Reprint of: Flow filtering and the physical sources of aerodynamic sound

The physical sources of sound are expressed in terms of the non-radiating part of the flow. The non-radiating part of the flow can be obtained from convolution filtering, as we demonstrate numerically by using an axi-symmetric jet satisfying the Navier-Stokes equations. Based on the frequency spectrum of the source, we show that the sound sources exhibit more physical behaviour than sound sources based on acoustic analogies. To validate the sources of sound, one needs to let them radiate within the non-radiating flow field. However, our results suggest that the traditional Euler operator linearized about the time-averaged part of the flow should be sufficient to compute the sound field. © 2010 Published by Elsevier Ltd.

Finite element solution of Navier Stokes equations adapted to a priori error estimates

The paper is based on qualitative properties of the solution of the Navier-Stokes equations for incompressible fluid, and on properties of their finite element solution. In problems with corner-like singularities (e.g. on the well-known L-shaped domain) usually some adaptive strategy is used. In this paper we present an alternative approach. For flow problems on domains with corner singularities we use the a priori error estimates and asymptotic expansion of the solution to derive an algorithm for refining the mesh near the corner. It gives very precise solution in a cheap way. We present some numerical results.

Long range exhaustion-a mathematical model for the axisymmetric air flow of a local exhaust ventilation hood assisted by a turbulent radial jet

Abstract-Mathematical modelling techniques are used to predict the axisymmetric air flow pattern developed by a state-of-the-art Banged exhaust hood which is reinforced by a turbulent radial jet flow. The high Reynolds number modelling techniques adopted allow the complexity of determining the hood's air Bow to be reduced and provide a means of identifying and assessing the various parameters that control the air Bow. The mathematical model is formulated in terms of the Stokes steam function, ψ, and the governing equations of fluid motion are solved using finite-difference techniques. The injection flow of the exhaust hood is modelled as a turbulent radial jet and the entrained Bow is assumed to be an inviscid potential flow. Comparisons made between contours of constant air speed and centre-line air speeds deduced from the model and all the available experimental data show good agreement over a wide range of typical operating conditions. | Mathematical modelling techniques are used to predict the axisymmetric air flow pattern developed by a state-of-the-art flanged exhaust hood which is reinforced by a turbulent radial jet flow. The high Reynolds number modelling techniques adopted allow the complexity of determining the hood's air flow to be reduced and provide a means of identifying and assessing the various parameters that control the air flow. The mathematical model is formulated in terms of the Stokes steam function, Ψ, and the governing equations of fluid motion are solved using finite-difference techniques. The injection flow of the exhaust hood is modelled as a turbulent radial jet and the entrained flow is assumed to be an inviscid potential flow. Comparisons made between contours of constant air speed and centre-line air speeds deduced from the model and all the available experimental data show good agreement over a wide range of typical operating conditions.

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.