The flame displacement speed: A key quantity for turbulent combustion and combustion instability

Future combustion power and propulsion systems may operate in premixed regime enabling reduced fuel burn and reduced pollutant emissions. The turbulent premixed regime in those future combustion systems is likely to be in the corrugated regime where modeling the flame as a thin interface propagating into the fresh gas is made possible. The flame displacement speed is thus a key quantity for turbulent combustion in this regime. This quantity is also important for combustion instabilities. Indeed, the flame displacement speed S d combined to the flow speed v determines the flame surface location by determining the flame surface speed w s . The flame surface location has shown to play a major role on combustion instabilities. Research work have also demonstrated the role of the flame displacement speed on the flame response which is used for subsequent combustion instability prediction. In this context, the derivation of flame speed models and flame transfer function models based on this quantity are required. This paper presents the theoretical derivation of flame transfer function coefficients for swirling premixed flames in this context. The derivation is based on the definition of the flame speed for turbulent flame, its perturbed form for oscillating flow, and the kinematic flame-flow speed budget. The obtained results are compared to previous literature data and discussed. The effect of the flame angle, id est the effect of the swirl number on the flame response is also investigated. This works motivates detailed local measurements and simulations to evaluate flow-flame speed budget terms.