无机材料学报 ›› 2025, Vol. 40 ›› Issue (12): 1387-1394.DOI: 10.15541/jim20250027
赵丽娟1,2(
), 谭哲1,2, 张晓光1,2(), 蒋国赛1,2, 陶然1,2, 潘德安2,3,4()
收稿日期:2025-01-18
修回日期:2025-04-15
出版日期:2025-12-20
网络出版日期:2025-05-09
通讯作者:
张晓光, 研究员. E-mail: zhangxg@bjut.edu.cn;作者简介:赵丽娟(1997-), 女, 博士研究生. E-mail: zhaolijuan97@163.com
基金资助:
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:摘要：
废加氢催化剂具有报废量大、颗粒完整度高等特性, 是再生催化剂载体的重要来源。现有废加氢催化剂回收技术大多关注其中的有价金属, 对于载体颗粒的回收研究较少。本研究针对条状废加氢催化剂颗粒难以通过传统筛分实现有效分级的关键问题, 创新性地提出采用流化床进行颗粒分级的策略。采用计算流体动力学(CFD)和离散单元模型(DEM)耦合模拟的研究方法, 结合响应面法(RSM)系统揭示了流化床分级的内在机理及工艺优化规律。研究表明, 流化床通过气固两相流态化作用可实现不同长径比颗粒的高效分级, 气体速度对分级效率的影响最为显著, 其次是进料流量, 进料口高度的影响相对较小。在一定的气体速度和进料口高度下, 存在进料流量阈值, 超过此值分级效率将会下降。通过建立Box-Behnken设计(BBD)模型, 确定当气体速度为10.45 m/s, 进料流量为7.50 t/h, 进料口高度为3.50 m时, 分级效率达到100%。本研究阐明了流化床分级过程的多物理场耦合机制, 为废加氢催化剂回收过程中的载体颗粒预分级工艺提供了理论参考。
中图分类号:
赵丽娟, 谭哲, 张晓光, 蒋国赛, 陶然, 潘德安. 废加氢催化剂颗粒分级数值模拟研究[J]. 无机材料学报, 2025, 40(12): 1387-1394.
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.
图1 (a)流化床模型以及(b)网格划分
Fig. 1 (a) Model and (b) mesh of fluidized bed
图2 (a1, b1)理论推导与(a2, b2)模拟仿真结果分析
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
图3 流化床中的气体速度分布
Fig. 3 Gas velocity distribution in fluidized bed Colorful figure is available on website
图4 (a1, a2)气体速度、(b1, b2)进料口高度和(c1, c2)进料流量对(a1, b1, c1)分级效率以及(a2, b2, c2)产品收集区最小粒径的影响
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
图5 模型残差分析
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
图6 响应面分析
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: $R e_{\mathrm{p}, \mathrm{CGM}}=\rho_{\mathrm{g}}\left|\boldsymbol{v}_{\mathrm{p}}-\boldsymbol{v}_{\mathrm{g}}\right| d_{\mathrm{p}, \mathrm{CGM}} / f_{\mathrm{CGM}} \mu_{\mathrm{g}}$ |
表S1 粗粒化CFD-DEM方法中的主要方程
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 |
表S2 符号命名
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 |
表S3 颗粒的组成
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 |
表S4 颗粒分级所需的临界气体速度
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 |
表S5 流化床模型验证的边界条件
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 |
表S6 BBD的三因素三水平设计
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 |
表S7 分级效率的RSM设计与仿真结果
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 |
表S8 模型拟合
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 |
表S9 回归方程方差
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 |
图S1 网格独立性验证
Fig. S1 Grid independence verification
图S2 每隔0.1 m截面的中点风速
Fig. S2 Midpoint gas velocity of the section every 0.1 m
图S3 流化床的产品收集区和颗粒分级区
Fig. S3 Product collection section and particle grading section of the fluidized bed
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