高超声速滑移流动机理研究
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摘要
高超声速临近空间飞行器的研究与设计必须细致考虑流动的稀薄气体效应的影响,需要精确预测流场特性及飞行器表面性质包括壁面热流量、压力和摩阻等,深入研究高超声速滑移流动机理包括理论分析、数值模拟和试验研究,开展高空高马赫数流动气动特性分析意义重大。本文采取的研究思路为程序编制,模型分析,数值模拟,最后是试验规划,这四部分的具体内容如下:
分析了分子方法、连续方法与混合方法在模拟高超声速滑移流动时的优势和不足,对比研究后认为,对于高超声速滑移流域的分析,采用N-S方程附加滑移模型,可以得到精度满意的结果,且计算代价较低,程序实现较为简单。本文根据流体动力学三维N-S方程,基于结构网格和有限体积法,运用M-AUSMPW+格式和LU-SGS隐式算法,编制了并行计算程序,通过与文献实验结果的对比,验证了程序的准确性。
对现有的主要滑移模型进行了细致的理论推导与分析,讨论了滑移模型的差别,通过数值模拟分析计算误差,认为改进型Maxwell滑移模型模拟效果相对较好。从分子运动论层次和流体动力学层次推导出高超声速滑移流动壁面热流计算模型,新增项从微观层次讲,表示单位时间、单位面积内由于分子碰撞而传入壁面的总能量;从宏观层次讲,表示单位时间内粘性应力输运的能量,并且从量级分析来看,新增项不可忽略。数值模拟结果显示,改进模型对热流的模拟效果有一定程度的改善。考察了壁面适应系数的研究进展,并指出了本文所研究的适应系数典型值。开展了高超声速滑移流气动热网格效应研究,表明在滑移流中壁面适应系数对热流收敛的影响并不显著,在滑移流区,一般取网格雷诺数为1-2即可。通过与两个高超声速滑移流动的实验数据的对比,验证了选用计算模型的准确性。
选取二维圆柱、三维球头、尖劈与平板等高超声速飞行器典型外形,对高超声速滑移流动流场特性与壁面特性进行了详细的数值模拟研究。通过选取0.5、0.75与1.0三种典型值,考察了壁面适应系数的影响;研究了来流马赫数对滑移流动的影响;通过选取来流努森数分别为0.002、0.01、0.05与0.25,研究了滑移流动区域上、下限内流动的变化规律。研究表明,努森数的增大使激波层增厚,粘性干扰作用增强,激波强度逐渐减弱,间断结构逐渐弱化;马赫数的增加强化了非平衡稀薄气体效应;壁面适应系数与粘性作用密切相关,适应系数的增大使粘性作用增强,非平衡稀薄气体效应减弱。最后,对高空高马赫数条件下耦合化学平衡效应的滑移流场特性展开了研究,表明考虑化学平衡效应使激波层变薄,波后压强升高,温度降低;壁面热流系数与滑移速度降低,且这一趋势随着稀薄程度的增大而加大。
对高超声速稀薄气体流动试验研究概貌进行了综述,从流场和气体/壁面界面两方面指出了研究中需要试验验证的地方,以此为基础,在理论分析与数值模拟的指导下,对高超声速滑移流动机理研究环境做了初步的规划,形成了针对高超声速滑移流的集流场显示、速度和温度测量以及气体/壁面相互作用研究的小型试验系统蓝图。
Rarefied gas effects have to be considered when doing the research and design of hypersonic flight vehicle in near space, in which accurate prediction of flow field and surface properties such as pressure, shear stress and heat flux are needed. Research on the mechanism of hypersonic slip flow must consist of mathematical analysis, numerical analysis and experimental research, and is of great importance resently. The research presented here in this dissertation has four main parts: CFD code debuging, mathematical model analysis, numerical analysis and experimental programming, which are detailed as follows:
The comparison of advantage and disadvantage among molecular method, continuum method and hybrid method on the hypersonic slip flow research are carried out, which points out that the N-S equation with slip bouindary model can get the satisfied accurate prediction while the computational cost is less expensive, and the code development relatively easy. This research developed a general 3D, parallel, structurted, finite-volume CFD code based on 3D N-S governing equations, using M-AUSMPW+ scheme and LU-SGS implicit time integration scheme. The comparison with experimental data, verified the code accuracy.
The main slip models are derived and analysed in detail, then the numerical experiments are presented to find out that the improved Maxwell model is relatively accurate and efficient. The hypersonic slip flow heat flux model are derived from both molecular level and hydrodynamics level, the additional term in the improved model are definite: from the microscopic view, it shows the whole energy transferred to the soild surface unit time and area due to the molecular collision, from the macroscopic view, it denotes the energy transferred by shear stress unit time, and the magnitude analysis indicates that the additional term can not be neglected. This heat flux computational model in some sense improves the numerical results. The progress and status reporting of gas/surface accommodation coefficients are presented as a guide of which typical values to choose for this research. The research on hypersonic slip flow grid effect for air heating problem are carried out, the results reveals that in slip flow, the accommodation coefficients have little impact on heat flux convergence which can be obtained using 1-2 grid Renold number. Through the comparison with two hypersonic slip flow experiments, the accuracy of computational model derived above are examined and certified.
The typical body of hypersonic flight vehicle such as 2D cylinder, 3D sphere, sharp-leading edge and zero-thickness flate plate are used in numerical analysis, and the hypersonic slip flow field properties and surface properties distributions (pressure, shear stress and heat flux) are simulated: Choose three typical values 0.5, 0.75 and 1.0 to study the effect of accommodation coefficients. The Mach number effects in slip flow are considered. Choose four typical Knudsen number, 0.002, 0.01, 0.05 and 0.25 to deeply study the regulations among slip flow regime. The reseach reviews that, the shock layer gets thicker when the Knudsen number becomes bigger, the shock discontinuous effects are getting weaker and the shock strength is weakened gradually. The rise of Mach number makes the rarefied gas effects stronger. The correlation between accommodation coefficients and viscous effects are found out, and the rise of the accommodation coefficients strengthen the viscous effects which weaken the rarefied gas effects. Then, research on the high space large mach number chemical-equilibrium slip flow are presented and indicate that in hypersonic slip flow regime, chemical-equilibrium effects make the shock layer thinner, pressure rise and temperature lower, the surface heat flux coefficient and slip velocity get smaller in which this trend becomes stronger as the Knudsen number rise.
The advancement of experimental research on hypersonic rarefied gas flow are summarized, and point out from flow field and gas/solid surface view the aspects that need to be examined in experiment, in other words, that difficult to calculate, and give detailed discreption on planar induced iodine fluorescence. On the basis above and the guide of mathematical analysis as well as numerical nanlysis, a preliminary programming for experimental environment on hypersonic slip flow are presented which integrates the flow field visualization, velocity and temperature measurement and gas/sueface interaction research, forming the small-size systemic blueprint for research on hypersonic slip flow.
分析了分子方法、连续方法与混合方法在模拟高超声速滑移流动时的优势和不足,对比研究后认为,对于高超声速滑移流域的分析,采用N-S方程附加滑移模型,可以得到精度满意的结果,且计算代价较低,程序实现较为简单。本文根据流体动力学三维N-S方程,基于结构网格和有限体积法,运用M-AUSMPW+格式和LU-SGS隐式算法,编制了并行计算程序,通过与文献实验结果的对比,验证了程序的准确性。
对现有的主要滑移模型进行了细致的理论推导与分析,讨论了滑移模型的差别,通过数值模拟分析计算误差,认为改进型Maxwell滑移模型模拟效果相对较好。从分子运动论层次和流体动力学层次推导出高超声速滑移流动壁面热流计算模型,新增项从微观层次讲,表示单位时间、单位面积内由于分子碰撞而传入壁面的总能量;从宏观层次讲,表示单位时间内粘性应力输运的能量,并且从量级分析来看,新增项不可忽略。数值模拟结果显示,改进模型对热流的模拟效果有一定程度的改善。考察了壁面适应系数的研究进展,并指出了本文所研究的适应系数典型值。开展了高超声速滑移流气动热网格效应研究,表明在滑移流中壁面适应系数对热流收敛的影响并不显著,在滑移流区,一般取网格雷诺数为1-2即可。通过与两个高超声速滑移流动的实验数据的对比,验证了选用计算模型的准确性。
选取二维圆柱、三维球头、尖劈与平板等高超声速飞行器典型外形,对高超声速滑移流动流场特性与壁面特性进行了详细的数值模拟研究。通过选取0.5、0.75与1.0三种典型值,考察了壁面适应系数的影响;研究了来流马赫数对滑移流动的影响;通过选取来流努森数分别为0.002、0.01、0.05与0.25,研究了滑移流动区域上、下限内流动的变化规律。研究表明,努森数的增大使激波层增厚,粘性干扰作用增强,激波强度逐渐减弱,间断结构逐渐弱化;马赫数的增加强化了非平衡稀薄气体效应;壁面适应系数与粘性作用密切相关,适应系数的增大使粘性作用增强,非平衡稀薄气体效应减弱。最后,对高空高马赫数条件下耦合化学平衡效应的滑移流场特性展开了研究,表明考虑化学平衡效应使激波层变薄,波后压强升高,温度降低;壁面热流系数与滑移速度降低,且这一趋势随着稀薄程度的增大而加大。
对高超声速稀薄气体流动试验研究概貌进行了综述,从流场和气体/壁面界面两方面指出了研究中需要试验验证的地方,以此为基础,在理论分析与数值模拟的指导下,对高超声速滑移流动机理研究环境做了初步的规划,形成了针对高超声速滑移流的集流场显示、速度和温度测量以及气体/壁面相互作用研究的小型试验系统蓝图。
Rarefied gas effects have to be considered when doing the research and design of hypersonic flight vehicle in near space, in which accurate prediction of flow field and surface properties such as pressure, shear stress and heat flux are needed. Research on the mechanism of hypersonic slip flow must consist of mathematical analysis, numerical analysis and experimental research, and is of great importance resently. The research presented here in this dissertation has four main parts: CFD code debuging, mathematical model analysis, numerical analysis and experimental programming, which are detailed as follows:
The comparison of advantage and disadvantage among molecular method, continuum method and hybrid method on the hypersonic slip flow research are carried out, which points out that the N-S equation with slip bouindary model can get the satisfied accurate prediction while the computational cost is less expensive, and the code development relatively easy. This research developed a general 3D, parallel, structurted, finite-volume CFD code based on 3D N-S governing equations, using M-AUSMPW+ scheme and LU-SGS implicit time integration scheme. The comparison with experimental data, verified the code accuracy.
The main slip models are derived and analysed in detail, then the numerical experiments are presented to find out that the improved Maxwell model is relatively accurate and efficient. The hypersonic slip flow heat flux model are derived from both molecular level and hydrodynamics level, the additional term in the improved model are definite: from the microscopic view, it shows the whole energy transferred to the soild surface unit time and area due to the molecular collision, from the macroscopic view, it denotes the energy transferred by shear stress unit time, and the magnitude analysis indicates that the additional term can not be neglected. This heat flux computational model in some sense improves the numerical results. The progress and status reporting of gas/surface accommodation coefficients are presented as a guide of which typical values to choose for this research. The research on hypersonic slip flow grid effect for air heating problem are carried out, the results reveals that in slip flow, the accommodation coefficients have little impact on heat flux convergence which can be obtained using 1-2 grid Renold number. Through the comparison with two hypersonic slip flow experiments, the accuracy of computational model derived above are examined and certified.
The typical body of hypersonic flight vehicle such as 2D cylinder, 3D sphere, sharp-leading edge and zero-thickness flate plate are used in numerical analysis, and the hypersonic slip flow field properties and surface properties distributions (pressure, shear stress and heat flux) are simulated: Choose three typical values 0.5, 0.75 and 1.0 to study the effect of accommodation coefficients. The Mach number effects in slip flow are considered. Choose four typical Knudsen number, 0.002, 0.01, 0.05 and 0.25 to deeply study the regulations among slip flow regime. The reseach reviews that, the shock layer gets thicker when the Knudsen number becomes bigger, the shock discontinuous effects are getting weaker and the shock strength is weakened gradually. The rise of Mach number makes the rarefied gas effects stronger. The correlation between accommodation coefficients and viscous effects are found out, and the rise of the accommodation coefficients strengthen the viscous effects which weaken the rarefied gas effects. Then, research on the high space large mach number chemical-equilibrium slip flow are presented and indicate that in hypersonic slip flow regime, chemical-equilibrium effects make the shock layer thinner, pressure rise and temperature lower, the surface heat flux coefficient and slip velocity get smaller in which this trend becomes stronger as the Knudsen number rise.
The advancement of experimental research on hypersonic rarefied gas flow are summarized, and point out from flow field and gas/solid surface view the aspects that need to be examined in experiment, in other words, that difficult to calculate, and give detailed discreption on planar induced iodine fluorescence. On the basis above and the guide of mathematical analysis as well as numerical nanlysis, a preliminary programming for experimental environment on hypersonic slip flow are presented which integrates the flow field visualization, velocity and temperature measurement and gas/sueface interaction research, forming the small-size systemic blueprint for research on hypersonic slip flow.
引文
[1]彭彪,张志峰,马岑睿,文科,宋亚飞[J].飞航导弹, 2011年第五期.
[2]李桦,田正雨,李伟.高超声速滑移流效应数值模拟方法分析[C].临近空间CFD研讨会,北京, 2010.
[3] Tsien H S. Superaerodynamics, mechanics of rarefied gases [J]. Aerospace Sci. Technol., 1964, 13 (12).
[4] Holman T D. Numerical Investigation of the Effects of Continuum Breakdown on Hypersonic Vehicle Surface Properties [D]. The University of Michigan, 2010.
[5] Cercignani C, Illner R, Pulvirenti M. The Mathematical Theory of Dilute Gases [M].北京:高等教育出版社, 2009..
[6] Burnett D. The Distribution of Molecular Velocities and The Mean Motion in a Nonuinform Gas [J]. Proc. Lond Math Soc., 1935.
[7] Grad H. On the Kinetic Theory of Rarefied Gases. [J]. Commun Pure Appl Math, 1949.
[8] Myong R S. Thermodynamically Consistent Hydrodynamic Computational Models for High-Knudsen-Number Gas Flows [J]. Phsics of Fluids, Volume 11, Number 9, 1999.
[9] Torrilhon M. Tow-Dimentional Bulk Microflow Simulations Based on Regularized Grad's 13-Moment Equations [J]. Multiscale Model Simul. 2006, 5(3).
[10] Myong R S. Impact of Computational Physics on Multi-Scale CFD and Related Numerical Algorithms [J]. Compers and Fluids, 2011.
[11] Bird G A. Gas Dynamics and the Direct Simulation of Gas Flows [M]. Oxford University Press, Oxford, 1994.
[12] Bird G A. Application of the DSMC Method to the Full Shuttle Geometry [R]. AIAA Paper 90-1392, 1990.
[13] Pham-Van-Diep, et al. Nonequilibrium Molecular Motion in a Hypersonic Shock Wave [J]. Science 1989, 245.
[14]沈青. MEMS稀薄气体内部流动模拟中的信息保存(IP)法[J].力学进展, 2006, 36(1).
[15] Shen C. Gas Flow in Micro Chanels-Experimental, Computational and Kinetic Theoretical Investigations [J]. Micro and Nanosystems, 2009, 1(3).
[16] Fan J, Sun Q. Kinetic Studies of Gas Flows [C]. ISCM II and EPMESC XII, 2009.
[17]胡远,陈松,孙泉华,樊菁.超声速平板绕流的全流域阻力特性研究[C].CSTAM 2010-0049, 2010.
[18] Sone Y. Kinetic Theory and Fluid Dynamics [M]. Birkhauser, 2002.
[19] Chen S, Doolen G D. Lattice Boltzmann Method for Fluid Flows [J]. Anuu. Rev. Fluid Mech. 1998.
[20] Reese J M, Gallis M A, Lockerby D A. New Direction in Fluid Dynamics: Non-Equilibrium Aerodynamic and Microsystem Flows [J]. Philosophical Transactions of The Royal Society (A): Mathematical, Physical and Engineering Sciences, 2003.
[21] Myong R S. Velocity Slip Effect in Low-Speed Microscale Gas [R]. AIAA Paper 2001-3076.
[22] Lockerby D A. Geometric and Constitutive Dependence of Maxwell's Velocity Slip Boundary Condition [R] ADA Report, 2005.
[23] Bailey. A Critical Review of The Drag Force On A Sphere In The Transition Flow Regime [R]. ADA Report, 2005.
[24] Lofthouse A J, Scalabrin L C, Boyd I D. Velocity Slip and Temperature Jump in Hypersonic Aerothermodynamics [R]. AIAA 2007-208, 2007.
[25] Maxwell J C. On Stresses in Rarefied Gases Arising from Inequilities of Temperature [J]. Philosophical Transactions of The Royal Society, 1879, 2(1).
[26] Gokcen T, MacCormack R W. Nonequilibrium Effects for Hypersonic Transitional Flows Using Continuum Approach [R]. AIAA Paper 1989-0461, 1989.
[27] Lockerby D A, Reese J M, Emerson D R, Barber R W. Velocity Boundary Condition at Solid Walls in Rareedgas Calculations [J]. Physical Review E, 70(017303), 2004.
[28] Lockerby D A, Reese J M, Gallis M A. Capturing the Knudsen Layer in Continuum-Fluid Models of Nonequilibrium Gas Flows [J]. AIAA Journal, 43(6), 2005.
[29] Cercignani C. Higher Order Slip According to the Linearized Boltzmann Equation [J]. Institute of Engineering Research Report AS-64-19, 1964.
[30] Deissler R. An Analysis of Second-Order Slip Flow and Temperature-Jump Boundary Conditions for Rarefied Gases [J]. Int. J.Heat Mass Transfer, 1965, 7.
[31] Beskod A, Karniadakis G. Rarefaction and Compressibility Effects in Gas Microflows [J]. J. Fluids Engin. 1996,11.
[32] Karniadakis G, Beskod A. Micro Flows [M]. New York: Springer-Verlag, 2002.
[33] Choong K O, Elaine S O. A New Hybrid Algorithm: Navier-Stokes as a DSMC Filter [R]. AIAA Paper 98-0849, 1998.
[34] Roveda R, Goldstein D B, Varghese P L. Unsteady Calculation of Slip Flow with 2-D Hybrid Euler/DSMC Numerical Approach [R]. AIAA Paper 98-0852, 1998.
[35] Nie X B, Chen S Y, et al. A Continuum and Molecular Dynamics Hybrid Methodfor Micro-and-Nano-Fluid Flow [J]. J. Fluid Mech. 2004.
[36] Schwartzentruber T E, Scalabrin L C, Boyd I D. Hybrid Particle-Continuum Simulations of Nonequilibrium Hypersonic Blunt-Body Flowfields [J]. Journal of Thermophysics and Heat Transfer, 2008, 22(1).
[37] Lilley C R, Macrossan M N. Methods for Implementing the Stream Boundary Condition in DSMC Computations [J]. International Journal for Numerical Methods in Fluids 42, 2003.
[38]陈懋章.粘性流体动力学基础[M].北京:高等教育出版社, 2002.
[39]阎超.计算流体力学方法及应用[M].北京:北京航空航天大学出版社, 2006.
[40] Liu M-S, Steffen J. A New Flux Splitting Scheme [J]. Journal of Computational Physics, 1993, Vol.107.
[41] Wada Y, Liou M-S. A Flux Splitting Scheme With High-Resolution and Robustness for Discontinuities [R]. AIAA 94-0083, 1994.
[42] Liou M-S. Progress Towards an Improved CFD Method: AUSM+ [R]. AIAA 95-1701,1995.
[43] Kim K H, Lee J H, Rho O H. An Improvement of AUSM Schemes by Introducing the Pressure-Based Weight Functions [J]. Computers and Fluids, 1998, 27(3).
[44] Kim K H, Kim C, Rho O H. Accurate Computations of Hypersonic Flows Using AUSMPW+ Scheme and Shock-Aligned Grid Technique [R]. AIAA 98-2442.
[45] Kim K H, Kim C. Accurate Efficient and Monotomic Numerical Methods for Multi-Dimensional Compressible Flows Part I: Spatial Discretization [J]. Journal of Computational Physics, 2005, 208.
[46] Yoon S, Jameson A. Lower-Upper Symmetric Gauss-Sediel Method for the Euler and Navier-Stokes Equations [J]. AIAA Journal, 1988, 26(9).
[47] Lee J H, Rho O H. Numerical Analysis of Hypersonic Viscous Flow about a Blunt Body Using Roe's FDS and AUSM+ Scheme [R]. AIAA 97-2054, 1997.
[48] Bayazitoglu Y, Tunc G. An Extension to the First Order Slip Boundary Conditions to Be Used in Early Transition Regime [R]. AIAA 2002-2779.
[49] Kennard E H. Kinetic Theory of Gasses [M]. New York: Mcgraw-Hill Book Co. Inc. 1938.
[50] Cercignani C. Mathematical Methods in Kinetic Theory [M]. New York: Plenum Press, 1990.
[51] Zheng Y, Reese J M, Scanlon T J, Lockerby D A. Scaled Navier-Stoke-Fourier Equations for Gas Flow and Heat Transfer Phenomena in Micro-and Nanosystems [C]. ICNMM 2006-96066, 2006.
[52] O'Hare L, Scanlon T J, Emerson D R, Reese J M. Evaluating Constitutive ScalingModels for Application to Compressible Microflows [J]. International Journal of Heat and Mass Transfer 51, 2008.
[53]李君哲,阎超,柯伦,张书庭.气动热CFD计算的格式效应研究[J].北京航空航天大学学报, 2003, 29(11).
[54]朱辉玉,王刚,孙泉华,樊菁.高超声速飞行气动热数值模拟的几个关键因素[C]. CSTAM 2010-0056, 2010.
[55] Bertin J J, Cummings R M. Critical Hypersonic Aerothermodynamic Phenomena [J]. Annual Review of Fluid Mechanics, 2006, 38.
[56]卞荫贵.气动热力学[M].中国科技大学出版社, 1997.
[57]栗弗席兹E M,皮塔耶夫斯基.物理动理学[M].北京:高等教育出版社, 2008.
[58] Hurlbut F C.气体与表面相互作用——最新的观察与解释[J].力学进展, 1997, 27(4).
[59] Rader D J, Trott W M, et al. Measurements of Thermal Accommodation Coefficients [C]. SAND 2005-6084, 2005.
[60] Yamaguchi H, Hanawa T, Yamamoto O, Matsuda Y, Egami Y, Niimi T. Experimental measurement on tangential momentum accommodation coefficient in a single microtube [J]. Microfluid Nanofluid, 05 February, 2011.
[61] Gronych T, Ulman R, Peksa L, Repa P. Measurements of the relative momentum accommodation coefficient for different gases with a viscosity vacuum gauge [J]. VACUUM, 73(2004), 275-279.
[62] Lofthouse A J, Boyd I D. Hypersonic Flow over a Flat Plate: CFD Comparison with Experiment [R]. AIAA 2009-1315, 2009.
[63]阎超,禹建军,李君哲.热流CFD计算中格式和网格效应若干问题研究[J].空气动力学学报, Vol 24, 2006.
[64] Siddiqui M S, Hoffmann K A, Chiang S T, Rutledge W H. A Comparative Study of The Navier-Stokes Solvers with Emphasis on The Heat Transfer Computations of High Speed Flows [R]. AIAA92-0835, 1992.
[65]黎作武,张涵信.高超声速航天飞行器气动热特性的数值模拟[C].第十届全国计算流体力学会议论文集.
[66] Chao Yan, Ruize Gao, Junzhe Li. A New Method for Estimating the First Normal Grid Spacing in Heat Flux Computations [R]. AIAA2009-832, 2009.
[67] Chpoun A, Lengrand J C, Heffner K S. Numerical and Experimental Investigation of Rarefied Compression Corner Flow [R]. AIAA 92-2900, 1992.
[68] Boylan D E. Laminar Heat Transfer on Sharp and Blunt Ten-Degree Cones in Conical and Parallel Low Density Flow [C]. Arnold Engineering Development Center, Tullahorna, TN, AEDC-TR-73-106, Aug. 1973.
[69] Lofthouse A J. Nonequilibrium Hypersonic Aerothermodynamics Using the Direct Simulation Monte Carlo and Navier-Stokes Models [D]. The University of Michigan, 2008.
[70]田正雨.高超声速流动的磁流体力学控制数值模拟研究[D].长沙:国防科技大学, 2008.04.
[71] Tannehill J C, Mugge P H. Improved Curve Fits for the Thermodynamic Properties of Equilibrium Air Suitable for Numerical Computation Using Time-Dependent or Shock-Capturing Methods [R]. NASA CR-2470, 1974.
[72] Jain A C, Woods H G. Investigation of Hypersonic Rarefied Flow on a Spherical Nose of the Aotv [R]. NASA-CR-179153, 1987.
[73] Muntz E P, Boyd I D, Ketsdever A. Rarefied Flow Testing in the 1990s: Mearuring Those Phenomena that are Difficult to Calculate [R]. AIAA 94-2631, 1994.
[74] Boyd I D, Holden M S, et al. Thermochemical Nonequilibrium Design Calculations for Detailed Hypervelocity Experiments in LENS Facility [R]. AIAA Paper 94-2403, 1994.
[75] Pham-Van-Diep, Muntz G C, et al. An Iodine Hypersonic Wind Tunnel for the Studiy of Nonequilibrium Reacting Flows [R]. AIAA Paper 92-0566, 1992.
[76] Hurlbut F. Rareifed Gas Research at Berkeley: Current Studies and Future Potentials [R]. AIAA 92-3971, 1992.
[77]戴金雯.载人飞船返回舱高空稀薄气动特性研究[D].长沙:国防科技大学, 2004, 10.
[78]王利,陆建江.激光—分子束—表面散射装置的研制[J].真空科学与技术, 1995.
[79] Cecil E, McDaniel J C. Planar Velocity and Temperature Measurements in Rarefied Hypersonic Flow Using Iodine LIF [R]. AIAA 2005-4695, 2005.
[80]李桂春.风洞试验光学测量方法[M].国防工业出版社, 2008.
[81]陈扬骎,杨晓华.激光光谱测量技术[M].华东师范大学出版社, 2006.
[2]李桦,田正雨,李伟.高超声速滑移流效应数值模拟方法分析[C].临近空间CFD研讨会,北京, 2010.
[3] Tsien H S. Superaerodynamics, mechanics of rarefied gases [J]. Aerospace Sci. Technol., 1964, 13 (12).
[4] Holman T D. Numerical Investigation of the Effects of Continuum Breakdown on Hypersonic Vehicle Surface Properties [D]. The University of Michigan, 2010.
[5] Cercignani C, Illner R, Pulvirenti M. The Mathematical Theory of Dilute Gases [M].北京:高等教育出版社, 2009..
[6] Burnett D. The Distribution of Molecular Velocities and The Mean Motion in a Nonuinform Gas [J]. Proc. Lond Math Soc., 1935.
[7] Grad H. On the Kinetic Theory of Rarefied Gases. [J]. Commun Pure Appl Math, 1949.
[8] Myong R S. Thermodynamically Consistent Hydrodynamic Computational Models for High-Knudsen-Number Gas Flows [J]. Phsics of Fluids, Volume 11, Number 9, 1999.
[9] Torrilhon M. Tow-Dimentional Bulk Microflow Simulations Based on Regularized Grad's 13-Moment Equations [J]. Multiscale Model Simul. 2006, 5(3).
[10] Myong R S. Impact of Computational Physics on Multi-Scale CFD and Related Numerical Algorithms [J]. Compers and Fluids, 2011.
[11] Bird G A. Gas Dynamics and the Direct Simulation of Gas Flows [M]. Oxford University Press, Oxford, 1994.
[12] Bird G A. Application of the DSMC Method to the Full Shuttle Geometry [R]. AIAA Paper 90-1392, 1990.
[13] Pham-Van-Diep, et al. Nonequilibrium Molecular Motion in a Hypersonic Shock Wave [J]. Science 1989, 245.
[14]沈青. MEMS稀薄气体内部流动模拟中的信息保存(IP)法[J].力学进展, 2006, 36(1).
[15] Shen C. Gas Flow in Micro Chanels-Experimental, Computational and Kinetic Theoretical Investigations [J]. Micro and Nanosystems, 2009, 1(3).
[16] Fan J, Sun Q. Kinetic Studies of Gas Flows [C]. ISCM II and EPMESC XII, 2009.
[17]胡远,陈松,孙泉华,樊菁.超声速平板绕流的全流域阻力特性研究[C].CSTAM 2010-0049, 2010.
[18] Sone Y. Kinetic Theory and Fluid Dynamics [M]. Birkhauser, 2002.
[19] Chen S, Doolen G D. Lattice Boltzmann Method for Fluid Flows [J]. Anuu. Rev. Fluid Mech. 1998.
[20] Reese J M, Gallis M A, Lockerby D A. New Direction in Fluid Dynamics: Non-Equilibrium Aerodynamic and Microsystem Flows [J]. Philosophical Transactions of The Royal Society (A): Mathematical, Physical and Engineering Sciences, 2003.
[21] Myong R S. Velocity Slip Effect in Low-Speed Microscale Gas [R]. AIAA Paper 2001-3076.
[22] Lockerby D A. Geometric and Constitutive Dependence of Maxwell's Velocity Slip Boundary Condition [R] ADA Report, 2005.
[23] Bailey. A Critical Review of The Drag Force On A Sphere In The Transition Flow Regime [R]. ADA Report, 2005.
[24] Lofthouse A J, Scalabrin L C, Boyd I D. Velocity Slip and Temperature Jump in Hypersonic Aerothermodynamics [R]. AIAA 2007-208, 2007.
[25] Maxwell J C. On Stresses in Rarefied Gases Arising from Inequilities of Temperature [J]. Philosophical Transactions of The Royal Society, 1879, 2(1).
[26] Gokcen T, MacCormack R W. Nonequilibrium Effects for Hypersonic Transitional Flows Using Continuum Approach [R]. AIAA Paper 1989-0461, 1989.
[27] Lockerby D A, Reese J M, Emerson D R, Barber R W. Velocity Boundary Condition at Solid Walls in Rareedgas Calculations [J]. Physical Review E, 70(017303), 2004.
[28] Lockerby D A, Reese J M, Gallis M A. Capturing the Knudsen Layer in Continuum-Fluid Models of Nonequilibrium Gas Flows [J]. AIAA Journal, 43(6), 2005.
[29] Cercignani C. Higher Order Slip According to the Linearized Boltzmann Equation [J]. Institute of Engineering Research Report AS-64-19, 1964.
[30] Deissler R. An Analysis of Second-Order Slip Flow and Temperature-Jump Boundary Conditions for Rarefied Gases [J]. Int. J.Heat Mass Transfer, 1965, 7.
[31] Beskod A, Karniadakis G. Rarefaction and Compressibility Effects in Gas Microflows [J]. J. Fluids Engin. 1996,11.
[32] Karniadakis G, Beskod A. Micro Flows [M]. New York: Springer-Verlag, 2002.
[33] Choong K O, Elaine S O. A New Hybrid Algorithm: Navier-Stokes as a DSMC Filter [R]. AIAA Paper 98-0849, 1998.
[34] Roveda R, Goldstein D B, Varghese P L. Unsteady Calculation of Slip Flow with 2-D Hybrid Euler/DSMC Numerical Approach [R]. AIAA Paper 98-0852, 1998.
[35] Nie X B, Chen S Y, et al. A Continuum and Molecular Dynamics Hybrid Methodfor Micro-and-Nano-Fluid Flow [J]. J. Fluid Mech. 2004.
[36] Schwartzentruber T E, Scalabrin L C, Boyd I D. Hybrid Particle-Continuum Simulations of Nonequilibrium Hypersonic Blunt-Body Flowfields [J]. Journal of Thermophysics and Heat Transfer, 2008, 22(1).
[37] Lilley C R, Macrossan M N. Methods for Implementing the Stream Boundary Condition in DSMC Computations [J]. International Journal for Numerical Methods in Fluids 42, 2003.
[38]陈懋章.粘性流体动力学基础[M].北京:高等教育出版社, 2002.
[39]阎超.计算流体力学方法及应用[M].北京:北京航空航天大学出版社, 2006.
[40] Liu M-S, Steffen J. A New Flux Splitting Scheme [J]. Journal of Computational Physics, 1993, Vol.107.
[41] Wada Y, Liou M-S. A Flux Splitting Scheme With High-Resolution and Robustness for Discontinuities [R]. AIAA 94-0083, 1994.
[42] Liou M-S. Progress Towards an Improved CFD Method: AUSM+ [R]. AIAA 95-1701,1995.
[43] Kim K H, Lee J H, Rho O H. An Improvement of AUSM Schemes by Introducing the Pressure-Based Weight Functions [J]. Computers and Fluids, 1998, 27(3).
[44] Kim K H, Kim C, Rho O H. Accurate Computations of Hypersonic Flows Using AUSMPW+ Scheme and Shock-Aligned Grid Technique [R]. AIAA 98-2442.
[45] Kim K H, Kim C. Accurate Efficient and Monotomic Numerical Methods for Multi-Dimensional Compressible Flows Part I: Spatial Discretization [J]. Journal of Computational Physics, 2005, 208.
[46] Yoon S, Jameson A. Lower-Upper Symmetric Gauss-Sediel Method for the Euler and Navier-Stokes Equations [J]. AIAA Journal, 1988, 26(9).
[47] Lee J H, Rho O H. Numerical Analysis of Hypersonic Viscous Flow about a Blunt Body Using Roe's FDS and AUSM+ Scheme [R]. AIAA 97-2054, 1997.
[48] Bayazitoglu Y, Tunc G. An Extension to the First Order Slip Boundary Conditions to Be Used in Early Transition Regime [R]. AIAA 2002-2779.
[49] Kennard E H. Kinetic Theory of Gasses [M]. New York: Mcgraw-Hill Book Co. Inc. 1938.
[50] Cercignani C. Mathematical Methods in Kinetic Theory [M]. New York: Plenum Press, 1990.
[51] Zheng Y, Reese J M, Scanlon T J, Lockerby D A. Scaled Navier-Stoke-Fourier Equations for Gas Flow and Heat Transfer Phenomena in Micro-and Nanosystems [C]. ICNMM 2006-96066, 2006.
[52] O'Hare L, Scanlon T J, Emerson D R, Reese J M. Evaluating Constitutive ScalingModels for Application to Compressible Microflows [J]. International Journal of Heat and Mass Transfer 51, 2008.
[53]李君哲,阎超,柯伦,张书庭.气动热CFD计算的格式效应研究[J].北京航空航天大学学报, 2003, 29(11).
[54]朱辉玉,王刚,孙泉华,樊菁.高超声速飞行气动热数值模拟的几个关键因素[C]. CSTAM 2010-0056, 2010.
[55] Bertin J J, Cummings R M. Critical Hypersonic Aerothermodynamic Phenomena [J]. Annual Review of Fluid Mechanics, 2006, 38.
[56]卞荫贵.气动热力学[M].中国科技大学出版社, 1997.
[57]栗弗席兹E M,皮塔耶夫斯基.物理动理学[M].北京:高等教育出版社, 2008.
[58] Hurlbut F C.气体与表面相互作用——最新的观察与解释[J].力学进展, 1997, 27(4).
[59] Rader D J, Trott W M, et al. Measurements of Thermal Accommodation Coefficients [C]. SAND 2005-6084, 2005.
[60] Yamaguchi H, Hanawa T, Yamamoto O, Matsuda Y, Egami Y, Niimi T. Experimental measurement on tangential momentum accommodation coefficient in a single microtube [J]. Microfluid Nanofluid, 05 February, 2011.
[61] Gronych T, Ulman R, Peksa L, Repa P. Measurements of the relative momentum accommodation coefficient for different gases with a viscosity vacuum gauge [J]. VACUUM, 73(2004), 275-279.
[62] Lofthouse A J, Boyd I D. Hypersonic Flow over a Flat Plate: CFD Comparison with Experiment [R]. AIAA 2009-1315, 2009.
[63]阎超,禹建军,李君哲.热流CFD计算中格式和网格效应若干问题研究[J].空气动力学学报, Vol 24, 2006.
[64] Siddiqui M S, Hoffmann K A, Chiang S T, Rutledge W H. A Comparative Study of The Navier-Stokes Solvers with Emphasis on The Heat Transfer Computations of High Speed Flows [R]. AIAA92-0835, 1992.
[65]黎作武,张涵信.高超声速航天飞行器气动热特性的数值模拟[C].第十届全国计算流体力学会议论文集.
[66] Chao Yan, Ruize Gao, Junzhe Li. A New Method for Estimating the First Normal Grid Spacing in Heat Flux Computations [R]. AIAA2009-832, 2009.
[67] Chpoun A, Lengrand J C, Heffner K S. Numerical and Experimental Investigation of Rarefied Compression Corner Flow [R]. AIAA 92-2900, 1992.
[68] Boylan D E. Laminar Heat Transfer on Sharp and Blunt Ten-Degree Cones in Conical and Parallel Low Density Flow [C]. Arnold Engineering Development Center, Tullahorna, TN, AEDC-TR-73-106, Aug. 1973.
[69] Lofthouse A J. Nonequilibrium Hypersonic Aerothermodynamics Using the Direct Simulation Monte Carlo and Navier-Stokes Models [D]. The University of Michigan, 2008.
[70]田正雨.高超声速流动的磁流体力学控制数值模拟研究[D].长沙:国防科技大学, 2008.04.
[71] Tannehill J C, Mugge P H. Improved Curve Fits for the Thermodynamic Properties of Equilibrium Air Suitable for Numerical Computation Using Time-Dependent or Shock-Capturing Methods [R]. NASA CR-2470, 1974.
[72] Jain A C, Woods H G. Investigation of Hypersonic Rarefied Flow on a Spherical Nose of the Aotv [R]. NASA-CR-179153, 1987.
[73] Muntz E P, Boyd I D, Ketsdever A. Rarefied Flow Testing in the 1990s: Mearuring Those Phenomena that are Difficult to Calculate [R]. AIAA 94-2631, 1994.
[74] Boyd I D, Holden M S, et al. Thermochemical Nonequilibrium Design Calculations for Detailed Hypervelocity Experiments in LENS Facility [R]. AIAA Paper 94-2403, 1994.
[75] Pham-Van-Diep, Muntz G C, et al. An Iodine Hypersonic Wind Tunnel for the Studiy of Nonequilibrium Reacting Flows [R]. AIAA Paper 92-0566, 1992.
[76] Hurlbut F. Rareifed Gas Research at Berkeley: Current Studies and Future Potentials [R]. AIAA 92-3971, 1992.
[77]戴金雯.载人飞船返回舱高空稀薄气动特性研究[D].长沙:国防科技大学, 2004, 10.
[78]王利,陆建江.激光—分子束—表面散射装置的研制[J].真空科学与技术, 1995.
[79] Cecil E, McDaniel J C. Planar Velocity and Temperature Measurements in Rarefied Hypersonic Flow Using Iodine LIF [R]. AIAA 2005-4695, 2005.
[80]李桂春.风洞试验光学测量方法[M].国防工业出版社, 2008.
[81]陈扬骎,杨晓华.激光光谱测量技术[M].华东师范大学出版社, 2006.