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In this paper a two-phase (gas - solid particles) swirling turbulent flow in the separation chamber of a centrifugal apparatus is considered. The results of mathematical modeling of flow at different settings are shown. This paper presents a two-phase (gas - solids) swirling turbulent flow in the separation chamber of the centrifugal apparatus with an additional supply of gas (Fig. 1). Through the section A-A the gas flow is supplied with particles having radial and tangential velocity components. Through the section B-B an additional supply of gas without solid is provided. The flow in the vortex chamber is axisymmetric by its nature. Through the section C-C the swirling flow together with the gas fraction of fine particles leaves the working area of the vortex chamber. Through the section B-B the incoming gas stream filters larger particles of the particulate fraction, returning finer particles to the working zone of the classifier. Large particles, due to the predominance of the centrifugal force over the aerodynamic force, leave the vortex chamber through the cross section B-B. All solid walls of the apparatus can rotate about the axis O-Z, giving additional rotation of the gas flow with the solid phase and thereby aligning the field of circumferential velocity vector components. To describe the swirling gas flow in the separation chamber a set of the Reynolds equations is used. For its closure the generalized Boussinesq model is applied according to which the Reynolds stresses are considered to be proportional to the mean flow strain rate and the coefficient of eddy viscosity νt. Thus, the system of Reynolds equations in the cylindrical coordinate system in the conservative dimensionless form for an incompressible viscous fluid taking into account the axial symmetry (/ = 0) can be written as follows: r ((ur r)) + z ((uzr)) = 0; + j = 1;

Modeling of a two-phase swirling turbulent flow in the separation chamber of the centrifugal apparatus