博碩士論文 100221026 詳細資訊




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姓名 許文馨( Wen-Shin Shiu)  查詢紙本館藏   畢業系所 數學系
論文名稱
(Parallel Numerical Simulation of 3D Non-Newtonian Flows through Eccentric Annuli with Rotational Inner-Cylinder)
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摘要(中) 這問題是研究關於一個三維power-law非牛頓流體流經非同軸的環管狀體且內管會旋轉的流動情形。因為是非牛頓流體的關係,黏滯項也成了數值計算上非線性的來源之一,使得計算的複雜度增高。且此為三維的問題,計算量比二維大的可觀。我們用Galerkin/least squares finite element的方法去做空間上離散的動作;平行演算法上是用Newton-Krylov-Schwarz演算法為基礎,因此可執行大量的數值計算。我們提供了一個可以觀察三維流體的solver,而且不只可以觀察在全展流狀態下的流體流動情形,亦可以觀察發展中流體的流動情形。經過計算得到以下的數值結果:網格的收斂度測試、二維和三維的比較、一些物理量三維的呈現、非牛頓影響的入口長度,以及平行運算的效能討論。
摘要(英) This work is about a numerical study of 3D flow of an inelastic power-law fluid through eccentric annuli with
inner cylinder rotation. The nonlinearity due to the shear-rate dependent viscosity and the truly 3D flow behavior makes us to solve the flow problem challenging and
parallel computing is necessary to handle such compute-intensive task. We use Galerkin/least squares finite element formulation for the spatial discretization, and the resulting large sparse nonlinear system of equations is solved by a Newton-Krylov-Schwarz algorithm that is suitable for large scale computing. In this study, we investigate the behavior of flow under different values of power law index and the Reynolds number ratios between axial and azimuthal directions within both of the developing and developed regions.
We provide some numerical results including the grid independent test, a comparison between 2D and 3D cases,
3D plots for physical quantities of flows, non-Newtonian effect on entrance length, and parallel performance
study.
關鍵字(中) ★ 非牛頓流體
★ power-law模型
★ GLS
★ NKS
★ 入口長度
關鍵字(英) ★ non-Newtonian
★ power-law model
★ GLS
★ NKS
★ entrance length
論文目次 Contents
Tables viii
Figures ix
Nomenclature xii
1 Introduction 1
2 Flow models, discretization, and solution algorithm 4
2.1 Problemstatement 4
2.2 Galerkin/least squares ?nite element formulation 6
2.3 Newton-Krylov-Schwarzalgorithm 8
3 Numerical results 12
3.1 Gridindependenttest 12
3.2 A comparison between 2D-REA and 3D-REA cases without axial velocity 15
3.3 3Dplotsofphysicalquantitiesof?ows 20
3.4 Non-Newtonianeffectonentrancelength 20
3.5 Ef?ciency study and parallel performance of NKS 28
4 Concluding remarks 31
Bibliography 32
AppendixA 34
AppendixB 44
參考文獻 [1] Online cubit users manual, 2009. http://cubit.sandia.gov/documentation.html.
[2] S Balay, K. Buschelman, W.D. Gropp, D. Kaushik, M.G. Knepley, L.C. McInnes, Smith B.F., and H. Zhang. Petsc web page, 2014. http://www.mcs.anl.gov/petsc.
[3] R.B. Bird, R.C. Armstrong, and O. Hassager. Dynamics of Polymeric Liquids, Vol
1: Fluid Mechanics. John Wiley and Sons, 1987.
[4] E. Brujan. Cavitation in Non-Newtonian Fluids: With Biomedical and Bioengineer?ing Applications. Springer, 2011.
[5] X.-C. Cai, W.D. Gropp, D.E. Keyes, R.G. Melvin, and D.P. Young. Parallel Newton-Krylov-Schwarz algorithms for the transonic full potential equation. SIAM J. Sci. Comput., 19:246–265, 1998.
[6] R.P. Chhabra and J.F. Richardson. Non-Newtonian Flow and Applied Rheology: Engineering Applications. Butterworth-Heinemann, 2011.
[7] W.C. Chin. Computational Rheology for Pipeline and Annular Flow. Elsevier, 2001.
[8] J.E. Dennis and R.B. Schnabel. Numerical Methods for Unconstrained Optimization and Nonlinear Equations. Society for Industrial and Applied Mathematics, 1996.
[9] R. N. Elias, A.L.G.A. Coutinho, and M.A.D. Martins. Inexact Newton-type methods for the solution of steady incompressible viscoplastic ?ows with the supg/pspg ?nite element formulation. Comput. Methods Appl. Mech. Engrg., 195:3145–3167, 2006.
[10] M.P. Escudier, I.W. Gouldson, P.J. Oliveira, and F.T. Pinho. Effects of inner cylinder rotation on laminar ?ow of a newtonian ?uid through an eccentric annulus. Inter. J. Heat Fluid Flow, 21:92–103, 2000.
[11] M.P. Escudier, P.J. Oliveira, and F.T. Pinho. Fully developed laminar ?ow of purely viscous non-newtonian liquids through annuli including the effects of eccentricity and inner-cylinder rotation. Int. J. Heat Fluid Flow, 23:52–73, 2002.
[12] P. Fang, R.M. Manglik, and M.A. Jog. Characteristics of laminar viscous shear-thinning ?uid ?ows in eccentric annular channels. J. Non-Newtonian Fluid Mech., 84:1–17, 1999.
[13] L.P. Franca and S.L. Frey. Stabilized ?nite element methods. II: The incompressible Navier-Stokes equations. Comput. Methods Appl. Mech. Engrg., 99:209–233, 1992.
[14] T.J.R. Hughes. The Finite Element Method : Linear Static and Dynamic Finite Element Analysis. Dover Publications, 2000.
[15] F-.N. Hwang, C.-Y. Wu, and X.-C. Cai. Numerical simulation of three-dimensional blood ?ows using domain decomposition method on parallel computer. J. Chin. Soc. Mech. Eng., 31:199–208, 2010.
[16] G. Karypis, R. Aggarwal, K. Schloegel, V. Kumar, and R. Shekhar. Metis home page, 2009. http://wwwusers.cs.umn.edu/karypis/metis/.
[17] A. Klawonn and L.P. Pavarino. Overlapping Schwarz methods for mixed linear elasticity and Stokes problems. Comput. Methods Appl. Mech. Engrg., 165:233– 245, 1998.
[18] R.M. Manglik and P. Fang. Effect of eccentricity and thermal boundary conditions on laminar fully developed ?ow in annular ducts. Inter. J. Heat and Fluid Flow, 16:298–306, 1995.
[19] B.R Munson, D.F. Young, T.H. Okiishi, and W.W. Huebsch. Fundamentals of Fluid Mechanics. John Wiley & Sons, 2010.
[20] R.G. Owens and T.N. Phillips. Computational Rheology. Imperial College Press, 2002.
[21] E.E. Prudencio, R. Byrd, and X.-C. Cai. Parallel full space SQP Lagrange-Newton-Krylov-Schwarz algorithms for PDE-constrained optimization problems. SIAM J. Sci. Comput., 27:1305–1328, 2006.
[22] J.N. Reddy and D.K. Gartling. The Finite Element Method in Heat Transfer and Fluid Dynamics. CRC press, 2001.
[23] Y. Saad. Iterative Methods for Sparse Linear Systems. Society for Industrial and Applied Mathematics, 2003.
[24] Y. Saad and M.H. Schultz. GMRES: A generalized minimal residual algorithm for solving nonsymmetric linear systems. SIAM J. Sci. Stat. Comput., 7(3):856–869, 1986.
[25] B.F. Smith, P.E. Bjorstad, and W. Gropp. Domain Decomposition: Parallel Mul?tilevel Methods for Elliptic Partial Differential Equations. Cambridge University Press, 1996.
[26] S. Wan, D. Morrison, and I.G. Bryden. The ?ow of Newtonian and inelastic non-Newtonian ?uids in eccentric annuli with inner-cylinder rotation. Theor. Comput. Fluid Dyn., 13:349–359, 2000.
指導教授 黃楓南(Feng-Nan Hwang) 審核日期 2014-1-28
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