Boundary-Layer Stability Analysis for Sharp Cones at Zero Angle-of-Attack

摘要

The stability characteristics of an uncooled sharp cone at zero angle of attack have been calculated at an edge Mach number of 6.8 and a stagnation temperature of 728 K (1310 R) using spatial normal modes. Transformed flat-plate boundary-layer profiles were used for the mean flow. By a consideration of both two-dimensional and oblique waves, it has been determined that instability at this Mach number is primarily a two-dimensional second-mode instability. Comparisons with available stability experiments show that the calculated unstable frequencies were present in the experiments, but the measured amplification rates differ from the calculated. A band of unstable high frequencies above the second-mode region that starts at about R=1400 is not accounted for by the theory. Comparisons of amplitude-growth curves for both cones and flat plates at March numbers 4.5, 5.8 and 6.8 show that the most unstable normal modes on a cone have at least as much total growth as on a flat plate at Mach 4.5 and more total growth at the other two Mach numbers. Keywords: Boundary layer stability; Hypersonic linear stability theory; Hypersonic cone stability.