Swirling mean flow effect on fan-trailing edge broadband noise in a lined annular duct

The present study aims at investigating the effect of a swirling mean flow and a lined annular duct on rotor trailing-edge noise. The objectives are to investigate these effects on the eigenvalues and a tailored Green's function on one hand and on the realistic case of the fan trailing-edge noise on the other hand. Indeed, the mean flow in between the rotor and the stator of the fan is highly swirling. Moreover, interstage liners are used to reduce the noise produced by the fan stage. The extension of Ffowcs-Williams & Hawkings' acoustic analogy in a medium at rest with moving surfaces, of Goldstein's acoustic analogy in a hardwall circular duct with uniform mean flow and of Rienstra & Tester's Green's function in an annular lined duct with uniform mean flow to a swirling mean flow in an annular duct with liner is introduced. First, the eigenvalues and the Green's function are investigated showing a strong effect of the swirl and of the liner. Second, a rotor trailing-edge noise model accounting for both the effects of the annular duct with lined walls and the swirling mean flow is developed and applied to a realistic fan rotor with different swirling mean flows (and as a result different associated blade stagger angles). The benchmark cases are built from the Boeing 18-inch Fan Rig Broadband Noise Test. In all cases the swirling mean flow has a strong effect on the absolute noise level. The overall liner insertion loss is little changed by the swirl in the studied cases.

A general mass law for broadband energy harvesting

It is well known that the power absorbed by a linear oscillator when excited by white noise base acceleration depends only on the mass of the oscillator and the spectral density of the base motion. This places an upper bound on the energy that can be harvested from a linear oscillator under broadband excitation, regardless of the stiffness of the system or the damping factor. It is shown here that the same result applies to any multi-degree-of-freedom nonlinear system that is subjected to white noise base acceleration: for a given spectral density of base motion the total power absorbed is proportional to the total mass of the system. The only restriction to this result is that the internal forces are assumed to be a function of the instantaneous value of the state vector. The result is derived analytically by several different approaches, and numerical results are presented for an example two-degree-of-freedom-system with various combinations of linear and nonlinear damping and stiffness. © 2013 The Author.