Linear stability of confined mixing layer
-
摘要: 针对超声速边界层/混合层组合流动,利用可压缩线性稳定性理论研究了流动的线性失稳特性。基本流场选取了具有不同速度特征的两股来流,采用双曲正切的混合层剖面叠加可压缩边界层自相似性解剖面构造。重点考察了混合层中心与壁面距离、对流马赫数等参数对组合流动稳定性特征的影响,其中壁面采用绝热壁面。混合层中心与壁面的距离为5~15倍的边界层厚度,混合层的对流马赫数为0.6~1.2。结果表明:该组合流动中存在独特的多重不稳定模态,并相互影响;且其不稳定模态随着壁面距离及对流马赫数的变化呈现出不同的主导行为。Abstract: Linear stability analysis was utilized to investigate the stability characteristics of a supersonic boundary/mixing layer confluent flow. The basis flow was designed as a mixing layer with hyperbolic-tangent profile over a compressible boundary layer with similar solution profile. Special attention was paid to the influence of wall distance and convective Mach number on the stability of this field, of which adiabatic wall condition was used. The distance from mixing layer center to the wall ranged from 5 to 15 times boundary layer thickness, and the convective Mach number varied from 0.6 to 1.2. It was found that novel multi-unstable modes existed in the confluent flow and the dominant modes showed different manners with varying wall distance and convective Mach number.
-
Key words:
- linear stability /
- mixing layer /
- boundary layer /
- convective Mach number /
- fast mode /
- slow mode
-
[1] 杨茵,陈迎春,李栋.多段翼混合边界层改变对流场的影响研究[J].航空工程进展,2016,7(1):30-37.YANG Yin,CHEN Yingchun,LI Dong.Influence of confluent boundary layer changing for multi-element airfoils flow field[J].Advances in Aeronautical Science and Engineering,2016,7(1):30-37.(in Chinese) [2] 王旭东,高峰,王应洋,等.超燃燃烧室支板喷注器燃料掺混优化数值分析[J].弹箭与制导学报,2016,36(1):93-98.WANG Xudong,GAO Feng,WANG Yingyang,et al.Numerical optimization analysis of fuel-air mixing for a supersonic combustor with strut injector[J].Journal of Projectiles,Rockets,Missiles and Guidance,2016,36(1):93-98.(in Chinese) [3] YOU Yancheng,LUEDEKE H,HANNEMANN K.Injection and mixing in a scramjet combustor:DES and RANS studies[J].Proceeding of the Combustion Institute,2013,34(2):2083-2092. [4] FU Jia,YI Shihe,WANG Xiaohu,et al.Experimental study on supersonic film cooling on the surface of a blunt body in hypersonic flow[J].Chinese Physics:B,2014,23(10):319-326. [5] SHI Xiaotian,LIU Fengjun,HU Ning,et al.Supersonic film cooling simulation with a discontinuous galerkin method[R].AIAA-2017-2248,2017. [6] 朱杨柱,易仕和,田立丰,等.带喷流的超声速光学头罩流动显示[J].北京航空航天大学学报,2013,39(1):105-108.ZHU Yangzhu,YI Shihe,TIAN Lifeng,et al.Flow visualization of supersonic optical dome with jet[J].Journal of Beijing University of Aeronautics and Astronautics,2013,39(1):105-108.(in Chinese) [7] MICHAEL A K,MARKUS J K,HERBERT O.Influence of cooling-gas properties on film-cooling effectiveness in supersonic flow[J].Journal of Spacecraft and Rockets,2015,52(5):1443-1455. [8] FEDOROV A V ,SOUDAKOV V G,LEYVA I A.Stability analysis of high-speed boundary layer flow with gas injection[R].AIAA-2014-2498,2014. [9] 周恒,赵耕夫,流动稳定性[M].北京:国防工业出版社,2004. [10] LEES L,LIN C C.Investigation of the stability of the laminar boundary layer in a compressible fluid[R].NACA TN 1115,1946. [11] MACK L M.Boundary layer linear stability theory[R].AGARD Report No.709,1984. [12] FEDOROV A V,TUMIN A.Branching of discrete modes in high-speed boundary layers and terminology issues[R].AIAA-2010-5003,2010. [13] MICHALKE A.On the inviscid instability of the hyperbolic-tangent velocity profile[J].Journal of Fluid Mechanics,1964,19(4):543-556. [14] RAGAB S A,WU J L.Linear instabilities in two-dimensional compressible mixing layers[J].Physics of Fluids,1989,1(6):957-966. [15] JACKSON T,GROSCH C.Inviscid spatial stability of a compressible mixing layer[R].NASA CR 181855,1989. [16] DAY M J,REYNOLDS W C,MANSOUR N M.The structure of the compressible reacting mixing layer:insights from linear stability analysis[J].Physics of Fluids,1998,10(4):993-1007. [17] 沈清,王强,庄逢甘.超声速平面剪切层声辐射涡模态数值分析[J].力学学报,2007,39(1):7-14.SHEN Qing,WANG Qiang,ZHUANG Fenggan.Numerical analysis of acoustic radiation vortical modes in a spatially evolving supersonic plane shear layer[J].Chinese Journal of Theoretical and Applied Mechanics,2007,39(1):7-14.(in Chinese) [18] GREENOUGH J A,RILEY J J.The effects of walls on a compressible mixing layer[R].AIAA 89-0372,1989. [19] HU F Q.A Numerical study of wave propagation in a confined mixing layer by eigenfunction expansions[J].Physics of Fluids,1993,5(6):1420-1426. [20] HUDSON D A,LONG L N,MORRIS P J.Computation of a confined compressible mixing layer[R].AIAA 95-2173,1995. [21] LIOU W W,LIU F J.Spatial linear instability of confluent wake/boundary layers[J].AIAA Journal,2001,39(11):2076-2081. [22] LIOU W W,LIU F J.Compressible linear stability of confluent wake/boundary layers[J].AIAA Journal,2003,41(12):2349-2356. [23] 刘智勇,袁湘江,刘小勇,等.超声速边界层/混合层组合流动的稳定性分析[J].力学学报2014,46(1):28-36.LIU Zhiyong,YUAN Xiangjiang,LIU Xiaoyong,et al.Stability analysis of supersonic boundary/mixing layers confluent flow[J].Chinese Journal of Theoretical and Applied Mechanics,2014,46(1):28-36.(in Chinese) [24] GAO Jun,LUO Jisheng.Mode decomposition of nonliear eigenvalue problems and application in flow stability[J].Applied Mathematics and Mechanics,2014,35(6):667-674. [25] MALIK M R.Numerical methods for hypersonic boundary layer stability[J].Journal of Computational Physics,1990,86:376-413. [26] MALIK M R,CHUANG S,HUSSAINI M Y.Accurate numerical solution of compressible linear stability equation[J].Zeitschrift Für Angewandte Mathematik und Physik Zamp,1982,33(2):189-201.
点击查看大图
计量
- 文章访问数: 650
- HTML浏览量: 2
- PDF量: 562
- 被引次数: 0