Active control of nonlinear pressure oscillations in combustion chambers

A theoretical analysis of active control of nonlinear acoustic instabilities in combustion chambers is developed in this article. The formulation starts with a generalized wave equation that describes the dynamic behavior of second-order nonlinear oscillations with distributed feedback actions. Control inputs are provided by the burning of the injected seconday fuel in the chamber, with its instantaneous mass flow rate modulated by a proportionalplus-integral (PI) controller located between the pressure sensor and the fuel injection mechanism. Various nonlinear stability characteristics, including the existence and stability of limit cycles, are studied analytically using the method of time averaging. In addition, an optimization procedure is developed for selecting controller gains. Nomenclature Anij = parameters associated with nonlinear acoustic coupling a = speed of sound in mixture Bnij = parameters associated with nonlinear acoustic coupling b = spatial distribution of burning of control fuel, Eq. (5b), Cv - constant-volume specific heat for two-phase mixture c = amplification factor of sensor output Dni = linear parameters, Eq. (11) Eni = linear parameters, Eq. (11) e - error signal between desired response and actual measurement