Selection of structural parameters for a cylindrical hydrocyclone for degassing of heterogenous liquid media based on results of numerical modeling

Abstract

Recommendations for optimization of structural parameters of a cylindrical hydrocyclone used to degas heterogeneous liquid media possessing non-Newtonian properties are set forth on the basis of results of numerical modeling. The mathematical degassing model takes into account the effect of inertial and Coriolis forces, and the associated liquid mass during the movement of a gas bubble. A system of differential equations in partial derivatives, which describes the degassing of heterogeneous media in a hydrocyclone, is reduced to ordinary differential equations, and is solved by the numerical method. The influence exerted on the degassing process by structural parameters of a cylindrical hydrocyclone and rheologic properties of the liquid is analyzed.Yablonskii [1] solves the problem of the film flow of a non-Newtonian liquid in a cylindrical direct-flow hydrocyclone by a numerical method using complete equations of rheodynamics. The problem of the degassing of heterogeneous liquid systems possessing non-Newtonian properties was solved in [2-6]; however, a description of the degassing process in a hydrocyclone during the film flow of a non-Newtonian liquid with a freely forming surface on the basis of solution of a complete system of rheodynamics equations with consideration of the associated liquid mass and the action of inertial and Coriolis forces has not been given until now, and is of significant theoretical and applied interest.The purpose of the present study is to select structural parameters of a cylindrical hydrocyclone for the degassing of heterogenous liquid media on the basis of results of numerical analysis.A cylindrical hydrocyclone in which the liquid film has minimal thickness is best suited for the degassing of heterogeneous liquid media; this ensures high degassing effectiveness, whereas a significant increase in the thickness of the liquid film occurs in the conical section of the housing in a cylindrical-conical hydrocyclone.The hydrocyclone consists of a cylindrical housing in which a non-Newtonian liquid containing gas bubbles is introduced tangentially via an inlet pipe mounted in its upper section. On rotating, the liquid that has entered the housing of the hydrocyclone flows downward along its walls, possessing radial v r , circumferential v ϕ , and axial v z velocity components. Gas bubbles are driven from the liquid by Archimedes centripetal force into a foam layer on the surface of the film.

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).…”