Eddy Diffusivity near a Bubble Plume

For my masters work, I studied mixing near a bubble plume as part of a project to investigate the effectiveness of aerators for mixing a combined-sewer overflow reservoir for the city of Chicago. As part of this project, we conducted deep water bubble plume experiments in a lock on the Snake River in Washington (the data from which never got used due to a decision to go with surface aerators).

For some light reading, you can download my master's thesis here.

Or you can download the short version in Water Resources Research here.

Profiles of eddy diffusivity and the rate of dissipation of temperature variance were inferred from
temperature microstructure measurements near a bubble plume at the center of a tank with
diameter 13.7 m and maximum depth 8.3 m. This set of profiles is one of only two experimentally
derived datasets of the eddy diffusivity near a bubble plume, and the other comes from a much
smaller vessel. Bubble plumes, which are created by injecting gas into a liquid, are used for mixing and aeration in many engineering applications, including mixing gases into steel melts in
metallurgy, providing gases to oxidation reactors in chemical engineering, and destratifying
reservoirs in civil engineering. The eddy diffusivity measures the mixing due to the bubble plume.
The eddy diffusivity is typically computed numerically.

The eddy diffusivity was calculated using two methods commonly used in oceanography. The
Osborn-Cox (1972) model uses the rate of dissipation of temperature variance and the Osborn
(1980) model uses the rate of dissipation of turbulent kinetic energy. Both these dissipation rates
can be determined from the microstructure measurements. The dependence of the eddy diffusivity on these parameters subjects these results to the uncertainties and issues of determining dissipation rates from microstructure data.

Using six datasets, containing between 18 and 51 profiles, ensemble averaged profiles of the eddy diffusivity were calculated. These data represent flow rates of 0.1 – 0.6 L/s and radii of 1.2 to 4 m. Because there were differences in tank sizes and air flow rates in bubble plume studies, the profiles were qualitatively compared to the current literature. This analysis shows that despite the differences, the magnitude of the eddy diffusivity is similar to that found in these other studies. Additionally there is a non-monotonic dependence of the eddy diffusivity on the radial distance, a trend which is also observed in numerical studies. If the eddy diffusivity is assumed to equal the eddy viscosity, the radial profiles of the eddy diffusivity can be used to compute a tank-averaged eddy viscosity, or a bulk effective viscosity. The current values of the bulk effective viscosity fall within the range predicted by the bulk effective viscosity models.

Comparison of the bulk eddy diffusivity from the present study and numerical simulations with the bulk effective viscosity models of Mazumdar (1989) and Sahai & Guthrie (1982a). The data symbols are as follows: ●, present data; ○, Grevet et al. (1982); +, Sahai & Guthrie (1982a); Δ, Sahai & Guthrie (1982b); ´, Sheng & Irons (1993). The dashed line represents the bulk effective viscosity model of Sahai & Guthrie (1982a), and the dash-dot line represents the model of Mazumdar (1989). The data are plotted using the source strength parameter M_H from Asaeda & Imberger (1993).