Centrally Ignited Expanding Flames in Laminar and Turbulent Media

Moshe Matalon, University of Illinois at Urbana-Champaign

Usage Details

The propagation of two and three-dimensional expanding turbulent flames is to be examined within the context of the hydrodynamic theory of premixed flames using a hybrid Navier-Stokes/Level-Set methodology, adept at handling multivalued and disjointed surfaces. Within this context, the flame is treated as a surface of density discontinuity separating fresh combustible mixture from the burnt gas, propagating at a speed dependent upon local curvature and hydrodynamic strain. For mixtures with Lewis numbers above criticality, thermo-diffusive effects have a stabilising influence which largely affect the flame at small radii. The amplitude of these disturbances initially decay and only begin to grow once a critical radius is reached. This instability is hydrodynamic in nature and is a consequence of thermal expansion. Through linear stability analysis, predictions of critical flame radius at the onset of instability have been obtained as functions of Markstein length and thermal expansion coefficients. Consistent with linear theory, simulations have shown the flame initially remaining stable and the existence of a particular mode that will be first to grow and later determine the cellular structure observed experimentally at the onset of instability.

A sensitivity analysis, based on mixtures with different Markstein numbers and thermal expansion ratios, is to be performed to investigate early flame kernel development in addition to its long-time evolution. The focus will be to understand the effect of turbulent flow characteristics (intensity and integral length scale) and the Darrieus-Landau instability on the burning rate with the intention of deriving scaling laws for the turbulent flame speed based on Damköhler's first hypothesis. Specifically, the role of flame-stretch will be assessed on the turbulent flame speed. Recent work indicates that incorporating this effect for mixtures with positive Markstein lengths provides more precise estimates of the turbulent flame speed. Finally, the flame-turbulence interaction will also be inferred from statistical quantities based on vorticity, strain-rate and flame topology.