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Two approaches for simulating the burning surface in gas dynamics by means boundary conditions and right sides in the equations involving Dirac delta function are discussed. A comparison of numerical steady-state solutions and the exact ones in one-dimensional approximation is performed for two approaches. It is shown that the numerical solutions obtained with the finite-difference scheme of first order accuracy on the base of two considered approaches converge to each other when the mesh refinement is applied. The numerical solution for the steady state problem coincides with the analytical one, if the pressure at the boundary cell face is set equal to the pressure in the center of the boundary cell.

A study has been made of ways of optimum distribution of particles of dispersed metal in the solid-propellant charge with a cylindrical central channel, which is fi rmly fastened to the case. The effi ciency of combustion of this metal has been analyzed. Consideration has been given to the infl uence of the dynamic nonequilibrium of two-phase fl ow on the optimum distribution of metal particles in the indicated charge in the approximation of one-dimensionality of the fl ow fi eld. Introduction.One key problem in designing solid-propellant rocket engines (SPREs) is to raise the energy efficiency of the propellant. Composite solid propellants widely used in SPREs at present contain such metals as aluminum, magnesium, and beryllium as fuel additions. These additions contribute to the increase in the specifi c momentum and to the improvement of the combustion stability of a solid propellant.It is common knowledge that metal additions, on the one hand, lead to an improvement of the energy characteristics of a composite solid propellant owing to their high combustion temperature, and, on the other, are the source of the specific-momentum loss by the incomplete combustion of metal particles and of their velocity lag behind the gas phase, particularly in the case of small SPREs and SPREs without a nozzle. The specifi c-momentum loss by incomplete combustion can be decreased due to the redistribution of metal particles inside the solid-propellant charge in accordance with structural features of the charge and the SPRE.It is as early as 40 years ago that investigations started to address the problem of increasing specifi c momentum due to the redistribution of metal inside a solid-propellant charge. For example, in Japan in 1976, a patent was registered for a solid-fuel composition, in which the redistribution of metal inside the charge in the form of a cylindrical cartridge with a channel was implemented through a change in the particles size [1]. It was demonstrated that for a solid-propellant charge with a 5 to 30 ratio between the channel′s length and its diameter, the redistribution of particles by size (the fi rst 44% of the charge length is occupied by particles of size 50-150 μm, the second 28%, by particles of size 20-50 μm, and the third 28%, by particles with a size smaller than 20 μm) can ensure an increase of 4-7% in the momentum compared to the uniform distribution of all the particles in the solid-propellant charge. The specifi c momentum can also be increased through the redistribution of metal due to the change in its mass fraction. The infl uence of the redistribution of metal particles by mass fraction on their combustion effi ciency was investigated numerically in [2] under the assumption that the mass fraction of the metal particles z(X) varies linearly along the channel. It was shown that there is an optimum slope of the z(X) straight line, which ensures the maximum combustion effi ciency for a prescribed mass of metal in the propellant charge. The combustion effi ciency of aluminum in an SPRE was ana...

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This paper reports on the ways of allocating the metal particles in the propellant grain of tube cross-sectional type to provide maximum combustion efficiency of metal. Two-dimensional flow field and the burning rate law govern a transport of the burning metal particles. The analytical correlation for the optimum allocation of metal particles in the case-bounded propellant grain of tube cross-sectional type under the assumption of equilibrium two-phase flow is deduced.