Taylor-diffusion-controlled combustion in ducts - Liñán, Amable; Rajamanickam, Prabakaran; Weiss, Adam D.; Sánchez, Antonio L. (Combustion theory and modelling, 2020)
An analysis is presented for the Burke-Schumann flame established when a fuel tank discharges with mean velocity U along a circular duct of radius a filled initially with air. Attention is focused on effects of interactions of shear with transverse diffusion resulting in enhanced longitudinal dispersion. The analysis accounts for preferential-diffusion effects arising for non-unity values of the fuel Lewis number , with the Peclet number based on the thermal diffusivity taken to be of order unity for generality. The solution to the associated Taylor-dispersion problem is described for times much larger than the characteristic diffusion time across the pipe , when the flame is embedded in a mixing region of increasing longitudinal extent moving with the mean velocity. At leading order in the limit , the longitudinal flame location, the burning rate, and the peak temperature are found to be a function of the effective Lewis number , whose value changes from for to for . As a result of this variation, the flame exhibits preferential-diffusion effects that depend fundamentally on , with important implications in designs of microcombustion devices employing narrow channels and pipes.