摘要
针对在叶轮机械内对效率影响显著的边界层转捩问题,本文结合已有的风洞实验数据,通过求解PSE方程,给出了一套可有效分析、预测、评价边界层稳定性的数值求解方法。
本文推导了正交曲线坐标系下稳定性PSE方程,使稳定性方程扩展为适合叶轮机械表面型线的正交曲线坐标系计算,并给出了稳定性方程离散和数值差分求解的方式。在现有叶栅叶片表面静压分布实验数据基础上,结合曲线坐标系下Falkner- Skan- Cooke方程求解叶栅表面边界层的平均流动解。将求解结果作为初值带入到稳定方程中。编制了整个求解过程的计算程序。稳定性方程特征值求解分别采用全局法和区域法方法。应用eN模型作为边界层转捩预测和稳定性比较的数值判据以评定叶栅内边界层流动的稳定性。并将以上算法应用于透平和压气机叶片表面边界层稳定性分析中。
本文计算分析了600Mw超临界汽轮机高压第八级汽轮机动叶及静叶两套叶栅吸力面边界层流动的稳定性及变冲角性能,两套叶栅均采用后部加载叶型。稳定性分析表明,在涡轮叶栅中,叶栅中部流动最为稳定,而两端壁附近的流动相对不稳定。
通过分析后部加载叶栅的变冲角特性,可以发现,当冲角改变后,叶栅两端壁边界层所受的影响最为显著,而叶栅中部边界层几乎不随冲角变化。由此看来,采用后部加载叶型,使叶片吸力面压力点移到60%轴向弦长之后,可有效推迟转捩发生,提高叶栅表面边界层稳定性,以及削弱叶栅的冲角对气流变化的敏感性。
为了研究来流条件变化对调节级喷嘴叶栅边界层稳定性的影响,计算了600Mw超临界汽轮机调节级喷嘴叶栅边界层流动的稳定性。结果表明,外界条件的改变在很大程度上影响叶栅表面边界层流动的稳定性。当来流速度增加时,雷诺数会随之增加,并导致流动稳定性变差。若通过改变叶栅几何尺寸,保持雷诺数不变,只增加马赫数,来流马赫数的增加会在一定程度上提高流动稳定性。另外,来流扰动频率也是影响叶栅边界层稳定性的重要因素。当扰动频率发生变化时,存在一个扰动放大率的最大极值点,在极值点附近扰动最容易放大,边界层也最容易发生转捩。
本文还探讨了在常见叶栅的改型设计中,二次流的变化对边界层流动稳定性影响。在对具有大扩张角外端壁的涡轮静叶栅的流动稳定性计算中发现,在该类涡轮静叶栅中,具有大扩张角的外端会引起叶栅顶部边界层增厚,转捩甚至分离,降低叶顶附近流动的稳定性。在该类涡轮静叶栅中如果叶顶采用前掠叶片,可削弱外端壁大子午扩张角对叶片顶部区域流动产生的不利影响。
本文最后讨论了叶片弯曲对扩压叶栅壁面边界层流动稳定性的影响,分析了直叶片和具有不同弯曲角的弯叶片叶栅的吸力面和压力面边界层流动的稳定性。结果表明在压气机中采用弯叶片,可改善压气机叶栅吸力面两端边界层流动,同时会降低吸力面中部边界层流动的稳定性。只有合理匹配选择弯叶片才能有效提高叶栅的整体性能。
The transition of boundary layer from laminar to turbulent plays an important role in turbine machine. Solving Parabolized Stability Equations(PSE), a numerical method is presented in this dissertation, which is based on wind tunnel experiment date to analyze, predict and estimate the boundary flow stability.
A stability PSE equation is developed in the dissertation. In order to generalize the equation for geometries with curved blade surfaces, an orthogonal curvilinear coordinate system is introduced. The numerical discretization and the finite diffence scheme are both proposed. Based on experiment date of blade surface pressure distribution, the mean parameters of the boundary flow can be solved with the Falkner- skan- Cooke equation in curvilinear coorinate system. The results are then used to be the initial parameters for the stability equations. Numercal solution codes are developed, in which the global and local methods are both used. The eN method is used for the criterion of the boundary flow stability and transition prediction in the blade cascade boundary flow stability problem. All of these methods can be used in stability analysis of both tubine and compressor blades.
The off-design performances of stator and rotor blades in the 8th stage of 600Mw supercritical steam turbine and their boundary flow stabilities are all analyzed in this dissertation. Two sets of blades are both aft-loaded profile. It is shown in the result that the flow at the mid span of blade is relatively steady, while the flow near the endwall is relatively unstable.
To analyze the influence of incoming flow on the boundary layer stability, computation is performed in the governing-stage guide vane of 600Mw super-critical steam. It is shown that when the incidence is changed, the boundary flow near the endwall is remarkably affected, but the flow at the mid span is not changed conspicuously. These results indicate that using aft-loaded cascade, the lowest pressure point on blade suction surface is moved to be about 60% axial chord, the transition is put off, the stability of cascade surface is enhanced and the incidence sensitivity is weakend effectively.
In order to investigate the influence of external flow parameter on the boundary flow stability, the blade surface boundary flow stability of the governing-stage guide vane in 600Mw supercritical steam turbine is computated. It is shown in the result that the disturbance of external flow patameter clearly affects the stability of the blade surface flow. When inlet flow velocities are increased, the Reynold number is increased also. The increase of the Reynold number leads to the decrease of the flow stability. If increasing the inlet Mach number and keeping the Reynold number constant, the stability should be increased with the Mach number. Furthermore, the external disturbing frequency is important influencing factors of stability. When the disturbing frequency is changed, there exists a local maximal disturbing magnification. Near this point the disturbance is easily magnified, so the flow transition is easy to occur.
The influence of the second flow on the boundary flow stability in general designed blade is also discussed in this dissertation. From the computation of the boundary flow stability in the diffused meridional flow passage, it is found that the difussed meridional passage thickens the boundary flow in the blade tip and discreases the flow stability there. If the forwardly swept blade is used, the negative effect on stability in blade tip is able to be descreased.
Finally, the effect of boundary flow stability in a diffuser cascade with bowed blade is discussed. The boundary flow stabilities on the suction and pressure surfaces in both the straight and bowed blades are solved. It is shown that the boundary flow stability near the endwall of the bowed blade suction surface is enhanced, but that at the mid span is reduced. So the performence of cascade can be enhanced by selecting appropriate bowed angles.
引文
1 张涵信,周恒. 流体力学基础研究. 世界科技研究与发展(院士论坛).2001, 32(1): 15~19
2 Roberto Sosaa, Guillermo Artanab. Steady Control of Laminar Separation over Airfoils with Plasma Sheet Actuators. Journal of Electrostatics. 2006, (64): 604~610
3 Trevor Young , Brian Mahony, Bryan Humphreys, Ernst Totland, Alan McClafferty, Julie Corish. Durability of Hybrid Laminar Flow Control (HLFC) Surfaces. Aerospace Science and Technology. 2003, (7): 181~190
4 Thibert JJ, Reneaux V, Schmitt V. Onera. Activities in Drag Reduction. Congr. Int. Council Aeron. Sci.. 1990, (17): 1053~1064
5 Ronald D. Joslin. Aircraft Laminar Flow Control. Annual Review of Fluid Mechanics. 1998, vol. 30: 1~29
6 Jerome Hoepffner, Mattias Chevalier, Thomas R. Bewley, Dan S. Henningson. State Estimation in Wall-Bounded Flow Systems. Part 1. Perturbed Laminar Flows. J. Fluid Mech.. 2005, 534: 263~294
7 Robert J-P. Hybrid Laminar Flow Control: A Challenge for a Manufacturer. Proc. Eur. Forum Laminar Flow Tech..1992, (1): 294~308
8 W. McCormack, O. R. Tuttyt, E. Rogers, P. A. Nelson. Optimization Based Control Of Boundary Layer Transition-Theory And Experimentation. The Institution of Electrical Engineers. 1998
9 Jan Pralits. Optimal Design of Natural and Hybrid Laminar Flow Control on Wings, Technical Reports from Royal Institute of Technology Department of Mechanics. SE-100 44 Stockholm, Sweden, 2003,(10)
10 T.M. Younga, B. Humphreysb, J.P. Fieldingc. Investigation of Hybrid Laminar Flow Control (HLFC) Surfaces. Aircraft Design. 2001, (4): 127~146
11 P.J. Schmid, and D.S.Henningson. Stability and Transition in Shear Flows. New York, Springer-Verlag, 2000
12 P. G. Drazin, W. H. Reid. Hydrodynamic Stability. Cambridge University Press, 1981, 1~250
13 J. O. Hinze. Turbulence. Second Ed.. McGraw-Hill, New York, 1998:1~40
14 是勋刚. 湍流. 天津大学出版, 1992: 20~30
15 H. Tennekes and J. L. Lumley. A First Course in Turbulence. MIT Press, Cambridge, MA, 1983
16 David C. Wilcox. Turbulence Modeling for CFD. Second Edition. DCW Industries, 2004, 3: 5~10
17 P. De. Palma. Accurate Numerical Simulation of Compressible Transitional Flows in Turbomachinery. AIAA JOURNAL. 2002, 40(4): 702~708
18 唐登斌,夏浩. 有限振幅 T-S 波在非平行边界层中的非线性演化研究. 应用数学和力学. 2002 年,6 月
19 S. V. Manuilovich. Propagation of a Tollmien-Schlichting Wave over the Junction between Rigid and Compliant Surfaces. Fluid Dynamics. 2004, 39(5): 702–717
20 N. K. Kyriakides, E. G. Kastrinakis, S. G. Nychas, A. Goulas. A Bypass Wake Induced Laminar/Turbulent Transition. Eur. J. Mech. B/Fluids. 1999, 18: 1049~1065
21 G. V. Petrov. Generation of the Tollmien-Schlichting Wave in a Supersonic Boundary Layer by Two Sinusoidal Acoustic Waves. Journal of Applied Mechanics and Technical Physics. 2002, 43(1): 63~68
22 P. Wassermann, M. Kloker. Mechanisms and Passive Control of Crossflow-Vortex-induced Transition in a Three-dimensional Boundary Layer. J. Fluid Mech. 2002,456: 49~84
23 Valery G. Chernoray, Alexander V. Dovgal, Victor V. Kozlov, Lennart L?fdahl. Secondary Instability of Stationary Vortex Packets in a Swept Wing Boundary Layer. XXI ICTAM, 15–21. 2004, (8) Warsaw, Poland
24 N. Vinod, Rama Govindarajan. Aspects of the Laminar-Turbulent Transition in Axisymmetric Boundary Layers. XXI ICTAM, Warsaw, Poland .2004, (8)
25 I. J. Wygnanski, and F. H. Champagne. On Transition in a Pipe. Part 1: the Origin of Puffs and Slugs and the Flow in a Turbulent Slug. J. Fluid Mech. 1973, 59: 281~335
26 V. C. Patel, M. R. Head. Some Observations on Skin Friction and Velocity Profiles in Full Developed Pipe and Channel Flows. J. Fluid Mech. 1969, 38: 181~201
27 L. N. Trefethen, A. E. Trefethen, S. C. Reddy, T. A. Driscoll. Hydrodynamic Stability without Eigenvalues. Science. 1993, 261: 578~584
28 S. Grossmann. The Onset of Shear Flow Turbulence. Reviews of Modern Physics. 2000, 72: 603~618
29 A. G. Darbyshire, T. Mullin. Transition to Turbulence in Constant Mass Flux Pipe Flow. J. Fluid Mech. 1995, 289: 83~114
30 郑哲敏,周恒,张涵信,黄克智,白以龙. 21 世纪初的力学发展趋势. 力学进展. 1995, 25(4): 433~441
31 P.C. Stainback, J.B. Anders, W.D. Harvey, A.M. Cary, J.E.Harris. An Investigation of Boundary Layer Transition on the Wall of a Mach 5 Nozzle. AIAA Paper. 1974(1): 74~136
32 S.P. Wikison, S. G. Anders, F. J. Chen, J. A. White. Status of NASA Langley Quiet Flow Facility Developments. AIAA Paper 94-2498, June 1994
33 S.P. Schnieder, and C.E. Haven. Quiet- Flow Ludwieg Tube for High-speed Transition Research. AIAA J. 1995, 33(4): 688~693
34 S.P. Wilkinson. A Review of Hypersonic Boundary Layer Stability Experiments in a Quiet Mach 6 Wind Tunnel. AIAA Paper 97-1819. 1997, (6)
35 T.P. Brogan, A. Demetriades. Influence of Sidewall Transition on Measured Free Stream Noise in a Two-Dimensional Supersonic Tunnel. AIAA Paper 98-2614, 1998, (6)
36 Torence Patrick Brogan. Effects of Surface Heating on Stability and Transition in A Supersonic Nozzle Boundary Layer. Ph.D. Dissertation in Engineering, Montana State University, Bozeman, Montana. January 1999.
37 D. Arnal, G. Casalis. Laminar-turbulent Transition Prediction in Three-Dimensional Flows. Progress in Aerospace Sciences. 2000, 36: 173~191
38 Robert G. Jacobs. Bypass Transition Phenomena Studied by Computer Simulation. Ph.D. Dissertation, Stanford University. January 2000
39 George Chimonas. Pressure Gradient Amplification of Shear Instabilities in the Boundary Layer. Dynamics of Atmospheres and Oceans. 2003, 37: 131~145
40 A. Pantokratoras. Further Results on the Variable Viscosity on Flow and Heat Transfer to a Continuous Moving Flat Plate. International Journal of Engineering Science. 2004, 42: 1891~1896
41 范绪萁,楼卓时. 二维平板可压缩边界层的二次稳定性分析. 应用数学和力学. 1999, 20(5): 486~490
42 袁湘江,周恒,赵耕夫. 超声速高超声速球锥绕流的边界层稳定性特点初探. 空气动力学学报. 1999, 17(1): 98~104
43 Roger L. Kimmel. Aspects of Hypersonic Boundary-Layer Transition Control. 41st Aerospace Sciences Meeting and Exhibit, AIAA 2003-772. 2003, (1)
44 Erik Janke, Ponnampalam Balakumar. On The Stability Of three-Dimensional Boundary Layers Part 1: Linear and Nonlinear Stability. NASA /CR - 1999-209330, ICASE Report No. 99-16
45 Erik Janke, Ponnampalam Balakumar. On the Stability Of Three-Dimensional Boundary Layers Part 2: Secondary Instability. NASA/CR-1999-209341, ICASE Report No. 99-19
46 Jeppe Johansen. Unsteady Airfoil Flows with Application to Aeroelastic Stability. Riso National Laboratory, Roskilde, Denmark. 1999, (10)
47 Z. Wang, K.S. Yeo, B.C. Khoo. Spatial Direct Numerical Simulation of Transitional Boundary Layer over Compliant Surfaces. Computers & Fluids. 2005, 34: 1062~1095
48 S. Scott Collis, Sanjiva K. Lele. Receptivity to Surface Roughness Near a Swept Leading Edge. J. Fluid Mech. 1999, 380: 141~168
49 Corke T. C., Bar-Sever A., Morkovin M. V..Experiments on Transition Enhancement by Distributed Roughness.Phys. Fluids. 1986, 29(10): 3199~ 3213
50 A. Boiko, K. Westin, B. Klingmann, Kozlov V., Alfredsson, P.. Experiments in a Boundary Layer Subjected to Free Stream Turbulence. Part 2. The Role of TS-waves in the Transition Process. J. Fluid Mech.. 1994. 281: 219~245
51 A. Bakchinov, G. Grek, B. Klingman, V. Kozlov. Transition Experiments in a Boundary Layer with Embedded Streamwise Vortices. Phys. Fluids. 1995, 7(4): 820~832
52 H. P. Greenspan, D.J. Benney. On Shear Layer Instability Breakdown and Transition. J. Fluid Mech.. 1963, 15: 133~153
53 M. T.Landahl.Wave Mechanics of Breakdown. J. Fluid Mech. 1972, 56, 775~802
54 Y. S. Kachnov, V. Y. Levchenko. The Resonant Interaction of Disturbances at Laminar Turbulent Transition in a Boundary Layer. J. Fluid Mech. 1984, 138: 209~247
55 V. I. Brodulin, Y. S. Kachanov. Role of the Mechanism of Local Secondary Instability in K Breakdown of Boundary Layer. Izv. Sib. Otd. Akad. Nauk SSSR. Ser. Tekh. Nauk. 18, 65-77(in Russian) English translation: Sov. J. Appl. Phys. 1989, 3(2): 70~81
56 V. I. Brodulin, Y. S. Kachanov. Experimental Study of Soliton-like Coherent Structures in Boundary Layer. Proc. Scientific Methodological Seminar on Ship Hydrodynamics, 19th session, 2:99-1-99-10. Varna: Bulg. Ship Hydrodyn. Centre. 1990
57 Ludwig Christian Haber, B.S., M.S.. Investigation of Dynamics in Turbulent Swirling Flows Aided by Linear Stability Analysis. Doctor of Philosophy in Mechanical Engineering, the Faculty of the Virginia Polytechnic Institute and State University. 2003
58 王伟志,唐登斌. Falkner-Skan 流空间演化的二次稳定性研究. 空气动力学学报. 2002, 20(4):477~482
59 H. Bippes. Basic experiments on transition in three-dimensional boundary layers dominated by crossflow instability. Prog. Aerospace Sci.. 1999,35: 363~412
60 H. Deyhle, H.Bippes. Disturbance growth in an unstable Three -Dimensional Boundary Layer and its Dependence on Environmental Conditions. J. Fluid Mech.. 1996, 316: 73~113
61 T. Lerche.Experimental investigations of nonlinear wave interactions and secondary instability in three-dimensional boundary-layer flow. In Advances in Turbulence VI (ed. S. Gavrilakis, L. Machiels & P. A.Monkewitz), Proc. Sixth European Turbulence Conf., Lausanne, Switzerland, Kluwer. 1996
62 W. S. Saric, Jr. Carrillo, Reibert M. S.. Nonlinear Stability and Transition in 3-D Boundary Layers. Meccanica. 1998, 33: 471~489
63 W. S. Saric, H. L. Reed, E. B.White. Stability and Transition of Three-Dimensional Boundary layers. Annu. Rev. Fluid Mech.. 2003, 35: 413~440
64 E. B. White, W. S. Saric. Secondary Instability of Crossflow Vortices. J. Fluid Mech. (submitted). 2003
65 Y. Kohama, Y. Kodashima, H. Watanabe. Randomization Process in Crossflow Instability Dominant Three-Dimensional Boundary-LayerTransition. In Laminar-Turbulent Transition (ed. R. Kobayashi), Proc. IUTAM Symp. Sendai, Japan. Springer. 1995
66 M. Kawakami, Y. Kohama, M. Okutsu. Stability Characteristics of Stationary Crossflow Vortices in Three-Dimensional Boundary Layer. AIAA Paper 99-0811. 1999
67 M. R. Malik, F. Li, M. M. Choudhari, Chang C.-L. Secondary Instability of Crossflow Vortices and Swept-Wing Boundary-Layer Transition. J. Fluid Mech.. 1999, 399: 85~115
68 M. R. Malik, F. Li, C.-L. Chang. Crossflow Disturbances in Three-Dimensional Boundary Layers: Nonlinear Development, Wave Interaction and Secondary Instability. J. Fluid Mech.. 1994, 268: 1~36
69 M. R. Malik, F. Li, C.-L. Chang. Nonlinear Crossflow Disturbances and Secondary Instabilities in Three-Dimensional Boundary Layers. In Nonlinear Instability and Transition in Three-Dimensional Boundary Layers. (ed. P. W. Duck & P. Hall), Proc. IUTAM Symp. Manchester, UK . Kluwer. 1996: 257~266
70 T. S. Haynes. H. L. Reed. Computations in Nonlinear Saturation of Stationary Crossflow Vortices in a Swept-Wing Boundary Layer. AIAA Paper 96-0182. 1996
71 T. S. Haynes, H. L Reed.. Simulation of Swept-Wing Vortices Using Nonlinear Parabolized Stability Equations. J. Fluid Mech. 2000, 405: 325~349
72 E. Janke, P. Balakumar. On the Secondary Instability of Three-Dimensional Boundary Layers. Theoret. Comput. Fluid Dyn.. 2000, 14:167~194
73 W. Koch, F. P. Bertolotti, A. Stolte, S. Hein. Nonlinear Equilibrium Solutions in a Three-Dimensional Boundary Layer and Their Secondary Instability. J. Fluid Mech.. 2000, 406: 131~174
74 W. Koch. On the Spatio-Temporal Stability of Primary and Secondary Crossflow Vortices in a Three-Dimensional Boundary Layer. J. Fluid Mech. 2002, 456: 85~111
75 赵 耕 夫 . 论 可 压 缩 边 界 层 线 性 稳 定 性 的 分 歧 . 力 学 学 报 . 1997, 29(1):24~28
76 Peter Wassermann, Markus Kloker. Transition Mechanisms Induced by Traveling Crossflow Vortices in a Three-Dimensional Boundary Layer. J. Fluid Mech. 2003, 483: 67~89
77 Peter Wassermann, Markus Kloker. Mechanisms and Passive Control of Crossflow Vortex Induced Transition in a Three-Dimensional Boundary Layer. J. Fluid Mech.. 2002, 456: 49~84
78 Nobutake Itoh. Non-Parallel Stability Analysis of Three-Dimensional Boundary Layers along an Infnite Attachment Line. Fluid Dynamics Research. 2000, 27: 143~161
79 M. V. Ustinov. Receptivity of the Inclined-Cylinder Attachment-Line Boundary Layer to Vortex Perturbations. Fluid Dynamics. 2004, 39(6):908~919
80 P. Hall, M. R. Malik, D. I. A. Poll. On the Stability of an Infnitely Swept Attachment Line Boundary Layer. Proc. R. Soc. Lond A.1984, 395:229~345
81 V. Theoflis. Spatial Stability of Incompressible Attachment-Line Flow. Theoret. Comput. Fluid Dynamics. 1995, 7:159~171
82 D. I. A. Poll. Transition in the Infnite Swept Attachment Line Boundary Layer. The aeronautical quarterly. 1979, 30:607~629
83 J. C. Juillen, D. Arnal. Experimental Study of Boundary Layer Suction Effects. In Kobayashi, R., editor, Laminar turbulent transition, Springer. 1995: 174~179
84 D. C. Sorensen. Implicit Application of Polynomial Flters in a K-step Arnoldi Method. SIAM J. Matrix Anal. Appl..1992, 13:357~385
85 Hall, Philip, Seddougui, O. Sharon. Wave Interactions in a Three-Dimensional Attachment- Line Boundary Layer. J. Fluid Mech., 1990, 217: 367~390
86 R. S. Lin, M. R. Malik. The Stability of Incompressible Attachment- Line Boundary Layers—A 2D-Eigenvalue Approach. AIAA-94-2372. 1994
87 R. S. Lin, M. R. Malik. Stability and Transition in Compressible Attachment - Line Boundary-Layer Flow. SAE Paper 952041. 1995
88 Ronald D. Joslin. Direct Numerical Simulation of Evolution and Control of Linear and Nonlinear Disturbances in Three-Dimensional Attachment-Line Boundary Layers. NASA Technical Paper 3623, 1997, (2)
89 D.I.A. Poll. The Development of Intermittent Turbulence on a Swept Attachment Line including the Effects of Compressibility. Aeronaut. Quart. XXXIV. 1983: 1~23
90 E. Benard, R.K. Cooper, A. Sidorenko. Transitional and Turbulent Heat Transfer of Swept Cylinder Attachment Line in Hypersonic Flow. International Journal of Heat and Mass Transfer. 2006, 49: 836~843
91 B.A. Singer. Modelling the transition region. NASA report, CR-4492, 1993
92 D. Arnal. Laminar-turbulent transition. T.K.S. Murthy (Ed.), Computational Methods in Hypersonic Aerodynamics, Kluwer Academic Publishers. 1991, 233~264
93 D.A. Dilley. Evaluation of CFD Turbulent Heating Prediction Techniques and Comparison with Hypersonic Experimental Data. NASA report CR-2001-21-837. 2001
94 A. I. Semisynov, A. V. Fedorov, V. E. Novikov, N. V. Semionov, A. D. Kosinov. Stability and Transition on a Swept Cylinder in a Supersonic Flow. J. Appl. Mech. Tech. Phys.. 2003, 44 (2): 212~220
95 C. P. Coleman, D. I. A. Poll, J. A. Laub, S. W. D. Wolf. Leading Edge Transition on a 76° Swept Cylinder at Mach Number 1.6. AIAA Paper 96-2082, 1996: 1~12
96 L. Gaillard, E. Benard, T. Alziary de Roquefort. Smooth Leading Edge Transition in Hypersonic Flow. Exp. Fluids. 1999, 26: 169~176
97 D. I. A. Poll. Skin Friction and Heat Transfer at an Infinite Swept Attachment Line. Aeronaut. Quart. XXXII, 1981: 299~318
98 F. Bellone. New models for the Prediction of Attachment-Lines Behaviour at Hypersonic Speeds. Ph. D. Thesis, Cranfield, No.51–14447. 2002
99 John W. Elliott, Andrew P. Bassom. The Effect of Wall Cooling on Compressible G?rtler Vortices. Eur. J. Mech. B – Fluids. 2003, 19: 37~68.
100 P. Hall, M. Malik. The Growth of G?rtler Vortices in Compressible Boundary Layers. J. Eng. Math.. 1989, 23: 239~251
101 A.H. Dando, S.O. Seddougui. The Compressible G?rtler Problem in Two- Dimensional Boundary Layers. IMA J. Appl. Math.. 1993, 51: 27~67
102 S.B. Rozhko, A.I. Ruban. Criss-cross Interaction in Three-Dimensional Boundary Layers. Izv. Akad. Nauk SSSR, Mekh. Zhidk. Gaza. 1987, 3: 42~50
103 A. I. Ruban. Propagation of Wave Packets in the Boundary Layer on a Curved Surface. Izv. Akad. Nauk SSSR, Mekh. Zhidk. Gaza. 1990, 2: 59~68.
104 S.B. Rozhko, A.I. Ruban, S.N. Timoshin. Interaction of the Three-Dimensional Boundary Layer with a Stretched Obstacle. Izv. Akad. Nauk SSSR, Mekh. Zhidk. Gaza. 1988, 1: 39~48
105 M. Choudhari, P. Hall, C. Streett. On Spatial Evolution of Long-Wavelength G?rtler Vortices Governed by a Viscous-inviscid Interaction. Q. J. Mech. Appl. Math. 1994, 47: 207~229
106 V. V. Bogolepov, I. I. Lipatov. On the Asymptotic Theory of G?rtler Vortices in a Boundary Layer. Zh. Prikl. Mekh. I Tekh. Fiz..1992, 3: 58~62
107 Aihara, Y., Koyama, H.. Nonlinear Development and Secondary Instability of Gortler Vortice. In Stability in the Mechanics on Continua, ed F. H. Schroeder, Berlin: Springer- Verlag. 1982: 345~354
108 Y. Aihara Y. T., Ito A.. Generation Development and Distortion of Longitudinal Vortices in Boundary Layers Along Concave and Flat Plates. In Laminar-Turbulent Transition. ed V. V. Kozlov, New York:Springer-Verlag. 1985: 447~454
109 P. Hall. The Nonlinear Development of Gortler Vortices in Growing Boundary Layers. Fluid Mech.. 1988, 193: 243~266
110 J. P. Denier, P. Hall. On the Nonlinear Development of the Most Unstable Gorlter Vortex Mode. J. Fluid Mech.. 1991, 231: 615~663
111 A. S. Sabry, T. C. Liu. Longitudinal Vorticity Elements in Boundary Layers: Nonlinear Development from Initial Gorlter Vortices. J. Fluid Mech..1991, 231: 615~663
112 Nobutake Itoh. A Non-Parallel Theory for Gortler Instability of Falkner–Skan Boundary Layers. Fluid Dynamics Research. 2001, 28: 383~396
113 J. A. Ekaterinaris, M. S.Chandrasekhara, M. F. Platzer. Analysis of Low Reynolds Number Airfoil Flows. Journal of Aircraft. 1995: 625~630
114 U. Mehta, K. C. Chang, T. Cebeci. Relative Advantages of Thinlayer Navier-Stokes and Interactive Boundary-Layer Procedures. Tech. Rep.,NASA, Technical Memorandum. 1985
115 B.J. Holmes, C.J. Obara, G.M. Gregorek, M.J. Homan, R.J. Freuhler. Flight Investigation of Natural Laminar Flow on the Bellanca Skyrocket II. SAE Pap.830717. 1983
116 B.J. Holmes, C.J. Obara, G.L. Martin, C.S. Domack. Manufacturing Tolerances for Natural Laminar Flow Airframe Surfaces. SAE Pap. 850863. 1985
117 D. Arnal, M. Habiballah, E. Coustols. Th_eorie de L'instabilit_e Laminaire et Crit_eres de Transition En _ecoulement Bi-et Tridimensionnel. La Recherche A_erospatiale No. 1984-2. 1984
118 Y. Bora Suzen, P. G. Huang. Predictions of Separated and Transitional Boundary Layers Under Low-Pressure Turbine Airfoil Conditions Using an Intermittency Transport Equation, AIAA 2001-0446. 2001
119 Andreas Krumbein, German Aerospace Center (DLR), Braunschweig, Germany. On Modeling of Transitional Flow and its Application on a High Lift Multi-Element Airfoil Configuration. AIAA 2003-724. 2003
120 Mark R. Anderson. Aerodynamic Modeling for Global Stability Analysis. AIAA Atmospheric Flight Mechanics Conference and Exhibit, AIAA 2002-4805. 2002, (8)
121 姚文秀,蔡春培,赵烈,王发民,赵桂萍. 可压缩流动稳定性方程求解与转捩预测. 计算物理. 1999, 16(3): 295~301
122 A. M. Savill. Some Recent Progress in The Turbulence Modeling of By-pass Transition. Near-Wall Turbulent Flows, edited by R.M.C. So, C.G. Speziale and B.E. Launder, Elsevier Science Publishers B.V.. 1993: 829~848
123 A.M. Savill. Further Progress in The Turbulence Modeling of By-pass Transition. Engineering Turbulence Modeling and Experiments 2, Edited by W. Rodi and F. Martelli, Elsevier Science Publishers B. V.. 1993: 583~592
124 K. J. A. Westin. R. A. Henkes. Application of Turbulence Models to Bypass Transition. Journal of Fluids Engineering. 1997, 119: 859~866
125 J. P. Gostelow, A. R. Blunden, G. J. Walker. Effects of Free-Stream Turbulence and Adverse Pressure Gradients on Boundary Layer Transition. ASME Journal of Turbomachinery. 1994, 116: 392~404
126 W. J. Solomon, G. J. Walker, J. P. Gostelow. Transition Length Prediction for Flows with Rapidly Changing Pressure Gradients ASME Paper ASME-95-GT-241, International Gas Turbine and Aeroengine Congress; Exposition, Houston, Texas. 1995, (6): 5~8
127 K. K. Chen, N. A. Thyson. Extension of Emmons' Spot Theory to Flows on Blunt Bodies. AIAA Journal. 1971, 9(5): 821~825
128 J. Steelant, E. Dick. Modeling of Bypass Transition with Conditioned Navier-Stokes Equations Coupled to an Intermittency Transport Equation. International Journal for Numerical Methods in Fluids. 1996, 23: 193~220
129 S. Dhawan, R. Narasimha. Some Properties of Boundary Layer During the Transition from Laminar to Turbulent Flow Motion. Journal of Fluid Mechanics. 1958, 3: 418~436
130 S. Grossmann. The Onset of Shear Flow Turbulence. Reviews of Modern Physics. 2000, 72: 603~618
131 L. N. Trefethen, A. E. Trefethen, S. C. Reddy, T. A. Driscoll. Hydrodynamic Stability without Eigenvalues, Science. 1993, 261: 578~584
132 J. S. Baggett, T. A. Driscoll, L. N. Trefethen. A Mostly Linear Model of Transition to Turbulence. Phys. Fluids. 1995, 7: 833~846
133 F. Waleffe. Transition in Shear Flows, Nonlinear Normality Versus Nonnormal Linearity. Phys. Fluids. 1995, 7: 3060-~3066
134 J. S. Baggett, L. N. Trefethen. Low-Dimensional Modes of Subcritical Transition to Turbulence. Phys. Fluids. 1997, 9: 1043~1053
135 S. J. Chapman. Subcritical Transition in Channel Flows. J. Fluid Mech. 2002 451: 35~97
136 L. N. Trefethen, S. J. Chapman, D. S. Henningson, A. Meseguer, T. Mullin, F. T. M. Nieuwstadt. Threshold Amplitudes for Transition to Turbulence in a Pipe. Numer. Anal. Rep. 00/17, Oxford University Comp. Lab. 2000
137 A. Meseguer. Streak Breakdown Instability in Pipe Poiseuille Flow. Phys. Fluids. 2003, 15: 1203~1213
138 B. Hof, A. Juel, T. Mullin. Scaling of the Turbulence Transition Threshold in a Pipe. Physical Review letters. 2004, 91: 244~502
139 J. R. Cho, M. K. Chung.. A k-ω-ε Equation Turbulence Model Journal of Fluid Mechanics. 1992, 237: 301~322
140 Y. B. Suzen, P. G. Huang. Modeling of Flow Transition Using an Intermittency Transport Equation. NASA- CR- 1999- 209313. 1999
141 T. W. Simon, S. Qiu, K. Yuan. Measurements in a Transitional Boundary Layer Under Low-Pressure Turbine Airfoil Conditions. NASA-CR-2000-209957. 2000
142 Y. B. Suzen, G. Xiong, P.G. Huang. Predictions of Transitional Flows in Low-Pressure Turbines Using an Intermittency Transport Equation. AIAA – 2000 – 2654, Fluids, Denver Colorado. 2000, (6)
143 Y. B. Suzen, P. G. Huang. Modeling of Flow Transition Using an Intermittency Transport Equation. Journal of Fluids Engineering. 2000, 122: 273~284
144 L. S. Hultgren, R. J. Volino. Separated and Transitional Boundary Layers Under Low-Pressure Turbine Airfoil Conditions. NASA TM in preparation. 2000
145 R. J. Volino, L.S. Hultgren. Measurements in Separated and Transitional Boundary Layers Under Low-Pressure Turbine Airfoil Conditions. ASME /IGTI Paper 2000-GT-0260. 2000
146 F. R. Menter. Two-Equation Eddy-Viscosity Turbulence Models for Engineering Applications. AIAA Journal. , 1994, 32(8): 1598~1605
147 李家春. 现代流体力学发展的回顾与展望. 力学进展. 1995, 25(4): 442~540
148 B.J. Abu-Gharmam, R. Shaw. Natural Transition of Boundary Layers-The Effects of Turbulence, Pressure Gradient, and Flow History. Journal of Mechanical Engineering Science. 1980, 22(5): 213~228
149 W. B. Roberts. Calculation of Laminar Separation Bubbles and Their Effect on Airfoil Performance. AIAA Journal, 1980, 18(1): 25-31
150 R. L. Davis, J. E. Carter, E. Reshotko. Analysis of Transitional Separation Bubbles on Infinite Swept Wings. AIAA Journal, 1987, 25(3): 421~428
151 H-S Dou. Energy Gradient Theory of Hydrodynamic Instability. Presented at the Third International Conference on Nonlinear Science, Singapore, revised version also in: International Journal of Non-Linear Mechanics, accepted and in press, 2005
152 H-S Dou. Viscous Instability of Inflectional Velocity Profile. Recent Advances in Fluid Mechanics, Proc. of the 4th Inter. Conf. on Fluid Mech., July 20~23, 2004, Dalian, China; Tsinghua University Press & Springer-Verlag. 2004: 76~79
153 R. R. Mankbadi. Transition, Turbulence, and Noise. Kluwer, Boston. 1994, 21~49
154 Carlo Cossu, Luca Brandt. On Tollmien–Schlichting-Like Waves in Streaky Boundary Layers. European Journal of Mechanics B/Fluids. 2004, 23: 815~833
155 Gaemus Edward Collins. The Orr-Sommerfeld Equation: Classical and Modern Techniques. Degree of Doctor of Philosophy in Mathematics, University of California Santa Barbara. 2002, 3~41
156 V. N. Bobochko. An Orr-Sommerfeld Equation with a First-Order Differential Turning Point. Differential Equations. 2003, 39(2): 182~191
157 Wu-Ting Tsai, Mei-Ying Lin. Stability Analysis on the Initial Surface-Wave Generation Within an Air-Sea Coupled Shear Flow. Journal of Marine Science and Technology. 2004, 12(3): 200~208
158 Rama Govindarajan, R. Narasimha. Accurate Estimate of Sisturbance Amplitude Variation from Solution of Minimal Composite Stability Theory. Theor. Comput. Fluid Dyn. 2005, 19(4): 229~235
159 Chau-Lyan Chan. The Langley Stability and Transition Analysis Code (LASTRAC) : LST, Linear & Nonlinear PSE for 2-D, Axisymmetric, and Infinite SweptWing Boundary Layers. AIAA 2003-974. 2003
160 罗俊荣,沈清,张涵信. 二维超声速剪切层的非线性失稳过程分析. 空气动力学学报. 2002, 20(3):282~288
161 P. Moresco, T. Alboussière. Stability of B?dewadt–Hartmann layers. European Journal of Mechanics B/Fluids. 2004, 23: 851~859
162 A. A. Maslov, S.G. Mironov, T.V. Poplavskaya, B.V. Smorodskii. Stability of the Hypersonic Shock Layer on a Flat Plate. Fluid Dynamics. 2004, 39(2):181~188
163 Smith AMO, Gamberoni N.. Transition, Pressure Gradient and Stability Theory. Report ES 26388, Douglas Aircraft Co., El Segundo, California. 1956
164 Van Ingen JL. A Suggested Semi-Empirical Method for the Calculation of Boundary Layer Transition Region. Report UTH-74, Univ. of Techn., Dept. of Aero. Eng., Delft. 1956
165 M.R. Ruith, P. Chen, E. Meiburg. Development of Boundary Conditions for Direct Numerical Simulations of Three-dimensional Vortex Breakdown Phenomena in Semi-infinite Domains. Computers & Fluids. 2004, 33: 1225~1250
166 Li Jiang, Chau-Lyan Chang, Meelan Choudhari, Chaoqun Liu. Instability-wave Propagation in Boundary-Layer Flows at Subsonic Through Hypersonic Mach Numbers. Mathematics and Computers in Simulation. 2004, 65: 469~487
167 Arnal D.. Prediction Based on Linear Theory. In: Progress in Transition Modelling. AGARD Report. 1993, 793
168 T. Cebeci, K. Stewartson. On Stability and Transition in Three-Dimensional Flows. AIAA Journal. 1980, 18(4):398~405
169 M. Drela, and M. B. Giles. Viscous-Inviscid Analysis of Transonic and Low Reynolds Number Airfoils. AIAA J..1986, 25(10)
170 T. Cebeci. Essential Ingridients of a Methods for Low Reynolds Number Airfoils. AIAA J..1988, 27(12)
171 H. Stock, E. Degenhart. A Simplified en Method for Transition Prediction in Two-dimensional Incompressible Boundary Layers. Z. Flugwiss Weltraumforsch. 1989, 13
172 E.D. Petersen. Graenselags stabilitet. Master’s thesis. Danish Technical University, AFM-EP 91-01. 1991
173 N. A. Olesen. Laminar/Turblent Omslagsmodel for Graenselagsstromninger. Master’s thesis. Danish Technical University, AFMEP 94-02. 1994
174 P. Dini, M.S. Selig, Maughmer M. D.. Simplified Linear Stability Transition Prediction Method for Separated Boundary Layers. AIAA J.. 1992, 30(8): 1953~1961
175 黄志澄. 空天飞机的边界层转捩. 气动实验与测量控制. 1994, 8(1):1~9
176 H. L. Reed, W. S. Saric, D. Arnal. Linear Stability Theory Applied to Boundary Layers. Annu. Rev. Fluid Mech. 1996, 28: 389~428
177 W. Saric. Personal Communication. Arizona State University, Tempe AZ. 2001
178 M.Choudhari, C.-L.Chang, C. L. Streett, P. Balakumar. Integrated Transition Prediction: A Case Study in Supersonic Laminar Flow Control. AIAA paper 2003-0973, 41st Aerospace Sciences Meeting and Exhibit, Reno, Nv. 2003, (1)
179 M. Drela. Two-Dimensional Transonic Aerodynamic Design and AnalysisUsing the Euler Equations. Ph.D. Dissertation, MIT GTL Rept.. 1986, 187(2)
180 G. Gleyzes, J. Cousteix, J.L. Bonnet. A Calculation Method of Leading-Edge Sepatation Bubbles, in Numerical and Physical Aspects of Aerodynamic Turbulent Flows II. edited by T. Cebeci, Springer-Verlag, New York. 1984
181 H. W. Stock, E. Degenhart. A Simplified en Method for Transition Prediction in Two-Dimensional, Incompressible Boundary Layers. Z. Flugwiss, Weltraumforschung. 1989, 12: 16~30
182 J. R. Dagenhart. Amplified Crossflow Disturbances in Laminar Boundary Layer on Swept Wings with Suction. NASA TP 1902. 1981, (11)
183 D. Arnal. Boundary Layer Transition: Predictions Based on Linear Theory, in Special Course on Progress in Transition Modeling. AGARD Rept. 193, 1994, (4): 1:63
184 J. D. Crouch, L. L. Ng. Variable N-Factor Method for Transition Prediction in Three-Dimensional Boundary Layers. AIAA Journal. 2000, 38(2): 211~216
185 唐建斌. 非平行边界层稳定性问题研究. 第五届湍流与流动稳定性学术会议. 1997, (5): 92~96
186 P. ANDERSSON, D. S. HENNINGSON, A. HANIFI. On a Stabilization Procedure for the Parabolic Stability Equations. Journal of Engineering Mathematics.1998, 33: 311~332
187 Rama Govindarajan, R. Narasimha. Estimating Amplitude Ratios In Boundary Layer Stability Theory: A Comparison Between Two Approaches. J. Fluid Mech. 2001, 439: 403~412
188 Thorwald Herbert. Parabolized Stability Equations. Annu. Rev. Fluid. Mech. 1997, 29: 245~283
189 Jan Pralits. Optimal Design of Natural and Hybrid Laminar Flow Control on Wings. Technical Reports from Royal Institute of Technology Department of Mechanics SE-100 44 Stockholm, Sweden
190 Erik Janke. On the Secondary Instability of Three-Dimensional Boundary Layers. Theoret. Comput. Fluid Dynamics. 2000, 14: 167~194
191 S.Scott Collis. A Computational Investigation of Receptivity in High-Speed Flow Near a Swept Leading-Edge.A Dissertation Submitted to the Department of Mechanical Engineering and the Committee on Graduate Studies of Stanford University in Partial Fulfillment of the Requitements for the Degree of Doctor of Philosophy
192 郭乃龙. 三维不可压边界层抛物化稳定性方程的椭圆特性研究. 航空学报. 1999, 20(2): 104~10
193 J. O. Pralits, C. Airiau, A. Hanifi, D.S. Henningson.. Sensitivity Analysis Using Adjoint Parabolized Stability Equations for Compressible Flows. Flow, Turbulence and Combustion. 2000, 65: 321~346
194 M. Langlois, G. Casalis, D. Arnal. On the Practical Application of the PSEApproach to Linear Stability Analysis. Aerospace Science and Technology. 1998, (3): 167~176
195 Justin Moston., Philip A. Stewart, Stephen J. Cowley. On the Nonlinear Growth of Two-Dimensional Tollmien-Schlichting Waves in a Flat Plate Boundary Layer. Under consideration for publication in J. Fluid Mech.
196 Meelan Choudhari, Chau-Lyan Chang, Craig Streett, P. Balakumar. Integrated Transition Prediction: a Case Study in Supersonic Laminar Flow Control. AIAA 2003-973. 2003(1)
197 Ian Frigaard, Cherif Nouar, On Three-Dimensional Linear Stability of Poiseuille Flow of Bingham Fluids. PHYSICS OF FLUIDS. 2003, 15(10): 2843~2850
198 周恒. 流动稳定性弱非线性理论的进一步改进. 中国科学. 1997, 27(12): 1111~1118
199 D. L. Harrar II, M. R. Osborne. Computing Eigenvalues Of Ordinary Differential Equations. ANZIAM J. 44 (E). 2003: C313~C334
200 L.C. Kaufman. The LZ Algorthm to Solve the Generalized Eigenvalue Problem. SIAM J. Numer Anal. 1974, 11:997~1024
201 D. L. Harrar II, M. R. Osborne. Computing Eigenvalues of Ordinary Differential Equations. ANZIAM J. 44 (E). 2003: C313~C334
202 Gerard L.G.. Sleijpen, Jasper van den Eshof. On the Use of Harmonic Ritz Pairs in Approximating Internal Eigenpairs. Linear Algebra and its Applications. 2003, 358: 115~137
203 Michiel E. Hochstenbach, Gerard L.G. Sleijpen. Two-sided and Alternating Jacobi–Davidson. Linear Algebra and its Applications. 2003, 358: 145~172
204 Xiaolin Zhong, Mahidhar Tatineni. High-Order Non-Uniform Grid Schemes for Numerical Simulation of Hypersonic Boundary-Layer Stability and Transition. Journal of Computational Physics. 2003, 190: 419~458
205 Orhan Ayd?n, Ahmet Kaya. Laminar Boundary Layer Flow over a Horizontal Permeable Flat Plate. Applied Mathematics and Computation. 2005, 161: 229~240
206 Asai Asaithambi. A Second-order Finite-Difference Method for the Falkner–Skan Equation. Applied Mathematics and Computation. 2004, 156: 779~786
207 Timo Betcke, Heinrich Voss. A Jacobi–Davidson-Type Projection Method for Nonlinear Eigenvalue Problems. Future Generation Computer Systems. 2004, 20: 363~372
208 王伟志. 非平行流边界层稳定性问题研究. 南京航空航天大学博士论文. 2002: 19~36
209 张伟. 600MW 超临界汽轮机静叶设计技术实验验证. 哈尔滨工业大学硕士学位论文. 2006: 29~30
210 李雅武. 600MW 超临界汽轮机动叶设计技术实验验证. 哈尔滨工业大学硕士学位论文. 2006: 25~26
211 万秉忠. 超临界汽轮机调节级导叶设计技术的实验与数值研究. 哈尔滨工业大学硕士论文. 2006: 21~22
212 安柏涛,韩万金,王仲奇. 子午扩压对环形叶栅流道内旋涡发生和发展的影响. 航空动力学报. 2000,15(4):361~365
213 安柏涛,韩万金,王松涛,王仲奇.大扩张角子午流道型线对损失的影响. 推进技术. 2001,22(3):211~214
214 安柏涛,韩万金,王松涛,王仲奇.子午扩张流道中叶片积叠线形式对损失的影响. 推进技术. 2002,23(2):100~104
215 王仲奇,苏杰先,钟兢军. 弯曲叶片栅内减少能量损失机理研究的新进展. 工程热物理学报. 1994, 15(2):147~152
216 钟兢军,苏杰先,王仲奇. 压气机叶栅中应用弯叶片的研究. 航空动力学报. 1998,13(1): 7~12
217 陈绍文,陈浮,冯冬民,王仲奇. 叶片弯曲对不同折转角扩压叶栅冲角特性的影响. 航空动力学报. 2007, 22(3): 406~411