以數值與實驗探討旋轉流體中泰勒牆與旋轉圓柱之交互影響

Abstract

中文摘要 許多在旋轉流豐饒有趣的現象中，科氏力所扮演的關鍵角色尤引人入勝。 本文旨在以數值計算與實驗量測分析，探討其中兩種流場結構的互制行為。其一，池盆渦漩為具背景渦度下的一種吸入式渦漩，其強烈的中心渦漩結構與颱風結構十分相似；其二，泰勒柱則為具背景渦度影響下的地形效應，能夠在地形垂直方向產生封閉的流場。以上兩種旋轉流的現象皆已為文獻廣泛地探討，然而從事兩者間互制行為的研究始自於本實驗室。 先前的研究中所使用之模型為一圓柱狀的旋轉水槽，其底板的中心鑿有一個小出水孔(用以產生池盆渦漩)，上板正中則倒置一圓形柱體(期以誘發泰勒柱現象)，而這樣的布置的確導致新的發現。除了固體邊界的艾克曼層及其湧升行為外，我組測定了圓柱下方與出水孔間的多層渦漩結構，尤其是首度確認了泰勒牆的存在，以及沿其外側爬升的強大泰勒湧升流。 本研究將擴大此項研究成果，探討倒置一圓柱於上板中心與其對應於底板的正投影面積在不同於背景之旋轉速率下對泰勒牆的影響。於數值計算模擬的工具使用有限體積分析套裝軟體ANSYS Fluent求解旋轉座標下的不可壓縮Navier-Stokes 方程式的定常解，探討圓柱長度-兩板間距比(h/H)，高度比範圍為0.3、0.5、0.7以及無圓柱作為對照組；圓柱與其對應底面轉速-背景轉速比(ω/Ω)，旋轉速度比之探討範圍由無相對旋轉速度至 8/3。另實驗中的流線與流場分布資訊將以螢光染料顯影以及粒子影像測速(PIV)的方法測量。 研究中發現，當圓柱旋轉的方向與背景旋轉方向相同時，泰勒牆會徑向擴張，且其高度與厚度亦隨著圓柱轉速增加；反之當圓柱旋轉方向與背景旋轉方向相反時，泰勒牆會徑向收縮，其高度與厚度則隨圓柱轉速增加而減少。

ABSTRACT There are lots of exciting phenomenon in rotating fluids, and the critical role which Coriolis force play is the most fascinating. The aim of this study is to investigate the interactions between two flow structures among vortices with numerical analysis and experimental measurements. The first one is the bathtub vortex driven by a drain-source under rotating background vorticity, which vortex structure is similar to that of typhoon; the other is the Taylor column, which is a topography effect that forms closed-loop flow field above terrain structures under rotating background. Both rotating flows mentioned above has long been studied broadly in the literature, but the work of studying their interactions has just recently began in our laboratory. In the previous study, the tub model has a tiny drain hole located at the center of bottom wall to generate bathtub vortex; and a cylinder is fixed on the center of top wall to induce Taylor column effect, which indeed leads to a new discovery. In addition to the Ekman layer on surfaces of solid boundary and its upwelling behavior, our team have determined the multi-layered vortex structure between the cylinder and drain hole. Moreover, the existence of Taylor wall and a strong Taylor upwelling that climbs along outside of Taylor wall has first been confirmed. This study is an extension of previous work, which consider the cylinder and its corresponding vertical projection area on the bottom wall rotating asynchronously to the background rotation. Steady-state solution of Navier-Stokes equation is solved under the rotating reference frame with finite volume method analysis software ANSYS Fluent, and some significant parameters for discussions are the height ratio of cylinder to distance between top and bottom walls (h/H), which are 0.3, 0.5, 0.7 and without cylinder as contrast; and the angular velocity ratio of cylinder and its corresponding area on the bottom wall to background rotation (ω/Ω), which ranges from -8/3 to 8/3. On the other hand, streak line patterns and flow field velocity profiles are measured using fluorescent dye visualization and Particle Image Velocimetry (PIV) in the experiment. The results show that along with the increasing angular velocity of cylinder, when it rotates in the same direction as the rotating tub, the Taylor wall radially expands and its height and width increases; when the cylinder rotates in the opposite direction, the Taylor wall contracts and its height and width reduces.