Spatial coherence of pipe vibrations induced by an internal turbulent flow

Whereas the spatial coherence of wall pressure and vibratory fields induced by turbulent boundary layers (TBLs) on flat plates have been studied at extent, their equivalents for cylindrical structures still need further investigation. To that end, this work develops a semi-analytical model which is valid for infinite cylindrical shells filled with a heavy fluid and excited by an internal TBL. The cylindrical shell can be also coupled to two ring stiffeners that account for the flanges generally used to connect a pipe to other portions of a circuit. The cross-spectrum density (CSD) function of the shell radial accelerations is estimated from the system circumferential sensitivity functions and the CSD of the wall pressure field induced by the TBL. The spatial coherence of the pipe vibration field is therefore analysed for a pipe with and without flanges. This is of critical importance for applications such as non-intrusive techniques for detecting acoustic sources inside pipes, like beamforming using arrays of accelerometers. If the pipe conveys a flow, the beamforming efficiency can strongly deteriorate because of the background noise induced by the TBL, which pollutes the coherence signal between sensors. The effects that the spatial coherence could have on the beamforming results of a line of point sensors (accelerometers) and a ring of wire sensors (piezoelectric coiled wires) are also investigated in this paper.