汽轮机内湿蒸汽两相凝结流动的数值研究
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摘要
汽轮机内发生的自发凝结现象,一方面引起不平衡态热力学损失,降低了汽轮机级的效率,同时还可能因为改变汽流参数的分布并同流场中边界层分离、激波等各种复杂现象互相作用而产生附加损失。对汽轮机内湿蒸汽两相凝结流动进行研究,以凝结理论设计汽轮机叶片对提高蒸汽透平效率具有重要意义。
对湿蒸汽两相不平衡凝结流动进行了数值研究,基于成核和水滴生长理论建立了欧拉/欧拉坐标系下的凝结流动数值模型。应用n阶Moment方法建立了均质成核液相数值模型,基于杂质核表面的冠状成核过程建立了非均质凝结的数值模型。采用二阶TVD格式离散,时间推进法求解。
基于传热传质过程耦合求解方法提出了一种水滴生长的修正模型。在水滴生长的初始阶段,液滴处于自由分子流区域,初始液滴半径增长至一定程度时处于连续流区域。汽轮机中的大多数凝结水滴落入两者之间过渡区的范围,但此区域中液滴生长缺乏精确的数学描述模型。针对过渡区求解困难的问题,推导了适合于连续流区域和自由分子流区域的传质系数表达式,应用传热传质耦合求解方法得到水滴增长率。在自由分子流区域、连续流区域及两者之间的过渡区具有较高的计算精度。
对缩放喷管和二维叶栅中凝结流动的进行了数值研究,与文献中提供的实验数据进行了对比。计算结果正确反映了凝结产生的压力突跃和水滴分布规律。潜热的释放会导致叶栅出口马赫数的降低,改变叶栅出口气流角,使流场中激波系重新分布,并在吸力面尾缘附近产生较明显的流动分离现象。这些现象改变了汽流参数的分布并产生各种附加损失。在非均质凝结流动中,杂质核的存在使得凝结可以在较小过冷度下发生,压力突跃减弱并向平衡流发展。
提出了通过控制叶片吸力面型线和尾缘点形状控制凝结过程的方法。凝结过程对汽流膨胀率敏感。通过修改叶片型线,减小吸力面喉部附近的局部膨胀率,可以使成核过程更平稳,降低边界层分离程度和尾迹涡强度,减弱尾迹涡中水滴对主流相变过程的扰动程度,保证叶栅下游水滴分布均匀性和汽流携带水滴的稳定性。通过改变尾缘点形状,降低压力面尾缘处局部汽流膨胀率,可以使尾迹中水滴数的数量级降低。
研究了凝结对汽轮机级内流动的影响。凝结过程可能会改变叶栅的汽流出口气流角,对透平级的通流能力和做功能力造成影响。进口参数不同会使凝结位置不同,凝结可能会发生在静叶或动叶中,从而对动叶进气角产生不同的影响趋势。设计初始成核级时,需要根据流动情况,进行叶型的设计。
In low pressure turbine stage, the presence of homogeneous condensation leads to problems of losses in turbine efficiency. Pressure distribution change caused by condensation and the interaction between nucleation and some sophiticate phenomenon would introduce some addition loss. Therefore, the research on wet steam flows is very important to the design of wet steam turbines.
Numerical simulation of condensing flow was performed. An Eulerian/Eulerian model was developed for calculation of the wet steam flows with spontaneous conden-sation. The process of condensation was calculated by quadrature method of n order moments. The model of hetgeneous nucleation based on convex spherical substrate surface nucleation was performed. The numerical algorithm is established with the high resolution TVD scheme and the time-marching technique is adapted.
A correction water droplet growth theory based on Langmuir-Maxwell model is introduced. In the initial stage of droplets growth, droplets are in the molecular regimes. And if droplets are larger than the mean free path, droplets are in the continuum regimes. But in low pressure turbine, droplets are almost in transition regimes between molecular regimes and continuum regimes. Accurate mathematical model is absent in the regimes. An equation for the mass transfer embracing continuum and molecular regimes is given. The droplet growth rate can be determined by simultaneous solve heat and mass transfer equation. Calculation is accurate in molecular regimes and continuum regimes and the transition region.
Numerical simulation is performed for homogeneous condensation in wet steam two-phase flows in Laval nozzle and turbine cascade, good agreement was obtained between the numerical results and experimental data. Pressure rise and droplets distribution are showed in the result. Latent heat release in condensing flow would decrease the exit Mach number, change the flow angle and induce boundary layer separation. Shock wave would redistribute. Then additional loss would be caused. The character of heterogeneous flow is studied, condensation happened in low supercooling Particles in the steam have remarkable influence on condensing flow. The heterogeneous condensation leads to the removal of the pressure rise and approaches an equilibrium profile.
The method of controlling condensation in cascade is introduced. It has been known that the nucleating and growth processes are sensitive to expansion rate. In nucleating flow, the suctionside blade profile line downstream of throat should be straight, and then the steam expands slowly, the strenth of boundary layer separation and wake votex can be reduced and the droplets distribution is uniform. The droplets number magnitude in wake can be reduced by reducing local expansion rate near trailing edge.
In cascade, the outlet flow angle in condensing flow departures from the value designed by traditional single-phase design method. This leads to inducing additional aerodynamics losses and undesirable effects to the through-flow capacity of the cascade. With different inlet parameter, nucleation would occur in nozzle or moving blade, and the inlet flow angle of moving blade would change to different trend. In designing primary nucleation stage, the blade design should be on the base of flow condition.
对湿蒸汽两相不平衡凝结流动进行了数值研究,基于成核和水滴生长理论建立了欧拉/欧拉坐标系下的凝结流动数值模型。应用n阶Moment方法建立了均质成核液相数值模型,基于杂质核表面的冠状成核过程建立了非均质凝结的数值模型。采用二阶TVD格式离散,时间推进法求解。
基于传热传质过程耦合求解方法提出了一种水滴生长的修正模型。在水滴生长的初始阶段,液滴处于自由分子流区域,初始液滴半径增长至一定程度时处于连续流区域。汽轮机中的大多数凝结水滴落入两者之间过渡区的范围,但此区域中液滴生长缺乏精确的数学描述模型。针对过渡区求解困难的问题,推导了适合于连续流区域和自由分子流区域的传质系数表达式,应用传热传质耦合求解方法得到水滴增长率。在自由分子流区域、连续流区域及两者之间的过渡区具有较高的计算精度。
对缩放喷管和二维叶栅中凝结流动的进行了数值研究,与文献中提供的实验数据进行了对比。计算结果正确反映了凝结产生的压力突跃和水滴分布规律。潜热的释放会导致叶栅出口马赫数的降低,改变叶栅出口气流角,使流场中激波系重新分布,并在吸力面尾缘附近产生较明显的流动分离现象。这些现象改变了汽流参数的分布并产生各种附加损失。在非均质凝结流动中,杂质核的存在使得凝结可以在较小过冷度下发生,压力突跃减弱并向平衡流发展。
提出了通过控制叶片吸力面型线和尾缘点形状控制凝结过程的方法。凝结过程对汽流膨胀率敏感。通过修改叶片型线,减小吸力面喉部附近的局部膨胀率,可以使成核过程更平稳,降低边界层分离程度和尾迹涡强度,减弱尾迹涡中水滴对主流相变过程的扰动程度,保证叶栅下游水滴分布均匀性和汽流携带水滴的稳定性。通过改变尾缘点形状,降低压力面尾缘处局部汽流膨胀率,可以使尾迹中水滴数的数量级降低。
研究了凝结对汽轮机级内流动的影响。凝结过程可能会改变叶栅的汽流出口气流角,对透平级的通流能力和做功能力造成影响。进口参数不同会使凝结位置不同,凝结可能会发生在静叶或动叶中,从而对动叶进气角产生不同的影响趋势。设计初始成核级时,需要根据流动情况,进行叶型的设计。
In low pressure turbine stage, the presence of homogeneous condensation leads to problems of losses in turbine efficiency. Pressure distribution change caused by condensation and the interaction between nucleation and some sophiticate phenomenon would introduce some addition loss. Therefore, the research on wet steam flows is very important to the design of wet steam turbines.
Numerical simulation of condensing flow was performed. An Eulerian/Eulerian model was developed for calculation of the wet steam flows with spontaneous conden-sation. The process of condensation was calculated by quadrature method of n order moments. The model of hetgeneous nucleation based on convex spherical substrate surface nucleation was performed. The numerical algorithm is established with the high resolution TVD scheme and the time-marching technique is adapted.
A correction water droplet growth theory based on Langmuir-Maxwell model is introduced. In the initial stage of droplets growth, droplets are in the molecular regimes. And if droplets are larger than the mean free path, droplets are in the continuum regimes. But in low pressure turbine, droplets are almost in transition regimes between molecular regimes and continuum regimes. Accurate mathematical model is absent in the regimes. An equation for the mass transfer embracing continuum and molecular regimes is given. The droplet growth rate can be determined by simultaneous solve heat and mass transfer equation. Calculation is accurate in molecular regimes and continuum regimes and the transition region.
Numerical simulation is performed for homogeneous condensation in wet steam two-phase flows in Laval nozzle and turbine cascade, good agreement was obtained between the numerical results and experimental data. Pressure rise and droplets distribution are showed in the result. Latent heat release in condensing flow would decrease the exit Mach number, change the flow angle and induce boundary layer separation. Shock wave would redistribute. Then additional loss would be caused. The character of heterogeneous flow is studied, condensation happened in low supercooling Particles in the steam have remarkable influence on condensing flow. The heterogeneous condensation leads to the removal of the pressure rise and approaches an equilibrium profile.
The method of controlling condensation in cascade is introduced. It has been known that the nucleating and growth processes are sensitive to expansion rate. In nucleating flow, the suctionside blade profile line downstream of throat should be straight, and then the steam expands slowly, the strenth of boundary layer separation and wake votex can be reduced and the droplets distribution is uniform. The droplets number magnitude in wake can be reduced by reducing local expansion rate near trailing edge.
In cascade, the outlet flow angle in condensing flow departures from the value designed by traditional single-phase design method. This leads to inducing additional aerodynamics losses and undesirable effects to the through-flow capacity of the cascade. With different inlet parameter, nucleation would occur in nozzle or moving blade, and the inlet flow angle of moving blade would change to different trend. In designing primary nucleation stage, the blade design should be on the base of flow condition.
引文
[1]Moore M J, Sieverding C H. Two-phase steam flow in turbines and separators. Hemisphere Publishing Corporation.1976.
[2]Moore M J, Sieverding C H. Aerothermodynamics of low pressure steam turbines and condensers. Hemisphere Publishing Corporation.1987.
[3]斯蒂弗H G著,徐华舫译.气体动力学基本原理,高速流体中的凝结现象.科学出版社.1988.
[4]蔡颐年,王乃宁.湿蒸汽两相流.西安交通大学出版社.1985.
[5]李亮,丰镇平,陈红梅,等. 凝结理论在汽轮机设计中应用的探讨. 热力透平,2005,34(1)：36-40.
[6]Kermani M J, Gerber A G. A general formula for the evaluation of thermodynamic and aerodynamic losses in nucleating steam flow. International Journal of Heat and Mass Transfer,2003,46(17):3265-3278.
[7]White A J. Numerical investigation of condensing steam flow in boundary layers. International Journal of Heat and Fluid Flow,2000,21(6):727-734.
[8]Schneerr G H, Heiler M, Winkler G. Hign-speed flows with condensation. AMIF-ESF Workshop:Computing methods for two-phase flows. Centre Langevin, Aussois, France, January 12-14,2000.
[9]Winkler G, Schnerr G H. Nucleating unsteady flows in low-pressure steam turbine stages. Proceedings of the Institution of Mechanical Engineers, Part A:Journal of Power and Energy,2001,215(6):773-781.
[10]Adam S, Schnerr G H. Instabilities and bifurcation of non-equilibrium two-phase flows. Journal of Fluid Mechanics,1997,348:1-28.
[11]Sejna M. Numerical modeling of unsteady wet steam flow. Z Angew Math Mech,1993,73(6):578-581.
[12]White A J, Senoo S. Numerical simulation of unsteady wet steam flows with non-equilibrium condensation in the nozzle and the steam turbine. ASME joint US-European fluid engineering summer meeting,2006.
[13]Skillings S A, Walters P T, Moore M J. A study of supercritical heat addition as potential loss mechanism in condensing steam turbines. Proceedings of the Institution of Mechanical Engineers, Part C,1987,259(87).
[14]Sejna M, Lain J. Numerical modeling of wet steam flow with homogeneous condensation on unstruced triangular Meshes. Z Angew Math Mech,1994,74(5): 375-378.
[15]Matsuo K, Kawagoe S, Sonoda K, Setoguchi T. Oscillations of laval nozzle flow with condensation (Part 2, On the mechanism of oscillations and their amplitudes). Bulletin of JSME,1985,28(235):88-93.
[16]Delale C F, Schnerr G H. Transient effects of nucleation in steady and unsteady condensing flows. Int. J. Multiphase Flow,1996,22(4):767-781.
[17]Skill ings S A, R Jackson. A robust time-marching solver for one dimensional nucleating steam flows. International Journal of Heat and Fluid Flow,1987,8(2): 139-144.
[18]Whirlow D K, Mccloskey T J, Davids J, En S, Kadambi J R, Farn C Flow instabilities in low pressure turbine blade passages. ASME paper 84-JPGC-GT-14, 1984.
[19]Damazh S. A, Deich M E, Almulki D S, Ismali N. The motion of saturated and wet steam in channels with a backstep. Teploenergetika,1990,37(5):68-72.
[20]Guha A. Thermal choking due to nonequilibrium condensation. ASME, Transactions, Journal of Fluids Engineering,1994,106(3):599-604.
[21]泡拉契克H,西格RJ著徐华舫译. 气体动力学基本原理E激波的相互作用. 科学出版社,1988.
[22]White A J, Young J B, Walters P T. Experimental validation of condensing flow theory for a stationary cascade of steam turbine blades. Philosophical Transactions:Mathematical, Physical and Engineering Sciences,1996,345(1): 59-88.
[23]王乃宁,张志刚. 汽轮机热力设计.Beijing水利电力出版社.1987.
[24]Ford I J. Statistical mechanics of nucleation:a review. Proceedings of the Institution of Mechanical Engineers, Part C:Journal of Mechanical Engineering Science,2004,218(8):883-899.
[25]Courtney W G. Remarks on homogeneous nucleation. Journal of Chemical Physics,1961,35:2249-2250.
[26]Hale B. The scaling of nucleation rates. Metallurgical and Materials Transactions A,1992,23(7):1863-1868.
[27]Kantrowitz A. Nucleation in very rapid vapor expansions. The Journal of Chemical Physics,1951,19:1097-1100.
[28]Wolk J, Strey R. Homogeneous nucleation of H2O and D2O in comparison:The isotope effect. J Phys Chem. B,2001,105(47):11683-11701.
[29]Young J B. The spontaneous condensation of steam in supersonic nozzles. Physico Chemical Hydrodynamics,1982,3(1):57-82.
[30]Heiler M. Instationare Phanomene in homogen/heterogen kondensierenden Dusen-und Turbinenstromungen. Dissertation, Fakultat fur Maschinenbau, Universitat Karlsruhe,1999.
[31]Hill P G. Condensation of water vapour during supersonic expansion in nozzles. Journal of Fluid Mechanics,1966,25(03):593-620.
[32]Delale C F, Meier G E A. A compasison of nucleation theories by the asymptotic solution of condensing nozzle flows. Acta Mechanica,1996,117(1):23-32.
[33]Bakhtar F, Young J B, Et Al. Classical nucleation theory and its application to condensing steam flow calculations. Journal of Mechanical Engineering Science, 2005,219(C12):1315-1333.
[34]Peters F, Meyer K. Measurement and interpretation of growth of mono-dispersed water droplets suspended in pure vapor. International Journal of Heat and Mass Transfer,1995,38(17):3285-3293.
[35]Bakhtar F, Mashmoushy H, Buckley J. On the performance of a cascade of turbine rotor tip section blading in wet steam Part 1:generation of wet steam of prescribed droplet sizes. Proceedings of the Institution of Mechanical Engineers, Part C:Journal of Mechanical Engineering Science,1997,211(7):519-529.
[36]Bakhtar F, Mashmoushy H, Jadayel O. On the performance of a cascade of turbine rotor tip section blading in wet steam Part 2:Wake Traverses. Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science,1997,209(7):169-177.
[37]Bakhtar F, Mashmoushy H, Jadayel O C. On the Performance of a Cascade of Turbine Rotor Tip Section Blading in Wet Steam. Part 2:Wake Traverses. Proc Instn Mech Engrs Part C,1997,211:639-649.
[38]Bakhtar F, Mashmoushy H, Jadayel O C. On the Performance of a Cascade of Turbine Rotor Tip Section Blading in Wet Steam. Part 2:Surface Pressure Distributions. Proc Instn Mech Engrs Part C,1997,211:531-540.
[39]Bakhtar F, Ebrahimi M, Webb R A. On the performance of a cascade of turbine rotor tip section blading in nucleating steam-Part 1:Surface Pressure Distributions. Proceedings of the Institution of Mechanical Engineers, Part C, 1995,209:115-124.
[40]Bakhtar F, Ebrahimi M, Bamkole B O. On the performance of a cascade of turbine rotor tip section blading in nucleating steam-Part 2:Wake Traverses. Proceedings of the Institution of Mechanical Engineers, Part C,1995,209(2):169-177.
[41]Bakhtar F, Mahpeykar M R. On the Performance of a Cascade of Turbine Rotor Tip Section Blading in Nucleating Steam, Part 3:Theoretical Treatment. Proc Instn Mech Engrs Part C,1997,211(3):195-210.
[42]黄跃,蔡颐年. 膨胀率对Laval喷管超音速湿蒸汽流动凝结过程的影响. 西安交通大学学报,1984(02)：51-61.
[43]蔡小舒,Renner. M, Stetter. H.跨音速流自发凝结水滴的测量. 流体力学实验与测量,1999,13(3)：65-69.
[44]蔡小舒,宁廷保,牛风仙,等.300MW直接空冷汽轮机低压末级鼓风态流场及湿度测量. 中国电机工程学报,2008,28(26)：8-13.
[45]蔡小舒,牛凤仙,宁廷保,等.300MW直接空冷汽轮机低压末级湿蒸汽测量研究. 中国电机工程学报,2009,29(2)：1-7.
[46]蔡小舒,汪丽莉,欧阳新. 低压汽轮机内湿蒸汽两相流测量. 上海汽轮机,2002(1)：23-29.
[47]蔡小舒,徐峰,宁廷保,等. 直接空冷汽轮机末级蒸汽异质／均质成核凝结过程的在线测量. 动力工程,2008,28(6)：865-870.
[48]蔡小舒,苏海林.5MW实验汽轮机内湿蒸汽两相流实验研究. 热力透平,2004,33(4)：216-222.
[49]蔡小舒,汪丽莉,欧阳新,等. 一种新型的测量汽轮机内湿蒸汽两相流的集成化探针系统. 工程热物理学报,2001,22(6)：743-746.
[50]蔡小舒王乃宁.能同时测量低压汽轮机内流场和湿度的联合探针的研制及实验研究. 动力工程,1999,19(3)：55-58.
[51]张弘,蔡小舒,王夕华.汽轮机内湿蒸汽实验测量技术现状.热力透平,2007,36(1)：1-7.
[52]宁廷保,蔡小舒,尚志涛,等. 一种新型汽轮机湿蒸汽测量探针系统. 热力发电,2008,37(7)：65-68.
[53]沈建琪,蔡小舒,于彬. 消光起伏自相关频谱法颗粒测量技术. 工程热物理学报,2006,27(5)：795-798.
[54]盛德仁,黄雪峰,陈坚红,等.一种基于布拉格光纤光栅测量湿蒸汽两相流湿度场的新方法. 中国电机工程学报,2005,25(05)：136-140.
[55]苏海林,蔡小舒,Messner J, Eyb G.试验汽轮机末级内湿蒸汽流动特性的实验研究.中国电机工程学报,2004,24(09)：257-261.
[56]汪丽莉,蔡小舒,欧阳新,汽轮机湿蒸汽两相流中大水滴速度的实验研究,中国工程热物理学会第十届年会多相流学术会议论文集.2001： 青岛.58-64.
[57]汪丽莉蔡小舒. 汽轮机湿蒸汽两相流中水滴尺寸研究进展. 上海理工大学学报,2003,25(4)：307-312.
[58]汪丽莉,蔡小舒,欧阳新. 汽轮机内湿蒸汽两相流流场的实验研究. 动力工程,2003,23(2)：2270-2274.
[59]王娜,张弘,蔡小舒. 二次水滴可视化探针的设计. 热力透平,2006,35(2)：79-82.
[60]马庆芬. 旋转超音速凝结流动及应用技术研究：[博士学位论文]. 大连：大连理工大学,2009.
[61]王美利. 高速膨胀流动中的非平衡凝结及其对流场影响的研究：[博士学位论文]. 合肥：中国科技大学,2006.
[62]Snoeck J. Calculation of Mixed Flows with Condensation in One Dimensional Nozzle. Aero-Thermodynamics of Steam Turbines, ASME,1981:11-18.
[63]Bakhtar F, M. T. Mohammadi Tochai. An Investigation of two-dimensional flows of nucleating and wet steam by the time-marching method. Int. J. Heat & Fluid Flow,1980,2(1):5-18.
[64]Bakhtar F. A study of nucleating and wet steam flows in high pressure steam turbines. Proceedings of the Institution of Mechanical Engineers,1979,190: 545-559.
[65]Bakhtar F. On the solution of supersonic blade-to-blade flows of nucleating steam by the time-marching method. Proceedings of the Institution of Mechanical Engineers,1984:C82-84.
[66]Bakhtar F. Nucleation phenomena in flowing high-pessure steam - Part 2: Theoretical analysis. Proceedings of the Institution of Mechanical Engineers, Part A,1990,204:233-242.
[67]Bakhtar. F, Webb R A, Shojaee-Fard M H, Siraj M A. An investigation of nucleation flows of steam in a cascade of turbine blading. Transaction of the ASME.1993,115:128-134.
[68]Bakhtar F, Zidi K. On the self diffusion of water vapour. Proceedings of the Institution of Mechanical Engineers, Part C,1985,199(C2):159-164.
[69]Bakhtar F, Mahpeykar M R, Abbas K K. An investigation of nucleating flows of steam in a cascade of turbine blading-theoretical treatment. J ASME Fluid Eng, 1995,117:138-144.
[70]Bakhtar F, So K S. A study of nucleating flow of steam in a cascade of supersonic blading by the time-marching method. International Journal of Heat & Fluid Flow,1991,12(1):54-62.
[71]Guha A, Young J B, Time-marching prediction of unsteady condensation phenomena due to supercritical heat addition, in The Institution of Mechanical Engineers Conference on Turbomachinery:Latest Developments in a changing Scene.1991, Institution of Mechanical Engineers:London.167-177.
[72]Guha A, J Young. The effect of flow unsteadiness on the homogeneous nucleation of water droplets in steam turbines. Philosophical Transactions:Physical Sciences and Engineering,1994,349(1691):445-472.
[73]Guha. A, Computation. Analysis and theory of two-phase flows. The Aeronautical Journal,1998,102(1012):71-82.
[74]White A J. A comparison of modelling methods for polydispersed wet-steam flow. International Journal for Numerical Methods in Engineering,2003,57(6): 819-834.
[75]White A J, Hounslow M J. Modelling droplet size distributions in polydispersed wet-steam flows. International Journal of Heat and Mass Transfer,2000,43(11): 1873-1884.
[76]White A J, Young J B. Time-marching method for the prediction of two-dimensional, unsteady flows of condensing steam. Journal of Propulsion and Power,1993,9(4):579-587.
[77]White A J, Hounslow M J. Modelling droplet size distributions in polydispersed wet-steam flows. International Journal of Heat and Mass Transfer,2000,43: 1873-1884.
[78]Young J B. Semi-analytical techniques for investigating thermal non-equilibrium effects in wet steam turbines. International Journal of Heat and Fluid Flow,1984, 5(2):81-91.
[79]Young J B. The condensation and evaporation of liquid droplets in a pure vapour at arbitrary Knudsen number. International Journal of Heat and Mass Transfer, 1991,34(7):1649-1661.
[80]Young J B. Two-dimensional, nonequilibrium, wet-steam calculations for nozzles and turbine cascades. Journal of Turbomachinery,1992,114:569-579.
[81]Young J B, Yeoh C. Non-equilibrium streamline curvature throughflow calculations in wet steam turbines. Transactions of the ASME Series A, Journal of Engineering for Power,1982, 104:489-496.
[82]Huang L, Young J B. An analytical solution for the Wilson point in homogeneously nucleating flows. Proceedings:Mathematical, Physical and Engineering Sciences,1996,452(1949):1459-1473.
[83]Gerber A G. Two-phase Eulerian/Lagrangian model for nucleating steam flow. Journal of Fluids Engineering,2002,124:465-475.
[84]Gerber A G, Mousavi A. Representing polydispersed droplet behavior in nucleating steam flow. Journal of Fluids Engineering,2007,129:1404-1414.
[85]Gerber A G, Kermani M J. A pressure based eulerian/eulerian multi-phase model for non-equilibrium condensation in transonic steam flow. International Journal of Heat and Mass Transfer,2004,47:2217-2231.
[86]Dykas S. Numerical calculation of the steam condensing flow. TASK Quarterly, 2001,5(4):519-535.
[87]Dykas S. Prediction of losses in the flow through the last stage of low-pressure steam turbine. International Journal for Numerical Methods in Fluids,2007,53(6): 933-945.
[88]Yamamoto S. Computation of practical flow problems with release of latent heat. Energy,2005,30(2-4):197-208.
[89]丰镇平李亮李国君. 汽轮机湿蒸汽两相凝结流动数值研究的现状与进展. 上海汽轮机,2002,2：1-10.
[90]俞茂铮,陈孝隆.存在自发凝结的超音速湿蒸汽双相流.西安交通大学学报,1983,17(1)：23-31.
[91]李亮,程代京,丰镇平,等.汽轮机湿蒸汽级中凝结流动的三维数值分析.工程热物理学报,2006,27(4)：571-573.
[92]Zhenping FENG, Liang LI, Guojun LI, Yoshio Shikano, Numerical simulation of three- dimensional transonic two-phase flows with spontaneous condensation. Proceeding of International Conference on Power Engineering. Xi'an, China, Oct. 8-12,2001:812-819.
[93]李亮,丰镇平,李国君. 透平级内动静干涉对凝结特性影响的数值研究. 工程热物理学报,2007,28(s1)：89-92.
[94]李亮,丰镇平,李国君. 一维喷管中存在自发凝结的跨音速湿蒸汽两相流动数值模拟. 工程热物理学报,2001,22(6)： 703-705.
[95]李亮,丰镇平,李国君. 平面叶栅中的湿蒸汽两相凝结流动数值模拟. 工程热物理学报,2002,23(3)：309-311.
[96]李亮,丰镇平,李国君. 湿蒸汽中超临界加热引起的非定常凝结流动一维数值分析. 自然科学进展,2003,13(2)：210-212.
[97]李亮丰镇平李国君. 出气边形状对叶栅中凝结流动影响机理的数值研究. 工程热物理学报,2003,24(5)：767-769.
[98]李亮,李国君,丰镇平.湿蒸汽两相流动的数值方法及其在喷管中的应用.西安交通大学学报,2001,35(11)：113 1-1134.
[99]吴晓明,李国君,丰镇平,李亮.SST k-co-kp两相湍流模型及其在湿蒸汽凝结流动数值模拟中的应用.西安交通大学学报,2007,41(5)：526-529.
[100]吴晓明,李亮,李国君,等. 基于双流体模型的湿蒸气凝结流动三维数值模拟. 热能动力工程,2007,22(4)：367-370.
[101]巫志华,李亮,丰镇平.三维湿蒸汽自发凝结流动的数值模拟. 动力工程,2006,26(6)：814-817.
[102]巫志华,李亮,丰镇平. 低压汽轮机三维叶栅通道内湿蒸汽两相流动的数值模拟与分析. 工程热物理学报,2007,28(5)：763-765.
[103]巫志华,李亮,丰镇平. 湿蒸汽两相流动问题的耦合求解. 工程热物理学报,2005,26(4)：578-580.
[104]陈红梅,李亮,丰镇平,等.一维喷管中湿蒸汽非均质凝结流动的研究. 工程热物理学报,2004,25(3)：395-398.
[105]陈红梅李亮丰镇平李国君.透平级中自发凝结及叶栅中非均质凝结流动的初步研究. 工程热物理学报,2005,26(s)：65-68.
[106]张冬阳,蔡虎,蒋洪德.蒸汽凝结对透平流动和几何参数的影响.汽轮机技术,1999,41(6)：339-341.
[107]张冬阳蒋洪德刘建军. 考虑若干影响的一元蒸汽凝结流数值解. 工程热物理学报,2001,22(S1)：25-39.
[108]张冬阳刘建军蒋洪德.三维湿蒸汽流动快速准确数值模拟方法及应用. 工程热物理学报,2003,24(2)：262-264.
[109]张冬阳.非平衡态湿蒸汽流动快速准确数值模拟方法研究：[博士学位论文].北京：中国科学研究院,2002.
[110]林智荣.蒸汽及燃气透平内部真实气体流动问题的研究：[博士学位论文]. 北京：清华大学,2005.
[11 1]林智荣,袁新.自发凝结流动数值模拟方法及其在Laval喷管中的应用.工程热物理学报,2006,27(1)：42-44.
[112]Kosolapov Y S. Calculation of spontaneously condensing steam flows in a plane turbine cascade. Fluid Dynamics,1995,30(6):926-933.
[113]David W, Oxtoby. Homogeneous nucleation:theory and experiment. J Phys: Condens,1992, Matter 4:7627-7650.
[114]Katz J. Homogeneous nucleation theory and experiment:A survey. Pure and applied chemistry,1992,64:1661-1661.
[115]M C C, Luijten. Nucleation and droplet growth at high pressure. PhD thesis. Department of Fluid Dynamics, Eindhoven University of Technology, 1998.
[116]Ford I J. Nucleation theorems, the statistical mechanics of molecular clusters, and a revision of classical nucleation theory. Physical Review E,1997,56(5): 5615-5629.
[117]Girshick S, Chiu C. Kinetic nucleation theory:A new expression for the rate of homogeneous nucleation from an ideal supersaturated vapor. The Journal of Chemical Physics,1990,93:1273-1277.
[118]Fisher M. The theory of condensation and the critical point. Physics,1967,3: 255-283.
[119]Kiang C S, Stauffer D, Walker G H, Puri O P, Wise J J, Patterson E M. A reexamination of homogeneous nucleation theory. Journal of Atmospheric Sciences,1971,28:1222-1232.
[120]Reiss H, Kegel W K, Katz J. Resolution of the problems of replacement free energy,1/S, and internal consistency in nucleation theory by consideration of the length scale for mixing entropy. Physical Review Letters,1997,78(23): 4506-4509.
[121]Lothe J, Pound G M. Reconsiderations of nucleation theory. The Journal of Chemical Physics,1962,36:2080-2085.
[122]Reiss H. Treatment of droplike clusters by means of the classical phase integral in nucleation theory. Journal of Statistical Physics,1970,2(1):83-104.
[123]Reiss H, Katz J L, Cohen E R. Translation-Rotation paradox in the theory of nucleation. The Journal of Chemical Physics,1968,48:5553.
[124]FederJ, Russell K C, Lothe J, Pound G M. Homogeneous nucleation and growth of droplets in vapours. Advances in Physics,1966,15(57):111-178.
[125]Wyslouzil B E, Seinfeld J H. Nonisothermal homogeneous nucleation. The Journal of Chemical Physics,1992,97(4):2661-2669.
[126]Dillman A, Meier G E A. A refined droplet approach to the problem of homogeneous nucleation from the vapour phase. J. Chem. Phys,1991,94:3872-3884.
[127]Heist R H, Reiss H. Investigation of the homogeneous nucleation of water vapor using a diffusion cloud chamber. The Journal of Chemical Physics,1973,59: 665-671.
[128]Anderson R J, Miller R C, Kassne[J], Hagen D E. A study of homogeneous condensation-freezing nucleation of small water droplets in an expansion cloud chamber. Journal of the Atmospheric Sciences,1980,37(11):2509-2520.
[129]Fletcher N H. Size effect in heterogeneous nucleation. The Journal of Chemical Physics,1958,29:572-576.
[130]Lee T D. Surface characterization by heterogeneous nucleation from the vapor. PhD thesis. Harvard University,1998
[131]Knudsen M. Maximum rate of vaporization of mercury. Ann Phys,1915,47: 697-708.
[132]Gyarmathy G. The spherical droplet in gaseous carrier streams:review and synthesis. Multiphase science and technology,1981-1982,1(1-4):99-279.
[133]Prast B. Condensation in supersonic expansion flows:theory and numerical evaluation. Eindhoven:Stan Ackermans Institute, Ontwerpers opleiding Computational Mechanics,1997.
[134]Mei Y, Guha A. Modification of the upwind schemes for the computation of condensing two-phase flows. Proceedings of the Institution of Mechanical Engineers, Part A:Journal of Power and Energy,2006,220(7):809-814.
[135]Peter V. Propagation of small disturbances in wet steam. In Proceedings of the 5th Conference on Steam Turbines of Large Output, Plzen, Czech Republic,1972, 35-50.
[136]Put F, Kelleners P H, Hagmeijer R, et Al. Numerical simulation of condensing real gas flows. Proceedings of CFD2001 3rd International Symposium on Computational Technologies for Fluid/Thermal/Chemical Systems with Industrial Applications,2001.
[137]Bolm D, Kerpicci H, Ren J, Surken N. Homogeneous and heterogeneous nucleation in a nozzle guide vane of a LP-steam Turbine.4th European Conference on Turbomachinery. Firenze, Italy,2001.
[138]Hienola A, Vehkamaki H K, Riipinen I, Kulmala M. Homogeneous vs heterogeneous nucleation in water-dicarboxylic acid systems. Atmos Chem Phys,2009,9:1873-1881.
[139]Jian Z Y, Jie W Q. Criterion for judging the homogeneous and heterogeneous nucleation. Metallurgical and Materials Transactions A,2001,32(2):391-395.
[140]Kotake S, Glass I I. Condensation of water vapour on heterogeneous nuclei in a shock tube. UTIAS Report,1976,207-210.
[141]Petr V, M Kolovratnik. Heterogeneous effects in the droplet nucleation process in 1p steam turbines.4th European Conference on Turbomachinery.2001. Firenze, Italy:783-792.
[142]Qian M, Ma J. Heterogeneous nucleation on convex spherical substrate surfaces: A rigorous thermodynamic formulation of Fletcher's classical model and the new perspectives derived. The Journal of chemical physics,2009,130(21): 214-709
[143]Harten A. High resolution schemes for hypersonic conservation laws. Journal of Computational Physics,1983,49(3):357-393.
[144]阎超.计算流体力学方法及应用.北京： 北京航空航天大学出版社.2006.
[145]张涵信,沈孟育. 计算流体力学—差分方法的原理和应用. 北京： 国防工业出版社.2003.
[146]Mashmoushy H, Mahpeykar M R, Bakhtar F. Studies of nucleating and wet steam flows in two-dimensional cascades. Proceedings of the Institution of Mechanical Engineers.,2004,218(8):843-858.
[147]Slater S, Leeming A D, Young J B. Particle deposition from two-dimensional turbulent gas flows. International Journal of Multiphase Flow,2003,29(5): 721-750.
[148]Dinh C V, Ruggles S G, Vogan J H. Bucket for the last stage of turbine. United States Patents.5393200,1995-2-28.
[2]Moore M J, Sieverding C H. Aerothermodynamics of low pressure steam turbines and condensers. Hemisphere Publishing Corporation.1987.
[3]斯蒂弗H G著,徐华舫译.气体动力学基本原理,高速流体中的凝结现象.科学出版社.1988.
[4]蔡颐年,王乃宁.湿蒸汽两相流.西安交通大学出版社.1985.
[5]李亮,丰镇平,陈红梅,等. 凝结理论在汽轮机设计中应用的探讨. 热力透平,2005,34(1)：36-40.
[6]Kermani M J, Gerber A G. A general formula for the evaluation of thermodynamic and aerodynamic losses in nucleating steam flow. International Journal of Heat and Mass Transfer,2003,46(17):3265-3278.
[7]White A J. Numerical investigation of condensing steam flow in boundary layers. International Journal of Heat and Fluid Flow,2000,21(6):727-734.
[8]Schneerr G H, Heiler M, Winkler G. Hign-speed flows with condensation. AMIF-ESF Workshop:Computing methods for two-phase flows. Centre Langevin, Aussois, France, January 12-14,2000.
[9]Winkler G, Schnerr G H. Nucleating unsteady flows in low-pressure steam turbine stages. Proceedings of the Institution of Mechanical Engineers, Part A:Journal of Power and Energy,2001,215(6):773-781.
[10]Adam S, Schnerr G H. Instabilities and bifurcation of non-equilibrium two-phase flows. Journal of Fluid Mechanics,1997,348:1-28.
[11]Sejna M. Numerical modeling of unsteady wet steam flow. Z Angew Math Mech,1993,73(6):578-581.
[12]White A J, Senoo S. Numerical simulation of unsteady wet steam flows with non-equilibrium condensation in the nozzle and the steam turbine. ASME joint US-European fluid engineering summer meeting,2006.
[13]Skillings S A, Walters P T, Moore M J. A study of supercritical heat addition as potential loss mechanism in condensing steam turbines. Proceedings of the Institution of Mechanical Engineers, Part C,1987,259(87).
[14]Sejna M, Lain J. Numerical modeling of wet steam flow with homogeneous condensation on unstruced triangular Meshes. Z Angew Math Mech,1994,74(5): 375-378.
[15]Matsuo K, Kawagoe S, Sonoda K, Setoguchi T. Oscillations of laval nozzle flow with condensation (Part 2, On the mechanism of oscillations and their amplitudes). Bulletin of JSME,1985,28(235):88-93.
[16]Delale C F, Schnerr G H. Transient effects of nucleation in steady and unsteady condensing flows. Int. J. Multiphase Flow,1996,22(4):767-781.
[17]Skill ings S A, R Jackson. A robust time-marching solver for one dimensional nucleating steam flows. International Journal of Heat and Fluid Flow,1987,8(2): 139-144.
[18]Whirlow D K, Mccloskey T J, Davids J, En S, Kadambi J R, Farn C Flow instabilities in low pressure turbine blade passages. ASME paper 84-JPGC-GT-14, 1984.
[19]Damazh S. A, Deich M E, Almulki D S, Ismali N. The motion of saturated and wet steam in channels with a backstep. Teploenergetika,1990,37(5):68-72.
[20]Guha A. Thermal choking due to nonequilibrium condensation. ASME, Transactions, Journal of Fluids Engineering,1994,106(3):599-604.
[21]泡拉契克H,西格RJ著徐华舫译. 气体动力学基本原理E激波的相互作用. 科学出版社,1988.
[22]White A J, Young J B, Walters P T. Experimental validation of condensing flow theory for a stationary cascade of steam turbine blades. Philosophical Transactions:Mathematical, Physical and Engineering Sciences,1996,345(1): 59-88.
[23]王乃宁,张志刚. 汽轮机热力设计.Beijing水利电力出版社.1987.
[24]Ford I J. Statistical mechanics of nucleation:a review. Proceedings of the Institution of Mechanical Engineers, Part C:Journal of Mechanical Engineering Science,2004,218(8):883-899.
[25]Courtney W G. Remarks on homogeneous nucleation. Journal of Chemical Physics,1961,35:2249-2250.
[26]Hale B. The scaling of nucleation rates. Metallurgical and Materials Transactions A,1992,23(7):1863-1868.
[27]Kantrowitz A. Nucleation in very rapid vapor expansions. The Journal of Chemical Physics,1951,19:1097-1100.
[28]Wolk J, Strey R. Homogeneous nucleation of H2O and D2O in comparison:The isotope effect. J Phys Chem. B,2001,105(47):11683-11701.
[29]Young J B. The spontaneous condensation of steam in supersonic nozzles. Physico Chemical Hydrodynamics,1982,3(1):57-82.
[30]Heiler M. Instationare Phanomene in homogen/heterogen kondensierenden Dusen-und Turbinenstromungen. Dissertation, Fakultat fur Maschinenbau, Universitat Karlsruhe,1999.
[31]Hill P G. Condensation of water vapour during supersonic expansion in nozzles. Journal of Fluid Mechanics,1966,25(03):593-620.
[32]Delale C F, Meier G E A. A compasison of nucleation theories by the asymptotic solution of condensing nozzle flows. Acta Mechanica,1996,117(1):23-32.
[33]Bakhtar F, Young J B, Et Al. Classical nucleation theory and its application to condensing steam flow calculations. Journal of Mechanical Engineering Science, 2005,219(C12):1315-1333.
[34]Peters F, Meyer K. Measurement and interpretation of growth of mono-dispersed water droplets suspended in pure vapor. International Journal of Heat and Mass Transfer,1995,38(17):3285-3293.
[35]Bakhtar F, Mashmoushy H, Buckley J. On the performance of a cascade of turbine rotor tip section blading in wet steam Part 1:generation of wet steam of prescribed droplet sizes. Proceedings of the Institution of Mechanical Engineers, Part C:Journal of Mechanical Engineering Science,1997,211(7):519-529.
[36]Bakhtar F, Mashmoushy H, Jadayel O. On the performance of a cascade of turbine rotor tip section blading in wet steam Part 2:Wake Traverses. Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science,1997,209(7):169-177.
[37]Bakhtar F, Mashmoushy H, Jadayel O C. On the Performance of a Cascade of Turbine Rotor Tip Section Blading in Wet Steam. Part 2:Wake Traverses. Proc Instn Mech Engrs Part C,1997,211:639-649.
[38]Bakhtar F, Mashmoushy H, Jadayel O C. On the Performance of a Cascade of Turbine Rotor Tip Section Blading in Wet Steam. Part 2:Surface Pressure Distributions. Proc Instn Mech Engrs Part C,1997,211:531-540.
[39]Bakhtar F, Ebrahimi M, Webb R A. On the performance of a cascade of turbine rotor tip section blading in nucleating steam-Part 1:Surface Pressure Distributions. Proceedings of the Institution of Mechanical Engineers, Part C, 1995,209:115-124.
[40]Bakhtar F, Ebrahimi M, Bamkole B O. On the performance of a cascade of turbine rotor tip section blading in nucleating steam-Part 2:Wake Traverses. Proceedings of the Institution of Mechanical Engineers, Part C,1995,209(2):169-177.
[41]Bakhtar F, Mahpeykar M R. On the Performance of a Cascade of Turbine Rotor Tip Section Blading in Nucleating Steam, Part 3:Theoretical Treatment. Proc Instn Mech Engrs Part C,1997,211(3):195-210.
[42]黄跃,蔡颐年. 膨胀率对Laval喷管超音速湿蒸汽流动凝结过程的影响. 西安交通大学学报,1984(02)：51-61.
[43]蔡小舒,Renner. M, Stetter. H.跨音速流自发凝结水滴的测量. 流体力学实验与测量,1999,13(3)：65-69.
[44]蔡小舒,宁廷保,牛风仙,等.300MW直接空冷汽轮机低压末级鼓风态流场及湿度测量. 中国电机工程学报,2008,28(26)：8-13.
[45]蔡小舒,牛凤仙,宁廷保,等.300MW直接空冷汽轮机低压末级湿蒸汽测量研究. 中国电机工程学报,2009,29(2)：1-7.
[46]蔡小舒,汪丽莉,欧阳新. 低压汽轮机内湿蒸汽两相流测量. 上海汽轮机,2002(1)：23-29.
[47]蔡小舒,徐峰,宁廷保,等. 直接空冷汽轮机末级蒸汽异质／均质成核凝结过程的在线测量. 动力工程,2008,28(6)：865-870.
[48]蔡小舒,苏海林.5MW实验汽轮机内湿蒸汽两相流实验研究. 热力透平,2004,33(4)：216-222.
[49]蔡小舒,汪丽莉,欧阳新,等. 一种新型的测量汽轮机内湿蒸汽两相流的集成化探针系统. 工程热物理学报,2001,22(6)：743-746.
[50]蔡小舒王乃宁.能同时测量低压汽轮机内流场和湿度的联合探针的研制及实验研究. 动力工程,1999,19(3)：55-58.
[51]张弘,蔡小舒,王夕华.汽轮机内湿蒸汽实验测量技术现状.热力透平,2007,36(1)：1-7.
[52]宁廷保,蔡小舒,尚志涛,等. 一种新型汽轮机湿蒸汽测量探针系统. 热力发电,2008,37(7)：65-68.
[53]沈建琪,蔡小舒,于彬. 消光起伏自相关频谱法颗粒测量技术. 工程热物理学报,2006,27(5)：795-798.
[54]盛德仁,黄雪峰,陈坚红,等.一种基于布拉格光纤光栅测量湿蒸汽两相流湿度场的新方法. 中国电机工程学报,2005,25(05)：136-140.
[55]苏海林,蔡小舒,Messner J, Eyb G.试验汽轮机末级内湿蒸汽流动特性的实验研究.中国电机工程学报,2004,24(09)：257-261.
[56]汪丽莉,蔡小舒,欧阳新,汽轮机湿蒸汽两相流中大水滴速度的实验研究,中国工程热物理学会第十届年会多相流学术会议论文集.2001： 青岛.58-64.
[57]汪丽莉蔡小舒. 汽轮机湿蒸汽两相流中水滴尺寸研究进展. 上海理工大学学报,2003,25(4)：307-312.
[58]汪丽莉,蔡小舒,欧阳新. 汽轮机内湿蒸汽两相流流场的实验研究. 动力工程,2003,23(2)：2270-2274.
[59]王娜,张弘,蔡小舒. 二次水滴可视化探针的设计. 热力透平,2006,35(2)：79-82.
[60]马庆芬. 旋转超音速凝结流动及应用技术研究：[博士学位论文]. 大连：大连理工大学,2009.
[61]王美利. 高速膨胀流动中的非平衡凝结及其对流场影响的研究：[博士学位论文]. 合肥：中国科技大学,2006.
[62]Snoeck J. Calculation of Mixed Flows with Condensation in One Dimensional Nozzle. Aero-Thermodynamics of Steam Turbines, ASME,1981:11-18.
[63]Bakhtar F, M. T. Mohammadi Tochai. An Investigation of two-dimensional flows of nucleating and wet steam by the time-marching method. Int. J. Heat & Fluid Flow,1980,2(1):5-18.
[64]Bakhtar F. A study of nucleating and wet steam flows in high pressure steam turbines. Proceedings of the Institution of Mechanical Engineers,1979,190: 545-559.
[65]Bakhtar F. On the solution of supersonic blade-to-blade flows of nucleating steam by the time-marching method. Proceedings of the Institution of Mechanical Engineers,1984:C82-84.
[66]Bakhtar F. Nucleation phenomena in flowing high-pessure steam - Part 2: Theoretical analysis. Proceedings of the Institution of Mechanical Engineers, Part A,1990,204:233-242.
[67]Bakhtar. F, Webb R A, Shojaee-Fard M H, Siraj M A. An investigation of nucleation flows of steam in a cascade of turbine blading. Transaction of the ASME.1993,115:128-134.
[68]Bakhtar F, Zidi K. On the self diffusion of water vapour. Proceedings of the Institution of Mechanical Engineers, Part C,1985,199(C2):159-164.
[69]Bakhtar F, Mahpeykar M R, Abbas K K. An investigation of nucleating flows of steam in a cascade of turbine blading-theoretical treatment. J ASME Fluid Eng, 1995,117:138-144.
[70]Bakhtar F, So K S. A study of nucleating flow of steam in a cascade of supersonic blading by the time-marching method. International Journal of Heat & Fluid Flow,1991,12(1):54-62.
[71]Guha A, Young J B, Time-marching prediction of unsteady condensation phenomena due to supercritical heat addition, in The Institution of Mechanical Engineers Conference on Turbomachinery:Latest Developments in a changing Scene.1991, Institution of Mechanical Engineers:London.167-177.
[72]Guha A, J Young. The effect of flow unsteadiness on the homogeneous nucleation of water droplets in steam turbines. Philosophical Transactions:Physical Sciences and Engineering,1994,349(1691):445-472.
[73]Guha. A, Computation. Analysis and theory of two-phase flows. The Aeronautical Journal,1998,102(1012):71-82.
[74]White A J. A comparison of modelling methods for polydispersed wet-steam flow. International Journal for Numerical Methods in Engineering,2003,57(6): 819-834.
[75]White A J, Hounslow M J. Modelling droplet size distributions in polydispersed wet-steam flows. International Journal of Heat and Mass Transfer,2000,43(11): 1873-1884.
[76]White A J, Young J B. Time-marching method for the prediction of two-dimensional, unsteady flows of condensing steam. Journal of Propulsion and Power,1993,9(4):579-587.
[77]White A J, Hounslow M J. Modelling droplet size distributions in polydispersed wet-steam flows. International Journal of Heat and Mass Transfer,2000,43: 1873-1884.
[78]Young J B. Semi-analytical techniques for investigating thermal non-equilibrium effects in wet steam turbines. International Journal of Heat and Fluid Flow,1984, 5(2):81-91.
[79]Young J B. The condensation and evaporation of liquid droplets in a pure vapour at arbitrary Knudsen number. International Journal of Heat and Mass Transfer, 1991,34(7):1649-1661.
[80]Young J B. Two-dimensional, nonequilibrium, wet-steam calculations for nozzles and turbine cascades. Journal of Turbomachinery,1992,114:569-579.
[81]Young J B, Yeoh C. Non-equilibrium streamline curvature throughflow calculations in wet steam turbines. Transactions of the ASME Series A, Journal of Engineering for Power,1982, 104:489-496.
[82]Huang L, Young J B. An analytical solution for the Wilson point in homogeneously nucleating flows. Proceedings:Mathematical, Physical and Engineering Sciences,1996,452(1949):1459-1473.
[83]Gerber A G. Two-phase Eulerian/Lagrangian model for nucleating steam flow. Journal of Fluids Engineering,2002,124:465-475.
[84]Gerber A G, Mousavi A. Representing polydispersed droplet behavior in nucleating steam flow. Journal of Fluids Engineering,2007,129:1404-1414.
[85]Gerber A G, Kermani M J. A pressure based eulerian/eulerian multi-phase model for non-equilibrium condensation in transonic steam flow. International Journal of Heat and Mass Transfer,2004,47:2217-2231.
[86]Dykas S. Numerical calculation of the steam condensing flow. TASK Quarterly, 2001,5(4):519-535.
[87]Dykas S. Prediction of losses in the flow through the last stage of low-pressure steam turbine. International Journal for Numerical Methods in Fluids,2007,53(6): 933-945.
[88]Yamamoto S. Computation of practical flow problems with release of latent heat. Energy,2005,30(2-4):197-208.
[89]丰镇平李亮李国君. 汽轮机湿蒸汽两相凝结流动数值研究的现状与进展. 上海汽轮机,2002,2：1-10.
[90]俞茂铮,陈孝隆.存在自发凝结的超音速湿蒸汽双相流.西安交通大学学报,1983,17(1)：23-31.
[91]李亮,程代京,丰镇平,等.汽轮机湿蒸汽级中凝结流动的三维数值分析.工程热物理学报,2006,27(4)：571-573.
[92]Zhenping FENG, Liang LI, Guojun LI, Yoshio Shikano, Numerical simulation of three- dimensional transonic two-phase flows with spontaneous condensation. Proceeding of International Conference on Power Engineering. Xi'an, China, Oct. 8-12,2001:812-819.
[93]李亮,丰镇平,李国君. 透平级内动静干涉对凝结特性影响的数值研究. 工程热物理学报,2007,28(s1)：89-92.
[94]李亮,丰镇平,李国君. 一维喷管中存在自发凝结的跨音速湿蒸汽两相流动数值模拟. 工程热物理学报,2001,22(6)： 703-705.
[95]李亮,丰镇平,李国君. 平面叶栅中的湿蒸汽两相凝结流动数值模拟. 工程热物理学报,2002,23(3)：309-311.
[96]李亮,丰镇平,李国君. 湿蒸汽中超临界加热引起的非定常凝结流动一维数值分析. 自然科学进展,2003,13(2)：210-212.
[97]李亮丰镇平李国君. 出气边形状对叶栅中凝结流动影响机理的数值研究. 工程热物理学报,2003,24(5)：767-769.
[98]李亮,李国君,丰镇平.湿蒸汽两相流动的数值方法及其在喷管中的应用.西安交通大学学报,2001,35(11)：113 1-1134.
[99]吴晓明,李国君,丰镇平,李亮.SST k-co-kp两相湍流模型及其在湿蒸汽凝结流动数值模拟中的应用.西安交通大学学报,2007,41(5)：526-529.
[100]吴晓明,李亮,李国君,等. 基于双流体模型的湿蒸气凝结流动三维数值模拟. 热能动力工程,2007,22(4)：367-370.
[101]巫志华,李亮,丰镇平.三维湿蒸汽自发凝结流动的数值模拟. 动力工程,2006,26(6)：814-817.
[102]巫志华,李亮,丰镇平. 低压汽轮机三维叶栅通道内湿蒸汽两相流动的数值模拟与分析. 工程热物理学报,2007,28(5)：763-765.
[103]巫志华,李亮,丰镇平. 湿蒸汽两相流动问题的耦合求解. 工程热物理学报,2005,26(4)：578-580.
[104]陈红梅,李亮,丰镇平,等.一维喷管中湿蒸汽非均质凝结流动的研究. 工程热物理学报,2004,25(3)：395-398.
[105]陈红梅李亮丰镇平李国君.透平级中自发凝结及叶栅中非均质凝结流动的初步研究. 工程热物理学报,2005,26(s)：65-68.
[106]张冬阳,蔡虎,蒋洪德.蒸汽凝结对透平流动和几何参数的影响.汽轮机技术,1999,41(6)：339-341.
[107]张冬阳蒋洪德刘建军. 考虑若干影响的一元蒸汽凝结流数值解. 工程热物理学报,2001,22(S1)：25-39.
[108]张冬阳刘建军蒋洪德.三维湿蒸汽流动快速准确数值模拟方法及应用. 工程热物理学报,2003,24(2)：262-264.
[109]张冬阳.非平衡态湿蒸汽流动快速准确数值模拟方法研究：[博士学位论文].北京：中国科学研究院,2002.
[110]林智荣.蒸汽及燃气透平内部真实气体流动问题的研究：[博士学位论文]. 北京：清华大学,2005.
[11 1]林智荣,袁新.自发凝结流动数值模拟方法及其在Laval喷管中的应用.工程热物理学报,2006,27(1)：42-44.
[112]Kosolapov Y S. Calculation of spontaneously condensing steam flows in a plane turbine cascade. Fluid Dynamics,1995,30(6):926-933.
[113]David W, Oxtoby. Homogeneous nucleation:theory and experiment. J Phys: Condens,1992, Matter 4:7627-7650.
[114]Katz J. Homogeneous nucleation theory and experiment:A survey. Pure and applied chemistry,1992,64:1661-1661.
[115]M C C, Luijten. Nucleation and droplet growth at high pressure. PhD thesis. Department of Fluid Dynamics, Eindhoven University of Technology, 1998.
[116]Ford I J. Nucleation theorems, the statistical mechanics of molecular clusters, and a revision of classical nucleation theory. Physical Review E,1997,56(5): 5615-5629.
[117]Girshick S, Chiu C. Kinetic nucleation theory:A new expression for the rate of homogeneous nucleation from an ideal supersaturated vapor. The Journal of Chemical Physics,1990,93:1273-1277.
[118]Fisher M. The theory of condensation and the critical point. Physics,1967,3: 255-283.
[119]Kiang C S, Stauffer D, Walker G H, Puri O P, Wise J J, Patterson E M. A reexamination of homogeneous nucleation theory. Journal of Atmospheric Sciences,1971,28:1222-1232.
[120]Reiss H, Kegel W K, Katz J. Resolution of the problems of replacement free energy,1/S, and internal consistency in nucleation theory by consideration of the length scale for mixing entropy. Physical Review Letters,1997,78(23): 4506-4509.
[121]Lothe J, Pound G M. Reconsiderations of nucleation theory. The Journal of Chemical Physics,1962,36:2080-2085.
[122]Reiss H. Treatment of droplike clusters by means of the classical phase integral in nucleation theory. Journal of Statistical Physics,1970,2(1):83-104.
[123]Reiss H, Katz J L, Cohen E R. Translation-Rotation paradox in the theory of nucleation. The Journal of Chemical Physics,1968,48:5553.
[124]FederJ, Russell K C, Lothe J, Pound G M. Homogeneous nucleation and growth of droplets in vapours. Advances in Physics,1966,15(57):111-178.
[125]Wyslouzil B E, Seinfeld J H. Nonisothermal homogeneous nucleation. The Journal of Chemical Physics,1992,97(4):2661-2669.
[126]Dillman A, Meier G E A. A refined droplet approach to the problem of homogeneous nucleation from the vapour phase. J. Chem. Phys,1991,94:3872-3884.
[127]Heist R H, Reiss H. Investigation of the homogeneous nucleation of water vapor using a diffusion cloud chamber. The Journal of Chemical Physics,1973,59: 665-671.
[128]Anderson R J, Miller R C, Kassne[J], Hagen D E. A study of homogeneous condensation-freezing nucleation of small water droplets in an expansion cloud chamber. Journal of the Atmospheric Sciences,1980,37(11):2509-2520.
[129]Fletcher N H. Size effect in heterogeneous nucleation. The Journal of Chemical Physics,1958,29:572-576.
[130]Lee T D. Surface characterization by heterogeneous nucleation from the vapor. PhD thesis. Harvard University,1998
[131]Knudsen M. Maximum rate of vaporization of mercury. Ann Phys,1915,47: 697-708.
[132]Gyarmathy G. The spherical droplet in gaseous carrier streams:review and synthesis. Multiphase science and technology,1981-1982,1(1-4):99-279.
[133]Prast B. Condensation in supersonic expansion flows:theory and numerical evaluation. Eindhoven:Stan Ackermans Institute, Ontwerpers opleiding Computational Mechanics,1997.
[134]Mei Y, Guha A. Modification of the upwind schemes for the computation of condensing two-phase flows. Proceedings of the Institution of Mechanical Engineers, Part A:Journal of Power and Energy,2006,220(7):809-814.
[135]Peter V. Propagation of small disturbances in wet steam. In Proceedings of the 5th Conference on Steam Turbines of Large Output, Plzen, Czech Republic,1972, 35-50.
[136]Put F, Kelleners P H, Hagmeijer R, et Al. Numerical simulation of condensing real gas flows. Proceedings of CFD2001 3rd International Symposium on Computational Technologies for Fluid/Thermal/Chemical Systems with Industrial Applications,2001.
[137]Bolm D, Kerpicci H, Ren J, Surken N. Homogeneous and heterogeneous nucleation in a nozzle guide vane of a LP-steam Turbine.4th European Conference on Turbomachinery. Firenze, Italy,2001.
[138]Hienola A, Vehkamaki H K, Riipinen I, Kulmala M. Homogeneous vs heterogeneous nucleation in water-dicarboxylic acid systems. Atmos Chem Phys,2009,9:1873-1881.
[139]Jian Z Y, Jie W Q. Criterion for judging the homogeneous and heterogeneous nucleation. Metallurgical and Materials Transactions A,2001,32(2):391-395.
[140]Kotake S, Glass I I. Condensation of water vapour on heterogeneous nuclei in a shock tube. UTIAS Report,1976,207-210.
[141]Petr V, M Kolovratnik. Heterogeneous effects in the droplet nucleation process in 1p steam turbines.4th European Conference on Turbomachinery.2001. Firenze, Italy:783-792.
[142]Qian M, Ma J. Heterogeneous nucleation on convex spherical substrate surfaces: A rigorous thermodynamic formulation of Fletcher's classical model and the new perspectives derived. The Journal of chemical physics,2009,130(21): 214-709
[143]Harten A. High resolution schemes for hypersonic conservation laws. Journal of Computational Physics,1983,49(3):357-393.
[144]阎超.计算流体力学方法及应用.北京： 北京航空航天大学出版社.2006.
[145]张涵信,沈孟育. 计算流体力学—差分方法的原理和应用. 北京： 国防工业出版社.2003.
[146]Mashmoushy H, Mahpeykar M R, Bakhtar F. Studies of nucleating and wet steam flows in two-dimensional cascades. Proceedings of the Institution of Mechanical Engineers.,2004,218(8):843-858.
[147]Slater S, Leeming A D, Young J B. Particle deposition from two-dimensional turbulent gas flows. International Journal of Multiphase Flow,2003,29(5): 721-750.
[148]Dinh C V, Ruggles S G, Vogan J H. Bucket for the last stage of turbine. United States Patents.5393200,1995-2-28.