High frequency combustion instability is one of the major issues of liquid rocket engines. A linear stability analysis is conducted to the combustion chamber by a three dimensional computational aeroacoustics solver in the time domain. The coupling between the combustion process and acoustics is realized by a classical pressure time lag model introduced by Crocco. A stability map is obtained and the most dominant modes are identified. An improved multi-pole broadband impedance model is adopted to study the damping effect of cavity by a recursive convolution technique. A continuous approximation to the resistance and reactance of acoustic cavity is fitted by a vector fitting method. It is shown that, high frequency combustion instability can be predicted properly in the time domain and the most dominant modes can be captured on condition that the parameters of the pressure time lag model are reasonable. The improved multi-pole broadband impedance model can be successfully implemented to study the damping effect of cavities to the most dominant modes.
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