透明的紊流底床載傳輸:以折射率近似的材料研究內部流場及其結構

Turbulent bed-load made transparent: internal flow structure from refractive-index-matched experiments

倪瑋傑(Wei-Jay Ni)

指導教授 ： 卡艾瑋

共同指導教授 ： 楊馥菱 ； 吳富春

國立臺灣大學/工學院/土木工程學研究所/博士(2018年)

https://doi.org/10.6342/NTU201804057

摘要

紊流底床載傳輸是改變地貌的主要地球物理現象之一，它不像懸浮載中的固體主要由湍流支持，也不像土石流藉由固體顆粒間的碰撞主導固體顆粒。紊流、顆粒間的碰撞和固液交互作用力在紊流底床載傳輸中相互影響且不可忽略。為理解這些耦合機制，我們進行一系列的物理實驗，研究在理想條件下之紊流底床載傳輸: 牛頓液體於穩定和近均勻的紊流流場條件下在矩形通道中流經可沖蝕底床之底床載傳輸，我們於水槽實驗中應用了三個實驗邊界條件:光滑牆壁光滑槽底、光滑壁面粗糙槽底和粗糙壁面粗糙槽底預期看到不同之流場變化。實驗材料選擇折射率近似的物質─固體顆粒採用相同粒徑之球形聚甲基丙烯酸甲酯(PMMA)顆粒，液體則採用染色之對位傘花烃 (para-cymene)，藉此特性可對水槽全斷面進行內部成像分析測量。在成像測量中，我們使用橫向鐳射掃描來獲得固體和液體於水槽全斷面的運動資料，另外開發縱向掃描法以獲得掃描體積內之固體體積比分布。在此基礎上，我們採用體積相平均法計算高解析度的固相和液相的平均速度分布和固體濃度分佈。影像測量結果與水槽的出口通量比對確認滿足守衡條件。我們通過將斷面上之流場強度分佈劃分為傳輸域、總流通域和清液域，計算與輸砂率相關的因素，得出輸砂率組成因素與運動學無因次參數:流度數，與動力無因次參數: 希爾斯數的關係符合對數方程。最後以光滑壁面邊界的兩組實驗資料，假設二相均為連續體且斷面方向速度、濃度均勻分布，計算並建立固液兩相動量平衡方程中每一項的實驗垂直剖面資料，發現需考慮對流加速項才可得到滿足力平衡並進而計算出固液兩相之剪切應力分布與阻力分布。由這些應力剖面資料我們測試分子運動學理論和阻力關係經驗式，本研究證實在穩態紊流底床載傳輸、雷諾數介於約5000-12000之條件下，除濃度過低與過高之固體傳輸層外，其固體正向與剪切應力滿足分子動力學理之本構關係，我們還發現源自孔隙介值流和顆粒流體化試驗的阻力關係經驗式，經考慮顆粒擾動速度之貢獻後可描述於紊流底床載傳輸二相於相對流場中之阻力關係。

關鍵字

折射率近似實驗 ； 紊流底床載傳輸 ； 粒子追蹤測速學

並列摘要

The bed-load transport is one of the major geophysical phenomena that change the landscape, it doesn't like suspended-load transport for which the solid is primarily supported by turbulence, and it doesn't like the debris flow which is dominated by the collisions between solid grains. The mechanism of turbulence, granular collisions, and inter-phase forces all play a role and mutually influence each other in the turbulence bed-load transport, and none of these can be neglected. To understand these coupled mechanism, we conducted series of physical experiments to explore the turbulent bed-load transport under idealized conditions: steady and nearly uniform turbulent flow of Newtonian liquid over erodible and identical deposits in a rectangular channel, we applied 3 boundary conditions to the experiments: smooth wall smooth floor, smooth wall rough floor and rough wall rough floor. The refractive-index-matched materials, the identical and spherical PMMA beads as solid grains and para-cymene as the liquid, were adopted and were applied the internal imaging measurements to the liquid-granular flow. For imaging measurements, we used transverse laser scans to acquire the motion of solid and liquid over the channel cross-section, and we developed longitudinal scans method to obtain the solid fraction distribution over the channel cross section. With the measurements, we calculated the averaged velocity distribution of solid and liquid phases, the solid fraction distributions by the volumetric phase-averaging approach with high resolution. The results were validated by measured discharges from the channel outlet and in good agreement. The internal flow structures were characterized by dividing the flow into transport domain, flow domain, and clear liquid domain to calculate the factors related to transport rate, we found the relationship between the factors composing transport rate and kinematic parameter, Mobility number, and dynamic parameter, Shields number. Further, for the experiments of the smooth wall cases, we established each term of the momentum balance equations for solid and liquid phases, we found that the convective acceleration term might be large and need to be considered, the shear stress profiles of solid and liquid were also obtained. From those profiles we tested the stress relation described by kinetic theory and the drag relation by empirical law, we confirmed that for steady state turbulent bed-load transport, and with Reynolds number range 5000-12000, the solid stresses could be described by the constitutive relations of the kinetic theory. We also found that the drag force relation derived from fixed pack and fluidization cell could be applied to turbulent bed-load if the contribution from solid velocity fluctuation was considered.

並列關鍵字

RIM experiment ； turbulent bed-load transport ； Particle tracking velocimetry

參考文獻

Allen, B., and Kudrolli, A. (2017). Depth resolved granular transport driven by shearing fluid flow. Phys. Rev. Fluids 2, 024304.

Ancey, C., Davison, A. C., Bohm, T., Jodeau, M., and Frey, P. (2008). Entrainment and motion of coarse particles in a shallow water stream down a steep slope. J. Fluid Mech. 595, 83--114.

Anderson, T. B., and Jackson, R. (1967). Fluid mechanical description of fluidized beds. Equations of motion. Ind. Engng Chem. Fundam. 6, 527--539.

Armanini, A., Capart, H., Fraccarollo, L., and Larcher, M. (2005). Rheological stratification in experimental free-surface flows of granular-liquid mixtures. J.~Fluid Mech. 532, 269--319.

Asano, T. (1995). Sediment Transport under Sheet-Flow Conditions. J. Waterway, Port, Coastal, Ocean Eng. 121, 239--246.