簡易檢索 / 詳目顯示

回結果列表
研究生： 朱迪諾
Dedy - Zulhidayat Noor
論文名稱： 沉侵邊界法於流固耦合作用之應用研究
Boundary Method to Fluid-Structure Interaction Problems
指導教授： 陳明志
Ming-Jyh CHERN
口試委員: 趙修武
Shiu-Wu Chau
張倉榮
none
朱佳仁
none
洪子倫
none
學位類別： 博士
Doctor
系所名稱： 工程學院 - 機械工程系
Department of Mechanical Engineering
論文出版年： 2010
畢業學年度： 98
語文別： 英文
論文頁數： 107
中文關鍵詞： 沉浸邊界法 、固體體積 、虛擬力 、虛擬熱源
外文關鍵詞： Immersed boundary, virtual force, heat source, fluid-structure interaction
相關次數： 點閱：231  下載：5 
分享至:
查詢本校圖書館目錄 查詢臺灣博碩士論文知識加值系統 勘誤回報

    • 這個方法主要是將一在流場中靜止愛動中的固體在每一離時間步驟先以流體方式來求解，接著在流場中被固體所佔有的空間於動量方程式中加上一虛擬力，籍以求解此固體對流體造成的作用力。同理，若固體為具有熱源之物體，也可在具流場中被固體佔有之區域的能量方程式中加上虛擬熱源。此沉浸邊界模式首先應用於一已事先知道運動尻跡與方式的固體與流體之交互作用。接著此模式也成功應用於預測一受流體作用而運動之固體，例如一在重力場中自由落下之橢圓物體受空氣影響而造成不同的運動模式，因此可知本研究所建立之沉浸邊界模式可有效地應用於流固耦合作用。

    An immersed boundary method with both virtual and heat source is developed here to solve Navier-Stokes and the associated energy transport equations. the key point of this novel nemerical method is that the solid object, stationary or moving, is first treated as fluid governed by Navier-Stokes equations for velocity and pressure, and by energy transport equation for temperature in every time step. An additional virtual force term is then compensated to the right hand side of mementum equations at the solid object region to make it acting mechanically like a solid rigid body immersed tn fluid exactly. Likewise, an additional virtual heat source term is applied to the right hand side of energy equation at the solid object region. For the case of moving objects without a prescribed velocity, the motion of object is tracked in Lagrangian reference by the equations of linear and angular momentum. We simulated some well-known and interesting cases to demonstrated the capability of the proposed method in handling fluid-structure interactions

    CONTENTS CHINESE ABSTRACT . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . i ABSTRACT . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . i ACKNOWLEDGEMENTS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . iii CONTENTS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . iii NOMENCLATURES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . viii LIST OF TABLES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xi LIST OF FIGURES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xiv 1 INTRODUCTION 1 1.1 Motivations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1.2 Literature review and the current method . . . . . . . . . . . . . . . . . . 4 1.3 Synopsis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10 2 MATHEMATICAL FORMULAE AND NUMERICAL METHOD 13 2.1 The governing equations . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13 2.2 The methods to solve the Navier-Stokes and energy equations . . . . . . . 14 2.2.1 Discretization of the diffusive terms . . . . . . . . . . . . . . . . . . 14 2.2.2 Discretization of convective terms . . . . . . . . . . . . . . . . . . . 16 CONTENTS 2.2.3 Temporal discretization . . . . . . . . . . . . . . . . . . . . . . . . . 17 2.2.4 Pressure-velocity coupling . . . . . . . . . . . . . . . . . . . . . . . 18 2.3 Hardware and computational time . . . . . . . . . . . . . . . . . . . . . . . 19 2.4 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20 3 VALIDATION OF IN-HOUSE NUMERICAL CODE FOR THE NAVIER- STOKES AND ENERGY EQUATIONS 21 3.1 Problem description and numerical procedures . . . . . . . . . . . . . . . . 24 3.1.1 Problem description . . . . . . . . . . . . . . . . . . . . . . . . . . 24 3.1.2 The governing equations . . . . . . . . . . . . . . . . . . . . . . . . 24 3.1.3 Validation of the in-house numerical code . . . . . . . . . . . . . . . 27 3.2 Numerical results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30 3.2.1 Flow patterns . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30 3.2.2 Isothermal profiles and average Nusselt numbers . . . . . . . . . . . 42 3.3 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49 4 IMMERSED BOUNDARY METHOD 51 4.1 The immersed boundary method with a prescribed motion of a solid body 53 4.2 The immersed boundary method without a prescribed motion of a solid body 56 4.3 The immersed boundary method for heat transfer problems . . . . . . . . . 57 4.4 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61 5 UNIFORM FLOW PAST STATIONARY OBJECTS 63 5.1 The flow past a stationary circular cylinder . . . . . . . . . . . . . . . . . . 63 5.2 The flow past two stationary circular cylinders in tandem . . . . . . . . . . 66 CONTENTS 5.3 The flow past two stationary side-by-side circular cylinders . . . . . . . . . 68 5.4 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69 6 FLUID-STRUCTURE INTERACTION PROBLEMS WITH HEAT TRANS- FER 71 6.1 Forced convection over a heated circular cylinder . . . . . . . . . . . . . . 71 6.2 Natural convection in a square enclosure with a heated circular cylinder . . 74 6.3 Mixed convection in a square enclosure with a moving heated circular cylinder 77 6.4 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83 7 FREELY FALLING OBJECTS 85 7.1 Sedimentation of cylinders . . . . . . . . . . . . . . . . . . . . . . . . . . . 85 7.2 Freely falling ellipses . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 88 7.3 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 95 8 CONCLUSIONS AND FUTURE WORK 97 8.1 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 97 8.2 Future works . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 99 BIBLIOGRAPHY . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101 PUBLICATIONS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 109

    [1] Versteeg, H.K. and Malalasekera, W., 1995, An Introduction to Computational Fluid Dynamics. Longman Group Ltd., Sussex, England.

    [2] Source : http://www.me.jhu.edu/lefd/turbo/introduction.html.

    [3] Source : http://www.friendship.system.com.

    [4] Thompson, J.F., Warsi, Z.U.A., and Mastin, C.W., 1985, Numerical Grid Generation : Fundamentals and Applications, Elsevier Science Publishing Co. Inc.

    [5] Karman, S.L. , 1995, SPLITFLOW: A 3d unstructured Cartesian/prismatic grid
    CFD code for complete geometries. AIAA Paper, pp. 95-0343.

    [6] Wang, Z.J., 1998, A quadtree-based adaptive Cartesian/quad grid °ow solver forNavier-Stokes equations. Computers and Fluids 27 No. 4, pp. 529-549.

    [7] Fujimoto, K., and Fujii, K., 2007, Optimization-based robust feature preserving technique for body-fitted Cartesian grid method. Proceedings of 10th ISGG Conference on Numerical Grid Generation, Crete, Greece.

    [8] Fujimoto, K., Fujii, K. and, Wang, Z.J., 2009, Improvements in the reliability and effciency of body-fitted Cartesian grid method. 47th AIAA Aerospace Sciences Meeting Including The New Horizons Forum and Aerospace Exposition, Orlando Florida, USA.

    [9] Hirt, C.W., Amsden, A.A., and Cook, J.L., 1974, An arbitrary Lagrangian-Eulerian computing method for all °ow speeds. Journal of Computational Physics 14, pp. 227-253. Reprinted in 1997 Journal of Computational Physics 135, 203-216.

    [10] Bailey, D., Berndt, M., Kucharik, M., and Shashkov, M., 2009, Reduced-dissipation remapping of velocity in staggered arbitrary Lagrangian-Eulerian methods. Journal of Computational and Applied Mathematics.

    [11] Kucharik, M., Liska, R., and Shashkov, M., 2006, Conservative remapping and ALE methods for plasma physics. Proceedings of HYP 2004, Tenth International Conference on Hyperbolic Problems: Theory, Numerics, Applications 2, editors Asakura, F.,Kawashima,S. Matsumura,A. Nishibata, S. and Nishihara, K. Yokohama publishers,
    ISBN 4-946552-22-7.

    [12] Benson, D.J., 1992, Computational methods in Lagrangian and Eulerian hydrocodes.
    Computer Methods in Applied Mechanics and Engineering 99, pp. 235-394.

    [13] Kjellgren, P., and Hyvarinen, J., 1998, An arbitrary Lagrangian-Eulerian ‾nite element method. Computational Mechanics 21, pp. 81-90.

    [14] Peery, J.S., and Carrol, D.E., 2000, Multi-material ALE methods in unstructured grids. Computer Methods in Applied Mechanics and Engineering 187, pp. 591-619.

    [15] Peskin, C.S., 1972, Flow patterns around heart valve: a numerical method. Journal of Computational Physics 10, pp. 252-271.

    [16] Goldstein, D., Handler, R., and Sirovich, L., 1993, Modeling and no-slip flow boundary with an external force field. Journal of Computational Physics 105, pp. 354-366.

    [17] Saiki, E.M. and Biringen, S., 1996, Numerical simulation of a cylinder in uniform flow: application of a virtual boundary method. Journal of Computational Physics 123, pp. 450-365.
    [18] Lai, M.C. and Peskin, C.S., 2000, An immersed boundary method with formal secondorder accuracy and reduced numerical viscosity. Journal of Computational Physics 160, pp. 705-719.

    [19] Su, S.W., Lai, M.C., and Lin, C.A., 2007, An immersed boundary technique for simulating complex flows with rigid boundary. Computers and Fluids 36, pp. 313-324.

    [20] Yusof, J.M., 1996, Interaction of massive particles with turbulence. PhD. Dissertation, Dept. of Mechanical and Aerospace Engineering, Cornell Univ.

    [21] Ye, T., Mittal, R., Udaykumar, H.S. and Shyy, W., 1999, An accurate Cartesian grid method for viscous incompressible flows with complex immersed boundaries. Journal of Computational Physics 156, pp. 209-240.

    [22] Fadlun, E.A., Verzicco, R., Orlandi, P. and Yusof, J.M., 2000, Combined immersed-boundary finite-difference method for three dimensional complex °ow simulations.Journal of Computational Physics 161, pp. 35-60.

    [23] Tseng, Y.H. and Ferziger J.H., 2003, A ghost-cell immersed boundary method for flow in complex geometry. Journal of Computational Physics 192, pp. 593-623.

    [24] Zhang, N. and Zheng, Z.C., 2007, An improved direct-forcing immersed-boundary method for finite difference applications. Journal of Computational Physics 221, pp. 250-268.

    [25] Paravento, F., Pourquie, M.J., and Boersma, B.J., 2007, An immersed boundary method for complex flow and heat transfer. Flow Turbulence Combustion. 80, pp.187-206.

    [26] Vega, A.P., Pacheco, J.R., and Rodic, T., 2007, A general scheme for the boundary conditions in convective and diffusive heat transfer with immersed boundary methods. Journal of Heat Transfer 129, pp. 1506-1516.

    [27] Pan, D., 2006, An immersed boundary method on unstructured Cartesian meshes for incompressible flows with heat transfer. Numerical Heat Transfer: Part B 49, pp. 277-297.

    [28] Wang, Z., Fan, J., and Luo, K., 2008, Combined multi-direct forcing and immerse boundary method for simulating flows with moving particles. International Journal of Multiphase Flow 34, pp. 283-302.

    [29] Uhlmann, M., 2005, An immersed boundary method with direct forcing for the simulation of particulate flows. Journal of Computational Physics 209, pp. 448476.
    [30] Dhole, S.D., Chhabra, R.P., and Eswaran, V., 2006, A numerical study on the forced convection heat transfer from an isothermal and isoflux sphere in the steady symmetric flow regime. International Journal of Heat and Mass Transfer 49, pp. 984-994.

    [31] Noor, D.Z., Chern, M.J., and Horng, T.L., 2009, An immersed boundary method to solve fluid-solid interaction problems, Computational Mechanics 44, pp. 447-453.

    [32] Noor, D.Z., Kanna, P.R., and Chern, M.J., 2009, Flow and heat transfer in a driven square cavity with double-sided oscillating Lids in Anti-Phase, International Journal of Heat and Mass Transfer 52, pp. 3009-3023.

    [33] Gupta, M.M. and Manohar, R.P., 1979, Boundary approximations and accuracy in viscous flow computations. Journal of Computational Physics 31, pp. 265-288.

    [34] Benjamin, A.S. and Denny, V.E., 1979, On the convergence of numerical solutions for 2-D flows in a cavity at large Re. Journal of Computational Physics 33, pp. 340-358.

    [35] Ghia, U., Ghia, K.N., and Shin, C.T., 1982, High-Re solutions for incompressible flow using the NavierStokes equations and a multigrid method. Journal of Computational Physics 48, pp. 387-411.

    [36] Schreiber, R. and Keller, H.B., 1983, Driven cavity flows by e±cient numerical techniques. Journal of Computational Physics 49, pp. 310-333.

    [37] Barragy, E. and Carey, G.F., 1997, Stream function-vorticity driven cavity solutions using p finite elements. Computers and Fluids 26, pp. 453-468.

    [38] Aydin, M. and Fener, R.T., 2001, Boundary element analysis of driven cavity flow for low and moderate Reynolds numbers. International Journal for Numerical Methods in Fluids 37, pp. 45-64.

    [39] Peng, Y.F., Shiau, Y.H., and Hwang, R.R., 2003, Transition in a 2-D lid-driven cavity flow. Computers and Fluids 32, pp. 337-352.

    [40] Erturk, E., Corke, T.C., and Gokcol, C., 2005, Numerical solutions of 2-D steady incompressible driven cavity flow at high Reynolds numbers. International Journal for Numerical Methods in Fluids 48, pp. 747-774.

    [41] Soh, W.H. and Goodrich, J.W., 1988, Unsteady solution of incompressible Navier-Stokes equations. Journal of Computational Physics 79, pp. 113-134.

    [42] Iwatsu, R., Hyun, J.M., and Kuwahara, K., 1992, Numerical simulation of flow driven by a torsionally- oscillating lid. Journal of Fluid Engineering. 114, pp. 143-151.

    [43] Nishimura, T. and Kunitsugu, K., 1997, Fluid mixing and mass transfer in two-dimensional cavities with time-periodic lid velocity. International Journal of Heat and Fluid Flow 18, pp. 497-506.

    [44] Sriram, S., Deshpande, A.P., and Pushpavanam, S., 2006, Analysis of spatiotemporal variations and flow structures in a periodically driven cavity. Journal of Fluid Engineering. 128, pp. 413-420.

    [45] Khanafer, K.M., Al-Amiri, A.M., and Pop, I., 2007, Numerical simulation of unsteady convection in a driven cavity using an externally exited sliding lid. European Journal of Mechanics. B/Fluids 26, pp. 669-687.

    [46] Kuhlmann, H.C., Wanschura, M., and Rath, H.J., 1997, Flow in two-sided lid-driven cavities: non-uniqueness, instabilities and cellular structures. Journal of Fluid Mechanics. 336, pp. 267-299.

    [47] Albensoeder, S. and Kuhlmann, H.C., 2002, Three-dimensional instability of two counter-rotating vortices in a rectangular cavity driven by parallel wall motion. European Journal of Mechanics B/Fluids 21, pp. 307-316.

    [48] Albensoeder, S. and Kuhlmann, H.C., 2003, Stability balloon for the double-lid-driven cavity flow. Physics of fluids 15, pp. 2453-2456.

    [49] Luo, W.-J. and Yang, R.-J., 2007, Multiple fluid flow and heat transfer solutions in a two sided lid-driven cavity. International Journal of Heat and Mass Transfer 50, pp. 2394-2405.

    [50] Hirt, C.W., Nichols, B.D., and Romero, N.C., 1975, SOLA - A Numerical Solution Algorithm for Transient Fluid Flow, LA-5852 technical report, Los Alamos Scientific Laboratory, USA.

    [51] Jeong, J. and Hussain, F., 1995, On the identification of a vortex. Journal of Fluid Mechanics. 285, pp. 69-94.

    [52] Guermond, J.-L., Migeon, C., Pineau, G., and Quartapelle, L., 2002, Start-up flows in a three dimensional cavity of aspect ratio 1:1:2 a Re = 1000. Journal of Fluid Mechanics. 450, pp. 169-199.

    [53] Branicki, M. and Moffatt, H.K., 2006, Evolving eddy structures in oscillatory Stokes flows in domains with sharp corners. Journal of Fluid Mechanics. 551, pp. 63-92.

    [54] Coutanceau, M. and Bouard, R., 1977, Experimental determination of the main features of the viscous flow in the wake of a circular cylinder in uniform translation. Journal of Fluid Mechanics Part 1. Steady °ow, 79, pp. 231-256.

    [55] Tritton, D.J., 1959, Experiments on the flow past a circular cylinder at low Reynolds number. Journal of Fluid Mechanics 6, pp. 547-567.

    [56] Williamson, C.H.K., 1996, Vortex dynamic in the cylinder wake. Annual Review Fluid Mechanics. 28, pp. 477-539.

    [57] Borthwick, A.G.L., 1986, Comparison between two finite difference schemes for computing the flow around a cylinder. International Journal for Numerical Methods in Fluids 6, pp. 275-290.

    [58] Chern, M.J., Borthwick A.G.L., and Taylor, R., 2005, Pseudospectral element model for free surface viscous flows. The International Journal of Numerical Methods for Heat and Fluid Flow 15, pp. 517-554.

    [59] Dennis S.C.R. and Chang G.Z., 1970, Numerical solutions for steady flow past a circular cylinder at Reynolds numbers up to 100. Journal of Fluid Mechanics 42, pp. 471-489.

    [60] Rosenfeld, M., Kwak. P., and Vinokur, M., 1991, Unsteady incompressible Navier-Stokes equations. Journal of Computational Physics 94, pp. 102-137.

    [61] Ye, T., Mittal, R., Udaykumar, H.S., and Shyy, W., 1993, An accurate Cartesian grid method for viscous incompressible flows with complex immersed boundaries. Journal of Computational Physics 156 pp. 209-240.

    [62] Rajani, B.N and Majundar, S., 1993, Numerical simulation of laminar flow past a circular cylinder . Applied Mathematical Modelling 33 3 pp. 1228-1247.

    [63] Zdravkovich, M., 1997, Flow Around Circular Cylinders., Oxford University Press, Oxford, UK.

    [64] Goldstein, D., Handler, R., and Sirovich, L., 1995, Direct numerical simulation of turbulent flow over a modelled riblet covered surface. Journal of Computational Physics 302, pp. 333.

    [65] Hurlbut, S.E., Spaulding, M.L., and White, F.M., 1982. Numerical solution for laminar two dimensional flow about a cylinder oscillating in a uniform stream. Trans ASME, Journal of Fluids Engineering 104, pp. 214-222.

    [66] Kalitzin, G. and Iaccarino, G., 2003, Toward immersed boundary simulation of high Reynolds number flows. Annual Research Briefs, Center for Turbulence Research pp. 369-378.

    [67] Diaz, A. and Majumdar, S., Numerical computation of flow around a circular cylinder, Technical Report, PS II Report, BITS Pilani, India.

    [68] Meneghini, J.R., Saltara, F., Siqueira, C.L.R, and Ferrari. Jr.J., 2001, A Numerical simulation of flow in interference between two circular cylinders in tandem and side-by-side arrangements. Journal of Fluids and structures 15, pp. 327-350.

    [69] Verzicco, R., Yusof, J.M., Orlandi, P., and Haworth, D., 2000, Large eddy simulation in complex geometric configurations using boundary body forces. AIAA J. 38 (3), pp. 427-433.

    [70] Yusof, J.M., 1997, Combined immersed-boundary/B-spline methods for simulations of flow in complex geometries. Annual Research Briefs, Center for Turbulence Research, pp. 317-327.

    [71] Kim, J., Kim, D. and Choi, H., 2001, An immersed-boundary finite-volume method for simulations of flow in complex geometries. Journal of Computational Physics 171, pp. 132-150.

    [72] Eckert, E.R.G. and Soehngen, E., 1952, Distribution of heat transfer coefficients around circular cylinder in cross flow at Reynolds number from 20 to 500. Trans. ASME 75, pp. 343-347.

    [73] Moukalled, F. and Acharya, S., 1996, Natural convection in the annulus between concentric horizontal circular and square cylinder. Journal of Thermophysics Heat Tansfer 10, pp. 524-531.

    [74] Shu, C., Xue, H., and Zhu, Y.D., 2001, Numerical study of natural convection in an eccentric annulus between a square outer cylinder and a circular inner cylinder using DQ method. International Journal of Heat and Mass Transfer 44, pp. 3321-3333.

    [75] Kim, B.S., Lee, D.S., Ha, M.Y., and Yoon, H.S., 2008, A numerical study of natural convection in a square enclosure with a circular cylinder at different vertical locations. International Journal of Heat and Mass Transfer 51, pp. 1888-1906.

    [76] Sadat, H. and Couturier, S., 2000, Performance and accuracy of a meshless method for laminar natural convection. Numerical Heat Transfer, Part B 37, pp. 455-467.

    [77] Choi, H.G., 2000, Splitting method for the combined formulation of the fluid-particleproblem. Computer Methods in Applied Mechanics and Engineering 190, pp. 1367-1378.
    [78] Hu, H.H., Joseph, D.D., and Crochet, M.J., 1992, Direct simulation of fluid particle motions, Theoretical and Computational Fluid Dynamics 3, pp. 285-306.

    [79] Perrin, A. and Hu, H.H., 2006, An explicit finite-difference scheme for simulation of moving particles, Journal of Computational Physics 212, pp. 166-187.

    [80] Fortes, F., Joseph, D.D., and Lundgren, T.S., 1987, Non-linear mechanics of fluidization of beds of spherical particles, Journal of Fluid Mechanics. 177, pp. 467-483.

    [81] Belmonte, A., Eisenberg, H., and Moses, E., 1998, From flutter to tumble: Inertial drag and Froude similarity in falling paper. Physics Review Letter. 81, 2 pp. 345-348.

    [82] Mahadevan, L., Ryu, W.S., and Samuel, A.D., 1999, Tumbling chards, Physic of Fluids 11, 1 pp. 1-3.

    [83] Pesavento, U. and Wang, Z. J., 2004, Falling paper: Navier-Stokes solutions, model of fluid forces and center of mass elevation, Physical Review Letters 93, pp. 1-4.

    [84] Jin, C. and Xu, K., 2008, Falling paper: Numerical study of the unsteady aerodynamics of freely falling plates, Communications in Computational Physics 3, pp. 834-851.

    [85] Kolomenskiy, D. and Schneider, K., 2009, A Fourier spectral method for the NavierStokes equations with volume penalization for moving solid obstacles, Jornal of Computational Physics 228, pp. 5687-5709.

    [86] Finn, D.L., 2007, Falling paper and flying business cards, SIAM News 40, pp. 1-3.

    [87] Maxwell, J.C., 1940, Scientific papers of Maxwell J.C., (Dover, New York) 1, pp. 115

    QR CODE