Study On Transition In A Hypersonic Swept Blunt Plate Boundary Layer

Transition prediction is very important to hypersonic vehicles design.Crossflow instability is a typical and important instability mechanism in the swept flow.The wall boundary condition of previous studies is mainly adiabatic wall condition,and the crossflow mode dominates in the evolution.However,adiabatic wall condition represents the state of the aircraft flying for a long time,when the wall temperature do not reach adiabatic temperature,the isothermal wall condition is more reasonable.Because of the wall cooling effect,the first-mode disturbances are stabilized,while the second-mode instability is significantly enhanced.The growth rate of second mode is larger than that of crossflow mode,and the effect of the second mode disturbance on the transition needs to be considered at this time.In this paper,the isothermal swept blunt plate model is selected to study the instability characteristics of the second mode disturbances,mainly study the nonlinear interaction between two second mode disturbances with the same frequency and the influence of the stationary crossflow vortex initial amplitude on the transition position.The main conclusion is summarized as follows:1.The traditional nonlinear parabolized stability equation(NPSE)is improved.When solving the streamwise wavenumber,the iterative method is no longer used for all disturbances.All disturbances are divided into two types according to their importance: dominant waves and nondominant waves.The streamwise wavenumbers of the nondominant waves are obtained using the phase-locked method,while those of the dominant waves are obtained using an iterative method.The improved NPSE avoids divergence when the disturbances imposed at the inlet no longer play a leading role or nonlinear interaction is strong,it increases the robustness and can be used to simulate the evolution of disturbances in hypersonic boundary layers.2.The growth rate of the second mode is larger than that of the crossflow mode in isothermal wall condition.This paper finds the nonlinear interaction of two second mode disturbances with same frequency generates a new zero frequency disturbance,called forced solution.And the solution obtained by linear stability theory called eigenvalue solution.The profile of the forced solution is similar to that of the second mode disturbances,but not the crossflow mode disturbances.The evolution of the forced solution is independent of the initial amplitude of crossflow mode disturbances.The growth rate of forced solution is much larger that of crossflow and second mode eigenvalue solution,and it is mechanism for the second mode disturbances to promote transition.3.Considering the effect of the second mode disturbance on the forced solution.It is found that the second mode disturbance affects the evolution of the forced solution by changing the magnitude of the mean flow distortion.The effect of maximum value of two second mode disturbances initial amplitude is much larger than that of the product of two second mode disturbances initial amplitude.The amplitude of the forced solution can be predicted using magnitude analysis through the amplitude of the second-mode disturbances,and the theoretical predictions are consistent with those of the NPSE when the second mode disturbances are unstable.The effects of different spanwise wavenumbers and frequencies of the second mode disturbances on the forced solution evolution are studied.It is found that no matter the second mode disturbances are in the growth zone at the entrance or not,the amplitude of the forced solution increases rapidly in the computational domain upstream region.The peak amplitude of the forced solution in stable second mode disturbances,however,is smaller than that when the second mode disturbances are unstable.When the second mode disturbancse are removed,the forced solution will not disappear immediately,but it also cannot maintain itself at a long time.Instead,it gradually transforms into the eigenvalue solution and evolves downstream.This explains why the theoretical derivation results are inconsistent with the NPSE results when the second mode disturbances are attenuated.4.Study the effect of stationary crossflow vortices with different initial amplitudes on the transition position.It is found that the amplitude of the stationary crossflow vortex will affect the evolution of the second mode disturbance,which in turn affects the transition position.When the initial amplitude of the stationary crossflow vortex is small,the stationary crossflow vortex promotes the transition;when the initial amplitude of the stationary crossflow vortex is large,the stationary crossflow vortex will suppress the second mode disturbances,which causes the starting position of saturate moves downstream.At the same time,the stationary crossflow vortex will roll the second mode disturbances energy away from the wall surface,causing the transition position to move downstream and suppress the transition.