STATISTICS AND STRUCTURE OF GRANULAR FLOW-THROUGH A VERTICAL PIPE

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 wavele t coefficients; which roughly correspond to the density increments ove r a given scale, are constructed. It is revealed that PDFs for the spa rse and uniform flow were Gaussian distribution over wide scales. On t he other band, those of uniform but dense flow were exponential distri butions and the time series signals had strong correlations between ad jacent 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 change d their shape according to the scales one observes. On large scales, t hey were Gaussian. As the length scale became smaller; PDFs were gradu ally deformed from Gaussian to exponential. It implies the existence o f intermittent density waves, which reminds us of fully developed turb ulence.