Flame initiated by a heated wall: A new mode of propagation in mixtures below the flammability limit

A new mode of flame propagation from a wall with an imposed temperature in a mixture below the flammability limit is described theoretically and numerically. We consider a simple chemistry model in which the reaction rate vanishes at a temperature below some critical cut-off temperature. Unlike the standard mode, in which the flame propagates at a constant velocity through the unburned mixture, and which is not possible under the conditions under consideration, in the new mode the flame propagates at a rate inversely proportional to the square root of time. Self-sustaining flame propagation in the new mode is possible at wall temperatures below the cut-off temperature, even in the case of a cold wall. It is shown that the value of the fuel Lewis number is determinant: the new mode of propagation exists only if L e < 1 . An analytical solution for this new mode is proposed, showing excellent agreement with the numerical results. Novelty and significance statement For the first time, a new type of solutions for the propagation of a combustion wave in a mixture below the flammability limit is obtained. For the cases under consideration, the standard well-known flame solution, when the flame propagates with constant velocity along the unburned mixture, turns out to be impossible. The propagation velocity in the new regime is inversely proportional to the square root of time. An asymptotic analytical solution is obtained and it is shown that the fuel Lewis number is the controlling parameter, and that the new propagation mode is possible only in mixtures with fuel Lewis number less than unity. Excellent agreement between numerical and analytical results is demonstrated. The results are relevant for safety in the storage and handling of lean hydrogen–air or, more generally, hydrogen-containing mixtures.