A numerical study on sound radiation from circular duct with cold flow

Abstract

The characteristics of sound radiation from the end of duct can be described by the reflection coefficient and end correction, which may be influenced by the flow velocity of medium and the wall thickness of duct. In this study, an approach based on solving the two-dimensional (2-D) axisymmetric frequency domain linearized Navier-Stokes equations (LNSEs) is proposed to determine the reflection coefficient and end correction of circular duct with clod flow. The numerical predictions are compared with theoretical results and published measurements, and good agreements are observed which verifies the accuracy of the present approach. Furthermore, the influences of flow velocity, velocity profile and wall thickness on sound radiation are examined numerically. The results indicate that in the presence of flow, the magnitude of reflection coefficient exceeds unity and the value of end correction at low Helmholtz number ka is much lower than that in the absence of flow. The numerical predictions for artificially constructed infinitely thin shear layer demonstrate that the velocity profile in jet affects the reflection coefficient and lowers the value of end correction. Numerical simulations of circular ducts with varying wall thicknesses and termination geometries reveal that the limit value of end correction as $ka\to 0$ converges to a common constant, provided the terminations preserve the characteristics of shear layer at the duct lip. Finally, expressions of reflection coefficient and end correction are presented by using the piecewise polynomial fitting method based on the numerical predictions.