Similarity between chaos analysis and frequency analysis of pressure fluctuations in fluidized beds

In literature the dynamic behavior of fluidized beds is frequently characterized by spectral analysis and chaos analysis of the pressure fluctuations that are caused by the gas-solids flow. In case of spectral analysis, most often the power spectral density (PSD) function is quantified, for example, by the frequency at the largest power and/or by the power-law fall-off at the higher frequencies. In case of chaos analysis, most often the correlation entropy (or Kolmogorov entropy) is used to characterize the fluidized bed dynamics. In this paper, it is shown theoretically that a relationship exists between the correlation entropy and the PSD function. This relationship is experimentally verified by a large set of experimental pressure fluctuation data from slugging, bubbling, and circulating fluidized beds. It is shown that the correlation entropy is linearly proportional to the average frequency that is obtained from the PSD function. As the average frequency can be directly interpreted in terms of the physical phenomena underlying the pressure fluctuations, the average frequency is suggested as a first, simple, characteristic of fluidized bed dynamics. (C) 2004 Elsevier Ltd. All rights reserved.