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The article develops a stochastic model of suspensions separation in hydrodynamic filter. Suspensions separation in the filter is carried out due to hydrodynamic force action on suspension flow (first stage of separation) and filtering through a porous membrane (second stage). Pivoting perforated partition is put into filter in front of the porous filtering membrane to increase effectiveness of suspensions separation at stage one. Complex Couette flow develops in the gap between filter bowl and the perforated partition. Specific modes of flow in the gap produce Taylor vortex, size and intensity of which depend on parti-tion’s rotation speed and flow velocity. It produces a flow currently known as Couette-Taylor flow. Multidirectional Taylor vortex arising in the mainstream disrupts its hydrodynamics and creates turbulence. Given such flow, calculation of hard phase separation with use of determinate models can be an error as does not include stochastic processes. The article presents a new analytical model of suspensions separation, which takes in stochastic (probabilistic) separation processes and is based on the theory of Markovian processes. Equations of diffusion type, particularly the Fokker-Planck-Kolmogorov equation, are offered to describe process of suspensions separation in hydrodynamic filters with pivoting perforated partition.

Currently, intensification of the filtering processes in media characterized by high concentration of solid particles remains of great interest in many sectors, such as oil production, oil refining, chemical, medical and food industries. One of the reasons that impede filtering could be the high viscosity level of the dispersion medium. It is known that the filtering rate is inversely proportional to viscosity; therefore, filtering of viscous liquids would be carried out much slower. In addition, filtering media characterized by high concentration of solid particles leads to higher costs for creating the process driving force, fast pores fouling in the filtering material and the need for frequent regeneration of the filtering material. Many media characterized by high viscosity, such as mineral oils, polymer solutions and melts, heavily polluted waters tend to reduce the flow section of the porous material channel; and, as a result, hydraulic characteristics are changing and regeneration of the filtering material is hampered. Therefore, replacement of the filtering material is required, which increases the costs. It is possible to intensify the filtering process by ensuring the suspension preliminarily preparing, for example, by increasing the medium temperature or decreasing the suspension viscosity, as well as adding a suitable solvent. In many technological processes such methods are unacceptable. Design, development and study of devices that allow increasing the filtering material service life and reducing energy consumption to create the required pressure gradient while maintaining the device compactness and ensuring the required fineness of filtration still remains a topical task. This paper is proposing to use filtering in combination with cleaning in centrifugal and vibration fields created in hydrodynamic filters. Centrifugal forces field in the hydrodynamic filter is formed due to liquid tangential introduction into the apparatus and rotation of the cylindrical porous filter partition. The method differs from other technologies by creating a potential flow in the apparatus annular zone within the centrifugal forces field. Such flow organization allows purging up to 80% of polluting substances from the media under cleaning by the centrifugal force mechanism; and such substances are removed from the filter without deposition on the filter partition. This would reduce the load on filter material and increase its service life. Vibration of the filtering partition provided for in its structure makes it possible to destroy the sediment layer thereon and to direct the sediment into the filtrate flow. Thus, the proposed hydrodynamic filter is provided with the self-regeneration ability.

The possibility of applying the probabilistic-statistical method for theoretical calculation of characteristics related to suspensions separation in self-cleaning hydrodynamic filters with a rotating filter element has been demonstrated. It has been shown that the change in characteristics of the suspensions separation in hydrodynamic filters with a rotating filter element can be satisfactorily described based on equations of diffusion type, in particular, using the Fokker–Planck–Kolmogorov equation. The main parameters of the separation process in hydrodynamic filters with a rotating filter element have been determined.

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