The Modeling of Fuel Mass Fraction Variance Transport in Turbulent Stratified Flames: A Direct Numerical Simulation Study

Abstract

Three-dimensional compressible simplified chemistry-based direct numerical simulations (DNS) of statistically planar turbulent stratified flames at global equivalence ratios ⟨φ⟩ = 0.7 and ⟨φ⟩ = 1.0 have been carried out to analyze the statistical behavior of the transport of the variance of the Favre fuel mass fraction fluctuations (where , and are Reynolds average, Favre mean, and Favre fluctuation of a general quantity q where ρ is the gas density) in the context of Reynolds-averaged Navier-Stokes (RANS) simulations. It has been found that algebraic expressions are inadequate for predicting in low Damköhler number combustion, and a transport equation for may need to be solved. The statistical behaviors of and the unclosed terms of the transport equation (i.e., the terms originating from turbulent transport T ₁ , reaction rate T ₃ , and molecular dissipation D ₂) have been analyzed in detail. It has been found, that T ₃ and D ₂ remain leading order contributors to the transport in all cases, whereas, the contribution of T ₁ remains small in ⟨φ⟩ = 1.0 cases, but plays a more important role in ⟨φ⟩ = 0.7 cases. Through an a-priori DNS analysis, the modeling of T ₁, T ₃, and D ₂ has been addressed in detail. A model has been identified for T ₁, which provides satisfactory agreement with the DNS data. The models for T ₃ and D ₂, which were originally proposed for high Damköhler number flames, have been modified for low Damköhler combustion in the context of RANS simulations, and the predictions of the modified models are found to be in good agreement with the corresponding quantities extracted from the DNS data.

The authors are grateful to EPSRC UK for financial assistance.