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1 ( ) , i i i i i i i i m u u dp B u v yB x y dx y y             (3) Abstract: The oil-water flows are multiphase because these liquids are mutually immiscible; therefore such flows are difficult for mathematical modeling and experimentalstudy. Peculiarities of the turbulent two-phase and multiphase flows of the mutually immiscible liquids and averaged differential equations for their modeling are considered. Such equations were first derived by Prof. A.I. Nakorchevski as an alternative to a number of the well-known averaged multiphase dynamics equations. The main difference of the new method was in an averaging of the Navier-Stokes equations by phases and components in time instead of the widely spread spatial averaging in multiphase mechanics. What was more, the introduction of the so-called functionindicator of the phases in a flow allowed recognizing the phases in their movement in a multiphase mixture, both theoretically and experimentally. For the experimentalstudy, the special micro sensor was invented and created, which was successfully applied. In this paper, the method of Nakorchevski is described in application to some multiphase tasks, and a discussion is presented as concern to advantages of the method for study of turbulent two-phase flows of water-oil immiscible mixture, as well as many other similar mixtures, where it is important to know the peculiarities of the phases’ movement and their mixing in a multiphase flow.

Approaches for Mathematical Modeling and Experimental Study of the Turbulent Flows of Mutually Immiscible Liquids (Oil-Water)