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    题名: 5:1矩形方柱氣動力數值模擬
    其它题名: Numerical simulation of turbulent flow around a 5:1 rectangular cylinder
    作者: 黃昱賓;Huang, Yu-Bin
    贡献者: 淡江大學航空太空工程學系碩士班
    李世鳴;Lee, Shi-Min
    关键词: 紊流;Turbulent Flow;BARC;MAC;K-ε-E;FRAM;Tensor Viscosity
    日期: 2011
    上传时间: 2011-12-28 19:20:03 (UTC+8)
    摘要: 本文利用計算流體力學方法,來探討一個比例為5:1的矩形鈍體(Bluff body),此模型比例是根據義大利風工程協會所制定的『a Benchmark on the Aerodynamics of a Rectangular 5:1 Cylinder』的統一基準計畫,簡稱為BARC計畫。利用同一基準模型來分析流場通過鈍體外型後所造成的流場分離及迴流現象,才能有效地和不同數值模擬及實驗來比較,進而能實際應用到工業上對於建築物外型的評估和分析。

    吾人所分析的是不可壓縮紊流流場問題,控制方程式是採用了時間平均Navier-Stokes方程式,而紊流模式是採用了Launder和Spalding 的K-ε-E 紊流模式,近壁模式則採用壁面函數法(Wall function)。數值方法是利用求解原始變數的方法,配合Marker- and-Cell(MAC)變數分配法將壓力和速度交錯分佈,並配合使用非均勻的網格來節省計算時間和網格總數。

    離散動量及紊流傳輸方程式中,本文以二階準確離散對流及時間項,離散算則以空間中央差分為基準結合時間前進,並引入張量黏滯法(Tensor Viscosity Method)將時間項離散提升到二階準確,再運用FRAM通量限制法(Filtering Remedy and Methodology)來過濾偽振盪現象的產生,使不符合FRAM限制條件的計算變數利用一階上風法來取代處理。計算程序以顯性法求解動量方程式的速度值,配合壓力修正迭代過程來修正速度值,使最後能得到一個同時滿足於動量和連續方程式的速度與壓力場。

    為驗證本文程式的離散方法,吾人以流場通過1:1正方形方柱問題,藉由週期性渦漩剝離流場的分析,證明本文程式所使用的紊流模式和離散方法,確實對於此類型的紊流流場分析具有適用性。確認本文程式的適用性,吾人才實際分析5:1的矩形鈍體外型。由計算結果顯示,本文程式能確切的呈現出流場週期性的渦漩剝離現象,以及方柱側面、後方的渦漩迴流現象,皆能詳實地呈現出來,並和商業軟體Fluent、實驗數據比對史徹赫數(Strouhal number)。最後吾人並且依序的利用程式計算出外型比例為2:1、3:1及4:1的結構流場分析,並將其渦漩產生情形放在一起呈現比較。
    In this study, we use the numerical method to simulate the turbulent flow around a rectangular cylinder with chord-to-depth ratio equal to 5. The aim of this benchmark is to provide a contribution to the analysis of the turbulent. This BARC (a Benchmark on the Aerodynamics of a Rectangular 5:1 Cylinder) problem originated with the Italian National Association for Wind Engineering (ANIV). In spite of the simple geometry, it is believed that the problem is interested not only for the purpose of fundamental research, but also to provide useful information on the aerodynamics of a wide range of bluff bodies (e.g. high-rise buildings).

    The governing equations are Navier-Stokes equations coupled with K-ε-E turbulence mode equation together with near-wall treatment (wall function). Computations are performed on a nonuniform and staggered MAC (marker-and-cell) grid system.

    The transport equations are discretized by three steps. In the first step, forward time and central space is applied, and then tensor term is added to stabilize the solution and to reach second order accuracy in time. Finally, FRAM procedure is introduced to remove nonphysical oscillations.

    First, we calculate the turbulent flow over cube problems. The computed results show that the scheme is suitable for simulation of turbulent flow. Second, we simulated the flow around a 5:1 rectangular cylinder and vortex shedding past rectangular cylinder problem. The computed results indicate that present study gives good agreement with other studies from BARC database and FLUENT (commercial CFD software). Finally, we also calculate the 1:1, 2:1, 3:1 and 4:1 rectangular cylinder problem and we compare result with the flow situation and vortex shedding in 5:1 rectangular cylinder problem.
    显示于类别:[航空太空工程學系暨研究所] 學位論文

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