A Mean-Line Flow Model of Viscous Liquids in a Vortex Pump

The axial, radial and tangential velocity profiles of six fluids were extracted from computational fluid dynamics simulation results at points in a pump chamber 1 mm distant from the blades in a vortex pump at the specific speed of 76. The critical radius was specified in the axial velocity radial profiles to determine the impeller inlet and outlet at six viscosities and part-load, design, and over-load points. A mean-line flow model and hydraulic loss model were built from the profiles. The incidence, incidence loss in the inlet, deviation angle, and slip factor in the outlet were calculated. The impeller theoretical head, pump hydraulic efficiency and volumetric efficiency were analyzed. It was shown that the axial, radial and tangential velocity profiles relate closely to the flow rate as usual, but also the viscosity, especially at low flow rates and in the inlet. The low flow rate and viscosity lead to near zero axial and radial velocities, a faster tangential velocity than the blade speed, negative incidence, and a small incidence loss coefficient in the inlet. The dimensionless critical radius ranged within 0.77–0.89 and reduces with the increasing flow rate and viscosity. The mean slip factor is between 0.11 and 0.20 and rises with the increasing flow rate and viscosity. The mean incidence loss coefficient is within 0.0020–0.15 and augments with the increasing flow rate but increases with the decreasing viscosity under part-load conditions. The theoretical head estimated by using the fluid tangential velocity between the outlet of the impeller and the inlet of the chamber is more reasonable.