Skip to main content Accessibility help
×
Home

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)...

Abstract

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.

Copyright

Corresponding author

Email address for correspondence: ramong@technion.ac.il

References

Hide All
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
MathJax
MathJax is a JavaScript display engine for mathematics. For more information see http://www.mathjax.org.

JFM classification

Metrics

Full text views

Total number of HTML views: 0
Total number of PDF views: 0 *
Loading metrics...

Abstract views

Total abstract views: 0 *
Loading metrics...

* Views captured on Cambridge Core between <date>. This data will be updated every 24 hours.

Usage data cannot currently be displayed