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 a n analytical model and experimental measurements. The study is restricted t o quasi-two-dimensional diaphragms with a sharp-edged rectangular aperture at conditions for which the acoustic source region can be considered compac t. The compactness of the source can be realized under two conditions: eith er 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 f ocus 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 q uasi-steady theory are compared with measurements of the reflection and tra nsmission coefficients of a diaphragm. The theoretical model is based on Ro nneberger's model for a step-wise expansion (D. Ronneberger 1967, Acustica 19, 222-235) and Bechert's description of an orifice used as an anechoic pi pe termination (Bechert 1980 Journal of Sound and Vibration 70, 389-405). A n 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 resu lts 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 l ow frequencies the model and the experimental results are in good agreement . Significant deviations appear only when the Strouhal number reaches unity . (C) 2001 Academic Press.