具顆粒負載之兩相紊流為工業應用或者自然現象上常見的物理機制，由於同時具有可視為連續體之負載流場與分散之固態顆粒紊流擾動本性，因此使得其物理問題更為複雜，這也使得實際在模擬計算上有其困難存在，尤其是在於顆粒交互作用不可忽略的狀態之下。在於本研究中採用Eulerian-Lagrangian架構，且在於顆粒模擬方面，使用Lagrangian顆粒追蹤法搭配決定論法之雙體碰撞硬球模式（binary collision hard-sphere models）來進行具考量顆粒碰撞行為之顆粒運動追蹤，而於流體方面流場之紊流效應使用雷諾平均納威爾－史托克（Reynolds-Averaged Navier-Stokes, RANS）法之紊流模式加以考量，並且以顆粒源項法（particles source in cell, PSI-cell）考量負載顆粒對於流場所造成之影響。
由於要考量顆粒之交互影響效應，因此在於演算法沒有特別處理的狀況之下其計算量將會隨著顆粒數量呈現平方成長，也因如此使得要考量顆粒之交互影響效應之顆粒負載流場，往往使數值模擬的實作僅能侷限於少量之顆粒數量以內。本研究針對顆粒搜索之問題提出一種高效率具有區域搜索特性之顆粒碰撞搜索演算法，並且深入探討在於不同的輔助搜索格點 的輔助參照之下對於顆粒模擬之計算效率之影響。而結果也呈於 座落於 到 之間有著最佳的計算效率。在於此方法之下也使得決定論法用於大量顆粒且使用硬球模式考量顆粒相互碰撞效應的兩相流模擬更可得以實作。本研究中的第二部分為使用決定論法直接追蹤模擬所有顆粒來進行兩種類不同流場型態的顆粒負載流場，分別為完全發展之垂直渠道流場與背向階梯流。除了驗證PSI-cell方法在於顆粒造成之紊流調劑效應外，本研究中也針對紊流擴散效應、粗糙壁面碰撞、顆粒相互碰撞效應以及入口初始條件對於顆粒運動行為分別進行探討。研究中也發顆粒碰撞效應與粗糙壁面的碰撞對於垂直渠道流場中對於顆粒分散現象之影響十分顯著，尤其在於相對大尺寸之顆粒。研究結果指出在於顆粒反應時間與顆粒平均碰撞時間的比值 的條件下，顆粒碰撞效應就會成不可忽略的主導效應之一。而於模擬結果中也指出壁面粗糙度條件確實對於顆粒運動行為有著明顯的影響，因此壁面粗糙度以及粗糙壁面碰撞效應也是顆粒負載流場模擬中需要考量的重點。在於背向階梯流場的模擬當中也發現顆粒的入口條件的考量也會對於 的模擬結果有著顯著的影響。而研究中也證實在於顆粒之 的條件之下，顆粒會受到入口的慣性之影響而難以捲入角落迴流區。

Particle-laden flows widely appear in many engineering practices and physical phenomena. Since both dispersed phase and carrier fluid have their own statistical natures of turbulence, numerical simulations of particle-laden flows are very difficult to reliably and accurately predict. An Eulerian-Lagrangian approach in which the carrier-fluid flow field is solved with a low-Reynolds-number turbulence model while the deterministic Lagrangian method together with binary-collision hard- sphere model is applied for the solution of particle motion. Effects of inter-particle collisions and particle-wall collisions under different extents of wall roughness on particle dispersion are addressed in this thesis.
In the first part of this study, a cost-effective searching collision pairs among particles algorithm which can be suitable for unstructured meshes system and easy to parallelize is developed. The results show that the values of in the calculations using the range from to can provide a higher computational efficiency in the Lagrangian particles tracking algorithm. A quantitative parametric study of the physical mechanisms and conditions which might affect the particles’ dispersion, including the turbulence dispersion, inter-particle collisions, rough-wall effects on the particle-wall collisions, and particles’ inlet conditions are also discussed. The results show that the inter-particle collisions can not be ignored under the conditions of . The influence of wall roughness on particle-wall collisions should also be able taken into account, particularly for large particles. The simulation results also found that only particles with Stokes numbers less than unity can be dispersed into the corner recirculation region in the backward-facing step flow.

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