Two-dimensional unsteady analysis of fluid forces on a whirling centrifugal impeller in a volute

Destabilizing fluid forces on a whirling centrifugal impeller rotating in a volute were observed. A quasisteady analysis neglecting shed vorticity or an unsteady analysis without a volute does not predict the existence of such destabilizing fluid forces on a whirling impeller. The effects of a volute and the shed vorticity are considered. We treat cases when an impeller with an infinite number of vanes rotates with a constant velocity omega and its center whirls with a constant eccentric radius epsilon and a constant whirling velocity psi. It is assumed that: (1) the number of the vanes is so large that the impeller can be treated as an actuator impeller in which the flow is perfectly guided; (2) flow is inviscid, incompressible and two dimensional; (3) the eccentricity epsilon is so small that unsteady components can be linearized; (4) vorticity is transported on a prescribed mean flow, the operating point is near design flow rate; and (5) the volute can be represented by a curved plate.