跳到主要內容

臺灣博碩士論文加值系統

(18.204.56.185) 您好!臺灣時間:2022/08/17 15:28
字體大小: 字級放大   字級縮小   預設字形  
回查詢結果 :::

詳目顯示

我願授權國圖
: 
twitterline
研究生:康有評
研究生(外文):Kang, Yu-Ping
論文名稱:雙噴流鈍體燃燒器非預混火焰結構之尺度效應研究
論文名稱(外文):Scale Effect on Nonpremixed Turbulent Flame Structure of Bluff-body Burners with Concentric Jets
指導教授:楊鏡堂楊鏡堂引用關係
指導教授(外文):Prof. Yang, Jing-Tang
學位類別:博士
校院名稱:國立清華大學
系所名稱:動力機械工程學系
學門:工程學門
學類:機械工程學類
論文種類:學術論文
論文出版年:2002
畢業學年度:90
語文別:中文
論文頁數:200
中文關鍵詞:鈍體燃燒器阻塞比
外文關鍵詞:PLIFSBluff-body burnerblockage
相關次數:
  • 被引用被引用:2
  • 點閱點閱:189
  • 評分評分:
  • 下載下載:0
  • 收藏至我的研究室書目清單書目收藏:1
本文採用實驗分析方法,系統性地變化鈍體尺寸與燃燒器出口條件,研究雙噴流圓盤鈍體燃燒器尺度大小對後方非預混火焰結構之效應。藉由中心燃料噴流與外環空氣噴流之出口速度、動量與質量流率的調整,建立不同阻塞比之火焰模式分區圖,並且成功地應用Schlieren光學系統、溫度量測系統、雷射都卜勒測速儀(LDV)及平面雷射誘發螢光質譜儀(PLIFS),探討空氣環流阻塞比(BR)、雙噴流出口速度比(γ)、動量比(MR)及質量流率比(QR)等控制參數對流場結構、熱結構與反應結構之影響。
尾流火焰結構之觀察顯示,較大的阻塞比可延緩火焰跳脫現象的發生,但阻塞比太大時,其延緩能力反而變得不穩定;當中心噴流出口速度(動量)固定時,阻塞比愈大,跳脫火焰因空氣環流出口速度(動量)增加所導致的吹熄現象愈不易發生。然而,當中心噴流質量流率固定時,阻塞比愈大,跳脫火焰因空氣環流出口質量流率增加所導致的吹熄現象反而容易產生。
尾流火焰之流場特性研究顯示,雙噴流鈍體燃燒器尾流場之流場結構可區分成五種典型的模態:分別是(a) ADV模態:迴流區流場結構由ADV (air-driven vortex)所主導;(b) A-FDV模態:流場結構由ADV與FDV (fuel-driven vortex)共同控制;(c) F-ADV模態:流場結構由FDV與ADV所共同主導,且中心噴流已穿透迴流區;(d) E-ADV模態:迴流區流場結構由中心噴流攫取效應(entrainment)與ADV共同主導;(e) HE-ADV模態:流場結構仍由中心噴流攫取效應與ADV主導,但由於中心噴流之高剪應力(high shear stress)作用增強,迴流區尺寸明顯變小。
阻塞比太小時,外環空氣之迴流能力較弱,易導致空氣主導渦漩受中心噴流牽引而拉長;較大阻塞比時,迴流區之無因次軸向高度受出口動量比主導,與阻塞比無關,但流場結構則隨阻塞比不同而有所改變;對於中心噴流主導火焰(F-ADV模態與E-ADV模態流場),固定出口動量比時,較大的紊流強度皆集中分佈於中心線兩側,其強度隨著阻塞比增加而遞減;無因次雷諾應力的正極值亦分佈於中心線兩側,與紊流強度分佈趨勢一致,但其負極值則分佈於空氣主導渦漩外側剪流層,與紊流強度分佈趨勢相反。
尾流火焰之熱與反應結構研究顯示,在ADV模態流場,氫氧自由基螢光強度分佈與溫度分佈極為吻合,侷限於迴流區內,但較大的OH基強度是沿著空氣迴流渦漩剪流層分佈;A-FDV模態時,較大的OH基螢光強度分佈於迴流區域內之右側、FSP (forward stagnation point)上游之中心噴流兩側及FSP下游之中心線區域,最大反應強度發生於空氣主導渦漩內側剪流層與中心線交會處,與高紊流強度分佈一致;F-ADV模態流場,主要反應區的位置與A-FDV模態者類似,但中心線區域之OH基螢光強度增強許多,顯示富油燃燒反應時,較大的紊流強度可增加燃燒反應。此流場之高溫區域正巧分佈在高OH基螢光強度範圍的兩側,顯示熱結構與反應結構有密切的關聯;在E-ADV模態時,由於中心噴流速度增加,燃氣混合的滯留時間變短,降低反應能力,使得中心噴流上的OH基螢光強度減弱;在HE-ADV模態時,隨著中心噴流攫取效應增大,反應強度會逐漸減弱並往迴流區上游推進,熱結構與反應結構分佈位置趨於一致。
在相同速度比下,雖然空氣外環流速度一樣,但阻塞比較大時,其空氣渦漩逆流動量反而較小,使得朝鈍體表面逆向前進的迴流渦漩,易受中心噴流的強力吸引而轉向往下游而去。因此,反應區域向流速較慢、滯流時間較長的迴流區上游推進,高溫也因而在此產生;此外,在迴流區內較大的OH基螢光強度分佈與高紊流強度分佈之間,阻塞比愈小時兩者相關性愈大,但較大的OH基螢光強度分佈與高溫分佈範圍,則隨著阻塞比增大而更趨於一致。
對不同的阻塞比,其OH基螢光分佈位置與反應強度隨著速度比而變遷的趨勢皆相同,但是當阻塞比愈大時,此現象也愈顯著;OH基螢光分佈範圍與反應強度亦會隨著質量流率比而改變,但其遷移的趨勢則隨著阻塞比增大而變得較緩和。當出口速度比固定時,動量比會隨著阻塞比增大而提高,但當質量流率比固定時,動量比反而會隨著阻塞比增大而降低。由此顯示,阻塞比、速度比與質量流率比皆為影響氫氧自由基反應區域遷移與反應強度改變之重要因素,但其背後主導的控制參數則為動量比值。
目 錄
頁次
摘要 i
誌謝 iv
目錄 v
圖表目錄 viii
符號說明 xvii
第一章 前言 1
1.1 研究動機 1
1.2 文獻回顧 4
1.2.1 迴流區特性 4
1.2.2 流場結構分析 5
1.2.3 燃燒反應對流場特性之影響 7
1.2.4 火焰型態與燃燒場特性 8
1.2.5 大尺度渦漩結構對混合之作用 9
1.2.6 雷射誘發螢光法之應用 11
第二章 實驗裝置與方法 15
2.1 實驗裝置 15
2.1.1 測試區與供氣系統 15
2.1.2 流場觀測系統 16
2.1.3 速度量測系統 17
2.1.4 溫度量測系統 22
2.1.5 氫氧自由基平面雷射誘發螢光系統 23
2.2 實驗方法 30
2.2.1 火焰影像觀察 32
2.2.2 速度場量測 32
2.2.3 溫度場量測 34
2.2.4 平面雷射誘發螢光影像觀察 34
第三章 尾流火焰結構之觀察 37
3.1 火焰型態變化 37
3.2 火焰型態分區圖 39
3.3 Schlieren 影像分析 42
第四章 尾流火焰之流場特性 44
4.1 固定阻塞比之燃燒流場特性 45
4.1.1 燃燒流場結構 45
4.1.2 燃燒流場之紊流性質 48
4.2 固定速度比之燃燒流場特性 55
4.2.1 燃燒流場結構 55
4.2.2 燃燒流場之紊流性質 57
4.3 固定動量比之燃燒流場特性 59
4.3.1 燃燒流場結構 59
4.3.2 燃燒流場之紊流性質 60
4.4 固定質量流率比之燃燒流場特性 61
4.4.1 燃燒流場結構 61
4.4.2 燃燒流場之紊流性質 63
第五章 尾流火焰之熱與反應結構 66
5.1 固定阻塞比之溫度場與反應結構分析 66
5.1.1 平均溫度與溫度擾動量分佈 66
5.1.2 燃燒反應強度分佈 70
5.2 固定速度比之溫度場與反應結構分析 74
5.2.1 平均溫度與溫度擾動量分佈 74
5.2.2 燃燒反應強度分佈 75
5.3 固定動量比之溫度場與反應結構分析 78
5.3.1 平均溫度與溫度擾動量分佈 78
5.3.2 燃燒反應強度分佈 79
5.4 固定質量流率比之溫度場與反應結構分析 80
5.4.1 平均溫度與溫度擾動量分佈 80
5.4.2 燃燒反應強度分佈 81
第六章 結論與展望 84
6.1 結論 84
6.2 未來展望 88
第七章 參考文獻 90
作者簡歷 197
著作目錄 199
Bakrozis, A. G., Papailiou, D. D., and Koutmos, P., 1999, "A Study of the Turbulent Structure of a Two-Dimensional Diffusion Flame Formed Behind a Slender Bluff-Body," Combustion and Flame, Vol. 119, pp. 291-306.
Ballal, D. R., Chen, T. H., and Schmoll, W. J., 1989, "Fluid Dynamics of a Conical Flame Stabilizer," J. Engineering for Gas Turbines and Power, Vol. 111, pp. 97-102.
Beer, J. M., and Chigier, N. A., 1983, Combustion Aerodynamics, Robert E. Krieger, Malabar, Fla., Chapter 1 and Chapter 3.
Bill, R. G. and Tarabanis, K., 1986, "The effect of Premixed Combustion on the Recirculation Zone of Circular Cylinders," Combustion Science and Technology, Vol. 47, pp. 39-53.
Carmody, T., 1964, "Establishment of the Wake Behind a Disk," Trans. ASME, J. Basic Engineering, Vol. 86, pp. 869-882.
Chen, R. H., Driscoll, J. F., Kelly, J., Namazian, M., and Schefer, R. W., 1990, "A Comparsion of Bluff-Body and Swirl-Stabilized Flames," Combustion Science and Technology, Vol. 71, pp. 197-217.
Chen, T. H. and Goss, L. P., 1991, "Statistical OH-Zone Structures of Turbulent Jet Flames from Liftoff to Near-Blowout," Combustion Science and Technology, Vol. 79, pp. 311-324.
Chen, Y. C., Chang, C. C., Pan, K. L., and Yang, J. T., 1998, "Flame Lift-off and Stabilization Mechanisms of Nonpremixed Jet Flames on a Bluff-body Burner, " Combustion and Flame, Vol. 115, pp. 51-65.
Chigier, N. A. and Beer, J. M., 1964, "The Flow Region Near the Nozzle in Double Concentric Jets," Trans. ASME, J. Basic Engineering, Vol. 86, pp. 797-804.
Chigier, N., 1989, "Velocity Measurements in Inhomogeneous Combustion Systems," Combustion and Flame, Vol. 78, pp. 129-151.
Chin, L. P. and Tankin, R. S., 1991, "Vortical Structure in a 2-D Vertical Bluff-Body Burner," Combustion Science and Technology, Vol. 80, pp. 207-229.
Daily, J. W., 1997, "Laser Induced Fluorescence Spectroscopy in Flames," Progress in Energy and Combustion Science, Vol. 23, pp. 133-199.
Davies, T. W. and Beer, J. M., 1970, "Flow in the Wake of Bluff-Body Flame Stabilizers," Thirteenth Symposium (International) on Combustion, The Combustion Institute, Pittsburgh, pp. 631-638.
Durao, D. F. G. and Whitelaw, J. H., 1978, "Velocity Characteristics of the Flow in the Near Wake of a Disk," J. Fluid Mechanics, Vol. 85, pp. 369-385.
Durst, F., Melling, A., and Whitelaw, J. H., 1981, Principles and Practice of Laser Doppler Anemometry, Academic Press, London, Chapter 4 and Chapter 10.
Dyer, M. J. and Crosley, D. R., 1982, "Two-Dimensional Imaging of OH Laser-Induced Fluorescence in a Flame," Optics Letters, Vol. 7, pp. 382-384.
Eckbreth, A. C., 1988, Laser Diagnostics for Combustion Temperature and Species, Abacus Press, Cambridge, Mass., pp. 9-25.
Eckbreth, A. C., Bonczyk, P. A., and Verdieck, J. F., 1979, "Combustion Diagnostics by Laser Raman and Fluorescence Techniques," Progress in Energy and Combustion Science, Vol. 5, pp. 253-322.
Figliola, R. S. and Beasley, D. E.,1995, Theory and Design for Mechanical Measurements, John Wiley & Sons, New York, Chapter 4.
Fujii, S. and Eguchi K., 1981, "A Comparsion of Cold and Reacting Flows Around a Bluff-Body Flame Stabilizer," Trans. ASME, J. Fluids Engineering, Vol. 103, pp. 328-334.
Gutmark, E., Parr, T. P., Hanson-Parr, D. M., and Schadow, K. C., 1989, "Azimuthal Structure of an Annular Diffusion Flame," Combustion and Flame, Vol. 75, pp. 229-240.
Hanson, R. K., 1986, "Combustion Diagnostics : Planar Imaging Techniques," Twenty-first Symposium (International) on Combustion, The Combustion Institute, Pittsburgh, pp. 1677-1691.
Hedly, A. B. and Jackson, E. W., 1965, "Recirculation and its Effects in Combustion Systems," J. the Institute of Fuel, Vol. 38, pp. 209-297.
Heitor, M. V., Taylor, A. M. K. P., and Whitelaw, J. H., 1988, "Velocity and Scalar Characteristics of Turbulent Premixed Flames Stabilized on Confined Axisymmetric Baffles," Combustion Science and Technology, Vol. 62, pp. 97-126.
Hirano, A., Ippommastu, M., and Tsujishita, M., 1992, "Two-dimensional digital Imaging of the CH Distribution in a Natural Gas/Oxygen Flame at Atmospheric Pressure and Detection of A-state Emission by means of C-state Excitation," Optics Letters, Vol. 17, No. 4, pp. 303-304.
Huang, R. F. and Lin, C. L., 1994a, "Characteristic Modes and Thermal Structure of Nonpremixed Circular-Disc Stabilized Flames," Combustion Science and Technology, Vol. 100, pp. 123-139.
Huang, R. F. and Lin, C. L., 1994b, "Visualized Flow Patterns of Double Concentric Jets at Low Annular Velocities," AIAA J., Vol. 32, pp. 1868-1874.
Huang, R. F. and Lin, C. L., 1997, "Flow Characteristics and Shear-Layer Vortex Shedding of Double Concentric Jets," AIAA J., Vol. 35, pp. 887-892.
Huang, R. F., Yang, J. T., and Lee, P. C., 1997, "Flame and Flow Characteristics of Double Concentric Jets," Combustion and Flame, Vol. 108, pp. 9-23.
Huang, R. F. and Lin, C. L., 2000, "Velocity Fields of Nonpremixed Bluff-Body Stabilized Flames," Trans. ASME, J. Energy Resources Technology, Vol. 122, pp. 88-93.
Hunt, J. C. R., Abell, C. J., Peterka, J. A., and Woo, H., 1978, "Kinematical Studies of the Flows Around Free or Surface-Mounted Obstacles; Applying Topology to Flow Visualization," J. Fluid Mechanics, Vol. 86, pp. 179-200.
Kanury, A. M., 1975, Introduction to Combustion Phenomena, Gordon and Breach Science Publishers, New York, pp. 247-249.
Kimoto, K., Shiraishi, I., and Matsumoto, R., 1981, "Structure of Turbulent Jet Flame Stabilized in Annular Air Jet," Combustion Science and Technology, Vol. 25, pp. 31-41.
Launder, B. E. and Spalding, D. B., 1972, Lectures in Mathematical Models of Turbulence, Academic Press, New York.
Lewis, B. and Von Elbe, G., 1961, Combustion, Flames and Explosions of Gases, 2nd ed., Academic Press, New York.
Li, X. and Tankin, R. S., 1987, "A Study of Cold and Combusting Flow Around Bluff-Body Combustors," Combustion Science and Technology, Vol. 52, pp. 173-206.
Locke, R. J., Hicks, Y. R., Anderson, R. C., and Ockunzzi, K. A., 1996, "OH Imaging in a Lean Burning High-Pressure Combustor," AIAA J., Vol. 34, pp. 622-624.
Masri, A. R. and Bilger, R. W., 1984, "Turbulent Diffusion Flames of Hydrocarbon Fuels Stabilized on a Bluff Body," Twentieth Symposium (International) on Combustion, The Combustion Institute, Pittsburgh, pp. 319-326.
Moreau, P. and Boutier, A., 1976, "Laser Velocimeter Measurements in a Turbulent Flame," Sixteenth Symposium (International) on Combustion, The Combustion Institute, Pittsburgh, pp. 1747-1755.
Mueller, C. J. and Schefer, R. W., 1998, "Coupling of Diffusion Flame Structure to an Unsteady Vortical Flow-Field," Twenty-seventh Symposium (International) on Combustion, The Combustion Institute, Pittsburgh, pp. 1105-1112.
Mungal, M. G., Dimotakis, P. E., and Broadwell, J. E., 1984, "Turbulent Mixing and Combustion in a Reacting Shear Layer," AIAA J., Vol. 22, pp. 797-800.
Paul, K. C., 1970, Separation of Flow, Pergamon Press, New York, pp. 336-451.
Paul, P. H. and Dec, J. E., 1994, "Imaging of Reaction Zones in Hydrocarbon-Air Flames by Use of Planar Laser-Induced Fluorescence of CH," Optics Letters, Vol. 19, pp. 998-1000.
Paul, P. H. and Hanson, R. K., 1990, "Applications of Planar Laser-Induced Fluorescence Imaging Diagnostics to Reacting Flows," Twenty-sixth Joint Propulsion Conference, AIAA-90-1848.
Pitz, R. W. and Daily, W., 1983, "Combustion in a Turbulent Mixing Layer Formed at a Rearward-Facing Step," AIAA J., Vol. 21, pp. 1565-1570.
Pope, S. B., 1990, "Computations of Turbulent Combustion : Progress and Challenges," Twenty-third Symposium (International) on Combustion, The Combustion Institute, Pittsburgh, pp. 591-612.
Prade, B. and Lenze, B., 1992, "Experimental Investigation in Extinction of Turbulent Non-Premixed Disk Stabilized Flames," Twenty-fourth Symposium (International) on Combustion, The Combustion Institute, Pittsburgh, pp. 369-375.
Quagliaroli, T. M., Laufer, G., Krauss, R. H., and McDaniel Jr., J. C., 1993, "Laser Selection Criteria for OH Fluorescence Measurements in Supersonic Combustion Test Facilities," AIAA J., Vol. 31, pp. 520-526.
Roquemore, W. M., Britton, R. L., and Sandhu, S. S., 1983, "Dynamic Behavior of a Bluff-Body Diffusion Flame," AIAA J., Vol. 21, pp. 1410-1417.
Roquemore, W. M., Tankin, R. S., Chiu, H. H. and Lottes, S. A., 1986, "A Study of a Bluff-Body Combustor Using Laser Sheet Lighting," Experiments in Fluids, Vol. 4, pp. 205-213.
Schefer, R. W., Namazian, M., and Kelly, J., 1987, "Velocity Measurements in a Turbulent Non-Premixed Bluff-Body Stabilized Flame," Combustion Science and Technology, Vol. 56, pp. 101-138.
Schefer, R. W., Namazian, M., and Kelly, J., 1989, "Comparison of Turbulent-Jet and Bluff-Body Stabilized Flames," Combustion Science and Technology, Vol. 67, pp. 123-146.
Schefer, R. W., Namazian, M., and Kelly, J., 1990, "CH, OH and CH4 Concentration Measurements in a Lifted Turbulent Jet Flames," Twenty-third Symposium (International) on Combustion, The Combustion Institute, Pittsburgh, pp. 669-676.
Schulte, G., Pein, R., and Högl, A., 1986, "Temperature and Concentration Measurements in a Solid Fuel Ramjet Combustion Chamber," J. Propulsion, Vol. 3, No. 2, pp. 114-120.
Seitzman, J. M. and Hanson, R. K., 1993, "Comparison of Excitation Techniques for Quantitative Fluorescence Imaging of Reacting Flows," AIAA J., Vol. 31, pp. 513-519.
Seitzman, J. M., ng t, A., Paul, P. H., and Hanson, R. K., 1990, "Imaging and Characterization of OH Structures in a Turbulent Nonpremixed Flame," Twenty-third Symposium (International) on Combustion, The Combustion Institute, Pittsburgh, pp. 637-644.
Takahashi, F. and Schmoll, W. J., 1990, "Lifiting Criteria of Jet Diffusion Flames," Twenty-third Symposium (International) on Combustion, The Combustion Institute, Pittsburgh, pp. 677-683.
Takahashi, F., Schmoll, W. J., Trump, D. D. and Goss, L. P., 1996, " Vortex-Flame Interactions and Extinction in Turbulent Jet Diffusion Flames," Twenty-sixth Symposium (International) on Combustion, The Combustion Institute, Pittsburgh, pp. 145-152.
Tangirala, V. and Driscoll, J. F., 1988, "Temperatures within Non-premixed Flames : Effects of Rapid Mixing Due to Swirl," Combustion Science and Technology, Vol. 60, pp. 143-162.
Taylor, A. M. K. and Whitelaw, J. H., 1984, "Velocity Characteristics in the Turbulent Near Wakes of Confined Axisymmetric Bluff Bodies," J. Fluid Mechanics, Vol. 139, pp. 391-416.
Tsau, F. H. and Strahle, W. C., 1988, "Prediction of Turbulent Combustion Flow Fields Behind a Backward Facing Step," AIAA Paper, AIAA-88-340.
Watson, K. A., Lynos, K. M., Donbar, J. M., and Carter, C. D., 1999, "Scalar and Velocity Field Measurements in a Lifted CH4-Air Diffusion Flame," Combustion and Flame, Vol. 117, pp. 257-271.
West, G. S. and Apelt, C., 1982, "The Effect of Tunnel Blockage and Aspect Ratio on the Mean Flows Past a Circular Cylinder with Reynolds Numbers Between 104 and 105," J. Fluid Mechanics, Vol. 114, pp.361-377.
Williams, F. A., 1988, Combustion Theory, 2nd ed., Addison-Wesley, New York, pp. 503-509.
Winterfeld, G., 1964, "On Processes of Turbulent Exchange Behind Flame Holders," Tenth Symposium (International) on Combustion, The Combustion Institute, Pittsburgh, pp. 1265-1275.
Yang, J. T. and Tsai, G. L., 1993, "Near-Wake Flow of a V-Gutter with Slit Bleed," Trans. ASME, J. Fluids Engineering, Vol. 115, pp. 13-20.
Yang, J. T., Yen, C. W., and Tsai, G. L., 1994, "Flame Stabilization in the Wake Flow of a Slit V-Gutter," Combustion and Flame, Vol. 99, pp. 288-294.
Yang, J. T., Chang, C. C., and Lin, M. T., 1995, "Effects of Central Jet Velocity on Non-premixed Flame of a Gas Burner with a Disc Stabilizer," The Ninth Congress and Exposition on Gas Turbines in Cogeneration and Utility, Industrial and Independent Power Generation, Vienna, Austria, Paper 95-CTP-44.
Yang, J. T. and Yen, C. W., 1996, "Reacting Flow over a Non-Traditional V-Gutter," Combustion Science and Technology, Vol. 112, pp. 95-117.
Yang, J. T., Pan, K. L. and Chang, C. C., 1997, "Effects of Recirculating Annular-Air Flow on Dynamics of Wake Flame Around a Circular Disc," Proceedings of the Sixteenth International Colloquium on the Dynamics of Explosion and Reactive Systems, Cracow, Poland, pp. 120-123.
Yang, J. T., Chang, C. C., and Pan, K. L., 2002a, "Flow Structures and Mixing Mechanisms behind A Disc Stabilizer with A Central Fuel Jet," Combustion Science and Technology, Vol. 174(3), pp. 95-126.
Yang, J. T., Chang, C. C., Pan, K. L., Kang, Y. P., and Lee, Y. P., 2002b, "Thermal Analysis and PLIF Imaging of Reacting Flow behind a Disc Stabilizer with a Central Fuel Jet," Combustion Science and Technology, Vol. 174(3), pp. 73-94.
張家齊, 1996, 鈍體燃燒器之同心雙噴流火焰結構研究, 國立清華大學動力機械工程學系博士論文.
陳建安, 1998, 二相紊流於背向階梯後之混合機制, 國立清華大學動力機械工程學系博士論文.
錢文生, 2000, 圓盤鈍體熱流場與燃燒反應之交互作用研究, 國立清華大學動力機械工程學系碩士論文.
QRCODE
 
 
 
 
 
                                                                                                                                                                                                                                                                                                                                                                                                               
第一頁 上一頁 下一頁 最後一頁 top