Modelling of ensemble-averaged premixed flame front under harmonic oscillation

Combustion instabilities are one of the most important operability issues associated with low-NOx combustion technology. This paper develops numerical and theoretical analyses of the nonlinear dynamics of harmonically-forced turbulent premixed flames that drive thermoacoustic combustion instability. A key objective of this work is to develop a model that enables tracking of ensemble-averaged turbulent flame fronts. A previous study introduced an equation for modeling the ensemble-averaged turbulent flame dynamics, in which the turbulent flame speed model used a turbulent Markstein length to account for the effect of flame-brush curvature on the propagation speed. This study improves upon the previous modelling by introducing an additional modeling parameter – an effective convection speed – that is required in order to account for nonlinearity associated with turbulent transport. Three-dimensional simulations of the harmonically-forced flame dynamics are performed using the G-equation approach and a flow field involving stochastic velocity fluctuations. The new model equation provides an improved description of the ensemble-averaged flame dynamics that is in close agreement with the G-equation simulation results. Through asymptotic analysis, explicit expressions are derived for the un-curved turbulent flame speed, the turbulent Markstein length, and the effective convection speed. The asymptotic models that have been derived give accurate predictions of the flame dynamics in the vicinity of the flame holder. More general solutions are also derived for flame dynamics in the far field and these provide a basis for general modeling of turbulent flame speeds in harmonically-forced flow