| It is very important to predict the transition accurately for hypersonic vehicle design.In high altitude flight,the main transition path is natural transition.Accurate prediction of natural transition depends on a comprehensive and in-depth understanding of the characteristics of disturbance instability in the boundary layer.In subsonic and low Mach numbers(usually less than 2.2)supersonic boundary layers,there is usually a single unstable mode,and good progress has been made in the related flow instability and transition prediction problems.However,in hypersonic flow(Mach number is usually greater than 4),there are many unstable modes in the boundary layer.The evolution of disturbance waves are complicated,therefore the stability and transition problems need further study.In order to predict the transition accurately,the instability characteristics of multiple unstable modes in the hypersonic boundary layer and the mode transformation between them are studied.On this basis,the effects of real gas effects and non-parallelism on instability and transition prediction are studied.The following results are obtained:1?The instability characteristics of the second mode and supersonic mode in the boundary layer with Mach number Ma=4.5 to 8 are studied using the linear stability theory(LST).The relationship between the second mode and supersonic mode and the generalized inflection point of the basic flow is analyzed.It is found that the generalized inflection point in the boundary layer near the outer edge of the boundary layer has a significant effect on the instability,and when the velocity is less than1-1/Ma,unstable supersonic modes will appear.Based on the free stream dispersion relation,the variation characteristics of the growth rate when the disturbance changes from subsonic to supersonic are explained theoretically.Two types of supersonic modes are found:the one propagates to far-field(called radiation mode)while the other is propagating to the wall.The radiation mode is more unstable,which is the dominant mode.It is found that there are two forms of existence for the supersonic mode,one is directly changed from the subsonic second mode,the other originates from _rc(28)1-1/Ma and forms a branch of independent mode.The supersonic modes are added to Fedorov's theoretical framework of the fast and slow modes in the boundary layer,and the complete description of the mode variation in the hypersonic boundary layer is given.The results of the perturbation evolution show that when the second mode perturbation evolves into the supersonic mode,the sound waves are radiated gradually from the relative sonic line to the free stream.When using LST to predict the supersonic mode,radiation boundary conditions should be used in the far-field.The range of far-field acoustic field can be determined by using the dispersion relation.Because of its spontaneous sound radiation characteristics,slow acoustic waves in the free stream cannot be swallowed into the boundary layer.2?Chemical reactions such as dissociation of the air will occur due to the high temperature in the hypersonic boundary layer.Considering the high temperature chemical reaction of air,the N-S equation solver and the PSE method with chemical equilibrium are established.Considering the chemical equilibrium,the stability analysis and transition prediction of the high Mach number(8-15)boundary layer are carried out.Stability analyses show that when considering the real gas effects,the unstable region of the first mode decreases obviously,the maximum growth rate of the second mode increases,and the third mode with higher frequency appears earlier and the supersonic mode becomes more unstable.The e~N transition predictions indicate that the second mode dominates the transition,and the third mode has little effect on the transition position.In the Mach number range from 8 to 12,the N-factor envelope becomes larger and the transition is promoted.However,when the Mach number exceeds 12,the N-factor envelope becomes smaller and the transition is delayed.The N-factor envelope decreases gradually with increasing altitude or Mach number.Considering the real gas effects,new generalized inflection points are found in the boundary layer for the high Mach number flow with adiabatic wall,which leads to the appearance of the new unstable supersonic mode.The PSE method is used to study the evolution characteristics of the second mode and supersonic mode in high Mach number flow.It is found that the superposition of supersonic mode and second mode causes the amplitude of perturbation wave to increase obviously downstream of the second mode,which can greatly promote the transition.3?The expanded parabolized stability equation(EPSE)is improved.Conservation relation is added to the original EPSE equation,which solves the multiple eigenvalue problem of the original EPSE.What's more,the accuracy is greatly improved,and the perturbation amplitude of the unstable wave in the strong non-parallel boundary layer can be calculated accurately.As a local stability analysis tool,the improved EPSE can be easily applied to a general 3D boundary layer transition prediction. |
PDF Full Text Request