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Acoustic oscillations driven by boundary mass exchange

  • Avshalom Offner (a1) (a2), Rui Yang (a2), Daniel Felman (a2) (a3), Nimrod Elkayam (a1) (a2), Yehuda Agnon (a1) (a2) (a3) (a4) and Guy Z. Ramon (a1) (a2) (a3)...


Thermoacoustic instability – self-sustained pressure oscillations triggered by temperature gradients – has become an increasingly studied topic in the context of energy conversion. Generally, the process relies on conductive heat transfer between a solid and the fluid in which the generated pressure oscillations are sustained. In the present study, the thermoacoustic theory is extended to include mass transfer; specifically, the working fluid is modified so as to incorporate a ‘reactive’ gas, able to exchange phase with a solid/liquid boundary through a sorption process (or through evaporation/condensation), such that most heat is transferred in the form of latent heat rather than through conduction. A set of differential equations is derived, accounting for phase-exchange heat and mass transfer, and de-coupled via a small-amplitude asymptotic expansion. These equations are solved and subsequently manipulated into the form of a wave equation, representing the small perturbation on the pressure field, and used to derive expressions for the time-averaged, second-order heat and mass fluxes. A stability analysis is performed on the wave equation, from which the marginal stability curve is calculated in terms of the temperature difference, $\unicode[STIX]{x0394}T_{onset}$ , required for initiation of self-sustained oscillations. Calculated stability curves are compared with published experimental results, showing good agreement. Effects of gas mixture composition are studied, indicating that a lower heat capacity of the inert component, combined with a low boiling temperature and high latent heat of the reactive component substantially lower $\unicode[STIX]{x0394}T_{onset}$ . Furthermore, an increase in the average mole fraction of the reactive gas, $C_{m}$ strongly affects onset conditions, leading to $\unicode[STIX]{x0394}T_{onset}\sim 5\,^{\circ }\text{C}$ at the highest value of $C_{m}$ achievable under atmospheric pressure. An analysis of the system limit cycle is performed for a wide range of parameters, indicating a systematic decrease in the temperature difference capable of sustaining the limit cycle, as well as a significant distortion of the acoustic wave form as the phase-exchange mechanism becomes dominant. These findings, combined, reveal the underlying mechanisms by which a phase-exchange engine may produce more acoustic power than its counterpart ‘classical’ thermoacoustic system, while its temperature difference is substantially lower.


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Arnott, W. P., Bass, H. E. & Raspet, R. 1992 Specific acoustic impedance measurements of an air-filled thermoacoustic prime mover. J. Acoust. Soc. Am. 92 (6), 34323434.10.1121/1.404167
Arnott, W. P., Belcher, J. R., Raspet, R. & Bass, H. E. 1994 Stability analysis of a helium-filled thermoacoustic engine. J. Acoust. Soc. Am. 96 (1), 370375.10.1121/1.410486
Bird, R. B., Stewart, W. E. & Lightfoot, E. N. 2007 Transport Phenomena, 2nd edn. Wiley.
Ceperley, P. H. 1979 A pistonless Stirling engine – the traveling wave heat engine. J. Acoust. Soc. Am. 66 (5), 15081513.10.1121/1.383505
Dowling, A. P. & Morgans, A. S. 2005 Feedback control of combustion oscillations. Annu. Rev. Fluid Mech. 37 (1), 151182.10.1146/annurev.fluid.36.050802.122038
Fleifil, M., Annaswamy, A. M., Ghoneim, Z. A. & Ghoniem, A. F. 1996 Response of a laminar premixed flame to flow oscillations: a kinematic model and thermoacoustic instability results. Combust. Flame 106 (4), 487510.10.1016/0010-2180(96)00049-1
Hiller, R. A. & Swift, G. W. 2000 Condensation in a steady-flow thermoacoustic refrigerator. J. Acoust. Soc. Am. 108 (4), 15211527.10.1121/1.1289664
Keller, J. J. 1995 Thermoacoustic oscillations in combustion chambers of gas turbines. AIAA J. 33 (12), 22802287.10.2514/3.12980
Landau, L. D. & Lifshitz, E. M. 1959 Fluid Mechanics. Pergamon.
Majer, V. & Svoboda, V. 1985 Enthalpies of Vaporization of Organic Compounds: A Critical Review and Data Compilation. Blackwell Scientific.
Meir, A., Offner, A. & Ramon, G. Z. 2018 Low-temperature energy conversion using a phase-change acoustic heat engine. Applied Energy 231, 372379.10.1016/j.apenergy.2018.09.124
Noda, D. & Ueda, Y. 2013 A thermoacoustic oscillator powered by vaporized water and ethanol. Am. J. Phys. 81 (2), 124126.10.1119/1.4766940
Poling, B. E., Prausnitz, J. M. & O’Connell, J. P. 2001 The Properties of Gases and Liquids. McGraw-Hill.
Raspet, R., Slaton, W. V., Hickey, C. J. & Hiller, R. A. 2002 Theory of inert gas-condensing vapor thermoacoustics: propgation equations. J. Acoust. Soc. Am. 112 (4), 14141422.10.1121/1.1508113
Rijke, P. L. 1859 Notiz über eine neue Art, die in einer an beiden Enden offenen Röhre enthaltene Luft in Schwingungen zu versetzen. Ann. Phys. 183 (6), 339343.10.1002/andp.18591830616
Rott, N. 1969 Damped and thermally driven acoustic oscillations in wide and narrow tubes. Z. Angew. Math. Phys. 20 (2), 230243.10.1007/BF01595562
Slaton, W. V., Raspet, R., Hickey, C. J. & Hiller, R. A. 2002 Theory of inert gas-condensing vapor thermoacoustics: transport equations. J. Acoust. Soc. Am. 112 (4), 14231430.10.1121/1.1508114
Sondhauss, C. 1850 Ueber die Schallschwingungen der Luft in erhitzten Glasröhren und in gedeckten Pfeifen von ungleicher Weite. Ann. Phys. 155 (1), 134.10.1002/andp.18501550102
Swift, G. W. 1988 Thermoacoustic engines. J. Acoust. Soc. Am. 84 (4), 11451180.10.1121/1.396617
Swift, G. W. 1992 Analysis and performance of a large thermoacoustic engine. J. Acoust. Soc. Am. 92 (3), 15511563.10.1121/1.403896
Swift, G. W. 2002 Thermoacoustics: A Unifying Perspective for Some Engines and Refrigerators. Acoustic Society of America.
Tsuda, K. & Ueda, Y. 2015 Abrupt reduction of the critical temperature difference of a thermoacoustic engine by adding water. AIP Adv. 5 (9), 097173.10.1063/1.4932036
Tsuda, K. & Ueda, Y. 2017 Critical temperature of traveling- and standing-wave thermoacoustic engines using a wet regenerator. Appl. Energy 196, 6267.10.1016/j.apenergy.2017.04.004
Ward, W. C. & Swift, G. W. 1994 Design environment for low amplitude thermoacoustic engines. J. Acoust. Soc. Am. 95 (6), 36713672.10.1121/1.409938
Weltsch, O., Offner, A., Liberzon, D. & Ramon, G. Z. 2017 Adsorption-mediated mass streaming in a standing acoustic wave. Phys. Rev. Lett. 118 (24), 244301.10.1103/PhysRevLett.118.244301
Yazaki, T., Iwata, A., Maekawa, T. & Tominaga, A. 1998 Traveling wave thermoacoustic engine in a looped tube. Phys. Rev. Lett. 81 (15), 31283131.10.1103/PhysRevLett.81.3128
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