The effect of the flame phase on thermoacoustic instabilities

摘要

This paper concerns the influence of the phase of the heat release response on thermoacoustic systems. We focus on one pair of degenerate azimuthal acoustic modes, with frequency coo. The same results apply for an axial acoustic mode. We show how the value phi(0) and the slope -tau of the flame phase at the frequency coo affects the boundary of stability, the frequency and amplitude of oscillation, and the phase phi(qp) between heat release rate and acoustic pressure. This effect depends on phi(0) and on the nondimensional number tau omega(0), which can be quickly calculated. We find for example that systems with large values of tau omega(0) are more prone to oscillate, i.e. they are more likely to have larger growth rates, and that at very large values of two the value phi(0) of the flame phase at coo does not play a role in determining the system's stability. Moreover for a fixed flame gain, a flame whose phase changes rapidly with frequency is more likely to excite an acoustic mode.