Analysis of the wave scattering from turbulent premixed flame

The purpose of this study is to lay a foundation for theoretical investigation of acoustic wave interactions with turbulent premixed flames. Such interactions affect the characteristic unsteadiness of combustion processes, e.g., combustion instabilities. Scattered acoustic waves are generated by the interaction with a wrinkled, moving flame front while the shape of flame front is also distorted by the scattered wave fields.; The significance of this work is that, although a great deal of studies have been reported for acoustic wave-flame interactions, no analysis has been performed to analytically evaluate the coherent and incoherent energy amplification/damping due to the transient interaction of acoustic waves and turbulent flames in three-dimensional space. In this thesis 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 flame's unsteady motion. Five (5) dimensionless parameters that govern this net acoustic energy were determined: rms height of flame front, s&d5; = K0sigma, correlation length of flame front,l˜c = K0 lc, incident wave frequency, f˜ 0 = f0tc, the ratio of flame's diffusion time to flame front's correlation time, tau = tr/tc, and incidence angle. The dependence of net acoustic energy upon these dimensionless parameters is illustrated by numerical simulations in case of Gaussian statistics of flame front. The major factors that determine amplification/damping of the total net energy are f˜0 and incidence angle; Amplification occurs when f˜0 ≥ 1 or at near-critical anlges. tau and l˜c have a significant effect on the total energy balance only for a large value (>>1) of f˜0. Coherent (incoherent) energy is damped (amplified) with the square of rms height.; The 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. Thus, this result is in partial agreement with heuristic arguments made in prior studies that the flame response to equivalence ratio oscillations increases as the mixture becomes leaner.