Account of heat convection by Rayleigh streaming in the description of wave amplitude growth and stabilization in a standing wave thermoacoustic prime-mover.

Abstract

This study focuses on the transient regime of wave amplitude growth and stabilization occuring into a standing wave thermoacoustic engine. Experiments are performed on a standing wave thermoacoustic oscillator. They show that the transient regime leading to steady state sound exhibits complicated dynamics, like the systematic overshoot of wave amplitude before its final stabilization, and the spontaneous and periodic switch on/off of the thermoacoustic instability at constant heat power supply. A simplified model is presented which describes wave amplitude growth from the coupled equations governing thermoacoustic amplification and unsteady heat transfer. In this model, the assumption of a one-dimensional temperature profile is retained and the equations describing heat transfer through the thermoacoustic core are coupled to that describing wave amplitude growth. These equations include the simplified description of two processes saturating wave amplitude growth, i.e. thermoacoustic heat pumping by acoustic waves and heat convection by Rayleigh streaming. It is notably shown that both effects could be responsible of the observed overshoot process.