Chemical Closure Model for Fractal Flamelets

Abstract A chemical closure model for premixed turbulent flames is proposed and tested by analysis and numerical computation for flames with vanishingly small density change. The model is based on the assumption that reaction zones can be modeled as thin sheets—flamelets—and that the geometry of these sheets can be represented by fractal surfaces. The model expression for mean fuel consumption rate is 〈ω〉=C R ρ〈δY f u L 〉 f (lƒ/η) D−2l F −1 〈C〉(1−〈c〉) with ƒ given by ƒ=[1−(1−A t −1 4 R 1 −3 4 ) exp (−A t 1 4 R 1 −1 4 u′/〈ul〉 f )] and l η =A t 1 4 R 1 3 4 where D is the fractal dimension of the flamelet surface and is the new parameter introduced by the fractal geometry assumption. This model is tested in simplified analyses of normal and oblique flames with good results. The oblique flame analysis provides new insight into the definition of the turbulent burning velocity. Numerical computations are performed with a conditioned second-order closure scheme, and the chemical closure model performance is found to be good. Computed results with a gradient transport model for species diffusion show that turbulent fluxes are significantly under predicted in comparison with the second-order closure results.