Freely Propagating Hydrogen Flames
Freely-propagating lean premixed hydrogen flames spontaneously develop into the well-known cellular burning structures, where the fuel consumption and heat release are highly variable along the "flame surface" (which, incidently, becomes significantly harder to define unambiguously). The instabilities at play in this system saturate quickly and result in robust, slowly evolving cellular burning features which prevent the establishment of a true steady solution. However, in our simulations, we employ a simple computational strategy to fix the mean location of the evolving flame, allowing us to achieve a quasi-steady flame configuration for analysis. Here, we explore the structure of three premixed hydrogen-air flames: stoichiometric and lean flat steady flames (one-dimensional), and a time-dependent lean freely-propagating (two-dimensional) case.
The simulations presented here are based on a low Mach number formulation of the reacting flow equations. The methodology treats the fluid as a mixture of perfect gases. We use a mixture-averaged model for differential species diffusion and ignore Soret, Dufour, gravity and radiative transport processes.
The flow configuration we consider initializes a flat laminar flame in a square domain, 8cm by 8cm, oriented so that the flame propagates downward. A cold fuel-air premixture enters the domain through the bottom boundary, and hot combustion products exit the domain through the top. The remaining computational boundaries are periodic. Along the inflow face we specify a mean inflow velocity. The simulations are run until the flames are statistically stabilized.
Tracing through the flame surface locally along integral curves of the temperature gradient, one finds that profiles of various chemical species and heat release resemble those of flat steady flames across a broad range of inlet fuel mixtures. This is consistent with characterizing the effect of differential diffusion and non-unity Lewis number as a local modification of fuel equivalence ratio. The distribution of heat deposition into the gas due to convection, conduction, diffusion (heat transfer accompanying differential species diffusion) and chemical reactions are evaluated for the flat steady cases, and used as normalizing scales to quantify and understand the behavior of the freely-propagating case.
The figure on the left shows the distribution of heat deposition into the gas due to convection, conduction, diffusion and chemical reactions along normals of an isotherm (T= 1144 K). The broad spread in the profiles is due to the thermo-diffusively unstable nature of hydrogen combustion. The scatter plot in the figure on the right shows that the shape of heat release of the freely propagating flame resembles that of the flat steady flame.
More details will appear in an upcoming paper by Xinfeng Gao, Marc S. Day and John B. Bell, Characterization of Flat and Freely Propagating Hydrogen Flames
John B. Bell, Robert K. Cheng, Marcus S. Day and Ian G. Shepherd, "Numerical Simulation of Lewis Number Effects on Lean Premixed Turbulent Flames". [pdf]