A New Method for Numerical Calculation of Pressure Gradient of Unsteady Flow of a Viscoelastic Fluid in Eccentric Annulus

摘要

Finite Volume Method (FVM) was used to discrete governing equations of unsteady flow of secondorder fluid with variable coefficients in eccentric annulus with the inner cylinder reciprocating axially, in which a fully implicit scheme was taken on time integral, and Alternating Direction Implicit (ADI) method to solve the discrete equation group. Using HPAM aqueous solution, the numerically calculated pressure gradients were compared with the experimentally measured ones, and coincidences of the comparisons were compared with those calculated by using the other two old methods. The results show that the new method presented is testified to be correct and the coincidences between the calculated pressure gradients and the measured ones, using the new method, are better than those using the old methods; moreover, the numerical calculating procedure of the new method is much more simple and convenient and calculating speed is faster. This study is of certain significance in practical engineering for optimizing the working parameters of beam pumping unit and the energy saving of production system of the unit.