Numerical Analysis of Heat Transfer Performance of Jet Impingement on a plate with Attached Porous Medium
鄭豐嘉、吳佩學，陳慶耀
E-mail: [email protected]
ABSTRACT
Jet impinging is an important cooling/heat transfer technique in the industries, such as industrial drying, metal and glass annealing, secondary cooling in iron casting, laser cooling, plasma cutting cooling, gas turbine blade cooling, and cooling of microelectronics.
Nowadays, enhancement techniques for jet impingement heat transfer are still under intense investigation by academic researchers.
In this numerical study, jet impingement on a bare flate plate was used as a basic case, and the heat transfer enhancement of jet impingement on a flate plate with attached porous medium with or without a center hole was investigated. The effects of the porous medium geometry and properties on heat transfer were also examined. Appropriate numerical models were firstly determined by comparing the computational results with various models with existing numerical and experimental data in the literature. The appropriate models were then employed in the computation for the geometries used in this study. Computational results show that an attached porous medium with a center hole can effectively enhance jet impingement heat transfer. On the other hand, an attached porous medium without a center hole has detrimental effect. In addition, the center hole geometry and permeability have the most influential effects. The best center hole geometry should allow flow to effectively penetrate into porous medium for heat exchange. Permeability should be higher at low porosity and lower at high porosity for better heat transfer.
Keywords : jet impingement, heat transfer enhancement, porous medium, center hole, porosity, permeability Table of Contents
簽名頁 授權書 iii 中文摘要 v 英文摘要 vi 誌謝 viii 目錄 ix 圖目錄 xi 表目錄 xiii 符號說明 xiv 第一章 導論 1 1.1 前言 1 1.2 研究動機與研究目的 3 1.3 文獻回顧 5 第二章 統御方 程式 15 2.1 各模擬幾何形狀 15 2.2 基本假設 15 2.3 統御方程式 16 2.4 邊界條件 21 第三章 數值方法 24 3.1 格點系統 24 3.2 數值方法 24 3.3 離散方法 26 3.4 速度與壓力連結 29 3.5 收斂條件 34 3.6 鬆弛因子 34 第四章 紊流模式之選擇與平板噴射 之模擬結果 37 4.1 選擇紊流模式的依據 37 4.2 平板噴射使用各種紊流模式的Nu數與實驗比較 42 4.3 加入基材無加多孔介質 的平板噴射模擬與實驗比43 4.4 衝擊噴射使用雷諾應力模式的紊流動能與實驗比45 4.5 加入多孔介質平板噴射模擬與其他 文獻流場比較45 第五章 中心挖洞的多孔塊用於平板噴射的散熱性能分析 56 5.1 數值模擬邊界與模型參數 56 5.2數值模 擬Nu的比較結果與分析 57 第六章 結論 67 參考文獻 68 附錄一 77
REFERENCES
【1】Beitelmal, A.H., Saad, M.A.,Patel, C.D., 2000," The effect of -inclination on the heat transfer between a flate surface and an -impinging two-dimensional air jet," Inter national Journal of -Heat and Fluid Flow, Vol.21, pp. 156-163 【2】張中興，「多孔介質流之流場與熱傳性質之 分析(Investigatim of -Flow and Thermal Properties of Porous Medium Flow)」，中興 大學機械工程研究所碩士論文(1996) 【3】Jiang, P.X., Ren, Z.P., Wang, B.X., 1999," Numerical simulation -of forced convection heat transfer in porous plate channels -using thermal equilibrium and nonthermal equilibrium models," -Numerical Heat Transfer,Vol. 35, pp. 99-113 【4】Lee, D.Y., Vafai, K., 1999," Comparative analysis of jet -impingement and microchochannel cooling for high heat flux -applica tions," International Journal of Heat and Mass Transfer, -Vol. 42, pp.
1555-1568 【5】黃新鉗,「加裝多孔凸塊以增強熱傳效率之研究（A Study of -Thermal Enhancement by Adding Porous Block Under -Impinging Jet）」,交通大學機械工程研究所博士論文(1997) 【6】San, J.Y., Huang, C.H., Shu, M.H., 1997," Impingement cooling -of a confined circular air jet," International Journal of Heat and -Mass Transfer, Vol. 40, pp. 1355-1364 【7】Voke ,P.R., Gao, S., 1997," Numerical study of heat transfer from -an impinging jet," International Journal of Heat and Mass -Transfer, Vol. 41, pp. 671 680 【8】Shu, J.J., Wilks, G.., 1996," Heat transfer in the flow of a Cold , -two-dimensional vertical liquid jet against a hot,horizontal -plate," International Journal of Heat and Mass Transfer, Vol. 39, -pp. 3367-3379 【9】Francis, N.D., Wepfer, W.J., 1996," Jet impingement drying of a -moist porous solid," International
Journal of Heat and Mass -Transfer, Vol. 39, pp. 1911-1923 【10】謝文政, 「具上限制板之紊流三維五噴射撞擊流場數值模擬 分析
（Numerical Simulation and Analysis of Three-Dimension -Turbulent Impinging Flow Field from Confined Five Jets）」, 逢 甲大學機械工程研 究所碩士論文(1999) 【11】陳宗榮,「具橫向流之三維紊流雙噴射撞擊平板流場數值模 擬與分析」中原大學機械工程研究所碩士論 文(1997) 【12】Jiang, P.X., Ren, Z.P., 2001," Numerical investigation of -forced convection heat transfer in porous media using a -thermal non-equilibrium model," International Journal of Heat -and Fluid Flow, Vol. 22, pp. 102-110 【13】Lee, D.Y., Vafai, K., 1999," Analytical characterization and -conceptual assessment of solid and fluid temperature -differentials in porous media," International Journal of Heat -and Mass Transfer, Vol.42, pp. 423-435 【14】Ould-Amer, Y., Chikh, S., Bouhadef, K., Lauriat, G., 1998," -Forced convection cooling enhancement by use of porous -materials," Internation al Journal of Heat and Fluid Flow, Vol. -19, pp. 251-258 【15】Chen, Y.C., Chung, J.N., Wu, Y.F., 2000,"
Non-Darcy mixed convection in a vertical channel filled with a porous medium," -International Journal of Heat and Mass Transfer, Vol. 43, pp.
-2421-2429 【16】Jiang, P.X., Wang, Z., Ren, Z.P., Wang, B.X., 1999," -Experimental research of fluid flow and convection heat -transfer in plate channels filled with glass or metallic -particles," Experimental Thermal and Fluid Science 20, pp. -45-54 【17】Jiang, P.X., Fan, M.H., Si, G.S., Ren, Z.P., 2001," -Thermal-hydraufic performance of small scale micro-channel -and porous media heat-exchangers," International Journal of -Heat and Mass Transfer, Vol. 44, pp. 1039-1051 【18】Bhattacharya, A., Calmidi, V.V., Mahajan, R.L., 2002," -Thermophysical properties of high porosity metal foams," -International Journal of Heat and Mass Transfer, Vol. 45, pp. -1017-1031 【19】Yang, J.H.,and Lee, S.L., 1999,"
Effect of anisotropy on -transport phenomna in anisotropic porous media," -International Journal of Heat and Mass Transfer, Vol. 42, pp.
-2673-2681 【20】Lee, S.L.,and Yang, J.H., 1997," Modelling of effective thermal -conductivity for a nonhomogeneous anisotropic porous -medium," International Journal of Heat and Mass Transfer, -Vol. 41, pp. 931-937 【21】Chen, C.Y., Wang, L., Kurosaki, Y., 2001," Numerical -simulations of heat transfer in porous media with effect of -heterogeneities," 【22】Kim, S.J.,and Jang, S.P.,2002," Effects of Darcy number, the -Prandtl number, and the Reynolds number on local thermal -non-equilibrium," International Journal of Heat and Mass Transfer, Vol. 45, pp.
3885-3896 【23】Fu, W.S.,and Huang, H.C., 1999," Effect of a random porosity -model on heat transfer performance of porous media,"
-International Journal of Heat and Mass Transfer, Vol. 42, pp. -13-25 【24】Hansen, L.G.,and Webb, B.W., 1993," Air jet impingement heat -transfer from modified surfaces", International Journal of -Heat and Mass Transfer, Vol. 36, pp. 989-997 【25】Merci, B., Dick, E., 2002," Heat transfer predictions with a cubic -k-ε model for axisymmetric turbulent jets impinging onto a -flat plate," International Journal of Heat and Mass Transfer, -Vol. 46, pp. 469-480 【26】Behnia, M., Durbin, S., and Durbin, P. A., 1998," Prediction of -heat transfer in an axisymmetric turbulent jet impinging on a -flatplate," International Journal of Heat and Mass Transfer, -Vol. 41,pp. 1845-1855 【27】Prakash, M., Turan, O.F., Li, Y., Mahoney, J.,and Thorpe, G. -R.,2001," Impinging round jet studies in a cylindrical -enclosure with and without a porous layer : Part I-Flow -visualizations and simulations," Chemical Engineering -Science, Vol. 56,pp. 3855-3875 【28】Shu, J. J., Wilks, G., 1996," Heat transfer in the flow of a cold, -two-dimensional vertical liquid jet against a hot, horizontal -plate," International Journal of Heat and Mass Transfer, Vol. -39, pp.
3367-3379 【29】Shi, Y., Ray, M.B., and Mujumdar, A. S., 2002," Effects of -prandtl number on impinging jet heat transfer under a -semi-confined turbulent slot jet," International Comm. of Heat -and Mass Transfer, Vol. 29, pp. 929-938 【30】Shi, Y.L., Ray, M.B., and Mujumdar, A.S., 2003," Effects of -prandtl number on impinging jet heat transfer under a -semi-confined laminar slot jet," International Comm. of Heat -and Mass Transfer, Vol. 30, pp. 455-464 【31】Shuja, S.Z., Yilbas, B.S., and Budair M. O., 2001," Local -entropy generation in an impinging jet : minimum entropy -concep evaluating various turbulence models," Comput. -Methods Appl. Mech. Engrg., Vol. 190, pp. 3623-3644
【32】Chiriac, V. A., Ortega, A., 2002," A numerical study of the -unsteady flow and heat transfer in a transitional confined slot -jet impinging on an isothermal surface," International Journal -of Heat and Mass Transfer, Vol. 45, pp. 1237-1248 【33】Chen, C.H., 1998," Mixed convection heat transfer from a -horizontal plate with variable surface heat flux in a porous -medium," Heat and Mass Transfer, Vol. 34, pp. 1-7 【34】Fu, W.S., Huang, H.C., 1997," Thermal performances of -different shape porous blocks under an impinging jet," -International Journal of Heat and Mass Transfer, Vol. 40, pp. -2261-2272 【35】Chalupa, C., Chen, M., Modi, V.,and West, A., 2001," High -Schmidt mass transfer in a turbulent impinging slot-jet flow," -International Journal of Heat and Mass Transfer, Vol. 44, pp. -3775-3785 【36】Lee, D. H., Won, S. Y., Kim, Y. T., and Chung Y. S., 2002," -Turbulent heat transfer from a flat surface to a swirling round -impinging jet," International Journal of Heat and Mass -Transfer, Vol. 45, pp. 223-227 【37】Meola, C., Luca, L., and Carlomagno, G. M., 1996," Influence of -shear layer dynamics on impingement heat transfer," -Experimental Thermal and Fluid Science, Vol. 13, pp. 29-37 【38】Gau, C., Sheu, W. Y., and Shen, C. H., 1997," Impingement -cooling flow and heat transfer under acoustic excitations," -Journal of Heat Transfer, Vol. 119, pp. 810-817 【39】Lee, J., Lee, S. J., 1999," The effect of nozzle aspect ratio on -stagnation region heat transfer characteristics of elliptic -impinging jet," International Journal of Heat and Mass -Transfer, Vol. 43, pp. 555-575 【40】Liu, T., Sullivan, J. P., 1996," Heat transfer and flow structures in -an excited circular impinging jet,"
International Journal of -Heat and Mass Transfer, Vol. 39, pp. 3695-3706 【41】Fitzgerald, J., Garimella, S. V., 1998," A study of the flow field -of a confined and submerged impinging jet," International -Journal of Heat and Mass Transfer, Vol. 41, pp. 1025-1034 【42】Fitzgerald, J. A., Garimella, S. V., 1997," Flow field effects on -heat transfer in confined jet impingement," Journal of Heat -Transfer, Vol. 119, pp. 630-632 【43
】Sheriff, H. S., Zumbrunnen, D. A., 1994," Effect of flow -pulsations on the cooling effectiveness of an impinging jet," -Journal of Heat Transfer, Vol. 116, pp. 886-895 【44】Seyed-Yagoobi, J., Narayanan, V., and Page, R. H., 1998," -Comparision of heat transfer characteristics of radial jet -reattachment nozzle to in-line impinging jet nozzle," Journal -of Heat Transfer, Vol. 120, pp. 335-341 【45】Baughn, J. W., Hechanova, A.
E.,and Yan, X., 1985," An -Experimental study of entrainment effects on the heat transfer -from a flat surface to a heated circular impinging jet,"
Journal -of Heat Transfer, Vol. 113, pp. 1023-1025 【46】Bizzak, D. J.,and Chyu, M. K., 1995,"Use of laser-induced -fluorescence thermal
imaging system for local jet impingement --heat transfer measurement," International Journal of Heat and -Mass Transfer, Vol. 38, pp. 267-274
【47】-Breugem, W. P., Boersma, B. J., 2002,"The turbulent flow over a -permeable wall," Center for Turbulence Research Proceedings -of the Summer Program 【48】Chikh, S., Boumedien A., Bouhadef, K., and Lauriat, G., -1998,"Analysis of fluid flow and heat transfer in a channel with -intermittent heated porous blocks," Heat and Mass Transfer, -Vol. 33, pp. 405-413 【49】Jiang, P. X., Ren, Z. P., 2001,"Numerical investigation of forced -convection heat transfer in porous media using a thermal -non-equilibrium model," International Journal of Heat and -Fluid Flow, Vol. 22, pp. 102-110 【50】Fu, W. S., Huang, H. C., 1999,"Effects of random porosity model -on heat transfer performance of porous media," International -Journal of Heat and Mass Transfer, Vol. 42, pp. 13-25 【51】Angirasa, D., Peterson, G. P., 1999,"Forced convection heat -transfer augmentation in a channel with a localized heat source -using fibrous materials," ASME J. Electronic packaging, Vol.
-121, No.1, pp. 1-7 【52】Prakash, M., Turan, O. F., Li, Y., Mahoney, J., and Thorpe, G. R., -2001," Impinging round jet studies in a cylindrical enclosure -with and with and without a porous layer: Part I－Fiow -visualization and simulations", Chemical Engineering Science, -Vol. 56, pp.
3855-3878 【53】Jiang, P. X., Fan, M. H., Si, Z. P., and Ren, Z. P., 2001,"Thermal -－hydraulic performance of small scale micro-channel and -porous-media heat-exchangers," International Journal of Heat -and jass Transfer, Vol. 44, pp. 1039-1051 【54】Jiang, P. X., Wang, Z., Ren, Z.
P., and Wang B. X., 1-999,"Experimental research of fluid and convection heat -transfer in plate channel filled with glass or metallic particles,"
-Experimental Thermal and Fluid Science, Vol. 20, pp. 45-54 【55】Bhattacharya, A.,Calmidi, V. V., and Mahajan, R. L., -2002,"Thermophsical properties of high porosity metal -foams," International Journal of Heat and Mass Transfer, Vol. -45, pp. 1017-1031 【56】FLUENT 6 User's Guide Volume 1-4,Tutorial Guide Volume 1-2 始用手冊
