Analysis of the distribution and attenuation of acoustic energy flux in lined duct containing inhomogeneous medium by the finite difference method

The internally generated noise which can be attenuated by liners when propagating in piping-system can be modelled by acoustic waves travelling in an infinite two-dimensional lined duct with an inhomogeneous medium. Since the duct is lined, all acoustic parameters and disturbances are complex, and this complicates the resolution of the mathematical formulation of the problem. In this paper and using the finite difference method, we analyse the behaviours of acoustic energy flux in a rectangular lined duct containing temperature and mean flow gradients for upstream and downstream propagation. Some results are presented for the separated and combined effects of these inhomogeneous factors on the attenuation rate. These results show that cooling the duct wall further strengthens the attenuation in downstream propagation and improves it in upstream propagation.