Aeroacoustic response of a slit-shaped diaphragm in a pipe at low Helmholtz number, 1: quasi-steady results

The aeroacoustic response of a diaphragm in a pipe is studied by means of an analytical model and experimental measurements. The study is restricted to quasi-two-dimensional diaphragms with a sharp-edged rectangular aperture at conditions for which the acoustic source region can be considered compact. The compactness of the source can be realized under two conditions: either a low Strouhal number and a jet Mach number of the order unity; or a low jet Mach number and a Strouhal number of order unity. In this paper, the focus is on the first case. The second case of low Mach number and Strouhal number of order unity is discussed in a companion paper. The results of a quasi-steady theory are compared with measurements of the reflection and transmission coefficients of a diaphragm. The theoretical model is based on Ronneberger's model for a step-wise expansion (D. Ronneberger 1967, Acustica19, 222–235) and Bechert's description of an orifice used as an anechoic pipe termination (Bechert 1980 Journal of Sound and Vibration70, 389–405). An important phenomenon associated with the flow through a diaphragm is the so-called vena contracta effect. This effect is analyzed theoretically as a function of diaphragm opening and jet Mach number by using analytical results for a Borda tube. This allows the use of the theory up to Mach numbers of unity in the free jet downstream of the diaphragm. It is shown that at low frequencies the model and the experimental results are in good agreement. Significant deviations appear only when the Strouhal number reaches unity

Starting transient of the flow through an in-vitro model of the vocal folds

An exact theory of voiced sound production can be useless. An exact numerical calculation is, in fact, a detailed experiment, which does not by itself provide any insight. For example a detailed numerical simulation cannot be used to obtain data compression or real-time sound synthesis. By contrast the most simple models available such as source/filter models are already quite versatile tools. As the available computational power increases we would like to use more complex models. Physical modeling is a guide to generate models with a limited number of parameters with limited ranges of plausible values, determined from physiological data. A physical model should have a reasonable balance in the degree of sophistication used to describe the various elements such as: mechanical system, flow, articulation, and so on. The aim of our long-term research is to test the most simple fluid dynamic theories by means of accurate in vitro experiments, providing the specialist with a range of models rather than a specific model. Our research program was triggered by request of colleagues from the Institute for Perception Research anxious to evaluate the relevance of the work of Teager [1,2]. Based on our earlier experience on natural gastransport systems and on musical acoustics we started by a literature study [3]. We certainly agree with Teager that a more systematic description of the flow can be useful. However, some of his research proposals are highly disputable. For example, it may be fascinating to place a hot wire in our mouth and observe the complex flow signal obtained during phonation. However, we will never be able to relate such data to any quantitative theory because we have no information about the flow channel geometry nor on the position of the hot wire. This makes in vivo experiments with hot wires rather frustrating. As fluid dynamicists we were much more impressed by simple in vitro experiments with fixed geometry [4,5] or oscillating models [6,7]. Based on the difficulties that we had already encountered in oscillating valves models [8], we decided to focus on fixed rigid geometries. We decided to introduce an unsteadiness of the flow by driving the model with a valve as we had done earlier for the organ pipe [9,10] . As we knew how difficult quantitative measurements are, we started by considering a smoothly converging two-dimensional flow channel with a sharp-edged termination. Steady and unsteady flow measurements were carried out in this geometry to check the calibrations of our pressure gauges and of our hot wires. (Even steady wall pressure measurements should always be checked because of potential problems with pressure holes.) While the sharp edged geometry is not physiologically relevant it allows detailed two-dimensional point vortex simulation because we know that vortex shedding occurs at the sharp edges and is described by a Kutta condition [11]. We actually are still working on this reference geometry. It is rather obvious that the glottis is smoothly shaped and that we should therefore develop a theory describing the flow through lip-like channels. A first step in this direction was carried out by Belfroid [12] followed by Pelorson etal. [13-15]. Using this set-up we now produced quite realistic flow pulses as shown in Figure 3-1. In the present chapter we give an informal description of the results we have obtained until now. More precise information both concerning the theory and the experiments is found in the papers previously quoted. We focus on the glottis. The interesting subject of the aeroacoustics of the vocal tract is not considered. A discussion of literature available on this subject is given in our earlier paper [3] and the recent review of Davies etal. [16]

Quasisteady aero-acoustic response of orifices

The low frequency response of orifices (slit, circular diaphragm, and perforated plate) in the presence of mean flow is well predicted by a quasisteady theory. A refinement is brought to the theory by considering a Mach number dependent vena contracta coefficient. The measurements of the vena contracta coefficient of a slit agree well with the simple analytical expression existing in the case of the Borda tube orifice. The measured scattering matrix coefficients do not depend strongly on the geometry of the element. If the frequency is increased the moduli remain relatively unaffected while the arguments exhibit a complex behavior which depends on the geometry. From these considerations an anechoic termination efficient at high mass flow is designed

Lithographic apparatus, device manufacturing methods, mask and method of characterizing a mask and/or pellicle

A thick pellicle is allowed to have a non-flat shape and its shape is characterized to calculate corrections to be applied in exposures to compensate for the optical effects of the pellicle. The pellicle may be mounted so as to adopt a one-dimensional shape under the influence of gravity to make the compensation easier

Introduction to aeroacoustics and self-sustained oscillations of internal flows

\u3cp\u3eAfter a review of basic equations of fluid dynamics, the Aeroacoustic analogy of Lighthill is derived. This analogy describes the sound field generated by a complex flow from the point of view of a listener immerged in a uniform stagnant fluid. The concept of monopole, dipole and quadrupole are introduced. The scaling of the sound power generated by a subsonic free jet is explained, providing an example of the use of the integral formulation of the analogy. The influence of the Doppler Effect on the radiation of sound by a moving source is explained. By considering the noise generated by a free jet in a bubbly liquid, we illustrate the importance of the choice of the aeroacoustic variable in an aeroacoustic analogy. This provides some insight into the usefulness of alternative formulations, such as the Vortex Sound Theory. The energy corrolary of Howe based on the Vortex Sound Theory appears to be the most suitable theory to understand various aspects of self-sustained oscillation due to the coupling of vortex shedding with acoustic standing waves in a resonator. This approach is used to analyse the convective energy losses at an open pipe termination, human whistling, flow instabilities in diffusers, pulsations in pipe systems with deep closed side branches and the whistling of corrugated pipes.\u3c/p\u3