Please use this identifier to cite or link to this item: http://hdl.handle.net/11455/1666
標題: 垂直與傾斜平板尾流渦漩剝離及流場控制
Vortex Shedding and Lock-on for a Rotationally Oscillating Flat Plate
作者: 方元政
Cheng, Fang Yuan
關鍵字: Vortex Shedding;渦漩剝離;Lock-on;Rotationally Oscillating;Flat Plate;互鎖;旋轉振盪;平板
出版社: 機械工程學系
摘要: 
本文以實驗量測及數值模擬探討平板尾流渦漩剝離的特性及互鎖的現象。實驗主要是量測尾流渦漩剝離頻率、表面壓力、平板的受力及尾流渦漩結構,並利用煙線可視化的技巧來觀察近尾流場的結構。數值模擬則選擇旋度與流線函數(vorticity and stream function formulation)型式之二維納維爾-史托克斯方程式,模擬的重點在於瞭解互鎖過程的流場細微變化。
實驗是在開放式的風洞中進行,模型為不同尺寸的平板,阻塞率在K=4.3- 26.2%。雷諾數則在3.5103與3.2104之間。首先針對平板靜止時,討論史卓赫數隨傾角、切角及雷諾數的變化,並且包括阻塞效應對流場的影響。實驗發現在適當的定義特徵長度及阻塞率的校正下,可得到一組通用的史卓赫數約為0.1600.003。在具阻塞效應的流場下,本實驗利用動量缺陷法來估算平板的阻力係數,結果發現在平板後方三至六倍的平板寬度內,估算的阻力係數相較於由平板表面壓力積分所得到的之值,其差異小於5%。
在互鎖特性的探討上,實驗選擇來回旋轉振盪方式,主動控制平板的渦漩剝離,旋轉中心為平板的中心點。討論的方向著重在於互鎖的機制、互鎖的過程及互鎖前後流場的變化。實驗的互鎖區域包括主區帶互鎖及諧和帶互鎖。在互鎖的機制上,發現垂直平板與傾斜平板恰好相反,若以高頻方式逼近互鎖,垂直平板的互鎖機制是以振盪頻率吸收渦漩剝離頻率之能量以達互鎖,而傾斜平板則是以振盪頻率壓抑渦漩剝離頻率之能量以達互鎖;如果以低頻方式逼近互鎖時,垂直平板的互鎖機制是以振盪頻率壓抑渦漩剝離頻率之能量以達互鎖,而傾斜平板則是以振盪頻率吸收渦漩剝離頻率之能量以達互鎖。結果也顯示以振盪頻率吸收渦漩剝離頻率之能量流場較易達到互鎖狀態;且在相同的振幅下,互鎖後振盪頻率的能量會高於以振盪頻率壓抑渦漩剝離頻率之能量以達互鎖時之能量。在互鎖狀態下,不同的振盪頻率將改變起始渦漩的結構及位置,而影響平板的背壓。由表面壓力量測配合流場可視化觀察,發現較短的渦漩形成長度及靠近渦漩中心都會造成較低的背壓。本實驗亦量測不同振盪頻率下,平板運動位移與渦漩剝離間的相位差,協助瞭解起始渦漩剝離隨振盪頻率所造成的變化。
本研究亦採用交替方向隱式法處理計算面上的旋度函數及流線函數,針對垂直平板在Re=100時,模擬渦漩互鎖流場隨時間的變化。模擬的結果與實驗具有相同的互鎖過程及互鎖機制,在相同的振盪振幅下,以高頻逼近較易達到互鎖,互鎖所需要的時間也較短。互鎖後,由於起始渦漩的形成長度會隨著振盪頻率的加快而縮短,所以平板的阻力係數擾動量會隨著振盪頻率的加快而增大,但渦漩中心隨著振盪頻率的加快漸往平板尖端移動,所以平板中心渦度擾動量則會隨之變小。在互鎖邊界的特性上,高頻逼近區的斜率會低於低頻逼近區。

The vortex shedding and lock-on induced by rotational oscillation of a flat plate normal and inclined to a uniform stream in its neutral position have been studied experimentally and numerically. The shedding frequency, lock-on bands, unsteady surface pressures, mean drag and vortical structure of the near wake are described.
The experiments were performed in an open-type wind tunnel with a square test-section of 305 mm305 mm and 1100 mm in length. A total of six flat plate models with blockage ratios in the range K = 4.3- 26.2% were tested in the present study for Reynolds numbers between 3.5103-3.2104. By the use of a correction factor to account for the effect of bevel angle, a universal Strouhal number of 0.1600.003 can be obtained for inclined angles =10-90 for the stationary flat plate. It appears that for the Reynolds numbers presented, the only significant effect of blockage is to produce an increase in the local free-stream velocity. Accordingly, the effect of blockage on drag coefficient and Strouhal number can be corrected by employing the common correction formula. The present study also determines the drag coefficients of the models with significant blockage effect using the momentum defect method.
The onset of lock-on, which depends on the combination of the frequency and amplitude of the forcing, is examined by using spectral analysis of the wake velocity. Three lock-on flow regimes are studied in detail. These include the primary lock-on regime that occurs when the ratio of forcing frequency to natural shedding frequency comes close to unity, and two subharmonic regimes 1/2 and 1/3 harmonics. Moreover, the lock-on state can be reached via a frequency higher or lower than the natural frequency. For a normal flat plate, the route leading to the lock-on state via a higher-frequency approach is found to ‘attract' the vortex shedding frequencies, whereas the lower-frequency approach ‘suppresses' the vortex shedding frequency other than the forcing one. However, for an inclined plate, the route leading to lock-on via higher-frequency or lower-frequency approach is observed opposite to that for the normal plate. Furthermore, the higher and lower frequency approaches to lock-on significantly alter the phase and structure of the shed vortices. Consequently, the base pressures exhibit different distributions in response to the vortex formation immediately behind the plate.
A finite difference simulation of the vortex shedding and lock-on for a rotationally oscillating flat plate at Re = 100 is computed by solving the unsteady two-dimensional Navier-Stokes equations in the vorticity-stream function form. The Strouhal number and vortical structure, which are evaluated for the stationary normal plate at Re=100, 126 and 500, reflect excellent agreement with both the experimental and numerical data available. Behavior of the route to vortex lock-on is also investigated. It is found that both the time from stationary to lock-on situation and vortex formation length decrease with increasing forcing frequency. The character of limits of lock-on regime is found in good agreement with present experimental results. An approach to lock via a higher-frequency is easier than via a lower frequency.
URI: http://hdl.handle.net/11455/1666
Appears in Collections:機械工程學系所

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