Radiation of cylindrical duct acoustic modes with flow mismatch

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

“…at the engine exhaust of a flying plane, when jets of gases escape into the outer space). This case, called "the exhaust problem" in the literature, was considered by Savkar (1975) and Munt (1977), who have obtained the solution by means of the Wiener-Hopf method. As one of the aims of this paper is to check whether their main finding concerning existence of a zone of relative silence (weakening of the propagation of the plane wave on the axis and in its vicinity) is observed also for the medium velocity of the range of tens of meters per second, we recall assumptions of their model below.…”

“…Strong pressure exerted on manufacturers to produce quieter systems resulted in extensive theoretical, numerical and experimental research work on the problem leading to elaboration of more exact and thorough description of the acoustic field phenomena reflecting the real conditions in which these appliances operate with better accuracy. This was achieved by the use of more complicated mathematical models, accounting for diffraction at the duct outlet and presence of higher wave modes (Levine, Schwinger, 1948;Weinstein, 1969;Snakowska, Wyrzykowski, 1986;Homicz, Lordi, 1975;Joseph, Morfey, 1999), flow of the medium inside the duct (Savkar, 1975;Munt, 1977;1990) or in the whole space (Sinayoko et al, 2010). In each case was accomplished by solving appropriate wave equation (either with or without flow) with adequate boundary conditions.…”

“…principal mode) and Lansing et al (1970) (for higher modes). The next step towards making theoretical model closer to real-life conditions was made by Mani, Savkar and Munt, who considered acoustic transmission properties of a jet pipe with subsonic flow inside, separated from the ambient, stagnant or co-flowing fluid by a vortex layer (Mani, 1973;Savkar, 1975;Munt, 1977;1990). Munt, in his earlier study, considered the sound radiated into the far field, and in the latter -the reflection coefficient for the plane wave and other duct modes.…”

“…This way, by assuming α = 0, the flow of the medium is limited to the inside of the duct and its extension along the duct axis, while the ambient gas remains still. Approximate theories considering difference in flow speed between the jet and ambient gas were also presented by Mani (1973) and Savkar (1975). In his paper, Mani considered a semiinfinite rectangular duct.…”

“…Obviously, the motion of the medium exterior to the duct strongly depends on the direction of flow (in or from the duct), which in turn depends on the way the fan is operating (suction or blowing mode). In the theoretical model (Savkar, 1975;Munt, 1977;1990) based on the solution obtained by means of the Wiener-Hopf method the diffraction of sound at the open end is accounted for but the flow outside is limited to the extension of the duct and so it is assumed to be uniform and of the same velocity as inside the duct. Nevertheless, the results obtained in the experiments carried out by the present author 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.…”