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1. 天津大学 力学系, 天津 300072;
2. 中国空气动力研究与发展中心 空气动力学国家重点实验室, 绵阳 621000

Effect of sweep angle on stability and transition in a swept-wing boundary layer
SUN Pengpeng1, HUANG Zhangfeng1,2
1. Department of Mechanics, Tianjin University, Tianjin 300072;
2. State Key Laboratory of Aerodynamics, China Aerodynamics Research and Development Center, Mianyang 621000, China
Abstract:The stability and transition of swept-wing boundary layers have important reference value to the design and optimization of airfoil. The sweep angle is one of the key parameters to the cross-flow instability of swept-wing boundary layers. Based on the NACA0012 airfoil profile, the mean flow of a swept-wing boundary layer was calculated by numerically solving the three-dimensional compressible Navier-Stokes equation, then the neutral curve and the growth curve of unstable Toumien-Schlisting wave were obtained by solving the Orr-Sommerfeld equation to study the effect of the sweep angle, and the transition position was predicted by applying eN method. Study shows that with the increase of sweep angle, both the strength of the cross-flow and the amplification factor n of the disturbance amplitude increase firstly and then decrease, and the strength of the cross-flow reaches its peak value when the sweep angle is in the range of 40° to 50°. The N factor predicted by eN method is the largest one when the sweep angle is about 50°, implying that with which angle, the induce disturbance with a smaller amplitude can easily lead to the occurrence of transition.
Key words: sweep angle     swept-wing     hydrodynamic stability     linear stability theory (LST)     eN method
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 图 1 模型坐标示意图 Fig. 1 Sketch map of model coordinate
1.2 线性稳定性问题及方法

1.3 转捩预测的eN方法

1.4 研究对象

2 结果分析 2.1 结果验证

 图 2 计算网格示意图 Fig. 2 Sketch map of computational domain

 模型 流向点数 法向点数 总网格数/105 grid-1 720 300 2.16 grid-2 1 000 400 4.00 grid-3 1 200 500 6.00

 图 3 3种不同网格数模型的流向速度剖面及压力系数 Fig. 3 Profile of flow velocity and pressure coefficient for three kinds of models with different grid number

 图 4 压力系数曲线 Fig. 4 Pressure coefficient curves
2.2 基本流分析

 图 5 后掠角不同时的速度剖面及压力系数 Fig. 5 Profile of velocity and pressure coefficient under different sweep angles

 图 6 横流坐标系下速度剖面 Fig. 6 Profile of velocity in cross-flow coordinate
2.3 特征值和特征函数

 Λ/(°) -αi β=1 β=2 β=3 10 -0.005 797 -0.000 429 0.000 464 15 -0.002 104 0.005 156 0.006 881 20 0.001 622 0.010 861 0.013 037 25 0.005 466 0.016 256 0.018 445 30 0.009 326 0.021 146 0.022 821 40 0.016 912 0.028 986 0.027 137 45 0.020 580 0.031 592 0.025 659 50 0.024 066 0.032 686 0.019 476 60 0.029 470 0.023 393 -0.030 135

 图 7 扰动波(β=1,ω=0)的特征函数 Fig. 7 Eigen-function of disturbance wave (β=1,ω=0)
2.4 中性曲线

 图 8 中性稳定曲线 Fig. 8 Neutral stability curve
2.5 增长率及幅值演化曲线

x0=25作为稳定性分析的参考位置,图 9 (b)给出了不同后掠角下该扰动波的幅值演化曲线.虽然在后掠角为30°~45°时驻波的中性曲线所包围的不稳定波的范围最大,但是后掠角为30°~40°时的增长率偏小,相应的幅值放大指数n值也偏小.当后掠角Λ≤50°时,n值随后掠角的增大而增大.但后掠角为60°时,由于其增长的流向范围较小,其n值会有所降低.后掠角为50°时扰动幅值放大指数n达到最大值.该结论与Boltz等[5]和Haynes[6]的发现一致.

 图 9 驻波(β=2,ω=0)增长率及幅值演化曲线 Fig. 9 Growth rate and growth curve of stationary wave (β=2,ω=0)
2.6 N值曲线及转捩预测

 图 1 转捩预测eN方法的N值曲线 Fig. 1 N factor in eN method

eN方法是一种半经验的转捩预测方法,发生转捩的N值需要由实验测量并做出进一步的假定.当计算得到的N值大于预设的N值时即可判定发生了转捩.研究表明,当扰动波的无量纲幅值达到来流的20%就会发生转捩[21].表 3给出了当扰动波放大指数达到给定N值时发生转捩的位置.可以看出,若给定发生转捩的预设值N=9,则后掠角小于30°时不会发生转捩;后掠角大于40°时,随着后掠角的增大,转捩位置向机翼前缘移动.

 Λ/(°) 流向位置x N=7 N=8 N=9 N=10 10 ― ― ― ― 15 ― ― ― ― 20 ― ― ― ― 25 ― ― ― ― 30 274.5 ― ― ― 40 120.0 151.5 198.5 307.0 45 99.0 121.0 149.5 193.0 50 86.5 103.0 124.0 152.5 60 71.0 82.5 97.0 125.5

 Λ/(°) x=150 x=200 x=250 x=300 N A0 N A0 N A0 N A0 10 0.11 1.8×10-1 0.19 1.7×10-1 0.25 1.6×10-1 0.28 1.5×10-1 15 1.16 6.3×10-2 1.47 4.6×10-2 1.67 3.8×10-2 1.78 3.4×10-2 20 2.63 1.4×10-2 3.15 8.6×10-3 3.47 6.2×10-3 3.66 5.1×10-3 25 4.10 3.3×10-3 4.80 1.6×10-3 5.21 1.1×10-3 5.46 8.5×10-4 30 5.50 8.2×10-4 6.34 3.5×10-4 6.84 2.1×10-4 7.13 1.6×10-4 40 7.96 7.0×10-5 9.01 2.4×10-5 9.62 1.3×10-5 9.96 9.5×10-6 45 9.00 2.5×10-5 10.12 8.1×10-6 10.74 4.3×10-6 11.12 3.0×10-6 50 9.92 9.8×10-6 11.07 3.1×10-6 11.71 1.6×10-6 12.10 1.1×10-6 60 10.29 6.8×10-6 10.39 6.1×10-6 10.39 6.1×10-6 10.39 6.1×10-6
3 结 论

1) 后掠机翼边界层中横流强度随后掠角的增大先增加后减小.当后掠角为40°~50°时横流强度存在最大值,在机翼头部靠近前缘位置(x=100左右),后掠角为45°时横流强度最强.

2) 后掠角为30°~45°时,扰动波的不稳定区域最大,不稳定驻波的展向波数范围最大.

3) 随着后掠角的增大,扰动波幅值放大指数n先增加后减小.后掠角在50°左右转捩预测eN方法计算的N值最大,引起转捩发生的初始扰动幅值最小,最易发生转捩.

4) 给定预设值N,转捩发生的位置随后掠角的增大逐渐向机翼前缘移动.

 [1] 周恒, 赵耕夫. 流动稳定性[M].北京: 国防工业出版社, 2004: 77-78. Zhou H, Zhao G F.Hydrodynamic stability[M].Beijing: National Defense Industry Press, 2004: 77-78(in Chinese). Click to display the text [2] 徐国亮, 符松. 可压缩横流失稳及其控制[J].力学进展, 2012, 42(3): 262-273. Xu G L, Fu S.The instability and control of compressible cross flows [J].Advances in Mechanics, 2012, 42(3): 262-273(in Chinese). Cited By in Cnki (2) [3] Joslin R D. Overview of laminar flow control[M].Hampton, Virginia: National Aeronautics and Space Administration, Langley Research Center, 1998: 3-7. Click to display the text [4] 吴永健. 横流不稳定性实验研究[D].南京: 南京航空航天大学, 2002. Wu Y J.Experimental study on crossflow instabilities in the boundary-layer of swept wing[D].Nanjing: Nanjing University of Aeronautics and Astronautics, 2002(in Chinese). Cited By in Cnki (1) [5] Boltz F W, Kenyon G C, Allen C Q.Effects of sweep angle on the boundary-layer stability characteristics of an untapered wing at low speeds[J].National Aeronautics and Space Administration, NASA Technical Note, 1960: D-338. Click to display the text [6] Haynes T S. Nonlinear stability and saturation of crossflow vortices in swept-wing boundary layers[D].Arizona: Arizona State University, 1996. Click to display the text [7] Dagenhart J R, Saric W S.Crossflow stability and transition experiments in swept-wing flow[M].National Aeronautics and Space Administration, Langley Research Center, 1999: 7-8. Click to display the text [8] Bippes H. Basic experiments on transition in three-dimensional boundary layers dominated by crossflow instability[J].Progress in Aerospace Sciences, 1999, 35(4): 363-412. Click to display the text [9] Bippes H, Müller B, Wagner M.Measurements and stability calculations of the disturbance growth in an unstable three-dimensional boundary layer[J].Physics of Fluids A: Fluid Dynamics(1989-1993), 1991, 3(10): 2371-2377. Click to display the text [10] Bippes H, Wiegel M, Bertolotti F.Experiments on the control of crossflow instability with the aid of suction through perforated walls[C]//IUTAM Symposium on Mechanics of Passive and Active Flow Control.Berlin: Springer, 1999, 53: 165-170. Click to display the text [11] Malik M R, Liao W, Li F, et al.DRE-enhanced swept-wing natural laminar flow at high Reynolds numbers, AIAA-2013-0412[R].Reston: AIAA, 2013. Click to display the text [12] Saric W S, Carrillo R B, Reibert M S.Nonlinear stability and transition in 3-D boundary layers[J].Meccanica, 1998, 33(5): 469-487. Click to display the text [13] Saric W S, Reed H L, White E B.Stability and transition of three-dimensional boundary layers[J].Annual Review of Fluid Mechanics, 2003, 35(1): 413-440. Click to display the text [14] 左林玄, 王晋军. 弹性与后掠角对三角翼绕流结构的影响[J].实验流体力学, 2008, 22(2): 29-33. Zuo L X, Wang J J.The effects of flexibility and sweep angle on flow around cropped delta wing[J].Journal of Experiments in Fluid Mechanics, 2008, 22(2): 29-33(in Chinese). Cited By in Cnki (1) [15] 马宝峰, 刘沛清, 魏园.大迎角下机翼后掠角对近耦合鸭式布局增升及流态的影响[J].实验流体力学, 2005, 19(3): 73-78. Ma B F, Liu P Q, Wei Y.Effects of wing sweep on lift-enhancement and flow patterns of close-coupled canard-configurations at high incidence[J].Journal of Experiments in Fluid Mechanics, 2005, 19(3): 73-78(in Chinese). Cited By in Cnki (4) [16] 刘杰, 刘沛清, 闫指江.中等后掠角三角翼前缘双涡结构的形成机理数值研究[J].空气动力学学报, 2012, 30(6): 767-771. Liu J, Liu P Q, Yan Z J.Numerical investigations of formation mechanism about a dual leading-edge vortex of a delta wing with medium leading-edge sweep angle[J].Acta Aerodynamica Sinica, 2012, 30(6): 767-771(in Chinese). Cited By in Cnki [17] 左岁寒, 杨永, 李栋.基于线性抛物化稳定性方程的后掠翼边界层内横流稳定性研究[J].计算物理, 2010, 27(5): 665-670. Zuo S H, Yang Y, Li D.Investigation on cross-flow instabilities in swept-wing boundary layers with linear parabolized stability equations[J].Chinese Journal of Computational Physics, 2010, 27(5): 665-670(in Chinese). Cited By in Cnki (3) [18] 左岁寒, 杨永, 李栋, 等.基于线化稳定性理论的后掠翼边界层内横流稳定性研究[J].航空计算技术, 2009, 39(4): 34-36. Zuo S H, Yang Y, Li D, et al.Study on crossflow instability of boundary layer on a swept wing based on linear stability theory[J].Aeronautical Computing Technique, 2009, 39(4): 34-36(in Chinese). Cited By in Cnki [19] 黄章峰, 逯学志, 于高通.机翼边界层的横流稳定性分析和转捩预测[J].空气动力学学报, 2014, 32(1): 14-20. Huang Z F, Lu X Z, Yu G T.Cross-flow instability analysis and transition prediction of airfoil boundary layer[J].Acta Aerodynamica Sinica, 2014, 32(1): 14-20(in Chinese). Cited By in Cnki [20] 韩步璋, 黄奕裔, 张其威, 等.NACA0012翼型跨音速测压实验研究[J].南京航空航天大学学报, 1987, 19(2): 92-102. Han B Z, Huang Y Y, Zhang Q W, et al.An experiment of pressure measurement for NACA0012 airfoil in a transonic wind tunnel[J].Journal of Nanjing Aeronautical Institute, 1987, 19(2): 92-102(in Chinese). Cited By in Cnki [21] Huang Z F, Cao W, Zhou H.The mechanism of breakdown in laminar-turbulent transition of a supersonic boundary layer on a flat plate-temporal mode[J].Science in China Series G: Mechanics and Astronomy, 2005, 48(5): 614-625. Click to display the text

#### 文章信息

SUN Pengpeng, HUANG Zhangfeng

Effect of sweep angle on stability and transition in a swept-wing boundary layer

Journal of Beijing University of Aeronautics and Astronsutics, 2015, 41(7): 1313-1321.
http://dx.doi.org/10.13700/j.bh.1001-5965.2014.0540