The Secondary Flow Of The Flow Of Viscoelastic Fluid In Annulus With The Inner Cylinder Executing A Planetary Motion

Under the behavior of production by screw pump of polymer flooding well, the pump rod rotates not only around its own axis but also around the axis of the oil tube, for the influences of its self-weight and decentralization, the flow of produced liquid in annulus between the pump rod and the oil tube could be regarded as flow of viscoelastic fluid in annulus with the inner cylinder executing a planetary motion. So, that researching on the flow of viscoelastic fluid in annulus with the inner cylinder executing a planetary motion has great significance in academic theory in the engineering.In this paper, to aim at viscoelastic fluid which rheological property can be described by constitutive equation of the second-order fluid with variable coefficients, the basic equations of the flow of second-order fluid with variable coefficients in annulus with the inner cylinder executing a planetary motion are established in bipolar system, the secondary flow distribution is calculated and analyzed numerically by the finite difference method.In theory, the non-inertia coordinate system is introduced and it makes that the analysis of the flow of the second-order fluid with variable coefficients in annulus with the inner cylinder executing a planetary motion being simplified greatly. Because of the continuity of the flow, the stream function is introduced and it makes that the numbers of the fluid dynamical basic equation is cut off one. Due to the exchange between the Descartes right-angle coordinate system and the bipolar coordinate system, it makes that the region which is wanted to calculated becomes from eccentric annular region to rectangle region. Thereby, the stream function-axial velocity equations and the boundary equations of this complex flow are established in the non-inertia bipolar coordinate system.In calculations, at the basis of the stream function-axial velocity equations and the boundary equations above, using the finite difference method, the numerical calculations of the distribution of the secondary flow of the second-order fluid with variable coefficients in eccentric annulus with the inner cylinder executing a planetary motion are made out, and the distribution of the secondary flow are plotted, and the relations between the distribution of secondary flow and eccentricity, the rotation and revolution velocities of the inner cylinder are analyzed. Taking Newtonian fluid for an example, it is proved that the distributions of secondary flow plotted by the numerical solution which is introduced in this paper coincide well with that plotted by analytical calculations. So it is believed that the numerical calculation method in this paper used in calculating the flow of the second-order fluid with variable coefficients in annulus with the inner cylinder executing a planetary motion is proper.