Natural convection heat transfer in confined porous media using body fitted curvilinear coordinates methods

• Main Authors: XIAO, SHI-WEN, 蕭世文
• Other Authors: CHEN, ZHAO-GUANG
• Format: Others
• Language: zh-TW
• Published: 1990
• Online Access: http://ndltd.ncl.edu.tw/handle/39792242977069664655

博士 === 國立成功大學 === 機械工程研究所 === 79 === The natural convection heat transfer in confined porous media is studied in this thesis using the body-fitted curvilinear coordinates system. Five problems are investigated: (1) Transient natural convection in a porous annulus between horizontal cylinders. (2) Transient natural convection about a heated corrugated plate embeded in an enclosed porous medium. (3) Transient natural convection for a heated horizontal bylinder in an enclosed porous medium. (4) Natural convection about a heated inclined plate mou ted on one side of an enclosed porous medium. (5) Natural convection in a vertical enclosure filled with a porous medium. The Brinkman-Darcy-Forchheimer equation is used as the momentum equation for all of the problems. A constant porosity medium is considered and the thermal dispersion effect is neglected in the first and sencond problems, while the nonuniform porosity and thermal dispersion effects are taken into consideration in the last three type of problems. The non-Darcian effects are included in the momentum equation, and the thermal dispersion effect is considered in the energy equation. The wall effect on porosity is approximated by an exponential function and its effect on thermal dispersion is modeled by a dispersive length. The governing equations in temperature are expressed in a body-fitted coordinates system, which were solved numerically by the finite difference method. In problem (1), the study covers four differentinitial and boundary conditions whichinclude the situations when (i) the porous annulus is initially at a uniform temperature, and the inner cylinder is suddenly changed to a higher temperature, (ii) the porous annulus is initially at a uniform temperature, and the outer cylinder is suddenly at a uniform temperature, and the inner cylinder is suddenly changed to a lower temperature, (iv) the porous annulus is initially at a uniform temperature, and the outer cylinder is suddenly changed to a higher temperature. The effects of eccentricity, eccentric angle, Rayleigh number, Darcy number, and radii ratio on the fluid flow and heat transfer characteristics are discussed. The radii ratio is also increased to infinite to simulate the case of a horizontal cylinder embedded in an infinite porous medium. In problem (2), the effects of modified Rayleigh number, Darcy number, Prandtl number, aspect ratio of the cavity, and plate position on the fluid flow and heat transfer characteristics are investigated. Their effects on the onset of free convection and the instability of the flow are also discussed. Finally, the flow and heat transfer characteristics of a corrugated plate and of a flate plate are compared. In problem (3), the effects of Rayleigh number, dimensionless particle diameter, aspect ratio of the cavity, nonuniform porosity and thermal dispersion on the flow and heat transfer rate are studied. With the effects of non-Darcian, nonuniform porosity, and thermal dispersion taken into consideration, it is found that the predicted Nusselt numbers are in better agreement with existing experimental data. In problem (4), the effects of dimensionless particle diameter, Rayleigh number, indlined angle of the cavity, eccentricity of the plate, nonuniform porosity, and thermal dispersion on the fluid flow and heat transfer are throughly investigated. The isotherms and streamlines for each 15O of inclined angle of the cavity are presented. At high Rayleigh number, a secondary vortex appears in the porous medium near the upper corner of the rectangular enclosure. The intensity of the vortex increases with the inclined angle of the cavity. The predicated Nusselt numbers are compared with existing experimental results. It is found that the computed Nusselt numbers based on the model with the effects of non-Darcian, nonuiform porosity, and thermal dispersion compare the best with experimental data. In problem (5), the effects of conductivity ratio of the fluid and solid phases, bulk and nonuniform porosities, thermal dispersion, Rayleighnumber, Prandtl number, dimensionless particle diameter, and aspect ratio of the cavity on the flow and heat transfer rate are studied. It is found that the effect of the thermal conductivity of the solid phase on the Nusselt number is more pronounced at olw Rayleigh numbers where the conduction heat transfer is predominant. The larger are the dimensionless particle diameter and Rayleigh number, the smaller is the influence of conductivity ratio. In addition, the isotherms and streamlines at different inclined angle of the cavity are compared with those of problem (4), and it is found that they are different from each other. In this problem, no secondary flow can be obtained when the inclined angle of the cavity is less than 90o. 本文主要以實體吻合曲線座標系統轉換法來探討在封閉有限空間內具多孔性介質的自 然對流熱傳特性，所研究的熱傳問題如下： ⑴兩水平圓柱套管間之多孔性介質內的暫態自然對流熱傳 ⑵鋸齒狀板在含有多孔性介質之矩形容器內的暫態自然對流熱傳 ⑶置於含有多孔性介質封閉容器中之水平圓管的暫態自然對流熱傳 ⑷裝有多孔性介質之傾斜矩形容器受局部加熱的自然對流熱傳 ⑸矩形封閉容器內的自然對流熱傳 在上述研究之問題中，都以Brinkman-Darcy -Forchheimer 方程式作為動量方程式， 第⑴、⑵類問題的解析係假設孔隙率為定值，且忽略熱擴散效應，後三類問題的解析 則將不均勻孔隙率與熱擴散的效應一併考慮，壁面對於孔隙率的效應，以指數函數的 型態來表示，而對於熱擴散係數的效應則採用擴散長度（dispersive lengty）的觀 念。對於所有問題的解析，都先將以渦旋函數、流線函數及溫度所表示的統制方程式 轉換到實體吻合曲線座標系統上，再以有限差分法做數值計算。 在第⑴個問題中，除了探討圓管偏心量、偏心角度、Rayleigh數值計算。 在第⑴個問題中，除了探討圓管偏心量，偏心角度、Rayleigh 數、達西數及圓管半 徑比等各種參數對流動及熱傳特性的影響外，同時也考慮內管較熱與內管較冷的情形 ，使能兼顧管線的保溫與保冷的狀況，並將圓管的半徑比提高到無窮大以模擬水平圓 管在無限大範圍之多孔性介質中的熱傳特性。 在第⑵個問題中，除了探討修飾Rayleigh數、達西數、普蘭特數、容器高寬比及板子 位置對於流動與熱傳特性的影響外，對於各參數對產生自然對流時機的影響以及產生 不穩定現象的時機等亦有所討論，並將鋸齒狀板與平板的流動與熱傳特性的差異作一 比較。 第⑶個問題中，主要探討Rayleigh數、無因次質點直徑、容器尺寸、不均勻孔隙率及 熱擴散效應等參數對流動與熱傳特性的影響，並將數值計算結果和前人的實驗研究結 果比較，發覺同時考慮非達西效應、不均勻孔隙率及熱擴散效應所得的數值計算結果 最接近實驗值。 第⑷個問題中主要探討無因次質點直徑、Rayleigh數、容器傾斜角、平板偏心度、不 均勻孔隙率及熱擴散效應等參數對流動與熱傳特性的影響，並將容器傾斜角度從0° 到90°每變化15°的等溫線與流線繪出，發現在Rayleigh數較高時都會有二次流產生 且其強度隨著傾斜角度的增加而增加，並取和前人實驗研究一致之條件做數值計算， 並和實驗結果比較，發覺以同時考慮非達西效應、不均勻孔隙率及熱擴散效應所得之 結果最接近實驗值。 第⑸個問題在探討液、固相熱傳導係數比、孔隙率、熱擴散效應、普蘭特數、質點直 徑及容器高寬比等參數對流動與熱傳特性的影響。結果顯示固相熱傳導係數對於紐塞 爾數的影響在低雷苪數而熱傳遞由熱傳導模式所主宰時更為顯著，無因次質點直徑及 雷芮數愈大時，液固相熱導模式所主宰時更為顯著，無因次質點直徑及雷芮數愈大時 ，液固相熱導係數比對熱傳率的影響愈小。除此之外，亦改變不同的容器傾斜角度， 結果顯示其流線與等溫線之分佈完全異於第⑷類問題者，而且在傾斜角小於90°時不 會再有第⑷類問題的二次流產生。