Two-dimensional global(BiGlobal)stability in the region of the minor axis is investigated in the case of hypersonic elliptic cones with major-minor axis ratios of 2:1 and 3:1 at Mach number 6.0,and the BiGlobal-e^(N) ...Two-dimensional global(BiGlobal)stability in the region of the minor axis is investigated in the case of hypersonic elliptic cones with major-minor axis ratios of 2:1 and 3:1 at Mach number 6.0,and the BiGlobal-e^(N) method is proposed to predict the transition location of the boundary layer.Matrix-free BiGlobal stability analysis is used to find unstable modes,including the Y-mode and the Z-mode.The growth rates in the streamwise-frequency plane for these modes are obtained.The Nmax all factor is proposed,which represents the maximum amplification factor that all BiGlobal unstable modes can reach.Using a comparison of the N_(max_all) factor with the transition location measured in a wind tunnel experiment for the 2:1 elliptic cone,the transition prediction criterion is determined,i.e.,N_(tr)=8.6.In the transition position,the amplification factors of several modes reach a level close to 8.6,which implies that none of them has the absolute superiority sufficient to cause the transition itself.Finally,the BiGlobal-e^(N) method is employed to predict the transition location in the region of the minor axis of the 3:1 elliptical cone.It is found that a larger major-minor axis ratio leads to stronger instability and an earlier transition.展开更多
Streamwise vortex instability is one of the most potent mechanisms for the transition of the three-dimensional boundary layers.By using the global stability analysis methods,stability characteristics of the leeward vo...Streamwise vortex instability is one of the most potent mechanisms for the transition of the three-dimensional boundary layers.By using the global stability analysis methods,stability characteristics of the leeward vortex over a blunt cone with an angle of attack under a typical wind tunnel condition are studied and are compared to the case with a smaller wall temperature ratio(corresponding to a flight condition).The vortical structure features inward and outward vortices,similar to that in the flight con-dition.Unlike the flight condition,the outward vortices appear stronger than the inward vortices,resulting in stronger outer-mode instabilities.Although the inner mode is heavily stabilized compared to the flight condition,it can still radiate apparent acoustics.The acoustic sources are computed based on Lighthill's acoustic analogy,showing that the entropy term measuring the deviation from the isentropic relation is dominant.While Mack second mode is shown to most likely trigger the transition in the flight condition,it is absent in the wind tunnel condition,and a shear-layer mode turns out to be the most dangerous instead.Moreover,the instability frequencies and growth rates of the wind tunnel case are much smaller than those of the flight case,indicating that wall heating may stabilize the leeward vortices.展开更多
基金supported by the National Key Research and Development Program of China(Grant No.2016YFA0401200)by the National Natural Science Foundation of China(Grant Nos.91952301,11672204,12072230,and 11732011).
文摘Two-dimensional global(BiGlobal)stability in the region of the minor axis is investigated in the case of hypersonic elliptic cones with major-minor axis ratios of 2:1 and 3:1 at Mach number 6.0,and the BiGlobal-e^(N) method is proposed to predict the transition location of the boundary layer.Matrix-free BiGlobal stability analysis is used to find unstable modes,including the Y-mode and the Z-mode.The growth rates in the streamwise-frequency plane for these modes are obtained.The Nmax all factor is proposed,which represents the maximum amplification factor that all BiGlobal unstable modes can reach.Using a comparison of the N_(max_all) factor with the transition location measured in a wind tunnel experiment for the 2:1 elliptic cone,the transition prediction criterion is determined,i.e.,N_(tr)=8.6.In the transition position,the amplification factors of several modes reach a level close to 8.6,which implies that none of them has the absolute superiority sufficient to cause the transition itself.Finally,the BiGlobal-e^(N) method is employed to predict the transition location in the region of the minor axis of the 3:1 elliptical cone.It is found that a larger major-minor axis ratio leads to stronger instability and an earlier transition.
基金supported by the National Natural Science Foundation of China(Grant No.92052301).
文摘Streamwise vortex instability is one of the most potent mechanisms for the transition of the three-dimensional boundary layers.By using the global stability analysis methods,stability characteristics of the leeward vortex over a blunt cone with an angle of attack under a typical wind tunnel condition are studied and are compared to the case with a smaller wall temperature ratio(corresponding to a flight condition).The vortical structure features inward and outward vortices,similar to that in the flight con-dition.Unlike the flight condition,the outward vortices appear stronger than the inward vortices,resulting in stronger outer-mode instabilities.Although the inner mode is heavily stabilized compared to the flight condition,it can still radiate apparent acoustics.The acoustic sources are computed based on Lighthill's acoustic analogy,showing that the entropy term measuring the deviation from the isentropic relation is dominant.While Mack second mode is shown to most likely trigger the transition in the flight condition,it is absent in the wind tunnel condition,and a shear-layer mode turns out to be the most dangerous instead.Moreover,the instability frequencies and growth rates of the wind tunnel case are much smaller than those of the flight case,indicating that wall heating may stabilize the leeward vortices.
