柏拉圖多面體顆粒在振動床內的運動行為之研究

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姓名

徐旻毓(Min-Yu Hsu) 查詢紙本館藏

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機械工程學系

論文名稱

柏拉圖多面體顆粒在振動床內的運動行為之研究

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至系統瀏覽論文 (2028-2-1以後開放)

摘要(中)

在顆粒體的振動研究中，顆粒形狀、振動頻率f與無因次振動加速度Γ是影響動力學行為的關鍵因素。本研究透過振動床實驗，調整不同振動條件，系統性的探討柏拉圖多面體顆粒與球體顆粒在形狀差異下的運動。本研究選取五種柏拉圖多面體，包括四面體、立方體、八面體、十二面體與二十面體，其圓球度分別為 0.6276、0.8172、0.8573、0.923、0.9523，單面面積依次為 9.81、5.45、3.90、2.41、1.40 ?mm?^2。本文分析圓球度、振動頻率與無因次振動加速度Γ對迴流強度、顆粒溫度及顆粒混合性的影響，並進一步探討柏拉圖多面體顆粒單面面積對顆粒流動的影響。研究結果表明，隨著Γ的增加（即振動床輸入能量的提升），顆粒的迴流強度與粒子溫度顯著增強。然而，在相同加速度條件下，振動頻率的提高會導致振幅減小，輸入能量下降，從而使迴流強度與粒子溫度降低。當圓球度增加時（單面面積降低），顆粒間的摩擦力減小，能量耗散減少，因此迴流強度與粒子溫度進一步提升。在 f=40 Hz 的振動條件下，立方體顆粒的迴流強度與粒子溫度顯著低於其他形狀的顆粒，甚至低於圓球度更低的四面體顆粒。透過分析粒子溫度隨振動床高度的變化，可以觀察到這一現象表明，在高頻低振幅條件下，立方體顆粒更容易在振動床容器底部堆積，限制其流動性與運動行為。此外，透過柏拉圖多面體顆粒與圓球的二元混合實驗發現，在高Γ條件下，因其輸入的能量較高，各形狀顆粒的最終混合度相近；而在低Γ條件下，因其輸入能量較小，故圓球度的影響提升，高圓球度顆粒相較於低圓球度顆粒更有利於混合效果的提升。

摘要(英)

In the study of granular vibration, particle shape, vibration frequency f, and dimensionless vibration acceleration Γ are critical factors influencing dynamic behavior. This study systematically investigates the dynamic behavior of Platonic solid particles and spherical particles with varying shapes through vibration bed experiments under different vibration conditions. Five Platonic solids were selected for the study, including tetrahedron, cube, octahedron, dodecahedron, and icosahedron, with sphericities of 0.6276, 0.8172, 0.8573, 0.923, and 0.9523, respectively, and corresponding single-face areas of 9.81, 5.45, 3.90, 2.41, and 1.40 ?mm?^2. This paper focuses on analyzing the effects of sphericity, vibration frequency, and dimensionless vibration acceleration on recirculation intensity, granular temperature, and particle mixing, while further exploring the role of the single-face area of Platonic solid particles. The results show that with an increase in Γ (i.e., enhanced energy input to the vibration bed), the recirculation intensity and granular temperature of the particles significantly increase. However, under the same acceleration conditions, increasing the vibration frequency reduces the amplitude, decreases the energy input, and consequently leads to a reduction in recirculation intensity and granular temperature. As sphericity increases (corresponding to a decrease in single-face area), the friction between particles is reduced, resulting in lower energy dissipation and further increases in recirculation intensity and granular temperature. Under the vibration condition of f=40 Hz, the recirculation intensity and granular temperature of cubic particles are significantly lower than those of other shapes, even lower than those of tetrahedral particles with lower sphericity. This indicates that, under high-frequency and low-amplitude conditions, cubic particles are more prone to accumulate at the bottom of the vibration bed container, restricting their mobility and dynamic behavior.
Additionally, binary mixing experiments of Platonic solid particles and spherical particles revealed that at high Γ values, the final mixing degree of all particle shapes is similar. However, under low Γ conditions, particles with higher sphericity achieve better final mixing than those with lower sphericity. This indicates that the dynamic behavior of high-sphericity particles under low-amplitude conditions is more conducive to enhancing the mixing effect. This study provides a comprehensive understanding of the combined effects of particle shape and vibration parameters on the dynamic behavior of granular flow, offering valuable insights for optimizing particle separation and mixing performance in vibration bed systems.

關鍵字(中)

★ 振動床
★ 柏拉圖多面體顆粒
★ 雙迴流

關鍵字(英)

★ Vibrating bed
★ Platonic polyhedral particles
★ Dual recirculation

論文目次

小寫符號 VII
大寫符號 VIII
希臘符號 IX
摘要 X
Abstracrt XI
第一章緒論 1
1.1 研究背景 1
1.1.1 顆粒流 1
1.1.2 柏拉圖多面體 2
1.2 文獻回顧 3
1.2.1 垂直振動床內的迴流現象 3
1.2.2 非球型顆粒與柏拉圖多面體顆粒研究 4
1.2.3 質點影像測速技術 6
1.2.4 圓球度 7
1.2.5 迴流強度與粒子溫度 7
1.2.6 Lacey mixing index 混和指數 9
1.3 研究動機與目的 9
第二章實驗設備、研究方法與實驗步驟 12
2.1 實驗設備 12
2.2 研究方法 15
2.2.1 質點影像測速技術與影像分析流程 16
2.2.2 分析方法 16
2.3 定義柏拉圖顆粒圓球度、單面面積 18
2.4 迴流強度 19
2.5 粒子溫度 19
2.6 Lacey mixing index 20
2.7 實驗步驟 21
第三章結果與討論 31
3.1 柏拉圖多面體顆粒在振動床中之迴流運動 31
3.1.1 速度向量圖 31
3.1.2 u平均速度與v平均速度隨x軸的變化 31
3.1.3 迴流強度與振動加速度及圓球度的關係 33
3.2 粒子溫度 36
3.2.1 柏拉圖多面體顆粒在不同振動條件下的粒子溫度 36
3.2.2 粒子溫度隨振動床高度的變化 37
3.3 柏拉圖多面體顆粒與圓球顆粒的混合 38
第四章結論 60
參考文獻 62

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指導教授

蕭述三(Shu-San Hsiau)

審核日期

2025-1-20

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