Direct numerical simulation of the coalescence of bubbles
Citation for published version (APA):
Baltussen, M. W., Deen, N. G., & Kuipers, J. A. M. (2012). Direct numerical simulation of the coalescence of bubbles. In Proceedings of the 22nd International Symposium on Chemical Reaction and Engineering (ISCRE 2012), 2-5 September 2012, Maastricht, The Netherlands
Document status and date: Published: 01/01/2012
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DIRECT NUMERICAL SIMULATION OF THE COALESCENCE OF BUBBLES
M.W. Baltussen, N.G. Deen and J.A.M. KuipersEindhoven University of Technology, Department of Chemical Engineering and Chemistry, Multiphase Reactors group
Summary
In industry, bubble columns are widely used. However, the knowledge on the hydrodynamics in the bubble column is limited. To increase this knowledge, computational fluid dynamics are used. In this research, the Volume of Fluid (VoF) model is used to study the coalescence of bubbles. Bubbles in the VoF model merge automatically when their surfaces share the same numerical grid cell. To determine, if the coalescence of the bubbles in the VoF model is physical, the results of the VoF model are compared to experimental results.
Keywords
Bubble columns, bubbly flow, Coalescence, Volume of Fluid model
Introduction
Bubble columns have various industrial applications, e.g. steam generators, chemical reactors, bioreactors [1]. The interaction between the liquid and the gas phase is one of the key elements for the design of bubble columns. These interactions are traditionally obtained from limited analytical solutions or empirical correlations obtained using time-consuming experiments. Due to the introduction of computational fluid dynamics, the interactions between the phases can be calculated for any situation [2].
Industrial sized bubble columns usually have a very large length scale, in the order of tens of meters. At this scale, it is not possible to resolve the flow of the fluids in full detail. Therefore, a multi-scale modeling approach, in which the larger scale models use accurate closures derived from the small scale models, is used to model industrial bubble columns [3].
Multi-scale modeling
The models of the multi-scale modeling approach form a hierarchy, as shown in Figure 1. The smallest scale model (O(102) bubbles) is the Direct Numerical Simulation (DNS). In this model, the Navier-Stokes equations are solved directly without any assumptions. From the model, closures for the bubble-liquid interactions can be determined [3]. To simulate intermediate scale bubble columns (O(106) bubbles), the Discrete Bubble Model (DBM) is used. In this model the bubbles are represented by Lagrangian spheres, while the liquid
Figure 1. The multi-scale modeling approach for bubble columns. A) the DNS, B) the DBM C) the Two-Fluid model flow field is simulated using the Navier-Stokes equations [3].
However, to simulate an industrial sized bubble column, the Two-Fluid model should be used. In this Euler-Euler model, both the liquid and the bubbles are simulated as interpenetrating fluids [3]. This work will focus on the interactions between the bubbles and the liquid. Therefore, a DNS model will be used.
The Volume of Fluid (VoF) model
There are many different DNS models. The Front Tracking model is not able to describe the coalescence of bubbles without the introduction of a sub-grid model. According to van Sint Annaland et al. (2005), the VoF model is able to describe the coalescence of bubbles even at high density and viscosity ratios, which are most relevant inindustrial applications. However, bubbles merge automatically in the VoF model when their surfaces share the same numerical grid cell. In this research, it is determined if the coalescence of the bubbles in the VoF model is physical [4].
To study this automatic coalescence of bubbles, a numerical study and experimental study is performed. The numerical and experimental results will be compared to validate the coalescence of bubbles in the VOF model. Some preliminary numerical results are shown in Figure 2.
References
[1] R.H. Chen, W.X. Tian, G.H. Su, S.Z. Qui, Y. Ishiwatari, Y. Oka, Numerical investigation on coalescence of bubble pairs rising in a stagnant liquid, Chem. Eng. Sci. 66 (2011), 5055-5063.
[2] W. Dijkhuizen, I. Roghair, M. van Sint Annaland, J.A.M. Kuipers, DNS of gas bubbles behaviour using an improved 3D front tracking model-Model development, Chem. Eng. Sci. 65 (2010), 1427-1437. [3] I. Roghair, Y.M. Lau, N.G. Deen, H.M.
Slagter, M.W. Baltussen, M. van Sint Annaland, J.A.M. Kuipers, On the drag of bubbles in bubble swarms at intermediate and high Reynolds numbers, Chem. Eng. Sci. 66 (2011), 3204-3211.
[4] M. Van Sint Annaland, N.G. Deen, J.A.M. Kuipers, Numerical simulation of gas bubbles behaviour using a three-dimensional volume of fluid method, Chem. Eng. Sci. 60 (2005), 2999-3011.
