The Fluctuating Forces Appropriate for the Calculation of Discrete Frequency Noise Generation in Subsonic Turbo-Machines

Abstract

Discrete frequency noise generation at blade passage frequency and its harmonics is a result of the aerodynamic interaction between successive rotors and stators. These interactions result in fluctuating forces on the rotor and stator blades which are equivalent to dipole sources radiating sound. This paper describes the importance of including airfoil cascade parameters and compressibility, even at low Mach numbers, in calculations of these fluctuating forces. The results are based upon solutions to the unsteady, compressible, two-dimensional partial differential equation which describe the flow disturbances generated by upstream obstructions being convected downstream past an airfoil cascade. The parameters include the cascade stagger angle, cascade solidity, reduced frequency, and the ratio of the number of upstream obstructions to downstream airfoils. The results indicate that isolated airfoil aerodynamics does not adequately describe these fluctuating forces; incompressible cascade aerodynamics is not adequate in the neighborhood of the resonance Mach number, but may be adequate at Mach number values both higher and lower than the neighborhood of the resonance Mach number. The extent of the neighborhood of this aerodynamic resonance, wherein compressibility and cascade effects are important, is a function of the flow and cascade parameters.