Analysis techniques for aeroacoustics:. noise source identification

P. Jordan

Institut Pprime, UPR-CNRS-3346,
Universite de Poitiers, ENSMA, France

1 Introduction

Aeroacoustic analysis is concerned with the problem of sound source mech­anism identification. Let us consider for a moment what we mean by this, because, depending on the context, the same terminology can be interpreted differently. Two different contexts for the analysis of an aeroacoustic sys­tem, or indeed a fluid flow system in general, are: (1) the kinematic context; and, (2) the dynamic context.

When we are interested in kinematics, we are concerned with description of the space-time structure of a fluid flow, and perhaps with phenomeno­logical explanations vis-a-vis our observation of that structure: this vortical structure interacted with that one to produce this or that result. Such kine­matic descriptions will very often be with regard to some observable; in aeroacoustics that observable is the radiated sound field: this vortical struc­ture interacted with that one to produce this or that property of the sound field.

Aeroacoustic theory was constructed from such a kinematic standpoint. Lighthill (1952) states on the second page of his seminal paper that he wishes to provide “…a general procedure for estimating the intensity of the sound produced in terms of the details of the fluid flow…”. He makes it clear that the search for sound source mechanisms, as he intends it, “is concerned with uncovering the mechanism of conversion of energy between…the kinetic energy of fluctuating shearing motions and the acoustic energy of fluctuating longitudinal motions.”. The “details of the fluid flow”, the “fluctuating shearing motions”, are considered as given.

However, if we are to consider more broadly the problem of source mech­anism identification, we realise that, in order to be able to speak clearly about source mechanisms we need to be able to speak clearly about fluid

R. Camussi (Ed.), Noise Sources in Turbulent Shear Flows: Fundamentals and Applications, CISM International Centre for Mechanical Sciences, DOI 10.1007/978-3-7091-1458-2_4,

© CISM, Udine 2013

dynamics mechanisms, and it is difficult to do so without placing ourselves in the context of dynamics: we would like to be able to explain why this vortical structure interacted with that one to produce this or that property of the sound field; i. e. we wish to discern the dynamic law that underpins the observed interactions, where sound production is concerned. Of course there is one very simple, correct, but not terribly useful, reply to such an inquiry: the Navier-Stokes equations constitute the underlying dynamic law, both of the “fluctuating shearing motions” of the turbulence and the “fluctuating longitudinal motions” of the sound field. But for high Reynolds number turbulence this law, and the space-time flow structure that it engenders, are—from the point of view of perspicacious phenomenological description, flow-state prediction, or design guidance—invariably too complex to be use­ful; we are thus forced to seek simplified models.

Lighthill (1952) provided us with a tool that allows the “fluctuating longitudinal motions” of the sound field to be modelled more simply, and then connected to the “fluctuating shearing motions” of the turbulence; but the same tool does not provide an analogous clarification with regard to how the latter should be modelled. His theory and its descendants are probably best thought of as means by which the connection between the two kinds of motion can be modelled; and by virtue of this connection-model, some insight can be provided regarding the kinematic structure of the underlying flow motions. However, these theories cannot inform with regard to the dynamic law of the “fluctuating shearing motions” that underpin sound radiation.

These lectures are concerned with the exposition of an analysis method­ology which, while it uses aeroacoustic theory as a central tool, attempts to take the problem of source mechanism identification beyond the kine­matic limits imposed by that theory. The methodology, whose objective is source mechanism identification on both kinematic and dynamic levels (implicit is assumption is that the Navier-Stokes dynamics can be mod­elled in a simplified manner, that simplification being specifically tailored with respect to the acoustic observable), is largely an exercise in system re­duction, and relies both on theoretical considerations and signal-processing tools. The document has therefore been organised as follows. In the next section, §2, an overview of aeroacoustic theory is provided; we focus on the earliest (Lighthill (1952)) and most recent theoretical developments (Gold­stein (2003), Goldstein (2005), Sinayoko et al. (2011)). This is followed by a discussion, in section §3, of the source modelling problem, the bulk of the attention being focused on ‘coherent structures’. It is in this section that the analysis methodology evoked above is outlined. Example implementa­tions of the methodology are presented in section §4, where two specific case studies are considered. The various signal processing tools used to support the analysis methodology, and which are implemented in section §4 without detailed explanation, form the basis of section §5. Finally, a brief outline of two reduced-order dynamical modelling approaches is given in section §6.

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