Generate QR code
Open Access
Subscription Access
Modulus of complex acoustic impedance of air in a cylindrical closed volume: calculation using numerical simulation
https://doi.org/10.32446/0368-1025it.2022-11-65-71
Abstract
The problem of the infl uence of the effect of heat transfer between air inside a closed volume with heat-conducting walls and the external environment, as well as the infl uence of waves refl ected from the walls, on the magnitude of the acoustic impedance of air in a cylindrical closed volume with heat-conducting and heat-insulated walls is considered using numerical modeling. The numerical algorithm used in the study is based on the regularized Navier-Stokes equations with quasi-gas dynamic approach taking into account the viscosity of the air. The modulus of acoustic impedance of air calculated by simulation in a closed volume with heat-conducting walls showed a good match with the analytical formula confi rmed experimentally for low and infrasound frequencies of sound oscillations. The results are relevant both for the primary calibration of measurement microphones by the pressure reciprocity method and the pistonphone method, and for the study of acoustic processes in liquid and gaseous media by numerical simulation.
About the Author
D. V. Golovin
Russian Metrological Institute of Technical Physics and Radio Engineering
Russian Federation
Russian Federation
Dmitrii V. Golovin
Mendeleevo, Moscow region
References
1. Ballantine S., Journal of the Acoustical Society of America, 1931, vol. 3, no. 8. https://doi.org/10.1121/1.1901925
2. Daniels F. B., Journal of the Acoustical Society of America, 1947, vol. 19, no. 4, pp. 569–571. https://doi.org/10.1121/1.1916522
3. Русаков И. Г. Термодинамическая поправка в методе насоса // Труды комиссии по акустике. 1955. Т. 8. С. 76–81. [Rusakov I. G., Termodinamicheskaia popravka v metode nasosa, Trudy komissii po akustike, 1955, vol. 8, pp. 76–81. (In Russ.)]
4. Burkhard M. D., Biagi F., Cook R. K., Corliss E. L. R., Koidan W., Journal of the Acoustical Society of America, 1954, vol. 26, no. 5, p. 935. https://doi.org/10.1121/1.1927953
5. Gerber H., Journal of the Acoustical Society of America, 1964, vol. 36, no. 8, pp. 1427–1434. https://doi.org/10.1121/1.1919219
6. Frederiksen E., Reduction of Heat Conduction Error in Microphone Pressure Reciprocity Calibration, Bruel and Kjaer Technical Review, 2001, no. 1, pp. 14–23.
7. Vincent P., Rodrigues D., Larsonnier F. et al., Metrologia, 2019, vol. 56, no. 1, 015003. https://doi.org/10.1088/1681-7575/aaee28
8. Волков К. Н., Дерюгин Ю. Н., Емельянов В. Н. и др. Методы ускорения газодинамических расчётов на неструктурированных сетках. М.: ФИЗМАТЛИТ, 2014. 536 с. [Volkov K. N., Deriugin Iu. N., Emelianov V. N., et. al., Metody uskoreniia gazodinamicheskikh raschetov na nestryktyrirovannykh setkakh [Methods of acceleration of gas dynamic calculations on unstructured grids], Moscow, Fizmatlit Publ., 2014, 536 p. (In Russ.)]
9. Абалакин И. В., Бобков В. Г., Козубская Т. К. Разработка метода расчёта течений с малыми числами Маха на неструктурированных сетках в программном комплексе NOISEtte // Математическое моделирование. 2017. Т. 29. № 4. C. 101–112. [Abalakin I. V., Bobkov V. G., Kozubskaya T. K., Mathematical Models and Computer Simulations, 2017, no. 9, pp. 688– 696. https://doi.org/10.1134/S2070048217060023 ]
10. Turkel E., Annual Review of Fluid Mechanics, 1999, vol. 31, pp. 385–416. https://doi.org/10.1146/annurev.fl uid.31.1.385
11. Chorin A. J., J. of Computational Physics, 1967, vol. 2, no. 1, pp. 12–26. https://doi.org/ 10.1016/0021-9991(67)90037-X
12. Rogers S. E., Kwak D., Kiris C., AIAA Journal, 1991, vol. 29, no. 4, pp. 603–610. https://doi.org/10.2514/3.10627
13. Rogers S. E., Kwak D., Applied Numerical Mathematics, 1991, vol. 8, no. 1, pp. 43–64. https://doi.org/10.1016/ 0168-9274(91)90097-J
14. Roe P. L., J. of Computational Physics, 1981, vol. 43, no. 2, pp. 357–372. https://doi.org/10.1016/0021-9991(81)90128-5
15. Rieper F., J. of Computational Physics, 2011, vol. 230, no. 13, pp. 5263–5287. https://doi.org/10.1016/j.jcp.2011.03.025
16. Li X-S., Gu C-W., J. of Computational Physics, 2008, vol. 227, no. 10, pp. 5144–5159. https://doi.org/doi.org/10.1016/j.jcp.2008.01.037
17. Liou M.-S., Steffen C. J., J. of Computational Physics, 1993, vol. 107, no. 1, pp. 23–39. https://doi.org/10.1006/jcph.1993.1122
18. Liou M.-S., J. of Comp. Phys. 1996, vol. 129, no. 2, pp. 364– 382. https://doi.org/10.1006/jcph.1996.0256
19. Liou M.-S., J. of Computational Physics, 2006, vol. 214, no. 1, pp. 137–170. https://doi.org/10.1016/j.jcp.2005.09.020
20. Балашов В. А., Савенков Е. Б. Численное исследование квазигидродинамической системы уравнений для расчёта течений при малых числах Маха // Журнал вычислительной математики и математической физики. 2015. Т. 55. № 10. C. 1773–1782. https://doi.org/10.7868/S0044466915100063 [Balashov V. A., Savenkov E. B., Comput. Math. and Math. Phys., 2015, vol. 55, pp. 1743–1751. https://doi.org/10.1134/S0965542515100061 ]
21. Головин Д. В. Моделирование инфразвукового пистонфона // Труды Института системного программирования РАН. 2020. Т. 32. № 5. C. 181–198. https://doi.org/10.15514/ISPRAS-2020-32(5)-14 [Golovin D. V., Simulation of infrasound pistonphone, Proceedings of ISP RAS, 2020, vol. 32, iss. 5, рр. 181–198. (In Russ.)]
22. Головин Д. В. Численное моделирование звукового давления для системы калибровки измерительных микрофонов типа LS // Математическое моделирование. 2021. Т. 33. № 10. C. 96–108. https://doi.org/10.20948/mm-2021-10-07 [Golovin D. V., Math. Models Comput. Simul., 2022, no. 14, pp. 419– 426. https://doi.org/10.1134/S2070048222030061 ]
23. Елизарова Т. Г. Квазигазодинамические уравнения и методы расчёта вязких течений. М.: Научный Мир, 2007 [Elizarova T. G., Quasi-Gas Dynamic Equations, Springer-Verlag, Berlin, Heidelberg, 2009, 286 p. https://doi.org/10.1007/978-3-642-00292-2 ]
24. Шеретов Ю. В. Динамика сплошных сред при пространственно-временном осреднении. М., Ижевск: НИЦ «Регулярная и хаотическая динамика», 2009. 400 c. [Sheretov Iu.V., Dinamica sploshnyh sred pri prostranstvenno-vremennom osrednenii [Dynamics of continuous environments with space-time averaging], Moscow, Izhevsk, NITS “Reguliarnaia i haoticheskaia dinamica” Publ., 2009, 400 p. (In Russ.)]
Review
For citations:
Golovin D.V. Modulus of complex acoustic impedance of air in a cylindrical closed volume: calculation using numerical simulation. Izmeritel`naya Tekhnika. 2022;(11):65-71. (In Russ.) https://doi.org/10.32446/0368-1025it.2022-11-65-71
Views:
105
Email this article 