Analysis of the flow in grooved pumps with specified pressure boundary conditions

In this study the numerical method is employed to examine the flow in pumps with spiral grooves. A methodology suitable for the use of unstructured grids is developed. In order to have the greatest feasibility, the governing equations are formulated in such a manner that the grids are allowed to rotate with the rotor. Different from common practices, pressures are specified on the inlet and the outlet boundaries. Therefore, special treatments are required to calculate the mass flow rate and the inlet and outlet velocities. The methodology developed here is assessed via comparison with existing measurements and good agreement is obtained. Examination of pump parameters reveals that in order to obtain maximum flow rate, both the spiral angle and the groove height need to be carefully determined. The force balance over the entire flow channel shows that for a fixed pressure rise across the pump, the pressure difference between side walls is proportional to tangent of the spiral angle and the groove width, but inversely proportional to the groove height and the rotor length. These relationships can roughly be seen in the calculated results.