Stability and ambiguous representation of shock wave discontinuity in thermodynamically nonideal media

The nonlinear analysis of the behavior of a shock wave on a Hugoniot curve fragment that allows for the ambiguous representation of shock wave discontinuity has been performed. The fragment under consideration includes a section where the condition L > 1 + 2M is satisfied, which is a linear criterion of the instability of the shock wave in media with an arbitrary equation of state. The calculations in the model of a viscous heat-conductive gas show that solutions with an instable shock wave are not implemented. In the one-dimensional model, the shock wave decays into two shock waves or a shock wave and a rarefaction wave, which propagate in opposite directions, or can remain in the initial state. The choice of the solution depends on the parameters of the shock wave (position on the Hugoniot curve), as well as on the form and intensity of its perturbation. In the two-dimensional and three-dimensional calculations with a periodic perturbation of the shock wave, a “cellular” structure is formed on the shock front with a finite amplitude of perturbations that does not decrease and increase in time. Such behavior of the shock wave is attributed to the appearance of the triple configurations in the inclined sections of the perturbed shock wave, which interact with each other in the process of propagation along its front.     

单晶铜中冲击波阵面结构的数值模拟研究

 用分子动力学方法模拟计算了在初始温度为0 K时单晶铜中的冲击波结构，相互作用势采用铜的嵌入原子势（EAM），模拟计算结果表明即使是在初始温度为0 K的FCC晶体中，冲击波波阵面后的区域也会向平衡态演化。局域分析表明冲击波阵面后区域的压力、粒子速度、应变和温度随时间逐步变化到稳定态，在所研究的冲击波强度（约262 GPa）下，波后区域的平均压力、粒子速度、应变均在约1 ps内逐渐上升并达到稳定值。动能温度在波阵面处始终为最大值，随着冲击波的传播，波后非零温度区域逐渐扩大，不同时刻的粒子速度分布函数说明波后区域逐渐向热力学平衡态演化，并最终达到热力学平衡，进一步的分析说明局域平衡是系统向平衡态演化的基本过程。     

Interaction between a composite compression wave and a vortex in a thermodynamically nonideal medium

A numerical analysis is presented of two-dimensional interaction between a transverse vortex and a composite compression wave that can exist in a thermodynamically nonideal medium. It is shown that the interaction of a composite wave involving a “neutrally stable” shock with a vortex generates weakly damped outgoing acoustic waves; i.e., the shock is a source of sound. This phenomenon increases the post-shock acoustic noise level in an initially turbulent flow.     

On the Structure Stability of a Neutrally Stable Shock Wave in a Gas and on Spontaneous Emission of Perturbations

Journal of Experimental and Theoretical Physics - We analyze the stability of the structure of a neutrally stable shock wave, which is also referred to as a spontaneously emitting shock wave. We...     

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.     

Dissipative Instability of Shock Waves

A new condition is obtained for the linear instability of a plane front of an intense shock wave in an arbitrary medium, which is determined by the finiteness of the viscosity. It is shown that the shock front instability occurs due to dissipative instability of the flow behind the front, which is analogous to the flow instability in the boundary layer. It is found that in the low-viscosity limit, one-dimensional longitudinal perturbations increase much faster than two-dimensional (corrugation) perturbations. The results are compared with the available data of experimental observation and numerical simulation of instability of shock waves. The comparison shows a better agreement between the new absolute shock instability as compared to the condition of such instability in the classical D’yakov theory disregarding viscosity.     

Restless rays, steady wave fronts

Observations of underwater acoustic fields with vertical line arrays and numerical simulations of long-range sound propagation in an ocean perturbed by internal gravity waves indicate that acoustic wave fronts are much more stable than the rays comprising these wave fronts. This paper provides a theoretical explanation of the phenomenon of wave front stability in a medium with weak sound-speed perturbations. It is shown analytically that at propagation ranges that are large compared to the correlation length of the sound-speed perturbations but smaller than ranges at which ray chaos develops, end points of rays launched from a point source and having a given travel time are scattered primarily along the wave front corresponding to the same travel time in the unperturbed environment. The ratio of root mean square displacements of the ray end points along and across the unperturbed wave front increases with range as the ratio of ray length to correlation length of environmental perturbations. An intuitive physical explanation of the theoretical results is proposed. The relative stability of wave fronts compared to rays is shown to follow from Fermat's principle and dimensional considerations.     

磁化尘埃等离子体中的冲击波及其横向扰动稳定性

利用双曲函数法得到ZKB方程的一组冲击波解,并对波在横向扰动下的动力学稳定性进行研究.对冲击波解进行线性稳定性分析,并构造高精度的有限差分格式求解所得本征值问题.结果表明：对于正耗散的情形,该冲击波在线性意义下稳定;对于负耗散情形,该冲击波在线性意义下不稳定.构造有限差分格式对受扰动的冲击波进行非线性动力学演化,结果表明：对于正耗散的情况,该冲击波是稳定的.     

Reverse undercompressive shock structures in driven thin film flow

We show experimental and computational evidence of a new structure: an undercompressive and reverse undercompressive shock for draining films driven by a surface tension gradient against gravity. The reverse undercompressive shock is unstable to transverse perturbations while the leading undercompressive shock is stable. Depending on the pinch-off film thickness, as controlled by the meniscus, either a trailing rarefaction wave or a compressive shock separates from the reverse undercompressive shock.     

Additive noise induces front propagation

The effect of additive noise on a static front that connects a stable homogeneous state with an also stable but spatially periodic state is studied. Numerical simulations show that noise induces front propagation. The conversion of random fluctuations into direct motion of the front's core is responsible of the propagation; noise prefers to create or remove a bump, because the necessary perturbations to nucleate or destroy a bump are different. From a prototype model with noise, we deduce an adequate equation for the front's core. An analytical expression for the front velocity is deduced, which is in good agreement with numerical simulations.     

凝聚炸药爆轰波在高声速材料界面上的折射现象分析

凝聚炸药爆轰在边界高声速材料约束下传播时,爆轰波会在约束材料界面上产生复杂的折射现象.本文针对凝聚炸药爆轰波在高声速材料界面上的折射现象展开理论和数值模拟分析.首先通过建立在爆轰ZND模型上的改进爆轰波极曲线理论给出爆轰波折射类型,然后发展一种求解爆轰反应流动方程的基于特征理论的二阶单元中心型Lagrange计算方法来数值模拟典型的爆轰波折射过程.从改进爆轰波极曲线理论和二阶Lagrange方法数值模拟给出的结果看出,凝聚炸药爆轰波在高声速材料界面上的折射类型有四种:反射冲击波的正规折射、带束缚前驱波的非正规折射、带双Mach反射的非正规折射、带λ波结构的非正规折射.     

Shock wave chemistry

Abstract

Shock wave chemistry, a new scientific trend, deals with investigations of chemical aspects of the substance state under this new type of effect. Indeed, shock wave effect is not a greater imposition than pressure and temperature actions. Characteristic features of the effect are the tremendous rates of substance loading and subsequent unloading. The effects result in a substance in a strongly non- equilibrium state. The lifetime of the state is governed by the relaxation process of those phenomena which are provoked by shock waves in the substance. For instance, in the case of substance consisting of complex molecules with a large number of internal degrees of freedom, differing strongly in excitation times, all kinetic parts of the shock energy are at first absorbed by the translational degrees of freedom inside the shock wave front. Then, the energy is redistributed to the vibrational degrees of freedom. The non-equilibrium state time is not longer than the excitation time of the most slowly excited vibrational degrees of freedom (10¹⁰-10^?9 s). The same order of magnitude is the relaxation time of liquid substance polarization caused by dipolar molecules mechanically turning under the shock discontinuity zone effect. In polymers the zone turns some separate groups of polymer molecule atoms. In such a case the relaxation period, on the contrary, may last as long as it can. As far as “hot are concerned, their lifetime is determined by thermal relaxation regularities and it depends on their size. The hot spots in solids appear during the shock compression process at the sites of an imperfect substance structure. In liquids the hot spots can orighate when a shock wave front passes through negative density fluctuations. It transforms the fluctuations of very small size and of high probability into some positive temperature regions of large size and extremely low probability at equilibrium state behind the wave front. The hot spots in perfect solids (possibly in liquids too) appear due to the effect of shear stresses in shock front. Pointed and lengthy defects of solid structure occur under the effect. The lengthy defects appear in the shock wave front due to the transition from one-dimensional to volume compression. The transition takes place if the wave intensity is larger than the dynamic elastic limit of the solid under investigation. In brittle materials the transition results in their grinding into fragments and in the relative displacement of the fragments. Some liquid melted layers of substance appear between the fragments in the process of displacement. Their lifetime is also determined by the thermal relaxation regularities and probably is small. Nevertheless, the layers obviously govern the spall strength of brittle solids and promote solid-phase shock reactions. The defects created in solids by the shock effect can exist for a very long time if the solid substance residual temperature is lower than its recrystallization temperature. Therefore, solid substance treatment by shocks of proper intensity can increase their chemical reactivity.     

Cell-like structure of unstable oblique detonation wave from high-resolution numerical simulation

A comprehensive numerical study was carried out to investigate the unsteady cell-like structures of oblique detonation waves (ODWs) for a fixed Mach 7 inlet flow over a wedge of 30° turning angle. The effects of grid resolution and activation energy were examined systematically at a dimensionless heat addition of 10. The ODW front remains stable for a low activation energy regardless of grid resolution, but becomes unstable for a high activation energy featuring a cell-like wave front structure. Similar to the situation with an ordinary normal detonation wave (NDW), a continuous increase in the activation energy eventually causes the wave-front oscillation to transit from a regular to an irregular pattern. The wave structure of an unstable ODW, however, differs considerably from that of a NDW. Under the present flow condition, triple points and transverse waves propagate downstream, and the numerical smoke-foil record exhibits traces of triple points that rarely intersect with each other. Several instability-driving mechanisms were conjectured from the highly refined results. Since the reaction front behind a shock wave can be easily destabilized by disturbance inherent in the flowfield, the ODW front becomes unstable and displays cell-like structures due to the local pressure oscillations and/or the reflected shock waves originating from the triple points. The combined effects of various instability sources give rise to a highly unstable and complex flow structure behind an unstable ODW front.     

Measurement of density, temperature, and electrical conductivity of a shock-compressed nonideal nitrogen plasma in the megabar pressure range

Kinematic and thermodynamic parameters of shock-compressed liquid nitrogen are measured behind the front of a plane shock wave using plane wave and hemispherical shock wave generators. In these experiments, high values of compression parameters (shock-compressed hydrogen density? ≈ 3.25 g/cm³ and temperature T≈ 56000 K at a pressure of P ≈ 265 GPa) are attained. The density, pressure, temperature, and electrical conductivity of the nonideal plasma of shock-compressed liquid nitrogen are measured. A nearly isochoric behavior of the nitrogen shock adiabat is observed in the pressure range P = 100–300 GPa. The thermodynamics of shock-compressed nitrogen is an alyzed using the model of the equation of state in the quasi-chemical representation (SAHA code) as well as the semiempirical wide-range equation of state developed at the Institute of Experimental Physics. Experimental results are interpreted on the basis of calculations as the fixation of the boundary of transition of shock-compressed nitrogen from the polymer phase to the state of a strongly nonideal plasma at P ≈ 100 GPa, ? ≈ 3.4 g/cm³.     

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。     

Excitable front geometry in reaction-diffusion systems with anomalous dispersion

Two-dimensional excitable systems with anomalous dispersion provide a discrete set of interpulse distances for the stable propagation of planar wave trains. Numerical simulations show that the trailing front of a pulse pair can undergo transitions between these stable distances. In response to localized perturbations, the trailing front converges towards one of numerous, sigmoidal shapes. Their transition segments move at constant speeds and can collide and fuse with each other. A complementing kinematic analysis of the front dynamics yields a reaction-diffusion-like equation.     

Nonlinear thermomagnetic waves in the resistive state of superconductors

The evolution of thermomagnetic perturbations in the resistive state of superconductors is considered. A qualitative pattern of the formation and further development of nonlinear stationary structures that describe the final stage of thermal and electromagnetic perturbations in a superconductor is investigated. The wave propagation velocity and the wave front width in a superconductor are estimated.     

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.     

界面追踪方法中的激波限制器研究

针对多介质流体界面追踪(Front Tracking)方法,通过在界面处构造Riemann问题,研究激波限制器应用过程中的若干基本问题.针对气-气和气-水界面问题,通过比较平均守恒误差、L₁误差和激波强度随参数的变化情况,给出激波限制器参数可以在0.3附近选取.同时,通过理论分析和数值算例发现,当有激波接近界面时,选择激波波后状态作为界面处Riemann问题的初始状态,数值模拟结果较满意.