Linear stability and resolvent analyses of a bluff-body stabilized flame with conjugate heat transfer

Conjugate heat transfer is a challenging fluid-structure coupling problem that can significantly influence flame stabilization and thermoacoustic instabilities. To properly capture combustion phenomena that involve conjugate heat transfer, careful modeling of chemical reactions in the fluid domain and heat transfer in the solid body is necessary and remains an active research topic. To this end, we derived a strongly-coupled method with a monolithic weak formulation to investigate the conjugate heat transfer between an anchored flame and a thermal conductive cylinder by means of linear stability analysis and resolvent analysis. We conduct parameter continuation with the Damkohler number to construct a bifurcation diagram and identify multiple baseflow states, including blow-off, anchored flame, and flashback. Linear stability analysis reveals the presence of a single unstable, non-oscillatory eigenmode for the base states on the anchored flame branch. This eigenmode plays a pivotal role in driving the bifurcation. Subsequently, resolvent analysis is performed to examine the amplification behavior of the fluid-solid coupled system under external forcing, showing that heat fluctuations are maximized when heat transfer between the fluid and solid is minimized.