In order to investigate the effect of circumferential non-uniform fluid parameters and heat release on thermoacoustic instabilities

Chebyshev method was applied to axial and radial directions and Fourier method was applied to circumferential direction in the linear Euler equations. Resonant frequencies and acoustic fields of a duct were obtained by this method for validation and further investigations. At last

after some calculation for circumferential non-uniform heat release

it is verified that some symmetrical circumferential non-uniform conditions can be simplified to uniform conditions. But this approximation would bring errors if the circumferential non-uniform distribution is strong in case of asymmetrical distribution.