Numerical Simulation of Turbulent Flame Structure with Non-unity Lewis Number

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Abstract
A numerical simulation of the response of a premixed flame to various randomly defined two-dimensional flow fields is performed in order to obtain an insight into Lewis number effects in turbulent premixed combustion. A one-step reaction with a large, but finite, activation energy in the limit of zero heat release is assumed.The numerical simulation uses vortex dynamics to describe the velocity field, while the scalar field is computed on a mesh.The flow field integral length scale is typically ten times the flame thickness, and the r.m.s. velocity fluctuation is of the order of the flame velocity. Ensemble averages are taken over a total number of 30 realization for Le of 1/2 and 37 realizations for Le of 2, where the Lewis number is Le = λ/(ρcpD). Since the density is kept constant, there is no feedback from the reacting scalar field to the velocity field. For the Le of 1/2 case, there is a clear manifestation of the thermo-diffusive instability mechanism leading to a cellular flame front structure, while for Le of 2, the thermo-diffusive effect reduces the hydrodynamic disturbances of the front.The scalar variable that best characterizes the flame dynamics is the excess enthalpy, which we define with respect to an undisturbed planar flame. The numerical results are analyzed statistically. The probability density functions of the progress variable and the excess enthalpy are interpreted on the basis of the observed flame response. The dissipation terms and the reaction rate in the onedimensional balance equations for the mean scalars and their variances are also given. Flame stretch enhances differential diffusion as shown by a significant correlation between strain-rate and excess enthalpy.