Heckl M., Howe M.

A theoretical model is presented to predict the stability of a Rijke tube from a Green’s function analysis. The Rijke tube is modelled as an open-ended tube with a blockage (compact compared with the wavelength) and jump in cross-section. Its Green’s function is calculated for various source and observer positions. In the region near the blockage the flow is assumed to be incompressible; on either side of the blockage, acoustic wave propagation is assumed. The velocity potentials of the incompressible and acoustic regions are matched by continuity of pressure and volume flow. A linear heat release function (relating perturbations in heat release to those of velocity) is considered. Oscillations in the Rijke tube are modelled by an integral equation involving the Green’s function. The growth rates are predicted from this integral equation and given in terms of properties of the heat release and of the Green’s function.