Unsteady combustion modeling of energetic solids

The classical, linearized quasi-steady (QS) theory of unsteady combustion of homogeneous energetic solids is examined. In particular, the activation energy asymptotic (AEA) approximation in the condensed phase is investigated. Single step, zeroth order, AEA decomposition with non-zero Jacobian parameter (n_s≠O) is shown to be a superior condensed phase model compared with the common, simple Arrhenius surface pyrolysis (n_s=O) model. Favorable comparison with T-burner and laser-recoil response function data for double base propellant provides evidence for the zeroth order decomposition model. These results and additional numerical investigation show that the response function can be influenced by condensed phase unsteady effects at frequencies as low as 1/4 the characteristic condensed phase reaction layer frequency (which for moderate pressures can be well below the gas phase characteristic frequency). This suggests that at moderate pressures (10-100 atm) condensed phase reaction zone unsteadiness should be considered before, or at least in conjunction with, gas phase unsteadiness. At frequencies low enough that the complete (gas and condensed) QS assumption is valid the incomplete (condensed-phase only) zeroth order decomposition model, when augmented by steady state experimental burning rate sensitivity data to supply the missing gas phase information, appears very promising for modeling transient burning.