Abstract
When cool flames, or indeed any exothermic chemical reaction, occur in a fluid inside an unstirred vessel, the heat from the reaction often induces temperature gradients and consequently motion, i.e., natural convection. The intensity of the resulting flow is governed by the Rayleigh number (Ra). This work simulates numerically the behavior of Sal'nikov's reaction, P → A → B, under the influence of natural convection in an unstirred spherical reactor. This reaction is the simplest to exhibit the thermokinetic oscillations characterizing cool flames. The behavior of this system can be represented on a three-dimensional regime diagram, whose axes are ratios of the characteristic timescales (τ) for chemical reaction, diffusion (of both heat and mass), and natural convection. Previous work has identified a region of oscillations on this diagram in the purely diffusive limit, when Ra = 0. This work extends this analysis to the general 3D space, where diffusion and natural convection are both important. A region in which oscillations are observed has been found for fixed values of the first-order rate constants for Sal'nikov's reaction. There is a distinct change in the shape of the region of oscillations around the critical value of Ra ∼ 500, when natural convection becomes important. When diffusion dominates transport (Ra < 500), the boundaries between oscillatory and nonoscillatory solutions are largely independent of the ratio of timescales τstep 2 / τconvection and agree well with the values found previously in the purely diffusive limit. When natural convection is important (Ra > 500), the oscillations occur over a wider range of parameters than is the case for a diffusive system. The presence of natural convection also leads to various, more complex behaviors than are seen in the diffusive or well-mixed limits. A region in the regime diagram was found where the oscillations in temperature and the concentration of A have small amplitudes and a frequency that is quite different from those generated in a well-mixed system. It is possible that these oscillations are caused by natural convection, i.e., are not thermokinetic oscillations produced by the chemical reaction. It was also found that sometimes the oscillations in the temperature and the concentration of A are in phase; more generally they are in anti-phase. The evolution of nonoscillatory behavior with relatively small increases in temperature was found to be always fairly similar, regardless of the intensity of natural convection. The shape of the temperature profile along the vertical axis of the reactor did, however, change with the intensity of natural convection. Finally, the nonoscillatory solutions with a large rise in temperature in the presence of natural convection were found to be very much like those seen in the purely diffusive limit for small times, due to the relatively long induction time (∼3.5 s in a vessel with diameter 0.1 m) for the onset of natural convection. © 2008 The Combustion Institute.