基于不可压缩流场条件下低Mach数流动诱发声辐射的分析及定量预测

In simulations of flows at low Mach number, the incompressible Navier-Stokes equations are typically solved instead of the compressible equations. This results in significant computational savings, since the continuity and momentum equations time step can be solved independent of the energy equation, and the time step is limited only by the convective velocity and not the acoustic velocity. However this approach eliminates acoustics waves from the problem, which may be important to some applications. Therefore, how to precisely predict aerodynamic sound based on incompressible flow fields is the purpose of the present study. The main research contents include four parts as follows. 1) Of the acoustic analogy aspect, a theoretical analysis of the difference between the aerodynamic pressure and acoustic pressure will be carried out. Based on this analysis a more reliable and precise numerical estimation of aerodynamic sound radiation based on surface dipole source will be presented, and a comparison to volume quadruple source models will be made in the study of flow-induced cylinder noise. 2) Governing equations of aeroacoustics based on aerodynamic/acoustic splitting technique will be derived, and will be used to investigate the convection and refraction effects of mean flows on the sound waves by comparing to the acoustic analogy approach in studying flow-induced cylinder noise problems. 3) In the study of broadband aerodynamic sound, the coupling relation between pressure fluctuations and velocity fields will be theoritically deduced, and effort will be made to improve the existing models of wall pressure fluctuations. The flow-induced pipe noise will be investigated both numerically and experimentally as an example of broadband aeroacoustic problems. 4）As an integrated application of this study, quantitative prediction of the tonal and broadband hydrodynamic noise of a centrifugal pump will be carried out. This study contributes to a better knowledge of the mechanism of aerodynamic sound generation in low Mach number flow regimes; thus it offers theoretical basis and guiding principles for future study of aerodynamic noise control.

低Mach数流动计算通常使用不可压缩Navier-Stokes方程，只需求解连续方程和动量方程且计算时间步长不受声速限制，从而节省计算量。然而此途径把声波问题排除在外，声波问题在很多应用中相当重要。基于不可压缩流场如何定量预测流动产生的声辐射是本项目的研究主旨。研究内容包括四部分：1）在声比拟方面，理论分析流体动力学压力与声学压力的区别，在此基础上提出基于偶极子面源气动声辐射的更合理数值算法，并与四极子体源法进行比较；2）推导小扰动与平均流相分离的控制方程，用于定量预测柱体绕流声，以研究平均流对声波的对流折射影响；3）在宽频气动声预测方面，推导压力波动与速度场的耦合关系，改进现有壁面压力波动半经验模型，以管道流动噪声为例进行数值与实验研究；4）作为研究的综合应用，定量预测离心泵的离散及宽频水动噪声。本项目的研究成果有助于更深入认识低速流动噪声的产生机理，进而为其控制提供理论基础与指导原则。

本项目以低Mach数流动诱发气动声辐射为研究目标，分析不可压缩流场的扰动特性，并基于气动声混合法预测进行声辐射定量研究。首先，利用非齐次波动方程的Kirchhoff积分公式对Lighthill方程进行求解，进而得到Curle公式。其次，理论分析了不可压缩流场水动压力波动（近场伪声）的特性，分析其与声学压力的不同之处。再次，以亚临界三维圆柱绕流的气动噪声为研究对象，基于不可压缩流场数值模拟，研究Lighthill声类比理论中偶极子及四极子源模型在预测低Mach数流动气动声的可靠性及准确性。选择不同流场内部（可穿透）面作为声源面，通过时域积分FW-H方程得到声远场声压并与实验数据比较分析，以研究可穿透声源面FW-H法预计的精确性。最后，作为综合应用，研究了离心泵内部非定常流场的压力波动及其引发的水动噪声。

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