Statistics and Structure of Granular Flow through a Vertical Pipe

Abstract

Time series signals of several flowing patterns of granular particles (rough sand) through a vertical pipe have been analyzed by the wavelet expansion method. Probability distribution functions (PDFs) of wavelet coefficients, which roughly correspond to the density increments over a given scale, are constructed. It is revealed that PDFs for the sparse and uniform flow were Gaussian distribution over wide scales. On the other hand, those of uniform but dense flow were exponential distributions and the time series signals had strong correlations between adjacent length scales. PDFs of density waves were a little more complex: When the resistance force due to the medium air was weak, they were Gaussian. When it became strong, however, PDFs of density waves changed their shape according to the scales one observes. On large scales, they were Gaussian. As the length scale became smaller, PDFs were gradually deformed from Gaussian to exponential. It implies the existence of intermittent density waves, which remi...