Computer Simulation of the Flow of Non-Newtonian Two-Phase Media in Areas of Complex Geometry

Computer modeling of the flow of two-phase non-Newtonian media in areas of complex geometry, which are often elements of various technological equipment, is considered. The basis of computer modeling is a mathematical model of the flow of non-Newtonian two-phase media in channels and pipes with various curved walls. To construct a mathematical model of the flow of non-Newtonian two-phase media, the equations of conservation of mass and momentum of the mechanics of heterogeneous media were used with the corresponding closing relations for the force of interphase interaction and the rheological law of the state of the medium. Simplified equations taking into account flow features close to one-dimensional, written in an orthogonal coordinate system associated with the flow area, are solved numerically using a modified method of equal flow surfaces. An algorithm for numerical flow calculations was constructed for computer simulation of the process. In numerical calculations, the location and number of surfaces of equal flow rates varied in a wide range, taking into account the characteristics of the flow, and reasonable input (initial) values of the longitudinal velocity on the streamlines were specified. Numerical calculations were carried out for areas of parabolic and conical shapes, taking into account the inlet section of the flow and the influence of the centrifugal force field. A computational experiment was performed for various values of channel parameters, the rheological law of the state of the medium and flow regimes of a two-phase medium. As a result, it was found that in the initial section the flow is transformed from an initial flat profile to a parabolic one. Flow velocities slow down near the channel walls, and accelerate in the center of the flow region. Because of this, in the initial section of the flow region, the stream lines are bent. Knowledge of the velocity field of the carrier phase makes it possible to determine the trajectories of motion of the dispersed phase, which is a determining factor for many technological processes. The constructed mathematical model that describes the hydrodynamic situation in the flow region allows us to conduct a computational experiment to calculate the flow of two-phase non-Newtonian media in curved channels and pipes of complex geometry using the modified method of equal flow surfaces. In this case, specific shapes of the flow region are specified by specifying the corresponding Lame coefficients for the flow region. Based on computer modeling, various flow regimes and the influence of various geometric characteristics of the channel, mass forces, and parameters of the rheological law of the state of the medium on the hydrodynamic flow conditions were studied. At different values of the nonlinearity parameters in the power law of state, the influence of the centrifugal force, with its increase, has a stronger effect on the hydrodynamic situation in the channel. The results of computer modeling make it possible to pose and solve problems of optimal hardware design of the corresponding technological processes.