Direct numerical simulation analysis of flame surface density equation in non-premixed turbulent combustion

Abstract

In flame surface density models used in turbulent cmbustion, the flame is described as a collection of laminar flame elements quantified in terms of available flame surface per unit volume Σ ¯ . A modeled transport equation for this central quantity was first derived from phenomenological considenrations [6] for non-poremixed turbulent combustion. More recently, an exact but unclosed transport equation for the density of a propagating surface has been established, leading to improvements in premixed turbulent combustion modeling. The same general framework, together with concepts borrowed from Vervisch et al. [16] may be used to describe non-premixed turbulent combustion. In the opresent work, two equivalent transport equations for the flame surface density Σ ¯ corresponding to the stoichiometric iso‐level value of the mixture fraction Σ ¯ are analyzed. The first equation is similar to a PDF transport equation whereas the second one introduces the concept of an effective propagation speed. Flame surface density Σ ¯ and terms in Σ ¯ equations are examined using direct simulations of a two-dimensional spatial turbulent mixing layer. In a first step, our study is limited to a constant density flow without shear. Simple models are also proposed for the source and snk terms in the Σ ¯ equations.