Aerodynamics of Tsuji burners with augmented fuel injection

This study addresses the aerodynamics of Tsuji burners, involving a flame developing from the forward stagnation region of a cylindrical porous fuel injector placed in a uniform air stream with moderately large Reynolds number. Attention is focused on conditions under which the fuel-injection velocity is not sufficiently small compared with the outer air velocity for the boundary layer to remain attached to the cylinder surface. In the resulting flow, the flame is embedded in the thin mixing layer that forms at the surface separating the outer air stream from the fuel stream, both having, in general, different densities. The flow on the air side of the mixing layer is potential, while that on the fuel side is rotational because fuel injection generates vorticity through the requirement that fuel emerges normal to the cylinder surface. It is shown that introduction of a suitably density-weighted stream function reduces the problem to that of constant-density flow, with the density-square-root-weighted ratio of injection velocity to free-stream velocity Λ emerging as the only controlling parameter. The numerical solution, involving determination of the vorticity distribution through an iterative scheme, provides the structure of the flow, including the flame location and associated strain-rate distribution. Numerical results are presented for values of Λ ranging from small (Λ<<1) to large (Λ>>1) injection velocities. The inviscid results in the limit of vanishingly small injection velocities, Λ approaching zero, demonstrate that the outer air velocity never approaches the classical solution corresponding to potential flow around a solid cylinder (Λ=0), a result with important implications for the analysis of flames stabilized in Tsuji burners.