5.1 結論
本研究針對以往固液二相流的假設稍作修改，承襲 Chou et al.(2014)的理論架 構，並採用 Lagrangian 描述法來開發一套固液系統模式，其特點如下所列
粒初始濃度對於結果有顯著的差異。在濃度為 0.0128 的模擬結果中，各模式 的顆粒沉降速度大致相同，連流場也幾乎沒有差異。然而當濃度提高至 0.0512 後，雖沉降初期仍無顯著之差異，但經歷較長的沉降時間後，壓力耦合模式 的顆粒沉降速度明顯較其它兩者來得慢，尤其與附加質量耦合模式的差異最 為明顯，而兩者在理論架構上是差異最小的，因為壓力耦合模式已包含了附 加質量效應，即是說當顆粒濃度提高時，壓力耦合的影響會相當顯著，此結 果與 Chou et al.(2014)的結論相符合。
3. 為了測試本模式是否可模擬出其它流體力學的基礎物理現象，我們以異重流為 範例，嘗試模擬 Lock-exchange flow 此一典型異重流問題。過去的研究多是使 用 E-E 架構的數值模式來進行模擬，而本研究所開發的 E-L 架構模式亦成功 模擬出此現象，且能捕捉到其流動特性，如流體交界面處的渦漩，讓本模式 更加具有可靠性。
5.2 未來工作
有兩種顆粒碰撞模型較適合我們的模式，其一為 Apte et al.(2008)所使用的碰 撞模型，他們為顆粒定義一個碰撞範圍，對任意顆粒而言，在其碰撞範圍的 計算太耗時而暫不採用。其二為 Snider et al.(2001)採用的顆粒正向應力模型，
他們將顆粒間的作用力以顆粒體積分率的函數表示之，即是將顆粒整體視為 連體來解析此物理量，採用質點網格法的精神，先在尤拉網格上計算出顆粒 正向應力，再透過內插求得每個顆粒位置上的值。此法計算相對省時，且由 該文獻提供的模擬結果來看，此模型十分健全，能成功模擬出顆粒在底層堆 積的現象，因此我們打算朝這方向來建立本模式的顆粒碰撞模型。
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