(97c) Analysing and Interpreting Pressure Fluctuation Signals Measured in Fluidized Beds – a Brief Review

Authors: 
van Ommen, J. R., Delft University of Technology
Sasic, S., Chalmers University of Technology
Johnsson, F., Chalmers University of Technology
van der Schaaf, J., Eindhoven University of Technology
Gheorghiu, S., Center for Complexity Studies
Coppens, M. O., Rensselaer Polytechnic Institute


Pressure measurements are widely applied in fluidization research. When the sampling frequency is sufficiently high (~200 Hz), the measured pressure signal can yield much information about the bed dynamics. In recent years, a wide range of analysis methods have been proposed. In this paper, we briefly review these methods, with a focus on the development over the last decade. We divide the analysis methods into time domain methods, frequency domain methods, and state space methods.

Analysis in the time-domain is often the simplest approach. The standard deviation of pressure fluctuations is widely used, e.g. to identify the regime change from bubbling to turbulent fluidization. Higher-order moments are scarcely applied. The cycle time and its distribution are a useful and easy-to-calculate alternative to frequency analysis, giving information about the relevant time-scales. Some researchers have applied the rescaled range (Hurst) analysis, but, for the data we studied, this characteristic was not discriminative. The probability distribution of pressure fluctuations often follows a Student-t distribution, with a power-law slope for large-amplitude pressure fluctuations that can be associated to the bubble or void size distribution.

The most common frequency domain method is to calculate the power spectral density to identify characteristic frequencies of the bed fluctuation. In addition, this approach can be applied to represent the fluidized bed as a single or multiple oscillators with frequencies corresponding to peaks in the spectrum. The slope of the power spectrum at higher frequencies (either in a log-normal or a log-log representation) is an alternative, but rather cumbersome way for regime characterization. To capture transient effects at longer time scales (> 1 s), either the transient power spectral density or wavelet analysis can be applied.

State space analysis (?chaos analysis') became popular in the 1990s. It is difficult to give irrefutable evidence that fluidized beds exhibit low-dimensional chaotic behaviour. It has been shown that the information given by the frequently reported Kolmogorov entropy is equivalent to that of the more easily calculated average frequency, obtained in the frequency domain. However, methods closely associated to chaos theory, such as attractor comparison, are useful to characterize the nonlinear dynamics of fluidized beds with a higher sensitivity to small differences than other methods.