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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 | Fa-Lin Chen | en |
dc.contributor.author | 黃柏諺 | zh_TW |
dc.contributor.author | Bo-Yan Huang | en |
dc.date.accessioned | 2024-06-13T16:08:51Z | - |
dc.date.available | 2024-06-14 | - |
dc.date.copyright | 2024-06-13 | - |
dc.date.issued | 2024 | - |
dc.date.submitted | 2024-06-11 | - |
dc.identifier.citation | 1. Chen, C.F., Double-diffusive convection in an inclined slot. Journal of Fluid Mechanics, 1975. 72(4): p. 721-729.
2. Paliwal, R.C. and C.F. Chen, Double-diffusive instability in an inclined fluid layer. Part 1. Experimental investigation. Journal of Fluid Mechanics, 1977. 98(4): p. 755-768. 3. Chen, C.F. and R.D. Sandford, Stability of time-dependent double-diffusive convection in an inclined slot. Journal of Fluid Mechanics, 1980. 83(1): p. 83-95. 4. Paliwal, R.C. and C.F. Chen, Double-diffusive instability in an inclined fluid layer Part 2. Stability analysis. Journal of Fluid Mechanics, 1980. 98(4): p. 769-785. 5. Thangam, S., A. Zebib, and C.F. Chen, Double-diffusive convection in an inclined fluid layer. Journal of Fluid Mechanics, 1982. 116: p. 363-378. 6. Chen Y-M, Pearlstein AJ. Stability of free-convection flows of variable-viscosity fluids in vertical and inclined slots. Journal of Fluid Mechanics. 1989;198:513-541. 7. Chen, Y. M., & Liou, J. K. (1997). Time-dependent double-diffusive convection due to salt-stratified fluid layer with differential heating in an inclined cavity. International journal of heat and mass transfer, 40(3), 711-725. 8. Bergeon, A., K. Ghorayeb, and A. Mojtabi, Double diffusive instability in an inclined cavity. Physics of Fluids, 1999. 11(3): p. 549-559. 9. Chen, Z.-W., Y.-S. Li, and J.-M. Zhan, Onset of oscillatory double-diffusive buoyancy instability in an inclined rectangular cavity. International Journal of Heat and Mass Transfer, 2012. 55(13-14): p. 3633-3640. 10. Teamah, M. A., Sorour, M. M., El-Maghlany, W. M., & Afifi, A. (2013). Numerical simulation of double diffusive laminar mixed convection in shallow inclined cavities with moving lid. Alexandria Engineering Journal, 52(3), 227-239. 11. Williamson, N., Armfield, S. W., Lin, W., & Kirkpatrick, M. P. (2016). Stability and Nusselt number scaling for inclined differentially heated cavity flow. International Journal of Heat and Mass Transfer, 97, 787-793. 12. Hasnaoui, S., Amahmid, A., Raji, A., Beji, H., Hasnaoui, M., Dahani, Y., & Benhamed, H. (2018). Double-diffusive natural convection in an inclined enclosure with heat generation and Soret effect. Engineering Computations, 35(8), 2753-2774. 13. Thangam, S., A. Zebib, and C.F. Chen, Transition from shear to sideways diffusive instability in a vertical slot. Journal of Fluid Mechanics, 1981. 112(-1). 14. Chen, C.F. and F. Chen, Salt-finger convection generated by lateral heating of a solute gradient. Journal of Fluid Mechanics, 1997. 352: p. 161-176. 15. Kerr, O.S. and K.Y. Tang, Double-diffusive instabilities in a vertical slot. Journal of Fluid Mechanics, 1999. 392: p. 213-232. 16. Kerr, O.S., Oscillatory double-diffusive instabilities in a vertical slot. Journal of Fluid Mechanics, 2001. 426: p. 347-354. 17. Chan, C.L., W.-Y. Chen, and C. Chen, Secondary motion in convection layers generated by lateral heating of a solute gradient. Journal of Fluid Mechanics, 2002. 455: p. 1-19. 18. Krishnamurti, R., Double-diffusive interleaving on horizontal gradients. Journal of Fluid Mechanics, 2006. 558. 19. Chang, T.-Y., F. Chen, and M.-H. Chang, Three-dimensional stability analysis for a salt-finger convecting layer. Journal of Fluid Mechanics, 2018. 841: p. 636-653. 20. Legare, S., A. Grace, and M. Stastna, Double-diffusive instability in a thin vertical channel. Physics of Fluids, 2021. 33(11). 21. Huang, W.-Y. and F. Chen, Stability of the double-diffusive convection generated through the interaction of horizontal temperature and concentration gradients in the vertical slot. AIP Advances, 2023. 13(5). 22. Wu, C.-F. and F. Chen, Stability transition of a solute-stratified fluid in a vertical slot imposed with a horizontal temperature gradient. Physics of Fluids, 2023. 35(9). 23. C. B. Moler, G. W. Stewart, An algorithm for generalized matrix eigenvalue problems, Society for Industrial and Applied Mathematics, 1973. 241-256(10) | - |
dc.identifier.uri | http://tdr.lib.ntu.edu.tw/jspui/handle/123456789/92709 | - |
dc.description.abstract | 本論文建立了傾斜槽系統,其中槽高無限高,並以側向加熱的方式進行物理模型建構。其中,容器內液體存在著垂直濃度梯度,當 θ=0^° 為典型垂直槽系統,其中左壁為高溫、右壁為低溫,當角度 θ>0^° 時,下板為加熱壁;反之,當 θ<0^° 時,上板為加熱壁。本文是以垂直槽中的熱對流題目為啟發,加入傾角與模態轉換定義,並將分析結果與過往論文進行交叉比對,進而得到新的結論。
本論文旨在對自然對流系統進行線性穩定性分析。基於Boussinesq approximation的控制方程組,求解了基態解。隨後引入微小擾動,並透過正規模態展開分析其隨時間的發展,進而探討系統的穩定性。數值求解採用切比雪夫配置法計算特徵值。最終,根據所得中性穩定曲線繪製穩定性邊界圖,並與以往實驗結果對比,歸納出相應結論。 固定 Pr=6.7、Le=100 來模擬海洋情形,並修正了前人論文的錯誤。本論文引入了五個穩定模式,包含溫度浮力模式(TBM)、擴散浮力模式(DBM)、擴散剪力模式(DSM)、鹽指剪力模式(SSM)以及鹽指浮力模式(SBM)。在引入模態後,本文定義了穩定邊界圖的轉換點,並追尋了Wu and Chen所定義的模態轉換。本論文使用T2~T4 模態轉換點,並求得出漸進關係式,發現當穩定邊界圖過了最低點後,會隨著角度越大越來越穩定,也就是論文中所探討的大濃度梯度區間。也求得最低點臨界值與角度的漸進線關係式,然而本論文發現小濃度梯度與大濃度梯度呈現相反現象,因此最後探討小濃度梯度與角度變化造成的影響。本研究找到了關鍵角度 θ=〖65.8〗^° ,當角度增加到 〖65.8〗^° 時,系統會變得更加不穩定,也探討當角度為 〖65.8〗^° 時,跳動點會在 R_s=33.9 時消失。 | zh_TW |
dc.description.abstract | This paper establishes a tilted slot system, in which the slot height is infinitely high, and a physical model is constructed using lateral heating. In this system, there exists a vertical concentration gradient in the liquid inside the container. When θ=0^° , it represents a typical vertical slot system, with the left wall being high temperature and the right wall being low temperature. When the angle θ>0^° , the bottom plate is the heated wall; conversely, when θ<0^° , the top plate is the heated wall. This paper is inspired by the topic of thermal convection in vertical slots, adding the definition of inclination and mode transition, and comparing the analysis results with previous papers to obtain new conclusions.
The purpose of this paper is to conduct linear stability analysis of natural convection systems. Based on the control equations of the Boussinesq approximation, the base state solution is solved. Subsequently, small disturbances are introduced, and their temporal development is analyzed through a normal mode expansion to explore the stability of the system. The numerical solution uses the Chebyshev collocation method to calculate eigenvalues. Finally, based on the obtained neutral stability curve, a stability boundary diagram is drawn and compared with previous experimental results to summarize corresponding conclusions. The simulation of oceanic conditions is carried out with fixed Pr=6.7、Le=100 , and errors in previous papers are corrected. This paper introduces five stable modes, including temperature buoyancy mode (TBM), diffusion buoyancy mode (DBM), diffusion shear mode (DSM), salt finger shear mode (SSM), and salt finger buoyancy mode (SBM). After introducing the modes, this paper defines the transition points of the stable boundary diagram and explores the mode transition defined by Wu and Chen. This paper uses the T2~T4 mode transition points and obtains an asymptotic relationship, finding that as the stable boundary diagram passes its lowest point, it becomes increasingly stable with larger angles, which corresponds to the interval of large concentration gradients discussed in the paper. The paper also derives an asymptotic line relationship between the critical value at the lowest point and the angle. However, it is found that small concentration gradients and large concentration gradients exhibit opposite phenomena, so the paper finally explores the effects of changes in angle on small concentration gradients. This study identifies a critical angle of θ=〖65.8〗^° , at which the system becomes more unstable as the angle increases to 〖65.8〗^° .It also discusses that when the angle is 〖65.8〗^° , the jumping point disappears at R_s=33.9. | en |
dc.description.provenance | Submitted by admin ntu (admin@lib.ntu.edu.tw) on 2024-06-13T16:08:51Z No. of bitstreams: 0 | en |
dc.description.provenance | Made available in DSpace on 2024-06-13T16:08:51Z (GMT). No. of bitstreams: 0 | en |
dc.description.tableofcontents | 致謝 I
摘要 II Abstract III 目次 V 圖次 VI 表次 VI 符號說明 VII 第1章 緒論 1 1.1 文獻回顧 1 1.2 研究動機 8 第2章 理論模型 9 2.1 研究方法 9 2.2 數學模型建立 10 2.3 Boussinesq approximation 12 2.4 統御方程式 13 2.5 統御方程式之無因次化 14 2.6 基態流場 16 第3章 線性穩定性分析 23 3.1 微小擾動方程式(Small Perturbation Equation) 23 3.2 正規模態展開(Normal Modes Expansion) 25 3.3 Squire’s Transformation 27 3.4 二維線性穩定性分析 29 3.5 二維正規模態展開 31 第4章 數值分析 32 4.1 數值方法 32 4.2 切比雪夫配置法(Chebyshev Collocation Method) 33 第5章 結果與討論 37 5.1 程式碼驗證 37 5.2 不同角度的穩定性分析 38 5.2.1 穩定性邊界圖(Stability Boundary Curve)與比較 38 5.2.2 波數圖(Wave Number) 40 5.2.3 模態轉換和最低點探討 41 5.2.4 中性曲線圖(Neutral Curve) 51 第6章 結論與未來展望 55 參考文獻 57 | - |
dc.language.iso | zh_TW | - |
dc.title | 傾斜槽內溶質垂直分層流體層在溫度梯度作用下之雙擴散對流穩定特性分析 | zh_TW |
dc.title | Analysis of the stability characteristics of double diffusive convection in a fluid layer with solute vertical stratification in an inclined trough under the influence of temperature gradient | en |
dc.type | Thesis | - |
dc.date.schoolyear | 112-2 | - |
dc.description.degree | 碩士 | - |
dc.contributor.oralexamcommittee | 羅安成;張敏興 | zh_TW |
dc.contributor.oralexamcommittee | An-Cheng Ruo;Min-Hsing Chang | en |
dc.subject.keyword | 流體穩定學,雙擴散傾斜槽,模態轉換,切比雪夫配置法, | zh_TW |
dc.subject.keyword | Double Diffusion Tilted Slot,Fluid Stability,Mode Transition,Chebyshev Collocation Method, | en |
dc.relation.page | 59 | - |
dc.identifier.doi | 10.6342/NTU202401112 | - |
dc.rights.note | 同意授權(全球公開) | - |
dc.date.accepted | 2024-06-11 | - |
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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