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.

Factorial comparison of working memory models.

Three questions have been prominent in the study of visual working memory limitations: (a) What is the nature of mnemonic precision (e.g., quantized or continuous)? (b) How many items are remembered? (c) To what extent do spatial binding errors account for working memory failures? Modeling studies have typically focused on comparing possible answers to a single one of these questions, even though the result of such a comparison might depend on the assumed answers to both others. Here, we consider every possible combination of previously proposed answers to the individual questions. Each model is then a point in a 3-factor model space containing a total of 32 models, of which only 6 have been tested previously. We compare all models on data from 10 delayed-estimation experiments from 6 laboratories (for a total of 164 subjects and 131,452 trials). Consistently across experiments, we find that (a) mnemonic precision is not quantized but continuous and not equal but variable across items and trials; (b) the number of remembered items is likely to be variable across trials, with a mean of 6.4 in the best model (median across subjects); (c) spatial binding errors occur but explain only a small fraction of responses (16.5% at set size 8 in the best model). We find strong evidence against all 6 documented models. Our results demonstrate the value of factorial model comparison in working memory.

Wave propagation in a slowly-varying duct with mean vortical swirling flow

The propagation of unsteady disturbances in a slowlyvarying cylindrical duct carrying mean swirling flow is investigated using a multiple-scales technique. This is applicable to turbomachinery flow behind a rotor stage when the swirl and axial velocities are of the same order. The presence of mean vorticity couples acoustic and vorticity equations which produces an eigenvalue problem that is not self-adjoint unlike that for irrotational mean flow. In order to determine the amplitude variation along the duct, an adjoint solution for the coupled system of equations is derived. The solution breaks down where a mode changes from cut on to cut off. In this region the amplitude is governed by a form of Airy's equation, and the effect of swirl is to introduce a small shift in the origin of the Airy function away from the turning-point location. The variation of axial wavenumber and amplitude along the duct is calculated. In hard-walled ducts mean swirl is shown to produce much larger amplitude variation along the duct compared with a nonswirling flow. Mean swirl also has a large effect in ducts with finite-impedance walls which differs depending on whether modes are co-rotating with the swirl or counter rotating. © 2001 by A.J. Cooper, Published by the American Institute of Aeronautics and Astronautics, Inc.

A derivation of the asymptotic random-coding prefactor

This paper studies the subexponential prefactor to the random-coding bound for a given rate. Using a refinement of Gallager's bounding techniques, an alternative proof of a recent result by Altuǧ and Wagner is given, and the result is extended to the setting of mismatched decoding. © 2013 IEEE.