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Analysis of stability and trasitionin flat plate compressible boundary layers using linear stability theory

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2004
Atalayer, H. Senem
In this study, numerical investigations of stability and transition problems were performed for 2D compressible boundary layers over a flat plate in adiabatic wall condition. Emphasis was placed on linear stability theory. The mathematical formulation for 3D boundary layers with oblique waves including detailed theoretical information was followed by use of the numerical techniques for the solution of resulting differential system of the instability problem, consequently an eigenvalue problem. First, two-dimensional sinusoidal disturbances were analyzed at various Mach numbers including the subsonic, transonic, supersonic and even hypersonic flow speeds. In this case, the second mode (acoustic mode), namely the Mack mode, and its behavior with the increasing Mach number were visualized. The results were then compared with the available data in literature concluding with good agreements. Secondly, similar analysis was carried out for oblique waves. Here, not only the effect of flow speed but also the effect of wave orientation was demonstrated. For this purpose, instability problem was solved for several wave angles at each Mach number in the range of M=0 and M=5. In this respect, the angle at which the waves were most unstable was also obtained at each investigated flow speed. The resultant stability diagrams corresponding to M=4 and higher Mach numbers for which both first and the second modes appear revealed that plane waves were more stable than oblique waves for the Tollmien-Schlichting mode, however, this was the opposite for the acoustic mode where oblique waves were observed to be more stable. As a final step, estimation of the transition location was handled for the most unstable wave condition. Smith-Van Ingen transition method was applied as the prediction device. The results representing the influence of Mach number on transition Reynolds number were then