Scalar gradient and small-scale structure in turbulent premixed combustion

Abstract

Scalar gradient and small-scale structure in turbulent premixed combustion are investigated with emphasis on flame thickening. A Lagrangian-type equation for the evolution of the scalar gradient following an isoscalar surface is presented, which is useful in studying physical mechanisms for the scalar gradient evolution in premixed flames. The terms in the Lagrangian-type form of the scalar gradient equation are analyzed using direct numerical simulation data for statistically one-dimensional planar flames with high intensity turbulence. Two flames with Da<1 and Ka>1 are investigated. Results show that the curvature plays an important role in the evolution of the scalar gradient in turbulent premixed flames. The tangential strain rate, which is the major term to steepen the scalar gradient, is shown to be negatively correlated with the curvature due to the relation between the dilatation and the displacement speed of isoscalar surfaces. This represents the effects of heat release on the scalar gradient evolution. The relation between the dilatation and the displacement speed of isoscalar surfaces is also related to the presence of negative dilatation in premixed flames. The alignment characteristics of the flame normal with the principal axis of the strain are also investigated in relation to the characteristics of the tangential strain rate. Variations of the curvature, weighted by the density and the diffusivity, along the normal to the isosurfaces are found to be the major sink term in the scalar gradient equation and to have a negative correlation with the magnitude of the curvature. This provides evidence that smaller-scale wrinkling is more responsible for flame thickening. In the preheat zone, the tangential strain rate is balanced with the variation of the mass flux normal to the isosurface, and the strength of the thickening process is determined by the curvature variation term. In the reaction zone, the evolution of the scalar gradient is determined by the balance of the tangential strain rate and the curvature variation term. It is also shown that the thickening process in the reaction zone is much weaker than that in the preheat zone. In one of the simulated flames, a sudden drop of the strength of flame thickening in the reaction zone is observed.