Green's function model for a Rijke tube with a distributed heat source

Abstract

A Rijke tube is an open-ended tube with a compact heat source (flame or hot gauze) inside. The heat source is commonly modelled by the "nτ law", which assumes a point source releasing heat at a rate that is proportional to the velocity (delayed by a time lag τ) at the heat source. The present paper aims to extend this model to include distributed heat sources. A distributed source is simulated by a row of point sources with individual heat release rates and time lags. The acoustic processes in the tube will be modelled by Lighthill's acoustic analogy equation, combined with a Green's function approach. The occurrence of thermo-acoustic instabilities will be predicted for different properties of the heat source. Geometrical complications in the tube, such as a blockage and a jump in cross-section, as well as a jump in mean temperature, will be taken into account.