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AEROACOUSTICS
Journal of Sound and Vibration (1996) 190(3), 387–398
AEROACOUSTICS J. E. F W Department of Engineering, University of Cambridge, Cambridge CB2 1PZ, England (Received 1 November 1995) The development of aeroacoustics since the 1950s is reviewed. The role of E. J. Richards in this development, and especially his distinctive scientific skills and unique personal talents for making things happen, are essential parts of the story. 7 1996 Academic Press Limited
E. J. Richards was used to making his own show happen long before he came to Southampton. His style of choosing a topic, identifying the most able available team, cajoling and encouraging them to perform, and promoting their successes in the most influential circles that he had access to at the time was still evident in the charming energetic octogenerian that he became. He still asked poky questions, retained his urge to persuade others to accept and follow his convictions and continued to sing the praises of his team’s most recent success. There was real substance in the contribution he reported; what was being learnt at Southampton 40 years ago about aircraft noise was attracting international attention. He knew it was the most important aeronautical problem of the day, and it was to be the main focus of research in the Aeronautical Engineering Department he had come from industry to lead. His enthusiasm and drive inspired those who worked with him and he was most skilful at avoiding or outmanoeuvring those who failed to share his views—his team was protected from them. He was adept at avoiding the few who could do things better and continually adapted his goals to give himself a clear run free of interference from powerful competitors. Jet aircraft were entering civil aviation in the 1950s and their evident and enormous potential was threatened by their noise. Elfyn Richards, Vickers’ aerodynamicist contemplating the jets that were to succeed the Viscount that he had helped make a success of turbine power, knew the jet noise problem was important enough to provide the core of the research he would lead in his post-industrial academic life. He knew also that view was shared by the ministry responsible for British aviation and he was already acquainted with the characters in that ministry. Richards knew who to persuade, what line of reasoning they were susceptible to, and the importance of demonstrating progress and a determination to mount the necessary scale of effort to succeed. Richards was putting Southampton University on the aeronautical map and making the aircraft noise problem an important aeronautical research subject when I first met him to be interviewed for undergraduate admission in 1954. At that interview I became determined to follow him—in half an hour he had shown me more excitement and promise in aeronautical engineering than I had ever imagined could exist. My excitement must of course have been partly due to the fact that the interview resulted in a scholarship, but my admiration of his dynamic personality and his sense of mischievous fun has not been changed by anything since. I always enjoyed his company and admired his style. I was delighted when he offered to 387 0022–460X/96/080387+12 $12.00/0
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supervise my postgraduate studies—and it seemed natural that he arranged funding for that research. Jet noise was to be the research topic. I was to be taught by the leader of what seemed to me to be the world’s most successful jet noise research team, a team that included Alan Powell, whose lectures to undergraduates I had always found a model of logical clarity and precise exposition, a quality that pervades his prolific publication output of that period. The term ‘‘aeroacoustics’’ had not then been coined; ‘‘jet noise’’ and ‘‘sound generated aerodynamically’’ were the preferred titles. ‘‘Aerosonics’’ was favoured while Alan Powell led the UCLA school around 1960, but it was not until the 1970s that ‘‘aeroacoustics’’ was adopted as the descriptive title for all aspects of the many interactions that take place between sound and flow. Hydroacoustics is the underwater counterpart of the aeronautical problem, the sound of unsteady flow around submarines being as important in the naval context as the aircraft noise problem is to all within range of an airport. Richards was involved at the birth of aeroacoustics, when aircraft noise was first recognized to be a serious technical problem. It was perfectly natural that he should see it as a practical matter that could benefit from the attention of university engineering research. In the 1950s, acoustics was a declining subject activity in physics, architecture and electrical engineering departments, and there was little appreciation that it could contribute much to the jet noise problem. The engineers seemed to ignore the acousticians with their jargon of phons and decibels, and they ploughed on to rediscover much of what should have been fundamental scientific knowledge; it certainly would have been known in Lord Rayleigh’s day. Today the modern subject knows no bounds between aerodynamics, electronics, information technology, wave physics and mathematics, but 30 or 40 years ago it was the engineering programmes in which E.J. Richards was such a leading figure that reinvigorated the study of sound and emphasized its importance to modern life. At least that seemed to be the British view of the subject, a view that with the 20/20 vision of hindsight was not a totally accurate reflection of the global scene. But the British knew more about jet noise; it seemed only natural that they should know more about all aspects of jet propulsion. The early jets of the 1940s were noisy, noisy enough to be a really important problem a problem that had to be quantified and predicted and if possible controlled. Most early jet engines ran only on test beds and their noise was measured in close proximity to the machinery and exhaust flow. That there was a problem was clear, but test bed measurements gave little insight into how to bring order into the subject. Open air tests soon allowed the sound radiating away from jets to be measured [1, 2], and the jet flows produced by expanding compressed gases of various compositions through small nozzles became useful research facilities [3]. The instrumentation used for early measurements lacked the calibration and accuracy regarded as essential today, and the spectral analysis equipment rarely resolved more finely than the octave band. Being a new subject, the aeroacoustics of the early 1950s had no established discipline. Clearly important, but unfamiliar to scientistis and engineers alike, there was scope for anyone interested to contribute. There were no experts, and many of the enthusiastic contributors of experimental data and measurements at full scale felt unconstrained by any need to record values of the various operating parameters that might influence jet noise other than to quote a peformance measure of their particular device. The most popular noise measure was the radiated acoustic power, that clearly increased with the size and power of the jet flow. Big jets were noisier than small jets, fast jets noisier than slow jets. Expansion ratios across the propulsive nozzle were important, as were jet temperature, density and the speed of sound variations in the exhaust streams of jets with different propulsive gases. Choked jets made a qualitatively different noise, their piercing screech
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being much more irritating than the random rumbling noise of subsonic jet streams. But whether pressure ratio or jet Mach number mattered more than jet power or propulsive thrust, or how important the jet density was compared with the speed of sound or mean jet temperature, was far from clear. The problem had a range of possibly important defining parameters, and without some fundamental understanding of the physics little sense could be made of contradictory experimental measurements. That situation changed abruptly with the publication in 1952 of Lighthill’s pioneering paper, setting out a general theory of sound generated aerodynamically [4]. The paper was a masterpiece, elegantly expressed and making full use of the ordering ability of mathematical analysis. The subject was analyzed at its most fundamental level and he devised an exact theory of sound generation that carried the style and authority of the great scientists that had set out the science of sound some hundred years previously. Rayleigh or Stokes would surely have done the same had the need presented itself in their time. Now started a distinctly different era of aeroacoustics. The elegance and generality of Lighthill’s theory was awesome in its impact. Airflow in the absence of resonators and boundaries was proven to be equivalent in its sound-generating ability to a distribution of quadrupoles and, provided that these quadrupoles scaled with the variables defining the hydrodynamic mean flow, the power of the noise that it produced would scale on the eighth power of jet velocity. That was easy to check, and experimental confirmation of that velocity index was soon forthcoming. In fact, it is as if the eighth power law was taken as an accuracy check on experimental measurements and only those measurements that passed that test passed through the editors’ sieve to be published. Of course, the eighth power law could not go on for ever; the power of the propulsive jet itself only increases with the cube of jet velocity. That aspect was a puzzle in the light of the exactness of Lighthill’s analysis. And there were experimentalists who found it hard to believe that, despite its rigorous derivation, the eighth power law could really be right; some of their results gave a different sensitivity. It was probably that feeling of unease that prompted Richards to direct my research towards checking Lighthill’s theory, checking it by measuring the jet turbulence to see if it related to sound as the theory predicted. There was much for me to learn. I knew nothing useful about turbulence and the Lighthill theory called for knowledge of the turbulence stress tensor—whatever that might be. I was soon to become familiar with the tensors and to become in awe of the elegance of Lighthill’s formulation, but it surprised and disappointed me that I could not find anybody with recognizably useful knowlege of turbulence. That situation is not so different today. Lighthill knew that turbulent eddies convect and that convection of their associated acoustic sources would modify the radiated sound. His setting of the problem into a convected co-ordinate system revealed the main convective effects explicitly; there is a Doppler modification of frequency and the sound is preferentially beamed into the direction in which the frequency shift is greatest. He did not pursue the analysis for the coincident condition where the source propagates in some direction at exactly the speed of sound, and his jet noise scaling scheme specifically excluded that possibility. Nonetheless, if that scheme was applied at the coincident condition it predicted infinity. The novelty of Lighthill’s approach, the quadrupole nature of aerodynamic sources and his emphasis of convective effects and of the crucially important space–time structure of the fluctuating Reynolds stresses was hard for people to take and it was not surprising that attempts were soon made to approximate and simplify the problem. Under Richards the Southampton team had up to that time concentrated on measurement of aerodynamic sound [5], making good use of optical techniques, techniques that work best on sharp-fronted waves. The sound produced when a shock wave passes a vortex was the subject of early experiments and Alan Powell’s [6] visualization and explanation of jet
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screech was a landmark. But it was Lighthill’s demonstration of how the subject can progress when the physical problem is properly modelled and analyzed that led directly into the modern aeroacoustic approach, in which theory and experiment are inseparable. Alan Powell left Southampton for the U.S.A., where he formulated his theory of vortex sound [7], which has proved extremely helpful in understanding the aeroacoustics of geometrically simple low Mach number flows. My own postgraduate studies were enormously influenced by Herbert Ribner, a visitor to Southampton, who knew that flow/acoustic interaction effects were important to understanding the jet noise problem, and he also knew at that time the essential structure of the inappropriate approximation that led to the singular Lighthill convective amplification term. He too sought an alternative simpler view of the sound-generating properties of flow, but many remain to be convinced of the merits of his proposed alternative. Mo¨hring [8] derived a relationship between unsteady low Mach number vorticity and sound, a relationship striking in its apparent simplicity and which has proved an effective way of evaluating the noise made by a definite distribution of voriticty. Howe [9] rearranged the problem to highlight the aeroacoustic significance of density and entropy inhomogeneities at low Mach numbers. It was in 1955 that Curle [10] published his extension of Lighthill’s acoustic analogy to include the effect of flow boundaries, showing that boundary terms could provide effective mass and momentum injection into the flow, acoustically equivalent to monopole and dipole sources of fundamentally greater acoustic efficiency than Lighthill’s volume quadrupoles. The 108 increase in acoustic efficiency as bubbles form in turbulent liquids is a direct effect of the monopoles [11] and the dipoles accounting for unsteady surface loading are the essential source of subsonic propeller noise. The Lighthill/Curle approach relates sound exactly to integrals of surface and volume source terms and specifies precisely what these source terms are. Once they are known, so is the sound field. Lighthill encouraged the view that low Mach number sources might well be independent of their sound field, and that they could be estimated or measured to produce a prediction of what their induced sound would be. The U 8 law followed such a prediction, and Curle’s surface stresses and vibration terms would similarly yield U 6 and U 4 scaling laws, laws that though verified in experiment were laws that were actually prone to failure. Alan Powell [12] pointed out that turbulence bounded by a rigid plane would still produce only quadrupole sources and that in that case Curle’s surface sources amounted to nothing more than a specular reflection of the volumetric sources, the sound of which was augmented by the quadrupole sound of ‘‘image’’ turbulence. Powell had made evident the fact that the surface source terms could not generally be specified independently of sound. In those cases in which sound does affect the surface sources, although the acoustic analogy is exactly true it is probably of very little use. The sound has first to be known before its surface source distribution can be specified—the meaning of what comes before what and what causes what has at this stage been lost. The problem has to be approached from another direction. It is a most important requirement of robust acoustic analogies that they should separate the source from the sound, sound being defined as the linear response of the source’s environment; sound is the response—it is driven by the source. There is no uniqueness about sources. Many different sources are capable of generating the same sound, and it is not therefore surprising that alternative prescriptions of aerodynamic sources exist. Lighthill’s analogy pointed the way and provided a tool for understanding and predicting the acoustic consequences of turbulence embedded in an acoustic environment at rest. Other analogies will be better if the situation is essentially different from the model that Lighthill envisaged—though Lighthill’s analogy continues to provide precise identities between sound and flow, identities that may or may not be useful. So it is in the case of
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the low Mach number turbulent boundary layer making sound that disturbs the otherwise uniformly moving flow over a plane rigid surface. The unsteady turbulence stress tensor is the strength of the quadrupole source making sound that leaves the source to be heard after it has travelled relative to the moving stream and been reflected in the acoustic mirror of the constraining boundary surface. That is the best view of the problem, although before Powell recognized that approach many hoped to be able to ‘‘predict’’ the sound radiated by turbulent boundary layers by making use of unsteady surface pressure measurements made in boundary layer tunnel facilities—a much more complicated and yet-to-be-proven procedure. Structures in flow rarely operate satisfactorily if driven to vibrate so violently that non-linear effects are important. Most flow surfaces then, even though they may vibrate, are surfaces on which boundary conditions are linear and the surface source terms that Curle identified in the acoustic analogy are also linear. Linear surface source terms may look satisfactorily simple but, in the aeroacoustic context, they are very far removed from what is generally easily interpreted—unless the surfaces are small enough, small enough for their environmental field to be forced into a near-singular adjustment in conforming with the local surface constraints. And the fact that small rigid bodies, with no boundary motion and no conceivable way of energizing any environmental disturbance, can possibly be the dominant aeroacoustic source is still an aspect that some find confusing. If foreign bodies provide the only disturbance to the perfect acoustic environment, and if that environment is otherwise source-free with its sound field unaltered by volumetric sources, then there is no sound and no pressure variation on the bounding surface. This obvious fact, that still fluid surrounding a motionless body is at rest everywhere and at steady pressure, is an example of an important wave property that is not as well known as it might be. The normal velocity on the bounding surface determines the pressure everywhere, and in particular the boundary pressures. It is also true that surface pressure has the same field-determining property. Knowledge of either the normal velocity or of the surface pressure defines all aspects of a linear sound field completely. Knowledge of both gives no more information than knowledge of one, although it undoubtedly provides that information in a more usable from. The fact that Curle’s surface monopoles and dipoles somehow turn into something else is not so much of a mystery once it is appreciated that linear surface terms—which is what they are—are not to be specified arbitrarily and can contain very subtle features that are easily lost by approximation. The error in assuming that they are sources the properties of which can be specified independently of their sound and that they scale on hydrodynamic variables is what caused the trouble in the flat-plate case. Powell recognized the essential fact that the extended ‘‘source’’ terms are sound rather than sources of sound; resetting aeroacoustic boundary problems within the context of different theory then became inevitable [13]. However, acoustic terms will be very weak at low enough Mach numbers, and it is only when the surfaces are large enough to make the accumulated effect of all the weak sources mount up to something large that the surface source terms are sensitive to sound. Acoustically compact surfaces, surfaces of linear scale much smaller than any in the sound field, do provide very efficient acoustic sources that the Curle procedure describes precisely and robustly. In these compact source cases it does not matter which view of the source process is taken. Even the acoustic field on small enough bodies is set by the hydrodynamics of adjacent flow, the compressibility of the medium having a negligible effect [14]. Then it is perfectly reasonable to scale surface stresses on hydrodynamic variables, even though they are linear, and to determine their acoustic effect by evaluating Curle’s integrals. Even
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when there are nearby volumetric sources, the sound scattered by acoustically small foreign bodies can be evaluated by solving the wave equation under the specified source conditions accounting for the known boundary constraint. This could be done by seeking the Green function under those boundary constraints and convolving it with the known sources, or by determining the hydrodynamic boundary conditions for later use in the Curle integrals. The development of aeroacoustics to specify only the turbulent source activity and to solve for the field on boundary surfaces has definitely brought new aspects of the subject into the limelight. The boundaries diffract the field. The special case of diffraction, when the surfaces are small on the acoustic scale, is scattering. Compact surfaces scatter the near field of quadrupoles very effectively indeed. Ten years after the publication of his general theory Lighthill summarized the subject of sound generated aerodynamically to the Royal Socieity in the 1961 Bakerian Lecture [15]. Jet noise had by then become the major problem envisaged when the analogy was conceived, and there was ample confirmation that the turbulence of the jet mixing layer, that Lighthill had identified as being the main source of noise, was indeed just that. The basic characteristics he had assumed this turbulenece to have had been largely confirmed. Measurements using the 1 and 2 inch diameter jets and the hot wire and space–time correlation equipment that Richards had established at Southampton made important contributions to the build-up of data, and the Lighthill style of jet noise prediction had been satisfactorily extended to supersonic jet speeds [16]. The outstandingly important parameter determining overall noise was jet speed, the eighth power law proving accurate at the engine exhaust speeds of operational jet aircraft. Quieter engines would happen only if jet speed was lowered—and, since a lowering of jet velocity would improve propulsive efficiency, higher mass flow engines of lower specific thrust were what the industry needed, and they were coming on in the high by-pass ratio engines then under development. Theory and practice seemed to be in satisfactory agreement—although in fact the serious engineering study of jet noise was only just beginning. The initial drive to lower jet speeds certainly brought the hoped-for U 8 law returns, but the aircraft problem had become so acute that even greater improvements were needed, and the engine industry responded with even larger engines of lower specific thrust. These larger engines failed to achieve the expected noise reduction and that failure spurred a much closer look at the jet noise problem in the early 1960s. The lower speed jets, with flows more closely meeting the Lighthillian low Mach number model, did not conform with quadrupole scaling [17]. More efficient sources had come into prominence and those were less sensitive to changes in jet speed. Of course jet turbulence is not very far away from the jet pipe and its termination in the exhaust nozzle. The possible influence of that is ignored in the simple model. Could it possibly be important? The answer is ‘‘yes’’; its influence is crucial at low enough exhaust speed [18]. Steady jet flow produces steady propulsive thrust. Unsteady jet flow produces unsteady thrust, acoustically equivalent to an axial dipole and more effective than free jet turbulence by a factor proportional to the inverse square of Mach number. This would give a noise scaling with U 6. Having started on that theme a U 4 contribution soon becomes evident, because unsteady exhaust output is equivalent to an acoustic monopole. Both of these elements are consistent with data taken from engine measurements. Also, the noise generated inside the engine by unsteady combustion, turbomachinery and internal turbulence manifests itself as unsteady flow through the exhaust nozzle. That called for flow smoothing devices and sound-absorbent treatment of the internal engine surface—which have proved very effective and are now commonly found in modern engines, engines that are quieter, for the same duty, by at least a factor of 100 than the engines of 20 years ago.
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Turbulence near a pipe opening must subject the pipe to acoustic disturbance and cause pipe entry conditions to become unsteady and to support monopoles and dipoles at the exit plane. To estimate the importance of this effect to the jet noise problem, experimental model studies were conducted with turbulence generators near the nozzle exit. Supporting theoretical examples represented the turbulence by quadrupoles the characteristics of which scaled on hydrodynamic variables. Of course the details of the interaction depend on the orientation and position of the quadrupoles, but experiments and theory confirm the fact that the open pipe is acoustically equivalent to a dipole source and its sound scales with the sixth power of jet velocity. More precise representations of idealized vortical flow produced examples consistent with the result, but known exact unsteady flows are few and the examples necessarily highly idealized. Often the examples are two-dimensional—and so is their sound field. A pair of opposing parallel line vortices within a two-dimensional semi-infinite duct moves and can escape out of the duct, perturbing the otherwise steady condition as it escapes. The matched expansion technique can give a solution to the sound generated by the escaping vortex pair, and again that calculation confirms the effectiveness of the duct as a scatter of the hydrodynamic field into sound exterior and interior to the duct [19]. For the precisely defined simple vortex configuration the complete history of the disturbance is available, but that is of little practical interest other than confirming that the scaling derived through the acoustic analogy is consistent with the results for the definite example. All these nozzle/jet turbulence interaction studies fit together and give confidence that the different basic mechanisms responsible for the noise of jets at the lower exhaust speeds are being understood. A much more interesting aeroacoustic model problem considers the scattering ability of a semi-infinite rigid screen [20]. The two alternative approaches of evaluating the field scattered when the edge is close to a quadrupole source, and the specific example of a line vortex lying parallel to the edge and moving unsteadily from one side of the screen to the other [21], both indicate the edge scattering to be important—more important in fact that the dipole interaction with a compact surface. Edge-scattered sound scales on U 5 and there is experimental confirmation of that theoretical prediction. The noise control work on jet engines has been so successful that engines no longer dominate in all aspects of the aircraft noise problem near airports. The airframe itself makes noise and the noise of flow over a large transport aircraft in its landing configuration is strong and is a cause for practical concern [22]. It is much worse than the nice swishing noise one can experience when a glider is heard on its landing approach, but the basic causes of the noise are the same in both cases. The large aircraft is faster and heavier and cluttered with elaborate landing gear, and multiple slot and flap arrangements have been deployed to augment the lifting ability of its wing. It is now thought that the turbulent boundary layer flowing over the trailing edge of lifting surfaces is one of the main contributors to airframe noise, and that the characteristics (directionality frequency content and velocity sensitivity) of that noise are consistent with the edge scattering process, a process first investigated simply because it was one of the geometrical arrangements that were simple enough to yield to analytical treatment. The turbulence was represented by quadrupoles scaling on hydrodynamic variables and the induced wave field solved with proper account being taken of the boundary constraints on the semi-infinite screen. Definite aeroacoustic models in which either the quadrupoles, representing turbulence or unsteady vorticity, or the Powell and Mo¨hring representation of vortical flow sources, have been analyzed to build up an appreciation of how sound is created in flow over definite geometrically intricate surfaces. These studies were usually driven by underwater or aeronautical needs, but have resulted in understanding the quantitative detail of sound in wind instruments [9], as well as the essential mechanics of the less pleasant, practically
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important flow-induced sounds. The compact scattering cases are relatively simple— Curle’s scheme works well on them. But when extensive surfaces interact with flow the acoustic analogy solved subject to the diffraction effects of boundary constraints offers the only way forward. The sounds made when turbulent flow passes down channels of irregular shape and the noise of a ring vortex passing through an orifice are understood from such studies. The reason why the interaction of turbulence with sound-absorbent screens is noisy has been made clear and, indeed, the problem controlled in the light of that understanding. These studies have pointed to flow of an irregular fluid mixture as being especially prone to unsteadiness and to be more capable of making sound than the flow of materially homogeneous fluid; the noisy chuffing of a garden hose as flow starts and emerges as an intermittent mixture of air and water is an everyday example of that process. The essential cause of that noise is that non-uniform flow of density-inhomogeneous fluid cannot be steady. The heavier portions, being less easily accelerated than the lighter parts, move differently through the pressure gradient that drives changes in speed. That has important aeroacoustic consequences and Morfey’s [23] identification of the fact revealed one of the very few aerodynamic sound-generating mechanisms that had escaped Lighthill’s notice. And it is an important mechanism, being the dominant cause of mixing noise elements in very hot jets. What Lighthill had failed to cover was the case in which mass density variations are not simply proportional to pressure changes, but depend also on what the material is. The normal balance in sound, Dp=c 2Dr, is not held in a mixture of fluids, and the difference appears as an inhomogeneity in the governing equation, a dipole inhomogenity more efficient than the quadrupoles which Lighthill showed accounted for all source processes. Lighthill’s method is precise enough to extract this effect once it is recognized that an interface between two different material substances is a surface of singular density gradient—and, in essence, that eventually makes singular the strength density of the quadrupole needed to represent what is really a finite dipole source system. An inhomogeneous mixture is bound to occur at the turbulent interface between adjacent zones of different fluids. Violent ocean wave activity at the air/sea interface is an example, and an example that makes clear the need for another major physical constraint to be accounted for explicitly before an acoustic analogy can help. The sound sources are not there embedded in an infinitely extended homogeneous environment as Lighthill’s analogy requires; one half of space is completely different from the other. Sound generated in either half will be partly reflected and partly transmitted through the interface, a wave effect that must be dealt with properly and not left as acoustic influences in the source terms; that would render the analogy useless, because the ‘‘sources’’ could not be known in advance of the waves that the sources are assumed to create. Once the linear response of the ocean surface was incorporated into the analogy the aeroacoustic approach transformed our state of knowledge of the important oceanographic question of what underwater sound is generated at the ocean surface. Guo’s [24–26] fundamental work illustrated how cause and effect could be ordered and separated, and he demonstrated how one could get much further than before by regarding both surface waves and sound as two of the consequences of inhomogeneous source activity. The two are related, but it is not the relation of cause and effect implied in the classical wave studies that up to that time provided the only pointers to the underlying mechanics of the sound generation process. Again, it is the singularly abrupt flow changes that happen at any fixed position crossed by the moving air/water interface that makes the simple quadrupole representation inadequate. Those singular volume ‘‘sources’’ give rise to finite surface distributions that are linear in the disturbance amplitude, and to deal with them properly one needs the kind
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of procedure that Powell had introduced to avoid Curle sources on infinite planes. And in developing the techniques for the oceanic case the acoustic analogy became generalized; it not only modelled the flow-induced sound but it also dealt with the creation of other waves, surface gravity waves in particular. That development of aeroacoustics to give other natural linear motions the same standing as sound is probably important, but it is far too early to be sure. Before Guo showed better, ocean waves were looked on as potential sources of sound [27]—which of course they can be, being coupled to sound at the non-linear level. But the view of surface gravity waves and their associated sound as being related linearly because they were both generated together is a much more satisfactory and general approach. The depth of understanding that followed made obvious that the sound generated by surface waves was no more a real effect than the surface waves generated by sound; both views can be right, but neither is generally helpful [28]. The aeroacoustics of two adjacent fluids needs to account for the different natural responses of those fluids to a disturbing influence, and it should also account for the modes of linear response that might exist purely because of the relative disposition of those fluids. Density and speed of sound differences both affect the response, but the effect, large as it is, is not nearly as great as the changes which come from bulk motion of fluids at high Mach number. Sound is convected by flow and aeroacoustic modelling has to bring out that effect explicitly if at all possible. In 1953, Powell [6] had shown how the mechanism of supersonic jet screech depended on mean flow differences, differences between the jet interior and its surroundings and across shock waves in the jet. Mean shear has been viewed as a potential amplifier for jet noise since the subject began, and the sound-generating quadrupoles have always attracted workers to distinguish between the effects of mean flow/turbulence interaction and non-linear turbulence terms. High speed source convection has a profound influence that was explicitly incorporated into the acoustic analogy from the start, but refraction and the possible focusing of sound as different rays are brought together, because shear flow bends their differing acoustics paths, was more difficult to account for alongside the aeroacoustic source process. That the effects were there was never in doubt, but their modelling required the non-uniform flow to be featured within the fundamental linear operator prescribing how sound behaves, and it is a matter of judgement as to which aspect of the flow is emphasized first. One approach [29] extends Lighthill’s analogy to account for the different propagation characteristics within two adjacent streams in relative motion and, though more complicated than the original analogy, the extension retains the exactness characteristic of Lighthill’s method. Other schemes take into account the detailed profile of the mean flow and inevitably pay for that detail in increased complexity [30, 31]. The interface between two streams in relative motion is linearly unstable and any scheme that represents exactly the interface perturbations, produced by aeroacoustic sources, must deal with the resulting linear instability. The exact modelling accounting for interface effects within the analogy drives one into having to select between insisting on either the finiteness of the linear response to a disturbance or on the causality of that response; one cannot have both at the same time on an unstable interface. Since any theory in which the linear effect of a disturbance grows without bound is probably unworkable, the non-casual solution has been preferred and the implied existence of the sound field in advance of this source rationalized in the following way. Sound is the linear response of a flow perturbed by the non-linear source process, but if the flow is unstable that response quickly grows to become non-linear and so to become the source. There is no requirement, then, to presume that aeroacoustic sources induce only a causal response—finiteness is much to be preferred (though the finite response is also the causal one when the flow is stable). Both the two-part uniform flow and the continuously varying flow profile
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modifications of the acoustic analogy have had the effect of bringing the theory and practice of jet noise into much closer agreement [32, 33]. Measurable elements of the noise field are predictable without having to say much more about the nature of the turbulent sources than that they scale on hydrodynamical variables. Since the understanding and effective modelling of turbulence is so difficult, that robust property of advanced analogies is useful and, incidentally, implies that progress in the control of jet noise is not dependent on a solution of the turbulence problem. All these approaches regard the linear response of the flow, the sound that interacts with the flow before it escapes, as being separable from the source of sound. If that is not so, there are great difficulties still to be overcome before the mechanics of aerodynamic sound is adequately understood. Both the flow and the sound must then be recognized as imperfectly separated parts of the same phenomenon, and must be understood and modelled together through schemes that have yet to be devised. Numerical techniques are expected to provide the long-term answers, although there is no clear perception yet of what question is most usefully asked of the computational aeroacoustician. Of course it is possible to understand the way in which particular elements of the problem fit in; the linear instability waves on an evolving shear layer for example, with their near fields extending to become recognizable acoustic features of real jets [34]. But to believe that one induces the other misses the point. The near field and the instability wave are inseparably the same thing; one cannot exist without the other and the question of what made them and what needs to be done to avoid them, the dominantly important practical aeroacoustic question, cannot even be addressed from that approach. The confusing coexistence of source and sound is at its height in searching for the acoustic importance of shock waves. The flow over transonic helicopter blades supports embedded shock waves, as do imperfectly expanded supercritical jets, and the noise of both flows is commonly viewed as resulting from a source process involving the shocks. But the shocks are compressive waves, often quite well approximated by linear theory, i.e., they are virtually sound, and it is quite difficult to see the point of setting them up as known in advance and to be the source of, rather than the manifestation, of, sound. Prediction procedures that rely on known shock-attached boundary conditions [35] are nonetheless considered useful; more fundamental approaches that emphasize the acoustic content of shocks do not seem to have yet made much impact on the aeroacoustics community [36]. The aeroacoustics of propulsive flows, be they mixing flow or turbomachinery related, is still the subject of active research, the high speed rotor problem seriously limiting the acceptance of helicopters into the urban environment. And jet noise is possibly the most difficult problem that must be solved before a supersonic passenger airliner is environmentally acceptable. The work that is producing ever closer agreement of prediction and practice (work that has progressed very satisfactorily over the past 20 years) is sadly concentrated on the pure jet flows that are too noisy to be practical [37]. The fundamentally different silencing schemes that will be essential for future SST’s still remain but a gleam in their inventor’s eye. A serious search for the radically new is badly needed. In this sense, although the past 40 years have seen enormous strides in aeroacoustic technology, there remains today the same kind of aeroacoustical need that posed such a serious research challenge at the beginning of the jet age. The supersonic branch of civil aviation is similarly at risk because of noise. Forty years ago, Elfyn Richards took such needs as a personal challenge and the energy and drive he brought to the subject had great effects. He established a research centre second to none in its aeroacoustic importance. His Southampton Institute of Sound and Vibration Research is just the sort of fundamental free-thinking academic environment needed for creative innovation and that is possibly his greatest legacy. The ISVR is bound to contribute towards finding the new techniques
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needed to control the noise of the supersonic jet age. That is today’s dominant aeroacoustic challenge.
REFERENCES 1. F. B. G, 1958 Journal of the Royal Aeronautical Society 58(250), 223–231. Engine noise. 2. E. J. R 1953 Journal of the Royal Aeronautial Society 57(509), 318–342. Research on aerodynamic noise from jets and associated problems. 3. L. W. L and H. H. H, 1952 NACA TN 2757. Experimental studies of noise from subsonic jets in still air. 4. M. J. L 1952 Proceedings of the Royal Society, London A221(1107), 564–587. On sound generated aerodynamically: I. General theory. 5. A. P 1954 Aircraft Engineering XXVI (229), 2–9. A survey of experiments on jet noise. 6. A. P 1953 Journal of the Acoustical Society of America 25(3), 385–389. The noise of choked jets. 7. A. P 1964 Journal of the Acoustical Society of America 36(1), 177–195. Theory of vortex sound. 8. W. M¨ 1978 Journal of Fluid Mechanics 85, 685–691. On vortex sound at low Mach number. 9. M. S. H 1975 Journal of Fluid Mechanics 71(4), 625–673. Contributions of the theory of aerodynamic sound, with application to excess jet noise and the theory of the flute. 10. N. C, 1955 Proceedings of the Royal Society of London, A231(1187), 505–514. The influence of solid boundaries upon aerodynamic sound. 11. D. G. C and J. E. F W 1969 Journal of Fluid Mechanics 36(3), 585–603. Sound generation by turbulent two-phase flow. 12. A. P 1960 Journal of the Acoustical Society of America 32(8), 982–990. Aerodynamic noise and the plane boundary. 13. D. G. C and F. G. L 1971 Journal of Fluid Mechanics 46(3), 577–597. On the scattering of aerodynamic noise. 14. D. G. C, 1975 Progress in Aerospace Science 16(1), 31–96. Basic principles of aerodynamic noise generation. 15. M. J. L 1962 Proceedings of the Royal Society, London A267(1329), 147–182. The Bakerian Lecture, 1961: sound generated aerodynamically. 16. J. E. F W 1963 Philosophical Transactions of the Royal Society, London A255(1061), 469–503. The noise from turbulence convected at high speed. 17. J. B. L, J. F. W, E. G and A. O. A 1968 Proceedings of AEOSR-UTIAS Symposium, Toronto, May 1968, 43–67. The development of engineering practices in jet, compressor, and boundary layer noise. 18. J. E. F W and C. G. G 1965 American Institute of Aeronautics and Astronautics Journal 3(4), 791–793. Noise of highly turbulent jets at low exhaust speeds. 19. J. E. F W and P. C 1973 Journal of Fluid Mechanics 58(1), 65–80. Radiation from line vortex filaments exhausting from a two-dimensional semi-infinite duct. 20. J. E. F W and L. H. H 1970 Journal of Fluid Mechanics 40(4), 657–670. Aerodynamics sound generation by turbulent flow in the vicinity of a scattering half plane. 21. D. G. C 1972 Journal of Fluid Mechanics 51(2), 148–155. Radiation from vortex filament motion near a half plane. 22. D. G. C 1994 in Aeoracoustics of Flight Vehicles, Theory and Practice Vol. 1: Noise Sources (H. H. Hubbard, editor), 391–447. Airframe noise, Woodburg, New York: Acoustical Society of America. 23. C. L. M 1973 Journal of sound and Vibration 31(4), 391–397. Amplification of aerodynamic noise by convected flow inhomogeneities. 24. T. P. G, 1987 Journal of Fluid Mechanics 181, 293–310. Waves induced by sources near the ocean surface. 25. T. P. G 1987 Journal of Fluid Mechanics 181, 311–328. On sound generation by weakly nonlinear interactions of surface gravity waves. 26. T. P. G, 1987 Journal of Fluid Mechanics 181, 329–347. Sound generation in the ocean by breaking surface waves.
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27. L. M. B, 1966 Izv. Atmospheric and Ocenaic Physics 2(9), 970–980. Underwater sound waves generated by surface waves in the ocean. 28. J. E. F W and Y. P. G 1991 in Mathematical Approaches in Hydrodynamics (T. Miloh, editor), 128–138. Standing waves on a compressible ocean. 29. A. P. D, J. E. F W, and M. E. G 1978 Philosophical Transactions of the Royal Society, London A288(1353), 321–349. Sound production in a moving stream. 30. O. M. P 1960 Journal of Fluid Mechanics 9(1), 1–28. On the generation of sound by supersonic turbulent shear layers. 31. G. M. L 1994 in Aeroacoustics of Flight Vehicles, Theory and Practice Vol. 1: Noise Sources (H. H. Hubbard, editor), 211–289. Jet noise, classical theory and experiments. Woodbury, New York: Acoustical Society of America. 32. M. E. G, 1994 in Aeroacoustics of Flight Vehicles, Theory and Practice Vol. 1: Noise Sources (H. H. Hubbard, editor), 291–310. Noise from turbulent shear flows. Woodburg, New York: Acoustical Society of America. 33. F. B 1976 Journal of Fluid Mechanics 74(2), 193–208. The far field of high frequency convected singularities in sheared flows, with an application to jet-noise prediction. 34. C. K. W. T, 1971 Journal of Fluid Mechanics 46(4), 757–768. Directional acoustic radiation from a supersonic jet generated by shear layer instability. 35. C. K. W. T and H. K. T 1982 Journal of Sound and Vibration, 81, 337–358. Shock associated noise of supersonic jets from convergent–divergent nozzles. 36. M. S. H and J. E. F W, 1978 Philosophical Transactions of the Royal Society, London A289(1358), 271–314. On the noise generated by an imperfectly expanded supersonic jet. 37. J. M. S, 1984 AIAA Paper 84-2275. Advances in high speed jet aeroacoustics.
AEROACOUSTICS J. E. F W Department of Engineering, University of Cambridge, Cambridge CB2 1PZ, England (Received 1 November 1995) The development of aeroacoustics since the 1950s is reviewed. The role of E. J. Richards in this development, and especially his distinctive scientific skills and unique personal talents for making things happen, are essential parts of the story. 7 1996 Academic Press Limited
E. J. Richards was used to making his own show happen long before he came to Southampton. His style of choosing a topic, identifying the most able available team, cajoling and encouraging them to perform, and promoting their successes in the most influential circles that he had access to at the time was still evident in the charming energetic octogenerian that he became. He still asked poky questions, retained his urge to persuade others to accept and follow his convictions and continued to sing the praises of his team’s most recent success. There was real substance in the contribution he reported; what was being learnt at Southampton 40 years ago about aircraft noise was attracting international attention. He knew it was the most important aeronautical problem of the day, and it was to be the main focus of research in the Aeronautical Engineering Department he had come from industry to lead. His enthusiasm and drive inspired those who worked with him and he was most skilful at avoiding or outmanoeuvring those who failed to share his views—his team was protected from them. He was adept at avoiding the few who could do things better and continually adapted his goals to give himself a clear run free of interference from powerful competitors. Jet aircraft were entering civil aviation in the 1950s and their evident and enormous potential was threatened by their noise. Elfyn Richards, Vickers’ aerodynamicist contemplating the jets that were to succeed the Viscount that he had helped make a success of turbine power, knew the jet noise problem was important enough to provide the core of the research he would lead in his post-industrial academic life. He knew also that view was shared by the ministry responsible for British aviation and he was already acquainted with the characters in that ministry. Richards knew who to persuade, what line of reasoning they were susceptible to, and the importance of demonstrating progress and a determination to mount the necessary scale of effort to succeed. Richards was putting Southampton University on the aeronautical map and making the aircraft noise problem an important aeronautical research subject when I first met him to be interviewed for undergraduate admission in 1954. At that interview I became determined to follow him—in half an hour he had shown me more excitement and promise in aeronautical engineering than I had ever imagined could exist. My excitement must of course have been partly due to the fact that the interview resulted in a scholarship, but my admiration of his dynamic personality and his sense of mischievous fun has not been changed by anything since. I always enjoyed his company and admired his style. I was delighted when he offered to 387 0022–460X/96/080387+12 $12.00/0
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supervise my postgraduate studies—and it seemed natural that he arranged funding for that research. Jet noise was to be the research topic. I was to be taught by the leader of what seemed to me to be the world’s most successful jet noise research team, a team that included Alan Powell, whose lectures to undergraduates I had always found a model of logical clarity and precise exposition, a quality that pervades his prolific publication output of that period. The term ‘‘aeroacoustics’’ had not then been coined; ‘‘jet noise’’ and ‘‘sound generated aerodynamically’’ were the preferred titles. ‘‘Aerosonics’’ was favoured while Alan Powell led the UCLA school around 1960, but it was not until the 1970s that ‘‘aeroacoustics’’ was adopted as the descriptive title for all aspects of the many interactions that take place between sound and flow. Hydroacoustics is the underwater counterpart of the aeronautical problem, the sound of unsteady flow around submarines being as important in the naval context as the aircraft noise problem is to all within range of an airport. Richards was involved at the birth of aeroacoustics, when aircraft noise was first recognized to be a serious technical problem. It was perfectly natural that he should see it as a practical matter that could benefit from the attention of university engineering research. In the 1950s, acoustics was a declining subject activity in physics, architecture and electrical engineering departments, and there was little appreciation that it could contribute much to the jet noise problem. The engineers seemed to ignore the acousticians with their jargon of phons and decibels, and they ploughed on to rediscover much of what should have been fundamental scientific knowledge; it certainly would have been known in Lord Rayleigh’s day. Today the modern subject knows no bounds between aerodynamics, electronics, information technology, wave physics and mathematics, but 30 or 40 years ago it was the engineering programmes in which E.J. Richards was such a leading figure that reinvigorated the study of sound and emphasized its importance to modern life. At least that seemed to be the British view of the subject, a view that with the 20/20 vision of hindsight was not a totally accurate reflection of the global scene. But the British knew more about jet noise; it seemed only natural that they should know more about all aspects of jet propulsion. The early jets of the 1940s were noisy, noisy enough to be a really important problem a problem that had to be quantified and predicted and if possible controlled. Most early jet engines ran only on test beds and their noise was measured in close proximity to the machinery and exhaust flow. That there was a problem was clear, but test bed measurements gave little insight into how to bring order into the subject. Open air tests soon allowed the sound radiating away from jets to be measured [1, 2], and the jet flows produced by expanding compressed gases of various compositions through small nozzles became useful research facilities [3]. The instrumentation used for early measurements lacked the calibration and accuracy regarded as essential today, and the spectral analysis equipment rarely resolved more finely than the octave band. Being a new subject, the aeroacoustics of the early 1950s had no established discipline. Clearly important, but unfamiliar to scientistis and engineers alike, there was scope for anyone interested to contribute. There were no experts, and many of the enthusiastic contributors of experimental data and measurements at full scale felt unconstrained by any need to record values of the various operating parameters that might influence jet noise other than to quote a peformance measure of their particular device. The most popular noise measure was the radiated acoustic power, that clearly increased with the size and power of the jet flow. Big jets were noisier than small jets, fast jets noisier than slow jets. Expansion ratios across the propulsive nozzle were important, as were jet temperature, density and the speed of sound variations in the exhaust streams of jets with different propulsive gases. Choked jets made a qualitatively different noise, their piercing screech
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being much more irritating than the random rumbling noise of subsonic jet streams. But whether pressure ratio or jet Mach number mattered more than jet power or propulsive thrust, or how important the jet density was compared with the speed of sound or mean jet temperature, was far from clear. The problem had a range of possibly important defining parameters, and without some fundamental understanding of the physics little sense could be made of contradictory experimental measurements. That situation changed abruptly with the publication in 1952 of Lighthill’s pioneering paper, setting out a general theory of sound generated aerodynamically [4]. The paper was a masterpiece, elegantly expressed and making full use of the ordering ability of mathematical analysis. The subject was analyzed at its most fundamental level and he devised an exact theory of sound generation that carried the style and authority of the great scientists that had set out the science of sound some hundred years previously. Rayleigh or Stokes would surely have done the same had the need presented itself in their time. Now started a distinctly different era of aeroacoustics. The elegance and generality of Lighthill’s theory was awesome in its impact. Airflow in the absence of resonators and boundaries was proven to be equivalent in its sound-generating ability to a distribution of quadrupoles and, provided that these quadrupoles scaled with the variables defining the hydrodynamic mean flow, the power of the noise that it produced would scale on the eighth power of jet velocity. That was easy to check, and experimental confirmation of that velocity index was soon forthcoming. In fact, it is as if the eighth power law was taken as an accuracy check on experimental measurements and only those measurements that passed that test passed through the editors’ sieve to be published. Of course, the eighth power law could not go on for ever; the power of the propulsive jet itself only increases with the cube of jet velocity. That aspect was a puzzle in the light of the exactness of Lighthill’s analysis. And there were experimentalists who found it hard to believe that, despite its rigorous derivation, the eighth power law could really be right; some of their results gave a different sensitivity. It was probably that feeling of unease that prompted Richards to direct my research towards checking Lighthill’s theory, checking it by measuring the jet turbulence to see if it related to sound as the theory predicted. There was much for me to learn. I knew nothing useful about turbulence and the Lighthill theory called for knowledge of the turbulence stress tensor—whatever that might be. I was soon to become familiar with the tensors and to become in awe of the elegance of Lighthill’s formulation, but it surprised and disappointed me that I could not find anybody with recognizably useful knowlege of turbulence. That situation is not so different today. Lighthill knew that turbulent eddies convect and that convection of their associated acoustic sources would modify the radiated sound. His setting of the problem into a convected co-ordinate system revealed the main convective effects explicitly; there is a Doppler modification of frequency and the sound is preferentially beamed into the direction in which the frequency shift is greatest. He did not pursue the analysis for the coincident condition where the source propagates in some direction at exactly the speed of sound, and his jet noise scaling scheme specifically excluded that possibility. Nonetheless, if that scheme was applied at the coincident condition it predicted infinity. The novelty of Lighthill’s approach, the quadrupole nature of aerodynamic sources and his emphasis of convective effects and of the crucially important space–time structure of the fluctuating Reynolds stresses was hard for people to take and it was not surprising that attempts were soon made to approximate and simplify the problem. Under Richards the Southampton team had up to that time concentrated on measurement of aerodynamic sound [5], making good use of optical techniques, techniques that work best on sharp-fronted waves. The sound produced when a shock wave passes a vortex was the subject of early experiments and Alan Powell’s [6] visualization and explanation of jet
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screech was a landmark. But it was Lighthill’s demonstration of how the subject can progress when the physical problem is properly modelled and analyzed that led directly into the modern aeroacoustic approach, in which theory and experiment are inseparable. Alan Powell left Southampton for the U.S.A., where he formulated his theory of vortex sound [7], which has proved extremely helpful in understanding the aeroacoustics of geometrically simple low Mach number flows. My own postgraduate studies were enormously influenced by Herbert Ribner, a visitor to Southampton, who knew that flow/acoustic interaction effects were important to understanding the jet noise problem, and he also knew at that time the essential structure of the inappropriate approximation that led to the singular Lighthill convective amplification term. He too sought an alternative simpler view of the sound-generating properties of flow, but many remain to be convinced of the merits of his proposed alternative. Mo¨hring [8] derived a relationship between unsteady low Mach number vorticity and sound, a relationship striking in its apparent simplicity and which has proved an effective way of evaluating the noise made by a definite distribution of voriticty. Howe [9] rearranged the problem to highlight the aeroacoustic significance of density and entropy inhomogeneities at low Mach numbers. It was in 1955 that Curle [10] published his extension of Lighthill’s acoustic analogy to include the effect of flow boundaries, showing that boundary terms could provide effective mass and momentum injection into the flow, acoustically equivalent to monopole and dipole sources of fundamentally greater acoustic efficiency than Lighthill’s volume quadrupoles. The 108 increase in acoustic efficiency as bubbles form in turbulent liquids is a direct effect of the monopoles [11] and the dipoles accounting for unsteady surface loading are the essential source of subsonic propeller noise. The Lighthill/Curle approach relates sound exactly to integrals of surface and volume source terms and specifies precisely what these source terms are. Once they are known, so is the sound field. Lighthill encouraged the view that low Mach number sources might well be independent of their sound field, and that they could be estimated or measured to produce a prediction of what their induced sound would be. The U 8 law followed such a prediction, and Curle’s surface stresses and vibration terms would similarly yield U 6 and U 4 scaling laws, laws that though verified in experiment were laws that were actually prone to failure. Alan Powell [12] pointed out that turbulence bounded by a rigid plane would still produce only quadrupole sources and that in that case Curle’s surface sources amounted to nothing more than a specular reflection of the volumetric sources, the sound of which was augmented by the quadrupole sound of ‘‘image’’ turbulence. Powell had made evident the fact that the surface source terms could not generally be specified independently of sound. In those cases in which sound does affect the surface sources, although the acoustic analogy is exactly true it is probably of very little use. The sound has first to be known before its surface source distribution can be specified—the meaning of what comes before what and what causes what has at this stage been lost. The problem has to be approached from another direction. It is a most important requirement of robust acoustic analogies that they should separate the source from the sound, sound being defined as the linear response of the source’s environment; sound is the response—it is driven by the source. There is no uniqueness about sources. Many different sources are capable of generating the same sound, and it is not therefore surprising that alternative prescriptions of aerodynamic sources exist. Lighthill’s analogy pointed the way and provided a tool for understanding and predicting the acoustic consequences of turbulence embedded in an acoustic environment at rest. Other analogies will be better if the situation is essentially different from the model that Lighthill envisaged—though Lighthill’s analogy continues to provide precise identities between sound and flow, identities that may or may not be useful. So it is in the case of
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the low Mach number turbulent boundary layer making sound that disturbs the otherwise uniformly moving flow over a plane rigid surface. The unsteady turbulence stress tensor is the strength of the quadrupole source making sound that leaves the source to be heard after it has travelled relative to the moving stream and been reflected in the acoustic mirror of the constraining boundary surface. That is the best view of the problem, although before Powell recognized that approach many hoped to be able to ‘‘predict’’ the sound radiated by turbulent boundary layers by making use of unsteady surface pressure measurements made in boundary layer tunnel facilities—a much more complicated and yet-to-be-proven procedure. Structures in flow rarely operate satisfactorily if driven to vibrate so violently that non-linear effects are important. Most flow surfaces then, even though they may vibrate, are surfaces on which boundary conditions are linear and the surface source terms that Curle identified in the acoustic analogy are also linear. Linear surface source terms may look satisfactorily simple but, in the aeroacoustic context, they are very far removed from what is generally easily interpreted—unless the surfaces are small enough, small enough for their environmental field to be forced into a near-singular adjustment in conforming with the local surface constraints. And the fact that small rigid bodies, with no boundary motion and no conceivable way of energizing any environmental disturbance, can possibly be the dominant aeroacoustic source is still an aspect that some find confusing. If foreign bodies provide the only disturbance to the perfect acoustic environment, and if that environment is otherwise source-free with its sound field unaltered by volumetric sources, then there is no sound and no pressure variation on the bounding surface. This obvious fact, that still fluid surrounding a motionless body is at rest everywhere and at steady pressure, is an example of an important wave property that is not as well known as it might be. The normal velocity on the bounding surface determines the pressure everywhere, and in particular the boundary pressures. It is also true that surface pressure has the same field-determining property. Knowledge of either the normal velocity or of the surface pressure defines all aspects of a linear sound field completely. Knowledge of both gives no more information than knowledge of one, although it undoubtedly provides that information in a more usable from. The fact that Curle’s surface monopoles and dipoles somehow turn into something else is not so much of a mystery once it is appreciated that linear surface terms—which is what they are—are not to be specified arbitrarily and can contain very subtle features that are easily lost by approximation. The error in assuming that they are sources the properties of which can be specified independently of their sound and that they scale on hydrodynamic variables is what caused the trouble in the flat-plate case. Powell recognized the essential fact that the extended ‘‘source’’ terms are sound rather than sources of sound; resetting aeroacoustic boundary problems within the context of different theory then became inevitable [13]. However, acoustic terms will be very weak at low enough Mach numbers, and it is only when the surfaces are large enough to make the accumulated effect of all the weak sources mount up to something large that the surface source terms are sensitive to sound. Acoustically compact surfaces, surfaces of linear scale much smaller than any in the sound field, do provide very efficient acoustic sources that the Curle procedure describes precisely and robustly. In these compact source cases it does not matter which view of the source process is taken. Even the acoustic field on small enough bodies is set by the hydrodynamics of adjacent flow, the compressibility of the medium having a negligible effect [14]. Then it is perfectly reasonable to scale surface stresses on hydrodynamic variables, even though they are linear, and to determine their acoustic effect by evaluating Curle’s integrals. Even
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when there are nearby volumetric sources, the sound scattered by acoustically small foreign bodies can be evaluated by solving the wave equation under the specified source conditions accounting for the known boundary constraint. This could be done by seeking the Green function under those boundary constraints and convolving it with the known sources, or by determining the hydrodynamic boundary conditions for later use in the Curle integrals. The development of aeroacoustics to specify only the turbulent source activity and to solve for the field on boundary surfaces has definitely brought new aspects of the subject into the limelight. The boundaries diffract the field. The special case of diffraction, when the surfaces are small on the acoustic scale, is scattering. Compact surfaces scatter the near field of quadrupoles very effectively indeed. Ten years after the publication of his general theory Lighthill summarized the subject of sound generated aerodynamically to the Royal Socieity in the 1961 Bakerian Lecture [15]. Jet noise had by then become the major problem envisaged when the analogy was conceived, and there was ample confirmation that the turbulence of the jet mixing layer, that Lighthill had identified as being the main source of noise, was indeed just that. The basic characteristics he had assumed this turbulenece to have had been largely confirmed. Measurements using the 1 and 2 inch diameter jets and the hot wire and space–time correlation equipment that Richards had established at Southampton made important contributions to the build-up of data, and the Lighthill style of jet noise prediction had been satisfactorily extended to supersonic jet speeds [16]. The outstandingly important parameter determining overall noise was jet speed, the eighth power law proving accurate at the engine exhaust speeds of operational jet aircraft. Quieter engines would happen only if jet speed was lowered—and, since a lowering of jet velocity would improve propulsive efficiency, higher mass flow engines of lower specific thrust were what the industry needed, and they were coming on in the high by-pass ratio engines then under development. Theory and practice seemed to be in satisfactory agreement—although in fact the serious engineering study of jet noise was only just beginning. The initial drive to lower jet speeds certainly brought the hoped-for U 8 law returns, but the aircraft problem had become so acute that even greater improvements were needed, and the engine industry responded with even larger engines of lower specific thrust. These larger engines failed to achieve the expected noise reduction and that failure spurred a much closer look at the jet noise problem in the early 1960s. The lower speed jets, with flows more closely meeting the Lighthillian low Mach number model, did not conform with quadrupole scaling [17]. More efficient sources had come into prominence and those were less sensitive to changes in jet speed. Of course jet turbulence is not very far away from the jet pipe and its termination in the exhaust nozzle. The possible influence of that is ignored in the simple model. Could it possibly be important? The answer is ‘‘yes’’; its influence is crucial at low enough exhaust speed [18]. Steady jet flow produces steady propulsive thrust. Unsteady jet flow produces unsteady thrust, acoustically equivalent to an axial dipole and more effective than free jet turbulence by a factor proportional to the inverse square of Mach number. This would give a noise scaling with U 6. Having started on that theme a U 4 contribution soon becomes evident, because unsteady exhaust output is equivalent to an acoustic monopole. Both of these elements are consistent with data taken from engine measurements. Also, the noise generated inside the engine by unsteady combustion, turbomachinery and internal turbulence manifests itself as unsteady flow through the exhaust nozzle. That called for flow smoothing devices and sound-absorbent treatment of the internal engine surface—which have proved very effective and are now commonly found in modern engines, engines that are quieter, for the same duty, by at least a factor of 100 than the engines of 20 years ago.
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Turbulence near a pipe opening must subject the pipe to acoustic disturbance and cause pipe entry conditions to become unsteady and to support monopoles and dipoles at the exit plane. To estimate the importance of this effect to the jet noise problem, experimental model studies were conducted with turbulence generators near the nozzle exit. Supporting theoretical examples represented the turbulence by quadrupoles the characteristics of which scaled on hydrodynamic variables. Of course the details of the interaction depend on the orientation and position of the quadrupoles, but experiments and theory confirm the fact that the open pipe is acoustically equivalent to a dipole source and its sound scales with the sixth power of jet velocity. More precise representations of idealized vortical flow produced examples consistent with the result, but known exact unsteady flows are few and the examples necessarily highly idealized. Often the examples are two-dimensional—and so is their sound field. A pair of opposing parallel line vortices within a two-dimensional semi-infinite duct moves and can escape out of the duct, perturbing the otherwise steady condition as it escapes. The matched expansion technique can give a solution to the sound generated by the escaping vortex pair, and again that calculation confirms the effectiveness of the duct as a scatter of the hydrodynamic field into sound exterior and interior to the duct [19]. For the precisely defined simple vortex configuration the complete history of the disturbance is available, but that is of little practical interest other than confirming that the scaling derived through the acoustic analogy is consistent with the results for the definite example. All these nozzle/jet turbulence interaction studies fit together and give confidence that the different basic mechanisms responsible for the noise of jets at the lower exhaust speeds are being understood. A much more interesting aeroacoustic model problem considers the scattering ability of a semi-infinite rigid screen [20]. The two alternative approaches of evaluating the field scattered when the edge is close to a quadrupole source, and the specific example of a line vortex lying parallel to the edge and moving unsteadily from one side of the screen to the other [21], both indicate the edge scattering to be important—more important in fact that the dipole interaction with a compact surface. Edge-scattered sound scales on U 5 and there is experimental confirmation of that theoretical prediction. The noise control work on jet engines has been so successful that engines no longer dominate in all aspects of the aircraft noise problem near airports. The airframe itself makes noise and the noise of flow over a large transport aircraft in its landing configuration is strong and is a cause for practical concern [22]. It is much worse than the nice swishing noise one can experience when a glider is heard on its landing approach, but the basic causes of the noise are the same in both cases. The large aircraft is faster and heavier and cluttered with elaborate landing gear, and multiple slot and flap arrangements have been deployed to augment the lifting ability of its wing. It is now thought that the turbulent boundary layer flowing over the trailing edge of lifting surfaces is one of the main contributors to airframe noise, and that the characteristics (directionality frequency content and velocity sensitivity) of that noise are consistent with the edge scattering process, a process first investigated simply because it was one of the geometrical arrangements that were simple enough to yield to analytical treatment. The turbulence was represented by quadrupoles scaling on hydrodynamic variables and the induced wave field solved with proper account being taken of the boundary constraints on the semi-infinite screen. Definite aeroacoustic models in which either the quadrupoles, representing turbulence or unsteady vorticity, or the Powell and Mo¨hring representation of vortical flow sources, have been analyzed to build up an appreciation of how sound is created in flow over definite geometrically intricate surfaces. These studies were usually driven by underwater or aeronautical needs, but have resulted in understanding the quantitative detail of sound in wind instruments [9], as well as the essential mechanics of the less pleasant, practically
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important flow-induced sounds. The compact scattering cases are relatively simple— Curle’s scheme works well on them. But when extensive surfaces interact with flow the acoustic analogy solved subject to the diffraction effects of boundary constraints offers the only way forward. The sounds made when turbulent flow passes down channels of irregular shape and the noise of a ring vortex passing through an orifice are understood from such studies. The reason why the interaction of turbulence with sound-absorbent screens is noisy has been made clear and, indeed, the problem controlled in the light of that understanding. These studies have pointed to flow of an irregular fluid mixture as being especially prone to unsteadiness and to be more capable of making sound than the flow of materially homogeneous fluid; the noisy chuffing of a garden hose as flow starts and emerges as an intermittent mixture of air and water is an everyday example of that process. The essential cause of that noise is that non-uniform flow of density-inhomogeneous fluid cannot be steady. The heavier portions, being less easily accelerated than the lighter parts, move differently through the pressure gradient that drives changes in speed. That has important aeroacoustic consequences and Morfey’s [23] identification of the fact revealed one of the very few aerodynamic sound-generating mechanisms that had escaped Lighthill’s notice. And it is an important mechanism, being the dominant cause of mixing noise elements in very hot jets. What Lighthill had failed to cover was the case in which mass density variations are not simply proportional to pressure changes, but depend also on what the material is. The normal balance in sound, Dp=c 2Dr, is not held in a mixture of fluids, and the difference appears as an inhomogeneity in the governing equation, a dipole inhomogenity more efficient than the quadrupoles which Lighthill showed accounted for all source processes. Lighthill’s method is precise enough to extract this effect once it is recognized that an interface between two different material substances is a surface of singular density gradient—and, in essence, that eventually makes singular the strength density of the quadrupole needed to represent what is really a finite dipole source system. An inhomogeneous mixture is bound to occur at the turbulent interface between adjacent zones of different fluids. Violent ocean wave activity at the air/sea interface is an example, and an example that makes clear the need for another major physical constraint to be accounted for explicitly before an acoustic analogy can help. The sound sources are not there embedded in an infinitely extended homogeneous environment as Lighthill’s analogy requires; one half of space is completely different from the other. Sound generated in either half will be partly reflected and partly transmitted through the interface, a wave effect that must be dealt with properly and not left as acoustic influences in the source terms; that would render the analogy useless, because the ‘‘sources’’ could not be known in advance of the waves that the sources are assumed to create. Once the linear response of the ocean surface was incorporated into the analogy the aeroacoustic approach transformed our state of knowledge of the important oceanographic question of what underwater sound is generated at the ocean surface. Guo’s [24–26] fundamental work illustrated how cause and effect could be ordered and separated, and he demonstrated how one could get much further than before by regarding both surface waves and sound as two of the consequences of inhomogeneous source activity. The two are related, but it is not the relation of cause and effect implied in the classical wave studies that up to that time provided the only pointers to the underlying mechanics of the sound generation process. Again, it is the singularly abrupt flow changes that happen at any fixed position crossed by the moving air/water interface that makes the simple quadrupole representation inadequate. Those singular volume ‘‘sources’’ give rise to finite surface distributions that are linear in the disturbance amplitude, and to deal with them properly one needs the kind
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of procedure that Powell had introduced to avoid Curle sources on infinite planes. And in developing the techniques for the oceanic case the acoustic analogy became generalized; it not only modelled the flow-induced sound but it also dealt with the creation of other waves, surface gravity waves in particular. That development of aeroacoustics to give other natural linear motions the same standing as sound is probably important, but it is far too early to be sure. Before Guo showed better, ocean waves were looked on as potential sources of sound [27]—which of course they can be, being coupled to sound at the non-linear level. But the view of surface gravity waves and their associated sound as being related linearly because they were both generated together is a much more satisfactory and general approach. The depth of understanding that followed made obvious that the sound generated by surface waves was no more a real effect than the surface waves generated by sound; both views can be right, but neither is generally helpful [28]. The aeroacoustics of two adjacent fluids needs to account for the different natural responses of those fluids to a disturbing influence, and it should also account for the modes of linear response that might exist purely because of the relative disposition of those fluids. Density and speed of sound differences both affect the response, but the effect, large as it is, is not nearly as great as the changes which come from bulk motion of fluids at high Mach number. Sound is convected by flow and aeroacoustic modelling has to bring out that effect explicitly if at all possible. In 1953, Powell [6] had shown how the mechanism of supersonic jet screech depended on mean flow differences, differences between the jet interior and its surroundings and across shock waves in the jet. Mean shear has been viewed as a potential amplifier for jet noise since the subject began, and the sound-generating quadrupoles have always attracted workers to distinguish between the effects of mean flow/turbulence interaction and non-linear turbulence terms. High speed source convection has a profound influence that was explicitly incorporated into the acoustic analogy from the start, but refraction and the possible focusing of sound as different rays are brought together, because shear flow bends their differing acoustics paths, was more difficult to account for alongside the aeroacoustic source process. That the effects were there was never in doubt, but their modelling required the non-uniform flow to be featured within the fundamental linear operator prescribing how sound behaves, and it is a matter of judgement as to which aspect of the flow is emphasized first. One approach [29] extends Lighthill’s analogy to account for the different propagation characteristics within two adjacent streams in relative motion and, though more complicated than the original analogy, the extension retains the exactness characteristic of Lighthill’s method. Other schemes take into account the detailed profile of the mean flow and inevitably pay for that detail in increased complexity [30, 31]. The interface between two streams in relative motion is linearly unstable and any scheme that represents exactly the interface perturbations, produced by aeroacoustic sources, must deal with the resulting linear instability. The exact modelling accounting for interface effects within the analogy drives one into having to select between insisting on either the finiteness of the linear response to a disturbance or on the causality of that response; one cannot have both at the same time on an unstable interface. Since any theory in which the linear effect of a disturbance grows without bound is probably unworkable, the non-casual solution has been preferred and the implied existence of the sound field in advance of this source rationalized in the following way. Sound is the linear response of a flow perturbed by the non-linear source process, but if the flow is unstable that response quickly grows to become non-linear and so to become the source. There is no requirement, then, to presume that aeroacoustic sources induce only a causal response—finiteness is much to be preferred (though the finite response is also the causal one when the flow is stable). Both the two-part uniform flow and the continuously varying flow profile
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modifications of the acoustic analogy have had the effect of bringing the theory and practice of jet noise into much closer agreement [32, 33]. Measurable elements of the noise field are predictable without having to say much more about the nature of the turbulent sources than that they scale on hydrodynamical variables. Since the understanding and effective modelling of turbulence is so difficult, that robust property of advanced analogies is useful and, incidentally, implies that progress in the control of jet noise is not dependent on a solution of the turbulence problem. All these approaches regard the linear response of the flow, the sound that interacts with the flow before it escapes, as being separable from the source of sound. If that is not so, there are great difficulties still to be overcome before the mechanics of aerodynamic sound is adequately understood. Both the flow and the sound must then be recognized as imperfectly separated parts of the same phenomenon, and must be understood and modelled together through schemes that have yet to be devised. Numerical techniques are expected to provide the long-term answers, although there is no clear perception yet of what question is most usefully asked of the computational aeroacoustician. Of course it is possible to understand the way in which particular elements of the problem fit in; the linear instability waves on an evolving shear layer for example, with their near fields extending to become recognizable acoustic features of real jets [34]. But to believe that one induces the other misses the point. The near field and the instability wave are inseparably the same thing; one cannot exist without the other and the question of what made them and what needs to be done to avoid them, the dominantly important practical aeroacoustic question, cannot even be addressed from that approach. The confusing coexistence of source and sound is at its height in searching for the acoustic importance of shock waves. The flow over transonic helicopter blades supports embedded shock waves, as do imperfectly expanded supercritical jets, and the noise of both flows is commonly viewed as resulting from a source process involving the shocks. But the shocks are compressive waves, often quite well approximated by linear theory, i.e., they are virtually sound, and it is quite difficult to see the point of setting them up as known in advance and to be the source of, rather than the manifestation, of, sound. Prediction procedures that rely on known shock-attached boundary conditions [35] are nonetheless considered useful; more fundamental approaches that emphasize the acoustic content of shocks do not seem to have yet made much impact on the aeroacoustics community [36]. The aeroacoustics of propulsive flows, be they mixing flow or turbomachinery related, is still the subject of active research, the high speed rotor problem seriously limiting the acceptance of helicopters into the urban environment. And jet noise is possibly the most difficult problem that must be solved before a supersonic passenger airliner is environmentally acceptable. The work that is producing ever closer agreement of prediction and practice (work that has progressed very satisfactorily over the past 20 years) is sadly concentrated on the pure jet flows that are too noisy to be practical [37]. The fundamentally different silencing schemes that will be essential for future SST’s still remain but a gleam in their inventor’s eye. A serious search for the radically new is badly needed. In this sense, although the past 40 years have seen enormous strides in aeroacoustic technology, there remains today the same kind of aeroacoustical need that posed such a serious research challenge at the beginning of the jet age. The supersonic branch of civil aviation is similarly at risk because of noise. Forty years ago, Elfyn Richards took such needs as a personal challenge and the energy and drive he brought to the subject had great effects. He established a research centre second to none in its aeroacoustic importance. His Southampton Institute of Sound and Vibration Research is just the sort of fundamental free-thinking academic environment needed for creative innovation and that is possibly his greatest legacy. The ISVR is bound to contribute towards finding the new techniques
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needed to control the noise of the supersonic jet age. That is today’s dominant aeroacoustic challenge.
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