Alexander M. Telengator

Influence of sublimation and pyrolysis on quasi-steady deflagrations in confined porous energetic materials

Deflagrations in porous energetic materials under confinement are generally characterized by a relatively rapid increase in the burning rate as the pressure difference, or overpressure, in the burned-gas region relative to that deep within the pores of the unburned solid increases. Specifically, there appears to be a range of overpressures in which the sensitivity, or slope, of the propagation speed as a function of overpressure transitions from relatively small to large values. This effect has been qualitatively attributed to the fact that a sufficient overpressure reverses the gas flow and thus allows the burned gas to permeate, and therefore preheat, the porous material. However, quantitative descriptions of both the process itself and the corresponding burning-rate dependencies have only recently been achieved. The present work reflects a further refinement in this analytical description in that the melt layer, which underlies several previous studies and is likely to exist only at modest overpressures, is replaced by sublimation and pyrolysis at the material surface, followed by an attached gas flame that converts the unburned gaseous reactants to final products. As a result, gaseous reactants as well as products now permeate the porous solid, thereby affecting the propagation speed significantly and modifying both the combustion-wave structure and the transition to convection-enhanced burning.

Stability of Quasi-Steady Deflagrations in Confined Porous Energetic Materials

Previous analyses have shown that unconfined deflagrations propagating through both porous and nonporous energetic materials can exhibit a thermal/diffusive instability that corresponds to the onset of various oscillatory modes of combustion. For porous materials, two-phase-flow effects, associated with the motion of the gas products relative to the condensed material, playa significant role that can shift stability boundaries with respect to those associated with the nonporous problem. In the present work, additional significant effects are shown to be associated with confinement. which produces an overpressure in the burned-gas region that leads to reversal of the gas flow and hence partial permeation of the hot gases into the unburned porous material. This results in a superadiabatic effect that increases the combustion temperature and consequently, the burning rate. Under the assumption of gas-phase quasi-steadiness, an asymptotic model is presented that facilitates a perturbation analysis of both the...

Intrusive-limit deflagrations in confined porous energetic materials

The deflagration of confined porous energetic materials is generally accompanied by an increasing pressure difference, or overpressure, between the burned gaseous products outside the porous solid and the unburned reactants deep within the pores of the material. Although for sufficiently small overpressures the overall structure of the combustion wave possesses a gaseous preheat region between the material surface and the gaseous reaction zone, at higher overpressures and/or sufficiently large surface reaction rates, there is a tendency for the surface temperature to approach the burned-gas temperature, causing the gaseous preheat region to disappear and the reaction zone to lie in the vicinity of the material surface. In this burning regime, there is a single merged reaction-zone structure in which both solid-surface and distributed gas-phase reactions occur. A large-activation-energy analysis of this wave structure is presented, complementing a previous study of the present model that assumed a positive standoff distance between the gaseous reaction zone and the solid material. An expression for the burning rate is derived, showing the expected transition from weak to strong pressure sensitivity in the burning-rate response as the over-pressure increases and convective preheating of the material begins to play a greater role. A fit of this burning-rate formula to relevant data for cyclotetramethylenetetranitramine C 4 H 8 N 8 O 8 , at less than 100% theoretical maximum density indicates reasonably good agreement with experimental results.

FINITE-RATE INTERPHASE HEAT-TRANSFER EFFECTS ON MULTIPHASE BURNING IN CONFINED POROUS PROPELLANTS

Deflagrations in porous solid propellants are often affected by an increasing pressure difference, or overpressure, between the burned-gas region and the gas deep within the pores of the material. As a result, there appears to be a relatively rapid change in the burning-rate response over a certain range of overpressures in which the sensitivity, or slope, of the propagation speed as a function of overpressure transitions from relatively small to large values. This is often referred to as a transition from “conductive” to “convective” burning, corresponding to the increased role played by convective gas transport relative to thermal diffusion in determining the propagation speed of the deflagration. In the present work, we consider the analysis of a two-temperature model in which finite-rate interphase heat-transfer effects also play an important role in determining the burning-rate eigenvalue. In particular, we revisit a physically relevant scenario in which the first effects of temperature nonequilibrium are felt in the thin multiphase reaction region, with the preheat zone remaining in thermal equilibrium to a first approximation. Expanding on previous asymptotic results that are further specialized to certain limiting parameter regimes, we consider a combination of analytical and numerical approaches to obtain solutions in the chemical boundary layer, and hence the burning-rate eigenvalue, for a significantly wider range of parameters. In particular, we are able to address a greater range of resistance to interphase heat transfer and thus determine an upper limit beyond which interphase temperature differences are no longer negligible in the preheat region. The main result is that, relative to earlier single-temperature models in which temperature-nonequilibrium effects are completely neglected, the burning-rate response exhibits a much sharper transition from the conduction- to the convection-dominated regime. This results from the ability of the reactive phase to retain a greater amount of the heat of reaction, causing a rapid increase in the reaction rate as the local temperature in that phase exceeds both the corresponding single-temperature value and even the final burned temperature.

Analysis of ignition of a porous energetic material

A theory of ignition is presented to analyse the effect of porosity on the time to ignition of a semi-infinite porous energetic solid subjected to a constant energy flux. An asymptotic perturbation analysis, based on the smallness of the gas-to-solid density ratio and the largeness of the activation energy, is utilized to describe the inert and transition stages leading to thermal runaway. As in the classical study of a nonporous solid, the transition stage consists of three spatial regions in the limit of large activation energy: a thin reactive–diffusive layer adjacent to the exposed surface of the material where chemical effects are first felt, a somewhat thicker transient–diffusive zone and, finally, an inert region where the temperature field is still governed solely by conductive heat transfer. Solutions in each region are constructed at each order with respect to the density-ratio parameter and matched to one another using asymptotic matching principles. It is found that the effects of porosity pro...

Combustion of porous energetic materials in the merged-flame regime

The structure and burning rate of an unconfined deflagration propagating through a porous energetic material is analyzed in the limit of merged condensed and gas-phase reaction zones. A global two-step reaction mechanism, applicable to certain types of degraded nitramine propellants and consisting of sequential condensed and gaseous steps, is postulated. Taking into account important effects due to multiphase flow and exploiting the limit of large activation energies, a theoretical analysis based on activation-energy asymptotics leads to explicit formulas for the deflagration velocity in a specifically identified regime that is consistent with the merged-flame assumption. The results clearly indicate the influences of two-phase flow and the multiphase, multi-step chemistry on the deflagration structure and the burning rate, and define conditions that support the intrusion of the primary gas flame into the two-phase condensed decomposition region at the propellant surface.

Ignition analysis of a porous energetic material: II. Ignition at a closed heated end

A continuation of an ignition analysis for porous energetic materials subjected to a constant energy flux is presented. In the first part (I), the analysis was developed for the case of an open-end, semi-infinite material such that gas flow, generated by thermal expansion, was directed out of the porous solid, thereby removing energy from the system. In the present study, the case of a closed end is considered, and thus the thermally induced gas flow is now directed into the solid. In these studies, an asymptotic perturbation analysis, based on the smallness of the gas-to-solid density ratio and the largeness of the activation energy, is utilized to describe the inert and transition stages leading to thermal runaway. In both cases it is found that the effects of porosity provide a leading-order reduction in the time to ignition relative to that for the non-porous problem, arising from the reduced amount of solid material that must be heated and the difference in thermal conductivities of the solid and gas...

Two-Temperature Effects on the Multiphase Burning of Confined Porous Propellants *

a relatively rapid change in the burning-rate response over a certain range of overpressures in which the sensitivity, or slope, of the propagation speed as a function of overpressure transitions from relatively small to large values. This is often referred to as a transition from “conductive” to “convective” burning, corresponding to the increased role played by convective gas transport relative to thermal diffusion in determining the propagation speed of the deflagration. In the present work, we consider the analysis of a two-temperature model in which finite-rate interphase heat-transfer effects also play an important role in determining the burning-rate eigenvalue. In particular, we revisit a physically relevant scenario in which the first effects of temperature nonequilibrium are felt in the thin multiphase reaction region, with the preheat zone remaining in thermal equilibrium to a first approximation. Expanding on previous asymptotic results that are further specialized to certain limiting parameter regimes, we consider a combination of analytical and numerical approaches to obtain solutions in the chemical boundary layer, and hence the burning-rate eigenvalue, for a significantly wider range of parameters. In particular, we are able to address a greater range of resistance to interphase heat transfer and thus determine an upper limit beyond which interphase temperature differences are no longer negligible in the preheat region. The main result is that, relative to earlier single-temperature models in which temperature-nonequilibrium effects are completely neglected, the burning-rate response exhibits a much sharper transition from the conduction- to the convection-dominated regime. This results from the ability of the reactive phase to retain a greater amount of the heat of reaction, causing a rapid increase in the reaction rate as the local temperature in that phase exceeds both the corresponding single-temperature value and even the final burned temperature.

Early Temperature-Nonequilibrium Effects on Multiphase Combustion of Confined Porous Energetic Materials *

Deflagrations in porous energetic materials are characterized by regions of two-phase flow where significant velocity and temperature differences between the gaseous and condensed phases act to modify the structure and propagation velocity of the combustion wave. In the present work, recent multiphase-flow models that describe propagating deflagrations under varying degrees of confinement, as represented by the pressure difference (or overpressure) between the burned and unburned regions, are reconsidered. We first summarize the results that are obtained in the single-temperature limit, and then go on to consider the early effects of temperature nonequilibrium on the burning-rate eigenvalue that are felt when such effects are still largely confined to the thin reaction region. Expanding on previous asymptotic results that show a significant increase in the sharpness of the well known transition from conduction- to convection-dominated burning, we consider the numerical solution of the inner reaction-zone problem for arbitrary values of the scaled interphase heat-transfer parameter. Employing a regularization technique to handle the complications that result from a regular singular point at the burned boundary, computational results are obtained that both validate the previous asymptotic regimes and suggest the spread of temperature nonequilibrium into the preheat region as the interphase heat-transfer coefficient is decreased.

Intrusive and Nonintrusive Deflagrations in Confined Porous Energetic Materials

The deflagration of confined porous energetic materials is generally accompanied by an increasing pressure difference, or overpressure, between the burned gaseous products outside the porous solid and the unburned reactants deep within the pores of the material. Although for sufficiently small overpressures the overall structure of the combustion wave possesses a gaseous preheat region between the material surface and the gaseous reaction zone, at higher overpressures and/or sufficiently large surface reaction rates, there is a tendency for the surface temperature to approach the burned-gas temperature, causing the gaseous preheat region to disappear and the reaction zone to lie in the vicinity of the material surface. In this burning regime, there is a single merged reaction-zone structure in which both solid-surface and distributed gas-phase reactions occur. A large-activation-energy analysis of both wave structures is presented, corresponding to positive (nonintrusive) and effectively zero (intrusive) stand-off distances between the gaseous reaction zone and the solid material. Expressions for the burning rate are derived, showing in each case the expected transition from weak to strong pressure sensitivity in the burning-rate response as the overpressure increases and convective preheating of the material begins to play a greater role. A fit of the intrusive burning-rate formula to corresponding data for HMX at less than 100% theoretical maximum density indicates reasonably good agreement with experimental results. *This paper is declared a work of the U.S. Government and is not subject to copyright protection in the United States.