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.
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.