Non-premixed combustion with swirl

The influence of a near-critical swirling flow on the shape of the Burke-Schumann reaction zone in a straight cylindrical chamber is investigated by asymptotic and numerical means. Two cases are considered. The first part of the study investigates the effect of swirl on the shape of a diffusion flame in the absence of heat release. The underlying assumptions are a high Reynolds number flow and infinite-rate chemistry. An asymptotic analysis is developed to study the way in which swirl at near-critical levels affects the fuel/oxidizer mixture mass fraction distribution. It is first shown that the leading-order changes of the velocity field from a columnar state can be described by a nonlinear reduced-order model. Then, these flow changes are used to calculate the corrections due to swirl to the classical Burke-Schumann flame structure. The asymptotic results are complemented by extensive direct numerical simulations at finite Reynolds numbers and a broader range of swirl. The numerical solutions agree with the asymptotic results at large values of the Reynolds numbers. The asymptotic and numerical computations are used to study the interaction between vortex breakdown and the size of the reaction zone in the case of no heat release.; The second part of the study reinstates the heat release, so as to describe the effects of thermal expansion. The effect of weak exothermicity is first examined by means of a small-disturbance approach. A computational study is then undertaken to consider the influence of order-unit heat release. The asymptotic study shows that weak exothermicity has a considerably larger effect on the flow structure. Also, the critical swirl ratio for transition to vortex breakdown of a reacting flow decreases with the increase of heat release. The numerical results agree with the trend of the asymptotic predictions for very small amounts of heat release. However, for larger amounts, the numerical results show that the critical swirl ratio increases with the amount of heat release. This shows that the asymptotic approach is limited to very small amounts of heat release. The numerical computations also show that when the swirl ratio approaches the critical level for the appearance of vortex breakdown, the reaction zone decreases in its length, expands radially, and becomes more compact near the pipe inlet.