ИСТИНА

Analysis of systems of differential equations describing two-speed flow of dispersed mixtures was carried out. Two types of systems were analyzed: with equal phases pressures, with different phases pressures. We investigated systems’ hyperbolicity and stability of stationary solutions. Firstly we analyzed the case with equal pressure of phases. We used a system of differential equations with stabilizing summands depending on gradients of stream parameters in inter-phase friction force. It was proven that stationary transitions from dripping flow to bubble flow are only possible in solutions with parameters discontinuities. For general case, we came up with a solution for a transition from dripping flow to bubble flow: discontinuous jump of parameters with further change to equilibrium values in bubble flow. Numerical calculations for different conditions were made. We proved that a model used nearly in every well-known research thermohydraulic program has significant flaws: for instance, it can lead to unstable solutions which require introduction of smoothing mechanisms and use of a very small step for description of regimes with a boundary of transition from bubble flow to dripping flow. Secondly we focused on the case with different pressures of phases. As a first step we analyzed the simplest test problem with analytical solution. It showed that formal transition from non-hyperbolic system of two equations to hyperbolic system of three equations (with exactly the same solutions as introduced parameter tends to zero) doesn’t solve the problem with non-hyperbolicity. Velocities of instability’s development in systems of two and three equations are analogous. We investigated the main patterns of a model of disperse mixtures flow.