On the low-frequency limit of flame transfer functions

The response of a premixed flame to quasi-steady flow perturbations is considered. It is found that in this low-frequency limit, constraints on the flame transfer function can be established from global conservation laws for mass, energy, and momentum. For example, the transfer function between velocity fluctuations and heat release of a perfectly premixed flame without fluctuations of equivalence ratio should be unity in the limit of zero frequency, while for a combustion system with constant mass flow rate of fuel, the transfer function should tend toward zero. It is demonstrated that these considerations can be employed to reduce the number of unknowns in analytical flame models or identify invalid modeling assumptions.