If a solid-body contour (Figure 2.1) has a sharp corner forming a convex angle γ < π, then an incompressible fluid flow around it cannot be unseparated. It is well known that for unseparated flow over a convex corner an unrealistic situation arises, when the speed of fluid elements increases without limit as the corner is approached. According to potential-flow theory, the speed is proportional to r−α, where α = (π − γ)/(2π − γ), and r is the distance to the corner O. The pressure decreases as the point O is approached and, according to Bernoulli's law, must become negative in some vicinity of the point.

The physical reason for flow separation from a corner is the viscosity of the medium. If the flow around the corner remained unseparated, then the fluid acceleration ahead of the point O would be accompanied by a deceleration downstream of that point. The boundary layer next to the wall immediately behind the corner would then be subjected to an infinitely large adverse pressure gradient, which would lead to flow separation. There can be an exception in the case of slight surface bending, when the adverse pressure gradient proves to be insufficient for boundary-layer separation. This case will be considered in Section 3, devoted to determining the conditions for the onset of separation. As will be shown, the unseparated state of the flow near the corner is maintained up to angles π − γ = O(Re−1/4). A further increase of the surface bending angle π − γ leads to boundary-layer separation.

To determine the sound produced by turbulence near an elastic boundary, it is necessary to know the response of the boundary to the turbulence stresses. These stresses not only generate sound but also excite structural vibrations that can store a significant amount of flow energy. The vibrations are ultimately dissipated by frictional forces, but they can contribute substantially to the radiated noise because elastic waves are “scattered” at structural discontinuities, and some of their energy is transformed into sound. Thus, flow-generated sound reaches the far field via two paths: directly from the turbulence sources and indirectly from possibly remote locations where the scattering occurs. The result is that the effective acoustic efficiency of the flow can be very much larger than for a geometrically similar rigid surface, even when only a small fraction of the structural energy is scattered into sound. Typical examples include the cabin noise produced by turbulent flow over an aircraft fuselage and the noise radiated from ship and submarine hulls, from duct flows, piping systems, and turbomachines [26]. Interactions of this kind are discussed in this chapter.

Sources Near an Elastic Plate

The simplest flexible boundary is the homogeneous, nominally flat, thin elastic plate, which supports structural modes in the form of bending waves. The effects of fluid loading are usually important in liquids, where the Mach number M is small, and in this section, it will be assumed that M ≪ 1 and, therefore, that mean flow has a negligible effect on the propagation of sound and plate vibrations.

Aerodynamic Sound

The sound generated by vorticity in an unbounded fluid is called aerodynamic sound [60, 61]. Most unsteady flows of technological interest are of high Reynolds number and turbulent, and the acoustic radiation is a very small by-product of the motion. The turbulence is usually produced by fluid motion relative to solid boundaries or by the instability of free shear layers separating a high-speed flow (such as a jet) from a stationary environment. In this chapter the influence of boundaries on the production of sound as opposed to the production of vorticity will be ignored. The aerodynamic sound problem then reduces to the study of mechanisms that convert kinetic energy of rotational motions into acoustic waves involving longitudinal vibrations of fluid particles. There are two principal source types in free vortical flows: a quadrupole, whose strength is determined by the unsteady Reynolds stress, and a dipole, which is important when mean mass density variations occur within the source region.

Lighthill's Acoustic Analogy

The theory of aerodynamic sound was developed by Lighthill [60], who reformulated the Navier–Stokes equation into an exact, inhomogeneous wave equation whose source terms are important only within the turbulent (vortical) region. Sound is expected to be such a very small component of the whole motion that, once generated, its back-reaction on the main flow is usually negligible. In a first approximation the motion in the source region may then be determined by neglecting the production and propagation of the sound.

Influence of Rigid Boundaries on the Generation of Aerodynamic Sound

The Ffowcs Williams–Hawkings equation (2.2.3) enables aerodynamic sound to be represented as the sum of the sound produced by the aerodynamic sources in unbounded flow together with contributions from monopole and dipole sources distributed on boundaries. For turbulent flow near a fixed rigid surface, the direct sound from the quadrupoles Tij is augmented by radiation from surface dipoles whose strength is the force per unit surface area exerted on the fluid. If the surface is in accelerated motion, there are additional dipoles and quadrupoles, and neighboring surfaces in relative motion also experience “potential flow” interactions that generate sound. At low Mach numbers, M, the acoustic efficiency of the surface dipoles exceeds the efficiency of the volume quadrupoles by a large factor ∼O(1/M2) (Sections 1.8 and 2.1). Thus, the presence of solid surfaces within low Mach number turbulence can lead to substantial increases in aerodynamic sound levels. Many of these interactions are amenable to precise analytical modeling and will occupy much of the discussion in this chapter.

Acoustically Compact Bodies [70]

Consider the production of sound by turbulence near a compact, stationary rigid body. Let the fluid have uniform mean density p0 and sound speed c0, and assume the Mach number is sufficiently small that convection of the sound by the flow may be neglected. This particular situation arises frequently in applications. In particular, M rarely exceeds about 0.01 in water, and sound generation by turbulence is usually negligible except where the flow interacts with a solid boundary [111].

Jets and shear layers are frequently responsible for the generation of intense acoustic tones. Instability of the mean flow over of a wall cavity excites “self-sustained” resonant cavity modes or periodic “hydrodynamic” oscillations, which are maintained by the steady extraction of energy from the flow. Whistles and musical instruments such as the flute and organ pipe are driven by unstable air jets, and shear layer instabilities are responsible for tonal resonances excited in wind tunnels, branched ducting systems, and in exposed openings on ships and aircraft and other high-speed vehicles. These mechanisms are examined in this chapter, starting with very high Reynolds number flows, where a shear layer can be approximated by a vortex sheet. We shall also discuss resonances where thermal processes play a fundamental role, such as in the Rijke tube and pulsed combustor. The problems to be investigated are generally too complicated to be treated analytically with full generality, but much insight can be gained from exact treatments of linearized models and by approximate nonlinear analyses based on simplified, yet plausible representations of the flow.

Linear Theory of Wall Aperture and Cavity Resonances

Stability of Flow Over a Circular Wall Aperture

The sound produced by nominally steady, high Reynolds number flow over an opening in a thin wall is the simplest possible system to treat analytically. Our approach is applicable to all linearly excited systems involving an unstable shear layer, and it is an extension of the method used in Section 5.3.6 to determine the conductivity of a circular aperture in a mean grazing flow.

Fluid motion in the immediate vicinity of a solid surface is usually controlled by viscous stresses that cause an adjustment in the velocity to comply with the no-slip condition and by thermal gradients that similarly bring the temperatures of the solid and fluid to equality at the surface. At high Reynolds numbers, these adjustments occur across boundary layers whose thicknesses are much smaller than the other governing length scales of the motion. We have seen how the forced production of vorticity in boundary layers during convection of a “gust” past the edge of an airfoil can be modeled by application of the Kutta condition (Section 3.3). In this chapter, similar problems are discussed involving the generation of vorticity by sound impinging on both smooth surfaces and surfaces with sharp edges in the presence of flow. The aerodynamic sound generated by this vorticity augments the sound diffracted in the usual way by the surface. However, the near field kinetic energy of the vorticity is frequently derived wholly from the incident sound, so that unless the subsequent vortex motion is unstably coupled to the mean flow (acquiring additional kinetic energy from the mean stream as it evolves) there will usually be an overall decrease in the acoustic energy: The sound will be damped. General problems of this kind, including the influence of surface vibrations, are the subject of this chapter. We start with the simplest case of sound impinging on a plane wall.

Damping of Sound at a Smooth Wall

Dissipation in the Absence of Flow

The thermo-viscous attenuation of sound is greatly increased in the neighborhood of a solid boundary where temperature and velocity gradients are large.

This book deals with that branch of fluid mechanics concerned with the production and absorption of sound occuring when unsteady flow interacts with solid bodies. Problems of this kind are commonly known under the heading of aerodynamic sound but often include more conventional areas of acoustics and structural vibration. Acoustics is here regarded as a branch of fluid mechanics, and an attempt has therefore been made in Chapter 1 to provide the necessary background material in this subject. Elementary concepts of classical acoustics and structural vibrations are also reviewed in this chapter. Constraints of space and time have required the omission or the curtailed discussion of several important subareas of the acoustics of fluid-structure interactions, including in particular many problems involving supersonic flow. The book should be of value in one or more of the following ways: (i) as a reference for analytical methods for modeling acoustic problems; (ii) as a repository of known results and methods in the theory of aerodynamic sound and vibration, which have tended to become scattered throughout many journal and review articles over the past forty or so years; and (iii) as a graduate level textbook. Chapter 1 and selected topics from Chapters 2 and 3 have been used for several years in teaching an advanced graduate level course on the theory of acoustics and aerodynamic sound.

Theoretical concepts are illustrated and sometimes extended by numerous examples, many of which include complete worked solutions. Every effort has been made to ensure the accuracy of formulae, both in the main text and in the examples. The author would welcome notification of errors detected by the reader and more general suggestions for improvements.

Scientific instruments carried aboard spacecraft often have to be equipped with mechanisms to operate shutters, protective covers, filter wheels, aperture changers and devices that focus, scan and calibrate, just as spacecraft themselves may have to be equipped with mechanisms such as deployable booms, reaction wheels and gas valves for manœuvrability, and driven shafts to steer antennae and solar arrays. This chapter focusses on the design principles of the former, treating them as a special branch of mechanical engineering, although somewhat paradoxically the system designer's first duty is to avoid the use of mechanisms wherever possible to reduce complexity and the risk of end–of–life failure.

We define a mechanism as a ‘system of mutually adapted parts working together’. It may provide useful relative movement, as for a focussing device in a photographic instrument. In the absence of a human operator, it may include a drive motor to overcome friction, or perhaps to perform controlled amounts of useful work. For example, the instrument might be a rock sample drill on a planetary lander. High powered machines such as rocket–engine turbopumps are not considered. The development of robotics (Yoshikawa, [1990]) for manufacturing industry has been widespread in an era in which the remotely directed manipulator arm has been useful in space.

The electronics are usually digital, and have been largely dealt with in Chapter 4 already. (In a functioning space mechanism they can be so well integrated that the combined system is described by some authors as ‘mechatronics’.)

For spacecraft and their instruments, the engineering disciplines of mechanical and structural design work together, and both are founded on the study of the mechanics of materials. We create designs, then prove (by calculation and test) that they will work in the environments of rocket launch and flight. Mechanisms, by definition having relatively–moving parts, are not the whole of mechanical design; they are interesting enough to get a later chapter of this book (Chapter 5) to themselves. But any mechanism is itself a structure of some kind, since it sustains loads. We therefore define structures, which are more general than mechanisms, as ‘assemblies of materials which sustain loads’. All structures, whether blocks, boxes, beams, shells, frames or trusses of struts are thereby included.

Mechanical design should begin by considering the forces which load the structural parts. The twin objectives are to create a structure which is (i) strong enough not to collapse or break, and (ii) stiffly resistant against deforming too far. The importance of stiffness as a design goal will recur in this chapter. Forces may be static, or dynamic; if dynamic, changing slowly (quasi–static) or rapidly, as when due to vibration and shock. The dynamic forces are dominant in rocket flight, and vibrations are a harsh aspect both of the launch environment and of environmental testing, generating often large dynamic forces. To analyse each mechanical assembly as a structure, we shall need the concept of inertia force to represent the reaction to dynamic acceleration.

The challenge of space

The dawn of the space age in 1957 was as historic in world terms as the discovery of the Americas, the voyage of the Beagle or the first flight by the Wright brothers. Indeed, the space age contains elements of each of these events. It is an age of exploration of new places, an opportunity to acquire new knowledge and ideas and the start of a technological revolution whose future benefits can only be guessed at. For these reasons, and others, space travel has captured the public's imagination.

Unfortunately, access to the space environment is not cheap either in terms of money or in fractions of the working life of an engineer or scientist. The design of space instruments should therefore only be undertaken if the scientific or engineering need cannot be met by other means, or, as sometimes happens, if instruments in space are actually the cheapest way to proceed, despite their cost. Designing instruments, or spacecraft for that matter, to work in the space environment places exacting requirements on those involved. Three issues arise in this kind of activity which add to the difficulty, challenge and excitement of carrying out science and engineering in space. First, it is by no means straightforward to design highly sophisticated instruments to work in the very hostile physical environment experienced in orbit. Secondly, since the instruments will work remotely from the design team, the processes of design, build, test, calibrate, launch and operate, must have an extremely high probability of producing the performance required for the mission to be regarded as a success.

The background

At the end of the nineteen sixties satellites characteristically had masses in the range 150 to 300 kg. By the end of the nineteen nineties many, if not most, satellites are being designed to mass budgets between one and ten metric tonnes. Satellites have expanded to fill the launchers available would be one conclusion. In fact, many changes have taken place during the past thirty years and most of these have led to a growth in satellite masses. The scientific problems being solved from space have grown more and more exacting in terms of the equipment required. As more is discovered, seemingly, more is left to be discovered and ever more sensitive instruments are demanded. Greater sensitivity usually requires large collecting areas, cooled telescopes or massive detectors, all strong factors in determining the mass of the payload. In the fields of Astronomy and Earth Observation the scientific problems seem best tackled by ‘Observatory Class’ missions in which a payload of five or ten separate instruments is compiled to provide the varied individual measurements necessary to address the mission objectives. In some cases these instruments could be launched on separate platforms if their observations could be properly coordinated, in other cases the full set of measurements must be simultaneous in space and time. Launch vehicles which are principally designed to meet the growing needs of geostationary communications satellites are available with the lift capability of many tonnes and so there has been little pressure to identify missions which can achieve the highest quality science from small, and hence inexpensive, satellites.