The Transition Prediction Of Boundary Layers On A Hypersonic Cone And The Improvement Of The E-N Method

For a successful design of hypersonic flying vehicles, the correct prediction of the skin friction and heat condition is essential, which in turn depends on the correct prediction of the transition location of the boundary layer. A sharp cone or a blunt nose cone is a typical fore-body of such vehicles. In this paper, the problem of transition prediction for supersonic and hypersonic boundary layers on a sharp or blunt nose cone at zero angle of attack or small angle of attack has been studied. Firstly, stability of a hypersonic boundary layer on a blunt cone with small nose bluntness at zero angle of attack has been investigated and the transition location was predicted by the e-N method. Secondly, the application of the e-N method to three-dimensional boundary layers is examined. For the transition prediction for a hypersonic sharp cone or cone with small bluntness, conventional e-N method does not yield correct result, even qualitatively, Then, based on our own previous works, new interpretation and essential improvement for the e-N method is proposed. Finally, the transition location of the boundary layers on the cones with different flow parameters, such as the angle of attack, the cone half angle and the Mach number of the coming flow etc. are predicted. The following conclusions can be drawn:1 For the transition of the boundary layer on a cone with small bluntness at zero angle of attack with Mach nember 6, although the maximum amplification rate for second mode waves is far bigger than those for the first mode waves, the second mode waves are not always responsible for the transition. The second mode waves do play a dominant role in the transition of boundary layers with isothermal wall, while the first mode waves would dominate the transition if the wall temperature condition is adiabatic. Thus, the wall temperature condition has a great influence on transition. For the boundary layer with adiabatic wall, transition happens about 60% further downstream from the nose of the cone, as compared with boundary layer with isothermal wall.2 ZARF is not unique in three-dimensional boundary layer. We have to seek the one that contains the fastest growing disturbance, and take it as the base for the implementation of the e-N method.3 For the transition of the boundary layer on a cone with small bluntness and angle of attack and with Mach number 6, conventional e-N method does not yield correct result, even qualitatively, while the improved e-N method can provide reasonable results. But it relies on the correct estimation of the initial amplitude of disturbances, which in turn relies on more flight data collection and analysis. The improved e-N method can also yield results well agree with those obtained by DNS.4 The transition prediction for boundary layers on cones with different key parameters such as angle of attack, cone half angle and the Mach number of the coming flow, have been made, to show the reliability of the modified e-N method.5 For the calculation of base flow, boundary layer equations can be used in the case of small angle of attack. Its computational cost is much smaller than those for DNS. However, the profiles on the leeward ray are questionable.