Mechanics on the Tip Clearance Loss of Impeller Blades

Abstract

For predicting the tip clearance loss of turbomachines, different equations are published in the literature based on different principles. In 1986 the present author postulated a new theory where the pressure loss consisted of two parts: the pressure loss induced by the drag force of the leaked flow, and the pressure loss to support the axial pressure difference without blades in the tip clearance zone. It has been suggested that the two losses were the same loss looked from two different viewpoints, or at least apart of the former was included in the latter or vice versa. In this paper the pressure loss due to the tip clearance is examined based on a macroscopic balance of forces, and the two kinds of loss are derived. Furthermore, it is shown that the former comes from the induced drag, which is parallel to the blade, while the latter comes from the missing blade force normal to the blade in the clearance zone. Because these two forces are mutally perpendicular, the two losses are entirely different in nature and they do not even partially overlap. It is also made clear quantitatively how the loss of the kinetic energy of leaked flow is related to the induced drag of the clearance flow.