摘要
固体燃料冲压发动机具有比冲高、结构简单、可靠性高、安全性好等优点,在未来超声速导弹和增程炮弹中具有广泛应用前景。本文采用理论研究、数值模拟和试验研究相结合的方法对发动机内部燃烧流动过程进行深入研究,进而开展工作过程仿真和一体化设计优化技术研究。
基于HTPB热分解及反应过程分析,建立了12组分、17反应的化学反应模型。采用二阶矩湍流燃烧模型,有效克服了常用的E—A模型、简化PDF模型等均无法正确描述固体燃料冲压发动机中化学反应速率和扩散速率处于同一量级的现象。在此基础上,采用雷诺平均N—S方程、BSL两方程湍流模型、化学非平衡方程和二阶矩湍流燃烧方程,建立了描述固体燃料冲压发动机燃烧室、补燃室和喷管内部燃烧流动过程的物理数学模型。
在数值模拟中,采用计算药柱表面层流底层导热率的方法计算燃面退移速率,与采用经验公式计算对流换热系数的方法相比更能反映出传热过程物理本质,有效地提高了计算精度。运用时间相关的LU-SGS方法,采用强耦合的全隐式有限体积进行离散,其中无粘对流项采用三阶MUSCL型差分的AUSMPW+格式,并应用最大特征值分裂,将矩阵运算转化为代数运算,大大缩短了计算时间。在此基础上,编制了数值模拟软件。通过数值模拟分析了台阶高度、空气总温、燃烧室空气流量等对发动机性能的影响规律。
在国内首次完成了无氧化剂固体燃料冲压发动机试验,发动机点火可靠,工作稳定。在国内首次采用三组元燃烧空气加热器和垂直软管连接方式,建立了新型固体燃料冲压发动机试验系统,推力测量精度高于采用轴向迷宫式密封连接方式;空气加热系统工作可靠性高,加热效率高。对不同总空气流量、燃烧室空气入口直径、燃烧室空气流量与总空气流量之比开展了试验研究。试验研究表明,总空燃比、补燃室压强和比冲随总空气流量减少而下降;减小燃烧室空气入口直径或增加燃烧室空气流量都使燃气流量上升,总空燃比和比冲下降。
在工作过程仿真分析时,考虑到辐射传热和壁面加质的影响,建立了燃面退移速率工作过程仿真模型。在此基础上,建立了固体燃料冲压发动机工作过程仿真模型,编制了仿真计算程序,详细分析了固体燃料冲压发动机不同工况和结构参数对性能参数的影响规律。分析研究表明,在飞行速度与发动机效率之间存在平衡关系,导弹总体设计时需对这两个参数进行优化;通过选择合适设计点,以保证导弹巡航飞行时推力平稳;固体燃料冲压发动机设计飞行工况为稳定工况,能根据巡航导弹飞行高度和速度变化进行自适应调节。
在发动机工作过程仿真分析的基础上,选取五个主要参数作为优化变量,建立了固体燃料冲压发动机一体化设计优化模型,结果表明优化方案可使导弹飞行距离提高24.8%。
Because of the virtues, such as high specific impulse, self-adaptive control property, simple structure and high security et., the solid fuel ramjet has extensive application foreground on supersonic missile and added-range projectile. The study on the combustion and flow behavior inside the motor is carried out through theoretical study, numerical simulation and experimental study. Moreover, the study on the simulation of the solid fuel ramjet operation process and the optimization of the motor design is carried out.
On the basis of the analysis of the decomposition and reaction process of HTPB, the 12 species 17 steps model is used. Because the chemical kinetics velocity and diffusion velocity are in the same magnitude in the solid fuel ramjet, the models, such as the E-A model, fast reaction simplified PDF model and finite reaction velocity simplified PDF model, can not mirror this phenomenon. Comparing with other models, the second-moment model is selected. Thus, the physicomathematical model is established to describe the combustion and flow behavior inside the combustion chamber, the second combustion chamber and the nozzle of the solid fuel ramjet. The three-dimensional Favre-averaged compressible turbulent N-S equations are used as the governing equations of the reacting flow, and the BSL two-equation turbulence equations are used for the turbulent flow, and the chemical non-equilibrium equations are used for the reaction rate, and the second-moment model is used for the turbulent combustion.
The key to numerical simulation is the calculation of the fuel regression rate. In many literatures, in order to achieve the fuel regression rate, the convective heat transfer coefficient is calculated to get the heat exchange rate, using many empirical formula and methods. In the thesis, the heat conductivity of the laminar sub-layer on the surface of the grain is calculated, which reflects the physical essence of the heat transferring. But it demands the higher computational accuracy. Time-dependent LU-SGS method and close coupled full implicit finite volume scheme are used. The AUSMPW+ based on the three-order MUSCL difference scheme is used for the inviscid operator, and the maximum eigenvalue splitting method is used to convert matrix operation to algebraic operation in order to shorten the computing time. Based on the above, a numerical simulation computing program is coded. It is analyzed the influence of the parameters, such as the step height, air total temperature, combustion air flux et.
For the first time in domestic, the solid fuel ramjet experiments with nonoxidizer propellant are performed. The experiments results prove that the ignition is reliable, and the motor works stably. A new style solid fuel ramjet test system is established adopting the three species combustion-air heater and vertical hose connection mode for the first time in domestic. The accuracy of thrust measurement of this test system is higher than that of the test system adopting the axial labyrinth seal connection mode, and the heater system has the virtues of high reliability and heating efficiency. The effect of factors, such as total air flow rate, the air inlet diameter of the combustion chamber, the ratio of the air flow rate of the combustion chamber to total air flow rate, on the performance is investigated experimentally. The experimental data shows that some parameters, such as the total air/fuel ratio, pressure in the second combustion chamber and specific impulse, decrease as the reduction of total air flow rate. Moreover, the hot gas flow rate increases as the reduction of the air inlet diameter or the increment of the air flow rate of the combustion chamber, which causes the reduction of the total air/fuel ratio and specific impulse.
Considering the radiative heat transfer and the effect of the mass addition from the wall on the convective heat transfer coefficient, the fuel regression rate simulation model is established. On the basis of the above, the operation process simulation model of the solid fuel ramjet is established. The simulation program is coded, and is used to analyze the effect of different structure parameters and operating condition on the performance in detail. It is showed that the specific impulse should be the maximum at the design height, not merely considering enhancing the performance of the inlet. The flight velocity must be optimized in the missile overall design procedure. A proper design point can make the thrust stable during the flight. The solid fuel ramjet has good adaptability, for it can adjust thrust with the change of the flight height and velocity.
On the base of the simulation analysis, five main parameters are selected as the optimize variables, and the design optimization model of the solid fuel ramjet is established. The optimize results show that the flight range increases 24.8 percent of the non-optimize results.
引文
[1]张玲翔.美国弹用冲压发动机技术的进展[J].飞航导弹,1998(11):38-43.
[2]W.H.Mermagen,R.J.Yalamanchili.Design and Development of a Ramjet Tank Training Round.8~(th) International Symposium of Ballistics.1988.
[3]Nusca,M.J.Chakravarthy,S.R.and Goldberg,U.C.Computational Fluid Dynamics Capability for Solid Fuel Ramjet Projectile[C].J.Propulsion Power,1990(3):256-262.
[4]R.Oosthuizen,J.J.du Buisson,G.E.Botha,Solid Fuel Ramjet(SFRJ)Propulsion for Artillery Projectile Applications-Concept Development Overview.19th International Symposium of Ballistics.2001.
[5]F.Dionisio,A.Stockenstrom.Aerodynamic Wind-Tunnel Test of a Ramjet Projectile.19th International Symposium of Ballistics.2001.
[6]R.G.Veraar,P.J.M.Elands,K.Andersson and Y.Nillsson.Overview of the Swedish-Dutch Co-operations Programme on Solid Fuel Ramjet Propelled Projectiles[C].18~(th) International Symposium of Ballistics.1998.
[7]R.G.Veraar and K.Andersson and Y.Nillsson.Flight Test Results of the Swedish-Dutch Solid Fuel Ramjet Porpelled Projectile.19~(th) International Symposium of Ballistics.2001.
[8]陈军,朱福亚,周长省.固体燃料冲压发动机在小口径弹药上的应用[J].弹道学报,1999(2):85-88.
[9]孙振宗.固体燃料冲压发动机试验研究.北京动力机械研究所.GF-A0034213G,1998.
[10]郭健,张为华,杨涛等.固体燃料冲压发动机研究进展[J].固体火箭技术,2003,26(2):8-11.
[11]谭建国,陈小前,杨涛,张为华.固体燃料冲压发动机燃速理论分析与数值模拟.航空动力学报,2000,15(2):201-204.
[12]Amnon Netzer and Alon Gany.Burning and Flameholding Characteristics of a Miniature Solid Fuel Ramjet Combustor.Journal Propulsion Power.1991.
[13]H.L.Jordan,H.R.Lips,Phil R.E.Experimental Investigation of a Solid Fuel Ramjet.Manuscript eingereicht,Hardthausen,German.1978.
[14]H.K.Ciezki and B.Schwein.Investigation of Gaseous and Solid Reaction Products in a Step Combustor using a Water-Cooled Sampling Probe.AIAA-96-2768.
[15]J.Richardson et.SFRJ Simulator Results:Experiment and Analysis in Cold Flow.AIAA-85-0329.
[16]P.J.M.Elands and P.A.O.G.korting.Combustion of Polyethylene in a Solid Fuel Ramjet-A Comparison of Computational and Experimental Results.AIAA-88-3043.
[17]Ronald G.Veraar and Alfons E.H.J.Mayer.The Role of the TNO Free Jet Test Facility in Solid Fuel.AIAA-2005-3828.
[18]Deborah Pelosi-Pinhas and Alon Gany.Solid Fuel Ramjet Regulation by Means of an Air Division Valve,ISABE 99-7245.
[19]Kyung-Soo Yang et.Numerical Study of Turbulent Flow Around a Rotating Cylinder with Backward-Facing Steps.AIAA-2001-0451.
[20]Tae-Ho Lee and Daejeon.A Study of the Flammability Limit of the Backward Facing Step Flow Combustion.AIAA-2000-3347.
[21]J.G.obbo-Ferreira et.Experimental Investigation of Polyethylene Combustion in a Solid Fuel Ramjet.AIAA-96-2698.
[22]Amnon Netzer and Alon Gany.Burning and Flame holding Characteristics of a Miniature Solid Fuel Ramjet Combustor.J.Propulsion Vol.7,No.3,1991.
[23]F.Dijkstra et.Ducted Rocket Combustion Experiments at Low Gas-generator Combustion Temperatures.AIAA-95-2415.
[24]James Nabity and Tony Walls et.Side-Dump Solid Fuel Ramjet Combustor Evaluation.AIAA-88-3072.
[25]R.Pein and F.Vinnemeier.Swirl and Fuel Composition Effects on Boron Combustion in Solid Fuel Ramjets.Journal of Propulsion and Power,Vol.8,No.3,1992.
[26]D.A.Duesterhaus et.Measurements in a Solid Fuel Ramjet Combustion with Swirl.AIAA-88-3045.
[27]A.M.Helmy et.Performance of Polycubanes in Solid Fuel Ramjet.AIAA-93-2591.
[28]F.J.Friedauer and C.Segal.Combustion of High Energy,High Density Fuels in a Ramjet Combustor.AIAA-96-3239.
[29]D.Netzer et.Regression and Combustion Characteristics of Boron Containing Fuels for Solid-Fuel Ramjets.Journal of Propulsion and Power,Vol.7,No.3,1991.
[30]H.K.Ciezki et.Investigation of the Combustion Process of Boron Particle Containing Solid Fuel Slabs in a Rearward Facing Step Combustor.AIAA-2000-3347.
[31]David W.Netzer.Modeling Solid-Fuel Ramjet Combustion.J.Spacecraft,Vol.14,No.12.
[32]P.J.Coelho,N.Duic,C.Lemos and M.G.Carvalho.Modelling of a Solid Fuel Combustion Chamber of a Ramjet Using a Multi-block Domain Decomposition Technique.Aerospace Science and Technology,No.2,1998.
[33]Charles A.Stevenson and David W.Netzer.Primitive-Variable Model Application to Solid-Fuel Ramjet Combustion.AIAA-81-4021.
[34]E.G.Plett and R.A.Stowe.Numerical Simulation of Solid Fuel Ramjet Missile Propulsive Performance.AIAA-95-2448.
[35]陈军.固体燃料冲压发动机工作过程研究[博士学位论文].南京:南京理工大学,1998.
[36]Ronald G.Veraar.RP~5:a Computer Program for Flight Performance Prediction of Solid Fuel Ramjet Propelled Projectiles.15th International Symposium of Ballistics.1995.
[37]Mel Human.A Missile Flight Simulation Using Interdisciplinary Coupling.AIAA-2001-4421.
[38]Benveniste Natan and Alon Gany.Combustion Characteristics of a Boron-Fueled Solid Fuel Ramjet with Aft-Burner.Journal of Propulsion and Power,Vol.9,No.5,1993.
[39]Rachel Ben-Arosh,Benveniste Natan,Elyeser Spiegler and Alon Gany.The Reacting Flowfield within a Supersonic Combustion Solid Fuel Ramjet.AIAA-97-2335.
[40]Abraham Comhen and Benveniste Natan.Experimental Investigation of a Supersonic Combustion Solid Fuel Ramjet.AIAA-97-3644.
[41]C.Vaught,M.Witt and D.Netzer.Investigation of Solid-Fuel,Dual-Mode Combustion Ramjets,Journal of Propulsion and Power,Vol.8,No.5,1992.
[42]李庆扬.常微分方程数值解法(刚性问题与边值问题).高等教育出版社.
[43]黎作武.含激波、旋涡和化学非平衡反应的高超声速复杂流场的数值模拟.中国空气动力研究与发展中心博士学位论文,1994.
[44]S.Eberhardt,S.Imlay.A Diagonal Implicit Scheme for Computing Flows with Finite-Rate Chemistry.AIAA 90-1577,1990.
[45]董维中.热化学非平衡效应对高超声速流动影响的数值计算与分析.北京航空航天大学博士学位论文,1996.
[46]倪鸿礼.运动激波与物体的干扰研究.中国空气动力研究与发展中心博士学位论文,1998.
[47]C.P.Li.Implicit Methods for Computing Chemically Reacting Flows.NASA TM-58274,1986.
[48]C.P.Li,T.C.Wey.Numerical Simulation of Hypersonic Flows Over an Aeroassist Flight Experiment Vehicle.AIAA-88-2675.
[49]L.T.Tam,C.P.Li.Three-Dimensional Thermo-chemical Non-equilibrium Flow Modeling for Hypersonic Flows.AIAA-89-1860.
[50]G.Palmer.An Improved Flux-Split Algorithm Applied to Hypersonic Flows in Chemical Equilibrium.AIAA-88-2693.
[51]G.Palmer.The Development of an Explicit Thermal-Chemical Non-equilibrium Algorithm and Its Application to Compute Three Dimensional AFE Flow-fields.AIAA 89-2701,1989.
[52]G.Palmer.Enhanced Thermo-Chemical Non-equilibrium Computations of Flow Around the Aeroassisted Flight Experiment Vehicle.AIAA-90-1702.
[53]T.R.Bussing,E.M.Murman.Finite Volume Method for the Calculation of Compressible Chemically Reacting Flows.AIAA-85-0331.
[54]J.S.Shuen.Upwind Differencing and LU Factorization for Chemical Non-equilibrium NS Equations.Journal of Computational Physics,Vol.99:235-250,1992.
[55]A.Jameson.Numerical Simulation of the Euler Equation by Finite Volume Methods Using Runge-Kutta Time Splitting.AIAA-81-1259.
[56]A.Harten.High Resolution Schemes for Hyperbolic Conservation Laws.Journal of Computational Physics,Vol.49:357-393,1983.
[57]S.Osher,S.R.Chakravarthy.High Resolution Schemes and Entropy Conditions.SIAM J.on Numerical Analysis,Vol.21(5):955-984,1984.
[58]P.L.Roe.Generalized Formation of TVD Lax-Wendroff Schemes.ICASE 84-53,1984.
[59]S.R.Chakravarthy,S.Osher.A New Class of High Accuracy TVD Schemes for Hyperbolic Conservation Laws.AIAA-85-0363.
[60]H.C.Yee.Generalized Formation of a Class of Explicit and Implicit TVD Schemes.NASA TM-86775,1985.
[61]H.C.Yee,G.H.Klopfer,J.L.Montagne.High Resolution Shock Capturing Schemes for Inviscid and Viscous Hypersonic Flows.NASA TM-100097,1988.
[62]A.Harten.Uniformly High Order Accurate Essentially Non-Oscillatory Schemes.Journal of Computational Physics,Vol.71(2):231-303,1987.
[63]A.Harten.ENO Schemes with Subcell Resolution.Journal of Computational Physics,Vol.83(3):148-184,1989.
[64]Chi-Wang Shu,S.Osher.Efficient Implementation of Essentially Non-Oscillatory Shock-Capturing Schemes.Journal of Computational Physics,1988.
[65]Chi-Wang Shu,S.Osher.Efficient Implementation of Essentially Non-Oscillatory Shock-Capturing Schemes Ⅱ.Journal of Computational Physics,Vol.83(1):32-78,1989.
[66]J.Y.Yang.Third-Order Non-Oscillatory Schemes for the Euler Equations.AIAA Journal,Vol.29(10):1611-1618,1991.
[67]J.Y.Yang,C.A.Hsu.High Resolution Non-Oscillatory Schemes for Unsteady Compressi- ble Flows.AIAA Journal,Vol.30(6):1570-1575,1992.
[68]A.G.Godfrey,C.R.Mitchell.Practical Aspects of Spatially High-Order Accurate Methods.AIAA Journal,Vol.31(9),1993.
[69]Fu Dexun,Ma Yanwen.Direct Numerical Simulation of Coherent Structure on the Compressible Mixing Layer.Proceeding of 1~(st) Asian CFD Conference,HongKong,1995.
[70]B.Van Leer.Towards the Ultimate Conservative Difference Scheme V:A Second Order Sequel to Godunov's Method.Journal of Computational Physics,Vol.32:101-136,1979.
[71]W.K.Anderson,J.L.Thomas,B.Van Leer.A Comparison of Finite Volume Flux Vector Splitting for the Euler Equations.AIAA-85-0122.
[72]J.L.Steger,R.F.Warming.Flux Vector Splitting of the Inviscid Gas-dynamic Equations with Application to Finite Difference Methods.Journal of Computational Physics,Vol.40:263-293,1981.
[73]赵兴艳等.LU-AUSM+混合格式在三维可压缩流动数值分析中的应用.西安交通大学学报.Vol.34,No.5.2000.
[74]K.H.Kim,C.A.Kim,O.H.Rho.Accurate Computations of Hypersonic Flows Using AUSMPW+ Scheme and Shock-Aligned Grid Technique.AIAA-98-2442.
[75]S.Gordon and B.J.McBride.Computer Program for Calculation of Complex Chemical Equilibrium Compositions,Rocket Performance,Incident and Reflected Shocks,and Chapman-Jouguet Detonations.NASA SP-273,1971.
[76]R.B.Bird,W.E.Stewart and E.N.Lightfoot.Transport Phenomena.John Wiley and Sons,New York,1960.
[77]C.R.Wilke.A Viscosity Equation for Gas Mixtures.Journal of Computational Physics,Vol.18,1950.
[78]D.K.Prabhu and J.C.Tannehill.A New PNS Code for Chemical Non-equilibrium Flows.AIAA-87-0284.
[79]H.A.Berman and J.D.Anderson.Supersonic Flow Over a Rearward Facing Step with Transverse Nonreacting Hydrogen Injection.AIAA-82-1002.
[80]S.Chapman and T.G.Cowling.The Mathematical Theory of Non Uniform Gases 2~(nd) ed.Cambridge University Press,New York,1958.
[81]F.R.Menter.Improved Two-Equation k-ω Turbulence Models for Aerodynamic Flows.NASA TM-103975,1992.
[82]F.R.Menter,Zonal.Two-Equation k-ω Turbulence Models for Aerodynamic Flows.AIAA-93-2906.
[83]W.P.Jones and B.E.Launder.The Calculation of Low-Reynolds-Number-Phenomena with a Two-Equation k-ω Model of Turbulence.Int.J.Heat Mass Transf,Vol.16:1119-1130,1973.
[84]D.L.Sondak and R.H.Pletcher.Application of Wall Functions to Generalized Nonortho- gonal Curvilinear Coordinate Sytems.AIAA-93-3107.
[85]D.C.Wilcox.Reassessment of the Scale-Determining Equation for Advanced Turbulence Models.AIAA Journal Vol.26:1299-1310,1988.
[86]F.P.Inglese and S.Acharya.An Improved k-ω Model for Compressible Flows.AIAA -96-0428.
[87]W.Shyy and V.S.Krishnamurty.Compressibility Effects in Modeling Complex Turbulent Flows.Progr.Aerospace Sci.Vol.33:587-645,1997.
[88]Mauro Valorani and Dimitrios Goussis.Explicit Time-Scale Splliting Algorithm for Stiff Problems:Auto-Ignition of Gasous Mictures behind a Steady Shock.Journal of Computa- tional Physics,Vol.169,No.1,2001.
[89]张仁编著.固体推进剂的燃烧与催化.国防科技大学出版社,1992.
[90]Martin J.Chiaverini et.Pyrolysis Behavior of Hybrid Rocket Solid Fuels under Rapid Heating Conditions.AIAA-97-3078.
[91]G.C.Cheng et.Numerical Simulation of the Internal Ballistics of a Hybrid Rocket Motor.AIAA-94-0554.
[92]张会强,陈兴隆,周力行等.湍流燃烧数值模拟研究的综述.力学进展,1999.
[93]周力行著.湍流气粒两相流动和燃烧的理论与数值模拟.科学出版社,1994.
[94]周力行著.多相湍流反应流体力学.国防工业出版社,2002.
[95]朱自强等编著.应用计算流体力学.北京航空航天大学出版社,1998.
[96]S.Obayashi and K.Kuwahara.LU Factorization of an Implicit Scheme for the Compressi-ble NS Equations.AIAA-84-1670.
[97]S.Yoon and A.Jameson.An LU-SSOR Scheme for the Euler and Navier-Stokes Equations,NASA CR-179556,1986.
[98]A.Jameson and S.Yoon.LU Implicit Scheme with Multiple Grid for the Euler Equations.AIAA-86-0105.
[99]H.F.Lehr.Experiments on Shock-Induced Combustion.Aeronautica Acta,Vol.17,1972.
[100]G.J.Wilson and R.W.MacCormack.Modeling Supersonic Combustion Using a Full- Implicit Numerical Method.AIAA-90-2307.
[101]M.Soetrisno and S.T.Imlay.Simulation of the Flow Field of a Ram Accelerator.AIAA -91-1915.
[102]J.Y.Choi,I.S.Jeung and S.Lee.Numerical Study of the Effect of Flow Conditions on Shock-Induced Combustion.AIAA-96-0345.
[103]J.K.Clutter,V.S.Krishnamurty and W.Shyy.Combustion and Turbulence Effect in Hypersonic Projectile Flows.AIAA-97-0897.
[104]J.K.Clutter,D.W.Mikolaitis and W.Shyy.Effect of Reaction Mechanism in Shock- Induced Combustion Simulations.AIAA-98-0274.
[105]傅维标,卫景彬编著.燃烧物理学基础.机械工业出版社,1984.
[106]刘兴洲主编.飞航导弹动力装置.宇航出版社,1992.
[107]于守志等编著.飞航导弹动力装置试验技术.宇航出版社,1990.
[108]王朝霞.锯齿型迷宫密封流场的数值模拟与实验研究[硕士学位论文].哈尔滨:哈尔滨工业大学,2002.
[109]S.Krishnan and Philmon George.Solid Fuel Ramjet Combustor Design.Prog.Aerospace Sci.Vol.34:219-256,1998.
[110]马庆芳等详.传热学.人民教育出版社,1979.
[111]王守范编著.固体火箭发动机燃烧与流动.北京工业学院出版社,1987.
[112]A.M.Krall and E.M.Sparrow.Turbulent Heat Transfer in the Separated,Reattached,and Redevelopment Regions of a Circular Tube.J.Heat Transfer 8.1966.
[113]J.Gobbo-Ferreira,M.G.Silva and J.A.Carvalho.Performance of an Experimental Polyethylene Solid Fuel Ramjet.Acta Astronautica Vol.45,No.1,1999.
[114]童秉纲等编.气体动力学.高等教育出版社,1989.
[115]P.Duveau and R.Thepot.Prediction Methods for Supersonic Inlets[R].ISABE91-7078.
[116]R.G.Lacau,P.Garnero and F.Gaible.Computation of Supersonic Air-intakes[R].ADA295492.
[117]潘荣霖等编著.飞航导弹自动控制系统.宇航出版社,1991.
[118]粟塔山等.最优化计算原理与算法程序设计.国防科技大学出版社,2002.
[119]崔金平,徐东来,蔡选义.某弹用二元混压式超音进气道设计与仿真.中国空空导弹研究院技术报告.
[120]R.K.Belew,M.D.Vose.Fourdation of Genetic Algorithms,4.San Francisco:Morgan Kaufman Publishers Inc.1997.
[121]M.Melanie.An Introduction to Genetic Algorithms.Cambridge:The MIT Press.1996.
[122]S.W.Mahfoud.Genetic drift in sharing methods.Proc 1~(st) IEEE Conf Evolutionary Computation.Nj:IEEE Press,1994.67-72.
[123]赵建民,夏智勋.高效全模式遗传算法研究.计算机与现代化,2004(11):4-6.
[124]孙瑞祥,屈梁生.遗传算法优化效率的定量评价.自动化学报,2000,26(4):382-384.
[125]李敏强,寇纪松.遗传算法的模式欺骗性分析.中国科学(E缉).2002,32(1):95-102.
[126]李敏强,寇纪松,林丹,李书全.遗传算法的基本理论与应用.科学出版社,2003.
[127]王炎,刘景录,孙一康.基于变尺度混沌优化策略的混合遗传算法.控制与决策,2002,17(6):958-960.