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標題: | 定量乾顆粒於傾斜平滑儲存槽內崩塌之動態及流變行為研究 Dynamics and Rheology of Finite Dry Granular Mass in Avalanche down an Inclined Smooth Reservoir |
作者: | Yung-Ta Huang 黃永達 |
指導教授: | 楊馥菱 |
關鍵字: | 乾顆粒材料,崩塌行為,控制體積分析,有效摩擦係數,μ-I流變關係式,應力稀化邊牆摩擦係數,邊牆μw-Iw關係式, dry granular material,avalanche,control volume analysis,effective friction coefficient,μ-I rheological law,particle rotation, |
出版年 : | 2015 |
學位: | 博士 |
摘要: | 本論文透過實驗與離散元素法模擬探究有限質量乾顆粒於平底傾斜儲存槽內崩塌之動態及流變行為,其首要目的是想探究針對穩態均勻顆粒流所提出描述有效摩擦係數(μ)與無因次慣性數(inertial number, I)之μ-I流變律是否也能在此非穩態、非均勻的顆粒流場中量測而得,再者,探究顆粒流與邊牆面之有效摩擦係數(μ_w)是否符合多數表面流理論模型中之假設,為一定值,最後,透過實驗於儲存槽邊牆所量得之流量隨時間變化率,校正模擬中使用之接觸模型的動件參數,並利用模擬結果檢視實驗中近二維控制體積分析所作假設之合理性,試著將實驗與模擬做結合。
實驗上,以高速攝影機於儲存槽牆邊記錄顆粒運動,所錄製之影像透過標定及追蹤求得顆粒速度,再透過面積加權平均,求得此顆粒流之顆粒總體密度ϕ(t,x,y)及流向、徑向速度分量U(t,x,y)與V(t,x,y)之瞬時空間分布,進一步以近二維控制體積分析顆粒之內摩擦力,進而求得μ^'-I之關係式,與既存穩態顆粒流之μ-I流變律近似,μ^'隨I單調遞增,驗證該流變律之推廣。 另外,我們透過可重現實驗於儲存槽邊牆所觀測的動態行為之平行化離散元素法,模擬相同尺寸及材料之崩塌流場,研究儲存槽中央、遠離牆面之顆粒體動態行為、摩擦力及相應之μ^'-I關係式,得到在I> 0.02時與邊牆動態相似、定性上吻合之結果,進而完備實驗的結果。然而,在I< 0.02的流場條件下發現μ^'隨I近似線性遞減之結果,顯示顆粒體於崩塌前期局部剪應力稀化之現象,也暗示了顆粒尺度之交互作用在此流況下與觀測到μ^'-I關係式的流況下之機制應有所不同,因此,針對μ^'隨I遞減之現象,我們提出一個考慮因剪應力引起膨脹之簡化力鏈結模型來描述。此外,我們計算出顆粒流之μ_w有深度衰退(depth weakening)的動態現象,非廣泛假設之常數,更隨邊牆之慣性數(I_w)單調遞增。 我們因而更進一步利用模擬資訊探究μ_w深度衰退、以及μ_w遠低於內摩擦係數μ之機制,發現當顆粒與邊牆除滑動接觸外,若同步發生旋轉或轉動接觸(spinning or rolling contact),將減輕顆粒體與固體邊界之摩擦力,有鑑於此,我們建立了一個模型來描述μ_w是如何隨著因顆粒轉動引起之速度與顆粒移動速度之比值參數(Ω)變化。 最後,從儲存槽邊牆與中央流場之數值可計算實驗中近二維控制體積分析,在近二維流場假設下,ϕ、U和V之低估程度,然而,非等向性之正向應力、以及在深度上偏離靜水壓公式(平均壓力隨深度單調遞增)飽和的現象,甚或非常數之邊牆摩擦係數均違反控制體積分析上的假設,由此發現探討實驗數據之誤差、並對相關分析提出修正及討論,以對狹窄空間中顆粒流之動態行為有更全面之了解。 This work investigates the dynamics and rheology for finite number of nearly identical dry glass spheres in avalanche down a narrow inclined reservoir of smooth frictional bed via both experiments and parallelized discrete element simulation. The objective is first to study if the μ-I rheology law that describes bulk internal friction coefficient, μ, as a monotonically increasing function of dimensionless inertial number, I, for steady uniform flows can also be extracted from a non-uniform transient flow. Second, examine the effective sidewall friction coefficient in which most theoretical studies have assumed a constant value in the application of surface flow modelling. Finally, as an attempt to integrate experiment and simulation, the experimentally measured bulk discharge rate is used to calibrate the contact parameters in simulation while the detailed flow information gained from simulation is utilized to evaluate the assumptions made in the control volume analysis of experimental data. High-speed imaging technique is employed to measure bulk transient dynamics at the reservoir sidewall from which individual spheres can be traced to achieve particle tracking velocimetry. The individual sphere information is coarse-grained to estimate continuous bulk solid volume fraction, ϕ(t,x,y), and streamwise and transverse velocity components,U(t,x,y)andV(t,x,y)which are then applied in a quasi-two-dimensional control volume analysis to estimate internal friction, T(t,x,y). These flow properties are further analyzed to seek bulk instantaneous friction coefficient, μ^', as a function of instantaneous flow inertial number and the obtained μ^'-I relation agrees qualitatively to that reported for steady flows, supporting its claim as a local rheology law and validating the applicability to unsteady flows. Complementary numerical simulation that reproduces the measured bulk dynamics at sidewall is conducted to extract flow information away from the sidewall and a μ^'-I in qualitative agreement to the measured data for I> 0.02 is obtained. A peculiar trend that μ^' decays almost linearly with I at small I< 0.02 is revealed, suggesting stress thinning at the onset of bulk motion which should be related to different micro- mechanisms than that giving rise to the robust μ^'-I relation. To describe the decay trend, a simplified model considering the shear-induced dilation of initially compressed one-dimensional force chain upon yielding has been developed, predicting a linear decay at small I. On the other hand, the effective sidewall friction coefficient, μ_w, is not a constant but degrades with flow depth and exhibits a monotonically increasing function of quasi-two-dimensional inertial number at the sidewall, I_w. The fact that rotation at one sphere center can divert surface relative velocity across the contact area to render lower sliding friction is considered to develop a model describing how μ_w drops with the ratio between rotation-induced velocity and sliding velocity, Ω. The numerical data provides the degree of underestimation for flow properties under the quasi-two-dimensional approximation in control volume analysis and reveals anisotropic normal stress and their saturating, not fully hydrostatic, depth profile in addition to the varying μ_w. These findings from numerical simulation are discussed and used to construct a more feasible control volume analysis with in-depth understanding of bulk dynamics in narrow frictional confinement. |
URI: | http://tdr.lib.ntu.edu.tw/jspui/handle/123456789/50127 |
DOI: | 10.6342/NTU201601894 |
全文授權: | 有償授權 |
顯示於系所單位: | 機械工程學系 |
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