新型翼片斜板取水头内部流场的数值模拟及分离性能研究
|
摘要
在构建低碳经济、倡导可持续发展的当今社会,水源热泵技术作为一种可靠的具有高效节能、减碳效果的可再生能源应用技术近年来在我国得到了迅速的发展。充足的水源和良好的水质条件是应用水源热泵技术的基础条件,论文以重庆主城区应用地表水源热泵技术为背景,从计算流体力学角度研究了专门针对嘉陵江、长江水质中含沙量过高而设计的新型翼片斜板取水头的内部流场及其对沙粒的分离性能,并探讨了不同入口水流速度、不同密度差、不同结构参数条件下翼片斜板取水头对固体颗粒的去除效果的优劣。
论文通过对固液两相流理论的研究与计算流体力学基本控制方程的分析,确立了采用湍流雷诺模型以及离散相模型对翼片斜板取水头中固液两相流进行数值模拟的计算方案,并以设计的中试装置的结构参数为基础对翼片斜板取水头的分离性能以及内部流场进行了数值模拟。
通过计算单一粒径颗粒在翼片斜板取水头内的分离效率,得到了该新型翼片斜板取水头的分离效率图,结果表明该翼片斜板取水头对10微米级以上粒径的颗粒去除率可达40%以上;通过计算得到的流场结果显示,有压流条件下的翼片斜板取水头内部流场呈明显的平行流动和环形流动两个区域,并且环形流动的翼片格子区域内的水流速度相比于平行流动的主流区要小很多,这一特殊的流场特性对于进入翼片格内的沙粒等固体颗粒物的去除非常有利;通过对比不同入口水流速度、固液两相间不同密度差条件下该新型取水头对固体颗粒的去除效率发现,水流速度和两相密度差这两大因素对取水头的去除效率都有较大影响。论文从取水头对固体颗粒的去除规律与试验结果进行了对比验证,结果表明数值计算所得到的结果与试验结果基本吻合,从而证明了我们所建立的计算模型和选择数值计算方案的正确性。
采用已被证实为正确的计算模型和数值计算方案就翼片斜板结构的主要结构参数(翼片格数N、翼片宽度B、斜板宽度h和斜板倾角θ)对固体颗粒的分离性能的影响作了研究,并就各参数对分离性能的影响作了定性分析,得出了使取水头出水所含颗粒最少时的结构参数值。
论文中研究有压流条件下翼片斜板结构的取水头的内部流场和固液两相流中固体颗粒的分离效率所确立的数值计算方法,能够为实际工程中设计的类似取水头部性能的研究提供一种新的思路和可靠的方法,具有一定的参考价值。
In modern society that builds low carbon economy and promotes sustainable development, as a reliable, energy efficient and carbon reducing renewable energy application technology, the water source heat pump technology (WSHP) has been developed rapidly in recent years in China. Sufficient water source and good water quality condition are the basic conditions for application of WSHP technology. Based on application of WSHP technology in Chongqing city, from the perspective of computational fluid dynamics, this paper studies the internal flow field and separation performance of the new water intake head with inclined vane plates designed for high sediment concentration in Jialing River and Yangtze River water, and discusses the performance of the new water intake head with inclined vane plates removing solids under the different inlet water velocity, the different density contrast, and the different structural parameters.
In this paper, through studying the liquid-solid two-phase flow theory and analyzing the basic equations of computational fluid dynamics, the numerical simulation method for solid-liquid two-phase flow in the water intake head with inclined vane plates by use of turbulent Reynolds Model and Discrete Phase Model was established, the separation performance and internal flow field of the new water intake head based on the designed structural parameters of pilot-plant are simulated.
By calculating the separation efficiency of single size particles in the new water intake head with inclined vane plates, its separation efficiency diagram was obtained. The results showed that the removal efficiency of particle that its size is more than 10 micron, can reach above 40% in this new water intake head. The computational flow field results showed that the internal flow field in the new water intake head with inclined vane plates is obvious parallel flow and annular flow., and the water velocity of annular flow in vane grid region is much lower than that of parallel flow in mainstream area, which is very favorable to remove sand and other solid particles in vane grid region. By comparing the removal efficiency under the conditions of different inlet water velocity and solid-liquid two phase density contrast, we found that water velocity and density contrast have great influence on the removal efficiency of this new water intake head. The laws of the new water intake head removing solid particles were compared with experiment results, which proved that the results of numerical calculation were almost the same as experiment results, and proved that our computation model and numerical calculation solution is correct.
The separation performance of water intake head with inclined vane plates removing particles influenced by its main structural parameters, including vane number N, vane width B, inclined plate width h, and inclined plate tilt angleθwas studied by use of the correct calculation model and numerical simulation solution that had been confirmed. Through qualitative analysis, the optimum structural parameter values to make effluent water contain minimum particles were obtained.
In this paper, we established a numerical calculation method of studying the internal flow field of the new water intake head with inclined vane plates and solid-liquid two phase separation efficiency of solid particles under the conditions of pressure flow, which provides a new idea and reliable methods for similar research on the performance of water intake head and has certain reference value in actual engineering design.
论文通过对固液两相流理论的研究与计算流体力学基本控制方程的分析,确立了采用湍流雷诺模型以及离散相模型对翼片斜板取水头中固液两相流进行数值模拟的计算方案,并以设计的中试装置的结构参数为基础对翼片斜板取水头的分离性能以及内部流场进行了数值模拟。
通过计算单一粒径颗粒在翼片斜板取水头内的分离效率,得到了该新型翼片斜板取水头的分离效率图,结果表明该翼片斜板取水头对10微米级以上粒径的颗粒去除率可达40%以上;通过计算得到的流场结果显示,有压流条件下的翼片斜板取水头内部流场呈明显的平行流动和环形流动两个区域,并且环形流动的翼片格子区域内的水流速度相比于平行流动的主流区要小很多,这一特殊的流场特性对于进入翼片格内的沙粒等固体颗粒物的去除非常有利;通过对比不同入口水流速度、固液两相间不同密度差条件下该新型取水头对固体颗粒的去除效率发现,水流速度和两相密度差这两大因素对取水头的去除效率都有较大影响。论文从取水头对固体颗粒的去除规律与试验结果进行了对比验证,结果表明数值计算所得到的结果与试验结果基本吻合,从而证明了我们所建立的计算模型和选择数值计算方案的正确性。
采用已被证实为正确的计算模型和数值计算方案就翼片斜板结构的主要结构参数(翼片格数N、翼片宽度B、斜板宽度h和斜板倾角θ)对固体颗粒的分离性能的影响作了研究,并就各参数对分离性能的影响作了定性分析,得出了使取水头出水所含颗粒最少时的结构参数值。
论文中研究有压流条件下翼片斜板结构的取水头的内部流场和固液两相流中固体颗粒的分离效率所确立的数值计算方法,能够为实际工程中设计的类似取水头部性能的研究提供一种新的思路和可靠的方法,具有一定的参考价值。
In modern society that builds low carbon economy and promotes sustainable development, as a reliable, energy efficient and carbon reducing renewable energy application technology, the water source heat pump technology (WSHP) has been developed rapidly in recent years in China. Sufficient water source and good water quality condition are the basic conditions for application of WSHP technology. Based on application of WSHP technology in Chongqing city, from the perspective of computational fluid dynamics, this paper studies the internal flow field and separation performance of the new water intake head with inclined vane plates designed for high sediment concentration in Jialing River and Yangtze River water, and discusses the performance of the new water intake head with inclined vane plates removing solids under the different inlet water velocity, the different density contrast, and the different structural parameters.
In this paper, through studying the liquid-solid two-phase flow theory and analyzing the basic equations of computational fluid dynamics, the numerical simulation method for solid-liquid two-phase flow in the water intake head with inclined vane plates by use of turbulent Reynolds Model and Discrete Phase Model was established, the separation performance and internal flow field of the new water intake head based on the designed structural parameters of pilot-plant are simulated.
By calculating the separation efficiency of single size particles in the new water intake head with inclined vane plates, its separation efficiency diagram was obtained. The results showed that the removal efficiency of particle that its size is more than 10 micron, can reach above 40% in this new water intake head. The computational flow field results showed that the internal flow field in the new water intake head with inclined vane plates is obvious parallel flow and annular flow., and the water velocity of annular flow in vane grid region is much lower than that of parallel flow in mainstream area, which is very favorable to remove sand and other solid particles in vane grid region. By comparing the removal efficiency under the conditions of different inlet water velocity and solid-liquid two phase density contrast, we found that water velocity and density contrast have great influence on the removal efficiency of this new water intake head. The laws of the new water intake head removing solid particles were compared with experiment results, which proved that the results of numerical calculation were almost the same as experiment results, and proved that our computation model and numerical calculation solution is correct.
The separation performance of water intake head with inclined vane plates removing particles influenced by its main structural parameters, including vane number N, vane width B, inclined plate width h, and inclined plate tilt angleθwas studied by use of the correct calculation model and numerical simulation solution that had been confirmed. Through qualitative analysis, the optimum structural parameter values to make effluent water contain minimum particles were obtained.
In this paper, we established a numerical calculation method of studying the internal flow field of the new water intake head with inclined vane plates and solid-liquid two phase separation efficiency of solid particles under the conditions of pressure flow, which provides a new idea and reliable methods for similar research on the performance of water intake head and has certain reference value in actual engineering design.
引文
[1]潘登.地表水源热泵技术在重庆的应用研究[D].重庆大学,硕士论文,2008.
[2]重庆市统计局等编.《重庆统计年鉴—2009》[M].北京:中国统计出版社,2009.
[3]重庆市发展改革委员会.重庆市资源与能源开发利用科技问题研究[R],2004.
[4]刘德彧.水源热泵系统的综合研究与工程应用[D].北方工业大学,硕士论文,2003.
[5] King, B. Experiences in the use of ground water-to-water heat pumps for building heating[C]. IEE Conference Publication, n 233, 329-332, 1984.
[6] Antero A M. Lakes as a heat source in cold climate[R]. In: International Congress of Refrigeration. Washington D C, 2003:1-8.
[7] A.L. Snijders. Aquifer Seasonal Cold Storage for Space Conditioning: Some Cost-effective Applications[J]. ASHRAE Transactions, 92, 11(3).
[8]李先瑞,刘笑.水源热泵与未利用能[C].全国暖通空调制冷2000年学术年会,2000:122-126.
[9]董孟能,姜涵,霍建辉,王晶,李怀玉.重庆江水水源热泵应用关键技术—取水及水质处理技术探讨[J].建设科技,2007.17,84～85.
[10]王子云,付祥钊,王永等.重庆市发展长江水源热泵的水源概况分析.重庆建筑大学学报,2008,30(1):92-94
[11]水利部长江水利委员会.长江泥沙公报[M],2006.
[12]王子云,付祥钊,仝庆贵.利用长江水作热泵系统冷热源的技术分析[J].中国给水排水. 2007.3: 6～9.
[13] H.I. Henderson, S.W. Carlson, M.K. Khattar, et al. The implications of the measured performance of variable flow pumping systems in geothermal and water loop heat pump applications. ASHRAE Trans. 106(2000)533-542.
[14] Heavener. Heating and Cooling System Using Groundwater[P]. United States Patent: 4427055, 1984-01-24.
[15] Kavanaugh S P. Design considerations for ground and water source heat pumps in southern climates [J]. ASHRAE Transactions, 1989, 95(1): 1139-1149.
[16] Kavanaugh S P, Pezent M C. Lake water applications of water-to-air heat pumps[J]. ASHRAE Transactions, 1990, 96(1):813-820
[17] Kavanaugh S P, Woodhouse J G, Carter J R. Test results of water-to-air heat pumps with high cooling efficiency for ground-coupled applications[J]. ASHRAE Transactions, 1991, 97:895-901.
[18] P. Tim, W. S. Joyce. Lake-source cooling[J]. ASHRAE Jounal, 2002, 44(4), 37-39.
[19]刘光远,陈兴华.俄罗斯热泵新技术简介[J].能源研究与利用,2001,(3):17-19.
[20] Büyükalaca O, Ekinci F, Yilmaz T. Experimental investigation of Seyhan River and dam lake as heat source-sink for a heat pump[J]. Energy, 2003, 28(2):157-169.
[21] S.W. Lang, W. Xu, T.S. Feng. Issues of design and application of the centralized air conditioning system with water source heat pump units [J]. HVAC 26(1)(1996)15-19.
[22] Yumrutas R, Unsal M.A computational model of a heat pump system with a hemispherical surface tank as the ground heat source. Energy, 2000, 25: 371-388.
[23]张勇,刘群生,李云苍.热泵技术的发展与应用[J].能源工程,2001,(4):32-35.
[24]蒋能照.空调用热泵技术及应用[M].北京:机械工业出版社,1997: 205-218.
[25]吕灿仁,马一太.运用热泵提高低温地热采暖系统能源利用率的分析[J].天津大学学报,1982,(4):1-8.
[26] Gao Z K.A study on the heating performance of ground-coupled heat pump[C].In: First International Conference on Energy Conversion and Energy Sources Engineering. Wuhan,1990:93-96.
[27] Gao Z K.A computer simulation of ground-coupled heat pump temperature field underground[C].In: First International Conference on Energy Conversion and Energy Sources Engineering.Wuhan, 1990:114-118.
[28]喻李葵,刘婷婷,彭建国等.地表水源热泵空调系统供暖模式优化方法[J].制冷与空调,2004,4(4):47-51.
[29]张海峰,茆磊,叶宏等.太阳能辅助地表水源热泵系统的性能模拟[C].制冷空调新技术进展——第四届全国制冷空调新技术研讨会论文集,南京,2005:795-798.
[30]陈晓,张国强,彭建国等.开式地表水源热泵在湖南某人工湖的应用研究[J].制冷学报,2006,27(3):10-13.
[31]钱剑峰,孙德兴,张承虎等.新型地表水源热泵及亟待解决的相关问题[C].全国暖通空调制冷2006学术年会资料集,合肥,2006:203-206.
[32]钱剑峰,孙德兴,吴荣华等.地表水源热泵辅助热源节能效果的分析[J].节能技术,2006,24(4):330-332.
[33]马最良,曹源.闭式环路水源热泵空调系统运行能耗的静态分析[J].哈尔滨建筑大学学报,1997,30 (6): 68-74.
[34]马最良,曹源.闭式环路水源热泵空调系统运行能耗的计算机动态模拟分析[J].哈尔滨建筑大学学报,1998,31(3): 57-63.
[35]陈晓,张国强,林宣军等.南方地区开式湖水源热泵的应用[C].中国制冷学会2005年制冷空调学术年会论文集,昆明,2005:370-374.
[36]严煦世,范瑾初.给水工程(第4版)[M].北京:中国建筑工业出版社, 1999:209-211.
[37]上海市政工程设计研究院.给水排水设计手册第3册—城镇给水(第二版)[S].北京:中国建筑工业出版社,2004:226-232.
[38]钟德铃,彭雪峰.介绍一种岸边式取水头部——悬臂真空罐取水头部[J].给水排水, 2002,28(7):13-15.
[39]唐明启.一种底栏栅结合干砌石形式的取水头部设计[J].中国给水排水,2008,25(2):44-46.
[40]董延衣.丘陵地区乡镇小型给水工程取水头部及取水口设计施工特点[J].西南给排水,1992,2:10-12.
[41]卢咏林.水下驱动自动防堵式水泵取水头[P].中国: ZL00230715.4,2001-06-20.
[42]李小林.双向防草除沙取水头[P].中国: ZL200520003650.8,2006-05-17.
[43]李保忠.防泥沙取水头[P].中国: ZL02229121.0,2003-04-09.
[44]陈滨.影响侧向流翼片斜板沉淀去浊效果因素的分析[J].给水排水,1992,01:15-18.
[45]刘百仓,马军,张素霞等.带翼片侧向流斜板沉淀池内颗粒沉降过程的数值模拟[J].给水排水,2007,33(11):139-142.
[46] S.V.Patankar. Numerical Heat Transfer and Fluid Flow[A].王福军.计算流体动力学分析—CFD软件原理与应用[M].北京:清华大学出版社,2004:4.
[47]王福军.计算流体动力学分析—CFD软件原理与应用[M].北京:清华大学出版社,2004:1-60.
[48]张红梅,李志鹏,高正明.连续高速分散混合器流体流动的数值模拟[J].北京化工大学学报,2005,32(6):5-8.
[49] Fluent Inc., FLUENT User’s Guide. Fluent Inc.,2003.
[50] Fluent Inc., FLUENT User Defined Function Manual. Fluent Inc.,2003.
[51]褚良银,陈文梅,戴光清等.水力旋流器[M].北京:化学工业出版社,1998.
[52]佟庆理.两相流动理论基础[M].北京:冶金工业出版社,1995.
[53]王绍亭,陈涛.动量热量与质量传递[M].天津:天津科学技术出版社,1986.
[54]岑可法.工程气固多相流动的理论及计算[M].杭州:浙江大学出版社,1990:80-85.
[55] C.J. Chen, S.Y. Jaw. Fundamentals of Turbulence Modeling[A].王福军.计算流体动力学分析—CFD软件原理与应用[M].北京:清华大学出版社,2004:4.
[56]陶文铨.数值传热学(第二版)[M].西安:西安交通大学出版社,2001.
[57] W.P. Jones, B.E. Launder. The calculation of low-Reynolds-number phenomena with a two-equation model of turbulence[A].王福军.计算流体动力学分析—CFD软件原理与应用[M].北京:清华大学出版社,2004:4.
[58]刘灿生,沈志恒,王绍文.翼片斜板沉淀实验研究[J].哈尔滨建筑工程学院学报, 1985,2:68-73.
[2]重庆市统计局等编.《重庆统计年鉴—2009》[M].北京:中国统计出版社,2009.
[3]重庆市发展改革委员会.重庆市资源与能源开发利用科技问题研究[R],2004.
[4]刘德彧.水源热泵系统的综合研究与工程应用[D].北方工业大学,硕士论文,2003.
[5] King, B. Experiences in the use of ground water-to-water heat pumps for building heating[C]. IEE Conference Publication, n 233, 329-332, 1984.
[6] Antero A M. Lakes as a heat source in cold climate[R]. In: International Congress of Refrigeration. Washington D C, 2003:1-8.
[7] A.L. Snijders. Aquifer Seasonal Cold Storage for Space Conditioning: Some Cost-effective Applications[J]. ASHRAE Transactions, 92, 11(3).
[8]李先瑞,刘笑.水源热泵与未利用能[C].全国暖通空调制冷2000年学术年会,2000:122-126.
[9]董孟能,姜涵,霍建辉,王晶,李怀玉.重庆江水水源热泵应用关键技术—取水及水质处理技术探讨[J].建设科技,2007.17,84～85.
[10]王子云,付祥钊,王永等.重庆市发展长江水源热泵的水源概况分析.重庆建筑大学学报,2008,30(1):92-94
[11]水利部长江水利委员会.长江泥沙公报[M],2006.
[12]王子云,付祥钊,仝庆贵.利用长江水作热泵系统冷热源的技术分析[J].中国给水排水. 2007.3: 6～9.
[13] H.I. Henderson, S.W. Carlson, M.K. Khattar, et al. The implications of the measured performance of variable flow pumping systems in geothermal and water loop heat pump applications. ASHRAE Trans. 106(2000)533-542.
[14] Heavener. Heating and Cooling System Using Groundwater[P]. United States Patent: 4427055, 1984-01-24.
[15] Kavanaugh S P. Design considerations for ground and water source heat pumps in southern climates [J]. ASHRAE Transactions, 1989, 95(1): 1139-1149.
[16] Kavanaugh S P, Pezent M C. Lake water applications of water-to-air heat pumps[J]. ASHRAE Transactions, 1990, 96(1):813-820
[17] Kavanaugh S P, Woodhouse J G, Carter J R. Test results of water-to-air heat pumps with high cooling efficiency for ground-coupled applications[J]. ASHRAE Transactions, 1991, 97:895-901.
[18] P. Tim, W. S. Joyce. Lake-source cooling[J]. ASHRAE Jounal, 2002, 44(4), 37-39.
[19]刘光远,陈兴华.俄罗斯热泵新技术简介[J].能源研究与利用,2001,(3):17-19.
[20] Büyükalaca O, Ekinci F, Yilmaz T. Experimental investigation of Seyhan River and dam lake as heat source-sink for a heat pump[J]. Energy, 2003, 28(2):157-169.
[21] S.W. Lang, W. Xu, T.S. Feng. Issues of design and application of the centralized air conditioning system with water source heat pump units [J]. HVAC 26(1)(1996)15-19.
[22] Yumrutas R, Unsal M.A computational model of a heat pump system with a hemispherical surface tank as the ground heat source. Energy, 2000, 25: 371-388.
[23]张勇,刘群生,李云苍.热泵技术的发展与应用[J].能源工程,2001,(4):32-35.
[24]蒋能照.空调用热泵技术及应用[M].北京:机械工业出版社,1997: 205-218.
[25]吕灿仁,马一太.运用热泵提高低温地热采暖系统能源利用率的分析[J].天津大学学报,1982,(4):1-8.
[26] Gao Z K.A study on the heating performance of ground-coupled heat pump[C].In: First International Conference on Energy Conversion and Energy Sources Engineering. Wuhan,1990:93-96.
[27] Gao Z K.A computer simulation of ground-coupled heat pump temperature field underground[C].In: First International Conference on Energy Conversion and Energy Sources Engineering.Wuhan, 1990:114-118.
[28]喻李葵,刘婷婷,彭建国等.地表水源热泵空调系统供暖模式优化方法[J].制冷与空调,2004,4(4):47-51.
[29]张海峰,茆磊,叶宏等.太阳能辅助地表水源热泵系统的性能模拟[C].制冷空调新技术进展——第四届全国制冷空调新技术研讨会论文集,南京,2005:795-798.
[30]陈晓,张国强,彭建国等.开式地表水源热泵在湖南某人工湖的应用研究[J].制冷学报,2006,27(3):10-13.
[31]钱剑峰,孙德兴,张承虎等.新型地表水源热泵及亟待解决的相关问题[C].全国暖通空调制冷2006学术年会资料集,合肥,2006:203-206.
[32]钱剑峰,孙德兴,吴荣华等.地表水源热泵辅助热源节能效果的分析[J].节能技术,2006,24(4):330-332.
[33]马最良,曹源.闭式环路水源热泵空调系统运行能耗的静态分析[J].哈尔滨建筑大学学报,1997,30 (6): 68-74.
[34]马最良,曹源.闭式环路水源热泵空调系统运行能耗的计算机动态模拟分析[J].哈尔滨建筑大学学报,1998,31(3): 57-63.
[35]陈晓,张国强,林宣军等.南方地区开式湖水源热泵的应用[C].中国制冷学会2005年制冷空调学术年会论文集,昆明,2005:370-374.
[36]严煦世,范瑾初.给水工程(第4版)[M].北京:中国建筑工业出版社, 1999:209-211.
[37]上海市政工程设计研究院.给水排水设计手册第3册—城镇给水(第二版)[S].北京:中国建筑工业出版社,2004:226-232.
[38]钟德铃,彭雪峰.介绍一种岸边式取水头部——悬臂真空罐取水头部[J].给水排水, 2002,28(7):13-15.
[39]唐明启.一种底栏栅结合干砌石形式的取水头部设计[J].中国给水排水,2008,25(2):44-46.
[40]董延衣.丘陵地区乡镇小型给水工程取水头部及取水口设计施工特点[J].西南给排水,1992,2:10-12.
[41]卢咏林.水下驱动自动防堵式水泵取水头[P].中国: ZL00230715.4,2001-06-20.
[42]李小林.双向防草除沙取水头[P].中国: ZL200520003650.8,2006-05-17.
[43]李保忠.防泥沙取水头[P].中国: ZL02229121.0,2003-04-09.
[44]陈滨.影响侧向流翼片斜板沉淀去浊效果因素的分析[J].给水排水,1992,01:15-18.
[45]刘百仓,马军,张素霞等.带翼片侧向流斜板沉淀池内颗粒沉降过程的数值模拟[J].给水排水,2007,33(11):139-142.
[46] S.V.Patankar. Numerical Heat Transfer and Fluid Flow[A].王福军.计算流体动力学分析—CFD软件原理与应用[M].北京:清华大学出版社,2004:4.
[47]王福军.计算流体动力学分析—CFD软件原理与应用[M].北京:清华大学出版社,2004:1-60.
[48]张红梅,李志鹏,高正明.连续高速分散混合器流体流动的数值模拟[J].北京化工大学学报,2005,32(6):5-8.
[49] Fluent Inc., FLUENT User’s Guide. Fluent Inc.,2003.
[50] Fluent Inc., FLUENT User Defined Function Manual. Fluent Inc.,2003.
[51]褚良银,陈文梅,戴光清等.水力旋流器[M].北京:化学工业出版社,1998.
[52]佟庆理.两相流动理论基础[M].北京:冶金工业出版社,1995.
[53]王绍亭,陈涛.动量热量与质量传递[M].天津:天津科学技术出版社,1986.
[54]岑可法.工程气固多相流动的理论及计算[M].杭州:浙江大学出版社,1990:80-85.
[55] C.J. Chen, S.Y. Jaw. Fundamentals of Turbulence Modeling[A].王福军.计算流体动力学分析—CFD软件原理与应用[M].北京:清华大学出版社,2004:4.
[56]陶文铨.数值传热学(第二版)[M].西安:西安交通大学出版社,2001.
[57] W.P. Jones, B.E. Launder. The calculation of low-Reynolds-number phenomena with a two-equation model of turbulence[A].王福军.计算流体动力学分析—CFD软件原理与应用[M].北京:清华大学出版社,2004:4.
[58]刘灿生,沈志恒,王绍文.翼片斜板沉淀实验研究[J].哈尔滨建筑工程学院学报, 1985,2:68-73.