小型燃气轮机传热效应研究
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摘要
伴随着小型燃气轮机日益广泛的应用以及其尺度的不断缩小,燃机传热效应越来越明显,此时若对气体流动过程继续沿用绝热的处理方法,必导致燃机的设计估算误差。热量从燃机高温端(主要是透平)传入低温端(主要是压气机),会带来一系列的副作用,包括压气机、透平乃至燃机整体性能都会受到影响。本文的主要内容即是针对非绝热“背靠背”小型燃气轮机,研究内部传热效应对性能的影响,通过热力学模型分析,阐述其传热机理,建立非转实验台,以CFD、实验等手段对燃机传热现象进行模拟和验证,进而考查相关隔热措施,指导改进非绝热小燃机设计。
     首先,本文在前人工作的基础上,推导分析了压气机和涡轮非绝热运行工况热力学模型。基于一定假设,定义三种不同的效率表达式,即为绝热效率、非绝热效率和传热效率。发现测量效率(即非绝热效率)不能准确反映部件的实际气动能力,它对压气机和涡轮实际气动效率的估计均存在偏差,而传热效率可视为实际气动效率。文章具体分析了影响各种效率改变的因素及变化趋势。
     本文采用ANSYS CFX软件对MarkⅡ叶片进行流热耦合验证计算并与实验值比较,研究表明虽然流热耦合计算的精度受湍流模型、转捩模型、网格密度等诸项因素制约,但相比非耦合计算,其结果更加接近真实值,完全满足工程计算要求。流热耦合计算的准确应用,将大大推动非绝热燃机的设计效率。
     本文以真实“背靠背”小燃机为模型,以相似准则为基准,自行设计了非转模型实验台,并且搭建了实验台软硬件测试系统。基于非转实验台进行传热实验考查,测量了不同工况条件实验件压气机、涡轮通道的壁面温度分布,并与数值计算结果进行对比,两组结果吻和得较好,进一步验证流热耦合计算的有效性。另一方面,考查了不同隔热方式的隔热效果,发现降低空隙辐射强度是工程上较为有效和可行的一种方法,从而给真实燃机的隔热设计提供了参考。
     本文针对某“背靠背”80kW非绝热小燃机建立三维整机计算模型,进行了CFD数值模拟。对比不同计算方式结果发现,绝热计算与耦合计算对流场影响的差别主要体现在温度场的不同上,而对流场内的压力场及其他参数影响不太明显。同时对有无隔热情况也进行了耦合计算比较,可以看到,采用有隔热耦合计算,燃机热效应明显减弱,这又一次验证了隔热设计对非绝热燃机的有效性。
     最后,为了使压气机性能与透平更好地相匹配,对非绝热压气机修改设计指标,并尝试进行了气动改进设计。新设计压气机提高了通流能力,并且减小了扩压器尺寸。计算结果表明,改进设计的压气机传热效应有所降低,取得一定效果。
The small gas turbine is being used more widely accompany with its scale getting smaller and smaller, so the heat effect of gas turbine is more and more obvious nowadays. If we treat the gas flow as an adiabatic procedure, some mistakes of gas turbine design will be made. Because of the heat transfer from the hot side (mainly turbine) to the cold side (mainly compressor), many side-effects appear, such as the performance of compressor, turbine and the whole engine will be affected. The main work of this article is to investigate the inside heat transfer effect on the performance of non-adiabatic "back to back" small gas turbine. The thermodynamic model is analyzed to describe the mechanism of the heat transfer, and a non-rotating experiment rig is built to validate the heat transfer phenomenon by CFD or experiment. Further more the heat insulation method will be researched, and the design of non-adiabatic small gas turbine will be improved.
     First, on the work before, this article builds a non-adiabatic thermodynamic model of compressor and turbine. Based on certain assumptions, three different definitions of efficiency were proposed, that is adiabatic efficiency, diabatic efficiency and heat efficiency. It is found that the measurement efficiency (i.e. diabatic efficiency) can not describe the components' actual aerodynamic power, and it estimates the aerodynamic efficiency in error. Meanwhile the heat efficiency can be treated as actual aerodynamic efficiency. This article discusses the factors affect the efficiency and their relationship.
     The ANSYS CFX software is used in this article to investigate the fluid-thermal coupling CFD method of MarkⅡtest case and compare with experimental data. The research shows that even though the precision of fluid-thermal coupling numerical simulation is restricted by turbulence model, transition model and mesh density, its result is closer to real value compare to non-couple numerical simulation, and it meets the engineering demands. So the fluid-thermal coupling CFD method will promote the design of non-adiabatic small gas turbine greatly.
     Based on real "back to back" small gas turbine, using similarity criterion, a non-rotating model experiment rig, together with hardware and software test system, is built. Heat transfer experiment is carried out on this test rig, and the temperature distribution on compressor and turbine wall in different conditions is measured. The experiment data conform to CFD result very well, which proved the validity of fluid-thermal coupling CFD method. On the other hand, the effect of different heat insulation method are investigated, and it is found that reducing the radiation intensity of interspace is a effective way in engineering, which will provide the experience for real gas turbine.
     This article practices the CFD numerical simulation of an 80kW "back to back" non-adiabatic small gas turbine 3D model. Comparing the results, the difference of adiabatic simulation and coupling simulation is mainly reflected on temperature field, rather than pressure field or other field. Meanwhile, it is different in the situation that with or without heat insulation. It can be seen from the simulation result that with heat insulation the heat effect of gas turbine is obviously weaker, and this proves the validity of heat insulation design for non-adiabatic small gas turbine.
     Finally, for making the compressor match the turbine well, the design target of non-adiabatic small gas turbine is changed, and new aerodynamic design is tried. The new design compressor improves the through-flow capability, and reduces the size of diffuser. The simulation result shows that the heat effect of new design compressor is braked, which makes progress.
引文
[1]李孝堂,候凌云,杨敏.现代燃气轮机技术[M].航空工业出版社,2006.
    [2]方昌德,马春燕.航空发动机的发展历程[M].北京:航空工业出版社,2007.
    [3]黄国平.微型涡轮发动机顶层设计研究[J].航空动力学报,2003,18(6):832-838.
    [4]薛元.超微型燃烧器的研究现状及进展[M].2002.
    [5]程昭武.世界飞机100年[M].北京:国防工业出版社,2002.
    [6]EARLY M.Small Engine Component Technology Study Final Report[M]//175078 N C.1991.
    [7]侯晓春.小发燃烧技术的研究与发展[M].21世纪航空动力发展研讨会.2000.
    [8]袁培益.论航空发动机的一个新领域——微型涡轮发动机[M].CSAA 95-PN-013.1995.
    [9]刁正纲.微型燃气轮机走向商业化[J].燃气轮机技术,2000,12
    [10]翁一武等.先进微型燃气轮机的特点和应用前景[J].热能动力工程,2003,3
    [11]勒智平.微型燃气轮机发电在我国的应用前景[J].电力学报,2004,67
    [12]赵士杭.线概念的微型燃气轮机的发展[J].燃气轮机技术,2001,6
    [13]温殿忠.离心压气机先进技术[M]//95-PH-015 C.1995.
    [14]张颖,王蔚,田丽,et al.微流动的尺寸效应[J].微纳电子技术,2008,45(1):33-37.
    [15]HO.C,方新.微电子机械系统和流体流动[J].力学进展,1998,28(2):250-272.
    [16]VERSTRAETE T,ALSALIHI Z,VAN DEN BRAEMBUSSCHE R A.Multidisciplinary optimization of a radial compressor for micro gas turbine applications,Montreal,Que.,Canada,F,2007[C].American Society of Mechanical Engineers,New York,NY 10016-5990,United States.
    [17]杨世铭,陶文铨.传热学[M].北京:高等教育出版社,1999.
    [18]韩介勤,桑迪普.杜达,斯瑞纳斯.艾卡德.燃气轮机传热和冷却技术[M].西安交通大学出版社,2005.
    [19]BRADSHAW P.Effect of Free-Steem Turbulence on Turbulent Shear Layers[M].Aeronautical Research Council,paper35468.1974.
    [20]MCDONALD H,KRESKOVSKY J P.Effect of Free-Stream Turbulence on the Turbulent Boundary Layer[J].International Journal of Heat and Mass Transfer,1979,26:31-36.
    [21]HANCOCK P E,BRADSHAW P.The effect of Free-Steam Turbulence on Turbulent Boundary Layers[J].ASME Journal of Fluids Engineering,1983,105:284-289.
    [22]BLAIR M F.Influence of Free-Stream Turbulence on Turbulent Boundary Layer Heat transfer and Mean Profile Development.Part Ⅰ:Experimental Data.Part Ⅱ:Analysis of Results[J].ASME Journal of Turbomachinery,1983,105:33-47.
    [23]THOLE K A,BOGARD D G.Enhanced Heat Transfer and Shear Stress Due to High Free-Streanm Turbulence[J].ASME Journal of Turbomachinery,1995,117:418-423
    [24]BLAIR M F.Influence of Free-Stream Turbulence on Boundary Layer Structures in Accelerating Flow with Heat Transfer[J].ASME Journal of Engineering for Power,1982,104:743-750.
    [25]MAYLE R E,BLAIR M F,KOPPER F C.Turbulent Boundary Layer Heat Transfer on Curved Surfaces[J].ASME Journal of Heat Transfer,1979,101:521-525.
    [26]KESTORAS M D,SIMON T W.Effect of Free-Stream Turbulence Intensity on a Boundary Layer Recovering from Concave Curvature Effects[J].ASME Journal of Turbomachinery,1995,117:206-214.
    [27]KESTORAS M D,SIMON T W.Turbulent Transport Measurements in a Heated Boundary Layer:Combined Effects of Free-Stream Turbulence and Removal of Concave Curvature[J].ASME Journal of Turbomachinery,1997,119:206-214.
    [28]BLAIR M F.An Experimental Study of Heat Transfer in a Large-Scale Turbine Rotor Passage[J].ASME Journal of Turbomachinery,1994,116:1-13.
    [29]BOGARD D G,SCHMIDT D L,TABBITA M.Characterization and Laboratory Simulation of Turbine Airfoil Surface Roughness and Associatied Heat Transfer[M].ASME 96-GT-386.1996.
    [30]KODAR B A,YAGLOM A M.Heat and Mass Transfer laws for Fully Turbulent Wall Flows[J].International Journal of Heat and Mass Transfer,1972,15:29-51.
    [31]蒋章焰林汪.高性能航空发动机传热技术[M].国防工业出版社,2005.
    [32]AMES.F.E.Influence of Large-Scale High-Intensity Turbulence on Vane Heat Transfer[J].ASME Journal of Turbomachinery,1997,119:23-30.
    [33]NEALY D A,MIHELC M S,HYLTON L D,et al.Measurements of Heat Transfer Distribution over the Surface of Highly Loaded Turbine Nozzle Guide Vaneds[J].ASME Journal of Engineering for Gas Turbines and Power,1984,106:149-158.
    [34]ABUAF N,BUNKER R S,LEE C P.Effects of Surface Roughness on Heat Transfer and Aerodynamic Performance of Turbine Airfoils[J].ASME Journal of Turbomachinery,1998,120:522-529.
    [35]DOORLY D J.Modeling the Unsteady Flow in a Turbine Rotor Passage[J].ASME Journal of Turbomachinery,1988,110:27-37.
    [36]EPSTEIN A H.Millimeter-scale,MEMS gas turbine engines,Atlanta,GA,United States,F,2003[C].American Society of Mechanical Engineers,New York,NY 10016-5990,United States.
    [37]KANG S,MATSUNAGA M,JOHNSTON J P,et al.Micro-scale radial-flow compressor impeller made of silicon nitride-Manufacturing and performance,Atlanta,GA,United States,F,2003[C].American Society of Mechanical Engineers,New York,NY 10016-5990,United States.
    [38]ONISHI T,BURGUBURU S,DESSORNES O,et al.Numerical design and study of a MEMS-based micro turbine,Reno-Tahoe,NV,United States,F,2005[C].American Society of Mechanical Engineers,New York,NY 10016-59°0,United States.
    [39]SIRAKOV B T.Characterization and Design of Non-adiabatic Micro-compressor Impeller and Preliminary Design of Self-sustained Micro Engine System[D];Massachusetts Institute of Technology,2005.
    [40]GONG Y,SIRAKOV B T,EPSTEIN A H,et al.Aerothermodynamics of micro-turbomachinery,Vienna,Austria,F,2004[C].American Society of Mechanical Engineers,New York,NY 10016-5990,United States.
    [41]MALOBABIC M,MOBARAK A,RAUTENBERG M.Influence of heat transfer between turbine and compressor on the performance of small turbocharger[M].GTS J International Gas Turbine Congress.Tokyo,Japan.1983:566-574.
    [42]MALOBABIC M,RAUTENBERG M.Adiabatic and non-adiabatic efficiencies of small turbochargers[M].International Gas Turbine Congress.Tokyo,Japan.1987:57-64.
    [43]RAUTENBERG M,KAMMER N.On the thermodynamics of non-adiabatic compression and expansion processes in turbomachines[M].5th Inernational conference for mechanical power engineering.Cairo,Egypt.1984.
    [44]HAGELSTEIN D,BEYER B,LUBKE H P.Heuristical View on the Non-adiabatic Coupling System of Combustion Engine and Turbocharger[M].IMechE International Conference on Turbocharging and Turbochargers.London,UK.2002.
    [45]BOHN D,MORITZ N,WOLFF M.Conjugate flow and heat transfer investigation of a turbo charger:Part Ⅱ-Experimental results,Atlanta,GA,United States,F,2003[C].American Society of Mechanical Engineers,New York,NY 10016-5990,United States.
    [46]CHAPMAN K S,NGURU R,SHULTZ J.Simplified Methodology to Correct Turbocharger Field Measurements For Heat Transfer and Other Effects[M].GRI-02/0156.2002.
    [47]SHAABAN S.Experimental Investigation and Extended Simulation of Turbocharger Non-adiabatic Performance[D].Hannover;Hannover University,2004.
    [48]BRAEMBUSSCHE R A V D.Micro Gas Turbines-A Short Suvey of Design Problems[M]//RTO-EN-AVT-131.2005.
    [49]MONROE M A,EPSTEIN A H,KUMAKURA H,et al.Component integration and loss sources in 3-5 KW gas turbines,Reno-Tahoe,NV,United States,F,2005[C].American Society of Mechanical Engineers,New York,NY 10016-5990,United States.
    [50]VERSTRAETE T,ALSALIHI Z,VAN DEN BRAEMBUSSCHE R A.Numerical study of the heat transfer in micro gas turbines,Barcelona,Spain,F,2006[C].American Society of Mechanical Engineers,New York,NY 10016-5990,United States.
    [51]TOM VERSTRAETE,ALSALIHI Z.Multidisciplinary Optimization of Micro-gasturbines taking into account Internal Heat transfer[M].IGTC2007 TS-029.Tokyo.2007.
    [52]黄国平,梁德旺,马向东,et al.微型涡轮发动机传热效应的建模分析与实验研究[J].航空学报,2008,29(3):542-547.
    [53]李宇,邹正平,叶建,et al.二维流热耦合数值模拟程序及方法研究[J].燃气涡轮试验与研究,2007,20(2):18-26.
    [54]郭立新,李志强,温立刚,et al.直接耦合法模拟计算活塞温度场[J].内燃机,2008,3:15-18
    [55]VIJAY.K.Heat Transfer Research on Gas Turbine Airfoils at NASA GRC Garg[J].International Journal of Heat and Fluid Flow,2002,23(2):109-136.
    [56]YONG J B,WILCOCK R C.Modeling the Air-Cooled Gas Turbine:Rart 1-General Thermodynamics[J].Journal of Turbomachinery,2002,124(2):207-213.
    [57]DUNN M G 2001 International Gas Turbine Institute Gas Turbine Scholar Lecture:Convective Heat Transfer and Aerodynamics in Axial Flow Turbines[J].Journal of Turbomachinery,2001,123(4):637-686.
    [58]NICKLAS M.Film-Cooled Turbine Endwall in a Transonic Flow Field:Part 2-Heat Transfer and Film-Cooling Effectiveness[J].Journal of Turbomachinery,2001,123(4):720-729.
    [59]PERELMAN T L.On Conjugated Problems of Heat Transfer[J].International Journal of Heat Mass Transfer,1961,3:293-303.
    [60]BOYLE R J,SIMON F F.Mach Number Effects on Turbine Blade Transition Length Prediction[M].ASME 1998.
    [61]李海滨.涡轮叶栅中的冷气掺混及气热耦合研究[D].哈尔宾;哈尔宾工业大学,2002.
    [62]WILLIAM D Y,JAMES,H.LAYLEK.Three-Dimensional Conjugate Heat Transfer Simulation of an Internally-Cooled Gas Turbine Vane[M].ASME.GT2003-38551.2003.
    [63]TAKASHI YAMAE T Y,SHUNJI ENOMOTO.Conjugate Simulation of Flow and Heat Conduction with a New Method of Faster Calculation[M].ASME.GT-2004-53680.2004.
    [64]JOHN A.VERDICCHIO J W C,NICK J.HILLS.Coupled Fluid/Solid Heat Transfer Computation for Turbine Descs[M].ASME.GT2001-0205.2001.
    [65]HAN Z X D B H.Simulations Prediction of External Flow-Field and Temperature in Internally Cooled 3-D Turbine Blade Material[M].ASME.2000-GT-253.2000.
    [66]李海滨,冯国泰.叶轮机械中的多场耦合分析技术[J].航空发动机,2002,2
    [67]GRAHAM R W.Fundamental Mechanics That influence the Estimate of Heat Transfer to Gas Turbine Blade[M].ASME 79-HT-43.1979.
    [68]SHARMA O P,NGUYEN P,NI R H,et al.Aerodynamics and Heat Transfer Analysis of a Low Aspect Ratio Turbine[M].AIAA-87-1916.1987.
    [69]DUNN M G,MARTIN H L,STANEK M J.Heat Flux and Pressure Measurements and Comparison with Prediction for a Low Aspect Ratio Turbine Stage[J].ASME,Jof Turbomachinery,1986,108(1):108-115.
    [70]ABHARI R S,GUENETTE G R,EPSTEIN.A H,et al.Comparison of Time-Resolved Turbine Rotor Blade Heat Transfer Measurements and Numerical Calculations[M].ASME 91-GT-268.1991.
    [71]HONGJUN LI A J K.Numerical Prediction of Fluid Flow and Heat Transfer in Turbine Blades with Internal Cooling[M].AIAA 94-2933.1994.
    [72]BOHN.D.E.B,V.J.3-D Conjugate Calculations of Convective Cooled Turbine Blades with Serpentine-Shaped and Ribbed Channels[M].ASME 99-GT-220.1999.
    [73]BOHN D E,BECKER.3-D Conjugate Flow and Heat Transfer Calculations of Film-Cooled Turbine Guide Vane at Different Operation Conditions[M].ASME 97-GT-23.1997.
    [74]BOHN D E,TOM HEUER.Conjugater Flow and Heat Transfer Calculation of a High-pressure Turbine Nozzle Guide Vane[M].AIAA2001-3304.2001.
    [75]HYLTON L D,MILHEC,M.S.,TURNER,E.R.,NEALY,D.A.,YORK,R.E.:NASA CR 168015,1983.
    [76]蔡毅,邓化愚,等.涡轮叶片型面外换热系数计算方法[J].燃气涡轮试验与研究, 1993,6(3):14-21.
    [77]蔡毅,刘松龄,等.涡轮叶片外换热系数计算方法和比较[J].燃气涡轮试验与研究, 1995.1:1-8.
    [78]倪志军,刘松龄.涡轮叶片型面外换热系数的数值计算[J].航空发动机,1997,2:35-41.
    [79]李海滨,冯国泰.叶轮机械中的多场耦合分析技术[J].航空发动机,2002,2:51-56.
    [80]姜澎,黄洪雁,冯国泰.空气冷却涡轮叶片气热耦合数值计算[J].哈尔滨工业大学学报,2006,38(12):2036-2038.
    [81]冯国泰,黄家骅,等.涡轮发动机三维多场耦合数值仿真的数学模型[J].上海理工大 学学报,2001,23(3):189-192.
    [82]黄海波.涡轮叶片中流场和温度场计算及实验研究[D].北京;中国科学院工程热物理研究所,2002.
    [83]周志翔,李维.涡轮叶片流-固耦合热分析[M].航空推进技术验证计划论文集.2004:177-184.
    [84]周驰,冯国泰,王松涛.涡轮叶栅气热耦合数值模拟[J].工程热物理学报,2003,24(2):224-227.
    [85]胡捷.燃气轮机透平导叶闭式蒸汽冷却研究[D].北京;中国科学院工程热物理研究所,2008.
    [86]李宇,邹正平,叶健,et al.二维流热耦合数值模拟程序及方法研究[J].燃气涡轮试验与研究,2007,20(2):18-26.
    [87]任玉新,陈海昕.计算流体力学基础[M].北京:清华大学出版社,2006.
    [88]郑捷庆,邹锋.CFD软件在工程流体力学教学中的应用[J].中国现代教育装备,2007,10:119-121.
    [89]姚征,陈康民.CFD通用软件综述[J].上海理工大学学报,2002,24(2):137-144.
    [90]许蕾,罗会信.基于ANSYS ICEM CFD和CFX数值仿真技术[J].铸造工程,2009,33(1):41-43.
    [91]CHANG K-C,SHYU M-J.Revisiting the Reynolds-averaged energy equation in near-wall turbulence models[J].International Journal of Heat and Mass Transfer,2000,43(5):665-676.
    [92]CHOW W K,LI J.Numerical simulations on thermal plumes with k-[epsilon]types of turbulence models[J].Building and Environment,2007,42(8):2819-2828.
    [93]CIOFALO M,COLLINS M W.k-epsilon Predictions of Heat Transfer in Turbulent Recirculating Flows Using an Improved Wall Treatment[J].Numerical Heat Transfer,Part B:Fundamentals,1989,15(1):21-47.
    [94]HIRAOKA H,OHASHI M.A(k-[epsilon])turbulence closure model for plant canopy flows[J].Journal of Wind Engineering and Industrial Aerodynamics,In Press,Corrected Proof(
    [95]贺旭照,赵慧勇,乐嘉陵.考虑可压缩与热传导的壁面函数边界条件及其应用[J].空气动力学学报,2006,24(4):450-453.
    [96]MORYOSSEF Y,LEVY Y.Unconditionally positive implicit procedure for two-equation turbulence models:Application to k-[omega]turbulence models[J].Journal of Computational Physics,2006,220(1):88-108.
    [97]雷雨冰,袁亚雄,赵坚行.壁面函数在复杂流场计算中的应用[J].弹道学报,2003, 15(2):1-5.
    [98]PARK T S,SUNG H J,SUZUKI K.Development of a nonlinear near-wall turbulence model for turbulent flow and heat transfer[J].International Journal of Heat and Fluid Flow,2003,24(1):29-40.
    [99]王运良,徐忠.使用不同壁面函数对紊流流场计算结果的影响[J].流体工程,1993,21(12):26-29.
    [100]RUMSEY C L.Apparent transition behavior of widely-used turbulence models[J].International Journal of Heat and Fluid Flow,2007,28(6):1460-1471.
    [101]ANSYS EUROPE L.ANSYS CFX-Solver Modeling Guide[M].2006.
    [102]ANSYS EUROPE L.FLUENT 6.3 User's Guide[M].2006.
    [103]F.R.MENTER.A Correlation-Based Transiton Model Using Local Variables:Part Ⅰ-Model Formulation[M].ASME.GT2004-53452.2004.
    [104]沈青等.力学中的相似方法与量纲理论[M].北京:科学出版社,1982.
    [105]邱绪光.实用相似理论[M].北京:北京航空学院出版社,1988.
    [106]中华人民共和国国家标准.流量测量节流装置用孔板、喷嘴和文丘里管测量充满圆管的流体流量[M].1991.
    [107]陈锡辉,张银鸿.LabVIEW 8.2程序设计[M].北京:清华大学出版社,2007.
    [108]沈煜欣,刘建军.考虑热传导的厘米级微型离心压气机设计与数值分析[M].中国工程热物理学会2008年会.天津.2008.
    [109]夏恭枕,石玉珍.中国航空材料手册:结构钢 不锈钢[M].北京:中国标准出版社,1988.
    [110]马丽群,陈汉平.封闭漫射灰腔内辐射模型的应用[J].上海交通大学学报,1999,33(3):305-308.
    [111]葛绍岩,那鸿悦.热辐射性质及其测量[M].北京:科学出版社,1989.
    [112]INCROPERA F P,DEWITT D P.Thermal radiation heat transfer[M].Washington:Hemisphere Publishing Corporation,1996.
    [113]薛莹莹,白敏丽,吕继组.隔热材料导热系数预测及其在发动机排气管隔热中的应用[J].内燃机学报 2007,5
    [114]《航空发动机设计手册》总编委会.航空发动机设计手册(第8册)[M].北京:航空工业出版社,2000.
    [115]M.左克罗.,J.霍夫曼著.,王汝涌等译.气体动力学(上册)[M].北京:国防工业出版社,1984.
    [116]李瑞遐,何志庆.微分方程数值方法[M].上海:华东理工大学出版社,2005.
    [117]章本照,印建安,张宏基.流体力学数值方法[M].北京:机械工业出版社,2003.
    [118]罗曼芦,王兆华.气体动力学[M].上海交通大学出版社,1989.
    [119]潘锦珊.气体动力学基础[M].西北工业大学出版社,2000.
    [120]MATHEWS J H,FINK K D.数值方法(MATLAB版)[M].北京:电子工业出版社,2008.

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