SMALL BUBBLE CLOUD CONFIGURATION EFFECT ON ADDED MASS FOR EULER-EULER MODELING

The development of clean energy is a worldwide concern. Hydropower is a leading source for renewable energy generation. In spite of its contribution in decreasing world ecological problems such as climate change and greenhouse gas emissions, hydropower dams can have a negative impact for local river wildlife. The low oxygen level in the reservoir can then be harmful to the aquatic life downstream from the hydropower dam. Using aerating turbines is a solution to drastically reduce this impact.

To develop more efficient and ecological turbines, understanding of the mechanics of the bubble clouds is essential. Due to the complexity of the two-phase flow configurations, modeling the physics of the phenomena driving the mixing of bubbles in turbines is still a challenge. One important factor, in existing two-phase flow models, is modeling small bubble dispersion. In two-phase flows, the dispersion of bubbles comes from different sources such as turbulence, local pressure conditions and bubble-bubble interactions. In this study, we model the effect of added mass fluctuations on the dispersion of bubbles.

A first glimpse of the mechanisms at play comes from the study of two bubbles rising side-by-side. The effects of added mass and induced added mass drive bubbles away from each other [1,2]. The added mass fluctuation is considered as a variable mass problem. Thus, a “Meshchersky” force appears from the spatial variation of the added mass. For the Euler-Lagrange model, we observed the dispersion effect of the “Meshchersky” force on the bubble cloud. However, for the Euler-Euler approach, actual added mass models do not consider local variations of the added mass due to local bubble distribution. Therefore, the dispersion effect of the “Meshchersky” force cannot be captured.

Within this framework, our objective is to develop an added mass model that considers local bubble configurations by introducing the void fraction gradient. The void fraction gradient allows us to account for the asymmetry of the bubble cloud around a single central bubble. This methodology allows a more consistently added mass effect, as well as “Meshchersky” forces, to be included in hydrodynamic models. Thus, this approach can be implemented in a Euler-Euler model that considers the dispersion of small bubbles caused by the effect of added mass.

[1] C. Béguin, E. Pelletier, S. Etienne, 2016, Added Mass in a Bubbly Flow: Void Fraction and Wall Influence, European Journal of Mechanics B/ Fluids, 56, 28-45.

[2] L.M. Milne-Thomson, 1968, Theoretical Hydrodynamics, Dover, New-York.