GENERAL SOLUTION FOR INTERACTION OF SOLITARY WAVES INCLUDING HEAD-ON COLLISIONS

A general solution of the Boussinesq equation is presented which solves the problem of interaction of any number of right-going and left-going solitary waves.The solution relies on the exact solu- tion of Gardner,Greene,Kruskal,and Miura(1967),and has the same degree of accuracy as that solution, but has a wider scope of application.It is much simpler than,but as accurate as,Hirota's exact solu- tion(1973)of the Boussinesq equation,to which the present solution is compared for the simplest case of two solitary waves in head-on collision.

ON HEAD-ON COLLISION BETWEEN TWO GKDV SOLITARY WAVES IN A STRATIFIED FLUID

In this paper,using the reductive perturbation method combined with the PLK method and two-parameter expansions,we treat the problem of head-on collision between two solitary waves described by the generalized Korteweg-de Vries equation (the gKdV equation) and obtain its second-order approximate solution.The results show that after the collision,the gKdV solitary waves preserve their profiles and during the collision,the maximum amplitute is the linear superposition of two maximum amplitudes of the impinging solitary waves.

HEAD-ON COLLISION BETWEEN TWO mKdV SOLITARY WAVES IN A TWO-LAYER FLUID SYSTEM

In this paper, based on the equations presented in [2], the head-on collision between two solitary waves described by the modified KdV equation (the mKdVequation, for short) is investigated by using the reductive perturbation method combined with the PLK method. These waves propagate at the interface of a two-fluid system, in which the density ratio of the two fluids equals the square of the depth ratio of the fluids. The second order perturbation solution is obtained. It is found that in the case of disregarding the nonuniform phase shift, the solitary waves preserve their original profiles after collision, which agrees with Fornberg and Whitham's numerical result of overtaking collision[6] whereas after considering the nonuniform phase shift, the wave profiles may deform after collision.

Head-on collision between two hydroelastic solitary waves with Plotnikov-Toland's plate model

Head-on collision between two hydroelastic solitary waves propagating at the surface of an incompressible and ideal fluid covered by a thin ice sheet is analytically studied by means of a singular perturbation method. The ice sheet is represented by the Plotnikov-Toland model with the help of the special Cosserat theory of hyperelastic shells and the Kirchhoff-Love plate theory,which yields the nonlinear and conservative expression for the bending forces. The shallow water assumption is taken for the fluid motion with the Boussinesq approximation. The resulting governing equations are solved asymptotically with the aid of the Poincaré-Lighthill-Kuo method,and the solutions up to the third order are explicitly presented. It is observed that solitary waves after collision do not change their shapes and amplitudes. The wave profile is symmetric before collision, and it becomes, after collision, unsymmetric and titled backward in the direction of wave propagation. The wave profile significantly reduces due to greater impacts of elastic plate and surface tension. A graphical comparison is presented with published results, and the graphical comparison between linear and nonlinear elastic plate models is also shown as a special case of our study.

Fracture mechanism of a cylindrical shell cut by circumferential detonation collision

The failure mechanism of a cylindrical shell cut into fragments by circumferential detonation collision was experimentally and numerically investigated.A self-designed detonation wave regulator was used to control the detonation and cut the shell.It was found that the self-designed regulator controlled the fragment shape.The macrostructure and micro-characteristics of fragments revealed that shear fracture was a prior mechanism,the shell fractured not only at the position of detonation collision,but the crack also penetrated the shell at the first contact position of the Chapmen-Jouguet(C-J)wave.The effects of groove number and outer layer thickness on the fracture behavior were tested by simulations.When the thickness of the outer layer was 5e18 mm,it has little effect on fragmentation of the shell,and shells all fractured at similar positions.The increase of the groove number reduced the fracture possibility of the first contact position of the C-J wave.When the groove number reached 7 with a 10 mm outer layer(1/4 model),the fracture only occurred at the position of detonation collision and the fragment width rebounded.

Modeling of nonlinear envelope solitons in strongly coupled dusty plasmas:Instability and collision

Modeling of instability and collision of nonlinear dust-acoustic（NDA） envelope solitons in strongly coupled dusty plasmas（SCDPs） is theoretically investigated. The SCDPs consists of strongly correlated negatively variable-charged dust grains and weakly correlated Boltzmann electrons and ions. Using the derivative expansion perturbation technique, a nonlinear Schr dinger-type（NLST） equation for describing the propagation of NDA envelope solitons is derived. Moreover,the extended Poincar′e–Lighthill–Kuo（EPLK） method is employed to deduce the analytical phase shifts and the trajectories after the collision of NDA envelope solitons. In detail, the results show that both modulation instability and phase shift after collision of NDA envelope solitons will modify with the increase in the effects of the viscosity, the relaxation time, and the dust charge fluctuation. Crucially, the modeling of dust-acoustic envelope solitons collision, as reported here, is helpful for understanding the propagation of NDA envelope solitons in strongly coupled dusty plasmas.

Nonreciprocal Head-on Collision Between Two Nonlinear Solitary Waves in Granular Metamaterials with an Interface

In this work,the head-on collision and transmission with nonreciprocal properties of opposite propagating solitary waves are studied,in which the interface between different granular chains is considered.Due to the discontinuity of two periodic granular systems,the transmitted and reflected solitary waves are produced.The head-on collision appears at the interface and the reductive perturbation method is applied to derive the generated solitary waves.According to the derivation and numerical simulation,we can find that the transmitted and reflected solitary waves can propagate with the same speed when they locate at the same chain.Moreover,the influences of both the arrangement and prestress are discussed.It is found that the amplitude and velocity of solitary waves become larger because of a bigger prestress,which result in the nonreciprocal collision and transmission in the granular mechanical metamaterials.This study is expected to be helpful for the design and application of elastic wave metamaterials and mechanical diodes with nonlinear solitary waves.

起爆方式对爆轰波传播特性的影响研究

为探究爆轰波碰撞对爆轰压力分布规律的影响,采用理论推导、数值模拟和现场试验相结合的方法,分析了不同起爆方式下炸药内部和外部爆轰压力的变化规律。研究结果表明:爆轰波发生碰撞后,依次产生正碰撞、斜碰撞及马赫反射现象,最大爆轰压力可达到稳定爆轰压力的3倍以上;采用对称双线性起爆方式时,土体聚能侧所受爆轰压力是起爆侧的2.74倍,轴向所受爆轰压力较单侧线性起爆方式提升了75%。基坑爆破试验结果表明:采用对称双线性起爆方式时,沿爆轰波碰撞聚能方向呈一字型布置起爆,炮孔间的贯通效果相较于单侧线性起爆方式得到了明显提升。

连续旋转爆震波传播过程研究(Ⅱ):双波对撞传播模式

在喷孔-喷孔和环缝-喷孔对撞式喷注模型发动机上,采用H2/O2热射流切向喷注的起爆方式进行了H2/air组合的连续旋转爆震试验,根据高频压力测量和高速摄影观测结果对爆震波传播过程进行了分析。试验发现了短暂的和可长时间维持的双波对撞传播现象,在该传播模式下燃烧室内存在两个爆震波头,但传播方向相反,周期性发生对撞,其高频压力振荡特征跟测压点距对撞点的夹角相关。初步分析了双波对撞传播过程的形成机制,认为在爆震波顶部能否形成混合气体层是实现该传播模式的关键。

爆轰波对碰驱动下平面铅飞层对碰区动载行为实验研究

采用高速光学照相和脉冲X光照相技术,对滑移爆轰波对碰驱动下平面铅飞层对碰区的动载行为进行了实验研究。实验结果显示,在爆轰波对碰区铅飞层出现了类似射流状超前凸起的现象,对碰区凸起呈现出速度和密度有明显差别的多层分区结构。凸起头部速度较高,运动过程中因自身的速度梯度及与周围空气的相互作用,呈现出明显的散碎、雾化特征,体密度远低于初始密度。凸起根部速度相对较低、密度较高,但随时间的推移仍迅速转变为非密实状态。对碰爆轰波的波剖面结构,以及材料的强度和冲击熔化可能是主导对碰区动载行为的主要因素。

变壁厚药型罩对爆轰波对撞EFP成型影响的数值模拟研究

基于线性装药结构,在两端面顶部棱线中点同时起爆方式下,相向而行的爆轰波在装药对称面发生对撞,产生更高的爆轰压力作用于中部的药型罩上,使药型罩中形成有利于沿中线闭合的速度梯度,最终形成高速EFP。利用非线性动力学分析软件AUTODYN-3D,设计中间厚两边薄的变壁厚药型罩,边缘壁厚为0.5 mm、罩顶壁厚在1.4~2.4 mm内的6种结构,研究其EFP成型状态和各项性能参数,通过对比分析得出罩顶壁厚在1.6~2.0 mm之间侵彻体成型效果好,侵彻能力强。从而对新型高效毁伤战斗部的设计提供指导意义。

爆轰波对碰驱动下加环紫铜圆管对碰区变形特性研究

针对爆轰波对碰驱动下金属圆管对碰区易出现过早断裂的问题,以加环紫铜(T2)圆管作为研究对象,利用高速分幅摄影、脉冲X光照相、VISAR三种测试技术,对其在爆轰波对碰驱动下的变形及破坏过程进行了观测。实验结果显示:在紫铜圆管对碰部位增加保护环结构,可以有效推迟该部位圆管的破裂时间。但同时也发现:加保护环后圆管对碰区会出现射流状超前突起现象。由高速摄影结果与X光照相结果对比分析证实:射流状超前突起物质为圆管表面微喷颗粒与空气冲击波混合形成的雾状结构。另外,采用DYNA3D程序对实验模型进行了模拟,计算结果与实验结果符合较好。最后,利用DYNA3D程序就保护环倒角变化对金属圆管对碰区壳体破裂的影响特征进行了初步分析。

激波与爆轰波对撞的数值模拟研究

采用二阶精度NND差分格式和改进的二阶段化学反应模型模拟了爆轰波与激波的对撞过程,研究了不同强度入射激波对爆轰过渡区域的影响.当对撞激波较弱时,透射爆轰波演变主要受流动膨胀作用的影响,可划分为对撞影响区、爆轰恢复区和稳定发展区3个阶段,在爆轰恢复区和稳定发展区,前导激波压力经历一个过冲、然后向稳定爆轰过渡的过程,表现了爆轰波熄爆和再起爆的物理特征,当对撞激波较强时,可燃混合气体的高热力学参数导致了更高的化学反应活化程度,形成了弱爆轰向稳定爆轰的直接转变.

两点起爆双槽聚能装药的模拟及实验研究

为了研究双槽聚能装药结构中采用两点起爆方式对聚能射流的影响,运用数值仿真及实验论证相结合的方法,进行了两点起爆下聚能射流的形成及侵彻研究。模拟结果表明:LS-DYNA 2D有限元软件可以较好模拟出一点和两点起爆爆轰波波形、爆轰波的碰撞、聚能射流的形成,验证了爆轰波碰撞引起爆轰压力的大幅增大,两点起爆形成聚能射流速度和长度均大于一点起爆。实验结果证明在工业炸药双槽聚能装药中采用两点起爆方式能起到增强爆轰强度、增大聚能射流侵彻能力的效果。

激波绕射碰撞加速诱导爆轰的数值模拟

基于单步化学反应的Euler方程和对激波(爆轰波)、接触间断具有良好捕捉效果的Roe/HLL混合格式以及自适应网格技术,模拟了激波在方形管中与方块障碍物相互作用,并发生绕射碰撞来诱导爆轰的过程。结果表明,弱激波在绕经方块时,形成上、下绕射激波并在方块尾部发生碰撞,生成局部高温高压点,可加快爆轰的形成;而当管内阻塞比超过一定值时,由于碰撞激波太弱则不能触发爆轰。

双波对撞模态下的液态燃料旋转爆轰发动机推力测试研究

在环形阵列式连续旋转爆轰发动机上,以汽油/富氧空气为工质,分析了双波对撞模态下爆轰波自持的传播特征、时域频域特征和爆轰波高度,测量了发动机模型在双波对撞模态下的一维推力。试验结果表明:在富氧空气(34.3%O_2和65.7%N_2)流量为945.3 g/s、汽油流量为84.3 g/s、当量比为0.82的工况下,爆轰波平均传播频率为2.174 k Hz,平均传播速度为1 051 m/s,爆轰波高度在55~70 mm之间,有效推力为607.3 N,单位面积推力8.587×104N/m2,燃料比冲为735.1 s.推力曲线表明:双波对撞模态下发动机推力波动较大,推力围绕推力平均值振荡,稳定工作阶段发动机振动频率与爆轰波传播频率基本一致。

多模LEFP成型机理与侵彻威力研究

为研究多模3种毁伤元的成型特点和侵彻威力,建立了多点起爆LEFP数值模拟模型,用LS-DYNA软件模拟了一端起爆、中心起爆和两端同时起爆3种起爆方式下LEFP成型过程。利用威力试验,测试了3种起爆方式下靶板的切口形态和侵彻深度,讨论了3种毁伤元在不同炸高下侵彻能力的差异。数值模拟结果表明,一端和中心起爆侵彻体呈线性,在大炸高下易飞散;两端同时起爆时,根据爆轰波对撞理论,两个爆轰波对撞产生超压,形成高速侵彻体,在大炸高下仍具有较强的毁伤威力。同时根据3种基本毁伤元成型特点,可在装药上设置多个起爆点,通过控制起爆点数量、位置和时序形成不同数量、速度和飞散方向的高速EFP毁伤元。实验结果表明,侵彻深度符合数值模拟的侵彻体形成规律。

连续旋转爆震波传播模态试验

通过保持空气流量不变、改变H2／air当量比开展了连续旋转爆震对比试验，发现随当量比的降低出现三种传播模态：在较高的当量比（0．90～1．86）下，连续旋转爆震波以同向传播模态传播；在较低的当量比（≈0．75）下，则以双波对撞模态传播；在中间工况，则以上述混合模态维持传播。分析了不同传播模态下的高频压力特征，并初步分析了传播模态的转换机制：当量比较高时，爆震强度较高，传播过程中的损失和速度亏损相对较小，爆震波以同向传播模态维持传播；当量比较低时，爆震强度较低，传播过程中的损失和速度亏损较大，此时无法维持同向传播模态，而以双波对撞模态传播，这是由于双波对撞模态中的激波对撞产生高温环境，有利于燃烧放热，其可能是连续旋转爆震的极限传播模态。

两端起爆下曲率药型罩线性装药的成型特性（英文）

为提高线性爆炸成型弹丸(LEFP)的威力,设计了一种带曲率结构的药型罩线性成型装药。采用数值模拟方法研究了两端起爆下LEFP成型过程及曲率半径对其影响规律,并进行了脉冲X光试验。结果表明,两端起爆时爆轰波对碰,使爆轰波有效地向LEFP运动方向汇聚,有利于曲率药型罩闭合,但曲率半径越大,越难闭合。LEFP稳定时形态良好,头部速度可达2 100m/s,药型罩利用率约87%,试验结果验证了两端起爆下曲率药型罩线性装药形成大威力LEFP的可行性和有效性。

爆轰波碰撞聚能效应及其数值分析

为了掌握爆轰波碰撞时的爆压和能量汇聚的规律,对爆轰波各种碰撞的爆压变化进行研究。首先基于爆轰波碰撞理论分析.得出爆轰波在正碰撞、斜碰撞和马赫反射三种条件下的爆压变化,确定马赫反射发生的条件,然后绘制入射角、偏离角和反射角间的关系曲线。应用Ls-dyna数值软件对爆轰波碰撞产生马赫反射的过程进行模拟。对比模拟和理论计算结果得知.对于多方指数为2.4的铵油炸药,马赫反射发生在斜爆轰波入射角为46.4°时,此时马赫波后压强达到最大值13.2 GPa,并在马赫波后形成高压区域。