| By numerical simulation, the evolutions of the disturbances are investigated in hyersonic boundary layer on a blunt cone at a small angle of attack (AOA).By using the streamwise pressure gradient on the edge of the boundary layer instead of the one in the boundary layer, traditional technique for the one in parabolized Navier-Stokes (PNS) equation solution was improved, for the use of PNS as basic flows for stability analysis of hypersonic flows.We investigated the evolutions of the disturbances with small and finite amplitude, respectively. first,the linear stability theory (LST) is verified in the hypersonic 3-dimensional boundary layer; second, inducing two groups of disturbances with different frequencies at inlet, non-symmetrical transiton along the azimuthal direction on blunt cone at small AOA is investigated; third, the nonlinear characters of the second mode disturbances in the flow is studied; then, the evolutions of wave-packet disturbances with finite amplitude in blunt cone at zero-AOA are simulated, and the results are compared with the ones of the same kind disturbances in small AOA blunt cone, hyperconic and incompressible flat bounary layer. And the following conclusions can be drawn:1. The boundary layer on a blunt cone at small AOA can be seperated into two regions by different 3-dimensional feature. In the windward and side region (φ= 0 ~。-135~。), the boundary layer changes bluntly, and LST predicts the growth well; in the region near the leeward, the bounday layer changes shapely, with the evolution of the disturbance is 3-D, but LST can also provide a good prediction when the 3-D waves are considered which the spanwise wavelength is one half of the length of the region with a sharp variation in the flow field on the leeward.2. The waves which are linearly decaying can grow by the nonlinear effect when the main disturbance grow to a large enough amplitude, but the main wave can also grow linearly with a distance. When the amplitude of the main wave reached about 0.05-0.1, nonlinear feature can be seen obviously. The rule is in existance on the windray, sideray, and leeray.3. Transition onset distributions along the azimuthal direction are obtained. It shows that transition onset is relevant to frequencies and amplitudes of the disturbances at the inlet, and is decided by the amplitudes of the most unstable waves at the inlet. According to this, the phenomenon leeside-forward and windside-after over a circular cone at non-zero AOA in most experiments can be explained. Also, it can explain the indentation of transition curve in theφ=150 ? meridian plane.4. On the windray and sideray, disurbance with equal amplitude along azimuthal direction can become wave-pack distribution in the downstream, and then small scale 3-D disturbances can be excited. The stational parts of the disturbances are stationary streamwise streaky structures, which haveφ/π≈0.014-0.016 spanwise scale. And growth of the non-stational parts should connect with the secondary instability theory.5. At zero AOA, wave-pack disturbances at inlet also can excite small scale 3-D structures in the downstream and the spanwise wave length is same. The disturbances at inlet are more concentrated, and these structures exited earlier. Compared with the evolutions of the wave-packet waves in hypersonic and incompressible flat, the generation of this kind of disturbance is a special phenomenon in hypersonic boundary layer.6. The sharp 3-D basic flow leads to 3-D disturbances on the leeray. When the waves grow higher enough, higher harmonic waves will be excited and it makes the flow"cell-like". Then, it will lead to a transition to turbulence. The scale of 3-D disturbances on the leeray is relevant to the 3-D feature of the basic leeward flow, which is larger than the one on the windray and sideray.
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