Michael S. Howe

Acoustics of Fluid–Structure Interactions

Preface 1. Introduction 2. Aerodynamic sound in unbounded flows 3. Sound generation in a fluid with rigid boundaries 4. Sound generation in a fluid with flexible boundaries 5. Interaction of sound with solid structures 6. Resonant and unstable systems References.

Compact Green's functions extend the acoustic theory of speech production

Abstract A brief tutorial discussion of the method of compact Greens functions applied to sources of sound in the vocal tract is given. A vocal tract transfer function may be regarded as a specialized Greens function. However, a Greens function enables detailed analysis of the transfer of energy from the hydrodynamic mode of fluid motion into sound. Source regions within the vocal tract often are small compared to the acoustic wavelength, which leads to a simplified model of the acoustics of the source region. This permits calculation of a ‘compact’ Greens function. In this approach much of the classical acoustic theory of speech production remains unchanged. The method is illustrated by the calculation of the sound source when a vortex is swept past an obstruction in the vocal tract. This is discussed in terms of the differences between the pressure sources of sibilant fricative production and of voicing and aspiration.

Effect of a downstream ventilated gas cavity on turbulent boundary layer wall pressure fluctuation spectraa)

An analytical and experimental investigation is made of the effect of a 2-D ventilated gas cavity on the spectrum of turbulent boundary layer wall pressure fluctuations upstream of a gas cavity on a plane rigid surface. The analytical model predicts the ratio of the wall pressure spectrum in the presence of the cavity to the blocked wall pressure spectrum that would exist if the cavity were absent. The ratio is found to oscillate in amplitude with upstream distance (−x) from the edge of the cavity. It approaches unity as −ωx∕Uc→∞, where ω is the radian frequency and Uc is the upstream turbulence convection velocity. To validate these predictions an experiment was performed in a water tunnel over a range of mean flow velocities. Dynamic wall pressure sensors were flush mounted to a flat plate at various distances upstream from a backward facing step. The cavity was formed downstream of the step by injecting carbon dioxide gas. The water tunnel measurements confirm the predicted oscillatory behavior of the ...

Source-tract interaction with prescribed vocal fold motion.

An equation describing the time-evolution of glottal volume velocity with specified vocal fold motion is derived when the sub- and supra-glottal vocal tracts are present. The derivation of this Fant equation employs a property explicated in Howe and McGowan [(2011) J. Fluid Mech. 672, 428-450] that the Fant equation is the adjoint to the equation characterizing the matching conditions of sub- and supra-glottal Greens functions segments with the glottal segment. The present aeroacoustic development shows that measurable quantities such as input impedances at the glottis, provide the coefficients for the Fant equation when source-tract interaction is included in the development. Explicit expressions for the Greens function are not required. With the poles and zeros of the input impedance functions specified, the Fant equation can be solved. After the general derivation of the Fant equation, the specific cases where plane wave acoustic propagation is described either by a Sturm-Liouville problem or concatenated cylindrical tubes is considered. Simulations show the expected skewing of the glottal volume velocity pulses depending on whether the fundamental frequency is below or above a sub- or supra-glottal formant. More complex glottal wave forms result when both the first supra-glottal fundamental frequencies are high and close to the first sub-glottal formant.

Comments on single-mass models of vocal fold vibration

Proposed mechanisms for single-mass oscillation in the vocal tract are examined critically. There are two areas that distinguish single-mass models: in the sophistication of the air flow modeling near the oscillator and whether or not oscillation depends on acoustic feedback. Two recent models that do not depend on acoustic feedback are examined in detail. One model that depends on changing flow separation points is extended with approximate calculations.

Lectures on the Theory of Vortex-Sound

The theory of vortex sound is introduced. From Lighthill’s acoustic analogy, it is shown how vorticity and entropy fluctuations can be seen as sources of sound. The use of the compact Green’s functions is introduced to compute the vortex sound. As an example of the method presented, this theory is applied to pressure transients generated by high-speed trains.

The suction force on the vocal folds as an energy source for vibration and as an acoustic source.

It has been shown that single‐degree‐of‐freedom vibration of sprung shutters in a duct with a source of constant pressure is enabled when there is a change in separation point position on the shutters [M. S. Howe and R. S. McGowan, Fluid Dyn. Res. in press]. In this scenario, the flow is supposed to separate on the upstream side of the shutters as they open and on the downstream side as they close. Energy is inputted from the flow into the shutters as the shutters close because of a suction force necessary to turn a potential flow around the edge of each shutter. This suction force is also called the Coanda force in the aerodynamics literature. This time variable suction force is a dipole source of sound that is distinct from drag force source that has already been discussed [M. S. Howe and R. S. McGowan, J. Fluid Mech. 592, 367–392 (2007)]. With these theoretical considerations, an equation analogous to Fant’s equation for the glottal jet can be derived to explore glottal jet kinematics and the effect of...

Nonlinear flow‐structure coupling in a mechanical model of the vocal folds and the subglottal system.

An analysis is made of the nonlinear interaction between flow in a mechanical model of the subglottal vocal tract and a model of the vocal folds. The mean flow through the system is produced by a “lung cavity” that is assumed to be steadily contracting. The lungs are connected to a subglottal tube of length L. The model for the vocal folds is at the other end of the subglottal tube. This model is a simple, self‐exciting single‐mass mathematical model of the vocal folds used to investigate the sound generated within the subglottal domain and the unsteady volume flux from the glottis. In the case when the absorption of sound by the lungs is presumed small and when the subglottal tube behaves as an open ended resonator (when L is as large as half the acoustic wavelength) a mild increase in volume flux is predicted. However, the strong appearance of second harmonics of the acoustic field is predicted at intermediate lengths, when L is roughly a quarter of the acoustic wavelength. In the cases of large lung da...

Vortex shedding and the voice source

The voice source is primarily an acoustic dipole produced by the fluctuating drag on the vocal folds [Zhao, Zhang, Frankel et al., J. Acoust. Soc. Am. 112, 2134–2146 (2002)]. In this paper the unsteady drag is determined theoretically in terms of the vorticity shed from the vocal folds. The principal source of acoustic energy is glottal‐jet vorticity lying within an axial distance downstream of the glottis of less than about the glottal width. The vortex drag dipole is equivalent to the volume velocity source traditionally assumed to be located at the glottis. In addition, there exists a true, but weaker fluctuating volume source associated with volumetric changes of the vocal folds region. The relationship between the voice source dipole and sibilant fricative dipoles will be discussed. Our findings will be presented in a largely qualitative manner, so that the few equations used in the presentation can be understood physically. [Work partially supported by NIDCD‐004688.]

Area oscillations of a bias‐flow aperture, with application to phonation

A thin baffle plate in a mean flow duct partitions the tube into high‐ and low‐pressure regions. The plate spans the whole cross section of the duct and is pierced by a small aperture, through which a nominally steady bias flow is maintained by the mean pressure differential. Sound is generated when the flow is disturbed by imposed, small amplitude cross‐sectional area fluctuations of the aperture. For irrotational flow the radiation is determined by the input impedances of the tube on each side of the aperture, and energy flowing into the acoustic field is equal to the work done on the fluid by the suction force at the edge of the aperture. For high Reynolds number flow of a real fluid (modeled by the imposition of a Kutta condition) much of the work goes into the production of vorticity, the unsteady volume flow is greatly reduced, and at low frequencies there can be a substantial oscillating drag force on the plate [M. S. Howe, Proc. R. Soc. London, Ser. A 366, 205–233 (1979)]. The application of these...