流动噪声不仅是湍流研究中的重要问题，也是影响水下航行器隐身性的关
键因素。基于 Heaviside 函数的 Ffowcs Williams 与 Hawkings (FWH) 声比拟方法
是常用的声比拟方法之一。该方法将适用于自由空间噪声预测的 Lighthill 声比
拟理论推广到考虑运动边界的噪声预测中。提高 FWH 声比拟方法的准确性与效
率是流动噪声计算的重要任务。
针对 FWH 声比拟方法的准确性与计算效率问题。本文考虑了 FWH 声比拟
方法的积分面截断以及声源输入的误差对计算所得声压的影响，由此提出了四
极子源与单极子源的修正方法。考虑到传统频域方法因计算量巨大难以应用于
运动物体辐射噪声或者运动观测点接收噪声的计算，本文构造了高效的频域远
场噪声求解方法。在此基础上，本文基于紧致声源假设研究了水下航行器标模
SUBOFF 的远场辐射噪声特性。主要的创新性工作包括：
1. 提出了一种适用于亚声速流动的频域四极子修正模型，抑制了四极子源
穿出积分面导致的虚假噪声。该模型考虑了前人工作中忽略的四极子源对流速
度等于或者大于声波相速度的情况，解决了传统的级数形式模型在计算上游观
测点噪声时出现的发散问题。在四极子声源冻结的假设下，该模型可以收敛到单
一面积分的形式，由此避免了模型中 Lighthill 应力张量高阶导数的计算。进一步
的，我们考虑了模型中的关键参数四极子源对流速度的影响，提出了基于关联函
数的非均匀四极子修正模型。与常用的均匀模型相比，非均匀模型改善了钝体绕
流远场噪声指向性的计算结果。最后，我们从四极子源滤波的角度揭示了虚假噪
声的产生机理：积分面截断导致不发声的冻结涡波中产生了奇异的四极子源，进
而导致了虚假噪声。
2. 提出了一种满足质量守恒的 FWH 积分，抑制了极低马赫数下质量守恒误
差对声压计算的影响。通过采用格林函数高阶导数的远场近似，我们对 FWH 积
分的单极子项进行了多极子展开，发现展开式的首项与穿过积分面的质量通量
成正比，而次项与动量脉动相关。在极低马赫数下，即使微弱的虚假质量通量也
会导致严重的单极子项计算误差。因此，我们在低马赫数下提出了一种不依赖于
质量通量的 FWH 积分。我们在对转涡和亚临界圆柱绕流算例中进行了验证，
发 现在极低马赫数条件下，舍弃单极子展开式的第一项有效地抑制了远场噪声对
积分面位置的依赖性。
3. 提出了两种不同的频域 FWH 积分计算方法，分别适用于运动声源和运动
观测点的噪声计算。对于运动声源问题，当前的频域 FWH 积分在计算宽谱噪声
或者多频噪声时需要逐个频率进行时间积分，计算量巨大。我们提出了一种高效
计算方法，可用于处理二维和三维的宽频噪声预测问题。应用格林函数的时频
域分解，并采用了非均匀快速傅里叶变换，我们得到了一种无需逐个频率进行时
间积分的频域 FWH 积分。在计算频率数量较多的情况下，与传统的频域方法相
比，我们提出的方法能够显著提高计算效率。对于运动观测点问题，我们同样采
用了时频域分解的方法，避免了需要逐个时刻进行频率积分的复杂计算。我们通
过单极子和偶极子等标准算例，证明了所提出的方法在不同来流马赫数和不同
运动形式的远场观测点噪声计算中的可行性和准确性。
4. 发现了全附体水下航行器标模绕流的远场辐射声压指向性特征，揭示了
指向性形成机制。我们模拟了全附体水下航行器标模 SUBOFF 周围的湍流流动
和辐射噪声，成功捕捉到了全附体 SUBOFF 周围的流动结构，包括：艇体、指挥
台和尾舵的曲面边界层；指挥台和尾舵引起的边界层局部分离；指挥台和尾舵形
成的剪切层；剪切层与艇体边界层之间的相互干扰以及尾迹中的不同尺度的涡
结构。此外，我们利用 FWH 积分计算了 SUBOFF 标模的远场辐射声压。我们发
现横截面上的辐射声压方向在一段时间内偏离垂直方向，在 45（或 225）度夹角
方向上形成了高压区。基于远场条件和低马赫数下的紧致声源假设，我们揭示了
引起这种指向性偏移的升力偶极子和侧向力偶极子的相消干涉和相长干涉机制。

Flow-generated sound is not only a crucial issue in turbulence research but also a key factor affecting the stealthiness of underwater vehicles.The Ffowcs Williams and Hawkings (FWH) acoustic analogy method, on the basis of the Heaviside function, is one of the commonly used acoustic analogy theories.The FWH acoustic analogy method extends Lighthill's acoustic analogy theory, which is suitable for sound prediction in free space, to prediction of sound generated by moving boundaries. Enhancing the accuarcy and computational efficiency of the FWH analogy method is crucial for prediction of flow-generated sound.

Addressing the accuarcy and computational efficiency of the FWH analogy method, this thesis considers the effects of truncation of the source region and errors in the source input on predicted sound. We propose correction methods for quadrupole and monopole source terms. Considering the huge computational burden associated with conventional frequency-domain methods, when predicting radiated noise from moving sources or received by moving observers, this thesis develops efficient frequency-domain sound prediction methods for both scenarios. Furthermore, based on the compact source region assumption, this thesis investigates the far-field radiated sound generated from the submairne model SUBOFF. The primary innovations and contributions of this work can be summarized as follows:

1. A frequency-domain quadrupole correction model applicable to subsonic flows is proposed. This model mitigates spurious noise caused by quadrupole sources crossing through the integral surface. We resolve the divergence issue in conventional series-like models at upstream observers by accounting for the condition where the convective velocity of quadrupole sources is smaller than the phase velocity of sound waves. Under the assumption of the frozen flow hypthosis, the proposed model converges to a single-surface integral, eliminating the requirement for computation of high-order derivatives of the Lighthill stress tensor. Furthermore, we investigate the influence of a critical parameter, the convective velocity of quadrupole sources, and propose a non-uniform model based on correlation function. Compared to the commonly used uniform model, the non-uniform model yields improved results of far-field sound directivity for bluff bodies. Finally, we explain the generation of spurious noise from the perspective of quadrupole source filtering: truncation of the source region leads to singular quadrupole sources from non-radiating vortical waves and thus resulting in spurious noise.

2. A mass-conserved FWH integral is proposed to suppress the effects of spurious mass flux on predicted sound. By employing a far-field approximation of Green's function's high-order derivatives, we expand the monopole source term of the FWH integral into a series of multipole terms. We find that the first term of the expansion is proportional to the mass flux through the integral surface, while the second term is related to momentum fluctuations. At very low Mach numbers, a weak artificial mass flux can lead to significant errors of the monopole source term. Therefore, we propose a FWH integral independent of the mass flux at low Mach numbers.
 We validate this method by using cases involving vortex pairs and subcritical flow over a circular cylinder, demonstrating that discarding the first term of the expansion effectively reduces the dependency of far-field sound on the integral surface's position.

3. Two distinct frequency-domain FWH integral calculation methods are proposed for predicting sound generated from moving sources and received by moving observers, respectively. For moving source problems, the methods requires an expensive time integration at each frequency. We propose an efficient method suitable for prediction of broadband sound in both two-dimensional and three-dimensional cases. By decomposing the Green's function into the time- and frequency-dependent components and applying a non-uniform fast Fourier transform, we obtain a frequency-domain FWH integral that does not require time integration at each frequency. When dealing with a large number of discrete frequencies, our proposed method significantly improves computational efficiency compared to the conventional frequency-domain method. For moving observer problems, we likewise employ a decomposition of the Green's funtion, thus avoiding the need for time-domain frequency integration. Through validation on standard cases involving monopole and dipole sources, we demonstrate the feasibility and accuracy of the proposed methods for far-field sound prediction under various freestream Mach numbers and in different kinds of motions.

 4.  We find the far-field sound directivity of a fully appended submarine model and reveal the mechanism resulting in the directivity. We simulate the turbulent flow around a fully appended submarine model (SUBOFF) and its radiated noise. We successfully capture the flow structures around the SUBOFF body, including the turbulent boundary layer on the hull, flow separation induced by the sail and stern, shear layers, interaction between the shear layer and turbulent boundary layer, and various scales of vortical structures in the wake. Additionally, we compute the far-field sound by using the FWH acoustic analogy method. We find that the directivity of the dipole sources on the cross-sectional plane deviates from the vertical direction over a certain time period, resulting in regions of low sound pressure at angles of 45 degrees (or 225 degrees). Based on the far-field conditions and the compact source assumption at low Mach numbers, we reveal that this deviation results from interference between lifting dipole and side force dipole.