Aerodynamics of Tsuji Burners with Augmented Fuel Injection

Abstract

ABSTRACT Tsuji burners, in which flames may be anchored in the forward stagnation region of a cylindrical porous fuel injector placed in a uniform air stream, are addressed here for moderately large Reynolds numbers. 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 forward part of 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 usually is rotational because exit conditions for the fuel injection generate vorticity, for example, by imposing a requirement that the fuel must emerge normal to the cylinder surface, which is the condition analyzed herein. 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 emerging as the only controlling parameter. The numerical solution, involving determination of the vorticity distribution in the inviscid fuel flow through an iterative scheme, provides the structure of the flow, including the mixing-layer location and the inviscid-flow strain rate there. Numerical results are presented for values of ranging from small () to large () injection velocities. The inviscid results in the limit of vanishingly small injection velocities ( approaching zero) demonstrate that, unlike the prediction of the potential-flow solution, when the fuel-side flow is rotational the outer air velocity never approaches the classical solution corresponding to potential flow around a solid cylinder (), a result affecting the interpretation of analyses of experiments involving flames stabilized on Tsuji burners as the boundary layer is blown off. In particular, with rotational fuel-side flow, the streamline separating the fuel and oxidizer regions lies farther from the cylinder surface, resulting in a larger near-quiescent wake and a lower strain rate along the separating streamline.