Measurements of the impedance matrix of a thermoacoustic core: Applications to the design of thermoacoustic engines

Abstract

The successful design of a thermoacoustic engine depends on the appropriate description of the processes involved inside the thermoacoustic core (TAC). This is a difficult task when considering the complexity of both the heat transfer phenomena and the geometry of the porous material wherein the thermoacoustic amplification process occurs. An attempt to getting round this difficulty consists in measuring the TAC transfer matrix under various heating conditions, the measured transfer matrices being exploited afterward into analytical models describing the complete apparatus. In this paper, a method based on impedance measurements is put forward, which allows the accurate measurement of the TAC transfer matrix, contrarily to the classical two-load method. Four different materials are tested, each one playing as the porous element allotted inside the TAC, which is submitted to different temperature gradients to promote thermoacoustic amplification. The experimental results are applied to the modeling of basic standing-wave and traveling-wave engines, allowing the prediction of the engine operating frequency and thermoacoustic amplification gain, as well as the optimum choice of the components surrounding the TAC.

Weakly Nonlinear Propagation in Thermoacoustic Engines: A Numerical Study of Higher Harmonics Generation up to the Appearance of Shock Waves

“…Thermoacoustic pumping is well described analytically for simple pore shapes [9], or with hybrid analytic/experimental approaches for more complex materials [10,11]. Acoustic streaming is accounted for in models by higher-order developments of the basic equations [12,13], and experimental solutions are implemented to limit its effects [14,15].…”

Parameter estimation for the characterization of thermoacoustic stacks and regenerators

“…Therefore, acoustic propagation through the TAC is only characterized by the four complex elements T ij of its matrix, which depend on the frequency of acoustic oscillations, on the geometrical and thermophysical properties of the stack and heat exchangers, and on the assigned temperature distribution along the TAC. In previous works, we performed the measurements of the T-matrices of various TAC by means of two different methods, namely a classical two-load method [28] and another method based on the use of an acoustic impedance sensor [29]. As a result, experimental data for different kinds of TAC equipped with different stack materials (ceramic catalyst, stainless steel grids, RVC and NiCr foams) are now available, which are obtained for different values of heat power supply in the frequency range 30 Hz-500 Hz.…”

“…In the following, we give a brief description of this element and of the experimental procedure used for measuring its transfer matrix (for a complete description of the measurements methods, the reader can find more details in Refs. [28,29] The acoustic properties of the TAC can be characterized by means of the so-called transfer matrix [30] (T-matrix), which gives a relationship between the complex amplitudes of acoustic pressure and acoustic velocity at both sides of the TAC. More precisely,…”

“…In previous studies [28,29], we presented an experimental setup for the measurements of the acoustical transfer matrix of a TAC under various heating conditions, and we used the experimental data to predict the onset of self-sustained oscillations of any thermoacoustic device equipped with the TAC characterized beforehand. However, such a black box approach does not provide information about the inside of the thermoacoustic core, and therefore the main objective of this study is to evaluate an inverse method approach to get information about the acoustical and thermal properties of the stack/regenerator.…”

“…However, such a black box approach does not provide information about the inside of the thermoacoustic core, and therefore the main objective of this study is to evaluate an inverse method approach to get information about the acoustical and thermal properties of the stack/regenerator. More precisely, the purpose of the present paper is (1) to propose a theoretical description of the TAC and (2) to make use of the experimental results from [28,29] so as to adjust parameters which are generally hard to evaluate (tortuosity, heat exchange coefficient . .…”