迎风表面三维积冰的数学模型与计算方法研究
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摘要
当飞机进入含有过冷水滴的云层时,机翼和发动机进口等迎风表面会产生结冰现象,导致机翼升力减小阻力增大、发动机推力降低甚至损坏等,给飞行安全带来很大的危害,因此关于飞机/发动机迎风表面的积冰研究受到了很大的关注。目前,国外对二维积冰的研究已经比较成熟,但对三维积冰(如机翼两端以及发动机进口等)的研究还在进行之中;国内关于二维积冰的数值研究已有较多的文献报道,但对三维积冰的数值模拟研究尚处于探索阶段。本文将研究三维积冰的数学模型,发展相应的计算方法,开发三维积冰的数值模拟程序。
本文首先发展了一个三维积冰模型,并据此开发了相应的积冰模拟程序。该积冰模型考虑了霜冰积冰、明冰积冰和不结冰三种情况;对明冰表面的未凝结薄水膜建立了控制方程,通过数值求解模拟其流动,克服了传统Messinger模型对水膜流动处理过于粗糙的缺点;模型中还考虑了两个相交表面角区的耦合积冰。据此所开发的积冰模拟程序可以自动判断不同来流条件下的积冰形态,并给出不同时刻的冰层厚度和水膜流动信息。
其次,本文发展了一套将自主开发程序与商业软件相结合的三维积冰计算方法,提高了三维积冰数值模拟的效率。即:利用自主开发程序进行局部水收集系数的计算以及冰层生长和冰层表面水膜流动的数值模拟,借助于ICEM、CFX和UG等软件进行网格划分、稀疏两相流场计算和三维冰形构建等工作,实现了整个积冰数值模拟过程—“网格自动划分-两相流场自动更新-冰层生长和水膜流动模拟-冰层表面坐标确定和冰形构建”—的循环。
再次,本文对冰层-空气对流换热、冰层-基底导热、水膜回流区以及水膜前锋区的处理等具体问题进行了细致的研究,并据此进一步完善了所开发的积冰模拟程序。
在上述工作的基础上,本文通过对文献提供的一些典型对比算例的计算,初步验证了本文所建立的三维积冰模型是合理的,所发展的计算方法是可行的,据此所开发的积冰模拟程序是基本可靠的。
最后,本文数值模拟了机翼-机身、机翼自由端、发动机进口支板和整流罩等部件的简化模型上的积冰过程,初步揭示了这些典型迎风表面上三维积冰的特点,显示了本文所开发程序的三维积冰模拟能力,为飞机/发动机迎风表面的积冰预测提供了一种方法和手段。
When the aircraft flys into the clouds with supercooled water droplets, ice accretion occurs on the up-wind surfaces, such as airfoil and engine-inlet. The ice on the airfoil leads to lift decrease and drag increase. The ice on the engine-inlet leads to thrust lost and even engine damage. All these reduce the safty of the flight. So, much attention has been paid on the study of the ice accretion on up-wind surfaces. The simulation of 2D ice accretion has been well done while the 3D simulation is just under research in the abroad. Many papers about 2D icing simulation have been published while the 3D icing simulation is just at the beginning in our country. The current research aims at developing an icing model and corresponding calculational methodology for 3D ice accretion, and also developing a 3D ice simulating program.
Firstly, a 3D icing model and the simulating program is developed. The model concerns three cases: rime ice, glaze ice and no ice. In this model, the control equations for the shallow water film flow are built. So the water flow is numerically simulated based on the equations. This is a big progress compared to the Messinger icing model in which the water flow is simply treated. The ice accretion on the corner of two intersecting surfaces is also concerned in the current model. The 3D ice simulating program is developed based on the icing model. The program can estimate which kind of ice will accrete uder different climate conditions. And it can provide the ice thickness and the informations of water flow at different time.
Secondly, a calculational methodology for the 3D ice simulation is developed. In this methodology, the water collection efficiency, the ice accretion and water flow on the ice layer are simulated with the program developed in this paper. The grid genetation, two-phase flow computation and ice surface construction are done with ICEM, CFX and UG respectively. The ice simulation process, grid generation-twophase flow computation-ice accretion and water flow simulation-ice surface construction, is completed with the program and softwares. So the 3D icing simulation efficiency is enhanced.
Thirdly, some improvements are added into the ice simulating program based on some detailed research about the heat convection between air flow and ice layer, the conduction between substrate and ice layer, the water flow in the reback area, the“front”of the water film, et al.
Then, many icing examples are simulated and the results are compared to that provided in the published papers. Good agreement proves the icing model is logical, the calculational methodology is feasible, and the program developed in this paper is credible.
Finally, the ice accretion on three simplified structures is numerically simulated. These three structures simulate the airfoil-the body of aircraft, the airfoil tip, the fairing and its strut in the engine-inlet respectively. The primary results show the characteristics of icing on these up-wind surfaces. The simulation work also shows the 3D ice simulating ability of the program developed in this paper. The research in this paper provides an approach for predicting the ice on the up-wind surfaces of the aircraft/aero-engine.
本文首先发展了一个三维积冰模型,并据此开发了相应的积冰模拟程序。该积冰模型考虑了霜冰积冰、明冰积冰和不结冰三种情况;对明冰表面的未凝结薄水膜建立了控制方程,通过数值求解模拟其流动,克服了传统Messinger模型对水膜流动处理过于粗糙的缺点;模型中还考虑了两个相交表面角区的耦合积冰。据此所开发的积冰模拟程序可以自动判断不同来流条件下的积冰形态,并给出不同时刻的冰层厚度和水膜流动信息。
其次,本文发展了一套将自主开发程序与商业软件相结合的三维积冰计算方法,提高了三维积冰数值模拟的效率。即:利用自主开发程序进行局部水收集系数的计算以及冰层生长和冰层表面水膜流动的数值模拟,借助于ICEM、CFX和UG等软件进行网格划分、稀疏两相流场计算和三维冰形构建等工作,实现了整个积冰数值模拟过程—“网格自动划分-两相流场自动更新-冰层生长和水膜流动模拟-冰层表面坐标确定和冰形构建”—的循环。
再次,本文对冰层-空气对流换热、冰层-基底导热、水膜回流区以及水膜前锋区的处理等具体问题进行了细致的研究,并据此进一步完善了所开发的积冰模拟程序。
在上述工作的基础上,本文通过对文献提供的一些典型对比算例的计算,初步验证了本文所建立的三维积冰模型是合理的,所发展的计算方法是可行的,据此所开发的积冰模拟程序是基本可靠的。
最后,本文数值模拟了机翼-机身、机翼自由端、发动机进口支板和整流罩等部件的简化模型上的积冰过程,初步揭示了这些典型迎风表面上三维积冰的特点,显示了本文所开发程序的三维积冰模拟能力,为飞机/发动机迎风表面的积冰预测提供了一种方法和手段。
When the aircraft flys into the clouds with supercooled water droplets, ice accretion occurs on the up-wind surfaces, such as airfoil and engine-inlet. The ice on the airfoil leads to lift decrease and drag increase. The ice on the engine-inlet leads to thrust lost and even engine damage. All these reduce the safty of the flight. So, much attention has been paid on the study of the ice accretion on up-wind surfaces. The simulation of 2D ice accretion has been well done while the 3D simulation is just under research in the abroad. Many papers about 2D icing simulation have been published while the 3D icing simulation is just at the beginning in our country. The current research aims at developing an icing model and corresponding calculational methodology for 3D ice accretion, and also developing a 3D ice simulating program.
Firstly, a 3D icing model and the simulating program is developed. The model concerns three cases: rime ice, glaze ice and no ice. In this model, the control equations for the shallow water film flow are built. So the water flow is numerically simulated based on the equations. This is a big progress compared to the Messinger icing model in which the water flow is simply treated. The ice accretion on the corner of two intersecting surfaces is also concerned in the current model. The 3D ice simulating program is developed based on the icing model. The program can estimate which kind of ice will accrete uder different climate conditions. And it can provide the ice thickness and the informations of water flow at different time.
Secondly, a calculational methodology for the 3D ice simulation is developed. In this methodology, the water collection efficiency, the ice accretion and water flow on the ice layer are simulated with the program developed in this paper. The grid genetation, two-phase flow computation and ice surface construction are done with ICEM, CFX and UG respectively. The ice simulation process, grid generation-twophase flow computation-ice accretion and water flow simulation-ice surface construction, is completed with the program and softwares. So the 3D icing simulation efficiency is enhanced.
Thirdly, some improvements are added into the ice simulating program based on some detailed research about the heat convection between air flow and ice layer, the conduction between substrate and ice layer, the water flow in the reback area, the“front”of the water film, et al.
Then, many icing examples are simulated and the results are compared to that provided in the published papers. Good agreement proves the icing model is logical, the calculational methodology is feasible, and the program developed in this paper is credible.
Finally, the ice accretion on three simplified structures is numerically simulated. These three structures simulate the airfoil-the body of aircraft, the airfoil tip, the fairing and its strut in the engine-inlet respectively. The primary results show the characteristics of icing on these up-wind surfaces. The simulation work also shows the 3D ice simulating ability of the program developed in this paper. The research in this paper provides an approach for predicting the ice on the up-wind surfaces of the aircraft/aero-engine.
引文
[1]裘燮刚,韩凤华.飞机防冰系统[M].北京:航空专业教材编审组, 1996:
[2] Kind R J, Potapczuk M G. Experimental and computational simulation of in-flight icing phenomena[J]. Progress in Aerospace Science, 1998, 34(1):275-345.
[3] Addy H E, Potapczuk M G, Sheldon D W. Modern airfoil ice accretions[R]. AIAA-97-0174.1997.
[4] Brumby R E. The effect of wing Ice contamination on essential flight characteristics.[R]. AGARD-CP-496.1991.
[5] Lynch F T, Khodadoust A. Effects of ice accretions on aircraft aerodynamics[J]. Progress in Aerospace Science, 2001, 37(8):669-767.
[6] Ranaudo R J, Mikkelsen K L, Knight R C. Performance degradation of a typical twin Engine commuter type aircraft in measured natural icing conditions[R]. AIAA-84-0179.1984.
[7] Gray V H. Prediction of aerodynamic penalties caused by ice formations on various airfoils[R]. NASA-TN D-2166.1964.
[8] Cole J A, Sand W R. Statistical study of aircraft icing accidents[R]. AIAA-91-0558.1991.
[9] Velloci A L. Financial report of aviation market[R]. Aviation Weed and Space Technology-2011.
[10] Ruff G A, Berkowitz B M. User's manual for the NASA lewice ice accretion prediction code(LEWICE)[R]. NASA-CR-185129.1990.
[11] Wright W B, Gent R W, Guffond D. DRA/NASA/ONERA collaboration on icing research partⅡ- prediction of airfoil ice accretion[R]. NASA-CR-202349.1997.
[12] Hedde T, Guffond D. Development of a three-dimensional icing code, comparison with experimental shapes[R]. AIAA-92-0041.1992.
[13] Mingione G, Brandi V, Esposito B. Ice accretion prediction on multi-element airfoils[R]. AIAA-1997-0177.1997.
[14] Bourgault Y, Habashi W G, Beaugendre H. Development of a shallow water icing model in FENSAP-ICE[R]. AIAA-99-0246.1999.
[15]沈维道,蒋智敏,童钧耕.工程热力学(第三版)[M].北京:高等教育出版社, 2000:
[16] Bowden D T, Gensemer A E, Skeen C A. Engineering Summary of Airframe Icing Technical Data[M]. Washington,D.C.: Federal Aviation Administration, 1963:
[17]胡娅萍.航空发动机进口部件积冰的数值模拟研究[D],南京:南京航空航天大学.博士学位论文.2008.
[18]易贤.飞机积冰的数值计算与积冰试验相似准则研究[D],绵阳:中国空气动力学研究与发展中心.博士学位论文. 2007.
[19]金维明,王炳仁,刘健文.飞机发动机积冰原因探讨[J].气象, 1997, 23(2):8~11.
[20] Hansman R J. The influence of ice accretion physics on the forecasting of aircraft icing conditions. Third International Conference on the Aviation Weather System[C], Anahiem, CA, 1989.
[21]裘燮纲,余小章.微引射防冰腔热力计算[J].航空学报, 1994, 15(9):1110-1113.
[22] Potapczuk M G, Berkowitz B M. An Experimental Investigation of Multi-Element Airfoil Ice Accretion and Resulting Performance Degradation[R]. AIAA-89-0752.1989.
[23] Bragg M B, Broeren A P, Blumenthal L A. Iced-airfoil aerodynamics[J]. Progress in Aerospace Sciences, 2005, 41(1):323-362.
[24] Myers T G, Hammond D W. Ice and water film growth from incoming supercooled droplets[J]. International Journal of Heat and Mass Transfer, 1999, 42(1):2233-2242.
[25] Papadakis M, Hung K E, Giao T. Vu e a. Experimental Investigation of Water Droplet Impingement on Airfoils, Finite Wings, and an S-Duct Engine Inlet[R]. NASA/TM-2002-211700.2002.
[26] Silveira R A d, Maliska C R, Estivam D A. Evaluation of Collection Efficiency Methods for Icing Analysis[R]. COBEM-2003-1810.2003.
[27] Messinger B L. Equilibrium temperature of an unheated icing surface as a function of airspeed[J]. Journal of Aeronautical Science, 1953, 20(1):29-42.
[28] Wright W B, Bidwell C S. Additional improvements to the NASA Lewis ice accretion code LEWICE[R]. AIAA-95-0752.1995.
[29] Hansman R H, Turnock S T. Investigation of surface water behavior during glaze ice accretion[J]. journa of aircraft, 1989, 26(2):140-147.
[30] Colin S, Pinella D, Garrison P. Ice accretion calculations for a commercial transport using the LEWCE3D, ICEGRID3D and CMARC programs[R]. AIAA-99-0250.1999.
[31] Potapczuk G M. LEWICE/E: An Euler based ice accretion code[R]. NASA-TM-105389.1992.
[32] Hedde T, Guffond D. Improvement of the ONERA 3D icing code,comparisoin with 3D exprimental shapes[R]. AIAA-93-0169.1993.
[33] Hedde T, Guffond D. ONERA three-dimensional icing model[J]. AIAA Journal, 1995, 33(6):1038-1045.
[34] Fortin G, Ilinca A, Laforte J L. Prediction of 2D airfoil ice accretion by bisection method and by rivulets and beads modeling[R]. AIAA-2003-1076.2003.
[35] Beaugendre H, Morency F, Habashi W G. ICE3D, FENSAP-ICE'S 3D in flight ice accretion module[R]. AIAA-2002-0385.2002.
[36] Bourgault Y, Boutanios Z, Habashi W G. Three-dimensional Eulerian approach to droplet impingement simulation using FENSAP-ICE,part1: model algorithm, and validation[J]. Journal of Aircraft, 2000, 37(1):95-103.
[37] Croce G, Beaugendre H, Habashi W G. CHT3D: FENSAP-ICE conjugate heat transfer computations with droplet impingement and runback effects[R]. AIAA-2002-0386.2002.
[38] Morency F, Beaugendre H, Habashi W G. FENSAP-ICE: a study of the effect of ice shapes on droplet impingement[R]. AIAA-2003-1223.2003.
[39] Potapczuk M G, Gerhart P M. Progress in development of a Navier-Stokes solver for evaluation of iced airfoil performance[R]. AIAA-1985-0410.1985.
[40] Scott J N, Hankey W L, Giessler F J. Navier-Stokes solution of the flow fied over ice accretion shapes[R]. AIAA-87-0099.1987.
[41] Potapczuk M. Numerical analysis of a NACA0012 airfoil with leading edge ice accretions[R]. AIAA-87-0101.1987.
[42] Cebeci T. The calculation of flow over iced airfoils[R]. AIAA-88-0112.1988.
[43] Scott J N, Gielda T P, Hankey W L. Navier-Stokes solutions of flowfield characteristics produced by ice accretion[R]. AIAA-88-0290.1988.
[44] Potapczuk M G. Navier-Stokes analysis of airfoils with leading edge ice accretions[R]. NASA Contractor report-191008.1993.
[45] Bangalore A, Phaengsook N, Sankar L N. Application of a third order upwind scheme to viscous flow over clean and iced wings[R]. AIAA-94-0485.1994.
[46] Caruso S C. Three-dimensional unstructured mesh procedure for iced wing flowfield and droplet trajectory calculations[R]. AIAA-94-0486.1994.
[47] Chung J, Choo Y, Reehorst A. Navier-Stokes analysis of the flowfield characteristics of an ice contaminated aircraft wing[R]. AIAA-99-0375.1999.
[48] Huebsch W W, Rothmayer A P. Unsteady Navier-Stokes Simulation Of Flow Past Surface Ice Geometries[R]. AIAA-2000-0232.2000.
[49] Kumar S, Loth E. Detached eddy simulations of an iced-airfoil[R]. AIAA-2001-0678.2001.
[50] Glockner? P S, Naterer G F, Venn G. Two-equation turbulence modeling of external flow past helicopter engine bay cooling inlets[R]. AIAA-2002-2965.2002.
[51] Zhu B, Chi X, Shih T I-P. Computing Aerodynamic Performance of 2-D Iced Airfoils with StructuredGrids[R]. AIAA-2003-1071.2003.
[52] Pan J P, Loth E. Detached eddy simulations for airfoil with ice shapes[R]. AIAA-2004-0564.2004.
[53] Chi X, Li Y, Chen H. A comparative study using CFD to predict iced airfoil aerodynamics[R]. AIAA-2005-1371.2005.
[54] Chi X, Williams B, Crist N. 2-D and 3-D CFD Simulations of Clean and Iced Wings[R]. AIAA-2006-1267.2006.
[55] McClain S T, Vargas M, Kreeger R E. Heat Transfer from Roughness Elements and Protuberances, Part II-Correlations for Protuberance Heat Transfer[R]. AIAA-2006-1083.2006.
[56] Kreeger R E, Vargas M. Heat Transfer over Roughness Elements Larger than the Boundary Layer[R]. AIAA-2005-5186.2005.
[57] Hansman R J, Reehorst A, Sims J. Analysis of surface roughness generation in aircraft ice accretion[R]. AIAA-92-0298.1992.
[58] Shin J. Characteristics of surface roughness associated with leading edge ice accretion[R]. AIAA-94-0799.1994.
[59] anderson D N, Shin J. Characterization of ice roughness from simulated icing encounters[R]. AIAA-1997-0052.1997.
[60] Anderson D N, Hentschel D B, Ruff G A. Measurement and Correlation of Ice Accretion Roughness[R]. AIAA-98-0486.1998.
[61] Tsao J C, Rothmayer A P. A mechanism for ice roughness formation on an airfoil leading edge, contributing to glaze ice accretion[R]. AIAA-1998-485 1998.
[62] Reshotko E, Tumin A. investigation of the role of transient growth in roughness-induced transition[R]. AIAA-2002-2850.2002.
[63] Tsao J C. Cross Flow Effects on Glaze Ice Roughness Formation[R]. AIAA-2003-1219.2003.
[64] Matheis B D, Rothmayer A P. Impact of Underlying Surface Roughness On Water Mass Transport[R]. AIAA-2003-1220.2003.
[65] Rothmayer A P. On the Creation of Ice Surface Roughness by Interfacial Instabilities[R]. AIAA-2003-972.2003.
[66] Wirogo S, Srirambhatla S. An eulerian method to calculate the collection efficiency on two and three dimensional bodies[R]. AIAA-2003-1073.2003.
[67] Cals M P, Henry R, Guffond D. Icing simulation in 3D duct : experiments and numerical simulation[R]. AIAA-2000-233.2000.
[68]卜雪琴,林贵平.基于CFD的水收集系数及防冰表面温度预测[J].北京航空航天大学学报, 2007, 33(10):1182-1185.
[69] Bragg M B, Gregorek G M. An analytical approach to airfoil icing[R]. AIAA-81-0403.1981.
[70] Kim J J, Elangovan R. An efficient numerical computation scheme for stiff equations of droplet trajectories[R]. AIAA-86-0407.1986.
[71] Maltezos D G, Osonitsch C, Shaw R J. Particle trajectory computer program for icing analysis of axisymmetric bodies(a progress report)[R]. AIAA-1987-0027.1987.
[72] Mohler S R, Bidwell C S. Comparision of two-dimensional and three-dimensional droplet trajectory calculations in the vicinity of finite wings[R]. AIAA-92-0645.1992.
[73] Caruso S C. LEWICE droplet trajectory calculations on a parallel computer[R]. AIAA-1993-0172.1993.
[74] Breer M D, Goodman M P. Three-dimensional water droplet trajectory code validation using an ECS inlet geometry[R]. NASA contractor report-191097.1993.
[75] Bidwell C S, Mohler S R. Collection efficiency and ice accretion calculations for a sphere, a swept MS(1)-317 wing, a swept NACA-0012 wing tip,an axisymmetric inlet, and a Boeing 737-300 inlet[R]. AIAA-1995-755.1995.
[76] Bourgault Y, Habashi W G, Dompierre J. An Eulerian approach to supercooled droplets impingement calculations[R]. AIAA-1997-0176.1997.
[77] Boutanios Z, Bourgault Y, Habashi W G. 3D droplets impingement analysis around an aircrafts's nose and cockpit using FENSAP-ICE[R]. AIAA-1998-200.1998.
[78] Rutkowski A, Wright W B, Potapczuk M. Numerical Study of Droplet Splashing and Re-impingement[R]. AIAA-2003-388.2003.
[79] Bidwell C S, Papadakis M. Collection Efficiency and Ice Accretion Characteristics of Two Full Scale and One 1/4 Scale Business Jet Horizontal Tails[R]. NASA/TM-2005-213653.2005.
[80] Tan S C, Papadakis M. Droplet Breakup, Splashing and Re-Impingement on An Iced Airfoil[R]. AIAA-2005-5185.2005.
[81] Tong X L, Luke E A. Eulerian simulations of icing collection efficiency using a singularity diffusion model[R]. AIAA-2005.
[82] Saeed F, Brette C, Fregeau M. A Three-Dimensional Water Droplet Trajectory and Impingement Analysis Program[R]. AIAA-2005-4838.2005.
[83] Domingos R H, Santos L C d C, Antunes A P. Analysis of a CFD procedure for water collection evaluation[R]. AIAA-2006-1269.2006.
[84] Quero M, Hammond D W, Purvis R. Analysis of Super-cooled Water Droplet Impact on a Thin Water Layer and Ice Growth [R]. AIAA-2006-0466.2006.
[85] Luliano E, Brandi V, Mingione G. Water impingement prediction on multi-element airfoils by means of Eulerian and Lagrangian approach with viscous and inviscid air flow[R]. AIAA-2006-1270.2006.
[86] MacArthur C D, Keller J L, Luers J K. Mathematical modeling of ice accretion on airfoils[R]. AIAA-82-0284.1982.
[87] Yamaguchi K, Hansman R J. Heat transfer on accreting ice surfaces[R]. AIAA-90-0200.1990.
[88] Yamaguchi K, Hansman R J, Kazmierczak M. Deterministic multi-zone ice accretion modeling[R]. AIAA-91-0265.1991.
[89] Wright W B. Advancements in the LEWICE ice accretion model[R]. AIAA-93-0171.1993.
[90] Eberhardt S, Ok H. Aircraft Icing Predictions Using an Efficient, Incompressible Navier-Stokes Solver[R]. AIAA-1994-609.1994.
[91] Tran P, Brahimi M T, Paraschivoiu I. ice accretion on aircraft wings with thermodynamic effects[R]. AIAA-94-0605.1994.
[92] Velazquez M T, Hansman R J. Implementation of combined feather and surface-normal ice growth models in LEWICE/X[R]. AIAA-95-0753.1995.
[93] Snellen M, Boelens O J, Hoeijmakers H W M. A computational method for numerically simulating ice accretion[R]. AIAA-97-2206.1997.
[94] Bragg M B, Lee S, Henze C M. Heat-transfer and freestream turbulence measurements for improvement of the ice accretion physical model[R]. AIAA-1997-53.1997.
[95] Tsao J C, Rothmayer A P. Triple-Deck Simulation of Surface Glaze Ice Accretion[R]. AIAA-22-0234.2000.
[96] Tao Y X, Xu G, Mansoor A M. Development of Ice Accretion Model Using Modular Approach[R]. AIAA-2001-0682.2001.
[97] Myers T G. An extension to the Messinger model for aircraft icing[J]. AIAA Journal, 2001, 39(2):211-218.
[98] Anderson D N, Tsao J C. Evaluation and validation of the Messinger freezing fraction[R]. AIAA-2003-1218.2003.
[99] Fortin G, Laforte J L, Beisswenger A. Prediction of Ice Shapes on NACA0012 2D Airfoil[R]. SAE 2003-01-2154.2003.
[100] Myers T G, Charpin J P F, Thompson C P. Slowly accretion ice due to supercooled water impactingon a cold surface[J]. Physics of Fluids, 2002, 14(1):240-256.
[101] Potapczuk M G, Papadakis M J, Vargas M. LEWICE modeling swept wing ice accretion[R]. AIAA-2003-730.2003.
[102] Domingos R H, Santos L C d C, A P Antunes e a. Analysis of a CFD procedure for water collection evaluation[R]. AIAA-2006-1269.2006.
[103] PSchuster E, Gambill J M, Fisher M S. Computational icing analysis of aircraft inlets[R]. AIAA-92-3178.1992.
[104] Schuster E P, Gambill J M, Fisher M S. Computational icing analysis of aircraft inlets[R]. AIAA-92-3178.1992.
[105] Al-Khalil K M, T G Keith J, Witt K J D. Icing calculations on a typical commercial jet engine inlet nacelle[R]. AIAA-94-0610.1994.
[106] Bidwell C S. Collection efficiency and ice accretion calcultions for a Boeing 737-300 inlet[R]. NASA technical memorandum-107347.1996.
[107] Mingione G, Brandi V, Saporiti A. A 3D Ice Accretion Simulation Code[R]. AIAA-99-0247.1999.
[108] Hamed A, Das K, Basu D. Numerical simulations of ice droplet trajectories and collection efficiency on aero-engine rotating machinery[R]. AIAA-2005-1248.2005.
[109] Venkataramani K S, Mallina R V, Shamara P A, et al. Dynamics of Icing in Aircraft Engines[R]. AIAA-2007-905.2007.
[110] Eberhardt S, Kim B, Ok H. BUWICE-an interactive icing program applied to engine inlets[R]. AIAA-1992-3179.1992.
[111] Lee S, Loth E, Broeren A. Simulation of icing on a cascade of stator blades[R]. AIAA-2006-0208.2006.
[112] Das K. Numerical simulations of icing in turbomachinery[D], university of Cincinnati.Ph. D. 2006.
[113] Das K, Hamed A, Basu D. Ice shape prediction for turbofan rotating blades[R]. AIAA-2006-0209.2006.
[114]韩风华,张朝民,王跃欣.飞机机翼表面水滴撞击特性计算[J].北京航空航天大学学报, 1995, 21(3):16-21.
[115]韩风华,左颜声,李东亮.飞机风挡防冰热载荷计算[J].航空学报, 1995, 16(1):33-37.
[116]常士楠,王长和,韩风华.飞机天线罩结冰情况研究[J].航空学报, 1997, 18(4):423-426.
[117]常士楠,韩风华.飞机发动机进气道前缘热气防冰器性能分析[J].北京航空航天大学学报, 1999, 25(2):201-203.
[118]杨倩,常士楠,袁修干.发动机进气道水滴撞击特性分析[J].北京航空航天大学学报, 2002,28(3):362-365.
[119]杨倩,常士楠,袁修干.水滴撞击特性的数值分析方法研究[J].航空学报, 2002, 23(2):173-176.
[120]张大林,杨曦,昂海松.过冷水滴撞击结冰表面的数值模拟[J].航空动力学报, 2003, 18(1):87-91.
[121]张强,胡利,曹义华.过冷水滴撞击三维机翼的数值模拟[J].航空动力学报, 2009, 21(6):1345-1350.
[122]易贤,王开春,桂业伟.结冰面水滴收集率欧拉计算方法研究及应用[J].空气动力学学报, 2010, 28(5):596-601.
[123]易贤,朱国林,王开春等.翼型积冰的数值模拟[J].空气动力学学报, 2002, 20(4):428-433.
[124]易贤,朱国林.考虑传质传热效应的翼型积冰计算[J].空气动力学学报, 2004, 22(4):490-493.
[125]陈维健,张大林.飞机机翼结冰过程的数值模拟[J].航空动力学报, 2005, 20(6):1010-1017.
[126]陈维健,张大林.瘤状冰结冰过程的数值模拟[J].航空动力学报, 2005, 20(3):472-476.
[127]张大林,陈维健.飞机机翼表面霜状冰结冰过程的数值模拟[J].航空动力学报, 2004, 19(1):137-141.
[128]付斌,孙志国,朱程香等.机翼表面结冰热力学模型[J].工程热物理学报, 2010, 31(10):1727-1730.
[129]孙志国,朱程香,付斌等.二维翼型结冰数值模拟[J].航空动力学报, 2010, 25(7):1485-1490.
[130]朱程香,孙志国,付斌等.水滴多尺寸分布对水滴撞击特性和结冰增长的影响[J].南京航空航天大学学报, 2010, 42(5):620-624.
[131]王汪峰,夏健,田书玲.基于非结构动态网格的翼型积冰过程数值模拟[J].航空学报, 2009, 30(12):2269-2274.
[132]蒋胜炬,李凤蔚.基于N-S方程的翼型结冰数值模拟[J].西北工业大学学报, 2004, 22(5):559-562.
[133]桑为民,蒋胜矩,李凤蔚.翼型冰增长和结冰影响的数值模拟研究[J].应用力学学报, 2008, 25(3):371-374.
[134]周志宏,李凤蔚,李广宁.基于两相流欧拉方法的翼型结冰数值模拟[J].西北工业大学学报, 2010, 28(1):138-142.
[135]冯文梁,李杰,张威.基于变形网格技术的翼型结冰数值模拟研究[J].西北工业大学学报, 2008, 26(5):550-555.
[136]陈科,曹义华.简化的积冰热力学模型及其应用[J].航空计算技术, 2008, 38(1):36-39.
[137]陈科,曹义华,潘星.改进的翼型积冰数值模拟方法[J].航空动力学报, 2007, 22(11):1814-1819.
[138]张强,曹义华,胡利.翼型表面明冰的数值模拟[J].航空动力学报, 2009, 24(1):91-97.
[139]张强,曹义华,李栋.采用欧拉两相流法对翼型表面霜冰的数值模拟[J].北京航空航天大学学报, 2009, 35(3):351-354.
[140]常士楠,艾素霄,陈余等.一种飞机机翼表面结冰过程仿真方法[J].系统仿真学报, 2008, 20(10):2538-2545.
[141]常士楠,洪海华,张玉珠.结冰模拟与AEDC方法有效性的验证[J].北京航空航天大学学报, 2009, 35(6):692-696.
[142]杨胜华,林桂平.霜冰生长过程的数值模拟[J].计算机工程与设计, 2010, 31(1):191-194.
[143]钟国华,孙晓峰.基于浸入式边界方法的二维结冰机翼的数值模拟[J].航空动力学报, 2009, 24(8):1752-1758.
[144]盛强,邢玉明,何超.基于CFD的机翼结冰过程分析[J].航空计算技术, 2009, 39(2):37-40.
[145]李国知,胡利,张瑞民等.直升机旋翼桨叶翼型积冰的数值模拟[J].直升机技术, 2008, 155(3):78-81.
[146]陈维建.飞机机翼结冰的数值模拟研究[D],南京:南京航空航天大学.博士学位论文. 2007.
[147]杜雁霞,桂业伟,肖春华等.飞机结冰过程的传热研究[J].工程热物理学报, 2009, 30(11):1923-1925.
[148]杜雁霞,桂业伟,肖春华等.飞机结冰过程的液/固相变传热研究[J].航空动力学报, 2009, 24(8):1824-1830.
[149]张强,曹义华,钟国.飞机机翼表面霜冰的三维数值模拟[J].航空动力学报, 2010, 25(6):1303-1309.
[150]易贤,桂业伟,朱国林.飞机三维积冰模型及其数值求解方法[J].航空学报, 2010, 31(11):2152-2158.
[151]王世忠.航空发动机进口支板的积冰机理和数值模拟研究[D],南京:南京航空航天大学.硕士学位论文. 2003.
[152] ANSYS CFX-Solver Theory Guide-Multiphase Flow Theory[R]. ANSYS, Inc.2006.
[153]王福军.计算流体动力学分析[M].北京:清华大学出版社, 2006:
[154] Riley J, Mcdowall R. An investigation of the effect of number of time steps on ice shapes calculated by an ice accretion code[R]. DOT/FAA/AR-02/1.2002.
[155] Moriarty J A, Schwartz L W, Tuck E O. Unsteady spreading of thin liquid films with small surface tension[J]. Physics of Fluids, 1991, 3(5):733-742.
[156] Morency F, Tesok F, Paraschivoiu I. Anti-Icing System Simulation using CANICE[J]. Journal of Aircraft, 1999, 36(6):999-1006.
[157] Papadakis M, Rachman A, Wong S C, et al. Water Impingement Experiments on a NACA 23012 Airfoil with Simulated Glaze Ice Shapes[R]. AIAA-2004-565.2004.
[158] Shin J, Bond T H. Results of an icing test on a NACA0012 airfoil in the NASA Lewis icing research tunnel[R]. AIAA-92-0647.1992.
[159] Shin J, Bond T H. Experimental and computational ice shapes and resulting drag increase for a NACA0012 airfoil[R]. NASA-TM-105743.1992.
[2] Kind R J, Potapczuk M G. Experimental and computational simulation of in-flight icing phenomena[J]. Progress in Aerospace Science, 1998, 34(1):275-345.
[3] Addy H E, Potapczuk M G, Sheldon D W. Modern airfoil ice accretions[R]. AIAA-97-0174.1997.
[4] Brumby R E. The effect of wing Ice contamination on essential flight characteristics.[R]. AGARD-CP-496.1991.
[5] Lynch F T, Khodadoust A. Effects of ice accretions on aircraft aerodynamics[J]. Progress in Aerospace Science, 2001, 37(8):669-767.
[6] Ranaudo R J, Mikkelsen K L, Knight R C. Performance degradation of a typical twin Engine commuter type aircraft in measured natural icing conditions[R]. AIAA-84-0179.1984.
[7] Gray V H. Prediction of aerodynamic penalties caused by ice formations on various airfoils[R]. NASA-TN D-2166.1964.
[8] Cole J A, Sand W R. Statistical study of aircraft icing accidents[R]. AIAA-91-0558.1991.
[9] Velloci A L. Financial report of aviation market[R]. Aviation Weed and Space Technology-2011.
[10] Ruff G A, Berkowitz B M. User's manual for the NASA lewice ice accretion prediction code(LEWICE)[R]. NASA-CR-185129.1990.
[11] Wright W B, Gent R W, Guffond D. DRA/NASA/ONERA collaboration on icing research partⅡ- prediction of airfoil ice accretion[R]. NASA-CR-202349.1997.
[12] Hedde T, Guffond D. Development of a three-dimensional icing code, comparison with experimental shapes[R]. AIAA-92-0041.1992.
[13] Mingione G, Brandi V, Esposito B. Ice accretion prediction on multi-element airfoils[R]. AIAA-1997-0177.1997.
[14] Bourgault Y, Habashi W G, Beaugendre H. Development of a shallow water icing model in FENSAP-ICE[R]. AIAA-99-0246.1999.
[15]沈维道,蒋智敏,童钧耕.工程热力学(第三版)[M].北京:高等教育出版社, 2000:
[16] Bowden D T, Gensemer A E, Skeen C A. Engineering Summary of Airframe Icing Technical Data[M]. Washington,D.C.: Federal Aviation Administration, 1963:
[17]胡娅萍.航空发动机进口部件积冰的数值模拟研究[D],南京:南京航空航天大学.博士学位论文.2008.
[18]易贤.飞机积冰的数值计算与积冰试验相似准则研究[D],绵阳:中国空气动力学研究与发展中心.博士学位论文. 2007.
[19]金维明,王炳仁,刘健文.飞机发动机积冰原因探讨[J].气象, 1997, 23(2):8~11.
[20] Hansman R J. The influence of ice accretion physics on the forecasting of aircraft icing conditions. Third International Conference on the Aviation Weather System[C], Anahiem, CA, 1989.
[21]裘燮纲,余小章.微引射防冰腔热力计算[J].航空学报, 1994, 15(9):1110-1113.
[22] Potapczuk M G, Berkowitz B M. An Experimental Investigation of Multi-Element Airfoil Ice Accretion and Resulting Performance Degradation[R]. AIAA-89-0752.1989.
[23] Bragg M B, Broeren A P, Blumenthal L A. Iced-airfoil aerodynamics[J]. Progress in Aerospace Sciences, 2005, 41(1):323-362.
[24] Myers T G, Hammond D W. Ice and water film growth from incoming supercooled droplets[J]. International Journal of Heat and Mass Transfer, 1999, 42(1):2233-2242.
[25] Papadakis M, Hung K E, Giao T. Vu e a. Experimental Investigation of Water Droplet Impingement on Airfoils, Finite Wings, and an S-Duct Engine Inlet[R]. NASA/TM-2002-211700.2002.
[26] Silveira R A d, Maliska C R, Estivam D A. Evaluation of Collection Efficiency Methods for Icing Analysis[R]. COBEM-2003-1810.2003.
[27] Messinger B L. Equilibrium temperature of an unheated icing surface as a function of airspeed[J]. Journal of Aeronautical Science, 1953, 20(1):29-42.
[28] Wright W B, Bidwell C S. Additional improvements to the NASA Lewis ice accretion code LEWICE[R]. AIAA-95-0752.1995.
[29] Hansman R H, Turnock S T. Investigation of surface water behavior during glaze ice accretion[J]. journa of aircraft, 1989, 26(2):140-147.
[30] Colin S, Pinella D, Garrison P. Ice accretion calculations for a commercial transport using the LEWCE3D, ICEGRID3D and CMARC programs[R]. AIAA-99-0250.1999.
[31] Potapczuk G M. LEWICE/E: An Euler based ice accretion code[R]. NASA-TM-105389.1992.
[32] Hedde T, Guffond D. Improvement of the ONERA 3D icing code,comparisoin with 3D exprimental shapes[R]. AIAA-93-0169.1993.
[33] Hedde T, Guffond D. ONERA three-dimensional icing model[J]. AIAA Journal, 1995, 33(6):1038-1045.
[34] Fortin G, Ilinca A, Laforte J L. Prediction of 2D airfoil ice accretion by bisection method and by rivulets and beads modeling[R]. AIAA-2003-1076.2003.
[35] Beaugendre H, Morency F, Habashi W G. ICE3D, FENSAP-ICE'S 3D in flight ice accretion module[R]. AIAA-2002-0385.2002.
[36] Bourgault Y, Boutanios Z, Habashi W G. Three-dimensional Eulerian approach to droplet impingement simulation using FENSAP-ICE,part1: model algorithm, and validation[J]. Journal of Aircraft, 2000, 37(1):95-103.
[37] Croce G, Beaugendre H, Habashi W G. CHT3D: FENSAP-ICE conjugate heat transfer computations with droplet impingement and runback effects[R]. AIAA-2002-0386.2002.
[38] Morency F, Beaugendre H, Habashi W G. FENSAP-ICE: a study of the effect of ice shapes on droplet impingement[R]. AIAA-2003-1223.2003.
[39] Potapczuk M G, Gerhart P M. Progress in development of a Navier-Stokes solver for evaluation of iced airfoil performance[R]. AIAA-1985-0410.1985.
[40] Scott J N, Hankey W L, Giessler F J. Navier-Stokes solution of the flow fied over ice accretion shapes[R]. AIAA-87-0099.1987.
[41] Potapczuk M. Numerical analysis of a NACA0012 airfoil with leading edge ice accretions[R]. AIAA-87-0101.1987.
[42] Cebeci T. The calculation of flow over iced airfoils[R]. AIAA-88-0112.1988.
[43] Scott J N, Gielda T P, Hankey W L. Navier-Stokes solutions of flowfield characteristics produced by ice accretion[R]. AIAA-88-0290.1988.
[44] Potapczuk M G. Navier-Stokes analysis of airfoils with leading edge ice accretions[R]. NASA Contractor report-191008.1993.
[45] Bangalore A, Phaengsook N, Sankar L N. Application of a third order upwind scheme to viscous flow over clean and iced wings[R]. AIAA-94-0485.1994.
[46] Caruso S C. Three-dimensional unstructured mesh procedure for iced wing flowfield and droplet trajectory calculations[R]. AIAA-94-0486.1994.
[47] Chung J, Choo Y, Reehorst A. Navier-Stokes analysis of the flowfield characteristics of an ice contaminated aircraft wing[R]. AIAA-99-0375.1999.
[48] Huebsch W W, Rothmayer A P. Unsteady Navier-Stokes Simulation Of Flow Past Surface Ice Geometries[R]. AIAA-2000-0232.2000.
[49] Kumar S, Loth E. Detached eddy simulations of an iced-airfoil[R]. AIAA-2001-0678.2001.
[50] Glockner? P S, Naterer G F, Venn G. Two-equation turbulence modeling of external flow past helicopter engine bay cooling inlets[R]. AIAA-2002-2965.2002.
[51] Zhu B, Chi X, Shih T I-P. Computing Aerodynamic Performance of 2-D Iced Airfoils with StructuredGrids[R]. AIAA-2003-1071.2003.
[52] Pan J P, Loth E. Detached eddy simulations for airfoil with ice shapes[R]. AIAA-2004-0564.2004.
[53] Chi X, Li Y, Chen H. A comparative study using CFD to predict iced airfoil aerodynamics[R]. AIAA-2005-1371.2005.
[54] Chi X, Williams B, Crist N. 2-D and 3-D CFD Simulations of Clean and Iced Wings[R]. AIAA-2006-1267.2006.
[55] McClain S T, Vargas M, Kreeger R E. Heat Transfer from Roughness Elements and Protuberances, Part II-Correlations for Protuberance Heat Transfer[R]. AIAA-2006-1083.2006.
[56] Kreeger R E, Vargas M. Heat Transfer over Roughness Elements Larger than the Boundary Layer[R]. AIAA-2005-5186.2005.
[57] Hansman R J, Reehorst A, Sims J. Analysis of surface roughness generation in aircraft ice accretion[R]. AIAA-92-0298.1992.
[58] Shin J. Characteristics of surface roughness associated with leading edge ice accretion[R]. AIAA-94-0799.1994.
[59] anderson D N, Shin J. Characterization of ice roughness from simulated icing encounters[R]. AIAA-1997-0052.1997.
[60] Anderson D N, Hentschel D B, Ruff G A. Measurement and Correlation of Ice Accretion Roughness[R]. AIAA-98-0486.1998.
[61] Tsao J C, Rothmayer A P. A mechanism for ice roughness formation on an airfoil leading edge, contributing to glaze ice accretion[R]. AIAA-1998-485 1998.
[62] Reshotko E, Tumin A. investigation of the role of transient growth in roughness-induced transition[R]. AIAA-2002-2850.2002.
[63] Tsao J C. Cross Flow Effects on Glaze Ice Roughness Formation[R]. AIAA-2003-1219.2003.
[64] Matheis B D, Rothmayer A P. Impact of Underlying Surface Roughness On Water Mass Transport[R]. AIAA-2003-1220.2003.
[65] Rothmayer A P. On the Creation of Ice Surface Roughness by Interfacial Instabilities[R]. AIAA-2003-972.2003.
[66] Wirogo S, Srirambhatla S. An eulerian method to calculate the collection efficiency on two and three dimensional bodies[R]. AIAA-2003-1073.2003.
[67] Cals M P, Henry R, Guffond D. Icing simulation in 3D duct : experiments and numerical simulation[R]. AIAA-2000-233.2000.
[68]卜雪琴,林贵平.基于CFD的水收集系数及防冰表面温度预测[J].北京航空航天大学学报, 2007, 33(10):1182-1185.
[69] Bragg M B, Gregorek G M. An analytical approach to airfoil icing[R]. AIAA-81-0403.1981.
[70] Kim J J, Elangovan R. An efficient numerical computation scheme for stiff equations of droplet trajectories[R]. AIAA-86-0407.1986.
[71] Maltezos D G, Osonitsch C, Shaw R J. Particle trajectory computer program for icing analysis of axisymmetric bodies(a progress report)[R]. AIAA-1987-0027.1987.
[72] Mohler S R, Bidwell C S. Comparision of two-dimensional and three-dimensional droplet trajectory calculations in the vicinity of finite wings[R]. AIAA-92-0645.1992.
[73] Caruso S C. LEWICE droplet trajectory calculations on a parallel computer[R]. AIAA-1993-0172.1993.
[74] Breer M D, Goodman M P. Three-dimensional water droplet trajectory code validation using an ECS inlet geometry[R]. NASA contractor report-191097.1993.
[75] Bidwell C S, Mohler S R. Collection efficiency and ice accretion calculations for a sphere, a swept MS(1)-317 wing, a swept NACA-0012 wing tip,an axisymmetric inlet, and a Boeing 737-300 inlet[R]. AIAA-1995-755.1995.
[76] Bourgault Y, Habashi W G, Dompierre J. An Eulerian approach to supercooled droplets impingement calculations[R]. AIAA-1997-0176.1997.
[77] Boutanios Z, Bourgault Y, Habashi W G. 3D droplets impingement analysis around an aircrafts's nose and cockpit using FENSAP-ICE[R]. AIAA-1998-200.1998.
[78] Rutkowski A, Wright W B, Potapczuk M. Numerical Study of Droplet Splashing and Re-impingement[R]. AIAA-2003-388.2003.
[79] Bidwell C S, Papadakis M. Collection Efficiency and Ice Accretion Characteristics of Two Full Scale and One 1/4 Scale Business Jet Horizontal Tails[R]. NASA/TM-2005-213653.2005.
[80] Tan S C, Papadakis M. Droplet Breakup, Splashing and Re-Impingement on An Iced Airfoil[R]. AIAA-2005-5185.2005.
[81] Tong X L, Luke E A. Eulerian simulations of icing collection efficiency using a singularity diffusion model[R]. AIAA-2005.
[82] Saeed F, Brette C, Fregeau M. A Three-Dimensional Water Droplet Trajectory and Impingement Analysis Program[R]. AIAA-2005-4838.2005.
[83] Domingos R H, Santos L C d C, Antunes A P. Analysis of a CFD procedure for water collection evaluation[R]. AIAA-2006-1269.2006.
[84] Quero M, Hammond D W, Purvis R. Analysis of Super-cooled Water Droplet Impact on a Thin Water Layer and Ice Growth [R]. AIAA-2006-0466.2006.
[85] Luliano E, Brandi V, Mingione G. Water impingement prediction on multi-element airfoils by means of Eulerian and Lagrangian approach with viscous and inviscid air flow[R]. AIAA-2006-1270.2006.
[86] MacArthur C D, Keller J L, Luers J K. Mathematical modeling of ice accretion on airfoils[R]. AIAA-82-0284.1982.
[87] Yamaguchi K, Hansman R J. Heat transfer on accreting ice surfaces[R]. AIAA-90-0200.1990.
[88] Yamaguchi K, Hansman R J, Kazmierczak M. Deterministic multi-zone ice accretion modeling[R]. AIAA-91-0265.1991.
[89] Wright W B. Advancements in the LEWICE ice accretion model[R]. AIAA-93-0171.1993.
[90] Eberhardt S, Ok H. Aircraft Icing Predictions Using an Efficient, Incompressible Navier-Stokes Solver[R]. AIAA-1994-609.1994.
[91] Tran P, Brahimi M T, Paraschivoiu I. ice accretion on aircraft wings with thermodynamic effects[R]. AIAA-94-0605.1994.
[92] Velazquez M T, Hansman R J. Implementation of combined feather and surface-normal ice growth models in LEWICE/X[R]. AIAA-95-0753.1995.
[93] Snellen M, Boelens O J, Hoeijmakers H W M. A computational method for numerically simulating ice accretion[R]. AIAA-97-2206.1997.
[94] Bragg M B, Lee S, Henze C M. Heat-transfer and freestream turbulence measurements for improvement of the ice accretion physical model[R]. AIAA-1997-53.1997.
[95] Tsao J C, Rothmayer A P. Triple-Deck Simulation of Surface Glaze Ice Accretion[R]. AIAA-22-0234.2000.
[96] Tao Y X, Xu G, Mansoor A M. Development of Ice Accretion Model Using Modular Approach[R]. AIAA-2001-0682.2001.
[97] Myers T G. An extension to the Messinger model for aircraft icing[J]. AIAA Journal, 2001, 39(2):211-218.
[98] Anderson D N, Tsao J C. Evaluation and validation of the Messinger freezing fraction[R]. AIAA-2003-1218.2003.
[99] Fortin G, Laforte J L, Beisswenger A. Prediction of Ice Shapes on NACA0012 2D Airfoil[R]. SAE 2003-01-2154.2003.
[100] Myers T G, Charpin J P F, Thompson C P. Slowly accretion ice due to supercooled water impactingon a cold surface[J]. Physics of Fluids, 2002, 14(1):240-256.
[101] Potapczuk M G, Papadakis M J, Vargas M. LEWICE modeling swept wing ice accretion[R]. AIAA-2003-730.2003.
[102] Domingos R H, Santos L C d C, A P Antunes e a. Analysis of a CFD procedure for water collection evaluation[R]. AIAA-2006-1269.2006.
[103] PSchuster E, Gambill J M, Fisher M S. Computational icing analysis of aircraft inlets[R]. AIAA-92-3178.1992.
[104] Schuster E P, Gambill J M, Fisher M S. Computational icing analysis of aircraft inlets[R]. AIAA-92-3178.1992.
[105] Al-Khalil K M, T G Keith J, Witt K J D. Icing calculations on a typical commercial jet engine inlet nacelle[R]. AIAA-94-0610.1994.
[106] Bidwell C S. Collection efficiency and ice accretion calcultions for a Boeing 737-300 inlet[R]. NASA technical memorandum-107347.1996.
[107] Mingione G, Brandi V, Saporiti A. A 3D Ice Accretion Simulation Code[R]. AIAA-99-0247.1999.
[108] Hamed A, Das K, Basu D. Numerical simulations of ice droplet trajectories and collection efficiency on aero-engine rotating machinery[R]. AIAA-2005-1248.2005.
[109] Venkataramani K S, Mallina R V, Shamara P A, et al. Dynamics of Icing in Aircraft Engines[R]. AIAA-2007-905.2007.
[110] Eberhardt S, Kim B, Ok H. BUWICE-an interactive icing program applied to engine inlets[R]. AIAA-1992-3179.1992.
[111] Lee S, Loth E, Broeren A. Simulation of icing on a cascade of stator blades[R]. AIAA-2006-0208.2006.
[112] Das K. Numerical simulations of icing in turbomachinery[D], university of Cincinnati.Ph. D. 2006.
[113] Das K, Hamed A, Basu D. Ice shape prediction for turbofan rotating blades[R]. AIAA-2006-0209.2006.
[114]韩风华,张朝民,王跃欣.飞机机翼表面水滴撞击特性计算[J].北京航空航天大学学报, 1995, 21(3):16-21.
[115]韩风华,左颜声,李东亮.飞机风挡防冰热载荷计算[J].航空学报, 1995, 16(1):33-37.
[116]常士楠,王长和,韩风华.飞机天线罩结冰情况研究[J].航空学报, 1997, 18(4):423-426.
[117]常士楠,韩风华.飞机发动机进气道前缘热气防冰器性能分析[J].北京航空航天大学学报, 1999, 25(2):201-203.
[118]杨倩,常士楠,袁修干.发动机进气道水滴撞击特性分析[J].北京航空航天大学学报, 2002,28(3):362-365.
[119]杨倩,常士楠,袁修干.水滴撞击特性的数值分析方法研究[J].航空学报, 2002, 23(2):173-176.
[120]张大林,杨曦,昂海松.过冷水滴撞击结冰表面的数值模拟[J].航空动力学报, 2003, 18(1):87-91.
[121]张强,胡利,曹义华.过冷水滴撞击三维机翼的数值模拟[J].航空动力学报, 2009, 21(6):1345-1350.
[122]易贤,王开春,桂业伟.结冰面水滴收集率欧拉计算方法研究及应用[J].空气动力学学报, 2010, 28(5):596-601.
[123]易贤,朱国林,王开春等.翼型积冰的数值模拟[J].空气动力学学报, 2002, 20(4):428-433.
[124]易贤,朱国林.考虑传质传热效应的翼型积冰计算[J].空气动力学学报, 2004, 22(4):490-493.
[125]陈维健,张大林.飞机机翼结冰过程的数值模拟[J].航空动力学报, 2005, 20(6):1010-1017.
[126]陈维健,张大林.瘤状冰结冰过程的数值模拟[J].航空动力学报, 2005, 20(3):472-476.
[127]张大林,陈维健.飞机机翼表面霜状冰结冰过程的数值模拟[J].航空动力学报, 2004, 19(1):137-141.
[128]付斌,孙志国,朱程香等.机翼表面结冰热力学模型[J].工程热物理学报, 2010, 31(10):1727-1730.
[129]孙志国,朱程香,付斌等.二维翼型结冰数值模拟[J].航空动力学报, 2010, 25(7):1485-1490.
[130]朱程香,孙志国,付斌等.水滴多尺寸分布对水滴撞击特性和结冰增长的影响[J].南京航空航天大学学报, 2010, 42(5):620-624.
[131]王汪峰,夏健,田书玲.基于非结构动态网格的翼型积冰过程数值模拟[J].航空学报, 2009, 30(12):2269-2274.
[132]蒋胜炬,李凤蔚.基于N-S方程的翼型结冰数值模拟[J].西北工业大学学报, 2004, 22(5):559-562.
[133]桑为民,蒋胜矩,李凤蔚.翼型冰增长和结冰影响的数值模拟研究[J].应用力学学报, 2008, 25(3):371-374.
[134]周志宏,李凤蔚,李广宁.基于两相流欧拉方法的翼型结冰数值模拟[J].西北工业大学学报, 2010, 28(1):138-142.
[135]冯文梁,李杰,张威.基于变形网格技术的翼型结冰数值模拟研究[J].西北工业大学学报, 2008, 26(5):550-555.
[136]陈科,曹义华.简化的积冰热力学模型及其应用[J].航空计算技术, 2008, 38(1):36-39.
[137]陈科,曹义华,潘星.改进的翼型积冰数值模拟方法[J].航空动力学报, 2007, 22(11):1814-1819.
[138]张强,曹义华,胡利.翼型表面明冰的数值模拟[J].航空动力学报, 2009, 24(1):91-97.
[139]张强,曹义华,李栋.采用欧拉两相流法对翼型表面霜冰的数值模拟[J].北京航空航天大学学报, 2009, 35(3):351-354.
[140]常士楠,艾素霄,陈余等.一种飞机机翼表面结冰过程仿真方法[J].系统仿真学报, 2008, 20(10):2538-2545.
[141]常士楠,洪海华,张玉珠.结冰模拟与AEDC方法有效性的验证[J].北京航空航天大学学报, 2009, 35(6):692-696.
[142]杨胜华,林桂平.霜冰生长过程的数值模拟[J].计算机工程与设计, 2010, 31(1):191-194.
[143]钟国华,孙晓峰.基于浸入式边界方法的二维结冰机翼的数值模拟[J].航空动力学报, 2009, 24(8):1752-1758.
[144]盛强,邢玉明,何超.基于CFD的机翼结冰过程分析[J].航空计算技术, 2009, 39(2):37-40.
[145]李国知,胡利,张瑞民等.直升机旋翼桨叶翼型积冰的数值模拟[J].直升机技术, 2008, 155(3):78-81.
[146]陈维建.飞机机翼结冰的数值模拟研究[D],南京:南京航空航天大学.博士学位论文. 2007.
[147]杜雁霞,桂业伟,肖春华等.飞机结冰过程的传热研究[J].工程热物理学报, 2009, 30(11):1923-1925.
[148]杜雁霞,桂业伟,肖春华等.飞机结冰过程的液/固相变传热研究[J].航空动力学报, 2009, 24(8):1824-1830.
[149]张强,曹义华,钟国.飞机机翼表面霜冰的三维数值模拟[J].航空动力学报, 2010, 25(6):1303-1309.
[150]易贤,桂业伟,朱国林.飞机三维积冰模型及其数值求解方法[J].航空学报, 2010, 31(11):2152-2158.
[151]王世忠.航空发动机进口支板的积冰机理和数值模拟研究[D],南京:南京航空航天大学.硕士学位论文. 2003.
[152] ANSYS CFX-Solver Theory Guide-Multiphase Flow Theory[R]. ANSYS, Inc.2006.
[153]王福军.计算流体动力学分析[M].北京:清华大学出版社, 2006:
[154] Riley J, Mcdowall R. An investigation of the effect of number of time steps on ice shapes calculated by an ice accretion code[R]. DOT/FAA/AR-02/1.2002.
[155] Moriarty J A, Schwartz L W, Tuck E O. Unsteady spreading of thin liquid films with small surface tension[J]. Physics of Fluids, 1991, 3(5):733-742.
[156] Morency F, Tesok F, Paraschivoiu I. Anti-Icing System Simulation using CANICE[J]. Journal of Aircraft, 1999, 36(6):999-1006.
[157] Papadakis M, Rachman A, Wong S C, et al. Water Impingement Experiments on a NACA 23012 Airfoil with Simulated Glaze Ice Shapes[R]. AIAA-2004-565.2004.
[158] Shin J, Bond T H. Results of an icing test on a NACA0012 airfoil in the NASA Lewis icing research tunnel[R]. AIAA-92-0647.1992.
[159] Shin J, Bond T H. Experimental and computational ice shapes and resulting drag increase for a NACA0012 airfoil[R]. NASA-TM-105743.1992.