Numerical study of thermoacoustic Taconis oscillations

Abstract

This paper studies quantitatively a thermoacoustic field by the Taconis oscillations with finite amplitude in a helium-filled, quarter-wavelength tube. Numerical simulations are performed based on the one-dimensional theory in the boundary-layer approximation developed in a previous paper [N. Sugimoto and D. Shimizu, Phys. Fluids 20, 104102 (2008)] by solving initial- and boundary-value problems for a smooth step temperature distribution. It is found that the variations in the density, temperature, and entropy are so significant that the mean values deviate from the respective values in quiescent state. The mean acoustic energy flux and mean heat flux are calculated not only in the main-flow region but also in the boundary layer. The mean convective heat flux appears locally in the main-flow region due to higher-order nonlinear effects. While the total heat flux into the gas vanishes per one period, the local heat flux flows into the gas over a middle part of the tube.