Coupling relationship between flame variation and acoustic velocity variation was established by G-equation method for combustor with the central body

the mathematical function of combustion heat release model was obtained. In early work

the heat release model was usually derived with the premise of ignoring the combustion expansion effect and the influence of equivalence ratio or temperature on thermo-acoustic instability was studied discretely

This model was developed invoking the combustion expansion effect

which is very different from early work. Result showed that it was the turbulent flame velocity but not the combustion expansion effect the response of heat release strongly. When turbulent flame velocity was fixed

the density expansion rate had very weak influence on the magnitude of the transfer between the heat release rate and acoustic perturbation

and no influence on the phase at all; but when the turbulent flame velocity was changed

both of the magnitude and phase of the transfer function were strongly influenced. Then acoustic modal analysis with the heat release model was carried out to determine the natural frequencies and their corresponding growth rate. At last the influence of the equivalence ratio and inlet air temperature on combustion instability was discussed successively. The cloud chart of stable zones and instable zones were developed

which is very useful to understand and control thermo-acoustic instability.