Definition of heater location to drive maximum amplitude acoustic oscillations in a Rijke tube

Abstract

This paper presents an analysis that defines the heater location to drive maximum amplitude acoustic oscillations in a Rijke tube. The analysis is based on the mathematical formulation of the Rayleigh criterion and, although applied to a simple geometry, it can be extended to investigate driving in geometries for which the acoustic characteristics are known. For a Rijke tube of length L, driven by a combustion process, it was calculated theoretically that maximum amplitude oscillations occur for the heater bed located at a) $\text{L}\text{4}$ for the fundamental mode; b) $\text{L}\text{8}$ and $\text{5L}\text{8}$ for the second harmonic; and c) $\text{L}\text{12}$, $\text{5L}\text{12}$, and $\text{3L}\text{4}$ for the third harmonic, where the distances are measured from the bottom of the tube. These results were checked experimentally, using a basket of burning wood, for the sections $\text{L}\text{4}$, $\text{L}\text{8}$, $\text{5L}\text{8}$, and $\text{L}\text{12}$. It was verified that acoustic oscillations can be excited in a Rijke tube with its heater element located in certain positions in the upper half.