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完整後設資料紀錄
DC 欄位 | 值 | 語言 |
---|---|---|
dc.contributor.advisor | 陳發林 | zh_TW |
dc.contributor.advisor | Falin Chen | en |
dc.contributor.author | 陳韋廷 | zh_TW |
dc.contributor.author | Wei-Ting Chen | en |
dc.date.accessioned | 2023-08-09T16:44:45Z | - |
dc.date.available | 2023-11-09 | - |
dc.date.copyright | 2023-08-09 | - |
dc.date.issued | 2023 | - |
dc.date.submitted | 2023-07-18 | - |
dc.identifier.citation | 1. J. S. Turner, Buoyancy Effects in Fluids, Cambridge University Press, (1979).
2. W. S. Jevons, On the cirrous form of cloud., London, Edinburgh, and Dublin Philos, Mag. J. Sci., 4th Series, 14, 22–35 (1857). 3. Radko, Timour, Double-Diffusive Convection, Cambridge University, (2013). 4. L. Rayleigh, Investigation of the character of the equilibrium of an incompressible heavy fluid of variable density, Proc. London Math. Soc., 14, 170–177 (1883). 5. H. A. Stommel, A. B. Arons, and D. Blanchard, An oceanographic curiosity: the perpetual salt fountain, Deep-Sea Res., 3, 152–153 (1956). 6. M. E. Stern, The “salt-fountain” and thermohaline convection, Tellus, 12,172–175 (1960). 7. H. E. Huppert, J. S. Turner, Double-diffusive convection, J. Fluid Mech., 106, 299–329 (1981). 8. J. S. Turner, Multicomponent convection, Annu. Rev. Fluid Mech., 17, 11–44 (1985). 9. S. Thorpe, P. Hutt, R. Soulsby, The effect of horizontal gradients on thermohaline convection, J. Fluid Mech., 38(2), 375-400 (1969). 10. C. F. Chen, D. G. Briggs, R. A. Wirtz, Stability of thermal convection in a salinity gradient due to lateral heating, Int. J. Heat Mass Transf., 14, 57–65 (1971). 11. C. F. Chen, Onset of cellular convection in a salinity gradient due to a lateral temperature gradient, J. Fluid Mech., 63, 563–576 (1974). 12. H. E. Huppert, J. S. Turner, Ice blocks melting into a salinity gradient, J. Fluid Mech., 100, 367–384 (1980). 13. I. G. Choi, S. A. Korpela, Stability of the conduction regime of natural convection in a tall vertical annulus, J. Fluid Mech., 99, 725-738 (1980). 14. Y. M. Chen, A. R. Pearlstein, Stability of free-convection flows of variable-viscosity fluids in vertical and inclined slots, J. Fluid Mech., 198, 513-541 (1989). 15. C. F. Chen, F. Chen, Salt-finger convection generated by lateral heating of a solute gradient, J. Fluid Mech., 352, 161–176 (1997). 16. J. Lee, S. H. Kang, Y. S. Son, Experimental study of double-diffusive convection in a rotating annulus with lateral heating, Int. J. Heat Mass Transf., 42, 821-832 (1999). 17. C. L. Chan, W. Y. Chen, C.F. Chen, Secondary motion in convection layers generated by lateral heating of a solute gradient, J. Fluid Mech., 455, 1–19 (2002). 18. T. Y. Chang, F. Chen, M. H. Chang, Three-dimensional stability analysis for a salt-finger convecting layer, J. Fluid Mech., 841, 636-653 (2018). 19. C. C. Wang, F. Chen, On the double-diffusive layer formation in the vertical annulus driven by radial thermal and salinity gradients, Mech. R. C., 125, 103991 (2022). 20. W. Y. Huang, F. Chen, Stability of the double-diffusive convection generated through the interaction of horizontal temperature and concentration gradients in the vertical slot, AIP Advances, 13, 055215 (2023). 21. J. E. Hart, On sideways diffusive instability, J. Fluid Mech., 49, 279-288 (1971). 22. I. T. Dolapci, Chebyshev collocation method for solving linear differential equations, Mathematical and Computational Application, 9, 107-115 (2004). 23. C. B. Moler, G. W. Stewart, An algorithm for generalized matrix eigenvalue problems, Society for Industrial and Applied Mathematics, 10, 241-256 (1973). 24. R. F. Bergholz, Instability of steady natural convection in a vertical fluid layer, J. Fluid Mech., 84, 743-768 (1978). | - |
dc.identifier.uri | http://tdr.lib.ntu.edu.tw/jspui/handle/123456789/88366 | - |
dc.description.abstract | 本論文的理論模型建立在一套高同心圓柱間隙中且水平徑向具有溫度及濃度梯度存在之系統,其內圓柱維持溫度、濃度高;外圓柱維持溫度、濃度低,通過徑向溫度梯度和濃度梯度之間的相互競爭作用將會形成連續的渦流且系統伴隨著產生三種不同類型的雙擴散不穩定性,分別為溫度、鹽指及雙擴散。本文藉由穩定性理論推導和Matlab數值分析方法,收集數據並整理分析出一套此系統的參數圖。
本研究利用時間不穩定性(temporal instability)的線性穩定性理論,探討在內外圓柱軸對稱的情況下,改變普朗特數(Pr)、路易斯數(Le)、內外圓柱半徑比以及溫度、濃度差對於此系統的不穩定性影響。透過固定Le改變Pr以及固定Pr改變Le且固定不同的半徑比進行計算,以龐大的數據量支持,可以發現所得到的穩定性邊界圖會分成三大區域,分別為溫度擴散區(thermal diffusive)、鹽指區(salt-finger)、雙擴散區(double-diffusive)。 透過溫度擴散區以及雙擴散區的數據發現此系統存在模態的轉換,系統會隨著Pr以及Le的增加,從臨界波數較大的剪力模態(shear mode)轉換為臨界波數較小的浮力模態(buoyancy mode)且中性曲線的極值發生跳動的改變,故本研究著重於分析此二區域,在固定Le改變Pr的情況下得出了Pr跳動點對於半徑比的關係式;在固定Pr改變Le的情況下得出了Le跳動點對於半徑比的關係式。 | zh_TW |
dc.description.abstract | The theoretical model of this thesis is based on a system of high concentric cylindrical gaps with radial temperature and concentration gradients. The inner cylinder maintains the high temperature and the high concentration; the outer cylinder maintains the low temperature and the low concentration. The continuous vortices will be formed through the competition between the radial temperature gradient and the concentration gradient, and the system will be accompanied by three different types of double-diffusive instabilities: thermal, salt-finger and double-diffusive. In this thesis, the stability theory derivation and Matlab numerical methods are used to collect data and set up a parameter diagrams of the system.
In this thesis, we using the linear stability theory of temporal instability. In the case of axisymmetric mode, the effect of changing Prandtl number(Pr), Lewis number(Le), ratio of inner and outer cylinder radii, temperature and concentration on the instability of the system is discussed. By changing Pr, fixing Le and changing Le, fixing Pr and fixing different radius ratios for calculation. With the huge amount of data support, it can be found that the stability boundary diagram will be divided into three major regions: thermal diffusive region, salt-finger region and double-diffusive region. Through the data of the thermal diffusion region and the double-diffusive region, we found that there is a transition of the mode in the system. With the increase of Pr and Le, the system will transform from the shear mode with a high critical wavenumber to the buoyancy mode with a low critical wavenumber and the extreme value of the neutral curve will jump. Therefore, this thesis focuses on the analysis of these two regions. In the case of fixing Le and changing Pr, the relational expression of Pr jumping point to radius ration is obtained; in the case of fixing Pr and changing Le, the relational expression of Le jumping point to radius ration is obtained. | en |
dc.description.provenance | Submitted by admin ntu (admin@lib.ntu.edu.tw) on 2023-08-09T16:44:45Z No. of bitstreams: 0 | en |
dc.description.provenance | Made available in DSpace on 2023-08-09T16:44:45Z (GMT). No. of bitstreams: 0 | en |
dc.description.tableofcontents | 致謝 I
摘要 II Abstract III 目錄 V 圖目錄 VII 表目錄 VIII 符號說明 IX 第一章 緒論 1 1.1 研究背景 1 1.2 文獻回顧 5 1.3 研究動機 8 1.4 研究方法 9 第二章 理論模型 10 2.1 模型描述 10 2.2 Boussinesq approximation 11 2.3 統御方程式 12 2.4 邊界條件與初始條件 13 2.5 統御方程式之無因次化 14 2.6 流場基態解 16 第三章 線性穩定性 20 3.1 微小擾動方程式(Small perturbation equation) 20 3.2 正規模態展開(Normal modes expansion) 21 第四章 數值分析 24 4.1 頻譜分析法(Spectral method) 24 4.2 Chebyshev Collocation method 24 4.3 展開階數N收斂測試 27 4.4 程式碼驗證 28 第五章 結果與討論 30 5.1 中性曲線與邊界圖 30 5.2 普朗特數Pr影響 32 5.2.1 穩定性邊界圖 32 5.2.2 溫度擴散區隨Pr的變化 34 5.3 路易斯數Le影響 39 5.3.1 穩定性邊界圖 39 5.3.2 雙擴散區隨Le的變化 41 第六章 結論與未來展望 46 6.1 結論 46 6.2 未來展望 47 參考文獻 48 | - |
dc.language.iso | zh_TW | - |
dc.title | 普朗特數和路易斯數對環流中雙擴散穩定性之影響 | zh_TW |
dc.title | Effect of Prandtl number and Lewis number on the double-diffusive stability in an annulus flow | en |
dc.type | Thesis | - |
dc.date.schoolyear | 111-2 | - |
dc.description.degree | 碩士 | - |
dc.contributor.oralexamcommittee | 牛仰堯;施陽正 | zh_TW |
dc.contributor.oralexamcommittee | Yang-Yao Niu;Yang-Cheng Shih | en |
dc.subject.keyword | 穩定性分析,雙擴散對流,圓柱座標系,極值跳動,模態轉換, | zh_TW |
dc.subject.keyword | stability analysis,double-diffusive convection,cylindrical coordinate system,jump of extreme value,mode transition, | en |
dc.relation.page | 50 | - |
dc.identifier.doi | 10.6342/NTU202301367 | - |
dc.rights.note | 同意授權(限校園內公開) | - |
dc.date.accepted | 2023-07-19 | - |
dc.contributor.author-college | 工學院 | - |
dc.contributor.author-dept | 應用力學研究所 | - |
顯示於系所單位: | 應用力學研究所 |
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