Acoustic waves propagating through nonuniform flows are subject to convection and refraction. Most noise prediction schemes use a linear wave operator to capture these effects. However, the wave operator can also support instability waves that, for a jet, are the well-known Kelvin-Helmholtz instabilities. These are convective instabilities that can completely overwhelm the acoustic solution downstream of the source location. A general technique to filter out the instability waves is presented. A mathematical analysis is presented that demonstrates that the instabilities are suppressed if a time-harmonic response is assumed, and the governing equations are solved by a direct solver in the frequency domain. Also, a buffer-zone treatment for a nonreflecting boundary condition implementation in the frequency domain is developed. The outgoing waves are damped in the buffer zone simply by adding imaginary values of appropriate sign to the required real frequency of the response. An analytical solution to a one-dimensional model problem, as well as numerical and analytical solutions to a two-dimensional jet instability problem, are provided. They demonstrate the effectiveness, robustness, and simplicity of the present technique.

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Fan-wake/outlet-guide-vane interaction broadband noise in turbofan jet engines is studied. The mechanism and some issues are first discussed using a two-dimensional gust-prediction model. An oblique gust-prediction model is then developed. Quasi-three-dimensional unsteady lift is calculated using a two-dimensional equivalence method. It is coupled with annular duct modes to obtain the sound power spectrum density. Spanwise turbulence integral length scales and their impact on power spectrum density predictions are investigated. A spanwise integration limit suitable for the complete frequency range is proposed. The model is validated using the NASA Source Diagnostic Test data. Sound power scaling with vane count B is examined. If solidity is maintained, the cascade response does not converge on the single-airfoil response, even for low vane counts. The sound power varies inversely with B at low frequency; it scales with B at very high frequency. The power spectrum density trend with the fan tip Mach number M T is also identified. It scales with M 5 T if turbulence intensity in the fan wake scales "ideally" with M T. At offdesign conditions, fan wakes are not ideal; therefore, different speed trends apply. M 3.3 T scaling is found to best fit the Source Diagnostic Test data and the prediction.

An analysis is presented which treats the noise generation from an axial flow fan row by given forces including the effects of a moving medium. The linearization of Euler’s equations to yield tractable problems for fan noise is discussed. The three-dimensional problem is decomposed into several two-dimensional problems. Finally, full details are given of a two-dimensional analysis to predict the amounts of acoustic energy, at the blade passing frequency and its harmonics, radiated up and downstream of a blade row due to its interaction with a neighboring row.

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