摘要
湍流是一种极为复杂的流动状态，直至现在，人们对湍流机理的认识尚不完善，仍在探索之中。湍流问题又是在工程技术中经常涉及到的重要难题，如何精确数值模拟湍流的复杂流场，成了湍流研究的一个重要目标。近些年发展起来的大涡模拟方法受到人们特别关注，本文采用该方法进行了航空燃气涡轮相关的湍流流场的精确数值模拟与拟序结构的机理性研究，这是与发动机性能的提高密切相关的，其研究工作是具有重要的理论意义和工程应用价值。
文中发展了高精度、高效率的可压缩流大涡模拟算法，主要包括：
1）导出可压缩流大涡模拟控制方程和无需近壁修正的动态亚格子模型，并在大涡模拟算法中引进计算低马赫数的先进预处理技术，扩展了可压缩流大涡模拟算法的应用范围。
2）在数值解法中，为了确保空间离散数值通量的高精度，对流项采用六阶WENOSYM格式离散、粘性项采用六阶紧致格式离散，并导出了紧致格式的相应系数；为了简化隐式迭代的矩阵形式，提出应用预处理之后的简化Roe Jacobians矩阵形式，推动了隐式预处理技术在工程中的应用。
3）为了更好的给定适用于壁湍流大涡模拟的进口扰动，采用一种先进的合成涡方法，经过计算检验，确认其仅需很短的计算域就可以得到完全发展湍流，为大涡模拟在工程上应用提供了适用的进口边界条件。
深入进行了相关的湍流边界层流场拟序结构及流动特性研究，主要包括：
1）分析了平板槽道湍流边界层内层的拟序结构。把计算得到的拟序结构特征参数与Cantwell B. J.的平壁湍流边界层拟序结构参数做了对比，以及将流场统计平均值与经验公式及DNS解作对比，得到了基本一致的结果；对于计算中发现的两种发卡涡包结构，经与实验结果对比，证实了其结构的合理性；在对拟序涡结构时空演化研究中，详细地展示出单侧涡腿的发卡涡的形成过程。上述对平壁湍流中发卡涡研究中的新成果，尚未见诸其他文献。
2）探讨了横向射流场中的发卡涡结构及射流脉冲控制发卡涡结构的优化气膜冷却方法。通过对稳定工况平板横向射流场的大涡模拟数值解的研究，分析了流场中典型的发卡涡对于射流场的影响，及发卡涡的发展演化过程，在此基础上结合其他文献的研究成果，从控制发卡涡的角度提出了射流进口方波脉冲控制优化气膜冷却的方法，并对不同脉冲频率下的射流场进行了大涡模拟计算分析，初步得到了方波脉冲使得发卡涡间歇出现，无发卡涡的间歇区间与射流出口脉冲波的“波谷”相对应的结论。此间歇区间的提出可以为今后涡轮气膜冷却设计提供一种新的思路。
3）展示了无气膜冷却和带气膜冷却的MT1涡轮导叶流场中不同转捩模式的拟序结构形态。通过对流场大涡数值模拟的研究，展示了叶片吸力面无气膜射流时激波诱导下分离转捩过程和湍流中的发卡涡无序且密集的分布形态，文中称此形态为发卡涡“森林”，研究了位于涡轮导叶不同位置的气膜射流在叶片表面产生的射流拟序结构的形态，显示了逆转捩过程影响下的涡拉伸结构。展示上述转捩过程的近壁涡结构形态，这种在高压涡轮的研究中还是第一次。
显然，本文进行的大涡模拟算法与湍流拟序结构的研究是密切相关的，高精度、高效率的可压缩流大涡模拟算法为湍流拟序结构的研究提供了技术支持，而槽道湍流、横向射流及涡轮导叶壁面流场的拟序结构和机理的研究为大涡模拟在涡轮中的实际应用提供了研究基础和理论依据。
Turbulence is a kind of very complex flow. Up until now, people on the understanding of themechanism of turbulence is not perfect, still in the exploration. Turbulence in the engineeringtechnology question also often involves the important problem. How accurate numerical simulation ofturbulence complex flow field, the turbulent research become into one of the most important goals. Inrecent years the development of Large Eddy Simulation method is special attention by people. In thisarticle, Large Eddy Simulation was used to carry out the accurate numerical simulation of turbulentflow field and the Basic theory research of Coherent structure，which turbulent flow field has closerelations with air gas turbine，and the improvement of the performance of the engine is closely relatedto its research work. It is has important theoretical significance and application value.
Compressible flow Large Eddy Simulation algorithm with high precision and high efficiencywas developed in the paper, its content mainly includes：
1) The governing Equations of the non-dimensional Large Eddy Simulation and dynamicsub-grid scale model specific form of this article is derived in the general curvilinear coordinatesystem. Then the preconditioned algorithm is used in the code to expand the scope of the program'scalculation, so that it can calculation of transonic flows and low-Mach number flows, such as the flowfield of turbine vane with the film cooling.
2) The finite volume methods take advantage of the integral form of the governing equation toachieve a algebraic discrete approximation for numerical calculations. In order to ensure generatednumber the discrete error did not exceed the influence of the sub-grid scale model, the numerical fluxwas calculated by six order precision WENOSYM scheme and Compact scheme. The WENOSYMscheme was adopted on calculation of the Convection flux. The Compact scheme was adopted oncalculation of the viscous flux and the specific coefficient was deduced.
In this paper, the implicit Newton iteration scheme was used for temporal discretization. Thenthe analytical S-W Jacobians formula and simplify Roe Jacobians formula of implicit Jacobiansmatrix was deduced. The engineering practicability of Roe Jacobians matrix was confirmed. Thiswork makes a good evolution for the implicit method.
3) In the process of computation, a given imported disturbance in the boundary layer is using asynthetic vortex approach. The computation result shows that the flow in calculation domaindeveloped turbulence after a short development section. The application of the approach is theengineering application of positive preparation.
The turbulent boundary layers fields related to Coherent structure and the flow characteristicswere further research in the paper. Its content mainly includes:
1）Coherent structure in the inner layer of the flat channel turbulent boundary layer is analyzed.Solution of the flow field statistical average was compared with the empirical formula and DNS result,and the characteristic parameters of large eddy coherent structures was compared with Cantwell’sparameters. The results of comparison were very well. The two kinds of hairpin vortex packetstructures of the calculated results were compared with experimental results to confirm its structure.Studying the temporal evolution process of coherent vortex structures, the hairpin vortices withunilateral vortex leg formation process was discussed. This conclusion of the hairpin vortices in theflat-wall turbulence is still not seen in the literature.
2）Hairpin vortex structure of the Jet into Cross-flow and the method of Pulsation optimizing filmcooling efficiency was discussed. On the research of the flat basis, the flow field of the Jet inCross-flow that was applied in the gas turbine film cooling is studied. Through the analysis of thestructure and development of the hairpin vortices in flow field, the flow’s characteristics of the Jet inCross-flow were learned. Then combined with the literatures, the idea that the hairpin vortices in themain body of jet are control by the pulsed jet is proposed. Through the analysis of the pulsed jet flowfield simulation results, the initial conclusions are that the pulsation controls the intermittent existenceof the hairpin vortices’ group and the interval between the hairpin vortices’ groups corresponding tothe frequency of pulsation.
3）Coherent structure form In the transition process on flow filed of MT1turbine vane is to show.Flow fields of the MT1turbine guide vane with film cooling and without film cooling were simulated.Without film cooling, coherent structures of shock-induced separated flow transition were showed onthe suction side of the blade. With film cooling, the forms of coherent structures that was produced byfilm cooling jet in different locations on blade surface were researched, and the influence thatcurvature of wall surface has an effect on jet’s structures were discussed, and the vortex stretching byinfluence of reverse transition were shown.
Obviously, in this paper the Large Eddy Simulation algorithm and to the research of theturbulence’s Coherent structure are closely related. The Large eddy simulation Algorithm providestechnical support for the research of Coherent structure, and the research provides researchfoundation and the theoretical basis for the practical application of the LES in flow field of turbinevane, that the research is related with flow field of flat，the Jet into Cross-flow，and the turbine vane.
引文
[1]张兆顺.湍流.北京:国防工业出版社,2002.
[2]陈懋章.粘性流体动力学基础.北京:高等教育出版社,2004.
[3]是勋刚.湍流.天津:天津大学出版社,1994.
[4] Corrsin S, Kistler A L. The free-stream boundaries of turbulent flows. NACA TN3133,1955.
[5]范保春,董刚,张辉.北京:湍流控制原理.国防工业出版社,2011:47~100.
[6] Kline S J, Reynolds W C, Schraub F A, et al. The structure of turbulent boundary layer. J. FluidMech.,1967,30:741-773.
[7]林建忠.湍流的拟序结构.上海:机械工业出版社,1995.
[8] Head M R, Bandyopadhyay P. New aspects of turbulent boundary layer structure,1981,107(4):297~337.
[9] Raupach M R. Conditional statistics of reynolds stress in rough-wall and smooth-wall turbulentboundary layers,1981,108:363~382.
[10] Cantwell B J. Organized motions in turbulent flows. Annual Review of Fluid Mechanics,1981,(13):457.
[11] Robinson S K. Coherent motions in turbulent boundary layer. Annual Review of Fluid Mechanics,1991,72:336~339.
[12] Tsinober A, Kit E, Dracos T. Experimental investigation of the field of velocity gradients inturbulent flows.1992,242:169~192.
[13] Saddoughi S G, Veeravalli S V. Local isotropy in turbulent boundary layers at high reynoldsnumber.1994,268:333~372.
[14] Adrian R J, Meinhart C D, Tomkins C D. Vortex organization in the outer region of the turbulentboundary layer. J. Fluid Mech.,2000,422:1~54.
[15] Liu Z, Adrian R J, Hanratty T J. Large-scale modes of turbulent channel flow: transport andstructure. J. Fluid Mech.,2001,448:53~80.
[16] Delo C J, Kelso R M, Smits A J. Three-dimensional structure of a low-reynolds-numberturbulent boundary layer,2004,512:47~83.
[17] Sheng J, Malkiel E, Katz J. Buffer layer structures associated with extreme wall stress events in asmooth wall turbulent boundary layer. J. Fluid Mech.,2009,633:17~60.
[18] Dennis D J C, Nickels T B. Experimental measurement of large-scale three-dimensionalstructures in a turbulent boundary layer. Part1: Vortex packets. J. Fluid Mech.,2011,673:180~217.
[19]张德良.计算流体力学教程.高等教育出版社,2010:32～34.
[20] Bradshaw P. Turbulence modeling with application to turbomachinery. Prog. Aerospace Sci.,1996,32:575~624.
[21] Sagaut P, Deck S, Terracol M. Multiscale and multiresolution approaches in turbulence. London:Imperial College Press,2006.
[22] Pope S B. Turbulent flows. Cambridge: Cambridge University Press,2000.
[23] Orszag S A, Patterson G S. Numerical simulation of three-dimensional homogeneous isotropicturbulence. Physical Review Letters,1972,28:76~79.
[24] Kim J, Moin P, Moser R. Turbulence statistics in fully developed channel flow at low Reynoldsnumber. J. Fluid Mech.,1987,177:133-166.
[25] Wallace J. Highlights of fifty years of turbulent boundary layer research. Turbulence ColloquiumMarseille,2011.
[26] Moin P, Mahesh K. Direct numerical simulation: a tool in turbulence research. Annu. Rev. FluidMech.,1998,30:539~578.
[27] Jimenez J, Hoyas S, Simens M P,et al. Turbulent boundary layers and channels at moderateReynolds numbers. J. Fluid Mech.,2010,657:335~360.
[28] Wu Xiaohua, Moin P. Direct numerical simulation of turbulence in a nominally zero-pressuregradient flat-plate boundary layer. J. Fluid Mech,2009,630:5~41.
[29] Wu Xiaohua. Establishing the generality of three phenomena using a boundary layer withfreestream passing wakes. J. Fluid Mech.,2010,664:193~219.
[30] Zaki T, Durbin P A. Continuous mode transition and the effects of pressure gradient. J. FluidMech.,2006,563:357~388.
[31] Krishnan L, Sandham N D. Strong interaction of a turbulent spot with a shock-induced separationbubble. Phys. Fluids,2007,19(016102):1~11.
[32]陈林,唐登斌,刘小兵,等.边界层转捩过程中环状涡和尖峰结构的演化.中国科学G辑:物理学力学天文学,2009,Vol.39(10):1520～1526.
[33]陈林,唐登斌,刘超群.转捩边界层中次生流向涡演化的数值研究.应用数学和力学,2011,Vol.32(4):428～436.
[34] CHEN Lin, TANG DengBin, LU Ping, et al. Evolution of the vortex structures and turbulentspots at the late-stage of transitional boundary layers.2011, Vol.54(5):986~990.
[35]陈林,唐登斌,刘超群.转捩边界层中流向条纹的新特性.物理学报,2011,Vol.60(9):094702.
[36] Wu X, Durbin P A. Evidence of longitudinal vortices evolved from distorted wakes in a turbinepassage. J. Fluid Mech.,2001,446:199-228.
[37] Wissink J G, Rodi W. Direct numerical simulations of transitional flow in turbomachinery.Journal of Turbomachinery,2006,128:668-678.
[38] Wagner C, Hüttl T, Sagaut P. Large-eddy simulation for acoustics. Cambridge: CambridgeUniversity Press,2007.
[39] Sagaut P. Large eddy simulation for incompressible flows: an introduction,3rd Edition. Berlin:Springer-Verlag,2006.
[40]张兆顺.湍流大涡数值模拟的理论与应用.清华大学出版社,2008.
[41] Berselli L C, Iliescu T, Layton W J. Mathematics of Large Eddy Simulation of Turbulent Flows.Springer Berlin Heidelberg New York,2006.
[42] Lesieur M, Metais O, Comte P. Large-eddy simulation of turbulence. Cambridge: CambridgeUniversity Press,2005.
[43] Jarrin N. Synthetic inflow boundary conditions for the numerical simulation of turbulence,[Ph.D.Dissertation]. Manchester, United Kingdom: School of Mechanical, Aerospace and CivilEngineering,The University of Manchester,2008.
[44] Addad Y, Laurence D, Talotte C, et al. Large eddy simulation of a forward-backward facing stepfor acoustic source identification. International Journal of Heat and Fluid Flow,2003,24:562~571.
[45] Kraichnan R H. Eddy viscosity in two and three dimensions. J. Atmos. Sci.,1976,33:1521~1536.
[46] Speziale C G, Erlebacher G, Zang T A, et al. The subgrid-scale modeling of compressibleturbulence. Phys. Fluids,1988,31(4):940~942.
[47] Moin P, Squires K, Cabot W, et al. A dynamic subgrid-scale model for compressible turbulenceand scalar transport. Phys. Fluids A,1991,3(11):2746~2757.
[48] Erlebacher G, Hussaini M Y, Speziale C G, et al. Toward the large-eddy simulation ofcompressible turbulent flows. J. Fluid Mech.,1992,238:155~185.
[49] Vreman B, Geurts B, Kuerten H. Subgrid-modeling in LES of compressible flow. Appl. Sci. Res.,1995,54:191~203.
[50] Piomelli U. Large-eddy simulation: achievements and challenges. Progress in AerospaceSciences,1999,35:335~362.
[51] Pope S B. Ten questions concerning the large-eddy simulation of turbulent flows. New Journal ofPhysics,2004,35(6):1~24.
[52] Yan H, Knight D, Zheltovodov A. Large-eddy simulation of supersonic flat-plate boundarylayers using the monotonically integrated large-eddy simulation (MILES) technique. Journal ofFluids Engineering,2002,124:868~875.
[53] Grinstein F F. Vortex dynamics and entrainment in rectangular free jets. Journal of FluidMechanics,2001,437:69~101.
[54] Grinstein F F, Fureby C. Recent progress on MILES for high Reynolds number flows. Journal ofFluids Engineering,2002,124:848~861.
[55] Schlatter P, Stolz S, Kleiser L. LES of transitional flows using the approximate deconvolutionmodel. Int. J. Heat and Fluid Flow,2004,25:549~558.
[56] Rembold B, Kleiser L. Noise prediction of a rectangular jet using large-eddy simulation. AIAAJournal,2004,42:1823~1831.
[57] Loginov M S, Adams N A, Zheltovodov A A. Large-eddy simulation ofshock-wave/turbulent-boundary-layer interaction. J. Fluid Mech.,2006,565:135~169.
[58] Cui G, Xu C, Fang, L, et al. A new subgrid eddy-viscosity model for large-eddy simulation ofanisotropic turbulence. J. Fluid Mech.,2007,582:377~397.
[59] Gravemeier V. A consistent dynamic localization model for large eddy simulation of turbulentflows based on a variational formulation. Journal of Computational Physics,2006,218:677~701.
[60] You D, Moin P. A dynamic global-coefficient subgrid-scale eddy-viscosity model for large-eddysimulation in complex geometries. Phys. Fluids,2007,19(10):1~8.
[61] Moin P. Advances in large-eddy simulation methodology for complex flows. Journal of Heat andFluid Flow,2002,23:710~720.
[62] Rodi W. DNS and LES of some engineering flows. Fluid Dynamics Research,2006,38:145~173.
[63] Kobayashi T. Large eddy simulation for engineering applications. Fluid Dynamics Research,2006,38:84~107.
[64] Bouffanais R. Advances and challenges of applied large-eddy simulation. Computers&Fluids,2010,39:735~738.
[65] You D, Mittal R, Wang M, et al. Computational methodology for large-eddy simulation oftip-clearance flows. AIAA Journal,2004,42:271~279.
[66] You D, Wang M, Moin P, et al. Vortex dynamics and low-pressure fluctuations in thetip-clearance flow. Journal of Fluids Engineering,2007,129:1002~1014.
[67] Hirsch C. Numerical computation of internal and external flows, Vol.1: fundamentals ofcomputational fluid dynamics,2nd Edition. Burlington: Butterworth-Heinemann,2007.
[68] Pitsch H. Large-Eddy simulation of turbulent combustion. Annu. Rev. Fluid. Mech.,2006,38:453~482.
[69] Sescu A. Towards computational aeroacoustics prediction of realistic turbofan broadband noiseusing synthetic turbulence modeling,[Ph.D. Dissertation]. The University of Toledo,2011.
[70]赵海洋,刘伟,万国新,等.加权基本无振荡格式研究进展.力学季刊,2005,26(1):87～94.
[71] Titarev V A, Toro E F. Finite-volume WENO schemes for three-dimensional conservation laws.Journal of Computational physics,2004,201:238~260.
[72] Matin M P, Taylor E M, Wu M, et al. A bandwidth-optimized WENO scheme for the effectivedirect numerical simulation of compressible turbulence. Journal of Computational physics,2006,220:270~289.
[73] Lele S K. Compact finite difference schemes with spectral-like resolution. Journal ofComputational Physics,1992,103:16~42.
[74] Fu Dexun, Ma Yanwen. On efficiency and accuracy of numerical methods for solving theaerodynamics equations. Proceedings of the International Symposium on Computational FluidDynamics,1989.
[75] Fu Dexun, Ma Yanwen. High Resolution Schemes. Computation Fluid dynamics review,1995.
[76] Lacor C, Smirnov S, Baelmans M. A finite volume formulation of compact central schemes onarbitrary structured grids. Journal of Computational Physics,2004,198:535~566.
[77] Crabb D, Durao F G. A round jet normal to cross-flow. Journal of Fluid Engineering,1981,103(1):142~153.
[78]Goldstein R J, Eckert R G. Effect of surface roughness on film cooling performance. Journal ofEngineering for Gas Turbine and Power,1998,114(10):747~755.
[79] Fric T F, Roshko A, Vortical structure in the wake of a transverse jet. Journal of Fluid Mechanics,1994,279:1~47.
[80] Sherif S A, Pletcher R H. Measurements of the flow and turbulent characteristics of round jets incrossflow. Journal of Fluid Engineering,1989,111:165~171.
[81] Karagozian A R. An analytical model for the vorticity associated with a transverse jets. AIAA J.,1986,24:429~436.
[82] Hahn S, Choi H. Unsteady simulation of jets in a cross flow. Journal of Computational Physics,1997, V134:342~356.
[83] Muldoon F, Acharya S. Numerical investigation of the dynamical behavior of a row of squarejets in crossflow over a surface. ASME Paper No.99-GT-217,1999.
[84] Yuan L, Street R L, Ferziger J H. Large eddy simulations of a round jet in crossflow. Journal ofFluid Mechanics,1999,379:71~104.
[85] Kapadia S, Roy S. Detached eddy simulation of turbine blade cooling. AIAA PaperNo.2003-3632,2003.
[86] Acharya S. Large Eddy Simulations and Turbulence Modeling for Film Cooling.NASA/CR-1999-209310,1999.
[87] Acharya S, Tyagi M, Hoda A. Flow and heat transfer predictions for film cooling, heat transfer ingas turbine systems, Ann. N.Y. Acad. Sci.,2001,934:110~125.
[88] Tyagi M, Acharya S. Large eddy simulation of film cooling flow from an Inclined cylindrical Jet.Journal of Turbomachinery,2003,125:734~742.
[89] Lavrich P L, Chiappetta L M. An investigation of jet in a cross flow for turbine film coolingapplications. East Hartford: United Technologies Research Center, UTRC Report No.90-04,1990.
[90] Sinha A K, Bogard D G, Crawford M E. Film-cooling effectiveness downstream of a single rowof holes with variable density ratio. Journal of Turbomachinery,1991,113:442~449.
[91] Liu K L, Pletcher R H, Large eddy simulation of discrete-hole film cooling in a flat plateturbulent boundary layer. AIAA Paper No.2005-4944,2005.
[92]Majander P, Siikonen T. Large eddy simulation of a round jet in a crossflow. International Journalof Heat and Fluid Flow,2006,27:402~415.
[93] Guo X, Schr der W, Meinke M, Large eddy simulations of film cooling flows. Computers&Fluids,2006,35:587~606.
[94] Ioulia V I, Sanjiva K L. Large eddy simulation of film-cooling above the flat surface with a largeplenum and short exit holes. AIAA Paper No.2006-1102,2006.
[95] Pietrzyk J R, Bogard D G, Crawford M E. Hydrodynamic measurements of jets in crossflow forgas turbine film cooling applications. Journal of Turbomachinery,1989,111:139~145.
[96] Rozati A, Tafti D K. Effect of coolant-mainstream blowing ratio on leading edge film coolingflow and heat transfer-LES Investigation. International Journal of Heat and Fluid Flow,2008,29:857~873.
[97] Mendez S, Nicoud F. Large-eddy simulation of a bi-periodic turbulent flow with effusion.Journal of Fluid Mechanics,2008,598:27~65.
[98] Renze P, Schr der W, Meinke M. Large eddy simulation of film cooling flows with variabledensity jets. Flow Turbulence Combust,2008,80:119~132.
[99]郭婷婷,刘建红,李少华,等.气膜冷却流场的大涡模拟.中国电机工程学报,2007,27(11):83～87.
[100]郭婷婷,邹晓辉,刘建红,等.扇形喷孔气膜冷却流场的大涡模拟.动力工程,2008,28(2):185～189.
[101]刘斌,任丽芸,叶建,等.方孔横向射流的大涡模拟研究.航空科学技术,2009,(2):40～43.
[102]刘宁,孙纪宁.基于大涡模拟分析气膜冷却的湍流场.航空动力学报,2010,25:1971～1977.
[103] Richard H P, Liu K L, Qin Z H, et al. Application of large eddy simulation to cooling and flowproblems in aeropropulsion systems. Arlington: Air Force Office of Scientific Research,ISU-MEP-CFD-0904,2004.
[104] Sieverding C H. Recent progres standing of basic aspects of secondary flows in turbine bladepassages. Journal of Engineering Gas Turbines Power,1985,107:248~257.
[105] Langston L S. Secondary flows in axial turbines-a review. Annals of the New York Academy ofSciences,2006,934:11~26.
[106] Jahanmier M. Boundary layer transitional flow in gas turbines,[Research report]. G teborg,Sweden, Chalmers university of technology,2011.
[107]陈懋章.航空叶轮机的气动力学问题.航空航天工业部科技情报研究所,压气机文集,1989,272~283.
[108] Ronald S B. A review of shaped hole turbine film-cooling technology. Journal of Heat Transfer,2005,127:441~453.
[109] Wang H P, Olson S J, Goldstein R J, et al. Flow visualization in a linear turbine cascade of highperformance turbine blades, ASME J. Turbomachinery,1997,119:1~8.
[110] Mayle R E. The role of laminar-turbulent transition in gas turbine engines. ASME Journal ofTurbomahcinery,1991,113:509~536.
[111] Mayle R E. Unsteady Multimode Transition in Gas Turbine Engines. AGARD PEP80,1992.
[112] Halstead D E, Wisler D C, Okiishi T H, et al. Boundary layer development in axial compressorsand turbines: part1of4-composite picture. ASME J. Turbomach.,1997,119:114~127.
[113] Halstead D E, Wisler D C, Okiishi T H, et al. Boundary layer development in axial compressorsand turbines: part2of4-compressors. ASME J. Turbomach.,1997,119:426~444.
[114] Halstead D E, Wisler D C, Okiishi T H, et al. Boundary layer development in axial compressorsand turbines: part3of4-LP turbines. ASME J. Turbomach.,1997,119:225~237.
[115]Halstead, D. E., Wisler, D. C., Okiishi, T. H., et al. Boundary layer development in axialcompressors and turbines:part4of4-computations and analyses. ASME J. Turbomach.,1997(119):128–139
[116]Schulte V, Hodson H P. Unsteady wake-induced boundary layer transition in high lift LPturbines. ASME J. Turbomach,1998,120:28~35.
[117] Koyabu E, Funazaki K, Kimura M. Effects of periodic wake passing upon bypass Transition ofblade boundary layer and unsteady loss. Proceedings of the International Gas TurbineCongress-Tokyo,2003.
[118] Anthony R J, Jones T V, LaGraff J E. High frequency surface heat flux imaging of bypasstransition. Transactions of the ASME, J. of Turbomachinery,2005,127:241~250.
[119] Schlichting H, Gersten K, Boundary layer theory.8thRevised and Enlarged Edition,2000.
[120] Spalart P R, Strelets M K. Mechanisms of transition and heat transfer in a separation bubble.Journal of Fluid Mechanics,2000,403:329~349.
[121] Volino R J. Separated flow transition under simulated low-pressure turbine airfoil conditions:Part2-turbulence spectra. ASME Journal of Turbomachinery,2002,124:656~664.
[122] Volino R J. Separated flow transition under simulated low-pressure turbine airfoil conditions:part1-mean flow and turbulence statistics. ASME Journal of Turbomachinery,2002,124:656~664.
[123] Volino R J, Hultgren L S. Measurements in separated and transitional boundary layers underlow-pressure turbine airfoil conditions. Transactions of the ASME, J. of Turbomachinery,2001,123:189~197.
[124] Mick W J, Mayle R E. Stagnation film cooling and heat transfer, including its effect within thehole pattern. ASME J. of Turbomachinery,1988,110:66~72.
[125] Houtermans R, Coton T, Arts T. Aerodynamic performance of a very high lift LP turbine bladewith emphasis on separatin perdiction. ASME Journal of Turbomachinery,2004,126:406~413.
[126] Warren J M, Metzger D E. Heat transfer with film cooling in the presence of laminarizingmainstream. ASME Paper72-HT-11,1972.
[127] Hodson H P. Boundary layer and loss measurements on the rotor of an axial-flow turbine.ASME J.of Engineering for Gas Turbines and Power,1984,106:391~399.
[128] Raverdy B, Mary I, Sagaut P, et al. High-resolution large-eddy simulation of flow aroundlow-pressure turbine blade, AIAA J.,2003,41:390~397.
[129]吴子牛.计算流体力学基本原理.北京:科学出版社,2001.
[130] Wang Xiao. A preconditioning algorithm for turbo machinery viscous flow simulation,[Ph. D.Dissertation].Mississippi:The Mississippi State University,2005.
[131] Vreman B, Geurts B, Kuerten H. A priori tests of large eddy simulation of compressible planemixing layer, J. Eng. Math.,1995,29:299~327.
[132] Knight D, Zhou G, Okong'o N, et al. Compressible large eddy simulation using unstructuredgrids. AIAA Paper98-0535,1998.
[133]《数学手册》编写组.数学手册.北京:高等教育出版社,1979.
[134]关晖.湍流射流的大涡模拟及其动力学特性研究,[博士学位论文].江苏南京:河海大学,2005.
[135] Moin P, Kim J. Numerical investigation of turbulent channel flow, J.Fluid Mech.,1982,118:341~356..
[136] Yakhot A, Orszag S A, Yakhot V, et al. Renormalization group formulation of large-eddysimulation. J.Sci.Comput,1989,(4):139~145..
[137] Lesieur M. Turbulence in fluids. Martinus Nijhoff, Dordrecht, The Netherlands,1987.
[138] Germano M, Piomelli U, Moin P, et al. A dynamic subgrid-scale eddy viscosity model.Phys.Fluids A3,1991:1760~1781.
[139] Spyropoulos T, Blaisdell A. Large eddy simulation of a spatially evolving compressibleboundary layer flow. AIAA. Paper97-0429.
[140] Squires D. Dynamic subgrid scale modeling of compressible turbulence. Annual ResearchBriefs, Center for Turbulent Research.:207-233
[141] Lilly D K. A proposed modiflcation of the Germano subgrid scale closure method. Phys, Fluids,1992, A4:633~657.
[142] Yang K S, Ferziger J H. Large-eddy simulation of turbulent obstacle flow using a dynamicsubgrid-scale model. AIAA Journal,1993,31(8):1406~1413.
[143] Zang Y, Street R.L, Koseff J R. A dynamic mixed subgrid-scale model and its application toturbulent recirulating flows. Phys.Fluids,1993, A5(12):3186~3196.
[144] Najjar F M, Tafti D K. Study of discrete test filters and finite difference approximations for thedynamic subgrid-scale stress model. Physics of Fluids,1996,8(4):1076~1088.
[145] Wang Xiao, Sheng Chunhua. Numerical study of a preconditioned algorithm for rotational flows.AIAA-2005-5126, Proceedings of the17th AIAA Computational Fluid DynamicsConference.Westin Harbor Castle, Toronto, Ontario, Canada:2005.
[146] Chorin A J, A numercial method for solving incompressible viscous flow problems. Journal ofComputation Physics,1967,(2):12~26.
[147] Briley W R, McDonald H, Shamroth S J. A low mach number euler formulation and applicationto time iterative LBI scheme, AIAA J.,1983,21(10):1467~1469.
[148] Turkel E. Acceleration to a steady state for the euler equations. ICASE Report84~32,1984.
[149] Choi D, Merkle C L. Application of time-iterative schemes to incompressible flow. AIAAJournal,1985,23(10):1518~1524.
[150] Choi D, Merkle C L. The application of preconditioning to viscous flows. Journal ofComputational Physics,1993,105:207~223.
[151] Turkel E. Preconditioned mehtods for solving the incompressible and low speed compressibleequations. Journal of Computational Physics,1987,72:277~298.
[152] Turkel E. Review of preconditioning methods for fluid dynamics. Applied NumericalMathematics,1993,12:257~284.
[153] Wang W, Pletcher R H. On the large eddy simulation of a turbulent channel flow withsignificant heat transfer. Phys Fluids,1996,8(12):54~66.
[154] Chidambaram N, Pletcher R H. A collocated-grid fully coupled algorithm for large eddysimulation of incompressible and compressible flows. Number Heat transfer Part B,2000,37:1~23.
[155] Lessani B, Ramboer J, Lacor C. Efficient large-eddy simulation of low mach number flowsusing preconditioning and multigrid. Int J Comput Fluid Dyn,2004,(3):221~233.
[156] Alkishriwi N, Meinke M, Schroder W. A large-eddy simulation method for low mach numberflows using preconditioning and multigrid. Computers&Fluids,2006(35):1126-1136.
[157] Briley W R, Taylor L K, Whitfield D L. High-resolution viscous flow simulations at arbitrarymach number. Journal of Computational Physics,2003,184(1):79~105.
[158]傅德薰,马延文.计算流体力学.北京:高等教育出版社,2002:11-197.
[159]陶文铨.数值传热学.西安:西安交通大学出版社,2001:15-186.
[160] Blazek J. Computational fluid dynamics: principles and applications,2nd Edition. Amsterdam:Elsevier,2005.
[161] Anderson W K, Thomas J L, Van Leer B. Comparison of finite volume flux vector splitting foreuler equations. AIAA Journal,1986,(24):1453~1460.
[162] Garnier E, Mossi M, Sagaut P, et al. On the use of shock capturing schemes for large eddysimulation. J Comp Phys,1999,153:273-311.
[163]朱君,赵宁.一种MWENO格式的构造和应用.空气动力学学报,2005,23(3):330~333.
[164] Chen J P. Unsteady three-dimensional thin-layer navier-stokes solutions for turbomachinery intransonic Flow,[Ph. D. Dissertation]. Mississippi: Mississippi State University,1991.
[165] Antony J.Time dependent calculations using multigrid with application to unsteady flows pastairfoils and wings. AIAA paper91-1956,1991.
[166]史万里,葛宁,SHENG Chunhua.计算全马赫数下粘性流动的隐式算法.空气动力学学报,2009,27(5):566~571.
[167]陈国良.并行算法实践.北京:高等教育出版社,2000.
[168]都志辉.高性能计算并行编程技术--MPI并行程序设计.北京:清华大学出版社,2001.
[169] Niceno B. An unstructured parallel algorithm for large eddy and conjugate heat transfersimulations,[Ph. D. Dissertation]. Delft: Delft University.2001.
[170] Haller G. An objective definition of a vortex. Journal of Fluid Mechanics,2005,525:1~26.
[171] Wu J Z, Xiong A K, Yang Y T. Axial stretching and vortex definition. Physics of Fluids,2005,17:1~4.
[172] Dubief Y, Delcayre F. On coherent-vortex identification in turbulence. Journal of Turbulence,2000,11:1~22.
[173] Bohr E. Inflow generation technique for large eddy simulation of turbulent boundary layers,[Ph.D. Dissertation]. New York: Rensselaer Polytechnic Institute Troy,2005.
[174] Shan H, Jiang L, Zhao W, et al. Large eddy simulation of flow transition in a supersonicflat-plate boundary layer. Reno,NV:37thAIAA Aerospace Sciences Meeting and Exhibit.1999:11~14.
[175] Liu Chaoqun. High performance computation for DNS/LES. Applied Mathematical Modelling,2006,30:1143~1165.
[176] Druault P, Lardeau S, Bonnet J P, et al. Generation of three-dimensional turbulent inletconditions for large-eddy simulation. AIAA Journal,2004,42(3):447~456.
[177] Spalart P R. Direct simulation of a turbulent boundary layer up to Reθ=1410. Journal of FluidMechanics,1988,187:61~98.
[178] Lund T S, Wu X, Squires K D. Generation of turbulent inflow data for spatially-developingboundary layer simulations. J. Comp. Phys,1998,140:233~258.
[179] Sagaut P, Garnier E, Tromeur E, et al. Turbulent inflow conditions for large-eddy simulation ofcompressible wall-bounded flows. AIAA Journal,2004,42(3):469~477.
[180] Hoshiya M. Simulation of multi-correlated random processes and application to structuralvibration problems. Proc. JSCE,1972, No.204:121~128.
[181] Kondo K, Murakami S, Mochida A. Generation of velocity fluctuations for inflow boundarycondition of LES. Journal of Wind Engineering and Industrial Aerodynamics,1997,67:51~64.
[182] Sandham N D, Yao Y F, Lawal A A. Large-eddy simulation of transonic turbulent flow over abump. Inernational Journal of Heat and Fluid Flow,2003,24:584~595.
[183] Jarrin N, Benhamadouche S, Laurence D, et al. A Synthetic-eddy-method for generating inflowconditions for large-eddy simulations. Stockholm: Symposium on Hybrid RANS-LES Methods,2005.
[184] Schoppa W, Hussain F. Numerical study of near-wall coherent structures and their control inturbulent boundary layers. Sixteenth International Conference on Numerical Methods in FluidDynamics, Springer-Verlag:1998, Volume515. ISBN978-3-540-65153-6.
[185] Schoppa W, Hussain F. Coherent structures generation in near-wall turbulence. J. Fluid Mech.,2002,453:57~108.
[186] Herbert T. Secondary instability of boundary laryers. Annu. Rev. Fluid Mech.,1998,20:487~526.
[187]史万里,葛宁,葛松林.斜管横向射流的大涡模拟并行计算.中国航空学会第一届航空发动机数值仿真与数字化设计学术交流会,北京,2008:187-190.
[188] Haven B A, Kurosaka M. Kidney and anti-kidney vortices in cross flow jets. J.Fluid Mech,1997,352:27~64.
[189]吴介之,马晖扬,周明德.涡动力学引论.北京:高等教育出版社,1993:77～78.
[190] Yuen C H N, Martinez-Botas R F. Film cooling characteristics of a single round hole at variousstreamwise angles in a crossflow: PartΙ effectiveness. International Journal of Heat and MassTransfer,2003,46:221~235.
[191] Zhou J, Adrian R J, Balachandar S, et al. Mechanism for coherent packets of hairpin vortices inchannel flow. J. Fluid. Mech.,1999, vol.387:353~396.
[192] Abhari R S. Impact of rotor-stator interaction on turbine blade film cooling. Journal ofTurbomachinery,1996,118:123~133.
[193] Burdet A, Abhari R S. Influence of near hole pressure fluctuation on the thermal protection of afilm-cooled flat plate. Journal of Heat Transfer,2009, Vol.131/022202-1.
[194] Abhari R S, Epstein A H. An experimental study of film cooling in a rotating transonic turbine.ASME J. Turbomach.,1994,116:63–70.
[195] Heidmann J D, Lucci B L, Reshotko E. An experimental study of the effect of wake passing onturbine blade film cooling. ASME J. Turbomach.,1997,123(2):214~221.
[196] Bons J P, Rivir R B, MacArthur C D, et al. The effects of unsteadiness on film coolingeffectiveness. Proceedings of the33rd AIAA Aerospace Scences Meeting, Reno, NV, Paper No.AIAA95-0306,1995.
[197] Ligrani P M, Gong R, Cuthrell J M, et al. Bulk flow pulsations and film cooling—I. injectantbehavior. Int. J. Heat Mass Transfer,1996,39:2271~2282.
[198] Ligrani P M, Gong R, Cuthrell J M, et al. Bulk flow pulsations and film cooling—II. flowstructure and film effectiveness. Int. J. Heat Mass Transfer,1996,39:2283~2292.
[199] Bell C M, Ligrani P M, Hull W A, et al. Film cooling subject to bulk flow pulsations: effects ofblowing ratio, freestream velocity, and pulsation frequency. Int. J. Heat Mass Transfer,1999,42:4333~4344.
[200] Gad-el-Hak M, Pollard A, Bonnet J P. Flow Control Fundamentals and ractices. Germany:Springer-Verlag Berlin Heidelberg,1998.
[201] Ekkad S V, Ou S, Rivir R B. Effect of jet pulsation and duty cycle on film cooling from a singlejet on a leading edge model. ASME Paper IMECE2004-60466.
[202] Coulthard S M, Volino R J, Flack K A. Effect of jet pulsing on film cooling, part1:effectiveness and flowfield temperature results. ASME Journal of Turbomachinery,2006,129:232~246.
[203] Coulthard S M, Volino R J, Flack K A. Effect of jet pulsing on film cooling, part2: heattransfer results. ASME Turbo Congress and Expo2006, Barcelona, Spain,2006.
[204] Kartuzova O, Danila D, Ibrahim M B. CFD simulation of jet pulsation effects on film cooling offlat plates. ASME paper GT2008-50284.
[205] Rutledge J L, King P I, Rivir R. CFD predictions of pulsed film cooling heat flux on a turbineblade edge. ASME paper IMECE2008-67276.
[206]康顺,马丽.脉动冷却流对冷却孔出口附近流动结构的影响.工程热物理学报,2008,29(9):1483～1485.
[207] Muldoon F, Acharya S. DNS study of pulsed film cooling for enhanced cooling effectiveness.International Journal of Heat and Mass Transfer,2009,52:3118~3127.
[208] Salvadori S, Montomoli F, Martelli F. Aerothermal study of the unsteady flow field in atransonic gas turbine with inlet temperature distortions. Journal of Turbomachinery,2011,133:031030-1.
[209]Montomoli F, Adami P, Gatta S D. Conjugate heat transfer modelling in film cooled blades.Proceedings of ASME Turbo Expo2004Power for Land, Sea, and Air, Vienna, Austria,2004.
