超声速尾涡的稳定性分析

从Ｎ－Ｓ方程出发，通过正则模方法，研究了超声速尾涡的绝对／对流不稳定性性质．计算了流动的稳定性特征随马赫数Ｍ，周向波数ｎ．，轴向自由流速度Ｗ０和旋转度ｑ等流动参数的变化规律，找到了绝对／对流不稳定区域的边界．通过比较发现，马赫数的增加使流动由绝对不稳定向对流不稳定乃至稳定转化．在所计算的参数范围，周向波数的增加加速了这一转化过程，而且，轴向速度的增加，同样使流动向着稳定的方向转化．同时还分析了不同旋拧程度的流动受可压缩影响的不同．这些结果对于了解旋拧流动稳定性的物理机理以及进行流动控制都有着重要意义．

STABILITY ANALYSIS ON SUPERSONICTRAILING-LINE VORTEX

In recent years there has been a great deal of interests in the stability of swirlingflows. It is because of not only the significance to the enhancement of supersonic mixing butalso the important applications to many practical flows such as the trailing-line vortices behindan aircraft. The absolute/convective instability of incompressible swirling flows and the temporalinstability of compressible swirling flows have been fully explored, whereas the absolute/convectiveinstability of compressible swirling flows remains nuclear. In this paper, the absolute/convectiveinstability of a supersonic trailing-line vortex is studied for the first time. The normal modemethod is applied to linearized N-S equations for disturbances. The obtained stability equationsare solved by the Chebyshev spectral collocation method combined with the QZ algorithm to givethe complex dispersion relation w = w(a), where a is complex axial wave number and w is complexfrequency. The absolute growth rate w_0,i is the imaginary part of w at the point with vanishinggroup velocity dw/dk = 0. Various stability characteristics of the flow along with the variationof Mach number M, azimuthal wave number n, axial free velocity w_0 and swirling ratio q areobtained. Like incompressible case, the axial velocity strongly influence the absolute/convectiveinstability of supersonic trailing-line vortex. The absolute growth rate is largest when there isa reverse flow (W_0 = 0.8), and reduces more quickly than incompressible case as axial velocitydeficit decreases (w_0 increases). The flow is less unstable and changes from absolute unstable toconvectively unstable or even stable as Mach number increases. Also, the absolute growth ratereduces as azimuthal wave number increases from n = l, and this tendency is more appreciable athigher Mach numbers. The boundary between absolutely unstable region and convectively unstableregion on the M-q plane is given. It shows that the swirl can significantly enhance the absolutegrowth rate only in certain range of swirling ratio q = 0.2 ~ 0.5. All these results are significantto the investigation of enhancement of supersonic mixing.