Wavelet denoising and nonlinear analysis of solids concentration signal in circulating fluidized bed riser

Particles,particle aggregates,and reactor walls complicate the dynamic microstructures of circulating fluidized beds(CFBs).Using local solids concentration data from a 10-m-high and 76.2-mm-inner-diameter riser with FCC(Fluid Catalytic Cracking)particles(dp=67μm,ρp=1500 kg/m^3),this paper presents an improved denoising process for use before nonlinear chaos analysis.Using the soft-threshold denoising method in the wavelet domain with experimental empty bed signals as base data to estimate the denoising threshold,an efficient denoising algorithm was proposed and used for the dynamic signals in CFBs.Analysis shows that for the local solids concentration time series,high-frequency fluctuations may be one of the system properties,while noise interference can also make a low-frequency contribution.An exact denoising method is needed in such cases.The correlation dimension and Kolmogorov entropy were calculated using denoised data and the results showed that the particle behavior in the CFB is highly complex.Generally,two correlation dimensions coexist in a low-flux CFB.The first correlation dimension is low and corresponds to small-scale fluctuations that reveal a high-frequency pseudo-periodic movement,but the second correlation dimension is high and corresponds to large-scale fluctuations that indicate multi-frequency movements,including particle aggregation and breakage.At the same axial level,the first correlation dimensions change slightly with radial position,and the main tendency is high at the center but slightly lower near the wall.However,the second correlation dimensions show large changes along the radial direction,are again high in the core region,and after r/R≥0.6(r as radial position,R as radius of the riser),the dimensions clearly drop down.This indicates that the particle behavior is more complex and has higher degrees of freedom at the center,but clusters near the wall are restrained to some degree because of wall effects.

Effect of bed size on the gas-solid flow characterized by pressure fluctuations in bubbling fluidized beds

Pressure fluctuations in four bubbling fluidized beds having different bed sizes (three square cross-sections of 5, 10, and 15 cm in side length, and one rectangular cross-section of 2 × 10 cm2) were measured at four axial positions (P1, P2, P3, and P4). Several characteristic indicators of the flow specifically of the pressure were calculated. In terms of these characteristic indicators, the effect of bed size on flow behavior was investigated. The results show that in the fully fluidized state, the pressure drop is slightly higher in smaller beds, but the pressure drops in the 10- and 15-cm beds are close. The 15-cm bed has the lowest pressure-fluctuation amplitude. The amplitudes at P1 and P2 in the lower part of the bed are very close for bed sizes below 10 cm, but the amplitude at P3 near the bed surface increases with decreasing bed size. No general trend was observed regarding the effect of bed size on skewness and kurtosis of the pressure for all four axial heights. For the average, standard deviation, skewness, and kurtosis of the pressure at P4, the values are close for the two small beds (2 × 10 and 5 × 5 cm2) and the two large beds (10 × 10 and 15 × 15 cm2), and hence the effect of bed size separates the beds into two groups. In the fully fluidized state, for P1, P2, and P3, the Kolmogorov entropy and the dominant frequency both increase with increasing bed size, but in the pseudo-2D bed both are between the values for the 5- and 10-cm beds.