臺灣博碩士論文加值系統

密閉矩形盒中具溫差之雙圓柱之自然對流現象
學生：鄭偉駿 指導教授：王立文
元智大學機械工程研究所
摘 要
本研究主要是藉助實驗方法來探討具雙圓柱矩形封閉區域中，溫度及濃度梯度所引起的自然對流之流場形態以及圓柱附近的垂直溫度分佈。
研究動機起因於結晶成長過程中組成不均勻的現象非常嚴重，因此對於過程中熱量及質量的傳遞應作充分了解。
本文所作實驗，將兩圓柱賦予溫度差和濃度差，其它邊界保持絕緣。所以，本研究又分兩部分：
（1） 矩形盒水平放置,即兩圓柱為一左一右之自然
對流現象。
（2） 矩形盒垂直放置,即兩圓柱為一上一下之自然
對流現象。
工作中工作溶液為硫酸銅水溶液。溫度梯度由兩個不同溫度的恒溫水槽來維持。濃度梯度是由電化學方法造成的，即利用電解方法形成不同濃度的邊界層。對於矩形密閉容器內流場現象，採用雷射光暗影（shadowgraphy）來觀察流場，並以相機拍照記錄以利分析。
順向流場在加入質傳後因為流體堆積的關係，通常會有interface的產生，而逆向流場在溫度傳遞速率與濃度傳遞速率不均勻的情況下通常會有鹽手指的產生。在質傳遞率方面，在固定Gr,m的情況下，當Gr,t增加時，質傳遞率(Sh)會隨之增加。且順向的質傳遞率比逆向的質傳遞率高。而在矩形盒垂直放置時質傳遞率又比矩形盒水平放置時質傳遞率高。
本實驗中
Ar=0.625 Gr,t=2.41 ×105 ~ 7.23 ×105
Gr,m=1.82 ×106 N=-2.52~7.55
Sc=1700~2300 Pr=6.0~7.0

Thermosolutal Convection in a Rectangular Enclosure with Dual Cylinders
Student: Wei-Chun Jeng Adviser: Lin-Wen Wang
Department of Mechanical Engineering
Yuan-Ze University
ABSTRACT
The purpose of present study is to investigate flows pattern, temperature and concentration distributions resulting from buoyancy force due to a combination of temperature and species convection effects in a rectangular enclosure with dual cylinders inside.
In the process of crystal growth, the non-homogeneous phenomenon would become more and more serious. So to know the sufficient understanding of heat and mass transports is indispensable.
In this experiment, the temperature and concentration differences are made between two cylinders and the insulation is kept all over the margin. Cupric Sulphate solution is selected as the working fluid. Two constant temperature baths keep the temperature gradient. Concentration gradient is controlled via electrochemical system. In order to visualize the flow, the shadowgraph technique is used. Electrical measurements will be used to obtain mass transfer rates and to infer a Sherwood number. We can find that in the cooperating case, the interface is shown due to the fluid accumulation after imposing the mass transport. However, in the opposing case, the salt finger is found owing to the difference between the thermal diffusive velocity and mass diffusive velocity.
This study can be divided into two parts:
(1) The enclosure is placed horizontally, and convection is established where one cylinder is inserted right next to the other.
(2) The enclosure is placed vertically, and convection is established where one cylinder is inserted beneath the other.
The range of the parameters in this study are Ar=0.625
Gr,t=2.41 ×105 ~ 7.23 ×105 Gr,m=1.82 ×106
N=-2.52~7.55 Sc=1700~2300 Pr=6.0~7.0

目錄
摘要-----------------------------------------------------------I
圖目錄--------------------------------------------------------IX
符號說明------------------------------------------------------XI
一 前言-------------------------------------------------------1
1.1 研究動機-----------------------------------------------1
1.2 實驗的應用---------------------------------------------1
1.3 研究文獻探討-------------------------------------------2
二 實驗設計與方法---------------------------------------------5
2.1 溫度梯度的建立-----------------------------------------5
2.2 濃度梯度的建立-----------------------------------------6
2.3 實驗裝置-----------------------------------------------8
2.4 實驗過程-----------------------------------------------9
2.5 流場觀察----------------------------------------------10
2.6 雷射光暗影法------------------------------------------10
2.7 溫度量測之方法----------------------------------------11
2.8 濃度量測之方法----------------------------------------11
2.9 本實驗密閉矩形盒之邊界條件----------------------------11
2.10 本實驗溫度及濃度之量測點-----------------------------12
三 實驗結果與討稐-------------------------------------------13
3.1 第一類例順向流場流場型態(N=7.55，Gr,t=2.41 ×105)--13
Case 1：左熱右冷左陰極右陽極---------------------13
Case 2：下熱上冷下陰極上陽極---------------------14
Case 3：上熱下冷上陰極下陽極---------------------15
3.2 第一類例逆向流場流場型態(N=7.55，Gr,t=2.41 ×105)---16
Case 4：左熱右冷左陽極右陰極---------------------16
Case 5：上熱下冷上陽極下陰極---------------------16
Case 6：下熱上冷下陽極上陰極-------------------17
3.3 第二類例順向流場流場型態(N=2.52，Gr,t=7.23 ×105)---18
Case 7：左熱右冷左陰極右陽極---------------------18
Case 8：下熱上冷下陰極上陽極---------------------19
Case 9：上熱下冷上陰極下陽極---------------------20
3.4 第二類例逆向流場流場型態(N=2.52，Gr,t=7.23 ×105)---20
Case 10：左熱右冷左陽極右陰極--------------------20
Case 11：上熱下冷上陽極下陰極--------------------21
Case 12：下熱上冷下陽極上陰極--------------------21
3.5 流場的溫度分佈(N=7.55，Gr,t=2.41 ×105)------------------22
Case 1：左熱右冷左陰極右陽極---------------------22
Case 2：下熱上冷下陰極上陽極---------------------23
Case 3：上熱下冷上陰極下陽極---------------------23
Case 4：左熱右冷左陽極右陰極---------------------24
Case 5：上熱下冷上陽極下陰極---------------------24
Case 6：下熱上冷下陽極上陰極---------------------25
3.6 流場的濃度分佈(N=7.55，Gr,t=2.41 ×105)------------------25
Case 1：左熱右冷左陰極右陽極---------------------25
Case 2：下熱上冷下陰極上陽極---------------------26
Case 3：上熱下冷上陰極下陽極---------------------26
Case 4：左熱右冷左陽極右陰極---------------------26
Case 5：上熱下冷上陽極下陰極---------------------27
Case 6：下熱上冷下陽極上陰極---------------------27
3.7 質傳遞率分析------------------------------------------28
四 結論
4.1第一類例順向流場流場型態結論---------------------29
4.2第一類例逆向流場流場型態結論---------------------29
4.3第二類例順向流場流場型態結論---------------------29
4.4第二類例逆向流場流場型態結論---------------------30
參考文獻-------------------------------------------------------------------------31

參考文獻
1.S.Ostrach, "Natural Convection with Combined Buoyancy Forces", Physico Chem. Hydrodyn, Vol.1, pp.233-247, 1980.
2.H. Stommel, A. B. Arons and D. Blanchard, "An Ocean graphical Curiosity the Perpetual Salt Fountain", Deep. Sea Res.15, 275-280, 1956.
3.J.S.Turner, "The Behavior of a Stable Salinity Gradient Heated from Below", J. Fluid Mech. Vol. 33, pp.183-200, 1968.
4.J.Lee, M.T. Hyun and K.W. Kim, "Confined Natural Convection Due to Lateral Heating in a Stably Stratified Solution", Int. J. Heat and Mass Transfer, 31,No.10, 1969-1977, 1990.
5.L.W.Wang and D.J. Sun, "Convection Mass Transfer in Enclosures with Vertical Temperature and Concentration" J. of National Cheng-Kung University, Vol.20,pp.313-322, 1985.
6.J.Chang, T.F. Lin and C.H. Chien, "Unsteady Thermosolutal Opposing Convection of A Liquid-Water Mixture in a Square Cavity-I, Flow Formation and Heat and Mass Transfer Characteristics" Int. J. of Heat and Mass Transfer Vol.36, No.5, pp.1315-1331, 1993.
7.J.A.Weaver and R. Viskanta, "Natural Convection in Binary Gases Due to Horizontal Thermal and Solutal Gradients", J. Heat Transfer, Vol.133 pp.141-147, 1991.
8.C.Gau and K.H.Wu, "A Non intrusive Technique for Concentration Distribution Measurement in Enclosure", Experiment Heat Transfer , Vol. 2, pp. 215-226, 1989.
9.L.W.Wang, "Combined Thermal and Mass Transfer by Free Convection in Low Aspect Ratio Enclosures", Ph.D. Thesis, Case Western Reserve University, Ohio, U.S.A., 1983.
10.Y.Kamotani, L.W.Wang, S. Ostrach and H.D. Jiang, "Experimental Study of Natural Convection in Shallow Enclosures with Horizontal Temperature and Concentration Gradients", Int. J. Heat Mass Transfer, Vol.28, No.1, pp. 165-173, 1985.
11.C.R.Wilke, M. Eisenberg and C.W.Tobias, "Correlation of Limiting Currents under Free Convection Conditions", J. of the Electrochemical Society, Vol. 100, pp.513-523, 1953.
12.V.G.Levich , Physicochemical Hydrodynamics. Prentice-Hall , 1962.
13.T.Mizushina,The Electrochemical Method in Transport Phenomena.Adv.Heat Transfer 7.pp.87-161, 1971.
14.J.S.Newman , Electrochemical Systems. Prentice-Hall, 1973.
15.A.A.Wragg , Free Convection Mass Transfer at Horizontal Electrodes , Electric chemical acta , Vol 13 , pp.2159-2165
, 1968.
16.L.W.Wang , C.T.Chen and J.J.Chen , Flow-patterns of Convection'' in Enclosure with Vertical Temperature and Concentration in Gradients. Presented at the joint ASME/JSME Thermal Engineering Conference , mar, 1987.
17.S.Ostrach , 1983，Fluid Mechanics in Crystal Growth the 1982 Free-man Scholar Lecture , Journal of Fluids Engineering , Vol.105，pp.5-20 , 1982.
18.C.F.Chen , D. G. Briggs and R. A. Wirtz, "Stability of Thermal Convection in a Salinity Gradient Due to Lateral Heating", Int. J. Heat Mass Transfer, Vol.14, pp. 57-65, 1971
19.K.Kamakura, "Experimental and Numerical Analyses of Double Diffusive Natural Convection Heated and Cooled from Opposing Vertical Walls with an Initial Condition of a Vertically Linear Concentration Gradient" Int. J. Heat and Mass Transfer, Vol. 36, pp.2125-2134, 1993
20.J.Chang, T.F.Lin and C.H.Chien, "Unsteady Thermosolutal Opposing Convection of A Lique-Water Mixture in a Square Cavity-I, Flow Formation and Heat and Mass Transfer Characteristics" Int. J. of Heat and Mass Transfer Vol.36, No.5, pp.1315-1331, 1993
21.J.Lee, M.T. Hyun and K.W. Kim, "Natural Convection in Confined Fluids with Combined Horizontal Temperature and Concentration Gradients", Int. J. Heat and Mass Transfer, 31,No.10,1969-1977, 1988
22. C. Gau and K.H. Wu, "A Nonintrusive Technique for Concentration Distribution Measurement in Enclosure", Experiment Heat Transfer , Vol. 2, pp.215-226, 1989
23.呂俊嘉，「溫度梯度與濃度梯度互相垂直之熱質自然對流實驗研究」,私立元智工學院,碩士論文,民國83年。
24.李慶中，「高、低展弦比之矩形盒內質熱梯度相互垂直之自然對流研究」,私立元智工學院,碩士論文,民國84年。