Calculation of flow rate for flow of the second-order fluid having variable coefficients in annulus with the inner cylinder executing a planetary motion

The governing equations of the flow of the second-order fluid having variable coefficients in annulus with the inner cylinder executing a planetary motion are established, and the flow rate calculation formula is given in this paper. The governing equations are calculated numerically by the finite difference method, on the base of above results, the laminar flow rate is numerically calculated using simpson integration formula. Influences of the revolution and the rotation velocity of the inner cylinder, the eccentricity and the pressure gradient in annulus on the flow rate are analyzed. The results show that the eccentricity and pressure gradient are main influence factors. The experiments for the flow of Hydrolyzed Polyacrylamide (HPAM) aqueous solution which can be regarded as the second-order fluid having variable coefficients in annulus with the inner cylinder executing a planetary motion are carried out, the theoretical flow rate calculated numerically is compared with those measured practically, the even relative percent error between them is smaller than 5%, it verifies that the governing equations, flow rate calculated formula and the relevant numerical calculation method given in this paper for the flow of the second-order fluid having variable coefficients in annulus with the inner cylinder executing a planetary motion are correct.