The combustion instability is investigated computationally for a multi-injector rocket engine using the flamelet progress variable (FPV) model. A C++ code is developed based on OpenFOAM 4.0 to apply the combustion model. Flamelet tables are generated for methane/oxygen combustion at the background pressure of $200$ bar using a 12-species chemical mechanism. A power law is determined for rescaling the reaction rate for the progress variable to address the pressure effect. The combustion is also simulated by the one-step-kinetics (OSK) method for comparison with the FPV approach. A study of combustion instability shows that a longitudinal mode of $1500$ Hz and a tangential standing wave of $2500$ Hz are dominant for both approaches. While the amplitude of the longitudinal mode remains almost the same for both approaches, the tangential standing wave achieves a larger amplitude in the FPV simulation. A preliminary study of the resonance in the injectors, which is driven by the longitudinal-mode oscillation in the combustion chamber, is also presented.
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