Experimental Verification of the Theoretical Model of Sound Radiation from an Unflanged Duct with Low Mean Flow

The paper deals with experimental verification of results provided by theoretical approach to the
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.