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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