The role of natural convection on cool flames and autoignition

Analysis of natural convection in a horizontal slot formed by two corrugated isothermal plates has been carried out. The analysis is limited to subcritical Rayleigh numbers$Ra$where no secondary motion takes place in the absence of corrugations. The corrugations have a sinusoidal form characterized by the wavenumber, the upper and lower amplitudes and the phase difference. The most intense convection occurs for corrugation wavelengths comparable to the slot height; it increases proportionally to$Ra$and proportionally to the corrugation height. Placement of corrugations on both plates may either significantly increase or decrease the convection depending on the phase difference between the upper and lower corrugations, with the strongest convection found for corrugations being in phase, i.e. a ‘wavy’ slot, and the weakest for corrugations being out of phase, i.e. a ‘converging–diverging’ slot. It is shown that the shear forces would always contribute to the corrugation build-up if erosion was allowed, while the role of pressure forces depends on the location of the corrugations as well as on the corrugation height and wavenumber, and the Rayleigh number. Placing corrugations on both plates results in the formation of a moment which attempts to change the relative position of the plates. There are two limiting positions, i.e. the ‘wavy’ slot and the ‘converging–diverging’ slot, with the latter being unstable. The system would end up in the ‘wavy’ slot configuration if relative movement of the two plates was allowed. The presence of corrugations affects the conductive heat flow and creates a convective heat flow. The conductive heat flow increases with the corrugation height as well as with the corrugation wavenumber; it is largest for short-wavelength corrugations. The convective heat flow is relevant only for wavenumbers of$O(1)$, it increases proportionally to$Ra^{3}$and proportionally to the second power of the corrugation height. Convection is qualitatively similar for all Prandtl numbers$Pr$, with its intensity increasing for smaller$Pr$and with the heat transfer augmentation increasing for larger$Pr$.

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A scaling analysis of Sal'nikov's reaction, P→A→B, in the presence of natural convection and the diffusion of heat and matter

Proceedings of The Royal Society A Mathematical Physical and Engineering Sciences ◽

10.1098/rspa.2005.1459 ◽

2005 ◽

Vol 461 (2059) ◽

pp. 1999-2020 ◽

Cited By ~ 12

Author(s):

A.N Campbell ◽

S.S.S Cardoso ◽

A.N Hayhurst

Keyword(s):

Activation Energy ◽

Natural Convection ◽

Chemical Reaction ◽

Reaction Diffusion ◽

Scaling Analysis ◽

Spherical Vessel ◽

Convection Diffusion ◽

Cool Flames ◽

Theoretical Predictions ◽

Active Intermediate

Sal'nikov's chemical reaction is very simple; it consists of two consecutive first-order steps, producing a product B from a precursor P via an active intermediate A, in P→A→B. The first step is assumed to be thermoneutral, with zero activation energy, while the second step is exothermic and has a positive activation energy. These properties make this mechanism one of the simplest to display thermokinetic oscillations, as seen in cool flames. We consider a pure gas, P, undergoing Sal'nikov's reaction in a closed spherical vessel, whose walls are held at a constant temperature. Natural convection becomes significant once the temperature is high enough for the Rayleigh number to reach approximately 10 3 . The subsequent behaviour of the system depends on the interaction between convection, diffusion of heat and mass, and chemical kinetics. By examining the governing equations, we develop and evaluate scales for the characteristic velocity, concentration of the intermediate A and the temperature rise during the progress of the reaction. These scales depend on the characteristic time-scales for the interacting phenomena of chemical reaction, diffusion and natural convection. Our theoretical predictions are verified by full numerical simulation for the two limiting cases when transport is dominated, respectively, by diffusion and natural convection.

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