The interaction of a laminar diffusion flame with two- and three-dimensional vortex structures is considered, in which the flame becomes severely distorted and is strained in its own plane. Fast chemical kinetics and unity stoichiometry are assumed. The resulting curved flame sheets are treated by applying the boundary layer approximation locally until neighboring flame sheets come sufficiently close to interact and consume the intervening reactant, thus creating a core of combustion products with external isolated flame sheets.
The simplest example is the deformation of a diffusion flame by a viscous vortex of circulation Γ. For large Γ the radius of the core of combustion products increases in proportion to Γ1/3D1/6t1/2, where D is the binary diffusivity, indicating the overall transport quantity to be Γ2/3D1/3. The augmentation of reactant consumption due to the presence of the vortex is time-independent and behaves as Γ2/3D1/3.
The interaction of a laminar flame with a viscous vortex undergoing constant axial straining also is examined. The growth of the core radius has the similarity relation ϒ · ~ Γ1/3D1/6[(1-e-εt)1/2]/ε1/2 indicating that the core eventually reaches a steady state size. The core continues to store products and the outer flame arms continue to consume reactants independently of time, however, due to axial extension. Hence there exist two different time scales governing the development of the flame: one associated with the flame-vortex interaction and one associated with the external strain rate.
The effect of the release of heat (and subsequent density change) by the reaction on flame structure is examined by considering the interaction of a diffusion flame with a vortex undergoing a density change at the core. The decreased core density shifts the entire flowfleld radially outward, causing the burned core to be increased in size, while the radius of the unburned core decreases as [ρ1/ρ2 + 1]-1/6, where ρ1 is the reactant density and ρ2 is the product density. The augmented consumption rate of the flame also is reduced, since the flame is being strained further from the viscous core and thus to a lesser extent.
