Title: Solution of bubble number density with breakage and coalescence in a bubble column by Least-Squares Method

Authors: Zhengjie Zhu, Carlos A. Dorao, Hugo A. Jakobsen

Addresses: Department of Chemical Engineering, Norwegian University of Science and Technology, K5-220, Sem Salands vei 4, Trondheim 7491, Norway. ' Department of Energy and Process Engineering, Norwegian University of Science and Technology, VTL 341, Kolbjorn Hejes vei 1A, Trondheim 7491, Norway. ' Department of Chemical Engineering, Norwegian University of Science and Technology, K5-209, Sem Salands vei 4, Trondheim 7491, Norway

Abstract: A steady-state model has been built for an air-water bubble column. The bubble number density constitutive equation has been formulated through integrating the bubble transport equation. Proper kernels for bubble breakage and coalescence rate have been chosen. The momentum balance of the gas phase is included in the model which leads to a set of non-linear differential equations. The model has been successfully solved by using the Least-Squares Method (LSM) with high accuracy and fast convergence. The successive iteration has been applied to the linearised equation set. The model shows excellent agreements with experimental data.

Keywords: air-water bubble column; LSM; least-squares method; PBE; population balance equation; chemical reactors; bubble number density; bubble breakage; bubble coalescence; steady-state modelling.

DOI: 10.1504/PCFD.2009.027375

Progress in Computational Fluid Dynamics, An International Journal, 2009 Vol.9 No.6/7, pp.436 - 446

Available online: 21 Jul 2009 *

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