Figure 5. Pressure drop across the fluidized bed versus superficial gas
velocity
at (a) T = 20°C, (b) T = 200°C, (c) T = 400°C, and (d) T = 600°C.
4.3 Minimum fluidization velocity
(\(\mathbf{U}_{\mathbf{\text{mf}}}\))
Under ambient conditions, silica particles used in our experiments are
typically Geldart B particles. Therefore, the minimum bubbling velocity\(U_{\text{mb}}\) should be the same as the minimum fluidization
velocity (\(U_{\text{mf}}\)). To determine \(U_{\text{mf}}\), we
followed pressure drops across the fluidized bed versus superficial gas
velocity as shown in Figure 5. It is normally accepted that the point,
where the intersection of extrapolated line of pressure drop across the
packed bed and that of the total pressure drop across the full fluidized
bed, as can be seen in Figure 5, is regarded as the minimum fluidization
point.41 Based on the pressure-drop versus superficial
gas velocity curves, we could obtain \(U_{\text{mf}}\) = 3.60, 2.92,
2.48, and 2.40 cm/s for T= 20, 200, 400, and 600°C, respectively.
Apparently, under the ambient condition (T= 20 °C), \(U_{\text{mf}}\)and \(U_{\text{mb}}\) are coincided.
\(U_{\text{mf}}\) is compared with the empirical correlations, showing
that the dimensionless Ergun equation can be used to predict\(U_{\text{mf}}\) for Geldart B particles with reasonably good agreement
even at high temperature41:
\(\frac{1.75}{\varnothing\varepsilon_{\text{mf}}^{3}}\text{Re}_{\text{mf}}^{2}+150\frac{1-\varepsilon_{\text{mf}}}{\varnothing^{2}\varepsilon_{\text{mf}}^{3}}\text{Re}_{\text{mf}}=Ar\)(13)
where the Reynolds number and Archimedes number are respectively defined
as
\(\text{Re}_{\text{mf}}=\frac{d_{p}\rho_{g}U_{\text{mf}}}{\mu}\) (14)
\(Ar=\frac{d_{p}^{3}\rho_{g}\left(\rho_{p}-\rho_{g}\right)g}{\mu^{2}}\)(15)
Note that \(\varnothing\) is the sphericity of particles,\(\varepsilon_{\text{mf}}\ \)is the void fraction at minimum
fluidization, \(\rho_{p}\) is the particle density, \(\rho_{g}\) is the
gas density, \(d_{p}\) is the Sauter mean diameter of particles, \(\mu\)is the gas viscosity, and \(g\) is the gravitational constant.
Figure 6 compares the measured \(U_{\text{mf}}\) with the predicted\(U_{\text{mf}}\ \)via Eq. (13). As can be seen, at relatively low
operating temperature (T= 20 and 200oC), the measured\(U_{\text{mf}}\) agrees well with the predicted \(U_{\text{mf}}\). At
relatively high temperatures, however, the pronounced deviation between
the measured and predicted \(U_{\text{mf}}\) can be observed. Note that
in Eq. (13) the effects of gas density and viscosity are taken into
account, which implicitly reflects the influence of high temperature via
the change in gas properties. It can be argued that at relatively low
temperature, the influence of temperature on fluidization of silica
particles is mainly exerted via the change in gas properties. At even
higher temperature (T = 400 and 600oC), other
impact factors, such as enhanced cohesive inter-particle forces, may
play an increasingly important role.