Numerical Prediction of Trailing Edge Noise at Low Reynolds Number with Modified Trailing Edges of a NACA 0015 Airfoil

Authors

  • Mohamed Ibren Department of Mechanical Engineering, Kulliyyah of Engineering, International Islamic University Malaysia, Kuala Lumpur, 53100, Malaysia
  • Amelda Dianne Andan Department of Mechanical Engineering, Kulliyyah of Engineering, International Islamic University Malaysia, Kuala Lumpur, 53100, Malaysia
  • Waqar Asrar Department of Mechanical Engineering, Kulliyyah of Engineering, International Islamic University Malaysia, Kuala Lumpur, 53100, Malaysia

DOI:

https://doi.org/10.37934/cfdl.16.8.6494

Keywords:

Low-Reynolds Number, NACA0015 Airfoil, Aeroacoustics, Trailing-Edge Noise, Serration, Comb

Abstract

Global concern about high noise levels in areas near airports and wind farms has generated interest from various groups due to factors such as potential health problems and dissatisfaction among the local community. To accommodate this worthwhile plan of further reducing overall noise levels, some researchers are working on lowering the contribution of trailing-edge noise. The original scientific contribution of this study lies on understanding the efficiency of various trailing edge designs such as baseline, serrations, comb and comb-serrated, across different angles of attack and Reynolds numbers, while also addressing the limitations of existing geometrical models for trailing edges. The study intends to examine the performance of these different configurations, with an emphasis on their effect on acoustic responses. By utilizing large-eddy simulation and applying the Ffowcs-Williams and Hawkings models for noise prediction, an investigation was conducted to assess the impact of these trailing edge configurations on radiated noise at a low Reynolds number of 1.6× 105. The numerical predictions of lift coefficient and surface pressure fluctuations are compared and validated with a published study and experimental data, showing satisfactory results. Further analysis of these study has demonstrated that prominent peaks at lower frequencies (<103) are observed, which are identified as the characteristic frequencies. Moreover, results showed irregular broadband noise (300 - 600 Hz) with increased noise and shifting peak frequency as angle of attack rose. The serrated trailing edge design notably reduced noise levels by roughly 21 dB, especially for low frequencies. Comb-serration increased high-frequency noise by about 9 dB for angles of attack at 0, -1, and -20, and achieved a reduction of approximately 9 dB for angles of attack at 1 and 20. On the other hand, the directivity pattern showed that the maximum noise level is observed to predominantly radiate at an azimuth angle of around 90 degrees for all the cases, ranging from 900 to 2700, indicating that the majority of the source's acoustic energy is being emitted on the suction and pressure sides of the airfoil.

Downloads

Download data is not yet available.

Author Biographies

Mohamed Ibren, Department of Mechanical Engineering, Kulliyyah of Engineering, International Islamic University Malaysia, Kuala Lumpur, 53100, Malaysia

mohamed.ibren@gmail.com

Amelda Dianne Andan, Department of Mechanical Engineering, Kulliyyah of Engineering, International Islamic University Malaysia, Kuala Lumpur, 53100, Malaysia

ameldadianne@iium.edu.my

Waqar Asrar, Department of Mechanical Engineering, Kulliyyah of Engineering, International Islamic University Malaysia, Kuala Lumpur, 53100, Malaysia

waqar@iium.edu.my

References

Roslan, Siti Amni Husna, Zainudin A. Rasid, and Ahmad Kamal Ariffin. "Extended blade element momentum theory for the design of small-scale wind turbines." Journal of Advanced Research in Applied Mechanics 101, no. 1 (2023): 62-75. https://doi.org/10.37934/aram.101.1.6275

Celik, Alper, J. Luke Bowen, and Mahdi Azarpeyvand. "Effect of trailing-edge bevel on the aeroacoustics of a flat-plate." Physics of Fluids 32, no. 10 (2020). https://doi.org/10.1063/5.0024248

Wang, Lei, Xiaomin Liu, and Dian Li. "Noise reduction mechanism of airfoils with leading-edge serrations and surface ridges inspired by owl wings." Physics of Fluids 33, no. 1 (2021). https://doi.org/10.1063/5.0035544

Chong, Tze Pei, and Elisa Dubois. "Optimization of the poro-serrated trailing edges for airfoil broadband noise reduction." The Journal of the Acoustical Society of America 140, no. 2 (2016): 1361-1373. https://doi.org/10.1121/1.4961362

Vemuri, S. H., Xiao Liu, B. Zang, and Mahdi Azarpeyvand. "On the use of leading-edge serrations for noise control in a tandem airfoil configuration." Physics of Fluids 32, no. 7 (2020). https://doi.org/10.1063/5.0012958

Ramli, Muhammad Ridzwan, Wan Mazlina Wan Mohamed, Hamid Yusoff, Mohd Azmi Ismail, Ahmed Awaludeen Mansor, Azmi Hussin, and Aliff Farhan Mohd Yamin. "The Aerodynamic Characteristics Investigation on NACA 0012 Airfoil with Owl’s Wing Serrations for Future Air Vehicle." Journal of Advanced Research in Fluid Mechanics and Thermal Sciences 102, no. 1 (2023): 171-183. https://doi.org/10.37934/arfmts.102.1.171183

Jefferies, R. "Continuous Lower Energy, Emissions and Noise (CLEEN) Program." In USACA Spring Association Meeting, 21 May. 2013.

Dobrzynski, Werner. "Almost 40 years of airframe noise research: what did we achieve?." Journal of aircraft 47, no. 2 (2010): 353-367. https://doi.org/10.2514/1.44457

Kallas, Siim, Máire Geoghegan-Quinn, M. Darecki, C. Edelstenne, T. Enders, E. Fernandez, and P. Hartman. "Flightpath 2050 Europe’s vision for aviation." Report of the high level group on aviation research, European commission, Brussels, Belgium, Report No. EUR 98. 2011.

Camussi, Roberto, and Gareth J. Bennett. "Aeroacoustics research in Europe: The CEAS-ASC report on 2019 highlights." Journal of Sound and Vibration 484 (2020): 115540. https://doi.org/10.1016/j.jsv.2020.115540

Chin, Wen Jun, Kai Sheng See, Yu Han Ng, Jie Ling Gan, and Sing Yee Lim. "Technologies for Indoor Noise Attenuation: A Short Review." Progress in Energy and Environment (2019): 1-10.

Gély, Denis, and Gareth J. Bennett. "Aeroacoustics research in Europe: The CEAS-ASC report on 2018 highlights." Journal of Sound and Vibration 463 (2019): 114950. https://doi.org/10.1016/j.jsv.2019.114950

World Health Organization. Environmental noise guidelines for the European region. World Health Organization. Regional Office for Europe, 2018.

Uppu, Shiva Prasad, and Naren Shankar Radha Krishnan. "Turbulent Airflows over Serrated Wings: A Review on Experimental and Numerical Analysis." Journal of Advanced Research in Fluid Mechanics and Thermal Sciences 109, no. 1 (2023): 27-40. https://doi.org/10.37934/arfmts.109.1.2740

Ibren, Mohamed, Amelda Dianne Andan, Waqar Asrar, and Erwin Sulaeman. "A Review on Generation and Mitigation of Airfoil Self-Induced Noise." Journal of Advanced Research in Fluid Mechanics and Thermal Sciences 90, no. 1 (2022): 163-178. https://doi.org/10.37934/arfmts.90.1.163178

Kroeger, Richard A., H. D. Gruschka, and Tibor C. Helvey. Low speed aerodynamics for ultra-quiet flight. Air Force Flight Dynamics Laboratory, Air Force Systems Command, United States Air Force, 1972. https://doi.org/10.1063/5.0012958

Sarradj, Ennes, Christoph Fritzsche, and Thomas Geyer. "Silent owl flight: bird flyover noise measurements." AIAA journal 49, no. 4 (2011): 769-779. https://doi.org/10.2514/1.J050703

Graham, R. R. "The silent flight of owls." The Aeronautical Journal 38, no. 286 (1934): 837-843. https://doi.org/10.1017/S0368393100109915

Herr, Michaela, Karl-Stephane Rossignol, Jan Delfs, Nicolas Lippitz, and Michael Mößner. "Specification of porous materials for low-noise trailing-edge applications." In 20th AIAA/CEAS aeroacoustics conference, p. 3041. 2014. https://doi.org/10.2514/6.2014-3041

Sandberg, R. D., L. E. Jones, N. D. Sandham, and P. F. Joseph. "Direct numerical simulations of tonal noise generated by laminar flow past airfoils." Journal of Sound and Vibration 320, no. 4-5 (2009): 838-858. https://doi.org/10.1016/j.jsv.2008.09.003

Andan, Amelda Dianne, and Duck-Joo Lee. "Discrete Tonal Noise of NACA0015 Airfoil at Low Reynolds Number." Journal of Advanced Research in Fluid Mechanics and Thermal Sciences 53, no. 1 (2019): 129-145.

Rossian, Lennart, Roland Ewert, and Jan W. Delfs. "Numerical investigation of porous materials for trailing edge noise reduction." International Journal of Aeroacoustics 19, no. 6-8 (2020): 347-364. https://doi.org/10.1177/1475472X20954410

Lee, Seongkyu, and Jessica G. Shum. "Prediction of airfoil trailing-edge noise using empirical wall-pressure spectrum models." AIAA Journal 57, no. 3 (2019): 888-897. https://doi.org/10.2514/1.J057787

Oberai, Assad A., Farzam Roknaldin, and Thomas JR Hughes. "Computation of trailing-edge noise due to turbulent flow over an airfoil." AIAA journal 40, no. 11 (2002): 2206-2216. https://doi.org/10.2514/2.1582

Wang, Meng, and Parviz Moin. "Computation of trailing-edge flow and noise using large-eddy simulation." AIAA journal 38, no. 12 (2000): 2201-2209. https://doi.org/10.2514/2.895

Wagner, Siegfried, Rainer Bareiss, and Gianfranco Guidati. Wind turbine noise. Springer Science & Business Media, 2012.

Afshari, Abbas, Ali A. Dehghan, and Mahdi Azarpeyvand. "Novel three-dimensional surface treatments for trailing-edge noise reduction." AIAA Journal 57, no. 10 (2019): 4527-4535. https://doi.org/10.2514/1.J058586

Moreau, Danielle J., Laura A. Brooks, and Con J. Doolan. "The effect of boundary layer type on trailing edge noise from sharp-edged flat plates at low-to-moderate Reynolds number." Journal of Sound and Vibration 331, no. 17 (2012): 3976-3988. https://doi.org/10.1016/j.jsv.2012.04.016

Chen, Nanshu, Hanru Liu, Qian Liu, Xingyu Zhao, and Yangang Wang. "Effects and mechanisms of LES and DDES method on airfoil self-noise prediction at low to moderate Reynolds numbers." AIP Advances 11, no. 2 (2021). https://doi.org/10.1063/5.0038183

Lee, Seongkyu. "The effect of airfoil shape on trailing edge noise." Journal of Theoretical and Computational Acoustics 27, no. 02 (2019): 1850020. https://doi.org/10.1142/S2591728518500202

Oerlemans, Stefan, Pieter Sijtsma, and B. Méndez López. "Location and quantification of noise sources on a wind turbine." Journal of sound and vibration 299, no. 4-5 (2007): 869-883. https://doi.org/10.1016/j.jsv.2006.07.032

Brooks, Thomas F., D. Stuart Pope, and Michael A. Marcolini. Airfoil self-noise and prediction. No. L-16528. 1989.

Moreau, Danielle J., and Con J. Doolan. "Noise-reduction mechanism of a flat-plate serrated trailing edge." AIAA journal 51, no. 10 (2013): 2513-2522. https://doi.org/10.2514/1.J052436

Barone, Matthew Franklin. "Survey of techniques for reduction of wind turbine blade trailing edge noise." (2011). https://doi.org/10.2172/1029824

Hubbard, Harvey H. "Aeroacoustics of flight vehicles: Theory and practice. volume 1. noise sources." NASA reference publication 1258 (1991).

Gregory, Nigel, and C. L. O'reilly. "Low-speed aerodynamic characteristics of NACA 0012 aerofoil section, including the effects of upper-surface roughness simulating hoar frost." (1970).

Oerlemans, Stefan, and Gerard Schepers. "Prediction of wind turbine noise directivity and swish." In Third International Meeting on Wind Turbine Noise, pp. 17-19. 2009.

Amiet, Roy K. "Noise due to turbulent flow past a trailing edge." Journal of sound and vibration 47, no. 3 (1976): 387-393. https://doi.org/10.1016/0022-460X(76)90948-2

Howe, Michael S. "Trailing edge noise at low Mach numbers." Journal of Sound and Vibration 225, no. 2 (1999): 211-238. https://doi.org/10.1006/jsvi.1999.2236

Gruber, Mathieu, Phillip Joseph, and Mahdi Azarpeyvand. "An experimental investigation of novel trailing edge geometries on airfoil trailing edge noise reduction." In 19th AIAA/CEAS aeroacoustics conference, p. 2011. 2013. https://doi.org/10.2514/6.2013-2011

Lyu, Benshuai, Mahdi Azarpeyvand, and Samuel Sinayoko. "Prediction of noise from serrated trailing edges." Journal of Fluid Mechanics 793 (2016): 556-588. https://doi.org/10.1017/jfm.2016.132

Stalnov, Oksana, Paruchuri Chaitanya, and Phillip F. Joseph. "Towards a non-empirical trailing edge noise prediction model." Journal of Sound and Vibration 372 (2016): 50-68. https://doi.org/10.1016/j.jsv.2015.10.011

Chase, David M. "Noise radiated from an edge in turbulent flow." AIAA journal 13, no. 8 (1975): 1041-1047. https://doi.org/10.2514/3.60502

Williams, JE Ffowcs, and L. H. Hall. "Aerodynamic sound generation by turbulent flow in the vicinity of a scattering half plane." Journal of fluid mechanics 40, no. 4 (1970): 657-670. https://doi.org/10.1017/S0022112070000368

Howe, Michael S. "A review of the theory of trailing edge noise." Journal of sound and vibration 61, no. 3 (1978): 437-465.https://doi.org/10.1016/0022-460X(78)90391-7

Brooks, Thomas F., and T. H. Hodgson. "Trailing edge noise prediction from measured surface pressures." Journal of sound and vibration 78, no. 1 (1981): 69-117. https://doi.org/10.1016/S0022-460X(81)80158-7

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 (2018): 560-591. https://doi.org/10.1017/jfm.2018.377

Jones, L. E., and R. D. Sandberg. "Acoustic and hydrodynamic analysis of the flow around an aerofoil with trailing-edge serrations." Journal of Fluid Mechanics 706 (2012): 295-322. https://doi.org/10.1017/jfm.2012.254

Arce León, Carlos, Roberto Merino-Martínez, Daniele Ragni, Francesco Avallone, and Mirjam Snellen. "Boundary layer characterization and acoustic measurements of flow-aligned trailing edge serrations." Experiments in fluids 57 (2016): 1-22. https://doi.org/10.1007/s00348-016-2272-z

Avallone, Francesco, Stefan Pröbsting, and Daniele Ragni. "Three-dimensional flow field over a trailing-edge serration and implications on broadband noise." Physics of Fluids 28, no. 11 (2016). https://doi.org/10.1063/1.4966633

Dassen, T., R. Parchen, J. Bruggeman, and F. Hagg. "Results of a wind tunnel study on the reduction of airfoil self-noise by the application of serrated blade trailing edges." (1996).

Oerlemans, Stefan, Murray Fisher, Thierry Maeder, and Klaus Kögler. "Reduction of wind turbine noise using optimized airfoils and trailing-edge serrations." AIAA journal 47, no. 6 (2009): 1470-1481. https://doi.org/10.2514/1.38888

Gruber, Mathieu. "Airfoil noise reduction by edge treatments." PhD diss., University of Southampton, 2012.

Chong, Tze Pei, and Alexandros Vathylakis. "On the aeroacoustic and flow structures developed on a flat plate with a serrated sawtooth trailing edge." Journal of Sound and Vibration 354 (2015): 65-90. https://doi.org/10.1016/j.jsv.2015.05.019

León, Carlos Arce, Roberto Merino-Martínez, Daniele Ragni, Francesco Avallone, Fulvio Scarano, Stefan Pröbsting, Mirjam Snellen, Dick G. Simons, and Jesper Madsen. "Effect of trailing edge serration-flow misalignment on airfoil noise emissions." Journal of Sound and Vibration 405 (2017): 19-33. https://doi.org/10.1016/j.jsv.2017.05.035

Avallone, Francesco, Stefan Pröbsting, and Daniele Ragni. "Three-dimensional flow field over a trailing-edge serration and implications on broadband noise." Physics of Fluids 28, no. 11 (2016). https://doi.org/10.1063/1.4966633

Gruber, Mathieu, Phillip Joseph, and Tze Chong. "On the mechanisms of serrated airfoil trailing edge noise reduction." In 17th AIAA/CEAS aeroacoustics conference (32nd AIAA aeroacoustics conference), p. 2781. 2011. https://doi.org/10.2514/6.2011-2781

Jaworski, Justin W., and Nigel Peake. "Aeroacoustics of silent owl flight." Annual Review of Fluid Mechanics 52 (2020): 395-420. https://doi.org/10.1146/annurev-fluid-010518-040436

Szőke, Máté, Daniele Fiscaletti, and Mahdi Azarpeyvand. "Uniform flow injection into a turbulent boundary layer for trailing edge noise reduction." Physics of Fluids 32, no. 8 (2020). https://doi.org/10.1063/5.0013461

Geyer, Thomas, Ennes Sarradj, and Christoph Fritzsche. "Measurement of the noise generation at the trailing edge of porous airfoils." Experiments in fluids 48 (2010): 291-308. https://doi.org/10.1007/s00348-009-0739-x

Bae, Youngmin, and Young J. Moon. "Effect of passive porous surface on the trailing-edge noise." Physics of Fluids 23, no. 12 (2011). https://doi.org/10.1063/1.3662447

Ali, Syamir Alihan Showkat, Mahdi Azarpeyvand, and Carlos Roberto Ilário Da Silva. "Trailing-edge flow and noise control using porous treatments." Journal of Fluid Mechanics 850 (2018): 83-119. https://doi.org/10.1017/jfm.2018.430

Finez, Arthur, Marc Jacob, Emmanuel Jondeau, and Michel Roger. "Broadband noise reduction with trailing edge brushes." In 16th AIAA/CEAS aeroacoustics conference, p. 3980. 2010. https://doi.org/10.2514/6.2010-3980

Herr, Michaela, and Werner Dobrzynski. "Experimental Investigations in Low-Noise Trailing Edge Design." AIAA journal 43, no. 6 (2005): 1167-1175. https://doi.org/10.2514/1.11101

Clark, Ian A., W. Nathan Alexander, William Devenport, Stewart Glegg, Justin W. Jaworski, Conor Daly, and Nigel Peake. "Bioinspired trailing-edge noise control." AIAA Journal 55, no. 3 (2017): 740-754. https://doi.org/10.2514/1.J055243

Jawahar, Hasan Kamliya, Qing Ai, and Mahdi Azarpeyvand. "Experimental and numerical investigation of aerodynamic performance for airfoils with morphed trailing edges." Renewable Energy 127 (2018): 355-367. https://doi.org/10.1016/j.renene.2018.04.066

Talboys, Edward, Thomas F. Geyer, and Christoph Brücker. "An aeroacoustic investigation into the effect of self-oscillating trailing edge flaplets." Journal of Fluids and Structures 91 (2019): 102598. https://doi.org/10.1016/j.jfluidstructs.2019.02.014

Chong, Tze Pei, and Phillip F. Joseph. "An experimental study of airfoil instability tonal noise with trailing edge serrations." Journal of Sound and Vibration 332, no. 24 (2013): 6335-6358. https://doi.org/10.1016/j.jsv.2013.06.033

León, Carlos Arce, Roberto Merino-Martínez, Daniele Ragni, Francesco Avallone, Fulvio Scarano, Stefan Pröbsting, Mirjam Snellen, Dick G. Simons, and Jesper Madsen. "Effect of trailing edge serration-flow misalignment on airfoil noise emissions." Journal of Sound and Vibration 405 (2017): 19-33. https://doi.org/10.1016/j.jsv.2017.05.035

Chong, T. P., P. F. Joseph, and M. Gruber. "Airfoil self noise reduction by non-flat plate type trailing edge serrations." Applied Acoustics 74, no. 4 (2013): 607-613. https://doi.org/10.1016/j.apacoust.2012.11.003

Bohn, A. J. "Edge noise attenuation by porous-edge extensions." In 14th aerospace sciences meeting, p. 80. 1976. https://doi.org/10.2514/6.1976-80

Potter, C. An experiment to examine the effect of porous trailing edges on the sound generated by blades in an airflow. American Institute of Aeronautics and Astronautics, 1968.

Herr, Michaela, and Johann Reichenberger. "In search of airworthy trailing-edge noise reduction means." In 17th AIAA/CEAS Aeroacoustics Conference (32nd AIAA Aeroacoustics Conference), p. 2780. 2011. https://doi.org/10.2514/6.2011-2780

Sarradj, Ennes, and Thomas Geyer. "Noise generation by porous airfoils." In 13th AIAA/CEAS Aeroacoustics Conference (28th AIAA Aeroacoustics Conference), p. 3719. 2007. https://doi.org/10.2514/6.2007-3719

Geyer, Thomas, Ennes Sarradj, and Christoph Fritzsche. "Porous airfoils: noise reduction and boundary layer effects." International journal of aeroacoustics 9, no. 6 (2010): 787-820. https://doi.org/10.1260/1475-472X.9.6.787

Geyer, Thomas F., and Ennes Sarradj. "Trailing edge noise of partially porous airfoils." In 20th AIAA/CEAS aeroacoustics conference, p. 3039. 2014. https://doi.org/10.2514/6.2014-3039

Zhang, Minghui, and Tze Pei Chong. "Experimental investigation of the impact of porous parameters on trailing-edge noise." Journal of Sound and Vibration 489 (2020): 115694. https://doi.org/10.1016/j.jsv.2020.115694

Geyer, Thomas Fritz, and Ennes Sarradj. "Self noise reduction and aerodynamics of airfoils with porous trailing edges." In Acoustics, vol. 1, no. 2, pp. 393-409. MDPI, 2019. https://doi.org/10.3390/acoustics1020022

Revell, James, James Revell, Herbert Kuntz, Frank Balena, Clifton Horne, Bruce Storms, Robert Dougherty et al. "Trailing-edge flap noise reduction by porous acoustic treatment." In 3rd AIAA/CEAS aeroacoustics conference, p. 1646. 1997. https://doi.org/10.2514/6.1997-1646

Bernicke, Paul, R. A. D. Akkermans, Varun B. Ananthan, Roland Ewert, Jürgen Dierke, and Lennart Rossian. "A zonal noise prediction method for trailing-edge noise with a porous model." International Journal of Heat and Fluid Flow 80 (2019): 108469. https://doi.org/10.1016/j.ijheatfluidflow.2019.108469

Wagner, Claus, Thomas Hüttl, and Pierre Sagaut, eds. Large-eddy simulation for acoustics. Vol. 20. Cambridge University Press, 2007. https://doi.org/10.1017/CBO9780511546143

Storey, R. C., S. E. Norris, and J. E. Cater. "Modelling turbine loads during an extreme coherent gust using large eddy simulation." In Journal of Physics: Conference Series, vol. 524, no. 1, p. 012177. IOP Publishing, 2014. https://doi.org/10.1088/1742-6596/524/1/012177

Kim, Sung-Eun. "Large eddy simulation using an unstructured mesh based finite-volume solver." In 34th AIAA fluid dynamics conference and exhibit, p. 2548. 2004. https://doi.org/10.2514/6.2004-2548

Smagorinsky, Joseph. "General circulation experiments with the primitive equations: I. The basic experiment." Monthly weather review 91, no. 3 (1963): 99-164. https://doi.org/10.1175/1520-0493(1963)091<0099:GCEWTP>2.3.CO;2

Germano, Massimo, Ugo Piomelli, Parviz Moin, and William H. Cabot. "A dynamic subgrid‐scale eddy viscosity model." Physics of Fluids A: Fluid Dynamics 3, no. 7 (1991): 1760-1765. https://doi.org/10.1063/1.857955

Zhao, Dan, Nuomin Han, Ernest Goh, John Cater, and Arne Reinecke. Wind turbines and aerodynamics energy harvesters. Academic Press, 2019.

Lighthill, Michael James. "On sound generated aerodynamically I. General theory." Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences 211, no. 1107 (1952): 564-587. https://doi.org/10.1098/rspa.1952.0060

Lighthill, Michael James. "On sound generated aerodynamically II. Turbulence as a source of sound." Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences 222, no. 1148 (1954): 1-32. https://doi.org/10.1098/rspa.1954.0049

Williams, JE Ffowcs, and David L. Hawkings. "Sound generation by turbulence and surfaces in arbitrary motion." Philosophical Transactions for the Royal Society of London. Series A, Mathematical and Physical Sciences (1969): 321-342. https://doi.org/10.1098/rsta.1969.0031

Shen, Wen Zhong, Weijun Zhu, and Jens Nørkær Sørensen. "Aeroacoustic computations for turbulent airfoil flows." AIAA journal 47, no. 6 (2009): 1518-1527. https://doi.org/10.2514/1.40399

Published

2024-03-31

Issue

Section

Articles

Most read articles by the same author(s)