黏彈流體於靜態混合器中混合的數值研究

Abstract

本研究透過COMSOL Multiphysics計算軟體進行數值模擬。在層流條件下，利用稀薄質傳法(Transport of Diluted Species)，計算黏彈流體於靜態混合器中流場和濃度場，並進而分析其混合效果及壓降。本文所選用之混合器元件共有兩種，分別為SMX元件及突縮圓管(Sudden Contraction Tube，簡稱SCT)元件。通過調整元件種類、排列、及元件中的幾何參數，並選用不同黏度之流體，和不同流體模型(以反應不同程度之彈性效應)進行計算，以探討其對混合效果的影響。 經本文的研究，可得以下結論：(1)經與實驗比較，採用黏彈模型(如Giesekus Model)較採用剪切稀化模型(如Carreau Model)所得的計算結果更能與實驗結果相符，後者約低估了18%的混合效果；但前者卻需多耗約5倍計算時間、且兩種模型的計算結果定性相符，故建議如作靜態混合器參數的最佳化研究，可採用剪切稀化模型。(2)如使用標準SMX靜態混合器對黏彈流體或較黏牛頓流體進行混合，其最佳化幾何設計參數可採用文獻上提出的設計公式，Np=2/3Nx-1 和 Nθ=90，其中Nx為跨越流道寬度的橫桿數目，Np為沿著流道的平行橫桿數目，Nθ為相鄰兩橫桿之間的角度。唯由該公式可得多於一組的設計參數，宜選擇較少桿件那組以降低混合器壓降，最終得出 Nx=6、Np=3、Nθ=90；對於黏度較低(如水)之流體，使用商業標準之SMX混合器，即可達到最有效的混合。(3)相較於SMX靜態混合器，SMX+SCT混合器在能量耗損方面明顯增加，需根據具體應用來選擇合適的混合器。(4)隨著魏森貝格數(Weissenberg Number)的增加，流體的彈性效應增強，能量耗損也隨之減少，流體的混合效果獲得改善。 本研究為設計高效能的靜態混合器提供理論基礎，對提升工業製程中的混合效率具有重要意義，不僅可應用於化工、製藥、食品加工等傳統工業，還有助推動新興領域如生物工程和材料科學中的應用。

Numerical simulations were performed for studying the flow field and concentration field of viscoelastic fluids in static mixers, and thus the mixing performance and pressure drop were analyzed, using Transport of Diluted Species Method, with the aid of COMSOL Multiphysics, under laminar conditions. Two mixing elements were employed, the SMX element and the Sudden Contraction Tube (SCT) element. The mixing performance was analyzed for varied mixers with different combinations of mixing elements (different types and arrangements), using different fluids with different viscosities, and different constitutive models accounting for various elastic effects. Several findings are as follows. (1) The calculations using the viscoelastic model (such as the Giesekus Model, which accounts more appropriate the elastic effect) are more consistent with the experimental results than those using the shear thinning model (such as the Carreau Model), and the latter underestimates the mixing effect by about 18%. However, the calculation time using the Giesekus Model is about 5 times longer than that using the Carreau Model, and both calculations are qualitatively similar. Therefore, it is recommended to use the shear thinning model for optimization research on static mixer parameters. (2) For the widely-used SMX static mixer in industry, the universal design rule, Np=2/3Nx-1 and Nθ=90, proposed in the literature, can be applied for the mixing of viscoelastic fluids and viscous Newtonian fluids, according to the present calculation. Here Nx represents the number of cross-bars over the width of mixer, Np represents the number of parallel cross-bars per element, and Nθ represents the angle between opposite cross-bars. However, the design rule can yield multiple sets of design parameters, and the set with fewer bars should be chosen for smaller pressure drop across the mixer. The final parameters for mixing optimization is Nx=6、Np=3、Nθ=90. For fluids with lower viscosity (such as water), using the commercial standard SMX mixer can achieve the most efficient mixing. (3) Compared to the SMX static mixer, the SMX+SCT mixer has significantly higher energy consumption, so the appropriate mixer should be selected based on the specific application. (4) As the Weissenberg number increases, the elastic effects of the fluid are enhanced, resulting in reduced energy consumption and improved mixing performance. This study provides a theoretical basis for designing high-efficiency static mixers, which is of great significance for improving the mixing efficiency in industrial processes. It can be applied not only in traditional industries such as chemical engineering, pharmaceuticals, and food processing, but also in emerging fields such as bioengineering and materials science.