J. E. Ffowcs Williams

‘Crackle’: an annoying component of jet noise

The paper describes an investigation of a subjectively distinguishable element of high speed jet noise known as ‘crackle’. ‘Crackle’ cannot be characterized by the normal spectral description of noise. It is shown to be due to intense spasmodic short-duration compressive elements of the wave form. These elements have low energy spread over a wide frequency range. The crackling of a large jet engine is caused by groups of sharp compressions in association with gradual expansions. The groups occur at random and persist for some 10 −1 s, each group containing about 10 compressions, typically of strength 5 × 10 −3 atmos at a distance of 50 m. The skewness of the amplitude probability distribution of the recorded sound quantifies crackle, though the recording process probably changes the skewness level. Skewness values in excess of unity have been measured; noises with skewness less than 0·3 seem to be crackle free. Crackle is uninfluenced by the jet scale, but varies strongly with jet velocity and angular position. The jet temperature does not affect crackle, neither does combustion. Supersonic jets crackle strongly whether or not they are ideally expanded through convergent-divergent nozzles. Crackle is formed (we think) because of local shock formation due to nonlinear wave steepening at the source and not from long-term nonlinear propagation. Such long-term effects are important in flight, where they are additive. Some jet noise suppressors inhibit crackle.

The active control of vortex shedding

This paper describes an active method of controlling vortex shedding from a circular cylinder at Reynolds number 400. The control was effected by an acoustic feedback of signals taken from hot-wires in the wake of the cylinder. The velocity fluctuation at the nominal vortex shedding frequency is reduced throughout the wake, in places by more than 30 decibels. Reduced also is the harmonic content though those elements were not excited from the control signal. Shedding could be suppressed by switching on the controller, the effect taking two or three vortex shedding periods to take hold. Similarly, when the controller was switched off, the natural state was recovered in about ten cycles.

Active stabilization of compressor surge

This paper describes the stabilization of compressor surge by an active method. It is known that surge follows when small disturbances grow in an unstable compression system, and that small growth can be modelled through a linear stability analysis. An active element is here introduced to counter any tendency to instability and the control law governing the active stabilizer is determined from linear theory. We follow precisely the suggestion put forward by Epstein et al. (1986) and verify that their theory conforms to practice. The theory is verified in an experiment on a compression system whose plenum volume is controlled. Suppression of the flow instability was achieved by switching on the controller and the compressor was made to operate stably on a part of its characteristic beyond the nature stall line. Furthermore the controlled compressor is much more resilient to external disturbances than is the natural case. The controller is even effective on deep surge – a feature of great interest but hardly predictable from the Epstein et al. initiative for this kind of study.

Boundary-layer pressures and the Corcos model: a development to incorporate low-wavenumber constraints

This paper re-examines the theoretical arguments that indicate the structure of the pressure field induced on a flat surface by boundary-layer turbulence at low Mach number. The long-wave elements are shown to be dictated by the acoustics of the flow, and the limit of the acoustic range is the coincidence condition of grazing waves where the spectrum is singular and proportional to the logarithm of the flow scale. The surface spectrum is shown to be proportional to the square of frequency at low-enough frequency and to the square of wavenumber at those low wavenumbers with subsonic phase speed. The similarity model successfully used by Corcos for the main convective elements of the field is used in this paper to model the turbulent sources of pressure, not the pressure itself, so that a Corcos-like description of the pressure spectrum is derived that is consistent with constraints imposed by the governing equations. This results in a fairly compact specification of the pressure spectrum with yet-undetermined constants, which must be derived from experiment. Despite an extensive search of published data on the pressure field, it is concluded that existing information is an inadequate basis for setting those constants and that new free field experiments are needed. Boundary layers formed on gliders or buoyant underwater bodies offer the most promising source of such data. The paper concludes with a study of how large flush-mounted transducers discriminate against the local flow noise field and i t is shown that they do so at a rate of 9 decibels per doubling of transducer diameter. This different conclusion from Corcos’ correct 6 decibel rate for small transducers is entirely due to the low- wavenumber constraints on the spectrum, which are misrepresented in the simple similarity model. This result, which conforms with the constraints imposed by the weak compressibility of the fluid, is the same as that later suggested by Corcos for transducers that are large on the boundary-layer scale.

The generation of sound by density inhomogeneities in low Mach number nozzle flows

This paper discusses the sound generated when an inhomogeneity in density is convected in a low Mach number steady flow through a contraction in a duct of infinite extent, and also when the inhomogeneity exhausts through a nozzle into free space. The analyses of Candel (1972) and Marble (1973) for the case of duct flow were based on a frequency decomposition of the incident inhomogeneity and cannot adequately deal with sharp-fronted inhomogeneities and entropy spots. However, the practical difficulties of this earlier work can be avoided at low flow Mach numbers by conducting the analysis in terms of an approximate expression for the acoustic Greens function in the manner described by Howe (1975). This method also permits a considerable extension of the range of the earlier investigations to the determination of the sound generated when the inhomogeneity is swept out of a nozzle orifice into free space. It is shown that the acoustic pressure perturbations developed in a duct at a contraction are in general proportional to the fractional difference between the density of the inhomogeneity and that of the mean flow times a typical mean flow pressure level, and are due principally to the fluctuation in thrust accompanying the passage of the inhomogeneity through the region of variable pressure gradient. The pressure waves generated at a nozzle orifice and radiated into free space are O ( M 0 ) smaller, where M 0 is a mean flow Mach number based on the speed of sound in the jet.

Active cancellation of pure tones in an excited jet

This paper describes the results of experiments conducted on a circular jet simultaneously excited by two different acoustic tones. By varying the phase between two signals at harmonically related frequencies, control can be exercised on the process of harmonic generation sometimes the process being virtually destroyed. This is shown to be so for both harmonic and subharmonic generation, but the latter is more difficult to control.

Active stabilization of compressor instability and surge in a working engine

We have applied feedback control to the compressor of a 45 kW auxiliary power unit. Using this, the engine is able to deliver more than 10 percent extra shaft power before surge occurs. We achieve control by suppressing a nonaxisymmetric flow phenomenon in the diffuser of the centrifugal ompressor. Control is effected by modulating a small extra air flow into the impeller. We present results of modeling and analysis suggesting that linear feedback control will be sufficient to stabilize a compression system, even when both axisymmetric surge and rotating stall are present as possible instabilities

Bubbles as sources of ambient noise

It has been shown that the main mechanism which produces the Knudsen region of the ambient noise spectrum is the free oscillations of bubbles. Some experimental results which seem to confirm these facts and to refute various alternative theories involving spray impacts and turbulent forcing of bubble oscillations are described. The results show that the mechanism which excites the bubbles is their formation at the surface; once a bubble has been formed and has radiated the excess energy resulting from its formation, it is more or less silent. It is possible for extremely violent conditions to re-excite bubbles by breaking them into smaller fractions, but it is not clear how important this process would be in the ocean. How the entrainment process imparts energy to the bubble is discussed. >

On resonant nonlinear bubble oscillations

If a bubble were produced with an initial surface distortion, the energy carried by surface modes could be converted to other modes by nonlinear interaction, a conversion that provides a possible mechanism of second generation by bubbles. Longuet-Higgins (1989 a,b ) has argued that volume pulsation would be excited at twice the frequency of the distortion mode and that the response to such excitation is ‘surprisingly large’ when its frequency is close to the natural resonance frequency of the volumetrical mode. It is shown in this paper that this is feasible only if the driving system is sufficiently energetic to supply the energy involved in those volume pulsations, and that this is not generally the case. In the absence of external sources, the sum of energies in the interacting modes cannot exceed the initial bubble energy; an increase in one mode is always accompanied by a decrease in another. In contrast to any expectation of significant pulsations near resonance, we find that, once modal coupling is admitted, the volumetrical pulsation has very small amplitude in comparison with that of the initial surface distortion. This is because of the constraint of energy, a constraint that becomes more severe once damping is admitted. Our conclusion therefore is that the distortion modes of a bubble are unlikely to be the origin of an acoustically significant bubble response.

On the possibility of turbulent thickening of weak shock waves

This paper examines the possible thickening of an initially sharp sonic boom by the turbulence it encounters in passing to the ground. Three apparently different viewpoints, all indicating substantial thickening, are shown to be actually identical and to give an irrelevant upper bound on wave thickness. All three approaches describe only the apparent mean diffusion induced by random convection of a sharp wave about its nominal position. Although a wave-front folding mechanism ultimately accounts for an apparent thickening as individual rays are weakened and tangled by turbulence, this process is too slow to be effective in the practical boom situation. The paper then considers what linear thickening of a wave packet results from propagation trough atmospheric turbulence and concludes that, in the relevant limit, a wave may be thickened by a factor of about 2 at the most. The conclusion is therefore reached that atmospheric turbulence cannot be the cause of the thousandfold discrepancy between the measured wave fronts and their Taylor thickness.