Alan Powell

Theory of Vortex Sound

Physical arguments are followed by mathematical developments to show how aerodynamic sound is generated as a result of the movement of vortices, or of vorticity, in an unsteady fluid flow. Changes in circulation or area of a vortex ring give rise to a dipole sound field, the former being illustrated by oscillating flow about a fixed sphere, and the latter by a simple model for the aeolian tone attributable to the stretching of vortex rings. Because in a free flow there can be no change of the total vortex strength (circulation times area), there is no net dipole strength, but each moving element of vorticity still causes local dipolelike flow; each element of moving vorticity acts with some equal and opposite movement elsewhere in the flow so that together they form an oblique quadrupole, although the total effect must be reducible to an assembly of lateral quadrupoles. A cardinal result is that the vorticity in a slightly compressible fluid can be considered to induce the whole flow field, both the hydro...

On the Edgetone

The feedback mechanism of classical low‐speed edgetones in which the action at the edge is interpreted as an acoustical source is developed in detail. A theoretical development indicating that the acoustic field is primarily due to the dipole associated with the fluctuating fluid force on the edge has been verified. It is the hydrodynamic field of the dipole which disturbs the jet, whose instability characteristics are shown to depend acutely on the Reynolds and Strouhal numbers, and the orifice‐edge distance. The gain criterion is developed in detail, it being shown how the eigenfrequencies (which can form no algebraic sequence) arise; the lower limit to the orifice‐edge distance is discussed, yielding an estimate of the “linear” instability of the stream. The amplitude of the established edgetone depends on the nonlinear behavior of large‐amplitude stream disturbances and the corresponding upper limit to the edge force proves to be in satisfactory agreement with measurements, thus yielding acceptable expressions for the sound pressure. Multiple tones and the circumstances of the hysteretic frequency jumps are discussed. The basic action depends only on Reynolds number for geometrically similar systems, while the sound power depends on the cube of the Mach number also.

Aerodynamic Noise and the Plane Boundary

In an earlier paper entitled “Thoughts on Boundary Layer Noise” (Aeronautical Research Council Report 16727, 1954), it was pointed out that while the fluctuating pressures exerted upon a rigid boundary by a contiguous unsteady flow can be shown in a formal manner to generate sound as of a distribution of dipoles, it can be argued by means of the reflection principle that all such dipole effects cancel out in the case of the boundary being plane; yet observations of aeolian tones adequately confirm the presence of effective dipole‐like generators in that case. Here the image principle is developed in a rigorous manner and the apparent paradox is resolved with the help of an extension of Lighthills and Curles analyses to include boundaries which are not wholly immersed in the noise‐generating flow. In particular, it is shown that the pressures exerted on a plane boundary are simply reflections of the quadrupole generators of the flow itself; thus the pressure dipoles account for an enhancement of the quad...

The sound-producing oscillations of round underexpanded jets impinging on normal plates

The results of acoustical and optical experiments in which ‘‘moderately’’ underexpanded sonic round jets impinge on flat plates normal to the jet axis are presented and analyzed. Periodic unstable oscillations of the jet flow, with the resultant radiation of sound of discrete frequencies, occur over a wide variation of control parameters, namely, pressure ratio, plate size, and spacing of the plate from the jet nozzle. For ‘‘small’’ plates, the principal oscillations with λ/D about 4 (λ=acoustic wavelength, D=nozzle diameter) occur when the standoff shock wave lies in a pressure recovery region of the periodic cellular structure of the choked jet and is, therefore, highly unstable; then the oscillations have key characteristics in common with the high‐harmonic excitation of Hartmann’s acoustic air‐jet generator. An analogous feedback mechanism in the standoff zone is suggested in which pressure waves reflected from the plate trigger the motion of the unstable shock wave. For ‘‘large’’ plates, acoustic fee...

On the Fatigue Failure of Structures due to Vibrations Excited by Random Pressure Fields

On the assumption that the forced modes of vibration of a structure, subjected to pressure fluctuations random in time and space, can be approximated by the composition of the motions of the uncoupled natural modes, a general analysis is made using the ideas of vibration theory and spectrum analysis. The power spectrum, and hence the rms value, of any quantity depending linearly upon structural distortions is derived and it involves a quantity (called the “joint acceptance”) concerning the spacewise structure of the pressure field and of the geometry of the modes of vibration. It is shown how this result may be used (on assuming “normal” randomness) to estimate the fatigue life on the hypothesis of cumulative damage.

Observations of the oscillation modes of choked circular jets

Under‐expanded jets exhausting from convergent circular nozzles are known to emit a powerful acoustic tone called screech. The steady decrease of the screech frequency with increasing pressure ratio is interrupted by four frequency jumps as the mode of jet instability changes successively from an axially symmetric (varicose, torroidal) one labeled A1 (varicose, torroidal), to another but similar one labeled A2, a sinuous (lateral, flapping) one B, a helical one C, and finally one that is identified here as a sinuous one, D. Digital FFT analyses disclose the simultaneous presence of associated secondary tones about 25 dB weaker than the dominant ones, the frequency of these secondary tones forming smooth continuations of the dominant tones. As a secondary tone connects the dominant B and D modes, it is inferred that these are actually the same mode interrupted by the helical mode C. However, their detailed behavior is significantly different: the plane of oscillation of B appears to have a preferred orient...

The Noise of “Choked” Jets

The noise of a jet changes character after the pressure ratio exceeds the critical value appropriate to sonic exit velocity, the general roar being dominated by a loud “whistling” or “screeching.” Schlieren photographs show that sound waves of ultrasonic frequency are caused by the transition of the initially laminar boundary layer to turbulence, and also by this turbulence interacting with the shock waves of the flow, Larger disturbances have also been noted, involving both the jet stream and some of the air external to the jet, and these also give rise to sound waves which have been photographed it is these which are held responsible for the audible effects A two‐dimensional study has shown the latter phenomenon to be enhanced, and it is shown how the system of disturbances is self‐maintained by virtue of sound waves creating initially small disturbances at the jet exit. The directionality of the sound field has been predicted and found in agreement with experiment, and the dimensions of the motion are ...

Some Experiments concerning the Hole and Ring Tone

Discrete‐frequency tones can be generated when objects obstruct the path of an axially symmetric jet. An experimental study of this phenomenon was conducted when the objects were (1) a flat plate perpendicular to the jet axis, there being a hole in the plate of the same diameter as the jet orifice and concentric with the jet, and (2) a ring whose plane was perpendicular to the jet axis and whose diameter was equal to that of the jet orifice. The tone from the former geometry is the hole tone and that from the latter, not previously observed, is the ring tone. The mechanism of tone generation appears to be very similar to that of the edge tone, although presently only qualitative explanations can be offered for certain aspects of the phenomena. The axially symmetric jet systems are sensitive to very weak acoustic reflections.

On the Aerodynamic Noise of a Rigid Flat Plate Moving at Zero Incidence

The aerodynamic noise resulting from the subsonic flow over a flat rigid plate at zero incidence has three origins. “Surface” noise due to fluctuating surface pressure is postulated to vanish by the authors image argument, except near the edges of the plate, where it is more appropriately called edge noise. Of dipole nature, its acoustic power depends on the velocity raised to between the fourth and fifth power, and consequently is to be expected to be of prime importance at low enough speeds. The contribution from fluctuating shear stresses is likely to be much smaller and so has been neglected. Quadrupole radiation takes place from from the turbulence of the boundary layer, producing layer noise and also from the turbulent wake, producing wake noise. Together, the latter two are suggested to have a spectrum with a single peak, bounded by slopes like f2 and f−7/4. Their noise power depends on nearly the eighth power of velocity, so is of increasing importance with speed. Analytical details rest on simil...

Transmission of Random Sound and Vibration through a Rectangular Double Wall

The existence of many modes of vibration in a complex system makes a detailed classical analysis almost intractable. However, when excited by broad‐band random noise, the detailed response characteristics may be overlooked and statistical properties such as mean‐square values and power spectra provide a measure of the vibration. The existence of classes of similarly excited modes allows theories of room acoustics and thermodynamics to be applied successfully. For sound transmission through a rectangular double wall, this technique gives results that agree within experimental error of measured transmission loss, much better than do conventional loss estimates. Both theory and experiment confirm that the product of modal density, average joint acceptance of the first panel, and the ratio of radiation to total resistance of the second panel are the most important characteristics in determining the transmission characteristics of the wall.