Ignition time in the stretched-flow field

Ignition times in a typical stretched-flow field counterflow system are calculated for both initially unmixed and premixed gases. To simplify the calculation, ideal gases with equal velocities are assumed, and asymptotic analysis for the limit of large activation energy is developed in order to reduce the six parameters which control the field. The solution of the present unsteady problem is uniquely determined in terms of initial conditions. Mixing and heat transfer should increase as the flow velocity increases, and therefore the ignition time is expected to decrease. However, in both cases of unmixed and premixed gases, the ignition time increases as the stretch rate, which is proportional to the flow velocity, increases. This indicates that a long induction time is required to reach a reaction intense enough for ignition. At a certain large flow stretch rate, the ignition time becomes infinite and ignition can no longer take place. Previously, such an ignitable limit was discussed as a function of flame temperature variation with flow velocity, but in this analysis it is derived for ignition time variation.