Modelling the response of Turbulent CH4-Air premixed flame using Resolvent Analysis

An understanding of the flame transfer function (FTF) is essential for predicting the onset of combustion instabilities in gas turbine combustors, where flow oscillations excited by acoustic forcing drive burning area and heat-release oscillations that can couple unfavourably with combustor acoustic modes. The heatrelease response is expensive to characterize directly through time resolved simulation, motivating reduced order approaches that operate on a single time-averaged mean flow. In the present work, we develop and critically assess a resolvent analysis (RA) based reduced order model for the FTF of a turbulent premixed methane air round jet flame (φ=0.8, T_u=800 K, Re≈1500), with the time-averaged base flow obtained from explicit-filtering large eddy simulation (EFLES) of the unforced flame. Two aspects of the RA formulation are examined systematically: the passive versus active treatment of the flame i.e., whether coherent reaction rate fluctuations are dropped or retained in the linearised species/energy equations and the choice of heatrelease rate closure across four models of increasing physical detail (a global Arrhenius model, ARR-A; a Bayesian calibrated modified Arrhenius model with a cold-boundary correction, ARR-B; and global and local Eddy Break-Up models, EBUG and EBUL). RA-predicted FTF gain and phase are validated against harmonically forced LES over St=[0.2,1.2], and the spatial structure of the leading RA response modes is compared against SPOD modes extracted from the same forced LES. FTF phase is recovered robustly by all four models up to St≈0.8, since the leading velocity response mode and hence the convective phase speed governing flame surface wrinkling is set almost entirely by the mean vorticity and density field and shows weak dependence on the heatrelease closure. FTF gain is far more model dependent: the passive ARR-B model gives the best overall quantitative match to LES, with excellent agreement at St=0.2 where non-linear flame tip pocket shedding is negligible, while both EBU models underpredict gain across the full St range because their reaction rate is a function of progress variable and density alone, giving identically zero sensitivity to temperature and fuel mass fraction fluctuations. The resolvent gain spectrum collapses toward strongly low rank behaviour with increasing St a single mode pair recovers 99% of the response for St≥0.6, while three mode pairs are needed at St=0.2 and the Arrhenius-type models produce systematically higher gains than the EBU models owing to their spatially extended sensitivity field. Switching from the passive to the active formulation leaves the velocity response essentially unchanged but qualitatively alters the thermochemical response: temperature and species fluctuations, which propagate downstream as undamped travelling waves in the passive case, decay beyond the flame brush in the active case, in closer qualitative agreement with the LES SPOD modes. This improved qualitative fidelity does not, however, translate into better FTF gain prediction the active formulation degrades gain agreement for every model examined, a result traced to the single free parameter in each heatrelease closure being calibrated only against the mean heatrelease field, with no constraint on the local dynamic sensitivities that the active formulation feeds back into the linear operator. The overall picture that emerges is that RA provides a reliable and computationally efficient framework for predicting FTF in axisymmetric premixed-flame configurations. The results further establish a clear pathway toward improved quantitative gain prediction through reaction-rate closures that represent the local dynamic sensitivities of the flame more faithfully, enabling increasingly predictive low-order models from time-averaged base flows. Further work is needed to improve the active flame approach by developing reaction rate closures that capture both the mean heatrelease field and the local dynamic sensitivities governing flame response feedback.

Speaker : SATYAM CHAUHAN

Research Supervisor :  Santosh Hemchandra