本研究應用大尺度渦流法並配合Lagrangian型之顆粒運動方程式來探討紊流流場與固體顆粒之間的兩相交互作用。所測試的流場為一完全發展之垂直渠道流，其雷諾數基於半個渠道高度及摩擦速度 (friction velocity) 為180及640。流體中所載具之三種固體顆粒， Lycopodium，玻璃及銅，其密度均遠大於氣相流體密度但是其直徑卻小於Kolmogorov length scale。氣相流場以大尺度渦流法求解，所採用的次格點尺度模式為dynamic mixed model。每一個固體顆粒均以Lagrangian法追蹤以求得每一瞬間之顆粒位置與速度。雖然本文所探討的問題為顆粒稀薄之流場，但仍將顆粒與顆粒間的碰撞納入考量。碰撞對的搜尋採用deterministic方法而碰撞後的狀態則由硬球模式 (hard-sphere model) 來決定。本論文目地著重於探討 (1)紊流流場結構對顆粒分布之影響；(2)顆粒間的碰撞與壁面粗糙度對顆粒運動及紊流調制 (turbulence modulation) 之影響；(3)顆粒影響紊流調制之機制。
研究結果發現，在近牆區，具有較小Stokes數之顆粒容易受sweep事件的影響而朝壁面方向運動，然而大部分脫離壁面朝向渠道中心運動的此類顆粒卻又容易陷入ejection-like的環境中而無法離開。此一紊流對小Stokes數顆粒的作用使得大量的顆粒累積在近牆區中並產生preferential concentration的現象。此外，考慮顆粒與顆粒間的碰撞可增強顆粒在垂直壁面方向的混合效應，防止顆粒聚集成群並使得流向方向顆粒平均速度的分佈曲線較為平緩。顆粒與顆粒間的碰撞將會加大兩相間的速度差，由此進一步地增強紊流衰減的程度。紊流強度因顆粒的存在而減弱或可歸因於兩個原因，一則直接由顆粒阻力所造成，另一者則由透過改變紊流能量傳遞或產生的機制而造成。和實驗值相比，本研究之計算低估了顆粒與流體間的速度差，導致所計算的顆粒阻力偏低，因而所得之紊流衰減量較實驗值為低。此外，顆粒的存在會抑制雷諾剪應力的強度使得紊流動能的源項(production term)減弱。雖然顆粒的存在會增強小尺度紊流的強度，但藉由影響紊流的結構及增加Kolmogorov length scale卻會增加能量耗散的程度。因此，整體來說紊流強度會因顆粒的存在而被削弱。由於整體紊流強度隨顆粒負載比(mass loading ratio)的增加而降低，dynamic mixed model所計算之模式常數Cs也隨之降低以反應由大尺度傳遞到小尺度能量之減少。除此之外，本文也發現壁面粗糙程度的高低亦會影響紊流調制量，其影響紊流流場的機制則類似於考慮顆粒間的碰撞所造成的影響。考慮壁面粗糙度可增強近牆區之紊流強度並抑制渠道中心區域之紊流。增強或抑制紊流強度之轉換點則取決於壁面粗糙程度，壁面粗糙度越高則此一轉換點越接近壁面，換言之，紊流強度受到抑制的區域越廣。

The interactions between turbulence flow and particle motion are investigated using Large eddy simulation in a vertical, fully-developed channel flow at two Reynolds numbers 180 and 644 which are based on the half-channel width and friction velocity. The flows are loaded separately with three classes of spherical, heavy particles with diameters smaller than the Kolmogorov length scale. The gas-phase flow field is obtained by the large eddy simulation (LES) incorporated with the dynamic mixed model. Each individual particle is tracked by a Lagrangian method. Inter-particle collisions are taken into consideration by using a deterministic collision detection method and the hard sphere model. The objective of this work is to investigate the influences of turbulence structure on particle dispersion, the effect of inter-particle collisions on the gas phase, mechanisms responsible for turbulence modulation, and the effect of particle-wall interactions on both phases.
Particles with small Stokes numbers tend to transport toward the wall by the sweep events and be trapped in the ejection-like environments. This process accumulates particle along the low speed streaks in the near-wall region. The inter-particle collisions cannot be ignored even in particle-dilute cases. Indeed, consideration of the inter-particle collisions in the modeling can enhance the particle transverse mixing and increase the attenuation of fluid turbulence. Attenuation of turbulence kinetic energy is due to either the particle drag effect or the modification on the transport mechanism of turbulence kinetic energy. The suppression of Reynolds stresses with increasing mass loading ratio decreases the production rate of turbulent kinetic energy. As a result, the energy contented in the fluid decreases. However, the effect of particles on gas-phase turbulence is not uniform for all scales. Presence of particles suppresses turbulence at large scales, while it increases the energy contained at small scales. The turbulence spatial structure is modified by which the energy flux to dissipative scales is increased. The model constant predicted by the dynamic mixed model becomes smaller and the Kolmogorov length scale becomes larger with increasing mass loading ratios. In addition, in the case of lower wall roughness, the effect of wall roughness enhances turbulence in most regions of the channel except at the channel centre where turbulence intensity is attenuated. In contrast, for a channel with high wall roughness, strong turbulence attenuation across most of the channel is observed

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