封闭腔湍流自然对流修正k-ε模型及其应用
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摘要
自然对流是由于流体的温度差或浓度差引起了密度差,在重力或其它力场作用下形成升浮力而产生的一种流体流动和对流传热现象。
封闭腔中自然对流由于在建筑节能、电子元器件的冷却、太阳能集热器设计、核反应器设计等领域中的普遍应用而受到了广泛关注。在过去的几十年中,为了深入理解封闭腔中自然对流流动与传热过程,人们开展了大量的实验和数值研究工作,但是封闭腔中湍流自然对流数值分析的结果与实验结果之间依然存在较大差异。随着计算机能力和计算方法的发展,数值分析方法越来成为不可缺少的研究手段。因此,进一步对封闭腔内湍流自然对流模型进行研究非常必要。
已发表的研究结果表明无论用高雷诺数κ-ε模型还是低雷诺数κ-ε模型对封闭腔内湍流自然对流问题进行计算时所得结果与实验结果之间均存在较大差异。本文针对这一现状开展了一系列工作。
1.为了获得数值结果和实验结果产生较大差异的原因,对自然对流和强迫对流从动量传递与热量传递之间的比拟关系方面进行了分析。发现自然对流流动边界层与温度边界层之间不存在比拟关系,从而不能像强迫对流一样用αt=νt/σt封闭能量方程中的-ρcpuiT。
2.提出了一求解封闭腔湍流自然对流换热的高低混合κ-ε模型,将由该模型所得结果与实验数据进行了对比。结果表明该模型在对湍流自然对流换热的预测精度上虽达到一定改善,但还需要进一步提高。
3.为了对高低混合κ-ε模型进行进一步改进,提出修正湍流普朗特数方案σt=1+Pr,并形成湍流修正κ-ε模型。将该模型所得结果与实验数据进行了对比,发现用修正κ-ε模型在Ra>109条件下获得封闭腔内空气湍流自然对流换热的平均Nu数与实验值之间的相对偏差平均值降低到了8.43%,同时在108≤Ra≤109时所得结果与其它文献中的数值结果很接近。
4.将修正κ-ε模型用于兰州地区住宅供暖换热器传热特性分析。在满足室内供暖温度要求的情况下,获得了外墙类型、室外环境条件、换热器面积、邻室传热等因素对换热器传热性能的影响规律、换热器表面温度、换热器提供的热量、室内流场、温度场等特征。
Acted by field force like gravity force, natural convection is induced by the buoyancy force resulting from temperature difference or concentration difference. It is a fluid flow and heat transfer phenomenon commonly occurring in many cases.
Natural convection in enclosures has been received considerable atteinstruments, solar energy collectors design and nuclear reactor design. Significant numbers of experimental and numerical works had been carried out in the past decades with an attempt to deeply understand the turbulent flow and heat transfer in enclosures. However, the discrepancies between the numerical results and the experimental results of the turbulent natural convection in enclosure are still significant. With developing of computer power and numerical method, the numerical analysis, as a study method, becomes more and more indispensable. So, it is worth making more efforts to study turbulent model for natural convection in enclosures.
A great numbers of the published investigations on turbulent natural convection in enclosures indicate that the discrepancy between the numerical results and the experimental results is significant using both the high-Reynolds-number k-ε model and the low-Reynolds-number k-ε model. Based on this situation, a series of works have been done in this dissertation:
1. To find the reason that the discrepancy exists between the numerical results and the experimental results, the differences of forced convection and natural convection are analyzed from the aspect of the analogy between momentum transfer and heat transfer. According to the analysis, it is found that the definition of, at=vt/σt, should not be used to enclose the turbulent heat flux,-ρcpuT'in energy equation because the analogy between flow boundary layer and thermal boundary layer does not exist in natural convection.
2. A composited k-ε model to resolve the turbulent natural convection heat transfer in enclosures is proposed. The composited k-ε model is used to numerically analyze the characteristics of fluid flow and heat transfer of natural convection in an air-filled enclosure. The numerical results are compared with the published experimental results and the numerical results, respectively. The results indicate that the composited k-ε model has a higher prediction accuracy than other models in some aspects, but the composited k-ε model should be further improved.
3. To improve the accuracy of the composited k-ε model, turbulent Prandtl number is modified into σt=1+Pr, and then a revised turbulent model is formed. The revised turbulent model is used to analyze the characteristics of turbulent natural convection in enclosure and the results are compared with the published experimental results and numerical results, respectively. The comparisons indicate that the revised k-ε model can accurately predict the heat transfer characteristics of the hot and cold wall under the condition of Ra>109. Especially, when109 4. The revised k-ε model is used to numerically analyze the heat transfer characteristics of a heat exchanger used in a typical room for heating in Lanzhou region. More details of the effects of outerwall types, outerdoor environment conditions, heat exchanger surface area, heat transfer between neighbour rooms on the heat transfer characteristics of the heat exchanger, the surface temperature of the heat exchanger and the heat quantity supplied by the hat exchanger, the flow field and temperature field of the room arc obtained.
封闭腔中自然对流由于在建筑节能、电子元器件的冷却、太阳能集热器设计、核反应器设计等领域中的普遍应用而受到了广泛关注。在过去的几十年中,为了深入理解封闭腔中自然对流流动与传热过程,人们开展了大量的实验和数值研究工作,但是封闭腔中湍流自然对流数值分析的结果与实验结果之间依然存在较大差异。随着计算机能力和计算方法的发展,数值分析方法越来成为不可缺少的研究手段。因此,进一步对封闭腔内湍流自然对流模型进行研究非常必要。
已发表的研究结果表明无论用高雷诺数κ-ε模型还是低雷诺数κ-ε模型对封闭腔内湍流自然对流问题进行计算时所得结果与实验结果之间均存在较大差异。本文针对这一现状开展了一系列工作。
1.为了获得数值结果和实验结果产生较大差异的原因,对自然对流和强迫对流从动量传递与热量传递之间的比拟关系方面进行了分析。发现自然对流流动边界层与温度边界层之间不存在比拟关系,从而不能像强迫对流一样用αt=νt/σt封闭能量方程中的-ρcpuiT。
2.提出了一求解封闭腔湍流自然对流换热的高低混合κ-ε模型,将由该模型所得结果与实验数据进行了对比。结果表明该模型在对湍流自然对流换热的预测精度上虽达到一定改善,但还需要进一步提高。
3.为了对高低混合κ-ε模型进行进一步改进,提出修正湍流普朗特数方案σt=1+Pr,并形成湍流修正κ-ε模型。将该模型所得结果与实验数据进行了对比,发现用修正κ-ε模型在Ra>109条件下获得封闭腔内空气湍流自然对流换热的平均Nu数与实验值之间的相对偏差平均值降低到了8.43%,同时在108≤Ra≤109时所得结果与其它文献中的数值结果很接近。
4.将修正κ-ε模型用于兰州地区住宅供暖换热器传热特性分析。在满足室内供暖温度要求的情况下,获得了外墙类型、室外环境条件、换热器面积、邻室传热等因素对换热器传热性能的影响规律、换热器表面温度、换热器提供的热量、室内流场、温度场等特征。
Acted by field force like gravity force, natural convection is induced by the buoyancy force resulting from temperature difference or concentration difference. It is a fluid flow and heat transfer phenomenon commonly occurring in many cases.
Natural convection in enclosures has been received considerable atteinstruments, solar energy collectors design and nuclear reactor design. Significant numbers of experimental and numerical works had been carried out in the past decades with an attempt to deeply understand the turbulent flow and heat transfer in enclosures. However, the discrepancies between the numerical results and the experimental results of the turbulent natural convection in enclosure are still significant. With developing of computer power and numerical method, the numerical analysis, as a study method, becomes more and more indispensable. So, it is worth making more efforts to study turbulent model for natural convection in enclosures.
A great numbers of the published investigations on turbulent natural convection in enclosures indicate that the discrepancy between the numerical results and the experimental results is significant using both the high-Reynolds-number k-ε model and the low-Reynolds-number k-ε model. Based on this situation, a series of works have been done in this dissertation:
1. To find the reason that the discrepancy exists between the numerical results and the experimental results, the differences of forced convection and natural convection are analyzed from the aspect of the analogy between momentum transfer and heat transfer. According to the analysis, it is found that the definition of, at=vt/σt, should not be used to enclose the turbulent heat flux,-ρcpuT'in energy equation because the analogy between flow boundary layer and thermal boundary layer does not exist in natural convection.
2. A composited k-ε model to resolve the turbulent natural convection heat transfer in enclosures is proposed. The composited k-ε model is used to numerically analyze the characteristics of fluid flow and heat transfer of natural convection in an air-filled enclosure. The numerical results are compared with the published experimental results and the numerical results, respectively. The results indicate that the composited k-ε model has a higher prediction accuracy than other models in some aspects, but the composited k-ε model should be further improved.
3. To improve the accuracy of the composited k-ε model, turbulent Prandtl number is modified into σt=1+Pr, and then a revised turbulent model is formed. The revised turbulent model is used to analyze the characteristics of turbulent natural convection in enclosure and the results are compared with the published experimental results and numerical results, respectively. The comparisons indicate that the revised k-ε model can accurately predict the heat transfer characteristics of the hot and cold wall under the condition of Ra>109. Especially, when109
引文
[1]过增元.国际传热研究前沿——微细尺度传热.力学进展,2000,30(1)：1-6.
[2]G. P. Peterson, An introduction to heat pipes-Modeling, Testing, and Applications. John Wiley &Sons, INC. New York,1994.
[3]王瑞平.平板型太阳能集热器效率分析.西安科技学院学报,2002,22(3)：362-366.
[4]赵春江,王恒龙.新型平板式集热器的设计和性能.上海交通大学学报,2004,38(10)：1656-1659.
[5]苏文佳,左然,张志强等.太阳能平板集热/储热系统.太阳能学报,2008,29(8)：449-453.
[6]张静敏,张华,卢峰等.太阳能烟囱集热器性能影响的试验研究.太阳能学报,2008,29(4)：993-998.
[7]李荣敏.热通道玻璃幕墙内部气流组织的研究：(硕士学位论文).上海：上海交通大学,2007.
[8]魏世雄.热通道玻璃幕墙数值模拟研究与优化设计：(硕士学位论文).上海：东华大学,2005.
[9]程义华,撒世忠,周亚素等.带遮阳百叶热通道幕墙的热工数学模型.建筑热能通风空调,2006,25(4)：10-15.
[10]Susanti L, Homma H, Matsumoto H, et al. A laboratory experiment on natural ventilation through a roof cavity for reduction of solar heat gain. Energy and Building,2008,40:2196-2206.
[11]马文驹,郑云.双扩散对流与晶体生长.力学进展,1991,21(2)：219-225.
[12]Yu Huiping, Sui Yunkang, Wang Jing, et al. Numerical Simulation of the natural convection influence on silicon single srysta 1 by CZ. Journal of synthetic crystals,2006,35(4):695-701
[13]宇慧平,隋允康,张峰翊等.紊流模型模拟分析旋转对提拉大直径单晶硅的影响.人工晶体学报,2004,33(5)：835-840.
[14]Papakonstantinou K A, Kiranoudis C T, Markatos N C. Computational analysis of thermal comfort:the case of the archaeological museum of Athens. Applied Mathematical Modelling,2000,24:477-494.
[15]Batchelor G K. Heat transfer by free convection across a closed cavity between vertical boundaries at different temperatures. Q. Appli. Math,1954,12:209-233.
[16]Poots G. Heat transfer by laminar free convection in enclosed plane gas layers. Q. Appl. Math,1958, 11:257-273.
[17]Aziz K and Hellums J D. Numerical solutions of the dimensional equations of motion for laminar natural convection. Phys. Fluids,1967,10:314-324.
[18]De Vahl Davis G. Laminar natural convection in an enclosed rectangular cavity. Int. J. Heat Mass Transfer,1968,11:1675-1693.
[19]MacGregor R K and Emery A F. Free convection through vertical plane layers-moderate and high Pr number fluids. ASME J. Heat Transfer,1969,91:391-403.
[20]Mallinson G D and De Vahl Davis G. Three-dimensional natural convection in a box:a numerical study. J. Fluid Mech,1977,83:1-31.
[21]Henkes R A W M. Natural convection flow in a square cavity calculated with low-Reynolds number turbulence models. International Journal of Heat Mass Transfer,1991,34:377-388.
[22]Henkes R A W M, Lankhost A M and Hoogendoorn C J. Structure of the laminar natural convection flow in a square cavity heated from the side for infinitely large Rayleigh number. Proc. ASME Winter Annual Meeting, Natural Convection in Enclosures, HTD-99,1988:9-16. NC36-24
[23]Corcione M. Effects of the thermal boundary conditions at the sidewalls upon natural convection in rectangular enclosures heated from bellow and cooled from above. Int. J. Therm. Sci,2003,42:199-208.
[24]Nader Ben Cheikh, Brahim Ben Beya,Taieb Lili. Influence of thermal boundary conditions on natural convection in a square enclosure partially heated from below, International communications in Heat and Mass Transfer,2007,34:369-379.
[25]Ganzarolli M M, Milanez L F. Natural convection in rectangular enclosures heated from below and symmetrically cooled from the sides. Int. J. Heat Mass Transfer,1995,38:1063-1073.
[26]Ramos R A V, Milanez L F. Numerical and experimental analysis of natural convection in cavity heated from below, Proceedings of 11th IHTC, vol.3, Kyongju, Korea,1998.
[27]Sezai I, Mohamad A. Natural convection from a discrete heat source on the bottom of a horizontal enclosure. Int. J. Heat Mass Transfer,2000,43:2257-2266.
[28]Sarris I E, Lekakis I, Vlachos N S. Natural convection in rectangular tanks heated locally from bellow. Int. J. Heat Mass Transfer,2004,47:3549-3563.
[29]Calgagni B, Marsili F, Paroncini M. Natural convective heat transfer in square enclosures heated from below. Appl. Therm. Eng,2005,25:2522-2531.
[30]Aydin O, Yang W J. Natural convection in enclosures with localized heating from below and symmetrical cooling from sides. Int. J. Numer. Methods Heat Fluid Flow,2000,10(5):519-529.
[31]Sharif M A R, Mohammad T R. Natural convection in cavities with constant flux heating at the bottom wall and isothermal cooling from the sidewalls. Int. J. Therm. Sci,2005,44:865-878.
[32]Hamady J F, Lloyd J R, Yang H Q, et al. Study of local natural convection heat transfer in an inclined enclosure. Int. J. Heat Mass Transfer,1989,32:1697-1708.
[33]Elsherbiny S M. Free convection in inclined air layers heated from above. Int. J. Heat MassTransfer, 1996,39:3925-3930.
[34]Erenburg V, Gelfgat A Y, Kit E, et al. A. Solan, Multiple states, stability and bifurcations of natural convection in a rectangular cavity with partially heated vertical walls. J. Fluid Mech,2003,492:63-89.
[35]Leong W H, Hollands K G T, Brunger A P. Experimental Nusselt numbers for a cubical-cavity benchmark problem in natural convection. Int. J. Heat Mass Transfer,1999,42:1979-1989.
[36]Wakashima S, Saitoh T S. Benchmark solutions for natural convection in a cubic cavity using the high-order time-space methods. Int. J. Heat Mass Transfer,2004,47:853-864.
[37]Yucel N, Ozdem A H. Natural convection in partially divided square enclosures. Heat Mass Transfer, 2003,40:167-175.
[38]Ampofo F. Turbulent natural convection in an air filled partitioned square cavity. Int. J. Heat Fluid Flow,2004,25:103-114.
[39]Shi X, Khodadadi J M. Laminar natural convection heat transfer in a differentially heated square cavity due to a thin fin on the hot wall. J. Heat Transfer,2003,125:624-634.
[40]Ostrach S, Raghavan C. Effect of stabilizing thermal gradients on natural convection in rectangular enclosures. J. Heat Transfer,1979,101:238-243.
[41]Shiralkar G S, Tien G L. A numerical study of the effect of a vertical temperature difference imposed in a horizontal enclosure. Numer. Heat Transfer,1982,5:185-197.
[42]Ravi M R, Henkes R A W M, Hoogendoorn C J. On the high Rayleigh-number structure of steady laminar natural-convection flow in a square enclosure. J. Fluid Mech.,1994,262:325-351.
[43]Ha M Y, Mi Jung Jung. A numerical study on three-dimensional conjugate heat transfer of natural convection and conduction in a di.erentially heated cubic enclosure with a heat-generating cubic conducting body. International Journal of Heat and Mass Transfer,2000,43:4229-4248.
[44]Kim D M, Viskanta R. Heat transfer by conduction, natural convection and radiation across a rectangular cellular structure. Int. J. Heat Fluid Flow,1984,5 (4):205-213.
[45]Kaminski D A, Prakash C. Conjugate natural convection in a square enclosure:effect of conduction in one of the vertical walls. Int. J. Heat Mass Transfer,1986,29 (12):1979-1988.
[46]Du Z G, Bilgen E. Coupling of wall conduction with natural convection in a rectangular enclosure. Int. J. Heat Mass Transfer,1992,35 (8):1969-1975.
[47]Liaqat A, Baytas A C. Conjugate natural convection in a square enclosure containing volumetric sources. Int J. Heat Mass Transfer,2001,44:3273-3280.
[48]Ben-Nakhi A, Mahmoud M. Conjugate natural convection in the roof cavity of heavy construction building during summer. Applied Thermal Engineering,2007,27:287-298.
[49]House J M. Beckermann C, Smith T F. Effect of a centered conducting body on natural convection heat transfer in an enclosure. Numerical Heat Transfer, Part A,1990,18:213-225.
[50]Oh J Y, Ha M Y, Kim K C. Numerical study of heat transfer and flow of natural convection in an enclosure with a heat-generating conducting body. Numerical Heat Transfer, Part A,1997,31:289-304.
[51]Ha M Y, Jung M J, Kim Y S. A numerical study on transient heat transfer and fluid flow of natural convection in an enclosure with a heat-generating conducting body. Numerical Heat Transfer, Part A,1999, 35:415-434.
[52]Ben Yedder R, Bilgen E. Laminar natural convection in inclined enclosures bounded by a solid wall. Heat and Mass Transfer,1997,32:455-462.
[53]Muneer T, Abodahad N, Gilchrist A. Combined conduction, convection and radiation heat transfer model for double-glazed windows. Proc CIBSE A18,1997:183-191.
[54]Ismail K A R, Salinas C T, Henriquez J G. Comparison between PCM filled glass windows and absorbing gas filled windows. Energy Build,2008,40:710-719.
[55]Onur N, Sivrioglu M, Turgut O. An experimental study on air window collector having a vertical blind for active solar heating. Solar Energy,1996,57:375-80.
[56]Etzion Y, Erell E. Controlling the transmission of radiant energy through windows:a novel ventilated reversible glazing system. Build Environ.,2000,35:433-444.
[57]Tanimoto J, Kimura K. Simulation study on an air flow window system with an integrated roll screen. Energy Build,1997,26:317-325.
[58]Ismail K A R, Salinas C T, Henriquez J R. A comparative study of naturally ventilated and gas filled windows for hot climates. Energy Conversion and Management,2009,50:1691-1703.
[59]徐铁锁,金虹,赵兴国,等.方腔内水平和竖直平板自然对流换热的数值计算.东北电力学院学报,1994,14(3)：83-86.
[60]夏吉良,辛明道,张洪济.单个局部内热源和外部加热同时作用时封闭空腔内的自然对流换热.重庆大学学报,1990,13(4)：23-33.
[61]陈礼,李隆健,底部离散加热、顶部冷却的二维空腔内高宽比对自然对流的影响.重庆大学学报,1994,17(1)：7-12.
[62]王秋旺,王育清,陶文铨,等.几何位置对封闭方腔内水平孤立平板自然对流换热的影响.工程热物理学报,1994,15(2)：195-199.
[63]徐明海,王秋旺,林梅,陶文铨.方腔尺寸对封闭方腔内多块孤立平板自然对流换热影响的数值分析.工程热物理学报,1999,20(6)：742-745.
[64]张浙,杨世铭,刘伟,等.矩形封闭空间内非饱和多孔介质自然对流的近似分析解.上海交通大学学报,1996,30(2)：1-7.
[65]张浙,杨世铭.矩形封闭空间内湿多孔介质自然对流的非达西效应.上海交通大学学报,1996,31(2)：56-60.
[66]杨沫,李少华,徐志明,等.三维方腔内竖直平板自然对流的数值模拟.工程热物理学报,1996,17(2)：209-212.
[67]李娜,李志信,过增元.封闭空间内小尺度等温竖板自然对流的三维效应.上海理工大学学报,2003,25(3)：218-220.
[68]战乃岩,杨茉,徐沛巍.封闭腔导热辐射与自然对流耦合换热的数值研究.中国科学：技术科学,2010,40(9)：1052-1060.
[69]Markatos N C, Pericleous K A. Laminar and turbulent natural convection in an enclosed cavity. Int. J. Heat Mass Transfer,1984,27:755-772.
[70]Ozoe H, Mouri A, Ohmuro M, et al. Numerical calculations of Iaminar and turbulent natural convection in water in rectangular channels heated and cooled isothermally on the opposing vertical walls. Int. J. Heat Mass Transfer,1985,28:125-138.
[71]Henkes R A W M, Hoogendoorn C J. Comparison of turbulence models for the natural convection boundary layer along a heated vertical plate. International Journal of Heat Mass Transfer,1989,32: 157-169.
[72]Nobile E, M.Sousa A C and Barozzi G S. Turbulent buoyant flows in enclosures, Proc.9th Int. Heat Transfer Conf.,1990,2:543-548.
[73]Barakos G, Mitsoulis E, Assimacopoulos D. Natural convection flow in a square cavity revisited: Laminar and turbulent models with wall functions. Int. J. Num. Meth. Fluids,1994,18:695-719.
[74]Henkes R A W M, Hoogendoorn C J. Comparison exercise for computations of turbulent natural convection in enclosures. Numer. Heat Transfer B,1995,28:59-78.
[75]Chen Q. Prediction of Room Air Motion by Reynolds-Stress Models. Building and Environment,1996, 31:233-244.
[76]Lankhorst A M, Hoogendoorn C J. Numerical computation of high Rayleigh number natural convection and prediction of hot radiator induced room air motion. Applied Scientific Research,1989, 47(4):301-322.
[77]Xu W, Chen Q, Nieuwstadt F T M. A new turbulence model for near-wall natural convection. International Journal of Heat and Mass Transfer,1998,41:3161-3176.
[78]Versteegh T A M, Nieuwstadt F T M. Scaling of free convection between two differentially heated infinite vertical plates. In:Turbulent Shear Flow,1996. [79]Sharif M A R, Liu W. Numerical study of turbulent natural convection in a side-heated square cavity at various angles of inclination. Numer. Heat Transfer, Part A,2003,43:693-716.
[80]Ben Yedder R, Bilgen E. Turbulent natural convection and conduction in enclosures bounded by a massive wall. International Journal of Heat and Mass Transfer,1995,38(10):1879-1891.
[81]Geniy V, Kuznetsov, Mikhail Sheremet A. Numerical simulation of turbulence natural convection in a rectangular enclosure having finite thickness walls. International Journal of Heat and Mass Transfer,2010, 53:163-177.
[82]Ben-Nakhi A, Mahmoud M. Conjugate turbulent natural convection in the roof enclosure of a heavy construction building during winter. Applied Thermal Engineering,2008,28:1522-1535. [83]Ben-Nakhi A, Mahmoud A M, Mahmoud M A, t al. Improving thermal performance of the roof enclosure of heavy construction buildings. Applied Energy,2008,85:911-930.
[84]赵秉文,刑荣鹏,张世将.矩形方腔湍流自然对流数值模拟研究.浙江理工大学学报,2008,25(4)：457-461.
[85]耿文广.考虑交叉耦合扩散效应时多物理场自然对流传热传质研究：(博士学位论文).济南：山东大学,2009.
[86]Henkes R A W M and Hoogendoom C J. Turbulent natural convection in enclosures:A computational and experimental benchmark study. Proc. Eurothenn Sem.22, EETI, Paris,1993.
[87]Fedorov A G and Viskanta R. Turbulent natural convection heat transfer in an asymmetrically heated vertical parallel-plate. Int. J. Heat Mass Transfer,1997,40 (16):3849-3860.
[88]Yasuo Hattori, Toshihiro Tsuji, Yasutaka Nagano, et al. Turbulence characteristics of natural convection boundary layer in air along a vertical plate heated at high temperatures. International Journal of Heat and Fluid Flow,2006,27:445-455.
[89]Ferreira V G, Mangiavacchi N, Tome M F, et al, Numerical simulation of turbulent free surface flow with two-equation k-ε eddy-viscosity models. Int. J. Numer. Meth. Fluids,2004,44:347-375.
[90]Kenjeres S, Hanjalic K. LES, T-RANS and hybrid simulations of thermal convection at high Ra numbers. International Journal of Heat and Fluid Flow,2006,27:800-810.
[91]Hsieh K J, Lien F S. Numerical modeling of buoyancy-driven turbulent flows in enclosures. International Journal of Heat and Fluid Flows,2004,25:659-670.
[92]Gray D D, Giorgin A. The validity of the Boussinesq approximation for liquids and gases. Int J Heat Transfer,1976,19:545-551.
[93]Chen C J, Jaw S Y. Fundamentals of turbulence modeling. Washington DC:Taylor&Francis,1998.
[94]程俊国,张洪济,张慕瑾等.高等传热学.重庆：重庆大学出版社,1990.
[95]Nachtsheim P R. Stability of free convection boundary-layer flows. NASA TN D-2089,1963.
[96]陶文铨.数值传热学.第二版.西安：西安交通大学出版社,2001.
[97]Rodi W. Turbulence models and their application in hydrolics,2nd ed. Netherlands, IAHR,1984:9-64.
[98]Jones W P, Launder B E. The prediction of laminarization with a two-equation model of turbulence. Int. J. Heat Mass Transfer,1972,15:301-311.
[99]Henkes R A W M. Natural Convection Boundary Layer, Ph.D thesis, Delft University of technology, 1990.
[100]Tsuji T, Nagano Y. Velocity and temperature measurements in a natural convection boundary layer along a vertical plat plate. Experimental Thermal Fluid Sci.,1989,2:208-215.
[101]Yu B, Ozoe H. Comparison of eight differential low-Reynolds-number k-models computed for natural convection in Czocharalski configuration. J. Mater Procc. Manuf. Sci.,1999,8:162-185.
[102]Tian Y S, Karayiannis T G. Low turbulence natural convection in an air filled square cavity, Part Ⅰ: the thermal and fluid flow fields. International Journal of Heat and Mass Transfer,2000,43:849-866.
[103]Jaw S Y, Chen C J. Present status of k-ε models and their applications. In:Chen C. J., Shih C., Lienau J., Kung R. J. eds. Flow modeling and turbulence measurement. Rotterdam:A A Bolkema,1996: 295-304.
[104]COSTA J J. Test of several versions for the k-ε type turbulence modeling of internal mixed convection flows. International Journal of Heat and Mass Transfer,1999,42:4391-4409.
[105]Chen Q. Comparison of different k-ε models for indoor air flow computations. Numerical Heat Transfer Part B,1995,28:353-369.
[106]Ciofalo M, Collins M W. k-ε predictions of heat transfer in turbulent reciuculating flows using an improved wall treatment. Numerical Heat Transfer, Part B,1989,15:21-47.
[107]Ramadhyani S. Two-equation and second-moment turbulence models for convective heat transfer. In:Minkowycz W. J., Sparrow E.M. eds. Advances in numerical heat transfer. Washington D.C.:Taylor & Francis,1997,1:171-199.
[108]So R M C, Zhang H S, Speciale C G. Near-wall modling of the dissipation rate equation. AIAA J, 1991,29(12):2069-2076.
[109]Nesic S, Adamopoulos G, Postlethwaite J, et al. Modeling of turbulent flow an mass transfer with wall function and low Re number closures. The Canadian Journal of Chemical Engineering,1993,71: 28-34.
[110]Chien K Y. Predictions of channel and boundary layer flows with a low-Reynolds-number two-equation model of turbulence. AIAA J,1982,20:33-38.
[111]Liu F, Wen J X. Development and validation of an advaced turbulence model for buoyancy driven flows in enclosures. International Journal of Heat and Mass Transfer,1999,42:3967-3981.
[112]符松.非线性湍流模式研究及进展.力学进展,1995,25(3)：318-327.
[113]Ince N Z, Launder B E. On the computation of buoyancy-driven turbulent flows in rectangular enclosures. International Journal of Heat and Fluid Flow,1989,10(2):110-117.
[114]Yap C. Turbulent heat and momentum transfer in recirculating and impinging flows:[dissertation].
Faculty of Technology, Univrsity of Manchestr, UK,1987. [115]Blosch E, Shyy W. The role of mass conservation in pressure-based algorithms. Numerical Heat Transfer, Part B,1993,24:415-429.
[116]Kim J, Moin P. Application of a fractional step method to incompressible Navier-Stokes equations. Journal of Computational Physics,1985,59:308-323.
[117]Kwak D, Chang J C, Shanks S P, et al. A three dimensional Navier-Stokes flow slover using primitive variables. AIAA Jounal,1986,24:390-396.
[118]Braaten M E, Shyy W. Comparison of iterative and direct method for viscous flow calculations in body-fitted coordinates. International Journal of Numerical Methods in Fluids,1986,6:325-349.
[119]Tao W Q, Qu Z G, He Y L. A novel segregated algorithm for incompressible fluid flow and heat transfer problems-CLEAR (coupled and linked equations algorithm revised). Part 1:Mathematical formulation and solution procedure. Numerical Heat Transfer, Part B,2004,45(1):1-18.
[120]Tao W Q, Qu Z G, He Y L. A novel segregated algorithm for incompressible fluid flow and heat transfer problems-CLEAR (coupled and linked equations algorithm revised). Part 2:Applications examples. Numerical Heat Transfer, Part B,2004,45(1):19-48.
[121]Shyy W, Mittel R. Solution methods for the incompressible Navier-Stokes equations//Johnson R W. The handbook of Fluid Dynamics, Boca Raton:CRC Press,1998,31:1-31.
[122]Hortmann M, Peric M, Scheuerer G. Finite volume multigrid prediction of laminar natural convection: Benchmark solutions. Int. J. Num. Meth.Fluids,1990,11:189-207.
[123]Patankar S V. Numerical heat transfer and fluid flow, pp.330-351, Hemisphere, New York,1980
[124]Ampofo F. Turbulent natural convection of air in a non-partitioned and partitioned cavity with differentially heated vertical and conducting horizontal walls. Experimental Thermal and Fluid Science, 2005,29:137-157.
[125]Ampofo F, Karayiannis T G. Experimental benchmark data for turbulent natural convection in an air filled square cavity. International Journal of Heat and Mass Transfer,2003,46:3551-3572.
[126]Kays W M. Turbulent Prandtl number-where we are? ASME J Hcat Transfer,1994,116:284-295.
[127]Miyamoto M, Kajino H, Kurima J, et al. Development of turbulence characteristics in a vertical free convection boundary layer, NC34,323-328, Vol.2, Proc. Seventh International Heat Transfer Conference, Munchen, Hemisphere Publishing Washington DC,1982.
[128]Fujii M, Fujii T. Numerical calculation of turbulent free convection along a vertical plate. Trans. JSME,1977,43(374):3825-3834.
[129]陆亚俊,马最良,邹平华.暖通空调.北京：中国建筑工业出版社,第二版,2007.
[130]刘艳峰,刘加平.建筑外壁面换热系数分析.西安建筑科技大学学报,2008,40(3)：407-412.
[131]单寄平.空调负荷实用计算法.北京：中国建筑工业出版社,1989.
[132]中国建筑学会建筑物理分会,围护结构隔热计算中的外表面换热系数取值[c]//陈启高.建筑物理学学术论文选集.北京：中国建筑工业出版社,2004：171-174.
[133]孟庆林,陈启高,冉茂宇,等.关于蒸发换热系数h的证明.太阳能学,1999,20(2)：216-219.
[2]G. P. Peterson, An introduction to heat pipes-Modeling, Testing, and Applications. John Wiley &Sons, INC. New York,1994.
[3]王瑞平.平板型太阳能集热器效率分析.西安科技学院学报,2002,22(3)：362-366.
[4]赵春江,王恒龙.新型平板式集热器的设计和性能.上海交通大学学报,2004,38(10)：1656-1659.
[5]苏文佳,左然,张志强等.太阳能平板集热/储热系统.太阳能学报,2008,29(8)：449-453.
[6]张静敏,张华,卢峰等.太阳能烟囱集热器性能影响的试验研究.太阳能学报,2008,29(4)：993-998.
[7]李荣敏.热通道玻璃幕墙内部气流组织的研究：(硕士学位论文).上海：上海交通大学,2007.
[8]魏世雄.热通道玻璃幕墙数值模拟研究与优化设计：(硕士学位论文).上海：东华大学,2005.
[9]程义华,撒世忠,周亚素等.带遮阳百叶热通道幕墙的热工数学模型.建筑热能通风空调,2006,25(4)：10-15.
[10]Susanti L, Homma H, Matsumoto H, et al. A laboratory experiment on natural ventilation through a roof cavity for reduction of solar heat gain. Energy and Building,2008,40:2196-2206.
[11]马文驹,郑云.双扩散对流与晶体生长.力学进展,1991,21(2)：219-225.
[12]Yu Huiping, Sui Yunkang, Wang Jing, et al. Numerical Simulation of the natural convection influence on silicon single srysta 1 by CZ. Journal of synthetic crystals,2006,35(4):695-701
[13]宇慧平,隋允康,张峰翊等.紊流模型模拟分析旋转对提拉大直径单晶硅的影响.人工晶体学报,2004,33(5)：835-840.
[14]Papakonstantinou K A, Kiranoudis C T, Markatos N C. Computational analysis of thermal comfort:the case of the archaeological museum of Athens. Applied Mathematical Modelling,2000,24:477-494.
[15]Batchelor G K. Heat transfer by free convection across a closed cavity between vertical boundaries at different temperatures. Q. Appli. Math,1954,12:209-233.
[16]Poots G. Heat transfer by laminar free convection in enclosed plane gas layers. Q. Appl. Math,1958, 11:257-273.
[17]Aziz K and Hellums J D. Numerical solutions of the dimensional equations of motion for laminar natural convection. Phys. Fluids,1967,10:314-324.
[18]De Vahl Davis G. Laminar natural convection in an enclosed rectangular cavity. Int. J. Heat Mass Transfer,1968,11:1675-1693.
[19]MacGregor R K and Emery A F. Free convection through vertical plane layers-moderate and high Pr number fluids. ASME J. Heat Transfer,1969,91:391-403.
[20]Mallinson G D and De Vahl Davis G. Three-dimensional natural convection in a box:a numerical study. J. Fluid Mech,1977,83:1-31.
[21]Henkes R A W M. Natural convection flow in a square cavity calculated with low-Reynolds number turbulence models. International Journal of Heat Mass Transfer,1991,34:377-388.
[22]Henkes R A W M, Lankhost A M and Hoogendoorn C J. Structure of the laminar natural convection flow in a square cavity heated from the side for infinitely large Rayleigh number. Proc. ASME Winter Annual Meeting, Natural Convection in Enclosures, HTD-99,1988:9-16. NC36-24
[23]Corcione M. Effects of the thermal boundary conditions at the sidewalls upon natural convection in rectangular enclosures heated from bellow and cooled from above. Int. J. Therm. Sci,2003,42:199-208.
[24]Nader Ben Cheikh, Brahim Ben Beya,Taieb Lili. Influence of thermal boundary conditions on natural convection in a square enclosure partially heated from below, International communications in Heat and Mass Transfer,2007,34:369-379.
[25]Ganzarolli M M, Milanez L F. Natural convection in rectangular enclosures heated from below and symmetrically cooled from the sides. Int. J. Heat Mass Transfer,1995,38:1063-1073.
[26]Ramos R A V, Milanez L F. Numerical and experimental analysis of natural convection in cavity heated from below, Proceedings of 11th IHTC, vol.3, Kyongju, Korea,1998.
[27]Sezai I, Mohamad A. Natural convection from a discrete heat source on the bottom of a horizontal enclosure. Int. J. Heat Mass Transfer,2000,43:2257-2266.
[28]Sarris I E, Lekakis I, Vlachos N S. Natural convection in rectangular tanks heated locally from bellow. Int. J. Heat Mass Transfer,2004,47:3549-3563.
[29]Calgagni B, Marsili F, Paroncini M. Natural convective heat transfer in square enclosures heated from below. Appl. Therm. Eng,2005,25:2522-2531.
[30]Aydin O, Yang W J. Natural convection in enclosures with localized heating from below and symmetrical cooling from sides. Int. J. Numer. Methods Heat Fluid Flow,2000,10(5):519-529.
[31]Sharif M A R, Mohammad T R. Natural convection in cavities with constant flux heating at the bottom wall and isothermal cooling from the sidewalls. Int. J. Therm. Sci,2005,44:865-878.
[32]Hamady J F, Lloyd J R, Yang H Q, et al. Study of local natural convection heat transfer in an inclined enclosure. Int. J. Heat Mass Transfer,1989,32:1697-1708.
[33]Elsherbiny S M. Free convection in inclined air layers heated from above. Int. J. Heat MassTransfer, 1996,39:3925-3930.
[34]Erenburg V, Gelfgat A Y, Kit E, et al. A. Solan, Multiple states, stability and bifurcations of natural convection in a rectangular cavity with partially heated vertical walls. J. Fluid Mech,2003,492:63-89.
[35]Leong W H, Hollands K G T, Brunger A P. Experimental Nusselt numbers for a cubical-cavity benchmark problem in natural convection. Int. J. Heat Mass Transfer,1999,42:1979-1989.
[36]Wakashima S, Saitoh T S. Benchmark solutions for natural convection in a cubic cavity using the high-order time-space methods. Int. J. Heat Mass Transfer,2004,47:853-864.
[37]Yucel N, Ozdem A H. Natural convection in partially divided square enclosures. Heat Mass Transfer, 2003,40:167-175.
[38]Ampofo F. Turbulent natural convection in an air filled partitioned square cavity. Int. J. Heat Fluid Flow,2004,25:103-114.
[39]Shi X, Khodadadi J M. Laminar natural convection heat transfer in a differentially heated square cavity due to a thin fin on the hot wall. J. Heat Transfer,2003,125:624-634.
[40]Ostrach S, Raghavan C. Effect of stabilizing thermal gradients on natural convection in rectangular enclosures. J. Heat Transfer,1979,101:238-243.
[41]Shiralkar G S, Tien G L. A numerical study of the effect of a vertical temperature difference imposed in a horizontal enclosure. Numer. Heat Transfer,1982,5:185-197.
[42]Ravi M R, Henkes R A W M, Hoogendoorn C J. On the high Rayleigh-number structure of steady laminar natural-convection flow in a square enclosure. J. Fluid Mech.,1994,262:325-351.
[43]Ha M Y, Mi Jung Jung. A numerical study on three-dimensional conjugate heat transfer of natural convection and conduction in a di.erentially heated cubic enclosure with a heat-generating cubic conducting body. International Journal of Heat and Mass Transfer,2000,43:4229-4248.
[44]Kim D M, Viskanta R. Heat transfer by conduction, natural convection and radiation across a rectangular cellular structure. Int. J. Heat Fluid Flow,1984,5 (4):205-213.
[45]Kaminski D A, Prakash C. Conjugate natural convection in a square enclosure:effect of conduction in one of the vertical walls. Int. J. Heat Mass Transfer,1986,29 (12):1979-1988.
[46]Du Z G, Bilgen E. Coupling of wall conduction with natural convection in a rectangular enclosure. Int. J. Heat Mass Transfer,1992,35 (8):1969-1975.
[47]Liaqat A, Baytas A C. Conjugate natural convection in a square enclosure containing volumetric sources. Int J. Heat Mass Transfer,2001,44:3273-3280.
[48]Ben-Nakhi A, Mahmoud M. Conjugate natural convection in the roof cavity of heavy construction building during summer. Applied Thermal Engineering,2007,27:287-298.
[49]House J M. Beckermann C, Smith T F. Effect of a centered conducting body on natural convection heat transfer in an enclosure. Numerical Heat Transfer, Part A,1990,18:213-225.
[50]Oh J Y, Ha M Y, Kim K C. Numerical study of heat transfer and flow of natural convection in an enclosure with a heat-generating conducting body. Numerical Heat Transfer, Part A,1997,31:289-304.
[51]Ha M Y, Jung M J, Kim Y S. A numerical study on transient heat transfer and fluid flow of natural convection in an enclosure with a heat-generating conducting body. Numerical Heat Transfer, Part A,1999, 35:415-434.
[52]Ben Yedder R, Bilgen E. Laminar natural convection in inclined enclosures bounded by a solid wall. Heat and Mass Transfer,1997,32:455-462.
[53]Muneer T, Abodahad N, Gilchrist A. Combined conduction, convection and radiation heat transfer model for double-glazed windows. Proc CIBSE A18,1997:183-191.
[54]Ismail K A R, Salinas C T, Henriquez J G. Comparison between PCM filled glass windows and absorbing gas filled windows. Energy Build,2008,40:710-719.
[55]Onur N, Sivrioglu M, Turgut O. An experimental study on air window collector having a vertical blind for active solar heating. Solar Energy,1996,57:375-80.
[56]Etzion Y, Erell E. Controlling the transmission of radiant energy through windows:a novel ventilated reversible glazing system. Build Environ.,2000,35:433-444.
[57]Tanimoto J, Kimura K. Simulation study on an air flow window system with an integrated roll screen. Energy Build,1997,26:317-325.
[58]Ismail K A R, Salinas C T, Henriquez J R. A comparative study of naturally ventilated and gas filled windows for hot climates. Energy Conversion and Management,2009,50:1691-1703.
[59]徐铁锁,金虹,赵兴国,等.方腔内水平和竖直平板自然对流换热的数值计算.东北电力学院学报,1994,14(3)：83-86.
[60]夏吉良,辛明道,张洪济.单个局部内热源和外部加热同时作用时封闭空腔内的自然对流换热.重庆大学学报,1990,13(4)：23-33.
[61]陈礼,李隆健,底部离散加热、顶部冷却的二维空腔内高宽比对自然对流的影响.重庆大学学报,1994,17(1)：7-12.
[62]王秋旺,王育清,陶文铨,等.几何位置对封闭方腔内水平孤立平板自然对流换热的影响.工程热物理学报,1994,15(2)：195-199.
[63]徐明海,王秋旺,林梅,陶文铨.方腔尺寸对封闭方腔内多块孤立平板自然对流换热影响的数值分析.工程热物理学报,1999,20(6)：742-745.
[64]张浙,杨世铭,刘伟,等.矩形封闭空间内非饱和多孔介质自然对流的近似分析解.上海交通大学学报,1996,30(2)：1-7.
[65]张浙,杨世铭.矩形封闭空间内湿多孔介质自然对流的非达西效应.上海交通大学学报,1996,31(2)：56-60.
[66]杨沫,李少华,徐志明,等.三维方腔内竖直平板自然对流的数值模拟.工程热物理学报,1996,17(2)：209-212.
[67]李娜,李志信,过增元.封闭空间内小尺度等温竖板自然对流的三维效应.上海理工大学学报,2003,25(3)：218-220.
[68]战乃岩,杨茉,徐沛巍.封闭腔导热辐射与自然对流耦合换热的数值研究.中国科学：技术科学,2010,40(9)：1052-1060.
[69]Markatos N C, Pericleous K A. Laminar and turbulent natural convection in an enclosed cavity. Int. J. Heat Mass Transfer,1984,27:755-772.
[70]Ozoe H, Mouri A, Ohmuro M, et al. Numerical calculations of Iaminar and turbulent natural convection in water in rectangular channels heated and cooled isothermally on the opposing vertical walls. Int. J. Heat Mass Transfer,1985,28:125-138.
[71]Henkes R A W M, Hoogendoorn C J. Comparison of turbulence models for the natural convection boundary layer along a heated vertical plate. International Journal of Heat Mass Transfer,1989,32: 157-169.
[72]Nobile E, M.Sousa A C and Barozzi G S. Turbulent buoyant flows in enclosures, Proc.9th Int. Heat Transfer Conf.,1990,2:543-548.
[73]Barakos G, Mitsoulis E, Assimacopoulos D. Natural convection flow in a square cavity revisited: Laminar and turbulent models with wall functions. Int. J. Num. Meth. Fluids,1994,18:695-719.
[74]Henkes R A W M, Hoogendoorn C J. Comparison exercise for computations of turbulent natural convection in enclosures. Numer. Heat Transfer B,1995,28:59-78.
[75]Chen Q. Prediction of Room Air Motion by Reynolds-Stress Models. Building and Environment,1996, 31:233-244.
[76]Lankhorst A M, Hoogendoorn C J. Numerical computation of high Rayleigh number natural convection and prediction of hot radiator induced room air motion. Applied Scientific Research,1989, 47(4):301-322.
[77]Xu W, Chen Q, Nieuwstadt F T M. A new turbulence model for near-wall natural convection. International Journal of Heat and Mass Transfer,1998,41:3161-3176.
[78]Versteegh T A M, Nieuwstadt F T M. Scaling of free convection between two differentially heated infinite vertical plates. In:Turbulent Shear Flow,1996. [79]Sharif M A R, Liu W. Numerical study of turbulent natural convection in a side-heated square cavity at various angles of inclination. Numer. Heat Transfer, Part A,2003,43:693-716.
[80]Ben Yedder R, Bilgen E. Turbulent natural convection and conduction in enclosures bounded by a massive wall. International Journal of Heat and Mass Transfer,1995,38(10):1879-1891.
[81]Geniy V, Kuznetsov, Mikhail Sheremet A. Numerical simulation of turbulence natural convection in a rectangular enclosure having finite thickness walls. International Journal of Heat and Mass Transfer,2010, 53:163-177.
[82]Ben-Nakhi A, Mahmoud M. Conjugate turbulent natural convection in the roof enclosure of a heavy construction building during winter. Applied Thermal Engineering,2008,28:1522-1535. [83]Ben-Nakhi A, Mahmoud A M, Mahmoud M A, t al. Improving thermal performance of the roof enclosure of heavy construction buildings. Applied Energy,2008,85:911-930.
[84]赵秉文,刑荣鹏,张世将.矩形方腔湍流自然对流数值模拟研究.浙江理工大学学报,2008,25(4)：457-461.
[85]耿文广.考虑交叉耦合扩散效应时多物理场自然对流传热传质研究：(博士学位论文).济南：山东大学,2009.
[86]Henkes R A W M and Hoogendoom C J. Turbulent natural convection in enclosures:A computational and experimental benchmark study. Proc. Eurothenn Sem.22, EETI, Paris,1993.
[87]Fedorov A G and Viskanta R. Turbulent natural convection heat transfer in an asymmetrically heated vertical parallel-plate. Int. J. Heat Mass Transfer,1997,40 (16):3849-3860.
[88]Yasuo Hattori, Toshihiro Tsuji, Yasutaka Nagano, et al. Turbulence characteristics of natural convection boundary layer in air along a vertical plate heated at high temperatures. International Journal of Heat and Fluid Flow,2006,27:445-455.
[89]Ferreira V G, Mangiavacchi N, Tome M F, et al, Numerical simulation of turbulent free surface flow with two-equation k-ε eddy-viscosity models. Int. J. Numer. Meth. Fluids,2004,44:347-375.
[90]Kenjeres S, Hanjalic K. LES, T-RANS and hybrid simulations of thermal convection at high Ra numbers. International Journal of Heat and Fluid Flow,2006,27:800-810.
[91]Hsieh K J, Lien F S. Numerical modeling of buoyancy-driven turbulent flows in enclosures. International Journal of Heat and Fluid Flows,2004,25:659-670.
[92]Gray D D, Giorgin A. The validity of the Boussinesq approximation for liquids and gases. Int J Heat Transfer,1976,19:545-551.
[93]Chen C J, Jaw S Y. Fundamentals of turbulence modeling. Washington DC:Taylor&Francis,1998.
[94]程俊国,张洪济,张慕瑾等.高等传热学.重庆：重庆大学出版社,1990.
[95]Nachtsheim P R. Stability of free convection boundary-layer flows. NASA TN D-2089,1963.
[96]陶文铨.数值传热学.第二版.西安：西安交通大学出版社,2001.
[97]Rodi W. Turbulence models and their application in hydrolics,2nd ed. Netherlands, IAHR,1984:9-64.
[98]Jones W P, Launder B E. The prediction of laminarization with a two-equation model of turbulence. Int. J. Heat Mass Transfer,1972,15:301-311.
[99]Henkes R A W M. Natural Convection Boundary Layer, Ph.D thesis, Delft University of technology, 1990.
[100]Tsuji T, Nagano Y. Velocity and temperature measurements in a natural convection boundary layer along a vertical plat plate. Experimental Thermal Fluid Sci.,1989,2:208-215.
[101]Yu B, Ozoe H. Comparison of eight differential low-Reynolds-number k-models computed for natural convection in Czocharalski configuration. J. Mater Procc. Manuf. Sci.,1999,8:162-185.
[102]Tian Y S, Karayiannis T G. Low turbulence natural convection in an air filled square cavity, Part Ⅰ: the thermal and fluid flow fields. International Journal of Heat and Mass Transfer,2000,43:849-866.
[103]Jaw S Y, Chen C J. Present status of k-ε models and their applications. In:Chen C. J., Shih C., Lienau J., Kung R. J. eds. Flow modeling and turbulence measurement. Rotterdam:A A Bolkema,1996: 295-304.
[104]COSTA J J. Test of several versions for the k-ε type turbulence modeling of internal mixed convection flows. International Journal of Heat and Mass Transfer,1999,42:4391-4409.
[105]Chen Q. Comparison of different k-ε models for indoor air flow computations. Numerical Heat Transfer Part B,1995,28:353-369.
[106]Ciofalo M, Collins M W. k-ε predictions of heat transfer in turbulent reciuculating flows using an improved wall treatment. Numerical Heat Transfer, Part B,1989,15:21-47.
[107]Ramadhyani S. Two-equation and second-moment turbulence models for convective heat transfer. In:Minkowycz W. J., Sparrow E.M. eds. Advances in numerical heat transfer. Washington D.C.:Taylor & Francis,1997,1:171-199.
[108]So R M C, Zhang H S, Speciale C G. Near-wall modling of the dissipation rate equation. AIAA J, 1991,29(12):2069-2076.
[109]Nesic S, Adamopoulos G, Postlethwaite J, et al. Modeling of turbulent flow an mass transfer with wall function and low Re number closures. The Canadian Journal of Chemical Engineering,1993,71: 28-34.
[110]Chien K Y. Predictions of channel and boundary layer flows with a low-Reynolds-number two-equation model of turbulence. AIAA J,1982,20:33-38.
[111]Liu F, Wen J X. Development and validation of an advaced turbulence model for buoyancy driven flows in enclosures. International Journal of Heat and Mass Transfer,1999,42:3967-3981.
[112]符松.非线性湍流模式研究及进展.力学进展,1995,25(3)：318-327.
[113]Ince N Z, Launder B E. On the computation of buoyancy-driven turbulent flows in rectangular enclosures. International Journal of Heat and Fluid Flow,1989,10(2):110-117.
[114]Yap C. Turbulent heat and momentum transfer in recirculating and impinging flows:[dissertation].
Faculty of Technology, Univrsity of Manchestr, UK,1987. [115]Blosch E, Shyy W. The role of mass conservation in pressure-based algorithms. Numerical Heat Transfer, Part B,1993,24:415-429.
[116]Kim J, Moin P. Application of a fractional step method to incompressible Navier-Stokes equations. Journal of Computational Physics,1985,59:308-323.
[117]Kwak D, Chang J C, Shanks S P, et al. A three dimensional Navier-Stokes flow slover using primitive variables. AIAA Jounal,1986,24:390-396.
[118]Braaten M E, Shyy W. Comparison of iterative and direct method for viscous flow calculations in body-fitted coordinates. International Journal of Numerical Methods in Fluids,1986,6:325-349.
[119]Tao W Q, Qu Z G, He Y L. A novel segregated algorithm for incompressible fluid flow and heat transfer problems-CLEAR (coupled and linked equations algorithm revised). Part 1:Mathematical formulation and solution procedure. Numerical Heat Transfer, Part B,2004,45(1):1-18.
[120]Tao W Q, Qu Z G, He Y L. A novel segregated algorithm for incompressible fluid flow and heat transfer problems-CLEAR (coupled and linked equations algorithm revised). Part 2:Applications examples. Numerical Heat Transfer, Part B,2004,45(1):19-48.
[121]Shyy W, Mittel R. Solution methods for the incompressible Navier-Stokes equations//Johnson R W. The handbook of Fluid Dynamics, Boca Raton:CRC Press,1998,31:1-31.
[122]Hortmann M, Peric M, Scheuerer G. Finite volume multigrid prediction of laminar natural convection: Benchmark solutions. Int. J. Num. Meth.Fluids,1990,11:189-207.
[123]Patankar S V. Numerical heat transfer and fluid flow, pp.330-351, Hemisphere, New York,1980
[124]Ampofo F. Turbulent natural convection of air in a non-partitioned and partitioned cavity with differentially heated vertical and conducting horizontal walls. Experimental Thermal and Fluid Science, 2005,29:137-157.
[125]Ampofo F, Karayiannis T G. Experimental benchmark data for turbulent natural convection in an air filled square cavity. International Journal of Heat and Mass Transfer,2003,46:3551-3572.
[126]Kays W M. Turbulent Prandtl number-where we are? ASME J Hcat Transfer,1994,116:284-295.
[127]Miyamoto M, Kajino H, Kurima J, et al. Development of turbulence characteristics in a vertical free convection boundary layer, NC34,323-328, Vol.2, Proc. Seventh International Heat Transfer Conference, Munchen, Hemisphere Publishing Washington DC,1982.
[128]Fujii M, Fujii T. Numerical calculation of turbulent free convection along a vertical plate. Trans. JSME,1977,43(374):3825-3834.
[129]陆亚俊,马最良,邹平华.暖通空调.北京：中国建筑工业出版社,第二版,2007.
[130]刘艳峰,刘加平.建筑外壁面换热系数分析.西安建筑科技大学学报,2008,40(3)：407-412.
[131]单寄平.空调负荷实用计算法.北京：中国建筑工业出版社,1989.
[132]中国建筑学会建筑物理分会,围护结构隔热计算中的外表面换热系数取值[c]//陈启高.建筑物理学学术论文选集.北京：中国建筑工业出版社,2004：171-174.
[133]孟庆林,陈启高,冉茂宇,等.关于蒸发换热系数h的证明.太阳能学,1999,20(2)：216-219.