Sound Radiation from a Circular Duct with Axial Temperature Gradients and Mean Flow

An analytic analysis has been carried out to investigate the effects of temperature on the sound radiation from an unchanged circular duct with mean flow by using a Wiener-Hopf technique. The problem is split into two domains, i.e., internal and external to the duct. The solution allows for any form of temperature distribution inside the duct, and the domain solutions were matched on the duct termination. The required split function was obtained by direct numerical integration with an appropriate indentation to the branch points. The computed results for uniform temperature distribution in the duct agreed well with published experimental data as well as the numerical calculations. The results show that the modulus of pressure reflection coefficients at the duct exit decreases as the temperature or flow velocity in the duct increases.