矢量气动声学的理论研究进展及应用

气动声学的声比拟理论以密度、声压等标量为波动算子变量，建立非齐次波动方程，描述流体运动及与边界作用诱发声音的辐射，但标量无法直接描述声能量的传播过程和途径.在流体力学研究中，标量用于描述当前当地的物质状态，而矢量用于描述质量和能量的传输.借鉴上述思想，开展了矢量气动声学的研究，概述矢量气动声学的理论研究进展及应用，主要包括:（1）以声粒子速度为变量，采用声比拟理论的思想直接从Navier-Stokes方程出发推导建立了气动声学的矢量波动方程及两种频域解；（2）综合利用声压和声粒子速度的积分解，直接求解声源周围的瞬时和有功声强矢量场，直观显示声能量的传播途径，应用于旋转声源辐射声能量的传播分析，揭示了亚音速旋转声源辐射声能量的3种传播模式:螺旋模式、声学黑洞模式和R-A模式；（3）采用球谐级数展开方法建立旋转点/紧凑声源辐射噪声的声压和声粒子速度的频域解析解，在此基础上推导了声功率谱的频域解析解，建立了识别旋转叶片声源在空间域和频域分布特征的方法；（4）综合利用矢量气动声学方法和等效源方法，显示声源和散射边界周围声强矢量场的分布特征和能量传播途径，直接揭示了阻抗边界主要的吸声位置以及直接计算得到阻抗边界的吸收声功率. 

Research Advancement and Application on Vector Aeroacoustics

In acoustic analogy theory, the perturbation of density or acoustic pressure is used as variable of the wave operator to describe the noise generated from fluid and its interaction with solid surfaces, but it is unable to directly describe the acoustic energy propagation with the acoustic scalars. In fluid mechanics, scalars are used to characterize the instantaneous and local states of fluid, while vectors are used to describe the transfers of mass and energy. Inspired by this idea, the vector aeroacoustics was developed and this paper presented the overview of recent advancement on this research. Some advancements were as summarized as follows. (1) The vector wave equation of aeroacoustics and the corresponding solutions have been proposed, in which the acoustic velocity was regarded as the variable of the wave operator. (2) The acoustic intensity vector field around rotating sources was visualized, revealing the following three radiation modes of acoustic energy:spiral mode, R-A mode and acoustically black-hole mode. (3) Analytical acoustic power spectrum formulations for the rotating point sources have been developed to identify the spatial and frequency features of the source on rotating blades. (4) Vector aeroacoustics method and the equivalent source method were combined to show the acoustic intensity vectors around the sources and scattering surfaces, visualizing the primary absorption position as well as calculating the acoustic power absorbed by impedance surfaces.