The mechanism of lean limit flame extinction

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

“…They showed that the stretch has a maximum at the tip of the flame, on the axis of the tube, which is the place where extinction begins at the flammability limit [2], and that the maximum stretch scaled with the inverse of the transit time of the gas across a planar flame propagating in the mixture (a dimensionless stretch or Karlovitz number) is a quantity of order unity. These results led von Lavante and Strehlow [10] to propose that flame stretch is the main cause of extinction of an upward propagating flame. Building on results derived for a planar flame in a stagnation point flow, Buckmaster and Mikolaitis [11] arrived at the conclusion that, at the flammability limit, the dimensionless stretch should have a certain critical value which depends on Lewis number of the fuel.…”

“…Noticing that flame stretch increases the final combustion temperature and thus strengthens the flame when the Lewis number of the fuel (Le) is smaller than unity [7], which is the case with their mixtures, these authors (see also von Lavante and Strehlow [10]) suggest that a flame propagating upwards in a tube can exist at fuel concentrations below the minimum at which a planar unstretched flame can exist. This would explain the low flammability limits obtained in narrow tubes, where the flame stretch is high.…”

“…Von Lavante and Strehlow [10] approximately computed the flow of the fresh gas above an upward propagating flame and the flame stretch, which is due mainly to the strain rate of the fresh gas flow. They showed that the stretch has a maximum at the tip of the flame, on the axis of the tube, which is the place where extinction begins at the flammability limit [2], and that the maximum stretch scaled with the inverse of the transit time of the gas across a planar flame propagating in the mixture (a dimensionless stretch or Karlovitz number) is a quantity of order unity.…”

“…This is contrary to the experimental results of Refs. [2,6,10], among others. The condition proposed in [11] relies on the assumption that convection should never bring burnt gas to the reaction region of the flame, which needs not be satisfied in a finite region around the flame tip.…”

A new type of steady and stable, laminar, premixed flame in ultra-lean, hydrogen–air combustion

“…These observations are associated with the determination of flammability limits such as by the United States Bureau of Mines [9,10], which considered the propagation of flames in vertical tubes. The lean flammability limits for hydrogen-air mixtures determined in this way are about φ = 0.1 (4% volume of fuel) for upwardly propagating flames [9], and φ = 0.23 (9%) for downwardly propagating flames [3, p. 10].…”