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Research Papers: Gas Turbines: Combustion, Fuels, and Emissions

Determination of the Instantaneous Fuel Flow Rate Out of a Fuel Nozzle

[+] Author and Article Information
Tongxun Yi1

Department of Mechanical and Nuclear Engineering, Pennsylvania State University, University Park, PA 16802tzy1@psu.edu

Domenic A. Santavicca

Department of Mechanical and Nuclear Engineering, Pennsylvania State University, University Park, PA 16802

1

Corresponding author.

J. Eng. Gas Turbines Power 132(2), 021503 (Oct 30, 2009) (7 pages) doi:10.1115/1.3155784 History: Received October 16, 2008; Revised March 23, 2009; Published October 30, 2009

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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Figures

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Figure 1

Acoustic experiment setup

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Figure 2

Measured and predicted pressure 2.5 cm upstream of the fuel injector. (a) Straight tubing (0.98 m); (b) bending tubing with two 90 deg sharp turns with zero radii (1.02 m). For both tests, the air flow rate is 50.9 SLPM, and the forcing input amplitude is 1.8 V.

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Figure 3

(a) Normalized amplitude of the instantaneous mass flux; (b) phase lag between the instantaneous mass flux and pressure at x0=−2.5 cm; (c) ratio of the mass changing rate to the inflow acoustic mass flux; and (d) normalized amplitude of the instantaneous mass flux at different forcing input amplitudes, namely, 0.8 V, 1.2 V, and 1.6 V

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Figure 4

Spatial distribution of specific acoustic impedance (forcing input amplitude of 1.8 V and zero mean flow)

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Figure 5

Spatial distribution of specific acoustic impedance (forcing input amplitude of 1.8 V and mean flow of 50.9 SLPM)

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Figure 6

Effects of forcing input on specific acoustic impedance (zero mean flow)

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Figure 7

Effects of forcing input on specific acoustic impedance (mean flow of 50.9 SLPM)

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Figure 8

Effects of mean flow on specific acoustic impedance (forcing input amplitude of 1.0 V)

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Figure 9

Measurements versus prediction for dynamic pressure 0.04 m upstream of the fuel nozzle. The mean fuel pressure is 138 kPa. The sound speed is taken as 1100 m/s. Three pressure transducers are installed at 1.04 m, 0.57 m, and 0.04 m upstream of the fuel nozzle, respectively.

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