臺灣博碩士論文加值系統

本研究應用高階通量限制函數對純電暈風與複合式電暈風之物理場之耦合計算優化，達到提升計算精確性與穩定性，使模擬結果與實驗結果更為匹配。在以有限容積法為基礎的數值計算方法模擬梯度變化極大的情況時(例如階梯函數)，傳統的離散方法常會產生數值擴散或數值震盪等問題，前者會使計算精度降低，後者會使計算不穩定甚至導致發散，本文所使用之高階通量函數具有偵測局部梯度變化，並依據偵測結果調整離散方法，使計算結果不致於產生過大的數值擴散與震盪，此方法能有效克服計算電暈風現象所遇到的難處：在放電電極尖端附近區域的電荷密度分布與速度分布會因電暈現象產生極大的梯度變化。
本研究針對電暈風現象測試數種不同之高階通量限制函數，分析各種限制函數對於計算電暈風現象的穩定性與準確性，並透過與實驗數據比對趨勢，選擇Van-Leer法作為分析所使用之高階通量限制函數。
模擬結果與實驗結果相比，因為二維假設導致模擬結果之衝擊現象可能較實驗強，進而使熱傳係數在所有條件下均高於實驗量測結果；在模擬結果中發現，電暈風熱傳增強之機制是受衝擊冷卻現象所主導，純電暈風能在加熱板中心形成較強的衝擊流現象，而複合式電暈風的振動雖然會使會使主要衝擊區域增加，但最大局部熱傳係數會下降約30%。基於以上結果，純電暈風具有較好的整體散熱效果，而複合式電暈風具有較均勻的散熱效果。

In this study, a higher-order flux limitation function was used to optimize the coupling calculations under the physical field of pure corona wind and composite corona wind, so as to improve the accuracy and stability of the calculation and make the simulation results more closely match the experimental results. When the numerical calculation method based on the finite volume method is used to simulate a situation where the gradient changes greatly (such as a step function), the traditional discrete method often produces problems such as numerical diffusion or numerical oscillation. The former will reduce the calculation accuracy, and the latter will make the calculation unstable or even cause divergence. . The high-order flux function used in this article can detect local gradient changes and adjust the discrete method based on the detection results so that the calculation results do not cause excessive numerical diffusion and oscillation. This method can effectively overcome the difficulties encountered in the calculation of the corona wind phenomenon：There is a great gradient change of the charge density distribution and velocity distribution in the area near the tip of the discharge electrode due to the corona phenomenon.
This study tested several different high-order flux limitation functions for the corona wind phenomenon, analyzed and compared the stability and accuracy of various limitation functions when calculating the corona wind phenomenon, and compared them with experimental data to select appropriate limits. Function to analyze the phenomenon of pure corona wind and composite corona wind, and compares the trend with experimental data to select the Van-Leer method used in the analysis.
After comparing the simulation results with the experimental results, it was found that the two-dimensional hypothesis would cause the impact phenomenon in the simulation results to be stronger than the experimental results, thereby making the heat transfer coefficient higher than the experimental measurement results under all conditions. It is shown that the mechanism of enhanced heat transfer from corona wind is dominated by the impact cooling phenomenon. Pure corona wind energy forms a strong impinging flow phenomenon in the center of the heating plate. Although the vibration of the composite corona wind will increase the main impact area, the maximum local heat transfer coefficient will decrease by about 30%. Based on the above results, pure corona wind has a better overall heat dissipation effect, while composite corona wind has a more uniform heat dissipation effect.

摘要 i
ABSTRACT ii
誌謝 iv
目錄 v
圖目錄 vii
表目錄 x
符號說明 xi
第一章 緒論 1
1-1前言 1
1-2電暈放電 2
1-3電液動力學基本公式 3
1-4電暈風現象之文獻回顧 4
1-5靜電致動器之文獻回顧 9
1-6複合式電暈風之文獻回顧 10
1-7研究方向 12
第二章 數學模型 13
2-1懸臂樑統御方程式 13
2-2 ALE座標系 15
2-3統御方程式（Governing Equation） 16
2-3-1流場統御方程式 16
2-3-2電場統御方程式 16
第三章 數值方法 19
3-1傳輸方程式之離散化（Discretization） 19
3-2速度與壓力耦合 24
3-2-1計算面上質量流率 25
3-2-2壓力修正式 26
3-2-3求解壓力修正式 27
3-3邊界條件（Boundary Condition） 29
3-3-1速度場邊界條件 29
3-3-2溫度場邊界條件 29
3-3-3電場邊界條件 30
3-4收斂標準 30
3-5計算步驟 31
第四章結果與討論 33
4-1幾何條件 33
4-2網格獨立性測試 33
4-3離散法測試 34
4-4純電暈風之數值模擬結果 34
4-5複合式電暈風之數值模擬結果 36
4-6純電暈風與複合式電暈風之模擬結果比較 37
4-7電暈風之模擬結果與實驗結果比較 38
第五章 結論 40
參考文獻 42
附圖 47
附表 88

[1] Robinson, M., 1961, "Movement of air in the electric wind of the corona discharge," Transactions of the American Institute of Electrical Engineers, Part I: Communication and Electronics, 80(2), pp. 143-150.
[2] Kibler, K. G., and Carter, H. G., 1974, "Electrocooling in gases," Journal of Applied Physics, 45(10), pp. 4436-4440.
[3] Mitchell, A. S., and Williams, L. E., 1978, "Heat transfer by the corona wind impinging on a flat surface," Journal of Electrostatics, 5, pp. 309-324.
[4] Hartmann, G., 1984, "Theoretical Evaluation of Peek's Law," IEEE Transactions on Industry Applications, IA-20(6), pp. 1647-1651.
[5] Peek, F. W., 1929, "Dielectric Phenomena In High Voltage Engineering," pp. 52-80.
[6] Bondar, H., and Bastien, F., 1986, "Effect of neutral fluid velocity on direct conversion from electrical to fluid kinetic energy in an electro-fluid-dynamics (EFD) device," Journal of Physics D: Applied Physics, 19(9), p. 1657.
[7] Elmoursi, A. A., and Speck, C. E., 1990, "Simulation of space charge in unbounded geometries," IEEE Transactions on Industry Applications, 26(2), pp. 384-392.
[8] Owsenek, B. L., Seyed-Yagoobi, J., and Page, R. H., 1995, "Experimental Investigation of Corona Wind Heat Transfer Enhancement With a Heated Horizontal Flat Plate," Journal of Heat Transfer, 117(2), pp. 309-315.
[9] Metwally, I. A., 1996, "Factors affecting corona on twin-point gaps under dc and ac HV," IEEE Transactions on Dielectrics and Electrical Insulation, 3(4), pp. 544-553.
[10] Owsenek, B. L., and Seyed-Yagoobi, J., 1997, "Theoretical and Experimental Study of Electrohydrodynamic Heat Transfer Enhancement Through Wire-Plate Corona Discharge," Journal of Heat Transfer, 119(3), pp. 604-610.
[11] Zebboudj, Y., and Ikene, R., 2000, "Positive corona inception in HVDC configurations under variable air density and humidity conditions," Eur. Phys. J. AP, 10(3), pp. 211-218.
[12] Anagnostopoulos, J., and Bergeles, G., 2002, "Corona discharge simulation in wire-duct electrostatic precipitator," Journal of Electrostatics, 54(2), pp. 129-147.
[13] Yan, Y. Y., Zhang, H. B., and Hull, J. B., 2004, "NUMERICAL MODELING OF ELECTROHYDRODYNAMIC (EHD) EFFECT ON NATURAL CONVECTION IN AN ENCLOSURE," Numerical Heat Transfer, Part A: Applications, 46(5), pp. 453-471.
[14] Ohyama, R., Aoyagi, K., Kitahara, Y., and Ohkubo, Y., 2007, "Visualization of the local ionic wind profile in a DC corona discharge field by laser-induced phosphorescence emission," Journal of Visualization, 10(1), pp. 75-82.
[15] Kasayapanand, N., 2007, "Numerical modeling of the effect of number of electrodes on natural convection in an EHD fluid," Journal of Electrostatics, 65(7), pp. 465-474.
[16] Zhao, L., and Adamiak, K., 2009, "Effects of EHD and External Airflows on Electric Corona Discharge in Point-Plane/Mesh Configurations," IEEE Transactions on Industry Applications, 45(1), pp. 16-21.
[17] Adamiak, K., 2013, "Numerical models in simulating wire-plate electrostatic precipitators: A review," Journal of Electrostatics, 71(4), pp. 673-680.
[18] Wu, J., Traoré, P., and Louste, C., 2013, "An efficient finite volume method for electric field–space charge coupled problems," Journal of Electrostatics, 71(3), pp. 319-325.
[19] 黃昱翔, 2015, "電暈放電產生之電液動流場數值模擬," 國立交通大學.
[20] 藍朝成, 2015, "靜電振動應用於離子風散熱之研究," 國立交通大學.
[21] Hin-Leung, C., and Wise, K. D., 1988, "An ultraminiature solid-state pressure sensor for a cardiovascular catheter," IEEE Transactions on Electron Devices, 35(12), pp. 2355-2362.
[22] Najafi, K., and Suzuki, K., "A novel technique and structure for the measurement of intrinsic stress and Young's modulus of thin films," Proc. IEEE Micro Electro Mechanical Systems, , Proceedings, 'An Investigation of Micro Structures, Sensors, Actuators, Machines and Robots', pp. 96-97.
[23] Kamisuki, S., Fujii, M., Takekoshi, T., Tezuka, C., and Atobe, M., "A high resolution, electrostatically-driven commercial inkjet head," Proc. Proceedings IEEE Thirteenth Annual International Conference on Micro Electro Mechanical Systems (Cat. No.00CH36308), pp. 793-798.
[24] Jo-Ey, W., Lang, J. H., and Schmidt, M. A., "An electrostatically-actuated MEMS switch for power applications," Proc. Proceedings IEEE Thirteenth Annual International Conference on Micro Electro Mechanical Systems (Cat. No.00CH36308), pp. 633-638.
[25] Legtenberg, R., Gilbert, J., Senturia, S. D., and Elwenspoek, M., 1997, "Electrostatic curved electrode actuators," Journal of Microelectromechanical Systems, 6(3), pp. 257-265.
[26] Hu, Y. C., Chang, C. M., and Huang, S. C., 2004, "Some design considerations on the electrostatically actuated microstructures," Sensors and Actuators A: Physical, 112(1), pp. 155-161.
[27] 許維仁, 2013, "低功率靜電式離子風振動電子散熱裝置," 國立交通大學.
[28] 黃鈺傑, 2016, "結合離子風與靜電振動增強散熱之數值模擬," 國立交通大學.
[29] 魏廷凱, 2018, "結合電暈風及靜振動於一新型熱傳增強方式之實驗分析與數值模擬," 國立交通大學.
[30] Tsui, Y.-Y., and Wu, T.-C., 2008, "A Pressure-Based Unstructured-Grid Algorithm Using High-Resolution Schemes for All-Speed Flows," Numerical Heat Transfer, Part B: Fundamentals, 53(1), pp. 75-96.
[31] Leonard, B. P., 1979, "A stable and accurate convective modelling procedure based on quadratic upstream interpolation," Computer Methods in Applied Mechanics and Engineering, 19(1), pp. 59-98.
[32] Gaskell, P. H., and Lau, A. K. C., 1988, "Curvature-compensated convective transport: SMART, A new boundedness- preserving transport algorithm," International Journal for Numerical Methods in Fluids, 8(6), pp. 617-641.
[33] Harten, A., 1983, "High resolution schemes for hyperbolic conservation laws," Journal of Computational Physics, 49(3), pp. 357-393.
[34] Sweby, P. K., 1984, "High Resolution Schemes Using Flux Limiters for Hyperbolic Conservation Laws," SIAM Journal on Numerical Analysis, 21(5), pp. 995-1011.
[35] van Leer, B., 1974, "Towards the ultimate conservative difference scheme. II. Monotonicity and conservation combined in a second-order scheme," Journal of Computational Physics, 14(4), pp. 361-370.
[36] van Albada, G. D., van Leer, B., and Roberts, W. W., 1997, "A Comparative Study of Computational Methods in Cosmic Gas Dynamics," Upwind and High-Resolution Schemes, M. Y. Hussaini, B. van Leer, and J. Van Rosendale, eds., Springer Berlin Heidelberg, Berlin, Heidelberg, pp. 95-103.
[37] N.A.Kaptsov, 1947, "Elektricheskie Yavleniya v Gazakh i Vakuume," Moscow,OGIZ.
[38] Roth, J. R., 1995, "Industrial Plasma Engineering," Institute of Physics Publishing, p. 149.