Journal articles: 'Acoustic Hawking radiation'

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Carusotto, Iacopo, and Roberto Balbinot. "Acoustic Hawking radiation." Nature Physics 12, no. 10 (August 15, 2016): 897–98. http://dx.doi.org/10.1038/nphys3872.

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Zhou, Shiwei, and Kui Xiao. "Hawking radiation of analogous acoustic black holes." Modern Physics Letters A 35, no. 28 (July 30, 2020): 2050236. http://dx.doi.org/10.1142/s0217732320502363.

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Propagation of sound waves in a flowing fluid can be viewed as a minimally coupled massless scalar field propagating in curved spacetime. The analogue Hawking radiation from a spherically symmetric acoustic black hole and a (2 + 1)-dimensional rotating acoustic black hole are investigated respectively in Damour–Ruffini’s method. The emission rate and Hawking temperature are obtained, which are related to acoustic black holes parameter.

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Balbinot, Roberto, and Alessandro Fabbri. "The Hawking Effect in the Particles–Partners Correlations." Physics 5, no. 4 (September 27, 2023): 968–82. http://dx.doi.org/10.3390/physics5040063.

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We analyze the correlations functions across the horizon in Hawking black hole radiation to reveal the correlations between Hawking particles and their partners. The effects of the underlying space–time on this are shown in various examples ranging from acoustic black holes to regular black holes.

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PARENTANI, RENAUD. "WHAT DID WE LEARN FROM STUDYING ACOUSTIC BLACK HOLES?" International Journal of Modern Physics A 17, no. 20 (August 10, 2002): 2721–25. http://dx.doi.org/10.1142/s0217751x02011679.

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The study of acoustic black holes has been undertaken to provide new insights about the role of high frequencies in black hole evaporation. Because of the infinite gravitational redshift from the event horizon, Hawking quanta emerge from configurations which possessed ultra high (trans-Planckian) frequencies. Therefore Hawking radiation cannot be derived within the framework of a low energy effective theory; and in all derivations there are some assumptions concerning Planck scale physics. The analogy with condensed matter physics was thus introduced to see if the asymptotic properties of the Hawking phonons emitted by an acoustic black hole, namely stationarity and thermality, are sensitive to the high frequency physics which stems from the granular character of matter and which is governed by a non-linear dispersion relation. In 1995 Unruh showed that they are not sensitive in this respect, in spite of the fact that phonon propagation near the (acoustic) horizon drastically differs from that of photons. In 2000 the same analogy was used to establish the robustness of the spectrum of primordial density fluctuations in inflationary models. This analogy is currently stimulating research for experimenting Hawking radiation. Finally it could also be a useful guide for going beyond the semi-classical description of black hole evaporation.

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Zhang, Li-Chun, Huai-Fan Li, and Ren Zhao. "Hawking radiation from a rotating acoustic black hole." Physics Letters B 698, no. 5 (April 2011): 438–42. http://dx.doi.org/10.1016/j.physletb.2011.03.034.

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Visser, Matt. "Acoustic black holes: horizons, ergospheres and Hawking radiation." Classical and Quantum Gravity 15, no. 6 (June 1, 1998): 1767–91. http://dx.doi.org/10.1088/0264-9381/15/6/024.

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Fagnocchi, Serena. "Correlations of Hawking radiation in acoustic black holes." Journal of Physics: Conference Series 222 (April 1, 2010): 012036. http://dx.doi.org/10.1088/1742-6596/222/1/012036.

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Kim, Wontae, and Hyeonjoon Shin. "Anomaly analysis of Hawking radiation from acoustic black hole." Journal of High Energy Physics 2007, no. 07 (July 27, 2007): 070. http://dx.doi.org/10.1088/1126-6708/2007/07/070.

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BÉCAR, RAMÓN, PABLO GONZÁLEZ, GUSTAVO PULGAR, and JOEL SAAVEDRA. "HAWKING RADIATION VIA ANOMALY AND TUNNELING METHOD BY UNRUH'S AND CANONICAL ACOUSTIC BLACK HOLE." International Journal of Modern Physics A 25, no. 07 (March 20, 2010): 1463–75. http://dx.doi.org/10.1142/s0217751x10048081.

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We study the Hawking radiation by Unruh's and canonical acoustic black hole from the viewpoint of anomaly cancelation method developed by Robinson and Wilczek and by the simple and physically intuitive picture given by the tunneling mechanism.

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Liberati, Stefano, Giovanni Tricella, and Andrea Trombettoni. "Back-Reaction in Canonical Analogue Black Holes." Applied Sciences 10, no. 24 (December 11, 2020): 8868. http://dx.doi.org/10.3390/app10248868.

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We study the back-reaction associated with Hawking evaporation of an acoustic canonical analogue black hole in a Bose–Einstein condensate. We show that the emission of Hawking radiation induces a local back-reaction on the condensate, perturbing it in the near-horizon region, and a global back-reaction in the density distribution of the atoms. We discuss how these results produce useful insights into the process of black hole evaporation and its compatibility with a unitary evolution.

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Barceló, Carlos, Stefano Liberati, and Matt Visser. "Towards the Observation of Hawking Radiation in Bose–Einstein Condensates." International Journal of Modern Physics A 18, no. 21 (August 20, 2003): 3735–45. http://dx.doi.org/10.1142/s0217751x0301615x.

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Acoustic analogues of black holes (dumb holes) are generated when a supersonic fluid flow entrains sound waves and forms a trapped region from which sound cannot escape. The surface of no return, the acoustic horizon, is qualitatively very similar to the event horizon of a general relativity black hole. In particular Hawking radiation (a thermal bath of phonons with temperature proportional to the "surface gravity") is expected to occur. In this note we consider quasi-one-dimensional supersonic flow of a Bose–Einstein condensate (BEC) in a Laval nozzle (converging-diverging nozzle), with a view to finding which experimental settings could magnify this effect and provide an observable signal. We discuss constraints and problems for our model and identify the issues that should be addressed in the near future in order to set up an experiment. In particular we identify an experimentally plausible configuration with a Hawking temperature of order 70 n K; to be contrasted with a condensation temperature of the order of 90 n K.

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Eskin, G. "Hawking radiation from acoustic black holes in two space dimensions." Journal of Mathematical Physics 59, no. 7 (July 2018): 072502. http://dx.doi.org/10.1063/1.4996765.

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Das, Arpan, Shreyansh S. Dave, Oindrila Ganguly, and Ajit M. Srivastava. "Hawking radiation from acoustic black holes in relativistic heavy ion collisions." Physics Letters B 817 (June 2021): 136294. http://dx.doi.org/10.1016/j.physletb.2021.136294.

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Eskin, G. "Hawking type radiation from acoustic black holes with time-dependent metric." Reports on Mathematical Physics 88, no. 2 (October 2021): 161–74. http://dx.doi.org/10.1016/s0034-4877(21)00067-7.

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Carusotto, Iacopo, Serena Fagnocchi, Alessio Recati, Roberto Balbinot, and Alessandro Fabbri. "Numerical observation of Hawking radiation from acoustic black holes in atomic Bose–Einstein condensates." New Journal of Physics 10, no. 10 (October 2, 2008): 103001. http://dx.doi.org/10.1088/1367-2630/10/10/103001.

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16

Zhang, Baocheng. "Thermodynamics of Acoustic Black Holes in Two Dimensions." Advances in High Energy Physics 2016 (2016): 1–8. http://dx.doi.org/10.1155/2016/5710625.

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It is well-known that the thermal Hawking-like radiation can be emitted from the acoustic horizon, but the thermodynamic-like understanding for acoustic black holes was rarely made. In this paper, we will show that the kinematic connection can lead to the dynamic connection at the horizon between the fluid and gravitational models in two dimensions, which implies that there exists the thermodynamic-like description for acoustic black holes. Then, we discuss the first law of thermodynamics for the acoustic black hole via an intriguing connection between the gravitational-like dynamics of the acoustic horizon and thermodynamics. We obtain a universal form for the entropy of acoustic black holes, which has an interpretation similar to the entropic gravity. We also discuss the specific heat and find that the derivative of the velocity of background fluid can be regarded as a novel acoustic analogue of the two-dimensional dilaton potential, which interprets why the two-dimensional fluid dynamics can be connected to the gravitational dynamics but it is difficult for four-dimensional case. In particular, when a constraint is added for the fluid, the analogue of a Schwarzschild black hole can be realized.

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Xue, She-Sheng. "Cosmological constant, matter, cosmic inflation and coincidence." Modern Physics Letters A 35, no. 15 (April 14, 2020): 2050123. http://dx.doi.org/10.1142/s0217732320501230.

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We present a possible understanding to the issues of cosmological constant, inflation, dark matter and coincidence problems based only on the Einstein equation and Hawking particle production. The inflation appears and results agree to observations. The CMB large-scale anomaly can be explained and the dark-matter acoustic wave is speculated. The entropy and reheating are discussed. The cosmological term [Formula: see text] tracks down the matter [Formula: see text] until the radiation-matter equilibrium, then slowly varies, thus the cosmic coincidence problem can be avoided. The relation between [Formula: see text] and [Formula: see text] is shown and can be examined at large redshifts.

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Carr, Bernard, Kazunori Kohri, Yuuiti Sendouda, and Jun’ichi Yokoyama. "Constraints on primordial black holes." Reports on Progress in Physics 84, no. 11 (November 1, 2021): 116902. http://dx.doi.org/10.1088/1361-6633/ac1e31.

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Abstract We update the constraints on the fraction of the Universe that may have gone into primordial black holes (PBHs) over the mass range 10−5 to 1050 g. Those smaller than ∼1015 g would have evaporated by now due to Hawking radiation, so their abundance at formation is constrained by the effects of evaporated particles on big bang nucleosynthesis, the cosmic microwave background (CMB), the Galactic and extragalactic γ-ray and cosmic ray backgrounds and the possible generation of stable Planck mass relics. PBHs larger than ∼1015 g are subject to a variety of constraints associated with gravitational lensing, dynamical effects, influence on large-scale structure, accretion and gravitational waves. We discuss the constraints on both the initial collapse fraction and the current fraction of the dark matter (DM) in PBHs at each mass scale but stress that many of the constraints are associated with observational or theoretical uncertainties. We also consider indirect constraints associated with the amplitude of the primordial density fluctuations, such as second-order tensor perturbations and μ-distortions arising from the effect of acoustic reheating on the CMB, if PBHs are created from the high-σ peaks of nearly Gaussian fluctuations. Finally we discuss how the constraints are modified if the PBHs have an extended mass function, this being relevant if PBHs provide some combination of the DM, the LIGO/Virgo coalescences and the seeds for cosmic structure. Even if PBHs make a small contribution to the DM, they could play an important cosmological role and provide a unique probe of the early Universe.

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Kholodov, Pavel, and Stéphane Moreau. "Identification of Noise Sources in a Realistic Turbofan Rotor Using Large Eddy Simulation." Acoustics 2, no. 3 (September 22, 2020): 691–706. http://dx.doi.org/10.3390/acoustics2030037.

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Large Eddy Simulation is performed using the NASA Source Diagnostic Test turbofan at approach conditions (62% of the design speed). The simulation is performed in a periodic domain containing one fan blade (rotor-alone configuration). The aerodynamic and acoustic results are compared with experimental data. The dilatation field and the dynamic mode decomposition (DMD) are employed to reveal the noise sources around the rotor. The trailing-edge radiation is effective starting from 50% of span. The strongest DMD modes come from the tip region. Two major noise contributors are shown, the first being the tip noise and the second being the trailing-edge noise. The Ffowcs Williams and Hawkings’ (FWH) analogy is used to compute the far-field noise from the solid surface of the blade. The analogy is computed for the full blade, for its tip region (outer 20% of span) and for lower 80% of span to see the contribution of the latter. The acoustics spectrum below 6 kHz is dominated by the tip part (tip noise), whereas the rest of the blade (trailing-edge noise) contributes more beyond that frequency.

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Zhang, X., X. X. Chen, and C. L. Morfey. "Acoustic Radiation from a Semi-Infinite Duct With a Subsonic Jet." International Journal of Aeroacoustics 4, no. 1-2 (January 2005): 169–84. http://dx.doi.org/10.1260/1475472053730075.

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The radiation of high-order spinning modes from a semi-infinite exhaust duct is studied numerically. The issues involved have applications to noise radiation from the exhaust duct of an aircraft engine. The numerical method is based on solutions of linearised Euler equations (LEE) for propagation in the duct and near field, and the acoustic analogy for far field radiation. A 2.5D formulation of a linearised Euler equation model is employed to accommodate a single spinning mode propagating over an axisymmetric mean flow field. In the solution process, acoustic waves are admitted into the propagation area surrounding the exit of an axisymmetric duct and its immediate downstream area. The wave admission is realised through an absorbing non-reflecting boundary treatment, which admits incoming waves and damps spurious waves generated by the numerical solutions. The wave propagation is calculated through solutions of linearised Euler equations, using an optimised prefactored compact scheme for spatial discretisation. Far field directivity is estimated by solving the Ffowcs Williams-Hawkings equations. The far field prediction is compared with analytic solutions with good agreement.

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Resende Coelho, Gustavo, James D. Goldschmidt, Henry J. Tingle, Peter G. Ifju, Ukeiley Lawrence, Ben Goldman, Maicon Secchi, and Steven A. Miller. "Aeroacoustic and aerodynamic interaction effects between electric vertical takeoff and landing rotors." Journal of the Acoustical Society of America 152, no. 4 (October 2022): A258. http://dx.doi.org/10.1121/10.0016201.

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Electric vertical take-off and landing (eVTOL) aircraft are characterized by their unconventional wing and electric rotor configurations, which involve both side-by-side and tandem rotor configurations. These configurations create unique aerodynamic and acoustic flow-fields. We numerically investigate the interaction effects between rotor pairs as well as their individual and combined acoustic radiation. We examine horizontal and vertical spacing, rotor tilt angles, and forward flight effects. Performance is characterized by thrust coefficient, blade passage frequency (BPF) sound pressure level (SPL), and overall sound pressure level (OASPL). This study is performed with a mid-fidelity aerodynamic solver, Dust, which is used to predict the aerodynamic flow-field. The tonal acoustic pressure at observer positions is predicted via the Farassat F-1A solution of the Ffowcs Williams and Hawkings equation utilizing the aerodynamic flow-field. The configurations studied show strong aerodynamic interaction effects in thrust, as well as out-of-plane acoustic radiation from the aft rotor. Base predictions of thrust and noise are validated via experimental measurement. As rotor separation decreases, we observe that aft rotor thrust decreases and BPF SPL increases. The most forward rotor, however, is marginally impacted by the interactions. [This research is supported by Archer Aviation Inc.]

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Shen, Weiqi, and Steven A. E. Miller. "Validation of a High-Order Large Eddy Simulation Solver for Acoustic Prediction of Supersonic Jet Flow." Journal of Theoretical and Computational Acoustics 28, no. 03 (September 2020): 1950023. http://dx.doi.org/10.1142/s2591728519500233.

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A high-order large eddy simulation (LES) code based on the flux reconstruction (FR) scheme is further developed for supersonic jet simulation. The FR scheme provides an efficient and easy-to-implement way to achieve high-order accuracy on an unstructured mesh. The order of accuracy and the shock capturing capability of the solver are validated with the isentropic Euler vortex and Sod’s shock tube problem. A heated under-expanded supersonic jet case from NASA’s Small Hot Jet Acoustic Rig (SHJAR) database is used for validation. The turbulence statistics along the nozzle centerline and lip-line are examined. We predict the acoustic radiation with the Ffowcs Williams and Hawkings method, which is integrated with our solver. The far-field acoustic predictions show reasonable agreement with the experimental measurement in the upstream and downstream directions, where the shock-associated noise and the large-scale turbulent mixing noise are dominant, respectively.

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YUAN, Mingchuan, Huixun SUN, Zhibin LI, Qingfeng NIU, and Feng FAN. "Numerical calculation and analysis of aero-acoustic characteristics of tilt rotor in different tilt angles." Xibei Gongye Daxue Xuebao/Journal of Northwestern Polytechnical University 42, no. 2 (April 2024): 205–13. http://dx.doi.org/10.1051/jnwpu/20244220205.

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The numerical calculation model for the aero-acoustic analysis of a tilt rotor was established by combining the free wake method and the FW-H (Ffowcs Williams-Hawkings) equation. The numerical method was validated by using the tilt rotor′s aero-acoustic test results. The aero-acoustic characteristics of dual tilt rotors that take into account the force and moment trim of an aircraft in its typical transition path were calculated. The unsteady air load of a rotor blade and its noise data in different observational positions were acquired. The acoustic directivity and sound pressure level of the tilt rotor in its different tilt angles were analysed. The results show that: the acoustic directivity characteristics of an isolate tilt rotor and dual tilt rotors were quite different due to the superposition and offset during noise radiation; the sound pressure level first increases and then decreases along with the rotor′s tilt angle; the maximum sound pressure level occurs at the tilt angle of 30 degree; the acoustic directivity and sound pressure level in different tilt angles vary due to multiple factors such as the Mach number at the rotor tip, air load and rotor orientation.

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Bernardini, Giovanni, Jacopo Serafini, Sandro Lanniello, and Massimo Gennaretti. "Assessment of Computational Models for the Effect of Aeroelasticity on BVI Noise Prediction." International Journal of Aeroacoustics 6, no. 3 (September 2007): 199–222. http://dx.doi.org/10.1260/147547207782419570.

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This paper deals with the computational analysis of acoustic fields generated by helicopter rotors when Blade-Vortex Interactions (BVI) occur. The prediction procedure starts from the determination of the steady periodic blade deformations. Then, the BVI-affected, unsteady aerodynamics solution is obtained by a potential-flow boundary integral formulation suited for aeronautical configurations experiencing blade-wake impingements. It is applicable to blades with arbitrary shape and motion and evaluates both wake distortion and blade pressure field. Finally, the noise field radiated by the rotor is computed through an aeroacoustic tool based on the Ffowcs Williams and Hawkings equation. The numerical investigation examines the sensitivity of BVI noise prediction on the aeroelastic model applied for the calculation of blade deformations, and assesses the accuracy of the results through correlation with experimental data concerning a helicopter main rotor in descent flight. Noise predicted is examined in terms of both acoustic pressure signatures and noise radiation characteristics.

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Rahier, Gilles, and Christophe Peyret. "Approximate computation of acoustic reflection and shadow effects using the Kirchhoff method." Acta Acustica 8 (2024): 58. http://dx.doi.org/10.1051/aacus/2024041.

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The article presents a fairly simple way to take solid bodies into account in acoustic radiation calculations using integral methods, while still using the free-space Green’s function. The approach is based on the Kirchhoff method and on a locally plane reflection assumption. It can be applied to both analytical noise sources and acoustic disturbances provided by numerical simulations, to fixed or mobile noise sources, concentrated or widely spread in a moving medium. The time-domain formulation is an important advantage for periodic signals rich in harmonics (rotors or propellers impulsive noise) and for broadband signals (profile or jet noise). The formulation and calculation algorithm are described in detail. The method’s accuracy and limitations are shown first by comparing the results with analytical solutions for the acoustic scattering of a point source by a sphere, for a fluid at rest. An application example is then given for a wing in a Mach 0.5 flow, and the results are compared with the numerical solution of the linearized Euler equations, in the presence of a mean flow. In addition, the article proposes expressions for direct calculation of the pressure gradient by Kirchhoff and Ffowcs Williams-Hawkings surface formulations.

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Morfey, C. L., S. V. Sorokin, and G. Gabard. "The effects of viscosity on sound radiation near solid surfaces." Journal of Fluid Mechanics 690 (December 1, 2011): 441–60. http://dx.doi.org/10.1017/jfm.2011.449.

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AbstractAlthough the acoustic analogy developed by Lighthill, Curle, and Ffowcs Williams and Hawkings for sound generation by unsteady flow past solid surfaces is formally exact, it has become accepted practice in aeroacoustics to use an approximate version in which viscous quadrupoles are neglected. Here we show that, when sound is radiated by non-rigid surfaces, and the smallest dimension is comparable to or less than the viscous penetration depth, neglect of the viscous-quadrupole term can cause large errors in the sound field. In addition, the interpretation of the viscous quadrupoles as contributing only to sound absorption is shown to be inaccurate. Comparisons are made with the scalar wave equation for linear waves in a viscous fluid, which is extended using generalized functions to describe the effects of solid surfaces. Results are also presented for two model problems, one in a half-space and one with simple cylindrical geometry, for which analytical solutions are available.

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Chen, Yung-Wei, Cheng-Cheng Pan, Yi-Hsien Lin, Chao-Feng Shih, Jian-Hong Shen, and Chun-Ming Chang. "Acoustic Field Radiation Prediction and Verification of Underwater Vehicles under a Free Surface." Journal of Marine Science and Engineering 11, no. 10 (October 8, 2023): 1940. http://dx.doi.org/10.3390/jmse11101940.

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This study aimed to examine the acoustic field radiated by propellers and underwater vehicles. For the verification of sound radiation in underwater vehicles, numerical methods are widely used in addition to experiments and propeller blade frequencies for calculation and validation. Numerical convergence and accuracy are more important for near-field and far-field problems. This paper uses the boundary element method (BEM) to assess the convergence of the finite volume method (FVM). In this study, the FVM, including the Reynolds-averaged Navier–Stokes method and the Ffowcs Williams–Hawkings (FW-H) acoustic model, is used to investigate the influence of various geometric inflows on the hydrodynamic and noise performance of the propeller. Then, the sound radiation of the FVM is compared with the BEM at the far field to determine the number of meshed elements. Furthermore, spectral analysis is being conducted to examine the noise generated by the underwater vehicle and propeller. The objective is to investigate the influence of the free surface on propeller efficiency. After verifying the numerical simulation, the results indicate that a relationship can be established between water pressure and propeller thrust under specific conditions. This relationship can be used to estimate the magnitude of propeller thrust at different water depths. The simulated results of propeller thrust, torque coefficient, propulsion efficiency, and sound radiation in this study are consistent with experimental values. This demonstrates the accuracy and practicality of the findings of numerical procedures in engineering applications.

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Dai, Wen-Qiang, Xu Zheng, Zhi-Yong Hao, Yi Qiu, Heng Li, and Le Luo. "Aerodynamic noise radiating from the inter-coach windshield region of a high-speed train." Journal of Low Frequency Noise, Vibration and Active Control 37, no. 3 (January 7, 2018): 590–610. http://dx.doi.org/10.1177/1461348417747178.

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The aerodynamic noise has been the dominant factor of noise issues in high-speed train as the traveling speed increases. The inter-coach windshield region is considered as one of the main aerodynamic noise sources; however, the corresponding characteristics have not been well investigated. In this paper, a hybrid method is adopted to study the aerodynamic noise around the windshield region. The effectiveness of simulation methods is validated by a simple case of cavity noise. After that, the Reynolds-averaged Navier–Stokes simulation is used to obtain the characteristics of flow field around the windshield region, which determine the aerodynamic noise. Then the nonlinear acoustic solver approach is employed to acquire the near-field noise, while the Ffowcs-Williams/Hawking equation is solved for far-field acoustic propagation. The results indicate that the windshield region is approximately an open cavity filled with severe disturbance flow. According to the analysis of sound pressure distribution in the near-acoustic field, both sides of the windshield region appear symmetrical two-lobe shape with different directivities. The results of frequency spectrum analysis indicate that the aerodynamic noise inside inter-coach space is a typical broadband one from 100 Hz to 5k Hz, and most acoustic power is restricted in the low-medium frequency range (below 500 Hz). In addition, the acoustic power in the low frequency range (below 100 Hz) is closely related to the cavity resonance with the resonance peak frequency of 42 Hz. The overall sound pressure level at different speeds shows that the acoustic power grows approximately 5th power of the train speed. Two forms of outside-windshields are designed to reduce the noise around the windshield region, and the results show the full-windshield form is better in noise reduction, which apparently eliminates interior cavity noise of inter-coach space and lessens the overall sound pressure level on the sides of near-field by about 13 dB.

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Li Volsi, Pietro, Gianluigi Brogna, Romain Gojon, Thierry Jardin, Hélène Parisot-Dupuis, and Jean-Marc Moschetta. "Analysis of MAV Rotors Optimized for Low Noise and Aerodynamic Efficiency with Operational Constraints." Fluids 9, no. 4 (April 19, 2024): 96. http://dx.doi.org/10.3390/fluids9040096.

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The rapid growth of drone use in urban areas has prompted authorities to review airspace regulations, forcing drone manufacturers to anticipate and reduce the noise emissions during the design stage. Additionally, micro air vehicles (MAVs) are designed to be aerodynamically efficient, allowing them to fly farther, longer and safer. In this study, a steady aerodynamic code and an acoustic propagator based on the non-linear vortex lattice method (NVLM) and Farassat’s formulation-1A of the Ffowcs Williams and Hawkings (FW-H) acoustic analogy, respectively, are coupled with pymoo, a python-based optimization framework. This tool is used to perform a multi-objective (noise and aerodynamic efficiency) optimization of a 20 cm diameter two-bladed rotor under hovering conditions. From the set of optimized results, (i.e., the Pareto front), three different rotors are 3D-printed using a stereolithography (SLA) technique and tested in an anechoic room. Here, an array of far-field microphones captures the acoustic radiation and directivity of the rotor, while a balance measures the aerodynamic performance. Both the aerodynamic and aeroacoustic performance of the three different rotors, in line with what has been predicted by the numerical codes, are compared and guidelines for the design of aerodynamically and aeroacoustically efficient MAV rotors are extracted.

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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 (September 11, 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 accelerated by a 3-D FMM to reduce computational cost. The proposed method is referred to as Fast FW-H in this work. The performance and efficiency of the proposed methodology are demonstrated using several examples. First, aeroacoustic predictions for the cases of a stationary acoustic monopole, moving acoustic monopole and stationary acoustic dipole in a uniform flow are studied, generally showing good agreement with the analytical solutions. Second, the sound field radiating from a flow passing a finite-length circular cylinder and the propeller of an unmanned aerial vehicle (UAV) during forward flight are studied, and the computed results obtained via the FW-H and Fast FW-H methods in the time domain with a stationary, permeable surface are compared. The overall computational efficiency of the sound field solutions obtained via the Fast FW-H method is found to be approximately two times faster than the computational efficiency of the original FW-H method, indicating that this proposed approach can be an accurate and efficient computational tool for modelling far-field aeroacoustic problems.

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Li, Zhengnong, and Jianan Li. "Numerical Simulation Study of Aerodynamic Noise in High-Rise Buildings." Applied Sciences 12, no. 19 (September 21, 2022): 9446. http://dx.doi.org/10.3390/app12199446.

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In order to study the aerodynamic noise on the surfaces of high-rise buildings under the action of strong winds, this paper numerically simulated the sound pressure field on the surface of a high-rise building using the large-eddy simulation method combined with the acoustic analog method of FW-H (Ffowcs Williams–Hawkings) equation and obtained the intensity radiation distribution of sound pressure on the surface of the building to further identify the area with the maximum sound pressure intensity of the noise radiation and thus achieve the purpose of locating noise source. The accuracy of the numerical simulation results for aerodynamic noise obtained in this paper was then verified by comparing with the acoustic wind tunnel experimental results. The locations of noise source obtained by numerical simulation and acoustic wind tunnel experiment were in good agreement. The sound pressure intensity pulsation time course was measured by the acoustic wind tunnel experiment, and the noise sound pressure level spectrum of each part of the building surface was obtained by fast Fourier transform (FFT). Furthermore, the spectral characteristics of the noise sound pressure level were analyzed. The results of the sound pressure level spectrum of aerodynamic noise obtained from the numerical simulation were compared with the acoustic wind tunnel experimental results, which were found to be very similar. The analysis of the sound pressure level spectrum of aerodynamic noise on the building surface reveals that the numerical simulation results in the middle- and high-frequency bands of the spectrum are in good agreement with the acoustic wind tunnel experimental results, but there is a difference between those in the low-frequency bands and the acoustic wind tunnel experimental results. The microphone array used to locate the noise source in the acoustic wind tunnel was found to suffer non-eliminable measurement errors, which might be a potential reason for a reasonably slight difference between the experimental and numerical simulation results. The background noise in the low-frequency band of the acoustic wind tunnel sound pressure level spectrum was relatively large, while there was basically no background noise in the numerical simulation. This paper shows that the numerical simulation method combined with large-eddy simulation and acoustic analogy (FW-H) can calculate the aerodynamic noise intensity at various points on the surfaces of high-rise buildings and reasonably predict the location of sound source. In addition, the numerical simulation results are similar to the acoustic wind tunnel experimental results in most frequency bands.

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Malefaki, Iro, and Kostas Belibassakis. "A Novel FDTD–PML Scheme for Noise Propagation Generated by Biomimetic Flapping Thrusters in the Ocean Environment." Journal of Marine Science and Engineering 10, no. 9 (September 3, 2022): 1240. http://dx.doi.org/10.3390/jmse10091240.

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Biomimetic flapping-foil thrusters can operate efficiently while offering desirable levels of thrust required for the propulsion of a small vessel or an Autonomous Underwater Vehicle (AUV). These systems have been studied both as main propulsion devices and for augmenting ship propulsion in waves. In this work, the unsteady hydrofoil loads are used to calculate the source terms of the Ffowcs Williams–Hawkings (FW-H) equation which is applied to model noise propagation in the underwater ocean acoustic environment. The solution provided by a simplified version of the Farassat formulation in free space is extended to account for a bounded domain and an inhomogeneous medium, characterizing the sea acoustic waveguide. Assuming the simplicity azimuthal symmetry of the environmental parameters, a numerical model is developed based on a Finite Difference Time Domain (FDTD) scheme, incorporating free-surface and seabed effects, in the presence of a variable sound speed profile. For the treatment of the outgoing radiating field, a Perfectly Matched Layer (PML) technique is implemented. Numerical results are presented illustrating the applicability of the method.

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Wei, Aibo, Shunhao Wang, Xu Gao, Limin Qiu, Lianyan Yu, and Xiaobin Zhang. "Investigation of unsteady cryogenic cavitating flow and induced noise around a three-dimensional hydrofoil." Physics of Fluids 34, no. 4 (April 2022): 042120. http://dx.doi.org/10.1063/5.0088092.

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In this paper, the Large Eddy Simulation (LES) combined with the Schnerr–Sauer cavitation model and the permeable Ffowcs Williams–Hawkings (FW-Hpds) acoustic analogy approach are introduced to study the unsteady cavitation behaviors and the radiated noise characteristics of the transient liquid nitrogen (LN2) cavitating flow around a NACA66 (National Advisory Committee for Aeronautics) hydrofoil. Satisfactory agreement is obtained between the numerical predictions and experimental measurements. The cavitation noise is predicted based on the sound radiation theory for spherical bubbles and compared with the sound pressure levels of non-cavitating flow from the FW-Hpds equation. It is found that the cavity volume acceleration is directly responsible for driving the generation of cavitation noise, and the sound pressure caused by the development of LN2 cavitation is shown to vary with the periodic pulsing cavity volume evolution, indicating a strong link between cavity evolutions and radiated noises. The transient cavitation structures of the sheet and cloud cavitation are well captured, and the evolution features of the cavities and vortex structures are analyzed in detail. The collapse of the detached small cloud cavity downstream is the main mechanism for generating intense acoustic impulses for both sheet and cloud cavitation. While the strong interaction between the re-entrant jet and the main flow results in violent pressure fluctuations, and thus produces instantaneous extreme dipole noise, which accounts for another distinctive mechanism to induce intense acoustic impulses for cloud cavitation, the presented study provides a deep understanding of the nature of cavitation-dominated noise for cryogenic cavitating flow.

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Lyrintzis, Anastasios S. "Surface Integral Methods in Computational Aeroacoustics—From the (CFD) Near-Field to the (Acoustic) Far-Field." International Journal of Aeroacoustics 2, no. 2 (April 2003): 95–128. http://dx.doi.org/10.1260/147547203322775498.

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A review of recent advances in the use of surface integral methods in Computational AeroAcoustics (CAA) for the extension of near-field CFD results to the acoustic far-field is given. These integral formulations (i.e. Kirchhoff's method, permeable (porous) surface Ffowcs-Williams Hawkings (FW-H) equation) allow the radiating sound to be evaluated based on quantities on an arbitrary control surface if the wave equation is assumed outside. Thus only surface integrals are needed for the calculation of the far-field sound, instead of the volume integrals required by the traditional acoustic analogy method (i.e. Lighthill, rigid body FW-H equation). A numerical CFD method is used for the evaluation of the flow-field solution in the near field and thus on the control surface. Diffusion and dispersion errors associated with wave propagation in the far-field are avoided. The surface integrals and the first derivatives needed can be easily evaluated from the near-field CFD data. Both methods can be extended in order to include refraction effects outside the control surface. The methods have been applied to helicopter noise, jet noise, propeller noise, ducted fan noise, etc. A simple set of portable Kirchhoff/FW-H subroutines can be developed to calculate the far-field noise from inputs supplied by any aerodynamic near/mid-field CFD code.

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Song, Yang, Pingjian Ming, and Bo Xun. "Research on similarity law of the flow-induced noise of the submarine." Journal of the Acoustical Society of America 156, no. 6 (December 1, 2024): 4010–23. https://doi.org/10.1121/10.0034606.

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Flow-induced noise is a complex source that significantly impacts submarines' stealth performance. While previous studies have provided valuable insights into the acoustic radiation of scaled-down submarine models, addressing the flow noise of full-scale prototypes has remained a daunting challenge. To bridge this gap, the research team undertook an extensive investigation to unveil the elusive similarity law of flow noise in both small and large-scale submarine models. By leveraging computational algorithms and turbulence models, the flow field of the submarine model was simulated, and the Kirchhoff and Ffowcs Williams–Hawkings model was employed to calculate the submarine's flow noise. This comprehensive study meticulously considered various influential factors, including Mach number, Reynolds number, etc., ultimately formulating a similarity correlation formula for submarine flow noise. The findings of this study revealed several key insights, including the minimal impact of accessories on submarine flow noise similarity, the adherence of the frequency of submarine flow noise to the Helmholtz number, and the intricate relationship between sound pressure level similarity law with Mach and Reynolds number. Ultimately, this study introduces and summarizes the submarine flow noise similarity law. This law enables the estimation of real-scale model flow noise by using small-scale model flow noise as a reference.

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Zhang, Chunyu, Qiang Xu, He Yang, Zilong Peng, Jiangqiao Li, and Jialiang Zhou. "Experimental Study and Numerical Simulation of Radiated Noise from Unmanned Underwater Vehicle." Polish Maritime Research 31, no. 4 (December 1, 2024): 131–41. https://doi.org/10.2478/pomr-2024-0057.

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Abstract This paper focuses on the research of the radiation noise of underwater unmanned vehicle (UUV), which is one of the most important indicators for evaluating the performance of underwater unmanned equipment. Integrating experimental study and numerical calculations, this paper investigates the underwater radiated noise characteristics and hydrodynamic properties of the propeller of UUV. Firstly, an open-water radiated noise experiment is conducted. To ensure the accuracy of acoustic test, the UUV are held stationary during the experiment. Then, the hydrodynamic performance of a propeller in a steady flow field is calculated using Computational Fluid Dynamics (CFD). Finally, the noise in the unsteady flow field is calculated using the Ffowcs Williams-Hawkings (FW-H) equation. The results show that the propeller, as the main noise source when the UUV is working, exhibits distinct characteristic line spectra in the frequency response curve. By comparing the numerical and experimental results, it was found that the overall trend of the sound pressure level is similar. But the line spectrum characteristics of the numerical results between 100 and 400 Hz are more obvious, mainly because the simulation model is more idealized compared to the experimental tests. The study further examines the hydrodynamic characteristics, propeller noise, and directional characteristics of UUV under different operating conditions.

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Delbari, Seyed Hamid, Amir Nejat, Mohammad H. Ahmadi, Ali Khaleghi, and Marjan Goodarzi. "Numerical modeling of aeroacoustic characteristics of different savonius blade profiles." International Journal of Numerical Methods for Heat & Fluid Flow 30, no. 6 (June 19, 2019): 3349–69. http://dx.doi.org/10.1108/hff-12-2018-0764.

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Purpose This study aims to carry out numerical modeling to predict aerodynamic noise radiation from four different Savonius rotor blade profile. Design/methodology/approach Incompressible unsteady reynolds-averaged navier-stokes (URANS) approach using gamma–theta turbulence model is conducted to obtain the time accurate turbulent flow field. The Ffowcs Williams and Hawkings (FW-H) acoustic analogy formulation is used for noise predictions at optimal tip speed ratio (TSR). Findings The mean torque and power coefficients are compared with the experimental data and acceptable agreement is observed. The total and Mono+Dipole noise graphs are presented. A discrete tonal component at low frequencies in all graphs is attributed to the blade passing frequency at the given TSR. According to the noise prediction results, Bach type rotor has the lowest level of noise emission. The effect of TSR on the noise level from the Bach rotor is investigated. A direct relation between angular velocity and the noise emission is found. Practical implications The savonius rotor is a type of vertical axis wind turbines suited for mounting in the vicinity of residential areas. Also, wind turbines wherein operation are efficient sources of tonal and broadband noises and affect the inhabitable environment adversely. Therefore, the acoustic pollution assessment is essential for the installation of wind turbines in residential areas. Originality/value This study aims to investigate the radiated noise level of four common Savonius rotor blade profiles, namely, Bach type, Benesh type, semi-elliptic and conventional. As stated above, numbers of studies exploit the URANS method coupled with the FW-H analogy to predict the aeroacoustics behavior of wind turbines. Therefore, this approach is chosen in this research to deal with the aeroacoustics and aerodynamic calculation of the flow field around the aforementioned Savonius blade profiles. The effect of optimal TSR on the emitted noise and the contribution of thickness, loading and quadrupole sources are of interest in this study.

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Zhu, Weijun, Jiaying Liu, Zhenye Sun, Jiufa Cao, Guangxing Guo, and Wenzhong Shen. "Numerical Study on Flow and Noise Characteristics of an NACA0018 Airfoil with a Porous Trailing Edge." Sustainability 15, no. 1 (December 24, 2022): 275. http://dx.doi.org/10.3390/su15010275.

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An airfoil with a porous trailing edge has a low noise emission; thus, using a porous medium is a good technique for further reduction of wind turbine noise. In this paper, to reduce airfoil trailing edge noise while minimizing the negative influence of a porous medium on aerodynamic performance, a new filling method is proposed such that a porous medium is only used in the suction side half of the trailing edge, which is more sensitive to the noise generation. The large eddy simulation (LES) technique for flow and the Ffowcs Williams and Hawkings (FW-H) method for acoustics are used. At a Reynolds number of 2.63 × 105 and various angles of attack, an NACA0018 airfoil profile with a porous trailing edge covering 20% of the chord is studied under two porous configurations, namely a fully porous and a suction-side porous trailing edge type. The results show that the flow direction, velocity magnitude, and their distributions along the boundary layer of the two porous airfoils are significantly modified due to the presence of the porous medium. The fluctuation of the pressure coefficient and the increase in the boundary layer thickness are significant at low angles of attack. As compared to the solid airfoil counterpart, the noise radiation from the newly proposed suction-side porous airfoil achieves a noise reduction of 4.3 dB at an angle of attack α = 0°, and a noise reduction of 4.07 dB at an angle of attack α = 2°.

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Su, Taoyong, Yang Lu, Jinchao Ma, and Shujun Guan. "Electrically Controlled Rotor Blade Vortex Interaction Airloads and Noise Analysis Using Viscous Vortex Particle Method." Shock and Vibration 2019 (November 6, 2019): 1–15. http://dx.doi.org/10.1155/2019/9678970.

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An electrically controlled rotor (ECR), also called a swashplateless rotor, replaces a swashplate with a trailing-edge flap system to implement primary rotor control. To investigate the aerodynamic characteristics of an ECR in blade-vortex interaction (BVI) condition, an analysis model based on the viscous vortex particle method, ECR blade pitch equation, and the Weissinger-L lifting surface model is established. In this model, the ECR wake flow field vorticity is discretized as multiple vortex particles, and the vorticity-velocity form of the Navier-Stokes equation is solved to simulate the transport diffusion of the vorticity. The flap motion-inducing blade-pitch movement is obtained by solving the ECR blade-pitch movement equation via the Runge–Kutta fourth-order method. On the basis, BVI noise radiation of an ECR is evaluated using the Ffowcs Williams and Hawkings (FW-H) equation. Based on the present prediction model, the aerodynamic and acoustic characteristics of a sample ECR in BVI condition are analyzed. The results show that since the BVI event of the ECR on the advancing side is mainly caused by the interaction between the flap tip vortex and the blade, the blade spanwise range of ECR BVI occurrence on the advancing side is smaller than that of the conventional rotor. In addition, the magnitude of the maximum sound pressure level on the advancing side as well as on the retreating side of the ECR is also different from that of the conventional rotor, which is consistent with the difference in the airloads between the ECR and conventional rotor. Furthermore, a study was performed to examine the effect of the pre-index angle on the BVI-induced airloads and noise. The amplitude of the impulsive airloads of the ECR on the advancing side is increased with the increase in pre-index angle, while the amplitude of the impulsive airloads of the ECR on the retreating side is decreased. Indeed, when the pre-index angle of the sample ECR is 8 degrees, the retreating-side noise radiation lobe is almost disappeared. In addition, the different intensity of wake vorticity is the main reason for the differences of the BVI-induced airloads and noise among the ECR with different pre-index angles.

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Liu, Enbin, Shanbi Peng, and Tiaowei Yang. "Noise-silencing technology for upright venting pipe jet noise." Advances in Mechanical Engineering 10, no. 8 (August 2018): 168781401879481. http://dx.doi.org/10.1177/1687814018794819.

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When a natural gas transmission and distribution station performs a planned or emergency venting operation, the jet noise produced by the natural gas venting pipe can have an intensity as high as 110 dB, thereby severely affecting the production and living environment. Jet noise produced by venting pipes is a type of aerodynamic noise. This study investigates the mechanism that produces the jet noise and the radiative characteristics of jet noise using a computational fluid dynamics method that combines large eddy simulation with the Ffowcs Williams–Hawkings acoustic analogy theory. The analysis results show that the sound pressure level of jet noise is relatively high, with a maximum level of 115 dB in the low-frequency range (0–1000 Hz), and the sound pressure level is approximately the average level in the frequency range of 1000–4000 Hz. In addition, the maximum and average sound pressure levels of the noise at the same monitoring point both slightly decrease, and the frequency of the occurrence of a maximum sound pressure level decreases as the Mach number at the outlet of the venting pipe increases. An increase in the flow rate can result in a shift from low-frequency to high-frequency noise. Subsequently, this study includes a design of an expansion-chamber muffler that reduces the jet noise produced by venting pipes and an analysis of its effectiveness in reducing noise. The results show that the expansion-chamber muffler designed in this study can effectively reduce jet noise by 10–40 dB and, thus, achieve effective noise prevention and control.

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Avallone, F., W. C. P. van der Velden, D. Ragni, and D. Casalino. "Noise reduction mechanisms of sawtooth and combed-sawtooth trailing-edge serrations." Journal of Fluid Mechanics 848 (June 8, 2018): 560–91. http://dx.doi.org/10.1017/jfm.2018.377.

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Trailing-edge serrations are add ons retrofitted to wind-turbine blades to mitigate turbulent boundary-layer trailing-edge noise. This manuscript studies the physical mechanisms behind the noise reduction by investigating the far-field noise and the hydrodynamic flow field. A conventional sawtooth and a combed-sawtooth trailing-edge serration are studied. Combed-sawtooth serrations are obtained by filling the empty space between the teeth with combs (i.e. solid filaments). Both serration geometries are retrofitted to a NACA 0018 aerofoil at zero degree angle of attack. Computations are carried out by solving the explicit, transient, compressible lattice Boltzmann equation, while the acoustic far field is obtained by means of the Ffowcs Williams and Hawkings analogy. The numerical results are validated against experiments. It is confirmed that the combed-sawtooth serrations reduce noise more than the conventional sawtooth ones for the low- and mid-frequency range. It is found that the presence of combs affects the intensity of the scattered noise but not the frequency range of noise reduction. For both configurations, the intensity of the surface pressure fluctuations decreases from the root to the tip, and noise sources are mainly located at the serrations root for the low- and mid-frequency range. The presence of the filaments generates a more uniform distribution of the noise sources along the edges with respect to the conventional serration. The installation of combs mitigates the interaction between the two sides of the aerofoil at the trailing edge and the generation of a turbulent wake in the empty space between teeth. As a result, the inward (i.e. from the serration edge to the centreline) and outward (i.e. from the serration centreline to the edge) flow motions, due to the presence of the teeth, are mitigated. It is found that the installation of serrations affects the surface pressure fluctuations integral parameters. Both the spanwise correlation length and convective velocity of the surface pressure fluctuations increase with respect to the baseline straight configuration. When both quantities are similar to the one obtained for the straight trailing edge, the effect of the slanted edge is negligible, thus corresponding to no noise reduction. It is concluded that the changes in sound radiation are mainly caused by destructive interference of the radiated sound waves for which a larger spanwise correlation length is beneficial. Finally, the difference between measurements and the literature is caused by an incorrect modelling of the spanwise correlation length, which shows a different decay rate with respect to the one obtained for a straight trailing edge.

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"Modified Metrics of Acoustic Black Holes: A Review." Physical Science & Biophysics Journal 7, no. 1 (January 5, 2023): 1–13. http://dx.doi.org/10.23880/psbj-16000245.

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In this brief review, we will address acoustic black holes arising from quantum field theory in the Lorentz-violating and non-commutative background. Thus, we consider canonical acoustic black holes with effective metrics for the purpose of investigating Hawking radiation and entropy. We show that due to the generalized uncertainty principle and the modified dispersion relation, the Hawking temperature is regularized, that is, free from the singularity when the horizon radius goes to zero. In addition, we also find logarithmic corrections in the leading order for entropy.

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Dave, Shreyansh S., Oindrila Ganguly, P. S. Saumia, and Ajit Mohan Srivastava. "Hawking radiation from acoustic black holes in hydrodynamic ﬂow of electrons." Europhysics Letters, August 29, 2022. http://dx.doi.org/10.1209/0295-5075/ac8d71.

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Abstract Acoustic black holes are formed when a ﬂuid ﬂowing with subsonic velocities, accelerates and becomes supersonic. When the ﬂow is directed from the subsonic to supersonic region, the surface on which the normal component of ﬂuid velocity equals the local speed of sound acts as an acoustic horizon. This is because no acoustic perturbation from the supersonic region can cross it to reach the subsonic part of the ﬂuid. One can show that if the ﬂuid velocity is locally irrotational, the ﬁeld equations for acoustic perturbations of the velocity potential are identical to that of a massless scalar ﬁeld propagating in a black hole background. One, therefore, expects Hawking radiation in the form of a thermal spectrum of phonons. There have been numerous investigations of this possibility, theoretically, as well as experimentally, in systems ranging from cold atom systems to quark-gluon plasma formed in relativistic heavy-ion collisions. Here we investigate this possibility in the hydrodynamic ﬂow of electrons. Resulting Hawking radiation in this case should be observable in terms of current ﬂuctuations. Further, current ﬂuctuations on both sides of the acoustic horizon should show correlations expected for pairs of Hawking particle.

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Sakalli, I., A. Övgün, and K. Jusufi. "GUP assisted Hawking radiation of rotating acoustic black holes." Astrophysics and Space Science 361, no. 10 (September 13, 2016). http://dx.doi.org/10.1007/s10509-016-2922-x.

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Recati, A., N. Pavloff, and I. Carusotto. "Bogoliubov theory of acoustic Hawking radiation in Bose-Einstein condensates." Physical Review A 80, no. 4 (October 7, 2009). http://dx.doi.org/10.1103/physreva.80.043603.

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Anacleto, M. A., F. A. Brito, and E. Passos. "Hawking radiation and stability of the canonical acoustic black holes." Annals of Physics, May 2023, 169364. http://dx.doi.org/10.1016/j.aop.2023.169364.

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Horstmann, B., B. Reznik, S. Fagnocchi, and J. I. Cirac. "Hawking Radiation from an Acoustic Black Hole on an Ion Ring." Physical Review Letters 104, no. 25 (June 24, 2010). http://dx.doi.org/10.1103/physrevlett.104.250403.

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Vieira, H. S., and V. B. Bezerra. "Acoustic black holes: massless scalar field analytic solutions and analogue Hawking radiation." General Relativity and Gravitation 48, no. 7 (June 10, 2016). http://dx.doi.org/10.1007/s10714-016-2082-x.

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Gerace, Dario, and Iacopo Carusotto. "Analog Hawking radiation from an acoustic black hole in a flowing polariton superfluid." Physical Review B 86, no. 14 (October 4, 2012). http://dx.doi.org/10.1103/physrevb.86.144505.

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Balbinot, Roberto, Alessandro Fabbri, Serena Fagnocchi, Alessio Recati, and Iacopo Carusotto. "Nonlocal density correlations as a signature of Hawking radiation from acoustic black holes." Physical Review A 78, no. 2 (August 19, 2008). http://dx.doi.org/10.1103/physreva.78.021603.

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Journal articles on the topic 'Acoustic Hawking radiation'

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