摘要
压气机性能的进一步的提高很大程度上依赖于我们对其内部非定常流动机理及相应损失机制的认识。数值模拟的方法在这方面发挥着日益重要的作用,但是还面临很多问题。本文将在计算压气机内部复杂非定常流动的数值方法和合理衡量压气机的损失等方面开展工作,并基于这些工作,对跨声速压气机级Rotor35/Stator37内的损失进行分析。
在数值方法方面,构造了以下三个不同程度上反应多维效应的数值格式,(1)将精度和稳健性都已得到广泛认可的二维旋转迎风格式推广为三维。(2)通过在计算数值通量时近似求解完整的流体力学方程来体现多维效应的影响,本文构造了多维输运格式。对于粘性流动,该格式无粘通量的计算能够考虑粘性通量的影响。(3)基于线化多维欧拉方程的次特征线理论构造了考虑无限多方向影响的局部演化迦辽金格式。这三种方法的共同特点是相对于已有的考虑多维效应的格式更加简单、高效,且可以直接推广到非结构网格的计算。本文将三维旋转迎风格式格式应用到自行开发的多级叶轮机械模拟程序中。数值验证表明多维格式在模拟跨声速压气机内复杂流动方面有一定优势。
在衡量压气机内损失方面,本文基于热力学定律,在有用功分析的框架提出了一种相比现有损失评估方法更适于非定常流场局部损失分析的损失评估参数-损失功,其强度量-损失功强度便于用来将流场结构与损失联系起来。这两个参数物理意义明确,能够被用来方便的、定量的研究局部区域内由于不可逆过程导致的熵产引起的损失。相比于先前同类方法,这两个参数能够考虑具体流动结构对于局部熵增的影响,从而能够更准确的衡量局部自身熵产的大小。这两个参数为压气机的设计、优化和改型提供了一个有效工具。
To further improve the performance of the compressor in the aero-engine and other gas-turbines, it is of great importance that the mechanism of the unsteady flow in the compressor is well understood. In this thesis, efforts are devoted to developing advanced numerical methods to simulate the complex unsteady flow field in the compressor and constructing reasonal parameters to measure the loss in the compressor. Based on the achievements in these two aspects, the unsteady loss in a one-stage transonic compressor is analyzed.
In the aspect of numerical method, three numerical schemes which can take multi-dimensional effects into account are developed. 1) Extension of a two-dimensional rotated Riemann solver, which has already proven its excellent robustness, to three-dimensional system. 2) A multi-dimensional upwind scheme was developed by computing the numerical fluxes at cell interfaces through solving full governing equations. This scheme can include the viscous contribution during the evaluation of the inviscid fluxes of the Navier-Stokes equations. 3)A finite volume local evolution Galerkin (FVLEG) method which is based on the bicharacteristics for linear (or linearized) hyperbolic systems were derived. The common advantages of the three schemes are simple, efficient and can be extended to unstructured grid directly. The 3D rotated Riemann solver has been already integrated into our in-house code for the compressor simulation. The numerical simulations show that the multi-dimensional scheme has better abilities to capture the discontinuities in the transonic compressor flow field.
The previously developed loss audit parameters coming from the steady compressor design system do not fit the measurements of the loss generation in some local regions. The values of these parameters usually reflect the accumulating loss of a fluid element or a system. Because flows in compressor are essentially unsteady and because it is meaningful to know the influence of some design modifications on the local loss, it is therefore necessary to develop new methods to measure the loss generation in particular region of the flow field. Based on the first and second laws of thermodynamics, an expression of irreversibility for arbitrary control volume has been derived under exergy analysis framework. The intensity of the irreversibility thus computed reveals relationship between the loss generation and flow structures. Irreversibility and its intensity can provide relevant information in compressor design and optimization.
引文
[1] Nicholson, J H. Experimental and theoretical studies of the aerodynamic and thermal performance of modern gas turbine blades. D.Phil. Thesis, University of Oxford, 1981.
[2] Greitzer E M. Thermodynamics and Fluid Mechanics of Turbomachinery. Volume II, NATO AS 1 Series, Series E: Applied Sciences, No.9713, 1985.
[3]陆亚钧.叶轮机械非定常流动.北京航空航天大学出版社,1991.
[4] Van Zante DE, To WM, Chen JP. Blade Row Interaction Effects on the Performance of a Moderately Loaded NASA Transonic Compressor Stage, ASME 2002-GT-30575, 2003.
[5] Huu, Duc Vo. Role of Tip Clearance Flow on Axial Compressor Stability, D.Phil. Thesis, M.I.T., Mechanical Department of Aeronautics and Astronautics, 2001.
[6]宁方飞,“考虑真实几何复杂性的跨声压气机内部流动的数值模拟”,博士学位论文,北京航空航天大学,2002.
[7]蒋康涛,“低速轴流压气机旋转失速的数值模拟研究”,博士学位论文,中国科学院工程热物理研究所,2004.
[8] Godunov S. Finite difference methods for numerical computation of discontinuous solutions of the equations of fluid dynamics. Math Sb 47:271–90, 1959.
[9] Van Leer B. Towards the ultimate conservative difference scheme V. J. Comput. Phys., 32:101–36, 1979.
[10] Harten A, Lax P. A random choice finite difference scheme for hyperbolic conservation laws. J. Numer. Anal., 18:289–315, 1981.
[11] Roe P. Approximate Riemann solvers, parameter vectors, and difference schemes. J. Comput. Phys., 43:357–72, 1981.
[12] Harten A, Hyman JM. Self adjusting grid methods for one-dimensional hyperbolic conservation laws. J. Comput. Phys., 50:235–69, 1983.
[13] Huynh HT. Accurate upwind methods for the Euler equations. J. Numer. Anal., 32:1565–619, 1995.
[14] Deconinck H, Paill`ere H, Struijs R, and Roe P. Multi-dimensional upwind schemes based on fluctuation splitting for systems of conservation laws, Comput. Mech., 11 (5-6): 323-340, 1993.
[15] Van Leer B. Flux-vector splitting for the Eular equations, Lecture Notes in Physics, 170, 507-512, 1982.
[16] Collela P. Multi-dimensional upwind methods for hyperbolic conservation laws, J. Comput. Phys. 87, 171-200, 1990.
[17] Langseth J O, LeVeque R J. A wave propagation method for three-dimensional hyperbolic conservation laws, J. Comput. Phys., 165, 126-166, 2000.
[18] LeVeque R J. Wave propagation algorithms for multi-dimensional hyperbolic systems, J. Comput. Phys., 131, 327-353, 1997.
[19] Billet S, Toro E F. On WAF-type schemes for multi-dimensional Riemann solver for Euler equations of gas dynamics, J. Comput. Phys., 130, 1-24, 1997.
[20] Fey M. Multi-dimensional upwinding. Part II. Decomposition of the Euler equations into advection equations, J. Comput. Phys., 143,181-199, 1998.
[21] Noelle S. The MOT-ICE: a new high-resolution wave-propagation algorithm for multi-dimensional systems of conservative laws based on Fey's method of transport, J. Comput. Phys., 164, 283-333, 2000.
[22] Luká?ová-Medvid’ová, SaibertováJ, Warnecke G. Finite volume evolution Galerkin methods for nonlinear hyperbolic systems, J. Comput. Phys., 183, 533-562, 2002.
[23] Brio M, Zakharian A R, Webb G M. Two-dimensional Riemann solver for Euler equations of gas dynamics. J. Comput. Phys., 167, 177-195, 2001.
[24] Kurganov A, Petrova G. A third-order semi-discrete genuinely multi-dimensional central scheme for hyperbolic conservation laws and related problems, Numer. Math., 88, 683-729, 2001.
[25] Denton JD, Singh UK. Time marching methods for turbomachinery flow calculation, Numerical methods in applied fluid dynamics, A 82-15826 04-3, 2004.
[26] Denton JD. The Calculation of Three-dimessional Viscous Flow Through Multistage Turbomachines, J. Turbomach., 114:18-26, 1992.
[27] Adamczyk JJ. Aerodynamic Analysis of Multistage Turbomachinery Flows in Support of Aerodynamic Design, J. Turbomach., 122:189-217, 2000.
[28] Rhie CM, etal. Development and Application of a Multistage Navier-Stokes Solver. Part.E: Multistage Modelling Using Bodyforces and Deterministic Stresses, ASME 95-GT-342, 1995.
[29] GILES M. Calculation of unsteady wake/rotor interaction, J. Propul. Power., 4:356-362, 1988.
[30] Rai MM. Three-Dimensional Navier–Stokes Simulations of Turbine Rotor–Stator Interaction, Part– methodology, J. Propul. Power., 5:305-311, 1989.
[31] Giles M. Stator/rotor interaction in a transonic turbine, J. Propul. Power., 6:621-627, 1988.
[32] Erdos JI, Alzner E, McNally W. Numerical Solution of Periodic Transonic Flow Through a Fan Stage, AIAA Journal, 15: 1559-1568, 1977.
[33] Chen T, Vasanthakumar P, He L. Analysis of unsteady blade row interaction using nonlinear harmonic approach, J. Propul. Power., 7:651-658, 2001.
[34] Ning Wei, He Li. Computation of unsteady flows around oscillating blades using linear and nonlinear harmonic Euler methods, The 1997 International Gas Turbine & Aeroengine Congress & Exposition; Orlando, FL, USA; 02-05 June 1997.
[35] Yao J, Jameson A, Alonso JJ, Liu F. Development and validation of a massively parallel flow solver for turbomachinery flows, J. Propul. Power., 17(3), 659-668, 2000.
[36] Rai MM. Navier-Stokes Simulations of Rotor-Stator Interactions Using Patched and Overlaid Grids, J. Propul. Power., 3(5):387-396, 1987.
[37] Chassaing JC, Gerolymos GA, Vallet I. Reynolds-Stress Model Dual-Time-Stepping Computation of Unsteady Three-Dimesional Flows, AIAA Journal, 41: 1882-1894, 2003.
[38] Menter, F R. Improved Two-Equation Turbulence Models for Aerodynamic Flows, NASA-TM-103975, 1992.
[39] Schobeiri M. Turbomachinery Flow physics and Dynamic Performance, Springer-Verlag Berlin Heidelberg, 2005.
[40] Jameson A. Schmidt W, Turkel E, Numerical Solutions of the Euler Equations by Finite Volume Methods Using Runge-Kutta Time-Stepping Schemes, AIAA 81-1259, 1981.
[41] Jameson A. Time Dependent Calculations Using Multigrid with Applications to Unsteady Flows Past Airfoils and Wings, AIAA 91-1596.
[42] Ni RH. A Multiple Grid Scheme for Solving the Euler Equations, Proc. AIAA 5th Computational Fluid Dynamics Conference, Palo Alto, 257-264, 1981.
[43] Thompson JF. Weatherill NP. Aspects of Numerical Grid Generation: Current Science and Art, AIAA Paper 93-3539, 1993.
[44] Rai MM. Three-Dimensional Navier-Stokes Simulations of Turbine Rotor-Stator Interaction, NASA TM 100081, 1988.
[45] Chen JP, Briley WR. A Parallel Flow Solver for Unsteady Multiple Blade Row Turbomachinery Simulations, ASME 2001-GT-348, 2001.
[46] Bradshaw P. Turbulence Modeling with Application to Turbomahcinery, Progr. Aero. Sci., 32:575-624, 1996.
[47] Denton JD. Lessons from Rotor37, Journal of Thermal Science, 6(1):1-13, 1996.
[48] Dunham J. CFD Validation for Propulsion System Components (La Validation CFD des Organes des Propulseurs), AGARD-AR-355, 1998.
[49] Ren YX. A robust shock-capturing scheme based on rotated Riemann solvers, Comput. Fluid., 32, 1379-1403, 2003.
[50] Dumbser M, Moschetta J, Gressier J. A matrix stability analysis of the carbuncle phenomenon, J. Comput. Phys., 197, 647-670, 2004.
[51] Sermeus K, Deconinck H. Solution of steady Euler and Navier–Stokes equations using residual distribution schemes, 33rd Computational Fluid Dynamics Course, VKI Lecture Series 2003-05, 2003.
[52]朱自强等.应用计算流体力学,北京:北京航空航天大学出版社,1998.
[53] Quirk J. A contribution to the Great Riemann Solver Debate. Int. J. Numer. Meth. Fluid. Dyn., 18:555–74, 1988.
[54] Toro E. Riemann solvers and numerical methods for fluid dynamics. New York: Springer-Verlag, 1999.
[55] Shu C-W, Osher SJ. Efficient implementation of essentially non-oscillatory shock capturing schemes. J. Comput. Phys., 77:439–71, 1988.
[56] LeVeque R J. Wave propagation algorithms for multi-dimensional hyperbolic systems, J.Comput. Phys., 131, 327-353, 1997.
[57] Pandolfi M, D2004.
[63] Luká?ová-Medvid’ová, SaibertováJ. Finite volume schemes for multi-dimensional hyperbolic systems based on the use of bicharacteristics, Applications of Mathematics, 51: 205-228, 2006.
[64] Zahaykah Y. Evolution Galerkin schemes and discrete boundary conditions for multidimensional first order systems, D. Phil. Thesis, University of Magdeburg, 2002.
[65] Arnone A, Liou M S, Povinelli L A. Multigrid calculation of three-dimensional viscous cascade flow,J. Propul. Power.,9(4),605-614, 1993.
[66] Arima T, Sonoda T, Shirotori M, Tamura A, Kikuchi K. A Numerical Investigation of Transonic Axial Compressor Rotor Flow Using a Low-Reynolds-Number K-e Turbulence Model, J. Turbomach., 121, 44-58, 1999.
[67] Chima R V. Calculation of Tip Clearance Effects in a Transonic Compressor Rotor,NASA TM-107216, 1996.
[68] Gerolymos G A, Neubauer J,Sharma V C, Vallet I. Improved prediction of turbomachinery flows using near-wall Reynolds-stress model, J. Turbomach., 124, 86-99, 2002.
[69] Gerolymos G A,Vallet I. Tip-clearance and secondary flows in a transonic compressor rotor, The 1998 International Gas Turbine & Aeroengine Congress & Exhibition; Stockholm,Sweden; 02-05 June 1998.
[70] Hah C,Loellbach J. Development of Hub Corner Stall and Its Influence on the Performance of Axial Compressor Blade Rows, J. Turbomach., 121, 67-77, 1999.
[71] Kazutoyo YAMADA,Masato FURUKAWA,Masahiro INOUE,and Ken-ichi FUNAZAKI,Numerical Analysis of Tip Leakage Flow Field in a Transonic Axial Compressor Rotor , Proceedings of the International Gas Turbine Congress 2003, Tokyo, 2003.
[72] Shabbir A, Celestina M L, Adamczyk J J, Strazisgar A J. The effect of hub leakage flow on two high speed axial flow compressor rotors, ASME 97-GT-346, 1997.
[73] Shabbir A, Zhu J. Celestina M. Assessment of Three Turbulence Models in A Compressor Rotor, ASME 96-GT-198, 1996.
[74] Reid L, Moore R D. Design and Overall Performance of Four Highly-Loaded, High-Speed Inlet Stages for an Advanced, High-Pressure-Ratio Core Compressor, NASA TP-1337. NASA, 1978.
[75] Reid L, Moore RD. Experimental Study of Low Aspect Ratio Compressor Blading, ASME 80-GT-6, 1980.
[76] Van Zante DE. Study of a wake recovery mechanism in a high-speed axial compressor stage, NASA/CR-1998-206594. NASA, 1998.
[77] Arnone A and Pacciani R. Rotor-Stator Interaction Analysis Using the Navier-Stokes Equations and a Multigrid Method, J. Turbomach., 118, 679-689, 1996.
[78] Jennions I K, Adamczyk J J. Evaluation of the interaction losses in a transonic turbine hp rotor/lp vane configuration, J. Turbomach., 119, 68-76, 1997.
[79] Van Zante D E, Hathaway M D, Okiishi T H. Recommendations for Achieving Accurate Numerical Simulation of Tip Clearance Flows in Transonic Compressor Rotors, J. Turbomach., 122(4):733-742, 2000.
[80] Van Zante D E, Adamczyk J J, Strazisar A J, Okiishi T H. Wake Recovery Performance Benefit in a High-Speed Axial Compressor, J. Turbomach., 124, 275-284, 2002.
[81] Wilcox DC. Reassessment of the scale-determining equation for advanced turbulence models, AIAA Journal, 26:1299–1310, 1988.
[82] Sanders AJ, Papalia J,Fleeter S. Multi-Blade Row Interactions in a Transonic Axial Compressor Part1-Stator Partical Image Velocimetry (PIV) Investigaton, J. Turbomach., 124, 10-18, 2002.
[83] Smith Jr L.H. Casing Boundary Layers in Multistage Axial-Flow Compressors, Flow Research on Blading, Elsevier, Amsterdam, 1969.
[84] Yu WS, Lakshminarayana B. Numerical Simulation of the Effects of Rotor-Stator Spacing and Wake/Blade Count Ratio on Turbomachinery Unsteady Flows, J. Fluids Eng., 117: 639-646, 1995.
[85] Layachi MY, Bolcs A. Effect of the axial spacing between rotor and stator with regard to the indexing in an axial compressor, ASME TURBO EXPO, 2001-GT-0592, 2001.
[86] Graf MB, Effects of stator pressure field on upstream rotor performance, MIT dissertation, 1996
[87] Graf MB, Effects of stator pressure field on upstream rotor performance, MIT dissertation, 1996.
[88] Supplee HH, The gas turbine: progress in the design and construction of turbines operated by gases of combustion, USA: J. B. Lippincott, 1910.
[89] Dunham JA, R.Howcll-Father of the British Axial Comprcssor, ASME 2000-GT-8, 2000.
[90] Freeman JH, Design of A Multi-spool, High-speed, Connter-Rotating, Aspirated Compressor, AD-A385286, 2000.
[91]陈慰章,叶轮机气动力学研究及其发展趋势,中国航空学会航空百年学术论坛动力分坛论文集(一),北京:中国航空学会动力专业分会, 2003.17-39.
[92]程荣辉,普惠公司的压气机设计技术,燃气涡轮试验与研究, 10(2):53-59, 1997.
[93] Wisler DC, Advanced Compressor and Fan Systems, lecture notes from UTSI short course Aeropropulsion, Dayton, OH, and December 7-11,1987.