臺灣博碩士論文加值系統

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 本文研究卡氏網格法 (Cartesian grid method) 於含複雜邊界流場之應用性能。流場藉由 Navier-Stokes 方程及連續方程求解得之，解答邏輯過程採用分步法 (Fractional Step Method) 。以卡氏網格解答流場過程中，含複雜邊界之障礙物則以 Ravoux 等人 [1] 發展的內嵌法 (Embedding Method) 處理之。本文數值方法以具二階精準度之中央插分法離散 Navier-Stokes 方程之空間項，時間項方面則利用 Adams-Bashforth 法處理對流項，以 Crank-Nicolson 法處理擴散項。本文首先以計算方型強曳穴流 (Square lid-driven cavity flow) 測試本文數值模式於簡單邊界流場之有效性。透過與 Ghia 等人 [2] 的研究結果比對，結果十分吻合，證實本文數值模式之正確性，本文並以不同尺度網格計算結果，證實本文數值模式應用於簡單邊界流場具2階精準度。隨後，本文以 Wannier Flow 測試內嵌法於含複雜邊界流場之應用性。透過不同尺度網格之計算結果與理論解比對，我們發現本文內嵌法具1.2階精準度。最後，我們應用內嵌法於渦漩逸出流場之抑制研究，經由控制圓柱之作用，主圓柱上卡門渦漩 (Karmann vortex) 幾達完全抑制之效果。
 In this paper, a Cartesian grid method is developed for simulating unsteady, viscous, incompressible flows with complex immersed boundaries. In solving the Navier-Stokes and continuity equations, a finite volume method is used in conjunction with a two-step fractional-step procedure. The key aspect in developing a Cartesian grid method for flow with complex geometries is imposition of bluff bodies. In this study, a simple concept of Immersed Boundary method is adopted by using distributed body forces in the Navier-Stokes equations instead of the existence of bluff solid bodies. Similar procession has been applied by Ravoux et al. [1] and they referred it as Embedding method. The present Cartesian grid method has been tested by two numerical examples to examine its numerical accuracy in two dimensional problems. By conducting computations and comparisons of square lid-driven cavity flow with variety of grid sizes, the accuracy of the present fractional step method for flow with simple geometries is revealed to be 2th order. Similarly, by conducting computations of Wannier Flow with varity of grid sizes and comparisons with analytic solution, it reveals the present Cartesian grid method for complex geometry flow is 1.2th order accuracy. Flow past two circular cylinders of different diameters is then simulated by present Cartesian grid method to investigate the suppression of vortex shedding problem. The application gave reasonable and satisfactory results comparable with the available experimental and numerical results in literature and showed the feasibility of the present model.
 目錄中文摘要 Ⅰ英文摘要 Ⅱ目錄 Ⅳ圖目錄 Ⅵ表目錄 Ⅸ符號索引 Ⅹ第一章 簡介 11.1 前言 11.2 文獻回顧 21.3 研究目的 31.4 本文大綱 3第二章 理論方法 52.1 分步法（Fractional Step Method） 52.2 內嵌法 (Embedding Method) 9第三章 數值方法驗證 113.1 分步法驗證-以穴流為測試流場 113.2 內嵌法驗證 - 以Wannier Flow為測試流場 22第四章 流過兩不同直徑圓柱之流場/逸出渦漩之抑制 26第五章 結論 33參考文獻 34
 參考文獻1. Ravoux, J.F., Nadim, A., and Haj-Hariri, H., “An Embedding Methodfor Bluff Body Flows: Interactions of Two Side-by-Side CylinderWakes,” Theoretical and Computational Fluid Dynamics, Vol. 16,pp. 433–466 (2003).2. Ghia, U., Ghia, K.N., and Shin, C.T., “High-Re solutions forincompressible flow using the Navier–Stokes equations and amultigrid method,” Journal of Computational Physics, Vol. 48, pp.387-411 (1982).3. Shiau, Y.H., Peng, Y.F., Hwang, R.R., andHu,C.K., “Multistability and symmetry breaking in the 2-D flowaround a square cylinder,” Physical Review E, Vol. 60, pp. 6188-6191 (1999).4. Peskin, C. S., “Flow patterns around heart valves: a digitalcomputer method for solving the equations of motion,” Ph.D.Dissertation, Departmemt of Physiology, Albert Einstein Collegeof Medicine, University Microfilms (1972).5. Viecelli, J.A., “A method for including arbitrary externalboundaries in the MAC incompressible fluid computing technique,”Journal of Computational Physics, Vol. 4, pp. 543-551 (1969).6. Hirt, C.W., and Nichols, B.D. “Volume of fluid (VOF) method fordynamics of free boundaries,” Journal of Computational Physics,Vol. 39, pp. 201-225 (1981).7. Ye, T., Mittal, R., Udaykumar, H.S., and Shyy, W., “An accurateCartesian grid method for viscous incompressible flows withcomplex immersed boundaries,” Journal of Computational Physics,Vol. 156, pp. 209-240 (1999).8. Choi, J.I., Oberoi, R.C., Edwards, J.R., and Rosati, J.A., “Animmersed boundary method for complex incompressible flows,”Journal of Computational Physics, Vol. 224, pp. 757-784 (2007).9. Peng, Y.F., Shiau, Y.H., and Hwang, R.R., “Transition in a 2-Dlid-driven cavity flow,” Computers & Fluids, Vol. 32, pp. 337-352(2003).10. Wannier, G.H., “A contribution to the hydrodynamics oflubrication,” Quarterly of Applied Mathematics, Vol. 8, No. 1(1950).11.Strykowski, B.J., and Sreenivasan, K.R., “On the formation andsuppression of vortex ‘shedding’ at low Reynolds numbers,”Journal of Fluid Mechanics, Vol. 218, pp. 71-107 (1990).12. H. Sakamoto, K. Tan, and H. Haniu, “An optimum suppression offluid forces by controlling a shear layer separated from a squareprism,” Journal of Fluids Enggineering, Vol. 113, pp. 183-189(1991).13. Sakamoto, H., and Haniu, H., “Optimum suppression of fluidforces acting on a circular cylinder,” Journal of FluidsEnggineering, Vol. 116, pp. 221-227 (1994).14. Dalton, C., Xu, Y., and Owen, J.C., “The Suppression of lift ona circular cylinder due to vortex shedding at moderate Reynoldsnumbers,” Journal of Fluids and Structures, Vol. 15, pp. 61-128(2001).15. Zhao, M., Cheng, L., Teng, B., and Liang, D., “Numericalsimulation of viscous flow past two circular cylinders ofdifferent diameters,” Applied Ocean Research, Vol. 27, pp. 39-55(2005).16. Delaunay, Y., and Kaiktsis, L., “Control of circular cylinderwakes using base mass transpiration,” Physics and Fluids, Vol.13, No. 11, pp. 3285-3302 (2001).17. Young, D.L., Huang, J.L., and Eldho, T.I., “Simulation oflaminar vortex shedding flow past cylinders using a coupled BEMand FEM model,” Computer Methods in Applied Mechanics andEngineering, Vol. 190, pp. 5975-5998 (2001).18. Lei, C., Cheng, L., and Kavanagh, K., “A finite differencesolution of the shear flow over a circular cylinder,” OceanEngineering, Vol. 27, pp. 271-290 (2000).
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