The Secondary Flow In The Flow Of Power-law Fluid In Annulus With The Inner Cylinder Executing A Planetary Motion

What is called that the annulus of the inner cylinder executing a planetary motion is: the inner cylinder which can form the annulus is not only rotating by the axis of itself, but also rotating by the axis of the outer cylinder in the annulus. The flow of non-Newtonian fluid in annulus with the inner cylinder executing a planetary motion is studied has great significance in academic theory and has great practical significance in the engineering. In this paper, the distribution of the secondary flow in the flow of Power-law fluid in　annulus with the inner cylinder executing a planetary motion is studied. In theory, the non-inertia coordinate system is introduced and it makes that the analysis of the flow Power-law fluid in annulus with the inner cylinder executing a planetary motion is 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 equation and the boundary equation of this complex flow are established in the non-inertia bipolar coordinate system. In calculations, at the basis of the stream function-axial velocity equation and the boundary equation above, using the finite difference method, the numerical calculations of the distribution of the secondary flow of Power-law fluid 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 conformations of secondary flow and the eccentric distance, the rotation and revolution velocities of the inner cylinder are analyzed. Taking Newtonian fluid as an example, it is proved that the distributions of secondary flow plotted by the numerical solution which is introduced in this paper are conformed well with that plotted by analytical calculations. So it is believed that the numerical calculation method this paper used in calculating the flow of Power-law fluid in annulus with the inner cylinder executing a planetary motion is proper.