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

Abstract

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.

Measurement of Heat Flow Transmitted through a Stacked-Screen Regenerator of Thermoacoustic Engine

“…This result indicates that r 0 should be used instead of r eff for better estimation of heat flow. Other earlier studies [29,31] have demonstrated that two effective radii are necessary to explain the viscous behavior and the thermal behavior in tortuous porous media because the viscous effects are governed by narrower regions of the channel, whereas the thermal effects are determined by wider regions [32,33]. Our experimentally obtained results provide another example representing the need of the effective thermal radius, in addition to the effective viscous radius.…”

Parameter estimation for the characterization of thermoacoustic stacks and regenerators

“…The stability of the algorithm has been checked by means of simulated experiments with artificial added noise and bias. For the acoustical problem (no heating), the estimation of the porosity, the tortuosity and the pore's inner radius of the stack/regenerator can be successfully achieved, but the estimation of a fourth parameter may make the algorithm unstable because an additional geometrical parameter would be correlated to the three above mentioned parameters (that is the reason why we did not account for the dynamic shape factors [26] in the description of acoustic propagation through the stack).…”

“…In the following, we derive the governing equations from which these T-matrices can be determined. Considering a piece of stack along which the temperature distribution T (x) is assigned, the extension of Rott's theory [14] to porous media proposed by Roh et al [26] can be used to derive the relationship between the complex amplitudes of acoustic pressure and volume velocity.…”

Influence of magnetic field on the periodically oscillating fluid inside a porous medium attached to a thick solid plate

“…Roh and Raspet [26] developed thermoacoustic theories for a random porous medium. Their theories included development of thermal and viscous functions, wave, and temperature distribution equation.…”