Bubble properties (bubble chord length, it's standard deviation, and bubble rising velocity) and pressure fluctuations have been measured in two and three phase fluidized beds.
The effects of superficial gas (0.02 - 0.10 m/s) and liquid (0.0 - 0.14 m/s) velocities, particle size (0.0, 1.0, 2.3, 6.0 mm) and electrolyte concentration (0.0 - 0.20 mol/l) on bubble properties and pressure fluctuations have been examined in a 0.376 m-ID x 2.1 m-high column.
Bubble properties have been measured by means of a U-shaped optical fiber probe with He-Ne laser generator. In two and three phase fluidized beds, bubble chord length and it's standard deviation increase with increasing gas velocity but decrease with an increase in liquid velocity and electrolyte concentration. Bubble rising velocity increases with increasing gas velocity and slightly decreases with increasing electrolyte concentration. The radial profile of bubble chord length and rising velocity have a shape of insignificant variation due to negligible wall effect.
Analysis and characterization of bubbling phenomena in two and three phase fluidized bed in terms of fluctuations of their state variables could yield useful fault diagnosis and control. Moreover, the bubbling phenomenon is probably most closely related to pressure fluctuations in the system. Hence, the analysis of pressure fluctuations should play a crucial role for developing diagnostic tools for the bubbling phenomenon.
The pressure fluctuation has been analyzed by resorting to the Fractal analysis: the time series of pressure fluctuation signals have been analyzed by means of correlation integral analysis, Lyapunov analysis, and the rescaled analysis based on the concept of fractional Brownian motion. From these analyses, correlation dimension, largest Lyapunov exponent, Hurst exponent have been obtained, respectively.
By means of new three parameters (correlation dimension, largest Lyapunov exponent, and Hurst exponent) it has been found that low order chaos exists in two and three phase fluidized beds and the characteristics of low order chaos have been quantified.
Among the Fractal analyses, Hurst exponent, H, has been most useful tool to detect the flow regime in two and three phase fluidized beds. In gas-liquid systems, Hurst exponent has been under 0.86 in churn turbulent flow regime and above 0.89 in bubbly flow regime and between 0.86 and 0.89 in transition regime. In three phase fluidized beds, Hurst exponent has been under 0.84 in bubble coalescing regime, above 0.88 in bubble breakup regime, and between 0.84 and 0.88 in the transition regime.
In two and three phase fluidized beds, Hurst exponent decreases with an increase in gas velocity but increases with increasing liquid velocity and electrolyte concentration. In three phase fluidized beds, Hurst exponent slightly decreases with the axial height from the distributor.
In gas-liquid systems, the obtained Hurst exponent has been correlated with the experimental variables as
$H=0.91U^{-0.055}_{G}U^{0.0535}_{L}C^{0.0058}_{NaCl}$
with correlation coefficient 0.92. H has the definite relationship with the bubble chord length.
In three phase fluidized beds, the obtained Hurst exponent has been correlated with the experimental variables as
$H=0.88d^{-0.020}_{p}U^{-0.056}_{G}U^{0.088}_{L}C^{0.012}_{NaCl}$
with correlation coefficient 0.89.
Moreover, according to Kolmogoroff's local theory of isotropic turbulence, the energy dissipation rate can be correlated with the dimensionless particle diameter, $d_p/D_T$, as the length scale and dimensionless liquid flow rate, $U_L/(U_L+U_G)$, as the velocity scale of micro eddies. The electrolyte concentration also is expressed in a dimensionless form as the ratio of electro conductivity of different NaCl concentration and tap water. Thus, H has been correlated in terms of these dimensionless parameters or scales to yield
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with correlation coefficient 0.91.
The dimensionless bubble chord length, $l_v/D_T$ has been correlated as a function of Hurst exponent as follow
$\frac{l_v}{D_T}=0.011H^{-0.551}$
with correlation coefficient 0.89.
