Taylor-diffusion-controlled combustion in ducts
Amable Liñán, Prabakaran Rajamanickam, Adam Weiss, Antonio L. Sánchez
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 LF, with the Peclet number Pe=Ua/Do based on the thermal diffusivity Do 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 a2/Do, 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′≫a2/Do, the longitudinal flame location, the burning rate, and the peak temperature are found to be a function of the effective Lewis number Leff=LF(1+Pe2/48)/(1+LF2Pe2/48), whose value changes from Leff=LF for Pe≪1 to Leff=1/LF for Pe≫1. As a result of this variation, the flame exhibits preferential-diffusion effects that depend fundamentally on Pe, with important implications in designs of microcombustion devices employing narrow channels and pipes.