Journal of Inorganic Materials ›› 2025, Vol. 40 ›› Issue (12): 1387-1394.DOI: 10.15541/jim20250027
• RESEARCH ARTICLE • Previous Articles Next Articles
ZHAO Lijuan1,2(
), TAN Zhe1,2, ZHANG Xiaoguang1,2(), JIANG Guosai1,2, TAO Ran1,2, PAN De’an2,3,4()
Received:2025-01-18
Revised:2025-04-15
Published:2025-12-20
Online:2025-05-09
Contact:
ZHANG Xiaoguang, professor. E-mail: zhangxg@bjut.edu.cn;About author:ZHAO Lijuan (1997-), female, PhD candidate. E-mail: zhaolijuan97@163.com
Supported by:CLC Number:
ZHAO Lijuan, TAN Zhe, ZHANG Xiaoguang, JIANG Guosai, TAO Ran, PAN De’an. Numerical Simulation of Particle Classification for Spent Hydrogenation Catalyst[J]. Journal of Inorganic Materials, 2025, 40(12): 1387-1394.
Fig. 1 (a) Model and (b) mesh of fluidized bed
Fig. 2 Analysis of (a1, b1) theoretical derivation and (a2, b2) simulation (a1, a2) dp=0.29 mm; (b1, b2) dp=2.19 mm. Colorful figures are available on website
Fig. 3 Gas velocity distribution in fluidized bed Colorful figure is available on website
Fig. 4 Effects of (a1, a2) gas velocity, (b1, b2) inlet height, and (c1, c2) feed flow on (a1, b1, c1) grading efficiency and (a2, b2, c2) minimum particle diameter in the product collection section Colorful figures are available on website
Fig. 5 Model residual analysis (a) Normal probability versus externally studentized residual; (b) Externally studentized residual versus predicted value; (c) Externally studentized residual versus run number; (d) Predicted value versus actual value. Colorful figures are available on website
Fig. 6 Response surface analysis (a1, a2) Factors gas velocity A and inlet height B; (b1, b2) Factors gas velocity A and feed flow C; (c1, c2) Factors inlet height B and feed flow C;(a1, b1, c1) Response surface; (a2, b2, c2) Contour plots. Colorful figures are available on website
| Average mass conservation equation: $\partial\left(\alpha_{\mathrm{g}} \rho_{\mathrm{g}}\right) / \partial t+\nabla \cdot\left(\alpha_{\mathrm{g}} \rho_{\mathrm{g}} \boldsymbol{v}_{\mathrm{g}}\right)=0$ |
|---|
| Average momentum conservation equation: $\partial\left(\alpha_{\mathrm{g}} \rho_{\mathrm{g}} \boldsymbol{v}_{\mathrm{g}}\right) / \partial t+\nabla \cdot\left(\alpha_{\mathrm{g}} \rho_{\mathrm{g}} \boldsymbol{v}_{\mathrm{g}} \boldsymbol{v}_{\mathrm{g}}\right)=-\alpha_{\mathrm{g}} \nabla P+\nabla \cdot\left(\alpha_{\mathrm{g}} \tau_{\mathrm{g}}\right)+F_{\mathrm{p} \rightarrow \mathrm{~g}}+\alpha_{\mathrm{g}} \rho_{\mathrm{g}} g$ |
| Velocity vector of the gas phase: $\tau_{\mathrm{g}}=\mu_{\mathrm{g}}\left(\nabla \boldsymbol{v}_{\mathrm{g}}+\nabla \boldsymbol{v}_{\mathrm{g}}^{T}\right)-2 / 3 \cdot\left(\nabla \boldsymbol{v}_{\mathrm{g}}\right) \boldsymbol{I}$ |
| Gas phase density: $\rho_{\mathrm{g}}=P_{\mathrm{g}} M / R_{\mathrm{g}} T$ |
| Momentum source term interacting with the particle phase: $F_{\mathrm{p} \rightarrow \mathrm{~g}}=-\sum_{p=1}^{n} F_{\mathrm{g} \rightarrow \mathrm{p}} / V_{\mathrm{C}}$ |
| Force generated by the gas phase on the particles: $F_{\mathrm{g} \rightarrow \mathrm{p}}=F_{\mathrm{D}}+F_{\nabla P}$ |
| Pressure gradient force $F_{\nabla P}$: $F_{\nabla P}=-V_{\mathrm{p}} \nabla P$ |
| Drag force calculation when using CGM: $F_{\mathrm{D}, \mathrm{CGM}}=1 / 2 \cdot\left(f_{\mathrm{CGM}}^{3} C_{\mathrm{D}} \rho_{\mathrm{g}} A^{\prime}\left|\boldsymbol{v}_{\mathrm{g}}-\boldsymbol{v}_{\mathrm{p}}\right|\left(\boldsymbol{v}_{\mathrm{g}}-\boldsymbol{v}_{\mathrm{p}}\right)\right)$ |
| Where $C_{D}$ is the drag coefficient, expressed as: $C_{\mathrm{D}}=\psi C_{\mathrm{D} 1}+(1-\psi) C_{\mathrm{D} 2}$ |
| Where $\psi$ is the mixing parameter, calculated by: $\psi=1 / \pi \cdot \tan ^{-1}\left[150 \cdot 1.75\left(0.8-\alpha_{\mathrm{g}}\right)\right]+0.5$ |
| Where $C_{\mathrm{D} 1}$ is expressed as: $C_{\mathrm{D} 1}=200 \alpha_{\mathrm{p}} / \alpha_{\mathrm{g}} \phi^{2} R e+7 / 3 \phi$ |
| Where $\psi$ is the sphericity of the particles, defined as: $\phi=A_{\mathrm{sph}} / A_{\mathrm{p}}$ |
| Where $C_{\mathrm{D} 2}$ is expressed as: $C_{\mathrm{D} 2}=\alpha_{\mathrm{g}}^{-1.65} \max \left\{24 / \alpha_{\mathrm{g}} R e_{\mathrm{p}} \cdot\left[1+0.15\left(\alpha_{\mathrm{g}} R e_{\mathrm{p}}\right)^{0.687}\right], 0.44\right\}$ |
| Particle relative Reynolds number $R e_{\mathrm{p}}$ when using CGM: $R e_{\mathrm{p}, \mathrm{CGM}}=\rho_{\mathrm{g}}\left|\boldsymbol{v}_{\mathrm{p}}-\boldsymbol{v}_{\mathrm{g}}\right| d_{\mathrm{p}, \mathrm{CGM}} / f_{\mathrm{CGM}} \mu_{\mathrm{g}}$ |
Table S1 Main equations in coarse-grained CFD-DEM method
| Average mass conservation equation: $\partial\left(\alpha_{\mathrm{g}} \rho_{\mathrm{g}}\right) / \partial t+\nabla \cdot\left(\alpha_{\mathrm{g}} \rho_{\mathrm{g}} \boldsymbol{v}_{\mathrm{g}}\right)=0$ |
|---|
| Average momentum conservation equation: $\partial\left(\alpha_{\mathrm{g}} \rho_{\mathrm{g}} \boldsymbol{v}_{\mathrm{g}}\right) / \partial t+\nabla \cdot\left(\alpha_{\mathrm{g}} \rho_{\mathrm{g}} \boldsymbol{v}_{\mathrm{g}} \boldsymbol{v}_{\mathrm{g}}\right)=-\alpha_{\mathrm{g}} \nabla P+\nabla \cdot\left(\alpha_{\mathrm{g}} \tau_{\mathrm{g}}\right)+F_{\mathrm{p} \rightarrow \mathrm{~g}}+\alpha_{\mathrm{g}} \rho_{\mathrm{g}} g$ |
| Velocity vector of the gas phase: $\tau_{\mathrm{g}}=\mu_{\mathrm{g}}\left(\nabla \boldsymbol{v}_{\mathrm{g}}+\nabla \boldsymbol{v}_{\mathrm{g}}^{T}\right)-2 / 3 \cdot\left(\nabla \boldsymbol{v}_{\mathrm{g}}\right) \boldsymbol{I}$ |
| Gas phase density: $\rho_{\mathrm{g}}=P_{\mathrm{g}} M / R_{\mathrm{g}} T$ |
| Momentum source term interacting with the particle phase: $F_{\mathrm{p} \rightarrow \mathrm{~g}}=-\sum_{p=1}^{n} F_{\mathrm{g} \rightarrow \mathrm{p}} / V_{\mathrm{C}}$ |
| Force generated by the gas phase on the particles: $F_{\mathrm{g} \rightarrow \mathrm{p}}=F_{\mathrm{D}}+F_{\nabla P}$ |
| Pressure gradient force $F_{\nabla P}$: $F_{\nabla P}=-V_{\mathrm{p}} \nabla P$ |
| Drag force calculation when using CGM: $F_{\mathrm{D}, \mathrm{CGM}}=1 / 2 \cdot\left(f_{\mathrm{CGM}}^{3} C_{\mathrm{D}} \rho_{\mathrm{g}} A^{\prime}\left|\boldsymbol{v}_{\mathrm{g}}-\boldsymbol{v}_{\mathrm{p}}\right|\left(\boldsymbol{v}_{\mathrm{g}}-\boldsymbol{v}_{\mathrm{p}}\right)\right)$ |
| Where $C_{D}$ is the drag coefficient, expressed as: $C_{\mathrm{D}}=\psi C_{\mathrm{D} 1}+(1-\psi) C_{\mathrm{D} 2}$ |
| Where $\psi$ is the mixing parameter, calculated by: $\psi=1 / \pi \cdot \tan ^{-1}\left[150 \cdot 1.75\left(0.8-\alpha_{\mathrm{g}}\right)\right]+0.5$ |
| Where $C_{\mathrm{D} 1}$ is expressed as: $C_{\mathrm{D} 1}=200 \alpha_{\mathrm{p}} / \alpha_{\mathrm{g}} \phi^{2} R e+7 / 3 \phi$ |
| Where $\psi$ is the sphericity of the particles, defined as: $\phi=A_{\mathrm{sph}} / A_{\mathrm{p}}$ |
| Where $C_{\mathrm{D} 2}$ is expressed as: $C_{\mathrm{D} 2}=\alpha_{\mathrm{g}}^{-1.65} \max \left\{24 / \alpha_{\mathrm{g}} R e_{\mathrm{p}} \cdot\left[1+0.15\left(\alpha_{\mathrm{g}} R e_{\mathrm{p}}\right)^{0.687}\right], 0.44\right\}$ |
| Particle relative Reynolds number $R e_{\mathrm{p}}$ when using CGM: $R e_{\mathrm{p}, \mathrm{CGM}}=\rho_{\mathrm{g}}\left|\boldsymbol{v}_{\mathrm{p}}-\boldsymbol{v}_{\mathrm{g}}\right| d_{\mathrm{p}, \mathrm{CGM}} / f_{\mathrm{CGM}} \mu_{\mathrm{g}}$ |
| Symbol | Physical significance |
|---|---|
| $g$ | Gas phase |
| $p$ | Particle phase |
| $\alpha_{\mathrm{p}}$ | Concentration of the particulate phase |
| $\rho_{\mathrm{g}}$ | Density of the gas phase |
| $\rho_{\mathrm{p}}$ | Density of the particulate phase |
| $V_{\mathrm{g}}$ | Velocity vector of the gas phase |
| $V_{\mathrm{p}}$ | Velocity vector of the particulate phase |
| $\tau_{\mathrm{g}}$ | Viscous stress tensor of the gas phase |
| $T$ | Temperature of the gas phase |
| $I$ | Identity matrix |
| $P_{g}$ | Pressure of the gas |
| $n$ | Number of particles inside the computational cell volume |
| $V_{C}$ | Computational cell volume |
| $F_{\mathrm{p} \rightarrow \mathrm{~g}}$ | Force generated by the particles on the gas phase |
| F_{\mathrm{g} \rightarrow \mathrm{~p}} | Force generated by the gas phase on the particulate phase |
| $F_{D}$ | Drag force |
| $F_{\nabla P}$ | Pressure gradient force |
| $V_{p}$ | Volume of the particle |
| $\nabla p$ | Local pressure gradient |
| $A'$ | Projected particle area in the flow direction |
| $f_{\mathrm{CGM}}$ | Scale factor of the coarse particle |
| $f_{\mathrm{D,CGM}}$ | Drag force of the coarse particle |
| $C_{D}$ | Drag coefficient |
| $\psi$ | Mixing parameter |
| $\phi$ | Sphericity of the particles |
| $A_{sph}$ | Surface area of a sphere with the same volume as the particle |
| $A_{p}$ | Actual surface area of the particle |
| $R e_{\mathrm{p}, \mathrm{CGM}}$ | Particle relative Reynolds number of the coarse particle |
| $d_{\mathrm{p}, \mathrm{CGM}}$ | Diameter of the coarse particle |
| $\mu_{\mathrm{g}}$ | Viscosity of gas phase |
| $d_{p}$ | Spherical equivalent diameter of the particle |
| $V_{HDS}$ | Volume of the spent hydrogenation (HDS) catalyst rod particle |
| $t$ | Graded time of the spent HDS catalyst particles |
| $G$ | Gravity of the spent HDS catalyst particles |
| $m$ | Mass of the spent HDS catalyst particles |
| $g$ | Acceleration due to gravity |
| $α$ | Acceleration of the particle |
| $V_{pi}$ | Velocity of a particle dropped from the inlet at i second |
| $V_{gi}$ | Cross-sectional gas velocity at i second |
| $α_{i}$ | Acceleration of a particle dropped from the inlet at i second |
| $L_{i}$ | Distance of a particle dropped from the inlet at i second |
| $\lambda$ | Gradation efficiency |
| $N_{1}$ | Number of the spent HDS catalyst particles with a diameter greater than 1.5 mm in the product collection section |
| $N_{2}$ | Total number of spent HDS catalyst particles in the product collection section |
Table S2 Nomenclature of the symbols
| Symbol | Physical significance |
|---|---|
| $g$ | Gas phase |
| $p$ | Particle phase |
| $\alpha_{\mathrm{p}}$ | Concentration of the particulate phase |
| $\rho_{\mathrm{g}}$ | Density of the gas phase |
| $\rho_{\mathrm{p}}$ | Density of the particulate phase |
| $V_{\mathrm{g}}$ | Velocity vector of the gas phase |
| $V_{\mathrm{p}}$ | Velocity vector of the particulate phase |
| $\tau_{\mathrm{g}}$ | Viscous stress tensor of the gas phase |
| $T$ | Temperature of the gas phase |
| $I$ | Identity matrix |
| $P_{g}$ | Pressure of the gas |
| $n$ | Number of particles inside the computational cell volume |
| $V_{C}$ | Computational cell volume |
| $F_{\mathrm{p} \rightarrow \mathrm{~g}}$ | Force generated by the particles on the gas phase |
| F_{\mathrm{g} \rightarrow \mathrm{~p}} | Force generated by the gas phase on the particulate phase |
| $F_{D}$ | Drag force |
| $F_{\nabla P}$ | Pressure gradient force |
| $V_{p}$ | Volume of the particle |
| $\nabla p$ | Local pressure gradient |
| $A'$ | Projected particle area in the flow direction |
| $f_{\mathrm{CGM}}$ | Scale factor of the coarse particle |
| $f_{\mathrm{D,CGM}}$ | Drag force of the coarse particle |
| $C_{D}$ | Drag coefficient |
| $\psi$ | Mixing parameter |
| $\phi$ | Sphericity of the particles |
| $A_{sph}$ | Surface area of a sphere with the same volume as the particle |
| $A_{p}$ | Actual surface area of the particle |
| $R e_{\mathrm{p}, \mathrm{CGM}}$ | Particle relative Reynolds number of the coarse particle |
| $d_{\mathrm{p}, \mathrm{CGM}}$ | Diameter of the coarse particle |
| $\mu_{\mathrm{g}}$ | Viscosity of gas phase |
| $d_{p}$ | Spherical equivalent diameter of the particle |
| $V_{HDS}$ | Volume of the spent hydrogenation (HDS) catalyst rod particle |
| $t$ | Graded time of the spent HDS catalyst particles |
| $G$ | Gravity of the spent HDS catalyst particles |
| $m$ | Mass of the spent HDS catalyst particles |
| $g$ | Acceleration due to gravity |
| $α$ | Acceleration of the particle |
| $V_{pi}$ | Velocity of a particle dropped from the inlet at i second |
| $V_{gi}$ | Cross-sectional gas velocity at i second |
| $α_{i}$ | Acceleration of a particle dropped from the inlet at i second |
| $L_{i}$ | Distance of a particle dropped from the inlet at i second |
| $\lambda$ | Gradation efficiency |
| $N_{1}$ | Number of the spent HDS catalyst particles with a diameter greater than 1.5 mm in the product collection section |
| $N_{2}$ | Total number of spent HDS catalyst particles in the product collection section |
| Diameter/mm | Percentage/% |
|---|---|
| 0.29 | 1.00 |
| 1.14 | 3.04 |
| 1.44 | 35.50 |
| 1.65 | 34.28 |
| 1.82 | 14.81 |
| 1.96 | 6.03 |
| 2.08 | 3.45 |
| 2.19 | 1.89 |
Table S3 Composition of particles
| Diameter/mm | Percentage/% |
|---|---|
| 0.29 | 1.00 |
| 1.14 | 3.04 |
| 1.44 | 35.50 |
| 1.65 | 34.28 |
| 1.82 | 14.81 |
| 1.96 | 6.03 |
| 2.08 | 3.45 |
| 2.19 | 1.89 |
| Diameter/mm | Velocity/(m·s-1) |
|---|---|
| 1.14 | 8.23 |
| 1.44 | 9.25 |
| 1.65 | 9.90 |
| 1.82 | 10.39 |
| 1.96 | 10.79 |
| 2.08 | 11.11 |
| 2.19 | 11.40 |
Table S4 Critical gas velocity required for particle gradation
| Diameter/mm | Velocity/(m·s-1) |
|---|---|
| 1.14 | 8.23 |
| 1.44 | 9.25 |
| 1.65 | 9.90 |
| 1.82 | 10.39 |
| 1.96 | 10.79 |
| 2.08 | 11.11 |
| 2.19 | 11.40 |
| Physical property | Value |
|---|---|
| fCGM | 7 |
| Particle temperature | 300 K |
| Gas velocity | 9.25 m/s |
| Feed flow | 1.25 t /h |
| Inlet height | 3.50 m |
Table S5 Boundary conditions of model validation for the fluidized graded bed
| Physical property | Value |
|---|---|
| fCGM | 7 |
| Particle temperature | 300 K |
| Gas velocity | 9.25 m/s |
| Feed flow | 1.25 t /h |
| Inlet height | 3.50 m |
| Independent variable | Unit | Symbol | Factor level | ||
|---|---|---|---|---|---|
| -1 | 0 | -1 | |||
| Gas velocity | m/s | A | 9.85 | 10.45 | 11.05 |
| Inlet height | m | B | 1.5 | 3.5 | 5.5 |
| Feed flow | t/h | C | 5 | 7.5 | 10 |
Table S6 Three-factor and three-level for BBD
| Independent variable | Unit | Symbol | Factor level | ||
|---|---|---|---|---|---|
| -1 | 0 | -1 | |||
| Gas velocity | m/s | A | 9.85 | 10.45 | 11.05 |
| Inlet height | m | B | 1.5 | 3.5 | 5.5 |
| Feed flow | t/h | C | 5 | 7.5 | 10 |
| NO. | Independent variable | Response value | ||
|---|---|---|---|---|
| Gas velocity, A/(m·s-1) | Inlet height, B/m | Feed flow, C/(t·h-1) | Grading efficiency, $\lambda$/% | |
| 1 | 10.45 | 3.5 | 7.5 | 100 |
| 2 | 9.85 | 1.5 | 7.5 | 75.37 |
| 3 | 11.05 | 5.5 | 7.5 | 100 |
| 4 | 10.45 | 3.5 | 7.5 | 100 |
| 5 | 10.45 | 3.5 | 7.5 | 100 |
| 6 | 11.05 | 3.5 | 10 | 100 |
| 7 | 10.45 | 5.5 | 10 | 100 |
| 8 | 9.85 | 3.5 | 10 | 76.56 |
| 9 | 10.45 | 1.5 | 10 | 100 |
| 10 | 10.45 | 3.5 | 7.5 | 100 |
| 11 | 10.45 | 5.5 | 5 | 100 |
| 12 | 9.85 | 5.5 | 7.5 | 81.17 |
| 13 | 10.45 | 1.5 | 5 | 100 |
| 14 | 11.05 | 3.5 | 5 | 100 |
| 15 | 9.85 | 3.5 | 5 | 78.24 |
| 16 | 10.45 | 3.5 | 7.5 | 100 |
| 17 | 11.05 | 1.5 | 7.5 | 100 |
Table S7 Design and simulation results of RSM of grading efficiency
| NO. | Independent variable | Response value | ||
|---|---|---|---|---|
| Gas velocity, A/(m·s-1) | Inlet height, B/m | Feed flow, C/(t·h-1) | Grading efficiency, $\lambda$/% | |
| 1 | 10.45 | 3.5 | 7.5 | 100 |
| 2 | 9.85 | 1.5 | 7.5 | 75.37 |
| 3 | 11.05 | 5.5 | 7.5 | 100 |
| 4 | 10.45 | 3.5 | 7.5 | 100 |
| 5 | 10.45 | 3.5 | 7.5 | 100 |
| 6 | 11.05 | 3.5 | 10 | 100 |
| 7 | 10.45 | 5.5 | 10 | 100 |
| 8 | 9.85 | 3.5 | 10 | 76.56 |
| 9 | 10.45 | 1.5 | 10 | 100 |
| 10 | 10.45 | 3.5 | 7.5 | 100 |
| 11 | 10.45 | 5.5 | 5 | 100 |
| 12 | 9.85 | 5.5 | 7.5 | 81.17 |
| 13 | 10.45 | 1.5 | 5 | 100 |
| 14 | 11.05 | 3.5 | 5 | 100 |
| 15 | 9.85 | 3.5 | 5 | 78.24 |
| 16 | 10.45 | 3.5 | 7.5 | 100 |
| 17 | 11.05 | 1.5 | 7.5 | 100 |
| Standard deviation | Mean | Coefficient of variance/% | R2 | Adj. R2 | Pred. R2 | Adeq Precision |
|---|---|---|---|---|---|---|
| 0.8397 | 94.78 | 0.8860 | 0.9968 | 0.9926 | 0.9481 | 38.9173 |
Table S8 Model fit statistics
| Standard deviation | Mean | Coefficient of variance/% | R2 | Adj. R2 | Pred. R2 | Adeq Precision |
|---|---|---|---|---|---|---|
| 0.8397 | 94.78 | 0.8860 | 0.9968 | 0.9926 | 0.9481 | 38.9173 |
| Source | Coefficient estimate | Sum of squares | Degree of freedom | Mean square | F value | P value |
|---|---|---|---|---|---|---|
| Model | - | 1516.81 | 9 | 168.53 | 239.00 | <0.0001 |
| A | 11.0825 | 982.57 | 1 | 982.57 | 1393.37 | <0.0001 |
| B | 0.725 | 4.21 | 1 | 4.21 | 5.96 | 0.0446 |
| C | -0.21 | 0.3528 | 1 | 0.3528 | 0.5003 | 0.5022 |
| AB | -1.45 | 8.41 | 1 | 8.41 | 11.93 | 0.0106 |
| AC | 0.42 | 0.7056 | 1 | 0.7056 | 1 | 0.3505 |
| BC | -8.71×10-16 | 0 | 1 | 0 | 0 | 1 |
| A2 | -11.0825 | 517.14 | 1 | 517.14 | 733.35 | <0.0001 |
| B2 | 0.2175 | 0.1992 | 1 | 0.1992 | 0.2825 | 0.6115 |
| C2 | -0.2175 | 0.1992 | 1 | 0.1992 | 0.2825 | 0.6115 |
Table S9 ANOVA results of the regression equation
| Source | Coefficient estimate | Sum of squares | Degree of freedom | Mean square | F value | P value |
|---|---|---|---|---|---|---|
| Model | - | 1516.81 | 9 | 168.53 | 239.00 | <0.0001 |
| A | 11.0825 | 982.57 | 1 | 982.57 | 1393.37 | <0.0001 |
| B | 0.725 | 4.21 | 1 | 4.21 | 5.96 | 0.0446 |
| C | -0.21 | 0.3528 | 1 | 0.3528 | 0.5003 | 0.5022 |
| AB | -1.45 | 8.41 | 1 | 8.41 | 11.93 | 0.0106 |
| AC | 0.42 | 0.7056 | 1 | 0.7056 | 1 | 0.3505 |
| BC | -8.71×10-16 | 0 | 1 | 0 | 0 | 1 |
| A2 | -11.0825 | 517.14 | 1 | 517.14 | 733.35 | <0.0001 |
| B2 | 0.2175 | 0.1992 | 1 | 0.1992 | 0.2825 | 0.6115 |
| C2 | -0.2175 | 0.1992 | 1 | 0.1992 | 0.2825 | 0.6115 |
Fig. S1 Grid independence verification
Fig. S2 Midpoint gas velocity of the section every 0.1 m
Fig. S3 Product collection section and particle grading section of the fluidized bed
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