近牆效應對水中墜落圓球影響之研究

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姓名

尹相勗(Xiang-Xu Yin) 查詢紙本館藏

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土木工程學系

論文名稱

近牆效應對水中墜落圓球影響之研究
(Near Wall Effect on the Falling Sphere in Water)

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至系統瀏覽論文 (2024-12-31以後開放)

摘要(中)

在許多流場問題中可能發生懸浮顆粒與邊牆之間的互制現象，譬如懸浮顆粒在管道中流動、人體血管內血球的運動以及河流中的泥沙傳輸等。本研究藉由實驗觀察不同密度圓球體在水箱內不同邊牆間距下的自由墜落現象，發現當壓克力球與邊牆的初始間距小於圓球體直徑D，圓球體的墜落軌跡會偏離鉛垂直線，先微幅地靠近側牆，在不碰撞邊牆下，又逐漸地偏離側牆，圓球墜落軌跡呈現S曲線。但鐵球在相同的邊牆間距下，墜落軌跡十分接近鉛垂直線。由圓球直徑和終端速度計算而得之雷諾數為1.8 x 10^4~ 1.4 x 10^5。本研究並利用RNG k–ε模式計算墜落球體周圍的流速和壓力，再採用沉浸邊界法計算墜落圓球的軌跡，並和實驗的結果比對。模擬的結果顯示：壓克力圓球靠近邊牆時，圓球左右兩側壓力不對稱，使得球體往側牆靠近，引發球體兩側的渦流逸散，使得圓球體往相反方向墜落。但鐵球的慣性大，墜落速度大，側向力無法使其偏離鉛垂線。為了深入探討邊牆效應給圓球的影響，我們藉由風洞實驗量測固定圓球在不同邊牆間距下，圓球表面的壓力，並利用大渦模式計算固定圓球周遭的流場和壓力分佈與實驗結果互相比對。本研究藉由模擬結果來定義一個無因次參數來量化側向力與重力之比，建立圓球側向力與邊牆間距之關係，以界定圓球體的墜落軌跡是否受側牆之影響。

摘要(英)

This study utilizes laboratory experiments and a fluid/solid coupled numerical model to investigate the near wall effect on a free-falling sphere in water. The falling trajectory of the acrylic sphere resemble a S-curve when the initial distance between the sphere and the vertical sidewall is smaller than the sphere diameter D. The sphere first moves slightly towards the sidewall without colliding with it, then gradually moves away from the sidewall. The falling trajectory of steel sphere close to a straight line. The Reynolds number can be expressed in terms of the sphere′s diameter and its terminal velocity, is in the range of Re = 1.8 x 10^4 ~ 1.4 x 10^5. In addition, an RNG k–ε model and the immersed boundary method are employed to simulate the flow field and pressure around the falling sphere. The Newton–Euler method is utilized to calculate the motion of the sphere. The simulated trajectories compared well with the experimental results. The simulation outcomes illustrate that the asymmetric pressure distribution on the left and right sides of the sphere propels the sphere towards the sidewall, and triggers vortex shedding around the sphere. Furthermore, the surface pressures of a fixed sphere are measured in a wind tunnel experiment to validate the near wall effect on the sphere. The simulation results of a Large eddy simulation also confirm that the near wall effect occurs when the gap is smaller than the sphere diameter. This study introduces a dimensionless force ratio to quantify the influence of the lateral force on the sphere’s trajectory.

關鍵字(中)

★ 邊牆效應
★ 墜落圓球
★ 大渦模式
★ RNG k–ε
★ 沉浸邊界法

關鍵字(英)

★ Sidewall effect
★ Fluid/Solid Interaction
★ Large eddy simulation
★ RNG k–ε model

論文目次

Abstract II
Contents III
Table Captions IV
Figure Captions V
Chapter 1. Introduction 1
Chapter 2. Numerical Model 4
2.1 Governing equations 4
2.2 Numerical Setup 8
2.3 Model Validation 9
Chapter 3. Results and Discussion 11
3.1 Near-wall effect on a fixed sphere in wind 11
3.2 Near-wall effect on a free-falling sphere in water 15
3.3 Sphere density 21
3.4 Comparison of single and two spheres 22
Chapter 4. Conclusions 25
References 27
Tables 31
Figures 34

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指導教授

朱佳仁

審核日期

2023-7-27

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