The radiation of sound waves from partially lined duct is treated by using the mode-matching method in conjunction with the Wiener-Hopf technique. The solution is obtained by modification of the Wiener-Hopf technique and involves an infinite series of unknowns which are determined from an infinite system of linear algebraic equations. Numerical solution of this system is obtained for various values of the problem parameters, whereby the effects of these parameters on the sound diffraction are studied. A perfect agreement is observed when the results of radiated field are compared numerically with a similar work existing in the literature.
A simple analytical method is developed to estimate frequencies of longitudinal modes in closed hard-walled ducts with discontinuities in a cross-sectional area. The approach adopted is based on a general expression for the acoustic impedance for a plane wave motion in a duct and conditions of impedance continuity at duct discontinuities. Formulae for mode frequencies in a form of transcendental equations were found for one, two and three discontinuities in a duct cross-section. An accuracy of the method was checked by a comparison of analytic predictions with calculation data obtained by use of numerical implementation based on the forced oscillator method with a finite difference algorithm.
Numerical methods are mostly used to predict the acoustic pressure inside duct systems. In this paper, the development of a numerical method based on the convected Helmholtz equation to compute the acoustic pressure inside an axisymmetric duct is presented. A validation of the proposed method was done by a comparison with the analytical formulation for simple cases of hard wall and lined ducts. The effect of the flow on the acoustic pressure inside these ducts was then evaluated by computing this field with different Mach numbers.
It is convenient to have a device and a method of generating single cut-on modes in cylindrical hard-walled waveguides or at least in laboratory models of such systems. This allows to examine, among other things, properties of various active and/or passive elements inserted in a cylindrical duct by testing them in conditions when the incident (input) wave comprises only one cut-on mode and determining the reflection and transmission coefficients for single selected incident modes. As it has been already demonstrated by the present authors, it is possible to generate single cut-on modes in a circular duct using a small (although increasing with mode order) number of acoustic monopoles arranged properly on a duct cross-section and driven with appropriate acoustic volume amplitudes and phases. Laboratory models of such sources are proposed in this paper and results of tests verifying their directional properties are presented. The other technical issue relating to practical utilization of the proposed method is the possible error introduced by the apparatus used for scanning the acoustic field inside the duct model. It is shown that insertion of the measuring probe changes the total energy radiated into the free space only by a fraction of a decibel.
problem of sound radiation from an unflanged duct with mean flow of the medium taking into account existence of all allowable wave modes and, in particular, occurrence of the so-called unstable wave, which results in decay of radiation on and in vicinity of the duct axis. The flow is assumed to be uniform with the source of flow located inside the duct, which is the case frequently occurring in industrial systems. Mathematical considerations, accounting for multimodal and multifrequency excitation and diffraction at the duct outlet, are based on the model of the semi-infinite unflanged hard duct with flow. In the experimental set-up a fan, mounted inside the duct served as the source of flow and noise at the same time modelled as an array of uncorrelated sources of broadband noise, what led to the axisymmetrical shape of the sound pressure directivity characteristics. The theoretical analysis was carried out for the root mean square acoustic pressure in the far-field conditions. Experimental results are presented in the form of the measured pressure directivity characteristics obtained for uniform flow directed inwards and outwards the duct compared to this observed for the zero-flow case. The directivity was measured in one-third octave bands throughout five octaves (500 Hz - 16 kHz) which, for a duct with radius of 0.08 m, corresponds to the range 0.74-23.65 in the reduced frequency ka (Helmholtz number) domain. The results obtained are consistent with theoretical solutions presented by Munt and Savkar, according to whom the weakening of the on-axis and close-to-axis radiation should take place in the presence of medium flow. Experimental results of the present paper indicate that this effect is observed even for the Mach number as low as 0.036.
Porous materials are used in many vibro-acoustic applications. Different models describe their perfor- mance according to material’s intrinsic characteristics. In this paper, an evaluation of the effect of the porous and geometrical parameters of a liner on the acoustic power attenuation of an axisymmetric lined duct was performed using multimodal scattering matrix. The studied liner is composed by a porous ma- terial covered by a perforated plate. Empirical and phenomenal models are used to calculate the acoustic impedance of the studied liner. The later is used as an input to evaluate the duct attenuation. By varying the values of each parameter, its influence is observed, discussed and deduced