让探索有迹，让求知有回响。Traces of discovery. Echoes of inquiry.

本研究通过受控缩比模型实验，考察地面表面处理与建筑存在对悬停无人机（UAV）声场的影响。实验以可跟踪的动态悬停无人机作为声源，在预设声源位置运行，沿线性传声器阵列及建筑上的局部接收位置测量声压级谱；并利用相应的动作捕捉记录验证声学采集时段内的静态悬停状态。实验设计旨在为相对传播比较提供受控的模型尺度基准，而非直接给出全尺度声压级预测。研究对比了四种环境条件——刚性地面或人工草皮覆盖地面，以及有建筑或无建筑——下的频谱差异。人工草皮作为相对于裸露亚克力地面的受控部分吸声表面处理，产生了一致的高频谱降低，沿主阵列的空间变化较弱；相比之下，建筑模型造成空间非均匀效应，建筑遮挡区内高频降低更强，而声源直接暴露区域的变化弱得多。两种效应在低频均不明显，此处绕射与相位敏感干涉更为重要。地面—建筑交互对频带平均声级影响有限，但在代表性窄带谱中仍可观察到局部频率选择性偏差。建筑附近的局部观测进一步表明，近结构频谱可能对局部声源—接收点几何关系及无人机悬停高度敏感。总体而言，这些结果为识别无人机噪声传播中频率依赖、空间结构化及局部化的频谱特征提供了可重复的缩比模型基准，并支撑城市空中交通噪声预测方法的发展与验证。

This study investigates how ground surface treatment and building presence influence the acoustic field of a hovering unmanned aerial vehicle (UAV) using a controlled scaled-model experimental setup. A tracked dynamically hovering UAV was used as the acoustic source and operated at prescribed source locations, and sound pressure level spectra were measured along a linear microphone array and at local on-structure receiver positions. The corresponding motion-capture records were used to verify the static-hover condition during the acoustic-recording windows. The experiment was designed to provide a controlled model-scale benchmark for relative propagation comparisons rather than to serve as a direct full-scale SPL prediction. Spectral differences were evaluated among four environmental conditions combining rigid or artificial grass-covered ground with building-present or no-building configurations. The artificial grass layer, used as a controlled partially absorptive surface treatment relative to the bare acrylic floor, produced a consistent high-frequency spectral reduction with weak spatial variation along the main array. In contrast, the model building produced a spatially non-uniform effect, with stronger high-frequency reduction in the building-shielded region and much weaker changes in the region with direct source exposure. Both effects were less pronounced at lower frequencies, where diffraction and phase-sensitive interference became more important. The ground–building interaction had limited impact on band-mean levels, although localized frequency-selective deviations remained observable in representative narrowband spectra. The local on-structure observations further showed that near-structure spectra can be sensitive to local source–receiver geometry and UAV hovering height. Overall, the results provide a repeatable scaled-model benchmark for identifying frequency-dependent, spatially structured, and localized spectral features in UAV noise propagation, and support the development and validation of urban air mobility noise prediction methods.

为研究边界层吸入（BLI）相关进气畸变对单级亚声速风扇气动与声学响应的影响，本文采用高保真格子玻尔兹曼方法/超大涡模拟（LBM/VLES）框架开展了系统性数值研究。在相同总体流量下，通过对比 BLI 进气构型与均匀进气构型，分析进气畸变的演化、其在风扇级内的传播以及相应的近场与远场声学响应。结果表明，S 形进气道内产生的低动量流在边界层发展、二次流与逆压梯度的共同作用下向下游逐步发展，在气动接口平面（AIP）形成显著的径向与周向不均匀性。进入风扇级后，畸变入流并非简单衰减，而是通过转子尾迹对流、转静子干涉与下游掺混持续重新分布。尽管截面平均的轴向输运能力仅略有变化，畸变入流仍导致不可逆损失增加，并使静子进口与出口处的空间不均匀性增强；同时强化了风扇级内的速度重分布、尾迹干涉与涡活动，使转子附近的非定常压力响应出现明显的周向调制。在近场，畸变入流使声压级（SPL）谱、瞬时压力脉动场与声能分布呈现更强的空间不均匀性。远场结果进一步揭示了明显的频率依赖性：200–1000 Hz 低频段与叶频（BPF）主导的离散分量对进气畸变最为敏感，而 1000–10000 Hz 频段及 2BPF 附近的响应相对较弱。特别地，低频声学效应主要表现为辐射指向性的重新分布，而非噪声水平的均匀升高。这些发现阐明了亚声速风扇在 BLI 进气畸变作用下的气动—声学耦合响应机理，可为 BLI 推进系统的气动评估与低噪声设计提供指导。

To investigate the effects of intake distortion associated with boundary layer ingestion (BLI) on the aerodynamic and acoustic responses of a single-stage subsonic fan, a systematic numerical study is conducted using a high-fidelity lattice Boltzmann method/Very Large Eddy Simulation (LBM/VLES) framework. The evolution of inlet distortion, its propagation through the fan stage, and the associated near-field and far-field acoustic responses are analyzed by comparing a BLI intake configuration with a uniform-inlet configuration at the same overall flow rate. The results show that the low-momentum flow generated within the S-shaped intake progressively develops downstream under the combined effects of boundary-layer development, secondary flow, and adverse pressure gradients, producing pronounced radial and circumferential non-uniformity at the aerodynamic interface plane (AIP). After entering the fan stage, the distorted inflow is not simply attenuated but undergoes continuous redistribution through rotor-wake convection, rotor–stator interaction, and downstream mixing. Although the section-averaged axial transport capability changes only slightly, the distorted inflow leads to increased irreversible loss and stronger spatial non-uniformity at the stator inlet and outlet. It also intensifies velocity redistribution, wake interaction, and vortical activity within the fan stage, resulting in a pronounced circumferential modulation of the unsteady pressure response near the rotor. In the near field, the distorted inflow produces stronger spatial non-uniformity in the sound pressure level (SPL) spectra, instantaneous pressure-fluctuation field, and acoustic-energy distribution. Far-field results further reveal a clear frequency dependence: the 200–1000 Hz low-frequency band and the blade-passing-frequency (BPF)-dominated tonal component are most sensitive to inlet distortion, whereas the responses in the 1000–10,000 Hz range and near 2BPF are comparatively weaker. In particular, the low-frequency acoustic effect is primarily manifested as a redistribution of radiation directivity rather than a uniform increase in noise level. These findings clarify the coupled aerodynamic and acoustic response mechanisms of a subsonic fan subjected to BLI-intake-induced distortion and provide guidance for the aerodynamic assessment and low-noise design of BLI propulsion systems.

点式安装的惯性作动器只能提供一个横向作用力，难以同时控制决定弯曲波运动的平动与转动状态。本文提出一种可编程惯性作动器单元，在 Euler–Bernoulli 梁的内部截面同时反馈这两种状态：由对称布置的加速度计对重构截面速度，两个空间分离的惯性力在不依赖外部反力框架、也不需要物理力矩作动器的前提下，合成一般耦合的虚拟边界阻抗。可调模拟滤波器实现反馈律，并采用代理模型辅助整定给出控制器参数，再用装配完成的梁–作动器模型加以验证。计入传感器与作动器基座质量后，得到的目标频率与实测值相差在 2% 以内。在第三、第四阶模态中，分别整定的双通道控制器使模型峰值迁移率降低 31.8 与 26.9 dB，实测的电压归一化监测响应分别降低 28.5 与 24.2 dB；数值降幅相较被动安装状态还多出约 22.3 与 23.8 dB。激光测振扫描确定了虚拟截面下游被抑制的响应区域，返回比测量支持闭环稳定性。反向波分量估计提供了补充证据，但尚不能给出吸声系数。在梁上方 20 mm 处进行的声压扫描显示近场有相应的降低。这些结果建立了一套紧凑、可重新整定的区域梁振动控制方案；声学验证目前仍限于所测近场。

A point-mounted inertial actuator supplies one transverse force, which limits the ability to control the translational and rotational states that govern the motion of flexural waves. In this study, a programmable inertial actuator unit that feeds back both states at an internal section of an Euler–Bernoulli beam is developed. A symmetric accelerometer pair reconstructs the section velocities, and two spatially separated inertial forces synthesize a generally coupled virtual boundary impedance without an external reaction frame or a physical moment actuator. Tuneable analogue filters realize the feedback law; surrogate-assisted tuning is used to propose controller parameters that are verified with the assembled beam–actuator model. The inclusion of sensor and actuator base masses yields target frequencies that are within 2% of experimentally derived values. In the third and fourth modes, separately tuned dual-channel controllers reduce the modelled peak mobility levels by 31.8 and 26.9 dB and the measured voltage-normalized monitor responses by 28.5 and 24.2 dB, respectively. The numerical reductions exceed those of the passive mounted state by approximately 22.3 and 23.8 dB. Laser vibrometer scans locate the suppressed response downstream of the virtual section, and return ratio measurements support closed-loop stability. Backwards-wave component estimates provide complementary evidence but do not identify an absorption coefficient. Pressure scans implemented 20 mm above the beam show an associated near-field reduction. These results establish a compact, retunable scheme for controlling regional beam vibration; the acoustic validation remains limited to the measured near field.

边界层吸入推进可提高飞行器气动效率，但也引入影响风扇流动与稳定性的进气畸变。本文在统一几何和边界条件下对比非定常雷诺平均 Navier–Stokes 模拟与大涡模拟，并分析三个代表性大涡模拟时刻，研究非定常响应与损失机制。相较前者，大涡模拟更详细地呈现畸变及内部涡结构，捕捉破碎涡系的生成和混合，并揭示静子轮毂附近角区分离与通流能力衰减等主要损失源。时序比较表明，畸变涡核的强度和形状虽随时间变化，其周向相位基本保持不变，在气动接口平面形成稳定畸变扇区。该扇区内转子接近临界入射角并发生局部分离，静子通道则呈现固定扇区内周向连续的损失分布。这些发现阐明了畸变引起的非定常损失机制，为定位损失区域及进气道—风扇一体化抗畸变设计提供数值指导。

Boundary layer ingestion (BLI) propulsion can improve aircraft aerodynamic efficiency, but also introduces inlet distortion that affects fan flow and stability. This study investigates the resulting unsteady flow response and loss mechanisms by performing a parallel comparison of unsteady Reynolds-averaged Navier–Stokes (URANS) and large-eddy simulation (LES) under unified geometry and boundary conditions, together with a time-sequence analysis of three representative LES instants. The results show that, compared with URANS, LES provides a more detailed depiction of the distortion pattern and internal vortical structures. LES captures the generation and mixing of fragmented vortex systems, and reveals corner separation near the stator hub and the decay of throughflow capacity, identifying major internal loss sources. The time-sequence comparison further shows that, although the distorted vortex core evolves in strength and shape, its circumferential phase remains essentially preserved, leading to a stable distorted sector at the aerodynamic interface plane. Within this sector, the rotor approaches critical incidence and triggers local separation, while the stator passages exhibit a sector-fixed, circumferentially continuous loss distribution. These findings clarify distortion-induced unsteady loss mechanisms in BLI fans and provide numerical guidance for locating loss regions and supporting distortion-tolerant design of intake–fan integrated systems.

FW–H 声类比广泛用于噪声预测，但大积分面和长声源时间历程会使后处理计算成本很高。本文面向配备深度计算单元（DCU，即 GPU 类加速器）的平台，提出基于 MPI 的多节点 FW–H 求解器。主机 CPU 负责数据准备、节点间通信和输入输出，主要计算量所在的 FW–H 积分卸载至 DCU。观察点、时间或频率样本及面元上的嵌套循环映射到三维线程网格，并通过分布式域分解减少各进程内存占用。典型二维和三维基准验证中，远场指向性的平均相对误差分别低于 0.15% 和 0.70%。在代表性二维频域基准中，相比经过优化的 32 核海光 C86 7185 CPU 实现，单张海光 DCU 的端到端加速最高达 21.2 倍，积分内核最高达 708 倍。该二维算例的 CPU 实现在较低至中等核数下近线性扩展，但接近 32 核时出现饱和；大型三维时域基准中，CPU 和 DCU 分别扩展至 128 核和 128 张 DCU 时仍表现良好，DCU 接近线性，部分配置达到超线性加速。分析表明，CPU 饱和主要与 MPI 开销和节点内资源竞争增加有关；DCU 超线性加速主要来自单设备任务减少后分块次数及主机—设备传输开销降低。基于额定功率的估算还表明，DCU 配置完成求解的能耗低于相应 CPU 配置。该实现为气动声学预测提供了准确、高效且可扩展的 FW–H 计算框架。

The Ffowcs Williams–Hawkings (FW–H) acoustic analogy is widely used for noise prediction, but large integration surfaces and long source-time histories can make the post-processing computationally expensive. To address this issue, we present a Message Passing Interface (MPI)-based multi-node implementation of the FW–H solver for platforms equipped with Deep Computing Units (DCUs), i.e., GPU-class accelerators. In this framework, host CPUs handle data preparation, inter-node communication, and I/O, while the computationally dominant FW–H integration is offloaded to the DCUs. The nested loops over observers, time/frequency samples, and surface elements are mapped onto a three-dimensional thread grid, and distributed domain decomposition is adopted to reduce the memory footprint on each rank. The implementation is validated on canonical two-dimensional and three-dimensional benchmarks, with mean relative errors in far-field directivity below 0.15% and 0.70%, respectively. For a representative 2D frequency-domain benchmark, a single Hygon DCU achieves an end-to-end speedup of up to 21.2 × over an optimized 32-core Hygon C86 7185 CPU implementation, and up to 708 × for the FW–H integration kernel. In this 2D case, the CPU implementation scales nearly linearly at low to moderate core counts but shows signs of saturation near 32 cores, whereas for the large 3D time-domain benchmark, both CPU and DCU implementations exhibit robust multi-node scalability up to 128 CPU cores and 128 DCUs, with the DCU path showing near-linear scaling and, in some configurations, superlinear speedup. Scalability analysis indicates that the CPU saturation trend is mainly associated with increasing MPI overhead and intra-node resource contention, whereas the superlinear DCU speedup arises primarily from reduced chunking and lower host–device transfer overhead as the per-device workload decreases. A rated-power-based estimate also suggests lower energy-to-solution for the DCU configurations than for the corresponding CPU configurations. Overall, the proposed multi-DCU implementation provides an accurate, efficient, and scalable framework for FW–H-based aeroacoustic prediction.

本文采用动量源计算框架，参数化研究圆柱在横向谐波扰动下的涡激振动与尾迹演化。扰动强度为自由来流速度的 1%–10%，约化速度从 1.0 扫描至 15.0。研究从振幅、水动力、相位动态及尾迹演化等方面分析不同约化速度区间内的响应。扰动强度的作用随区间显著变化：锁定前区间内，扰动增大振幅并触发尾迹由 2S 向 2P 模式转变；在所给文本缺失的特定条件下发生完全同步，所有测试扰动强度下均保持稳定振幅和 2P 脱涡模式。锁定区间内，结构振动略受抑制，但响应频率仍保持锁定。向失同步过渡时，内禀脱涡与外部扰动竞争使主锁定状态提前终止，形成低振幅分支，且扰动强度越高，外部主导作用越明显。失同步区间内，扰动增强尾迹动力学，并放大脱涡频率处的结构响应。研究阐明了横向扰动对圆柱涡激振动的多重作用，为海洋工程结构疲劳评估及振动控制提供参考。（所给文本中约化速度符号及完全同步条件缺失，待补原文公式。）

Employing a momentum-source computational framework, this study parametrically investigates the vortex-induced vibration (VIV) and wake evolution of a circular cylinder subjected to harmonic cross-flow perturbations with intensities ranging from 1% to 10% of the freestream velocity. The reduced velocity () is swept from 1.0 to 15.0. The perturbation-modulated response across different reduced velocity regimes is analyzed regarding vibration amplitude, hydrodynamic forces, phase dynamics, and wake evolution. The results indicate that the impact of perturbation intensity varies significantly across different reduced velocity regimes. Within the pre-lock-in regime, the perturbation amplifies the vibration amplitude and triggers a wake transition from 2S to 2P patterns. At [value missing in supplied text], full synchronization occurs. Under all tested perturbation intensities, the response maintains robust vibration amplitudes and a stable 2P shedding mode. Within the lock-in regime, although the structural vibration undergoes slight suppression, the response frequency remains firmly locked. In the transition towards desynchronization, the competition between intrinsic shedding and extrinsic perturbation forces an early termination of the primary lock-in state, leading to a low-amplitude branch. This extrinsic dominance becomes increasingly pronounced at higher perturbation intensities. In the desynchronized regime, the perturbation energizes the wake dynamics and amplifies the structural response at the vortex shedding frequency. These findings clarify the multifaceted role of cross-flow perturbations in the VIV of cylindrical structures, providing valuable insights for the fatigue assessment and VIV control of marine engineering systems. [The reduced-velocity symbol was also missing from the supplied text.]

采用传统时域方法求解周期非定常流动时，达到最终周期状态之前的长过渡过程常导致计算效率较低。本文通过实现对流单极子声源、频域阵风激励及无反射边界条件，将谐波平衡方法用于气动声学。测试包括均匀背景流中单极子声源、翼型俯仰振荡、阵风—翼型相互作用前缘噪声及阵风—叶栅响应。结果与解析及实验数据吻合良好，多数算例中的归一化均方根误差通常低于 10%。研究展示了谐波平衡方法在流体力学和气动声学中的广泛应用潜力。

Periodic unsteady flow problems often exhibit computational inefficiency when conventional time-domain methods are employed. This phenomenon can be attributed to the lengthy transition phase before reaching the ultimate periodic state. To address this problem, the harmonic balance method (HBM) is employed for aeroacoustic applications through the implementation of convective monopole sources, frequency-domain gust excitation, and nonreflective boundary conditions. A set of test cases is considered to evaluate this method, including monopole sources with uniform background flows, the pitching oscillations of airfoils, leading-edge noise of gust–airfoil interactions, and the response of gust–cascade interactions. The results show good agreement with analytical and experimental data, with normalized root-mean-square errors typically below 10% across most considered cases. The findings from this research demonstrate a comprehensive range of potential applications for HBM in the fields of fluid dynamics and aeroacoustics.

本文结合有限元分析（FEA）与统计能量分析（SEA），计算两腔阶梯声学管道的中频响应。腔室 1 尺寸为 0.644×0.045×0.045 m，腔室 2 为 0.17×0.02×0.02 m，两者同轴连接，由腔室 1 外端扬声器驱动。在全消声室内开展 178–11220 Hz 测试。按模态数量分类，腔室 1 在 1415–8913 Hz 内表现为一维与三维混合子系统，采用统计建模；腔室 2 保持一维特征，采用确定性建模。两者通过阻抗动态凝聚为单自由度的界面耦合。由阻抗管测得吸声系数推导内部损耗因子；声源表征在第一截止频率 3811 Hz 以下采用多传声器方法，更高频率采用平面波近似。腔室 1 的 SEA 解给出界面声压和体积速度，预计算传递函数用于预测腔室 2 测点声压。实验显示，两腔最大误差分别为 2.88 dB 和 3.02 dB。所提方法耗时 1009 s，相比耗时 20061 s 的全系统有限元计算快约 20 倍。

This work presents a fusion of finite element analysis (FEA) and statistical energy analysis (SEA) for calculating the mid-frequency response in a stepped acoustic duct comprising two chambers, Chamber 1 (0.644 × 0.045 × 0.045 m3) coupled to Chamber 2 (0.17 × 0.02 × 0.02 m3), arranged coaxially and driven by a loudspeaker at the outer end of Chamber 1. The system was tested in a fully anechoic room over 178 to 11220 Hz. Based on modal-number classification, Chamber 1 acted as a mixed 1D/3D subsystem over 1415 to 8913 Hz, and so was modeled statistically, whereas Chamber 2 remained 1D and was treated deterministically. The subsystems were coupled by an interface with impedance dynamically condensed to a single-degree-of-freedom. Absorption coefficients measured in an impedance tube were used to derive internal loss factors. Source characterization combined a multi-microphone approach for frequencies below the first cutoff at 3811 Hz and a plane-wave approximation for higher frequencies. The SEA solution for Chamber 1 yielded interface pressure and volume velocity, while pre-computed transfer functions predicted pressures at probe positions in Chamber 2. Experiments showed maximum errors of 2.88 dB in Chamber 1 and 3.02 dB in Chamber 2. The proposed method required 1009 s of computation, and is thus about 20 × faster than full-system FEA, which required 20061 s.

声衬是用于衰减和控制声传播的专用结构或表面材料。准确模拟不同掠流条件下的阻抗测量，对其性能优化十分重要。本文利用混合神经网络模型，提出适用于掠流入射管的高效阻抗反演方法，可在多种参数及工况下快速有效反演阻抗。基于 NASA 掠流入射管基准实验，采用有限元生成模型训练数据，并在单自由度声衬、CT57 声衬、多孔材料的解析结果及 NASA 实验数据上验证模型。各项验证表明，该方法有望成为实际、准确的阻抗反演及声衬优化工具。

Acoustic liners are specialized structures or surface materials designed to attenuate and control sound propagation. Accurate simulation of impedance measurement under different grazing flow conditions is essential for optimizing their performance. This paper presents an efficient impedance eduction method for a grazing incidence tube by using a mixed neural network model, which enables rapid and effective impedance eductions over a range of parametric values and working conditions. In a procedure based on the NASA grazing incidence tube benchmark experiment, the finite element method is applied to generate the dataset required for the model training process. The proposed mixed neural network model is demonstrated on the analytical results of several acoustic liners, including a single-degree-of-freedom liner, a CT57 liner, a porous material, and NASA experiment data. All the demonstrations highlight its potential and capability as a practical and accurate tool for impedance eduction and liner optimization.

风扇和压气机是航空发动机压缩系统的核心部件，其性能与稳定性直接影响发动机效率和运行安全。本文以涡扇发动机风扇及压气机为对象，对进气道、风扇和高压压气机第一级开展一体化非定常模拟，研究非轴对称静子（NAS）对下游流场及压缩部件性能、稳定性的影响。结果表明，风扇与压气机共同工作时，NAS 可显著改善复杂工况下的风扇性能，并提高压气机气动性能与稳定性。在相同修正转速下，压气机最大总压比和峰值效率分别提高 4.60% 和 0.92%，稳定裕度提高 30.63%。采用 NAS 后，压气机进口流场非均匀性及通道内低能流体显著减少，部分静子叶片压力面附近的流动分离得到抑制，静子内部总压损失降低 33.98%，从而显著改善压气机性能。

Fans and compressors are the core components of aviation engine compression systems, and the performance and stability of these components directly affect the efficiency and operational safety of an engine. In this study, the fan and compressor of a turbofan engine were taken as the research objects, and an integrated unsteady simulation was conducted for the intake, fan, and high-pressure compressor first stage. The influence of a non-axisymmetric stator (NAS) on the downstream flow field and the performance and stability of the compression components were both examined. The research results indicated that when the fan and compressor worked together, the NAS could significantly improve the fan performance under complex operating conditions and significantly enhance the aerodynamic performance and stability of the compressor. At the same corrected speed, the maximum total pressure ratio and the peak efficiency of the compressor were increased by 4.60% and 0.92%, respectively, and the stability margin was increased by 30.63%. After adopting the NAS, the non-uniformity of the inlet flow field of the compressor was significantly reduced, and the low-energy fluid in the compressor flow passage was effectively reduced. The flow separation near the pressure surface of some stator vanes is effectively suppressed, and the total pressure loss inside the compressor stator was reduced by 33.98%, which significantly improved the performance of the compressor.

电磁分流阻尼器可在较小分流电压下产生较大阻尼力，其在单自由度系统中的动态特性类似调谐吸振器。然而，其隔振性能受电子元件固有阻尼限制，通常需要负电阻分流电路提升阻尼效率和控制性能，而负电阻可能导致不稳定。本文提出将主动控制与被动分流结合的混合电磁分流阻尼器，无需负电阻即可获得可调阻尼及无条件稳定性。基于无量纲单自由度隔振模型，研究推导无阻尼系统在指定优化准则下的闭式最优参数，并采用自适应模拟退火粒子群算法优化有阻尼系统，揭示控制增益与电阻比的耦合机制。该方法在单自由度隔振平台上进行实验验证，理论与实测吻合良好。结果表明，该阻尼器具有优良低频隔振能力与稳健稳定性，为下一代高性能隔振系统提供理论与实践基础。（公开元数据未保留优化准则的数学公式，具体符号待原文核对。）

It is well known that electromagnetic shunt damper (EMSD) can generate substantial damping forces with relatively small shunt voltages and exhibit dynamic characteristics similar to those of a tuned vibration absorber in a single-degree-of-freedom (SDOF) system. However, their vibration-isolation performance is constrained by the intrinsic damping limitations of electronic components and typically requires negative-resistance (NR) shunt circuits to enhance damping efficiency and control performance. Such circuits, however, are prone to inducing system instability. To overcome these limitations, this study proposes a hybrid electromagnetic shunt damper (HEMSD) that integrates active control with passive shunting, enabling adjustable damping and unconditional stability without negative resistance. Based on a dimensionless SDOF vibration-isolation model, closed-form optimal parameters are derived for the undamped system under the [Formula: see text] optimization criterion. An adaptive simulated annealing particle swarm optimization (ASAPSO) algorithm is further employed to optimize the damped system and reveal the coupling mechanism between control gain and resistance ratio. The proposed method is experimentally validated on an SDOF vibration-isolation platform, showing excellent agreement between theoretical predictions and experimental measurements. The results confirm that the HEMSD exhibits superior low-frequency isolation capability and robust stability, providing a solid theoretical and practical foundation for the design of next-generation high-performance vibration-isolation systems.

为研究与海上应用相关的垂直轴风力机气动响应，本文基于冯·卡门谱生成二维可控合成来流，湍流强度（TI）最高为 30%，积分尺度 Λ 为 0.1–0.4 m。该理想化框架用于分离 TI 与 Λ 的影响，而非再现海上大气来流的全部复杂性。数值模拟捕捉湍流结构与旋转叶片相互作用，分析非定常流动、叶片载荷与尾迹动力学。TI 增大影响分离和再附，使峰值扭矩脉动最高增大 30%，但平均功率系数变化小于 2%；TI=30% 时，峰值法向力增加约 25%。频谱和模态分析揭示载荷由确定性向宽带随机性转变，主导力模态能量占比由 49% 降至 29%。较高 TI 还使尾迹恢复距离缩短约 40%，增强不对称性，并使第一主导尾迹模态能量占比从约 80% 降至 65%。相比之下，Λ 的作用次要，主要调节尾迹摆动。研究还发现尾迹模态与叶片气动载荷之间明确的频谱对应关系。

To investigate the aerodynamic response of vertical axis wind turbines (VAWTs) relevant to offshore applications, a two-dimensional controlled synthetic inflow based on the von Kármán spectrum is generated with turbulence intensity (TI) up to 30% and integral length scale (Λ) ranging from 0.1 to 0.4m. This idealized framework isolates the effects of TI and Λ rather than reproducing the full complexity of offshore atmospheric inflow. Numerical simulations capture the interactions between turbulent structures and rotating blades, enabling detailed analysis of unsteady flow features, blade forces, and wake dynamics. The results show that increasing TI affects flow separation and reattachment, markedly amplifying peak torque fluctuations by up to 30%, while the mean power coefficient varies by less than 2%. At TI=30%, the peak normal force increases by approximately 25%. Spectral and modal analyses reveal a transition from deterministic to broadband stochastic loading, with the energy of the dominant force mode decreasing from 49% to 29%. Furthermore, high TI shortens the wake recovery distance by approximately 40% and enhances wake asymmetry, reducing the energy of the first dominant wake mode from about 80% to 65%. In contrast, Λ plays a secondary role, primarily modulating wake meandering. Additionally, a distinct spectral correspondence is revealed between wake modes and blade aerodynamic loads.

本文提出利用图形处理器（GPU）高效实现高斯波束追踪（GBT）的方法，以突破传统 CPU 声学模拟的性能限制。算法在 NVIDIA RTX A6000 GPU 上实现并优化，显著提升高斯波束求和（GBS）性能。针对 GBT 固有的不规则控制流，利用 CUDA 动态并行在 GPU 上直接展开并调度嵌套循环。通过 NVIDIA Nsight Compute 驱动的性能分析与针对性优化，将 SM 吞吐率从 22.27% 提高至 33.32%，L1 缓存吞吐率从 13.15% 提高至 22.15%，L2 缓存吞吐率从 9.16% 提高至 21.26%。相较原始单线程 CPU 实现，GPU 加速的 GBS 算法最高达到 817 倍加速；在包含 16,384 条射线的城市环境场景中，完整计算流程达到 112 倍加速。研究还提出克服 GPU 显存限制的策略，使超出单内核约束的大规模射线数据能够高效处理，并建立系统性能评估方法，为 GPU 算法分析、调优及后续扩展奠定基础。

This study presents an efficient implementation of the Gaussian beam tracing (GBT) method utilizing graphics processing units (GPUs) to overcome the performance limitations of traditional CPU-based acoustic simulations. The algorithm was implemented and optimized on an NVIDIA RTX A6000 GPU, significantly enhancing the Gaussian beam summation (GBS) performance. We addressed the challenge of irregular control flows inherent to GBT by leveraging CUDA's dynamic parallelism to effectively flatten and dispatch nested loops directly on the GPU. Additionally, a profiling-driven optimization workflow using NVIDIA Nsight Compute enabled targeted improvements, raising SM throughput from 22.27% to 33.32%, L1 cache throughput from 13.15% to 22.15%, and L2 cache throughput from 9.16% to 21.26%. Consequently, the GPU-accelerated GBS algorithm achieved up to an 817× speedup compared to the original single-threaded CPU implementation, while the full computational pipeline reached 112× acceleration in a city-environment scenario involving 16,384 rays. Furthermore, this study introduces innovative strategies for overcoming GPU memory limitations, enabling efficient processing of large-scale ray datasets beyond single-kernel constraints. Finally, we establish systematic performance evaluation methodologies critical for analyzing and tuning GPU-accelerated algorithms, laying a foundation for future enhancements and scalability improvements.

低马赫数（M<0.3）流动与流致噪声研究具有重要科学意义。虽然声传播要求介质可压缩，常规低马赫数流动模拟却常假设流体不可压缩。本文研究 M=0.05–0.30 时圆柱绕流、阵风—翼型及湍流—翼型相互作用等典型构型，采用不可压缩和可压缩模型评估流动与声场预测性能，并利用 FW–H 方程预测远场噪声，与直接数值模拟比较。结果表明，不可压缩模型可预测升阻力，但不能捕捉声波传播，因此其近场声源不适用于可渗透面 FW–H 方程。固体表面积分形式虽能有效预测噪声，但对高频非紧致声学分量的解析仍不足。相比之下，可压缩模型在整个马赫数范围内，无论直接模拟还是 FW–H 声学计算均与参考数据高度一致。

Research on fluid dynamics and flow-induced noise at low Mach numbers (M<0.3) holds significant scientific importance. However, conventional numerical simulations for low Mach number flows often assume incompressible fluids, although the medium is compressible to allow sound wave propagation. In this study, we investigated sound generation from canonical flow configurations at low Mach numbers ranging from 0.05 to 0.30: flow around a cylinder, gust–airfoil interaction, and turbulence–airfoil interaction. Both incompressible and compressible numerical models were employed to assess their performance in predicting fluid dynamics and acoustic fields. Furthermore, the Ffowcs Williams and Hawkings (FW–H) equation is also employed to predict far-field noise radiation, which is further compared to direct numerical simulations. Our findings reveal that the incompressible model is able to predict drag and lift force but fails to capture sound wave propagation. Consequently, near-field sound sources from the incompressible model are unsuitable for the permeable-surface FW–H equation. Although the solid-surface integral form of the FW–H equation provides an effective approach for noise prediction, it exhibits deficiencies in accurately resolving high-frequency (non-compact) acoustic components. In contrast, the compressible model consistently yielded excellent agreement with the reference data across the entire Mach number range, both in direct numerical simulations and FW–H-based acoustic computations.

低马赫数（M<0.3）流致噪声准确预测受到两方面限制：不可压缩模型忽略弱可压缩性，而完全可压缩模型计算成本较高。本文通过圆柱绕流、阵风—翼型与湍流—翼型三个典型算例，系统评估保持声波的弱可压缩模型，并与不可压缩及完全可压缩模型比较，同时利用 FW–H 方程评估远场噪声。所有模型均能重现流体动力学场，但声学预测差异显著：弱可压缩和完全可压缩模型能够正确捕捉波传播并给出一致的远场预测，不可压缩模型则不能表示声辐射。马赫数低于 0.2 时，弱可压缩模型精度与完全可压缩模型相当；较高马赫数下，其等熵假设的适用性下降。研究明确了弱可压缩模型的有效范围，并强调低马赫数气动声学模拟考虑可压缩性的必要性。

Accurate prediction of flow-induced noise at low Mach numbers (M<0.3) is hindered by the omission of weak compressibility in incompressible formulations and the heavy computational load of fully compressible schemes. To address this gap, we systematically assess an acoustic-wave-preserving weakly compressible model through three canonical cases: flow over a circular cylinder, gust–airfoil interaction, and turbulence–airfoil interaction. For benchmarking, its performance is compared against incompressible and fully compressible models, with far-field noise additionally evaluated using the Ffowcs Williams–Hawkings equation. The comparisons reveal that while all models reproduce the hydrodynamic fields, their acoustic predictions differ markedly. In particular, the weakly compressible and fully compressible models correctly capture wave propagation and provide consistent far-field noise predictions, whereas the incompressible model fails to represent acoustic radiation. Furthermore, the weakly compressible model achieves accuracy comparable to the fully compressible model for Mach numbers below 0.2, but its isentropic assumption deteriorates at higher Mach numbers. Taken together, these findings not only clarify the validity range of the weakly compressible model but also underscore the necessity of accounting for compressibility effects in low-Mach-number aeroacoustic simulations.

多螺旋桨城市空中交通飞行器近年来受到广泛关注，但既有研究主要关注单个螺旋桨的气动噪声，对可能改变远场噪声指向性的机身声散射效应关注有限。本文开发高效声散射边界元求解器以弥补这一不足，并利用层次矩阵降低计算成本。基准算例显示，该求解器具有较高精度和良好的可扩展性。随后选取代表性飞行器模型，用旋转声源模拟螺旋桨噪声。结果表明，机身与螺旋桨组合构型中的屏蔽效应能够明显降低噪声并改变声能分布，说明低噪声城市空中交通飞行器设计需要考虑机身影响。

Urban aerial mobility (UAM) vehicles with multipropeller configurations have attracted considerable attention in recent years. However, previous investigations have mainly focused on the aerodynamic noise from individual propellers, with limited focus on the fuselage’s sound scattering effects which can alter the far-field noise directivity. In this work, an efficient boundary element solver for sound scattering was developed to fill this gap. The solver employs hierarchical matrices to save computational cost. The benchmark examples showed high accuracy and good scalability. A representative vehicle model was then chosen, and the propeller noise was simulated using rotating sources. Results show that the shielding effect in the fuselage/propeller configuration can produce an apparent noise reduction and redirect sound energy distribution, suggesting the importance of considering the fuselage in low-noise UAM development.

湍流与叶片前缘相互作用对螺旋桨气动及气动声学性能具有显著影响。除直接模拟湍流外，动量源方法等合成湍流方法也已广泛用于相关计算研究。然而，对于非周期扰动，即使诱导速度场无散，源区仍可能产生污染模拟结果的伪声。作为先前时间周期阵风研究的扩展，本文增加修正项，使无散条件在全局满足，并抑制不需要的声波。该方法具有简洁、灵活和通用的特点：可推导直接用于数值实现的显式源项，以生成非定常流动脉动；可将源项置于计算域内部，减少湍流对流的计算成本并兼容大多数边界条件；对于任意所需的各向同性或各向异性无散湍流场，可获得 Navier–Stokes 方程所需动量源的解析表达式。通过谐波阵风、高斯涡和随机湍流合成算例验证方法，并将不同频谱成分的合成速度与目标速度直接比较。研究系统考察了影响附加源分布的参数组合，最后评估来流湍流与薄翼型的气动相互作用，结果与解析解吻合良好。

The interaction between turbulence and blade leading edges is known to have a significant impact on the aerodynamic and aeroacoustic performance of propellers. In addition to directly simulating turbulence, synthetic turbulence, such as the momentum source method, has been developed as a popular method for studying this interaction process in computational fluid dynamics and computational aeroacoustics. However, it is found that for non-periodic disturbances, although the induced velocity field is divergence-free, spurious noise may be generated in the source region and contaminate simulation results. To address this issue, the present work proposes adding a correction term so that the divergence-free condition is satisfied globally and the unwanted acoustic waves are suppressed, as an extension to our previous work for time-periodic gusts [H. Jiang, Phys. Fluids 35, 096115 (2023)]. The strength of the proposed approach lies in its simplicity, flexibility, and generality. First, it derives explicit source terms, which are straightforward for numerical implementations, to generate unsteady flow fluctuations. Second, the sources can be added inside the computational domain, saving computational costs for turbulence convection and being compatible with most existing boundary conditions. Third, the proposed method can obtain analytical expressions for the needed momentum source of the Navier–Stokes equation subject to any desired isotropic or anisotropic divergence-free turbulence fields. The method has been verified by examples of synthesizing harmonic gusts, Gaussian eddies, and random turbulence. The synthetic velocity results characterized by different spectral components are directly compared to target velocity fields, verifying the proposed approach and showing its capability. Parameters that influence the distribution of added sources are systematically investigated to identify an optimal combination for different scenarios. Finally, the model is employed to evaluate the aerodynamic interaction between an incoming turbulence and a thin airfoil. The obtained results exhibit good correspondence with analytical solutions.

自行车比赛中的超车包含跟随前车和向侧方移动等过程，骑行者之间的流动相互作用对气动性能具有显著影响。已有实验与数值研究揭示了部分相对位置下的阻力变化。本文旨在给出完整超车路径上的气动功率等值图，详细描述不同相对位置的功率需求，以制定高效超车策略。气动结果由数值模拟获得，并通过风洞实验验证其准确性。研究采用改进的采样和数据拟合方法完善已有结果。结果表明，从尽可能靠近前车的位置开始超车，并在超越时保持较大的横向间距，是气动效率最高的策略。这些发现为竞技自行车中的最优超车策略提供了参考。

In cycling races, overtaking is a crucial maneuver that involves drafting behind and moving to the side of another cyclist. The flow interaction between the cyclists has a very significant impact on the aerodynamic performance. Previous experimental and numerical studies have shown the aerodynamic drag changes at certain relative positions between cyclists. This study aims at providing a comprehensive aerodynamic power contour along a complete overtaking path, detailing the power at different relative positions to develop efficient overtaking strategies. The aerodynamic results are obtained with numerical simulations, the accuracy of which is validated against wind tunnel experiments. Improved sampling and data-fitting approaches are employed to enhance previous findings. The results show that starting the overtaking maneuver closest to the leading cyclist and overtaking with a larger lateral separation is the most aerodynamically efficient strategy. These findings provide valuable insights into developing optimal overtaking strategies in competitive cycling races.

线性化欧拉方程是声学研究的基本控制方程之一。声学扰动相对背景流物理量很小，因此需要在长期计算中保持高精度并避免耗散与色散。通量重构是一种构造灵活的高阶数值方法，近年来广泛用于偏微分方程数值求解。本文针对一维线性化欧拉方程引入偏置数值通量，构造具有能量守恒特性的 ECFR 格式，以实现长时间高精度计算。通过理论推导与数值验证证明其保能性质，并讨论马赫数和偏置通量参数对性能的影响，同时分析稳定性并给出 CFL 数限制。该格式有助于获得高精度声学数值解，为飞机、潜艇和汽车噪声等复杂工程问题研究提供支持。

The Linearized Euler Equations (LEE) are one of the fundamental governing equations in acoustics research. Due to the relatively small magnitude of acoustic disturbances compared to the physical quantities of the background flow, ensuring highly precise solutions without dissipation and dispersion over time is essential. The Flux Reconstruction (FR) method, recognized as a high-order numerical method with flexible construction capabilities, has been extensively utilized in recent years for solving partial differential equations numerically. This paper introduces an offsetting numerical flux for one-dimensional LEE. Subsequently, it develops a flux reconstruction scheme with energy-conserving characteristics, referred to as the ECFR scheme, aimed at achieving high-precision numerical solutions for prolonged computations. The energy-conserving feature of the scheme is substantiated through theoretical derivation and further corroborated by numerical validation. Moreover, the impact of Mach numbers and the parameter of the offsetting flux on the scheme's performance is discussed. The stability of the scheme is also analyzed, with the limit of the CFL number being provided. The novel ECFR scheme facilitates obtaining high-precision acoustic numerical solutions, thereby providing strong support for the study of complex engineering problems such as aircraft, submarine, and automobile noise.

物理信息神经网络已显示出求解偏微分方程的能力，但传统模型未能区别处理训练数据中的时间和空间变量，并忽略数据点之间对动态系统建模至关重要的时间关系。本文分别基于 Transformer 与卷积长短期记忆网络提出两种新模型，采用编码器—解码器结构加强时空变量处理，并用高阶有限差分计算偏导数。这些计算通过 PyTorch 中的卷积实现，将物理与数学信息融入网络。研究在波动方程和雷诺平均 Navier–Stokes 方程上评估方法。结果表明，基于 Transformer 的模型在精度、效率与泛化能力方面均优于传统及 ConvLSTM 模型。

Physics-informed neural networks (PINNs) have been proven powerful for solving partial differential equations (PDEs). However, conventional PINNs fail handling time/space variables in the training data distinctly and overlook the temporal relationships among data points, which is critical for accurately modeling dynamic systems. To address this issue, this work proposes two novel PINN models based on the transformer and the convolutional long short-term memory (ConvLSTM) architectures, respectively. An encoder-decoder neural network structure is adopted to enhance handling of time-space variables and a high-order finite-difference method is used to compute partial derivatives. These computations are implemented using the convolution within the PyTorch framework that incorporates both physical and mathematical information into the neural networks. The efficacy of the proposed methods has been evaluated for the wave equation and the Reynolds-Averaged Navier-Stokes equations. Results suggest that the transformer-based PINN outperforms both the conventional and ConvLSTM-based PINN in terms of accuracy, efficiency and generalizability.

涡旋阵风是可能影响飞行器气动性能与稳定性的非定常流动扰动。由于湍流特性的复杂性和多样性，在流动模拟中生成真实涡旋阵风具有挑战性。本文提出一种利用动量源在流动模拟中生成涡旋阵风的新框架。该方法可在任意位置向来流施加所需的无散速度扰动，同时避免产生不需要的声波。方法从忽略黏性效应的线性化不可压缩动量方程出发，其频域形式为易于求解的常微分方程，再通过若干条件确定未知系数，得到生成一维和二维阵风的源项表达式。生成的速度场与指定阵风高度一致。研究系统考察了影响附加源分布的参数，以寻找适用于不同情形的较优组合。最后，利用该模型评估涡旋阵风与薄翼型之间的气动相互作用，结果与 Sears 模型的解析解吻合良好。

Vortical gusts are unsteady flow disturbances that can affect the aerodynamic performance and stability of aircraft. Generating realistic vortical gusts in flow simulations is challenging due to the complexity and diversity of turbulence characteristics. This paper introduces a novel framework for creating vortical gusts in flow simulations using momentum sources. The method can manipulate the incoming flow with any desired divergence-free velocity perturbation at any location and avoid unwanted acoustic waves in the meanwhile. It starts from a linearized incompressible momentum equation without viscous effects. The equation has a frequency-domain representation, which is an ordinary differential equation and easy to solve. Then, several conditions are imposed to determine unknown coefficients. Expressions of source terms producing one-dimensional and two-dimensional gusts are obtained. The generated velocity field is compared to the specified gust and shows outstanding agreement. Several parameters that affect the distribution of added sources are systematically studied to find a combination that can provide optimal performance in various scenarios. Finally, the model is used to assess the aerodynamic interaction of a vortical gust and thin airfoils. The results agree well with the analytical solutions provided by the Sears model.

用于城市空中交通的电动垂直起降飞行器近年来受到广泛关注。一些飞行器采用涵道螺旋桨以提高功率效率，但涵道也可能影响螺旋桨噪声的产生和辐射。本文通过系统数值研究评估短涵道对螺旋桨噪声辐射的影响。采用解析模型预测孤立螺旋桨噪声，并利用边界元方法考虑声散射效应，同时提出高效的数据聚类方法以加快整体噪声预测。通过对几何参数和螺旋桨安装位置开展参数研究，探索涵道用于低噪声飞行器的可行性。结果表明，阻挡效应在不同转速下均有利于噪声控制，将螺旋桨安装在涵道对称平面处能够实现最大的降噪效果。

Electric vertical and takeoff/landing vehicles for urban aerial mobility have attracted considerable attention in recent years. Some of these vehicles are equipped with ducted propellers to improve power efficiency, but the duct may also affect propeller noise generation and radiation. This work presents thorough numerical investigations to assess the importance of a short duct on propeller noise radiation. An analytical model is employed to predict noise emission from an isolated propeller, and the boundary element method is adopted to account for acoustic scattering effects. Additionally, an efficient data-clustering method is proposed to accelerate the overall noise prediction process. Parametric studies concerning geometries and the propeller's installation location are performed to exploit the duct's feasibility for low-noise vehicle development. Results suggest that the blocking effect can significantly benefit noise control for different rotating speeds, and installing the propeller at the symmetric plane of the duct can achieve the most noise reduction.

实际无人机叶片常由轻质材料制成，可能发生振动。本文数值研究了具有振动运动的螺旋桨叶片的气动及气动声学特性。采用声波保持人工可压缩性方法解析非定常湍流产生的声音，再利用 Ffowcs Williams–Hawkings 方程的积分解将声音投射至远场观察点。研究表明，小振幅周期叶片振动能够引起推力脉动；由于有效迎角周期变化，振动还会影响叶尖涡及近叶片流动结构。因此，旋转频率谐波处产生显著纯音噪声，并可向转子盘面的上游和下游传播。声源分析表明，新增纯音噪声主要来自叶片轴向运动引起的多普勒效应及推力脉动的影响。此外，高频宽带噪声对叶片振动似乎并不敏感。

In this work, we conduct a numerical investigation of aerodynamics and aeroacoustics of propeller blades with vibrations, which could occur in practical unmanned aerial vehicles as the blades are often made of lightweight materials. The simulations resolve the sound generation from the unsteady turbulent flows using an acoustic-wave preserved artificial compressibility method. Then, the sound projection to the far-field observers is made using an integral solution of the Ffowcs-Williams and Hawkings equation. The study shows that periodic blade vibrations with small amplitudes can lead to aerodynamic thrust fluctuations. The blade vibration also affects the generation of tip vortices and the near-blade flow structures due to the periodic change of the effective angle of attack. Consequently, significant tonal noise at the harmonics of rotational frequency is produced, and the noise can propagate to both upstream and downstream directions of the rotor disc plane. A noise source analysis is performed to identify the contribution of different noise components. Results show that the extra tonal noise is mainly caused by the Doppler effect due to the blade axial motion and the influence of the thrust fluctuations. Moreover, the study also suggests that the high-frequency broadband noise seems to be insensitive to the blade vibration.

截面翼型几何对螺旋桨气动声学特性具有决定性影响，但制造公差、磨损和加工技术限制会引入细小偏差，从而导致测量不确定性。本文在消声风洞中对直径 217.2 mm 的基准螺旋桨及其若干变型进行系统研究，通过改变有限尾缘厚度调整截面翼型，并用高精度数控加工保证细微几何差异。测力结果表明，气动性能对这些微小变化不敏感。当轴向来流速度低于 5 m/s 时，纯音和宽带噪声仅受到轻微影响；相比之下，有限尾缘厚度可以带来超过 3 dB 的明显降噪。研究还利用基于小波的波束形成方法分析声源特征，证实降噪源于叶尖附近尾缘噪声减弱。该研究有助于量化螺旋桨噪声测量的不确定性，并表明调整尾缘厚度可能成为实际降噪手段。

The geometry of the sectional airfoil has a determinative impact on the aeroacoustic characteristics of propellers. However, there are always slight deviations in the practical profiles due to manufacturing tolerance, wear loss, and limitations of processing techniques, which can potentially introduce uncertainties to aeroacoustic measurements. To this end, a systematic investigation is conducted on a benchmark propeller with a diameter of 217.2 mm and several of its variants in an anechoic wind tunnel. The variants are redesigned by modifying the sectional airfoil shapes with varying finite trailing-edge thicknesses. High-accuracy computer numerical control machining is employed to ensure the subtle geometrical differences between the blades. Force measurements indicate that the aerodynamic performances are insensitive to the slight variations of the sectional geometry, as expected. As for the acoustic performance, both the tonal and broadband noise are slightly affected when the axial flow speed is lower than 5 m/s. By contrast, a discernible noise reduction above 3 dB can be achieved due to the finite trailing-edge thickness. The noise source features are also investigated using a wavelet-based beamforming method, confirming that the noise reduction is caused by the weakened trailing-edge noise around the tip. This study is beneficial for the quantification of uncertainties in propeller noise measurements. It also suggests that adjusting trailing-edge thickness might be an useful approach in reducing propeller noise in practical applications.

固定桨距转子飞行器的气动声学特性不同于采用变桨距叶片的传统直升机。由于存在多种不确定因素和非定常性，准确预测转子噪声仍有挑战。本文研究转速偏差、转速脉动、叶片振动和几何不对称的声学影响。分析基于不同工况下的高效噪声计算，平均气动量采用叶素动量理论求得，并引入小振幅波动表征非定常及不确定因素。周期转速波动和叶片振动会产生显著附加纯音；随机波动和振动则提高较宽频段内的噪声水平，提示需要重新审视通常归因于湍流的转子宽带噪声源。这些影响依赖观察角度，在上游和下游方向更明显。叶片几何不对称可在轴频谐波处产生附加纯音。双转子噪声通常因干涉效应而对初始相位差和旋转方向敏感，但轻微转速差即可显著改变其特征。本文对这些实际因素进行了更全面的分析，并强调在多转子飞行器准确噪声预测中考虑它们的必要性。

The aeroacoustic characteristics of flying vehicles with pitch-fixed rotors differ from traditional helicopters with pitch-controlled rotor blades. Accurate predictions of rotor noise are still challenging because many uncertainty factors and unsteadinesses exist. This work investigates the aeroacoustic effects of rotational speed deviation, rotation speed fluctuation, blade vibration and blade geometric asymmetry. The analysis is based on the efficient computation of rotor noise under different working conditions. The mean aerodynamic variables are computed using the blade element moment theory, while small-amplitude fluctuations are introduced to account for the unsteadiness and uncertainty factors. It is shown that periodic rotation speed fluctuations and blade vibrations can produce significant extra tones. By contrast, if the fluctuations and vibrations are random, the noise level in a wide frequency range is increased. The intriguing result reminds us of the need to revisit the rotor broadband noise sources commonly attributed to turbulent flows. The influences are observer angle dependent, and the extra noise production is more significant in the upstream and downstream directions. The asymmetric blade geometry can cause extra tonal noise at the harmonics of the blade shaft frequency. The noise features of dual rotors are also investigated. Usually, the noise is sensitive to the initial phase difference and rotation directions due to the interference effect. However, the noise features are vastly altered if there are slight differences in the rotation speeds. Although the influences of some factors on rotor noise were already known, the present study provides a more comprehensive analysis of the problem. The results also highlight the need to consider these practical factors for accurate noise prediction of multi-rotor flying vehicles.

水下湍流与螺旋桨相互作用是重要噪声来源，其中常见噪声频谱隆起及蓝移，即草垛现象，但其产生机制仍不清楚，限制了噪声控制策略的发展。本文数值研究湍流与转子相互作用，将螺旋桨简化为叶栅，并将湍流表示为谐波阵风时间序列。通过阵风—翼型相互作用问题与 Sears 模型比较验证模拟。初步结果提示，来流扰动频谱与叶栅周期采样之间存在卷积相互作用机制，支持 Huang 在 AIAA Journal（2023）的理论分析。这有助于理解湍流吸入转子噪声的物理机制，并为下一代水下航行器设计提供参考。

The haystack phenomenon, i.e., humps and blue shifting in noise spectra, is commonly observed in the study of underwater turbulence-propeller interactions, which is a major contributor to noise radiation. However, its generation mechanism is still unclear, which is vital to develop noise control strategies. To address this issue, this work conducted numerical simulations concerning the interaction between turbulence and rotors. The propeller is simplified to a cascade model and the turbulence flow is represented by a time series of harmonic gusts for convenience. The simulations are validated against the Sears model for a gust-airfoil interaction problem. Initial results suggest a convolutional interaction mechanism between the spectra of incoming flow disturbances and the periodic sampling of the cascade, which approves the theoretical analysis from Huang (AIAA J. 2023). The results is helpful to understanding the physics of turbulence-ingestion rotor noise and designing the next generation underwater vehicles.

声波是水下航行器通信与探测的重要手段。水下环境中的声传播通常较复杂，存在小尺度湍流时尤为如此，传统波动方法的精确模拟可能需要过高计算成本。本文采用在效率、稳健性和精度方面具有优势的高斯波束追踪方法，研究涡影响下二维线声源声场的特征，并讨论声源频率、涡强度等因素的影响。结果表明，涡诱导的非均匀流场对声传播具有显著影响。

Sound waves are the most crucial tool of communication and detection for underwater vehicles. Wave propagation in underwater environment is usually complex, especially in the presence of small-scale turbulence. Conventional wave-based approaches may be computationally prohibitive for performing accurate simulations in such environments. In this work, the Gaussian beam tracing (GBT) method is adopted for its advantages in terms of efficiency, robustness and accuracy. The characteristics of sound field generated by a two-dimensional line source under the influence of vortex is investigated. The effects of factors such as source frequency and vortex intensity are discussed. The results show that the non-uniform flow field induced by vortex has significant influences on the sound propagation.

本文提出面向无人机的高效低噪声螺旋桨设计。首先采用计算气动声学方法研究三种叶片构型周围的流动与噪声辐射，流动由声波保持人工可压缩性方法计算，远场噪声通过求解 Ffowcs Williams–Hawkings 方程外推，并开展实验验证数值模拟与设计思路。数值和实验结果在气动效率、噪声频谱以及螺旋桨之间的差异方面吻合良好。与基准相比，两种新设计均能同时提高气动效率并降低噪声。较长弦长和较小半径有助于减少尾缘流动分离。定性声源分析进一步表明，宽带声源主要与叶片表面压力的时间导数有关，并集中在叶尖附近的尾缘。

This work presents a high-efficiency low-noise propeller design for unmanned aerial vehicles. Three different blade configurations are first investigated, using the computational aeroacoustic approach to recognize the flow around propellers and the noise emissions. The flow simulation is obtained by an acoustic-wave preserved artificial compressibility method, and the far-field noise is extrapolated by solving the Ffowcs-Williams and Hawkings equations. Experiments are also conducted to validate numerical simulations and the design philosophy. The comparison between numerical and experimental results confirms an encouraging agreement regarding aerodynamic efficiency, noise spectra and differences between propellers. The results show that two designed propellers can simultaneously improve aerodynamic efficiency and reduce noise emissions compared to the baseline propeller. It is observed that using a longer chord length and shorter propeller radius can reduce flow separation at the trailing edge. Furthermore, a qualitative noise-source analysis shows that broadband noise sources are primarily ascribed to the time-derivative of blade surface pressure and occur at the trailing edge near the tip.

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本文研究螺旋桨纯音噪声的辐射模态与效率。在球坐标下构建厚度噪声和载荷噪声模型，简化积分声源的数值计算。辐射场可分解并投影到球谐函数，分离声源与观察点位置，从而分析声场结构。球谐函数的奇偶性解释了推力仅产生关于旋转平面反对称声波的原因；声场的对称分量则来自厚度、阻力及叶片表面径向力。声源靠近旋转中心时，各模态辐射效率迅速衰减，说明低噪声螺旋桨应谨慎设计气动载荷的径向分布。该模型应用于无人机螺旋桨，取得与实验可靠吻合的结果，噪声计算输入流动量来自 CFD，实验数据在消声室获得。

This paper focuses on the radiation modes and efficiency of propeller tonal noise. The thickness noise and loading noise model of propellers has been formulated in spherical coordinates, thereby simplifying numerical evaluation of the integral noise source. More importantly, the radiation field can be decomposed and projected to spherical harmonics, which can separate source-observer positions and enable an analysis of sound field structures. Due to the parity of spherical harmonics, the proposed model can mathematically explain the fact that thrusts only produce antisymmetric sound waves with respect to the rotating plane. In addition, the symmetric components of the noise field can be attributed to the thickness, as well as drags and radial forces acting on the propeller surface. The radiation efficiency of each mode decays rapidly as noise sources approach the rotating center, suggesting the radial distribution of aerodynamic loadings should be carefully designed for low-noise propellers. The noise prediction model has been successfully applied to a drone propeller and achieved a reliable agreement with experimental measurements. The flow variables employed as an input of the noise computation were obtained with computational fluid dynamics (CFD), and the experimental data were measured in an anechoic chamber.

近年来，多旋翼无人机和城市空中交通飞行器受到广泛关注，其气动噪声问题也日益重要。基于物理的噪声预测工具有助于安静无人机设计。本文采用边界元求解器评估飞行中无人机机身对转子噪声的散射，并通过组合 Helmholtz 内部积分方程方法（CHIEF）处理可能的非唯一解。将方法用于真实机身构型后发现，低频下波的绕射使机身明显改变螺旋桨噪声辐射方向；高频下机身还可通过反射改变声场，产生明显降噪。

Multi-rotor powered drones and urban mobility vehicles (UMV) have received considerable attention over recent years and attracted ever-increasing interest in their aerodynamic noise. Physics-based prediction tools for aerodynamic noise are of importance to facilitate quiet drone designs. In this work, a boundary element method (BEM) based solver is employed to evaluate the scattering of the rotor noise of a flying drone fuselage. The possible non-uniqueness of the solution is tackled using a Combined Helmholtz Interior integral Equation Formulation (CHIEF). The proposed method is applied to evaluate the noise scattering by a realistic fuselage configuration. Results suggest that the fuselage can visibly redirect propeller noise radiation at low frequencies because of wave diffractions. The fuselage can also affect the sound field by wave reflections at high frequencies, producing an apparent noise reduction.

本文通过实验研究无人机在悬停、自旋、爬升、垂直飞行及巡航等代表性工况下的噪声特征。不同于可能受阵风、地面反射等不确定因素影响的室外实验，本研究在大型消声室内测量。采用覆盖 5.6 m×6.4 m 区域的地面矩形传声器阵列，以及侧墙上长 4.6 m 的线阵测量噪声及辐射指向性，并通过双目视觉系统实时追踪无人机运动。结果表明，飞行噪声对飞行高度、与观察者的相对距离和运动状态敏感。悬停时的噪声指向性与孤立螺旋桨相似，机身下方存在低噪声区域；巡航时，由于机身俯仰角，较高噪声区域出现在无人机后方。同步噪声与位置测量系统能够识别飞行试验中运动状态变化对应的声学响应。通过对噪声和运动追踪数据进行短时傅里叶分析，发现实时噪声谱图变化与螺旋桨转速变化之间存在相干关系。研究扩展了作者此前的工作，加深了对不同运行条件下无人机噪声特征的理解。

This work experimentally studies the noise features of flying drones under representative working conditions, including hover, spin, climb, vertical flight, and cruise. Being different from outdoor experiments where many uncertain factors, such as gust wind and ground reflections, could affect test results, measurements in this study were conducted in a large anechoic chamber. The noise was measured with a ground-based rectangular microphone array covering an area of 5.6 m×6.4 m and a 4.6 m linear array on the sidewall to account for emission directivity. A binocular vision tracking system was used to trace drones' motion in real-time. Results show that a flying drone's noise feature is sensitive to its flight altitude, relative distance from observers, and motion status. Interestingly, under hovering conditions, the noise directivity is similar to that of an isolated propeller, and a low-noise region is found underneath the fuselage. While for cruising flight, the region with higher noise levels is observed behind the drone due to the fuselage's pitch angle. More importantly, the synchronized systems for noise and position measurements allow finding of an acoustic response to any change in motion status across flight tests. A coherence between real-time changes in the noise spectrogram and variations of the propeller rotating speed is found, thanks to the short-time Fourier analysis of both noise and motion-tracking data. The present finding extends the authors' previous work, enabling a deeper understanding of general drone noise features under different operating conditions.

近几十年来，对螺旋桨气动噪声辐射的关注推动了声源识别研究及城市空中交通飞行器的发展。传统声学成像算法主要假设单极子声源，但现代气动声学理论认为螺旋桨噪声以偶极子载荷噪声为主。为获得物理一致的声源分布，本文提出基于运动偶极子声源的波束形成方法。该方法在时频域构建，可恢复声源强度和指向性三维分布的时间历程。以双叶螺旋桨基准算例评估声源识别能力，采用经测量验证的高保真模拟结果开展声源分析，以便核验声源位置与方向。结果表明，声源位于螺旋桨叶尖附近的尾缘，且指向性随频率变化。相较传统单极子方法，该方法在正确追踪声源方面具有优势，能够重构高速旋转螺旋桨的三维声源。流场与声学成像结果的一致性验证了方法的准确性，并显示其工业应用潜力。

The increasing attention to aerodynamic noise radiation from propellers has driven the interest in noise source identification and promoted the development of urban aerial vehicles over the last decades. Conventional acoustic imaging algorithms primarily assume monopole-type sources, but modern aeroacoustic theories have recognized that the dipole-type loading noise is dominant for propellers. To obtain physically consistent noise source distributions, we propose a moving dipole source-based beamforming method. The method is developed in the time-frequency domain to recover the time history of three-dimensional mapping for source strength and directivity, different to other techniques. The capability of the proposed method to identify noise sources is assessed by considering a two-bladed propeller benchmark. Instead of directly conducting experiments, we use results from high-fidelity numerical simulations, validated by measurements, to perform a noise source analysis. In this way, it is easier to verify the obtained source locations and directions. The results show that the noise sources are located on the trailing edge around the tip of the propeller, and the directivity varies with frequency. The proposed method exhibits competitive advantages in correctly tracing sources over conventional monopole-based methods. The proposed method can recover the three-dimensional noise sources for a high-speed rotating propeller. The consistency between the flow field and acoustic imaging results confirms the accuracy of the proposed method and suggests its potential in industrial applications.

本研究发现，在相同流动条件下，频谱可能呈现不同表现，构成迟滞现象。研究从现代动力系统角度分析结果，将边界层视为受迫振子，并将声波视为激励机制。通过引入分岔理论和庞加莱截面，研究自由来流速度变化时的动态过程。

This work reports that the frequency spectra can exhibit different behavior at the same flow condition, which constitutes the hysteresis phenomenon. Results are analyzed from the perspective of modern dynamical systems. The boundary layer is viewed as the forced oscillator, with the acoustic waves being the forcing mechanism. Both the bifurcation theory and the Poincar\'e section are introduced to investigate the dynamic process when freestream velocity changes.

本文提出一种超分辨率声学成像方法，可反演三维空间中的声源分布、强度与结构。该方法利用低频声场与高频平面波之间的非线性耦合突破分辨率限制。不同声源强度与频率下的重构结果验证了其能力。结果表明，该方法尤其适合低频声源成像，可增强声学成像试验的超分辨率分析能力，从而加深对水下及航空航天推进系统相关物理机制的认识。

This work reports a super-resolution acoustic imaging method that inverses source distribution, strength, and structure in three-dimensional space. The nonlinear coupling process between a low-frequency sound field and a high-frequency plane wave is endowed to break the resolution limit. The reconstructed results for different source strengths and frequencies demonstrate the capability of the proposed method. The results show that the proposed method is very suitable for low-frequency source imaging, which could strengthen the super-resolution analysis capability of acoustic imaging tests and, consequently, lead to deepened physical insights into various propulsion systems in underwater and aerospace systems.

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无人机应用广泛，并有望满足未来空中交通需求，因而成为重要研究课题。许多构型中转子会与上游物体尾流相互作用，这对气动及气动声学性能十分重要。对于多数小型无人机所处的低于 10⁵ 雷诺数范围，相关流动结构及声源研究仍然有限。本文采用 Spalart–Allmaras 延迟脱体涡模拟方法和基于 Farassat 1A 公式的声类比，在约 10⁴ 的低雷诺数下研究转子与翼型尾流的相互作用。结果表明，翼型轴向力和表面压力扰动与转子旋转紧密耦合；相互作用对转子叶片的影响取决于相对迎角。对与声源对应的表面压力脉动进行分析后发现，叶片通过频率及其谐波处的纯音噪声主要由周期相互作用产生，而高频噪声由转子尾缘的脱落涡产生。

Unmanned aerial vehicles (UAVs) have become an important research topic due to their wide range of applications and potential to meet the future air transportation demands. In many configurations of UAVs, the rotors interact with the wake of upstream bodies, which is of pivotal importance to the aerodynamic and aeroacoustic performance. The studies of flow structures and noise sources for rotors interacting with adjacent upstream bodies at Reynolds numbers lower than 105, which is the operating condition of most small UAVs, are limited. In the current study, numerical simulations are conducted to investigate the interaction between a rotor and the wake of an airfoil at low Reynolds numbers around 104 using the Spalart–Allmaras delayed detached eddy simulation method and acoustic analogy based on Farassat's formulation 1 A. The results show that the axial forces and the surface pressure perturbations of the airfoil are closely coupled with the rotor rotation. The effect of interaction on the rotor blades depends on the relative angle of attack. Furthermore, an analysis of the surface pressure fluctuations corresponding to the noise sources shows that the tonal noise at the blade passing frequency and its harmonics is mainly caused by periodical interaction, and the high-frequency noise is produced by the shedding vortex at the trailing edge of the rotor.

本文研究多旋翼飞行器常见推进螺旋桨的噪声数据处理方法。实验记录的噪声通常包含螺旋桨旋转、与湍流相互作用及其他随机因素产生的周期纯音和随机宽带成分。非定常转速、制造公差及流动扰动等因素使噪声具有时变特征。本文评估识别螺旋桨噪声确定性成分的方法，利用相邻旋转周期内噪声模式相似的特点，通过平均方法迭代去除随机成分。研究采用简单平均、指数加权移动平均和卡尔曼滤波平均三种方法。指数加权移动平均使用恒定权重，卡尔曼滤波方法的权重则迭代调整。将方法用于合成信号及计算气动声学模拟结果，验证其去除随机成分的能力，随后应用于实验数据，识别噪声信号的若干特征。

This study focuses on methods of processing the noise data of propulsive propellers commonly found on ubiquitous multi-rotor flying vehicles. The noise signals recorded in experiments typically contain periodic tonal and random broadband components produced by the rotational motion of the propellers, the interaction between the propellers and turbulence, and other random factors. Factors such as unsteady rotational speed, manufacturing tolerance and flow disturbance can exist, leading to time-varying characteristics of the noise signals. In this work, we made assessments of methods to identify the deterministic components of the noise signals of propellers. Considering that the different noise patterns within two adjacent periods (due to the rotation) are similar, we applied averaging methods to remove the random components iteratively. A total of three methods were employed in this work: simple averaging, exponentially weighted moving averaging, and Kalman filter averaging. The exponentially weighted moving averaging method uses a constant weight while the weighting parameter based on the Kalman filter approach is iteratively adjusted. The methods are applied to synthesized signals and results from the computational aeroacoustic simulations, demonstrating the capabilities of removing the random components. Then, the averaging techniques are also applied to the experimental results, and some characteristics of the noise signals are identified.

本文实验研究尾缘锯齿与薄多孔膜或绒面结构组合降低湍流边界层尾缘噪声的潜力。消声风洞实验以平板为基准，弦长雷诺数为 2×10⁵ 至 5×10⁵，并在前缘附近充分触发边界层转捩。研究测试了锯齿与未扰动尾流对齐及不对齐两种安装方式。传统锯齿在流动不对齐时降噪能力显著下降，组合结构则仅受轻微影响。所开发的新组合方案在尾缘锯齿周围布置锯齿状多孔绒面结构，优于未改进锯齿，在对齐和不对齐条件下、以边界层厚度定义的斯特劳哈尔数 0.3 至 1 的宽频范围内均可实现约 10 dB 降噪。同时，绒面结构使气动阻力增加约 30%–40%。进一步的热线尾流测量揭示了附加降噪能力的可能机制。

This study experimentally investigates the potential of using combinations of trailing edge serrations and thin porous membrane/velvet structures for turbulent boundary layer trailing edge noise reduction. The experiments were conducted in an anechoic wind tunnel, with a flat plate model as the baseline model. The chord-based Reynolds number ranged between 2×105 and 5×105, and the boundary layers were fully tripped near the leading edge. Two different installation methods were tested, where the serration structure was aligned/misaligned with the undisturbed wake flow. It was observed that the noise reduction capability of the conventional serrations deteriorates significantly when the serrations are misaligned with the flow, while the performances of the combined structures are only slightly affected by flow misalignment. A novel combined treatment is developed, in which the trailing edge serrations are surrounded by serrated porous velvet structures. This treatment is found to outperform the unmodified serrations and can achieve approximately 10 dB noise reduction in both flow-aligned and flow-misaligned conditions, within a wide frequency range corresponding to a boundary layer thickness-based Strouhal number Stδ between 0.3 to 1. A 30%–40% increase in the aerodynamic drag due to the velvet structures was observed. Further hotwire wake survey revealed the possible mechanisms for the additional noise reduction capability of the combined treatments.

本文利用统一变换方法研究带不同延伸段的有限刚性平板声散射，处理刚性、弹性、穿孔及多孔弹性等边界条件。通过宽频范围内对弹性、孔隙率和延伸长度开展参数研究，探索其耦合作用。结果表明，降噪可归因于平板两侧压差的衰减。对于带多孔弹性延伸段的有限平板，低频时（k0≤0.1，k0 为无量纲波数）孔隙率带来的降噪比弹性更显著；弹性总体有利于降噪，尤其与较低孔隙率结合时。高频时（k0≥10），较高弹性或较大孔隙率均可实现最大降噪，但降噪幅度仍小于低频。延伸长度在低频配合较大孔隙率、或在中高频配合较高弹性时更有效。研究揭示了有限刚性平板附加多孔弹性延伸段的降噪潜力，有助于理解降噪机制及优化实际延伸段设计。

This paper investigates sound scattering by a finite rigid plate with various extensions using the unified transform method. Different boundary conditions, including rigid, elastic, perforated, and poroelastic conditions are addressed thanks to this efficient method. Parametric studies for the elasticity, the porosity, and the extension length are also conducted over a wide frequency range to explore the combined effects of these variables. Results show that the observed noise reduction can be attributed to the attenuation of pressure difference across the plate. For the case of a finite plate with a poroelastic extension, at a low frequency (k0⩽0.1, where k0 is the non-dimensional wavenumber), porosity can achieve more noise reduction than elasticity. Elasticity generally enhances noise reductions, especially when combined with low porosities. At a high frequency (k0⩾10), the maximum noise reduction can be achieved through either high elasticity or large porosity, which is, however, still smaller than that at low frequencies. The extension length is more effective in noise reduction when applied with large porosity at a low frequency or high elasticity at a medium or high frequency. This study reveals the potential noise reduction by a poroelastic extension attached to a finite rigid plate, and helps shed more light on the noise reduction mechanisms as well as an optimal design of realistic poroelastic extensions.

本文实验研究利用上游涡流发生器提高尾缘锯齿降噪能力。实验采用弦长 100 mm 的 NACA 0012 翼型，在 0° 至 9° 的四种迎角及 20–50 m/s 来流速度下进行，弦长雷诺数为 1.3×10⁵ 至 3.3×10⁵。沿锯齿根部布置高度比 h/δ 为 0.125–0.25 的叶片式涡流发生器，其中 δ 为不安装发生器时的尾缘边界层厚度。用相控传声器阵列进行声学测量，用热线测量尾缘附近流动。声源积分频谱表明，在 3 kHz 以上高频段尾缘噪声平均降低约 2 dB。尾流测量识别出发生器产生的流向涡，并发现这些涡能够抵消锯齿根部横向流，从而改善锯齿性能。

This paper presents an experimental investigation on improving the noise reduction capability of trailing edge serrations using upstream vortex generators.Experiments were conducted for a 100 mm chord NACA 0012 airfoil at four angle of attack between 0 • and 9 • and flow speed ranging from 20 to 50 m/s.The Reynolds number based on the chord length ranges from 1.3 × 10 5 to 3.3 × 10 5 .Vane type vortex generators with various heights of h/δ = 0.125 -0.25 were placed along with the serration roots, where δ is the boundary layer thickness at the trailing edge without the vortex generators.The aeroacoustic measurements were made with a phased microphone array, and the aerodynamic measurements near the trailing edge were measured using a hot wire.The source integrated noise spectra showed on average 2 dB reduction in the trailing edge noise over high frequency range above 3 kHz.The generation of streamwise vortices by vortex generators can be identified in the wake measurement.These streamwise vortices were further found to counteract the cross-flow generated at the serration roots, hence improving the performance of the serration.

本文研究尾缘锯齿与无纺布多孔膜或绒面结构组合的降噪潜力。以平板为模型，在零迎角、弦长雷诺数 2×10⁵ 至 5×10⁵ 及充分触发转捩的边界层条件下开展消声风洞实验，并测试锯齿与未扰动尾流的不同对齐状态。流动不对齐显著削弱传统锯齿的降噪能力，但对组合结构影响较小。多孔膜会产生额外高频噪声，而多孔绒面能有效抑制高频噪声。具有锯齿尾缘的多孔绒面还带来附加低频降噪，可能源于其锯齿末端的额外相消干涉。最优组合在对齐及不对齐状态下均可在宽频范围内实现约 10 dB 降噪。进一步的热线尾流测量揭示了组合方案附加降噪能力的可能机制。

This work studies the trailing edge noise reduction potentials of combining trailing edge serrations and porous membrane/velvet structures made of non-woven fabrics. Anechoic wind tunnel experiments were conducted based on a flat plate model, at a chord-based Reynolds number between 2×10^5 a and 5×10^5 and zero angle of attack, with fully tripped boundary layers. Different alignment conditions between the serrations and the undisturbed wake flow were tested. It was observed that the noise reduction capability of the conventional serrations deteriorates significantly when the serrations were misaligned with the flow, while the performances of the combined structures were only slightly affected by misalignment. The porous membrane structure was found to generate extra high-frequency noise, while the porous velvet structure effectively suppressed the high-frequency noise. In addition, porous velvet structures with serrated trailing edge provided additional noise reduction at lower frequencies, which is likely due to the additional destructive interference at the serrated end of the porous velvet structure. The optimal combination could achieve approximately 10 dB noise reduction in a wide frequency range, in both flow-aligned and flow-misaligned conditions. Further hotwire wake survey revealed the possible mechanisms for the additional noise reduction capability of the combined treatments.

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声传递函数可高效处理不同边界条件和声源下的声学分析。研究首先提出用插值替代直接组装影响矩阵，以加速边界元分析；进一步结合本征正交分解与离散矩阵插值，构造新的频率插值算法。对预先计算的传递函数进行本征正交分解，构建降阶子空间，再在其中实施插值，同时提高存储与插值效率。除计算性能外，研究还分析误差界并通过数值实验验证准确性。本文主要利用声传递函数计算声散射，不同于由边界质点速度计算声压的常见应用。最后以无人机噪声散射问题展示方法能力。

The acoustic transfer function is a well-known concept for efficient computations of acoustic analysis with various boundary conditions and sound sources. It is first proposed to accelerate the boundary element analysis by interpolating instead of directly assembling influence matrices. To further improve its computational efficiency, a new frequency-interpolation algorithm is proposed by incorporating the proper orthogonal decomposition and a discrete matrix interpolation method. The former is imposed on those pre-computed transfer functions to construct a reduced-order subspace where the later interpolation is implemented, resulting in efficiency gain in both storage and interpolation. In addition to the computational performance, the error bound is also investigated to verify the accuracy via numerical experiments. In this work, the acoustic transfer functions are mainly employed to compute sound scattering, being different from the common applications of computing sound pressure induced by particle velocity at the boundary. Finally, the capability of the proposed method is demonstrated in a drone noise scattering problem.

尾缘锯齿能够降低航空发动机的湍流混合噪声，但关于其控制转子—静子组件入射声波散射的研究较少。为此，本文提出理论模型，预测均匀塞状流条件下带尾缘锯齿圆管的声波散射。模型将傅里叶级数展开引入 Wiener–Hopf 方法，是 Huang（2017）平板锯齿声散射工作的自然推广。流动管道问题会产生复杂得多的矩阵核，本文给出了相应的因式分解方法。模型与代表性构型下的数值模拟进行了比较，总体吻合良好，同时表现出适于快速预测的高效率。参数研究揭示了两种降噪机制：声能重新分配至新的、更高截止阶次的模态，以及锯齿多重散射产生的相消干涉。该模型有助于深入理解相关物理机制，并可在权衡气动影响后辅助低噪声航空发动机及流动管道系统的声学设计与优化。

It is well known that trailing-edge serrations, which are also known as chevrons, are able to reduce the turbulent mixing noise from an aeroengine. The study of the associated control capability of the scattering of incident waves from the rotor–stator assembly is rare. To address this issue, a theoretical model is proposed to predict sound wave scattering from a cylindrical pipe with trailing-edge serrations in the presence of plug flows. The model incorporates Fourier series expansion into the Wiener–Hopf method and, therefore, is a natural extension of the previous aerofoil work by Huang (2017, “Theoretical Model of Acoustic Scattering From a Flat Plate With Serrations,” J. Fluid Mech., 819, pp. 228–257). The nature of the flow duct problem, however, leads to a much more complicated matrix kernel, and the associated factorization method is given in this article. The proposed model is validated by comparison with the numerical simulations at certain representative setups, which show the overall agreements to be satisfactory. The comparisons also show that the proposed model is so efficient that it can enable rapid predictions. A series of parametric studies are performed to study the two mechanisms behind the noise reduction of a serrated flow duct. One is the redistribution of acoustic energy to new higher cutoff modes. The other is the destructive interference due to multiple scattering from serrations. Overall, the proposed model should be helpful in offering deep physical insights and would be able to assist the aeroacoustic design and optimization of new low-noise aeroengines and flow duct systems after considering the tradeoff with aerodynamic impacts.

本文提出分析帆在振荡泵动下推进性能的框架，该框架不同于传统扑翼分析。研究提出推进效率 ηs 与推进效能 ΔC̄x 等指标，它们不仅取决于气动力系数，也取决于帆航行器的运动条件。通过计算流体力学模拟，分析二维翼型在不同升沉及运动条件下的推进性能，说明采用这些指标的必要性。结果发现，泵动帆通常通过增加升力而非降低阻力来改善推进性能，因此，与扑翼不同，前缘涡的形成不一定损害泵动帆的推进效率。在某些航行条件下，由于航行器能够从风中提取能量，推进效率可以大于一。

This study presents a framework to analyze the propulsive performance of a sail under oscillatory pumping motion, which should be modified from the analysis framework for conventional flapping wings. A new set of metrics, including the propulsive efficiency ηs and efficacy ΔCx¯, which depend not only on the aerodynamic coefficient but also on kinematic conditions of the sailing vehicle, are proposed to characterize the propulsive performance of sail pumping. The necessity of the proposed metrics is illustrated by studying the propulsive performance of a two-dimensional airfoil under different heaving and kinematic conditions through computational fluid dynamic simulations. It was found that the sail pumping typically improves the propulsive performance by lift enhancement instead of drag reduction. Thus, the formation of leading-edge vortices may not be detrimental to the propulsive efficiency of a pumping sail, contrary to that for flapping wings. A propulsive efficiency greater than unity is achievable under certain sailing conditions because a sailing vehicle can extract energy from the wind.

对于带延伸段平板的声散射，传统 Wiener–Hopf 方法难以获得近场解或在低频范围收敛，统一变换方法可以解决这些问题。本文利用统一变换方法研究多孔弹性延伸段对有限平板声散射的影响，考察弹性、孔隙率与延伸长度的耦合作用及其降噪潜力。结果表明，低频下孔隙率比弹性带来更大的降噪效果；高频下二者均可实现最大降噪。延伸长度在低频配合较大孔隙率，或在中高频配合较大弹性时，对降噪更有效。研究旨在高效探索有限刚性平板附加多孔弹性延伸段的降噪潜力，并揭示相关机制。

For the sound scattering of a plate with an extension, the traditional Wiener-Hopf method is hard to obtain the near-field solution or converge in a low-frequency range. Recently, the unified transform method can be applied to address these problems. In this study, we investigate the effect of a poroelastic extension on the acoustic scattering of a finite plate using the unified transform method. The coupled effects of the elasticity, the porosity, and the extension length are investigated to explore the potential noise reduction of the design of a poroelastic extension. Results show that porosity can achieve more noise reduction than elasticity at lower frequencies. At high frequencies, both of them can achieve maximum noise reduction. The extension length is more effective in noise reduction when applied with large porosity at a low frequency or high elasticity at a medium or high frequency. The investigation aims to efficiently explore the potential noise reduction of the design of a poroelastic extension attached to a finite rigid plate and to shed some light on the associated noise reduction mechanisms.

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声学多频分析需求的增长要求更高效的算法。传统边界元方法适于研究复杂声散射问题，但宽频计算中多个频率下稠密矩阵求逆成本较高，限制了性能。本文将全阶问题投影至低阶子空间，在保持高保真度的同时显著减少计算时间，给出详细算法实现与性能比较，并讨论和解决常规边界元方法的非唯一解问题，以保证宽频范围预测准确。最后通过无人机噪声散射问题展示所提方法的能力。

Growing demand for multi-frequency analysis in acoustics calls for more efficient algorithms. Conventional boundary element method (BEM) is found to be a very promising tool for the investigation of complex acoustic scattering problems. However, the performance of BEM would be compromised for broadband set-ups due to an expensive inverse operation for a dense matrix at multiple frequencies. To address this issue, a new algorithm is proposed by projecting the full-order problem into a low-order subspace to significantly reduce the computational time while still maintaining the high-fidelity. Detailed algorithm implementations and performance comparisons are demonstrated, and the non-uniqueness issue of the conventional BEM is also discussed and solved to guarantee accurate wide-range predictions. The capability of the proposed method is finally demonstrated in a drone noise scattering problem.

锯齿结构最初用于抑制航空发动机喷口辐射的射流噪声，其相关流体力学机制已得到广泛研究。随着涵道比不断增大，风扇噪声相对于射流噪声的重要性逐渐提高，但外涵道尾缘锯齿能否衰减风扇噪声及其机制仍不明确。本文首先利用基于 Wiener–Hopf 方法的理论模型，对多种构型进行快速参数研究，结果表明锯齿也能有效降低风扇噪声散射。随后，对真实航空发动机的若干代表性构型开展高保真流动与声学计算，进一步证实锯齿的有效性。解析和数值结果均表明，锯齿会诱发声模态转换，尤其是由低阶模态向高阶模态转换，进而产生径向倏逝波，最终降低不同辐射角度的噪声。这些发现有望用于下一代低噪声航空发动机设计。

Chevrons, which are also known as serrations, are initially developed to suppress jet noise radiating from aero-engine nozzles. The associated fluid mechanics are already well known. Compared with jet noise, turbomachinery fan noise has become relatively more important along with the ever-increasing bypass ratio. However, it is still unclear whether the trailing-edge chevrons on the bypass duct would attenuate fan noise and, if the answer is yes, what is the associated mechanism. In this work, we first use a theoretical model based on the Wiener–Hopf method to rapidly conduct parametric studies across a number of different setups. The results from such a theoretical model suggest that the chevrons are also effective in the reduction of fan noise scattering. Next, we perform high-fidelity computational fluid and acoustic simulations for a realistic aero-engine with some representative setups, and the results further confirm the effectiveness of chevrons. Both analytical and numerical results show the associated noise control mechanism, that is, chevrons would induce acoustic mode conversion (especially from low modes to high modes), which shall further result in evanescent waves in the radial direction and the final noise reduction at various radiation angles. The findings may find applications in the next-generation low-noise aero-engine design.

本文提出解析与边界元混合方法，计算翼型叶栅与阵风相互作用噪声。假设翼型对来流阵风的声学响应取决于局部非均匀平均流，利用基于广义 Prandtl–Glauert 变换的解析解计算声产生，再用高效边界元方法求解其他翼型对辐射声的散射。研究提出平均化方法，高效计算叶栅周期格林函数。预测结果与平板叶栅数值模拟合理吻合，并讨论几何约束导致的截止特性，推导不同声模态阶次的临界阵风波长。零安装角时低频分量被限制在叶片间，非零安装角时则可能传播平面波。对于真实翼型叶栅，背景平均流由势流理论计算。忽略折射效应以及声学响应解析解中的近似会导致误差，但混合方法能够捕捉有限厚度产生的降噪效应，相比平板近似更接近数值解。

This paper presents a hybrid analytical and boundary element method to compute the airfoil cascade-gust interaction noise. We assume that the acoustic response of an airfoil to the oncoming gust depends on the locally non-uniform mean flow such that the analytical solution based on a generalised Prandtl-Glauert transformation is utilised to compute the sound generation. The radiation of sound from an airfoil is scattered by other airfoils, which is resolved by a high-efficiency boundary element method. An averaging approach is proposed to efficiently compute the periodic Green's function due to the cascade. The predicted results are validated against numerical simulations for flat plate cascades, and the results match reasonably well. The cut-off properties due to the geometry restriction are discussed, and the critical gust wavelengths for the different orders of acoustic mode are derived. The low-frequency components are trapped in the space between the blades if the stagger angle is zero, while the plane waves are likely to propagating otherwise. For cascades with real airfoil geometry, the background mean flows are computed based on the potential theory. The omission of the refraction effect and approximation errors in the analytical solution of the acoustic response can cause errors for real airfoils, but the hybrid method can capture the sound reduction due to the finite thickness, and yield closer agreement with the numerical solution than the flat plate.

本文在消声室中实验研究商用四旋翼的噪声特征，涵盖悬停、爬升、下降、巡航和偏航工况。受控环境避免了室外测试中的干扰因素。利用地面 8×9 矩形传声器阵列及竖直布置的八传声器线阵测量噪声：线阵揭示桨盘附近的声辐射特征，地面阵列提供声压级等值图，从而分析声源周向对称性和优先辐射方向。与噪声测量同步的双目视觉系统追踪无人机位置，联合声学和位置数据捕捉各飞行试验中的噪声特征变化。

The noise features of a commercial quad-copter were experimentally studied in an anechoic chamber. Flight conditions including hover, climb and descent, as well as cruise and yaw, were tested. The measurements were conducted in a controlled environment and factors that may affect outdoor testing were avoided. The drone noise was measured by a ground-based 8×9 rectangular microphone array, as well as a linear array composed of eight microphones placed vertically. The linear array provided insight to the sound radiation characteristics along the propeller plane and the ground array provided a contour map of the sound pressure levels, and this information brought insight to the azimuthal symmetry of the noise source as well as the preferred radiation direction. A binocular vision tracking system synchronized with the noise measurements, was used to trace the drone position. The combined noise and position data captured the changes in the noise characteristics across the flight tests. © 2019, American Institute of Aeronautics and Astronautics Inc, AIAA. All rights reserved.

本文提出计算真实翼型叶栅与湍流相互作用噪声的解析方法，采用两个关键假设：单个翼型产生的声音仅取决于局部平均流与涡旋阵风；各翼型仅对其他翼型辐射的声波发生散射。采用基于广义 Prandtl–Glauert 变换的真实翼型噪声解析解计算对来流阵风的声学响应，以考虑非均匀平均流影响。翼型间声散射由高效边界元方法求解。本文介绍该模型的主要步骤，零安装角平板叶栅的初步结果与高阶数值模拟吻合良好，为模型假设的有效性提供支持。

A analytical method is presented in this paper to compute the turbulence-cascade interaction noise with real airfoil geometry. Two key assumptions are made: 1) the property of sound generated by an airfoil only depends on the local mean flow and vortical gust; 2) each airfoil only scatters the sound waves radiated from other airfoils. A proposed analytical solution for the noise generated by a real airfoil can be utilised to compute the acoustic response to the oncoming vortical gusts. The analytical solution was developed based on a generalised Prandtl-Glauert transformation to account for the non-uniform mean flow effect. As for the interaction between the cascade airfoils, the sound scattering is resolved using the high-efficiency boundary element method. This abstract presents the principle steps in the proposed analytical model. Initial results for zero stagger angle flat plate cascades are computed, and match well with the high order numerical simulation results, giving us the confidence with the validities of the assumptions made in the analytical model. © 2019, American Institute of Aeronautics and Astronautics Inc, AIAA. All rights reserved.

随着多旋翼无人机快速发展，其噪声问题日益受到关注。安静无人机设计需要理解噪声产生与传播机制。本文利用自主开发的边界元求解器，提出评估飞行中无人机机身对转子噪声散射效应的高效框架。常规边界元方法的非唯一解问题通过组合 Helmholtz 内部积分方程方法（CHIEF）解决。预测工具被用于评估真实转子与机身构型的噪声辐射。该研究是无人机噪声整体研究的一部分，相关工作还包括飞行试验、消声风洞研究及解析和数值模拟。

With the rapid development of multi-rotor powered drones, the drone noise has received large attention over the recent years. The design of quiet drones calls for physical understanding of the drone noise generation and propagation. In this paper, we present an efficient framework to evaluate the scattering effect of the rotor noise off a flying drone fuselage using an in-house solver based on the boundary element method (BEM). The non-unique solution of the conventional BEM is tackled using a Combined Helmholtz Interior integral Equation Formulation (CHIEF). The prediction tool is applied to evaluate the noise radiated by a realistic rotor/fuselage configuration. This study is an element of an overall effort on the drone noise, including flying tests, anechoic wind tunnel studies, and analytical and numerical simulations. © 2019, American Institute of Aeronautics and Astronautics Inc, AIAA. All rights reserved.

新型声衬设计常采用具有非均匀阻抗分布的材料，因此需要新的建模与分析方法。本文建立理论模型，研究轴对称流动管道中管壁带半无限、周向非均匀声衬时的声波散射。将傅里叶级数展开引入 Wiener–Hopf 方法后，得到具有矩阵核的解析模型，再通过去极点法分解矩阵核以获得闭式解。研究还提出求解去极点技术相关留数的新数学方法，并通过与相应计算结果比较验证模型。该模型不仅揭示周向非均匀声衬与轴向硬—软界面的可能物理效应，也增强了对实际重要复杂构型的理论建模能力，可用于研究流动管道被动降噪的新型声衬设计。

Novel acoustic liner designs often incorporate new materials with non-uniform impedance distributions. Therefore, new methods are required for their modelling and analysis. In this paper, a theoretical model is developed to investigate the scattering of sound waves from an axially symmetrical flow duct with a semi-infinite, azimuthally non-uniform acoustic lining on the duct wall. More specifically, the incorporation of Fourier series expansions into the Wiener–Hopf method leads to an analytical model with a matrix kernel, which is further factorised by using the pole-removal method to obtain a closed-form solution. A new mathematical method is developed to solve the residues associated with the pole-removal technique. The proposed model has been verified and validated by comparing with corresponding computational results. In addition to shedding light on the possible physical effect of azimuthally non-uniform liners along with an axial hard–soft interface, the current model enhances the theoretical modelling capability for a complicated set-up of practical importance, and can be used to investigate new liner designs for passive noise control in flow ducts.

数值优化对低噪声航空发动机声衬设计十分有用。现代计算工具虽然能高效完成单次发动机噪声传播模拟，但宽频声衬优化需要成千上万次计算，其高昂成本使这些工具难以直接用于该任务。为使台式计算机能够开展快速优化，本文提出基于 Wiener–Hopf 方法的高效解析求解器。该方法虽能在秒量级给出预测，但通常采用均匀背景流中的理想直管假设，其实际适用性存在争议。本文利用该求解器优化半无限环形管道中的声衬，并将其降噪效果与针对非均匀背景流下实际发动机进气道、直接采用有限元求解器得到的优化声衬进行比较。两类求解器给出的近场和远场解几乎一致，说明所提优化策略兼具准确性和高效率。因此，该 Wiener–Hopf 求解器适用于实际构型的声衬优化，对低噪声航空发动机初步设计具有价值。

Numerical optimizations are very useful in liner designs for low-noise aeroengines. Although modern computational tools are already very efficient for a single aeroengine noise propagation simulation run, the prohibitively high computational cost of a broadband liner optimization process which requires hundreds of thousands of runs renders these tools unsuitable for such task. To enable rapid optimization using a desktop computer, an efficient analytical solver based on the Wiener–Hopf method is proposed in the current study. Although a Wiener–Hopf-based solver can produce predictions very quickly (order of a second), it usually assumes an idealized straight duct configuration with a uniform background flow that makes it arguable for practical applications. In the current study, we employ the Wiener–Hopf method in our solver to produce an optimized liner design for a semi-infinite annular duct setup and compare its noise-reduction effect with an optimized liner designed by the direct application of a numerical finite element solver for a practical aeroengine intake configuration with an inhomogeneous background flow. The near-identical near- and far-field solutions by the Wiener–Hopf-based method and the finite element solvers clearly demonstrate the accuracy and high efficiency of the proposed optimization strategy. Therefore, the current Wiener–Hopf solver is highly effective for liner optimizations with practical setups and is very useful to the preliminary design process of low-noise aeroengines.

声衬优化需要高效的仿真方法。本文针对 Wiener–Hopf 求解器提出一种高效、直接的算法，并利用图形处理器（GPU）的并行处理能力。该算法将 Wiener–Hopf 求解器的公式重新组织为适当的矩阵形式。这一常被忽视的思路十分简洁，却能显著提高计算效率。通过考察声衬管道和管道声辐射两类典型问题，研究展示了所提算法的优越计算性能，尤其是在使用 GPU 时。计算效率的提高表明，该算法及 GPU 技术具有应用于实际低噪声航空发动机设计与优化的潜力。

Acoustic liner optimization calls for very efficient simulation methods. A highly efficient and straightforward algorithm is proposed here for the Wiener–Hopf solver, which also takes advantage of the parallel processing capability of the emerging graphics processing unit (GPU) technology. The proposed algorithm adopts a simple concept that re-arranges the formulations of the Wiener–Hopf solver to appropriate matrix forms. This concept was often overlooked but is surprisingly succinct, which leads to a stunningly efficient computational performance. By examining the computational performance of two representative setups (lined duct and duct radiations), the current study shows the superior performance of the proposed algorithm, particularly with GPU. The much improved computational efficiency further suggests the potential of the proposed algorithm and the use of GPU for practical low-noise aircraft engine design and optimization.

本文将代理模型与 Wiener–Hopf 方法结合，提出用于掠流入射管的高效阻抗反演方法，可在一系列参数取值与工况下快速预测声学响应并有效反演阻抗。通过分别与理论结果、数值预测和实验测量比较，对该方法进行了验证。各项验证均表明，所提出的求解器具有用于声衬参数研究与优化的能力和潜力。

This paper presents an efficient impedance eduction method for grazing flow incidence tube by using a surrogating model along with the Wiener–Hopf method, which enables rapid acoustic predictions and effective impedance eductions over a range of parametric values and working conditions. The proposed method is demonstrated by comparing to the theoretical results, numerical predictions, and experimental measurements, respectively. All the demonstrations clearly suggest the capability and the potential of the proposed solver for parametric studies and optimizations of the lining methods.

本文建立理论模型，研究半无限声衬表面被等间距刚性接缝覆盖的流动管道声散射问题，该问题对低噪声航空发动机开发具有实际意义。主要贡献是结合傅里叶级数展开与 Wiener–Hopf 方法，对轴向声衬接缝作出严格解析描述。傅里叶级数用于描述半无限声衬表面的周期变化，准确表示接缝在周向的布局。相应矩阵核包含常数矩阵和对角矩阵，后者由一系列典型标量核组成，可通过标准 Wiener–Hopf 标量核分解获得闭式解。实现时采用无限傅里叶级数数值截断等合理近似，并与商业声学求解器结果比较验证。多个算例说明，模型能够揭示轴向及周向硬—软界面共同作用产生的关键声学效应。

In this paper we present a theoretical model to study sound scattering from flow ducts with a semi-infinite lining surface covered by some equally spaced rigid splices, which is of practical importance in the development of silent aeroengines. The key contribution of our work is the analytical and rigorous description of axial liner splices by incorporating Fourier series expansion and the Wiener–Hopf method. In particular, we describe periodic variations of the semi-infinite lining surface by using Fourier series that accurately represent the layout of rigid splices in the circumferential direction. The associated matrix kernel involves a constant matrix and a diagonal matrix. The latter consists of a series of typical scalar kernels. A closed-form solution is then obtained by using standard routines of Wiener–Hopf factorisation for scalar kernels. A couple of appropriate approximations, such as numerical truncations of infinite Fourier series, have to be adopted in the implementation of this theoretical model, which is validated by comparing favorably with numerical solutions from a commercial acoustic solver. Finally, several numerical test cases are performed to demonstrate this theoretical model. It can be seen that the proposed theoretical model helps to illuminate the essential acoustic effect jointly imposed by axial and circumferential hard–soft interfaces.

该论文的中文摘要尚未收录。

The English abstract has not yet been added.

本文提出理论模型，研究半无限声衬表面被等间距刚性接缝覆盖的流动管道声散射问题，这对低噪声航空发动机发展具有实际意义。主要贡献是结合傅里叶级数展开与 Wiener–Hopf 方法，对轴向声衬接缝进行严格解析描述。半无限声衬区域内沿周向周期分布的接缝用傅里叶级数表示，得到的矩阵核包括常数矩阵和对角矩阵；后者由若干标量核组成，可采用标准标量核分解程序处理。通过数值算例验证该理论模型，并利用多组参数研究揭示轴向及周向硬—软界面对声散射的关键影响。

A theoretical model is presented in this paper to study sound scattering from flow ducts with semi-infinite lining surface covered by equal-spaced rigid splices, which is of practical importance in developments of silent aeroengine. The key contribution of our work is the analytical and rigorous description of axial liner splices by incorporating Fourier series expansion and Wiener-Hopf method. The distribution of the circumferentially periodical splices in semi-infinite liner region is described using Fourier series. The resulted matrix kernel involves a constant matrix and a diagonal matrix, the latter of which consists of a couple of scalar kernels that a standard routines of scalar kernel factorization could be utilised. This theoretical model is validated by numerical test cases. The essential acoustic scattering effect imposed by axial and azimuthal hard-soft interfaces is illuminated with several parametric study cases.