Abstract
The distribution of perturbations of pressure and velocity in a rectangular resonator is considered. A resonator contains a gas where thermodynamic processes take place, such as exothermic chemical reaction or excitation of vibrational degrees of a molecule’s freedom. These processes make the gas acoustically active under some conditions. We conclude that the incident and reflected compounds of a sound beam do not interact in the leading order in the case of the periodic sound with zero mean pressure including waveforms with discontinuities. The acoustic field before and after forming of discontinuities is described. The acoustic heating or cooling in a resonator is discussed.Keywords:
standing waves, acoustically active gas, resonator, nonlinear propagation of sound.References
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16. Perelomova A. (2010), Nonlinear generation of nonacoustic modes by low-frequency sound in a vibrationally relaxing gas, Canadian Journal of Physics, 88, 4, 293–300, https://doi.org/10.1139/P10-011
17. Perelomova A. (2012), Standing acoustic waves and relative nonlinear phenomena in a vibrationally relaxing gas-filled resonator, Acta Acustica, 98, 713–721, http://dx.doi.org/10.3813/AAA.918552
18. Perelomova A., Pelc-Garska W. (2014), Standing waves and acoustic heating (or cooling) in resonators filled with chemically reacting gas, Archives of Acoustics, 39, 3, 403–410, https://doi.org/10.2478/aoa-2014-0044
19. Perelomova A., Pelc-GarskaW. (2011), Non-wave variations in temperature caused by sound in a chemically reacting gas, Acta Physica Polonica A, 120, 3, 455–461.
20. Zeldovich Ya.B., Raizer Yu.P. (1966), Physics of shock waves and high temperature hydrodynamic phenomena, Academic Press, New York.
2. Biwa T., Yazaki T. (2010), Observation of energy cascade creating periodic shock waves in a resonator, J. Acoust. Soc. Am., 127, 3, 1189–1192, http://dx.doi.org/10.1121/1.3291029
3. Chester W. (1964), Resonant oscillations in closed tubes, J. Fluid Mech., 18, 44–64, http://dx.doi.org/10.1017/S0022112064000040
4. Chu B.T. (1970), Weak nonlinear waves in nonequilibrium flows, [in:] Nonequilibrium flows, Wegener P.P. [Ed.], vol. 1, part 2, Marcel Dekker, New York.
5. Clarke J.F., McChesney A. (1976), Dynamics of relaxing gases, Butterworth, UK.
6. Hamilton M., Morfey C. (1998), Model equations, [in:] Nonlinear Acoustics, Hamilton M., Blackstock D. [Eds.], pp. 41–63, Academic Press, New York.
7. Kaner V.A., Rudenko O.V., Khokholov R.V. (1977) Theory of nonlinear oscillations in acoustic resonators, Sov. Phys. Acoust., 23, 5, 432–437.
8. Keller J.J. (1977), Nonlinear acoustic resonances in shock tubes with varying cross-sectional area, J. Appl. Math. Phys., 28, 107–122, http://dx.doi.org/10.1007/BF01590712
9. Makaryan V.G., Molevich N.E. (2007), Stationary shock waves in nonequilibrium media, Plasma Sources Sci. Technol., 16, 124–131.
10. Molevich N.E. (2001), Sound amplification in inhomogeneous flows of nonequilibrium gas, Acoustical Physics, 47, 1, 102–105, http://dx.doi.org/10.1134/1.1340086
11. Mortell M.P., Mulchrone K.F., Seymour B.R. (2009), The evolution of macrosonic standing waves in a resonator, International Journal of Engineering Sience, 47, 11–12, 1305–1314, http://dx.doi.org/10.1016/j.ijengsci.2008.10.012
12. Ochmann M. (1985), Nonlinear resonant oscillations in closed tubes – an application of the averaging method, J. Acoust. Soc. Am., 77, 1, 61–66, http://dx.doi.org/10.1121/1.391901
13. Osipov A.I., Uvarov A.V. (1992), Kinetic and gasdynamic processes in nonequilibrium molecular physics, Sov. Phys. Usp., 35, 11, 903–923, http://dx.doi.org/10.1070/PU1992v035n11ABEH002275
14. Parker D.F. (1972), Propagation of damped pulses through a relaxing gas, Phys. Fluids, 15, 256–262, http://dx.doi.org/10.1063/1.1693902
15. Rudenko O.V., Soluyan S.I. (2005), Theoretical foundations of nonlinear acoustics, Consultants Bureau, New York, https://doi.org/10.1002/jcu.1870060222
16. Perelomova A. (2010), Nonlinear generation of nonacoustic modes by low-frequency sound in a vibrationally relaxing gas, Canadian Journal of Physics, 88, 4, 293–300, https://doi.org/10.1139/P10-011
17. Perelomova A. (2012), Standing acoustic waves and relative nonlinear phenomena in a vibrationally relaxing gas-filled resonator, Acta Acustica, 98, 713–721, http://dx.doi.org/10.3813/AAA.918552
18. Perelomova A., Pelc-Garska W. (2014), Standing waves and acoustic heating (or cooling) in resonators filled with chemically reacting gas, Archives of Acoustics, 39, 3, 403–410, https://doi.org/10.2478/aoa-2014-0044
19. Perelomova A., Pelc-GarskaW. (2011), Non-wave variations in temperature caused by sound in a chemically reacting gas, Acta Physica Polonica A, 120, 3, 455–461.
20. Zeldovich Ya.B., Raizer Yu.P. (1966), Physics of shock waves and high temperature hydrodynamic phenomena, Academic Press, New York.
