Conditional moment closure modeling of extinction and re-ignition in turbulent non-premixed flames

The conditional moment closure approach is used to describe extinction and re-ignition events in turbulent non-premixed hydrocarbon combustion. It is well known that single conditional moment closure cannot correctly capture these phenomena and a second conditioning variable, sensible enthalpy, needs to be introduced to account for significant fluctuations around the singly conditioned mean. As a first step, the key closure assumptions are validated with the aid of direct numerical simulation with four-step chemistry. Simulations with an increasing degree of local extinction are used to assess the performance of first order closures for the highly non-linear chemical source terms. The results obtained with the doubly conditioned moment closure method are excellent for all cases, and conditional moment closure is capable of accurately predicting local extinction, the onset of re-ignition, and the occurrence of global extinction. Next, it is shown that the conditioned reaction rate terms can be modelled using presumed shape functions for the conditional moments in sensible enthalpy space, thus leading to a new closure for the reaction rate terms in the singly conditioned moment closure equations. Full closure can be based on a presumed β-distribution for the conditional PDF of sensible enthalpy, and the solution of an additional variance equation is needed.