Numerical multi-scale analysis of premixed-flame thermoacoustic instabilities with wall heat quenching

Recent experiments of premixed flames propagating from the open to the closed end of slender tubes have emphasized the importance of wall effects–of thermal and viscous nature–in the transition between various thermoacoustic regimes. However, limited experimental access to temperature and reaction-rate measurements impede a full understanding of the coupling between the acoustic and reactive characteristics of the flow. Contrarily, numerical simulations and mathematical modeling can provide extra information of heat-transfer processes and underlying flow properties in thermoacoustic problems. In the present work, a set of 2D numerical simulations of premixed flames in non-adiabatic channels reproduces the flame dynamics observed in experiments of stoichiometric methane-air flames, which remain representative of nearly equidiffusional flames propagating in slender channels. The numerical simulations validate existing one-dimensional models for flame acoustics at the tube-length scale, while at the flame-length scale they serve to explore the variations of two-dimensional acoustics and non-isothermal eigenfunctions that induce the deformation of the flame front, enhancing the corrugation of the reactive front near non-adiabatic walls. These facts become instrumental to provide a causality study on the origin and transition from primary to secondary thermoacoustic instabilities and their sensitivity to wall heat losses. Novelty and significance statement: This work’s simulations reproduce the intricate flame-wall interaction governing thermoacoustic instabilities in slender tubes and its sensitivity to wall cooling. In doing so, the capabilities of the simplified numerical simulations are successfully tested, rendering future analyses trustworthy and accessible. The separate contribution of thermal, viscous and hydrodynamic effects to the flow’s acoustic response, reveal the roles of convective acceleration at the preheat region and conductive heat transfer at the wall. The results validate the theoretical modeling of pressure eigenmodes through non-isothermal acoustics and highlight novel but fundamental contributing effects. In particular, the oscillating flame-edge quenching along with the identification of unsteady wall cooling contributes to understanding the role of heat-losses in the stability of micro-combustors, guiding strategies for the suppression of instabilities and the development of safer and more efficient devices.