Acoustic oscillations driven by boundary mass exchange

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.

PC-TAS: A design environment for phase-change and classical thermoacoustic systems

“…As a result, the thermoacoustic conversion can be enhanced. This effect has been demonstrated in recent studies of phase-change (or wet) thermoacoustic engines and refrigerators [7][8][9][10][11][12][13][14]. Furthermore, it has been predicted that the phase-change thermoacoustic conversion has the potential to increase the energy density of classical thermoacoustic devices by up to one order of magnitude, with an efficiency above 40% of Carnot limit, especially when working under small temperature differences [9,10].…”

“…However, after being studied for more than four decades, the room for further improving the performance through traditional pathways, such as improving acoustics, is becoming increasingly narrow, as clearly seen in travelling-wave devices where the achieved acoustic field is becoming close to ideal (i.e., near travelling-wave phase and large acoustic impedance) [3,4]. A promising approach for a breakthrough that significantly improves the performance of thermoacoustic systems is the use of phase-change thermoacoustic conversion [5][6][7][8][9][10]. In phasechange thermoacoustic devices, the working fluid is a mixture consisting of an ''inert'' gas and a ''reactive'' component, which undergoes periodical evaporation and condensation during the oscillation.…”

“…Based on the long-wavelength, low amplitude acoustic approximation, the full equations can be simplified into three ODEs. This simplified model was first developed by Raspet et al [5] and Slaton et al [6], and later extended by Weltsch et al [15] and Offner et al [7] to include other mass-exchange processes (e.g., absorption and adsorption). Here, we use the dimensional versions of the equations derived in Offner et al [7]:…”

“…η ν and η D are functions of phase change kinetics, geometry, and the liquid layer's capacity for absorbing additional molecules. Following Offner et al [7], for evaporation/condensation, they are both assumed to equal 1. C m is the mean mass fraction of the reactive component.…”

Multi-physics coupling in thermoacoustic devices: A review

“…The performance of phase-change travelling-wave TAEs was examined experimentally by Ueda [132] and Yang [133], who demonstrated much lower onset temperature differences and higher thermal efficiencies than the dry equivalents. Recently, Ramon et al [134][135][136] generalised the theory of thermoacoustics with mass exchange between the solid and a binary mixture comprising an inert (e.g., air) and a reactive component (e.g., water) in a thermod namic c cle. As shown in Figure 17, heat transfer between the gas mixture and solid is accompanied by mass transfer (gain or loss) due to phase change in the evaporation and condensation processes.…”