The Stability Analysis And Transition Estimation Of The Supersonic Boundary Layer Over Blunt Cone At Small Angle Of Attack

In this paper, the supersonic boundary layer over blunt cone at angle of attack(AOA) and Mach 6 is studied. DNS is done to get the base flow over various bluntcones and at several of AOA in the same incoming flow condition. Linear stabilitytheory (LST) is used to analyze the stability of the base flows. The LST results areverified by DNS of the small amplitude disturbance evolvement. The evolvementsof large amplitude disturbance are also computed by DNS for the elementary study ofthe transition estimation.When base flow is got by DNS, the computation time is markedly saved byrefining the computation scheme.The following conclusions are got by LST or DNS:1. The study of blunt effect of cone shows the following results: The blunteffect stabilizes flow field and moves the unstable region aftward. Theblunt nose can affect as long as 300 times of nose radius distance and theflow field agrees with the sharp cone case at the further location.2. The linear stability analysis of the boundary layer over the cone at AOAshows the following results: When the cone at AOA, the boundary becomesthinner on the windward and thicker on the leeward so that the frequency ofunstable wave changes on different meridian. The boundary layer becomesunstable the most downstream at zero AOA, such that the unstable regionmoves forward at AOA, and it moves faster on the leeward. Thedisturbance amplitude is computed by eNmethod, and the result shows that,at the same location, the disturbance growth greater on the leeward.3. The DNS of small disturbance evolvement shows the following results: Theevolvement of single wave is the same as the result of LST estimate, whichindicates LST can be applied to the 3D supersonic flow over blunt cone atsmall AOA. When the amplitude of single wave exceeds 0.07, thenonlinear effect becomes strong so that the LST fails. When multiplewaves exist in the same field, the evolvement of each wave agrees with thesingle case, which indicates that there is no remarkable interaction.4. The numerical study of transition estimation shows the following results: Transition occurs when the large disturbances are introduced at the inlet.Both the disturbance amplification and Cf curve can reflect the spot wheretransition begins, and the both can give the same location. The DNS resultsshow that the transition locations are seriously affected by the disturbancesat the inlet, so that the change of disturbance at the inlet can result indifferent transition location. On the transition beginning spot, theamplitudes of each wave are different, which are the 1.0~3.2% of thefreestream velocity, while the total amplitude is all about 5% of thefreestream velocity. Consequently, when we estimate the transitionlocation, it is more acceptable to use the total amplitude to fix the spot wheretransition begins.