Martin Summerfield

Nonsteady burning phenomena of solid propellants - Theory and experiments.

Abstract : Non-steady burning of solid propellants was investigated both theoretically and experimentally, with attention to combustion instability, transient burning during motor ignition, and extinction by depressurization. The theory is based on a one-dimensional model of the combustion zone consisting of a thin gaseous flame and a solid heat up zone. The non-steady gaseous flame behavior is deduced from experimental steady burning characteristics; the response of the solid phase is described by the time-dependent Fourier equation. Solutions were obtained for dynamic burning rate, flame temperature, and burnt gas entropy under different pressure variations; two methods were employed. First, the equations were linearized and solved by standard techniques. Then, to observe nonlinear effects, solutions were obtained by digital computer for prescribed pressure variations. One significant result is that a propellant with a large heat evolution at the surface is intrinsically unstable under dynamic conditions even though a steady-state solution exists. Another interesting result is that the gas entropy amplitude and phase depend critically on the frequency of pressure oscillation and that either near-isentropic or near-isothermal oscillations may be observable. Experiments with an oscillating combustion chamber and with a special combustor equipped for sudden pressurization tend to support the latter conclusion. (Author)

Starting Transient of Solid-Propellant ocket Motors with High Internal Gas Velocities

A comprehensive analytical model which considers time and space development of the flow field in solid propellant rocket motors with high volumetric loading density is described. The gas dynamics in the motor chamber is governed by a set of hyperbolic partial differential equations, that are coupled with the ignition and flame spreading events, and with the axial variation of mass addition. The flame spreading rate is calculated by successive heating-to-ignition along the propellant surface. Experimental diagnostic studies have been performed with a rectangular window motor (50 cm grain length, 5 cm burning perimeter and 1 cm hydraulic port diameter), using a controllable head-end gaseous igniter. Tests were conducted with AP composite propellant at port-to-throat area ratios of 2.0, 1.5, 1.2, and 1.06, and head-end pressures from 35 to 70 atm. Calculated pressure transients and flame spreading rates are in very good agreement with those measured in the experimental system.

Theory of Flame Front Propagation in Porous Propellant Charges under Confinement

Abstract : Ultra-high burning rates can be achieved by combustion of porous media. A theoretical model is developed to describe the flame propagation in a packed bed of granular propellant. The calculated pressure-time-distance transients, wave propagation speed, and mass fraction of propellant burned during flame propagation, all agree well with experimental data obtained for the same conditions. Results demonstrate that the combustion-generated strong pressure gradient causes the hot product gas to deeply penetrate the unburned region. A continental divide forms automatically in the pressure distribution as the wave progresses into the charge. In the particular case studied the flame front reaches a speed about 5000 times the normal propellant burning rate and continues to accelerate as the internal pressure increases. (Modified author abstract)

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).

Site and Mode of Action of Platonizers in Double Base Propellants

Certain metal organic salts (e.g., lead or copper salicylate) when used in double-base propellants induce desirable insensitivities of burning rate to pressure and initial temperature. To understand this, the combustion wave zones (luminous flame, dark, fizz, and surface reaction zones) were examined by means of photography and fine thermocouples (4fi bead). The metal salts significantly alter the surface and fizz zones. The surface zone accumulates carbonaceous material coincident with the appearance of an accelerated burning rate in the catalyzed case. No attendant change in surface heat release is detected. Coinciding with this carbonaceous layer occurrence are substantial (50-100%) increases in conductive feedback from the fizz zone. This latter effect is believed directly responsible for the altered burning behavior though its origin may lie in the altered surface chemistry.

A thermophysical mathematical model of steady-draw smoking and predictions of overall cigarette behavior

Abstract Manipulation of the effeluent smoke composition from a cigarette will be facilitated by a working model of the combustion and smoke formation process. A first step toward such a model is presented. For simplicity, the situation considered here is steady-draw smoking from ignition. A one-dimensional model of the actual two-dimensional burning process is derived from the usual conservation laws (mass, momentum, energy, species). The chemical processes are simplified by the concept of grouping of reactions. The model thus includes only a one-step char oxidation reaction and a one-step pyrolysis reaction; the kinetic parameters of these are obtained by thermal analysis of tobacco. Other input parameters, notably convective heat transfer coefficient, are measured values. Model predictions of the effects of flow rate and oxygen concentration on burning rate and pressure drop are compared with experiment. Reasonable agreement is found for these overall behavior parameters.

Theoretical examination of assumptions commonly used for the gas phase surrounding a burning droplet

A finite reaction-rate model is compared to three commonly used flame-sheet models. The latter differ in their treatment of the evaporation from the surface and the value used for the molecular weights in the evaporation law. All four models are applicable to both steady and unsteady burning of droplets. Further, they account for variations of droplet radii and allow for differences in ambient conditions. Numerical results (obtained forn-decane) show that if the radius of the droplet is 10^(−2) cm the thin-flame approximation is excellent at 10 atm if the droplet surface temperature is not close to either the boiling point or the ambient temperature. However, this approximation is unacceptable at 1 atm. Among the three flame-sheet models, the one using non equilibrium evaporation at the surface and individual molecular weights best approximates the finite reaction-rate theory. However, this agreement breaks down for smaller droplets with lower surface temperatures, or for air with a larger oxygen content. These conclusions are independent of the chosen kinetics. The Clausius-Clapeyron approximation is shown to be excellent away from the boiling point for R = 10^(−2) cm. However, as the droplet surface temperature approaches the boiling point, or the droplet radius decreases, this assumption leads to considerable errors in the evaporation rate and also distortion of the thermal layer. Even larger errors are obtained when an average molecular weight is used. Here, large underestimates of the evaporation rate and great distortions of the thermal layer of the droplet are obtained. In spite of these errors, all models agree well at wet-bulb conditions.

A study of some factors influencing the ignition of a liquid fuel pool

Abstract Two particular problems concerning the ignitability of a pool of liquid fuel are considered. First is the problem of defining the domain of ignitability of a pool of fuel at a superflash temperature subjected to a cross wind. It is postulated that this domain is bounded by the lean mixture limit or by the blowoff limit of the local fuel-air mixture, whichever is encountered first above the surface. This domain is calculated for a laminar boundary layer over a flat pool of fuel. The agreement between this predicted boundary and the boundary found here experimentally is generally quite good. Second is the problem of determining what factors control the ignitability of a liquid pool of fuel at a subflash temperature. The heating of such a pool to the point of ignition, by an energy source in the space above it, is retarded considerably by motion induced in the pool. Suppression of the motion enhances the ignitability markedly. The induced motion produces a vortex cell whose size depends on various fuel and igniter parameters. The driving force causing this fluid motion is postulated to be a combination of the forces resulting from buoyancy in the pool and surface tension gradient on the surface.

Aluminized Solid Propellants Burning in a Rocket Motor Flowfield

Combustion and agglomeration processes of aluminum particles emitted from the surface of an aluminized double-base propellant (NC/TMETN) were studied under rocket motor, crossflow conditions. High-speed color photographs (-2000 frames/s) were taken of burning AI/AI2O3 agglomerates forming on the surface, moving along the surface, and entering the flowfield. As an example, a propellant containing 6-^m Al burning at 7 MPa and 6 m/s crossflow produced a mean agglomerate size of about 250 ^m. Analysis of size distributions of the agglomerates leaving the surface revealed that the following parameters decrease with increasing pressure: collision frequency on the surface, the agglomerate stay time on the surface, and mean agglomerate size. Increasing the crossflow velocity decreased the mean agglomerate size. The propellants which contained the large aluminum particles (50 /*m vs 6 j*m) burned without the aluminum igniting or agglomerating on the surface.

The Mechanism of Super-Rate Burning of Catalyzed Double Base Propellants

Previous investigators have offered qualitative explanations for the large, pressure-dependent, burning behavior changes seen in nitrate ester propellants when lead or copper salts are added. The most developed qualitative models are those of Camp and of Powling and co-workers but both exhibit certain discrepancies with experiment. New evidence reported here derives from radiation-assisted burning tests in which the spectral content (particularly ultraviolet) of the impinging radiation was varied; contrary to the original hypothesis of Camp, the UV component of the radiation yielded no special burning rate enhancing effect. Experimental evidence recently presented by the authors shows that the burning rate enhancement by lead or copper compounds is a result of acceleration of the fizz zone reactions; this is accompanied by an increased production of carbonaceous material at the burning surface. Therefore it is hypothesized that the acceleration is due to a shift in equivalence ratio toward the stoichiometric when potentially burnable fuel molecules are instead carried through the fizz zone as solid carbon. A simplified mathematical model of this hypothesis is developed based on representing the equivalence ratio change as a shift from a single normal reaction pathway toward a second, more reactive pathway. This hypothesis successfully explains the appearance of a region of enhanced burning rate and its disappearance at higher pressures but it is shown that sudden disappearance (mesa burning), sometimes seen experimentally, requires a further mechanism whose nature is not yet clear.