Effect of Structural Parameters of a Cylindrical-Conical Hydrocyclone on the Separation Index of Suspensions with a Non-Newtonian Dispersion Medium

Abstract

A mathematical model that accounts for the effect of the Coriolis force on solid-phase particles is developed. The system of differential equations in partial derivatives, which describes the separation process, is reduced to a system of ordinary differential equations and is solved by a numerical method. It is established that an increase in the non-Newtonian properties of a dispersion medium will lead to an increase in the degree of thickening.The majority of procedures developed for analysis of separation in cylindrical-conical hydrocyclones [1-6] are based on the equation of the one-dimensional motion of a small solid spherical particle suspended in a viscous and incompressible turbulent flow.In many cases, suspensions separated in the chemical industry are non-Newtonian media, the effective viscosity of which decreases with increasing intensity of the rate at which they deform; this will exert an influence on the hydrodynamics of the vessels and the selection of their structural parameters corresponding to the optimal separation index. Romankov [7] and Vainshtein [8] have established that the rheologic equation of state of a non-Newtonian fluid is applicable to multiphase heterogeneous systems (in view of the Ostwald de Waele law). The author of this paper conducted a numerical investigation of the film flow of a non-Newtonian fluid in a cylindrical-conical hydrocyclone [9], which was based on solution of the complete equations of rheodynamics, and developed a procedure for analyzing the suspension of separations by pressurized flotation in a cylindrical hydrocyclone [10]; a procedure for analyzing the separation of suspensions with a non-Newtonian disperse medium by deposition in a cylindrical-conical hydrocyclone with a freely forming surface of liquid-phase, which is based on solution of the complete system of rheodynamics equations, however, is of considerable theoretical and applied interest.The hydrocyclone consists of a cylindrical chamber (into the upper part of which the suspension to be separated is delivered tangentially via an inlet pipe) and conical section. The height of the cylindrical chamber of the hydrocyclone is equal to its diameter. The suspension that has been delivered flows, by revolving, along the walls of the hydrocyclone downward at a velocity having radial v r , circumferential v ϕ , and axial v z components. Particles of solid phase are driven under centrifugal force back toward the wall of the vessel's housing, and are then removed via the discharge device of a lower overflow, through which the clarified suspension flows. The separation efficiency in the hydrocyclone is determined by the hydro-

Analysis of influence exerted by structural and regime parameters of cylindrical hydrocyclones on degassing efficiency of non-Newtonian media on the basis of regression model

“…A mathematical description of degassing in a hydrocyclone during the film flow of a non-Newtonian liquid with a freely forming surface, which is based on solution of a complete system of rheodynamics equations is developed in [8,9] with consideration of the liquid mass connected to the bubbles, and the effect on the bubbles in a centrifugal field of inertial and Coriolis forces.…”

“…As results of numerical modeling of degassing in a hydrocyclone have indicated [8,9], a cylindrical hydrocyclone in which the circumferential velocity component of the liquid is higher, and the film thickness of the liquid smaller as compared with a cylindrical-conical hydrocyclone is most suitable for degassing, and will ensure a highly effective process.…”

“…When calculations were performed on the basis of formula (1), the axial velocity component H g of the gas bubbles was assumed equal to the axial velocity component H l of the dispersion medium [7], since the inertia of the gas bubbles in the axial direction was disregarded in performing the calculations in [8,9].…”

“…Degassing of liquids exhibiting non-Newtonian properties in a hydrocyclone is characterized by the following determining similitude numbers [8,9]: (2) where Fr is the Froude number (separation factor), Re n is an analogy of the Reynolds number for non-Newtonian liquids characterizing the flow regime of the liquid film, Q 0 is a parameter of the dimensionless flow rate, Re ng is an analogy of the …”

“…The degree of approximation of the values of the degree of extraction S obtained using the mathematical model outlined in [8,9] and calculation on the basis of regression equation (3) was evaluated using the squared correlation index R squared , which can be calculated using the SPSS software package [13]. In executing the procedure for nonlinear regression in the SPSS package, the correlation index R squared amounted to 0.984; this indicates a good degree of approximation of the degree of extraction S obtained using the mathematical model to the values calculated from regression equation (3).…”