F. G. Leppington

Noise Source Mechanisms

Each property of a fluid flow is a function of position x and time t. The density ρ is the mass per unit volume. The specific volume, or volume per unit mass, is ρ−1. The velocity at a point is the speed and direction at which the fluid particle currently at that point is moving. The Eulerian approach considers conditions at a fixed point x as time progresses. The Lagrangian approach considers a particular fluid particle which occupies successively different locations x, as time progresses. Rates of change in a Lagrangian frame are rates of change as seen by an observer moving with the fluid velocity. This rate of change is written D/Dt. Thus

Thermoacoustic Sources and Instabilities

Thermoacoustics deals with the acoustics of flows in which the variation of entropy plays a significant role. A range of processes are thermoacoustic sources. For example, unsteady combustion, diffusion of heat and mass and turbulent two-phase flows all generate sound. Chapters 11 and 12 demonstrate how the Lighthill theory provides a convenient description of sound generation. There we saw in Equation (11.46), for example, that the Navier-Stokes equation and the equation of mass conservation may be combined to give an inhomogeneous wave equation for the density fluctuations. When investigating thermoacoustic source processes it is convenient to use the pressure perturbation as the dependent variable.

Flow Noise on Surfaces

A turbulent boundary-layer flow over a surface generates noise, which is usually referred to as flow noise. This Chapter deals with the prediction and properties of the fluctuating surface pressures induced by flow noise and investigates their spectral characteristics. This problem is particularly important in underwater acoustics, where a passive sonar system on a ship or submarine aims to detect and analyze weak sounds emanating from a distant source. However, when the vessel is in motion, the unsteady pressures generated by its turbulent boundary layer can obscure the incoming signal. There are other applications where flow noise is important. For example, the turbulent boundary layer over fuselage is a significant source of high- frequency sound within an aircraft cabin. But in this Chapter we will concentrate on the underwater geometry.

Wiener-Hopf Technique

This is a method for solving certain linear partial-differential equations subject to mixed boundary conditions on semi-infinite geometries. Equivalently, it is applicable to integral equations of convolution type, such as The method hinges on the use of complex Fourier transforms and exploits their known analyticity properties.

Effects of Motion on Acoustic Sources

An acoustic source in motion radiates a different sound field from that produced when the source is stationary. One effect of source motion is to cause a Doppler shift in frequency. This is well known and often observed. For example, the whistle of an approaching train appears to be of higher frequency to a stationary listener than when the train recedes. Another effect of source motion is to change the amplitude of the acoustic field. These effects can be illustrated by considering a moving acoustic monopole which is at a position xs(t) at time t. The pressure perturbation satisfies

Matched Asymptotic Expansions Applied to Acoustics

Many problems in acoustics contain a small dimensionless parameter e, and it is useful, both conceptually and from the point of view of numerical computation, to seek a solution in the form of a perturbation series. In the simplest case the series would proceed by integral powers of e, where, in a typical application, φ might be an acoustic potential or pressure and e a frequency parameter, or Helmholtz number. In most cases, however, the problem of determining the functions φ i is a singular perturbation problem, that is, one in which no single series like the one quoted will be valid both in the near field (where boundary data are specified and where surface loading may be of interest) and in the far field (where the signal directivity and level are required). Separate series must be developed describing the near and far fields, but neither can be completely constructed independently of the other because each series lacks sufficient boundary data for its unique determination.

Fluid-Loading Interaction with Vibrating Surfaces

When an elastic structure in contact with a fluid vibrates, unsteady pressures are generated in the fluid and exert a surface loading on the structure additional to that which may be exerted by mechanical excitation or by the surface pressures of a boundary layer formed over a perfectly rigid structure. The additional loading is referred to as “fluid loading”; it is a highly nonlocal loading, not necessarily connected with fluid compressibility or bulk fluid motion, which is crucial in determining many aspects of most structural acoustics problems in one part of parameter space or another. When the fluid loading is important (which, as we shall see, it is for some aspects of the acoustic or vibration fields even when the fluid density is small compared with that of the structure material) one is faced with a fully-cowpltd problem, involving transverse waves (and occasionally longitudinal waves) on the structure and their nonlocal coupling to either incompressible pressure fluctuations or compression waves in the fluid. Recently there has been considerable success in analytical studies of these problems, leading to simple and explicit descriptions of the structural and acoustic fields and the identification of resonance and other significant conditions, even under conditions of “heavy” fluid loading. The basic point of these notes is to illustrate in the simplest problem the roles played by the five essential competing mechanisms for plane elastic plates under static fluid loading, to illustrate how the balances between them are different for different aspects of the system response and in different parameter ranges, and to give a general asymptotic method which provides a powerful approach to fluid-loaded structure problems.

Asymptotic Evaluation of Integrals

This Chapter concerns methods of estimating certain integrals that depend on a large (or small) parameter. The essential idea in each case is to compare the given integral with a simpler one that can be evaluated exactly yet approximates closely to the original. In the most elementary case the integrand can be expressed as a Taylor series in increasing powers of the small parameter; if the approximating series is a uniformly good approximation to the integrand (for all values of the dummy variable of integration) it can be integrated term by term.

Propeller and Helicopter Noise

Plans for aircraft powered by high-speed prop fans means that propeller noise can be expected to be an increasingly important aeroacoustic source. Both the near and far acoustic fields of propellers are of interest, with the near field influencing unsteady airframe loading and passenger comfort, and the far field determining the noise level near airports. The propeller is also a major source of noise for underwater vehicles.

Fourier Transforms, Random Processes, Digital Sampling and Wavelets

Consider ordinary functions f(t) of a real variable t, −∞ 0. Then the half-range Fourier transform