Driving mechanisms in low order modeling of longitudinal combustion instability

Several test cases in the literature have shown that both transverse and longitudinal high frequency combustion instability can be driven by the injector dynamics. In these cases, pressure oscillations result into fluctuations of propellants mass flow rate, yielding to pulsing heat release. This fundamental mechanism is the focus of the present work, aiming to include this effect into a quasi-1D Eulerian model, for studies of longitudinal combustion instability. In particular, the injection dynamics is represented through a simplified formulation representing the core of the proposed response function. Moreover, the role of combustion efficiency, in order to recover the main limit cycle characteristics (frequency and amplitude), is also discussed. The obtained model is tested comparing the quasi-1D simulations against the experimental data of the Continuously Variable Resonance Combustor (CVRC) available in the literature, considering three different geometrical configurations, with different length of the oxidizer post. The proposed formulation is able to reasonably reproduce the unstable behavior as well as to provide a simple model explaining the mechanism leading to low average combustion efficiency during unstable operation.