AN ANALYTICAL DESIGN METHOD FOR LINEARIZED FREE-VORTEX TYPE FLOW IN TURBOMACHINES

摘要

An analytical solution based on the velocity perturbation method and radial equilibrium theory is derived for a 3-D axisymmetric flow through constant-diameter turbomachines with a free-vortex type tangential velocity distribution. The linearized equation of motion for inviscid flow is solved by approximation using an asymptotic expansion method. The derived solution sufficiently describes the behavior of the axial and radial velocities upstream and downstream near a blade row as well as the far field velocities. A new design method based on this analysis is presented to enable the designer to compute the velocity field near a blade row without directly solving the 3-D Euler equations for axisymmetric flow. The results of this analytical method demonstrate a very good agreement with the well-established streamline curvature method which is frequently used in turbomachinery design and analysis.