Numerical simulation of the upward propagation of a flame in a vertical tube filled with a very lean mixture.

Upwardpropagation of a premixed flame in averticaltubefilled with a very leanmixture is simulated numerically using a single irreversible Arrhenius reaction model with infinitely high activation energy. In the absence of heat losses and preferential diffusion effects, a curved flame with stationary shape and velocity close to those of an open bubble ascending in the same tube is found for values of the fuel mass fraction above a certain minimum that increases with the radius of the tube, while the numerical computations cease to converge to a stationary solution below this minimum mass fraction. The vortical flow of the gas behind the flame and in its transport region is described for tubes of different radii. It is argued that this flow may become unstable when the fuel mass fraction is decreased, and that this instability, together with the flame stretch due to the strong curvature of the flame tip in narrow tubes, may be responsible for the minimum fuel mass fraction. Radiation losses and a Lewis number of the fuel slightly above unity decrease the final combustion temperature at the flame tip and increase the minimum fuel mass fraction, while a Lewis number slightly below unity has the opposite effect.

Effects of radiation losses on very lean methane/air flames propagating upward in a vertical tube

The stationary upward propagation of a very lean methane/air flame in a long vertical tube open at the bottom and closed at the top is simulated numerically using a single overall chemical reaction to model combustion and assuming an optically thin gas and a transparent or non-reflecting tube wall to approximately account for radiation losses from CO2CO2 and H2OH2O. Buoyancy plays a dominant role in the propagation of these flames and causes a large region of low velocity of the burnt gas relative to the flame to appear below the flame front when the equivalence ratio is decreased. The size of this region scales with the radius of the tube, and its presence enhances the effect of radiation losses, which would be otherwise negligible for a standard flammability tube, given the small concentration of radiating species. Heat conduction is found to be important in the low velocity region and to lead to a conduction flux from the flame to the burnt gas that causes extinction at the flame tip for a value of the equivalence ratio near the flammability limit experimentally measured in the standard tube. The effect of radiation losses decreases with the radius of the tube. Numerical results and order-of-magnitude estimates show that, in the absence of radiation, a very lean flame front fails to propagate only after recirculation of the burnt gas extends to its reaction region and drastically changes its structure. This condition is not realized for the standard flammability tube, but it seems to account for the flammability limit measured in a tube of about half the radius of the standard tube.