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Ind. Eng. Chem. Res. 1997, 36, 4052-4074
REVIEWS Modeling of Vertical Bubble-Driven Flows Hugo A. Jakobsen,† Bente H. Sannæs,‡ Sverre Grevskott,‡ and Hallvard F. Svendsen*,‡ Norwegian Meteorological Institute, P.O. Box 43, Blindern, N-0313 Oslo, Norway, and Department of Chemical Engineering, Norwegian University of Science and Technology, NTNU, N-7034 Trondheim, Norway
Bubbly flows comprise a large number of different flow situations, e.g., dispersed pipe flows, flows in multiphase agitated tanks, flows in multiphase fixed- and fluidized-bed reactors, and typical bubble-column and loop-reactor flows. This paper focuses on bubble-driven flows. These are flow situations were the bubble movement itself is the main source of momentum to the flow field and are often characterized by low superficial liquid velocities, relatively high superficial gas velocities, and no mechanical support of the flow (e.g., agitation). Only vertical flow situations are considered. An overview of the verified forces acting on bubbles is given, and examples of both classical and more recent modeling approaches are shown. This include gravity, buoyancy, centrifugal forces, conventional Magnus and Saffman forces, form and friction drag, and added mass as well as turbulent migration and other instability mechanisms. Special emphasis is placed on mechanisms creating bubble movement in the radial direction. Important literature on the subject with regard to the use of computational fluid dynamics to model gas-driven bubbly flows is reviewed, and the various approaches are evaluated, i.e., dynamic vs steady-state descriptions and Euler/Lagrange vs Euler/Euler formulations. Results from steady-state Euler/ Euler simulations are given and discussed, and the demand for amplified modeling including more accurate and stable numerical solution schemes and algorithms is stressed. Introduction One would expect that the modeling of bubble-driven dispersed flows has developed significantly during the last 2 decades. In their review of two-phase flow models in 1984, Stewart and Wendroff (1984) concluded that no general agreement was reached as to the definite form of the governing equations and that a priori assumptions as to the nature of the flow regime had to be made. Although a number of modeling and experimental studies have been performed since then, covering many forms of bubbly flow and having definitely raised the general level of knowledge, one may still feel that Stewart and Wendroff’s conclusion is still valid. It seems that modeling of two-phase flow in pipes, at relatively high liquid velocities and for low gas fractions, has come a long way in being able to predict radial gas fraction profiles with good accuracy. Examples of this can be found in Beyerlein et al. (1985), Lahey (1990), Antal et al. (1991), and Zun et al. (1993). Dispersed flow under these conditions is in many ways simpler than bubble-driven flow. No recirculation of liquid and gas flows is set up, the void fractions are often low (
