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This paper treats the control of nonstationary oscillations of the pressure which arise in the combustion process of a Rijke tube. The low order model of a nonstationary combustion process in a Rijke tube with multiplicative feedback control function is considered, which is investigated by means of two-DOF coupled van der Pol oscillator. The self-excited oscillations in the combustion process are analysed by means of the Extended Lindstedt-Poincare (EL-P) method with multiple time scales. By applying the EL-P method, it is ascertained, that nonstationary oscillations are almost periodic with amplitude and phase, which are functions of the slow time scale. Without control of the fuel influx, the self excited oscillations can approach limit cycles. By applying the fuel control, the influence of control parameters on the quenching of the self excited oscillations is investigated in a phenomenon of competitive quenching and mutual synchronization with close frequencies and multiple harmonics, respectively.

Self-excited Oscillations and Fuel Control of a Combustion Process in a Rijke Tube