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1

Souliez, F. J., L. N. Long, P. J. Morris, and A. Sharma. "Landing Gear Aerodynamic Noise Prediction Using Unstructured Grids." International Journal of Aeroacoustics 1, no. 2 (2002): 115–35. http://dx.doi.org/10.1260/147547202760236932.

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Aerodynamic noise from a landing gear in a uniform flow is computed using the Ffowcs Williams-Hawkings (FW-H) equation. The time accurate flow data on the integration surface is obtained using a finite volume low-order flow solver on an unstructured grid. The Ffowcs Williams-Hawkings equation is solved using surface integrals over the landing gear surface and over a permeable surface away from the landing gear. Two geometric configurations are tested in order to assess the impact of two lateral struts on the sound level and directivity in the far-field. Predictions from the Ffowcs Williams-Haw
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2

Testa, C., S. Ianniello, F. Salvatore, and M. Gennaretti. "Numerical Approaches for Hydroacoustic Analysis of Marine Propellers." Journal of Ship Research 52, no. 01 (2008): 57–70. http://dx.doi.org/10.5957/jsr.2008.52.1.57.

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This paper is devoted to a theoretical and numerical hydroacoustic analysis of marine propellers. The use of the Ffowcs Williams-Hawkings equation is addressed and compared with a Bernoulli-based methodology, typically used in the naval context. A computational tool based on a boundary element formulation for the velocity potential is used to determine the hydrodynamic loads on the propeller blades. Then, both the Bernoulli and the Ffowcs Williams-Hawkings equations are used to evaluate the pressure far field. The role played by the incompressibility assumption is treated from theoretical and
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3

Ianniello, Sandro. "Quadrupole Noise Predictions Through the Ffowcs Williams-Hawkings Equation." AIAA Journal 37, no. 9 (1999): 1048–54. http://dx.doi.org/10.2514/2.832.

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4

Ianniello, Sandro. "Quadrupole noise predictions through the Ffowcs Williams-Hawkings equation." AIAA Journal 37 (January 1999): 1048–54. http://dx.doi.org/10.2514/3.14287.

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5

Ikeda, Tomoaki, Shunji Enomoto, Kazuomi Yamamoto, and Kazuhisa Amemiya. "Quadrupole Corrections for the Permeable-Surface Ffowcs Williams–Hawkings Equation." AIAA Journal 55, no. 7 (2017): 2307–20. http://dx.doi.org/10.2514/1.j055328.

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6

GUO, Y. P. "Application of the Ffowcs Williams/Hawkings equation to two-dimensional problems." Journal of Fluid Mechanics 403 (January 25, 2000): 201–21. http://dx.doi.org/10.1017/s0022112099006989.

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This paper discusses the application of the Ffowcs Williams/Hawkings equation to two-dimensional problems. A two-dimensional version of this equation is derived, which not only provides a very efficient way for numerical implementation, but also reveals explicitly the features of the source mechanisms and the characteristics of the far-field noise associated with two-dimensional problems. It is shown that the sources can be interpreted, similarly to those in three-dimensional spaces, as quadrupoles from turbulent flows, dipoles due to surface pressure fluctuations on the bodies in the flow and
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7

Zhou, Zhiteng, Hongping Wang, and Shizhao Wang. "Simplified permeable surface correction for frequency-domain Ffowcs Williams and Hawkings integrals." Theoretical and Applied Mechanics Letters 11, no. 4 (2021): 100259. http://dx.doi.org/10.1016/j.taml.2021.100259.

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8

Chen, Zhibo, and Aaron Towne. "An azimuthal Fourier domain formulation of the Ffowcs Williams and Hawkings equation." Journal of the Acoustical Society of America 150, no. 3 (2021): 1967–78. http://dx.doi.org/10.1121/10.0006234.

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9

Casalino, Damiano, Marc Jacob, and Michel Roger. "Prediction of Rod-Airfoil Interaction Noise Using the Ffowcs-Williams-Hawkings Analogy." AIAA Journal 41, no. 2 (2003): 182–91. http://dx.doi.org/10.2514/2.1959.

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10

Ianniello, Sandro. "Algorithm to Integrate the Ffowcs Williams-Hawkings Equation on Supersonic Rotating Domain." AIAA Journal 37, no. 9 (1999): 1040–47. http://dx.doi.org/10.2514/2.831.

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11

Ianniello, Sandro. "Algorithm to integrate the Ffowcs Williams-Hawkings equation on supersonic rotating domain." AIAA Journal 37 (January 1999): 1040–47. http://dx.doi.org/10.2514/3.14286.

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12

LOCKARD, DAVID P. "AN EFFICIENT, TWO-DIMENSIONAL IMPLEMENTATION OF THE FFOWCS WILLIAMS AND HAWKINGS EQUATION." Journal of Sound and Vibration 229, no. 4 (2000): 897–911. http://dx.doi.org/10.1006/jsvi.1999.2522.

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13

Ricciardi, Tulio R., William R. Wolf, and Philippe R. Spalart. "On the Application of Incomplete Ffowcs Williams and Hawkings Surfaces for Aeroacoustic Predictions." AIAA Journal 60, no. 3 (2022): 1971–77. http://dx.doi.org/10.2514/1.j061285.

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14

Brentner, Kenneth S. "A superior Kirchhoff method for aeroacoustic noise prediction: The Ffowcs Williams–Hawkings equation." Journal of the Acoustical Society of America 102, no. 5 (1997): 3183. http://dx.doi.org/10.1121/1.420848.

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15

Testa, C., S. Ianniello, and F. Salvatore. "A Ffowcs Williams and Hawkings formulation for hydroacoustic analysis of propeller sheet cavitation." Journal of Sound and Vibration 413 (January 2018): 421–41. http://dx.doi.org/10.1016/j.jsv.2017.10.004.

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16

Kusyumov, Alexander, Sergey Mikhailov, Sergey Kusyumov, Elena Romanova, and Georgios Barakos. "Some Peculiarities of Helicopter Main Rotor Aeroacoustic for Far-Field Observer." EPJ Web of Conferences 213 (2019): 02048. http://dx.doi.org/10.1051/epjconf/201921302048.

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Mathematical models for helicopter rotor acoustics are usually based on the Ffowcs Williams–Hawkings (FW–H) equation. The level of rotor noise is determined by geometry (thickness noise) of a flying vehicle and distributed blade loading (loading noise). Initially, the FW-H equation was obtained from Euler’s equations and does not depend on the viscosity of flow. In the present work the UH-1H helicopter is considered as a test case for numerical CFD simulation and comparison to experimental data.
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17

Wu, Jiafeng, Jianyun Yangzhou, Zhaokai Ma, and Xun Huang. "Numerical study of rotor unsteady forces and noise due to ingestion of grid-generated turbulence." Physics of Fluids 35, no. 1 (2023): 015141. http://dx.doi.org/10.1063/5.0132975.

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In many aeronautics and marine applications, the unsteady forces generated by propulsion rotors due to turbulence ingestion are a significant source of noise and create serious concerns. The understanding of rotor turbulence ingestion and the rotor noise generation mechanisms is vital to achieve an optimal design or apply noise control strategy. The current study is the first attempt to numerically investigate an underwater rotor ingesting grid-generated turbulence by large eddy simulation combined with the Ffowcs-Williams and Hawkings equation. The flow characteristics of two directly simulat
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18

Zhou, Zhiteng, Yi Liu, Hongping Wang, and Shizhao Wang. "Mass-Conserved Solution to the Ffowcs-Williams and Hawkings Equation for Compact Source Regions." Aerospace 10, no. 2 (2023): 148. http://dx.doi.org/10.3390/aerospace10020148.

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A mass-conserved formulation for the Ffowcs-Williams–Hawkings (FW–H) integral is proposed to suppress contributions of spurious mass flux to the far-field sound at very low Mach numbers. The far-field condition and compact-source region assumptions are employed. By using higher-order derivatives of Green’s function, an expansion of the integrand in the monopole term is performed. This expansion transforms the mass-flux like monopole term into a series including different orders of velocity moment. At very low Mach numbers, the zero-order term is exactly the contribution from the spurious mass
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19

Hong, Juan, Wei Chen, and Song Pin Wu. "Influence of Cavity Shape on Aerodynamic Noise by a Hybrid LES-FWH Method." Applied Mechanics and Materials 543-547 (March 2014): 358–61. http://dx.doi.org/10.4028/www.scientific.net/amm.543-547.358.

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The flow mechanism and radiate noise by a low-speed turbulent flow over an open cavity has been investigated computationally. After acquired the flow field data which is obtained by using Large Eddy Simulation, hybrid method that couples numerical flow computations with an implementation of the Ffowcs Williams-Hawkings equation is used to capture the flow induced noise. Different cavity length to depth ratios and configurations are used to investigate the influences of cavity deeps and configuration with an incoming flow of 50m/s. In this article, we also discussed the reduction method of cavi
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20

Bacak, Aykut, and Ali Pinarbasi. "Numerical Investigation of Acoustics Performance of Low- Pressure Ducted Axial Fan by Using Different Turbulence Models." ITM Web of Conferences 22 (2018): 01004. http://dx.doi.org/10.1051/itmconf/20182201004.

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In this article, capacity and acoustics parameters of low pressure ducted axial fan is numerically investigated with Realizable k-epsilon, k-w SST and DES turbulence models by using computational fluid dynamics software. One slice of six bladed axial fan operating at 3000 RPM is simulated periodically as low pressure ducted axial ventilation fan. Simulations are run for operating point on the performance curve for each turbulence models. Investigation of acoustics parameters are obtained Ffowcs-Williams Hawkings acoustic model to calculate sound pressure levels for related frequencies. Numeric
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21

Huang, Zhongjie, Leonidas Siozos-Rousoulis, Tim De Troyer, and Ghader Ghorbaniasl. "A time-domain method for prediction of noise radiated from supersonic rotating sources in a moving medium." Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 474, no. 2210 (2018): 20170089. http://dx.doi.org/10.1098/rspa.2017.0089.

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This paper presents a time-domain method for noise prediction of supersonic rotating sources in a moving medium. The proposed approach can be interpreted as an extensive time-domain solution for the convected permeable Ffowcs Williams and Hawkings equation, which is capable of avoiding the Doppler singularity. The solution requires special treatment for construction of the emission surface. The derived formula can explicitly and efficiently account for subsonic uniform constant flow effects on radiated noise. Implementation of the methodology is realized through the Isom thickness noise case a
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22

Schoder, Stefan, Clemens Junger, and Manfred Kaltenbacher. "Computational aeroacoustics of the EAA benchmark case of an axial fan." Acta Acustica 4, no. 5 (2020): 22. http://dx.doi.org/10.1051/aacus/2020021.

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This contribution benchmarks the aeroacoustic workflow of the perturbed convective wave equation and the Ffowcs Williams and Hawkings analogy in Farassat’s 1A version for a low-pressure axial fan. Thereby, we focus on the turbulence modeling of the flow simulation and mesh convergence concerning the complete aeroacoustic workflow. During the validation, good agreement has been found with the efficiency, the wall pressure sensor signals, and the mean velocity profiles in the duct. The analysis of the source term structures shows a strong correlation to the sound pressure spectrum. Finally, both
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23

Khelladi, Sofiane, and Farid Bakir. "A Consistency Test of Thickness and Loading Noise Codes Using Ffowcs Williams and Hawkings Equation." Advances in Acoustics and Vibration 2010 (July 4, 2010): 1–6. http://dx.doi.org/10.1155/2010/174361.

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The thickness noise predicted by the Ffowcs Williams and Hawkings (FW&H) equation depends on the normal velocity which is very sensitive to the meshing size. Isom showed that in far field a monopolar source is equivalent to a dipolar source induced by a uniform distribution of the load on the entire moving surface. The main objective of this paper is to determine a specific expression of Isom's thickness noise in time and frequency domains for subsonic fans. The scope of the proposed expression of Isom's thickness noise is to define a benchmark test of consistency for thickness and loading
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24

Nitzkorski, Zane, and Krishnan Mahesh. "A dynamic end cap technique for sound computation using the Ffowcs Williams and Hawkings equations." Physics of Fluids 26, no. 11 (2014): 115101. http://dx.doi.org/10.1063/1.4900876.

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25

Spalart, Philippe R., and Michael L. Shur. "Variants of the Ffowcs Williams - Hawkings Equation and Their Coupling with Simulations of Hot Jets." International Journal of Aeroacoustics 8, no. 5 (2009): 477–91. http://dx.doi.org/10.1260/147547209788549280.

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26

Ianniello, Sandro. "The Ffowcs Williams–Hawkings equation for hydroacoustic analysis of rotating blades. Part 1. The rotpole." Journal of Fluid Mechanics 797 (May 23, 2016): 345–88. http://dx.doi.org/10.1017/jfm.2016.263.

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This paper deals with the use of the Ffowcs Williams–Hawkings equation for hydroacoustic analysis of rotating blades, and the deep difference between the acoustic fields generated by aeronautical and marine devices in air and underwater. This dissimilarity does not depend on either the different fluid or the (although existing) geometric and structural difference of the blade: it is an intrinsic feature of the generating noise mechanisms related to rotating sources and is essentially due to the remarkable diversity of the rotational speed. It will be shown how the usual assumption of believing
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27

Naqavi, Iftekhar Z., Zhong-Nan Wang, Paul G. Tucker, M. Mahak, and Paul Strange. "Far-field noise prediction for jets using large-eddy simulation and Ffowcs Williams–Hawkings method." International Journal of Aeroacoustics 15, no. 8 (2016): 757–80. http://dx.doi.org/10.1177/1475472x16672547.

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28

Rahier, G., M. Huet, and J. Prieur. "Additional terms for the use of Ffowcs Williams and Hawkings surface integrals in turbulent flows." Computers & Fluids 120 (October 2015): 158–72. http://dx.doi.org/10.1016/j.compfluid.2015.07.014.

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29

Lidtke, Artur K., Stephen R. Turnock, and Victor F. Humphrey. "Characterisation of sheet cavity noise of a hydrofoil using the Ffowcs Williams–Hawkings acoustic analogy." Computers & Fluids 130 (May 2016): 8–23. http://dx.doi.org/10.1016/j.compfluid.2016.02.014.

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30

Epikhin, Andrey, Matvey Kraposhin, and Kirill Vatutin. "The numerical simulation of compressible jet at low Reynolds number using OpenFOAM." E3S Web of Conferences 128 (2019): 10008. http://dx.doi.org/10.1051/e3sconf/201912810008.

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The paper presents an analysis of various approaches for calculation gas-dynamic parameters and acoustic perturbations generated by a compressible jet at low Reynolds number (M = 0.9, Re = 3600). The jet flow parameters at selected conditions are well studied and can be used for validation of the numerical methods and schemes. The OpenFOAM software package with various approaches (solvers) such as pimpleCentralFoam, dbnsTurbFoam and new QGDFoam solver based on QGD-algorithms are considered. The results of time-averaged flow parameters and acoustic properties are compared with the experimental
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31

Huang, Surui, Kai Yang, Chengyuan Sun, and Leilei Shi. "Research on finite element model of rotor aerodynamicnoise in hovering state." Journal of Physics: Conference Series 2756, no. 1 (2024): 012009. http://dx.doi.org/10.1088/1742-6596/2756/1/012009.

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Abstract The helicopter has been widely used in many fields, and the rotor aerodynamic noise has gradually attracted attention. The non-homogeneous wave equation, Ffowcs Williams-Hawkings equation (FW-H equation) derived from hydrodynamic N-S equation, combined with RANS turbulence simulation, was used to simulate the sound field of NACA0012 airfoil-shape model in hovering state. On this basis, by changing the thickness and camber of the blade, the aerodynamic noise of the rotor under different airfoil profile thickness and camber is calculated. The results show that the change of airfoil thic
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32

Wang, Yanqing, Wei Kang, and Shilin Hu. "Aeroacoustic Analysis of Rapid Position Changing Process of Missile Seeker Equipment." Journal of Physics: Conference Series 2658, no. 1 (2023): 012034. http://dx.doi.org/10.1088/1742-6596/2658/1/012034.

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Abstract A two-dimensional CFD model of the rapid position-changing of missile seeker equipment is presented to study its aeroacoustic impact. By combining the computational fluid dynamics (CFD) with the Ffowcs Williams-Hawkings (FW-H) equation, the flow and related aeroacoustic features are analyzed under different flight Mach numbers and flight heights. The impact of seeker movement on the flow field and aerodynamic noise are highlighted. The results indicate that the spectrum peak of sound pressure level increases with the vortex shedding frequency as the flight Mach number increases. As th
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33

Tabrizi, Amir Bashirzadeh, and Binxin Wu. "The role of compressibility in computing noise generated at a cavitating orifice." International Journal of Aeroacoustics 18, no. 1 (2018): 73–91. http://dx.doi.org/10.1177/1475472x18812801.

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The computational fluid dynamics calculation can be accomplished by solving either compressible or incompressible Navier–Stokes equations to determine the flow-field variables of the noise source. The proper assumption depends on both the physical situation and the Mach number. Although in cavitating devices usually we are dealing with low Mach number flow, cavitation is an acoustic phenomenon that can be affected by compressibility. Cavitation behaves acoustically as a monopole and it is mentioned by some researchers that incompressible solution is sufficient to study the dipole sources. Howe
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34

Dunn, Mark H. "The acoustic analogy in four dimensions." International Journal of Aeroacoustics 18, no. 8 (2019): 711–51. http://dx.doi.org/10.1177/1475472x19890259.

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The classical acoustic analogy theory is incomplete in the sense that the original research on the subject focused only on the prediction of acoustic pressure. There were no provisions for predicting the three components of acoustic velocity which are needed as input for aeroacoustic scattering applications. This is because the scalar wave equations of Lighthill and Ffowcs Williams and Hawkings were derived from the fluid conservation equations by eliminating three of the four governing differential equations from which the acoustic velocity could have been obtained. Recently developed acousti
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35

Romik, Dawid, and Ireneusz Czajka. "Numerical Investigation of the Sensitivity of the Acoustic Power Level to Changes in Selected Design Parameters of an Axial Fan." Energies 15, no. 4 (2022): 1357. http://dx.doi.org/10.3390/en15041357.

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The noise generated by different types of fans used in the turbomachinery industry is a topic that has been studied for many years. However, researchers are still looking for a universal solution to reduce noise while maintaining the performance of these machines. This paper, as a contribution to the research, presents the results of numerical investigations of an axial fan installed in a pipeline with a circular cross-section. In particular, the focus was on investigating the sensitivity of the sound power level to changes in selected design and operational parameters of this fan. The simulat
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36

Cho, Yong, and Young J. Moon. "Discrete Noise Prediction of Variable Pitch Cross-Flow Fans by Unsteady Navier-Stokes Computations." Journal of Fluids Engineering 125, no. 3 (2003): 543–50. http://dx.doi.org/10.1115/1.1568356.

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The unsteady viscous flow fields of a cross-flow fan are computed by time-accurately solving the two-dimensional incompressible Navier-Stokes equations with the unstructured triangular mesh solver algorithms. Based on pressure fluctuation data acquired at the surfaces of 35 rotating blades and stabilizer, acoustic pressures are predicted by the Ffowcs Williams-Hawkings equation. The aerodynamic noise sources of the cross-flow fan are also identified by correlating the acoustic pressure fluctuations with the unsteady flow characteristics during one revolution of the impeller. The present method
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37

Ma, Yunpeng, and Na Guo. "A numerical study on the effects of design parameters on the acoustics noise of a high efficiency propeller." Aircraft Engineering and Aerospace Technology 91, no. 1 (2018): 30–37. http://dx.doi.org/10.1108/aeat-08-2017-0183.

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PurposeA numerical study on the aerodynamic noise generation of a high efficiency propeller is carried out.Design/methodology/approachThree-dimensional numerical simulation based on Reynolds averaged N-S model is performed to obtain the aerodynamic performance of the propeller. Then, the result of the aerodynamic analysis is given as input of the acoustic calculation. The sound is calculated using the Farassat 1A which was derived from Ffowcs Williams–Hawkings equation and is compared with the measurements.FindingsMoreover, the fan is modified for noise reduction by changing its geometrical pa
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38

Branda˜o, Mauri´cio P. "Towards the Unification of Acoustics and Fluid Mechanics." Applied Mechanics Reviews 42, no. 11S (1989): S20—S31. http://dx.doi.org/10.1115/1.3152392.

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A comprehensive study of a modern acoustic technique is presented. The conservation laws of mass, momentum, and surface boundary conditions are cast in the form of an inhomogeneous wave equation, known today as Ffowcs Williams and Hawkings’ equation. The result is general, capable of addressing three-dimensional, nonlinear, and unsteady flow problems of compressible and viscous fluids. The Green’s function solution is used to transform the differential equation into integral form. The formulation is then linearized and viscosity is neglected. The pressure distribution on the surface of the NAC
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39

Schoder, Stefan, and Manfred Kaltenbacher. "Hybrid Aeroacoustic Computations: State of Art and New Achievements." Journal of Theoretical and Computational Acoustics 27, no. 04 (2019): 1950020. http://dx.doi.org/10.1142/s2591728519500208.

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This paper collects the state of the art and the tremendous progress that has been made in hybrid modeling of aeroacoustic sound. Hybrid modeling is defined such that flow and acoustics are modeled separate and connected by an aeroacoustic model. The contributions will be classified with respect to the aeroacoustic models being developed, covering Lighthill’s analogy, Ffowcs Williams and Hawkings, vortex sound, linearized Euler equations (LEE), and different perturbation equations modeling flow induced sound. Within each topic, specific applications, such as jet noise, aircraft noise, ground m
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40

Zhu, Chunli, Hassan Hemida, Dominic Flynn, Chris Baker, Xifeng Liang, and Dan Zhou. "Numerical simulation of the slipstream and aeroacoustic field around a high-speed train." Proceedings of the Institution of Mechanical Engineers, Part F: Journal of Rail and Rapid Transit 231, no. 6 (2016): 740–56. http://dx.doi.org/10.1177/0954409716641150.

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The flow field and sound propagation around a three-coach 1/8th scale high-speed passenger train were obtained using a detached-eddy simulation and the Ffowcs-Williams and Hawkings acoustic analogy. The Reynolds number of flow based on the train height and speed was 2,000,000. The numerical results of the flow and aeroacoustic fields were validated using wind tunnel experiments and full-scale data, respectively. Features of overall sound pressure level, sound pressure level and A-weighted sound pressure level of typical measuring points are discussed. The sound propagated by a high-speed train
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41

IANNIELLO, S. "New perspectives in the use of the Ffowcs Williams–Hawkings equation for aeroacoustic analysis of rotating blades." Journal of Fluid Mechanics 570 (January 3, 2007): 79–127. http://dx.doi.org/10.1017/s002211200600293x.

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The Ffowcs Williams–Hawkings equation represents a standard approach in the prediction of noise from rotating blades. It is widely used for linear aeroacoustic problems concerning helicopter rotors and aircraft propellers and over the last few years, through the use of the so called porous (or permeable) surface formulation, has replaced the Kirchhoff approach in the numerical solution of nonlinear problems. Nevertheless, because of numerical difficulties in evaluating the contribution from supersonic sources, most of the computing tools are still unable to treat the critical velocities at whi
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42

Spalart, Philippe R., Kirill V. Belyaev, Mikhail L. Shur, Mikhail Kh Strelets, and Andrey K. Travin. "On the differences in noise predictions based on solid and permeable surface Ffowcs Williams–Hawkings integral solutions." International Journal of Aeroacoustics 18, no. 6-7 (2019): 621–46. http://dx.doi.org/10.1177/1475472x19878934.

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43

Zhang, Yadong, and Yijun Liu. "Fast Evaluations of Integrals in the Ffowcs Williams–Hawkings Formulation in Aeroacoustics via the Fast Multipole Method." Acoustics 5, no. 3 (2023): 817–44. http://dx.doi.org/10.3390/acoustics5030048.

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A new approach to accelerating the evaluation of monopole and dipole source integrals via the fast multipole method (FMM) in the time domain for general three-dimensional (3-D) aeroacoustic problems is presented in this paper. In this approach, the aeroacoustic field is predicted via a hybrid method that uses computational fluid dynamics (CFD) for near-field flow field calculations and the Ffowcs Williams–Hawkings (FW-H) acoustic analogy for far-field sound field predictions. The evaluation of the surface integrals of the monopole and dipole source terms appearing in the FW-H formulation is ac
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44

Long, Shuang Li, Hong Nie, and Xin Xu. "Aeroacoustic Study on a Simplified Nose Landing Gear." Applied Mechanics and Materials 184-185 (June 2012): 18–23. http://dx.doi.org/10.4028/www.scientific.net/amm.184-185.18.

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Simulation analysis and experiment research are performed on the aeroacoustic noise of a landing gear component in this paper. Detached Eddy Simulation (DES) is used to produce the flow field of the model. The Ffowcs-Williams/Hawkings (FW-H) equation is used to calculate the acoustic field. The sound field radiated from the model is measured in the acoustic wind tunnel. A comparison shows that the simulation results agree well with the experiment results under the acoustic far field condition. The results show that the noise radiated from the model is broadband noise. The directivity of the no
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45

Ji, Chun Hui, and Zhan Qiang Liu. "Aeroacoustic Performance Evaluation of Milling Cutters Based on the Flow Field on the Cutter Surface." Advanced Materials Research 188 (March 2011): 398–403. http://dx.doi.org/10.4028/www.scientific.net/amr.188.398.

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Many workers all over the world suffer significant hearing loss as well as psychological and physical stress as a result of exposure to high levels of aeroacoustic noise. Dipole sources are the major noise sources in aeroacoustic noise generation in rotating face milling cutters. A noise model based on the Ffowcs Williams-Hawkings Equation is used to predict aeroacoustic noise; the noise predicted was 2.5dB less than the experimental observations. Flow field of cutter surface was numerically simulated by the resolution of the Navier-Stokes equations (CFD) and five zones on cutter surface were
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Zhong, Guo, Jun Huang, and Mingxu Yi. "Design parameters improvement of helicopter ducted tail rotor." Aircraft Engineering and Aerospace Technology 90, no. 2 (2018): 237–45. http://dx.doi.org/10.1108/aeat-01-2017-0033.

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Purpose The purpose of this paper is to reduce the acoustic noise of helicopter ducted tail rotor. Design/methodology/approach To predict the noise accurately, a thin-body boundary element method (BEM)/Ffowcs Williams–Hawkings method is developed in this paper. It is a hybrid method combining the BEM with computational aeroacoustics and can be used efficiently to predict the propagation of sound wave in the duct. Findings Compared with the experimental results, the proposed method of acoustic noise is rather desirable. Practical implications Then several geometry parameters are modified to inv
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Branda˜o, Mauri´cio P. "Mixed Volume Boundary Element Approach for Aerodynamics." Applied Mechanics Reviews 44, no. 11S (1991): S36—S45. http://dx.doi.org/10.1115/1.3121370.

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A review is presented of theoretical methods in aerodynamics and aeroacoustics which lead to the present approach. A formulation is developed for the analysis of three-dimensional, unsteady, and viscous flows. The integral solution to the Ffowcs Williams and Hawkings equation mixes surface and volume contributions. The surface terms are treated following the traditional boundary element technique. Special care is taken in revealing the hidden singularities of curved surfaces. The volume terms are treated following a cell-based approach. The concept of finite-part of singular integrals is used
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48

Sampath, Karthikeyan, Shiv G. Kapoor, and Richard E. DeVor. "Modeling and Analysis of Aerodynamic Noise in Milling Cutters." Journal of Manufacturing Science and Engineering 129, no. 1 (2006): 5–11. http://dx.doi.org/10.1115/1.2335861.

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Aerodynamic noise generated in high speed face milling cutters is usually much higher than the noise exposure limit set by OSHA. Experiments were conducted on two different face milling cutters to understand the aerodynamic noise generation in face milling cutters. It is observed that dipole sources of noise are most important in determining the noise generation in rotating face milling cutters. The aerodynamic noise spectrum consists of discrete tones at the rotational frequency and a broad range of higher frequencies, with the broadband spectrum contributing significantly to overall noise. A
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Nitzsche, F., and D. G. Opoku. "Acoustic validation of a new code using particle wake aerodynamics and geometrically-exact beam structural dynamics." Aeronautical Journal 109, no. 1096 (2005): 257–67. http://dx.doi.org/10.1017/s0001924000000713.

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Abstract This paper describes the validation of a new code for prediction both aeroacoustic and aeroelastic behaviour of hingeless rotors. The structural component is based on a non-linear beam element model considering small strains and finite rotations, which uses a mixed variational intrinsic formulation. The aerodynamic component is built on a loworder panel method incorporating a vortex particle free-wake model. The aerodynamic and structural components are combined to form a closely coupled aeroelastic code that solves in the time-domain. The loading and thickness noise terms for the aer
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Najafi-Yazdi, Alireza, Guillaume A. Brès, and Luc Mongeau. "An acoustic analogy formulation for moving sources in uniformly moving media." Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 467, no. 2125 (2010): 144–65. http://dx.doi.org/10.1098/rspa.2010.0172.

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Acoustic analogy methods are used as post-processing tools to predict aerodynamically generated sound from numerical solutions of unsteady flow. The Ffowcs Williams–Hawkings (FW–H) equation and related formulations, such as Farassat’s Formulations 1 and 1A, are among the commonly used analogies because of their relative low computation cost and their robustness. These formulations assume the propagation of sound waves in a medium at rest. The present paper describes a surface integral formulation based on the convective wave equation, which takes into account the presence of a mean flow. The f
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