顆粒流對邊界磨損行為之研究:以實驗與理論

本研究針對顆粒流流經鬆軟堆積層造成淘刷及流經堅硬岩盤造成側向磨損的行為進行探討。對於鬆軟堆積層的淘刷，以兩種不同的實驗及理論進行比較驗證。理論方面，本研究以質量、動量方程式作為基礎，並使用動能方程式取代常見的侵蝕方程式作為第三條方程式，再使用深度積分簡化其方程式作為本研究之控制方程式。在實驗方面，分為長渠道實驗及滾筒實驗，實驗上皆以粒子影像分析方法記錄其流場。針對長渠道，以非穩態均勻流的假設簡化理論，並與長渠道實驗結果進行比較，其結果相當吻合。再以滾筒實驗進行穩態非均勻流之實驗，以理論驗證之。實驗結果與理論符合，並經由理論進行尺度分析，發現顆粒於滾筒內之運動行為可由一簡單無因次參數(En)控制。同時經由比較實驗與理論，可得出顆粒在滾筒內之運動模式存在兩值域，並由動能消散項控制其變化反應，根據理論推導後，與實驗結果一致。而關於顆粒流對於堅硬岩盤的磨損，因本研究以小尺度的實驗進行，為避免應力尺度的非線性變化，本研究以小尺度的實驗搭配地工離心機進行。利用地工離心機提升應力大小後，即可使用與現地尺度應力大小相同之材料進行岩盤磨損實驗，並透過三維攝影投影方式記錄其磨損變化。本研究再提出一簡化的磨損模式，以能量變化正比於磨損量之關係根據顆粒速度場計算其磨損量。最後，將模式預估的結果與實驗相比較，其結果成功預測了在局部的磨損形貌及整體的磨損量值。

關鍵字

動能方程式；深度積分方程式；尺度分析；地工離心機實驗

並列摘要

Granular avalanches flowing over loose beds evolve by gaining or losing grains through their basal boundary as stress and velocity change within the sheared layer. Kinetic energy dissipation results from internal dissipation and wall abrasion. By understanding the wall abrasion behavior, it is possible to build a bed rock erosion law. In this study both theory and experimental results are used to further understanding of granular avalanches and bed rock erosion. Experiments are performed in a vertical rotating drum which has a synthetic rock sample embedded into the wall and is used to simulate long period, steady bedrock erosion behavior. Through theory, we develop new depth-averaged equations assuming conservation of kinetic energy, mass and momentum to capture the flow process. For steady flows in rotating drums, we deduce two asymptotic regimes governed by a single dimensionless number, the Entrainment number, which controls flow geometry in the drum. Theoretical analysis is used to develop experimental design. Granular shear stress is scaled up by performing the experiments under enhanced gravity conditions in a geotechnical centrifuge. The velocity field are measured and compared with theoretical results. Through theory and the experiment observation, we develop an erosion model based on the kinetic energy exchanges. The proposed erosion model can be applied to both local erosion patterns and global erosion rates.

並列關鍵字

kinetic energy ； depth-averaged equation ； scaling analysis ； centrifuge experiments

參考文獻

Adrian, R.J. (1991): Particle-imaging techniques for experimental fluid mechanics. Annu. Rev. Fluid Mech., Vol. 23, pp. 261–304.

Ahn, H., Brennen, C.E., and Sabersky, R.H. (1991): Measurements of velocity, velocity fluctuation, density, and stresses in chute flows of granular materials. Transactions of the ASME, Vol. 58, pp. 792-803.

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Boateng, A.A., (1998): Boundary layer modeling of granular flow in the transverse plane of a partially filled rotating cylinder. Int. Journal of Multiphase Flow, Vol. 24(3), pp. 499-521.

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顆粒流對邊界磨損行為之研究:以實驗與理論

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