A method of analysis for three-dimensional viscous flow in centrifugal impellers

An analytical model is developed for steady, incompressible flow in shrouded centrifugal impellers of arbitrary design. The method is based on the assumption of an inviscid core flow with surrounding boundary layers on the passage walls. The core flow calculation, which is applicable to incompressible or subsonic compressible flow, employs a streamline curvature technique to solve the governing equations on two intersecting families of stream surfaces. By employing several hub-to-shroud and blade-to-blade stream surfaces whose coordinates are determined as part of the solution, a truly three-dimensional analysis is achieved. An orthogonal streamline coordinate system is used in the solution of boundary layer momentum integral equations which include the effects of rotation and streamline curvature. Simple models for the boundary layer crossflow velocity profiles and the secondary flow in the corner regions permits a step-by-step calculation of the boundary layers on the hub, shroud and blade surfaces.