Traveling and standing thermoacoustic waves in solid media

TL;DR

This study explores self-sustained traveling thermoelastic waves in solid rods with thermal gradients, revealing dominant traveling wave modes with higher growth rates than standing waves, and provides insights into energy conversion in solid-state thermoacoustic engines.

Contribution

It is the first numerical investigation of traveling wave thermoacoustic oscillations in solids, analyzing their energy dynamics and conditions for dominance over standing waves.

Findings

Traveling wave component becomes dominant as rod radius approaches thermal penetration depth.

Traveling TA waves have higher growth-rate-to-frequency ratios than standing waves.

Energy budgets elucidate the energy conversion processes in solid-state thermoacoustic systems.

Abstract

The most attractive application of fluid-based thermoacoustic (TA) energy conversion involves traveling wave devices due to their low onset temperature ratios and high growth rates. Recently, theoretical and numerical studies have shown that thermoacoustic effects can exist also in solids. However, these initial studies only focus on standing waves. This paper presents a numerical study investigating the existence of self-sustained thermoelastic oscillations associated with traveling wave modes in a looped solid rod under the effect of a localized thermal gradient. Configurations having different ratios of the rod radius $R$ to the thermal penetration depth $\delta_k$ were explored and the traveling wave component (TWC) was found to become dominant as $R$ approaches $\delta_k$. The growth-rate-to-frequency ratio of the traveling TA wave is found to be significantly larger than that of the standing wave counterpart for the same wavelength. The perturbation energy budgets are analytically formulated and closed, shedding light onto the energy conversion processes of solid-state thermoacoustic (SSTA) engines and highlighting differences with fluids. Efficiency is also quantified based on the thermoacoustic production and dissipation rates evaluated from the energy budgets.