液體渦流與下沉球體交互作用之雷射發光實驗

Abstract

本篇論文的目的是在探討固體球體在液體中運動所產生的渦流變化以及球體本身的軌跡變化。球體以某些固定的速度往下沉，球體的尾流將會形成渦場，而在不同的條件設定下，產生的渦會有些許的不同，尤其在高雷諾數的情況下。渦場是因為固體邊界層的黏滯力影響所 產生的，所以我們也考慮了固體邊界層對於渦場的行為產生的影響，進而觀察邊界層跟流體之間的相互作用。 實驗會分成兩個部分，第一部分我們會控制球的軌跡，以不同的速度往下沉，藉此觀察球體附近產生的流場和分析渦的軌跡；第二部分是讓固體球體不受任何拘束落下，在高雷諾數的情況下，紊流的影響會對球體產生比較嚴重的擾動，使得球體落下的時候不會是一條直線。 此實驗是個三維性非常強的一個實驗。此外本實驗可以利用特殊的液體解決了固體跟液體之間折射率的問題，再利用雷射激發的原理，可以在一個三維流況中，切出一個二維切面，讓我們方便在一個三維空間中觀察以及分析。 實驗分析是利用粒子影像分析的技術，在長時間曝光的影像下，可以觀察出液體中顆粒的軌跡，這可以用來代表整個流場；再利用PTV 方法，計算出速度場以及渦度場，這樣就可以更清楚了解固體和液體交互作用時，流場變化的一些更細部的資訊。為了使實驗更有完整性， 所取得的資訊也會跟數值模擬做部分的比較，藉此搭起實驗跟數值模擬之間更完美的結合。

The purpose of this thesis is to investigate the vortex structure brought by a solid sphere dropped in a liquid and to observe the coupled motions between the solid sphere and a liquid. When a solid sphere moved downward with some specific speed, the wake behind the sphere produced vortices. Under some different conditions, the trajectories of vortices are similar but a little different, especially in high Reynolds numbers. Vortex is generated because of the viscosity from the boundary layer, so we also want to observe the interactions between the boundary and the liquid. There are two parts in the experiment: in the first part we controlled the displacement of the sphere which dropped in different constant speeds, and then observed the flow field and vortices surrounding the sphere. In the second part we let the sphere drop freely. The movement of the sphere was interfered because the turbulence was more evident in high Reynolds numbers. In that situation, the trajectory of the sphere was not a straight line. Due to the experiment was a three dimensional experiment, the problem of refractive index was solved by using specific solid and liquid, so that we could observe and analyze the two dimensional phenomena in a three dimensional space. We used image processing methods to capture the trajectories of these bright spots seeding in a liquid. In the long exposure image, the trace of particles could stand for the flow field almost, and then use particle tracking velocimetry (PTV) to calculate the velocity field and vorticity field. So that we can understand the more detail information about the interaction between the solid sphere and the liquid. We needed numerical simulation to compare with the experiments to complete the investigation.