A Quasi-Three-Dimensional Finite Element Solution for Steady Compressible Flow Through Turbomachines

A quasi-three-dimensional solution method is presented for subsonic flows through turbomachines of arbitrary geometry. Principal equations are based on Wu’s formulation of flow on blade-to-blade and hub-to-shroud surfaces, modified such that the same hub-to-shroud principal equation is used for all types of stream surfaces. Blade-to-blade surfaces are assumed to be surfaces of revolution. A stream function is used as the field variable. The problem is solved by finite element method. An iterative solution is used to find the quasi-three-dimensional solution. Solutions at hub, tip, and midheight blade-to-blade surfaces are used to construct a mean hub-to-shroud surface and vice versa, until convergence is obtained. Results indicate that the developed technique is satisfactory for predicting the flow through turbomachine blades.