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TsAGI Science Journal
GROUP VELOCITY OF UNSTABLEWAVES IN A BOUNDARY LAYER AT SUPERSONIC SPEEDS
Vladimir Aleksandrovich Kuzminsky
Central Aerohydrodynamic Institute (TsAGI) 1, Zhukovsky str., Zhukovsky, 140180, Moscow region, Russia
Considered in this paper is a hydrodynamic stability of flow in a flat-plate boundary layer for incident flow Mach numbers M = 2.2 and M = 4.5 with displacement-thickness Reynolds numbers and Reδ* = 10,000 (Rex ≅ 0.896 × 106), respectively. Dependence of the group velocity vector on the wave vector absolute value K and the tilt angle ψ of the oblique wave vector for first and second stability modes were derived for the most increasing space disturbances. Amplification coefficients for the second mode at 0 ≤ ψ ≤ 20° are greater than maximum values for the first mode. Variation of group velocity with wave vector has a qualitatively different character for first and second modes, and it has a minimum value for the most increasing second-mode disturbances in the instability region. The direction of group velocity, which is the direction of amplification, varies from −1 to 2° in the instability region and coincides with the direction of incident flow at ψ = 0, 45 and 90. Presented here is a calculation of group velocity absolute value on the assumption of linear dependence between viscosity and temperature and with use of the Sutherland formula. The dependence between group velocity vector and tilt angle ψ of the oblique wave vector was obtained at M = 2.2 for the first mode. In this case, the direction of group velocity in the instability region varies from −6 to 4° and coincides with the direction of incident flow at values ψ = 0 and ψ ≅ 50°.
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