A. A. Charakhch’yan

Converging shock waves in porous media

We have numerically solved several problems related to converging shock waves, including (i) one-dimensional spherical and cylindrical waves with cumulation limited to a ball or cylinder of small radius and (ii) shock-wave flow in a cone-shaped solid target. The passage from a continuous loaded substance to a porous medium in these problems leads to a significant increase in both temperature and pressure in the sample. This character of pressure variation depending on the porosity qualitatively differs from the case of plane waves of constant intensity, for which an increase in the sample porosity under otherwise equal conditions of loading always leads to a decrease in the pressure.

Calculation of shock compression of porous media in conical solid-state targets with an outlet hole

The Godunov-type method that was earlier developed for the hydrodynamic equations of compressible media on regular grids is extended to the case of shock wave flows in elastoplastic porous media. The results of numerical simulations of a hypothetical experimental plant for checking the effect of an increased intensity of converging shock waves in porous media with increasing degree of porosity are presented. This effect was earlier discovered by numerical simulations.

Hydrodynamic simulation of converging shock waves in porous conical samples enclosed within solid targets

Axially symmetric flows with converging shock waves in conical solid targets of steel or lead filled by porous aluminum, graphite, or polytetrafluoroethylene under impact of an aluminum plate with the velocity from 2.5 to 9 km/s have been simulated numerically in the framework of the model of the hypoelastic ideal-plastic solid. Equations of state for all materials in question are used to describe thermodynamic properties of the impactor and target over a wide range of pressures and temperatures, taking into account phase transitions. The graphite-to-diamond transformation is taken into consideration based on a kinetic model. Three different convergent cone configurations of the targets either with a closed cavity or with an outlet hole are analyzed. An appreciable increase of the pressure and temperature within the target cavity as well as of the ejected material velocity on decreasing the initial density of a sample is demonstrated in the simulations. Numerical results that can be compared with possible...

On the role of heat conduction in the formation of a high-temperature plasma during counter collision of rarefaction waves of solid deuterium

This paper considers the problem of counter collision of rarefaction waves of solid deuterium produced by the simultaneous incidence of two identical shock waves on free surfaces located at a certain distance from each other. The motion of deuterium is described by the equations of one-velocity two-temperature hydrodynamics. The model of electron and ion heat transfer takes into account heat-flux relaxation. The parametric properties of the problem are investigated. It is shown that with decreasing distance between the free surfaces, the maximum temperature of the plasma ceases to depend on this parameter. At moderate distances between the free surfaces, the maximum plasma temperature becomes much lower than the temperature obtained earlier in the problem for the equations of nondissipative hydrodynamics. With increasing pressures in the incident shock wave, the maximum ion temperature increases linearly, reaching a value approximately equal to 160 · 106 K at 500 Mbar. In the case of a shock wave with a pressure of 50 Mbar at a gap of 2 mm between the free surfaces of deuterium, the yield of fusion neutrons increases roughly by a factor of 10 compared to the yield of neutrons in the case of no gap.

Mechanism of Amplification of Convergent Shock Waves in Porous Media

The effect of amplification of moderate-intensity converging shock waves in porous media with decreasing initial density, revealed by numerically solving the hydrodynamics equations, was demonstrated for ID converging waves and for a 2D problem of the compression of porous material in conical solid targets. The latter problem was also treated within the framework of the simplest model of dynamic deformation of solids, with consideration given to shear stresses. The calculation results for porous graphite, aluminum, and Teflon samples are presented. Both closed targets and targets with an outlet orifice were considered. When modeling the intense shock loading of graphite, its transformation into diamond was taken into account.

On the mechanism of pressure increase with increasing porosity of the media compressed in conical and cylindrical targets

The effect of porosity on the solution of the problem on a shock wave entering a porous medium is studied. The dependence of the wave parameters appearing under shock compression of porous graphite, aluminum, and polytetrafluoroethylene in a steel target with a cavity in the shape of a truncated cone on the relative initial density is investigated. For a steel target with a cylindrical cavity filled with graphite, the effect of increasing the peak pressure on the symmetry axis in the case when the solid graphite is replaced with porous one is investigated.

Continuous compression waves in the two-dimensional Riemann problem

The interaction between a plane shock wave in a plate and a wedge is considered within the framework of the nondissipative compressible fluid dynamic equations. The wedge is filled with a material that may differ from that of the plate. Based on the numerical solution of the original equations, self-similar solutions are obtained for several versions of the problem with an iron plate and a wedge filled with aluminum and for the interaction of a shock wave in air with a rigid wedge. The behavior of the solids at high pressures is approximately described by a two-term equation of state. In all the problems, a two-dimensional continuous compression wave develops as a wave reflected from the wedge or as a wave adjacent to the reflected shock. In contrast to a gradient catastrophe typical of one-dimensional continuous compression waves, the spatial gradient of a two-dimensional compression wave decreases over time due to the self-similarity of the solution. It is conjectured that a phenomenon opposite to the gradient catastrophe can occur in an actual flow with dissipative processes like viscosity and heat conduction. Specifically, an initial shock wave is transformed over time into a continuous compression wave of the same amplitude.

On a Heat Exchange Problem under Sharply Changing External Conditions

The heat exchange problem between carbon particles and an external environment (water) is stated and investigated based on the equations of heat conducting compressible fluid. The environment parameters are supposed to undergo large and fast variations. In the time of about 100 μs, the temperature of the environment first increases from the normal one to 2400 K, is preserved at this level for about 60 μs, and then decreases to 300 K during approximately 50 μs. At the same periods of time, the pressure of the external environment increases from the normal one to 67 GPa, is preserved at this level, and then decreases to zero. Under such external conditions, the heating of graphite particles of various sizes, their phase transition to the diamond phase, and the subsequent unloading and cooling almost to the initial values of the pressure and temperature without the reverse transition from the diamond to the graphite phase are investigated. Conclusions about the maximal size of diamond particles that can be obtained in experiments on the shock compression of the mixture of graphite with water are drawn.

Numerous experiment on impact compression of a mixture of graphite and water

This paper describes the problem of the behavior of a mixture of small graphite particles with water in the conditions of shock-wave action at a pressure of 32 GPa and a temperature of up to 1200–1600 K. Graphite particles at these pressures and temperatures are capable of transforming into cubic diamonds or at least into their hexagonal form that is lonsdaleite. It is shown that, for sufficiently small graphite particles of the order of 1 μm, their mixture with water for about 10 μs can heat up to the above-mentioned temperatures and undergo phase transformation, remain in those conditions for about 50 μs, and then efficiently cool down during the next 50 μs to the temperatures below 300 K, while remaining in the diamond phase.

Track method for the calculation of plasma heating by charged thermonuclear reaction products for axisymmetric flows

Integral formulas for the three-dimensional case that give the plasma heating rate per unit volume are obtained using the track method and by integrating the well-known Cauchy problem for the steady-state homogeneous kinetic equation in the Fokker–Planck approximation in the absence of diffusion of the distribution function in the velocity space and under the condition that the velocity of the produced particles is independent on the direction of their escape. It is shown that both integral formulas are equivalent and, in the case of space homogeneous coefficients, turn into the model of local plasma heating away from the domain boundary. In addition to the known direct track method, the inverse method based on the approximation of the integral formula is developed. It is shown that the accuracy of the direct method is significantly decreased in the vicinity of the symmetry axis for not very fine angular grids. In the inverse method, the accuracy is not lost. It is shown that the computational cost of the inverse method can be significantly reduced without the considerable reduction of the computation accuracy.