A Free-Lagrange method for unsteady compressible flow: simulation of a confined cylindrical blast wave

A Free-Lagrange numerical procedure for the simulation of two-dimensional inviscid compressible flow is described in detail. The unsteady Euler equations are solved on an unstructured Lagrangian grid based on a density-weighted Voronoi mesh. The flow solver is of the Godunov type, utilising either the HLLE (2 wave) approximate Riemann solver or the more recent HLLC (3 wave) variant, each adapted to the Lagrangian frame. Within each mesh cell, conserved properties are treated as piece-wise linear, and a slope limiter of the MUSCL type is used to give non-oscillatory behaviour with nominal second order accuracy in space. The solver is first order accurate in time. Modifications to the slope limiter to minimise grid and coordinate dependent effects are described. The performances of the HLLE and HLLC solvers are compared for two test problems; a one-dimensional shock tube and a two-dimensional blast wave confined within a rigid cylinder. The blast wave is initiated by impulsive heating of a gas column whose centreline is parallel to, and one half of the cylinder radius from, the axis of the cylinder. For the shock tube problem, both solvers predict shock and expansion waves in good agreement with theory. For the HLLE solver, contact resolution is poor, especially in the blast wave problem. The HLLC solver achieves near-exact contact capture in both problems. Received May 25, 1995 / Accepted September 11, 1995     

Shock wave attenuation by grids and orifice plates

The interaction of weak shock waves with porous barriers of different geometries and porosities is examined. Installing a barrier inside the shock tube test section will cause the development of the following wave pattern upon a head-on collision between the incident shock wave and the barrier: a reflected shock from the barrier and a transmitted shock propagating towards the shock tube end wall. Once the transmitted shock wave reaches the end wall it is reflected back towards the barrier. This is the beginning of multiple reflections between the barrier and the end wall. This full cycle of shock reflections/interactions resulting from the incident shock wave collision with the barrier can be studied in a single shock tube test. A one-dimensional (1D), inviscid flow model was proposed for simulating the flow resulting from the initial collision of the incident shock wave with the barrier. Fairly good agreement is found between experimental findings and simulations based on a 1D flow model. Based on obtained numerical and experimental findings an optimal design procedure for shock wave attenuator is suggested. The suggested attenuator may ensure the safety of the shelter’s ventilation systems.     

Simulation of blast wave propagation over a cylinder

A numerical study of the interaction of plane blast waves with a cylinder is presented. Computations are carried out for various blast-wave durations and comparisons are obtained with the corresponding results of planar shock-wave. Both inviscid and viscous results based on the solution of the Euler and Navier-Stokes equations are presented. The equations are solved by an adaptive-grid method and a second-order Godunov scheme. The shock wave diffraction over the cylinder is investigated by means of various contour plots, as well as, pressure and skin-friction histories. The study reveals that the blast-wave duration significantly influences the unsteady flow over the cylinder. The differences between the viscous and inviscid results are also discussed. Received 2 March 1996 / Accepted 28 February 1997     

Shock wave diffraction by a square cavity filled with dusty gas

A simple two-dimensional square cavity model is used to study shock attenuating effects of dust suspension in air. The GRP scheme for compressible flows was extended to simulate the fluid dynamics of dilute dust suspensions, employing the conventional two-phase approximation. A planar shock of constant intensity propagated in pure air over flat ground and diffracted into a square cavity filled with a dusty quiescent suspension. Shock intensities were and , dust loading ratios were and , and particle diameters were and {\rm \mu}$m. It was found that the diffraction patterns in the cavity were decisively attenuated by the dust suspension, particularly for the higher loading ratio. The particle size has a pronounced effect on the flow and wave pattern developed inside the cavity. Wall pressure histories were recorded for each of the three cavity walls, showing a clear attenuating effect of the dust suspension. Received 15 November 1999 / Accepted 25 October 2000     

Specific features of incident and reflected blast waves

On the basis of numerical modeling specific features of shock wave reflections were analyzed. It was found, that after diaphragm rupture self-modeling pressure and velocity distributions nearby the shock front establish. But in some special cases the temperature behind the shock front can rise. This peculiarity should be taken into account when performing experiments with high reactive gaseous mixtures. The temperature on the shock front and the velocity gradient behind it are uniform in the case of strong blast wave reflections. This effect is observed in the zone with an elevated temperature profile behind the incident blast wave. The reflected triangular waves conserve a quasi-self-modeling character by pressure. Typical experiments were carried out to verify the theoretical predictions. The effects of reflected wave acceleration in the case of triangular waves and the self-similar character of the pressure profiles were observed.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.     

Experimental and numerical studies of weak blast waves in air

Effects of viscosity and vibrational nonequilibrium on the profile of a weak, spherical N-wave in air are experimentally and numerically studied. Weak blast waves were generated, in a quiescent air dome, by spark discharges and exploding wires and observed by high frequency response microphones over 40 meters. Some similarity relationships were obtained from the blast wave experiments. For observed N-waves having less than 100 Pa peak overpressure, the peak overpressure p _f and the duration of the positive phaset _d+ are found to vary with the radial distance from the sourcer as p _f r ^–1.38 andt _d + r ^0.19, whilst the rise time of the blast wave t _f linearly increases with distance. Similar trends were also found for the negative phase of the blast wave. Numerical simulations were carried out to compare with the blast wave data. The Navier-Stokes equations for spherical symmetric flows were solved by coupling with a relaxation equation for vibrational excitation of oxygen using the random choice method (RCM) adapted to supercomputing with an operator splitting technique. The resultant N-wave profiles are in good agreement with the experimental results. The numerical results clearly indicate that the wave-easing process due to the dispersive effect of vibrational relaxation plays a dominant role in determining the rise time of the N-wave.This article was processed using Springer-Verlag T_EX Shock Waves macro package 1990.     

Jet and vortex flow induced by anisotropic blast wave: experimental and computational study

This paper discusses gas-dynamic aspects of intense explosions in uniform environments. In experiments, the energy of a laser is almost instantaneously released in a volume of air shaped as either a flattened or stretched cylinder generating a blast wave. Its shape evolves in time and ultimately becomes spherical. But momentum transferred to the air when the blast wave is strongly nonspherical is anisotropic. As a result, a subsonic jet and a vortex are induced and propagate along the symmetry axis or along the perpendicular plane, depending on the initial configuration of the blast wave. Simulations based on a free-Lagrangian method for a nonviscous gas are in good agreement with the experiments. Velocities, circulation, and positions of fluid particles found in computations give an insight into the causes and details of the flow. Two simultaneous and contrary processes take place – vorticity production by the anisotropic shock wave and baroclinical generation of vorticity at the boundary of the heated gas – which give rise to net circulation. Received 21 April 1997 / Accepted 27 June 1997     

Experimental and numerical studies of underwater shock wave attenuation

The attenuation of an underwater shock wave by a thin porous layer is studied both experimentally and numerically. The shock waves are generated by exploding 10 mg silver azide pellets and the pressures at different distances from the explosion center are measured. Measurements are also carried out with a gauze layer placed between the explosion source and the pressure gauge. The results with and without the gauze layer are compared evaluating the shock wave attenuation. Numerical simulations of the phenomenon are also carried out for a simple wave attenuation model. The results are compared with the experimental data. Despite the simple mathematical model of wave attenuation, the agreement between the experimental and numerical results is reasonable.Received: 22 October 2002, Accepted: 17 June 2003, Published online: 5 August 2003PACS: 47.11.+j, 47.40.Nm, 47.55.Mh     

Numerical simulation of blast flow fields induced by a high-speed projectile

Numerical investigations on the launch process of a projectile in a nearly realistic situation have been performed in this article. The Arbitrary Lagrangian–Eulerian (ALE) of Euler equations is solved by the AUSMDV scheme and the dynamic chimera grid technique are used for describing the moving of the projectile. Based on our numerical results, the muzzle blast flow field of the transient launch process of a projectile at a relative high Mach number of 3.0 has been visualized numerically, and the prominent characteristics including the propagation of first and second blast waves, the generation of bow shock wave and moving of the projectile, etc. have been discussed in detail.      

On the interaction and coalescence of spherical blast waves

The scaling and similarity laws concerning the propagation of isolated spherical blast waves are briefly reviewed. Both point source explosions and high pressure gas explosions are considered. Test data on blast overpressure from the interaction and coalescence of spherical blast waves emanating from explosives in the form of shaped charges of different strength placed in the vicinity of a solid propellant stack are presented. These data are discussed with regard to the scaling laws concerning the decay of blast overpressure. The results point out the possibility of detecting source explosions from far-field pressure measurements.      

脆性材料中应力波衰减规律与层裂实验设计的数值模拟

对混凝土、岩石类脆性材料的层裂实验进行了有限元模拟,研究了应力波在此类材料中传播的衰减规律,包括两类机制:弹性波因大尺寸试样的几何弥散产生的小幅度线性衰减、与应变率相关的黏塑性波因本构关系导致的指数衰减。在此基础上,提出了包含常数项的指数型应力波峰值拟合公式。建议采用可以忽略应力波衰减影响的细长形试样进行层裂实验。混凝土类脆性材料层裂破坏模拟结果显示,有限元模拟得到的层裂片厚度与一维应力波理论得到的结果非常吻合,验证了按一维应力波理论确定层裂强度的实验方法的有效性。通过对比3种不同入射波形下层裂片的形状和净拉应力波形,发现不对称的入射波形状更有利于实验获得平直的层裂断面和较准确的层裂强度。     

Constitutive modeling of aluminum foam including fracture and statistical variation of density

An existing constitutive model applicable for aluminum foam was evaluated. The model was implemented in LS-DYNA, and several test cases were analyzed and compared to experimental data. The numerical analyses consisted of foam subjected to both simple and more complex loading conditions where fracture was of varying importance. Therefore, simple fracture criteria were added to the model. Additionally, the inhomogeneities in the foam were modeled by incorporating the possibility of statistical variation of the foam density. The implemented model is efficient and robust, and gives satisfactory results compared with the experimental results.     

Importance of unsteady contributions to force and heating for particles in compressible flows. Part 2: Application to particle dispersal by blast waves

Particle dispersal by blast waves is an interesting phenomenon. A model problem, i.e., a sudden release of a compressed gas–particle mixture contained in a spherical container, is employed to investigate the fundamental physics of particle dispersal. The problem is simulated by the multiphase flow models proposed in Part 1 of this article that include unsteady contributions in momentum and energy exchange between gas and particles. At early times, when particles are accelerated in the expansion fan, unsteady force and heating contributions are much larger than the corresponding quasi-steady contributions. Consequently, neglecting unsteady contributions leads to significant errors in particle front location (the boundary of the particle cloud). The complex wave interactions in the flow have strong influence on the particle motion. As a result, the particle motion is a non-monotonic function of particle density or diameter and the evolution of particle concentration is non-uniform and unsteady.     

Shock-induced collapse of a cylindrical air cavity in water: a Free-Lagrange simulation

A Free-Lagrange CFD code is used to simulate the collapse of a cylindrical air cavity in water by a 1.9 GPa incident shock. The Lagrangian treatment allows the air/water interface to be tracked throughout the interaction. The incident shock is partially transmitted into the cavity, within which it experiences multiple reflections. The upstream cavity wall involutes to form a high-speed jet which, on impact with the far cavity wall, produces an intense blast wave. Heating of the gas within the cavity is highly non-isentropic, and is dominated by shock heating. The predicted final gas temperature is of order 12000 K, although the modelling assumptions used here lead to over-prediction of temperature during the later stages of collapse. Received 14 September 1999 / Accepted 28 June 2000     

激波作用下三维涡的形成及其界面捕捉计算

针对三维多介质可压缩流体,给出了可压缩多介质流体三维高精度数值计算方法,以及界面捕捉方程和带重新初始化的三维LevelSet方法,对初始压力间断和密度间断条件形成激波、接触间断以及稀疏波的三维复杂流场相互作用情况进行数值计算,给出流场中涡的形成过程和界面位置。并对计算方法进行理论验证。     

水平光面爆破激发地震波的成分及衰减特征

借助极化偏振分析方法,针对一组现场爆破实验,分析了水平光面爆破激发地震波的成分构成及特性,比较了不同波的衰减特征及各自对爆破振动的影响,并探讨了水平光面爆破的内在力学机理。结果表明,爆破振动中不同波的相对量值及主导波的类型均会随测点位置的改变而变化,爆源特性和沿传播路径的不同衰减共同决定波的成分构成及演化,各测点的优势振动方向也与波的成分构成密切相关。对于水平光面爆破,在光爆孔平面上,P波的影响可忽略,S波主要在竖直向振动,R波对水平及竖直向的振动均有贡献,其中水平向的振动主要由R波引起,而S波的竖直向振速在近区远高于R波,但归因于S和R波的不同衰减,R波在距离爆源22.5 m/kg^1/2(58~67 m)处开始主导竖直向的振动;在光爆孔平面外,P波的影响不可忽略,且在特定位置会成为优势波型。     

Numerical study of spherical blast-wave propagation and reflection

The objective of this study is to understand the flow structures of weak and strong spherical blast waves either propagating in a free field or interacting with a flat plate. A 5th-order weighted essentially non-oscillatory scheme with a 4th-order Runge-Kutta method is employed to solve the compressible Euler/Navier-Stokes equations in a finite volume approach. The real-gas effects are taken into account when high temperature occurs. A shock-tube problem with the real-gas effect is first tested in order to verify the solver accuracy. Moreover, unsteady shock waves moving over a stationary wedge with various wedge angles, resulting in different types of shock wave reflections, are also tested. It is found that the computed results agreed well with the existing data. Second, the propagation of a weak spherical blast wave, created by rupture of a high-pressure isothermal sphere, in a free field is studied. It is found that there are three minor shock waves moving behind the main shock. Third, the problem of a strong blast wave interacting with a flat plate is investigated. The flow structures associated with single and double Mach reflections are reported in detail. It is found that there are at least three local high-pressure regions near the flat plate. Received 27 July 2000 / Accepted 25 January 2002 – Published online 17 June 2002     

Shock wave reflection over wedges: a benchmark test for CFD and experiments

In the Shock Wave Journal Vol. 2, No. 4 a benchmark test for shock wave reflection over wedges was announced. International scientists who are interested in shock wave research were invited to participate. The benchmark test aimed at comparison of various advanced numerical schemes as well as experimental results. During the last three years more than twenty results, including both CFD and experiments, were collected from all over the world. Efforts contributed by these scientists made the present benchmark test reach to a standard of the state of the art of the computational fluid dynamics applied to the shock wave research. However, it was regrettable not to publish all the results collected due to limitation on the available page number. Received 5 November 1994 / Accepted 9 September 1996     

泡沫材料对冲击波的衰减特性

对冲击波与开式、闭式泡沫作用及其在空气中的传播特性开展实验研究,探讨不同结构的泡沫材料对冲击波衰减的力学特征。通过定量分析泡沫材料对冲击波的超压峰值、正冲量的损失,分析冲击波入射、反射、透射的正冲量。实验结果表明, 泡沫材料对冲击波的衰减体现在对冲击波的反射衰减等方面,其中开式泡沫对冲击波的衰减效果比闭式泡沫稍好,且它们衰减冲击波的具体力学过程也不尽相同。

     

截卵形弹水平入水的速度衰减及空泡扩展特性

用轻气炮设备对截卵形弹进行了速度在100~150 m/s的水平入水实验,利用高速相机记录了整个入水过程,获取了截卵形弹体在水中运动的速度衰减规律,并对平头弹、卵形弹及截卵形入水弹道稳定性及速度衰减规律进行了对比,对截卵形弹体入水形成的空泡扩展行为进行了理论研究,建立了关于空泡扩展的理论模型,得到了固定位置和固定时间处空泡扩展半径、速度分别与时间和侵彻距离的关系,实验数据与理论计算吻合很好。