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Aerodynamic Noise Generation – Reminder of Basic Principles
1.1 Introduction
Aerodynamic noise radiation from an unsteady flow is a dissipation mechanism by which a tiny part of the mechanical energy of the flow is converted into sound. The particularity of this acoustic dissipation in open-air aeroacoustic problems is that it propagates at large distances and contaminates the environment. Moreover the acoustic dissipation rate of aerodynamic noise is a very rapidly increasing function of the characteristic Mach number. Yet it is at a much lower order of magnitude than other forms of
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_2,
© CISM, Udine 2013
dissipation such as viscous losses. This makes the points of view of Fluid Dynamics and of Aeroacoustics differ. In absence of acoustic back-reaction, a flow can be most often described ignoring its acoustic dissipation, for what enters the scope of mechanical efficiency, losses, fuel consumption, and so on. In contrast describing the acoustic field requires a much higher level of accuracy. This remark holds for all unsteady flows encountered in aeronautics, turbomachinery, heating and ventilating engineering and ground transportation. More precisely the scope of this book reduces to the basic sound generating mechanisms which develop around bodies in translating motion because of some unsteadiness in the flow, provided by turbulence or instabilities.
As mentioned in chapter 1, the pioneering work of Sir M. J. Lighthill in the fifties (1952) addressing the problem of turbulence noise is generally considered the starting point for the investigation of aerodynamic noise. This work was next extended by Ffowcs Williams & Hawkings (1969) to include the presence of moving bodies in a flow. The basic idea is to define an acoustic analogy, by which the real problem involving a highly disturbed flow and moving solid surfaces is restated as a problem of linear acoustics in an unbounded uniform medium with some equivalent acoustic sources. The difficulty of solving exact, non-linear equations is then apparently avoided and replaced by the question of defining the equivalent sources. A crucial point is that there are different ways of deriving a wave equation from the equations of gas dynamics, leading to various analogies. Any analogy is based, first on the choice of the field variable the wave equation will govern, and secondly on the wave operator itself. Lighthill’s formulation and subsequent developments resort to the classical wave operator acting on the fluctuating density recognized as the relevant acoustic variable. Other choices can be proposed, each leading to a different definition of the equivalent source terms. Anyway, the difficulty inherent to the equations of gas dynamics cannot be escaped by just writing the equations in another way. The pseudo-wave equation of the acoustic analogy cannot be solved exactly because generally the equivalent source terms still include contributions of the field variable to be determined : the equation and the source terms are said implicit. Therefore the advantage of the formalism is enlightened only if simplifying assumptions are accepted, for instance making the source terms explicit by removing the acoustic field variable from them. This has the effect of discarding some part of the physics. The resulting approach is an interpretation. It is fruitful whenever the neglected phenomena are of secondary importance and the dominant mechanism is preserved in the process. Furthermore the degree of simplification of the source terms can also be a matter of available means of describing the flow. Finally different analogies are more suited in different practical problems, as already pointed in chapter 1. Because the interest of an acoustic analogy is to benefit from the formal simplicity of the standard Green’s function solving procedure, the classical wave equation was preferred historically. Ffowcs Williams & Hawkings’ formulation presented in this chapter and extensively applied in the aeroacoustic community obeys this strategy. But the idea of the analogy can be extended to more general propagation operators. Such extensions, more especially dealing with jet-noise applications, are described in subsequent chapters.
It must be stated clearly that the aim of an analogy is not essentially to provide very accurate results, but rather to infer general laws from the standard procedures associated with the classical wave equation. This may be sufficient to achieve low-noise design in engineering applications. However, a preliminary knowledge of the main flow features must be already available, either from experiments, Computational Fluid Dynamics (CFD) or theoretical considerations. What is the degree of required accuracy in the flow variables to get satisfactory acoustic results will be one of the key issues when applying the method. In other words tell me the flow I will tell you the sound.
