Low Frequency Combustion Instability Analysis in LRE by Using Double Time Lag Theory

The low frequency instability in LRE is modeled and analyzed using the double time lag model in the present work. To this end, the interaction between the fluctuations of injectors representing feed system oscillations on the one hand, and fluctuations of chamber pressure representing combustion oscillations on the other hand have been considered. The dynamics of chamber pressure is modeled through the double time lag or evaporization and mixing time lag model. This way, the low frequency instability boundary in liquid-gas and liquid-liquid engines is analyzed and their corresponding frequencies are determined. It is shown that increasing the pressure drop of injectors and gas residence time can stabilize the engine. Decreasing the mixing time in liquid-gas engines has a stabilizing effect, but this is not true for liquid-liquid engines. In these engines, the mixing time has different effects on the stability boundaries depending on the evaporization time of fuel and oxidizer. It is also concluded that low frequency instability can be initiated at special domains of frequency. The results are in agreement with the available theoretical and experimental results.