Influence of vane sweep on rotor-stator interaction noise.

Abstract

In this dissertation the influence of vane sweep on rotor-stator interaction noise is investigated. In an analytical approach, the interaction of a convected gust, representing the rotor viscous wake, with a cascade of finite span swept airfoils, representing the stator, is analyzed. The analysis is based on the solution of the exact linearized equations of motion. High-frequency convected gusts for which noise generation is concentrated near the leading edge of the airfoils are considered. In a preliminary study, the problem of an isolated finite span swept airfoil interacting with a convected gust is analyzed. Using Fourier transform methods and the Wiener-Hopf technique, an approximate solution for this problem is developed. Closed form expressions for the acoustic farfield are obtained and used in a parametric study to assess the effect of airfoil sweep on noise generation. Results indicate that sweep can substantially reduce the farfield noise levels for a single airfoil. Utilizing the single airfoil model, an approximate solution to the problem of noise radiation from a cascade of finite span swept airfoils interacting with a convected gust is derived. Only upstream radiated noise is considered. Neglecting the weak coupling between the adjacent leading edges at high frequencies, the cascade solution is constructed as a superposition of acoustic farfields emanating from an infinite number of isolated airfoils. A parametric study of noise generated by gust-cascade interaction is then carried out to assess the effectiveness of vane sweep in reducing rotor-stator interaction noise. The results of the parametric study show that, over a fairly wide range of conditions, sweep is beneficial in reducing noise levels. One conclusion of particular importance is that rotor wake twist or circumferential lean substantially influences the effectiveness of vane sweep. The orientation of the vane sweep must be chosen to enhance the natural phase lag caused by wake lean, in which case rather small sweep angles substantially reduce the noise levels.