Flow Of The Power-law Fluid In Variable Cross-section Annulus With The Rotating Inner Cylinder Having Uniform Distance Annulus Solid

In order to solving eccentric wearing in the production of the screw pump well, centering guides be installed on suker rod. The flow of produced liquid in annulus consisted of sucker rod having centering guides and oil pipe can be regarded as the flow of fluid in variable cross-section annulus with the rotating inner cylinder having uniform distance annulus solid. So research on the flow of fluid in variable cross-section annlus with the rotating inner cylinder having uniform distance annulus solid is of certain theoretical instruction and engineering significance for optimizing and designing the parameters of pump in screw pump production well.In this paper, the rheological properties of the produced liquid in screw pump production well are described by the model of power-law fluid. The governing equations and pressure drop equation of the flow of power-law fluid in variabel cross-section annulus with the rotating inner cylinder having uniform distance annulus solid under the cylindrical coordinate system are established, and the relative numerical calculation method were given in this paper. Taking HPAM aqueous solution for examples, the govering equations and the computational formula of pressure drop of the flow are numerically calculated. The influences of the geometry parameters of annulus solid and flow parameters on the distribution of stream function, the distribution of velocity and the pressure drop were analyzed.Based on the equations of motion of the flow of the power-law fluid in variable cross-section annulus with the rotating inner cylinder having uniform distance annulus solid under the cylindrical coordinate system, the Hanks's theory of the flow stability is introduced, then the mathematical expression of the stability parameter H of the flow of the power-law fluid in variable cross-section with the rotating inner cylinder having uniform distance annulus solid was deduced, the stability parameter H of the HPAM aqueous solution in variable cross-section annulus with the rotating inner cylinder having uniform distance annulus solid is numerically calculated and analyzed.Through the experiments of the flow of HPAM aqueous solution, the mass percentage concentration of which is 0.050%,0.100% and 0.125% respectively, in variable cross-cection annulus with the rotating inner cylinder having uniform distance annulus solid, based on the governing equation, computational formula of pressure drop, the formula of stability parameter H and the corresponding numerical methods established and presented, the pressure drop numerically calculated are compared with those experimentally measured, and the critical maximum value of the stability parameter H of the flow is determined. The results show that the maximum average relative errors between the pressure drop numerically calculated and those experimentally measured is 4.89%, so that the governing equation, the computational formula of pressure drop and the corresponding numerical methods established and presented in this paper can be testified to be correct, and the critical maximum value of the stability parameter H of the flow of the power-law fluid in variable cross-section annulus with the rotating inner cylinder having uniform distance annulus solid is 398.2.