| This study uses the reactive flow model equations to examine, via asymptotic and numerical analyses, the manner in which heat release resulting from premixed combustion alters the nature of near-critical, axisymmetric, swirling flows in a straight circular pipe. The asymptotic analysis focuses on steady states and confines attention to dilute premixtures and near-critical swirl levels. In this limited parameter space, a nonlinear small-disturbance approach is derived and produces analytical solutions of the reactant and flow fields. In the numerical study, exothermicity is finite, swirl levels vary over a broad range, and the transient problem is considered.; The results of the asymptotic analysis show that weak exothermicity has a considerably larger effect on the flow. In the absence of combustion the columnar vortex loses stability and breaks down via a transcritical bifurcation as the level of swirl rises beyond a critical value. Small heat release due to combustion 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 and breakdown states appear. As a result, the critical swirl for a weak combusting flow is smaller than that for the cold flow. For a certain range of swirl below this critical value, the solution branch is double-valued and yields two equilibria, one corresponding to a near-columnar state and the other hinting at the appearance of a large-amplitude structure. For heat release beyond a limit value the double-valued branch loses its fold, suggesting the gradual appearance of large-amplitude disturbances with increasing levels of swirl.; The numerical computations for relatively weak heat release show agreement with the asymptotic results. However, for larger heat release, it is found that increasing exothermicity shifts the critical swirl to higher levels. Computations also allow one to follow the appearance of large-scale structures in the flow. These structures are accompanied by significant changes in the fields of temperature and reactant concentration. These changes, along the pipe axis near the inlet region, increase with the swirl level, forming a hot central core of combustion products, that tends to move upstream toward the inlet, thereby allowing a shorter combustor. |
