Advances in Multiphase Flow and Heat Transfer

Volume: 3

Indexed in: Chemical Abstracts, EBSCO, Ulrich's Periodicals Directory

Multiphase flow and heat transfer have found a wide range of applications in several engineering and science fields such as mechanical engineering, chemical and petrochemical engineering, nuclear ...
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Nonlinear Dynamic Characteristics of Bubbling Fluidization

Pp. 300-331 (32)

Reza Zarghami, Navid Mostoufi, Rahmat Sotudeh-Gharebagh and Jamal Chaouki


Nonlinear time series analysis techniques were applied to characterise bubbling fluidization. The experiments were carried out in a laboratory scale fluidized bed, operated under ambient conditions and various sizes of particles, settled bed heights, measurement heights and superficial gas velocities. It was found that a minimum in average cycle frequency, wide band energy and entropy with an increase in the velocity corresponds to the transition between macro structures and finer structures of the fluidization system. This minimum was mostly found in the macro structures of the bubbling fluidization system. Hurst exponent of the pressure fluctuations showed that the fluidized bed has a bifractal behaviour. The reciprocal of the break point in the Hurst profile is similar to the domain frequency of the bed. The method of delays was used to reconstruct the state space attractor to carry out analysis in the reconstructed state space. The state space reconstruction parameters, i.e., time delay and embedding dimension, were determined and the results showed that their values are different for various types of methods introduced in literature. Chaotic behaviour of fluidized system was determined by introducing two nonlinear dynamic invariants, correlation dimension and entropy in different ways. The state-space analysis reflected that a low dimension behaviour of the bubbling fluidization system. The nonlinearity test showed that nonlinearity cannot be concluded at all gas velocities.


Nonlinear, pressure fluctuation, hurst exponent, chaotic attractor, entropy, correlation dimension.


School of Chemical Engineering, College of Engineering, University of Tehran, Tehran, Iran, Department of Chemical Engineering, Ecole Polytechnique de Montreal, Montreal, Canada