Formation of blast waves as a result of a low pressure domain decomposition

In this article the formation and propagation of blast wave as a result of a focusing of shock wave in a domain with low pressure and density are examined in the frame of an ideal gas model. We consider the decomposition of a pressure-density discontinuity on the boundary of the spherical (or cylindrical) domain which is filled by a gas whose pressure and density are lower than the pressure and density of gas that filling the external space. At initial moments of this decomposition the rarefaction wave propagates in the external space and the converging shock wave is formed in the domain of low pressure and density. The intensity of the converging shock wave gradually increases, and the wave transitions to the self-similar regime. After implosion, a diverging shock wave is formed which propagates through the disturbed gas. The values of wave intensity, wave impulse and other parameters for some magnitudes of initial parameters have been determined by means of numerical calculations. Received 10 August 1997 / Accepted 13 July 1998     

Simulation of converging cylindrical GPa-range shock waves generated by wire array underwater electrical explosions

Results of one-dimensional numerical simulations of the parameters of the converging strong shock wave generated by electrical underwater explosions of a cylindrical wire array with different array radii and different deposited energies are presented. It was shown that for each wire array radius there exists an optimal duration of the energy deposition into the exploding array, which allows one to maximize the shock wave pressure and temperature in the vicinity of the implosion axis. The simulation results agree well with the 130-GPa pressure in the vicinity of the implosion axis that was recently obtained, which strongly indicates the azimuthal symmetry of the converging shock wave at these extreme conditions. Also, simulations showed that using a pulsed power generator with a stored energy of ~200 kJ, the pressure and temperature at the shock wave front reaches ~220 GPa and 1.7 eV at 0.1 mm from the axis of implosion in the case of a 2.5 mm radius wire array explosion. It was found that, in spite of the complicated equation of state of water, the maximum pressure at the shock wave front at radius r can be estimated as P ≈ (P*(r*/r) ^α , where P* is the known value of pressure at the shock wave front at radius r* ≥ r and α is a parameter that equals 0.62±0.02. A rough estimate of the implosion parameters of the hydrogen target after the interaction with the converging strong shock wave is presented as well.     

Reflection of a ring shock wave from a rigid wall

A new type of an implosion has been observed experimentally and simulated in a numerical calculation: the formation of a quasi-spherical converging shock wave after the reflection of a ring shock wave from a solid wall. The conversion of the ring shock wave into the quasi-spherical converging shock wave intensifies the local implosion properties.This article was processed using Springer-Verlag T_EX Shock Waves macro package 1.0 and the AMS fonts, developed by the American Mathematical Society.     

聚心火焰与激波相互作用的数值研究

基于带化学反应的2维轴对称Euler方程,利用带有monotonized centered(MC)限制器的波传播算法,在两端敞开的圆桶中对惰性介质的聚心激波和氢气-空气混合物的聚心火焰与激波的相互作用进行了数值模拟。数值结果表明,在惰性介质中激波在轴心的每次汇聚均可成长为马赫干,马赫干的追赶使激波得到一定程度的增强,但整体还呈下降趋势。在氢气-空气混合物中,燃烧诱导的激波,由于与火焰的反复作用,使激波在轴心处产生马赫干的频率和强度皆高于惰性介质中的情形。同时,火焰在与激波的相互作用过程中发生失稳变形,使其形状呈扁平头部的蘑菇云。     

Numerical investigations of the porosity effect on the shock focusing process

The effect of cylindrical obstacles and the porosity in between them along the path of a converging cylindrical shock is studied through numerical simulations. An initially cylindrical converging shock wave is perturbed by cylindrical obstacles placed radially in its path. High pressures and temperatures are achieved as the shock wave is focused. Results show that the shape of the shock wave close to the point of convergence as well as the porosity and type of shock wave reflection the converging shock undergoes influence the peak values. Various configurations of the obstacle size and number are considered. The Guderley constant for each case is compared with previous reported experimental values.     

柱形汇聚激波冲击球形重气体界面的实验研究

采用高速纹影法实验研究了柱形汇聚激波与球形重气体界面相互作用的 Richtmyer-Meshkov不稳定性问题. 激波管实验段基于激波动力学理论设计, 将马赫数为1.2 的平面激波转化为柱形汇聚激波, 气体界面由肥皂膜分隔六氟化硫(内)和空气(外)得到. 采用高速摄影机在单次实验中拍摄激波运动的全过程, 对柱形激波的形成进行了实验验证, 并进一步观测了汇聚激波与球形气体界面相互作用过程中的波系发展和气体界面变形以及反射激波同已变形界面二次作用的流场演化. 结果表明: 当柱形汇聚激波穿过气泡界面以后, 气泡左侧界面极点沿激波传播方向保持匀速运动, 气泡右侧界面发展成为射流结构, 气泡主体发展成为涡环结构; 在反射激波的二次作用下, 流场中无序运动显著增强并很快进入湍流混合阶段.     

Stability of converging cylindrical shock waves

An experimental and numerical study was made of converging cylindrical shock waves. The goal of the present study was to clarify the movement and instability of the converging cylindrical shock waves. Experiments were conducted in an annular shock tube of 230 mm o.d. and 210 mm i.d. connected to a cylindrical test section of 210 mm diameter. Double exposure holographic interferometry was used to visualize the converging cylindrical shock waves. Incident shock Mach numbers ranged between 1.1 and 2.0 in air. A numerical simulation was conducted using the TVD finite difference scheme. It was found in the experiments that although the initial shock wave configuration looked cylindrical, it was gradually deformed with propagation towards the center and finally showed mode-four instability. This is attributable to the existence of initial disturbances which were introduced by the struts which supported the inner tube of the annular shock tube. This trend was significant for stronger shock waves indicating that at the last stage of shock wave convergence the initial perturbations of the converging cylindrical shock wave were amplified to form the triple point of Mach reflection. The numerical results correctly predicted the experimental trend.This article was processed using Springer-Verlag T_EX Shock Waves macro package 1990.     

The numerical simulations of explosion and implosion in air: use of a modified Harten's TVD scheme

Numerical simulations of explosion and implosion in air are carried out with a modified Harten's TVD scheme. The new scheme has a high resolution for contact discontinuities in addition to maintaining the good features of Harten's TVD scheme. In the numerical experiment of spherical explosion in air, the second shock wave (which does not exist in the one‐dimensional shock tube problem) and its subsequent implosion on the origin have been successfully captured. The positions of the main shock wave, the contact discontinuity and the second shock wave have shown satisfactory agreement with those predicted from previous analysis. The numerical results are also compared with those obtained experimentally. Finally, simulations of a cylindrical explosion and implosion in air are carried out. Results of the cylindrical implosion in air are compared with those of previous work, including the interaction of the reflected main shock wave with the contact discontinuity and the formation of a second shock wave. All these attest to the successful use of the modified Harten's TVD scheme for the simulations of shock waves arising from explosion and implosion. Copyright © 1999 John Wiley & Sons, Ltd.     

Experimental study of toroidal shock wave focusing in a compact vertical annular diaphragmless shock tube

The paper reports results of experiments regarding toroidal shock wave focusing in a vertical shock tube as a part of a series of converging shock wave studies. This compact vertical shock tube was designed to achieve a high degree of reproducibility with minimum shock formation distance by adopting a diaphragmless operating system. The shock tube was manufactured in the Institute of Fluid Science, Tohoku University. An aspheric lens shaped cylindrical test section was connected at the open end of the shock tube to visualize the diffraction and focusing of the toroidal shock wave released from the ring shaped shock tube opening. Pressure transducers were flush mounted on the shock tube’s test section to measure pressure histories at the converging test section. Double exposure holographic interferometry was employed to quantitatively visualize the shock waves. The whole sequence of toroidal shock wave diffraction, focusing, and its reflection from the symmetrical axis were successfully studied. The transition of reflected shock waves was observed.     

柱形汇聚几何中内爆驱动金属界面不稳定性

采用自研的高保真度爆轰与冲击动力学程序,对柱形汇聚几何中内爆驱动金属材料界面不稳定性的动力学行为,进行了数值模拟研究。结果表明,首次冲击后至约12 μs,界面发展以RM（Richtmyer-Meshkov）不稳定性为主;12 μs后至冲击波聚心反弹加载前,界面聚心运动处于加速减速状态,界面发展由RT (Rayleigh-Taylor)不稳定性主导;冲击波聚心反弹加载后,界面发展又由RM不稳定性主导。另外,还研究了初始条件（初始振幅、初始波长、钢壳初始厚度和几何构型）对柱形内爆驱动金属材料界面不稳定性的影响。结果显示:初始振幅较大时振幅增长也较大;初始波长较小（模数较大）时振幅增长较小,而且存在一个截止波长;钢壳厚度会抑制扰动增长,也存在一个截止厚度;几何汇聚效应会使扰动增长速度更快。     

An experimental investigation of the stability of converging cylindrical shock waves in air

An experimental study was made of the stability of converging cylindrical shock waves. The experiments were conducted on annular shock tubes equipped with a double exposure holographic interferometer in the Stoßwellenlabor, RWTH Aachen, and in the Institute of High Speed Mechanics, Tohoku University, Sendai, for shock Mach numbers of 1.1 to 2.1 in air. By comparing these two different shock tube experiments, it is found that in the former facility the mode-three instability is predominant at the center of convergence, whereas the mode-four instability appears in the latter setup. The instabilities are denoted in this way because the shock and the flow field behind it reveal a remarkable triangular and quadrangular symmetry, respectively. It is concluded that the converging cylindrical shock wave is always unstable and sensitive to the structure of the annular shock tube. Usefulness of holographic interferometry to this kind of shock wave research is also demonstrated.To Prof. Dr. sq. techn. Dr.-Ing. e.h. Fritz Schultz-Grunow on the occasion of his 80th birthday     

Focusing of weak shock waves in confined axisymmetric chambers

Theoretical study of a weak shock wave focusing process on a spherical region in confined 3-D axisymmetric chambers is presented. The chambers are elliptic or parabolic in the plane cross-section containing their axis of symmetry. In the elliptic case a spherical shock wave of constant strength generated at one of the focal points will reflect off the chamber wall and converge on a spherical region around the second focus of the chamber. It is shown that the pressure distribution on the converging spherical shock wave is not homogeneous. In the parabolic case two possibilities of shock generation are considered. In the first one a plane shock wave of constant intensity is send in the inner of the chamber. This shock wave with the plane perpendicular to the symmetry axis will after the reflection off the chamber wall transform to a spherical shock with non-homogeneous pressure distribution. Alternatively, a spherical shock of constant intensity generated at the focus of the paraboloidal chamber will after the reflection transform to a plane shock with non-homogeneous pressure distribution propagating in the outer of the chamber. The above mentioned problems are solved within the frame of the geometrical acoustics approximation and the flow fields as well as the non-uniform shock strengths behind the converging wave fronts are calculated.This article was processed using Springer-Verlag T_EX Shock Waves macro package 1.0 and the AMS fonts, developed by the American Mathematical Society.     

Controlling the form of strong converging shocks by means of disturbances

The influence of artificial disturbances on the behavior of strong converging cylindrical shocks is investigated experimentally and numerically. Ring-shaped shocks, generated in an annular cross sectional shock tube are transformed to converging cylindrical shocks in a thin cylindrical test section, mounted at the rear end of the shock tube. The converging cylindrical shocks are perturbed by small cylinders placed at different locations and in various patterns in the test section. Their influence on the shock convergence and reflection process is investigated. It is found that disturbances arranged in a symmetrical pattern will produce a symmetrical deformation of the converging shockfront. For example, a square formation produces a square-like shock and an octagon formation a shock with an octagonal front. This introduces an alternative way of tailoring the form of a converging shock, instead of using a specific form of a reflector boundary. The influence of disturbances arranged in non-symmetric patterns on the shape of the shockfront is also investigated.      

基于面积折减等效模型的光电倍增管水下内爆机理研究

光电倍增管(photomultiplier tube，PMT)是中微子探测器的核心部件，是由玻璃材料制成的内部真空的薄壳结构，排列在深水中工作，若一个PMT被压溃会产生内爆冲击波，会引起周围PMT发生殉爆。针对PMT内爆，建立了PMT内爆数值计算简化模型，并将计算与试验结果进行对比，验证简化模型的合理性。在此基础上，提出了基于面积折减等效模型的PMT内爆计算方法，通过等效模型分析了防护装置破口面积对PMT内爆的影响，得出随着防护装置破口面积的减小，水流碰撞发生PMT内爆的时刻相应提前，内爆产生的冲击波脉宽基本保持不变，冲击波压力峰值明显减小。该研究有利于找到有效的PMT内爆防护方法。     

The production and evolution of multiple converging radiative shock waves in gas-filled cylindrical liner z-pinch experiments

A cylindrical liner z-pinch configuration has been used to drive converging radiative shock waves into different gases. On application of a 1.4 MA, 240 ns rise-time current pulse, a series of cylindrical shocks moving at typical velocities of 20 km s^?1 are consecutively launched from the inside liner wall into an initially static gas-fill of density ～10^?5 g cm^?3. The drive current skin depth calculated prior to resistive heating was slightly less than the liner wall thickness and no bulk liner implosion occurred. Axial laser probing images show the shock fronts to be smooth and azimuthally symmetric, with instabilities developing downstream of each shock. Evidence for a radiative precursor ahead of the first shock was seen in laser interferometry imaging and time-gated, spatially resolved optical spectroscopy. The interferometry diagnostic was able to simultaneously resolve the radiative precursor and the density jumps at the shock fronts. Optical streak photography provided information on shock timing and shock trajectories and was used to gain insight into the shock launching mechanisms.     

The shock–vortex interaction patterns affected by vortex flow regime and vortex models

We have used a third-order essentially non-oscillatory method to obtain numerical shadowgraphs for investigation of shock–vortex interaction patterns. To search different interaction patterns, we have tested two vortex models (the composite vortex model and the Taylor vortex model) and as many as 47 parametric data sets. By shock–vortex interaction, the impinging shock is deformed to a S-shape with leading and lagging parts of the shock. The vortex flow is locally accelerated by the leading shock and locally decelerated by the lagging shock, having a severely elongated vortex core with two vertices. When the leading shock escapes the vortex, implosion effect creates a high pressure in the vertex area where the flow had been most expanded. This compressed region spreads in time with two frontal waves, an induced expansion wave and an induced compression wave. They are subsonic waves when the shock–vortex interaction is weak but become supersonic waves for strong interactions. Under a intermediate interaction, however, an induced shock wave is first developed where flow speed is supersonic but is dissipated where the incoming flow is subsonic. We have identified three different interaction patterns that depend on the vortex flow regime characterized by the shock–vortex interaction.      

流动肥皂膜气体界面及其在柱状汇聚激波作用下演化的实验研究

在Richtmyer-Meshkov(RM)不稳定性实验研究中,形成两种不同密度流体的初始扰动界面是前提和关健.本文提出了一种流动肥皂膜气体界面生成方法,其工作原理是由细丝构成的导流框从激波管实验段穿过,肥皂液从导流框的上端注入并在重力作用下在导流框中形成流动肥皂膜,膜的两测可以分别充入不同密度的气体从而形成稳定的气体...     

Focusing of strong shocks in an elliptic cavity

Focusing of strong shock waves in a gas-filled thin chamber with an elliptic boundary is investigated theoretically and numerically. The process of reflection and convergence of cylindrical shocks generated at one of the focal points of the chamber is studied by means of Whitham's theory of geometrical shock dynamics (1957, 1959). The current calculations are based on the modified version of this theory, which takes into account the non-homogeneous flow ahead of the advancing shock, Apazidis and Lesser (1996). There are two main results of the present study indicating a qualitatively different behavior of strong shocks as compared to the linear acoustic case. (1) - the form of the reflected shock is not cylindrical and (2) - the reflected, converging shock does not focus at the geometrical second focal point of the chamber. The dependence of the form of the reflected shock and the location of its focusing point on the strength of the shock and the eccentricity of the chamber is investigated.     

Numerical investigation of axisymmetric shock wave focusing over paraboloidal reflectors

The problem of a plane shock wave incident to a paraboloidal reflector is numerically investigated. The numerical solver used is developed by an improved, implicit, upwind total variation diminishing scheme in a finite-volume approach. The real-gas effect is taken into account if high temperature occurs. The solver is validated on four test problems. The complicated flow fields of axisymmetric shock wave focusing for different-depth reflectors at various incident shock Mach numbers are studied. An interesting result of a maximum pressure happening at the reflector center is found. This is due to the occurrence of an implosion phenomenon. A maximum temperature might occur at the reflector center or at other locations, depending on the incident shock Mach number and the reflector depth. Moreover, vortical flows induced by shock wave focusing and their formation mechanism are explored. It was found that the vortices near the reflector are caused by a ring-shaped shock/slipline interaction. Owing to the slipline on the symmetry axis, a jet flow is induced, resulting in the formation of vortices near the symmetry axis. Received 13 January 1998 / Accepted 10 November 1998     

Propagation of converging and diverging shock waves under isothermal condition

In this article the flows of perfect gas behind converging and diverging strong shock waves under isothermal condition in the cases of spherical and cylindrical symmetry are examined. A diverging shock wave is formed by energy supply according to a power law. These waves propagate in a uniform medium at rest and all conservation laws hold at the fronts of these shock waves. It was established that in the case of converging waves for any value of the ratios of specific heats the solution of the problem under consideration exists and is unique. When the problem has more than one solution. In the case of diverging shock waves the solution exists and is unique for any from the interval and any value of power in the energy input law. Received 4 August 1996 / Accepted 28 May 1996