The Instability And Transition Prediction Of Stationary Crossflow Vortices Over Supersonic Swept Elliptic Cylinders

Some experiments have shown that stationary crossflow vortices may cause transition over the first half of supersonic swept cylinders.And the general supersonic aircraft may have a long blunt swept leading edge which approximate a swept cylinder.If there is a transition in the leading edge,the supersonic aircraft state will have a great impact.The swept elliptic cylinders with infinite spanwise length are used as models to simulate the swept leading edges of supersonic aircraft at high altitude.By using the e~N method based on the linear stability theory,the influence of different length ratios of the upwind axis and vertical axis,Reynolds numbers and swept angles on the instability of stationary crossflow vortices on swept elliptic cylinders is studied systematically.The N-factor curves and the maximum N-factors at the outlet of computational region obtained by integrating the spatial growth rates of most unstable stationary crossflow vortices along the flow direction are seem as the standard to measure the strength of instability.The free flow conditions include the same condition as the cylinder in Archambaud,et al.'s experiment and flight conditions at different altitude.Conclusions are as follows:1)Increasing the length ratios of the upwind axis and vertical axis will enhance the instability of the stationary crossflow vortices.2)The instability of the stationary crossflow vortices is related to the Reynolds number and unit Reynolds number.The relationship between the instability and the Reynolds number is nearly liner.Referring to this relationship,the possibility of transition take place in similar conditions can be estimated rapidly.3)In the range of calculation,the swept angle has little effect on the instability of stationary crossflow vortices.The evolution of finite amplitude stationary crossflow vortices in swept cylinder boundary layer is studied.In the condition,H=20km,Mach number is 4,swept angle is 55~o,radius is 120mm.The conclusions are as follows:1)The LST can be used to predict the linear evolution of the disturbance amplitude.2)The NPSE can be used to predict the nonlinear phase before the amplitude reaches the first peak.But may fail in the prediction of the second peak.3)The evolution of the stationary crossflow vortices,the position where the nonlinear function and the position and amplitude of the first peak are related to the initial amplitude.And there is a certain law which can be used to rapidly gain the evolution of other stationary crossflow vortices with different initial amplitude.