An analytical study of the non-steady behavior of large combustors

The transient response of large burners depends primarily upon fluid mechanical adjustment rather than in time delays associated with transient chemical response. Examples of this behavior are the non-steady behavior of burners in utility boilers, and the low-frequency response of after burners in aircraft gas turbines. The non-steady behavior of a flame stabilized by a single-flame holder at the center of a long two-dimensional duct is investigated analytically when it is excited by periodic acoustic disturbances that approach the flame zone from either the upstream or downstream direction. The flame zone itself is considered acoustically compact. The problem is treated by an integral technique in which relevant equations are integrated across high-density and low-density portions of the gas separately; the two fields are then coupled across the thin flame front, the determination of its shape being part of the solution. Transmission and reflection coefficients were calculated for a range of flame velocities, burner inlet flow velocities, combustion temperature ratio and imposed acoustic frequency. The results showed that a considerably stronger pressure wave passed upstream of the flame than downstream, in the sense that could be expected from the different acoustic impedences of the hot and cold gas. Of most significance, however, was the very large (active) response of the burner at certain characteristic frequencies which corresponded to well-defined values of ωL/u_o where L is the length of the flame zone and u_o is the flow velocity upstream of the burner. It is indicated that these energetic response modes result from vorticity shed from the distorted flame which induces a propagating wave along the flame front