Effect of thermal expansion on flame propagation in channels with nonslip walls

Abstract

Propagation of premixed flames in narrow channels is investigated by means of extensive numerical simulations of a complete system of combustion and hydrodynamic equations, incorporating transport properties (thermal conduction, diffusion and viscosity) and Arrhenius chemical kinetics. The system includes mass conservation and Navier–Stokes equations as well as those for the energy and species balance. A flame propagates from the closed end of a channel to the open one. An initially planar flame front gets corrugated due to wall friction and thereby accelerates. It is shown that a flame exhibits an exponential state of acceleration only when the thermal expansion coefficient Θ exceeds a certain critical value Θ>Θc. The quantity Θc is tabulated as a function of the Reynolds number related to the flame propagation, Re, being Θc≈6 for Re=5∼20. The major flame characteristics such as the flame propagation speed and acceleration rate are scrutinized. It is demonstrated that the acceleration promotes with Θ but weakens with Re. In this respect, the present computational results support the theoretical prediction of Bychkov et al. Physical Review E 72 (2005) 046307 in a wide range of Θ and Re. While very good quantitative and qualitative agreement between numerical and theoretical results is found for realistically large thermal expansion, Θ⩾8, agreement deteriorates with decreasing Θ. Specifically, while the theory and modeling do not quantitatively agree for Θc<Θ<8, they nevertheless demonstrate a qualitative resemblance (the exponential state of acceleration). Finally, no exponential acceleration at Θ<Θc denotes that the theory completely breaks in that case, but this fits other works in the field and thereby allows reconciling various formulations on the flame acceleration.