三维扰动波的非平行边界层稳定性研究

NONPARALLEL STABILITY ANALYSIS OF THREE DIMENSIONAL DISTURBANCE WAVE IN BOUNDARY LAYERS

导出了三维扰动波的原始变量形式的抛物化稳定性方程（PSE）,研究了三维空间模态TS波的非平行边界层稳定性问题.采用了法向四阶紧致格式,以提高计算精度.通过给出不会导致奇性的坐标变换、修改外边界条件以及克服平行流初始值的瞬态影响和推进步长的限制,保证了计算的数值稳定.用补全元素带状矩阵法求解块三对角矩阵,大大提高了速度.计算结果清楚地显示了三维扰动波的演化过程和非平行性对边界层稳定性的影响,特别是,观察到非平行性对三维扰动波的影响,有时会使其稳定性出现逆转的现象.还研究了逆压梯度的作用.算例的结果与其他结果符合良好.

In this paper, the nonparallel stability of 3D TS waves for the spatial mode in the boundary layers is analyzed using parabolized stability equations (PSE), which are new effective approach to study the evolution of disturbance waves in the weakly nonparallel flows such as boundary layers. The governing equations are derived directly from full Navier-Stokes equations in primitive-variables form. Numerical computation is exact by using fourth-order compact scheme in normal-wise. The PSE is solved stably by using a nonsingularly mapped domain with modified outer boundary conditions, and overcome the step-size limitation and the transient phase introduced by the parallel initial solution by larger step size at beginning. The solver of single element band matrix with complement zero block is presented, which is quite efficient. The results presented clearly show the evolutions of the 3D TS waves and the effects of the nonparalellism on the stability of 3D waves in incompressible boundary layers. Paticularly, the nonparalell effects, which is found in the amplitude curves of TS waves with different spanwise wavenumber, can change stability characteristics of 3D disturbance wave from stability with parallel flow to instability with nonparallel flow under some conditions. The role of pressure gradient is also investigated. The results computated are quite consistent with available data.