Guided wave propagation in cylindrical ducts with elastic walls enclosing a fluid moving with a uniform velocity

Theoretical models for elastic wave propagation in fluid filled ducts normally neglects mean fluid flow. However, in many engineering applications the velocity of the fluid may influence the modal characteristics of the duct, for example in gas pipelines, turbomachinery applications and ventilation systems. Accordingly, the influence of a mean uniform fluid flow on acoustically driven duct wall vibration is analysed here for a cylindrical geometry. The semi-analytic finite element method is used to couple the elastodynamic wave equation for the duct wall to the convected wave equation for sound propagation in a uniform fluid flow. A one dimensional finite element approach is described and this is used to find the coupled eigenmodes for the duct. Under certain conditions, a uniform mean flow is seen to significantly affect the phase speed for different eigenmodes, and it is shown that this may cause energy to transfer from the fluid to the surrounding wall at frequencies much lower than those seen without mean flow. This behaviour has the potential to increase sound radiation from ducts at lower frequencies when mean flow is present.