高速三维边界层的横流不稳定性

CROSSFLOW INSTABILITY OF HIGH SPEED THREE DIMENSIONAL BOUNDARY LAYER 1)

用两点四阶差分格式研究旋转圆锥超音速三维边界层的横流不稳定性和壁面冷却对稳定性的影响数值结果表明，与二维边界层相比横流使三维边界层第一模式增长率增大，对第二模式影响很小；Ｍｅ＜４３第一模式最不稳定，Ｍｅ＞４３第二模式最不稳定；三维边界层最不稳定第二模式是三维波，二维边界层则为二维波；壁面冷却对第一模式起稳定作用。

There exist variety of instability in three dimensional boundary layer on swept wing, the cross-flow instability is dominant The flow over rotating cone is typical three dimensional boundary layer It has been shown that the experimental and theoretical results of rotating cone can be used to model cross flow instability of swept wing At high speeds, where even the basic flow calculations of swept wing are a problem, owe to it′s simple geometry, rotating cone become a suitable and valuable model to study cross flow instability of high speed three dimensional boundary layer on swept wing In this paper, a rotating sharp cone which located in a supersonic/hypersonic free stream at zero attack is used as a model to study the cross flow instability of high speed three dimensional boundary layer The purpose of present work is to investigate the different instability mechanism of two and three dimensional boundary layers and effect of wall cooling on the instability The basic boundary layer flow is calculated using box scheme and the instability eigenvalue problem is solved by a fourth-order accurate two-point finite difference scheme Since the calssical approximation method of thermodynamic parameters of the air has not enough accuracy for numerical analysis of high speed instability problem, a high degree polynomial is used to imitate the dependence on temperature of viscosity, conductivity, Prandtl number and specific heat from experimental data The numerical results show that the growth rates of cross-flow first mode are larger comparing with those in two-dimensional case and the influence of cross flow decreases as Mach number increases but the influence of cross-flow on the second mode is weakly The results also show that the instability with cross flow cover a much wider range of unstable frequencies than those without cross flow and the growth rates of travelling waves are larger than stationary waves, the most unstable stationary wave is approximately perpendicular to potential flow direction If M e<4 3 the most unstable disturbance is the first mode, if M e>4 3 it is the second mode In three dimensional boundary layer the most unstable second mode is oblique, in two dimensional boundary layer is two-dimensiona; Cooling the wall stabilizes the first mode, destabilizes the second mode