Nonequilibrium radiation of a strong shock wave

We examine the nonequilibrium radiation from the first negative band of the molecular nitrogen ion N ₂ ⁺ . The various N ₂ ⁺ ion excitation mechanisms are discussed. It is shown that for a shock wave velocity in air 8 km/sec the primary excitation mechanism is electronic impact.In conclusion the authors wish to thank V. K. Vertushkin and A. A. Gladkov for supplying the calculations on the structure of the normal compression shock and L. I. Ponomarev for helpful discussions.     

Finite element solution of the equations governing the flow of electrolyte in charged microporous membranes

Electrical double-layer effects are unimportant in flows through porous media except when the Debye length k^?1 is comparable in magnitude with the pore radius a. Under these conditions the equations governing the flow of electrolyte are those of Stokes, Nernst-Planck and Poisson. These equations are non-linear and require numerical solution. The finite element method provides a useful basis for solution and various algorithms are investigated. The numerical stability and errors of each scheme are analysed together with the development of an appropriate finite element mesh. The electro-osmotic flow of a typical electrolyte (barium chloride) through a uniformly charged cylindrical membrane pore is investigated and the ion fluxes are post-computed from the numerical solutions. The ion flux is shown to be strongly dependent on both zeta potential and pore radius, ka, indicating the effects of overlapping electrical double layers.     

Flow of a fully ionized gas with finite time for energy exchange between electrons and ions

The flow of a jet of a fully ionized gas with velocity ~5·10⁶ cm/sec is examined; the finite time of energy exchange between the electrons and ions is considered.The derived solution agrees well with experimental data on the behavior of the electron and ion temperatures in the zone behind the shock wave which forms in the ionized gas jet issuing from a channel.     

Reaching High Temperatures by Compressing a Vapor Bubble

The process of compression of a vapor bubble under the action of an instantaneously applied pressure is considered. The effect of initial parameters on compression dynamics is analyzed. Conditions of emergence of a shock wave inside the bubble are considered. It is shown that the temperature in the bubble is lower than 10⁴ K under uniform compression.     

Interaction of a wave with an obstacle in a multicomponent two-phase medium

The author's model [1] of a multicomponent liquid medium with nonlinear limiting compression diagrams and constant coefficient of viscosity is improved by the introduction of a coefficient of viscosity that varies during the deformation. The new model is used to obtain a numerical solution to the problem of the propagation of a plane wave produced by a shock load and the interaction of the wave with a fixed obstacle. Such a problem was solved earlier [2] in the case of a viscous medium for linear diagrams of static and dynamic compression and constant coefficient of viscosity. It is shown that the nonlinearity of the diagram of static compression leads with increasing pressure first to an increase in the reflection coefficient and then to a decrease of it. If the load has a sufficient duration, the initial section of the obstacle is subject to a succession of several waves, the number of which increases with increasing duration and amplitude of the load. The calculation was made for glycerine with air bubbles. It is assumed that at pressures up to 400·10⁵ N/m² glycerine is a linearly elastic medium In this case, the dynamic compression diagram of the two-component glycerine—gas-bubble medium is linear.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 3, pp. 183–187, May–June, 1981.I thank Yu. A. Sozonenko for discussion and valuable comments.     

Mathematical analysis of SOFC based on co-ionic conducting electrolyte

In co-ionic conducting solid oxide fuel cell (SOFC), both oxygen ion (O2) and proton (H+) can transport through the electrolyte, generating steam in both the an-ode and cathode. Thus the mass transport phenomenon in the electrodes is quite different from that in conventional SOFC with oxygen ion conducting electrolyte (O-SOFC) or with proton conducting electrolyte (H-SOFC). The generation of steam in both electrodes also affects the concentration over-potential loss and further the SOFC performance. However, no detailed modeling study on SOFCs with co-ionic electrolyte has been reported yet. In this paper, a new mathematical model for SOFC based on co-ionic electrolyte was developed to predict its actual performance considering three major kinds of overpotentials. Ohm’s law and the Butler-Volmer formula were used to model the ion conduction and electrochemical reactions, respectively. The dusty gas model (DGM) was employed to simulate the mass transport processes in the porous electrodes. Parametric simulations were performed to investigate the effects of proton transfer number (tH) and current density (jtotal) on the cell performance. It is interesting to find that the co-ionic conducting SOFC could perform better than O-SOFC and H-SOFC by choosing an appropriate proton transfer number. In addition, the co-ionic SOFC shows smaller difference between the anode and cathode concentration overpotentials than O-SOFC and H-SOFC at certain t H values. The results could help material selection for enhancing SOFC performance.     

Shock Compression of a Plate on a Wedged–Shaped Target

Problems of compression of a plate on a wedge–shaped target by a strong shock wave and plate acceleration are studied using the equations of dissipationless hydrodynamics of compressible media. The state of an aluminum plate accelerated or compressed by an aluminum impactor with a velocity of 5—15 km/sec is studied numerically. For a compression regime in which a shaped–charge jet forms, critical values of the wedge angle are obtained beginning with which the shaped–charge jet is in the liquid or solid state and does not contain the boiling liquid. For the jetless regime of shock–wave compression, an approximate solution with an attached shock wave is constructed that takes into account the phase composition of the plate material in the rarefaction wave. The constructed solution is compared with the solution of the original problem. The temperature behind the front of the attached shock wave was found to be considerably (severalfold) higher than the temperature behind the front of the compression wave. The fundamental possibility of initiating a thermonuclear reaction is shown for jetless compression of a plate of deuterium ice by a strong shock wave.     

Anomaly in the dynamic strength of austenitic stainless steel 12Cr19Ni10Ti under shock wave loading

Measurement results for the shock wave compression profiles of 12Cr19Ni10Ti steel and its dynamic strength in the strain rate range 10⁵–10⁶ s^?1 are presented. The protracted viscous character of the spall fracture is revealed. With the previously obtained data taken into account, the measurement results are described by a polynomial relation, which can be used to construct the fracture kinetics. On the lower boundary of the range, the resistance to spall fracture is close to the value of the true strength of the material under standard low-rate strain conditions; on the upper boundary, the spall strength is more than twice greater than this quantity. An increase in the temperature results in a decrease in both the dynamic limit of elasticity and the spall fracture strength of steel. The most interesting result is the anomaly in the dependence of the spall fracture strength on the duration of the shock wave compression pulse, which is related to the formation of deformation martensite near the growing discontinuities.     

A Three-Scale Model of pH-Dependent Flows and Ion Transport with Equilibrium Adsorption in Kaolinite Clays: II Effective-Medium Behavior

In part I (Lima et al., Transp Porous Media, 2009), a three-scale model governing the movement of an aqueous saline solution containing four monovalent species (Na⁺, H⁺, Cl^?, OH^?) in kaolinite clays was derived. Unlike purely macroscopic approaches, the novelty of the formulation relied on the double averaging of the nanoscopic electro- chemistry of particle/electrolyte solution interface ruled by the electrical double layer coupled with protonation/deprotonation reactions. The passage from the nano to the micro (pore)-scale gave rise to ion-sorbed concentrations and slip velocity at the solid/fluid interface which are coupled with the microscopic Stokes problem and Nernst–Planck equations governing the hydrodynamics and ion transport in the micropores. Application of a formal homogenization procedure led to macroscopic governing equations with effective electro-chemical parameters, such as retardation coefficients, electro-osmotic permeability, and electric conductivity. In this study, we reconstruct the constitutive laws of the macroscopic coefficients by solving the nano and microscopic closure problems. New generalized isotherms for Na⁺ and H⁺ ? OH^? sorption are build-up based on a perturbation approach and the limitations of classical Freundlich isotherm for modeling ion sorption at the solid/fluid interface are discussed. The macroscopic governing equations are discretized by the finite volume method and numerical simulations of a transient electroosmosis experiment for desalination of a clay sample by electrokinetics are presented.     

An equation of state for dense nitrogen

An empirical equation of state for nitrogen at high pressure and density is considered. It is shown that for nitrogen at densities greater than 0.6 g/cm³, by using available data [1–3] on static compression of gaseous nitrogen and shock compression of liquid nitrogen, it is possible to construct a Mie-Grüneisen type equation of state which gives a pressuredensity relationship close to experiment along the shock adiabat of liquid nitrogen and agrees with the calculations of other authors for temperature values beyond the shock-wave front [2–3]. Heat capacity, entropy, and Grüneisen coefficient values beyond the shock-wave front in liquid nitrogen are calculated.     

Nature of the surface heart transfer fluctuation in a hypersonic separated turbulent flow

This paper presents the results of an experimental study of the unsteady nature of a hypersonic separated turbulent flow. The nomimal test conditions were a freestream Mach number of 7.8 and a unit Reynolds number of 3.5×10⁷/m. The separated flow was generated using finite span forward facing steps. An array of flush mounted high spatial resolution and fast response platinum film resistance thermometers was used to make multi-channel measurements of the fluctuating surface heat trtansfer within the separated flow. Conditional sampling analysis of the signals shows that the root of separation shock wave consists of a series of compression wave extending over a streamwise length about one half of the incoming boundary layer thickness. The compression waves converge into a single leading shock beyond the boundary layer. The shock structure is unsteady and undergoes large-scale motion in the streamwise direction. The length scale of the motion is about 22 percent of the upstream influence length of the separation shock wave. There exists a wide band of frequency of oscillations of the shock system. Most of the frequencies are in the range of 1–3 kHz. The heat transfer fluctuates intermittently between the undisturbed level and the disturbed level within the range of motion of the separation shock wave. This intermittent phenomenon is considered as the consequence of the large-scale shock system oscillations. Downstream of the range of shock wave motion there is a separated region where the flow experiences continuous compression and no intermittency phenomenon is observed. The project supported by National Natural Science Foundation of China     

Efficiency of the induction interaction of a blob of conducting gas with an electrical circuit in which an external electromotive force is included

The possibility of increasing the efficiency of a magnetohydrodynamic energy conversion by including an external emf source in the operating winding is investigated. Values of the average electrical efficiency which can be obtained with the used operating winding are calculated. The possibility and the limits of regulating the efficiency by varying the magnitude of the external emf, the angle of the phase shift of the external emf relative to the currents in the ionized gas, and the magnitude of the excitation magnetic field for the known nature of the flow and the parameters of the gas are determined.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 2, pp. 143–146, March–April, 1971.     

Shock heating of plasma in a rapidly increasing magnetic field

The experimental excitation of intense collisionless shock waves (M 5) with subsequent plasma compression by the magnetic field of a shock coil is described. A magnetic plug > 20 kOe is produced in 100 × 10^–9 sec by a current generator, a long line with 250-kV water insulation and a characteristic impedance of l At an initial deuterium-plasma density of 2 × 10¹⁴ cm^–3, shock waves with a front width of 20c/₀₃and a velocity of 5 × 10₇ cm/sec are recorded. The ion energy after the accumulation, determined from the neutron yield, turns out to be 2 ke V. Axial shock waves excited by the plasma flow beneath the shock coil are observed.Translated from Zhurnal Prikladnoi Mekhaniki i Teknicheskoi Fiziki, Vol. 11, No. 2, pp. 28–38, March–April, 1970.The authors thank G. I. Budker and R. Z. Sagdeev for formulating the problem, R. I. Soloukhin for interest in the study, and S. P. Shalamov for construction of the apparatus.     

<Emphasis Type="Italic">L</Emphasis><Superscript>2</Superscript> Stability Estimates for Shock Solutions of Scalar Conservation Laws Using the Relative Entropy Method

We consider scalar nonviscous conservation laws with strictly convex flux in one spatial dimension, and we investigate the behavior of bounded L ² perturbations of shock wave solutions to the Riemann problem using the relative entropy method. We show that up to a time-dependent translation of the shock, the L ² norm of a perturbed solution relative to the shock wave is bounded above by the L ² norm of the initial perturbation.     

Method of determining the rheological and energy characteristics of the shock compression of metals

A method for determining the shear stress relaxation time and the heat release due to deformation of a material is developed based on the Kolsky technique using a split Hopkinson bar. The method was tested in experimental studies of the rheological and energy characteristics of AMg5 M aluminum alloy in the range of strain rates from 300 to 1500 s^?1. The relationship between the relaxation time and the thermal and internal energies of AMg5 M alloy during its shock compression was determined.     

Visualization of shock-wave formation processes during shock reflection at obstacles with multiple steps

According to standard textbooks on compressible fluid dynamics, a shock wave is formed by an accumulation of compression waves. However, the process by which an accumulated compression wave grows into a shock wave has never been visualized. In the present paper, the authors tried to visualize this process using a model wedge with multiple steps. This model is useful for generating a series of compression waves and can simulate a compression process that occurs in a shock tube. By estimating the triple-point trajectory angle, we demonstrated visually that an accumulated compression wave grows into a shock wave. Further reflection experiments over a rough-surface wedge confirmed the tendency for the triple point trajectory angle to reach the asymptotic value _s in the end.This work was first presented at the Symposium on Shock Waves, Japan 2002     

The reflected pressure field in the interaction of weak shock waves with a compressible foam

This paper deals with the waves that are reflected from slabs of porous compressible foam attached to a rigid wall when impacted by a weak shock wave. The interest is in establishing possible attenuation of the pressure field after a shock or blast wave has struck the surface. Foam densities from 14 to 38 kg/m³ were tested over a range of shock wave Mach numbers less than 1.4. It is shown that the initial reflected shock wave strength is accurately predicted by the pseudo-gas model of Gelfand et al. (1983), with a pressure ratio of approximately 80% of the value for reflection off a rigid wall. Evidence is presented of gas entering the foam during the early stages of the process. A second wave emerges from the foam at a later stage and is separated from the first by a region of constant velocity and pressure. This second wave is not a shock wave but a compression front of significant thickness, which emerges from the foam earlier than predicted by the pseudo-gas model. Analysis of the origin of this wave points to much more complex flows within the foam than previously assumed, particularly in an apparent decrease in average wave front speed as the foam is compressed. It is shown that the pressure ratio across both these waves taken together is slightly higher than that for reflection off a rigid wall. In some cases this compression wave train is followed by a weak expansion wave.This article was processed using Springer-Verlag T_EX Shock Waves macro package 1990.     

Shock response of a heavy tungsten alloy

This article describes the results of shock wave experiments performed on a heavy tungsten alloy containing W, Ni, and Fe in the ratio of 92.85:4.9:2.25 by weight. These experiments provide information about the shear strength under compression and tensile strength, as measured by the spall threshold, of this alloy to 24 GPa. The results of these experiments show that: (i) the magnitude of its Hugoniot elastic limit (HEL) is 2.76±0.26 GPa; (ii) this alloy deforms plastically above its HEL and thus retains its shear strength to 24 GPa; (iii) the spall strength of the alloy is found to be 1.9±0.4 GPa and is independent of the impact stress and duration of the shock compression pulse; and (iv) the tensile impedance of the alloy, determined from a new experiment designed to measure this impedance, is 68±10 Gg/m² s.     

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 · 10 ⁶ 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.