Shock Adiabatic Curve Research Articles

Application of a Theoretical Model of State Equation for Calculation of N2, O2, and CO2 Shock Adiabatic Curves

An improved version of the equation of state model for two-component fluid mixtures whose molecules interact with the Exp-6 type potential has been proposed in previous works. The thermodynamic parameters of N2, O2, and CO2 shock-wave compression are calculated using the equation of state model for two-component fluid mixtures based on perturbation theory. Products of compression of these substances are two-component mixtures. Analogous calculations are also performed using an effective one-fluid model. A comparison of the results obtained with the available experimental data and results of Monte Carlo simulation allows us to conclude that the proposed theoretical equation of state model is superior to effective one-fluid model in accuracy and reliably describes the thermodynamic properties of two-component fluid mixtures in a wide pressure and temperature ranges.

Dynamic deformation of soft soil media: Experimental studies and mathematical modeling

A complex experimental-theoretical approach to studying the problem of high-rate strain of soft soil media is presented. This approach combines the following contemporary methods of dynamical tests: the modified Hopkinson-Kolsky method applied tomedium specimens contained in holders and the method of plane wave shock experiments. The following dynamic characteristics of sand soils are obtained: shock adiabatic curves, bulk compressibility curves, and shear resistance curves. The obtained experimental data are used to study the high-rate strain process in the system of a split pressure bar, and the constitutive relations of Grigoryan’s mathematical model of soft soil medium are verified by comparing the results of computational and natural test experiments of impact and penetration.

The effect of a change in entropy on the form of the shock adiabatic curve of quasi-transverse elastic waves

The shock adiabatic curve of quasi-transverse shock waves in a slightly anisotropic elastic medium is considered. For waves whose intensity is not too high, the elastic potential of the medium Φ is represented by an expansion in series in the deformations and the change in entropy. Shock waves, when only the principal terms remain in the expansion of Φ which reveal the effects of non-linearity and anisotropy, have been investigated in detail in previous publications, but the effect of a change in entropy on the elastic properties of the medium was not taken into account. Below, these results are taken as the zeroth approximation and, using the method of linearization about the zeroth approximation, corrections due to succeeding terms of the expansion of Φ> are obtained. A model of a slightly non-linear elastic medium is considered in detail when, in addition terms in the form of cross products of the deformations and the entropy and the square of the change in entropy are taken into account in the expansion of Φ For such a medium, the changes in the form of the shock adiabatic curve and the position of the evolution parts in it, due to considering the effect of a jump in entropy in the shock wave, are obtained in explicit form.

The existence and uniqueness of self-similar solutions involving Jouguet points on the shock adiabatic curve

The self-similar solutions of one-dimensional unsteady equations of the hyperbolic type which express the conservation laws are considered. A number of special features have been revealed [1–4] in the non-linear theory of elasticity: the absence of uniqueness, the absence of a continuous dependence of a solution on the parameters and rapid changeovers of a wave of one type with the emission of a wave of another type. It has been shown that all of these phenomena have a common character and are associated with the presence of a “foreign” Jouguet point on the shock adiabat. The velocity of a shock wave of a certain type at this point is equal to the characteristic velocity downstream of a shock wave of another neighbouring and slower type. Hence, in the case of hyperbolic systems. which express the conservation laws. the possibility exists of judging the most important properties of self-similar solutions as a whole using certain properties of the shock adiabats.

Study of the stressed state of shock-compressed solids by the method of principal stresses

The conditions are analyzed for correct measurements by the method of principal stresses in solids compressed by a plane shock wave. The results are given for specific experimental structures. The principal stresses along the shock adiabatic curve for molybdenum, vanadium, steel 30KhGSA, and aluminum oxide ceramics have been found to differ by a constant amount in states above the Hugoniot elastic limit.

Shock waves in a weakly anisotropic elastic incompressible material

The effect of anisotropy on shock waves in an incompressible elastic medium is studied. No assumption is made here concerning the smallness of the deformations. Particular attention is paid to those materials for which the non-linear stress-strain relation has a point of inflection. The anisotropy is assumed to be small compared with the effect of the non-linear properties of the medium, but this turns out to be quite sufficient for new qualitative effects to be revealed. A set of states behind the shock wave (the shock adiabatic curve) for a specified state ahead of the shock wave as well as the velocity of motion of the shock wave front for an incompressible medium with small anisotropy of arbitrary form are found and investigated using conservation laws. The shock adiabatic curve is clearly presented in the case of the simplest actual form of anisotropy. The segments on it which correspond to the requirements of an evolutionary character and no decrease in the entropy are indicated.

Cold compression isotherm for carbon based on interatomic reaction potentials in the graphite-diamond system

Results are presented of calculating cold compression for carbon in the graphite-diamond system. The isotherm for graphite-diamond, the energy barrier for sp/sup 2/-sp/sup 3/ transition, the energy for the change in pi- and omega-bond length, the shock adiabatic curve, and the energy zone for phase transition are illustrated. It is shown that the fact of energy accumulation for the system, sufficient in order to overcome the potential barrier for transition of one carbon modification into another, is a condition for the possibility of this transition and its physical explanation.

Shock adiabatic curves of metals

Shock adiabatic curves of metals

Approximate equation of state of condensed substances

The functions entering into the equation of state of Mie-Gruneisen solids are constructed approximately. In [1] an approximate equation of state was proposed for solids whose adiabatic curves obey a linear relationship between the velocity of the shock wave D and the mass velocity U; the slope of the shock adiabatic curve was equal to 1.5. In the present work, the dimensionless variables proposed in [2] are used to construct an equation of state which is free from the above-mentioned limitation. The equation of state found is used to make calculations of the shock compression of porous metals, in particular, of copper, with values of the porosity not differing significantly from unity.

Shock compression of two-component paraffin-tungsten mixtures

Up to pressures of 2 mbar, curves have been recorded experimentally for the shock compression of paraffin and for two paraffin-tungsten mixtures, containing 66.2 and 84.0 wt.% tungsten. It is shown that over the whole range of pressures investigated experimentally, the mixture shock adiabatic curves satisfy the principle of additivity. Attention is called to the great potential of the method of weighting additives for the investigation of light media at high shock pressures. The criteria for the applicability of the principle of additivity have been analyzed.

One-dimensional electrohydrodtnamk flows with shock waves: PMM vol. 36. n≗5, 1972, pp. 866–873

Stationary one-dimensional electrohydrodynamic flows with shock waves in channels are analyzed for the case of an arbitrary interaction parameter. The criteria of existence of electrohydrodynamic flows with shock waves in which the electric field component normal to the wave front is continuous and that of existence of flows with discontinuities of the electric field in the shock wave are derived. A diagram is constructed in the velocity-electric field coordinate plane which makes it possible to determine the feasibility of obtaining one kind of flow or another by the velocity and the electric field intensity upstream of the shock wave front. An electrohydrodynamic shock adiabatic curve is constructed for a perfect gas.