Comparison of the properties of segregated layers in a bidispersed fluidized bed to those of a monodispersed fluidized bed

Since industrial fluidized-bed reactors typically operate with polydispersed particles, the ability to approximate such reactors as the superposition of corresponding monodispersed fluidized beds would greatly simplify their design and operation. To evaluate the validity of superposition of monodispersed reactor behavior, we evaluate the effects of bidispersity by comparing three-dimensional liquid-solid monodispersed and segregated bidipsersed fluidized beds. Simulations were conducted using the immersed boundary method with direct forcing in a periodic domain and with particle Reynolds numbers of 20–70 based on the largest particle diameter. We show that the volume fraction, kinematic wave speed, particle velocity fluctuations, and collisional and hydrodynamic stresses in the segregated layers of a bidispersed fluidized bed can be well approximated by the corresponding properties of a monodispersed fluidized bed. In the transition region between the layers, only the volume fraction and collision stresses monotonically decrease with height. At low Reynolds numbers, particle velocity fluctuations in the upper layers are the largest. As the particle Reynolds number increases, particle velocity fluctuations in the transition and lower layers become the largest sequentially. At intermediate particle Reynolds numbers, the hydrodynamic stresses in the transition region are greater than those in the upper and lower layers. As the particle Reynolds number increases, the difference between the hydrodynamic stresses in the transition layer and the two layers become more significant. This paper demonstrates that, despite the clear segregation into layers that behave, such as monodispersed beds, the transition region is governed by complex bidispersed mechanisms that cannot be explained in terms of the particle behavior in the segregated layers. Overall, particle dynamics of the segregated layers in the bidispersed fluidized bed can be approximated with the corresponding monodispersed layers. The result implies that industrial applications, such as wastewater treatment performance in bidispersed or polydispersed fluidized beds can be predicted with results from past numerical or experimental studies of monodispersed fluidized beds.

Figure 1

The three-dimensional computational domain, showing the bidispersed fluidized bed and the uniform inflow velocity profile. Particle positions are initialized with $1d_{p,1}$ spacing for the simulation with ${\mathrm{Re}}_p=40$ for FB-Bi-14.

Figure 2

Time series of the ensemble settling velocity ${\langle w_p\rangle }^{*}$ normalized by $u_0$ for ${\mathrm{Re}}_{p,1}=40$ for all cases simulated except FB-Mono-10.

Figure 3

Horizontally and time-averaged volume fraction ${\langle \overline{\varphi }\rangle }_{xy}^{*}$ as a function of normalized vertical position $z/d_{p,1}$ for different particle Reynolds numbers ${\mathrm{Re}}_{p,1}$. (a) FB-Mono-12. (b) FB-Bi-12. (c) FB-Mono-14. (d) FB-Bi-14.

Figure 4

PDF of particle vertical positions for the two-particle diameters in the case with ${\mathrm{Re}}_{p,1}=40$ for FB-Bi-12.

Figure 5

Porosity $1-\langle \overline{\varphi }\rangle$ as a function of ${\mathrm{Re}}_{p,1}$ for the simulated monodispersed and bidispersed cases. The lines were constructed based on fitting to the power-law equation (1).

Figure 6

Wave speed based on the autocorrelation as a function of ${\mathrm{Re}}_{p,1}$ for (a) $d_{p,1}$, (b) $d_{p,2}$, and (c) $d_{p,3}$.

Figure 7

Particle velocity fluctuations as a function of the fluidized-bed height $L_b$ for case FB-Mono-12 with (a) ${\mathrm{Re}}_{p,1}=30$ and (b) ${\mathrm{Re}}_{p,1}=60$.

Figure 8

Normalized particle velocity fluctuations as a function of ${\mathrm{Re}}_{p,1}$ for (a) $d_{p,1}/d_{p,2}=1.2$ and $d_{p,1}/d_{p,3}=1.4$ and $1-\langle \overline{\varphi }\rangle$ for (c) $d_{p,1}/d_{p,2}=1.2$ and (d) $d_{p,1}/d_{p,3}=1.4$.

Figure 9

Calculated integral timescale as a function of (a) simulated duration $N_{\tau }$ and (b) fluidized-bed height $L_b/d_{p,1}$ for case FB-Mono-12 with ${\mathrm{Re}}_{p,1}=40$.

Figure 10

Expected integral timescale as a function of ${\mathrm{Re}}_{p,1}$ for (a) $d_{p,1}/d_{p,2}=1.2$ and $d_{p,1}/d_{p,3}=1.4$.

Figure 11

Self-diffusivity as a function of ${\mathrm{Re}}_{p,1}$ for (a) $d_{p,1}/d_{p,2}=1.2$ and (b) $d_{p,1}/d_{p,3}=1.4$.

Figure 12

Normal contact stress and hydrodynamic stress as a function of vertical position for $d_{p,1}/d_{p,3}=1.40$ and with (a) ${\mathrm{Re}}_{1,p}=20$ and (b) ${\mathrm{Re}}_{1,p}=70$. Solid lines correspond to bidispersed fluidized-bed layers, and dotted lines correspond to monodispersed layers.

Figure 13

The computed normal contact stress and hydrodynamic stress as a function Reynolds number ${\mathrm{Re}}_{p,1}$. (a) Normal contact stress for $d_{p,1}/d_{p,2}=1.2$. (b) Hydrodynamic stress for $d_{p,1}/d_{p,2}=1.2$. (a) Normal contact stress for $d_{p,1}/d_{p,3}=1.4$. (a) Hydrodynamic stress for $d_{p,1}/d_{p,3}=1.4$.

Figure 14

Volume fraction fluctuation ${\varphi }^{\prime }$ as a function of time $t$ and vertical position $z$ at ${\mathrm{Re}}_p=60$ in the lower layer for case FB-Bi-12. (a) Unfiltered ${\varphi }^{\prime }$, (b) reconstructed low-pass filtered ${\varphi }^{\prime }$.

Figure 15

(a) Autocorrelation of the low-pass filtered volume fraction fluctuation ${\varphi }^{\prime }$ as a function of time $t$ and vertical position $z$ and (b) energy spectra of the reconstructed volume fraction fluctuation ${\varphi }^{\prime }$ as a function of wave-number $k$ and frequency $\omega$ at ${\mathrm{Re}}_p=60$ in the lower layer for case FB-Bi-12.

Figure 16

Wave speed derived from different approaches as a function of ${\mathrm{Re}}_{p,1}$ for case FB-Mono-12.