Reported is a practical method for accurate and fast determination of the instantaneous fuel flow rate out of a fuel injector. Both gaseous and liquid fuels are considered. Unsteady fuel flow rates introduced into a combustor can be caused by both self-excited pressure pulsations and fuel modulations. During combustion instability, the air flow rate into a combustor also varies in response to pressure pulsations. Accurate determination of the instantaneous fuel and air flow rates is important for both modeling and control of combustion instability. The developed method is based on the acoustic wave theory and pressure measurements at two locations upstream of a fuel injector. This method bypasses the complexities and nonlinearities of fuel actuators and fuel nozzles, and works for systems with slow-time-varying characteristics. Acoustic impedance of a gaseous fuel nozzle is found to be a function of multivariables, including the forcing frequency, the acoustic oscillation intensity, and the mean fuel flow rate. Thus, it is not an intrinsic property of the fuel injector alone. In the present study, sharp tubing bending with almost zero radii is found to have minimal effects on the distribution of 1D acoustic wave. This is probably because vortex shedding and recirculation at tubing corners do not alter the globally 1D characteristics of acoustic wave distribution. Different from the traditional two-microphone method, which determines the acoustic velocity at the middle locations of the two microphones, the present method allows the acoustic velocity, the acoustic mass flux, and the specific acoustic impedance to be determined along the fuel tubing or an air pipe.

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