超声速平面剪切层声辐射涡模态数值分析

NUMERICAL ANALYSIS OF ACOUSTIC RADIATION VORTICAL MODES IN A SPATIALLY EVOLVING SUPERSONIC PLANE SHEAR LAYER

对Mc=1．2二维超声速空间发展平面自由剪切层,进行了扰动模态及流动结构的数值分析．采用时空三阶改进MacCormack格式,差分求解可压缩扰动Navier-Stokes方程,直接数值模拟入口不同基频谐波扰动的非线性演化特征．采用空间线性稳定性理论证明,计算所促发的扰动波是声辐射涡模态．扰动参数及特征函数分析显示,声辐射涡模态是弱色散的快／慢两种外部模态,在扰动对流Mach数为超声速一侧呈膨胀／压缩状辐射．单频受迫扰动可无相差地促发多模态混合扰动波,而在自然扰动条件下,剪切层的稳定性受慢模态主导．

Disturbance modes and flow structures are numerically analyzed for a two-dimensional spatially evolving supersonic plane free shear layer at Mc = 1.2. The compressible disturbance Navier-Stokes equations are solved by using a modified MacCormack scheme, which is a third-order method in both temporal and spatial accuracies. Three primary harmonic-wave disturbances with different frequencies are superimposed upon the mean transverse velocities at inflow sections, and then their nonlinear developments are investigated by using the direct numerical simulation （DNS） method. Moreover, a spatial linear stability theory is also introduced, and it is shown that the induced disturbance waves obtained by the DNS method are of acoustic radiation vortical modes. The results from analyses of disturbance parameters and eigenfunctions reveal that the acoustic radiation vortical mode is an outer mode consisting of fast and slow modes, radiating in the supersonic disturbance convective Mach number side in the shear layer, with a series of expansion and compression fans. Single-frequency forcing disturbance can produce a multi-mode mixed disturbance wave without phase difference, while the slow mode is dominant in the shear layer for a natural disturbance.