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研究生:莊榮南
研究生(外文):Chuang, Jung-Nan
論文名稱:變黏度流體在同心及偏心圓環間自然對流研究
論文名稱(外文):Studies on Natural Convection of Variable Viscosity Fluids between Concentric and EccentricHorizontal Cylindrical Annuli
指導教授:邱澄彬
指導教授(外文):Chue Ching-Hwei
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
學門:工程學門
學類:電資工程學類
論文種類:學術論文
論文出版年:1998
畢業學年度:86
語文別:中文
論文頁數:87
中文關鍵詞:變黏度渦漩自然對流
外文關鍵詞:Variable ViscosityVortexNatural Convection
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本篇論文係藉由詳細的數值模擬,探討具有高普蘭特數的變黏度流體
在水平同心及偏心圓柱間之自然對流,因變黏度效應所引起的流場轉變及
熱傳變化問題。工作流體使用濃度分別為70、80、90%之甘油水溶液。參
考溫度分別在22.0、22.7及33.4℃,普蘭特數分別為158、405、720,對
於所有的流場之穩態解,使用雷利數範圍為2500 ~ 200000,半徑比為1.5
,偏心率為0~0.8。黏度-溫度之關係式使用四參數型式關係式來模擬。格
點系統使用修正後之Sorenson方法建立一組與邊界近乎正交之格線,以增
加數值計算的準確性,而後利用這組格線配合權函數法則數值方法,將統
制方程式化成離散式,再以連續鬆弛法(SOR)解流線方程式、以交錯直接
隱性法(ADI)解渦漩及溫度場。為了確保數值方法的精確性,先以一般定
黏度牛頓流體分析結果和參考文獻之結果作比較後,再進一步分析變黏度
流體熱傳特性。 本文主要分析變黏度效應對於流場、溫度場及熱傳率
的影響,並與定黏度流體比較,得知變黏度效應對於流場、溫度場及熱傳
率皆有明顯的影響;隨著雷利數之增加,流場會經歷幾種模態的過渡轉換
,當雷利數大於第一臨界雷利數時,原來的單一對流渦漩崩潰產生不穩定
之二級渦漩,當雷利數大於第二臨界雷利數時,二級渦漩崩潰,形成更小
且與二級渦漩反向旋轉的三級渦漩,若再增加雷利數,則流場由層流轉變
成完全紊流;變黏度效應使得流場溫度梯度變大,增強熱對流效果,提高
熱傳率;變黏度效應也使得流場較不穩定,且普蘭特數愈高流場愈不穩定
,愈早達到臨界狀態,臨界雷利數會隨著普蘭特數之增加而下降,且成線
性關係。另外本文亦探討偏心量對熱傳效果的影響,對於正偏心的幾何結
構可獲得較佳的熱傳效果,相反地負偏心的幾何結構較不利於自然對流發
展空間,使得熱傳效果降低。
A numerical simulation has been carried out to explore the
variable viscosity effects induced flow transition and heat
transfer modifications inthe natural convection of high Prandtl
number fluids with temperature-dependent viscosity between
concentric and eccentric horizontal cylindrical annuli. The
working fluids used in the present study are glycerine-water
solutions of 70, 80 and 90% glycerine, reference temperature is
fixed at 22.0, 22.7 and 33.4℃, respectively. The Prandtl number
at these reference temperature are 158, 405 and 720. During the
simulations, steady solutions of the entire flow field are
obtained for a range of Rayleigh number 2500 ~ 200000, for a
radius ratio of 1.5 and a range of eccentricity 0 ~ *0.8. A
four-parameter correlation for the variable viscosity is
adopted. The modified Sorenson''s method used to generate the
grid line, it can get the grid system with orthogonality along
all boundaries and enhance calculation accuracy, the grid system
goes along with weighting function scheme (WFS) to discrete the
general governing equation. The successive over-relaxation
method (SOR) is applied to solve stream function equation, the
alternating direction implicit method (ADI) is applied to solve
vorticity and energy equations. The flow patterns and the
Nusselt numbers are in good agreement with previous experimental
and numerical results in the constant viscosity cases. The
subject of this thesis is to analyze the influence of variable
viscosity effects on the flow field, temperature and heat
transfer, and compare to the constant viscosity cases. The
numerical results show that : There are some different flow
regimes occur as Rayleigh number increases, when Rayleigh number
is increased exceeding the first critical value, the unicellular
convection vortex breaks into a number of unsteady secondary
vortices. For Rayleigh number larger than the second critical
Rayleigh number, smaller counter-rotating convection cells
appear, which are called the tertiary vortices. As the Rayleigh
number is increased further, the tertiary flow breaks down and
leads to a fully irregular turbulent flow. The effects of
variable viscosity enhance the temperature gradient, the
convection and heat transfer of the flow field, and let the flow
become unstable. For larger Prandtl number, the flow is more
unstable and reaches critical state earlier, the critical
Rayleigh number shows a decreasing trend as the Prandtl number
of the fluid is increased. Moreover, the influence of
eccentricity on the flow field is also studied in this thesis,
it reveals that the positive eccentricity can improve the
average Nusselt number, but the negative eccentricity may not
promote the convection effect.
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