本文以流場可視化法及PIV量測法研究靜止外罩內同步旋轉雙圓盤間流場之動力特性。流場可視化法利用雷射光頁照射懸浮質點以顯現量測平面上之流動結構。雙圓盤間之流體會因圓盤與轉軸幾何變化關係及不同轉速而形成具規則外型之多邊形流動結構。多邊形流動結構之外型轉換受到雷諾數與轉軸幾何之影響：轉軸外徑較大時，造成流動結構外型轉換之雷諾數較小。多邊形流動結構與圓盤並不同步轉動，其轉動頻率相對於圓盤頻率之比值為—五邊形：0.8；四邊形：0.75；三角形：0.69；橢圓形：0.6。PIV量測獲得速度時序資料，以時間平均及相位解析法進行分析，得到速度場及紊流特性。速度時序資料以頻譜分析獲得定量化之流場特徵頻率，該特徵頻率與流場可視化所認知之現象一致。時間平均速度分佈之斜率隨徑向位置改變，自轉軸至外罩間可分為四個特徵區域：似固體轉動區(solid-body-rotation-like region)、過渡區(buffer region)、渦旋結構區(vortex region)及外罩影響區(shroud-influenced region)。相位解析法所獲得之相對速度向量及流線圖均顯示在多邊形流動結構與外罩間存在渦旋結構，且該渦旋結構之數量與多邊形流動結構之邊數相同。紊流分析將瞬時速度分解成時間平均項、週期性波動項及紊流擾動項，據以研究各擾動項對於流場中紊流特性之影響。分析結果顯示，整體擾動強度分佈區域內之極大及極小值位置與週期性波動強度一致。雷諾應力分析結果，流場中周向及徑向雷諾正向應力高於雷諾剪應力。而雷諾剪應力分佈極大值出現在過渡區與渦旋結構區之間，顯示該位置具有明顯紊流動量交換現象。Lagrangian時間與尺寸之積分尺度分佈與多邊形流動結構及流場特徵區域有明顯關係。

Flow characteristics in the interdisk midplane between two shrouded co-rotating disks were experimentally studied. A laser-assisted particle-laden flow-visualization method was used to identify the qualitative flow behaviors. Particle image velocimetry was employed to measure the instantaneous flow velocities. The flow visualization revealed rotating polygonal flow structures (hexagon, pentagon, quadrangle, triangle, and oval) existing in the core region of the interdisk spacing. There existed a difference between the rotating frequencies of the polygon and the disks. The rotating frequency ratio between the polygonal flow structure and the disks depended on the mode shapes of the polygonal flow structures—0.8 for pentagon, 0.75 for quadrangle, 0.69 for triangle, and 0.6 for oval. The radial distributions of the time-averaged and phase-resolved ensemble-averaged circumferential and radial velocities were presented. Five characteristic regions (solid-body-rotation-like region, buffer region, vortex region, and shroud-influenced region) were identified according to the prominent physical features of the flow velocity distributions. The phase-resolved, ensemble-averaged relative radial velocity profiles in the interdisk midplane at various phase angles exhibited grouping behaviors in three ranges of polygon phase angles (θ = 0 and α/2, 0 < θ < α/2, and ?悈\/2 < θ < α). Circumferential and radial turbulence intensities, Reynolds stresses, turbulence kinetic energy, correlation coefficients, as well as the Lagrangian integral time and length scales of turbulent fluctuations were analyzed and presented. Features of the turbulence properties were found to be closely related to the rotation motion of the inner and outer characteristic flow structures. The circumferential components of the turbulence properties exhibited local minima in the buffer region and maxima in the solid-body rotation and vortex regions, while the radial components of the turbulence intensity, turbulent normal stress, and Lagrangian integral turbulence time scale exhibited maximum values in the buffer region and relatively low values in the regions near the hub and the shroud.

中文摘要 i
英文摘要 ii
誌謝 iii
目錄 iv
符號索引 vii
表圖目錄 ix
第一章 緒論 1
1.1研究動機 1
1.2文獻回顧 2
1.3研究目的 8
第二章 實驗設備、儀器及方法 9
2.1 實驗設備與座標定義 9
2.1.1 實驗設備 9
2.1.2 試驗質點特性分析 11
2.1.3 實驗座標定義 13
2.2 實驗量測方法 13
2.2.1 雷射光頁與流場可視化法 13
2.2.2質點影像速度儀與速度量測方法 15
2.3 PIV速度分析 21
2.3.1 時間平均法 21
2.3.2 相位解析平均法 22
2.4 實驗不準度及誤差分析 24
2.5 實驗因次分析 25
第三章 流場模態與特徵變化 27
3.1 多邊形流動特徵結構 27
3.2 多邊形流動結構運動分析 34
3.3橫截面流場可視化結果 36
3.4 阻塞比(Rhd)對流場之影響 37
第四章 時間平均流場特性 39
4.1 雙圓盤間中心平面流場特性 39
4.2 雙圓盤間中心平面時間平均速度分佈與特徵 47
4.3 橫截面時間平均流場 55
第五章 相位解析平均流場特性 60
5.1 雙圓盤間中心平面相對速度場流動結構 61
5.2 雙圓盤間中心平面絕對速度之分佈與特徵 71
5.3渦度場 75
第六章 紊流分析 76
6.1流場擾動強度 77
6.2 雷諾應力與紊流動能 82
6.3 紊流積分尺度 85
第七章 結論與建議 90
7.1 結論 90
7.2建議 92
參考文獻 93

[1] Schlichting, H., Boundary Layer Theory, McGraw-Hill, New York, 1979.
[2] Batchelor, G. K., “Note on a class of solutions of the Navior-Stokes equations representing steady rotationally-symmetric flow,” Quart. J. Mech., Vol. 4, 1951, pp. 29-41.
[3] Greenspan, H., The Theory of Rotating Fluids, Cambridge University Press, Cambridge, 1969.
[4] Owen, J. M., Rogers, R., Flow and Heat Transfer in Rotating Disk Systems, Vol. 1: Rotor-Stator Systems, John Wily & Sons, New York, 1989.
[5] Childs, P. R. N., Rotating Flow, Butterworth-Heinemann, Burlington, USA, 2011.
[6] Crespo del Arco, E., Serre, E., Bontoux, P., Launder, B. E., “Stability, transition and turbulence in rotating cavities,” in Instability of Flows, Rahman M. (Ed.), WIT Press, Milton Keynes, UK, 2005.
[7] Akhmetov, D. G., Tarasov, V. F., “Structure and evolution of vortex cores,” J. Applied Mech. Tech. Physics, Vol. 27, No. 5, 1986, pp. 690-694.
[8] Lennemann, E., “Aerodynamics aspects of disk files,” IBM J. Res. Develope, Vol. 18, No. 6, 1974, pp. 480-488.
[9] Kaneko, R., Oguchi, S., Hoshiya, K., “Hydrodynamic characteristics in disk packs for magnetic storage,” Rev. Elect. Comm. Lab., Vol. 25, No. 11-12, 1977, pp. 1325-1336.
[10] Abrahamson, S. D., Eaton, J. K., Koga, D. J., “The flow between shrouded corotating disks,” Phys. Fluids, Vol. 1, No. 2, 1989, pp. 241-251.
[11] Schuler, C. A., Weber, U. B., Humphrey, J. A. C., Greif, R., “On the flow in the unobstructed space between shrouded corotating disks,” Phys. Fluids, Vol. 2, No. 10, 1990, pp. 1766-1770.
[12] Tzeng, H.-M., Munce, A. C., Crawforth, L., “Quantitative airflow visualization between shrouded corotating disks,” in Experimental and Numerical Flow Visualization, Khalighi B. (Ed.), Vol. 128, 1991, pp. 141-147.
[13] Funaki, J., Takizawa, K., Hirata, K., Yano, H., “Flow modes in gap between coaxial rotating disks,” Trans. Jpn. Soc. Mech. Eng. : Ser. B, Vol. 81, No. 588, 1995, pp. 2924-2929. (In Japanese)
[14] Herrero, J., Giralt, F., Humphery, J. A. C., “Influence of the geometry on the structure of the flow between a pair of corotating disks,” Phys. Fluids, Vol. 11, No. 1, 1999, pp. 88-94.
[15] Wu, S. C., Chen, Y. M., “Phase-averaged method applied to periodic flow between shrouded corotating disks,” Int. J. Rotating Mach., Vol. 9, No. 4, 2003, pp. 293-301.
[16] Tsai, Y. S., Chang, Y. M., Chang, Y. J., Chen, Y. M., “Phase-resolved PIV measurements of the flow between a pair of corotating disks in a cylindrical enclosure,” J. Fluids Structures, Vol. 23, No. 1, 2007, pp. 191-206.
[17] Picha, K. G., Eckert, E. R. G., “Study of the air flow between coaxial disks rotating with arbitrary velocities in an open or enclosed space,” in Proc. 3rd U. S. Nat. Congress of Applied Mechanics, ASME, New York, 1958, pp. 791-798.
[18] Flagan, R. C., Seinfeld, J. H., Fundamentals of Air Pollution Engineering, Prentice-Hall, New Jersey, 1988, pp. 290-357.
[19] Raffel, M., Willert, C., Kompehans, J., Particle Image Velocimetry: A Practicle Guide, Springer, Berlin Heidelberg, Germany, 1998.
[20] Adrain, R. J., “Particle-imaging techniques for experimential fluid mechanics,” Annu. Rev. Fluid Mech., Vol. 23, 1991, pp. 261-304.
[21] Adrian, R. J., “Twenty years of particle image velocimetry,” Exp. Fluids, Vol. 39, 2005, pp. 159-169.
[22] Grant, I. (Ed.), Selected Papers on Particle Image Velocimetry, The Society for Optical Engineering (SPIE), Washington, USA, 1994.
[23] Tsai, Y. S., On the Flow between A Pair of Corotating Disks in A Cylindrical Enclosure, PhD Thesis, National Taiwan University, 2006. (In Chinese)
[24] Perry, A. E., Lim, T. T., Chong, M. S., “The instantaneous velocity fields of coherent structures in co-flowing jets and wakes,” J. Fluids Mech., Vol. 101, 1989, pp. 243-256.
[25] Palmer, A. C., Dimensional Analysis and Intelligent Experimentation, World Scientific, Singapore, 2008.
[26] 談慶明，量綱分析，中國科學技術大學出版社，合肥，2005.
[27] Buckingham, E., “On physically similar systems: illustrations of the use of dimensional equations,” Phys. Rev., Vol. 4, 1914, pp. 345-376.
[28] Welsh, W. E., Hartenett, J. P., “Velocity measurements in the boundary layer and in the main flow between two coaxial disks rotating with equal velocities in air,” in Proc. 3rd U. S. Nat. Congress of Applied Mechanics, ASME, New York, 1958, pp. 847-855.
[29] Shirai, K., Yaguchi, Y., Buttner, L., Czarske, J., Obi, S., “Highly spatially resolving laser Doppler velocity measurements of the tip clearance flow inside a hard disk driver model,” Exp. Fluids, Vol. 50, 2011, pp. 573-586.
[30] Hirata, K., Furue, M., Sugawara, N., Funaki, J., “An experimental study of three-dimensional vortical structures between co-rotating disks,” J. Phys.: Conference Series, Vol. 14, 2005, pp. 213-219.
[31] Miura, T., Mizushima, J., “Stability of flow between two corotating disks in an enclosure,” Phys. Fluids, Vol. 19, 2007, pp. 068106-1 ~ 14.
[32] Mizushima, J., Sugihara, G., Miura, T., “Two modes of oscillatory instability in the flow between a pair of corotating disks,” Phys. Fluids, Vol. 21, 2009, pp. 014101-14.
[33] Humphrey, J. A. C., Chang, C. J., Li, H. W., Schuler, C. A., “Unobstructed and obstructed rotating disk flows: A summary review relevant to information storage systems,” Advances in Information Storage Systems, ASME, Vol. 1, 1991, pp. 79-110.
[34] Wu, S. J., The Flow between Corotating Disks with/without An Obstruction in A Cylindrical Enclosure, PhD Thesis, National Taiwan University, 2000. (In Chinese)
[35] Batchelor, G. K., An Introduction to Fluid Dynamics, Cambridge University Press, Cambridge, 1967.
[36] Rabaud, M., Couder, Y., “A Shear-flow instability in a circular geometry,” J. Fluid Mech., Vol. 136, 1983, pp.291-319.
[37] Cooley, J. W., Tukey, J. W., “An algorithm for the machine compution of complex Fourier Series,” Math. Comput., Vol. 19, 1965, pp. 277-301.
[38] Tzeng, H. M., Humphrey, J. A. C., “Corotating disk flow in an axisymmetric enclosure with and without a bluff body,” Int. J. Heat and Fluid Flow, Vol. 12, No. 3, 1991, pp. 194-201.
[39] Amemiya, K., Masuda, S., Obi, S., Tokuyama, M., Imai, S., “Flow between shrouded corotating disks,” Trans. Jpn. Soc. Mech. Eng. Ser. B, Vol. 66, No. 650, 2000, pp. 2559-2564. (In Japanese)
[40] Kong, D. W., Joo, W. G., Doh, D. H., “Visualization of the transitional flow patterns at the mid-span between shrouded co-rotating disks,” J. Visualization, Vol. 10, No. 4, 2007, pp. 381-388.
[41] Wu, S.-C., “A PIV study of co-rotating disks flow in a fixed cylindrical enclosure,” Exp. Thermal Fluid Sci., Vol. 33, No. 5, 2009, pp. 875-882.
[42] Gor, D., Humphrey, J. A. C., “Ventilated flow in the unobstructed space between corotating disks in a cylindrical enclosure,” Trans. ASME, J. Fluids eng., Vol. 115, Sep., 1993, pp. 398-407.
[43] Hide, R., Titman, C. W., “Detached shear layer in a rotating fluid,” J. Fluid Mech., Vol. 29, Part 1, 1967, pp. 39-60.
[44] Lighthill, M. J., “Attachment and separation in three-dimensional flow”, in Laminar Boundary Layers, Rosenhead L. (Ed.), Oxford University Press, Cambridge, 1963, pp. 72-82.
[45] Perry, A. E., Fairlie, B. D., “Critical points in flow patterns,” Adv. Geophys., Vol. 18, Part B, 1974, pp. 299-315.
[46] Hunt, J. C. R., Abell, C. J., Peterka, J. A., Woo, H., “Kinematical studies of the flows around free or surface-mounted obstacles; applying topology to flow visualization,” J. Fluid Mech., Vol. 86, No. 1, 1978, pp. 299-446.
[47] Tobak, M., Peake, D. J., “Topology of two-dimensional and three dimensional separation flows,” AIAA-79-1480, 1979.
[48] Tobak, M., Peake, D. J., “Topology of three-dimensional separated flows,” NASA-TM-81294, 1981.
[49] Chong, M. S., Perry, A. E., Cantwell, B. J., “A general classification of three-dimensional flow fields,” Phys. Fluids A, Vol. 2, No. 5, 1990, pp. 765-777.
[50] Hesselink, L., Helman, J., Ning, P., “Quantitative image processing in fluid mechanics,” Exp. Thermal Fluids Sci., Vol. 5, 1992, pp. 605-616.
[51] Coutanceau, M., Pineau, G., “Some typical mechanisms in the early phase of the vortex-shedding process from particle-streak visualization,” Atlas of visualization III, CRC press, 1997, pp. 43-68.
[52] Randriamampianina, A., Schiestel, R., Wilson, M., “The turbulent flow in an enclosed corotating disk pair: axisymmetric numerical simulation and Reynolds stress modeling,” Int. J. Heat and Fluid Flow, Vol. 25, 2004, pp. 897-914.
[53] Tennekes, H., Lumley J. L., A First Course in Turbulence, MIT Press, Cambridge, 1983.
[54] Pope, S. B., Turbulent Flows, Cambridge University Press, Cambridge, 2000.
[55] Evans, R. L., “Some turbulence and unsteadiness effects in turbomachinery”, in Turbulence in Internal Flow, Murphy S. N. B. (Ed.), Hemisphere Publishing, Washington D. C., 1977.
[56] Reynolds, W. C., Hussain, A. K. M. F., “The mechanics of an organized wave in turbulent shear flow. Part 3. Theoretical models and comparisons with experiments,” J. Fluid Mech., Vol. 54, Part 2, 1972, pp. 263-288.
[57] Kundu, P. K., Cohen, I. M., Dowling, D. R., Fluid Mechanics, Academic Press, Waltham, USA, 2012.
[58] 章梓雄、董曾南，黏性流體力學，清華大學出版社，北京，1998。
[59] Sheng, J., Meng, H., Fox, R. O., “A large eddy PIV method for turbulence dissipation rate estimation,” Chem. Eng. Sci., Vol. 55, 2000, pp. 4453-4434.
[60] Liu, X. H., Min, J., Pan, C. M., Gao, Z. M., Chen, W. M., “Investigation of turbulence kinetic energy dissipation rate in a stirred tank using large eddy PIV approach,” Chin. J. Process Eng., Vol. 8, No. 3, 2008, pp. 425-431.
[61] Elsner, J. W., Elsner, W., “On the measurement of turbulence energy dissipation,” Meas. Sci. Technol., Vol. 7, 1996, pp. 1334-1348.
[62] Taylor, G. I., “The spectrum of turbulence,” Proc. R. Soc. Lond. A, Vol. 164, 1938, pp. 476-490.
[63] Pinsky, M., Khain, K., Tsinober, A., “Accelerations in isotropic and homogeneous turbulence and Taylor’s hypothesis,” Phys. Fluids, Vol. 12, No. 12, 2000, pp. 3195-3204.