Turbulent Drift of Finely Dispersed Particles in Emulsions and Suspensions in Pressure Hydrocyclones
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Journal of Engineering Physics and Thermophysics, Vol. 93, No. 4, July, 2020
TURBULENT DRIFT OF FINELY DISPERSED PARTICLES IN EMULSIONS AND SUSPENSIONS IN PRESSURE HYDROCYCLONES A. G. Laptev, M. M. Basharov, and E. A. Lapteva
UDC 66.063.62
Consideration has been given to a mathematical model of turbulent drift of finely dispersed particles in the liquid phase of a hydrocyclone. With the two-layer model of a turbulent boundary layer and the coefficient of turbulent diffusion of the particles, the authors have obtained an expression for calculating the coefficient of the rate of particle transport from the flow core to the boundary of a viscous sublayer on the apparatus wall. On the basis of the expression for shear stress on the wall, which was written with a momentum-transfer coefficient, an expression has been obtained for calculating the average circular velocity in the hydrocyclone. The basic parameter of these expressions is the dynamic velocity, which is determined from the average rate of energy dissipation. Results of calculations of the coefficient of transport of particles, the average circular velocity, and the efficiency of separation of particles of diameter 6 μm (sand particles in oil) have been presented; a comparison of the results with experimental data has been made. Keywords: hydrocyclone, turbulent diffusion, transfer coefficients, separation efficiency. Introduction. Heterogeneous media are separated under the action of various forces. The acting force determines the structure of the apparatus and the field of its application. Separation in a hydrocyclone mainly occurs under the action of centrifugal forces. The regime of motion of a liquid in the apparatus is turbulent in nature. Therefore, turbulent diffusion of particles is predominantly toward the hydrocyclone wall. Hydrocyclones have been investigated in the works of A. I. Povarov, A. M. Kutepov, D. F. Kelsall, D. Bradly, A. B. Golovanchikov, A. B. Adel′shin, D. A. Baranov, and many others [1–3]. The objective of the present work is to develop a mathematical model of turbulent migration of finely dispersed particles, which is usually disregarded in traditional methods of calculation of hydrocyclones. The motion of suspended particles in a turbulent flow is characterized by greater intensity and complexity than in a laminar flow. This is due to the fact that under the influence of turbulent pulsations of a medium, the particles execute vibrational motions with respect to pulsation moles carrying them and random movements together with the moles of the medium. It is common knowledge that depending on the hydrodynamic conditions of the medium and the densities of interacting phases, it is only fairly large particles that are not involved in the medium′s turbulent pulsations. For smaller particles, account should be taken of turbulent pulsating motion [4–6]. The degree of entrainment of small particles by turbulent pulsations is characterized by the Stokes number (inertial parameter) and by the factor of inertia of the particles, i.e., at ωE
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