Effect of combustion on near-critical swirling flow

Abstract

This paper examines the manner in which heat release resulting from premixed combustion alters the nature of near-critical, axisymmetric, swirling flow in a straight circular pipe. Attention is confined to dilute premixtures so that exothermicity is weak and a small-disturbance approach applicable. The weak exothermicity is found to have a considerably larger effect on the flow. In the absence of combustion, the columnar solution loses stability via a transcritical bifurcation as the level of swirl rises beyond a critical value. Exothermicity splits the bifurcation portrait into two branches separated by a gap in the level of swirl; within this gap steady, near-columnar solutions cease to exist. As a result the critical value of swirl for a combusting flow is smaller than that for the cold flow. For a certain range of swirl below this critical value and for small enough heat release, the solution branch is double-valued and yields two equilibria, one corresponding to a near-columnar state and the other pointing to the appearance of a large-amplitude structure. For larger heat release the double-valued branch loses its fold, suggesting the gradual appearance of large-amplitude disturbances with increasing levels of swirl. The mechanism that governs the behaviour of the reactive flow with swirl, and the relevance of the results to combustion states with vortex breakdown, are also discussed.