超声速流动中非线性EASM湍流模式应用研究
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摘要
针对超声速复杂流动区域精确模拟的需要,发展了基于k-ω可压缩修正形式的非线性显式代数雷诺应力模式(EASM),提高了该模式对超声速复杂流动的数值模拟精度。通过对二维超声速凹槽和三维双椭球的数值计算表明,与SA和SST常规线性涡黏性湍流模式比较,非线性的EASM模式对大分离以及剪切层流动结构的刻画能力更精细,对剪切层再附区的压力及摩擦系数分布模拟更加精确;EASM模式能够准确地模拟二次激波引起的压强和热流分布情况。
To meet the needs of simulating complex supersonic flow regions accurately,the nonlinear explicit algebraic Reynolds stress model( EASM) based on the form of k-ω compressibility modification is developed.The numerical simulation accuracy of the model for supersonic flow is improved. The flows of 2-D supersonic cavity and 3-D hypersonic double ellipsoid are calculated by EASM. Compared with the conventional linear eddy viscosity models( SA and SST turbulence models),EASM has the potential ability to describe the flow structure of massive separation and shear layer in more sophisticated detail and simulate pressure and friction coefficient distribution in the region where shear layer reattaches more precisely. Distribution of pressure and heat flux induced by secondary shock wave are simulated accurately.
To meet the needs of simulating complex supersonic flow regions accurately,the nonlinear explicit algebraic Reynolds stress model( EASM) based on the form of k-ω compressibility modification is developed.The numerical simulation accuracy of the model for supersonic flow is improved. The flows of 2-D supersonic cavity and 3-D hypersonic double ellipsoid are calculated by EASM. Compared with the conventional linear eddy viscosity models( SA and SST turbulence models),EASM has the potential ability to describe the flow structure of massive separation and shear layer in more sophisticated detail and simulate pressure and friction coefficient distribution in the region where shear layer reattaches more precisely. Distribution of pressure and heat flux induced by secondary shock wave are simulated accurately.
引文
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[2]Menter F R.Two-equation eddy viscosity turbulence models for engineering applications[J].AIAA Journal,1994,32(8):1598-1605.
[3]赵勇,高云,王天霖,等.逆压梯度边界层未分离情况下的湍流模式适用性研究[J].计算力学学报,2016,33(3):357-361.(ZHAO Yong,GAO Yun,WANG Tian-lin,et al.Turbulence model applicability for boundary layer flow with adverse pressure gradient in attached case[J].Chinese Journal of Computational Mechanics,2016,33(3):357-361.(in Chinese))
[4]阎超,于剑,徐晶磊,等.CFD模拟方法的发展成就与展望[J].力学进展,2011,41(5):562-589.(YAN Chao,YU Jian,XU Jing-lei,et al.On the achievements and prospects for the methods of computational fluid dynamics[J].Advances in Mechanics,2011,41(5):562-589.(in Chinese))
[5]Gatski T B,Speziale C G.On explicit algebraic stress models for complex turbulent flows[J].Journal of Fluid Mechanics,1993,254(1):59-78.
[6]Johansson A,Wallin S.A new explicit algebraic Reynolds stress model[A].6t hEuropean Turbulence Conference[C].Lausanne,Switzerland,1996.
[7]Wallin S,Johansson A.An explicit algebraic Reynolds stress model for incompressible and compressible turbulent flows[J].Journal of Fluid Mechanics,2000,403:89-132.
[8]Pope S B.A more general effective-viscosity hypothesis[J].Journal of Fluid Mechanics,1975,72(2):331-340.
[9]You Y C,Buanga B,Hannemann V,et al.Evaluation of turbulence models in predicting hypersonic and subsonic base flows using grid adaptation techniques[J].Chinese Journal of Aeronautics,2012,25(3):325-334.
[10]赵慧勇,雷波,乐嘉陵.非线性EASM在激波与湍流边界层相互作用中的数值应用[J].航空动力学报,2011,26(4):860-866.(ZHAO Hui-yong,LEI Bo,LE Jia-ling.Numerical application of nonlinear EASM model to the interaction between shock waves/turbulent boundary layer[J].Journal of Aerospace Power,2011,26(4):860-866.(in Chinese))
[11]聂胜阳,高正红,黄江涛.EARSM和DRSM在亚音速旋涡流动中的应用[J].应用力学学报,2011,28(6):602-607.(NIE Sheng-yang,GAO Zheng-hong,HUANG Jiang-tao.Application of EARSM and DRSM in subsonic vortex flow[J].Chinese Journal of Applied Mechanics,2011,28(6):602-607.(in Chinese))
[12]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.(YAN Chao.The Computational Fluid Dynamics Method and Application[M].Beijing:Beijing University of Aeronautics and Astronautics Press,2006.(in Chinese))
[13]Wilcox D C.Turbulence Modeling for CFD[M].California:DCW Industries Inc,1998.
[14]耿云飞,阎超,徐晶磊,等.高超声速流动湍流模式评估[J].北京航空航天大学学报,2011,37(8):907-911.(GENG Yun-fei,YAN Chao,XU Jing-lei,et al.Turbulence modeling validation in hypersonic flows[J].Journal of Beijing University of Aeronautics and Astronautics,2011,37(8):907-911.(in Chinese))
[15]Settles G S,Williams D R,Baca B K,et al.Reattachment of a compressible turbulent free shear layer[J].AIAA Journal,1982,20(1):60-67.
[16]李素循.典型外形高超声速流动特性[M].北京:国防工业出版社,2007.(Li Su-xun.Hypersonic Flow Characteristics for Typical Shapes[M].Beijing:National Defense Industry Press,2007.(in Chinese))