摘要
非定常流和非定常设计是当前叶轮机械气动热力学领域研究的焦点之一。因此，本文尝试性地论述了非定常设计的两个重要组成：非定常流型和缘线匹配，并对它们进行了初步研究。由于叶轮机非定常实验的困难，CFD方法成为研究非定常流动的主要手段。本文以编制叶轮机流动时间精确模拟程序为开端，进行了以下研究工作：
一、作为实现非定常设计的软件基础，开发了能够对叶轮机内部流动进行多排、多通道时间精确模拟的二维和三维计算程序。鉴于缺乏相关的非定常实验数据，采用商业CFD软件FLUENT和NUMECA分别与二维和三维程序进行了互校。在应用于流动研究前，对所开发程序进行了网格无依赖和物理时间步长无依赖两个方面的研究，确定出适当的网格和物理时间步长配置。结果表明，所开发程序应用于叶轮机非定常流求解具有令人满意的精度。
二、非定常流型是叶轮机非定常气动设计中二维层面的重要技术，论文采用二维数值方法初步研究了这一问题。研究以一涡轮叶栅基元为对象，通过在入口边界施加非定常条件来模拟叶轮机内的非定常环境，结果显示了流动的非定常性对叶栅性能的影响，并与定常、准定常环境下的叶栅性能进行了对比，得出了尾迹亏损程度、进气角度和尾迹移动速度等因素影响叶栅性能的规律。此外，还对叶栅的升力滞回现象做出初步研究。以上工作初步展示了未来关于叶轮机非定常流型研究方面的部分内容。
三、二维时序效应属于非定常流型研究中的一个重要部分，论文通过对1.5级静／动／静布局的涡轮叶栅进行数值模拟，首先对时序效应进行了现象及机理研究；其后探索了叶排间轴向间距和动叶转速对时序效应的影响，发现两种因素均会给时序效应带来一些新的现象，比如时序效应提升效率潜力的变化，尾迹输运时间的变化等等。这一研究在促进对时序效应流动机理的认识继续深入的同时，进一步细化了时序效应的研究，为三维时序研究和应用提供有益的指导。
四、缘线匹配是叶轮机非定常气动设计三维层面上用于多排排间匹配的重要技术，也是本文的主要内容。因此，论文首先全面介绍了缘线匹配的理论基础、两种应用方式
摘要
及其初步验证。然后，作为对该理论继续验证和应用的实例，首次将时序效应纳入
缘线匹配框架之下，利用缘线匹配思路进一步拓展了时序效应潜力。通过修改二级
静叶的根、尖相位组合和修改一、二级静叶叶尖相位组合两种方式，使研究对象的
气动效率在从时序效应受益的基础上进一步获得提升。研究以三维CFD程序为工
具，采用缘线匹配应用中最为耗时的全优化方式，综合预估了包括效率在内的代表
叶轮机性能的多种参数的时均量和脉动量，显示出缘线匹配这一设计自由度在非定
常设计体系中所起到的重要作用。
Nowadays, unsteady flow and unsteady design are parts of the main focuses of turbomachinery aerodynamics research. Hence, the present dissertation attempts to discuss two important parts of unsteady design: Unsteady Flow Pattern and Edge Matching, on which preliminary investigations are performed. Because of the difficulty rising from experiment of unsteady turbomachinery flow, the author has to select CFD as a main method to conduct unsteady researches. Consequently, this dissertation begins with programming the time-accurate flow solvers and the main efforts are listed as follows:
1. To be the basis of fulfilling unsteady turbomachinery design, 2D and 3D Reynolds-Averaged N-S solvers are developed with the capabilities of simulating unsteady flow of turbomachine with multiple blade rows and passages. Due to lack of data from unsteady experiment, the 2D and 3D CFD codes are validated by comparing with FLUENT and NUMECA respectively. Before putting the codes into the following researches, studies about grid and time step dependence have been conducted. Reasonable grid and time step are determined so that the numerical results can be convinced. All these indicate that the codes are reliable for unsteady flow simulation.
2. Unsteady Flow Pattern is an important technique in 2D unsteady turbomachinery design.
A turbine cascade is adopted as an example in unsteady flow pattern study, in which time-accurate inlet profiles are imposed to produce the cascade unsteady flowfield. The effects of unsteady flow onto cascade performance are studied and compared with those of the equivalent steady and quasi-steady cases. The main concerns focus on how the wake defect, flow angle and wake moving speed in pitchwise influence the cascade performance. Also, 'time-lag' phenomenon of cascade lift is investigated preliminarily. All these researches display some aspects of unsteady flow pattern study introductorily in future.
3. As an important part of unsteady flow pattern study, 2D clocking effect is investigated on
a 1.5 stage turbine cascades with stator/rotor/stator configuration. Not only the knowledge about the mechanism of clocking effect is obtained, but also the influences of
axial gap and rotor rotating speed onto clocking effects are further demonstrated by 2D CFD simulations. Results show that the two kinds of influence both can bring some new phenomena onto clocking effect, such as the changing of potential in improving the efficiency of turbomachinery, changing of wake-transport time and so on. This study can not only advance the understanding of the mechanism of clocking effect, but also make the investigation on clocking effect more detailed, from which 3D clocking effect study and application will be benefited subsequently.
4. Edge Matching is an important technique in 3D unsteady turbomachinery design which mainly aimed at the 'matching' between multiple blade rows. To be an important part of this dissertation, it is introduced comprehensively about the theory of Edge Matching, two methods of manipulating and its preliminary validation firstly. Then, as an example to testify and apply the theory, a new idea is suggested that the clocking effects can be more perfect when they are taken into account in the frame of Edge Matching theory. In order to exemplify this potential, two ways of applying edge matching are selected: one is from combinations of hub and tip section of the second stator; the other is from combinations of the two tip sections of both two stators, the intention of which is to see if the turbine aerodynamic efficiency can be further promoted over the original well clocked one. 3D numerical optimizations are conducted based on the full-optimizing method, which is the most time-consuming one in the two manipulatin
g ways of Edge-Matching theory. Results show the importance of Edge Matching for further promoting the benefit of clocking effects. This indicates edge matching provided a new degree of design freedom for turbomachinery unsteady design.
引文
[1] 中国航空信息中心，21世纪初的航空科学技术，1999
[2] 工程热物理与能源利用，自然科学学科发展战略调研报告，第一版，北京：科学出版社，1995
[3] Layne, A.W., et.al, The US Department of Energy's Advanced Turbine Systems Program, ASME 98-GT-141, 1998
[4] 刘大响，抓住机遇迎接挑战实现航空动力跨越发展，燃气涡轮试验与研究，Vol．15(1)，2002：1-5
[5] P.C. Ruffles, Expanding the Horizons of Gas Turbines in Global Markets, ISABE paper 2001-1010, 2001
[6] Whittle, Sir Frank, The Early History of the Whittle Jet Propulsion Gas Turbine, Proc. Instn. Mech. Engrs., Vol. 152, 1945:419-535
[7] Ainley, D.G., Mathieson, G.C.R, An Examination of the Flow and Pressure Losses in Blade Rows of Axial Flow Turbines, Aeronautical Research Council R and M2891, 1955
[8] Wu, Chung-hua, A General Theory of Three-Dimensional Flow in Subsonic or Supersonic Turbomachines in Radial, Axial and Mixed-Flow Types, NACA TN2604, 1952
[9] Johnson, I.A., and Bullock, R.O., Aerodynamic Design of Axial-Flow Compressors, NASA SP-36,1965
[10] Horlock, J.H. and Denton, J.D., A Review of Some Early Design Practice using CFD and A Current Perspective, ASME paper GT2003-38973, 2003
[11] Wennerstrom, A.J. and Frost, G.R., Design of a 1500ft/sec, Transonic, High-Through-Flow, Single-Stage Axial-Flow Compressor with Low Hub/Tip Ratio, AFARL TR 76-59, 1976
[12] Denton, J.D., The Calculation of Three Dimensional Viscous Flow Through Multistage Turbomachines, ASME paper 90-GT-19, 1990
[13] Ni, R.H., et al, Prediction of 3D Multi-Stage Turbine Flow Field Using a Multiple-Grid Euler Solver, AIAA paper 89-0203, 1989
[14] Dawes, W.N., Towards Improved Through Flow Capability: The Use of 3D Viscous Flow Solvers
in a Multistage Environment, ASME paper 90-GT-18, 1990
[15] Rhie, C.M., et al, Development and Application of a Multistage Navier-Stokes Solver, Part 1: Multistage Modeling Using Body-Forces and Deterministic Stresses, ASME paper 95-GT-342, 1995
[16] 季路成，黄海波，陈江等，涡轮中的激波／叶排相互作用，工程热物理学报，Vol．23(2)，2002：163-166
[17] 季路成，轴流叶轮机转子／静子干扰非定常流动探索，博士学位论文，北京航空航天大学，1998
[18] Adamczyk, J.J., Model Equation for Simulating Flows in Multistage Turbomachinery, ASME paper 85-GT-220, 1985
[19] Adamczyk, J.J., Celestina, M.L. and Beach, T.A., Simulation of Three-Dimensional Viscous Flow within a Multistage Turbine, ASME paper 89-GT-152, 1989
[20] Giles, M.M, An Approach for Multi-Stage Calculations Incorporating Unsteadiness, ASME paper 92-GT-282,1992
[21] Hall, E.J., Aerodynamic Modeling of Multistage Compressor Flow Fields, ASME paper 97-GT-344, 1997
[22] 季路成，项林，陈江等，非定常环境下叶栅性能的数值研究，工程热物理学会年会论文，No．022012，2002
[23] Dean, R.C., On the Necessity of Unsteady Flow in Fluid Machines, ASME J. Basic Eng., 1959: 24-28
[24] Greitzer, E.M., An Introduction to Unsteady Flow in Turbomachines, Thermodynamics and Fluid Mechanics of Turbomachinery-Volume Ⅱ, 1997: 967-1024
[25] 唐狄毅，叶轮机非定常流，第一版，北京：国防工业出版社，1992
[26] Lefcourt, M.D., An Investigation into Unsteady Blade Forces in Turbomachines, ASME J. of Engineering for Power, 1965:345-354
[27] Hodson, H.P., An Inviscid Blade-to-Blade Prediction of a Wake-Generated Unsteady Flow, ASME paper 84-GT-43, 1984
[28] Hodson, H.P., Measurements of Wake-Generated Unsteadiness in the Rotor Passages of Axial Flow
Turbine, ASME paper 84-GT-189, 1989
[29] Wang, H.P., Olson, S.J., Goldstein, R.J. et al., Flow Visualisation in a Linear Turbine Cascade of High Performance Turbine Blades, ASME paper 95-GT-7, 1995
[30] Harrison, S., Secondary Loss Generation in a Linear Cascade of High-Turning Turbine Blades, ASME paper 89-GT-47, 1989
[31] 钟兢军，苏杰先，王仲奇，压气机叶栅壁面拓扑和二次流结构分析，中国工程热物理学术会议热机气动热力学学术会议，No．962050，1996
[32] Weyer, H.B.., Fundamentals of Flow Field Measurement Techniques, Thermodynamics and Fluid Mechanics of Turbomachinery-Volume Ⅰ, 1997:467-565
[33] Bynum, D., Ledford, R. and Smotherman, W., Wind Tunnel Pressure Measuring Techniques, AGARDograph No. 145, 1970
[34] Georgakisl, C., Bennett, I., and Ivey, P.C. Fast Response Probes Measuring Unsteady Flows in High-Speed Research Compressors, ASME paper GT2003-38160, 2003
[35] Setchell, R.E., Time Measurements in Turbulent Flames Using Raman Spectroscopy, AIAA paper 76-28, 1976
[36] Wernst, M.R., Zante, D.V. and Strazisar, T.J. et al., 3-D Digital PIV Measurements of the Tip Clearance Flow in an Axial Compressor, ASME paper GT-2002-30643, 2002
[37] 张玮，王元，徐忠，叶轮机械内部流动测量及动静相互作用的实验研究进展，流体机械，Vol．8，2001：6-10
[38] Denton, J.D., The Use of a Distributed Body Force to Simulate Viscous Effects in 3D Flow Calculations, ASME paper 86-GT-144, 1986
[39] Dawes, W.N., A Numerical Analysis of The Three-Dimensional Viscous Flow in a Transonic Compressor Rotor and Comparison with Experiment, ASME paper 86-GT-16,1986
[40] Subramanian, S.V. and Bozzola, R., Computation of Three-Dimension, Rotational Flow Through Turbomachinery Blade Rows for Improved Aerodynamic Design Studies, ASME paper 86-GT-26, 1986
[41] Chima, R.V. and Yokota, J.W., Numerical Analysis of Three Dimensional Viscous Internal Flows, NASA TM 100878, 1988
[42] Arnone, A., Viscous Analysis of Three-Dimensional Rotor Flow Using a Multigrid Method, ASME Journal of Turbomachinery, Vol. 116, 1994:435-445
[43] Davis, R.L., Shang, T., Buteau, J., et al, Prediction of 3D Unsteady Flow in Multi-Stage Turbomachinery Using an Implicit Dual-Time Step Approach, AIAA paper 96-2565, 1996
[44] Dorney, D.J., Sharma, O.P., A Study of Turbine Performance Increases Through Airfoil Clocking, AIAA paper 96-2816, 1996
[45] Nürnberger, D., Eulitz, F. Schmitt, S., et al, Recent Progress in the Numerical Simulation of Unsteady Viscous Multistage Turbomachinery Flow, ISABE paper 2001-1081, 2001
[46] Valkov, T. and Tan, C.S., Control of the Unsteady Flow in a Stator Blade Row Interacting with Upstream Moving Wakes, ASME paper 93-GT-23, 1993
[47] Wu, Chung-hua and Brown, C.A., A Theory of the Direct and Inverse Problems of Compressible Flow Past Cascade of Arbitrary Aerofoils, Journal of the Aeronautical Sciences, 1952:183-196
[48] Marsh, H., A Computer Program for the Through Flow Fluid Mechanics in an Arbitrary Turbomachine Using a Matrix Method, Aeronautical Research Council R. and M. No. 3509, 1968
[49] 杨策，蒋滋康，索沂生，时间推进方法在叶轮机械内部流场计算中的进展，力学进展，Vol．30(1)，2000：83-94
[50] Neumann, V.J. and Richtmyer, R.D., A Method for the Numerical Calculation of Hydrodynamic Shocks, Journal of Applied Physics, Vol. 21, 1950:232-257
[51] Denton, J.D., A Time Marching Method for Two- and Three-Dimensional Blade to Blade Flow, ARC R&M3775, 1974
[52] McDonald, P.W., The Computation of Transonic Flow Through Two-Dimensional Gas Trubine Cascades, ASME paper 71-GT-89, 1971
[53] Ni, R.H., A Multiple Grid Scheme for Solving the Euler Equations, AIAA Journal, Vol. 20(11), 1982:1565-1571
[54] 刘建军，蒋洪德，高分辨率有限体积LW格式，中国工程热物理学会第八届年会，No．922020，1992
[55] 刘建军，蒋洪德，用多重网格TVD—LW格式数值求解NS方程，中国工程热物理学会第九届年会，No．932012，1993
[56] MacCormack, R.W., The Effect of Viscosity in Hypervelocity Impact Catering. AIAA paper 69-345, 1969
[57] Jameson, A., Schmidt, W. and Turkel, E., Numerical Solutions of the Euler Equations by Finite Volume Methods using Runge-Kutta time Stepping Schemes, AIAA paper 81-1239, 1981
[58] Holmes, D.G. and Tong, S.S., A Three Dimensional Euler Solver for Turbomachinery Blade Rows, ASME paper 84-GT-79, 1984
[59] 周新海，朱方元，应用Navier-Stokes方程的叶栅粘性流动数值分析，工程热物理学报，Vol．9(2)，1988：230-235
[60] 居鸿斌，刘斌，向一敏，一个新的二步显隐差分格式及其反射边界条件，中国工程热物理学第七届年会，No．902027，1990
[61] Denton, J.D., An Improved Time Marching Method for Turbomachinery Flow Calculation, ASME paper 82-GT-239, 1982
[62] Arts, T., Cascade Flow Calculations using a Finite Volume Method, VKI L.S.-05, 1982
[63] Beam, R.M., Warming, R.F., An Implicit Factored Scheme for the Compressible Navier-Stokes Equations, AIAA Journal, Vol. 16(4), 1978:393-402
[64] MacCormack, R.W., A Numerical Method for Solving the Equation of Compressible Viscous Flow, AIAA paper 81-0110, 1981
[65] Weber, K.F., Delaney, R.A., Viscous Analysis of Three-Dimensional Turbomachinery Flow on Body Conforming Grids using an Implicit Solver, ASME paper 91-GT-286, 1991
[66] Yokota, J.A., Diagonally Inverted LU Implicit Multigrid Scheme for the Three Dimensional Navier-Stokes Equations, AIAA Journal, Vol. 28(9), 1990:1642-1660
[67] Towne, C.E., Schwab, J.R. and Bui, T.T., Proteus Three-Dimensional Navier-Stokes Computer Code-Version 1.0, Volumel-Analysis Description, NASA-TM-106337, 1993
[68] 郭延虎，跨音速叶轮机械中三维粘性流场结构的数值研究，博士学位论文，北京：清华大学，1996
[69] 袁新，可压缩粘性流动中双方程湍流模型选择，工程热物理学报，Vol．19(4)，1998：427-432
[70] Jameson, A., Time Dependent Calculations Using Multigrid with Applications to Unsteady Flows Past Airfoils and Wings, AIAA paper 91-1596, 1991
[71] Arnone, A. and Pacciani, R., Rotor-Stator Interaction Analysis using the Navier-Stokes Equations and a Multigrid Method, ASME paper 95-GT-177, 1995
[72] He, L., New Two-Grid Acceleration Method for Unsteady Navier-Stokes Calculations, AIAA Journal of Propulsion and Power, Vol. 9(2), 1993
[73] Jorgenson, P. and Chima, R., An Unconditionally Stable Runge-Kutta Method for Unsteady Flows, AIAA paper 89-0205, 1989
[74] Rai, M.M., Navier-Stokes Simulations of Rotor/Stator Interaction using Patched and Overlaid Grids, Journal of Propulsion, Vol. 3(5), 1987:387-396
[75] Rai, M.M. and Madavan, N.K., Multi-Airfoil Navier-Stokes Simulations of Turbine Rotor-Stator Interaction, AIAA paper 88-0361, 1988
[76] Erdos, J.I. and Alzner, E., Computation of Unsteady Transonic Flows Through Rotating and Stationary Cascades, NASA CR-2900, 1977
[77] He, L., An Euler Solution for Unsteady Flows around Oscillating Blades, Journal of Turbomachinery, Vol. 112, 1990:714-722
[78] Giles, M.M., UNSFLO: A Numerical Method for Unsteady Inviscid Flow in Turbomachinery, Technical Report 195, MIT Gas Turbine Laboratory, 1988
[79] Giles, M.M., Non-Reflecting Boundary Conditions for the Euler Equations, CFDL-TR-88-1, 1988
[80] 季路成，陈江，黄海波，徐建中，关于叶轮机时均(准四维)和非定常(四维)气动设计体系的初步诠释，中国工程热物理学会2002年学术会议，No．022011，2002
[81] He, L., Chen, T., et al, Analysis of Rotor-Rotor and Stator-Stator Interferences in Multi-Stage Turbomachines, ASME paper 2002-GT-30355, 2002
[82] Kerrebrock, J.L. and Mikolajczak, A.A., Intra-Stator Transport of Rotor Wakes and Its Effects on Compressor Performance, Journal of Engineering for Power, Vol. 92(4), 1970:359-368
[83] Butler, T.L., Sharma, O.P., Joslyn, H.D., et al., Redistribution of an Inlet Temperature Distortion in an Axial Flow Turbine Stage, Journal of Propulsion and Power, Vol. 5(1), 1989:64-71
[84] Krouthen, B., and Giles, M. B., "Numerical Investigation of Hot Streaks in Turbines", AIAA paper 88-3015, 1988
[85] Rai, M.M. and Dring, R.P., Navier-Stokes Analyses of the Redistribution of Inlet Temperature
Distortions in a Turbine, Journal of Propulsion and Power, Vol. 6, No. 3, 1990:276-282
[86] Sharma, O.P., Pickett, G.F., Ni, R.H., Assessment of Unsteady Flows in Turbomachines, ASME paper 90-GT-150, 1990
[87] Dorney, D.J., Davis, R.L., Edwards, D.E., et al., Unsteady Analysis of Hot Streak Migration in a Turbine Stage, AIAA paper 90-2354, 1990
[88] Takahashi, R.K., and Ni, R.H., Unsteady Euler Analysis of the Redistribution of and Inlet Temperature Distortion in a Turbine, AIAA paper 90-2262, 1990
[89] Dorney, D.J. and Davis, R.L., Numerical Simulation of Turbine 'Hot Spot' Alleviation Using Film Cooling, AIAA paper 92-3309, 1992
[90] Dorney, D.J. and Gundy-Burlet, K.L., Hot Streak Clocking Effects in a 1-1/2 Stage Turbine, ASME paper 95-GT-202, 1995
[91] Schubauer, G.B. and Klebanoff, P.S., Contributions on the Mechanics of Boundary Layer Transition, NACA TN 3489, 1955
[92] Gostelow, J.P., Walker, G.J., Solomon, W.J., et al., Investigation of the Calmed Region Behind a Turbulent Spot, ASME paper 96-GT-489, 1996
[93] Speidel, L., Effect of Periodic Disturbances of the Upstream Flow on the Laminar Boundary Layer, Zeitung für Flugwissenschaften, Vol. 9, 1957
[94] Schulte, V., Unsteady Separated Boundary Layers in Axial-flow Turbomachinery, PhD Dissertation, Cambridge University, 1995
[95] Cumpsty, N.A., Dong, Y., and Li, Y.S., Compressor Blade Boundary Layers in the Presence of Wakes, ASME paper 95-GT-443, 1995
[96] Ladwig, M., Fottner, L., Experimental Investigations of the Influence of Incoming Wakes on the Losses of a Linear Turbine Cascade, ASME paper 93-GT-394, 1993
[97] Halstead, D.E., Wisler, D.C., Okiishi, T.H., et al., Boundary Layer Development in Axial Compressors and Turbines: Part 1: Composite Picture, Journal of Turbomachinery, Vol. 119, 1997: 114-127
[98] Tiedemann, M., Kost, F., Unsteady Boundary Layer Transition on a High Pressure Turbine Rotor Blade", ASME paper 99-GT-194, 1999
[99] Hodson, H.P., Huntsman, I., Steele, A.B., An Investigation of Boundary Layer Development in a Multistage LP Turbine, ASME paper 93-GT-310, 1993
[100] Walker, G.J. and Oliver, A.R., The Effect of Interaction Between Wakes from Blade Rows in an Axial Flow Compressor on the Noise Generated by Blade Interaction, ASME paper 72-GT-15, 1972
[101] Huber, F.W., Johnson, P.D., Sharma, O.P., et al., Performance Improvement through Indexing of Turbine Airfoils, Part 1—Experimental Investigation, ASME paper 95-GT-27, 1995
[102] Eulitz, F., Engel, K., Gebing, H., Numerical Investigation of the Clocking Effects in a Multistage Turbine, ASME paper 96-GT-26, 1996
[103] Cizmas, P.G.A., Dorney, D.J., Parallel Computation of Turbine Blade Clocking, International Journal of Turbo and Jet Engines, Vol. 16, 1999:49-60
[104] Cizmas, P.G.A., Dorney, D.J., The Influence of Clocking on Unsteady Forces of Compressor and Turbine Blades, ISABE paper 99-72, 1999
[105] Tiedemann, M., Kost, F., Some Aspects of Wake-Wake Interactions Regarding Turbine Stator Clocking, Transactions of ASME, Vol. 123, 2001:526-533
[106] Gombert, R., Hühn, W., Unsteady Aerodynamical Blade Row Interaction in a New Multistage Research Turbine-Part 1: Experimental Investigation, ASME paper 2001-GT-0306, 2001
[107] Dorney, D.J., Croft, R.R., Sondak, D.L., et al., Computational Study of Clocking an Embedded Stage in a 4-Stage Industrial Turbine, ASME paper 2001-GT-0509, 2001
[108] Arnone, A., Marconcini, M., Pacciani, R., et al., Numerical Investigation of Airfoil Clocking in a Three-Stage Low Pressure Turbine, ASME paper 2001-GT-0303, 2001
[109] Reinmller, U., Stephan, B., Schmidt, S., et al., Clocking Effects in a 1.5 Stage Axial Turbine-Steady and Unsteady Experimental Investigations Supported by Numerical Simulations, ASME paper 2001-GT-0304, 2001
[110] 候安平，周盛，轴流式叶轮机时序效应的机理探讨，航空动力学报，Vol．18(1)，2003：70-75
[111] 曾理江，昆虫运动仿生研究，科技日报，2002年5月9日，11版，2002
[112] 航空航天工业部高效节能发动机文集编委会主编，《高效节能发动机文集》第五分册，第一版，北京：航空工业出版社，1990
[113] 专利：叶轮机缘线的非定常匹配方法，2002
[114] Ji Lucheng, Chen Jiang, and Xu Jianzhong, Numerical Investigations about the Aerodynamic Performance of the Cascade in Unsteady Environment, ASME paper 2003-GT-38288, 2003
[115] Ji Lucheng, Chen Jiang, Li Wei, et. al., A New Freedom for Turbomahcinery Design: Edge-Matching Technique, ISABE paper 2003-1100, 2003
[116] 陈江，季路成，杨春信，叶轮机非定常气动设计的缘线匹配技术，航空动力举报，Vol．18(5)，2003：608-614
[117] 季路成，陈江，闫朝等，叶轮机设计的缘线匹配理论及方法，中国工程热物理学会气动热力学2003年学术会议论文，No．032005，2003
[118] 季路成，陈江，缘线匹配技术在轴流压气机设计中的应用探索，中国工程热物理学会气动热力学2003年学术会议论文，No．032087，2003
[119] 季路成，陈江，闫朝，缘线匹配理论在轴流透平设计中的应用探索，中国工程热物理学会气动热力学2003年学术会议论文．No．032088，2003
[120] Denton, J.D., Xu, L., The Effects of Lean and Sweep on Transonic Fan Performance, ASME paper GT-2002-30327, 2002
[121] Gallimore, S.J., Bolger, J.J., Cumpsty, N.A., et al., The Use of Sweep and Dihedral in Multistage Axial Flow Compressor Blading-Part Ⅰ: University Research and Methods Development, ASME paper GT-2002-30328, 2002
[122] 王仲奇，冯国泰，王松涛等，透平叶片中的二次流旋涡结构的研究，工程热物理学报，Vol．23(5)，2002：553-556
[123] Wang, S.T., Wang, Z.Q., Feng, G.T., Numerical Simulation of 3D Flow Field Structure in Turbine Cascade with Bowed Blades, ASME paper 2001-GT-30328, 2001
[124] Wellborn, S.R., Delaney, R.A., Redesign of a 12-Stage Axial-Flow Compressor using Multistage CFD, ASME paper 2001-GT-0351,2001
[125] Lyes, P.A., Ginder, R.B., Low-Speed Compressor Tests of Swept and Bowed Blade Designs, ISABE paper 99-7048, 1999
[126] 周盛等，叶轮机气动弹性力学引论，第一版，北京：国防工业出版社，1989
[127] 孙晓峰，周盛，气动声学，第一版，北京：北京航空航天大学动力学教材，1992
[128] Wilkinson, D.H., Calculation of Blade to Blade Flow in a Turbomachine by Streamline Curvature, Aeronautical Research Council Report and Memorandum, No. 3704, 1972
[129] Smith, D., and Frost, D.H., Calculation of the Flow past Turbomachine Blades, Proc. Ⅰ. Mech. E., 1969
[130] Zhao, X.L., Solution of Transonic Flow along SI Stream Surfaces Employing Non-Orthogonal Curvilinear Coordinates and Corresponding Non-Orthogonal Velocity Components, Ⅰ. Mech. E. Conf., 1984:183-189
[131] Caspar, J.A., Hobbs, D.E., and Davis, R.L., The Calculation of Two Dimensional Compressible Potential Flow in Cascades using Finite Area Techniques, AIAA 17th Aerospace Sciences Meeting, 1979
[132] 陈矛章，粘性流体动力学理论及紊流工程计算，第一版，北京：北京航空学院出版社，1986
[133] Fu, S., Rung, T., and Thiele, F., On the Realizability of Nonlinear Stress-Strain Relationship for Reynolds Stress Closures, Flow, Turbulence and Combustion, Vol. 60, 1999:333-359
[134] Hwang, C.B., and Lin, C.A., Improved Low-Reynolds-Number κ-ε Model Based on Direct Numerical Simulation Data, AIAA Journal, Vol. 36, 1998:38-43
[135] 陶文铨，计算传热学的近代进展，第一版，北京：科学出版社，2001
[136] Harten, A., High Resolution Schemes for Hyperbolic Conservation Laws, Journal of Computational Physics, Vol. 49, 1983:357-393
[137] Roe, P.L., and Baines, M.J., Asymptotic Behaviour of Some Non-Linear Schemes for Linear Advection, Notes on Numerical Fluid Mechanics, Vol. 7, 1984:283-290
[138] Roe, P.L., Some Contributions to the Modelling of Discontinuous Flows, Lectures in Applied Mathmatics, Vol. 22, 1985
[139] Johnson, G.M., Multiple-Grid Convergence Acceleration of Viscous and Inviscid Flow Computations, NASA TM, 1983
[140] Chima, R.V., and Johnson, G.M., Efficient Solution of the Euler and Navier-Stokes Equations with a Vectorized Multiple-Grid Algorithm, NASA TM, 1983
[141] 刘超群，多重网格法及其在计算流体力学中的应用，第一版，北京：清华大学出版社，1995
[142] Schulte, V., Hodson, H.P., "Unsteady Wake-Induced Boundary Layer Transition in High Lift LP
Turbines", ASME paper 96-GT-486, 1996
[143] 于海力，闫朝，季路成等，探讨一种叶轮机非定常流数值模拟的方法，工程热物理学报，Vol．24(1)，2003：46-48
[144] Liu, J.S., and Sockol, P.M., Unsteady Euler Cascade Analysis, AIAA paper 89-0322, 1989
[145] 祁明旭，丰镇平，轴流透平动静干涉的非定常效应及其对气动性能的影响，中国工程热物理学会学术会议论文，No．022029，2002
[146] Huang, H.Y., Yang, H.T., Feng, G.T., et al., Fully Clocking Effect in a Two-Stage Compressor, ASME paper GT2003-38867, 2003
[147] Martin, A., and Hirsch, Ch., Numerical Investigation of a 1-1/2 Axial Turbine Stage at Quasi-Steady and Fully Unsteady Conditions, ASME paper 2001-GT-0309, 2001
[148] Dixon, S.L., Fluid Mechanics, Thermodynamics of Turbomachinery, 3rd Edition, Great Britain: PERGAMON Press, 1978
[149] Smith,L.H., Wake Dissipation in Turbomachine[J], ASME J of Basic Engineering, Vol. 88D, 1966: 688-690
[150] Denton, J.D., Solution of the Euler Equations for Turbomachinery Flows-Part 2. Three Dimensional Flows, Thermodynamics and Fluid Mechanics of Turbomachinery-Volume 1, 1997: 313-347
[151] Thompkins, W.T., An Experimental and Computational Study of Flow in a Transonic Compressor Rotor, Ph.D. Thesis, M.I.T., 1976
[152] Denton, J.D., Lessons From Rotor 37, 3rd International Symposium on Aerothermodynamics of Internal Flows, 1996
[153] Granville, P.S., Baldwin-Lomax Factors for Turbulent Boundary Layers in Pressure Gradients, AIAA Journal, Vol. 25, 1987:1624-1627
[154] Jennions, I.K., and Turner, M.G., Three Dimensional Navier-Stokes Computations of Transonic Fan Flow using an Explicit Solver and an Implicit κ-ε Solver, ASME paper 92-GT-309, 1992
[155] Martinelli, L., and Jameson, A., Validation of Multigrid Method for Reynolds Averaged Equations, AIAA paper 88-0414, 1988
[156] Arnone, A., Marconcini, M., Scotti Del Greco, A., et al., Numerical Investigation of
Three-dimensional Clocking Effects in a Low Pressure Turbine, ASME paper GT2003-38414, 2003
[157] Denton, J.D., Loss Mechanisms in Turbomachines, I Mech E Conference Publications, 1987:1-14
[158] He, L., Modelling Issues for Computation of Unsteady Turbomachinery Flows, VKI Lecture Series 'Unsteady Flows in Turbomachines', 11-15, 1996:1-27
