Numerical simulation of self-excited thermoacoustic instabilities in a Rijke tube

Self-excited thermoacoustic instabilities or oscillations occur in confined geometries and result from a feedback loop between the heat transferred to the fluid from a heat source and the acoustics of the geometry. If the heat input is at times of high pressure, a self-amplification of acoustic fluctuations may lead to high pressure amplitudes. The effect can be observed in a Rijke tube, a straight tube with a heating element made from hot wires or gauze that provides the heat input. In the presence of a gas flow, pressure oscillations are excited at one of the tube's natural frequencies. Two different kinds of Rijke tubes are modelled by using a control volume based finite difference method to solve iteratively the unsteady conservation equations for mass, momentum and energy. The obtained results are in good agreement with experiments. Besides the general behaviour of the oscillating system, non-linear effects are also accounted for by the simulations. The non-linearities in the heat transferred to the fluid from the heat source were investigated. These determine the limit cycle amplitudes of the self-excited oscillations. (C) 1999 Academic Press.