INTRODUCTION

The compressor, which raises the pressure of the air before combustion, and the turbine, which extracts work from the hot pressurised combustion products, are at the very heart of the engine. Up to now we have assumed that it is possible to construct a suitable compressor and turbine without giving any attention to how this might be done. In this chapter an elementary treatment is given with the emphasis being to find the overall diameter of various components and the flow-path this entails, the number of stages of compressor and turbine, and suitable rotational speeds. The details of blade shape will not be addressed. Further information is obtainable at an elementary level in Dixon (1995) and at a more advanced level in Cumpsty (1989).

For the large engine that we are considering the most suitable compressor and turbine will be of the axial type. These are machines for which the flow is predominantly in the axial and tangential directions, and stand in contrast to radial machines for which the flow is radial at inlet or outlet.

Because the pressure rises in the direction of flow for the compressor there is always a great risk of the boundary layers separating, and when this happens the performance of the compressor drops precipitously and is said to stall. To obtain a large pressure rise (or, as it is more commonly expressed, pressure ratio) the compression is spread over a large number of stages.

INTRODUCTION

It would be possible to calculate the performance of an engine in the manner of Exercise 7.1 and 7.2 for every conceivable operating condition, e.g. for each altitude, forward speed, rotational speed of the components. This is not an attractive way of considering variations and it does not bring out the trends as clearly as it might. An alternative is to predict the variations by using the appropriate dynamic scaling – apart from its usefulness in the context of engine prediction, the application of dimensional analysis is illuminating. The creation of groups which are actually non-dimensional is less important than obtaining groups with the correct quantities in them. The reasoning behind these ideas is discussed in Chapter 1 of Cumpsty (1989). For compatibility with the usual terminology the phrase ‘dimensional analysis’ will be retained here.

Using the ideas developed on the basis of dynamic scaling it is possible to estimate the engine performance at different altitudes and flight Mach numbers when the engine is operating at the same non-dimensional condition. From this it is possible to assess the consequences of losing thrust from an engine and the provision that needs to be made to cope with this at either take off or cruise.

ENGINE VARIABLES AND DEPENDENCE

Figure 8.1 shows a schematic engine installed under a wing. The only effects of the pylon are assumed here to be the transmission of a force between the engine and the wing and the passage of fuel to the engine.

What is Vortex Sound?

Vortex sound is the sound produced as a by-product of unsteady fluid motions (Fig. 1.1.1). It is part of the more general subject of aerodynamic sound. The modern theory of aerodynamic sound was pioneered by James Lighthill in the early 1950s. Lighthill (1952) wanted to understand the mechanisms of noise generation by the jet engines of new passenger jet aircraft that were then about to enter service. However, it is now widely recognized that any mechanism that produces sound can actually be formulated as a problem of aerodynamic sound. Thus, apart from the high speed turbulent jet – which may be regarded as a distribution of intense turbulence velocity fluctuations that generate sound by converting a tiny fraction of the jet rotational kinetic energy into the longitudinal waves that constitute sound – colliding solid bodies, aeroengine rotor blades, vibrating surfaces, complex fluid–structure interactions in the larynx (responsible for speech), musical instruments, conventional loudspeakers, crackling paper, explosions, combustion and combustion instabilities in rockets, and so forth all fall within the theory of aerodynamic sound in its broadest sense.

In this book we shall consider principally the production of sound by unsteady motions of a fluid. Any fluid that possesses intrinsic kinetic energy, that is, energy not directly attributable to a moving boundary (which is largely withdrawn from the fluid when the boundary motion ceases), must possess vorticity. We shall see that in a certain sense and for a vast number of flows vorticity may be regarded as the ultimate source of the sound generated by the flow.

Vortex sound is the branch of fluid mechanics concerned with the conversion of hydrodynamic (rotational) kinetic energy into the longitudinal disturbances we call sound. The subject is itself a subsection of the theory of aerodynamic sound, which encompasses a much wider range of problems also involving, for example, combustion and ‘entropy’ sources of sound. The book is based on an introductory one-semester graduate level course given on several occasions at Boston University. Most students at this level possess an insufficient grasp of basic principles to appreciate the subtle coupling of the hydrodynamic and acoustic fields, and many are ill-equipped to deal with the novel analytical techniques that have been developed to investigate the coupling. Great care has therefore been taken to discuss underlying fluid mechanical and acoustic concepts, and to explain as fully as possible the steps in a complicated derivation.

A considerable number of practical problems occur at low Mach numbers (say, less than about 0.4). It seems reasonable, therefore, to confine an introductory discussion specifically to low Mach number flows. It is then possible to investigate a number of idealized hydrodynamic flows involving elementary distributions of vorticity adjacent to solid boundaries, and to analyze in detail the sound produced by these vortex–surface interactions. For a broad range of such problems, and a corresponding broad range of noise problems encountered in industrial applications, the effective acoustic sources turn out to be localized to one or more regions that are small compared to the acoustic wavelength.

The Acoustic Analogy

The sound generated by turbulence in an unbounded fluid is usually called aerodynamic sound. Most unsteady flows of technological interest are of high Reynolds number and turbulent, and the acoustic radiation is a very small byproduct of the motion. The turbulence is usually produced by fluid motion over a solid boundary or by flow instability. Lighthill (1952) transformed the Navier–Stokes and continuity equations to form an exact, inhomogeneous wave equation whose source terms are important only within the turbulent region. He argued that sound is a very small component of the whole motion and that, once generated, its back-reaction on the main flow can usually be ignored. The properties of the unsteady flow in the source region may then be determined by neglecting the production and propagation of the sound, a reasonable approximation if the Mach number M is small, and there are many important flows where the hypothesis is obviously correct, and where the theory leads to unambiguous predictions of the sound.

Lighthill was initially interested in solving the problem, illustrated in Fig. 2.1.1a, of the sound produced by a turbulent nozzle flow. However, his original theory actually applies to the simpler situation shown in Fig. 2.1.1b, in which the sound is imagined to be generated by a finite region of rotational flow in an unbounded fluid. This avoids complications caused by the presence of the nozzle.