The coupling between heat release oscillations produced by equivalence ratio fluctuations with combustor acoustic modes in lean premixed combustion systems, is a serious problem that limits the operation envelope of these devices. Such oscillations are produced by an oscillating pressure drop across air inlets and/or fuel injectors due to the presence of acoustic oscillations. This results in fluctuations in mass flow rates of air and/or fuel entering the combustor, thereby, changing the local equivalence ratio of the mixture at these injector/inlet locations. These perturbations in equivalence ratio are advected by the flow into the flame, causing its heat release to oscillate. Detailed reduced order models for the heat release response of premixed flames to equivalence ratio oscillations, based on this phenomenological picture, have been developed in the past. A key problem in validating these models is the ambiguity of interpretation of chemiluminescence signals when, the length scale of equivalence ratio fluctuations is smaller than the characteristic flame length. As such, the present work performs a DNS of a premixed methane-air flame, subject to unsteady forcing in upstream methane mass fraction. Predictions from prior reduced order modelling approaches are compared with present DNS results. The agreement between modelling and DNS predictions in the characteristics of flame response is good at low excitation frequencies and amplitudes. This agreement, however, degrades as forcing amplitude and frequency increase due to the influence of hydrodynamic coupling between the flow-fields on either side of the flame as well as damping of equivalence ratio perturbations by diffusion, on the dynamics of the flame.
Effect of equivalence ratio on premixed flame response to unsteady strain-rate and curvature