Thermoacoustic instability (TAI) is an undesirable phenomenon that can lead to sizeable structural vibration, noise pollution, and failure of the power systems. Therefore, it is required to understand the mechanism of TAI to predict and control it. In this study, to analyze the TAI, a two-dimensional (2D) computational fluid dynamics method has been developed for the vertical Rijke using Unsteady Reynolds averaged numerical simulation. To trigger the thermoacoustic instability, a trigger has been applied at the inlet boundary of the Rijke tube for a small duration (impulse time) using a user-defined function (UDF). The results have been observed to be in good agreement with published data. The effect of impulsive time of trigger on TAI has been analyzed. The limit cycle amplitude and frequency have been observed. The phase differences between the oscillation of pressure, velocity, and heat release have been calculated and they satisfy the Rayleigh criterion. The Rayleigh index and sound level in decibels have been calculated.