粘塑性靶板中冲击波的演化

讨论了粘塑性靶板中的一维应变波的传播规律。利用广义特征理论导出了应力波传播的特征线和特征关系。利用特征关系和冲击波阵面上的突跃条件，得出了冲击波在传播过程中的演化的规律，并以Ｂｏｄｎｅｒ－Ｐａｒｔｏｍ幂函数型粘塑性材料为例，计算和讨论了板中应力波传播规律的特点     

粘塑性变截面杆中冲击波的演化

讨论了粘塑性变截面杆中的一维应力波传播规律。在粘塑性本构理论框架的基础上,利用特征关系和冲击波阵面上的突跃条件,得出了冲击波在传播过程中的演化规律,包括其微分方程和解析表达式,并对Bodner和Johnson-Cook材料和不同收缩形式的杆中冲击波的演化规律进行了讨论,同时计算和讨论了杆中冲击波后方应力波传播规律的特点。     

On the energy conservation and critical velocities for the propagation of a ＂steady-shock＂ wave in a bar made of cellular material

The propagation of shock waves in a cellular bar is systematically studied in the framework of continuum solids by adopting two idealized material models, viz. the dynamic rigid, perfectly plastic, locking （D-R-PP-L） model and the dynamic rigid, linear hardening plastic, locking （D-R-LHP-L） model, both considering the effects of strain-rate on the material properties. The shock wave speed relevant to these two models is derived. Consider the case of a bar made of one of such material with initial length L 0 and initial velocity v i impinging onto a rigid target. The variations of the stress, strain, particle velocity, specific internal energy across the shock wave and the cease distance of shock wave are all determined analytically. In particular the ＂energy conservation condition＂ and the ＂kinematic existence condition＂ as proposed by Tan et al. （2005） is re-examined, showing that the ＂energy conservation condition＂ and the consequent ＂critical velocity＂, i.e. the shock can only be generated and sustained in R-PP-L bars when the impact velocity is above this critical velocity, is incorrect. Instead, with elastic deformation, strain-hardening and strain-rate sensitivity of the cellular materials being considered, it is appropriate to redefine a first and a second critical impact velocity for the existence and propagation of shock waves in cellular solids. Starting from the basic relations for shock wave propagating in D-R-LHP-L cellular materials, a new method for inversely determining the dynamic stress-strain curve for cellular materials is proposed. By using e.g. a combination of Taylor bar and Hopkinson pressure bar impact experimental technique, the dynamic stress-strain curve of aluminum foam could bedetermined. Finally, it is demonstrated that this new formulation of shock theory in this one-dimensional stress state can be generalized to shocks in a one-dimensional strain state, i.e. for the case of plate impact on cellular materials, by simply making proper replacements of the elastic and plastic constants.     

A simple physical theory of weak Mach reflection over plane surfaces

It is shown that simple physical principles coupled with the inviscid shock jump relations can be applied to the problem of weak Mach reflection to the extent that the triple point path can be predicted from the incident shock Mach number , gas specific heat ratio and the inclination angle of the reflecting surface to the shock normal. Comparison with the Euler code data and with experiments show close agreement for conditions both far and close to transition and that the general shape of the reflected and Mach stem shocks follow simple curves except in the neighbourhood of the triple point. The conflict at the triple point in matching the flow deflection angles and pressures across the contact discontinuity remains. It is shown however that the simple model presented here gives a close match to the cfd and experimental overall shock and contact surface shapes although it cannot predict these or the flow properties in any detail. Received 10 May 1999 / Accepted 17 December 1999     

Topology of elementary waves for mixed-type systems of conservation laws

We construct explicitly the fundamental wave manifold for systems of two conservation laws with quadratic flux functions. We describe the shock foliation for this manifold, as well as the singular set of the foliation. We subdivide the manifold into regions where the shock curves form trivial foliations. Sonic surfaces are identified as well. We establish the stability of shock curves underC ³ perturbations of the flux functions in the Whitney topology.In memoriam of Jean Martinet.     

Characteristics of an annular vertical diaphragmless shock tube

Abstract. This paper reports on the characteristics of a compact vertical diaphragmless shock tube, which was constructed and tested in the Shock Wave Research Center to study experimentally the behavior of toroidal shock waves. It is 1.15 m in height and has a self-sustained co-axial vertical structure consisting of a 100 mm i.d. outer tube and an 80 mm o.d. inner tube. To create a ring shaped shock wave between the inner and outer tubes, a rubber sheet is inserted to separate a high pressure driver gas from a test gas, which is bulged with auxiliary high pressure helium from the behind. When the rubber membrane is contracted by the sudden release of the auxiliary gas so as to break the seal, shock waves are formed. Special design features of the shock tube are described and their role in producing repeatable shock waves is discussed. Its special opening characteristics make possible the production of annular shaped shock waves that are unlikely met with a conventional tube that uses rupturing diaphragms. Performance of the shock tube is evaluated in terms of the shock wave Mach numbers and the measured flow properties. It eventually showed a higher degree of repeatability and the scatter in the shock wave Mach numbers Ms was found to be 0.2% for Ms ranging from 1.1 to 1.8. The shock wave Mach number so far measured agreed very well with the simple shock tube theory. Received 3 February 1999 / Accepted 6 April 2000     

The influence of single-pulse and tandem shock waves on bacteria

Tandem shock waves have shown to enhance kidney stone fragmentation during in vitro and in vivo extracorporeal shock wave lithotripsy (SWL). The purpose of this research was to study the influence of shock waves on the viability of two strains of bacteria in solution, and to verify if tandem shock waves increase microorganism death. A piezoelectric shock wave generator was modified to generate either standard (single-pulse) or tandem (dual-pulse) shock waves. E. coli and Listeria monocytogenes were exposed in vitro to thousands of standard shock waves. Another group was subjected to the same number of tandem shock waves with a delay of 450 μs. A third group was exposed to tandem shock waves having a 900-μs delay. No inactivation was observed for both microorganisms at up to 8,000 standard shock waves. About 40% of L. monocytogenes and 50% of E. coli were inactivated after treatment with tandem waves at a delay of 900 μs. Inactivation was less efficient for a delay of 400 μs. Our results could be useful in medicine, because infection stones are still a significant cause of morbidity and mortality after SWL. The use of tandem shock waves to treat persistent localized infections or as a novel non-thermal food-preservation method also might be possible.      

Shock wave propagation through a model one dimensional heterogeneous medium

We study the problem of impact-induced shock wave propagation through a model one-dimensional heterogeneous medium. This medium is made of a model material with spatially varying parameters such that it is heterogeneous to shock waves but homogeneous to elastic waves. Using the jump conditions and maximal dissipation criteria, we obtain the exact solution to the shock propagation problem. We use it to study how the nature of the heterogeneity changes material response, the structure of the shock front and the dissipation.     

Higher-order jump conditions for conservation laws

The hyperbolic conservation laws admit discontinuous solutions where the solution variables can have finite jumps in space and time. The jump conditions for conservation laws are expressed in terms of the speed of the discontinuity and the state variables on both sides. An example from the Gas Dynamics is the Rankine–Hugoniot conditions for the shock speed. Here, we provide an expression for the acceleration of the discontinuity in terms of the state variables and their spatial derivatives on both sides. We derive a jump condition for the shock acceleration. Using this general expression, we show how to obtain explicit shock acceleration formulas for nonlinear hyperbolic conservation laws. We start with the Burgers’ equation and check the derived formula with an analytical solution. We next derive formulas for the Shallow Water Equations and the Euler Equations of Gas Dynamics. We will verify our formulas for the Euler Equations using an exact solution for the spherically symmetric blast wave problem. In addition, we discuss the potential use of these formulas for the implementation of shock fitting methods.     

The formation of a secondary shock wave behind a shock wave diffracting at a convex corner

This paper deals with the formation of a secondary shock wave behind the shock wave diffracting at a two-dimensional convex corner for incident shock Mach numbers ranging from 1.03 to 1.74 in air. Experiments were carried out using a 60 mm 150 mm shock tube equipped with holographic interferometry. The threshold incident shock wave Mach number () at which a secondary shock wave appeared was found to be = 1.32 at an 81° corner and = 1.33 at a 120° corner. These secondary shock waves are formed due to the existence of a locally supersonic flow behind the diffracting shock wave. Behind the diffracting shock wave, the subsonic flow is accelerated and eventually becomes locally supersonic. A simple unsteady flow analysis revealed that for gases with specific heats ratio the threshold shock wave Mach number was = 1.346. When the value of is less than this, the vortex is formed at the corner without any discontinuous waves accompanying above the slip line. The viscosity was found to be less effective on the threshold of the secondary shock wave, although it attenuated the pressure jump at the secondary shock wave. This is well understood by the consideration of the effect of the wall friction in one-dimensional duct flows. In order to interpret the experimental results a numerical simulation using a shock adaptive unstructured grid Eulerian solver was also carried out. Received 1 May 1996 / Accepted 12 September 1996     

Weak shock waves in isotropic solids at finite temperatures up to the melting point

Propagation speeds and Rankine–Hugoniot relations for weak shock waves in isotropic solids are derived analytically in order to elucidate mechanical and thermal properties of the waves. In the analysis, we adopt a new continuum model for the solids, which takes into account explicitly microscopic thermal vibration of the constituent atoms. As the model is valid in a wide temperature range up to the melting point, we can discuss the relations at high temperatures even near the melting point. Typical numerical results are also shown and discussed as illustrations.      

Nonlinear wave propagation in binary mixtures of Euler fluids

In the present paper, we study the propagation of acceleration and shock waves in a binary mixture of ideal Euler fluids, assuming that the difference between the atomic masses of the constituents is negligible. We evaluate the characteristic speeds, proving that they can be separated into two groups: one is related to the case of a single Euler fluid, provided that an average ratio of specific heats is introduced; the other is new and related to the propagation speed due to diffusion. We evaluate the critical time for sound acceleration waves and compare its value to that of a single fluid. We then study shock waves, showing that three types of shock waves appear: sonic and contact shocks, which have counterparts in the single fluid case, and the diffusive shock, which is peculiar to the mixture. We discuss the admissibility of the shock waves using the Lax-Liu conditions and the entropy growth criterion. It is proved that the sonic and the characteristic shock obey the same properties as in the single fluid case, while for the diffusive shock there exists a locally exceptional case that is determined by a particular value of the concentration of the constituents, for which the genuine nonlinearity is lost and no shocks are admissible. For other values of the unperturbed concentration, the diffusive shock is stable in a bounded interval of admissibility.Received: 15 December 2002, Accepted: 28 June 2003 Correspondence to: T. RuggeriS. Simi: On leave from the Department of Mechanics, Faculty of Technical Sciences, University of Novi Sad, Serbia     

Lagrangian description of transport equations for shock waves in three-dimensional elastic solids

A set of transport equations for the growth or decay of theamplitudes of shock waves along an arbitrary propagation directionin three-dimensional nonlinear elastic solids is derived using theLagrangian coordinates.The transport equations obtained showthat the time derivative of the amplitude of a shock wave alongany propagation ray depends on (i) an unknown quantity immediatelybehind the shock wave,(ii) the two principal curvatures of theshock surface,(iii) the gradient taken on the shock surface ofthe normal shock wave speed and (iv) the inhomogeneous term.whichis related to the motion ahead of the shock surface.vanisheswhen the motion ahead of the shock surface is uniform.Severalchoices of the propagation vector are given for which the tran-sport equations can be simplified.Some universal relations,which relate the time derivatives of various jump quantities toeach other but which do not depend on the constitutive equationsof the material,are also presented.     

A high‐resolution scheme for compressible multicomponent flows with shock waves

A simple methodology for a high‐resolution scheme to be applied to compressible multicomponent flows with shock waves is investigated. The method is intended for use with direct numerical simulation or large eddy simulation of compressible multicomponent flows. The method dynamically adds non‐linear artificial diffusivity locally in space to capture different types of discontinuities such as a shock wave, contact surface or material interface while a high‐order compact differencing scheme resolves a broad range of scales in flows. The method is successfully applied to several one‐dimensional and two‐dimensional compressible multicomponent flow problems with shock waves. The results are in good agreement with experiments and earlier computations qualitatively and quantitatively. The method captures unsteady shock and material discontinuities without significant spurious oscillations if initial start‐up errors are properly avoided. Comparisons between the present numerical scheme and high‐order weighted essentially non‐oscillatory (WENO) schemes illustrate the advantage of the present method for resolving a broad range of scales of turbulence while capturing shock waves and material interfaces. Also the present method is expected to require less computational cost than popular high‐order upwind‐biased schemes such as WENO schemes. The mass conservation for each species is satisfied due to the strong conservation form of governing equations employed in the method. Copyright © 2010 John Wiley & Sons, Ltd.     

脉冲辐照下三维多向碳纤维编织复合材料热激波的实验研究

在“闪光二号”脉冲电子束加速器上,采用自行研制的保护环式石英压电传感器,对三维多向碳纤维编织复合材料的热激波传播特性开展了实验研究。结果表明: (1)在电子束能注量为382J/cm2 ~953J/cm2范围内,三维编织复合材料的热激波应力峰值在 97~406MPa之间,只是相同能注量下Ly-12铝的 8%左右,这表明该材料具有良好的衰减热激波的性能; (2)三维编织复合材料中的热激波,其波速较低(大约为 2. 78~3. 45km/s),只是Ly-12铝的 0. 4倍左右,其波形上升时间也比Ly-12铝的大; (3)热激波强度和能注量间近似有线性关系,但烧蚀质量却随能注量增加而增加,当能注量足够高时,质量亏损面密度几乎以指数方式增加。     

关于具有激波的流动的稳定性

<正> 1、引言 流体运动总是同时受动力学和热力学规律的约制,通常处理流动问题时这两方面的考虑也总是交织在一起,例如,为了定义描述流动现象的诸流动变量,首先要假定每个流体质点微团是处于热力学平衡态,即假定流动系统满足“局域热平衡”条件。这样才可以定义各“点”的压力、密度、熵等变量。由于流动系统同时又是一个热力学系统,因此它的     

Shock conditions for hypoelastic materials

The equations governing the motion of hypoelastic materials (and related models of non-Newtonian fluids) are not in conservation form. Hence there is no obvious formulation of Rankine-Hugoniot jump conditions across a shock. In this paper we demonstrate that a viscosity criterion can be used to obtain meaningful shock conditions. In particular, we discuss shocks of small amplitude. The shock conditions obtained will in general depend on the form of the viscosity term.Michael Renardy's research was supported by the National Science Foundation under Grant DMS-9008497.     

Repeated application of shock waves as a possible method for food preservation

In order to study the possibility of using underwater shock waves to cause death in non desired microorganisms found in certain foods, Escherichia coli in suspension was exposed to hundreds of shock waves on an experimental electrohydraulic shock wave generator. Using a parabolic reflector it was possible to produce a plane shock front and expose many test tubes to the action of the shock waves at the same time and under the same conditions. The amount of surviving bacteria was determined by plate counting for different numbers of applied shock waves. Pressure measurements using needle hydrophones are also reported. Experimental results indicate that electrohydraulically generated shock waves are capable of producing a significant reduction in an E. coli population. An increase in the applied shock wave number produced a nearly exponential reduction in the E. coli population. Received 8 April 1998 / Accepted 17 September 1998     

铅飞层中斜冲击波对碰马赫反射行为实验研究

采用线阵多普勒光纤探针测速技术(Doppler pins system,DPS)和高速光电分幅相机照相两种精密诊断技术,对铅飞层中斜冲击波对碰后的反射行为进行了观测。获得了飞层对碰部位速度-时间历史曲线和凸起形貌演化图像,给出了凸起轮廓发展演化过程、压力分布等实验数据和信息。结合冲击波反射理论,对铅飞层对碰区动力学现象进行了分析和解释,证实铅飞层中斜冲击波对碰后发生了马赫反射。     

An Approximate Roe-Type Riemann Solver for a Class of Realizable Second Order Closures

A realizable, objective second-moment turbulence closure, allowing for an entropy characterisation, is analyzed with respect to its convective subset. The distinct characteristic wave system of these equations in non-conservation form is exposed. An approximate solution to Ihe associated one-dimensional Riemann problem is constructed making use of approximate jump conditions obtained by assuming a linear path across shock waves. A numerical integration method based on a new approximate Riemann solver (flux-difference-splitting) is proposed for use in conjunction with either unstructured or structured grids. Test calculations of quasi one-dimensional flow cases demonstrate the feasibility of the current technique even where Euler-based approaches fail.