This work presents a novel computational model for the 3D flow in a rigid stator Progressing Cavity Pump (PCP), using an element based finite volume method, which includes the relative motion between rotor and stator. Usual flow models in PCPs consider a Poiseuille flow along the seal lines, i.e., along the positive clearance between cavities in order to predict the internal slip and then, the volumetric efficiency for different pressures, rotations and fluid viscosities. Furthermore, some attempts for more detailed models including computational solutions for the flow in simplified geometries can be encountered in literature. These approaches include, treating cavities as parallel plates or computing the flow between two static cavities, in all cases considering steady state flow, which is a strong hypothesis in this case. Nevertheless no models considering the solution for the full transient 3D Navier-Stokes equations and the relative motion between rotor and stator were encountered. The main challenge at this point was the imposition of the mesh motion and mesh generation process, mainly, because of the mesh quality control (element distortion) in regions near the seal lines, or in the clearance regions between rotor and stator.

The model developed is capable to predict accurately the volumetric efficiency and the viscous looses as well as provide detailed information of pressure and velocity fields inside this device. Furthermore, the present model could be used to predict the hydraulic performance of an elastomeric progressing cavity pump after stator wear or deformation and allow for the development of a computational model for the fluid-structure interaction which permits the analysis of the non-rigid stator case.

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