Turbulence Statistics and Structures of a Supersonic Boundary Layer by Direct Numerical Simulation

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 Re_θ 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.