高超声速流存在局部稀薄效应的一个判据及相应的流动特性
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摘要
对于近空间高超声速飞行器的研制,计算流体力学(CFD)起着非常重要的作用。但若流场中存在必须考虑气体稀薄效应的地方,传统的CFD就要做相应的改变,这时首先遇到的问题将是判断是否需要考虑气体的稀薄效应的判据应该是什么?[1]其次就是气体稀薄效应的影响表现在什么地方?如何在CFD中考虑这一效应?本文选取具有代表性的高超声速剪切流为研究对象,采用直接模拟Monte Carlo(DSMC)方法,对剪切强度和稀薄程度不断增强的流动,研究了分子运动速度分布函数以及剪切力的相应变化规律;找到了一个可以判别气体稀薄效应程度的无量纲参数Zh,以及传统连续介质模型下的剪切力和由DSMC所得剪切力随参数Zh的增大而出现的有规律性的差别。
Computational Fluid Dynamics(CFD)plays a very important role in the development of near space flying vehicles.However,at places where the rarefaction effect of the gas has to be considered,the conventional CFD has to be modified accordingly.Then the first question one has to answer is what would be the appropriate criterion for assessing if the rarefaction effect should be taken into consideration.And then what is the main manifestation of the rarefaction effect and how to consider this effect in CFD?In this paper,a typical hypersonic shear flow is studied by Direct Simulation Monte Carlo(DSMC).The probability density function and shear stress are investigated in details for different degrees of rarefaction and different shear strengths.A parameter Zh which can characterize the rarefaction effect is proposed,and the difference between the shear stresses obtained by the conventional continuum model and those obtained by DSMC is found to be increasing as the parameter Zh is increasing but follows a definite rule.
Computational Fluid Dynamics(CFD)plays a very important role in the development of near space flying vehicles.However,at places where the rarefaction effect of the gas has to be considered,the conventional CFD has to be modified accordingly.Then the first question one has to answer is what would be the appropriate criterion for assessing if the rarefaction effect should be taken into consideration.And then what is the main manifestation of the rarefaction effect and how to consider this effect in CFD?In this paper,a typical hypersonic shear flow is studied by Direct Simulation Monte Carlo(DSMC).The probability density function and shear stress are investigated in details for different degrees of rarefaction and different shear strengths.A parameter Zh which can characterize the rarefaction effect is proposed,and the difference between the shear stresses obtained by the conventional continuum model and those obtained by DSMC is found to be increasing as the parameter Zh is increasing but follows a definite rule.
引文
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[16]Eu B C.Kinetic theory and irreversible thermodynamics[M].Canada:John Wiley&Sons,Inc.,1992.
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[22]Fan J.Rarefied gas dynamics:Advances and applications[J].Advances in Mechanics,2013,43(2):185-201.(in Chinese)樊菁.稀薄气体动力学[J].进展与应用,力学进展,2013,43(2):185-201.
[23]Fan J,Shen C.Statistical simulation of low-speed rarefied gas flows[J].J Comput Phys,2001,167:393-412.
[24]Wu L,White C,Scanlon T C,et al.Deterministic numerical solutions of the Boltzmann equation using the fast spectral method[J].J Comput Phys,2013,250(1):27-52.
[25]Xu K,Huang J C.A unified gas-kinetic scheme for continuum and rarefied flows[J].J Comput Phys,2010,229(20):7747-7764.
[26]Li Z H,Zhang H X.Study on gas kinetic unified algorithm for flows from rarefied transition to continuum[J].J Comput Phys,2004,193(2):708-738.
[27]Li Z H,Zhang H X.Study on gas kinetic unified algorithm for flows from rarefied transition to continuum[J].Acta Aerodynamica Sinica,2003,21(3):255-266.(in Chinese)李志辉,张涵信.稀薄流到连续流的气体运动论统一算法研究[J].空气动力学学报,2003,21(3):255-266.
[28]Xu K.Direct modeling for computational fluid dynamics:construction and application of unified gas-kinetic schemes[M].World Scientific Publishing Co,2015.
[29]Chapman S,Cowling T.The mathematical theory of nonuniform gases[M].London:Cambridge Univ.Press,1970.
[30]Burnett D.The distribution of molecular velocities and the mean motion in a non-uniform gas[J].Proceedings of the London Mathematical Society,1936,2(1):382-435.
[31]Gu X J,Emerson D R.A high-order moment approach for capturing non-equilibrium phenomena in the transition regime[J].J Fluid Mech,2009,636:177.
[32]Myong R S.Thermodynamically consistent hydrodynamic computational models for high-Knudsen-number gas flow[J].Physic of Fluids,1999,11(9):2788-2802.
[33]Xiao H,Shang Y H,Wu D,et al.Nonlinear coupled constitutive relations and its validation for rarefied gas flow[J].Acta Aeronautica et Astronautica Sinica,2015,36(7):2091-2104.(in Chinese)肖洪,商雨禾,吴迪,等.稀薄气体动力学的非线性耦合本构方程理论及验证[J].航空学报,2015,36(7):2091-2104.
[2]Zhang S H,Li Q,Zhang L P,et al.The history of CFD in China[J].Acta Aerodynamica Sinica,2016,34(2):157-174.(in Chinese)张树海,李沁,张来平,等.中国CFD史(英文)[J].空气动力学学报,2016,34(2):157-174.
[3]Zhang H X.Investigations on fidelity of high order accurate numerical simulation for computational fluid dynamics[J].Acta Aerodynamica Sinica,2016,34(1):1-4.张涵信.关于CFD高精度保真的数值模拟研究[J].空气动力学学报,2016,34(1):1-4.(in Chinese)
[4]Tsien H S.Superarodynamics,mechanics of rarefied gas[J].J Aerospace Sci,1946,13:342.
[5]Kandlikar S G,Garimella S,Li D,et al.Heat transfer and fluid flow in minichannels and microchannels[M].Second Edition,Elsevier,2013.
[6]Shen Q.Rarefied gas dynamics[M].Beijing:National Defense Industry Press,2003.(in Chinese)沈青,稀薄气体动力学[M].北京:国防工业出版社,2003.
[7]Bird G A.Breakdown of translational and rotational equilibrium in gaseous expansions[J].AIAA J,1970,8(11):1998-2003.
[8]Boyd I D,Chen G,Candler G V.Predicting failure of the continuum fluid equations in transitional hypersonic flows[J].Phys Fluids,1995,7(1):210-219.
[9]Wang W L,Boyd I D.Predicting continuum breakdown in hypersonic viscous flows[J].Phys Fluids,2003,15(1):91-100.
[10]Sun Q H,Boyd I D,Candler G V.A hybrid continuum/particle approach for modeling subsonic,rarefied gas flows[J].J Comput Phys,2004,194(1):256-277.
[11]Li Z H,Li Z H,Li H Y,et al.Research on CFD/DSMC hybrid numerical method in rarefied flows[J].Acta Aerodynamica Sinica,2015,33(2):266-271.(in Chinese)李中华,李志辉,李海燕,等.过渡流区N-S/DSMC耦合计算研究[J].空气动力学学报,2015,33(2):266-271.
[12]Lockerby D A,Reese J M,Struchtrup H.Switching criteria for hybrid rarefied gas flow solvers[J].Proceedings of the Royal Society A:Mathematical,Physical and Engineering Science,2009,465(2105):1581.
[13]Grad H.On the kinetic theory of rarefied gases[J].Communications on Pure and Applied Mathematics,1949,2(4):331-407.
[14]Meng J P,Dongari N,Reese J M,et al.Breakdown parameter for kinetic modeling of multiscale gas flows[J].Phys Rev E,2014,89(6):63306.
[15]Meng J P,Zhang Y H,Shan X W.Multiscale lattice Boltzmann approach to modeling gas flows[J].Phys Rev E,2011,83(4):046701.
[16]Eu B C.Kinetic theory and irreversible thermodynamics[M].Canada:John Wiley&Sons,Inc.,1992.
[17]Camberos J,Schrock C,McMullan R,et al.Development of continuum onset criteria with direct simulation Monte-Carlo using Boltzmann’s h-theorem:review and vision[C]//9th AIAA/ASME Joint Thermophysics and Heat Transfer Conference,AIAA,2006:2006-2942.
[18]Xiao H,Myong R S,Singh S.A new near-equilibrium breakdown parameter based on the Rayleigh-Onsager dissipation function[J].AIP Conference Proceedings,2014,1628:527.
[19]Bird G A.Moleculargas dynamics and the direct simulation of gas flows[M].Oxford:Clarendon Press.1994.
[20]Bird G A.Recent advances and current challenges for DSMC[J].Computer Math Applic,1998,35:1-14.
[21]Shen C.Rarefiedgas dynamics:Fundamentals,simulations and Micro-flows[M].Springer,Berlin,2005.
[22]Fan J.Rarefied gas dynamics:Advances and applications[J].Advances in Mechanics,2013,43(2):185-201.(in Chinese)樊菁.稀薄气体动力学[J].进展与应用,力学进展,2013,43(2):185-201.
[23]Fan J,Shen C.Statistical simulation of low-speed rarefied gas flows[J].J Comput Phys,2001,167:393-412.
[24]Wu L,White C,Scanlon T C,et al.Deterministic numerical solutions of the Boltzmann equation using the fast spectral method[J].J Comput Phys,2013,250(1):27-52.
[25]Xu K,Huang J C.A unified gas-kinetic scheme for continuum and rarefied flows[J].J Comput Phys,2010,229(20):7747-7764.
[26]Li Z H,Zhang H X.Study on gas kinetic unified algorithm for flows from rarefied transition to continuum[J].J Comput Phys,2004,193(2):708-738.
[27]Li Z H,Zhang H X.Study on gas kinetic unified algorithm for flows from rarefied transition to continuum[J].Acta Aerodynamica Sinica,2003,21(3):255-266.(in Chinese)李志辉,张涵信.稀薄流到连续流的气体运动论统一算法研究[J].空气动力学学报,2003,21(3):255-266.
[28]Xu K.Direct modeling for computational fluid dynamics:construction and application of unified gas-kinetic schemes[M].World Scientific Publishing Co,2015.
[29]Chapman S,Cowling T.The mathematical theory of nonuniform gases[M].London:Cambridge Univ.Press,1970.
[30]Burnett D.The distribution of molecular velocities and the mean motion in a non-uniform gas[J].Proceedings of the London Mathematical Society,1936,2(1):382-435.
[31]Gu X J,Emerson D R.A high-order moment approach for capturing non-equilibrium phenomena in the transition regime[J].J Fluid Mech,2009,636:177.
[32]Myong R S.Thermodynamically consistent hydrodynamic computational models for high-Knudsen-number gas flow[J].Physic of Fluids,1999,11(9):2788-2802.
[33]Xiao H,Shang Y H,Wu D,et al.Nonlinear coupled constitutive relations and its validation for rarefied gas flow[J].Acta Aeronautica et Astronautica Sinica,2015,36(7):2091-2104.(in Chinese)肖洪,商雨禾,吴迪,等.稀薄气体动力学的非线性耦合本构方程理论及验证[J].航空学报,2015,36(7):2091-2104.