CFD simulation and wavelet transform analysis of vortex and coherent structure in a gas–solid fluidized bed

In a gas–solid fluidized bed, the particle vortexes play an important role in determining the heat transfer capability, while the coherent structures dominate the hydrodynamic characteristics of the turbulent flow field. A two-dimensional Eulerian–Eulerian model integrating the kinetic theory of granular flow (KTGF) is used to simulate the particle vertical fluctuating velocity in a gas–solid fluidized bed, based on which the continuous wavelet transform technique is for the first time introduced to analyze the particle vortex behavior. The results show that the time scale of a particle vortex has a linear relationship with the wavelet scale. Some particle vortexes perform periodic motion and merge with or separate from others until the end of the vortex period. As the superficial gas velocity and bed height increase, particle vortexes are stretched and their boundaries become unclear. Furthermore, to investigate the intermittency of the gas–solid flow field, the probability density function (PDF) of wavelet coefficients is computed. It is found that the wavelet coefficients and the probabilities of intermittent events both improve as the wavelet scale, superficial gas velocity and bed height increase. Since intermittency is caused by coherent structures in the flow field, the effects of coherent structures on the intermittency are studied through a coherent structure extracting method and the extended self-similarity (ESS) scaling law. Before extraction, wavelet coefficients at the same scale increase as the superficial gas velocity and bed height increase, while the scaling law curve at Ug=0.75 m/s deviates from those at other superficial gas velocities, but shows no obvious change with the bed height. After extraction, the discriminations of scaling law curves under different operating conditions are eliminated and all curves merge in one. The effects of bubble formation, their size and propagation on particle vortex behavior are also analyzed. Bubble motion becomes more violent as gas velocity and bed height increase, which enhance the particle vortex size and activity and coherent structure generation, leading to stronger intermittency of granular flow field. As gas velocity increases, the amplitude of pressure fluctuation first increases and then decrease, while one sharp peak changes to be uniform lower peaks. As bed height increases, the major frequency decreases slightly and the amplitude increases slightly. This work provides deep insights into the turbulent flow field in a gas–solid fluidized bed by CFD simulation and the continuous wavelet transform technique.

► We use CFD simulation and wavelet transform to analyze particle vortex behavior.
► The particle vortex time scale has a linear relationship with wavelet scale.
► The probability density function (PDF) of wavelet coefficients is computed.
► Coherent structures are investigated by extended self-similarity scaling law.
► Bubble motion and its effects on particle vortex behavior is studied.