A DNS study of the impact of gravity on spherically expanding laminar premixed flames

Abstract Determining laminar flame speeds from spherical flame experiments is difficult for low flame speeds, when the flame shapes quickly become non-spherical due to the influence of gravity. Direct Numerical Simulations (DNS) of spherically expanding laminar premixed flames whose motion is affected by buoyancy have been performed. A lean methane/air flame and a series of rich hydrogen/air flames diluted with molecular nitrogen are considered to investigate the effects of different fuels. All flames feature low flame speeds such that the gravitational force quickly leads to a strong deformation of the initially spherical shapes. To assess the effects of non-unity Lewis numbers in the hydrogen flames, an additional DNS of one hydrogen flame is conducted with unity Lewis numbers for all species. All DNS employ finite rate chemistry. The effect of buoyancy on the flame dynamics is found to be governed by the Richardson number, which describes the relative importance of buoyancy with respect to the flame expansion, unless significant variations of the flame propagation speed due to strain rate and curvature occur, as observed for the hydrogen/air flames with non-unity Lewis numbers. In contrast to spherical flames, the linear dependence of the flame’s displacement speed on stretch is not observed. Unless effects due to non-unity Lewis numbers prevail, the displacement speed is found to be proportional to strain rate and curvature, which vary independently along the flame front of a buoyant flame. Based on the DNS data, five techniques to determine the burning velocity of the unstretched premixed flame from data collected in buoyant flames are discussed. Among these techniques, a methodology based on flame volume, surface area, and surface-averaged curvature shows promising results with relative errors below 2% for flames where effects due to non-unity Lewis numbers are negligible.