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

The annulus in which the inner cylinder executes a planetary motion means that the inner cylinder not only rotates about its own axis, but also rotates about the axis of the outer cylinder in the annulus. Studying the flow of the non-Newtonian fluid in annulus with the inner cylinder executing a planetary motion is of certain theoretic and engineering significance. In this paper, the flow of a Power-law fluid in annulus with the inner cylinder executing a planetary motion is studied. Theoretically, the non-inertia motive coordinate system is introduced so that the analysis of flow of a power-law fluid in annulus with the inner cylinder executing a planetary motion is greatly simplified; the stream function is introduced due to the continuity of the flow so that the total number of variables of the fluid dynamic basic equations are reduced by one; according to the transformation from the Descartes coordinate system to the bipolar coordinate system, the required solution region is changed from the eccentric annular region to the rectangle region so that the boundary condition is greatly simplified. Therefore, the basic equations of flow of a power-law fluid in annulus with the inner cylinder executing a planetary motion are established in the non-inertia motive bipolar coordinate system. Calculationally, based on the basic equations mentioned above and by using the finite difference method, the distribution of the stream-function and the tangential velocity of the CMC aqueous solution, which can be regarded as a power-law fluid, of Couette flow in annulus are numerically calculated respectively; the distribution of the axial velocity of the CMC aqueous solution of Poseuille flow in annulus is numerically calculated; the distribution of the stream-function, the tangential velocity and the axial velocity of the CMC aqueous solution in annulus with the inner cylinder executing a planetary motion are also numerically calculated; and the distribution of the stream-function,the tangential velocity and the axial velocity are plotted. The relations of the distribution of the stream-function, the tangential velocity and the axial velocity with the revolution velocity, the rotation velocity of the inner cylinder and the eccentric distance are analyzed .The flow rate of the CMC aqueous solution in annulus with the inner cylinder executing a planetary motion is numerically calculated, and the relations of the flow rate and the revolution, the rotation velocity of the inner cylinder and the eccentric distance are analyzed. Taking the flow of a Newtonian fluid in annulus with the inner cylinder executing a planetary motion as an example, the distribution of stream-function, the tangential velocity and the axial velocity which are calculated by using the numerical method mentioned in this paper are compared with those which are calculated by using the analytical method, and the results are coincide very well. Experimentally, through the experiments of the flow of CMC aqueous solution in annulus with the inner cylinder executing a rotation motion and a revolution motion respectively and comparing the flow rate calculated by numerical method in this paper with those measured by the experiments, the mean relative errors between them are no more than ±5%. It shows that the basic equations of flow of a power-law fluid in annulus with the inner cylinder executing a planetary motion established in this paper, as well as the numerical method, are correct.