Individual phase holdup, bubble velocity, bubble chord length and its distribution in the radial direction of a 0.254m I.D. and 0.376 m-ID × 2.5 m high Plexiglas column of two and three phase fluidized beds have been studied.
The effects of liquid phase velocity (0.0-0.1 m/s), gas phase velocity (0.01-0.14 m/s) and particle size (0.4, 1.0, 2.3, 6.0 mm) on the bubble properties and local liquid velocity have been determined.
The Bubble properties and local liquid velocity have been measured by means of a U-shaped optical fiber probe and an electro-conductivity probe, respectively.
The gas phase holdup decreases with an increase in the radial distance in the bubble coalescing beds (dp=0.4, 1.0, 2.3 mm). However, the radial gas phase holdup profiles are found to be nearly flat in the bubble disintegrating bed (dp=6.0 mm). The radial profile of gas phase holdup can be expressed in terms of the dimensionless radial distance (r/R) and the average gas phase holdup as follows:
Two Phase Fluidized Beds:
$\bar{ε}_g = 0.34 U_g(1-1.7 U_1^{0.87})$
$ε_g =$\bar{ε}_g(\frac{3}{2}) (1-(\frac{r}{R})^4)$
Three Phase Fluidized Beds:
$ε_g = \bar{ε}_g (\frac{n+2}{n}) (1-(\frac{r}{R})^n)$
$\bar{ε}_g = 3.697d_p^{0.309} U_1^{-0.022} U_g^{0.701}$
$n = 409 d_p^{0.653}$
The bubble chord length and its velocity increase with an increase in gas phase velocity in two and three phase fluidized beds. However, the bubble chord length decreases slightly with the liquid phase velocity, but bubble rising velocity increases slightly with liquid phase velocity. The rate of increase in bubble chord length increases with an increase in particle size in three phase fluidized beds. The bubble chord length and its velocity have a maximum value at the center of column. The bubble chord length and its rising velocity have been correlated by the following equations:
Two Phase Fluidized Beds:
$1_v = 1_{vc}-(1_{vc}-1_{vw}) (\frac{r}{R})^{2.02}$
$1_{vc} = 0.023 U_g^{0.323} (1-24.82 U_1^{2.36})$
$1_{vw} = 6.85×10^{-3} U_g^{0.11}$
$U_B = U_{BC}-(U_{BC}-U_{BW}) (\frac{r}{R})^{1.56}$
$U_{BC} = 2.28 U_g^{0.35} (1+0.51 U_1^{0.48})$
$U_{BW} = 0.65 U_g^{0.29} (1+0.81 U_1^{0.72})$
Three Phase Fluidized Beds:
$\frac{1_{vc}-1_{v}}{1_{vc}}= \frac{1_{vc}-1_{vw}}{1_{vc}}(\frac{r}{R})^m$
$1_{vc} = 2.67×10^{-3} d_p^{-0.3} U_1^{-0.072} U_g^{0.221}$
$1_{vw} = 4.295×10^{-3} d_p^{-0.129} U_1^{-0.06} U_g^{0.124}$
$m = 3.770 d_p^{0.121}$
$U_B = \bar{U}_B \frac{k+2}{k} (1-(\frac{r}{R}^k)$
$\bar{U}_B = 1.772 d_p^{0.06} U_1^{0.024} U_g^{0.225}$
$k = 16.062 d_p^{0.228}$
The bubble chord length distribution is found to be log-normal. However, the bubble chord length distribution is found to be bimodal at the dimensionless distance (r/R) of 0.685 in the bubble coalescing beds.
The local liquid velocity can be predicted by the proposed modified wake model. The ratio of wake to gas phase holdup, the main parameter of the modified wake model decreases with an increase in gas velocity.
The turbulent viscosity estimated from the recirculation flow model increases with ann gas phase velocity in two and three phase fluidized beds. The turbulent viscosity can be correlated in term of operating parameters as follows:
$v_t = 0.0122 D_C^{0.352}d_p^{0.039}U_1^{0.32}$
