MATHEMATICAL MODELING OF NON-ISOTHERMAL FLOW OF TWO-PHASE ENVIRONMENT IN AREAS OF COMPLEX GEOMETRICAL FORM
Authors:   Kazan State Agrarian University, IBYATOV R.I. , AKHAMDIEV F.G. , GALIMOV R.A. ,   Kazan State University of Architecture and Civil Engineering, GALIEV D.M. ,   Kazan State Agrarian University
Published: November 2024

Mathematical modeling of non-isothermal flow of two-phase media in areas of complex geometric shape, which are often working units of various types of technological equipment, is considered. To construct a mathematical model describing the flow of a two-phase medium in channels and pipes of complex shape, the equations of conservation of mass, momentum and energy of the mechanics of multiphase media were used with the corresponding closing relations for the force of interphase interaction, the physical parameters of the two-phase medium and the rheological law of the state of the mixture in the form of the Ostwald-de Ville. The conservation equations, taking into account the flow features close to one-dimensional, are written in an orthogonal coordinate system associated with the region, which allows them to be significantly simplified. An algorithm for conducting a computational experiment has been constructed. As a numerical method for conducting a computational experiment, a modified method of equal flow surfaces was used. In this case, changes in the physical parameters of a two-phase medium depending on temperature are taken into account, which significantly complicates the calculations. Numerical calculations were carried out for areas of parabolic and conical shapes, which are determined in the general conservation equations written in a curvilinear orthogonal coordinate system by specifying the corresponding Lame coefficients. In this case, the location and number of equal flow surfaces varied over a wide range, and the input values of the longitudinal velocity and temperature on the streamlines were specified. A computational experiment was implemented for various values of the parameters of the flow region, the rheological law of the state of the medium, taking into account changes in the effective viscosity of the medium from temperature, heat transfer modes and the flow of a two-phase medium. As a result of the computational experiment, various flow regimes and the influence of various geometric characteristics of the flow region, mass forces, and parameters of the rheological law of the state of the medium on the hydrodynamic situation were studied. The various longitudinal velocity and temperature profiles specified at the input developed to a certain steady state, which do not depend on the choice of the initial profile. The temperature values of the medium on the streamlines monotonically approach their asymptotes. The locations of the asymptotic values are determined by the temperature values on the channel walls and the initial temperature of the medium at the inlet. At the same wall temperatures, a symmetrical pattern of heating of the medium is observed, but when the wall temperatures are different, no symmetry is observed. The results of mathematical modelling and computational experiment can be used in the calculation of various technological processes occurring in non-isothermal flows of two-phase media in areas of complex geometric shape.