Linear stability analysis was conducted in modal premixed combustor with bluff body flame holder. The software COMSOL Multiphysics was used to solve the three-dimensional Helmoholtz equation. The time lag model was the source term of equation. The periodic change of chemical reaction rate was studied by unsteady calculation for modal premixed combustor

and the unsteady heat release occurred at the top of the flame. The delay times of 0.6

0.3

0.9

0.6ms were obtained for equivalence ratios of 0.72

0.8

0.88 and 0.97 respectively in four cases based on the phase difference of pressure and temperature signals. The linear stability analysis obtained the real part and imaginary part of frequency of longitudinal mode for modal premixed combustor

and the negative imaginary part represented linear instability. The results show that the second

third

and fourth longitudinal modes are linear instability in the first five longitudinal modes. The imaginary part of the third longitudinal mode has the largest absolute value

indicating the largest growth rate in small disturbance. So there is the biggest possibility to occur linear unstable and combustion instability for the third longitudinal mode in disturbance.