Two methods for predicting instantaneous burning rates are described and compared: 1) theories based on models of the flame and 2) the Zeldovich-Novozhilov method which uses the steady- state burning rate data as functions of pressure p and initial temperature TO to deduce the appropriate nonsteady law for the heat feedback rate from the flame. The latter method offers the important advantage of not requiring detailed knowledge of the flame structure. Theoretical connections between the two methods are demonstrated. Burning rate data r(p,T0) were obtained for pressures from 1.3 to 40.0 atm and for initial temperatures from 130° to 350 °K. The primary limitation encountered in the application of the ZeldovichNovozhilov method is the inadequacy of techniques for obtaining r(p,To) at ambient temperatures below 150 °K. Calculated extinction boundaries agree with measured results for depressurization rates from 4,000 to 15,000 atm/sec and pressures from 20 to 60 atm. An interesting observation is that within a class of similar propellants, the propellant with a high temperature sensitivity of burning rate tends to extinguish more readily, ignite with greater difficulty, and be more prone to instability. A8 = B = c = E = h = H = k = m = n = 0[ ] = p = q = Qs = r = t = T = u = a. = /3,e = X = p =

Theory of dynamic extinguishment of solid propellants with special reference to nonsteady heat feedback law

In the first part, a review is offered of the intrinsic stability of pressure- or radiation-driven burning of solid propellants with chemically inert condensed phase. The two main approaches today available [flame modeling and the Zeldovich-Novozhilov (ZN) method] are both considered. Within the current quasi-steady homogeneous one-dimensional framework, the intrinsic burning stability boundaries and frequency of the self-sustained oscillatory solution predicted by several techniques are the same; the classical boundaries predicted by the ZN are somewhat extended. The intrinsic stability boundaries for pressure-driven or radiation-driven burning are identical in the limit of fully opaque condensed phase (surface absorption). However, the burning configurations are affected by the impinging radiant flux. Some peculiar effects of radiation assisted burning are illustrated. In the second part of this article, an extension is presented to chemical reactions volumetrically distributed in the condensed phase with a uniform heat release rate distribution. Frequency response functions and unbounded response limits are obtained; both recover the particular configuration of chemically inert condensed phase. Nomenclature A = nondimensional function, Eq. (31); Denison and Baum nondimensional parameter, Eq. (53); Krier-T'ien-Sirignano-Summerfield transient flame mode nondimensional parameter, Eq. (54) As = nondimensional function, Eq. (6) a = nondimensional function defined by Eq. (13) ax = average volumetric absorption coefficient, cm"1

Intrinsic combustion instability of solid energetic materials

During a rapid depressurization, the intensities of several spectral lines and the pressure are measured, simultaneous to the taking of high speed movie photographs of the propellant flame. The quenched surfaces of all samples are analysed with a scanning electron microscope. The 24% carboxyl terminated polybutadiene -+- 76 % 25 μ ammonium perchlorate propellant extinguishes permanently for initial depressurization rates exceeding ca. 7.5 × 103 atm/s, when the initial pressure is 45 atm. At the highest depressurization rates (>16 × 103 atm/s), the gaseous flame quenches immediately due to the adiabatic expansion. Lower rates of fall in pressure (7 × 103 to 16 × 103 atm/s) allow a second flame to develop after 5–7 ms, the relaxation time of the solid phase. This new flame is irregular and partially consumes the AP particles available on the propellant surface, depending on the imposed dP/dt. The driving mechanism is far from one-dimensional. The new flame goes out only at the end of the pressure t...

Depressurization Extinguishment of Composite Solid Propellants: Flame Structure, Surface Characteristics, and Restart Capability

The thermal effects of incident radiation on the burning characteristics of homogeneous solids are considered and the practical implications of these effects in solid rocket motors are assessed. The applicability of the equivalence principle (equivalence between radiation and initial temperature) is investigated experimentally and analytically. Experimental steady burning rates as a function of initial temperature and mean radiant flux are presented for a fine ammonium perchlorate (A P) composite propellant which indicate that the equivalence principle is accurate to within experimental error. The equivalence principle is also assessed analytically by considering the worst case conditions of condensed phase controlled burning. For deflagration and pyrolysis of solids controlled by condensed phase reactions it is shown that a modification of Ibiricu and Williams' high activation energy asymptotic burning rate expression allows consideration of the effect of incident radiation on steady burning rat...

Radiation-augmented combustion of homogeneous solids

Burning stability analyses of solid propellants are performed, within the framework of a thermal theory of monodimensional heterogeneous deflagration waves, from a linearized point of view. The frequency response function is determined both for pressure and radiation driven combustion waves. Two limiting schemes for the quasi-steady gas phase are implemented: distributed and sharp flame models. Work available from the literature in this field is reviewed, corrected, and extended. Particular attention is given to the connection between pressure and radiation driven admittance functions. Burning stability properties predicted from linear and nonlinear theories are compared. A way to rate experimentally the dynamic burning stability of condensed substances with optically opaque condensed phase and transparent flame is suggested.

Frequency response function of burning solid propellants

: A new theory for extinction by depressurization of AP composite propellants is employed to predict the rate of pressure decrease required to achieve flame-out and to rationalize the effects of various composition parameters on the ease of extinguishment The research is concentrated mainly on the 'temporary' extinguishment behavior of solid propellants, but a re- ignition theory is also presented Attention is given in this theory to the proper derivation of the nonsteady heat feedback from the gaseous flame zone to the burning surface Included in the model are the essential physical and chemical rate processes of the granular diffusion flame model, as deduced from the steady state burning characteristics A brief study of double-base propellants which indicates that they are considerably easier to extinguish than composite propellants concludes this report A rough model for the burning of double-base propellants is presented which further indicates the importance of the flame structure in determining the extinguishment characteristics of solid propellants

S. L. Turk

Papers

Extinguishment of solid propellants by rapid depressurization