Flow Stability And Wave Propagation In Hypersonic Three-dimensional Boundary Layers

With the rapid development of near space aircraft,boundary-layer instability and transition have received much attention.The investigation on two-dimensional(2-D)or axisymmetric boundary layers cannot meet the requirements in engineering because the three-dimensional(3-D)boundary layers are more common.Therefore,in order to offer theoretical guidance for engineering,it is necessary to make in-depth investigation on the stability of typical 3-D boundary layers.Based on the varying of the basic flow profiles in the spanwise direction,boundary layers can be categorized into four types,namely,boundary layers with no,slow,relatively fast and fast varying in the spanwise direction.In this paper,boundary layers with slow and fast varying in the spanwise direction are concerned to investigate the stability and wave propagation and the main conclusion are summarized as follows:1.Generalized growth rate(GGR)in the boundary layer is proposed and GGRs of 2-D waves in 2-D flow,3D wave of spatial mode and spatiotemporal waves are analyzed.The conservation relation of GGR is strictly deduced in theory and validated numerically.GGR conservation manifests that the existing ways of calculating disturbance growth rate in e N method can be unified,and all of them are the particular cases of GGR in essence.In addition,a convenient method of calculating disturbance growth rate is proposed.The knowledge about GGR of the disturbance is helpful to perfect the theoretical foundation of three-dimension e~Nmethod.2.A new method is proposed to predict the linear evolution of infinitesimal perturbations in 3D boundary layers with slow varying in the spanwise direction,named as RTPSE,in which the line-marching parabolized stability equation(PSE)is improved by applying the ray tracing(RT)theory.Two major improvements are achieved.One is that the marching line is predefined along the direction of group velocity.Another is that the variation of the spanwise wavenumber is predicted by RT theory.Direct numerical simulation(DNS)is performed to verify and validate the prediction by RTPSE in a 3-D supersonic boundary layer on a blunt cone with an angle of attack(AOA).Results show that RTPSE can accurately predict the variation of spanwise wavenumber and linear evolution of disturbances,implying that RTPSE is fully applicable to predict the linear evolution of disturbances in 3D boundary layers.3.The investigation on the relationship between the secondary instability of G?tler vortices in the downstream region and the fist/second mode in the upstream region is performed by Bi Global analysis,three-dimensional linear parabolized stability equations(3DLPSE)and DNS.It is shown from results that a one-to-one match between the secondary instability modes in the downstream region and the Mack modes in the upstream region can be found by Bi Global method.However,only dominant modes can reflect the characteristics of disturbance evolution in G?rtler vortices qualitatively even though multiple modes can be solved by Bi Global analysis.3DLPSE approach accurately predicts the process of Mack mode disturbance evolving into secondary instability of G?rtler vortices,and perfect agreement with results by DNS is obtained,indicating that 3DLPSE is a more effective tool.In addition,it is proved that secondary instability of stationary G?rtler vortices can originate from first/second Mack mode.4.The effect of stationary crossflow vortices with different amplitude on fast/slow mode and the evolution of fast/slow mode are investigated by 3DLPSE.It is found that crossflow vortices with small amplitude can stabilize the fast mode but destabilize the slow mode;however,crossflow vortices with large amplitude strongly destabilize these two disturbances,which is mainly caused by the spanwise shear of the distorted basic flow.A detailed analysis of the primary mechanism for the effect of the crossflow vortices on the fast/slow mode provides the evidence that the mean flow distortion(MFD)of the nonlinear crossflow vortex with small amplitude has a stabilizing effect on the fast/slow mode but MFD with large amplitude destabilizes these two disturbances because inviscid secondary instability occurs due to the general inflection arising at the outer edge of the distorted basic flow profile.In addition,it is demonstrated that the spanwise varying component of the crossflow vortices always dominates the evolution characteristics of fast/slow modes.5.Based on the cone with an AOA,the present calculation demonstrates that the second mode is the origin of secondary instability in stationary crossflow vortices and second mode with finite amplitude can promote the breakdown of stationary crossflow vortices.Therefore,second mode plays an active role in the breakdown process dominated by crossflow vortices.