Non-monotonic flame response behaviors in harmonically forced flames

Abstract

This paper describes an investigation into the nonlinear response of flames to harmonic forcing. The amplitude dependent response of the heat release to imposed forcing plays a key role in determining conditions where self-excited oscillations occur, and their amplitudes. This paper particularly focuses on the flame response amplitude. Several prior results, both experimental and theoretical have noted the saturating character of the flame response as the disturbance amplitude increases. In addition, some experiments have also shown more complex amplitude dependencies, including inflection points and even non-monotonic response behaviors. In the latter case, the flame response decreases with increasing disturbance amplitude over a range of amplitudes. This paper analyzes the conditions under which such non-monotonic behavior occurs. By expanding the unsteady heat release response in an expansion of the form, Q(t)=Q0+ϵQ1(t)+ϵ2Q2(t)+ϵ3Q3(t)+O(ϵ4), we show that non-monotonic behavior occurs when the phase between the O(ϵ3) term and the linear term fall in a certain band. The model is then applied to representative measured data from the literature where non-monotonic behavior is observed, to extract the different flame response contributions. Finally, results are presented from nonlinear premixed flame calculations to explicitly show the parameter regions where such behavior occurs.