中文摘要

本文研究重點在建立一流固耦合數值模型，此問題可以流固耦合通式： 表示，式中M為結構體之慣性矩陣(Inertia Matrix)，K為剛性矩陣(Stiffness Matrix)，F為流場作用於結構體之載荷，q為結構體之廣義座標(Generalized Coordinate)。本研究結合計算流體力學(Computational Fluid Dynamics)及有限元素法(Finite Element Method)，以前者計算流場作用於結構體之載荷，後者提供結構體之慣性與剛性矩陣來進行交互作用之數值模擬。由於結構體在每一瞬間均會因流場作用之載荷變動而產生變形，必須以動態格點法(Dynamic Grid)與幾何守恆律(Geometric Conservation Law)來處理此一介面網格變形。本文利用狀態過渡矩陣(State Transition Matrix)時間積分方法處理流體與結構交互作用的問題，以不可壓縮那威爾-史托克(Navier-Stokes)流體與一維線性繩索結構模型來進行流固交互作用之研究。本研究發展的流固耦合方法，可做為將來發展非線性大變形結構模型之參考。本研究驗證了流力、結構及交互作用模型之正確性，並應用於一彈性壁面(Flexible Wall)腔室開孔流場之數值模擬，分析了入流位置與開孔比例對於繩索變形與腔室壓力變化的影響。

Abstract

The objective of this work is to develop a numerical procedure that can solve a fluid/structure interaction problem, expressed by a general formula, . In this equation system, M and K are the inertia and stiffness matrices of the structure, respectively, F is the load vector exerted by the flow field on the structure, q is the general coordinate vector of the structure. In the present work, Computational Fluid Dynamic (CFD) and Finite Element Method (FEM) are integrated, foe which the former computes the loads acting on the structure and the latter provides the inertia and stiffness matrices in the modeling of the structure. To evaluate fluid-induced loads on the structure, the grid movement must be carefully treated for CFD computation during each time step. Dynamic grid technique that can strictly enforce the geometric conservation law has been employed to cope with the grid deformation of the interface. State transition matrix time integration method was used to march the fluid/structure system represented by an incompressible Navier-Stokes fluid and an one dimensional linear string model. The presently developed fluid/structure interaction scheme can serve as a basis for developing non-linear, large-deformation structure model in the future. The accuracy the proposed fluid/structure interaction scheme has been verified. A simulation of a cavity problem with a flexible wall and inlet, the relationship of inflow position, size of inlet, deformation of string and pressure variation of the cavity were analyzed.

參考文獻

1.Smith, R., Blick, E., Coalson, J., and Stein, P., “Thrombus Production by Turbulence,” Journal of Applied Physiology, Vol. 32, 1972, pp. 261-264.
2.Stein, P. D., and Sabbah, M. N, “ Measured Turbulence and Its Effect on Thrombus Formation,” Circulation Research, Vol. 35, 1974, pp. 608-614.
3.Sutera, S. P. and Mehrjardi, M. H., “ Deformation and Fragmentaion of Human Red Blood Cells in Turbulent Shear Flow,” Biophysical Journal, Vol. 15, 1975, pp. 1-11.
4.Sallam, A. M. and Hwang, N. H. C., “ Human Red Blood Cell Hemolysis in a Turbulent Shear Flow: Contribution of Reynolds Shear Stresses,” Biorheology, Vol. 21, 1984, pp. 783-797.
5.Williams, A. R., “ Release of Serotonin from Human Platelets by Acoustic Microstreaming.” Journal of the Acoustical Society of America, Vol. 56, No. 5, 1974, pp. 1640-1643.
6.Hung, T. C., Hochmuth, R. M., Joist, J. H., and Sutera, S. P., “Shear-Induced Aggregation and Lysis of Platelets,” ASAIO, Vol. 22, 1976, pp. 285-290.
7.Yaping Zhu, Kosala Wickramasinghe, and Nigel Francis, “Fluid Structure Interaction Modeling of Airbag Deployment Using PAM-FLOWTM/ PAM-CRASHTM Coupling,” AMERI-PAM, 1999.
8.T. Y. Chang and K. Sawamiphakdi, “Large Deformation Analysis of Laminated Shells by Finite Element Method,” Journal of Computers & Structures, Vol. 13, 1981, pp. 331-340.
9.Chorin, A. J., “A Numerical Methods for Solving Incompressible Viscous Flow Problems,”Journal of Computational Physics, Vol. 2, pp. 12-26, 1967.
10.Merkle, C. L. and Athavale, M., “Time Accurate Unsteady Incompressible Flow Algorithms Based on Artificial Compressibility,”AIAA Paper 87-1137, CFD Conf., July, 1987.
11.Pan., D. and Chakravathy, S. R., “Unified Formulation for Incompressible Flows,”AIAA Paper 89-0122, Reno, 1989
12.Roger, S. E., Kwak, D. and Kiris, “Navier-Stokes Equations for Steady-State and Time-Depedent Problems,”AIAA Paper 89-0463, 1989.
13.Vinokur, M., “An Analysis of Finite-Difference and Finite-Volume Formulations of Conservation Laws,”Journal of Computational Physics, Vol. 81, pp.1-52, 1989.
14.Roe, P. L., “Characteristic-Based Schemes for the Euler Equation,” Annual Reviews of Fluid Mechanics, Vol. 18, pp.337-365.
15.Pan, D. and Lomax, H., “A New Approximate LU Factorization Scheme for the Eeynolds-Averaged Navier-Stokes Equations,” AIAA Journal, Vol. 26, No. 2, pp.163-171, Feb, 1998.
16.Edwards, J. W., Bennett, R. M., Whitlow, W., Jr., and Seidel, D. A.,“Time-Marching Transonic Flutter Solutions Including Angle-of-Attack Effects,”AIAA Paper 82-0685, 1982.
17.Batina, J. J.,“Unsteady Euler Airfoil Solutions Using Unstructure Dynamics Meshes,”AIAA Paper 89-0115, 1989.
18.Huff, D. L., “Numerical Simulations of Unsteady, Viscous, Transonic Flow Over Isolated and Cascaded Airfoils Using a Deforming Grid,”AIAA Paper 87-1316, 1987.
19.D'souza, A.F. and Garg, V. K., “Advanced Dynamics: Modeling and Analysis,”Prentice-Hall, 1984.
20. 張智豪, “發展多元流體液面捕捉法以計算不可壓縮流具自由液面流場,”博士論文, 中華民國87年6月.
21.楊宜升, “以動態格點計算具自由液面流場,”碩士論文, 中華民國84年6月.
22.葉燉烟, “穿音速聲波激擾流場之非穩態空氣動力及空氣彈力特性,”博士論文, 中華民國81年12月.
23.陳森貴,“聲波顫振抑制法在無黏性及黏性穿音速葉柵流場之應用,”博士論文, 中華民國88年6月.
24.黃信昌, “以液面捕捉法計算液滴碰撞,”碩士論文, 中華民國89年6月.
25.王勋成, 邵敏,“有限單元法基本原理和數值方法,”清華大學出版社.