非均勻結構膠羽群在流場中的拖曳係數

本文以數值模擬方式探討膠羽結構及其濃度效應對其在流場中所受的拖曳力之影響。由於膠羽實際的組成結構相當複雜，為簡化問題，我們假設整個膠羽粒子為一具有不同穿透係數的雙層多孔性物質。實際的情形下，膠羽粒子在流體中運動時雷諾數往往高達數十以上，Stokes law將不再適用。本文使用的主控方程式包括描述流體在多孔體外運動的Navier-Stokes方程式及描述多孔體內運動的Darcy-Brinkman model，並以數值方法求解該組高度非線性的主控方程式。在探討膠羽濃度的方面，採用廣為接受的free surface cell model來模擬群體效應。吾人探討下列參數對膠羽拖曳力的影響，包括：膠羽群孔隙度ε、流體雷諾數Re及膠羽外內層之穿透度比k1/k2。藉由改變膠羽內、外層結構的穿透度，我們發現膠羽群在自由沉降時，在相同的雷諾數及平均穿透度下，結構愈不均勻的膠羽所受的拖曳力愈大，且在雷諾數較高時，由其拖曳係數對雷諾數之作圖觀察，偏離Stokes-law-like correlation的偏差值也愈大。藉由改變群體間的孔隙度，我們發現當膠羽彼此分佈愈鬆散(濃度低)，系統所造成的拖曳力愈小，由流線圖扭曲的程度觀察，對流現象愈趨明顯，偏離Stokes-law-like correlation的偏差值也愈大。

關鍵字

非均勻結構；膠羽濃度分布；細胞模型；兩層模型；拖曳係數

並列摘要

The influences of the structure of floc and its concentration on the hydrodynamic drag acting on it are investigated theoretically. Due to the fact that floc formation involves various nonlinear, random processes, its structure is of complicated nature. Here, a two-layer model is adopted to simulate the behavior of a floc where various possible floc structures are simulated by varying the permeability of each layer, and a cell model is used to model the behavior of a concentrated floc dispersion. Experimental evidence reveals that the Reynolds number associated with the sedimentation of floc can be on the order of ten, that is, the Stokes law is inapplicable. In this study, a Navier-Stokes equation governing the flow field outside a floc and a Darcy-Brinkman model describing the motion of fluid inside it are solved numerically based on a finite scheme. The influence of the key parameters of the problem under consideration, including the swarm voidage ε, the Reynolds number Re, and the permeability ratio k1/k2, k1 and k2 being respectively the permeability of the outer layer and the inner layer of a floc, on the drag acting on a floc are discussed. The results of numerical simulation reveal that the more heterogeneous the structure of floc, the greater the drag is. Also, the more heterogeneous the structure of a floc the more serious the deviation of the variation of drag against Re curve from a Stokes-law-like relation. The drag on a floc decreases with the decrease in its concentration, and, due to the convective flow of fluid, the distortion of streamlines between flocs becomes more serious, and the deviation of the variation of drag against Re curve from a Stokes-law like relation is more significant.

並列關鍵字

two-layer model ； drag coefficient ； cell model ； Concentrated floc dispersion ； nonuniform structure

參考文獻

[1] Hunter, R. J. (1989). Foundations of colloid science. Vol.1, Oxford Univ. Press, London

[2] Wu, R. M.; Lee, D. J. (1998). Hydrodynamic drag force exerted on a moving floc and its implication to free-settling tests. Water Res., 32, 760-768.

[5] Lee, D. J.; Chen, G. W.; Liao, Y. C.; Hsieh, C. C. (1996). On the free-settling test for estimating activated sludge floc density. Water Res., 30, 541-550.

[6] Beavers, S. G.; Joseph, D. D. (1967). Boundary condition at a naturally

permeable wall. J. Fluid Mech., 30, 197-207.

國際替代計量

非均勻結構膠羽群在流場中的拖曳係數

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