One-dimensional problem of nonlinear elasticity theory with a structural shock wave

Voronezh' Civil-Engineering Institute. Translated from Prikladnaya Mekhanika, Vol. 26, No. 1, pp. 103–108, January, 1990.     

One-dimensional compression of bounded volumes of a self-gravitating gas

Unsteady plane and spherically-symmetric self-gravitating gas flows are analytically and numerically studied. It is assumed that the gas is enclosed in a plane layer of finite thickness or in a bounded spherical volume. Two characteristic compression patterns are established, namely, a quasiperiodic regime in which gravitational equilibrium is attained and a fast compression regime with a many orders increase in the density. The quasiperiodic regime is realized when the layer thickness is fairly small as compared with the Jeans length. The fast compression occurs when the layer thickness is greater than the Jeans length.     

One-dimensional problem of water-oil displacement in a medium with fracture porosity

We consider the one-dimensional displacement of oil by water in a medium with fracture porosity. A special dependence of saturation on time is assumed, which approximates well the experimental curve. The position of the injected water front in the course of time is found for several flow rate variation laws.The author wishes to thank V. L. Danilov for his scientific guidance.     

One-dimensional steady-state flows of a rotating gas and zonal wind

A thin layer of an ideal gas on a solid gravitating sphere is considered with allowance for inertia forces. Flows are initiated by heating the solid spherical surface nonuniformly in latitudes. A solution in the form of a one-dimensional flow directed along the meridians is obtained. Assuming that the gas density is independent of the latitude, an exact solution is obtained for the one-dimensional flow in question. This solution has all the features of zonal winds existing in many planets of the Sun system including the possibility of existence of supperrotation, i.e., the regime for which the atmosphere moves more rapidly than the solid body of the planet.     

One-dimensional model for microscale shock tube flow

A one-dimensional model for the numerical simulation of transport effects in small-scale, i.e., low Reynolds number, shock tubes is presented. The conservation equations have been integrated in the lateral directions and three-dimensional effects have been introduced as carefully controlled sources of mass, momentum and energy, into the axial conservation equations. The unsteady flow of gas behind the shock wave is reduced to a quasi-steady flow by choosing a coordinate system attached to the shock. The boundary layer problem is thereby reduced to a laminar solution, similar to the Blasius solution, with the exception that the wall velocity can be nonzero. The resulting one-dimensional equations are then solved numerically using a two-step Lax-Wendroff/ MacCormack scheme with flux correction transport. For validation purposes, comparisons are performed against previously published shock structure and low Reynolds number shock tube experiments; good agreement is observed. The model has been used to predict the performance of a 10μm shock tube and the result of this simulation shows the possibility of shock wave disappearance at lower pressure ratios for a micro-scale shock tube.      

One-dimensional transonic gas flow in a wind tunnel with perforated walls

Near-sonic inviscid gas flow in the working section of a wind tunnel with perforated walls is investigated in the context of the one-dimensional theory with Darcy's boundary condition.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 6, pp. 143–148, November–December, 1988.     

Gas-dynamic shock waves in a relaxing gas

St. Petersburg State University, St. Petersburg 199004. Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 36, No. 3, pp. 92–97, May–June, 1995.     

One-dimensional theory of off-design supersonic gas jets

A method based on the quasi-one-dimensional treatment of off-design supersonic jet flow is presented, together with the results of calculating the parameters of the jet on the interval of adaptation to the external conditions in the immediate vicinity of the nozzle exit section. On the jet formation interval the region of flow with strong discontinuities (shocks) is replaced by a surface of discontinuity. The mixing effect is taken into account by means of a concentrated mass flux in the section of discontinuity. It is shown that taking into account the real properties of the jet flow on the formation interval makes it possible considerably to improve the accuracy of a number of important flow parameters and to obtain a series of quantitative results that coincide with the experimental data.Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No.1, pp. 48–56, January–February, 1993.The author is grateful to E. A. Kapustin for his interest in the work and useful discussions.     

One-dimensional response of sandwich plates to underwater shock loading

The one-dimensional shock response of sandwich plates is investigated for the case of identical face sheets separated by a compressible foam core. The dynamic response of the sandwich plates is analysed for front face impulsive loading, and the effect of strain hardening of the core material is determined. For realistic ratios of core mass to face sheet mass, it is found that the strain hardening capacity of the core has a negligible effect upon the average through-thickness compressive strain developed within the core. Consequently, it suffices to model the core as an ideally plastic-locking solid. The one-dimensional response of sandwich plates subjected to an underwater pressure pulse is investigated by both a lumped parameter model and a finite element (FE) model. Unlike the monolithic plate case, cavitation does not occur at the fluid-structure interface, and the sandwich plates remain loaded by fluid until the end of the core compression phase. The momentum transmitted to the sandwich plate increases with increasing core strength, suggesting that weak sandwich cores may enhance the underwater shock resistance of sandwich plates.     

The behavior of a gas bubble in a shock wave

The phenomenon of thermal relaxation of the gas bubbles in a fluid behind a shock front is analyzed. The approach to solving the problem of heat transfer between a gas bubble and a fluid developed by the author is used to obtain a solution describing the initial stage of bubble collapse behind the shock front.Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 5, pp. 187–189, September–October, 1993.     

One-dimensional shock wave interaction with rubber and low-porosity foam

One-dimensional interaction between a planar shock wave and a rubber or low-porosity foam is investigated experimentally and numerically. The considered polyurethane foam is of high density (ρ _c=290 kg/m³) and lowporosity (ϕ=0.76), and this corresponds to an intermediate condition between rubber and high-porosity foam. Stress-strain relations for the low-porosity foam are investigated by machine tests, which show larger deformation against compressive force and higher non-linearity in stress-strain curve as compared with rubber. Also the low-porosity foam shows a hysteresis cycle. Experiments on shock wave-foam interactions are conducted by using a shock tube. Experimental time history of the surface stress of the foam at the end of the shock tube does not show shock type stress increase, but continuous excessive stress rise can be seen, and then dumping vibration approaching to gas dynamic pressure of the reflected shock wave is followed, and the highest stress amounts about 3∼4 times of the pressure after the reflected gas dynamic shock wave. Interactive motions of gas and the low-porosity foam are analyzed using the Lagrangean coordinates system. An elastic model for a low-porosity foam is assumed to be a single elastic material with the measured stress-strain relation. Results of numerical simulations are compared with the shock tube experiments, which show essentially same stress variations with experimental results.     

Blowing of a foreign gas in a hypersonic viscous shock layer

We consider the problem of a hypersonic viscous flow of a nonreactive mixture of ideal gases around smooth thick bodies in the framework of a two-layer model of a thin shock layer for moderately small Reynolds numbers. We investigate the effect of blowing of a foreign gas through a permeable surface in the bow region of a spherical blunt body. We introduce a transformation of variables that gives a number of important advantages in the numerical solution of the problem under consideration. The problem of mass blowing from the surface of a body into a boundary layer has an extensive literature. The effect of blowing for moderately small Reynolds numbers has been considerably less studied [1–5], and in the majority of papers on this question either the critical point of a blunt body or the blowing of a gas homogeneous with the gas in the incoming flow is investigated.Moscow. Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 4, pp. 110–116, July–August, 1972.