臺灣博碩士論文加值系統

本論文使用Wilmanski梯度流理論，將內變數模組化，藉由梯度理論觀點考慮乾顆粒流內部的孔隙變化，探討這些顆粒內部的變化與限制。經熱力學分析，使用Müller-Liu熵增原理，完成本構變數在平衡態的表示式；使用準線性處理非平衡態部份，引用次塑性理論來表達內部摩擦效應與塑性影響。此論文模型是針對等容乾顆粒流，從一移動斜板上流下，得到解析解，最後與實驗結果對比 和 。對顆粒內部微結構的孔隙率作進一步討論。

In the present study the effect of the variation in porosity in dry granular matters is modeled by using the Wilmanski’s model. To obtain the complete constitutive equations, A thermodynamic analysis,based on the Müller-Liu entropy production principle, is performed to derive the equilibrium expressions of the constitutive variables. Non-equilibrium responses are proposed by means of a quasi-linear theory. The model is subsequently employed to study an isothermal dry granular slow flow down an inclined moving plane, of which the results are compared with the experimental results. It is seen that far dry granular flows with slow to moderate velocities, the Wilmanski’s model is sufficient to describe the effects induced by the variation in porosity, whilst for very rapid flows like avalanche the wilmanski’s model deliver inaccurate predictions of velocity and volume fraction profiles.

中文摘要.......... .......I
Abstract ................II
誌謝.....................III
目錄.....................IV
表目錄...................VI
符號說明.................VII
第一章 簡介..............1
1.1研究動機..............1
1.2顆粒物質..............1
1.3顆粒物質的特性........2
1.4應用..................8
1.5論文架構..............9
第二章 顆粒物質研究方法..11
2.1簡介..................11
2.2理論回顧..............11
2.3小結..................18
第三章 理論推導..........19
3.1理論簡介..............19
3.2平衡方程與本構變數........20
3.3熱力分析( thermodynamic analysis )........22
3.4額外熵通量( extra entropy flux )..........26
3.5熱力平衡( thermodynamic equilibrium ).....30
3.6非平衡反應( non-equilibrium responses )...33
3.7自由能( Helmholtz free energy )，黏性( viscosity )與次塑性( hypoplasticity )........34
第四章 數值計算方法與結果........37
4.1定義問題........37
4.2數值結果........49
第五章 結果與討論........56
參考文獻........59
附錄........62
簡歷........65

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