Noise Sources in Turbulent Shear Flows: Fundamentals and Applications

After a review of basic equations of fluid dynamics, the Aeroacoustic analogy of Lighthill is derived. This analogy describes the sound field generated by a complex flow from the point of view of a listener immerged in a uniform stagnant fluid. The concept of monopole, dipole and quadrupole are introduced. The scaling of the sound power generated by a subsonic free jet is explained, providing an example of the use of the integral formulation of the analogy. The influence of the Doppler Effect on the radiation of sound by a moving source is explained. By considering the noise generated by a free jet in a bubbly liquid, we illustrate the importance of the choice of the aeroacoustic variable in an aeroacoustic analogy. This provides some insight into the usefulness of alternative formulations, such as the Vortex Sound Theory. The energy corrolary of Howe based on the Vortex Sound Theory appears to be the most suitable theory to understand various aspects of self-sustained oscillation due to the coupling of vortex shedding with acoustic standing waves in a resonator. This approach is used to analyse the convective energy losses at an open pipe termination, human whistling, flow instabilities in diffusers, pulsations in pipe systems with deep closed side branches and the whistling of corrugated pipes.

The present chapter is dealing with some fundamentals of sound radiation from rigid moving bodies or bodies in a flow. The theoretical background of the analogy is reminded in a first part. According to Ffowcs Williams & Hawkings’ formulation the problem of sound generation by unsteady flows in the presence of solid surfaces is restated as a problem of linear acoustics with equivalent moving sources. Therefore the solving procedure is based on standard Green’s function technique. This procedure is detailed in the second part as a necessary background and source motion is considered a key feature of the radiation. Aspects inherent to the wave operator and specific aspects of acoustic sources on the one hand, and source physics and source motion on the other hand, are addressed separately for the sake of physical understanding. In the third part formal developments and dimensional analysis of Ffowcs Williams & Hawkings’ equation are proposed, both to highlight the flow features involved in sound generation and to point out the effects of motion. Some introductory topics have been presented in chapter 1 and are re-addressed for specific purposes.

This chapter provides an overview of the present understanding of jet noise from both an experimental and analytical viewpoint. First, a general review of experimental observations is provided. Only single axisymmetric jets are considered. Then a historical review of theoretical contributions to jet noise understanding and prediction is provided. The emphasis is on both the assumptions and shortcomings of the approaches, in addition to their successes. The present understanding of jet noise generation mechanisms and noise predictions is then presented. It is shown that there remain two competing explanations of many observed phenomena. The ability of the different approaches to predict jet noise is assessed. Both subsonic and supersonic jets are considered. Finally, recent prediction methods and experimental observations are described.

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-à-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.

The chapter is dedicated to the noise radiated by thin airfoils in either disturbed or homogeneous flows. This includes noise produced by impingement of upstream turbulence onto a leading edge, self-noise caused by boundary-layer turbulence scattering at the trailing edge and noise due to the formation of a vortex street in the near wake. Analytical modeling is proposed in the frequency domain, based on linearized theories of unsteady aerodynamics. The same mathematical background referred to as Schwarzschild’s technique is used for all mechanisms in order that the predicted trends can be compared. In a first step the analysis is focused on the derivation of the induced lift fluctuations, acting as the sources of sound according to Ffowcs Williams & Hawkings’ analogy. The radiation properties of isolated aerodynamic wave-numbers in the sources are discussed in a second step. Next a statistical declination of the formalism is introduced, relating the source statistics to the PSD of the acoustic pressure in the far field. Finally the statistical models are assessed against experimental data.

Boundary layer noise concerns the generation of acoustic waves as an effect of the interaction of a fluid with a moving surface. Several issues are related to the noise generation mechanisms in such a configuration. In the present description we focalize mainly onto the case of an infinite flat plate and two main distinct situations are considered. The first one deals with the prediction of the far field noise as accomplished from the classical integral theories, and the main formulations, including Curle’s approach, are briefly reviewed. A novel approach based on the computation of the surface transpiration velocity is also presented. The second aspect concerns the interior noise problem and it is treated from the view point of the fluid dynamic effects rather than from that of the structural dynamics. Attention is focused on the statistical properties of the wall pressure fluctuations and a review of the most effective theoretical models predicting statistical quantities is given. The discussion is completed by a short review of the pressure behavior in realistic situations, including the separated boundary layers in incompressible and compressible conditions and the effect of shock waves at transonic Mach numbers.

This chapter is focused on the interior noise caused by a Turbulent Boundary Layer (TBL) relative fluid flow over the flexible thin walls of an enclosure. This is a typical interior noise problem encountered in surface and air passenger transportation vehicles. When such vehicles travel at high speed, the airflow around the skin develops into a TBL. This phenomenon produces large pressure fluctuations that effectively excite the skin panels of the vehicle, which, in turn, radiate noise into the interior.

The formulation for the coupled structural–acoustic response to a TBL pressure field is first introduced for a general model problem given by a cylindrical cavity bounded by a thin flexible wall, which is immerged in a convected fluid that has developed a TBL. Structural vibration and sound radiation effects are expressed in terms of the Power Spectral Densities (PSD) of the wall flexural kinetic energy and cavity acoustic potential energy.

A reduced model problem is then analysed in detail by examining a small section of the enclosure flexible wall and assuming a heavily damped interior. In this case a simplified model is used, which considers a rigidly baffled flat panel with unbounded fluid domains on the two sides. The panel is excited on the exterior side by the pressure field generated by a TBL fluid flow and radiates sound on the interior side. To facilitate the analysis, the PSDs of the panel flexural kinetic energy and interior sound power radiation produced by the TBL pressure field are contrasted with those produced by harmonic acoustic plane waves, by a stochastic acoustic diffuse field and by the so called “rain on the roof” stochastic excitation.

The chapter is then completed with two sections illustrating the principal effects produced by mass, stiffness and damping passive treatments and structural–acoustic active systems on the panel. The first active system consists of an array of decentralised feedback loops with point sensor and actuator transducers while the second active system is composed by a single channel feedback loop with distributed sensor and actuator transducers.