Introduction

Experimental study of flow transition began with the famous pipe flow experiment [365], in which Reynolds took pipes of different diameters and fitted them carefully with bell-mouth shaped entry sections. In Chapter 4, one noted that favorable pressure gradient delays transition by attenuating disturbances. The bell-mouth accelerates the flow, and the resultant favorable pressure gradient stabilizes the flow. Apart from this, Reynolds took other precautions to note that the transition in the pipe flow depends upon the non-dimensional parameter, now known as the Reynolds number, Re = Vd/ν, where V is the centreline velocity and d is the diameter of the pipe. He found that with all extra precautions taken against disturbance growth, the flow can be kept laminar up to Re = 12, 830. It was also noted by Reynolds that this critical value is very sensitive to disturbances in the oncoming flow, before it enters the pipe. Although this might also indicate receptivity of the flow, Reynolds remarked that “this at once suggested the idea that the condition might be one of instability for disturbance of certain magnitude and stable for smaller disturbances.” The relation between input and output amplitudes during disturbance growth is a typical attribute of nonlinear instability. There are other flows, e.g. the Couette flow, which are found to be linearly stable for all Reynolds numbers. This prompted researchers [282, 298] to suggest nonlinear routes of instabilities for such flows. However, it is interesting to note that some authors [399] have stated without proof that “it is easy to verify that the nonlinear terms of the incompressible Navier–Stokes equations are energy preserving: the role of the nonlinear terms is the distribution, scattering and transfer of energy, but this reorganization is accomplished in a conservative manner. Energy growth or decay can only come from linear processes.” The presented explanation in this book is contrary to this point of view, with enough evidences provided to show the central and important role of nonlinearity in causing transition [471].

One of the constraints of classical linear instability theories performing local analysis is the adoption of the parallel flow assumption of the equilibrium flow. This has been addressed in review articles by Chomaz [93] and Theofilis [519], with the main emphasis on giving up on local analysis in favor of a global analysis.

Acoustic design of ductworks such as fluid machinery intake and exhaust systems usually requires a large number of iterations for concept validation and prototype development. The network approach is ideally suited for this purpose, but systematic search and optimization methods are indispensable for quick and efficient progress. The last chapter, Chapter 13, discusses the acceleration of iterative design calculations and handling uncertainties about model parameters. We also present an approach which brings an inverse perspective to the conventional target based acoustic design calculations.

Chapter 10 describes analytical actuator-disk models for the basic acoustic source mechanisms, namely, non-steady mass and heat injection and force application, applications of which are demonstrated on internal combustion engines, turbomachinery and combustion chambers.

Chambers and resonators are used as noise control devices in almost all industrial duct systems. In Chapter 5, transmission loss is defined and, using the acoustic models and the assembly techniques described in previous chapters, transmission loss characteristics of various chamber and resonator types are demonstrated. Also discussed are the calculation of the shell noise and mean pressure loss (or back pressure), which may impose trade-offs on effective use of these devices in duct-borne noise control.

Chapter 6 introduces the three-dimensional analytic theory of sound propagation in ducts and presents acoustic models of hard-walled and lined uniform ducts. Also discussed are the effects of gradual cross-section non-uniformity, circular curvature of the duct axis, and sheared and vortical mean flows.

Chapter 12 describes the contemporary measurement methods in duct acoustics. Acoustic measurements are necessary in order to validate theoretical models and also to develop acoustic models when theoretical approaches tend to be inadequate or impossible. The multiple wall-mounted microphone method is introduced from first principles and its applications to the measurement of the characteristics of acoustic sources and of passive system elements are described.

This chapter describes a block diagram based network approach for construction of acoustic models of duct systems from the simpler components in one dimension and three dimensions. This topic is considered early in the book, because it describes the format used in later chapters in mathematical representation of acoustic models of ductwork components and their assemblies.