在CO2地質封存過程中，超臨界CO2與地下鹵水在地層深處的復雜流動過程屬於多孔介質內流動。為了研究CO2在地質封存中與鹵水相互作用的復雜擴散和流動過程，對多孔介質中自由界面上的溶解驅動對流進行了數值模擬。采用Darcy-Cahn-Hilliard模型，結合特殊的密度和亥姆霍茲自由能分布，實現了兩種流體形成清晰界面的部分互溶特徵。采用高精度緊致有限差分格式，結合偽譜方法，模擬了二維多孔介質中的對流流動。通過與Hele–Shaw Cell的實驗結果進行對比，驗證了該數值方法的準確性。通過與完全互溶模擬結果的對比，證明了該方法可以獲得穩定的自由界面。數值模擬采用瑞利數(Rayleighnumber)在4.3×103 ~1.6 × 104範圍內進行。在此基礎上，分析了流型演變過程中羽流(plume)形成、羽流生長、羽流合並，羽流穩定和羽流衰減五個階段。測量了溶解速率的發展過程，可分為擴散、流量增長、合並、穩定流量和羽流衰減5個階段，分別對應於界面上羽流的演化和濃度分布。最後，將溶解速率分為自由對流、約束對流和羽流衰減三個階段。在自由對流階段內，溶解速率隨瑞利數的增加而減小，可以用指數公式Fs+=0.0198 + 2.59Ra−0.667表示，其中常數項為對流效應貢獻，指數項為擴散效應貢獻。而在約束對流和羽流衰減階段，溶解速率與瑞利數無關。在約束對流階段溶解速率隨時間變化大約保持在一個固定值0.0234。而在羽流衰減階段，溶解速率隨時間呈下降趨勢。羽流衰減階段溶解速率的模化過程，結合雙側Rayleigh-B´enard單元穩定對流的無因次流量的相關公式，得到無因溶解速率公式為Fs+=(he/cm)A(2A(t−6.6)+ 0.0394−2)−3/2。在系數A中加入修正因子a來表示底邊界的阻隔效應，模型公式可以準確地預測CO2在鹽水中的溶解速率和溶解量。

Modeling the Sediment-related hazardous flows is often a challenging task, because of the complex composition in the flow body and of the non-trivial flow paths the rugged topographies in the mountain area. In the approach by continuum mechanics, the models can be divided into three groups:
(a) Single-phase models
(b) Two-phase (quasi-two-phase or two-phase) models
(c) Multi-phase models
Among them, the single-phase models are the most popular and widely employed in engineering applications for hazard assessment. However, for the complexity of composition, its rheological behavior is highly non-linear and significantly different to the conventional Newtonian one. In the two-phase approach, the flow body is supposed to be composed of fluid and solid constituent. In the quasi-two-phase models, the relative velocity between the two constituents is assumed to be very small and the impacts of relative velocity between the phases are assumed to be negligible, so that only the coupled mixture momentum equation is present in the resultant model equations. As a matter of course, this kind of models is not able to describe the phenomenon of phase separation. By contrast, conservation of momentum for each phase is considered in the two-phase models. But there are apparently more equations to be evaluated. Taking into account the various concentration of the fine clay in the interstitial fluid in the fluid phase, the multi-phase models is proposed, where the individual velocity of the fine particles can be considered or assumed to be suspended in the fluid.
Most of the research concerning sediment-related hazardous flows focus on the rheological behaviors, i.e. the constitutive relations. In addition to the depth-averaged process for a high computational efficiency in hazard assessments, the model equations are mainly given in the Cartesian coordinates, where the down-slope direction is either horizontal or inclined with an angle to the horizon. However, the surface in mountain area is rugged and non-trivial, yielding the challenge of finding the appropriate coordinate system on the irregularly curved surface. The first trial is the introduction of a simple reference surface coinciding with the coordinate axes, above which shallow topography is added (Savage & Hutter, 1991; Koch et al., 1994; Gray et al., 1999). This concept has been improved by a curved and twisted coordinate system (Pudasaini & Hutter, 2003), where the valley is mimicked by a curved and twisted reference surface with the talweg lying on the projection of the master curve on the reference surface. The first complex curvilinear coordinates (terrain-fitted coordinate system) for arbitrary topography is proposed by Bouchut & Westdickenberg (2004). Integrating the unified coordinate method (Hui, 2004; Hui et al., 2010) with the BW coordinates, Tai et al. (2012, 2019), Tai & Kuo (2012) and Luca et al. (2016) suggested a nonconventional approach is proposed, where erosion/deposition can be easily integrated into the model equations without complicated transformation for the orientation of the velocity to the model axes. Although the terrain-fitted coordinate system is superior in describing the flow behaviors in the depth-averaged approach, the application of a terrain-fitted coordinate system is limited by the constrain of shallow curvature, i.e. the curvature radius should be sufficient large. This hurdle can be overcome by the concept of sub-topography over the smoothed topographic surface.
In the present study, we shall first brief the reason of employing the terrain-fitted coordinate system in comparison with the conventional Cartesian coordinates. After the introduction of the concept of the sub-topography for modeling the sediment-related hazardous flow over the rugged topographies, a general approach, which unifies the terrain-fitted coordinate system and Cartesian coordinate one, is suggested. Numerical examples are illustrated for highlighting the differences between the Cartesian approach and the one with sub-topography in terrain-fitted coordinate system. And a back-calculation of historical event (2009 Hsaiolin landslide event) will be shown for illustrating the high potential of engineering application.

臺灣各地山區經常因為地形坡度、土石量的大小及多寡、豪雨等引發坡地災害。在土石顆粒沿著陡峭的斜坡向下游流動的過程中，將會造成崩落之土石侵蝕土壤的現象，接著通過夾帶一些在土壤的土石來引發更大的災害，此過程會從最初的小流量發展為危險的大流量，因此侵蝕現象會在災害當中造成加劇的影響。本研究將實驗設置為一傾斜流槽，用實驗方式來模擬於山地斜坡上發生的坡地災害的現象。實驗設備將使用一開放式二維傾斜流槽裝置，以手動快速拉起擋板使崩塌床顆粒釋放至可侵蝕床中，同時以電子天平稱量流出流槽之顆粒。在本研究中，我們將利用改變不同顆粒床顆粒尺寸的實驗配置，並以不同的初始崩塌床寬高比來探討崩塌顆粒流至可侵蝕床後的侵蝕現象，實驗後分別藉由分析崩塌顆粒流的流場及可侵蝕床顆粒的流場來觀察不同顆粒尺寸與不同初始寬高比對於侵蝕的影響。
針對流場的整體流動行為從流出質量與質量流率來看，初始崩塌床寬高比的增加與顆粒床顆粒尺寸的增加都會造成較大的流出質量。然而流出質量的大小在某些情況下並沒有辦法正相關於流場中的侵蝕夾帶現象，這是因為被侵蝕挖掘出來的可侵蝕床顆粒，並不一定能夠有足夠的能量來流動足夠長的流動距離。接著我們將從影像上來觀察在流場中的整體流動過程中的顆粒運動行為。在流場中的崩塌床崩塌流動行為中，隨著初始崩塌床寬高比的增加，將會獲得比較短的流動時間、比較少的上游崩塌床殘留面積與比較深的流體深度。而這個現象同樣會發生在可侵蝕床顆粒尺寸較大的時候。在隨著時間發展的過程中，各個量化指標的變化率則會呈現先變大在變小的情況。從可侵蝕床的流動行為與崩塌床的流動行為中，我們則可以看到，隨著崩塌流動時間的發展，可以分成兩個階段，分別是劇烈變化階段與平緩發展階段。在可侵蝕床的崩塌流動行為中，受到崩塌床流動造成的影響，最終侵蝕面積會隨著初始崩塌床寬高比的增加與崩塌床顆粒尺寸的增加而變大。此外我們還發現到，崩塌床的位能能量損失率對於不同可侵蝕床顆粒尺寸的侵蝕面積會有不一樣的影響。此時，當可侵蝕床粒徑小的情況下，最終侵蝕面積與位能損失率呈現指數正相關；而當可侵蝕床粒徑較大時，則發現兩者呈現較小曲率的二次曲線關係。

本研究目的在於探討類二維旋轉鼓內不同轉速與不同非球形顆粒比例對於三元顆粒系統的顆粒分離機制與動態特性之影響。本實驗使用高速攝影機與數位攝影機進行拍攝與紀錄，經由粒子追蹤方法與影像處理技術來量測粒子的平均速度，平均粒子溫度，動態安息角與最終分離強度。實驗結果顯示當紅豆顆粒比例增加時，由於非球形顆粒形狀複雜的關係，會導致顆粒間互鎖效應增強，影響到顆粒的流動性，因此有提升紅豆顆粒的比例，顆粒的平均速度，平均粒子溫度，最終穩態分離強度下降，動態安息角上升的現象發生。本研究結果證實改變非球形顆粒比例對於因尺寸效應所導致的分離機制有重要的影響。

Granular material exhibits hysteric stick-slip behavior at the onset or extinction of a continuous motion. This phenomenon is closely tied with how static or moving grains experience different interactions with their neighbors to render distinctive internal friction properties. Researchers often characterizes this biphasic features in a uniform surface flow by measuring the flow height (Hstop) when the layer stops moving at a specific angle (θstop) and likewise when a static layer of thickness Hstart is set into motion at a different angle (θstart). While granular kinetic energy has been developed to estimate collisional stress components from individual grain dynamics, how frictional interactions play a role in a flow stress is yet unclear.
In order to estimate a stress field from lasting inter-particle friction, we develop a non-intrusive measurement technique by exploiting the birefringence of a photoelastic material. When under compression loading, the refractive index of a thin photoelastic disk changes accordingly so that a fringe pattern can be captured via proper polarized illumination, which provides us a means to observe the loaded frictional force network. In this study, we have developed a photoelastic granular chute flow facility to observe how the fringe intensity and structure change under different flow conditions that can be set by varying the chute angle and flow height. We have developed novel image processing algorithms to capture the mean fringe angle (α) and its strength by the gradient square (G2) method. Via static calibration, we obtain the σf--G2 and the τf--α relations to estimate the frictional stress components. In addition, we also develop an algorithm to achieve the Particle Tracking Velocimetry (PTV) to measure the bulk dynamic properties including its velocity, shear strain rate, granular temperature, and solid volume fraction so that the concurrent collisional stress components can be estimated. For this, we had to design a pendulum collision experiment to measure the coefficient of restitution for the photoelastic disks.
Based on the observation, the frictional stress developed primarily at the bottom of an inclined flow to resist gravity and maintain the particle structure. In contrast, the collisional stress is detected near the free surface to facilitate the flow by converting gravity into grain motions. We shall examine the frictional and the collisional normal and tangential stress components against the total stress predicted from a continuum model to evaluate the proposed methodology.

When a single particle is settling due to gravity in an unbounded fluid under the inertialess Stokes flow condition, a disturbance flow field v can be generated around the particle and decays as 1/r, where r is the distance to the particle. In a dilute sedimenting particle suspension where many particles are settling at the same time, this long range point-force character generally renders collective hydrodynamic interactions between the particles, making the ensemble average of the disturbance velocity v' grow indefinitely with the container size L as L^2. Batchelor (1970) first showed that this divergence can be successfully removed by the backflow renormalization in that the bottom wall of a container sets up a macroscopic backflow that necessarily grows as L2 to counterbalance the likewise point-force contribution for ensuring =0 macroscopically. For the velocity fluctuation delta_v which is the square root of the velocity variance ^1/2, Caflisch & Luke (1985) showed that delta_v also grows as L^1/2 without bound, in contrast to experimental observations which showed no such a divergence. However, from a conceptual point of view, It is rather puzzling that such a L^1/2 divergence in delta_v, the so-called Caflisch-Luke paradox, is not tamable while a much stronger L^2 divergence in can still be fully eliminated. This thus raises a question: can the macroscopic backflow effect in the latter be used to kill the divergence in the former? In this talk, I will demonstrate that the O( d^1/2) velocity fluctuation delta_v can indeed be made finite due to the suppression by the O( d^2) backflow effect in terms of a mesoscopic length much greater than the particle size a. In addition, this backflow suppression entails a natural cutoff length d~a*phi^1/3 that scales as the average particle separation in consistent with the experiment by Segré et al. (1997), where phi is the particle volume fraction.