Adiabatic pyrolysis of solid propellants

Abstract

Several one-step, irreversible, zero-order pyrolysis models (Arrhcnius, KTSS, and Merzhanov Dubovitskii high activation energy pyrolysis), commonly used to study adiabatic burning of energetic materials with arbitrary pressure and initial temperature, are revisited. Motivated by experimental and theoretical work performed in 1984 by students of this laboratory, a relationship among the several interplaying parameters is found under steadystate conditions. This relationship corresponds to the Jacobian of the sensitivity parameters used in the Zeldovich Novozhilov approach. If the Vieille steady burn rate law is enforced, consistency requires an explicit pressure dependence for both Arrhenius and KTSS pyrolysis. But if the normal (or Zeldovich) steady burn rate is enforced, no explicit pressure dependence is required for both Arrhenius and KTSS pyrolysis. Other constraints arise for the Merzhanov Dubovitskii pyrolysis model. The unifying concept for these different trends is the Jacobian consistency between the implemented steady pyrolysis and ballistic laws. The dependence of the pre-exponential factor on surface activation energy (known as kinetic compensation) is shown to be linear (Arrhenius) or almost linear (Merzhanov Dubovitskii), for any given experimental data set under steady burning. Experimental results are reported for a variety of solid propellants of different nature. NOMENCLATURE * Copyright © 1997 by Luigi DeLuca. Published by the American Institute of Aeronautics arid Astronautics, Inc. with permission. ' Professor, Dipartimento di Energetica; Fax: (39-2) 2399-3940, e-mail: DeLuca@icil64.cilea.it. Associate Fellow. ' Professor, Dipartimento di Matematica ' PhD. Candidate, Dipartimento di Energetica ' Lab. Technician, Dipartimento di Energetica MSc. Candidate, Dipartimento di Energetica a&, &(, = multiplicative factors denned by Eq. 3.3, Eq. 3.4 A, B = nondim. functions used in frequency response analysis Ac = multiplicative factor used in the Merzhanov-Dubovitskii pyrolysis, 1/s, in Eq. 2.3 AS, Bs = multiplicative factors defined by Eq. 2.1 (Arrhenius ), Eq. 2.2 (KTSS) c = specific heat, cal/g K £{...) = activation energy, cal/mole J5(...) = .Z?(...)/9J/T(...) , riondim. activation energy Is = external radiant flux intensity, cal/cmPs j = running counter, integer k = ZN steady sensitivity parameter defined in Eq. 6.3 ra = mass burn rate, g/crn s Ms = pre-exponential factor of Zeldovich (or normal) mass burn rate, g/cms, in Eq. 2.6 n = pressure exponent of ballistic steady burn rate defined by Eq. 2.4 n., = pressure exponent of pyrolysis law denned by Eq. 2.1 (Arrhenius ) and Eq. 2.2 (KTSS) IT-TS — pressure exponent of steady surface temperature defined by Eq. 3.1 p = pressure, atm Pref, Tref = reference pressure (68 atm), reference temperature (298 K) Q = heat release, cal/g (positive if exothermic) r =ZN steady sensitivity parameter denned in Eq. 6.4 rj, — burn rate, cm/s n,ref>TSiref = reference burn rate n(pref), reference surface temperature Ts(pTnf) 5R = universal gas constant; 1.987 cal/moleK T = temperature, K TI = initial propellant temperature, K ws = power of KTSS pyrolysis law, denned in Eq. 2.2 Greek Symbols a = thermal diffusivity, cm/s 8 = ZN Jacobian defined in Eq. 6.5 fj,, v = ZN steady sensitivity parameters defined in Eq. 6.2, Eq. 6.1 p = density, g/cm cTp = steady temperature sensitivity of burn rate, 1/K, denned by Eq. 2.4 T« = pressure exponent of surface temperature defined by Eq. 3.1 if} = variable defined in Eq. 4.19 Subscripts Arr = Arrhenius pyrolysis law bal = ballistic c = condensed g = gas hig = high KTSS = KTSS pyrolysis law low = low p = pressure pyr = pyrolysis ref = reference s = burn surface Vi = Vieille burn rate law Ze = Zeldovich burn rate law (...)1 = cold boundary value Superscripts (...) = steady-state value (...) = dimensional value (...) — average value