低雷諾數下流經有限長圓柱體之流場的端效應研究

Abstract

本篇文章架構為以實驗及計算的方式探討低雷諾數流場流體流經有限長度圓柱。 實驗在一個開放式水洞中進行，實驗液體為甘油，而計算模擬的部分使用的軟體為一般商用軟體Ansys Fluent。 Ar(aspect ratio number)的範圍為1.5到6，而雷諾數變化的範圍為Re=10-100我們固定Re探討不同的Ar所造成的影響，固定Ar討論不同Re的變化，在研究了不同Re的變化後，我們發現流況是穩定的且在尾流區域具有雙重對稱性的。 尤其要注意3維流況及橫向於圓柱軸方向之截面，在圓柱尾流區域會有兩種不同形式的流線交織再一起：一種為流體流經圓柱表面向下分離的橫向分流（transverse separation，TS）和從圓柱自由端面分離下來的縱向下沖流（longitudinal separation，LS）。 Ar=4圓柱在Re>50時流況與一般2D圓柱截然不同，在圓柱尾流區域會產生一個奇異點源，與橫向分離流動一起形成一個扭曲的星形圖案，奇異源位於縱向分離所形成的recirculation的中末端，而圓柱與奇異點的距離以d_s表示。 而此奇異點源的強度以SS=-∂v/∂y來表示當Re固定時，d_s隨直徑增加而增加，在Re=10時每根圓柱流況基本一致，隨著Re增加後方尾流區域不斷拉長，而SS在Re=100時當Ar<3後會有明顯的下降，Ar固定時 d_s隨著雷諾數增加而成長，而ss在Re>40後成長為非線性。

This article is to report on a joint numerical and experimental investigation of the vortex structures of flow past a circular cylinder of finite span in a range of low Reynolds numbers. The experiments were performed in an open water channel using the glycerol as the working fluid, while numerical simulations were carried out using the commercial code Ansys/Fluent. The aspect ratio Ar of the cylinder varies from 1.5to 6, and the Reynolds number Re varies from 10 to 100. Give a fixed Re we study the various cases of Ar, and given a fixed Ar we study the various cases of Re. In this regime of parameters, the flow is found to be steady, separated and doubly-symmetric. In particular, the 3-dimensional flow streamline pattern as well as its cross sections transverse to the cylinder axis are carefully examined. The streamlines are interweaved by two flow separations: separated flow over the round side of the cylinder (transverse separation, TS) and that around the two flat ends of cylinder (longitudinal separation, LS). At low Aspect Ratio On the middle cross-section, the flow pattern bears a great difference from the 2-dimensional flow (over a very long cylinder) that a singular source appears in the wake, together with TS to form a distorted star-shaped streamline pattern. The singular source is located in the farthest spot from the cylinder where recirculation of LS starts in the middle section; the normalized distance between the singular source and the cylinder is denoted by d_s. the strength of the singular source, denoted by SS=-∂v/∂y, The flow conditions of each cylinder are basically the same at Re = 10, and the wake area continues to elongate after increasing Re, while SS at Re = 100 will decrease significantly after Ar <3 When Ar is fixed, d_s grows by increasing the Reynolds number, and ss grows nonlinear after Re>40.