The Stability And Transition Prediction Of The Hypersonic Boundary Layer Over Blunt Cone Considering Real Gas Effects

In this paper, stability analysis and transition prediction of hypersonic boundarylayer over blunt cone considering high-temperature effects is investigated. The Machnumber is taken as6/8/10/20. According to the range of temperature of the aircraftsurface, the real gas effects of variable specific heat (vibrational excitation) and gasdissociation are considered, and then the appropriate numerical simulation method isput forward to obtain the mean flow. For different freestream Mach numbers and wallconditions, stability analysis on boundary layer over blunt cone are conducted basedon linear stability theory; transition location is predicted by the improved e-N method,and compared with that of constant specific heat. It is indicated that, the influence ofreal gas effects on stability and transition prediction of hypersonic boundary layer cannot be ignored. In calculation, the gas parameter is taken as the air parametercorresponding to different height. The following conclusions can be drawn:1. Two methods are put forward to compute the flow field considering real gaseffect of variable specific heat. The first method is introducing equivalentspecific heat ratio instead of constant specific heat ratio in the governingequation in the case of constant specific heat. The other method, theconvection flux of the N-S equation is splitted directly; the form differs fromthat of constant specific heat in the energy equation. The results of twomethods by DNS are the same with each other. The first method is appliedand operated simply, and can be applied to the condition of gas dissociation.2. It can be found from the comparison between the cases of variable specificheat and constant specific heat, for the same freestream Mach number andadiabatic wall condition, the influences of real gas effects of variable specificheat on the mean flow and stability are as follows: the location of thedetached shock in hypersonic flow over blunt cone is more nearer the surfaceof the cone, the temperature of the surface of the cone is lower; the maximumgrowth rate of the first and the second mode wave are increasing; the secondmode instability shifts to lower frequencies and the first mode to higherfrequencies. The real gas effect of variable specific heat causes the transitionlocation to move forward, no matter what the wall is adiabatic or isothermal. 3. Under the condition of isothermal wall in hypersonic boundary layer overblunt cone considering variable specific heat, it is indicated that, with thewall temperature reduces, the second mode instability is made to moreunstable and the first mode to stabilize; the critical Reynolds’ number of thetwo mode increase; the second mode instability shifts to higher frequenciesand the first mode to lower frequencies; the influence of real gas effects onthe first mode instability is more important than that on the second mode. Itis also found that the transition is led by the second mode wave and the lowerthe wall temperature is, the more backward the transition location is.4. Considering the influence of the freestream Mach number on the transitionlocation of hypersonic boundary layer over blunt cone, the cases of Mach6/8/10are investigated. It is found that, with the Mach number increases, thetransition location moves backward under the adiabatic wall condition andmoves forward under the isothermal wall condition of the same walltemperature.5. From the investigation of stability analysis and transition prediction ofhypersonic boundary layer over blunt cone considering the real gas effects ofgas dissociation, it can be indicated that: there appears more higher frequencyunstable mode wave with high Mach number, the maximum growth rate ofwhich is equivalent with that of the second mode; there is no2D first modeunstable wave; the maximum growth rate of the2D wave of the second modeis less than that of the3D wave. Generally speaking, the maximum growthrate considering gas dissociation is larger than that of constant specific heat,real gas effects broaden the frequency range of instability and shift theinstability to higher frequencies. Compared with the case of constant specificheat, the curve of the growth rate under the case of considering gasdissociation move down stream, with the peak increases; the envelope line ofN is larger, and this trend should be considered in choosing transitioncriterion.