Stretched vortex layer flamelet

Abstract

A new sub-grid flamelet model is developed based on a steady-state, viscous vortex layer with an imposed compressive strain orthogonal to both the vorticity and the shear force. The imposed normal strain results in the stretching of the vorticity in the direction orthogonal to the plane of the shear strain. The model has certain special features. (i) Non-premixed flames, premixed flames, or multi-branched flame structures are determined rather than prescribed. (ii) Three components of velocity exist although the flamelet model is two-dimensional. (iii) The effect of variable density is addressed in the flamelet model. The vortex-layer configuration distinguishes this model from recent models by this author that address flames in other practical and ubiquitous vortical structures: tube-like stretched vortices or vortices stretched in two directions. Thereby, the model collection available for application to vortical configurations found in turbulent combustion is increased. Solutions to the Navier-Stokes equations and the associated scalar equations governing the flamelet model are obtained without the boundary-layer approximation and demonstrate the impact of the new features of the model. The shear strain and vorticity are found not to affect the scalar profiles, mixing and burning rates, or the two velocity components orthogonal to the shear force; only the velocity parallel to the shear force is affected. The compressive strain rate is the influential constraint affecting the scalars and the other two velocity components. However, the vorticity is strongly affected by the scalar profiles. The relation to classical concepts for incompressible flow is discussed.