Shock-wave equation-of-state studies at Los Alamos

A history of the shock-wave equation-of-state (EOS) studies at Los Alamos is given. Particular emphasis is placed on the pioneering research in the 1950s where many of the experimental techniques and methods of analysis were developed, which we now take for granted. A brief review of shock-wave physics is given, which illustrates important hydrodynamic and thermodynamic concepts. Recent studies on the EOS of Ti are presented with emphasis on the-to- phase transition. VISAR wave profiles for polycrystalline Ni and singlecrystal Ni are presented to determine the strengths of these materials under pressure. Low-density polystyrene foam Hugoniot experiments are described and results analyzed.This article was processed using Springer-Verlag T_EX Shock Waves macro package 1990.     

Impact compression of piezoceramics

We investigated the dynamic compressibility of a piezoceramic composed of lead zirconatetitanate (LCT) and its depolarization by shock waves over the pressure range 100–500 kbar. We also observed the changes that persisted in the specimens after brief compression at pressures of 350 and 500 kbar. The dependence of the piezocurrent on time was used to calculate the dielectric permeability and conductivity of the ceramic beyond the shock-wave front over the pressure range investigated. This article discusses the possibility of a phase transition to the paraelectric phase in LCT during compression by a shock wave.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, Vol. 13, No. 2, pp. 106–110, March–April, 1971.The author wishes to thank R. M. Zaidel' for his helpful comments and A. N. Shuikin for his assistance in processing the experimental data.     

爆炸破片对防护液舱的穿透效应

分别对单发破片和双发破片同时穿透液舱的过程进行了数值计算,提出了破片穿透液舱的5个典型过程,分析了破片速度的衰减规律、液舱内板的响应及舱内液体中冲击波压力的叠加效应。结果表明:破片穿透液舱的过程中产生的冲击波和局部压力将作用在液舱内板上,双发破片打击时液体内部产生的冲击波有明显的叠加效应,高压区域的位置与破片间距有关,冲击波压力峰值和液舱内板受到的压力大于2倍的单发破片打击情况。     

Schlieren imaging of loud sounds and weak shock waves in air near the limit of visibility

A large schlieren system with exceptional sensitivity and a high-speed digital camera are used to visualize loud sounds and a variety of common phenomena that produce weak shock waves in the atmosphere. Frame rates varied from 10,000 to 30,000 frames/s with microsecond frame exposures. Sound waves become visible to this instrumentation at frequencies above 10 kHz and sound pressure levels in the 110 dB (6.3 Pa) range and above. The density gradient produced by a weak shock wave is examined and found to depend upon the profile and thickness of the shock as well as the density difference across it. Schlieren visualizations of weak shock waves from common phenomena include loud trumpet notes, various impact phenomena that compress a bubble of air, bursting a toy balloon, popping a champagne cork, snapping a wooden stick, and snapping a wet towel. The balloon burst, snapping a ruler on a table, and snapping the towel and a leather belt all produced readily visible shock-wave phenomena. In contrast, clapping the hands, snapping the stick, and the champagne cork all produced wave trains that were near the weak limit of visibility. Overall, with sensitive optics and a modern high-speed camera, many nonlinear acoustic phenomena in the air can be observed and studied.     

Effect of the adiabatic exponent on the reflection of shock waves

The effect of the adiabatic exponent on certain features of shock-wave reflection is analyzed with particular reference to the nature of the dependence of the critical angle on the incident wave intensity. The latter is shown to increase with increasing shock-wave intensity. Limit cases of weak shock waves at any arbitrary adiabatic exponent and of strong shock waves with the adiabatic exponent equal to unity are analytically investigated. Results of calculations of the critical angle for various adiabatic exponents throughout the possible range of incident wave intensities are presented.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, Vol. 11, No. 1, pp. 62–66, January–February, 1970.     

Shock-wave structure in the near zone upon explosion of spatial charges in air

Profiles and values of pressure in shock waves are determined for the case of spherical, linear, and spatial charges, such as a coil of a bulk spiral and plane annular coils and Archimedes’ spiral of various lenths, exploded in air. In the case of explosion of rings and spirals, a complex wave structure in the form of a sequence of several shock waves is registered near the charges along the spiral axes; a weaker attenuation of shock waves with distance and pressure amplitudes two to three times higher than in the case of a spherical charge of the same mass are observed. It was found that an increase in the length of a plane spiral does not lead to an increase in the maximum pressure in the shock wave at distances of the order of several pitches of the spiral from its plane. With distance from spatial charges of different shape but identical mass, the pressure values in the shock-wave fronts coincide and tend asymptotically to the parameters of a spherical explosion with a significant increase in the duration of a wave packet generated by the spatial charge. Dependences for evaluation of shock-wave pressure amplitudes in the near zone of the explosion are presented. Lavrent’ev Institute of Hydrodynamics, Siberian Division, Russian Academy of Sciences, Novosibirsk 630090. Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 41, No. 5, pp. 81–90, September–October, 2000.     

Over forty years of continuous research at UTIAS on nonstationary flows and shock waves

Analytical and experimental research on non-stationary shock waves, rarefaction waves and contact surfaces has been conducted continuously at UTIAS since its inception in 1948. Some unique facilities were used to study the properties of planar, cylindrical and spherical shock waves and their interactions. Investigations were also performed on shock-wave structure and boundary layers in ionizing argon, water-vapour condensation in rarefaction waves, magnetogasdynamic flows, and the regions of regular and various types of Mach reflections of oblique shock waves. Explosively-driven implosions have been employed as drivers for projectile launchers and shock tubes, and as a means of producing industrial-type diamonds from graphite, and fusion plasmas in deuterium. The effects of sonic-boom on humans, animals and structures have also formed an important part of the investigations. More recently, interest has focussed on shock waves in dusty gases, the viscous and vibrational structure of weak spherical blast waves in air, and oblique shock-wave reflections. In all of these studies instrumentation and computational methods have played a very important role. A brief survey of this work is given herein and in more detail in the relevant references.This article was processed using Springer-Verlag T_EX Shock Waves macro package 1990.     

The shock-wave structure in a two-velocity mixture of compressible media with different pressures

The problem of the shock-wave structure in a mixture of two compressible media with different velocities and pressures of components is considered. The problem is reduced to solving a boundary-value problem for two ordinary differential equations that describe the velocity relaxation and pressure equalization of the components. Using methods of the qualitative theory of dynamic systems on a plane, the existence and uniqueness of four types of waves are shown: (a) fully dispersed waves; (b) frozen-dispersed waves; (c) dispersed-frozen waves; (d) frozen waves of two-front configuration. A chart of solutions of the corresponding flow types is constructed in the plane of the following parameters: the initial velocity of the mixture and the initial volume concentration of one of the components. The numerical calculations conducted illustrate the obtained analytical structures of the shock wave. It is shown that the results obtained using the suggested mathematical model are in agreement with experimental data on the dependence of the velocity of the dispersed shock wave on the equilibrium pressure behind the shock-wave front for a mixture of silica sand and water. Institute of Theoretical and Applied Mechanics, Siberian Division, Russian Academy of Sciences, Novosibirsk 630090. Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 39, No. 2, pp. 10–19, March–April, 1998.     

Numerical models for afterburning of TNT detonation products in air

Afterburning occurs when fuel-rich explosive detonation products react with oxygen in the surrounding atmosphere. This energy release can further contribute to the air blast, resulting in a more severe explosion hazard particularly in confined scenarios. The primary objective of this study was to investigate the influence of the products equation of state (EOS) on the prediction of the efficiency of trinitrotoluene (TNT) afterburning and the times of arrival of reverberating shock waves in a closed chamber. A new EOS is proposed, denoted the Afterburning (AB) EOS. This EOS employs the JWL EOS in the high pressure regime, transitioning to a Variable-Gamma (VG) EOS at lower pressures. Simulations of three TNT charges suspended in a $26\,\hbox {m}^3$ explosion chamber were performed. When compared to numerical results using existing methods, it was determined that the Afterburning EOS delays the shock arrival times giving better agreement with the experimental measurements in the early to mid time. In the late time, the Afterburning EOS roughly halved the error between the experimental measurements and results obtained using existing methods. Use of the Afterburning EOS for products with the Variable-Gamma EOS for the surrounding air further significantly improved results, both in the transient solution and the quasi-static pressure. This final combination of EOS and mixture model is recommended for future studies involving afterburning explosives, particularly those in partial and full confinement.     

磁驱动飞片的一维磁流体动力学数值研究

磁驱动高速飞片技术是近年来发展的一种新型实验技术,在冲击波物理领域得到应用。该过程伴随着磁场扩散,并由此引起焦耳加热,使得飞片加载面的相状态发生变化,这决定了飞片厚度的范围。基于拉格朗日坐标系,利用磁流体动力学方程组、电阻率方程和状态方程数据库,对磁驱动铝飞片进行了一维磁流体动力学数值计算,获得了不同时刻铝飞片密度、温度的剖面分布,得到了磁场扩散速率随加载电流密度的变化关系。文章所选取的电导率方程只考虑到汽化点为止,对于等离子体形成的过程无法描述,如果要精确描述更高电流密度下的驱动过程,需考虑更为普适的电导率方程。磁场扩散速率随加载电流密度的变化存在转折点,在转折点前后可分别用两个线性关系表达式加以刻画。利用这些关系和冲击波物理相关知识,对磁压加载等熵驱动飞片实验样品厚度的选择进行了研究。     

Strength and elasticity of iron and copper at high shock-wave compression pressures

The elastic and strength parameters of iron and copper were determined experimentally at high shock-wave compression pressures of 1–2 Mbar. The attenuation of shock waves created by the impact of thin plates in blocks of the investigated materials was recorded in the experiments. The Poisson ratios, bulk moduli, shear moduli, and yield strength Y for iron at 1.11 and 1.85 Mbar and for copper at 1.22 Mbar were determined from the experimentally observed amplitudes and velocites of the unloading shock waves. The shape of the curve of the change of the yield strength of copper with an increase of pressures to states of shock-wave compression causing melting was determined on the basis of the results obtained and data of other investigators. The curve has a maximum at P 800 kbar corresponding to Y =280 kg/mm². The yield strengths for iron are located on the ascending branch of the curve Y(P) and are numerically equal to 110 kg/mm² at 1.11 Mbar and 270 kg/mm² at 1.85 Mbar. The measured values of Y exceed the yield strengths of uncompressed metals by a factor of 5–7. The authors also recorded a substantial increase of Poisson's ratios with increase of pressures in the investigated metals.Deceased.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 6, pp. 159–166, November–December, 1971.     

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.     

Application of digital phase-shift holographic interferometry to weak shock waves propagating at Mach 1.007

Digital phase-shift holographic interferometry was applied to visualize weak shock waves and related phenomena quantitatively. This method of interferometry is an improved version of double-exposure holographic interferometry using digital image processing and a phase shift method. The obtained interferograms were analyzed using the Carré method. To evaluate the applicability of the interferometry to quantitatively visualize the phenomena, density profiles behind weak spherical shock waves generated with 500 μg of silver azide were examined. The results of the numerical analysis performed with the hydrocode AUTODYN were compared with those of the experiment. The Mach number of visualized shock waves was estimated to be 1.007 ± 0.001 at the pressure transducer near the test section. At the shock fronts, the density difference between the experimental and numerical results was within 0.3%.     

Transient shock wave flows in tubes with a sudden change in cross section

This paper describes propagation of shock waves within circular cross-section shock tubes with a sudden area change in cross section. A dispersion-controlled scheme was used to solve the Euler equations assuming axisymmetric flows. For experimental visualizations an aspheric cylindrical test section was designed to keep collimated incident light rays parallel once they were reflected or refracted on the inner and outer surfaces of the test section. For effective comparisons with experimental results, equivalent numerical interferograms were constructed to demonstrate effectiveness of the numerical method and verify the observed shock-wave phenomena. The numerical method was used to calculate three further cases with variations of the initial shock-wave Mach number and the flow geometry to clarify the role of these parameters. Complex transient shock-wave phenomena, such as shock-wave reflection, shock/vortex interaction and shock-wave focusing were observed in these cases, and interpreted with shock wave theory. In addition, the research clearly shows that combination of CFD with experiments is effective to highlight physical phenomena in axisymmetric flows. Received 15 June 1996 / Accepted 20 December 1996     

Diffuse interface model for high speed cavitating underwater systems

High speed underwater systems involve many modelling and simulation difficulties related to shocks, expansion waves and evaporation fronts. Modern propulsion systems like underwater missiles also involve extra difficulties related to non-condensable high speed gas flows. Such flows involve many continuous and discontinuous waves or fronts and the difficulty is to model and compute correctly jump conditions across them, particularly in unsteady regime and in multi-dimensions. To this end a new theory has been built that considers the various transformation fronts as ‘diffuse interfaces’. Inside these diffuse interfaces relaxation effects are solved in order to reproduce the correct jump conditions. For example, an interface separating a compressible non-condensable gas and compressible water is solved as a multiphase mixture where stiff mechanical relaxation effects are solved in order to match the jump conditions of equal pressure and equal normal velocities. When an interface separates a metastable liquid and its vapor, the situation becomes more complex as jump conditions involve pressure, velocity, temperature and entropy jumps. However, the same type of multiphase mixture can be considered in the diffuse interface and stiff velocity, pressure, temperature and Gibbs free energy relaxation are used to reproduce the dynamics of such fronts and corresponding jump conditions. A general model, based on multiphase flow theory is thus built. It involves mixture energy and mixture momentum equations together with mass and volume fraction equations for each phase or constituent. For example, in high velocity flows around underwater missiles, three phases (or constituents) have to be considered: liquid, vapor and propulsion gas products. It results in a flow model with 8 partial differential equations. The model is strictly hyperbolic and involves waves speeds that vary under the degree of metastability. When none of the phase is metastable, the non-monotonic sound speed is recovered. When phase transition occurs, the sound speed decreases and phase transition fronts become expansion waves of the equilibrium system. The model is built on the basis of asymptotic analysis of a hyperbolic total non-equilibrium multiphase flow model, in the limit of stiff mechanical relaxation. Closure relations regarding heat and mass transfer are built under the examination of entropy production. The mixture equation of state (EOS) is based on energy conservation and mechanical equilibrium of the mixture. Pure phases EOS are used in the mixture EOS instead of cubic one in order to prevent loss of hyperbolicity in the spinodal zone of the phase diagram. The corresponding model is able to deal with metastable states without using Van der Waals representation.     

激波与堆积粉尘相互作用的数值模拟

基于双流体模型和测定的堆积粉尘的本构方程 ,利用AUSM+ 格式 ,对激波与堆积粉尘的相互作用进行了数值模拟。计算所反映的流场结构与实验图像一致。此外还对激波强度 ,颗粒材料密度等对流场的影响进行了讨论。     

Ab initio calculations of the equation of state of hydrogen in a regime relevant for inertial fusion applications

We describe ab initio electronic structure calculations (density functional theory molecular dynamics and coupled electron-ion quantum Monte Carlo) of the equation of state (EOS) of hydrogen in a pressure-temperature regime relevant for simulating the initial phase of an inertial confinement fusion capsule implosion. We find the computed EOS to be quite close to that of the most recent SESAME table (constructed by G. Kerley, 2003). A simple density-dependent but temperature-independent correction brings the 2003-Kerley EOS into excellent agreement with ours in the chosen region of the hydrogen phase diagram. Simulations of fusion ignition experiments on the National Ignition Facility (NIF) with this modified 2003-Kerley table are shown to produce results nearly indistinguishable from those of the 2003-Kerley EOS, which was used to design the capsule. In this sense, we do not expect that further improvements to the hydrogen EOS in this particular regime will impact the capsule design.     

Breakdown of a discontinuity,taking account of the real equation of state of the detonation products from a condensed explosive

The problem is considered concerning the breakdown of an arbitrary discontinuity, due to the emergence of a detonation wave at the boundary of a condensed explosive charge. The real equation of state of the detonation products of Hexogen was used in the numerical calculations. A u vs p diagram is constructed, which allows graphical calculations to be carried out of the discontinuity breakdown for different media. A comparison is carried out of the calculated values of the initial shock-wave velocities with the experimental data obtained at a certain distance from the explosive charge. It is shown that an increase of the pressure of the gas in which dispersion of the explosion products occurs leads to a reduction of the initial shock wave velocity and to an enhancement of its attenuation during its further motion in the shock tube.     

Accelerating piston action and plasma heating in high-energy density laser plasma interactions

In the field of high-energy density physics (HEDP), lasers in both the nanosecond and picosecond regimes can drive conditions in the laboratory relevant to a broad range of astrophysical phenomena, including gamma-ray burst afterglows and supernova remnants. In the short-pulse regime, the strong light pressure (>Gbar) associated ultraintense lasers of intensity I > 10¹⁸ W/cm² plays a central role in many HEDP applications. Yet, the behavior of this nonlinear pressure mechanism is not well-understood at late time in the laser–plasma interaction. In this paper, a more realistic treatment of the laser pressure ‘hole boring’ process is developed through analytical modeling and particle-in-cell simulations. A simple Liouville code capturing the phase space evolution of ponderomotively-driven ions is employed to distill effects related to plasma heating and ion bulk acceleration. Taking into account these effects, our results show that the evolution of the laser-target system encompasses ponderomotive expansion, equipartition, and quasi-isothermal expansion epochs. These results have implications for light piston-driven ion acceleration scenarios, and astrophysical applications where the efficiencies of converting incident Poynting flux into bulk plasma flow and plasma heat are key unknown parameters.     

On shock waves in a special class of thermoelastic solids

This paper describes a thermoelastic model for shock waves in uniaxial strain based on a subclass of the so-called materials of Mie–Grüneisen type. We compare the Hugoniot curve with the isotherms and isentropes for this model, and we construct the shock-wave solution to a simple impact problem.