A general numerical model based on the Zeldovich-Novozhilov solid-phase energy conservation result for unsteady solid-propellant burning is presented in this paper. Unlike past models, the integrated temperature distribution in the solid phase is utilized directly for estimating instantaneous burning rate (rather than the thermal gradient at the burning surface). The burning model is general in the sense that the model may be incorporated for various propellant burning-rate mechanisms. Given the availability of pressure-related experimental data in the open literature, varying static pressure is the principal mechanism of interest in this study. The example predicted results presented in this paper are to a substantial extent consistent with the corresponding experimental firing response data.

https://downloads.hindawi.com/journals/ijae/2008/826070.pdf

Transient Burning Rate Model for Solid Rocket Motor Internal Ballistic Simulations

Experimental and theoretical extinction of solid rocket propellants by fast depressurization

Dynamic burning behavior in solid propellant combustion often occurs under a rapid pressure excursion and is caused by the finite relaxation times required for the solid and/or gas phases to adjust their temperature profiles. The instantaneous burning rate under transient conditions may therefore differ significantly from the steady-state value corresponding to the instantaneous pressure. The purpose of this review is: (1) to report the state-of-the-art on dynamic burning studies; (2) to explain the detailed mechanism of dynamic burning; (3) to classify the existing theories to facilitate more direct comparison; (4) to point out the limitations of each model and its general validity; (5) to summarize the important experimental observations and theoretical results; and (6) to describe the difficulties involved in the study of dynamic burning effects so that the technological gaps of information needed in this area are made clear.

Review of dynamic burning of solid propellants in gun and rocket propulsion systems

Various factors and trends related to the presence of inert particles in the central core flow as a means to suppress axial-combustion-instability symptom development are numerically predicted for a composite-propellant cylindrical-grain motor. Individual transient internal-ballistic-simulation runs show the evolution of the axial pressure wave and associated base pressure shift for a given inert particle size and loading percentage, as initiated by a given pressure disturbance. The pressure wave's limit magnitude at a later reference time in a given firing simulation run is collected for a series of runs at different particle sizes and loadings and is mapped onto an attenuation trend chart in a format potentially useful for motor designers evaluating their specific motor design and particle loading requirements (and, in turn, allowing for less experimental test firings, if the numerical results are relatively accurate). When the effect of acceleration (through structural vibration of the propellant surface) on the combustion process is included in the numerical calculations, one observes substantial differences in burning and internal flow behavior in the presence of axial-pressure-wave activity, as reflected in individual firing simulations and the corresponding particle attenuation map. The predicted base pressure shift is more pronounced at lower particle loadings: for example, in conjunction with the pressure-wave magnitude being larger, when the propellant's burning process is substantially sensitive to normal acceleration. Whether the propellant's burning rate is acceleration-sensitive or not, the inert particles' presence in the central core flow is demonstrated to be an effective means of suppression, correlating with past experimental successes in the usage of particles. Particle/burning-surface interactions, which may also act to suppress pressure-wave development by changing the propellant's inherent frequency-dependent combustion response, are not explicitly accounted for in this study, although one or two of the combustion-response model's pertinent coefficients could be altered to reflect this change, given sufficient information in this regard.

Inert Particles for Axial-Combustion-Instability Suppression in a Solid Rocket Motor

An improved closed burner method

Response of three types of transient combustion models to gun pressurization

HYDRODYNAMIC aspects of the gun environment have been central to the theme of interior ballistics theory for over a century. Decoupled from a nontrivial description of propellant ignition and flamespread, the problem has been amenable to numerical solution for more than a decade. More recently, however, the occurrence of several catastrophic gun ammunition malfunctions has been linked to ignition-indu ced two-phase flow dynamics. A number of approaches have been pursued intensely to provide a solution to the combined twophase flow, ignition and flamespread interior ballistics problem. A detailed review of four such modeling efforts has been provided by Kuo. 1 Work reported herein relates to efforts aimed at reconciling experimental data with numerical predictions obtained using a computer code developed by Gough.2 Manipulation of poorly known input parameters or statements of constitutive physics was performed both to identify those parameters that most affect the calculated results and to draw useful inferences about the physical processes themselves. Considerable success has been demonstrated in attempts to simulate the performance of a Navy 5-in./54-caliber case gun; however, similar agreement with data obtained in an Army 155-mm howitzer was unattainable without substantial modifications to available input data. An attempt has been made to provide a physically motivated explanation for this difference in the level of agreement for the two configurations. Contents The Gough model, also known as the NOVA code, is a twophase flow treatment of the gun interior ballistic cycle, formulated under an assumption of quasi-one-dim ensional flow. Gas and particles are treated as interpenetrat ing media, with conservation equations derived using formal averaging techniques. Constitutive laws include a covolume equation of state for the gas and an incompressibl e solid phase. Compaction of an aggregate of particles is allowed, with intergranular stress represented as a function of propellant bed porosity. Interphase drag and heat transfer are represented by reference to empirical correlations for fixed and fluidized beds. Functioning of the igniter is included by providing as input an experimentall y determined mass injection rate as a function of position and time. Grain temperature follows from the convective heat-transfer correlation and unsteady heat conduction in the solid, with ignition based on a surface temperature criterion. Propellant combustion is then assumed

Flame Spreading in Granular Propellant: Comparison of Theory to Experiments

Another comment on the transient burning-rate model of Suhas and Bose

obtain a straight line for the portion of the curve which ought to be in the logarithmic region and plays no role in the model used to compute turbulent flows. To obtain the skin-friction coefficient from the slope of the straight-line portion of the curve, it is customary to assume that the von Karman constant retains its value for flows over smooth surfaces (see Ref. 2, p. 177). It is thus seen that the argument for parallel log-law portions for smooth and rough flows is an essential part of bringing the experimental data into tractable form. The shift Ay + employed by Rotta is simply the difference between the smooth and rough log-law portions of the curves on semilog plot as u + vs y + (see Fig. 4.29 and 4.30 of Ref. 1) and bears no relationship to the shift of virtual origin Az. The virtual origin y = 0 is a distance Az below the crests of the roughness elements. The y in Eqs. (7) and (9) in Mills paper are indeed measured from the virtual origin. Thus the contradiction in the eddy-viscosity formulas and the wall boundary conditions *'invented" by Mills does not exist. The appearance of Ay in Eq. (7) only affects the rate of approach to Eq. (9) when performing integration. However, this problem has been clearly overshadowed by the questions of where to start the solution and what the boundary conditions should be because the sublayer is reduced or nonexistent. It has been found by experience that the logarithmic boundary conditions, Eq. (9), are satisfactorily applied if >>^>50 and u0/ue >0.15 are satisfied simultaneously. Mills' objection 2 toward the end of his Comment simply states the obvious: Of course we are well aware that Eqs. (8) and (10) will have different forms for different roughness geometries (see Ref. 1, p. 129, Fig. 4.27). Unfortunately, so far only the sand-grain type roughness has been well researched and documented. Before we conclude, we would like to offer a word of caution. If the agreement between "theory" and all the available experimental data on the subject is quite good (so good that it may be difficult to beat these predictions by other turbulence models), it is perhaps advisable to be cautious in light of this agreement before raising objections which do not bear up under the weight of the theoretical, computational or experimental evidence.

Carl W. Nelson

Papers

Response of three types of transient combustion models to gun pressurization

Flame Spreading in Granular Propellant: Comparison of Theory to Experiments

Another comment on the transient burning-rate model of Suhas and Bose

Comment on "Pressure Dependence of Burning Rate of Composite Solid Propellants"