Taylor-diffusion-controlled combustion in ducts. Issue 6 (1st November 2020) - Liñán, Amable; Rajamanickam, Prabakaran; Weiss, Adam D.; Sánchez, Antonio L.
Abstract : 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 L F, with the Peclet number P e = U a / D o based on the thermal diffusivity D o taken to be of order unity for generality. The solution to the associated Taylor-dispersion problem is described for times t ′ much larger than the characteristic diffusion time across the pipe a 2 / D o, when the flame is embedded in a mixing region of increasing longitudinal extent moving with the mean velocity. At leading order in the limit t ′ ≫ a 2 / D o, the longitudinal flame location, the burning rate, and the peak temperature are found to be a function of the effective Lewis number L e f f = L F ( 1 + P e 2 / 48 ) / ( 1 + L F 2 P e 2 / 48 ), whose value changes from L e f f = L F for P e ≪ 1 to L e f f = 1 / L F for P e ≫ 1 . As a result of this variation, the flame exhibits preferential-diffusion effects that depend fundamentally on P e, with important implications in designs of microcombustion devices employing narrow channels and pipes.