Statistical Analysis of Displacement Speed in Turbulent Stratified Flames: A Direct Numerical Simulation Study

Abstract

Statistically planar turbulent stratified flames under different initial root mean square turbulent velocity fluctuation u′ levels are simulated for global equivalence ratios <φ> = 1.0 and <φ> = 0.7 using 3-dimensional compressible direct numerical simulations (DNS) with a modified single-step Arrhenius-type chemistry. For the simulations of stratified flames, a sinusoidal variation of equivalence ratio is introduced in the unburned reactants ahead of the flame. The simulation parameters are chosen in such a manner that the combustion situation belongs to the thin reaction zones regime in all cases. The DNS data has been used to analyze the statistical behavior of the displacement speed S d and its components (i.e., the reaction rate component S r , the normal molecular diffusion component S n , the tangential diffusion component S t , and the component arising due to reactant inhomogeneity S ξ) and their curvature and tangential strain rate dependence. The mean behavior of displacement speed S d and its local strain rate and curvature dependences have been analyzed in detail in terms of the statistical behaviors of the various components of displacement speed (i.e., S r , S n , S t , and S ξ). It has been observed that the contribution of S d due to reactant inhomogeneity S ξ is negligible in comparison to the other components and therefore S d is most significantly affected by the contribution of (S r + S n + S t ). The displacement speed S d statistics are presented in terms of its marginal probability density functions (PDFs) as well as its joint PDFs with curvature and tangential strain rate. It has been observed that S d shows a nonlinear negative correlation with curvature but the correlation strength decreases with increasing u′. The tangential strain rate response of S d has also been found to be dependent upon the turbulence velocity fluctuation level u′ with weak correlation in higher initial u′ cases and a modest positive correlation in the lower u′ cases. It has been found that the marginal PDFs of S r and S n in stratified flames show significant differences in comparison to the corresponding PDFs obtained for perfectly premixed flames with the same values of global equivalence ratio and u′. However, the local curvature and strain rate dependences of S d and its components are found to be qualitatively similar to the corresponding statistical behaviors obtained for perfectly premixed flames with the same values of global equivalence ratio and u′. It has been demonstrated that the curvature dependence of S d has important implications in the context of modeling the curvature stretch term in the Flame Surface Density transport equation.