Analysis of pressure fluctuations in fluidized beds. I. Similarities with turbulent flow

Experimental data for pressure fluctuation time series in a fluidized bed are analyzed by several distinct, but complementary methods. First, we compute a multiscale probability density function (PDF) for the successive increments of the data. The results demonstrate the evolution of the PDF from the short to long time scales, and indicate striking similarity to the Castaing equation that has been proposed for modeling velocity fluctuations in turbulent flows. Next, to further check the results we compute the structure function of the successive increments of the data. We find that the fluctuations exhibit multifractal behavior, which is also prevalent in turbulence. The multifractality implies that the pressure fluctuates differently over distinct time scales. To understand the origin of the multifractality, we use a powerful method of analysis, namely, the multifractal detrended fluctuation analysis (MF-DFA) in order to analyze the data. The results confirm the multifractal property of the data. To better understand the similarities between the pressure fluctuations in fluidized beds and velocity fluctuations in turbulent flow, and whether the multifractality is due to extended correlations in the data or because the PDF of the successive increments is broad, we also construct the shuffled and surrogate series for the data and analyze them by the MF-DFA method. Comparison of results for the original data with the shuffled and surrogate time series indicates that the correlations in the pressure are responsible for the multifractality of the data, rather than the broadness of the PDF.