Effect of solid-liquid stirring on membrane deformation in the slurry electrolysis tank
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摘要: 礦漿電解作為一種短流程濕法冶金工藝，隔膜袋在攪拌槳攪動及礦石的磨損下會產生變形，甚至出現破裂，嚴重制約了生產效率。針對該問題，基于單向流固耦合原理，采用計算流體力學與固體有限元相結合的方法對礦漿電解攪拌槽內隔膜變形規律進行了全三維解析。研究發現隔膜袋兩側壓差是導致變形的根本原因，最大變形量出現在垂直高度y=1.2 m位置處，且攪拌轉速越大，隔膜變形所需的最佳液位差越小。當陰極區壓力不足時，隔膜袋向內擠壓變形；壓力增加后，則向兩側鼓包。隔膜最大變形量隨流體域固體體積含量（SL）的增加先減小后增加，在SL=15%時，隔膜變形達到最小值226.7 mm；越靠近槽下部，SL對絕對壓力的影響越大。添加框架約束后，隔膜最大變形量減小到0.664 mm。通過可視化的解析，可以為礦漿電解工業控制提供參照。
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關鍵詞:
- 礦漿電解 /
- 流固耦合 /
- 隔膜變形 /
- 計算流體力學?有限元 /
- 壓強差
Abstract: As a short-process hydrometallurgical technology, slurry electrolysis (SE) collects the stirring that improves the suspension of ore, the membrane bag that acts as purifying, and the cathodic and anodic plates that promote ion migration in one tank. The stirring helps to maintain the ore suspended. As the SE tank is stirred, the membrane bag will deform and become damaged, severely limiting production efficiency. In this research, the one-way fluid-structure interaction (FSI) was used to examine the impact of the solid–liquid suspension on membrane deformation, which was based on the computational fluid dynamics (CFD) and solid finite element method (FEM). Through the full 3D quantitative analysis, the database of membrane deformation under various conditions was established. The membrane was extruded to the center during the initial stirring conditions, and the greatest deformation measured 891.66 mm. Primarily, membrane deformation was brought on by the pressure differential brought on by liquid velocity, solid concentration distribution, and liquid level. The maximum deformation of the membrane first decreased and then increased with the increased liquid level difference between the cathode and anode. With the upper fixed constraint, the maximum deformation of the membrane appears at y = 1.2 m. The larger the stirring speed is, the smaller the optimal liquid level difference required to minimize the membrane deformation. The stirring speed changes the overall pressure distribution by changing the dynamic pressure in the anode domain. The maximum deformation of the membrane decreases first and then increases with the increase of electrolyte density in the cathode domain. The membrane bag is extruded to the cathode domain when the pressure in the cathode region is insufficient because of the low electrolyte density in the cathode domain. When the cathode pressure increases, the membrane bag bulges to both sides, and the inner bulge is greater than the outer. With an increase in solid volume concentration (SL) in the anode domain, the maximum membrane deformation first reduces and subsequently increases. When SL = 15%, the membrane deformation reaches the minimum value of 226.7 mm. The closer to the bottom of the tank, the greater the influence of solid content on absolute pressure. The maximum membrane deformation is drastically decreased to 0.664 mm when the frame restrictions are considered. It can support the industrial control process via visual analysis.-
Key words:
- slurry electrolysis /
- fluid-solid interaction /
- membrane deformation /
- CFD?FEM /
- pressure difference
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圖 1 隔膜幾何模型. （a）三維模型；（b）隔膜俯視圖
Figure 1. Membrane geometry: (a) three-dimensional model; (b) vertical view
圖 2 隔膜變形云圖. (a) 三維視圖；(b) 俯視圖
Figure 2. Membrane deformation contours: (a) three-dimensional view; (b) vertical view
圖 3 (a) 混合相絕對壓力分布；(b) 槽內電解質速度分布（z=0 mm）
Figure 3. (a) Absolute pressure distribution of the mixture phase; (b) liquid velocity distribution (z = 0 mm plane)
圖 4 隔膜最大變形量隨陰陽區液位差變化曲線 (SL=12%)
Figure 4. Curve of the maximum deformation of membrane with the liquid level (SL = 12%)
圖 5 隔膜變形量隨液位差變化云圖. （a）Δl = 100 mm；（b）Δl = 120 mm；（c）Δl = 140 mm
Figure 5. Contours of membrane deformation versus liquid level : (a) Δl = 100 mm；(b) Δl = 120 mm；(c) Δl = 140 mm
The membrane on the left part of the impeller; N = 120 rad∙min?1; SL = 12%; d = 74 μm; ρ = 1227 kg·m?3
圖 6 絕對壓力隨液位差變化曲線
Figure 6. Curve of absolute pressure versus liquid level
N = 120 rad∙min?1; SL = 12%; d = 74 μm; ρ = 1227 kg·m?3
圖 7 隔膜變形隨陰極區電解液密度變化云圖. （a）ρ = 1268 kg?m?3；（b）ρ = 1330 kg?m?3；（c）ρ = 1372 kg?m?3；（d）ρ = 1392 kg?m?3；（e）ρ = 1413 kg?m?3；（f）ρ = 1455 kg?m?3.
Figure 7. Contours of membrane deformation versus electrolyte density in cathode domain: (a) ρ = 1268 kg?m?3; (b) ρ = 1330 kg?m?3; (c) ρ = 1372 kg?m?3; (d) ρ = 1392 kg?m?3; (e) ρ = 1413 kg?m?3; (f) ρ = 1455 kg?m?3.
The membrane on the left part of the impeller; N = 100 rad∙min?1; SL = 12%; d = 74 μm; $ \Delta l= $50 mm
圖 8 隔膜最大變形量隨陰極電解液密度變化曲線
Figure 8. Curve of the maximum deformation of membrane with the electrolyte density in cathode domain
圖 9 隔膜最大變形量隨固體體積含量變化
Figure 9. Curve of the maximum deformation of membrane versus solid volume fraction
The membrane on the left part of the impeller; N = 120 rad∙min?1; $ \Delta l= $50 mm; ρ = 1400 kg·m?3
圖 10 混合相的絕對壓力沿x軸變化曲線。（a）y=0.7 m；（b）y=1.2 m；（c）y=1.7 m（z = 0 m）
Figure 10. Curve of absolute pressure along x-axis: (a) y = 0.7 m；(b) y = 1.2 m；(c) y = 1.7 m (z =0 m)
圖 11 礦漿電解槽隔膜袋的框架約束. （a）隔膜框架位置；（b）隔膜變形云圖
Figure 11. Fixed support on the membrane in slurry electrolysis tank: (a) location of fixed support on the membrane; (b) contour of membrane deformation
表 1 隔膜主要尺寸及物性參數
Table 1. Size and physical parameters of the membrane
Parameter Value Parameter Value Membranes’ length, L/mm 2140 Nylon density/(kg?m?3) 1140 Membranes’ width, W/mm 174.6 Coefficient of thermal expansion/℃?1 0.000147 Membranes’ thickness, h/mm 5 Young’s modulus/Pa 1.06×109 Membranes’ off-bottom clearance/mm 600 Poisson’s ratio 0.35 Nylon yield strength/Pa 4.31×107 Bulk modulus/Pa 1.1778×109 Nylon ultimate strength/Pa 34.97×107 Shear modulus/Pa 3.9259×108 
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表 2 網格無關性驗證
Table 2. Mesh independence for the simulation
Mesh Case1 Case2 Case3 Case4 Elements number for the fluid domain 4461000 4461000 4461000 4461000 Nodes number for the solid domain 584338 726550 983518 1107450 Maximum deformation, mm 174.47 184.49 185.07 185.13
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