Analysis of the Wave Scattering From Turbulent Premixed Flame
Cho, Ju Hyeong
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A theoretical investigation of acoustic wave interactions with turbulent premixed flames was performed. Such interactions affect the characteristic unsteadiness of combustion processes, e.g., combustion instabilities. The small perturbation method (SPM) was utilized to evaluate the scattered fields as a result of the flame-wave interaction at the instantaneous wrinkling surface of a randomly moving turbulent flame. Stochastic analysis of ensemble-averaged net acoustic energy was conducted to examine coherent and incoherent acoustic energy amplification /damping by the interaction. Net acoustic energy flux out of the flame is due to two factors: the acoustic velocity jump due to unsteady heat release from flame. The other is the flames unsteady motion. Five(5) dimensionless parameters that govern this net acoustic energy were determined: rms height and correlation length of flame front, incident wave frequency, the ratio of flames diffusion time to flame fronts correlation time, and incidence angle. The dependence of net acoustic energy upon these dimensionless parameters was illustrated and discussed by numerical simulations in case of Gaussian statistics of flame front. The laminar flame response to equivalence ratio perturbations was also examined, showing that the overall heat release response is controlled by the superposition of three disturbances: heat of reaction, flame speed, and flame area. Heat of reaction disturbances dominate the flame response at low Strouhal numbers, roughly defined as (frequency x flame length)/(axial flow velocity). All three disturbances play equal roles at Strouhal numbers of O(1). In addition, the mean equivalence ratio exerts little effect upon this transfer function at low Strouhal numbers. At O(1) Strouhal numbers, the flame response increases with decreasing values of the mean equivalence ratio.