Nonlinear dynamics of unsteady premixed, planar flames

Resumen

The planar unsteady propagation of a premixed ñame front in a reactive mixture is investigated, in the diffusional-thermal limit, for a solid as well as for a gaseous mixture with the Lewis number of the limiting reactant larger than unity. The unsteadiness appears when the steady propagation becomes unstable on crossing the limit of stability. Cióse to this limit the propagation assumes the form of harmonic oscillations with a well defined time scale. But on moving deeper into the instability región, these oscillations, aithough still periodic, soon become complicated relaxational type pulsations, characterized by long periods with fíame front velocities lower than that corresponding to a steady ñame, bounded by very short stages with very large ñame front velocities. In the first part of the thesis, the structure of the reaction layer in these unsteady cases is addressed. It is shown that for large valúes of the Zel'dovich number the fíame maintains, even in the unsteady case, the classical dual structure with a thin quasisteady reactive layer embedded in reaction-free unsteady regions. The inner reactive layers, much thinner than the outer regions and quasisteady in the first approximation, are studied in detail following Liñán's earlier analysis of the premixed ñame regime of diffusion ñames. The problem of the unsteady propagation of the ñame is then formulated by replacing the inner zone by a discontinuity surface or reaction sheet with jump conditions across it provided by the previous analysis of the reaction zone structure. Thus the solution can be obtained by accounting for the effect of these discontinuity surfaces in the outer unsteady regions which are now free from the reaction terms. The second part of the thesis is devoted to the analysis of the dynamics with the reaction sheet formulation, of these unsteady ñames in the fully nonlinear, pulsating regime. The problem still contains a large parameter, the non-dimensional activation energy, and that poses considerable difnculties from the numerical point of view, since the solution involves, simultaneously, both large and small spatial scales which, in addition, evolve with time during each period. On departing from the stability limit, the propagation soon assumes a pulsating form, so each period is characterized by very short excursions with large ñame velocities, when the flame temperature grows over its adiabatic steady valué, followed by long stages with temperatures and ñame velocities significantly lower than the valúes corresponding to the steady flame. The time and length scales strongly varying with time are identified and used to genérate new rescaled independent variables for the reformulation of the problem, which now takes a form more amenable to be treated numerically. However, the resulting problem is still time dependent aithough the temporal as well as the spatial scales now vary much more smoothly along a period. This affords to obtain well resolved solutions, both spatially and in time. The general features of these unstable solutions are discussed at length. In addition, a number of analytical results are obtained which allow to explain the observed behaviour.