The necessary conditions for stable combustion of a powder in a half-closed chamber

The low-frequency stability of the steady-state combustion cycle is investigated in linear approximation for a powder in a half-closed chamber, taking account of incompleteness of combustion, heat losses at the walls, and dynamic erosion. The necessary conditions for stable combustion are obtained. Qualitative conclusions are drawn of the incompleteness of the chemical reactions taking place and of the destabilizing effect of thermal losses and erosion on the combustion process. Only two out of three possible steady-state mechanisms are stable. The existence of limits of combustion with respect to pressure is shown.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 6, pp. 90–98, November–December, 1972.     

Effect of condensed powder phase reactions on the stability of steady-state combustion processes

A study has been made of the low-frequency stability of powder combustion in a semiclosed chamber, working within the framework of a linear theory with account taken of condensed-phase (k-phase) inertia and evolution of thermal energy. The case treated is that of the first-order reaction. It is shown that k-phase exothermic chemical decomposition increases the stability of the combustion process. The results of numerical computations are interpreted.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 5, pp. 102–111, September–October, 1973.     

On the stability of shock waves in a continuous medium with a space charge

The stability of shock waves is discussed for a hydrodynamic model of motion of a continuous medium with a space electrical charge. The correctness of a mixed problem obtained by linearization of the hydrodynamic model and the equations of a strong discontinuity for electrohydrodynamic shock waves is proved. As is known, this indicates stability of this type of strong discontinuity in the model of a continuous medium considered. Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 39, No. 2, pp. 29–39, March–April, 1998.     

Equation for nonsteady-state combustion velocity of a powder

An integral equation is obtained for the nonsteady-state combustion velocity of a powder. It is shown that the effect of a variable tangential stream of gases on the rate of burning (nonsteady-state erosion) can be calculated in a similar way as for the change of pressure. The solution of the equation in linear approximation is considered (rate of burning differs slightly from steady-state).Translated from Zhurnal Prikladnoi Mekhaniki i Teknicheskoi Fiziki, No. 4, pp. 73–78, July–August, 1970.     

Ablation combustion of secondary powder explosives

The explosive transformation in a passive charge initiated by an air shock wave was studied using synchrotron diagnostics of density. It was found that in the passive charge, a compression wave capable of forming effective hot spots does not arise and classical initiation conditions do not occur. The development of the reaction can be attributed to the ablation combustion observed in studies of the initiation of secondary powder explosives by a spark and gaseous detonation.     

Stability of combustion of powder in a phenomenological model with nonadiabatic flame

A stability criterion for combustion of powder is obtained, taking into account the effect of the processes in the gas phase. It is shown that consideration of the effects of a nonadiabatic flame leads to the stability reserve of combustion being reduced and the natural frequency of vibrations being lowered. The effects thus found are physically explained by the radiation of a part of energy from the combustion zone with thermal and acoustic waves.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 6, pp. 82–87, November–December, 1973.Deceased.     

Nonlinear oscillations of combustion velocity of powder

The combustion of powder, where the surface temperature T_s depends on the pressure p and the initial temperature T₀, is studied under the condition of sinusoidally varying pressure. The nonlinearity of the heat conduction equation together with the dependence of the combustion velocity u and the surface temperature on both the pressure and initial temperature affects the zeroth harmonic and gives rise to higher harmonics in the combustion velocity and the temperature of the powder. The present paper considers the case of nonlinear resonance, when the frequency of the pressure fluctuations is close to the natural vibration frequency of the powder. It has been shown that an autonomous oscillatory regime of combustion is possible under constant pressure.The author wishes to thank Ya. V. Zel'dovich, G. I. Barenblatt, A. S. Kompaneits, and O. I. Leipunskii for fruitful discussion and advice.     

Experimental investigation of the hypersonic low-density flow past a half-closed cylindrical cavity

Hypersonic (M=21) flow past a half-closed cylindrical cavity with a beveled upstream-facing open end was experimentally investigated in a self-oscillatory regime. The Reynolds numbers, based on the largest dimension of the inlet orifice, were Re=8.5·10³ and 2.5·10⁴. The dependence of the pressure fluctuation intensity within the cavity on the fluctuation frequency and the angle between the oncoming stream and the plane of the inlet orifice was determined. The measured data were analyzed on the basis of existing models of fluctuation generation. An electron-beam technique was used to measure the distributions of the average and fluctuation densities in the outer stream. The amplitude and phase characteristics of the outer fluctuations were determined and their relation with the pressure fluctuations within the cavity was established.Novosibirsk. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 6, pp. 155–160, November–December, 1996.     

Two-dimensional stability of the combustion of condensed systems

The question of the combustion stability of condensed systems relative to curvature of the front is investigated in a linear approximation. Two of the simplest combustion models are examined, a gasless system and a model of flameless combustion of a solid fuel. In the first case, the combustion products are condensed, just as are the initial materials, and in the second the solid fuel is converted into a gas in which no chemical reactions occur. Boundaries of the stability of the stationary combustion mode are found. It is shown that gasless systems are less stable with respect to two-dimensional perturbations than to one-dimensional perturbations. For the flameless combustion model the result depends on the relationship between the thermophysical constants of the initial material and the products. The question of the influence of heat emission on the one-dimensional stability of the gasless composites is considered. An increase in the heat emission diminishes the stable combustion region, where a one-dimensional instability originates earlier than collapse of combustion occurs because of strong heat emission to the wall.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 5, pp. 51–59, September–October, 1971.     

On the stability of an elastic column positioned on an elastic half space

Summary Stability of a heavy elastic column loaded by a concentrated force at the top is analysed. It is assumed that the column is fixed to a rigid circular plate that is positioned on a homogeneous, isotropic, linearly elastic half-space. The constitutive equations for the column are assumed in the form that allows axial compressibility and takes into account the influence of shear stresses. It is shown that eigenvalues of the linearized equations determine the bifurcation points of the full non-linear system of equilibrium equations. Also, the type of bifurcation at the lowest eigenvalue is examined and shown that it could be both super-and sub-critical. The post-critical shape of the column is determined by numerical integration of the equilibrium equations. Received 13 June 1998; accepted for publication 12 November 1998     

On the convection of a cusp in elastic stability

Because of its dominant role in elastic stability, the unstable-symmetric bifurcation, or cusp catastrophe, is worthy of special study. We present here a systematic perturbation analysis of the cusped imperfection-sensitivity in a general bifurcational context, to examine its movement and deformation under the influence of further imperfection parameters. The elimination of passive coordinates allows explicit expressions to be derived for the horizontal and vertical shifts and the tilting of the primary two-thirds power-law cusp. The results throw new light on the earlier experiments of Roorda, which are re-examined in some detail. Contours of constant failure load in a two-dimensional imperfection space finally allow the worst types of compound imperfection to be identified.