楊德良Young, Der-Liang臺灣大學:土木工程學研究所魏子翔Wei, Tzu-HsiangTzu-HsiangWei2010-06-302018-07-092010-06-302018-07-092008U0001-3007200811290900http://ntur.lib.ntu.edu.tw//handle/246246/187583這一篇論文主旨是用混合理論來發展在傾斜平面上穩態的二維二相顆粒混合流之流動分層模型。在這一篇論文中所考慮的二相顆粒混合體包含了兩組不同型態的顆粒，一組是體積較大且重量較重的顆粒，而另一組是體積小且重量輕的顆粒。在應用混和理論推導分層模型的過程，顆粒間的交互作用力是關鍵的一環，所以我們考慮了廣義的流況，在交互作用力中加入了四種不同的分力：(1)是延伸自Gray和Thornton在2005年所發展的垂直尺寸分選機制；(2)是流線方向的尺寸分選機制；(3)是重力分選機制；(4)是不均勻動態壓力梯度所造成的影響。所考慮的動態壓力可以用勢流理論裡因為兩條流線的速度不同而造成的升力來解釋。了處理並分析這一個分層模型，本研究發展了一套數值模型來分析在不同流況下的各種顆粒混合流的分層狀況，並特別著重於了解新加入的分選機制如何影響原本主導分層行為的垂直尺寸分選機制。數值的結果顯示這些新加入的分選機制都阻礙了二相顆粒混合流垂直尺寸分選的過程，延長了原本分層模型達到完全分離的時間。其中，重力分選機制的影響最為明顯。研究發現分層作用會造成濃度分佈出現明顯的不連續，我們定義這種濃度的跳躍為「震波邊界」，而這些震波邊界的交點則定義為「三相點」。特別注意由於本研究的觀察區域隨著混合流的穩定流速前進，所以雖然三相點的絕對位置隨著混合流的移動而穩速前進，但其相對位置於觀察區域之中是固定的。此三相點的相對位置會決定最後的二相顆粒混合流的分層狀況，因此本研究亦追蹤不同流況下的三相點穩定位置。研究結果顯示流線方向的尺寸分選機制會使三相點向觀察區的下游方向移動，而不均勻動態壓力場的影響則會減緩震波邊界之不連續變化。This thesis applies the mixture theory to develop a two-dimensional segregation model for a steady binary granular flow down an inclined plane. The mixture considered here is composed a group of large and heavy granulates and another group of small and light granulates. The current model is an extension of the vertical size segregation model developed by Gray and Thornton (2005) by considering more general flow conditions. Streamwise size segregation and density segregation are included to the model by appropriate interaction force components. Further, a new force component is proposed in this thesis by considering the gradient of a hydrodynamic pressure field formed in the bulk and in the constituent phases when segregation occurs. This new force is inviscid in nature and can be interpreted as a lift force in the potential flow theory generated across two streamlines with different velocities. Such a dynamic pressure force contributes to the total interaction force between the constituents which is the key element in the mixture theory when applied to study the bulk segregation dynamics. numerical scheme has been developed to solve the generalized segregation model and employed to investigate the segregation dynamics under various flow conditions. Special efforts are made to examine how the newly introduced segregation mechanisms affect the dominating vertical size segregation, a feature that generally determines the bulk segregation behavior. In general, all these new mechanisms hinder the segregation process and thus prolong the settling time for a uniform mixture to transit to its fully-segregated state. Density segregation, however, has the most pronounced influence. The onset of segregation leads to jump in the flow concentration profile, which is described as a ‘shock boundary’ in this work. The intersection of these shock boundaries determines a ‘triple point’ in a reference frame that moves with the bulk. The position of this triple point thus characterizes the final segregation pattern. It is found that the streamwise segregation convects the triple point towards the downstream and the non-uniform hydrodynamic pressure field may blur the shock boundaries.Table of contains謝 I要 IIbstract IIIable of contains IVomenclature VIIigure list IXable list XIIhapter 1 Introduction 1.1 Motivation 1.2 Literature review 2.2.1 The mixture theory 2.2.2 Application of the mixture theory: the particle size segregation model by Gray and Thornton (2005) 3.3 Thesis Outline 9hapter 2 Governing equations 10.1 Introduction 10.2 Extension to include streamwise size segregation 11.3 Hydrodynamic pressure and the resulting interaction force 12.3.1 Bernoulli equation 12.3.2 The proportion function for the constituent hydrodynamic pressure 13.3.3 Interaction force induced by a non-uniform dynamic pressure field 14.3.4 A dynamic component of the interaction force 16.4 The Segregation Model 16.4.1 The Interaction force 16.4.2 The segregation model 17hapter 3 Numerical method 25.1 Numerical scheme 25.1.1 Simulation procedure 25.1.2 The initial conditions 27.1.3 The boundary conditions 27.2 Finite difference method 28.2.1 Introduction of finite difference method 28.2.2 Method of coupled matrix 29.2.4 Computation mesh 33.3 Shock capturing method 33.4 Determination of the steady state 34.4.1 The triple-point 34.4.2 Determination of the triple point 36.4.3 Determination of complete segregation 37.5 Mesh independence 37hapter 4 Simulation results and discussions 43.1 Vertical size segregation 43.1.1 Vertical size segregation 43.1.2 Flow geometry vs. vertical size segregation 46.2 Streamwise size segregation 51.2.1 Streamwise size segregation 51.2.2 Flow geometry vs. streamwise and vertical size segregation 53.3 Density segregation 58.3.1 Density segregation 58.3.2 Flow geometry vs. vertical size and density segregation 62.4 Hydrodynamic pressure 69.4.1 Hydrodynamic pressure effect 69.4.2 Flow geometry vs. hydrodynamic pressure effect and vertical size segregation 71.4.3 Hydrodynamic pressure effect vs. density and vertical size segregation 76.4.4 Hydrodynamic pressure effect vs. density, streamwise, and vertical size segregation 79.5 Conclusion and Remarks 81hapter 5 Conclusions 83eferences 85ppendix 86. Verification of the newly proposed interaction force due to non-uniform hydrodynamic pressure field in (2.13) 86. Non-dimensionalization procedure 87. Biconjugate Gradient Stabilized Method 903901596 bytesapplication/pdfen-US二相顆粒流混合理論重力分選機制尺寸分選機制動態篩選模型binary granular flowdensity segregationsize segregationkinetic sievingmixture theorythesishttp://ntur.lib.ntu.edu.tw/bitstream/246246/187583/1/ntu-97-R94521331-1.pdf