Improving the determination of bubble size histograms by wavelet de-noising techniques

Intrusive phase detection probes are widely used in association with numerical processing techniques to obtain bubble size distributions in two-phase bubbly flows. Under these circumstances, a numerical problem must be solved which consists in determining bubble size histograms from measured chord or pierced length histograms. This can be done by inverting a Fredholm integral operator of the first kind, which is known to be often ill conditioned, i.e. the solution will be extremely sensitive to small changes or errors in the input data. In practical situations, the ill conditioned nature of the problem may be critical, particularly because the signals delivered by phase detection probes always have noise and, also, when the construction of the chord histogram is based on restrictive assumptions such as the definition of threshold levels. These two issues are addressed in this work. Specifically, the application of a numerical de-noising technique based on orthogonal wavelet decomposition is described and compared with the classical Fourier de-noising technique. In addition, a new method is proposed for the extraction of pierced lengths based on the instantaneous frequency of the phase signal. Numerical experiments with artificial signals were carried out, aiming to test the proposed methodology and to delimit its range of applicability with respect to maximum allowable noise levels. Results confirm the advantage of the wavelet de-noising technique, mostly due to its ability of removing noise without a significant distortion of the edges of the signal from which the pierced lengths are determined.