Direct Numerical Simulation Of Supersonic Turbulent Boundary Layers Subject To Pressure Gradients

In this paper,direct numerical simulation is used to study the evolution of coherent structure,the organization of three-dimensional flow field and the statistical properties of turbulence in supersonic turbulent boundary layer under the effect of pressure gradients.In particular,the "divide and conquer" approach is adopted to decouple the effect of the wall curvature and the pressure gradient,so as to study the supersonic velocity of flat plate separately.At the same time,the pressure gradient effect of curvature wall coupling under the same wall pressure distribution is compared with that of pressure gradient effect alone.Compared with the boundary layer with zero pressure gradient(ZPG),the near-wall streaks are more likely to form patches with larger scale due to the existence of adverse pressure gradient(APG).The enhanced LSM is a typical flow structure in the outer bound-ary layer under bulk compression.The results show that Q4 event is dominant in the near wall region,and Q2 event is dominant in the rest of the boundary layer.Because of the existence of compression waves,the baroclinicity plays an important role in the forma-tion of near-wall velocity patches and the LSM in the outer layer.It is the driving force of high-speed fluid flow from the outer layer to the inner,and it also strengthens the trend of fluid flow from the inner layer to the outer layer.In flows over concave curvature wall,the generation of Gortler vortex is the main character of the flow field.This structure distorts the local density gradient,and the in-teraction between the density gradient and the concave induced compression produces baroclinicity,resulting in a large number of small-scale vortices generating over the con-cave wall,representing an amplification of local turbulence.The internal region of the concave boundary layer seems to be little affected by the Gortler instability,and rela-tively slow turbulence amplification is obtained through the baroclinic effect induced by the bulk compression.Even if there is no curvature of the wall,the response of the turbulent structure to the favorable pressure gradient(FPG)effect and the acompanied bulk dilatation shows an obvious two-layer(inner layer and outer layer)feature.The near-wall streaks are further separated in the spanwise direction and elongated in the flow direction.The velocity of the outer high-speed fluid is much higher than that of the near-wall low-speed fluid lifting away from the wall.Therefore,the low-speed fluid from the near wall region as well as the near wall instability cannot go further into the outermost boundary layer.Accordingly,in the boundary layer,especially in the outer layer,the entanglement of the adj acent streaks is suppressed and the small-scale motion is further reduced.It is shown that the spanwise streaks spacing of the convex curved wall flow is larger than that of the flat plate flow.The TKE profile and budget along the wall-normal direc-tion show a typical two-layer structure.In the outer layer,the turbulence is continuously suppressed along the curved wall.Compared with the outer layer,the inner-layer turbu-lence recovers more quickly,and performs locally in another approximate equilibrium of generation and dissipation.It is found that the two-layer structure is due to the bulk di-latation and the centrifugal effect caused by the curved wall,which limits the momentum and mass exchange between the inner and outer layer as well as between the outer layer and the bulk stream.The rapid recovery of the inner layer suggests an on-going impact of the near-wall instability.