Stability Analysis And Transition Control In Hypersonic Streamwise Vortices Over A Yawed Cone

Since a hypersonic near-space vehicle has incomparable advantages over conventional flighting vehicles,e.g.in maneuverability and flight altitude,the development of hypersonic vehicles is of great importance for the military applications.With the rapid development of hypersonic vehicles,the hypersonic boundary-layer stability and transition problems have received increased attention since they are criticle in prediction of aero thermodynamics of high-speed flying vehicles.In practical applications,the encountered flows are usually complex three-dimensional boundary layer flows,and hence the previous investigations on the traditional two-dimensional or axisymmetric boundary layer cannot satisfy the engineering needs.Therefore,it is crucial to deeply understand the stability characteristics of the typical three-dimensional boundary layers and to provide theoretical guidance for engineering transition prediction and flow control.The streamwise vortices structures in the leeward region of a cone at an angle of attack are typically three-dimensional boundary layer flows.Due to the angle of attack effect for a yawed cone,the shock intensity on the windward and leeward sides is largely inequal,resulting in strong pressure gradient in the spanwise direction of the cone model.This causes the streamlines converging from the windward surface to the leeward surface and a streamwise vortex structure is hence generated near the centerline of the leeward zone.In this paper,the streamwise vortex structure in the leeward region over a yawed cone at an angle of attack of 6 degrees is studied.Based on the global stability theory,the characteristics of the streamwise vortex boundary layer stability are studied comprehensively.The transition control in the streamwise vortex region is studied by using a three-dimensional smooth hump.The main conclusions are summarized as follows:1.Aiming at generally complicated three-dimensional boundary layers,a twodimensional global stability analysis method(i.e.the extended two-dimensional global stability analysis method(EBi-Global))that can consider the non-parallelism of the basic flow is established,and its accuracy is strictly verified.This method not only retains the advantages of the Bi-Global analysis method for solving local eigenvalue problems,but also considers the non-parallel effects of the base flow.As a result,the prediction results are more consistent with the DNS results.Because the EBi-Global accounts for the non-parallelism,it can provide more accurate inlet boundary conditions for the three-dimensional parabolic stability equation method(3DPSE).2.Aiming at the hypersonic streamwise vortex boundary layer in the leeward zone over a yawed cone,the boundary layer instability and transition mechanism are investigated.Two pairs of vortices(inner and outer vortices)are found for the first time in the streamwise vortex in the leeward region,and the nature of the vortices has an important influence on the instability of the streamwise vortex boundary layer.An inner mode and a modified Mack mode inside streamwise vortex boundary layers were identified for the first time using a two-dimensional spatial global stability analysis.By comparing direct numerical simulation(DNS)results and wind tunnel data.It was found that the inner modes dominate the transition only in a noisy environment,whereas the outer modes play a significant role in boundary layer transition under quiet freestream condition.Based on the eN method,the engineering transition criteria for streamwise vortexes over a yawed cone in different free-stream environments are given.3.A class of three-dimensional smooth hump with an analyzed control function is designed as a roughness on the yawed cone.The shape of the three-dimensional hump is adjustable,and it can smoothly join with the model wall,which is suitable for highprecision solvers.Based on the understanding of the transition mechanism of the streamwise vortex over a yawed cone,the influence of streaks induced by four humps with different heights on the stability of the streamwise vortex boundary layer is studied.It is found that the generation of new streaks can effectively enhance the original inward vortex structure and delay the formation and evolution of the outward vortex structure.The global stability analysis results show that the streaks will enhance the inner modes instability and suppress the outer modes instability.In particular,the dominant mode Z-S1 instability in the quiet environment is suppressed,and its growth rate and dominant frequency are reduced.It is worth noting that increasing the height of the hump will make the antisymmetric Mack mode more unstable due to the secondary streamwise vortex energy increases.The eN method based on global stability theory was used to predict the location of the transition along the centerline on the leeward side of the cone.It is found that the humps with the height of 0.153 and 0.267 times of local boundary layer thickness will result in a transition delay of 3%and 11%,respectively.