Theory of inert gas-condensing vapor thermoacoustics: propagation equation

Thermoacoustic Soret separation

In a fluid mixture in a channel with an axial time-averaged temperature gradient, high-amplitude oscillating flow can greatly increase the axial flux of thermal diffusion (Soret) separation of the components of the mixture. The enhancement occurs when the oscillating lateral temperature gradient greatly exceeds the axial gradient, causing a large oscillating concentration that can be favorably time-phased with the oscillating flow. This process can occur even with a negligible pressure oscillation or with a negligible temperature response to pressure, as is the case in most liquid solutions. The thermal boundary condition imposed by realistic solids on thermoacoustic liquids is imperfect, adding mathematical complications that are absent for typical gases, for which the solid surface is temporally isothermal. Compared with gas mixtures, the high Lewis number in typical liquid solutions reduces the separation flux associated with the time-averaged temperature gradient, but it also reduces the remixing associated with the time-averaged mole-fraction gradient. For large enough channels, the second-law separation efficiency is only slightly reduced from that of steady liquid Soret separation.

Merits and Demerits of ODE Modeling of Physicochemical Systems for Numerical Simulations

In comparison with the first-principles calculations mostly using partial differential equations (PDEs), numerical simulations with modeling by ordinary differential equations (ODEs) are sometimes superior in that they are computationally more economical and that important factors are more easily traced. However, a demerit of ODE modeling is the need of model validation through comparison with experimental data or results of the first-principles calculations. In the present review, examples of ODE modeling are reviewed such as sonochemical reactions inside a cavitation bubble, oriented attachment of nanocrystals, dynamic response of flexoelectric polarization, ultrasound-assisted sintering, and dynamics of a gas parcel in a thermoacoustic engine.

Analysis of the linear oscillation dynamics of Fluidyne engines

A Fluidyne engine is a liquid piston Stirling engine that uses thermally induced self-sustained oscillations of water and air that are filled in a looped tube and tuning column. It presents high potential for use as a low-temperature-difference Stirling engine with a simple structure. This study analyzes the linear oscillation dynamics of the Fluidyne from a thermoacoustic point of view, with particular emphasis on the local specific acoustic impedance of the working gas, which is given by the ratio of the complex amplitudes of the pressure and velocity oscillations in the regenerator of the Fluidyne. The frequency dependence of the specific acoustic impedance indicates that the gas in the regenerator region undergoes a thermodynamic cycle equivalent to the Stirling cycle when the oscillation frequency is equal to the natural oscillation frequency of the U-shaped liquid column in the Fluidyne. The analysis of the natural oscillation modes determined two key parameters for the desired specific acoustic impedance: the tuning column length and the connecting position to the loop. Experimental verification was achieved via measurements of the onset temperature ratio and acoustic field of a prototype Fluidyne engine.

Measurement of acoustic dissipation occurring in narrow channels with wet wall

The acoustic dissipation that occurs in a porous medium is experimentally investigated. Two conditions are tested. One is that the wall of the porous medium is wet by water, and the other is that it is dry. Experimental results show that water does not affect viscous dissipation; however, it affects the dissipation caused by pressure oscillation. Furthermore, it is found that the effect of water on the dissipation due to pressure oscillation increases with the temperature of the working gas. A theory that can consider the effect of condensation and evaporation on sound propagation is used to investigate the result. The theoretically and experimentally obtained values of dissipation are in good agreement. The reason for the effect of water is analyzed using the theory.

Adsorption-Mediated Mass Streaming in a Standing Acoustic Wave

Oscillating flows can generate nonzero, time-averaged fluxes despite the velocity averaging zero over an oscillation cycle. Here, we report such a flux, a nonlinear resultant of the interaction between oscillating velocity and concentration fields. Specifically, we study a gas mixture sustaining a standing acoustic wave, where an adsorbent coats the solid boundary in contact with the gas mixture. It is found that the sound wave produces a significant, time-averaged preferential flux of a "reactive" component that undergoes a reversible sorption process. This effect is measured experimentally for an air-water vapor mixture. An approximate model is shown to be in good agreement with the experimental observations, and further reveals the interplay between the sound-wave characteristics and the properties of the gas-solid sorbate-sorbent pair. The preferential flux generated by this mechanism may have potential in separation processes.

Effect of evaporation and condensation on a thermoacoustic engine: A Lagrangian simulation approach

Acoustic oscillations of a fluid (a mixture of gas and vapor) parcel in a wet stack of a thermoacoustic engine are numerically simulated with a Lagrangian approach taking into account Rott equations and the effect of non-equilibrium evaporation and condensation of water vapor at the stack surface. In a traveling-wave engine, the volume oscillation amplitude of a fluid parcel always increases by evaporation and condensation. As a result, pV work done by a fluid parcel is enhanced, which means enhancement of acoustic energy in a thermoacoustic engine. On the other hand, in a standing-wave engine, the volume oscillation amplitude sometimes decreases by evaporation and condensation, and pV work is suppressed. Presence of a tiny traveling-wave component, however, results in the enhancement of pV work by evaporation and condensation.

A model for sound propagation between two adsorbing microporous plates

A model describing the sound propagation between two infinite adsorbing plates is proposed in order to investigate the extension to the audible sound range of the Frequency Response method applied to the measurement of diffusion in micropores. The model relates adsorption parameters (i.e., diffusivity and equilibrium constant) to an acoustic quantity (i.e., propagation constant). The equations describing sound propagation in the presence of adsorbing boundaries are obtained on the basis of the classical Kirchhoff theory [(1868). Ann. Phys. (Leipzig) 134, 177-193]. The solution is derived using the Low Reduced Frequency Approximation method [Tijdeman, (1975). J. Sound Vib. 39, 1-33].

Acoustics and precondensation phenomena in gas-vapor saturated mixtures

Starting from fundamental hydrodynamics and thermodynamics equations for thermoviscous fluids, a new modeling procedure, which is suitable to describe acoustic propagation in gas mixtures, is presented. The model revises the boundary conditions which are appropriate to describe the condensation-evaporation processes taking place on a solid wall when one component of the mixture approaches saturation conditions. The general analytical solutions of these basic equations now give a unified description of acoustic propagation in an infinite, semi-infinite, or finite medium, throughout and beyond the boundary layers. The solutions account for the coupling between acoustic propagation and heat and concentration diffusion processes, including precondensation on the walls. The validity of the model and its predictive capability have been tested by a comparison with the description available in the literature of two particular systems (precondensation of propane and acoustic attenuation in a duct filled with an air-water vapor saturated mixture). The results of this comparison are discussed to clarify the relevance of the various physical phenomena that are involved in these processes. The model proposed here might be useful to develop methods for the acoustic determination of the thermodynamic and transport properties of gas mixtures as well as for practical applications involving gas and gas-vapor mixtures like thermoacoustics and acoustics in wet granular or porous media.

Acoustic fields in binary gas mixtures: mutual diffusion effects throughout and beyond the boundary layers

The acoustic behavior in thermo-viscous gas mixtures, both in proximity of walls and far from them (outside the boundary layers), involves deviations from the adiabatic and laminar movements in pure gases, which result from the influence of several diffusive fields, namely, shear, entropic, and concentration variation fields (their energy being provided by the acoustic field itself). Owing to the boundary conditions, that are slip condition, isothermal condition and concentration flux vanishing on the walls, a strong coupling between these fields occurs inside the boundary layers while their effects appear to be simple additive processes in the bulk of the medium. Although recent literature on this subject leads to interesting results, opening the way to several new issues [R. Raspet et al., J. Acoust. Soc. Am. 105, 65-73 (1999); R. Raspet et al., J. Acoust. Soc. Am. 112, 1414-1422 (2002); G. W. Swift and P. S. Spoor, J. Acoust. Soc. Am. 106, 1794-1800 (1999); D. A. Geller and G. W. Swift, J. Acoust. Soc. Am. 111, 1675-1684 (2002)], the results available still have limitations because they do not provide complete solutions for the propagative and diffusive fields throughout and beyond the boundary layers. The present work aims at providing these solutions in the whole domains considered. The results allow interpreting analytically the behavior of the fields above mentioned in closed cavities and ducts, and particularly in spherical cavities which are best suited to develop metrological applications.

Parallel capillary-tube-based extension of thermoacoustic theory for random porous media

Thermoacoustic theory is extended to stacks made of random bulk media. Characteristics of the porous stack such as the tortuosity and dynamic shape factors are introduced into the thermoacoustic wave equation in the low reduced frequency approximation. Basic thermoacoustic equations for a bulk porous medium are formulated analogously to the equations for a single pore. Use of different dynamic shape factors for the viscous and thermal effects is adopted and scaling using the dynamic shape factors and tortuosity is demonstrated. Comparisons of the calculated and experimentally derived thermoacoustic properties of reticulated vitreous carbon and aluminum foam show good agreement. A consistent mathematical model of sound propagation in a random porous medium with an imposed temperature is developed. This treatment leads to an expression for the coefficient of the temperature gradient in terms of scaled cylindrical thermoviscous functions.

Theory of inert gas-condensing vapor thermoacoustics: transport equations

The preceding paper [J. Acoust. Soc. Am. 112, 1414-1422 (2002)] derives the propagation equation for sound in an inert gas-condensing vapor mixture in a wet-walled pore with an imposed temperature gradient. In this paper the mass, enthalpy, heat, and work transport equations necessary to describe the steady-state operation of a wet-walled thermoacoustic refrigerator are derived and presented in a form suitable for numerical evaluation. The requirement that the refrigerator operate in the steady state imposes zero mass flux for each species through a cross section. This in turn leads to the evaluation of the mass flux of vapor in the system. The vapor transport and heat transport are shown to work in parallel to produce additional cooling power in the wet refrigerator. An idealized calculation of the coefficient of performance (COP) of a wet-walled thermoacoustic refrigerator is derived and evaluated for a refrigeration system. The results of this calculation indicate that the wet-walled system can improve the performance of thermoacoustic refrigerators. Several experimental and practical questions and problems that must be addressed before a practical device can be designed and tested are described.