RI 8607 The Theory of Flammability Limits - Radiative Losses and Selective Diffusional Demixing

The concept of limit burning velocities is being used to formulate a quantitative theory of flammability limits. Competing and complicating processes dissipate power from a combustion wave and quench propagation at some characteristically low limit velocity. Two earlier reports dealt with process (a), natural convection (RI 8127); and with process (b), conductive-convective wall losses (RI 8469). This report considers process (c), radiative losses, and process (d), selective diffusional demixing. The limit burning velocity for radiative losses is [(SU)c ~ e cp] It is normally not a significant process for premixed gas flames; however, for laminar flame propagation in a gravity-free environment, it is the only loss process present. Accordingly, limit velocities at zero gravity should be much lower than on earth, and premixed gases should be flammable over wider composition ranges. For highly emissive dusts, soot, or ash-forming flames, radiative losses are significant even under normal gravity conditions. Selective diffusional demixing is a complication that manifests itself in the form of cellular flame structures and wide gaps in composition between upward and downward propagation limits. It induces a burning velocity shift (?Su)d, causing the flame to behave as though it were richer or leaner than its initial composition, depending on whether the fuel or the oxidizer mole¬cule has the higher diffusivity. A simple pertubation analysis shows that the process generates stable cellular flames whenever [dsu] > 0, where ci is the concentration of the reactant with the higher diffusivity. The same analysis indicates that at the opposite stoichiometry, where [dcu] < 0, laminar structures are stabilized. A simple formula for the diameter of cellular flames is derived, which predicts that dcell should vary inversely with the product of the diffusivity difference Di -DJ, and the burning velocity slope [dc ]. Those predictions are in good agreement with the available data. Buoyancy forces for upward propagation induce flame front curvature, and hence buoyancy and selective diffusion are mutually supportive in upward propagation. Thus large gaps in composition between upward and downward limits are present in those composition domains where cellular flames are stable.