應用在高黏性牛頓及非牛頓流體混合之層流攪拌器性能參數分析與流場計算

Abstract

本文旨在應用計算流體力學(CFD)研究螺桿攪拌器與螺帶攪拌器內流體速度場與濃度場，以及攪拌器幾何尺寸(槽直徑、葉片螺距、葉片間隙、葉片寬度)對攪拌器性能參數(功率消耗、循環流量、混合效率、混合時間)的影響，同時也研究流體性質(牛頓流體與非牛頓流體)對攪拌器性能的影響，最後根據上述的結果得出最佳攪拌器幾何尺寸，以及攪拌器性能與尺寸關係式。 由於攪拌器攪拌的流體具有高黏性，本研究使用三維不可壓縮層流來模擬攪拌器內流場，計算網格為三維非結構性網格，計算方法為有限體積法。由於攪拌器葉片等轉速轉動使流場具有週期性的變動，因此假設流場為擬似穩態，為葉片旋轉至某一位置的瞬時狀態，並採用多重參考座標系，將葉片旋轉掃過的區域定為旋轉座標系，此區以外的區域定為靜止座標系，解完擬似穩態速度場再解非穩態濃度場以求得混合時間。牛頓流體選用的是葡萄糖漿，非牛頓流體則是使用”修正Herschel-Bulkley”模式來模擬三仙膠(具降伏應力的偽塑性流體)的流變學性質。 經研究後得知，當螺桿攪拌器攪拌牛頓流體葡萄糖漿時，尺寸在D/d=2.0, S/d=1.5, C/d=0.1時有最佳攪拌效率；攪拌降伏偽塑性流體三仙膠時，螺距在S/d=1.0時有最佳攪拌效率，但效率較攪拌牛頓流體時差。而螺帶攪拌器攪拌牛頓流體葡萄糖漿時，尺寸在W/d=0.25, S/d=0.7, C/d=0.06時有最佳攪拌效率；攪拌降伏偽塑性流體三仙膠時，螺距在S/d=1.0時有最佳攪拌效率，而且效率較攪拌牛頓流體時佳。最後我們並得到一個適用在較大範圍的功率數( )與幾何參數(W/d, S/d, C/d)的關係式。

The purpose of this paper was to study the 3D flow field in the mixing of Newtonian or non-Newtonian fluids with high viscosity in laminar flow region for screw impellers and helical ribbon impellers, which is analyzed using a computational fluid dynamics method. The velocity field is assumed to be in a quasi-steady state. The multiple reference frames were employed to model the rotation of impellers. The momentum and continuity equations were solved using finite volume method with unstructured grids. The glucose syrup was used as Newtonian fluid. The rheology of xanthan gum solution, a pseudoplastic fluid with yield stress, was approximated using the Herschel-Bulkley model. After the flow field was calculated, the unsteady-state concentration equation was solved to determined mixing time. The effects of impeller geometry (tank diameter, impeller pitch, impeller clearance, and impeller blade width) and fluid rheology on power consumption, circulation flow rate, mixing efficiency, and mixing time were also investigated. The optimum values of D/d (tank diameter to impeller diameter), S/d (impeller pitch to impeller diameter), C/d (impeller clearance to impeller diameter), W/d (impeller width to impeller diameter) ratios were determined on the minimum mixing time and power consumption can be expressed as functions of these ratios.

For the mixing of Newtonian fluids by screw impeller with draght tube, the optimum sizes are D/d=2.0, S/d=1.5, and C/d=0.1. While xanthan gum solution, a pseudoplastic fluid with yield stress, was mixed, the optimum screw impeller pitch is S/d=1.0. Helical ribbon impeller has optimum sizes W/d=0.25, S/d=0.7, and C/d=0.06 when mixing Newtonian fluids, and S/d=1.0 when mixing xanthan gum.