EFFECTS OF WAVY ROUGHNESS ON THE STABILITY OF A MACH 6.5 FLAT-PLATE BOUNDARY LAYER
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摘要: 高超声速边界层转捩会使飞行器表面热流和摩阻增加3 ~ 5倍, 极大影响高超声速飞行器的性能. 波纹壁作为一种可能的推迟边界层转捩的被动控制方法, 具有较强的工程应用前景. 文章研究了不同高度和安装位置的波纹壁对来流马赫数6.5的平板边界层稳定性的影响. 采用直接数值模拟(DNS)得到层流场, 并在上游分别引入不同频率的吹吸扰动以研究波纹壁对扰动演化的作用. 对于不同位置的波纹壁, 探究了其与同步点相对位置对其作用效果的影响, 与相同工况下光滑平板的扰动演化结果进行了对比, 发现当快慢模态同步点位于波纹壁上游时, 波纹壁会对该频率的第二模态扰动起到抑制作用. 当同步点位于波纹壁之中或者下游时, 波纹壁对扰动的作用可能因为存在两种不同的机制而使得结果较为复杂. 对于不同高度波纹壁, 发现高度较低的波纹壁, 其作用效果强弱与波纹壁高度成正相关, 而更高的波纹壁则会减弱其作用效果. 与DNS结果相比, 线性稳定性理论可以定性预测波纹壁对高频吹吸扰动的作用, 但在波纹壁附近的强非平行性区域误差较大.Abstract: Transition from laminar to turbulent flow of the hypersonic boundary layer can increase the wall friction coefficient and heat conduction coefficient by 3 ~ 5 times, which has a significant influence on flight performance and safety of hypersonic vehicles. Wavy roughness is a possible passive control method to delay hypersonic boundary layer transition, and is thus of engineering significance. In this paper we investigate the effort of finite-length wavy roughnesses with different locations and heights on the stability of a Mach 6.5 flat-plate boundary layer using direct numerical simulation and linear stability theory (LST). DNS is employed to obtain the laminar base flow, and to study the linear evolution of fixed-frequency disturbances parametrically introduced upstream by blowing and suction. The effects of the relative position of the fast/slow mode synchronization point and the wavy roughness are revealed. It is found that when the wavy roughness is placed upstream of a disturbance’s synchronization point, the disturbance is damped compared to the smooth surface case; when the disturbance’s synchronization point is within or slightly downstream of the wavy roughness, the disturbance is generally enhanced. The effects of heights of wavy roughnesses are also considered. For the wavy roughness with small heights compared to the boundary layer thickness, the effect of wavy roughness is positively correlated with the height of the wavy roughness, while the effect is weakened by the higher wavy roughness. Linear stability theory can predict well the effects of wavy roughness on high-frequency disturbances, but exhibits large discrepancies with DNS in predicting the behaviors of moderate and low-frequency disturbances. This indicates that the receptivity process and the strong non-parallel effect in the vicinity of the wavy roughness neglected by LST should play an important role.
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图 1 位于位置A处高0.4波纹壁的平板示意图
Figure 1. Sketch of the flat plate with height 0.4 wavy roughness located in position A
图 2 3种高度波纹壁及光滑平板流向速度云图
Figure 2. Contours of streamwise velocity in three wavy roughnesses with different heights and smooth surface case
图 3 不同高度波纹壁流向速度剖面对比
Figure 3. Streamwise velocity profiles of three different wavy roughnesses with different heights and Blasius flow
图 4 高度0.4波纹壁工况, 光滑平板及Blasius解在流向不同站位的速度剖面对比
Figure 4. Streamwise velocity profiles of height 0.4 wavy roughness case, smooth surface case, and Blasius flow at different positions
图 5 波纹壁和光滑壁的沿流向增长率对比图
Figure 5. Comparison of growth rate contours in wavy roughness case and smooth surface case
图 6 第二模态不同频率的光滑壁N值曲线对比, 其中彩色条带标注了3处波纹壁位置
Figure 6. N-factor evolutions for second modes with different frequencies, where colorful bands represent the regions of three wavy roughnesses
图 7 LST分析位置A处高0.4波纹壁工况和光滑平板N值曲线对比
Figure 7. Comparison of N-factors in the case of smooth surface and case of height 0.4 wavy roughness located in position A through LST analysis
图 8 压强扰动和温度扰动沿流向发展的云图
Figure 8. Contours of pressure and temperature disturbance evolutions along the streamwise direction
图 9 LST与DNS计算的沿流向扰动幅值演化对比, 扰动按照其最大幅值进行归一化
Figure 9. Comparison of disturbance amplitudes computed through LST and DNS. Disturbance amplitudes are normalized by the maximum of each amplitude
图 10 不同频率下快慢模态同步点位置, 圆圈符号为LST计算值, 曲线为拟合的近似公式xf 2 = C
Figure 10. Positions of synchronization points with different frequencies. The circle points are computed by LST and the continuous curve is fitted by function xf 2 = C
图 11 同步点位于波纹壁上游的工况与光滑平板扰动幅值对比, 绿色条带为波纹壁范围, 竖直点划线为同步点位置, 下同
Figure 11. Comparison of disturbance amplitudes in smooth surface and wavy roughness case when synchronization point is located upstream of the wavy roughness. The green band and vertical dot-dash lines represent the positions of wavy roughness and synchronization points respectively
图 12 同步点位于波纹壁之中的工况与光滑平板扰动幅值对比
Figure 12. Comparison of disturbance amplitudes in the smooth surface case and wavy roughness case when synchronization point is within the wavy roughness
图 13 同步点位于波纹壁下游的工况与光滑平板扰动幅值对比
Figure 13. Comparison of disturbance amplitudes in smooth surface case and wavy roughness case when synchronization point is located downstream of the wavy roughness
图 14 位置A处三种高度波纹壁工况扰动幅值对比
Figure 14. Comparison of disturbance amplitudes for three wavy roughnesses with different heights in position A
表 1 波纹壁参数研究的两组工况
Table 1. Details of two groups of wavy roughnesses with different locations or heights
Group Location Height Rekk I [100,125] 0.2 3.1 I [100,125] 0.4 13.7 I [100,125] 0.8 65.3 II [100,125] 0.4 13.7 II [150,175] 0.4 11.0 II [200,225] 0.4 9.4 
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表 2 3个位置波纹壁选取的扰动工况表, 其中绿色、蓝色和黄色的标注分别表示同步点位于波纹壁下游, 位于波纹壁之中和位于波纹壁上游
Table 2. Frequencies of disturbances for three wavy roughnesses with different positions. Where green, blue, and orange represent synchronization points that are located downstream of the wavy roughness, within the wavy roughness, or located upstream of the wavy roughness respectively
Position f/(kHz) A 80 90 100 110 120 130 140 150 155 160 170 180 190 200 B 80 90 100 110 120 123 126 130 140 150 160 170 C 80 90 100 108 110 120 130 140 150 160
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[1] 陈坚强, 涂国华, 张毅锋等. 高超声速边界层转捩研究现状与发展趋势. 空气动力学学报, 2017, 35(3): 311-337 (Chen Jianqiang, Tu Guohua, Zang Yifeng, et al. Hypersonic boundary layer transition: what we know, where shall we go. Acta Aerodynamica Sinica, 2017, 35(3): 311-337 (in Chinese) [2] Fedorov A. Transition and stability of high-speed boundary layers. Annual Review of Fluid Mechanics, 2011, 43: 79-95 doi: 10.1146/annurev-fluid-122109-160750 [3] Drazin PG, Reid WH. Hydrodynamic Stability, 2nd ed. Cambridge: Cambridge University Press, 2004 [4] Mack LM. Boundary-layer linear stability theory. AGARD Rep. 709, 1984 [5] Mack LM. Review of Linear Compressible Stability Theory. Stability of Time Dependent and Spatially Varying Flows. New York: Springer, 1987: 164-187 [6] 刘强, 涂国华, 罗振兵等. 延迟高超声速边界层转捩技术研究进展. 航空学报, 2022, 43(2): 125357 (Liu Qiang, Tu Guohua, Luo Zhenbing, et al. Progress in hypersonic boundary transition delaying control. Acta Aeronautica et Astronautica Sinica, 2022, 43(2): 125357 (in Chinese) doi: 10.7527/j.issn.1000-6893.2022.7.hkxb202207001 [7] Fedorov AV. Stabilization of hypersonic boundary layers by porous coatings. AIAA Journal, 2001, 39(4): 605-610 doi: 10.2514/2.1382 [8] 涂国华, 陈坚强, 袁先旭等. 多孔表面抑制第二模态失稳的最优开孔率和孔半径分析. 空气动力学学报, 2018, 36(2): 273-278 (Tu Guohua, Chen Jianqiang, Yuan Xianxu, et al. Optimal porosity and pore radius of porous surfaces for damping the second-mode instability. Acta Aerodynamica Sinica, 2018, 36(2): 273-278 (in Chinese) [9] Zhu WK, Shi MT, Zhu YD, et al. Experimental study of hypersonic boundary layer transition on a permeable wall of a flared cone. Physics of Fluids, 2020, 32: 011701 doi: 10.1063/1.5139546 [10] Zhu WK, Chen Xi, Zhu YD, et al. Nonlinear interactions in the hypersonic boundary layer on the permeable wall. Physics of Fluids, 2020, 32: 104110 doi: 10.1063/5.0028698 [11] Fong KD, Wang XW, Zhong XL. Numerical simulation of roughness effect on the stability of a hypersonic boundary layer. Computers & Fluids, 2014, 96: 350-367 [12] 周云龙. 考虑表面粗糙影响下的高超声速边界层稳定性研究. [硕士论文]. 长沙: 国防科技大学, 2019Zhou Yunlong. Study of the effect of surface roughness on the hypersonic boundary layer stability. [Master Thesis]. Changsha: Graduate School of National University of Defense Technology, 2019 (in Chinese) [13] Wu XS, Dong M. A local scattering theory for the effects of isolated roughness on boundary-layer instability and transition: transmission coefficient as an eigenvalue. Journal of Fluid Mechanics, 2016, 794: 68-108 doi: 10.1017/jfm.2016.125 [14] Dong M, Zhao L. An asymptotic theory of the roughness impact on inviscid Mack modes in supersonic/hypersonic boundary layers. Journal of Fluid Mechanics, 2021, 913: A22 [15] 董明. 边界层转捩预测中的局部散射理论. 空气动力学学报, 2020, 38(2): 286-298 (Dong Ming. Local scattering theory for transition prediction in boundary-layer flows. Acta Aerodynamica Sinica, 2020, 38(2): 286-298 (in Chinese) doi: 10.7638/kqdlxxb-2019.0140 [16] Brehm C, Dackermann T, Grygier F, et al. Numerical investigations of the influence of distributed roughness on blasius boundary layer stability//49th AIAA Aerospace Sciences Meeting including the New Horizons Forum and Aerospace Exposition, Orlando, Florida, 2011 [17] Tameike H, Yakeno A, Obayashi S. Influence of small wavy roughness on flat plate boundary layer natural transition. Journal of Fluid Science and Technology, 2021, 16(1): 1-10 [18] Fujii K. Experiment of the two-dimensional roughness effect on hypersonic boundary-layer transition. Journal of Spacecraft and Rockets, 2006, 43(4) : 731-738 [19] Si WF, Huang GL, Zhu YD, et al. Hypersonic aerodynamic heating over a flared cone with wavy wall. Physics of Fluids, 2019, 31: 051701 doi: 10.1063/1.5094388 [20] Si WF. The influence of wavy wall on hypersonic boundary layer instability over a flared cone. International Journal of Modern Physics B, 2020, 34: 14n16, 2040093 [21] Egorov IV, Novikov AV, Fedorov AV. Numerical modeling of the disturbances of the separated flow in a rounded compression corner. Fluid Dynamics, 2006, 41(4): 521-530 doi: 10.1007/s10697-006-0070-7 [22] Egorov IV, Novikov AV. Direct numerical simulation of supersonic boundary layer stabilization using grooved wavy surface//48th AIAA Aerospace Sciences Meeting Including the New Horizons Forum and Aerospace Exposition, Orlando, Florida, 2010 [23] Bountin D, Chimitov T, Maslov A, et al. Stabilization of a hypersonic boundary layer using a wavy surface. AIAA Journal, 2013, 51(5): 1203-1210 [24] Zhou YL, Liu W, Chai ZX, et al. Numerical simulation of wavy surface effect on the stability of a hypersonic boundary layer. Acta Astronautica, 2017, 140: 485-496 [25] Kirilovskiy SV, Poplavskaya TV. Hypersonic boundary layer stabilization by using a wavy surface. Journal of Physics: Conf. Series, 2017, 894: 012040 doi: 10.1088/1742-6596/894/1/012040 [26] Zhu WK, Gu DW, Si WF, et al. Instability evolution in the hypersonic boundary layer over a wavy wall. Journal of Fluid Mechanics, 2022, 943: A16 [27] Zhu WK, Gu DW, Zhu YD, et al. Generation of acoustic waves in the hypersonic boundary layer over a wavy wall. Physics, Mechanics & Astronomy, 2022, 65(3): 234711 [28] Gabín AM, Chávez M, Mena JG, et al. Wavy walls, a passive way to control the transition to turbulence. detailed simulation and physical explanation. Energies, 2021, 14: 3937 [29] 张存波, 罗纪生, 高军. 分布式粗糙度对马赫数为4.5的平板边界层稳定性的影响. 航空动力学报, 2016, 31(5): 1234-1241 (Zhang Cunbo, Luo Jisheng, Gao Jun. Effects of distributed roughness on Mach 4.5 boundary-layer transition. Journal of Aerospace Power, 2016, 31(5): 1234-1241 (in Chinese) [30] Muppidi S, Mahesh K. Direct numerical simulations of roughness -induced transition in supersonic boundary layers. Journal of Fluid Mechanics, 2012, 693: 28-56 doi: 10.1017/jfm.2011.417 [31] Giovanni AD, Stemmer C. Cross-flow-type breakdown induced by distributed roughness in the boundary layer of a hypersonic capsule configuration. Journal of Fluid Mechanics, 2018, 856: 470-503 doi: 10.1017/jfm.2018.706 [32] Reda DC. Review and synthesis of roughness-dominated transition correlations for reentry applications. Journal of Spacecraft and Rockets, 2022, 39(2): 161-167 [33] Reda DC, Wilder MC, Bogdanoff DW, et al. Transition experiments on blunt bodies with distributed roughness in hypersonic free flight. Journal of Spacecraft and Rockets, 2008, 45(2): 210-215 doi: 10.2514/1.30288 [34] Wilder MC, Reda DC, Prabhu DK. Transition experiments on blunt bodies with distributed roughness in hypersonic free flight in carbon dioxide//53rd AIAA Aerospace Sciences Meeting, Kissimmee, Florida, 2015 [35] Liang X, Li XL, Fu DX, et al. Effects of wall temperature on boundary layer stability over a blunt cone at Mach 7.99. Computers & Fluids, 2010, 39: 359-371 [36] Chen X, Chen JQ, Yuan XX, et al. From primary instabilities to secondary instabilities in Görtler vortex flows. Advances in Aerodynamics, 2019 , 1: 19 [37] Dong SW, Chen JQ, Yuan XX, et al. Wall pressure beneath a transitional hypersonic boundary layer over an inclined straight circular cone. Advances in Aerodynamics, 2020, 2: 29 [38] 李慧, 黄章峰. 局部凸起对可压缩平板边界层稳定性的影响. 航空动力学报, 2015, 30(1): 173-181 (Li hui, Huang Zhangfeng. Effort of local hump on stability of compressible boundary layer on flat plate. Journal of Aerospace Power, 2015, 30(1): 173-181 (in Chinese) doi: 10.13224/j.cnki.jasp.2015.01.024 [39] 陈曦. 高超声速边界层转捩问题研究. [博士论文]. 北京: 北京大学, 2018Chen Xi. Study on hypersonic boundary layer transition. [PhD Thesis]. Beijing: Peking University, 2018 (in Chinese)) [40] Chen X, Zhu YD, Li CB. Interactions between second mode and low-frequency waves in a hypersonic boundary layer. Journal of Fluid Mechanics, 2017, 820: 693-735 doi: 10.1017/jfm.2017.233 [41] Malik MR. Numerical methods for hypersonic boundary layer stability. Journal of Computational Physics, 1990, 86: 376-413 doi: 10.1016/0021-9991(90)90106-B [42] Chen X, Huang GL, Li CB. Hypersonic boundary layer transition on a concave wall: stationary Görtler vortices. Journal of Fluid Mechanics, 2019, 865: 1-40 doi: 10.1017/jfm.2019.24 [43] Tullio ND, Sandham ND. Influence of boundary-layer disturbances on the instability of a roughness wake in a high-speed boundary layer. Journal of Fluid Mechanics, 2015, 763: 136-165 -
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