In this paper, the effect of the non-normal nature of premixed flameacoustic interaction and the effect of internal flame dynamics on thermoacoustic instability are investigated. The thermoacoustic system is modeled by considering the acoustic momentum and energy equations together with the equation for the evolution of the flame front obtained from the kinematic G-equation. The linearised operator for this thermoacoustic system is non-normal leading to non-orthogonality of its eigenvectors.

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... orthogonal eigenvectors can cause transient growth in evolutions even when all the eigenvectors are decaying for a linearly stable case. Therefore, classical linear stability theory cannot predict the finite time transient growth observed in non-normal systems. A parametric study of the variation in transient growth due to change in parameters such as flame location and flame angle is performed. In addition to projections along the acoustic variables of velocity and pressure, the optimal initial condition for the self evolving system has significant projections along the variables for heat release rate. Nonlinear simulations show subcritical transition to instability and dominant mode shift for the present model. It is shown that low order models such as a time lag model or a lumped model for the heat release rate dynamics as a function of acoustic velocity cannot adequately capture the non-normal effects. The notion of phase between acoustic pressure and heat release rate as an indicator of stability is examined. Nomenclature = flame front displacement = axial velocity = flame angle = laminar flame speed = radius of duct = radius of burner = length of duct = heat release rate per unit surface area of flame = heat release rate per unit mass of mixture = surface area of flame = cross-sectional area of duct = co-ordinate along unperturbed flame front = co-ordinate along duct length 1 Graduate student. 2 Professor and Associate Fellow of AIAA.