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研究生:李信宏
研究生(外文):Hsin-Hung Lee
論文名稱:管壁對圓管中落球所引生流場之效應研究
論文名稱(外文):Boundary-wall effect on the flow generated by a sphere falling in a pipe
指導教授:伍次寅
學位類別:博士
校院名稱:國立臺灣大學
系所名稱:機械工程學研究所
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:2005
畢業學年度:94
語文別:中文
論文頁數:104
中文關鍵詞:圓球管壁效應穩定性阻力
外文關鍵詞:spherewall effectstabilitydrag
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本文主要在於探討軸對稱管內不可壓縮定常流流場的不穩定性與流場物理現象。流場的形式為管中央的軸中心線上置有一圓球,並以軸向速度為1當作管入口與壁面的邊界條件。此一物理模型除了可探討圓球垂直落入管中受壁面效應所造成的影響外,在不考慮重力項的情形下,本文之模式即等同於一般數值計算中,以有限域來模擬無窮域均勻自由流流經圓球的情形。而改變管球徑比(D/d)的大小即可探討數值模擬中將無限域截斷成有限域所造成的誤差影響。在數值方法上,本文採用虛擬壓縮性法(pseudo-compressibility)並配合有限體積法(finite volume formulation)來計算不可壓縮流場之奈維爾-史托克(Navier-Stokes)方程式的數值解。在空間離散方面採用TVD雙曲型守恆率之高解析算則,時間離散方面則採用LUSSOR隱式解法以求得穩定的收斂值。
在流場穩定性的分析方面,本文採用線性穩定(linear stability analysis)的分析方法,並配合ARPACK程式庫以求解特徵方程組的領導特徵值,以藉此判別流場的穩定與否。計算結果顯示隨著雷諾數的增加,流場首次不穩定是發生在對稱破壞分歧點(symmetry-breaking bifurcation point)上,而在D/d=20(模擬無窮域)下臨界雷諾數為209。接著在管徑逐漸縮小的情況下,會造成臨界雷諾數(critical Reynolds number)逐次的增加並在管球徑比(D/d)等於3時達到最高,但當小於3時臨界雷諾數則會急速的降低。
另外在流場及圓球阻力的計算上,本文考慮了8種不同的管球徑比與4種不同的雷諾數情形下的流場,並採用 、 、 三種不同的網格數目,而後利用Richardson外插法得到一較高階準確的圓球阻力數值結果。此結果將與他人的實驗及無窮域模擬作比較,最後並利用計算所得之結果,經曲線擬合推導出一修正後的阻力、管球徑比及雷諾數的相關方程式。而此式不但可以分析在有限管壁下圓球的受力情形,甚至在考慮無窮域流場的情形時,亦具有相當程度的參考價值。
This work is to study the instability and the physical phenomenon for the falling sphere problem (a steady, axisymmetric, uniform flow of Newtonian fluid passing an axially-located sphere in a pipe with a moving wall). For the sake of convenience in the numerical simulation, the coordinate is set on the sphere and applies the uniform flow as the inlet velocity, the no-slip condition on the fixed sphere and moving wall with the same velocity as well as the inlet axial velocity to be the boundary conditions to simulate the problem. The boundary configuration has two objectives. The first is to study the drag on the sphere, wake length, wake width and the flow stability affected by the wall when a sphere falls into the pipe. The second is to simulate the infinite fluid passing a sphere without considering the gravity in the different numerical finite domain, and examined the truncation effect in the numerical calculation.
For the flow stability, the linear stability analysis is applied to determine the critical Reynolds number for each pipe-to-sphere diameter ratio (D/d). The finite volume method with the TVD strategy and the LUSSOR implicit scheme are adopted to solve the incompressible Navier-Stokes equations with artificial compressibility to calculate the base flow solutions and examine the flow instability to three-dimensional modal perturbations. Finally, the ARPACK package is utilized to obtain the leading eigenvalue of the resulting perturbation eigenvalue problem. The numerical results reveal that the critical Reynolds number increases gradually with the decreasing diameter ratio (D/d), but drops suddenly when D/d<3. This phenomenon is found to be related to the large pressure gradient behind the sphere and rapid pressure drop of a global minimum-pressure ring in the wake. Additionally, the bifurcation condition and the critical Reynolds number in large diameter ratios (D/d 10) are found to be consistent with the results of Natarajan and Acrivos (1993), who investigated the stability of the flow passing a sphere in an unbounded domain.
For the computation of the flow field, four different Reynolds number ranging from 50 to 200 and eight different diameter ratios (D/d=1.5~20) are selected. The results show that the wake length would vary from monotonically decreasing to asymptotically decreasing when Reynolds number exceeds 100 and diameter ratio (D/d) below 5, but the wake width still remains the tendency of monotonic decrease. Finally, a least squared regression technique is applied to collapse the calculated results into a single expression exhibiting the functional relationship between the drag coefficient, Reynolds number and the diameter ratio.
摘要 …………………………………………………………………...…I
英文摘要 ………………………………………………………………III
目錄 ………………………………………………………………….…V
附表目錄 ………………………………………………………….…VIII
附圖目錄 …………………………………………………...……….…IX

第一章 序論
1.1 引言 …………………………………………………………...1
1.2 文獻回顧 ……………………………………………………...3
1.3 本文目的 ……………………………………………………...7
1.4 本文內容 ……………………………………………………...9

第二章 統御方程式
2.1 物理模型 …………………………………………………...11
2.2 統御方程式 …………………………………………….…..11
2.3 邊界條件 …………………………………………………...18

第三章 數值方法
3.1 空間離散 ……………………………………………….…..20
3.2 時間離散 ……………………………………………...…....26
3.3 收斂條件 ……………………………………………...…....31

第四章 流場穩定性分析
4.1 理論模式 ……………………………………………...…....33
4.2 Implicitly Restarted Arnoldi method ………………....…......36
4.3 結果與討論 …………………………………………...…....42

第五章 流場數值模擬與圓球阻力
5.1 基本算例的驗證與比較 ……………………………...…....48
5.2 不同管球徑比與雷諾數之流場現象比較與探討 …...…....49
5.2.1 大管球徑比之流場 …...….........................................49
5.2.2 小管球徑比之流場 …...….........................................51
5.3 圓球阻力受管壁及雷諾數影響之探討及阻力係數公 式 …...…...............................................................................53
5.4 尾流長度、寬度受管壁及雷諾數影響之探討 ...................56

第六章 結論與未來研究方向
6.1 結論 …...…............................................................................59
6.2 未來研究方向 .......................................................................61

參考文獻 ................................................................................................62
附表 ........................................................................................................66
附圖 ........................................................................................................70
附錄A. 圓柱座標下之擾動方程式 ....................................................103
Ataide, C.H., Pereira, F.A.R. and Barrozo, M.A.S. (1999), ‘Wall effects on the terminal velocity of spherical particles in Newtonian and non-Newtonian fluids’, Braz. J. Chem. Eng., Vol.16, pp.1-12.
Bagchi, P. and Balachandar, S. (2002), ‘Steady planar straining flow past a sphere at moderate Reynolds number’, J. Fluid Mech., Vol.466, pp.365-407.
Brown, P.P. and Lawler, D.F. (2003), ‘Sphere drag and settling velocity revised’, J. Environ. Eng-ASCE., Vol.129, pp.222-231.
Chen, Y.N., Yang, S.C. and Yang, J.Y. (1999), ‘Implicit weighted essentially non-oscillatory schemes for the incompressible Navier-Stokes equations’, Int. J. Numer. Meth. Fluids, Vol.31, pp.747-765.
Chorin, A.J. (1967), ‘A numerical method for solving incompre- ssible viscous flow problems ’, J. Comput. Phys., Vol.2, pp.12-26.
Chang, J.L.C., Kwak, D., Rogers, S.E. and Yang, R.J. (1988), ‘Numerical solution methods of incompressible flows and an application to the space shuttle main engine’, Int. J. Numer. Meth. Fluids, Vol.8, pp.1241-1268.
Cliffe, K.A., Garratt, T.J. and Spence, A. (1993), ‘Eigenvalues of the discretized Navier-Stokes equations with application to the detection of Hopf bifurcations’, Adv. Comput. Math. Vol.1, pp.337-356.
Cliffe, K.A., Spence, A. and Tavener, S.J. (2000), ‘O(2)-symmetry breaking bifurcation: with application to the flow past a sphere in a pipe ’, Int. J. Numer. Meth. Fluids, Vol.32, pp.175-200.
Clift, R., Grace, J.R., and Weber, M.E. (1978), ‘Bubbles, drops, and particles’, Academic, New York.
Dennis, S.C.R. and Walker, J.D.A. (1971), ‘Calculation of the steady flow past a sphere at low and moderate Reynolds numbers’, J. Fluid Mech., Vol.48, pp.771-789.
Flemmer, R.L.C. and Banks, C.L. (1986), ‘On the drag coefficient of a sphere’, Powder Technol., Vol.48, pp.217-225.
Fornberg, B. (1988), ‘Steady viscous flow past a sphere at high Reynolds numbers’, J. Fluid Mech., Vol.190, pp.471-489.
Fox, R.W. and Macdonald, A.T. (1998), ‘Introduction to fluid mechanics’, fifth edition, pp.450.
Ghidersa, B. and Dusek, J. (2000), ‘Breaking of axisymmetry and onset of unsteadiness in the wake of a sphere’, J. Fluid Mech., Vol.423, pp.33-69.
Goldburg, A. and Florsheim, B.H. (1966), ‘Transition and Strouhal number for the incompressible wake of various bodies’, Phys. Fluids, Vol.9, pp.45-50.
Harten, A. (1983), ‘High resolution schemes for hyperbolic conservation laws’, J.Comput. Phys., Vol.49, pp.357-393.
Hundsdorfer W. and Verwer, J.G. (2003), Numerical Solution of Time Dependent Advection Diffusion Reaction Equations, Springer Ser. Comput. Math. 33, Springer-Verlag, Berlin.
Johnson, T.A. and Patel, V.C. (1999), ‘Flow past a sphere up to a Reynolds number of 300’, J. Fluid Mech., Vol.378, pp.19-71.
Johansson, H. (1974), ‘A numerical solution of the flow around a sphere in a circular cylinder’, Chem. Eng. Commun., Vol.1, pp.271-280.
Kiya, M., Ishikawa, H. and Sakamoto, H. (2001), ‘Near-wake instabilities and vortex structures of three-dimensional bodies: a review’, J. wind eng. ind. Aerody., Vol.89, pp.1219-1232.
Laney, C.B. (1998), Computational Gasdynamics, Cambridge University Press, Cambridge, UK.
Lehoucq, R.B., Sorensen, D.C. and Yang, C. (1998), ARPACK USERS’ GUIDE:Solution of Large Scale Eigenvalue Problems by Implicitly Restarted Arnoldi Methods. SIAM, Philadelphia, PA.
LeVeque, R.J. (2002), Finite Volume Methods for Hyperbolic Problems, Cambridge University Press, Cambridge, UK.
Margarvey, R.H. and Bishop, R.L. (1961), ‘Transition ranges for three- dimensional wakes’, Can. J. Phys., Vol.39, pp.1418-1422.
Magarvey, R.H. and Maclatchy, C.S. (1965), ‘Vortices in sphere wakes’, Canadian J. Phys., Vol.43, pp.1649-1656.
Magnaudet, J., Rivero, M. and Fabre, J. (1995), ‘Accelerated flows past a rigid sphere or a spherical bubble. Part 1. Steady straining flow’, J. Fluid Mech., Vol.284, pp.97-135.
Mittal, R. (1999), ‘A Fourier Chebyshev spectral collocation method for simulation flow past spheresand spheroids’, Intl. J. Numer. Meths. Fluids, Vol.30, pp.921-937.
Modi, V.J. and Akutsu, T. (1984), ‘Wall confinement effects for spheres in the Reynolds number range of 30-2000’, J. fluids eng., Vol.106, pp.66-73.
Nakamura, I. (1976), ‘Steady wake behind a sphere’, Phys. Fluids, Vol.19, pp.5-8.
Natarajan, R. and Acrivos, A. (1993), ‘The instability of the steady flow past spheres and disks’, J. Fluid Mech., Vol.254, pp.323-344.
Oh, J.H. and Lee, S.J. (1988), ‘A study on the Newtonian fluid flow past a sphere in a tube’, Korean J. Chem. Eng., Vol.5, pp.190-196.
Pruppacher, H.R., Le Clair, B.P. and Hamiliec, A.E. (1970), ‘Some relations between drag and flow pattern of viscous flow past a sphere and a cylinder at low and intermediate Reynolds numbers’, J. Fluid Mech., Vol.44, pp.781-796.
Rivkind, V.Y., Ryskin, G.M. and Fishbein, G.A. (1976), ‘Flow around a spherical drop at intermediate Reynolds numbers’, Appl. Math. Mech., Vol.40, pp.687-691.
Roe, P.L. (1981), ‘Approximate riemann solvers, parameter vectors, and difference schemes’, J. comput. Phys., Vol.43, pp.357-372.
Roe, P.L. (1986), ‘Characteristic-based upwind scheme for the Euler equations’, Annu. Rev. Fluid Mech., Vol.18, pp.337-365.
Sorensen, D.C. (1992), ‘Implicit application of polynomial filters in a k-step Arnoldi method’, SIAM. J. Matrix. Anal., Vol.13, pp.357-385.
Taneda, S. (1956), ‘Experimental investigation of the wake behind a sphere at low Reynolds numbers’, J. Phys. Soc. Japan, Vol.11, pp.1104-1108.
Tavener, S.J. (1994), ‘Stability of the O(2)-symmetric flow past a sphere in a pipe’, Phys. Fluids A., Vol.6, pp.3884-3892.
Thompson, M.C., Leweke, T. and Provansal, M. (2001), ‘Kinematics and dynamics of sphere wake transition’, J. Fluids Struct., Vol.15, pp.575-585.
Tomboulides, A.G., Orszag, S.A. and Karniadakis, G.E. (1993), ‘Direct and large-eddy simulations of axisymmetric wakes’, AIAA-93-0546.
Tomboulides, A.G. and Orszag, S.A. (2000), ‘Numerical investigation of transitional and weak turbulent flow past a sphere’, J. Fluid Mech., Vol.416, pp.45-73.
Toro, E.F. (1999), Riemann Solvers and Numerical Methods for Fluid Dynamics, Springer-Verlag, Berlin.
Turton, R. and Levenspiel, O. (1986), ‘A short note on the drag correlation for spheres’, Powder Technol., Vol.47, pp.83-86.
Van Leer, B. (1979), ‘Towards the ultimate conservative difference scheme V, a second order sequel to Godunov’s method’, J. comput. Phys., Vol.32, pp.234-245.
Werner, B. and Spence, A. (1984), ‘The computation of symmetric breaking bifurcation points’, SIAM J. Numer. Anal., Vol.21, pp.388-399.
Wham, R.M., Basaran, O.A. and Byers, C.H. (1997), ‘Wall effects on flow past solid spheres at finite Reynolds number’, Chem. Eng. Sci., Vol.19, pp.3345-3367.
Wu, J.S. and Faeth, G.M. (1993), ‘Sphere wakes in still surroundings at intermediate Reynolds numbers’, AIAA J., Vol.31, pp.1448-1455.
Yang, J.Y., Yang, S.C., Chen, Y.N. and Hsu, C.A. (1998), ‘Implicit weighted ENO schemes for the three-dimensional incompressible Navier-Stokes equations’, J. comput. Phys, Vol.146, pp.464-487.
Yoon, S. and Jameson, A. (1987), ‘An LU-SSOR scheme for the Euler and Navier-Stokes equations’, AIAA-87-0600.
Yoon, S. and Jameson, A. (1988), ‘A lower-upper symmetric Gauss Seidel method for the Euler and Navier Stokes equations’, AIAA J. Vol.26 pp.1025-1026.
馮建忠 (2000), ‘脈衝流於非等截徑彈性管(動脈血管)中之流場模擬’,國立台灣大學機械工程研究所博士論文
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1. 王士峰(1985)。電腦化資訊系統開發程序-系統分析方法。書府,64-71。
2. 吳宗立(1996)。國民中學校務行政電腦化的展望。資訊與教育,52,39-44。
3. 吳清山、黃旭鈞 (2000)。學校推動知識管理策略初探。教育研究月刊,77,18-32。
4. 李美鶯 (2002)。從「知識管理」理論分析學校行政經營與管理之道。學校行政雙月刊,21,54-63。
5. 莊明昆 (2004)。學校e化的推行策略。師說,179,29-33。
6. 陳景蔚(1989)。現階段我國推展學校行政電腦化芻議。資訊與教育,14,43-47。
7. 黃美文、吳盛、劉旭榮(2000)。「臺灣企業導入電子商務發展情形之探討」。大仁學報,18,365-378。
8. 黃超陽(2001)。花蓮縣國民小學推行校務行政電腦化問題與對策。資訊與教育,82,64-74。
9. 甄曉蘭(1995)。合作行動研究-進行教育研究的另一種方式。嘉義師院學報,19,297-318 。
10. 蔡松齡(1990)。試由「科技整合」的觀點看「學校行政電腦化」。資訊與教育,15,32-35。
11. 蔡松齡(1990)。實際推動學校行政電腦化時所遇到之障礙及尋求解決之道。資訊與教育,18,16-21。
12. 鄭明長(1993)。系統分析在學校行政決定上的應用。教育研究,32,68-73。
13. 蘇聖義(1990)。效率e 上乘的電子化建置:企業內電子化實例-敬鵬工業企 業資源 規劃系統。工業自動化電子化,3,31-34。