Dynamics of Practical Premixed Flames, Part I: Model Structure and Identification

Abstract

For the analysis of thermoacoustic instabilities it is most important to determine the dynamic flame response to acoustic disturbances. Premixed flames are often modelled as single-input single-output system, where the “output” (the overall rate of heat release) responds to a single “input” variable (often the velocity at the exit of the burner nozzle). However, for practical premixed flames, where perturbations of pressure or velocity at the fuel injector will modulate the fuel equivalence ratio, the heat release rate will respond to fluctuations of equivalence ratio as well as nozzle mass flow rate. In this case, a multiple-input, single-output (MISO) model structure for the flame is appropriate. Such a model structure is developed in the present paper. Staged fuel injection as well as fuel line impedances can be taken into account, the integration with low-order or finite-element based models for stability analysis is straightforward. In order to determine unit impulse and frequency response functions for such a model structure, an identification scheme based on unsteady CFD calculation with broadband excitation followed by correlation analysis is proposed and validated successfully. Identification of MISO model coefficients is a challenging task, especially in the presence of noise. Therefore criteria are introduced which allow to ascertain a posteriori how well the identified model represents the true system dynamics. Using these criteria, it is investigated how excitation signal type, time series length and signal-to-noise ratio influence the results of the identification process. Consequences for passive design strategies based on multi-stage fuel injection and experimental work on practical premixed flame dynamics are discussed.