The Rijke Tube: A Green's Function Approach in the Frequency Domain

The stability behaviour of a Rijke tube is studied by a Green's function approach in the frequency domain. The tube is open at both ends. It contains an acoustically compact flame holder that blocks the acoustic motions; there is also a jump in cross-sectional area and in mean temperature. The oscillating part of the rate of heat release is modelled by a flame transfer function, i.e. the frequency-domain ratio of heat release rate to acoustic velocity. An equation for the complex eigenfrequencies is derived. Its solutions give the frequencies and growth rates of the acoustic modes in the tube. The approach is then used to study the effect of several flame transfer functions on the stability behaviour of the Rijke tube. The role of several parameters in these flame transfer functions is examined. Finally, the possibility is discussed whether one can discriminate between these transfer functions from measurements of the stability behaviour and frequencies in a simple Rijke tube set-up.