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http://tdr.lib.ntu.edu.tw/jspui/handle/123456789/33296完整後設資料紀錄
| DC 欄位 | 值 | 語言 |
|---|---|---|
| dc.contributor.advisor | 許文翰(Tony Wen-Hann Sheu) | |
| dc.contributor.author | Yu-Xin Lin | en |
| dc.contributor.author | 林禹鑫 | zh_TW |
| dc.date.accessioned | 2021-06-13T04:33:20Z | - |
| dc.date.available | 2012-08-01 | |
| dc.date.copyright | 2011-08-01 | |
| dc.date.issued | 2011 | |
| dc.date.submitted | 2011-07-27 | |
| dc.identifier.citation | [1] William K. George, Lectures in Turbulence for the 21st Century, Chalmers University of Technology, Gothenburg, Sweden.
[2] S. V. Ptankar, Numerical Heat Transfer and Fuild Flow, Hemisphere, New York, 1980. [3] U. Ghia, K. N. Ghia, C. T. Shin, High Re Solutions for imcompressible Flow Using the Navier-Stokes Equation and a Multigrid Method, J. Comp. Physics, Vol. 48, 387-411, 1982. [4] A. J. Baker, Finite element computational fluid mechanics, New York:McGraw-Hill, 1983. [5] J. Kim, P. Moin., Application of a fractional step method to incompressible Navier-Stokes equations, J. Comput. Phys., Vol. 59, 308-323, 1985. [6] V. Girault, P. A. Paviart, Finite element methods for Navier-Stokes equautions:Theory and algorithms, Springer Verlag, 1986. [7] O. Pironeau, Finite element methods fluids, John Wiely and Sons Inc., 1989. [8] Peter C. Chu, Chenwu Fan, A three-point combined compact difference scheme, J. Comput. Phys., Vol. 140, 370-399, 1998. [9] S. Chen, D. D. Holm, L. G. Margolin, R. Zhang, Direct numerical simulations of the Navier-Stokes alpha model, Physica D, Vol. 133, 66-83, 1999. [10] S. B. Pope, Turbulent Flows, Cambridge University Press. ISBN 978-0521598866., 2000. [11] D. D. Holm, Karman-Howarth Theorem for the Lagrangian averaged Navier-Stokes alpha model, Journal of Fluid Mechanics, Vol. 467, Issue 01, 205-214, 2001. [12] J. A. Domaradzki, D. D. Holm, Navier-Stokes-alpha model: LES equations with nonlinear dispersion, eprint arXiv:nlin/0103036, 2001. [13] J. L. Guermond, J. T. Oden, S. Prudhomme, An interpretation of the Navier-Stokes-alpha model as a frame-indifferent Leray regularization, Physica D, Vol. 177, 23-30, 2003. [14] A. Cheskidov, Boundary Layer for the Navier-Stokes-alpha Model of Fluid Turbulence, Arch. Rational Mech. Anal., Vol. 172, 333-362, 2004. [15] E. Erturk, T. C. Corke, Numerical Solutions of 2-D Steady Incompressible Driven Cavity Flow at High Reynolds Numbers, Int. J. Numer. Meth. Fluids, Vol. 48, 747-774, 2005. [16] A. Cheskidov, D. D. Holm, E. Olson, E. S. Titi, On a Leray-α model of turbulence, Proc. R. Soc., 629-649, 2005. [17] 林瑞國, 不可壓縮黏性熱磁流之科學計算方法, 博士論文, 2005. [18] A. A. Ilyin, E. M. Lunasin, E. S. Titi, A modified-Leray-α subgrid scale model of turbulence, Nonlinearity, Vol. 19, 879-897, 2006. [19] E. Olson, E. S. Titi, Viscosity versus vorticity stretching : Global well-posedness for a family of Navier-Stokes-alpha-like models, Nonlinear Analysis, Vol. 66, 2427-2458, 2007. [20] Tony W. H. Sheu, P. H. Chiu, A divergence-free-condition compensated method for incompressible Navier–Stokes equations, Comput. Methods Appl. Mech. Engrg., Vol. 196, 4479–4494, 2007. [21] E. Lunasin, S. Kurien, E. S. Titi, Spectral scaling of the Leray-α model for two-dimensional turbulence, J. Phys. Math. Theor., Vol. 41, 344014, 2008. [22] L. G. Rebholz, A family of new, high order NS-α models arising from helicity correction in Leray turbulence models, J. Math. Anal. Appl., Vol. 342, 246-254, 2008. [23] P. H. Chiu, Tony W. H. Sheu, R. K. Lin, An effective explicit pressure gradient scheme implemented in the two-level non-staggered grids for incompressible Navier-Stokes equations, Journal of Computational Physics., Vol. 227, 4018-4037, 2008. [24] Tony W. H. Sheu, L. W. Hsieh, C. F. Chen, Development of a Three-point Sixth-order Helmholtz scheme, Journal of Computational Acoustics., Vol. 16, 343-359, 2008. [25] M. van Reeuwijk, H. J.J. Jonker, K. Hanjalic, Leray-α simulations of wall-bounded turbulent flows, International journal of Heat and Fluid Flow, Vol. 30, 1044-1053, 2009. [26] P. H. Chiu, Tony W. H. Sheu, On the development of a dispersion-relation-preserving dual-compact upwind scheme for convection-diffusion equation, Journal of Computational Physics., Vol. 228, 3640-3655, 2009. [27] W. Layton, C. C. Manica, M. Neda, L. G. Rebholz, Numerical analysis and computational comparisons of the NS-alpha and NS-omega regularizations, Comput. Methods Appl. Mech. Engrg., Vol. 199, 916-931, 2010. | |
| dc.identifier.uri | http://tdr.lib.ntu.edu.tw/jspui/handle/123456789/33296 | - |
| dc.description.abstract | 本論文主要是探討紊流模型之特性,並將分析之結果與原始不可壓縮黏性Navier-Stokes方程組做一比較。在求解統御方程式方面,論文是架構在二維正交座標系統上，並於非交錯式網格(non-staggered grids)上壓力與速度耦合配置方式下,採用有限差分方法(finite-difference method)來離散統御方程式,以期精確的求解流體力學方程式。
紊流模型的基礎,是建立在變更非線性不可壓縮Navier-Stokes方程中的對流項(convective term)或擴散項(diffusion term),藉由調整此兩項在動量方程式中所佔的比例,除了抑制其非線性的成長外,也希望能使用較少成本(較粗網格或較少計算時間),捕捉我們必須使用較高成本來計算非線性不可壓縮Navier-Stokes方程才能觀察到的流場狀況,這樣的作法我們稱之為規則化(regularization)。 本研究討論了Leray-alpha及Navier-Stokes-alpha兩種紊流模型,此兩種紊流模型除了方程形式類似外,也相同的改變動量方程式中的對流項。透過數值模擬,我們期望了解使用紊流模型的益處,以及與原始非線性不可壓縮Navier-Stokes方程之差異。 | zh_TW |
| dc.description.abstract | This thesis explores and analyzes the characteristics of Turbulence Models by comparing the results with original incompressible viscous Navier-Stokes equations.This thesis is constructed from the two-dimensional in orthogonal non-staggered grids in pressure and velocity coupling configuration mode, to discretize the governing equations by finite-difference method, to make computational fluid dynamic equations for precisely.
Turbulence model is based on the changes of nonlinear incompressible Navier-Stokes equations in convective terms or diffusion terms and adjust their ratio in the momentum equations.In addition, we want to suppress its non-linear growth, but also hope to use a less cost (coarse grid or less computing time) to obtain information about turbulent flow, rather than using a high cost to solve the nonlinear incompressible Navier-Stokes equations. This approach is called Regularization. This study discusses two turbulence models: Leray-alpha model and Navier-Stokes-alpha model. These two turbulence models are similar. They both change the momentum equations convection terms.Through numerical simulation, we expect to understand the benefits of there turbulence models. We also hope to know the differences between them and the original non-linear incompressible Navier-Stokes equations. | en |
| dc.description.provenance | Made available in DSpace on 2021-06-13T04:33:20Z (GMT). No. of bitstreams: 1 ntu-100-R98525048-1.pdf: 34254145 bytes, checksum: 0398e3618e89d01aa4b0a7cbfc4623c3 (MD5) Previous issue date: 2011 | en |
| dc.description.tableofcontents | 致謝--------------------------------------i
摘要--------------------------------------iv abstract-----------------------------------v 第一章 導論--------------------------------1 1.1 文獻回顧-------------------------------1 1.2 研究動機與目標-------------------------2 1.3 論文大綱-------------------------------3 第二章 紊流模型之介紹----------------------4 2.1 紊流模型之相關理論---------------------4 2.1.1 紊流理論-----------------------------4 2.1.2 紊流尺度理論-------------------------5 2.2 紊流模型之分類-------------------------7 第三章 紊流數學模型------------------------10 3.1 基本假設-------------------------------10 3.2 不可壓縮黏性之Navier-Stokes方程--------11 3.3 Helmholtz方程式------------------------12 3.4 紊流模型方程---------------------------13 3.4.1 Leray-alpha方程----------------------13 3.4.2 Navier-Stokes-alpha方程--------------15 3.5 邊界條件-------------------------------17 第四章 數值方法----------------------------18 4.1 時間之離散格式-隱式Euler方法-----------18 4.2 空間之離散格式-Combined Compact方法----19 4.2.1 二階偏導數項的緊緻格式---------------19 4.2.2 一階偏導數項的波數關係保持緊緻格式---20 4.3 壓力之離散格式-無散度補償方法----------24 4.4 壓力梯度之離散格式---------------------26 4.5 三點六階Helmholtz方程之求解格式--------28 4.6 程式計算流程---------------------------30 第五章 程式驗證----------------------------33 5.1 Navier-Stokes方程之驗證----------------33 5.1.1 穩態具實解之問題---------------------33 5.1.2 暫態具實解之問題---------------------34 5.1.3 高雷諾數拉穴流之問題-----------------34 5.2 Helmholtz方程之驗證--------------------36 5.2.1 具實解之問題-------------------------36 5.3 Leray-alpha方程之驗證------------------37 5.3.1 穩態具實解之問題---------------------37 5.3.2 暫態具實解之問題---------------------37 5.4 Navier-Stokes-alpha方程之驗證----------39 5.4.1 穩態具實解之問題---------------------39 5.4.2 暫態具實解之問題---------------------40 5.5 計算結果及討論-------------------------41 第六章 紊流模型之測試問題------------------62 6.1 拉穴流問題-----------------------------63 6.2 通道流問題-----------------------------67 6.3 後向階梯流問題-------------------------71 6.4 模擬結果及討論-------------------------76 6.4.1 截面速度的比較-----------------------76 6.4.2 對流項比上擴散項的比較---------------86 6.4.3 流量的比較---------------------------90 6.4.4 不可壓縮條件的比較-------------------93 6.4.5 規則化後流場速度與原始Navier-Stokes方程速度的比較-------------------------------------------95 6.4.6 收斂過程的比較-----------------------99 6.4.7 調整alpha的比較----------------------100 6.5 研究成果之結論-------------------------105 6.6 未來展望-------------------------------105 附錄A 不同形式的Leray-alpha方程------------107 附錄B 不同形式的Navier-Stokes-alpha方程----109 附錄C Navier-Stokes-alpha方程之推導--------112 附錄D Navier-Stokes-alpha方程之壓力離散格式-無散度補償方法-------------------------------------------114 參考文獻-----------------------------------116 | |
| dc.language.iso | zh-TW | |
| dc.subject | 非線性 | zh_TW |
| dc.subject | 規則化 | zh_TW |
| dc.subject | 對流項 | zh_TW |
| dc.subject | 不可壓縮黏性Navier-Stokes方程 | zh_TW |
| dc.subject | 紊流模型 | zh_TW |
| dc.subject | incompressible viscous Navier-Stokes equations | en |
| dc.subject | convection term | en |
| dc.subject | regularization | en |
| dc.subject | nonlinear | en |
| dc.subject | turbulence model | en |
| dc.title | 兩種Regularized NS方程之大渦紊流模型評估 | zh_TW |
| dc.title | Assessment study on two regularized Navier-Stokes models for simulating large-eddy turbulent flow | en |
| dc.type | Thesis | |
| dc.date.schoolyear | 99-2 | |
| dc.description.degree | 碩士 | |
| dc.contributor.oralexamcommittee | 陳宜良,李龍(Long Lee),蔣德普,游景皓 | |
| dc.subject.keyword | 不可壓縮黏性Navier-Stokes方程,紊流模型,非線性,規則化,對流項, | zh_TW |
| dc.subject.keyword | incompressible viscous Navier-Stokes equations,turbulence model,nonlinear,regularization,convection term, | en |
| dc.relation.page | 118 | |
| dc.rights.note | 有償授權 | |
| dc.date.accepted | 2011-07-27 | |
| dc.contributor.author-college | 工學院 | zh_TW |
| dc.contributor.author-dept | 工程科學及海洋工程學研究所 | zh_TW |
| 顯示於系所單位： | 工程科學及海洋工程學系 | |
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