Sensitivity analysis of transfer functions of laminar flames

The sensitivity of laminar premixed methane/air flames responses to acoustic forcing is investigated using direct numerical simulation to determine which parameters control their flame transfer function. Five parameters are varied: (1) the flame speed sL, (2) the expansion angle of the burnt gases α, (3) the inlet air temperature Ta, (4) the inlet duct temperature Td and (5) the combustor wall temperature Tw. The delay of the flame transfer function is computed for the axisymetric flames of Boudy et al. [1] and the slot flames of Kornilov et al. [2]. Stationary flames are first computed and compared to experimental data in terms of flame shape and velocity fields. The flames are then forced at different frequencies. Direct numerical simulations reproduce the flame transfer functions correctly. The sensitivity analysis of the flame transfer function is done by changing parameters one by one and measuring their effect on the delay. This analysis reveals that the flame speed sL and the inlet duct temperature Td are the two parameters controlling the flame delay and that any precise computation of the flame transfer function delay must first have proper models for these two quantities.