Acoustic analogy in swirling mean flow applied to predict rotor trailing-edge noise

The present study aims at accounting for swirling mean flow effects on rotor trailing-edge noise. Indeed, the mean flow in between the rotor and the stator of the fan or of a compressor stage is highly swirling. The extension of Ffowcs-Williams & Hawkings' acoustic analogy in a medium at rest with moving surfaces and of Goldstein's acoustic analogy in a circular duct with uniform mean flow to a swirling mean flow in an annular duct is introduced. It is first applied to tonal noise. In most cases, the swirl modifies the pressure distribution downstream of the fan. In several configurations, when the swirl is rather close to a solid body swirl, it is often sufficient to apply a simple Doppler effect correction when predicting the duct modes in uniform mean flow in order to predict accurately the noise radiated with swirl. However, in other realistic configurations, the swirling mean-flow effect cannot be addressed using this simple Doppler effect correction. Second, a rotor trailing-edge noise model accounting for both the effects of the annular duct and the swirling mean flow is developed and applied to a realistic fan rotor with different swirling and sheared 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 an effect. In some cases the a simple Doppler effect may address it, but, in other realistic configurations our acoustic analogy with swirl is needed. © 2012 by the authors. Published by the American Institute of Aeronautics and Astronautics, Inc.

A single FBAR-based temperature and pressure sensors

A novel temperature and pressure sensor based on a single film bulk acoustic resonator (FBAR) is designed. This FBAR support two resonant modes, which response opposite to the change of temperature. By sealed the back cavity of a back-trench membrane type FBAR with silicon wafer, an on-chip single FBAR sensor suitable for measuring temperature and pressure simultaneously is proposed. For unsealed device, the experimental results show that the first resonant mode has a temperature coefficient of frequency (TCF) of 69.5ppm/K, and the TCF of the second mode is -8.1ppm/K. After sealed the back trench, it can be used as a pressure sensor, the pressure coefficient of frequency (PCF) for the two resonant mode is -17.4ppm/kPa and -6.1 ppm/kPa respectively, both of them being more sensitive than other existing pressure sensors. © 2013 Trans Tech Publications Ltd, Switzerland.

The acoustic analogy in an annular duct with swirling mean flow

This paper is concerned with modelling the effects of swirling flow on turbomachinery noise. We develop an acoustic analogy to predict sound generation in a swirling and sheared base flow in an annular duct, including the presence of moving solid surfaces to account for blade rows. In so doing we have extended a number of classical earlier results, including Ffowcs Williams & Hawkings' equation in a medium at rest with moving surfaces, and Lilley's equation for a sheared but non-swirling jet. By rearranging the Navier-Stokes equations we find a single equation, in the form of a sixth-order differential operator acting on the fluctuating pressure field on the left-hand side and a series of volume and surface source terms on the right-hand side; the form of these source terms depends strongly on the presence of swirl and radial shear. The integral form of this equation is then derived, using the Green's function tailored to the base flow in the (rigid) duct. As is often the case in duct acoustics, it is then convenient to move into temporal, axial and azimuthal Fourier space, where the Green's function is computed numerically. This formulation can then be applied to a number of turbomachinery noise sources. For definiteness here we consider the noise produced downstream when a steady distortion flow is incident on the fan from upstream, and compare our results with those obtained using a simplistic but commonly used Doppler correction method. We show that in all but the simplest case the full inclusion of swirl within an acoustic analogy, as described in this paper, is required. © 2013 Cambridge University Press.

Comparison of acoustic velocity perturbation measurements using PIV vs. two-microphone technique

Understanding combustion instabilities requires accurate measurements of the acoustic velocity perturbation into injectors. This is often accomplished via the use of the two microphone technique, as this only requires two pressure transducers. However, measurements of the actual velocities emerging from the injectors are not often taken, leaving questions regarding the assumptions about the acoustic velocity. A comparison of velocity measured at downstream of the injector with that of two-microphone technique can show the accuracy and limitations of two-microphone technique. In this paper, velocity measurements are taken using both particle image velocimetry (PIV) and the two-microphone technique in a high pressure facility designed for aeroengine injector measurements. The flow is excited using an area modulation device installed on the choked end of the combustion chamber, with PIV measurements enabled by optical access downstream of the injector through a quartz tube and windows. Acoustic velocity perturbations at the injector are determined by considering the Fourier transformed pressure fluctuations for two microphones installed at a known distance upstream of the injector. PIV measurements are realized by seeding the air flow with micrometric water particles under 2.5 bar pressure at ambient temperature. Phase locked velocity fields are realized by synchronizing the acquisition of PIV images with the revolution of the acoustic modulator using the pressure signal measured at the face of injector. The mean velocity fluctuation is calculated as the difference between maximum and minimum velocities, normalized by the mean velocity of the unforced case. Those values are compared with the peak-to-peak velocity fluctuation amplitude calculated by the two-microphone technique. Although the ranges of velocity fluctuations for both techniques are similar, the variation of fluctuation with forcing frequencies diverges significantly with frequency. The differences can be attributed to several limitations associated with of both techniques, such as the quality of the signal, the signal/noise ratio, the accuracy of PIV measurements and the assumption of isentropic flow of the particle velocity from the plenum through the injector. We conclude that two-microphone methods can be used as a reference value for the velocity fluctuation in low order applications such as flame transfer functions, but not for drawing conclusions regarding the absolute velocity fluctuations in the injector. Copyright © 2013 by ASME.