Numerical calculation of unsteady flow of viscoelastic fluid in eccentric annulus

The governing equation, initial and boundary condition of unsteady flow of viscoelastic fluid in eccentric annulus with inner cylinder reciprocating axially under bipolar coordinate system, and the expression of average flow rate areintroduced in this paper. On the basis of numerically solving the governing equation by the finite volume method, the average flow rate of the unsteady flow of HPAM aqueous solution, which can be considered as the viscoelastic fluid, in eccentric annulus with the inner cylinder reciprocating axially, is numerically calculated, using the expression of average flow rate. The relative curves of average flow rate vs. pressure gradient, at different eccentricity of annulus and stroke and frequency of inner cylinder, are plotted. The influence of these three factors on average flow rate is analyzed. Comparison between average flow rate of the unsteady flow of viscoelastic fluid and that of power-law fluid is carried out. Results of the analysis may be good reference to the optimization of operating parameters of pumping units under polymer flooding conditions.