Turbulence Statistics and Structures of a Supersonic Boundary Layer by Direct Numerical Simulation
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摘要: 可压缩边界层转捩问题与湍流问题一直是制约高超声速飞行器发展的关键基础问题，也是近年来流体力学领域研究的热点问题.采用直接数值模拟方法，获得了空间发展的Ma=2.25超声速湍流边界层流场，通过对湍流边界层的发展状态进行评估，得出有效的Reynolds数Reθ范围约为2 600~4 600.对壁面摩阻系数开展了分解，获得了各分量的占比，对充分发展的湍流边界层进行1阶和高阶统计分析，包括形状因子、壁面律、平坦因子与偏斜因子、Reynolds应力、脉动涡量等，得到了剪切Reynolds数与动量Reynolds数之间的关系式，分析了湍流边界层壁面律的分层特性，发现湍流的间歇特性主要分布在y+ < 30的区域，并且法向速度脉动的间歇性远高于另外两者，3个方向上的Reynolds应力分布和涡量分布都存在较大差异.通过两点相关性分析和Lagrange涡结构，对近壁区湍流结构进行了分析，包括流向平面和展向平面，发现流向脉动速度的相关区域流向尺度较长，呈现狭长的特性，并且流向平面的相关系数与壁面存在一定的夹角；而在边界层外层，流向速度脉动相关区域的流向尺度变短而展向尺度增加，呈现宽胖型.研究结果进一步加深了对超声速湍流边界层的认识，为下一步湍流边界层的流动控制奠定了基础.Abstract: The transition and turbulence of compressible boundary layer are the key basic problems that restrict the development of hypersonic vehicle, and they are also the hot issues in the field of fluid dynamics in recent years. By using the direct numerical simulation method, the spatial development of the flow field of Ma=2.25 supersonic turbulent boundary layer was obtained. Through the evaluation of the development state of the turbulent boundary layer, the effective range of momentum Reynolds number Reθ is about 2 600~4 600. The skin friction coefficient was decomposed and the proportion of each component was analyzed. The first-order and high-order statistical analysis of the fully developed turbulent boundary layer was carried out, including shape factor, wall law, flatness and skewness, Reynolds stress, fluctuating vorticity, et al. The relation between shear Reynolds number and momentum Reynolds number was obtained and the stratification characteristics of the wall law of turbulent boundary layer were analyzed. It is also found that the inner intermittence is mainly distributed in the region of y+ < 30. The distributions of Reynolds stresses and vortices in three directions are quite different as well. Based on the two-point correlation analysis, the turbulent structures in different heights were detailed analyzed, including the streamwise plane and the spanwise plane. It is found that the distributions of two-point correlations of the streamwise fluctuating velocities in both X-Y plane and X-Z plane are featured by long and narrow characteristics and there is a certain angle between the correlation coefficients and the wall. In the outer part of the boundary layer, however, the streamwise scale of the correlation region becomes shorter and the spanwise scale increases, indicating that the scale of turbulent structures increases with the increase of distance from the wall. The results further deepen the understanding of supersonic turbulent boundary layer and lay a foundation for the flow control of turbulent boundary layer.
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图 2 瞬时流场的涡结构图
Figure 2. Vortex structure of instantaneous flow field (Q=0.01, colored by flow velocity)
图 4 不同流向位置的瞬时流场温度云图(y+=15)
Figure 4. Temperature distribution of instantaneous flow field at different flow positions(y+=15)
图 7 充分发展段的湍流边界层摩阻系数分解
Figure 7. Decomposition of skin friction coefficient in fully developed turbulent boundary layer
图 8 超声速湍流边界层不同Reynolds数之间的关系
Figure 8. Relations between various Reynolds numbers in supersonic turbulent boundary layer
图 9 超声速平板湍流边界层平均速度分布曲线
Figure 9. Mean velocity distribution curves of supersonic turbulent boundary layer
图 10 湍流边界层脉动速度的高阶统计矩
Figure 10. High order statistical moments of fluctuating velocity in turbulent boundary layer
图 11 超声速平板湍流边界层Reynolds正应力分布
Figure 11. Reynolds normal stress distribution in supersonic turbulent boundary layer
图 12 超声速平板湍流边界层涡量脉动强度分布(Reθ=4 080)
Figure 12. Distribution of vorticity fluctuation intensity in supersonic turbulent boundary layer
图 15 湍流边界层不同高度处流向速度脉动空间相关性沿展向的分布
Figure 15. Distributions of the two-point correlations in spanwise direction at various distances from the wall
图 16 法向高度为y/δ99=0.2的展向自相关函数
Figure 16. Distribution of the two-point correlations in spanwise direction at the height of y/δ99=0.2
图 17 两个平面流向自相关函数
Figure 17. Distributions of the two-point correlations in streamwise direction
图 18 流向位置为x=275δin处的不同法向高度X-Y平面空间相关系数分布
Figure 18. Distributions of the two-point correlations in streamwise plane
图 19 法向高度分别为y+=5和y+=15的两个平面的LCS结构
Figure 19. Lagrangian coherent structures in two planes at the heights of y+=5 and y+=15
表 1 超声速来流条件
Table 1. Inlet conditions of boundary layer
Ma∞ Re/in-1 T∞/K δin/mm Reθ Reδ* 2.25 6.35×105 169.4 0.45 1 145 6 084 
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