Reversibility and Entropy in Bubbling Fluidized Beds: A Recurrence-Based Analysis

Abstract

Nonlinear time series analysis techniques were applied to characterize bubbling fluidization. The delay method was used to reconstruct the state space attractor and analyze the reconstructed state space. The experiments were carried out in a laboratory-scale fluidized bed, operated under ambient conditions and with various sizes of particles, settled bed heights, measurement heights, and superficial gas velocities. The reversibility of the gas-solid fluidized bed hydrodynamics was investigated using pressure fluctuations by recurrence plot analysis. The anti-diagonal lines of the recurrence plot (RP) were regarded as a measure of reversibility. It was shown that the reversibility versus gas velocity has a concave shape in the bubbling regime. The highest reversibility occurs at velocities remarkably lower than the turbulent transition velocity. In addition, reversibility increases as the size of the particles increases. The Kolmogorov entropy was also estimated to confirm the reversibility analysis in the state space domain. In addition, the average cycle frequency and wideband energy in the frequency domain were also used to clarify the results in the state domain. It was found that a minimum in average cycle frequency, wideband 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 primarily found in the macro-structures of the bubbling fluidization system. These findings can provide a practical tool for the optimal design and operation of the fluidized bed.