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.

Summary: This paper presents the development of a computational-fluid-dynamics (CFD) model for the 3D transient two-phase flow within a progressing-cavity pump (PCP). The model implementation was only possible because of the meticulous mesh-generation and mesh-motion algorithm, previously published by the authors, which is briefly described herein. In this algorithm, a structured mesh was generated by defining all nodes’ positions and connectivities, for each rotor position by means of FORTRAN subroutines, which were embodied into ANSYS CFX software. The model is capable of predicting accurately the volumetric efficiency and the viscous losses, and it provides detailed information of pressure and velocity fields and void distribution along the pump. Such information could be of fundamental importance for product development and/or optimization for field operation. In field applications, the common situation is that in which the oil comes into the pump accompanied with free gas, which characterizes a multiphase flow. Simplified models on the basis of the calculation of the backflow or “slippage,” which is subtracted from the displaced flow rate, fail to characterize the PCP performance under multiphase conditions because the slip is variable along the pump. In this model, the governing equations were solved with an element-based finite-volume method in a moving mesh. The Eulerian-Eulerian approach, considering the homogeneous model, is used to model the flow of the gas/liquid mixture. The compressibility of the gas is taken into account, which is one of the main shortcomings in positive/constant displacement pumps. The effects of the different gas-volume fractions (GVFs) in pump volumetric efficiency, pressure distribution, power, slippage flow rate, and volumetric flow rate were analyzed, and some new insights are presented about the slippage in PCPs operating in multiphase conditions. The results show that the developed model is capable of reproducing pump dynamic behavior under multiphase-flow conditions performed early in experimental works.

A hybrid analytical-numerical approach based on the Generalized Integral Transform Technique is employed to simulate the laminar forced convection (hydrodynamically fully developed and thermally developing laminar flow) of power-law non-Newtonian fluids inside ducts with arbitrary shaped cross-sections. The analysis is illustrated through consideration of both right angularly and isosceles triangular ducts subjected to constant wall temperature as thermal boundary condition. Reference results for quantities of practical interest such as dimensionless average temperature and Nusselt numbers within the thermal entry region were produced for different values of power-law index and apex angles. Finally, critical comparisons are performed with results available in the literature for direct numerical and approximate approaches.