Critical ignition behind non-stationary curved shocks*

Gas ignition behind non-stationary curved shocks is treated analytically.  The competition between thermal heating and gasdynamic expansion along a particle path controls the ignition.  The relation between the Lagrangian rate of gas expansion and the shock dynamics parameters is established using the shock change equations.   The critical conditions for ignition are derived in closed form for ignition described by global one and two step kinetics in terms of the shock speed, curvature and acceleration.  Both models predict the same critical conditions for ignition in the limit of a high activation energy.  The closed form solutions for critical gas expansion rate preventing ignition predicted by these models are found in excellent agreement with results from real gas calculations for ignition behind shocks in hydrocarbon-air mixtures.   The model presented unifies previous models developed by Shepherd, Oppenheim and the author for critical ignition behind decaying shocks.