Theoretical And Experimental Study Of Heat Sound Source Localization In The Duct

Combustion instability is an important problem for the development of lean premixed combustion for low-NOx emission in practice.The combustion instability in the combustion chamber of the gas turbine would cause the large acoustic perturbations.Determining the position of the unsteady acoustic source with the pressure measured is beneficial for the monitor and the control of combustion instability.This paper established the relationship between the acoustic source and the pressure perturbations in the duct.The microphone array was used to measure the distribution of pressure in the duct and the acoustic inverse problem model was established to localize the heat acoustic source,which is an inverse problem of mathematical physics.The results would provide supports to the control of the combustion instability in the combustor.There are three parts in this thesis.The beamforming method was used to study the azimuthal localization and the plane localization of the sound source in the duct.The acoustic model of the monopole source in the duct was built,and the experimental rig was set up.In the experiments,the circular microphone array was used to measure the pressure.The results show that at low frequencies,the resolution is insufficient and side lobes exists.DAMAS can be used to improve the resolution and remove the side-lobes.When the frequency is close to a cut-on frequency of the spinning mode,the measured pressure is dominated by the single mode and the results rapidly deteriorate.An improved algorithm is developed to address this problem.The simulations and experiments results indicate that the accuracy of the localization is highly dependent on the number of the spinning modes that are able to propagate in the duct.Significant improvements can be achieved when the algorithm is applied in the near-cut-on condition.The reconstruction of the one-dimensional heat release rate was studied by simulation based on the thermo-acoustic inverse problem model.The relationship between the oscillation heat release rate and the pressure was represented as a Volterra integral equation of the first kind.The discretization method was applied to transform the integral equation into matrix form and the regularization method was proposed to stabilize the solution.The influence of discretization method,discretization steps and the regularization method was studied in the simulation.The results show that in the application,the mid-point discretization method and Tikhonov regularization should be applied.Based on the simulation research of the thermo-acoustic inverse problem,the experimental validation was studied.The Rijke combustion dynamic facility was built,and the The semi-finite probe system was used to measure the pressure perturbations in the duct and the calibration of the measurement system was studied before the experiments.The microphone array was mounted in the axial direction of the duct to measure the pressure distribution,and the distribution of the unsteady heat release rate was calculated based on the inverse model.The results show that the error in the pressure data may be amplified when the frequency is close to the resonant frequency of the duct,therefore,the regularization method should be applied.Furthermore,the thermo-acoustic inverse problem model considering the influence of the temperature was developed in this paper,and was used to achieve the sound source localization in the high temperature condition and the heat source localization when the combustion instability occurs.To validate the theory further,the model gas turbine combustor was designed and developed.The results indicate the measurement of the pressure can be used to localize the axial position of the heat release rate.