The role of heat transfer in radiant ignition/extinction behavior of homogeneous energetic solids has been studied computationally. A model has been developed based on simplified chemical kinetics, unsteady heat transfer processes in the solid phase, and quasi-steady heat transfer in the gas phase. The general behavior of ignition and extinction dynamics for a spatially uniform incident radiant flux has been simulated and explained in terms of unsteady heat transfer phenomena. Two critical heat flux levels for the incident radiation are identified. For fluxes between the critical values, there is an ignition corridor with upper and a lower limits on the allowable time for radiation exposure to achieve ignition. Below the lower critical flux there is no upper limit on the allowable exposure time to achieve ignition. Above the upper critical flux, stable ignition (self-sustained combustion on removal of the radiant flux) is not possible, that is, the ignition corridor becomes vanishingly small. The model explains the ignition corridor in terms of unsteady conductive, advective, and in-depth radiative heat transfer processes in the solid and quasi-steady conductive/advective processes in the gas-phase flame zone. Comparison is made with experimental data for go/no-go ignition behavior of cyclotetramethylene-tetranitramine (HMX).
Nomenclature
A c= condensed-phase kinetic preexponential factor B g = modified gas-phase kinetic preexponential factor C = specific heat of condensed phase, C p for gas E c = activation energy of condensed-phase decomposition E g = gas-phase activation energy F c,g = Zeldovich-Novozhilov functions f r = fraction of q r absorbed below surface reaction zone, exp(−K a X R ) f s = surface temperature gradient on condensed side K a = absorption coefficient of condensed phase k c,g = thermal conductivity L * = characteristic length defined by the ratio of free chamber volume to nozzle throat area m = mass flux P = pressure Q c,g = chemical heat release (positive exothermic) q c = conductive heat feedback to condensed phase q crit = critical heat fluxes for upper boundary of ignition corridor (low and high) q r = radiant heat flux R = universal gas constant r b = burning rate T = temperature T chem = temperature at which condensed-phase chemical reaction modeling begins T 0a = apparent initial temperature t = time X C = solid conduction zone length scale, α c /r b X R = surface reaction zone length scale X rad = absorption length scale, 1/K a x = coordinate normal to surface, positive into gas phase α c = thermal diffusivity in condensed phase