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 in fluctuations in propellant mass flow rate, which yields pulsing heat release. This fundamental mechanism is the focus of the present work, with the aim of including this effect in a quasi-1D nonlinear model of Euler equations suited to studies of longitudinal combustion instability. In particular, the injection dynamics is represented through a simplified formulation, which is the core of the proposed response function. The analysis also addresses the influence of combustion efficiency on the main characteristics of the resulting limit cycle (frequency and amplitude). The obtained model is tested comparing the quasi-1D simulations against the experimental data of the continuously variable resonance combustor available in the literature, considering three different geometrical configurations, with different lengths of the oxidizer post. The proposed formulation is capable of reasonably reproducing the unstable behavior, as well as providing a simple model that explains the mechanism that leads to a low average combustion efficiency during unstable operation.