installation for both the injection of compressed air for artificial mixing in winter and the injection of pure oxygen into the hypolimnion in summer (Figures 1 a and lb). Pure oxygen is used for hypolimnic oxygenation to prevent the accumulation of molecular nitrogen which can be toxic to fish [Fast and Hulquist, 1982].Both modes of operation are physically similar. The main difference between them consists in the choice of the initial bubble radius and the selection of either natural air or pure oxygen. During the winter the air bubbles have to be large enough to guarantee that the buoyancy force acts up to the lake surface. In contrast, for efficient oxygenation, the oxygen bubbles have to be small enough to dissolve completely in the oxygen-poor hypolimnion before entering the 3235 3236 WOEST ET AL.: BUBBLE PLUME MODELING FOR LAKE RESTORATION

Bubble momentum plume as a possible mechanism for an early breakdown of the seasonal stratification in the northern North Sea

“…Fluid in the bubble momentum plume appears to rise at an average 0.33 m/s, whereas the bubbles themselves rise at 0.25-0.30 m/s faster than the surrounding flow. The bubble-plume induced flow likely causes additional turbulent mixing and can generate entrainment of the surface mixed layer (Wüest et al, 1992). Therefore the data are consistent with the hypothesis that strong bubble plumes provide a mechanism that assists in breaking down of the seasonal thermocline.…”

“…Large natural bubble plumes from marine seepage ) and engineered bubble plumes such as used in lake destratification (Wüest et al, 1992) are associated with strong upwelling fluid motions. These motions are driven by the buoyancy flux, Q, which accelerates fluid vertically.…”

Tamanho de bolhas de ar formadas por difusores não porosos na água

“…Assim, os diâmetros estimados podem ser usados para avaliar importantes parâ-metros na modelagem de sistemas de aeração por ar difuso por meio de difusores não porosos, tais como o coefi ciente de transferência de massa (WÜEST et al, 1992;MCGINNINS & LITTLE, 2002) e a velocidade relativa das bolhas (LIMA NETO et al, 2008b, 2008d …”

“…Nesses tipos de sistemas torna-se importante determinar o tamanho das bolhas geradas, de forma que a hidrodinâmica e os processos de transferência de massa envolvidos possam ser modelados com precisão (WÜEST et al, 1992;MCGINNIS & LITTLE, 2002;LIMA NETO, 2012a, 2012b. O foco do presente artigo foi a determinação do tamanho das bolhas formadas a partir de difusores não porosos (ou difusores de bolhas grossas), os quais são menos susceptíveis ao problema da colmatação do que os difusores porosos, o que facilita o seu uso, por exemplo, em sistemas de aeração/destratificação de lagos e reservatórios.…”

Integral models for bubble, droplet, and multiphase plume dynamics in stratification and crossflow

“…For releases that do not include any ambient fluid, there needs to be an estimate of the initial amount of ambient water that mixes with the plume in the zone-of-flow-establishment; otherwise, the initial volume and momentum fluxes of the entrained fluid are undefined, and the solution fails. In these cases, we use the bubble plume Froude number initial condition proposed by Wüest et al [56] and detailed for the SPM in Socolofsky et al [8]. Alternatively, the zoneof-flow establishment could be considered, as in Premathilake et al [57].…”