S. A. Rashkovskii

Method of the model equation in the theory of unsteady combustion of a solid propellant

A model equation for the unsteady burning rate of a solid propellant is proposed and justified. In the frequency range of interest for practice, the proposed model agrees with the phenomenological theory of unsteady combustion, but it is even more convenient for applications because it reduces to an ordinary differential equation of the second order with respect to the burning rate. A parametric study of the transitional process in the solid-propellant rocket motor is performed with variations of the nozzle throat area in a wide range of solid propellant parameters. The model predicts oscillatory combustion regimes and propellant extinction in the case of a decrease in pressure. The boundary of stability of the transitional process in the coordinates “sensitivity of the burning rate to changes in pressure—sensitivity of the burning rate to changes in initial temperature.” It is demonstrated that the calculations performed with the use of this model are in qualitative and quantitative agreement with experimental data for a full-scale solidpropellant rocket motor.

Effect of the curvature of the burning surface of condensed energetic materials on the burning rate

Combustion of homogeneous condensed energetic materials (CEMs) with a curved burning surface is considered within the framework of the phenomenological theory of unsteady combustion. A dependence of the burning rate on the burning surface curvature is found. It is demonstrated that there exists a limiting surface curvature value above which self-sustained combustion is impossible. This limiting curvature depends on thermophysical and ballistic characteristics of CEMs. The existence of the limiting curvature of the burning surface offers an explanation of the critical conditions of combustion of homogeneous CEMs. Based on this hypothesis, the critical diameters of combustion of several homogeneous CEMs are calculated. The calculated results are in good agreement with available experimental data.

Combustion mechanism of mixtures of binders capable of self-sustained combustion with inert and active fillers

A single mechanism for the combustion of mixtures of binders capable of self-sustained combustion with inert or active fillers is proposed. A mathematical model for the combustion of such mixtures is developed which takes into account the curvature of the burning surface of binder layers and the associated change in its burning rate. Parametric studies of the model are performed, and the calculation results are compared with experimental data on the combustion of mixtures of active binders with SiO2, HMX, AP, and CL-20. It is shown that the proposed combustion mechanism and the developed model allow a unified explanation of all available experimental data for the class of compounds considered.

The mechanism of small-gas detonation in mechanically activated low-density powder mixtures

A mechanism of supersonic propagation of the energy-release wave in mechanically activated small-gas explosive powder mixtures is proposed. It is shown that, under certain conditions, this process exhibits all the signs of detonation and should be recognized as a kind of thereof. On the other hand, this kind of detonation is fundamentally different from classical detonation, e.g., in gases. Instead of a shock wave, the powder mixture features propagation of a compression wave, in which the powder exhibits densification due to the mutual displacement of particles rather than contraction of the particle material. A chemical reaction is initiated by the mutual friction of particles in the compression wave.

Discrete combustion waves of two-dimensional nanocomposites

A combustion model for a thin heat-conducting film with discrete, chemically active hot spots distributed on its surface is proposed. An equation describing the combustion of such a system is derived, and exact analytical solutions of this equation for periodic arrangement of hot spots on the film surface are found. The sensitivity of burning rate to changes in the initial temperature of the system depending on its main parameters is determined. It is shown that the system has critical parameters (film thickness, hot spot concentration, and initial temperature) that define the limits of its combustion. With large concentrations of hot spots on the film surface, it is theoretically possible to reach burning rates that significantly exceed the speed of sound in the ambient gas. The proposed combustion model provides a qualitative explanation of the high burning rate of mechanoactivated nanocomposites and allows one to understand the influence of mechanoactivation on combustion of powder mixtures.

Unsteady Combustion of Layered Condensed Systems. Parallel Burning of Components

A model of unsteady combustion of a “sandwich”:‐type layered condensed system consisting of parallel layers of simultaneously burning components capable of self‐sustaining combustion is considered. The response function of the mass burning rate of the system to periodic pressure oscillations with allowance for the interaction between the components caused by the difference between their burning rates is found. In the linear approximation, combustion of such systems under a rapid change in pressure is analyzed. It is shown that the pattern and duration of these processes depend on the ratio of the layer thickness of the slowly burning component and the thickness of its heated layer. It is found that bending of the burning surface of components in the course of unsteady combustion of the layered condensed system can substantially affect the pattern of its unsteady combustion as a whole, in particular, enhance or reduce its stability.

Effect of distributed injection of air into the afterburning chamber of a ram-rocket engine on the efficiency of combustion of boron particles

A mathematical model of combustion of boron particles in a ram-rocket engine is developed. The boron combustion efficiency for one-stage and two-stage injection of air into the afterburning chamber is calculated. It is demonstrated that two-stage injection of air sometimes allows the time of complete combustion of boron particles to be significantly reduced (by a factor of 1.5–3); thus, the fuel combustion efficiency in the ram-rocket engine can be increased. The simulated results are consistent with available experimental data.

Improving the completeness of combustion of boron particles in a solid-fuel ducted rocket owing to distributed air supply to the secondary combustor

A model of combustion of boron particles in ducted rocket using distributed air supply to the secondary combustor was developed for the first time. The completeness of boron combustion in ducted rocket using air supply to the secondary combustor through one outlet or two outlets (distributed air supply) was calculated. It was shown that, in some cases, distributed air supply significantly (by a factor of 1.5–3) decreases the time of complete combustion of boron particles and thereby increases the completeness of fuel combustion in ducted rocket. The modeling results agree with the known experimental data.

BIFURCATIONS OF THE FLOW CHARACTERISTICS OF AN ADJUSTABLE SUPERSONIC NOZZLE

A ground-based experimental study of the flow characteristic of an adjustable highaltitude nozzle was performed. It is shown that the flow characteristic of the adjustable nozzle can significantly depend on the design of its supersonic part and operation conditions. It is found that the operation such nozzles can involve different flow regimes of the working fluid depending on the position of the regulator; under certain conditions, there may be an abrupt change in the flow regime, which leads to an abrupt change (bifurcation) of the flow characteristic of the nozzle.