State equation of condensed matter at high pressure: <Emphasis Type="Italic">D-U</Emphasis> diagram approach

For solids and liquids, an equation of state is suggested at high pressures up to a few megabars, for densities greater than that at normal conditions and for temperatures up to the melting point. Shock wave loading test data are analyzed for 40 basic chemical elements, and they prove the state equation suggested, within the limits of test error. The method is based on the analysis of D-U diagrams where D is the shock wave velocity and U is the material velocity behind the shock wave (both with respect to the material in front of the shock wave). Based on the state equation suggested the velocity of shock wave is shown to be a linear function of the material velocity behind the shock wave, the function being a specific characteristic of the material and its structure. Most significant anomaly belonging to carbon, iron, ice, and water is explained by the formation of new phases at high pressure, with two new phases of iron, and one phase in the case of water. For water, a simple nearly exact equation of state is suggested for pressures from 0.1 MPa to 150 GPa. For pressures from 0.1 to 300 MPa, it fits very well the extremely complicated state equation of the American standard obtained by static tests, and for pressures from 2 to 50 GPa it fits well the data of shock wave tests. In the pressure range from 45 to 1500 GPa liquid water becomes solid, which equation of state coincides with that of alkaline metal sodium. The model of ideal solid as contrary to ideal gas is introduced, with internal energy of ideal solid depending only on stresses or strains (and only on pressure or density, at high pressures). The equations of state for iron, diamond, pyrolithic graphite, and for several phases of ice are as well derived based on test data.     

Mathematical simulation of the shock compression of porous molybdenum using a heterogeneous model

The shock compression of a heterogeneous material is numerically simulated. The physical model used for the simulation is based on a layered model of a porous material and consists of a set of thin matrix plates with a known equation of state that are separated by filler layers also with a known equation of state. The model is intended to calculate the parameters (pressure, temperature, mass velocity) of shock compression of the matrix and the filler of heterogeneous materials during their one-dimensional shock compression in terms of a developed hydrodynamic code. The adequacy of the proposed model is tested on porous molybdenum during shock-wave loading to a pressure of 15–70 GPa and a temperature of 4000 K.     

A model for shock waves in solids and evidence for a thermal catastrophe

Shock-wave experiments and computer simulations yield a linear relation between shock velocity and particle velocity. We show that a Mie-Grüneisen equation of state combined with the Hugoniot relations matches the computer results and the experiments and leads to an explanation of the generality of the linear velocity dependence. At high shock velocities the onset of a thermal catastrophe, which results in a maximum shock compression, is predicted from our model.     

辐射驱动冲击波速度被动式测量

在神光Ⅱ和神光Ⅲ原型装置上采用了辐射驱动冲击波速度被动式测量技术,对冲击波发光图像信噪比进行了理论分析和实验研究,结果表明:靶室内杂散光比冲击波信号至少强4个量级以上,是影响信噪比的关键因素。据此提出了信噪比控制技术,通过电磁屏蔽优化,采用了基于光触发的快时间分辨测量技术,提高了冲击波速度测量精度。基于冲击波测量辐射温度,对辐射驱动冲击波速度被动式测量技术进行了考核。实验测量的冲击波发光图像清晰,数据信噪比及冲击波速度和物理预期一致,验证了技术的可靠性。     

A conservative discrete compatibility-constraint low-Mach pressure-correction algorithm for time-accurate simulations of variable density flows

In this paper, we develop the discrete compatibility-constraint pressure-correction algorithm for transient simulations of variable density flows at low-Mach numbers. The constraint for the velocity field is constructed from a combination of the discrete equations of continuity and scalar (e.g. energy) transport, imposing that the newly predicted state must be compatible, in agreement with the equation of state. This way, mass and scalar conservation are guaranteed and the equation of state is exactly fulfilled at every time step. For comparison reasons, two other types of well-known pressure-correction algorithms are also used. The first class, denoted as continuity-constraint pressure-correction, is based on a constraint for the velocity field that is derived solely from the continuity equation. The second class, denoted as analytical compatibility-constraint pressure-correction, constructs the constraint from an analytical combination of the material derivative of the equation of state and the continuity and scalar equations. The algorithms are tested for three example fluid configurations: a single-fluid ideal gas, a two-fluid inert mixture and a two-fluid reacting mixture. The latter is special in the sense that the equation of state is non-linear and not everywhere differentiable. The continuity-constraint pressure-correction algorithm yields unstable solutions if density ratios are high. The analytical compatibility-constraint pressure-correction algorithm yields stable results, but the predicted states do not correspond to the equation of state. The discrete compatibility-constraint pressure-correction algorithm performs well on all test cases: the simulation results are stable and exactly match the equation of state.     

水中斜激波的传播

 利用水的简化物态方程讨论了水中斜激波波后流动马赫数、密度比、压强增量及冲击角与来流马赫数的关系,给出了一个无量纲化的激波极线方程;对附体激波转变为脱体激波及波后流动为等声速流的条件进行了讨论。     

氢及氘的宽区物态方程研究进展

氢是自然界最丰富的元素,是天体物理和惯性约束聚变（ICF）研究的重要对象。简要综述了国内外氢及氘宽区物态方程研究进展,特别评述了OMEGA激光装置上的最新冲击压缩 实验和理论模型的对比分析情况。在以往数据分析评估基础上,利用改进的化学自由能模型、第一原理数值模拟结果及多参数物态方程模型,构建了氢的宽区物态方程,适用温度、密度范围分别为20～108 K,10?7～2000 g/cm3。与已有多类实验如冲击压缩实验、静高压等温线实验、声速等实验结果对比表明,新构建的氢宽区物态方程具有较高的置信度,为天体物理、惯性约束聚变、国际热核实验堆等工程物理设计提供高精度的支撑数据。氢宽区物态方程的构建及验证方法亦可适用于其同位素氘,该方法构建的氘宽区物态方程与2019年最新发表的主雨贡纽、二次冲击雨贡纽数据的吻合程度明显优于当前国外模型。指出了未来研究需要关注的状态区域。     

Nonequilibrium processes in condensed media: Part 1. Experimental studies in light of nonlocal transport theory

Based on experimental research in shock loading of solid-state materials it is shown that among the important dynamic characteristics of the process, like spatial-temporal mass velocity profiles of shock waves, are the mass velocity variation, velocity defect, and structural instability threshold recorded in real time. Analysis of these characteristics depending on the strain rate, target thickness, and structural state of material demonstrates that conventional approaches of continuum mechanics fail to provide their adequate interpretation and simulation of shock wave processes. A new concept of shock wave processes in condensed media is proposed. The concept, being based on nonlocal nonequilibrium transport theory, allows describing the transition from elastic to hydrodynamic response of a medium depending on the loading rate and time. A nonstationary elastoplastic wave model is proposed for describing the relaxation of an elastic precursor and formation of a retarded plastic front during the wave propagation in a medium with regard to structural evolution. Analysis of the experimental data shows that the division of stresses and strains into elastic and plastic components is incorrect for shock loading.     

Use of the two-moment boundary condition in the problem of rarefied gas slip over a solid cylindrical surface

The slip velocity of a rarefied gas nonuniform in temperature and mass velocity is calculated for gas slip over the surface of a right circular cylinder. The calculation uses the two-moment boundary condition in an approximation linear in Knudsen number. Corrections to the slip velocity that are due to the interface curvature, volume temperature stresses, and nonuniform temperature distribution in the Knudsen layer are studied as func-tions of the accommodation coefficients in the first two moments of the distribution function. The Bhatnagar-Gross-Krook model of the Boltzmann kinetic equation is employed as the basic equation for the gas state.     

Non-invasive determination of shock wave pressure generated by optical breakdown

Shock waves generated by a laser-induced plasma were investigated using a pump-and-probe technique. Both 7-ns and 40-ps laser pulses at 1.06 m were employed to initiate breakdown in water. Two He-Ne laser beams were used as a velocity probe, allowing the accurate measurement of the shock velocity around the plasma. The maximum shock pressure was determined from the measured shock velocities, the jump condition and the equation of state for water. The conservation of the total momentum of the shock front was used to derive expressions for the shock velocity, particle velocity and shock pressure vs. the distance (r) from the center of the plasma. For a shock wave of spherical symmetry, the shock pressure is proportional to 1/r ². Our work shows that the expanding plasma initially induces a shock wave; the shock wave dissipates rapidly becoming an acoustic wave within 300–500 m.     

Brownian motion of massive skyrmions in magnetic thin films

We report on the thermal effects on the motion of current-driven massive magnetic skyrmions. The reduced equation for the motion of skyrmion has the form of a stochastic generalized Thiele’s equation. We propose an ansatz for the magnetization texture of a non-rigid single skyrmion that depends linearly with the velocity. By using this ansatz it is found that the skyrmion mass tensor is closely related to intrinsic skyrmion parameters, such as Gilbert damping, skyrmion-charge and dissipative force. We have found an exact expression for the average drift velocity as well as the mean-square velocity of the skyrmion. The longitudinal and transverse mobility of skyrmions for small spin-velocity of electrons is also determined and found to be independent of the skyrmion mass.     

Quantum‐Statistical Equation‐of‐State Models of Dense Plasmas: High‐Pressure Hugoniot Shock Adiabats

We present a detailed comparison of two self‐consistent equation‐of‐state models which differ from their electronic contribution: the atom in a spherical cell and the atom in a jellium of charges. It is shown that both models are well suited for the calculation of Hugoniot shock adiabats in the high pressure range (1 Mbar‐10 Gbar), and that the atom‐in‐a‐jellium model provides a better treatment of pressure ionization. Comparisons with experimental data are also presented. Shell effects on shock adiabats are reviewed in the light of these models. They lead to additional features not only in the variations of pressure versus density, but also in the variations of shock velocity versus particle velocity. Moreover, such effects are found to be responsible for enhancement of the electronic specific heat. (© 2007 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Analysis of the Intrinsic Uncertainties in the Laser-Driven Iron Hugoniot Experiment Based on the Measurement of Velocities

One of the most challenging tasks in the laser-driven Hugoniot experiment is how to increase the reproducibility and precision of the experimental data to meet the stringent requirement in validating equation of state models.In such cases,the contribution of intrinsic uncertainty becomes important and cannot be ignored.A detailed analysis of the intrinsic uncertainty of the aluminum-iron impedance-match experiment based on the measurement of velocities is presented.The influence of mirror-reflection approximation on the shocked pressure of Fe and intrinsic uncertainties from the equation of state uncertainty of standard material are quantified.Furthermore,the comparison of intrinsic uncertainties of four different experimental approaches is presented.It is shown that,compared with other approaches including the most widely used approach which relies on the measurements of the shock velocities of Al and Fe,the approach which relies on the measurement of the particle velocity of Al and the shock velocity of Fe has the smallest intrinsic uncertainty,which would promote such work to significantly improve the diagnostics precision in such an approach.     

三级炮加载技术在超高压状态方程研究中的应用

根据阻抗梯度飞片设计原则和超高速数值模拟技术设计出一种新的叠层波阻抗梯度飞片,并利用三级炮加载技术将Ta飞片加速至9 km/s以上,测量了Ta在超高压下的状态方程。三级炮实验实现了冲击波速度与粒子速度的同时测量,Ta的Hugoniot数据与文献中发表的数据具有很好的线性关系,说明三级炮加载技术适合于材料超高压状态方程研究。     

粘性物质中正激波稳定性分析

用线性稳定性理论,分析粘性物质中的正激波稳定性问题.粘性物质中任意强度的一维激波,其稳定性问题可归结为处理复数范围内的特征值问题,该特征值问题由两个一阶常微分方程及一个二阶常微分方程构成.这些常微分方程的系数依赖于流动的基本流场的物理量及其梯度.所获得的特征值问题由一个四阶精度的有限差分离散求解.分析考虑物质粘性的金属铝中的正激波稳定性,可以看出,正激波运动是稳定的,并且激波速度对波前和波后的小扰动量的衰减有相反的作用,而物质粘性有致稳的作用.     

Thermal diffusion shock waves

The Ludwig-Soret effect or thermal diffusion, which refers to the separation of liquid mixtures in a temperature gradient, is governed by a nonlinear, partial differential equation in space and time. It is shown here that the solution to the nonlinear differential equation for a binary mixture predicts the existence of shock waves completely analogous to fluid shocks and obeys an expression for the shock velocity that is an exact analogue of the Rankine-Hugoniot relations. Direct measurements of the time dependent, spatial absorption profile of a suspension of nanometer sized particles subjected to a sinusoidal temperature field generated by a pair of continuous laser beams, as well as self-diffraction experiments, show motion of the particles in agreement with the predictions of nonlinear theory.     

冲击波影响下的聚能射流侵彻扩孔方程

 当聚能射流侵彻速度大于靶板声速时,由于冲击波的产生导致波阵面后材料的状态参数发生改变,影响聚能射流的侵彻扩孔过程,致使波阵面前后不能直接应用伯努利方程求解。在考虑侵彻过程中冲击波影响的基础上,对射流轴向侵彻和径向扩孔的力学特性进行了分析,并对冲击波的传播和衰减进行了假设,着重探讨侵彻速度大于靶板声速时冲击波的影响。针对侵彻速度大于和小于靶板声速两种情况,建立了相应的侵彻模型,提出了一个新的聚能射流侵彻扩孔方程。将该方程与Szendrei-Held模型进行了比较,结果表明,新模型更符合Held等人的实验数据,冲击波对轴向侵彻的影响远小于对径向扩孔的影响。     

用于冲击诊断的成像速度干涉仪

为了诊断测量激光驱动冲击波,研制了具有空间分辨力的成像型速度干涉仪.该干涉仪主要包括输入部分、像传递部分及干涉部分,探测光采用波长为532 nm的单纵模激光.在靶位放置一分线板,经过测量,其空间分辨力小于10μm.基于天光KrF准分子激光系统的参数,设计并自制含有烧蚀层的单台阶金属靶,利用成像型速度干涉仪测量到了金属铝...     

Van der Waals状态方程可压缩多流体流动的PPM方法

基于流体体积分数的混合型多流体数值模型,将Piecewise Parabolic Method（PPM）方法应用于可压缩多流体流动的数值模拟,采用双波近似求解多流体van der Waals状态方程的Riemann问题．模拟高密度比且含有激波的可压缩多流体流动,典型的纯界面平移问题模拟结果表明,在接触间断的界面附近,压力和速度没有任何的振荡且界面数值耗散都被控制在2—3个网格之内;一维和二维算例表明,该数值方法可以有效地处理接触间断、激波和多维滑移线等物理问题,并能够比其它多流体数值方法更精细地模拟多流体交界面．