超声速和高超声速燃烧的数值研究
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摘要
为了研究HLLC黎曼求解器在超声速和高超声速燃烧问题中的适用性,对4个典型算例进行了数值模拟。基于多组分方程的完全N-S方程,对时间项和空间项离散分别采用2阶Runge-kutta方法和HLLC格式,考虑了H_2/Air燃烧的详细化学反应机理,用有限速率化学反应模型模拟燃烧现象。对Sod激波管问题和高超声速钝体绕流进行数值模拟,分析了流场内密度、压力和激波位置;对超声速燃烧和高超声速钝体激波诱导燃烧进行数值模拟,分析了流场内组分特性。数值模拟结果与实验结果或相关文献的计算结果吻合良好,表明了HLLC黎曼求解器在模拟复杂化学非平衡流场中能够准确地分析复杂的物理现象且具有较广的应用范围。
Four typical examples were numerically simulated to investigate the validity of HLLC Riemann solver in the application of supersonic and hypersonic combustion.Based on the perfect Navier-Stokes equations of multi-component equations,the convection fluxes was calculated by the HLLC scheme,while two-stage Runge-Kutta iterative method was used for time discretization.The detailed chemical reaction of H_2/Air was considered,and the finite-rate chemical-reaction model was applied to simulate the combustion.Sod shock-tube problems and hypersonic flow around blunt body were numerically simulated,and the flow-field density,pressure and shock-wave position were analyzed.The supersonic combustion and the combustion induced by hypersonic-blunt-body shock-wave were simulated,and the composition characteristics of flow field was analyzed.The numerical simulation results are in good agreement with the experimental results or the related literature.By the HLLC Riemann solver,the complex physical phenomena can be accurately analyzed,and the solver has wide application range in complex chemical non-equilibrium flow-field.
Four typical examples were numerically simulated to investigate the validity of HLLC Riemann solver in the application of supersonic and hypersonic combustion.Based on the perfect Navier-Stokes equations of multi-component equations,the convection fluxes was calculated by the HLLC scheme,while two-stage Runge-Kutta iterative method was used for time discretization.The detailed chemical reaction of H_2/Air was considered,and the finite-rate chemical-reaction model was applied to simulate the combustion.Sod shock-tube problems and hypersonic flow around blunt body were numerically simulated,and the flow-field density,pressure and shock-wave position were analyzed.The supersonic combustion and the combustion induced by hypersonic-blunt-body shock-wave were simulated,and the composition characteristics of flow field was analyzed.The numerical simulation results are in good agreement with the experimental results or the related literature.By the HLLC Riemann solver,the complex physical phenomena can be accurately analyzed,and the solver has wide application range in complex chemical non-equilibrium flow-field.
引文
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[19]张涵信,陈坚强,高树椿.H2/O2燃烧的超声速非平衡流动的数值模拟[J].宇航学报,1994,4(2):14-23.ZHANG Han-xin,CHEN Jian-qiang,GAO Shu-chun.Numerical simulation of supersonic non-equilbrium flows for H2/O2combustions[J].Journal of Astronautics,1994,4(2):14-23.(in Chinese)
[20]KIM K M,BAEK S W,HAN C Y.Numerical study on supersonic combustion with cavity-based fuel injection[J].International Journal of Heat and Mass Transfer,2004,47(2):271-286.
[21]VISWANATH R K.Comparison of chemical-kinetics models for predicting premixed and non-premixed flames:AIAA 2006-4745[R].Sacramento,CA:AIAA,2006.
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[23]SHANG H M,CHEN Y S,LIAW P,et al.Investigation of chemical kinetics integration algorithms for reacting flows:AIAA 1995-0806[R].Reno,NV:AIAA,1995.
[24]TORO E F.Riemann solvers and numerical methods for fluid dynamics:a practical introduction[M].London:Springer Science&Business Media,2013.
[25]KEMM F.A comparative study of TVD-limiters:well-known limiters and an introduction of new ones[J].International Journal for Numerical Methods in Fluids,2011,67(4):404-440.
[26]BURROWS M C,KURKOV A P.An analytical and experimental study of supersonic combustion of hydrogen in vitiated air stream[J].AIAA Journal,1973,11(9):1 217-1 218.
[27]LEHR H F.Experiments on shock-induced combustion[J].Astronautica Acta,1972,17:589-597.
[28]YUNGSTER S,EBERHARDT S,BRUCKNER A P.Numerical simulation of hypervelocity projectiles in detonable gases[J].AIAA Journal,1991,29(2):187-199.
[2]汪秋笑,黄东欣,孟华.甲烷-液氧超临界压力非预混湍流燃烧的数值模拟[J].航空学报,2016,31(7):2 132-2 143.WANG Qiu-xiao,HUANG Dong-xin,MENG Hua.Numerical simulation of CH4-LOx non-premixed turbulent combustion at supercritical pressures[J].Acta Aeronautica et Astronautica Sinica,2016,31(7):2 132-2 143.(in Chinese)
[3]周力行.两相燃烧的大涡模拟[J].中国科学:技术科学,2014,44(1):41-49.ZHOU Li-xing.Large-eddy simulation of two-phase combustion[J].Scientia Sinica Technologica,2014,44(1):41-49.(in Chinese)
[4]金台.超声速湍流燃烧多物理耦合的直接数值模拟研究[D].杭州:浙江大学,2015.JIN Tai.Supersonic turbulent combustion multi-physical coupled of direct numerical simulation studies[D].Hangzhou:Zhejiang University,2015.(in Chinese)
[5]KLIMENKO A Y,BILGER R W.Conditional moment closure for turbulent combustion[J].Progress in Energy and Combustion Science,1999,25(6):595-687.
[6]EIFLER P,KOLLMANN W.PDF prediction of supersonic hydrogen flames:AIAA 1993-0448[R].Reno,NV:AIAA,1993.
[7]BAURLE R A,GIRIMAJI S S.Assumed PDF turbulence-chemistry closure with temperature-composition correlations[J].Combustion and Flame,2003,134(1):131-148.
[8]PETERS N.Laminar flamelet concepts in turbulent combustion[C]//Symposium(International)on Combustion.Berlin:Elsevier,1988:1 231-1 250.
[9]罗坤,金台,卢树强,等.超音速氢气燃烧火焰结构特性的直接数值模拟[J].工程热物理学报,2012,33(11):2 010-2 014.LUO Kun,JIN Tai,LU Shu-qiang,et al.DNS of flame structure characteristics in a supersonic hydrogen combustion[J].Journal of Engineering Thermophysics,2012,33(11):2 010-2 014.(in Chinese)
[10]HARTEN A.High resolution schemes for hyperbolic conservation laws[J].Journal of Computational Physics,1983,49(3):357-393.
[11]张涵信.无波动、无自由参数的耗散差分格式[[J].空气动力学学报,1988,6(2):143-165.ZHANG Han-xin.Non-oscillatory and non-free-parameter dissipation difference scheme[J].Acta Aerodynamic Sincia,1988,6(2):143-165.(in Chinese)
[12]SHU C W.Essentially non-oscillatory and weighted essentially nonoscillatory schemes for hyperbolic conservation laws[M]//Advanced Numerical Approximation of Nonlinear Hyperbolic Equations.Berlin:Springer,1998:325-432.
[13]LIOU M S.A sequel to ausm:Ausm+[J].Journal of Computational Physics,1996,129(2):364-382.
[14]KIM K H,LEE J H,RHO O H.An improvement of AUSM schemes by introducing the pressure-based weight functions[J].Computers&Fluids,1998,27(3):311-346.
[15]KIM K H,KIM C,RHO O H.Accurate computations of hypersonic flows using AUSMPW+scheme and shock-aligned grid technique:AIAA 1998-2442[R].[S.l]:AIAA,1998.
[16]王伟臣,魏志军,张峤,等.后燃对火箭发动机羽流红外特性的影响[J].航空动力学报,2010,25(11):2 612-2 618.WANG Wei-chen,WEI Zhi-jun,ZHANG Qiao,et al.Influence of afterburning on infrared signature of rocket motor exhaust plume[J].Journal of Aerospace Power,2010,25(11):2 612-2 618.(in Chinese)
[17]韩省思,叶桃红,朱旻明,等.应用修正的k-ε模型研究超声速H2/Air燃烧[J].推进技术,2008,29(2):158-162.HAN Xing-si,YE Tao-hong,ZHU Min-ming,et al.Numerical simulation of supersonic H2/Air combustion appling modified k-εturbulence model[J].Journal of Propulsion Technology,2008,29(2):158-162.(in Chinese)
[18]刘君.化学动力学模型对H2/Air超燃模拟的影响[J].推进技术,2003,22(1):67-70.LIU Jun.Numerical study on chemical mechanism in supersonic H2/Air mixture gas flow[J].Journal of Propulsion Technology,2003,22(1):67-70.(in Chinese)
[19]张涵信,陈坚强,高树椿.H2/O2燃烧的超声速非平衡流动的数值模拟[J].宇航学报,1994,4(2):14-23.ZHANG Han-xin,CHEN Jian-qiang,GAO Shu-chun.Numerical simulation of supersonic non-equilbrium flows for H2/O2combustions[J].Journal of Astronautics,1994,4(2):14-23.(in Chinese)
[20]KIM K M,BAEK S W,HAN C Y.Numerical study on supersonic combustion with cavity-based fuel injection[J].International Journal of Heat and Mass Transfer,2004,47(2):271-286.
[21]VISWANATH R K.Comparison of chemical-kinetics models for predicting premixed and non-premixed flames:AIAA 2006-4745[R].Sacramento,CA:AIAA,2006.
[22]CHOI J Y,SHIN E,KIM C K.Numerical study of base-bleed projectile with external combustion[C]//41st AIAA/ASME/SAE/ASEE Joint Propulsion Conference&Exhibit.Ariiona:AIAA.2005:10-13.
[23]SHANG H M,CHEN Y S,LIAW P,et al.Investigation of chemical kinetics integration algorithms for reacting flows:AIAA 1995-0806[R].Reno,NV:AIAA,1995.
[24]TORO E F.Riemann solvers and numerical methods for fluid dynamics:a practical introduction[M].London:Springer Science&Business Media,2013.
[25]KEMM F.A comparative study of TVD-limiters:well-known limiters and an introduction of new ones[J].International Journal for Numerical Methods in Fluids,2011,67(4):404-440.
[26]BURROWS M C,KURKOV A P.An analytical and experimental study of supersonic combustion of hydrogen in vitiated air stream[J].AIAA Journal,1973,11(9):1 217-1 218.
[27]LEHR H F.Experiments on shock-induced combustion[J].Astronautica Acta,1972,17:589-597.
[28]YUNGSTER S,EBERHARDT S,BRUCKNER A P.Numerical simulation of hypervelocity projectiles in detonable gases[J].AIAA Journal,1991,29(2):187-199.