以離散元素法模擬斜坡顆粒流 撞擊障礙物 的震波現象

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蘇浚弘(Jun-Hong Su) 查詢紙本館藏

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機械工程學系

論文名稱

以離散元素法模擬斜坡顆粒流撞擊障礙物的震波現象

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至系統瀏覽論文 (2029-10-31以後開放)

摘要(中)

本研究採用離散元素法(Discrete Element Method, DEM)模擬顆粒體在滑道中撞擊兩種障礙物的流動與力學行為，分別為楔型障礙物與圓柱障礙物，分析障礙物對滑道中顆粒流傳輸性質與內部性質的影響。分析顆粒流的流動深度，流動速度，粒子溫度等物理量，及正向應力、剪應力與應力比的分佈，研究結果顯示：(1) 在楔型障礙物中，福祿數越大，模擬結果與理論解析解越接近，換言之滑道坡度越大，兩者更為接近。在圓柱障礙物中，福祿數越小，模擬結果與理論解析解越接近，表示滑道坡度越小兩者越接近；(2) 顆粒流撞擊障礙物產生不同的衝擊波，衝擊波型受到滑道傾角與半頂角的影響，有接觸波與非接觸波的產生，在圓柱障礙物中，衝擊波型與滑道傾角及直徑無關，皆產生非接觸波；(3) 因障礙物的影響，在兩種障礙物模擬中皆有顆粒滯留的現象產生，造成障礙物前方的流動深度上升，流動速度下降、粒子溫度升高及呈現較大的應力值，隨著障礙物尺寸越大，滯留現象也越早發生；(4) 在楔型障礙物中，上游處σxx/σzz震盪平均值皆為1，半頂角25°時在障礙物前方可觀察到最大應力比值接近6.5。在滑道底部τ /σzz中，上游處震盪平均值約為0.36，半頂角25°時在障礙物前方可觀察到最大應力比值接近0.75。在圓柱障礙物中，與楔型障礙物結論相同，σxx/σzz在上游處震盪平均值皆為1，滑道傾角20°時在障礙物前方可觀察到最大應力比值接近4.4。在滑道底部τ /σzz中，上游處震盪平均值約為0.36，滑道傾角35°時在障礙前方可觀察到最大應力比值接近0.76。

摘要(英)

This study employs the Discrete Element Method (DEM) to simulate the flow and mechanical behavior of granular materials impacting two types of obstacles in a chute: wedge-shaped obstacles and cylindrical obstacles. The study explores the effects of these obstacles on the transport properties and internal characteristics of the granular flow in the chute. The analysis includes the flow depth, flow velocity, granular temperature, as well as the distribution of normal stresses, shear stresses, and stress ratios. Major research findings are summarized below: (1) In the case of wedge-shaped obstacles, the larger the Froude number, the closer the DEM simulation results are to the theoretical analytical solutions; in other words, the greater the chute slope, the closer the results are. In the case of cylindrical obstacles, the smaller the Froude number, the closer the DEM simulation results are to the theoretical analytical solutions, indicating that the smaller the chute slope, the closer the results are; (2) Granular flow impacting the obstacles generates two types of shock waves (Contact and non-contact waves), with the shock wave type being influenced by the chute angle and the half-apex angle of the wedge-shaped obstacle. In the case of cylindrical obstacles, the shock wave type is independent of the chute angle and obstacle diameter, with non-contact waves always being created; (3) Due to the influence of the obstacles, both types of DEM simulations exhibit particle retention phenomena, leading to an increase in flow depth, a decrease in flow velocity, an increase in granular temperature, and higher stress values in front of the obstacles. As the obstacle size increases, the retention phenomena occur earlier; (4) In the case of wedge-shaped obstacles, the upstream average value of σxx/σzz is 1.0, and a maximum stress ratio close to 6.5 is observed in front of the obstacle at a half-apex angle of 25°. In the bottom of the chute, the upstream average value of τ /σzz is approximately 0.36, and a maximum stress ratio close to 0.75 is observed in front of the obstacle at a half-apex angle of 25°. For cylindrical obstacles, similar conclusions apply: the upstream average value of σxx/σzz is 1.0, and a maximum stress ratio close to 4.4 is observed in front of the obstacle at a chute angle of 20°. In the bottom of the chute, the upstream average value of τ /σzz is approximately 0.36, and a maximum stress ratio close to 0.76 is observed in front of the obstacle at a chute angle of 35°.

關鍵字(中)

★ 斜坡顆粒流
★ 楔型與圓柱障礙物
★ 離散元素模擬
★ 連體斜震波理論
★ 傳輸性質
★ 應力分佈

關鍵字(英)

★ granular chute flow
★ wedge-shaped and cylindrical obstacles
★ discrete element method
★ continuum theory of oblique shock wave
★ transport properties
★ stress distribution

論文目次

摘要 i
Abstract ii
目錄 iii
附表目錄 vi
附圖目錄 vii
附錄目錄 xiii
第一章緒論 1
1-1 研究背景 1
1-2 文獻回顧 1
1-3 研究動機 5
第二章研究方法 6
2-1 離散元素法 6
2-1-1 運動方程式 6
2-1-2 接觸力模型 8
2-1-3 臨界時間步 10
2-2 模型建立與模擬架構 11
2-2-1 離散元素模型 11
2-2-2 降低模數法 12
2-3 顆粒流傳輸性質 13
2-3-1 平均速度 13
2-3-2 擾動速度 13
2-3-3 粒子溫度 14
2-4 顆粒流內部性質 15
2-4-1 粒子體積佔有率 15
2-4-2 平均配位數 15
2-4-3 摩擦啟動因子 16
2-4-4 應力計算 16
2-5 斜震波理論 18
2-6 正震波理論 19
第三章結果與討論 26
3-1 障礙物尺寸與邊壁影響 26
3-1-1 楔型障礙物 26
3-1-2 圓柱障礙物 28
3-2 楔型障礙物對顆粒體在滑道中流動行為的影響 29
3-2-1 流動行為的分析 29
3-2-2 流動速度分佈與粒子溫度分佈 31
3-2-3 衝擊波型分析 32
3-2-4 顆粒滯留探討 33
3-3 圓柱障礙物對顆粒體在滑道中流動行為的影響 33
3-3-1 流動行為的分析 34
3-3-2 流動速度分佈與粒子溫度分佈 34
3-3-3 顆粒滯留探討 36
3-4 楔型障礙物對顆粒流的應力分析 36
3-4-1 流動方向正向應力 37
3-4-2 應力比 38
3-5 圓柱障礙物對顆粒流的應力分析 39
3-5-1 流動方向正向應力 39
3-5-2 應力比 40
第四章結論 81
參考文獻 83
附錄 86

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指導教授

鍾雲吉(Yun-Chi Chung)

審核日期

2024-10-4

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