The role of duct thickness on the quenching process of premixed flame propagation

The propagation of premixed laminar flame in ducts of circular cross-section considering a thermal-diffusive model is investigated numerically. Heat losses by conduction to the channels walls are taken into account using the thermally thin wall regime. The effects and the relationship between thickness and diameter of the tube with the flame speed propagation are studied and the quenching condition is obtained as a function of the heat-loss parameter. The mathematical model employs the axisymmetric energy and species equations. The calculations are based on a two-step chemistry, with an Arrhenius, energetically neutral, radical production reaction followed by an exothermic radical recombination reaction. For large values of the heat-loss parameter, the wall temperature is close to the free stream temperature and all the heat losses through the wall are convected away. No heat feedback occurs. On the other hand, for small values of the heat-loss parameter, a feedback mechanism occurs by transferring heat from the burned gas to the fresh mixture along the tube wall. For values of the heat-loss parameter of order unity, the heat feedback mechanism is able to sustain the flame propagation and the quenching condition disappears, producing an almost planar flame front as the propagation velocity reduces. For this two-step reaction mechanism, the radical species behaviour at the duct walls seems to have negligible effect on the quenching process.