# Experimental Study of Entrainment and Mixing of Renewable Active Particles in Fluidized Beds
## 3 Results and Discussion
### Particle Entrainment  
Particle entrainment is one of the fluid-dynamic characteristics that depend on the type of the actual solid fuel. Figure 6 presents the _accumulated entrained mass fraction_ of the investigated particles (SRF, bark, sunflower shell, and wheat shell) as function of the superficial gas velocity. This figure shows that there is a significant difference in the entrainment behaviors of the investigated particles. For example, the sunflower shells entrain from the bed in the highest degree; however, at very low velocity, the entrainment of wheat shell is the most intensive. The entrainment behaviors of the investigated SRF and bark samples are similar. However, the SRF is entrained relatively less than the bark at the low fluidization velocities, and more than the bark at elevated velocities. Also, the 50%-entrainment line shows that the velocity at which 50% of the investigated particles is entrained is higher for the larger particles (SRF and bark), irrespectively of their diverse densities. [PERSON] and [PERSON] [29] proposed an empirical-based chart for estimating the particle terminal velocity. This chart contains a set of curves offsetting by the degree of particle sphericity. Figure 7 show this chart, together with the data representing the renewable fuels as measured in the current work. The 50% entrainment data were taken from Figure 6 as they characterize well the sets of irregular particles. Figure 7 indicates that the investigated renewable fuels behave like low sphericity particles. More precisely, the curve running closest to the data gained from the SRF measurements corresponds to a sphericity of \(\phi_{\text{SRF}}=0.123\), and similar conclusions can be taken for all other investigated fuels. According to this, the characteristic sphericity of bark and wheat shell is \(\phi_{\text{Bark}}=\phi_{\text{W.Shell}}=0.043\), and that of sunflower shell can be well approximated by \(\phi_{\text{S.Shell}}=0.035\). In fluidized bed energy applications, the operating temperature is high and it depends on the conversion process e.g., incineration, gasification, pyrolysis, and carbonization. The present measurements were performed on a cold basis to avoid conversion of the active particles. Furthermore, we need to address exclusively the fluid dynamic phenomenon without complications that can result from the hot-condition. To over come this technical problem, we need to link the superficial velocity of the hot basis to the investigated cold basis superficial velocity range. This correction can be obtained from the similarity of the drag force between the hot basis and the cold basis. Therefore, the consequent  
Figure 6: Particle entrainment as function of the superficial air velocity of SRF, bark, sunflower shell, and wheat shell. (Error bars on the above figure represent the repeatability error, while the precision error of the measuring instruments are \(\pm\) 0.05 g for weight, and \(\pm\) 0.009 m/s for velocity)similarity of the particle Reynolds number (\(Re=\rho_{g}u_{g}d_{p}/\mu_{g}\)) is used to obtain the hot basis superficial velocity as follows:  
\[ \begin{split}& Re^{i}|_{T^{\circ}C}=Re|_{25^{\circ}C}\\ &\frac{\rho_{g}^{\prime}u_{g}^{\prime}d_{p}}{\mu_{g}^{\prime}}|_{ T^{\circ}C}=\frac{\rho_{g}u_{g}d_{p}}{\mu_{g}}|_{25^{\circ}C}\end{split}  \tag{1}\]  
Figure 8 shows the correction of the superficial velocity related to different operating temperatures. By this way, we can calculate the particles entrainment in hot basis, indirectly by first estimating the Re-equivalent cold superficial velocity from Figure 8. The, substitution with the superficial air velocity in Figure 6 to get the accumulated entrained mass fraction. For example, the incineration hot basis superficial velocity of 0.2 m/s can entrain the wheat shell at a rate of 73%. Figure 8: Superficial velocity correction related to the operating temperature.