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International Conference on Mathematical Modeling and Scientific Computing
April 2-6, 2001
Middle East Technical University and Selcuk University
Ankara and Konya, Turkey

Organizers
F. Bornemann (Munich University of Tecnology, Germany), H. Bulgak (Selcuk University, Konya, Turkey), V. Ganzha (Munich University of Technology, Germany), B. Karasozen (METU, Ankara, Turkey), A. Sinan (Selcuk University, Konya, Turkey), C. Zenger (Munich University of Technology, Germany)

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Engineering Applications of Nonlinear Systems: Turbulent two-phase upward flows through annnular ducts
by
Senem Ersahin
Department of Chemical Engineering, METU
Coauthors: Ahmet Erarslan (Department of Engineering Science, METU), Tulay A. Ozbelge (Department of Chemical Engineering, METU)

A simple mechanistic model to predict main flow characteristics of fully developed turbulent dilute liquid-solid mixtures through vertical concentric annuli has been formulated. The dilute liquid-solid slurry is treated as a single-phase fluid of locally variable density due to the presence of solid particles in the liquid-phase. The density distribution function is expressed in terms of the density of liquid and solid density variation coming from correlation of the experimental data of one of the authors. A general expression is obtained for the distribution of total shear stress in terms of pressure gradient in the longitudinal direction, wall shear stresses and radial position of zero shear stress. The laminar counterpart of the total shear is obtained from the law of viscosity and the turbulent counterpart is approximated with the help of Prandtl’s mixing length hypothesis. For grid nodes in the radial direction, highly nonlinear algebraic equations are written to predict one of the wall shear stresses, pressure drop, radial position of zero shear and the distribution of velocity across the flow area. Computer solutions of these nonlinear equations were achieved using Powell Hybrid method provided in MINPACK Package. Preliminary runs were carried out using 100 grid nodes in the radial direction to produce reliable results and on the average 1500 Powell iterations were required to attain convergence.

According to the results of the computations, number of iterations performed is found to be very sensitive to the start-up values of the radial location of zero shear. Radial locations of the maximum velocity and zero shear almost coincide and this location shifts towards the inner wall as the solid concentration is increased. If the solid concentration is kept constant, an increase in the flow rate shifts the position of maximum velocity towards the outer wall. The wall shear stresses change conversely in magnitude as the solid loading is changed and their ratio is observed to be dependent on the solid loading.

Date received: January 25, 2001

Copyright © 2001 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # cagk-32.