Spatial coherence of pipe vibrations induced by an internal turbulent flow

Abstract

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 semianalytical 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 crossspectrum 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.

Numerical analysis of vibroacoustic beamforming gains for acoustic source detection inside a pipe conveying turbulent flow

“…Only the coupling along the radial direction between the shell and the stiffener will be considered. The ring stiffener will be represented by a rod of circular curvature, as described in [12,16]. A cylindrical coordinate system (𝑥, r, 𝜃) is adopted, as in Fig.…”

“…It should be noted that the theoretical foundations of the model to be used below were recently presented in detail in [12] and validated through the independent experiments in [13]. For completeness, the outline of the model is presented herein for the case of the shell excited by the TBL.…”

“…An extension for the shell excited by a monopole source is then proposed in section 2.3. The readers are referred to [12] for further information and deeper insight on the theoretical derivations.…”

“…In section 2, we present the hypotheses and principles of the numerical model employed to compute the accelerations in the pipe surface induced by the turbulent flow and by the monopole source. The theoretical core of the model was recently presented in [12] and validated through the independent experiments in [13]. An extension is proposed herein to calculate the shell vibrations induced by the monopole source inside the fluid.…”

“…On the other hand, the MaxSNR beamforming technique [11], which is not relying on such hypothesis, exhibited remarkable gains (about 10 to 25 dB) for different positions of the source. The spatial coherence of the accelerometers' signals induced by an internal turbulent flow has been recently investigated in [12] using numerical modelling.…”