MATHEMATICAL SIMULATION OF THE FLOW OF A NON-NEWTONIAN TWO-PHASE MEDIUM IN A CHANNEL OF COMPLEX GEOMETRY

A mathematical model of the fl ow of a two-phase medium, whose state is defi ned by the nonlinear rheological equation, in a curvilinear channel of parabolic shape has been constructed. Numerical calculations of the fl ow of such a medium in this channel were performed with regard for the existence of its initial region and a centrifugal force in the channel. A computational experiment has been conducted, and, on its basis, diff erent regimes of fl ow of a liquid in the indicated channel were investigated depending on the rheological properties of the liquid, governed by the Ostwald–de Waele law of state, and on the hydrodynamic situation in this channel. The numerical calculations have shown that, in the process of development of a liquid fl ow in the channel, in its initial region, the plane velocity profi le of the fl ow is transformed into the parabolic one. In this case, the fl ow near the wall of the channel is decelerated, and the fl ow in the central region of the channel is, vice versa, accelerated. Because of this, in the initial region of the fl ow, its lines and the velocity fi elds on them have bends. The nonlinearity coeffi cient of a liquid substantially infl uences the shape of the velocity profi le of its fl ow. In the case of rotation of the channel around its symmetry axis, the velocity profi le of the liquid fl ow in it becomes asymmetrical.
A mathematical model of the fl ow of a two-phase medium, whose state is defi ned by the nonlinear rheological equation, in a curvilinear channel of parabolic shape has been constructed. Numerical calculations of the fl ow of such a medium in this channel were performed with regard for the existence of its initial region and a centrifugal force in the channel. A computational experiment has been conducted, and, on its basis, diff erent regimes of fl ow of a liquid in the indicated channel were investigated depending on the rheological properties of the liquid, governed by the Ostwald–de Waele law of state, and on the hydrodynamic situation in this channel. The numerical calculations have shown that, in the process of development of a liquid fl ow in the channel, in its initial region, the plane velocity profi le of the fl ow is transformed into the parabolic one. In this case, the fl ow near the wall of the channel is decelerated, and the fl ow in the central region of the channel is, vice versa, accelerated. Because of this, in the initial region of the fl ow, its lines and the velocity fi elds on them have bends. The nonlinearity coeffi cient of a liquid substantially infl uences the shape of the velocity profi le of its fl ow. In the case of rotation of the channel around its symmetry axis, the velocity profi le of the liquid fl ow in it becomes asymmetrical.
Author:  R. I. Ibyatov, F. G. Akhmadiev
Keywords:  mathematical simulation, curvilinear channel, non-Newtonian two-phase medium, computational experiment
Page:  1224