Simulating practical combustion systems requires the approximation of the interaction between turbulence, molecular transport and chemical reactions. Turbulent combustion models are used for this purpose, but their behavior is di cult to anticipate based on their mathematical formulations, making the use of numerical experimentation necessary. Therefore, the present work explores the e↵ect of three turbulent-combustion models, two eddy-viscosity models, and their parameters on a combustion problem which is notoriously di cult to model: flame extinction and reignition. For this purpose, two types of temporal jets are considered, and direct-numerical-simulation results are compared qualitatively with those from large-eddy simulations.
I. IntroductionCombustion devices such as piston engines, gas-turbine engines, afterburners, and furnaces operate in a turbulent-combustion mode, as opposed to laminar combustion. 1, 2 Turbulent combustion involves an interaction between chemical reactions, micromixing (molecular mixing), and turbulence that spans a broad range in spatiotemporal space. As a result, the full resolution of these physics with Direct Numerical Simulations (DNS) is currently computationally a↵ordable only for the simplest type of problems. Practical problems need to be simulated with mathematical formulations that approximate the above physics. These formulations are called turbulent-combustion models. Being models themselves, careful comparisons of their predictions with experiments or DNS is necessary, a topic which has a vast literature. 2-5 Nonetheless, there still remains various physics which have proven to be particularly di cult to model.The onset of flame blowout is a dangerous operating condition. It involves extinction and reignition, 6 both of which pose a di cult modeling challenge. To start with, convenient modeling assumptions about the rate controlling mechanism (mixing-controlled or reaction-controlled) no longer apply. Another di culty is the fact that some reignition mechanisms involve a distributed-reaction-like regime 7, 8 or a partially-premixed combustion mode. 9, 10 Therefore, for example, flamelet or conditional-moment-closure models designed exclusively for either premixed or nonpremixed combustion are not applicable, but may need to be modified to account for partially-premixed combustion, a task that has been conducted for flamelets. 11 Another challenge in modeling extinction and reignition is that molecular di↵usion plays a key role; not surprisingly, simulations of extinction and reignition with transported PDF (TPDF) methods, where micromixing is modeled, not resolved, are very sensitive to the type of micromixing model. 12 This type of model-parameter sensitivity is not restricted to TPDF. Moreover, some flames undergoing extinction and reignition exhibit PDFs of temperature with two peaks (i.e. not monomodal PDFs), 13, 14 a feature that cannot be captured ⇤ Senior Engineer, esteban@fastmail.us, AIAA Member.