Lifting Surface Theory of Axial Compressor Blade Rows: Part I-Subsonic Compressor

Abstract

The authors' three-dimensional, inviscid linearized lifting line theory of compressible flow past a lifting axial compressor rotor is developed into a lifting surface theory. A solution is constructed by distributing bound vortices of varying strength in the radial and chordwise directions over the surfaces of the rotor blades, and expressions are obtained for the induced velocities everywhere. The general solution shows features of axisymmetric throughflow actuator disk theory, in addition to describing the details of the flow dependent on the detailed blade loading and geometry. Attention is focused on the case where the relative Mach number is everywhere subsonic, and for this case, the quasi-two-dimensional approximation to the flow at each radial section is extracted from the general solution. The latter approximation is shown to consist of both the local flow due to an equivalent actuator disk and the local two-dimensional cascade flow at the section. Three-dimensional corrections to these approximations are then obtained, and are identified as being primarily due to the vortices concentrated in the blade wakes. Camber-line profiles corresponding to prescribed loading distributions are computed, and the influence of the wakes on these profiles demonstrated.