Numerical study of initiation of a combustion wave by an ignition kernel

The response of an infinite fuel system to the sudden deposition of energy into a spherically symmetric ignition kernel is studied. Using a highly idealized fuel chemistry model, the governing differential equations are solved numerically. Nondimensional parameters based on the size and temperature of the ignition kernel are developed and used to determine the boundary between decay of the ignition kernel and initiation of a combustion wave. It is shown that for ignition to occur, the radius of the hot gas kernel generated by the initial input of energy must exceed a thickness characteristic of a propagating combustion wave. The effect of changing the value of the Lewis number for a fixed energy input is investigated and is found to change the boundary between decay and wave propagation. Results are presented which show the effects of serveral of the model parameters on the position and velocity of the combustion wave as it develops.