Dependency of the slip phenomenon on the inertial forces inside radial runners

The slip phenomenon consists in the deviation of the fluid fl ow (r elative ve locity ve ctor) wi th re spect to th e blade congruent angles and is mainly due to the finite number of blades. For this reason, slip becomes significant in pumps operating as turbines (PaTs) being characterized by a lower number of blades compared to conventional turbines highlighting a shortcoming of these devices in energy recovery applications. Even though this topic has been widely investigated in the past for centrifugal pumps, it has been often neglected for hydraulic turbine applications. As described in the literature, a counter rotating vortex (known as eddy vortex) develops inside each vane of a rotating machine and its effect can be superimposed to the main flow characteristics. Moreover, the relative vorticity magnitude, which is twice the angular velocity under the hypothesis of inviscid, incompressible and irrotational flow, is constant regardless of the number of vanes. In this work, 3D inviscid steady flow numerical simulations of a purely radial impeller with zero-thickness blades, being designed according to a logarithmic spiral law, have been carried out with the purpose of bringing out the relationship between the flow deviation and the number of blades, neglecting viscous effects which could hinder the inertial ones. The results show a local deviation of the streamline downstream of the trailing edge when the flow is not confined by the blades. The effect of the flow deviation has been also evaluated by calculating the hydraulic performance of the runners. Four different runners have been investigated (with 28, 14, 7 and 3 blades) at their design point and rotating at two different angular velocities. This allowed to correlate the deviation with the inertial effect and to propose a least-squares fitting curve. As shown in previous works, the inclusion of the slip correction factor in 1-D PaT performance prediction models enhances their accuracy.