Analytical Study on Neutral Stability Analysis of Hypersonic Boundary Layers

摘要

The interaction of vorticity and acoustic modes of neutral stable waves in hypersonic boundary layers is investigated analytically. For subsonic disturbances, the difficulty in analyzing system properties of the instability of hypersonic boundary layers is due to the occurrence of the generalized inflection point, which is the essential singularity of the neutral stability problem. To alleviate the effect of singularity, the relative Mach number profile is first assumed as an indispensable physical characteristic, which is function of mean stream velocity, density and Mach number. With known profiles, the governing equation of the stability problem can be reduced to an eigenvalue problem with suitable boundary conditions. By introducing the WKB method, the characteristic equations that represent vorticity and acoustic modes can be derived. This study shows that eigenvalues, when appropriately normalized, depend on a single parameter Y, which is the product of the square of y{sub}s with the curvature of M{sup}2(y) evaluated at y{sub}s. For inflectional modes, the vorticity mode increases as Y{sup}(3/2), whereas the acoustic modes increase approximately as 1/Y. Then, using local perturbation method, the phenomena of curve veering and fluttering can be analyzed based on the eigenvalue loci. This study demonstrates that curve veering only appears in hypersonic boundary layers.