A comparison between measured and predicted complex intensity in a flanged cylindrical pipe

A hybrid finite element method is used to model wave propagation in a flanged cylindrical pipe containing a monopole source. Here, a modal expansion is used to represent sound propagation in the exterior domain and this avoids the use of perfectly matched layers normally found in commercial software packages. Complex intensity in the pipe is then obtained and the real part of the complex intensity is shown to represent the local travelling energy and the imaginary part the local oscillating energy. Results are presented in the plane wave region and at higher frequencies, where the first circumferential mode has cut-on. The predicted complex intensity is then compared to experimental measurements and generally good agreement is observed. From this it is seen that the interaction between the acoustic pressure in the plane wave and the acoustic particle velocity in the first circumferential mode mainly contributes to the transverse flow of energy flow in the pipe, whilst the interaction between the acoustic pressure in the first circumferential mode pressure and the acoustic particle velocity in the first circumferential mode contributes to energy oscillation.