Prediction of the heat-release transfer function of a premixed flame

This paper studies the effect of acoustic excitation on the heat release characteristics of a two dimensional premixed flame. Past researches have assumed the acoustic nearfleld and kinematics of the flame surface to be decoupled. However, recent studies by the authors have shown that the acoustic nearfleld is significantly affected by flame surface wrinkling and hence the coupling between flame surface kinematics and the acoustic field cannot be neglected. The acoustic velocity nearfleld of the flame surface is determined using a modified Boundary Integral Equation (BIE) to include the effects of flame front wrinkling on the acoustic field. A linearized G-equation is solved to obtain an expression for the flame surface wrinkling in terms of the acoustic velocity at the flame front. This equation is then solved simultaneously with the BIE using a Newton-Raphson scheme to obtain simultaneously, the flame surface shape and the acoustic velocity variation, for the case of a two-dimensional dump stabilized flame. The results show that the transfer function is controlled by two parameters, the flame Strouhal number and the half-angle at the apex of the flame (θ). The computed transfer function is compared with the transfer functions obtained assuming a one-dimensional axial velocity fluctuation and by neglecting kinematic coupling. The latter predicts transfer function magnitudes greater than unity. The inclusion of kinematic coupling however is observed to predict lower gain at low excitation Strouhal numbers when compared to the uncoupled case. The predicted magnitudes are seen to increase with decrease in θ. The predicted phase however, is observed to be insensitive to changes in θ.