Axial-mode solid-state thermoacoustic instability: An analytical parametric study

Abstract

Solid-state thermoacoustic (SSTA) instability refers to the occurrence of unstable thermoelastic oscillations of solid media when in presence of a spatial temperature gradient. Recently, theoretical and numerical studies have shown that both standing and traveling thermoacoustic waves can exist in solids. The many mechanisms available in solids to tailor either their physical or effective properties offer remarkable opportunities to enhance and tune the performance of SSTA devices. A thorough understanding of the functional relationships controlling the complex dynamics in solid-state thermoacoustics (SSTAs) is critical to design efficient SSTA machines. In this paper, we first recast the governing equations of SSTAs into dimensionless form; then, we develop accurate analytical approaches to solve for the mode shapes and complex frequencies for 1) a standing-wave fixed-mass SSTA rod, and 2) for a traveling-wave looped SSTA rod. It is found that the growth-rate-to-frequency ratio is governed by the dimensionless coefficient of thermal expansion (CTE), the Grüneisen parameter, the hot-to-cold temperature ratio, the normalized stage location and length, the dimensionless radius, the end mass ratio for the fixed-mass rod, and the thermal buffer segment (TBS) length for the looped rod. Based on these newly identified dimensionless parameters a thorough numerical analysis is conducted in order to shed light on the optimal design of SSTA devices.