Use of Condensed-Phase Reaction Models in Combustion Simulation of Energetic Materials

Abstract

The contribution of condensed-phase reaction kinetics to the overall combustion behavior of cyclotetramethylenetetranitramine is investigated in the context of a successful two-step chemical reaction scheme introduced by Ward, Son, and Brewster ("Role of Gas-and Condensed-We derive extensions of the activation energy asymptotics of the condensed-phase reaction from nthorder (0 n 1) kinetics to include 10 additional analytic reaction models. The results show that it is not possible to determine uniquely the condensed-phase reaction model by validating against steady-state burn rates and surface temperatures because the parameters of all models are sufficiently flexible to fit the experiments. However, the frequency-dependent transient response functions of mass burning rate to fluctuations in pressure and external radiation are somewhat more sensitive to the choice of kinetic model. The sensitivity of using different kinetic models to fit experimental T-burner data is more pronounced under conditions in which the surface temperature is low and no external radiation is applied. The power law model, which has the highest contribution to condensed-phase heat release, provides the best fit to transient combustion response functions. Nomenclature A c = Arrhenius preexponential factor B g = gas-phase frequency factor C p = heat capacity D g = gas-phase Damköhler number E = activation energy f = frequency of oscillating pressure/radiance f r = fraction of external radiation absorbed below surface reaction zone fY = condensed-phase reaction model K a = laser absorption coefficient of condensed phase k = nondimensional temperature sensitivity m = mass burning rate or mass flux m r = reference mass flux, 1 kg=m 2 s n = order of reaction P = pressure Q = heat release q = heat flux R = ideal gas constant R p = pressure-driven frequency response function R q = radiation-driven frequency response function r = @T s =@T 0 p r b = linear burn rate T = temperature W = molecular weight x = distance x g = gas flame characteristic thickness Y = mass fraction Y cc = critical mass fraction at burning surface = extent of conversion = r k, Jacobian parameter @ x y = @y=@x = thermal conductivity = homogeneous solution to energy equation with oscillating perturbation = pressure exponent or pressure sensitivity = solid density p = temperature sensitivity = nondimensional frequency c = rate of condensed-phase reaction ! = 2f, circular frequency Subscripts c = condensed phase f = flame g = gas l = liquid r = radiation s = surface = extent of conversion 0 = initial Superscript = nondimensional quantity