Statistics of velocity fluctuations of Geldart A particles in a circulating fluidized bed riser

The statistics of fluctuating velocity components are studied in the riser of a closed-loop circulating fluidized bed with fluid catalytic cracking catalyst particles. Our analysis shows distinct similarities as well as deviations compared to existing theories and bench-scale experiments. The study confirms anisotropic and non-Maxwellian distribution of fluctuating velocity components. The velocity distribution functions (VDFs) corresponding to transverse fluctuations exhibit symmetry, and follow a stretched-exponential behavior up to three standard deviations. The form of the transverse VDF is largely determined by interparticle interactions. The tails become more overpopulated with an increase in particle loading. The observed deviations from the Gaussian distribution are represented using the leading order term in the Sonine expansion, which is commonly used to approximate the VDFs in kinetic theory for granular flows. The vertical fluctuating VDFs are asymmetric and the skewness shifts as the wall is approached. In comparison to transverse fluctuations, the vertical VDF is determined by the local hydrodynamics. This is an observation of particle velocity fluctuations in a large-scale system and their quantitative comparison with the Maxwell-Boltzmann statistics.

Figure 1

Fluctuating horizontal VDF measured from the experiments (symbols) at different radial locations for PSRI1 (top) and PSRI2 (bottom). The solid line represents the stretched Gaussian distribution $P\left(c_x\right)\sim e^{-1.5|c_x{|}^{1.3}}$.

Figure 2

Deviation from Maxwellian distribution for PSRI1 at $r=0$ in. (top), $r=2$ in. (middle), and $r=4$ in. (bottom). Symbols represent the deviation calculated using the experimental data, and the solid line corresponds to the theoretical deviation from the Maxwell-Boltzmann distribution.

Figure 3

Deviation from Maxwellian distribution for PSRI2 at $r=0$ in. (top), $r=2$ in. (middle), and $r=4$ in. (bottom). Symbols represent the deviation calculated using the experimental data, and the solid line corresponds to the theoretical deviation from the Maxwell-Boltzmann distribution.

Figure 4

Fluctuating vertical VDF measured from the experiments (symbols) at different radial locations for PSRI1 (top) and PSRI2 (bottom). The solid line represents the Gaussian distribution $P\left(c_y\right)\sim e^{-|c_y{|}^2}$.