Effect of Le on transition to parametric instability in downward propagating flames

Flames propagating downward from open to closed end in a tube are prone to thermo-acoustic instability. At sufficiently high burning velocity (SL) two regimes of instability are observed, namely, primary instability (where initial cellular flame transitions to a flat flame) and a secondary instability (where flat flame transition to turbulent flame due to parametric instability of flame front). On further increasing SL flat flame is not observed and initial cellular flame directly transitions to parametric instability. This SL is called critical SL here. This work presents the effect of Le (Lewis number) on critical SL. Experiments reveal that larger Le condition has higher critical SL compared to lower Le condition. Theoretical calculations of instability of planar flame front in presence of acoustic forcing are presented. Effect of Le is successfully captured by the theory as predicted stability region of planar flame is narrower for lower Le as compared to higher Le. However, quantitative agreement for critical SL between experiments and theory is obtained only after applying a correction factor which is a function of and Le.