基于模态分解的轴对称超声速射流啸声产生位置数值分析

不完全膨胀超声速射流的势核中会产生准周期的激波栅格结构, 其与剪切层内拟序结构的相互作用会产生激波噪声. 啸声是主要向上游方向传播的、具有离散频率的高强度激波噪声, 其产生是受一种非线性的声反馈环机制驱动. 精确定位啸声的声源位置是定量理解啸声反馈环机制和发展准确的啸声预测模型的一个关键所在. 为了分析近场啸声, 本文采用高精度数值方法直接求解轴对称可压缩Navier-Stokes方程, 数值模拟了完全膨胀射流马赫数为1.10和1.15的圆形声速喷管欠膨胀超声速冷射流, 得到了A₁和A₂两种轴对称模态啸声. 通过傅里叶模态分解、本征模态分解和动态模态分解, 分析了射流时序压力场和速度场, 研究了啸声关联拟序流动结构的空间演化, 精确定位了轴对称模态啸声的声源位置. 研究表明: 啸声关联拟序流动结构存在饱和态区域, 啸声声波是在其饱和态区域产生并向外传播; 在本文所涉及的射流马赫数范围内, A₁和A₂两种轴对称模态啸声的有效声源位置分别是在第4和第3个激波栅格结构的尾缘. 

NUMERICAL STUDY ON THE GENERATION POSITION OF SCREECH TONE IN AXISYMMETRIC SUPERSONIC JET BASED ON MODAL DECOMPOSITION1)

For the imperfectly expanded supersonic jet, the quasi-periodic shock-cell structures in jet core interacts with the coherent structures in shear layer to generate shock-associated noise. Screech tone is the shock-associated noise component with discrete frequency and high intensity, and it propagates primarily toward upstream direction. Its generation is driven by a nonlinear acoustic feedback loop. The exact nature of screech-generation mechanism, including source positions, has remained an open question. Accurately locating the sound source position of screech tone is a key point to quantitatively understand the screech feedback loop mechanism and to develop exact screech prediction model. In this paper, numerical simulations of underexpanded supersonic cold jet issuing from a circular sonic nozzle are carried out through solving axisymmetric compressible Navier-Stokes equations directly, using fifth order finite difference weighted essentially non-oscillatory scheme and third order total variation diminishing Runge-Kutta scheme. The fully expanded jet Mach numbers are 1.10 and 1.15. The present numerical result is compared and in good agreement with the experimental result in the literature. The axisymmetric A₁ mode and A₂ mode screech tones are captured. The time sequential pressure field and velocity field of the jet are analysed through the Fourier mode decomposition, the proper orthogonal decomposition and the dynamic mode decomposition. The spatial evolution of screech-associated coherent flow structures are studied and the sound source positions of axisymmetric A₁ mode and A₂ mode screech tones are accurately located. The results show that each screech-associated coherent flow structure has its own saturation state region, where the screech waves generate and radiate outward. It is also found that the effective source positions of axisymmetric A₁ mode and A₂ mode screech tones are the trailing edges of the fourth and the third shock-cells respectively for the jet Mach numbers considered.