Compressible turbulent boundary layer (TBL) is a typical flow on the surface of high speed aircraft. The TBL with high Mach number and high Reynolds number has special phenomena. Under high Mach number, strong compressibility effect appears in the boundary layer, and the characteristics of statistics and coherent structures change. Under high Reynolds number, the outer large-scale structure becomes more and more important, and the interaction of the inner and outer coherent structure appears. In such extreme conditions, the influence of wall temperature is often accompanied, which makes the flow phenomenon more complex. So, the flow mechanism is not fully analyzed in the existing researches. At the same time, the simulation of these flows requires low-dissipation and high-robustness numerical scheme. This paper is divided into three parts. Firstly, the existing numerical scheme is further optimized, and then the flow mechanism of compressible turbulent boundary layer with high Mach number and high Reynolds number is deeply analyzed by direct numerical simulation.

1.In the first part of the work, we summarize the development of the weighted essentially non-oscillatory scheme (WENO) and develop a new WENO-PR scheme based on the WENO-Z scheme. The main idea is to increase the weight of the less smooth substencil in the WENO scheme which then is more linear to the original scheme and has less numerical dissipation. To achieve this goal, we optimize the high order smooth factor τ. In order to reduce the dissipation and ensure the robustness of the scheme together, the discontinuous sensitivity factor p is further optimized. Numerical characteristics of the new WENO-PR scheme are tested by several numerical tests.

2.The second part of the work, wall temperature effects on hypersonic flat-plate turbulent boundary layer are analyzed. The direct numerical simulation (DNS) database with free-stream Mach number Ma_∞=8 and two isothermal wall conditions (T_w/T_r=10.03 and 1.9) are considered.

(1)The influence of the wall temperature on compressibility effect and Reynolds shear stress are studied. The results show that wall cooling enhances the compressibility effect and the near-wall ejection and sweeping motions. The ejection motion is stronger than the sweeping motion, which is caused by the combined effect of the velocity fluctuation behaviors.

(2)The non-uniform temperature distribution (NUTD) on the coherent vortex surfaces is studied using conditional sampling technique. The coherent vortex surface is identified by the Ω-criterion and two characteristic sides of the vortex are defined. The results show that there is a significant difference of up to 20% between the characteristic sides. Furthermore, the velocity-temperature fluctuation correlations (-R_u'T'  and R_v'T' ) show that the temperature fluctuations are redistributed by the vortex rotational motion through -R_u'T'  and R_v'T', and then lead to the NUTD.

(3)The correlation between density and temperature fluctuations (ρ' and T') is studied. A fitting slope method and a two-dimensional correlation method are adopted to visualize the correlated behaviors. The results show that an adverse trend and a separated correlated structure are found in the buffer region, which can be treated as the effects of the local and surrounding correlation of ρ' and T'. Several statistics indicate that the extreme events are suppressed with wall cooling, meanwhile, the small-scale fluctuations are enhanced because of the reduced mean swirling strength and the increased radius of the vortical structures.

3.The third part of the work, the direct numerical simulation of turbulent boundary layer subjected to curved surface with high Reynolds number (Re_τ>1000) is carried out. The DNS database is established. The average and statistical characteristics of the boundary layer are analyzed. Firstly, the flow field is visualized in several aspects and abundant small-scale structures are observed. Then, the mean velocity profiles at different streamwise directions are studied. It is proved that there is no sinking phenomenon in the logarithmic law in the curved region. The statistical analyses show that when the Reynolds number is high enough, the turbulent intensities have the inner and outer peak. With the increase of the local Reynolds number, the inner peak increases gradually, and the outer peak becomes more and more obvious. At this time, Morkovin's hypothesis is partially invalid. The small-scale and large-scale streaks in the near wall and logarithmic law regions are studied. It is found that the latter is more important under the condition of high Reynolds number, which has an important influence on the near-wall one and the statistical characteristics of the flow field.