In-depth Absorption Research Articles

Fetal stress during labor

In a previous paper, radiant ignition of a surface-cooled reactive solid for small values of the ratio of the gas to solid thermal responsivity was analyzed. Here, these results are extended to moderate and large values of this ratio by treating the nondimensional activation temperature as a large parameter in an asymptotic analysis. Interior ignitions occur because in-depth absorption is taken into account. Graphs of ignition time are obtained for various responsivity ratios, thereby generalizing results reported by Linan and Williams. It is shown that the responsitivity ratio has a large influence on ignition time for surface absorption, but that, as the absorptivity decreases, the influence of the responsivity ratio rapidly diminishes.

Gas-Phase Ignition of a Solid with In-Depth Absorption of Radiation

Abstract In an earlier paper an asymptotic analysis was presented for the radiant ignition of a solid fuel that gasifies endothermically then reacts exothermically in the gas phase through a one-step Arrhenius process. The theory was restricted to surface absorption of the incoming radiation and to ignitions occurring during the stage of transport-controlled gasification which follows the stage of transition to gasification. These two restrictions are removed in the present paper. Emphasis is placed on determining the ignition time, defined as the interval between initiation of irradiation and thermal runaway. It is shown that if the gas is sufficiently reactive then ignition can occur early in the stage of transition to gasification and that decreasing the absorptivity of the solid increases the ignition time. Comparisons are made with results of earlier numerical integrations, demonstrating the existence of regimes in which the ignition time depends strongly on the ignition criterion adopted. Graphs are given containing results of a parametric study for the ignition time.

Influence of strong conductive gas-phase cooling on radiant ignition of a reactive solid

In a previous paper, radiant ignition of a surface-cooled reactive solid for small values of the ratio of the gas to solid thermal responsivity was analyzed. Here, these results are extended to moderate and large values of this ratio by treating the nondimensional activation temperature as a large parameter in an asymptotic analysis. Interior ignitions occur because in-depth absorption is taken into account. Graphs of ignition time are obtained for various responsivity ratios, thereby generalizing results reported by Linan and Williams. It is shown that the responsitivity ratio has a large influence on ignition time for surface absorption, but that, as the absorptivity decreases, the influence of the responsivity ratio rapidly diminishes.

Radiative ignition of double-base propellants. I - Some formulation effects

In this first paper of a two part study, the ignition response to arc image radiative heating (5 to 100 cal/cm sec) of several double-base propellants is examined; comparisons with certain AP and HMX propellants are made also. Ignition delay is affected by chemical factors in propellant formulation (stability of the condensed phase, reaction rate in the gas phase) and by optical factors in propellant formulation (opacifiers affecting reflectivity and in-depth absorption). The results show that comparisons of the chemical factors in the formulation can only be made properly when the optical factors are minimized (as by carbon addition). When optical factors are minimized by opacifying the propellant, one finds, in order of increasing ease of ignitability, the formulations tested fall as follows: HMX composite, AP composite, double base (noncatalyzed), double base (catalyzed).

A Radiative Ignition Model of a Solid Fuel

A theoretical model describing radiative ignition of a solid fuel is constructed and is numerically analyzed. The model includes the effects of gas phase reaction and a finite value of the absorption coefficient of the solid (in-depth absorption of incident radiation). It is found that the gas phase reaction must be included in the model in order to understand radiative ignition of a solid fuel and to find its ignition boundary. The in-depth absorption of the incident radiation by a solid fuel significantly affects the ignition delay time. The results indicate that there is a finite range of values for pyrolysis or gas phase reaction activation energy for which ignition will occur. This finding has a direct bearing on efforts to reduce material ignitability.

An Asymptotic Analysis of Radiant and Hypergolic Heterogeneous Ignition of Solid Propellants

Abstract An asymptotic analysis, in the limit of large activation energies, is presented for the ignition of a solid propellant undergoing an exothermic heterogeneous Arrhenius reaction with a gaseous oxidizer. The analysis is carried out for hypergolic or shock tube ignition conditions, and also for ignition under a radiant flux with in-depth absorption of the radiation. The asymptotic analysis illustrates how, for sufficiently large radiant fluxes, a short reaction stage, ending in thermal runaway, follows a much longer inert heating stage. A closed form expression is found to relate the ignition time to the radiant flux and physico-chemical propellant characteristics. An analytical expression is also found for the ignition time under hypergolic or shock tube ignition conditions. The existing numerical calculations of the ignition time, for hypergolic ignition cases and for ignition under a radiant flux with surface absorption, are very accurately correlated by the closed form expressions resulting from...

Radiant ignition of a reactive solid with in-depth absorption

An asymptotic analysis of the limit of large activation energy is presented for radiant ignition of asolid that experiences a one-step Arrhenius reaction in the condensed phase. Both constant and time-dependent radiant-energy fluxes are considered, and the complete range of values is covered for the absorption coefficient μ. It is shown that as μ increases, the structure of the transition stage, which follows the inert heat-conduction stage, passes from a thermal explosion without heat conduction, to a single transient heat-conduction zone with distributed chemical heat release, to a two-zone structure composed of a reactive-diffusive-absorptive zone near the surface and a transient-diffusive zone in the interior. For very high values of μ, the reactive-diffusive-absorptive zone further splits into a surface absorption zone and an interior reactive-diffusive zone, thereby reproducing results obtained previously for ignition by a surface-applied energy flux. The analysis shows that contrary to earlier expectation, the nondimensional absorption coefficient must be at least as large as the nondimensional activation energy for in-depth absorption to affect the ignition time negligibly.

Theory of Radiant and Hypergolic Ignition of Solid Propellants

Abstract A model is formulated for radiant ignition of a solid propellant, accounting for in-depth absorption of radiation and surface reaction between solid fuel and gaseous oxidizer. Mathematical solutions are obtained in the limit of infinite absorption coefficient. From calculated surface temperature histories, several ignition criteria are compared. Conditions are established under which the choice of ignition criterion influences ignition time; it is shown that ignition times based on constant ignition temperature can be greatly in error at high heating rates. From the dimensionless parametric solutions, dependence of ignition time on oxidizer concentration, pressure and other quantities is extracted. At low pressures and equal solid and gas temperatures, oxidizer mass fraction and pressure affect ignition time only through their effect on oxidizer concentration, but at high pressure or under shock-tube ignition conditions, the additional effect of pressure on transport properties becomes increasingly important. Chemical kinetics constitute the principal factor determining ignition time, while oxidizer diffusion rate imposes a limit on attainment of ignition without significantly affecting ignition time.