A new method is given for the analysis of unsteady flows through mixed flow impellers under an assumption of a two-dimensional flow in a representative flow surface of revolution. The flow is mapped to one around a two-dimensional annular cascade. If the thickness of the impeller flow passage changes in a certain functional form, the flow can be represented by using a two-dimensional potential flow in the mapping plane. For impellers with such a thickness distribution, small sinusoidal and/or large transient fluctuations of flow rate and/or rotational velocity are considered. Special attention is paid to the unsteady torque on the impeller. The unsteady torque is divided into three components—quasisteady, apparent mass and wake, and the effects of the geometry of the flow surface on each component are discussed. Apparent mass torque coefficients are determined for fluctuations of flow rate and rotational velocity. Stability of torsional vibration and surging are discussed from energy considerations.

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