Abstract
In this study, the modified Sauer cavitation model and Kirchhoff-Ffowcs Williams and Hawkings (K-FWH) acoustic model were adopted to numerically simulate the unsteady cavitation flow field and the noise of a three-dimensional NACA66 hydrofoil at a constant cavitation number. The aim of the study is to conduct and analyze the noise performance of a hydrofoil and also determine the characteristics of the sound pressure spectrum, sound power spectrum, and noise changes at different monitoring points. The noise change, sound pressure spectrum, and power spectrum characteristics were estimated at different monitoring points, such as the suction side, pressure side, and tail of the hydrofoil. The noise characteristics and change law of the NACA66 hydrofoil under a constant cavitation number are presented. The results show that hydrofoil cavitation takes on a certain degree of pulsation and periodicity. Under the condition of a constant cavitation number, as the attack angle increases, the cavitation area of the hydrofoil becomes longer and thicker, and the initial position of cavitation moves forward. When the inflow velocity increases, the cavitation noise and the cavitation area change more drastically and have a superposition tendency toward the downstream. The novelty is that the study presents important calculations and analyses regarding the noise performance of a hydrofoil, characteristics of the sound pressure spectrum, and sound power spectrum and noise changes at different monitoring points. The article may be useful for specialists in the field of engineering and physics.Keywords:
sound pressure spectrum, noise, sound power spectrum, numerical predictionReferences
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21. Li G., Shi L. (1997), Cavitation and cavitation erosion and their influencing factors [in Chinese], Journal of Petroleum University (Natural Science Edition), 21(1): 97–101, http://www.alljournals.cn/view_abstract.aspx?pcid=3C5CA5E51F7D0F8A&cid=3C5CA5E51F7D0F8A&jid=AFEA5AA653DB650F7CB44EE42E99DE56&aid=4D3C8AFBB3796195B9EA80098C763CE8&yid=5370399DC954B911&vid=&iid=&sid=&eid=&from_absract=1 (access: 11.09.2022).
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26. Plesset M. (1949), The dynamics of cavitation bubbles, Journal of Applied Mechanics, 16: 277–282.
27. Prentkovskis O., Tretjakovas J., Švedas A., Bieliatynskyi A., Daniunas A., Krayushkina K. (2012),
The analysis of the deformation state of the double-wave guardrail mounted on bridges and viaducts of the motor roads in Lithuania and Ukraine, Journal of Civil Engineering and Management, 18(5): 761–771, https://doi.org/10.3846/13923730.2012.731252
28. Prokopov V.G. et al. (1993), Effect of coating porosity on the process of heat-transfer with gas-hermal deposition, Powder Metallurgy and Metal Ceramics, 32(2): 118–121, https://doi.org/10.1007/BF00560034
29. Schnerr G.H., Sauer J. (2001), Physical and numerical modeling of unsteady cavitation dynamics, [in:] 4th International Conference on Multiphase Flow ICMF-2001, https://www.semanticscholar.org/paper/Physical-and-numerical-modeling-of-unsteady-Schnerr-Sauer/ed8c0ec44ddc18456eb4f32fb7aaf76605bd13aa (access: 17.09.2022).
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31. Singhal A.K., Athavale M.M., Li H., Jiang Y. (2002), Mathematical basis and validation of the full cavitation model, Journal of Fluids Engineering, 124(3): 617–624, https://doi.org/10.1115/1.1486223
32. Su Y., Dou F., Liu Y., Cui T. (2013), Study of non-cavitating propeller noise, Journal of Wuhan University of Technology (Transportation Science and Engineering), 37(5): 895–899, https://doi.org/10.3963/j.issn.2095-3844.2013.05.001
33. Sultanov K.S., Khusanov B.E., Rikhsieva B.B. (2020), Longitudinal waves in a cylinder with active external friction in a limited area, [in:] IV International Scientific and Technical Conference Mechanical Science and Technology Update (MSTU-2020), 1546: 012140, https://doi.org/10.1088/1742-6596/1546/1/012140
34. Wang G., Senocak I., Shyy W., Ikohagi T., Cao S. (2001), Dynamics of attached turbulent cavitating flow, Progress in Aerospace Science, 37(6): 551–581, https://doi.org/10.1016/S0376-0421%2801%2900014-8
35. Wang G., Ostoja-Starzewski M. (2007), Large Eddy simulation of a sheet/cloud cavitation on a NACA0015 hydrofoil, Applied Mathematical Modelling, 31(3): 417–447, https://doi.org/10.1016/j.apm.2005.11.019
36. Wang G.-Y., Zhang B., Huang B., Zhang M. (2009), Unsteady dynamics of cloud cavitating flows around a hydrofoil, Journal of Experiments in Fluid Mechanics, 23(3): 44–49, https://www.semanticscholar.org/paper/Unsteady-Dynamics-of-Cloud-Cavitating-Flowsaround-Wang-Zhang/0db160f3faecc68c656b97b6453252fba40eeded (access: 19.09.2022).
37. Wang W., Li Z., Liu M., Ji X. (2021), Influence of water injection on broadband noise and hydrodynamic performance for a NACA66 (MOD) hydrofoil under cloud cavitation condition, Applied Ocean Research, 115: 102858, https://doi.org/10.1016/j.apor.2021.102858
38. Wu J.Y., Wang G.Y., Shyy W. (2005), Time-dependent turbulent cavitating flow computations with interfacial transport and filter based models, International Journal for Numerical Methods in Fluids, 49(7): 739–761, https://doi.org/10.1002/fld.1047
39. Yang Q., Wang Y., Zhang Z. (2012), Assessment of the improved cavitation model and modified turbulence model for ship propeller cavitation simulation, Journal of Mechanical Engineering, 48(9): 178–785, https://doi.org/10.3901/JME.2012.09.178
40. Yang Q., Wang Y., Zhang Z., Hou G. (2014), Numerical prediction of cavitation inception radiated noise of contra-rotating propeller with non-uniform in flow, Shenghxue Xuebao/Acta Acustica, 39(5): 589–604.
41. Yang Q.-F., Wang Y.-S., Zhang Z.-H. (2011), Improvement and evaluation of numerical model for cavitation flow viscous simulation around propeller blade section, Transactions of Beijing Institute of Technology, 31(12): 1401–1407.
42. Zhang B.,Wang G., Huang B., Zhiyi Y. (2009), Numerical and experimental studies on unsteady shedding mechanisms of cloud cavitation, Chinese Journal of Theoretical and Applied Mechanics, 41(5): 651–659, https://doi.org/10.6052/0459-1879-2009-5-2008-152
43. Zwart P., Gerber A.G., Belamri T. (2004), A twophase flow model for prediction cavitation dynamics, [in:] 5th ICMF 2004 International Conference on Multiphase Flow.
2. Al-Obaidi A.R. (2019), Numerical investigation of flow field behaviour and pressure fluctuations within an axial flow pump under transient flow pattern based on CFD analysis method, Journal of Physics: Conference Series, 1279(1): 012069, https://doi.org/10.1088/1742-6596/1279/1/012069
3. Al-Obaidi A.R. (2020), Influence of guide vanes on the flow fields and performance of axial pump under unsteady flow conditions: Numerical study, Journal of Mechanical Engineering and Sciences, 14(2): 6570–6593, https://doi.org/10.15282/jmes.14.2.2020.04.0516
4. Al-Obaidi A.R., Mishra R. (2020), Experimental investigation of the effect of air injection on performance and detection of cavitation in the centrifugal pump based on vibration technique, Arabian Journal for Science and Engineering, 45(7): 5657–5671, https://doi.org/10.1007/s13369-020-04509-3
5. Beljatynskij A. Prentkovskis O., Krivenko J. (2010), The experimental study of shallow flows of liquid on the airport runways and automobile roads, Transport, 25(4): 394–402, https://doi.org/10.3846/transport.2010.49
6. Cao H., Fang S., Zhu Z. (2014), Numerical prediction and characteristic analysis of slow varying components of cavitation noise of propeller in non-uniform inflow, High-tech Communications, 24(3): 296–304, https://doi.org/10.3772/j.issn.1002-0470.2014.03.012
7. Chang F.N. (2011), The prediction of the viscous cavitation flow around a hydrofoil section, [in:] Proceedings of the Twenty First International Offshore and Polar Engineering Conference, 1: 989–994, https://onepetro.org/ISOPEIOPEC/proceedings-abstract/ISOPE11/All-ISOPE11/ISOPE-I-11-423/13400 (access: 21.09.2022).
8. Curle N. (1955), The influence of solid boundaries upon aerodynamic sound, Proceedings of the Royal Society of London, Series A, 231(1187): 505–514, https://doi.org/10.1098/rspa.1955.0191
9. Ducoin A., Astolfi J.A., Deniset F., Sigrist J.F., (2009), Computational and experimental investigation of flow over a transient pitching hydrofoil, European Journal of Mechanics – B/Fluids, 28(6): 728–743, https://doi.org/10.1016/j.euromechflu.2009.06.001
10. Ducoin A., Astolfi J.A., Gobert M.L. (2012), An experimental study of boundary-layer induced vibrations on a hydrofoil, Journal of Fluids and Structures, 32(3): 37–51, https://doi.org/10.1016/j.jfluidstructs.2011.04.002
11. Fan G. (2015), Research on Vibration and Acoustic Radiation Characteristics of Hydrofoil Flow, Shanghai, School of Mechanics and Power, Shanghai Jiao Tong University.
12. Fuji A., Kawakami D.T., Tsujimoto Y., Arndt R.E.A. (2007), Effect of hydrofoil shapes on partial and transitional cavity oscillations, Journal of Fluids Engineering, 129(6): 669–673, https://doi.org/10.1115/1.2734183
13. Hong F., Yuan J.P., Zhou B.L. (2017), Application of a new cavitation model for computations of unsteady turbulent cavitating flows around a hydrofoil, Journal of Mechanical Science and Technology, 31(1): 249–260, https://doi.org/10.1007/s12206-016-1227-x
14. Huang B., Wu Q., Wang G.-Y. (2018), Progress and prospects of investigation into unsteady cavitating flows [in Chinese], Drainage and Irrigation Mechanical Engineering, 36(1): 1–14, https://doi.org/10.3969/j.issn.1674-8530.17.0094
15. Ji B., Lou X.-W., Wu Y.-L., Liu S.-H., Xu H.-Y., Oshima A. (2010), Numerical investigation of unsteady cavitating turbulent flow around a full-scale marine propeller, Journal of Hydrodynamics, 22(5): 747–752, https://doi.org/10.1016/S1001-6058%2810%2960025-X
16. Kieldsen M., Arndt R.E.A., Effertz M. (2000), Spectral characteristics of sheet/cloud cavitation, Journal of Fluids Engineering, 122(3): 481–487, doi: 10.1115/ 1.1287854.
17. Korzhyk V., Bushma O., Khaskin V., Dong C., Sydorets V. (2017), Analysis of the current state of the processes of hybrid laser-plasma welding, [in:] Proceedings of the 2nd International Conference on Mechanics, Materials and Structural Engineering (ICMMSE 2017) “AER-Advances in Engineering Research”, pp. 80–90, https://doi.org/10.2991/icmmse-17.2017.14
18. Kubota A., Kato H., Yamaguchi H. (1992), A new modeling of cavitating flows: a numerical study of unsteady cavitation on a hydrofoil section, Journal of Fluid Mechanics, 240(1): 59–96, https://doi.org/10.1017/S002211209200003X
19. Leroux J.B., Astolfi J.A., Billard J.Y. (2004), An experimental study of unsteady partial cavitation, Journal of Fluids Engineering, 126(1): 94–101, https://doi.org/10.1115/1.1627835
20. Leroux J.B., Olivier C.D., Astolfi J.A. (2003), A joint experimental and numerical study of mechanisms associated to instability of partial cavitation on two-dimensional hydrofoil, Physics of Fluids, 17(5): 052101, https://doi.org/10.1063/1.1865692
21. Li G., Shi L. (1997), Cavitation and cavitation erosion and their influencing factors [in Chinese], Journal of Petroleum University (Natural Science Edition), 21(1): 97–101, http://www.alljournals.cn/view_abstract.aspx?pcid=3C5CA5E51F7D0F8A&cid=3C5CA5E51F7D0F8A&jid=AFEA5AA653DB650F7CB44EE42E99DE56&aid=4D3C8AFBB3796195B9EA80098C763CE8&yid=5370399DC954B911&vid=&iid=&sid=&eid=&from_absract=1 (access: 11.09.2022).
22. Lord Rayleigh O.M. F.R.S. (1917), VIII. On the pressure developed in a liquid during the collapse of a spherical cavity, The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science, 34(200): 94–98, https://doi.org/10.1080/14786440808635681
23. Neppiras E.A., Noltingk B.E. (1951), Cavitation produced by ultrasonics: Theoretical conditions for the onset of cavitation, Proceedings of The Physical Science Society, Section B, 64(12): 1032–1038, https://doi.org/10.1088/0370-1301/64/12/302
24. Noltingk B.E., Neppiras E.A. (1950), Cavitation produced by ultrasonics, Proceedings of the Physical Society, Section B, 63(9): 674–685, https://doi.org/10.1088/0370-1301/63/9/305
25. Nurtas M., Baishemirov Z., Tsay V., Tastanov M., Zhanabekov Z. (2020), Convolutional neural networks as a method to solve estimation problem of acoustic wave propagation in poroelastic media, News of the National Academy of Sciences of the Republic of Kazakhstan – Physico-Mathematical Series, 4(332): 52–60, https://doi.org/10.32014/2020.2518-1726.65
26. Plesset M. (1949), The dynamics of cavitation bubbles, Journal of Applied Mechanics, 16: 277–282.
27. Prentkovskis O., Tretjakovas J., Švedas A., Bieliatynskyi A., Daniunas A., Krayushkina K. (2012),
The analysis of the deformation state of the double-wave guardrail mounted on bridges and viaducts of the motor roads in Lithuania and Ukraine, Journal of Civil Engineering and Management, 18(5): 761–771, https://doi.org/10.3846/13923730.2012.731252
28. Prokopov V.G. et al. (1993), Effect of coating porosity on the process of heat-transfer with gas-hermal deposition, Powder Metallurgy and Metal Ceramics, 32(2): 118–121, https://doi.org/10.1007/BF00560034
29. Schnerr G.H., Sauer J. (2001), Physical and numerical modeling of unsteady cavitation dynamics, [in:] 4th International Conference on Multiphase Flow ICMF-2001, https://www.semanticscholar.org/paper/Physical-and-numerical-modeling-of-unsteady-Schnerr-Sauer/ed8c0ec44ddc18456eb4f32fb7aaf76605bd13aa (access: 17.09.2022).
30. Shin S., Hong J.-W., Nagarathinam D., Ahn B.-K., Park S.-G. (2021), Tip vortex cavitation and induced noise characteristics of hydrofoils, Applied Sciences (Switzerland), 11(13): 5906, https://doi.org/10.3390/app11135906
31. Singhal A.K., Athavale M.M., Li H., Jiang Y. (2002), Mathematical basis and validation of the full cavitation model, Journal of Fluids Engineering, 124(3): 617–624, https://doi.org/10.1115/1.1486223
32. Su Y., Dou F., Liu Y., Cui T. (2013), Study of non-cavitating propeller noise, Journal of Wuhan University of Technology (Transportation Science and Engineering), 37(5): 895–899, https://doi.org/10.3963/j.issn.2095-3844.2013.05.001
33. Sultanov K.S., Khusanov B.E., Rikhsieva B.B. (2020), Longitudinal waves in a cylinder with active external friction in a limited area, [in:] IV International Scientific and Technical Conference Mechanical Science and Technology Update (MSTU-2020), 1546: 012140, https://doi.org/10.1088/1742-6596/1546/1/012140
34. Wang G., Senocak I., Shyy W., Ikohagi T., Cao S. (2001), Dynamics of attached turbulent cavitating flow, Progress in Aerospace Science, 37(6): 551–581, https://doi.org/10.1016/S0376-0421%2801%2900014-8
35. Wang G., Ostoja-Starzewski M. (2007), Large Eddy simulation of a sheet/cloud cavitation on a NACA0015 hydrofoil, Applied Mathematical Modelling, 31(3): 417–447, https://doi.org/10.1016/j.apm.2005.11.019
36. Wang G.-Y., Zhang B., Huang B., Zhang M. (2009), Unsteady dynamics of cloud cavitating flows around a hydrofoil, Journal of Experiments in Fluid Mechanics, 23(3): 44–49, https://www.semanticscholar.org/paper/Unsteady-Dynamics-of-Cloud-Cavitating-Flowsaround-Wang-Zhang/0db160f3faecc68c656b97b6453252fba40eeded (access: 19.09.2022).
37. Wang W., Li Z., Liu M., Ji X. (2021), Influence of water injection on broadband noise and hydrodynamic performance for a NACA66 (MOD) hydrofoil under cloud cavitation condition, Applied Ocean Research, 115: 102858, https://doi.org/10.1016/j.apor.2021.102858
38. Wu J.Y., Wang G.Y., Shyy W. (2005), Time-dependent turbulent cavitating flow computations with interfacial transport and filter based models, International Journal for Numerical Methods in Fluids, 49(7): 739–761, https://doi.org/10.1002/fld.1047
39. Yang Q., Wang Y., Zhang Z. (2012), Assessment of the improved cavitation model and modified turbulence model for ship propeller cavitation simulation, Journal of Mechanical Engineering, 48(9): 178–785, https://doi.org/10.3901/JME.2012.09.178
40. Yang Q., Wang Y., Zhang Z., Hou G. (2014), Numerical prediction of cavitation inception radiated noise of contra-rotating propeller with non-uniform in flow, Shenghxue Xuebao/Acta Acustica, 39(5): 589–604.
41. Yang Q.-F., Wang Y.-S., Zhang Z.-H. (2011), Improvement and evaluation of numerical model for cavitation flow viscous simulation around propeller blade section, Transactions of Beijing Institute of Technology, 31(12): 1401–1407.
42. Zhang B.,Wang G., Huang B., Zhiyi Y. (2009), Numerical and experimental studies on unsteady shedding mechanisms of cloud cavitation, Chinese Journal of Theoretical and Applied Mechanics, 41(5): 651–659, https://doi.org/10.6052/0459-1879-2009-5-2008-152
43. Zwart P., Gerber A.G., Belamri T. (2004), A twophase flow model for prediction cavitation dynamics, [in:] 5th ICMF 2004 International Conference on Multiphase Flow.
