Aeroacoustic Response of a Slit-Shaped Diaphragm in a Pipe at Low Helmholtz Number, 1: Quasi-Steady Results

Abstract

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 "rst 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 re#ection and transmission coe$cients of a diaphragm. The theoretical model is based on Ronneberger's model for a step-wise expansion (D. Ronneberger 1967, Acustica 19, 222}235) and Bechert's description of an ori"ce used as an anechoic pipe termination (Bechert 1980 Journal of Sound and <ibration 70, 389}405). An important phenomenon associated with the #ow through a diaphragm is the so-called vena contracta e!ect. This e!ect 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. Signi"cant deviations appear only when the Strouhal number reaches unity.

Aeroacoustic Response of Diffusers and Bends: Comparison of Experiments With Quasi-Steady Incompressible Flow Models

“…The linear response of a sharp-edged open pipe termination is also well understood (Rienstra 1981;Cargill 1982;Munt 1990;Peters et al 1993). Similar data are now available for thin sharp-edged orifices (Ingard & Ising 1967;Cummings 1983;Durrieu et al 2001;Hofmans et al 2001). Recently, Dequand et al (2001) carried out a detailed study of the 908 bend with a sharp inner edge.…”

“…We used a fit of the Peters et al data for Z as proposed by Hofmans et al (2001). In the following two sections, the geometry of the configurations studied is described more accurately.…”

“…Quasi-Steady Flow Theories 3.2.1. Bends: incompressible quasi-steady flow theory At low Strouhal numbers pfD=U 0 ( 1, we can predict the scattering matrix defined in the previous section by means of a quasi-steady flow model as developed by Durrieu et al (2001) and Hofmans et al (2001) for the orifice. We compare our experimental data obtained for the bends at Strouhal numbers in the range 0Á35pfD=U 0 53 with an incompressible quasi-steady flow theory.…”

“…The experimental method and set-up used are described in detail by Peters et al (1993), Hofmans et al (2001) and Durrieu et al (2001). By means of the two-microphone method, the pressure reflection coefficient R p is measured as a function of the Mach number M ¼ U 0 =c 0 for different pipe discontinuities (Fig 1).…”

Frequency Response of Gas-Filled Tube With Minor Losses

“…From equations 2.17 through 2.21 a scattering matrix could be developed for an orifice using theory presented by Hofmans et al [7]. Modeling of an orifice is expanded from previous models by Hofmans to include compressibility effects and a dependence on Mach number for the vena contracta factor.…”