跳到主要內容

臺灣博碩士論文加值系統

(3.235.120.150) 您好!臺灣時間:2021/08/06 01:38
字體大小: 字級放大   字級縮小   預設字形  
回查詢結果 :::

詳目顯示

: 
twitterline
研究生:陳維霖
研究生(外文):Wei-LinChen
論文名稱:應用晶格波茲曼法結合大渦法模擬紊流強制對流熱傳問題
論文名稱(外文):Application of Lattice Boltzmann Method to Large Eddy Simulation of Turbulent convective heat transfer
指導教授:陳朝光陳朝光引用關係楊玉姿楊玉姿引用關係
指導教授(外文):Chao-Kuang ChenChao-Kuang Chen
學位類別:碩士
校院名稱:國立成功大學
系所名稱:機械工程學系碩博士班
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:2012
畢業學年度:100
語文別:中文
論文頁數:131
中文關鍵詞:晶格波茲曼法大渦模擬強制對流熱傳頂蓋驅動流背向階梯流場波形渠道
外文關鍵詞:lattice Boltzmann methodlarge eddy simulationconvective heat transferdriven cavitybackward facing stepwavy channel
相關次數:
  • 被引用被引用:2
  • 點閱點閱:183
  • 評分評分:
  • 下載下載:34
  • 收藏至我的研究室書目清單書目收藏:0
本文採用晶格波茲曼方法(Lattice Boltzmann Method,LBM),並結合大渦模擬來模擬高雷諾數(Reynolds number,Re)並具有熱傳效應的強制對流紊流場。晶格波茲曼方法由於數值穩定性的原因,大部分的研究都在低雷諾數的流場,
而本文利用了特殊的邊界條件處理方法及大渦模擬來解決此問題,因此可以模
擬高雷諾數的流場。

目前模擬紊流有三種方式,分別為直接數值模擬(Direct Numerical Simulation,DNS)、大渦數值模擬(Large Eddy Simulation,LES)及雷諾平均模擬(Reynolds Average Navier-Stokes Simulation,RANS)。本文採用大渦數值模擬(LES),其基本的理念是將物理量分成大尺度與小尺度的量,主要求解大尺度的物理量,而小尺度的擾動則建立模型來近似,此模型稱為亞格子模型。亞格子模型目前有數種模型,本文採用最簡單的亞格子渦黏及渦擴散模型,並使用Smagorinsky模式來得到渦黏及渦擴散系數,此模型的準確度在大多數的工程應用上是可被接受的。

本文模擬的問題包含頂蓋驅動流、背向階梯流場、波形渠道。流場皆假設為二維不可壓縮流,模擬的範圍涵蓋了層流及紊流。由於晶格波茲曼方程式為非穩態方程式,在求解紊流的時候無法得到穩態解,因此本文採用時間平均的方式得到時間平均解。本文研究的問題與已知文獻的實驗及模擬結果相比較,均非常吻合。

在頂蓋驅動流中,當Re≦7500時為層流,Re≧10000時為紊流,模擬結果與已有文獻進行渦中心位置的比較,結果非常吻合。在背向階梯流場中,當Re≦1200時為層流,1200〈 Re 〈6600時為過渡區,Re≧6600時為紊流,模擬結果與已有文獻進行再接觸點長度的比較,結果非常吻合。此外,並觀察其熱傳效應,在雷諾數高時有較好的對流熱傳效應。在波形渠道中,當Re≦500時為層流,Re≧3000時為紊流,並討論振幅波長比、雷諾數及普朗特數對表面摩擦係數與紐賽數的影響,結果顯示增加振幅波長比與提高雷諾數會提高表面摩擦係數,而提升雷諾數及普朗特數可以增加對流熱傳效應。
In this study, the Large Eddy Simulation (LES) is introduced into the Lattice Boltzmann Method (LBM), and applied to numerically solving high Reynolds number (Re) turbulent flows with convective heat transfer. For LBM simulations, due to the numerically instability in simulating high Reynolds number flow, most studies were focused on low Reynolds number flow. Present work adopts special method for boundary condition and coupled with LES to solve this problem. Therefore, it can be used to simulate high Reynolds number flows.
Typically, there are three numerical methods to simulate turbulence, namely Direct Numerical Simulation (DNS), Large Eddy Simulation, Reynolds Average Navier-Stokes Simulation (RANS), respectively. The basic concept of Large Eddy Simulation is to decompose the turbulent flow field into large and small scale parts. The large scale part is solved by Navier-Stokes equation, while the small scale part is solved by sub-grid scale (SGS) model. The SGS model used in this study is based on the most convenient model : Smagorinsky model, which includes vortex viscous and vortex diffusive form.
Simulations of this article include driven cavity flow, backward facing step flow, and flows in a wavy channel. This flow fields are considered as two-dimensional incompressible flow, include laminar and turbulent flows. Due to Lattice Boltzmann Equation is an unsteady equation, the steady solution can’t be obtained in the simulation of turbulent flows. Therefore, the time average solutions are calculated the numerical simulations. The results are compared with other experimental and numerical results, and obtained good consistency.
In driven cavity flow, the flow is laminar for Re≦7500, turbulent for Re≧10000, the simulation results are compared with reference for the position of vortex center, and present results have good consistency. In backward facing step flow, the flow is laminar for Re≦1200, transition for 1200〈 Re 〈6600, and turbulent for Re≧6600, the simulation results are compared with reference for reattachment length, and present results have good consistency. In addition, we observe the heat transfer, the flow have good convective heat transfer in high Reynolds number. In wavy channel flow, the flow is laminar for Re≦500, turbulent for Re≧3000. Reynolds number, Prandtl number and amplitude-wavelength ratio on the skin-friction and Nusselt number have been studied, the results show the amplitudes of the Nusselt number and the skin-friction coefficient increase with an increase in the Reynolds number and the amplitude-wavelength ratio, and the Nusselt number increases with an increase in the Reynolds number and Prandtl number.
中文摘要 I
Abstract III
誌謝 VI
目錄 VIII
表目錄 XI
圖目錄 XII
符號說明 XV
第一章、緒論 1
1-1晶格波茲曼法與紊流模擬之簡介 1
1-2晶格波茲曼法之文獻回顧 4
1-3晶格波茲曼法熱模型之文獻回顧 6
1-4大渦模擬法之文獻回顧 8
1-5頂蓋驅動流、背向階梯流場、波形渠道之文獻回顧 9
1-6本文架構 12
第二章、晶格波茲曼方法的基本理論 13
2-1 Boltzmann方程式 13
2-2晶格Boltzmann方程式與數值求解 15
2-2-1晶格Boltzmann方程式 15
2-2-2晶格Boltzmann方程式的數值求解 17
2-3晶格Boltzmann的速度模型 18
2-3-1 D2Q9模型 18
2-3-2 Chapman-Enskog展開及基本模型所對應之巨
觀方程式 22

2-4晶格Boltzmann的熱模型 27
2-4-1多組分流體的LBM被動標量模型 27
2-4-2 Chapman-Enskog展開及基本模型所對應之
巨觀方程式 29
2-5晶格Boltzmann方法的邊界處理 34
2-5-1反彈邊界 34
2-5-2動力學格式-非平衡態反彈格式 35
2-5-2平衡態方法 36
2-6晶格Boltzmann方法的單位轉換 37
第三章、晶格波茲曼方法結合大渦模擬的研究 48
3-1紊流問題 48
3-2大渦模擬的基本理論 50
3-3大渦模擬的統御方程式 52
3-4亞格子模型 54
3-5大渦模擬結合晶格波茲曼方法 56
第四章、數值模擬之結果與討論 62
4-1模擬問題之簡介 62
4-2後處理、邊界條件處理及收斂準則之介紹 63
4-2-1後處理之介紹 63
4-2-2邊界條件處理之介紹 65
4-2-3收斂準則之介紹 66
4-2-4時間平均處理 66
4-3頂蓋驅動流之數值模擬 67
4-3-1統御方程式 67
4-3-2幾何設定 68
4-3-3參數設定 68
4-3-4邊界條件設定 68
4-3-5頂蓋驅動流之結果與討論 69
4-4背向階梯流場之數值模擬 70
4-4-1統御方程式 70
4-4-2幾何設定 70
4-4-3參數設定 71
4-4-4邊界條件設定 71
4-4-5背向階梯流場之結果與討論 72
4-5波形渠道之數值模擬 78
4-5-1統御方程式 78
4-5-2幾何設定 78
4-5-3參數設定 79
4-5-4邊界條件設定 79
4-5-5波形渠道之結果與討論 81
第五章、結論與未來展望 126
5-1結論 126
5-2未來與展望 127
參考文獻 128
Armaly, B.F.,& Durst, F.,& Pereira, J.C.F., and Schonung, B., “Experimental and theoretical investigation of backward-facing step flow, J. Fluid. Mech. , Vol. 127, pp. 473–496., 1983.
Alexander, F. J., & Chen, S., & Stering, J. D., “Lattice Boltzmann thermohydrodynamics, Phys. Rev. E, Vol. 47, pp. R2249-2252, 1993.
Alawadhi, E. M., “Forced Convection Flow in a Wavy Channel With a Linearly Increasing Waviness at the Entrance Region, Journal of Heat Transfer, Vol. 131, pp. 011703-1 - 011703-7, 2009.
Bhatnagar, P.L., & Gross, E.P., & Krook, M., “A model for collision processes in gases. Ⅰ. Small amplitude processes in charged and nrutral one-component systems, Phys. Rev., Vol. 94(3), pp. 511-525, 1954.
Chapman, S.,& Cowling, T.G., “The mathematical theory of non-uniform gases, Cambridge: Cambridge University Press, 1970.
Chen, Hudong, & Chen, Shiyi, & Matthaeus, William H., “Recovery of the Navier-Stokes equations using a lattice-gas Boltzmann method, Phys. Rev. A, Vol. 45, pp. R5339-5342, 1992.
Chen, Shiyi, & Doolen, Gary D., “Lattice Boltzmann model for fluid flows, Annu. Rev. Fluid Mech., Vol. 30, pp. 329-364, 1998.
Chen, H.,& Kandasamy, s.,& Orszag,s., et al., Extended Boltzmann Kinetic Equation for Turbulent Flows, Science , Vol.301, pp.633-636., 2003.
Chen, S., A large-eddy-based lattice Boltzmann model for turbulent flow simulation, Applied Mathematics and Computation, Vol. 215, pp. 591–598, 2009.
Chang, S.C., “Lattice Boltzmann simulation of fluid flows with fractal geometry: An unknown-index algorithm, Journal of the Chinese Society of Mechanical Engineers, Vol.32, No.6, pp.523-531, 2011.
Dieter, A. Wolf-Gladrow, “Lattice-gas cellular autimata and lattice Boltzmann models, Springer, Germany, 2000.
Deardoff, J. W., The use of subgrid transport equations in a three-dimensional model of atmospheric turbulence,ASME J. Fluid Engineering, Vol. 95,pp. 429-438,1973.

Erturk, E.,& Corke, T. and Gokcol, C., “Numerical solutions of 2-D steady incompressible driven cavity flow at high Reynolds numbers, International Journal for Numerical Methods in Fluids, Vol. 48, pp. 747-74., 2005.
Erturk, E., “Numerical solutions of 2-D steady incompressible flow over
a backward-facing step, Part I: High Reynolds number solutions, Computers & Fluids, Vol. 37, pp. 633–655, 2008.
Erturk, E., “Discussions On Driven Cavity Flow, Int. J. Numer. Meth. Fluids, Vol 60: pp 275-294, 2009.
Grunau, Daryl, & Chen, Shiyi, & Eggert, Kenneth, “A lattice Boltzmann model for multiphase fluid flows, Phys. Fluids A, Vol. 5(10), pp. 2557-2562, 1993.
Guo, Zhaoli, & Zhao, T. S., “Lattice Boltzmann model for incompressible flows through porous media, Phys. Rev. E, Vol. 66, pp. 036304, 2002.
Guan, H., & Wu, C., Large-Eddy Simulations of turbulent flows with lattice Boltzmann dynamics and dynamical system sub-grid models “, Sci China Ser E-Tech Sci, vol. 52 , no. 3 ,pp. 670-679 , 2009.
Higuera, F. J.,& Jimenez J., “Boltzmann approach to lattice gas simulations. Europhysics Letters, Vol. 9(7), pp. 663–668, 1989.
Hou, S.,& Sterling, J.,& Chen, S., and Doolen, G. D., “A lattice Boltzmann subgrid model for high Reynolds number flows, in Pattern Formation and Lattice Gas Automata, edited by A. T. Lawniczak and R. Kapral, Fields Institute Communications Vol. 6 (AMS, Providence), pp. 151–166, 1996.
He, X.,& Luo, L.-S., A priori derivation of the lattice Boltzmann equation, Phys. Rev. E, Vol. 55, pp. R6333- R6336, 1997.
He, X.,& Luo, L.-S., “Theory of the lattice Boltzmann method: From the Boltzmann equation to the lattice Boltzmann equation, Phys. Rev. E, Vol. 56, pp. 6811-6817 , 1997.
He, Xiaoyi, & Chen, Shiyi, & Doolen, Gary D., “A novel thermal model for the lattice Boltzmann in incompressible limit, J. Comput. Phys., Vol. 146, pp. 282-300, 1998.


Jongebloed, L., “Numerical Study using FLUENT of the Separation and Reattachment Points for Backwards-Facing Step Flow, An Engineering Project Submitted to the Graduate Faculty of Rensselaer Polytechnic Institute in Partial Fulfillment of the Requirements for the degree of Master of Engineering, 2008.

McNamara, Guy R., & Zanetti, Gianluigi, “Use of the Boltzmann equation to simulate lattice-gas automata, Physical Review Letters, Vol. 61(20), pp. 2332-2335, 1988.
Peng, Y., & Shu, C., & Chew Y. T., “Simplified thermal lattice Boltzmann model for incompressible thermal flows, Phys. Rev. E, Vol. 68, pp. 026701, 2003.
Qian, Y. H., & d’Humiéres, D., & Lallemand, P., “Lattice BGK models for Navier-Stokes equation, Europhy. Lett., Vol. 17(6), pp. 479-484, 1992.
Rush, T. A.,& Newell, T.A.,& Jacobi, A.M., “An experimental study of flow and heat transfer in sinusoidal wavy passages, Int. J. Heat Mass Transfer, Vol. 42, 1541-1553, 1999.
Raabe, D., “Overview of the lattice Boltzmann method for nano- and microscale fluid dynamics in materials science and engineering, Modelling and Simulation in Materials Science and Engineering, Vol.12 , pp. R13-R46, 2004.
Smagorinsky, J., General circulation experiments with the primitive equations, i. the basic experiment. Monthly Weather Review, Vol. 91: pp 99-164, 1963.
Shan, X. & Chen, H., “Lattice Boltzmann model for simulating flows with multiple phases and components. Phys. Rev. E, Vol. 47, pp. 1815-1819, 1993.
Shan, Xiaowen, “Simulation of Rayleigh-Bénard convection using a lattice Boltzmann method, Phys. Rev. E, Vol. 55, pp. 2780-2788, 1997.
Succi, S., & Vergassola, M., & Benzi, R., “Lattice Boltzmann scheme for two-dimensional magnetohydrodynamics, Phys. Rev. A, Vol. 43(8), pp. 4521-4524, 2001.
Wang, C.C. and Chen, C.K., “Forced convection in a wavy-wall channel, International Journal of Heat and Mass Transfer, Vol. 45, pp. 2587-2595., 2002
Yu, H.,& Luo, L. S., & Girimaji, S S., “Scalar mixing and chemical reaction simulations using lattice Boltzmann method, International Journal of Computational Engineering Science, Vol.3, pp.73-87, 2002.
Ziegler, D. P., “Boundary conditions for lattice Boltzmann simulation, J. Stat. Phys., Vol. 71, pp. 1171-1177, 1993.
Zou, Qisu, & He, Xiaoyi, “On pressure and velocity boundary conditions for the lattice Boltzmann BGK model, Phys. Fluids, Vol. 9(6), pp. 1591-1598, 1997.
何雅玲、王勇、李慶,格子Boltzmann方法的理論及應用,北京:科學出版社,2008。
張兆順、崔桂香、許春曉,湍流大渦數值模擬的理論和應用,清華大學出版社,2008。
郭照立、鄭楚光,格子Boltzmann方法的原理及應用,北京:科學出版社,2008。
顏子翔,「應用晶格波茲曼法與場協同理論於不同阻礙物之背向階梯管道熱流分析」,國立成功大學博士論文,2006。
連結至畢業學校之論文網頁點我開啟連結
註: 此連結為研究生畢業學校所提供,不一定有電子全文可供下載,若連結有誤,請點選上方之〝勘誤回報〞功能,我們會盡快修正,謝謝!
QRCODE
 
 
 
 
 
                                                                                                                                                                                                                                                                                                                                                                                                               
第一頁 上一頁 下一頁 最後一頁 top
無相關期刊