Characterizing Particle Flow by Acoustic Emission

A simple theoretical model which captures the statistical nature of an acoustic emission (AE) signal generated by a stream of solid particles impinging on a flat solid surface is presented. It rests on well-known results dating back to the fundamental work by Hertz, which assumes the impact to be elastic, the particle to be spherical, and the surface on which the particle bounces perfectly flat. The average power of the signal is evaluated in two limits. In the first one, the frequency content of the signal is identical to that of the forces developed during impact. In the second limit, only the low frequency part of the source function contributes to the spectrum of the recorded signal, the transfer function of the measuring system acting as a low-pass filter. In this case, it is shown that the result has an immediate physical interpretation, although its practical relevance is still limited. Additional progress is accomplished by experimentally proving that the statistical average of the particles’ momentum may be replaced with the average flow velocity, a quantity that may be directly measured in real life situations. It is suggested that this simplified version of the theoretical result may provide a useful tool to characterize particle flow in systems of industrial interest.