以預測-修正型直接施力沈浸邊界法探討紊流中鋸齒型電漿制動器對翼型動態失速的影響

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研究生：	陸秉鍵 Ping-Chien Lu
論文名稱：	以預測-修正型直接施力沈浸邊界法探討紊流中鋸齒型電漿制動器對翼型動態失速的影響 Prediction-correction direct-forcing immersed boundary modeling of dynamic stall of airfoil under serrated plasma control in turbulent flow
指導教授：	陳明志 Ming-Jyh Chern
口試委員:	陳明志 Ming-Jyh Chern 王謹誠 Chin-Cheng Wang 林怡均 Yi-Jiun Lin
學位類別：	碩士 Master
系所名稱：	工程學院 - 機械工程系 Department of Mechanical Engineering
論文出版年：	2022
畢業學年度：	110
語文別：	英文
論文頁數：	81
中文關鍵詞：	流場控制、電漿制動器、平行計算、直接施力沉浸邊界法、鋸齒型電極、動態失速
外文關鍵詞：	Flow control, plasma actuator, parallel computing, direct-forcing immersed boundary method, serrated electrode, dynamic stall
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機翼中的升力伴隨著翼形攻角增加而增加。失速則是指當翼形的攻角增加至臨界攻角時，升力突然驟降的一個物理現象。動態失速是一個非線形的流體現象，因翼形攻角快速改變時所產生的機翼前緣渦流生成及運動，進而造成渦流延遲脫落的物理現象。使用電漿制動器作為主動式的流場控制，是近幾年來被廣泛研究的流場控制方法之一，透過主動式的電漿制動器可作為流場控制的方法之一，其目的是可以延遲失速現象的發生。

本研究以預測-修正型直接施力沉浸邊界法來模擬流體與機翼間的交互作用，該方法可以在不需要重建網格的情況下模擬複雜的流固耦合問題。同時使用紊流模型-大渦模擬法模擬紊流場現象，並以輕度失速模型模擬動態失速的現象。

本研究在驗證數值模式階段分為三部分，第一部分驗證流在雷諾數100,000的情況下經過固定翼的升/阻力的值與Ohtake的研究符合。第二部分驗證數值電漿制動器，此處以流經過平板上的電漿制動器的情況下的速度分佈圖與Shyy的數值模型一致，第三部分驗證機翼上的線/鋸齒型電漿制動器，此處以流經過不同攻角機翼的升/阻力值來驗證其線/鋸齒型電漿制動器的改善效果符合Yoon的研究結論。

本研究在動態失速情況下的研究，主要分成兩部分，第一部分證實在雷諾數100,000的情況下，線型電漿制動器在機翼弦長的0.1c位置可以有效提升機翼在翼型擺動的完整行程的升力/阻力比，並且分析其電漿制動器的頻率及電壓效應，發現改變電漿制動器的頻率在提升機翼的效果上會更為顯著。第二部分根據研究結果發現鋸齒型電漿制動器對於改善紊流邊界層的效果有顯著提升。使用鋸齒型30°電漿制動器可以比線型電漿制動器提高20%以上的升力/阻力比，因此證實其鋸齒型電漿制動器可達成降低能耗目的。此外，鋸齒型30°電漿制動器在翼型擺動的下擺區段開始時，會產生新的渦流模式，該模式可以發現適當的前緣渦旋大小及強度，將會有助於提升機翼的升力/阻力比。

Lift increases with the increasing angle of attack (AOA) of the airfoil. Lift suddenly falls down when the angle of attack of airfoil pitching up to the critical angle of attack, which called the stall. Dynamic stall is a non-linear fluid phenomenon. It results from the vortex generation and movement of the leading edge of the airfoil. When the AOA changes rapidly, it causes the vortex to delay and shed. Recently, the dielectric barrier discharge (DBD) actuator is used as active flow control which can delay stall and increase the lift-to-drag ratio.

In this study, the Direct Force Immersion Boundary method is utilized to simulate interaction between fluids and the pitching airfoil. This method is able to simulate the complex fluid-structure coupling problem without mesh regeneration. At the same time, the Smagorinsky model is used in the large eddy simulation method to simulate turbulence flow over an airfoil. The light stall model is established to simulate the dynamic stall phenomenon.

At the validation stage of the numerical model, this study is divided into three parts. The first part verifies that the values of lift and drag flow through the fixed wing at a Reynolds number of 100,000 are consistent with Ohtake et al. The second part verifies that the numerical DBD actuator, where the velocity profile with flow through the DBD actuator on the plate is consistent with Shyy's numerical model.
Validating the feasibility of line and serrated DBD actuators for applying flow through an airfoil with varying AOA. The effect of the line and serrated DBD actuators is similar to Yoon's results.

The present study is divided into two parts based on its research objectives. The first section investigated whether the DBD actuator installed at the position of the airfoil chord length of 1/10 could effectively improve the lift-to-drag ratio in a full stroke. Furthermore, the frequency and voltage effects of the line DBD actuator were studied, and it was discovered that changing the frequency had a better effect on the lift-to-drag ratio. The serrated DBD actuator significantly delayed the point of separation on the upper surface of the airfoil and generated a suitable scale of the leading-edge vortex (LEV) at the beginning of downstroke, according to the findings in the second section. According to the current study results, Saw 30° DBD actuator configuration can raise the lift-to-drag ratio by more 20% than line DBD actuator as well as reduce the energy consumption. When configuring the Saw 30° DBD actuator on the wing, it is found that a proper scale of LEV and magnitude of vorticity can improve the lift-to-drag ratio.

Chinese Abstract  . . . . . . . . . . . . . . . . . . . . . i
Abstract  . . . . . . . . . . . . . . . . . . . . . iii
Acknowledgements  . . . . . . . . . . . . . . . . . . . . . v
Contents  . . . . . . . . . . . . . . . . . . . . . vi
Nomenclature  . . . . . . . . . . . . . . . . . . . . .viii
List of tables  . . . . . . . . . . . . . . . . . . . . . xii
List of figures  . . . . . . . . . . . . . . . . . . . . . xii
Supplementary movies  . . . . . . . . . . . . . . . . . . . . . xvii
INTRODUCTION  . . . . . . . . . . . . . . . . . . . . . 1
1 Motivation  . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  . 1
2 Literature Review  . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2
2.1 Direct-forcing immersed boundary method . . . . . . . . . . . . . . . . . 2
2.2 Dynamic stall . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2
2.3 Dielectric barrier discharge actuator . . . . . . . . . . . . . . . . . . . 4
3 Synopsis  . . . . . . . . . . . . . . . .  . . . . . . .  . . . . . .. . . . .4
MATHEMATICAL FORMULAE AND NUMERICAL MODEL  . . . . . . . . . . . . . . . .  . . 6
1 LES Governing equations . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
2 Numerical methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
2.1 Prediction-correction DFIB method . . . . . . . . . . . . . . . . . . . . . 8
2.2 Lift and drag calculation . . . . . . . . . . . . . . . . . . . . . . . . . 10
3 Airfoil and pitching model . . . . . . . . . . . . . . . . . . . . .  . . . . 10
4 Dielectric barrier discharge actuator . . . . . . . . . . . . . . . . . . . . 12
5 Hybrid parallel programming . . . . . . . . . . . . . . . . . . . . . . . . . 13
6 Computational environment . . . . . . . . . . . . . . . . . . . . . . . . . . 14
RESULTS AND DISCUSSION . . . . . . . . . . . . . . . . . . .. . . . . . . . . . 17
1 Validation . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . 17
1.1 Grid independence . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
1.2 Flow past a stationary airfoil . . . . . . . . . . . . . . . . . . . . . . 20
1.3 Flow past plate with dielectric barrier discharge actuator . . . . . . . . 20
1.4 Flow control with various dielectric barrier discharge actuators . . . . . 26
2 Dynamic stall . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .31
2.1 Dynamic stall without plasma control . . . . . . . . . . . . . . . . ..  . 31
3 Line dielectric barrier discharge actuator . . . . . . . . . . . . . . . . . 31
3.1 Frequency effect . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31
3.2 Voltage effect . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34
3.3 Analysis of effect of line DBD actuator . . . . . . . . . . . . . . . . . . 39
4 Serrated dielectric barrier discharge actuator . . . . . . . . . . . . . . . . 40
4.1 Serrated angle effect . . . . . . . . . . . . . . . . . . . . . . . . . . . 49
CONCLUSIONS AND FUTURE WORKS . . . . . . . . . . . . . . . . . . . . . . . . . .58
1 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58
2 Future works . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .59
                                

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