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Importance of modelling bubble dynamics for calculations of bubble columns: LES combined with Lagrangian tracking

Banff International Research Station for Mathematical Innovation and Discovery

Talk: Plenary Abstract: Since many years CFD (computational fluid dynamics) is applied for numerical calculations of the very complex flows in bubble columns using the two-fluid approach as well as the Euler/Lagrange approach, both based on the point-particle approximation. Numerous different models have been proposed and used for describing the forces on bubbles, modelling bubble induced turbulence and transport of bubbles by turbulence structures. The dynamics of bubbles, i.e. oscillations and tumbling motion have not been considered so far. Such a model has been developed, implemented in the frame of Euler/Lagrange calculations and validated based on detailed experiments (Sommerfeld and Bröder 2009). In this framework, a CFD model is developed and implemented in an open source platform (OpenFOAM®), based on the Euler/Lagrange approach. Flow field and turbulence of the carrier phase was modelled by the Large Eddy Simulation (LES) approach, considering also bubble induced modification of sub-grid-scale (SGS) turbulence, described by the Smagorinsky model (Lain et al. 2002). In bubble tracking all relevant forces such as drag, gravity/buoyancy, transverse lift, pressure and added mass are considered. The time step for Lagrangian tracking is dynamically adapted according the local relevant time scales. The effect of sub-grid scale turbulence on bubble motion was described by a stochastic single-step Langevin equation, based on Lagrangian and Eulerian time scales (Lipowsky and Sommerfeld 2007). LES and Lagrangian tracking is done with different time steps governed by the respective time scales, so that within each LES time step multiple Lagrangian time steps are conducted. This procedure reduces computational time. Moreover, the bubble dynamics in the point-particle approximation was modelled by stochastic variations of bubble shape and orientation according to experimental observations. For that purpose a Langevin model is used for describing the development of the eccentricity and orientation having a correlated and a random part. The correlation function depends on the Lagrangian time step and the time scale of oscillation (Lunde and Perkins 1998). Drag and lift coefficients are calculated by considering bubble eccentricity. Additionally, the bubble direction of motion is altered by a Langevin random process in order to mimic bubble tumbling motion. Numerical simulations, including comprehensive parameter studies (e.g. different force correlations coupling between the phases and oscillation model parameters), were compared with experiments from Sommerfeld and Bröder (2009) using a laboratory bubble column with a diameter of 140 mm and a height of the water level of 650 mm. The conclusion from this study is that bubbly dynamics needs to be modelled in numerical calculations in order to correctly predict their behaviour which will be of immense importance when also considering mass transfer and chemical reaction.

Mathematics; Fluid mechanics; Mechanics of particles and systems; Fluid dynamics

video/mp4

Author affiliation: Martin-Luther-University Halle-Wittenberg

2017-02-07

Attribution-NonCommercial-NoDerivatives 4.0 International

http://hdl.handle.net/2429/60526

Unreviewed

http://creativecommons.org/licenses/by-nc-nd/4.0/