Scaling the flame transfer function of confined premixed conical flames

Abstract

The influence of confinement side walls on the response of premixed conical flames submitted to velocity disturbances is investigated experimentally and theoretically. When the flame is sufficiently confined, the burnt gases cannot fully expand at the nozzle outlet. In that case, the confinement ratio Cr=R0/R1 between the burner and flame tube radii and the burnt to unburnt gas volume expansion ratio E=ρu/ρb need to be taken into account in the description of the flame transfer function (FTF). The main effect of confinement is an acceleration of the fresh stream of reactants induced by the over-pressure of the confined burnt gases. Experiments on steady flames reveal that the flame height increases for increasing confinement ratios Cr, leading to a gain shift and a phase drop for the FTF. A theoretical analysis is conducted to model this acceleration and examine its impact on the steady flame shape and flame response to flow disturbances. The change in the FTF phase is shown to be related to a reduction of the mean time lag between heat release rate perturbations and velocity modulations induced by both the velocity acceleration in the fresh reactants and a change in the location of the steady flame front. An expression to scale the FTF of confined flames is derived based on a modification of the classical reduced frequency ω∗ used to scale the response of unconfined flames. This expression includes explicitly the confinement ratio Cr and the volume expansion ratio E. This new dimensionless number enables to plot FTF measured for different confinements with reasonable collapse. It may also be used to transpose FTF gathered on single burners to multiple injection configurations when the burnt gases cannot fully expand due to the presence of neighboring flames.