An Evaluation of Numerical Models for Temperature-Stabilized CH₄/Air Flames in a Small Channel

Abstract

Flames stabilized in a heated tube with a diameter on the order of the flame thickness (i.e., small Peclet number) are investigated with numerical models of differing formulations. Providing a benchmark for comparison, a two-dimensional detailed model that solves the full, elliptic Navier–Stokes equations assuming axisymmetry is implemented with detailed chemical kinetics. The solutions are compared to those obtained from a simpler one-dimensional volumetric model that relies on a constant Nusselt number assumption to account for the heat transfer between the gas and the wall. This volumetric model presents poor agreement with the detailed results with an average error of 231 K (18%) in wall temperature at the stabilization position. In an attempt to improve the modeling accuracy, the volumetric model is extended to account for the variations in the thermal boundary layer inside the reaction zone and the resulting enhanced flame-wall heat transfer. This extended volumetric model demonstrates significant improvements, given the considerable savings in computational time when compared to the detailed model, with errors smaller than 55 K (4.2%) in stabilization wall temperatures. The leading order effects influencing these flames are inferred based on the dissimilarities in the respective model formulations and on the accuracy of their predictions. Deviations between this improved model and the detailed model are further investigated to determine the influence of the neglected two-dimensional effects. The deviations are attributed to the differences in treatment of radial momentum and H species transport between the two models.