Unsteady Flow in the Far Field of an Isolated Blade Row

摘要

This report describes a theoretical investigation of the unsteady flow in the far field of an isolated two-dimensional blade row. In particular, analytic far-field solutions are derived for cascades operating at subsonic, transonic and supersonic inlet and exit Mach numbers. These solutions describe the velocity potential fluctuations associated with irrotational pressure (acoustic) disturbances, rotational velocity disturbances and the vorticity shed form blade trailing edges and convected along blade wakes. As such they provide the inlet and exit information needed for a successful numerical resolution of the unsteady flow through the cascade. As part of this investigation a convienent method for classifying unsteady excitations, based on the acoustic response in the far field, is provided. Also, analytical results are presented to illustrate subsonic and supersonic far-field acoustic response behavior and numerical solutions have been determined for subsonic compressor cascades to demonstrate partially the impact of unsteady far-field behavior on the aerodynamic response at a vibrating blade surface. Keywords: Cascades (Fluid dynamics); Unsteady velocity potential; Isolated two-dimensional blade row; Far field acoustic response; Vortical response; Subsonic transonic; Supersonic inlet/exit conditions.