Self-excited periodic combustion instabilities in a staged lean burn combustor could be generated by operating the combustor at single-sector,sector and full annular combustor test rigs,but differences existed in oscillation modes and frequencies.In order to investigate the differences and establish the relationship among them,and to verify the thermo-acoustic instability simulation method,experiments and numerical simulations of combustion instabilities were carried out on these three kinds of test rigs,the oscillation characteristics of different test rigs were obtained,and the results were compared between simulations and experiments.The results showed that there were two unstable modes in full annular combustor,while only one unstable mode existed in sector combustor and single-sector combustor.The single-sector and sector combustors can represent one of the unstable modes in full annular combustor,but cannot represent another unstable mode.The three-dimensional finite element method thermo-acoustic simulation method accurately predicted the combustion instabilities of these three different kinds of test rigs,and the predicted dimensionless unstable frequencies were consistent with the experimental results with an error within 2%.