Stochastic modeling of unsteady extinction in turbulent non-premixed combustion

Turbulent fluctuations of the scalar dissipation rate have a major impact on extinction in non-premixed combustion. Recently, an unsteady extinction criterion has been developed (Hewson, 2013) that predicts extinction dependent on the duration and the magnitude of dissipation rate fluctuations exceeding a critical quenching value; this quantity is referred to as the dissipation impulse. The magnitude of the dissipation impulse corresponding to unsteady extinction is related to the difficulty with which a flamelet is exintguished, based on the steady-state S-curve.In this paper we evaluate this new extinction criterion for more realistic dissipation rates by evolving a stochastic Ornstein–Uhlenbeck process for the dissipation rate. A comparison between unsteady flamelet evolution using this dissipation rate and the extinction criterion exhibit good agreement. The rate of predicted extinction is examined over a range of Damköhler and Reynolds numbers and over a range of the extinction difficulty. The results suggest that the rate of extinction is proportional to the average dissipation rate and the area under the dissipation rate probability density function exceeding the steady-state quenching value. It is also inversely related to the actual probability that this steady-state quenching dissipation rate is observed and the difficulty of extinction associated with the distance between the upper and middle branches of the S-curve.