靜態混合器中幾何結構對混合效率之影響

Abstract

本研究透過COMSOL Multiphysics 進行流體力學與質量傳輸的數值模擬，以探討SMX靜態混合器在不同的幾何結構和流體條件下之變異係數 (Coefficient of Variation, 以CoV表示)與壓降(Δp)，作為評估混合器性能之依據；CoV和Δp愈低者，混合器性能愈佳。SMX混合器元件由有規則相互交錯的橫桿組成，其中沿主流方向有Np支橫桿，橫跨主流方向有Nx支橫桿。本研究以矩形截面混合器流道為設計核心，系統性地分析Np和Nx之變化對混合器性能之影響。 本文首先以水為工作流體、並選定文獻及工業上常使用的(Np=3、Nx=8)結構進行探討，以比較圓形與方形截面流道對混合器性能造成的差異。結果顯示雖然方形截面者CoV值略高於圓形截面者，但其Δp也較低。如將方形截面者增加橫桿數至Nx=10，其CoV值及Δp均低於圓形截面者，此一結果展現方形截面混合器的潛力。為了減低壓降，本文引入文獻中在橫桿間加入空隙的設計、並就幾何參數Gr(定義為空隙與橫桿寬度間的比值)進行計算分析，結果顯示適度的空隙(約Gr≈0.1)會同時減少Δp和CoV值，而增強混合器性能。 本文亦模擬不同黏度的流體(水和甘油混合液，黏度由0.001~1.412Pa·s)在方形截面混合器(Np=3、Nx=10)的混合表現，發現黏度上升會造成CoV與Δp均上升；混合器中橫桿的數目須隨著黏度提升而減少、才能達至較佳的混合，表現出幾何與流體間存在著互相耦合的關係。此外，本研究也針對非牛頓流體(1% CMC溶液)進行分析，發現對於方形截面的SMX混合器，其內橫桿數目Np和Nx的優化選擇符合文獻中所提出的設計公式。最後，本研究引入突縮管結構於方形截面SMX混合器中，透過計算發現引入突縮管結構之整體效益不佳。 本研究提出了矩形截面SMX靜態混合器幾何結構在不同條件下之設計建議與應用潛力，期望可作為靜態混合器設計優化之參考。

Numerical simulations of fluid dynamics and mass transport inside, SMX static mixers were performed under various geometric configurations for different fluids using COMSOL Multiphysics, for accessing the mixer performance via the Coefficient of Variation (CoV) and pressure drop across the mixer (Δp), with lower CoV and Δp indicating better performance. The SMX mixer elements are composed of regularly interlaced crossing bars, with Np bars aligned along the main flow direction and Nx bars spanning across it. This study focuses on mixer with rectangular cross-section, and systematically investigates the influence of varying Np and Nx on mixer performance. First, a commonly structure in literature and industry (Np=3、Nx=8) was employed, using water as the working fluid, for studying the performance differences between circular and square cross-sections of the mixers. Results show that although the square cross-section exhibits slightly higher CoV, it also results in a lower Δp. By increasing the number of crossbars to (Np=3、Nx=10) in the square mixer, both CoV and Δp become lower than those of the circular counterpart with (Np=3、Nx=10), demonstrating the potential of using square mixer. To further reduce the pressure drop, a gap is introduced between the bars as suggested in the literature, and the geometric parameter Gr (defined as the ratio of the gap width to the bar width) is analyzed. The results indicate that a small gap size (approximately Gr≈0.1) could simultaneously reduce both CoV and Δp, enhancing the mixer performance. The mixing performance of fluids with different viscosities (water-glycerol mixtures with viscosities ranging from 0.001 to 1.412 Pa·s) was also studied in the square mixer with (Np=3、Nx=10). It is found that, both CoV and Δp increase. To achieve better mixing, the number of crossbars should be reduced with increasing viscosity, revealing a coupled relationship between mixer geometry and fluid properties. Additionally, simulations of a non-Newtonian fluid (1% CMC solution) show that the optimal selection of Np and Nx for square-section SMX mixers is consistent with design formulas proposed in the literature. Finally, the introduction of sudden contraction structures into the square SMX mixer was explored, but the result showed that the overall mixer performance was reduced due to a large increase in pressure-drop. This study provides some guidelines for the design of static SMX mixers, and highlights the application potential of mixers with rectangular cross-sections.