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     

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     

颗粒材料中致密波结构研究

采用一维两相流模型与相应颗粒构形应力函数,研究了致密波的形成及其结构．用简化两相流模型系统地讨论致密波对有关因素的依赖关系．分析指出：小于基体材料音速的致密波仅能在非理想颗粒材料中存在,从波前到波后,所有状态物理量光滑过渡．大于基体材料音速的致密波,波头可能存在间断．应力函数与致密粘性确定后,致密波速度决定致密波结构、宽度、终态压实度．采用一维两相流模型模拟了活塞驱动颗粒床形成致密波这一动态过程．用线方法（MOL）对该方程组求数值解．计算表明,经过短暂的非稳态过程,颗粒床中形成一稳态致密波．分析了活塞速度与初始孔隙率对致密波结构的影响,并对简化两相流模型与两相流模型的计算结果进行了对比．     

Enhancement of shock waves

The flow field developed behind a shock wave propagating inside a constant cross-section conduit is solved numerically for two different cases. First, when the density of the ambient gas into which the shock propagates has a logarithmic change with distance. In the second, and the more practical case, the ambient gas is composed of pairs of air–helium layers having a continually decreasing width. It is shown that in both cases meaningful pressure amplification can be reached behind the transmitted shock wave. It is especially so in the second case. By proper choice of the number of air–helium layers and their width reduction ratio, pressure amplification as high as 7.5 can be obtained.      

The isotope effect of gaseous hydrogen under shock compression

The shock compression method has been used to measure the Hugoniot data and shock temperature for gaseous hydrogen samples, covering the pressure range of 55-140 MPa and the temperature range of 3400-4500 K and with the initial conditions of P ₀ = 0.6 MPa, 1.2 MPa and T ₀ at room temperature. Spectral radiance histories emitted from shocked D ₂ and H ₂ + D ₂ (equimolar mixture) are monitored by a pyrometer system with seven wavelength channels. Theoretical calculations based on the Saha model with Debye-Hückel correction for the shock compression behavior of shocked gaseous samples are in good agreement with the measured Hugoniot data, but show slightly higher values for the shock temperature when comparing with experiments. An isotope effect relevant to these shocked hydrogen species has been found in the linear shock velocity vs particle velocity relation, in which the correlation factor between these hydrogen isotopes or hydrogen mixtures is simply of initial density dependence.Received: 8 December 2002, Accepted: 8 May 2003, Published online: 2 September 2003PACS: 62.50 + p, 31.30.GS, 51.90. + r     

A compact numerical algorithm for solving the time‐dependent mild slope equation

The mild slope equation has been widely used to describe combined wave refraction and diffraction. In this study, a new numerical algorithm is developed to solve the time‐dependent mild slope equation in a second‐order hyperbolic form. The numerical algorithm is based on a compact and explicit finite difference method that is second‐order accurate in both time and space. The algorithm has the similar structure to the leap‐frog method but is constructed on three time levels for the second‐order time derivative term. The numerical model has the capability of simulating transient wave motion by correctly predicting the speed of wave energy propagation, which is important for the real‐time forecast of the arrival time of storm waves generated in the far field. The model is validated against analytical solution for wave shoaling and experimental data for combined wave refraction and diffraction over a submerged elliptic shoal on a slope (Coastal Eng. 1982; 6 :255). Lastly, the realistic scale Homma's island (Geophys. Mag. 1950; 21 :199) is studied with the use of various wave periods of T = 720s, T = 120 s, and T = 24 s. These wave periods correspond to long, intermediate, and short waves for the given topography, respectively. Comparisons are made between numerical results and existing analytical solutions in terms of the wave amplification around the island, which serves as the indicator for the potential wave runup. Excellent agreements are obtained. The model runs on a PC (Pentium IV 1.8GHz) and the computer capacity allows the computation of a mesh system up to 3000 × 3000, which is equivalent to about 150 × 150 waves or a large area of 540km × 540km for a wave train with the period of T = 60 s. Copyright 2004 John Wiley & Sons, Ltd.     

Measurement of shock waves velocity in the air plasma of capacitively coupled RF discharge

The velocity of shock wave propagation in the air plasma of stationary capacitively coupled RF discharge at different gas pressure and charged particles concentration has been measured. It is shown, that the velocity of the shock wave increases at the increase of the concentration. Measurement results are brought to the universal dependence. Received 17 August 1998 / Accepted 10 December 1999     

双磁场IMPS粒子速度测试系统

动载下材料横向行为的直接实时测量,对于全面了解材料响应及其机理有重要意义。本文介绍了自行研制的双磁电磁ＩＭＰＳ粒子速度测试系统的工作原理、结构性能及初步实验结果。该装置基于Ｆａｒａｄａｙ电磁感应定律,可实时测量多点斜碰撞产生的纵向和横向质点速度波形,从而解决了压剪炮试验中的ｓ波测量问题。     

The reflected pressure field in the interaction of weak shock waves with a compressible foam

This paper deals with the waves that are reflected from slabs of porous compressible foam attached to a rigid wall when impacted by a weak shock wave. The interest is in establishing possible attenuation of the pressure field after a shock or blast wave has struck the surface. Foam densities from 14 to 38 kg/m³ were tested over a range of shock wave Mach numbers less than 1.4. It is shown that the initial reflected shock wave strength is accurately predicted by the pseudo-gas model of Gelfand et al. (1983), with a pressure ratio of approximately 80% of the value for reflection off a rigid wall. Evidence is presented of gas entering the foam during the early stages of the process. A second wave emerges from the foam at a later stage and is separated from the first by a region of constant velocity and pressure. This second wave is not a shock wave but a compression front of significant thickness, which emerges from the foam earlier than predicted by the pseudo-gas model. Analysis of the origin of this wave points to much more complex flows within the foam than previously assumed, particularly in an apparent decrease in average wave front speed as the foam is compressed. It is shown that the pressure ratio across both these waves taken together is slightly higher than that for reflection off a rigid wall. In some cases this compression wave train is followed by a weak expansion wave.This article was processed using Springer-Verlag T_EX Shock Waves macro package 1990.     

Interaction of a shock wave with a loose dusty bulk layer

The interaction of a planar shock wave with a loose dusty bulk layer has been investigated both experimentally and numerically. Experiments were conducted in a shock tube. The incident shock wave velocity and particle diameters were measured with the use of pressure transducers and a Malvern particle sizer, respectively. The flow fields, induced by shock waves, of both gas and granular phase were visualized by means of shadowgraphs and pulsed X-ray radiography with trace particles added. In addition, a two-phase model for granular flow presented by Gidaspow is introduced and is extended to describe such a complex phenomenon. Based on the kinetic theory, such a two-phase model has the advantage of being able to clarify many physical concepts, like particulate viscosity, granular conductivity and solid pressure, and deduce the correlative constitutive equations of the solid phase. The AUSM scheme was employed for the numerical calculation. The flow field behind the shock wave was displayed numerically and agrees well with our corresponding experimental results.      

An experimental investigation on the dynamic axial buckling of cylindrical shells using a Kolsky Bar

Several experiments were performed with a Kolsky Bar (Split Hopkinson Pressure Bar) device to investigate the dynamic axial buckling of cylindrical shells. The Kolsky Bar is a loading as well as a measuring device which can subject the shells to a fairly good square pulse. An attempt is made to understand the interaction between the stress wave and the dynamic buckling of cylindrical shells. It is suggested that the dynamic axial buckling of the shells, elastic or elasto-plastic, is mainly due to the compressive wave rather than the flexural or bending wave. The experimental results seem to support the two critical velocity theory for plastic buckling, withV _c1 corresponding to an axisymmetric buckling mode andV _c2 corresponding to a non-symmetric buckling mode. The project supported by National Natural Science Foundation of China     

Experimental investigation of the interaction between weak shock waves and granular layers

 The paper describes new experimental results regarding the pressure fields in front of and inside granular layers of different materials during their collision with weak shock waves. A variety of waves result from the shock wave-granular layer interaction. The pressure behind the reflected wave from the material interface approaches the equilibrium value, P ₅, which would have been reached had the shock wave reflected from a solid end-wall. The wave succession inside the layer depends solely on two processes: the complex interaction of the compaction wave with the granular material and the gas filtration, which affects the particles by the drag forces between the two phases. Inside a material with a permeability coefficient f>0.001 mm² the transmitted wave moves with a constant velocity which is largely governed by the gas filtration. For low permeability materials ( f<0.0003 mm²) the transmitted wave trajectory strongly depends on the compaction wave propagation. In such cases the compaction wave was found to be unsteady and its acceleration was higher in material having low material densities. The maximum compressive stress values, P _c , reached at the shock tube end-wall, covered by the materials under investigation, manifested as an unsteady pressure peak twice as large as the gas pressure P ₅, measured ahead of the layer. Comparing the present data with those available in the literature showed that the amplitude of the unsteady pressure peak was higher in materials having low effective densities, γ, and small permeability coefficients f. Contrary to flexible foams where the available experimental data indicated that the compressive stress in the post peak period converges to P ₅=P _g , the results obtained in the present study indicated that during the test time the compressive stress, P _s , was well preserved in the material and for most of the sample length its value was within the range P _s >P ₅>P _g . Received: 4 March 1996 / Accepted:26 September 1996     

Free surface flow under gravity and surface tension due to an applied pressure distribution: I Bond number greater than one-third

We consider steady free surface two-dimensional flow due to a localized applied pressure distribution under the effects of both gravity and surface tension in water of constant depth, and in the presence of a uniform stream. The fluid is assumed to be inviscid and incompressible, and the flow is irrotational. The behavior of the forced nonlinear waves is characterized by three parameters: the Froude number, F, the Bond number, τ > 1/3, and the magnitude and sign of the pressure forcing parameter ɛ. The fully nonlinear wave problem is solved numerically by using a boundary integral method. For small amplitude waves and F < 1 but not too close to 1, linear theory gives a good prediction for the numerical solution of the nonlinear problem in the case of bifurcation from the uniform flow. As F approaches 1, the nonlinear terms need to be taken account of. In this case the forced Korteweg-de Vries equation is found to be an appropriate model to describe bifurcations from an unforced solitary wave. In general, it is found that for given values of F < 1 and τ > 1/3, there exists both elevation and depression waves. In some cases, a limiting configuration in the form of a trapped bubble occurs in the depression wave solutions.     

气压对压力容器前壁超高速撞击损伤的影响

充气压力容器在超高速撞击下的典型损伤包括穿孔及其边缘的裂纹失稳破坏,会导致气体泄漏或爆炸,内压对容器前壁损伤的影响仍不明确。以不同内压的球形铝合金充气压力容器为研究对象,开展了球形铝合金弹丸超高速撞击实验和数值模拟计算,分析了内充气体压强对前壁穿孔形貌特征、穿孔直径、孔边环向应力等的影响规律和影响机理,讨论了气体冲击波的传播行为及影响前壁穿孔边缘裂纹失稳破坏的机制。结果表明:前壁穿孔边缘内翻边形貌与内压相关,内压越高,弯折程度越轻;穿孔直径与内充气体压强正相关,但气体对孔径的影响远小于容器壁厚及撞击速度的影响;穿孔边缘使裂纹失稳破坏的环向拉应力不仅受到后壁反射冲击波的影响,也与容器壁内应力波的传播有关,与内压成正比。     

Peristaltic transport of rheological fluid: model for movement of food bolus through esophagus

Fluid mechanical peristaltic transport through esophagus is studied in the paper.A mathematical model has been developed to study the peristaltic transport of a rheological fluid for arbitrary wave shapes and tube lengths.The Ostwald-de Waele power law of a viscous fluid is considered here to depict the non-Newtonian behaviour of the fluid.The model is formulated and analyzed specifically to explore some important information concerning the movement of food bolus through esophagus.The analysis is carried out by using the lubrication theory.The study is particularly suitable for the cases where the Reynolds number is small.The esophagus is treated as a circular tube through which the transport of food bolus takes place by periodic contraction of the esophageal wall.Variation of different variables concerned with the transport phenomena such as pressure,flow velocities,particle trajectory,and reflux is investigated for a single wave as well as a train of periodic peristaltic waves.The locally variable pressure is seen to be highly sensitive to the flow index "n".The study clearly shows that continuous fluid transport for Newtonian/rheological fluids by wave train propagation is more effective than widely spaced single wave propagation in the case of peristaltic movement of food bolus in the esophagus.     

The effect of porosity on shock interaction with a rigid, porous barrier

This work investigates the pressure amplification experienced behind a rigid, porous barrier that is exposed to a planar shock. Numerical simulations are performed in two dimensions using the full Navier–Stokes equations for a M = 1.3 incoming shock wave. An array of cylinders is positioned at some distance from a solid wall and the shock wave is allowed to propagate past the barrier and reflect off the wall. Pressure at the wall is recorded and the flowfield is examined using numerical schlieren images. This work is intended to provide insight into the interaction of a shock wave with a cloth barrier shielding a solid boundary, and therefore the Reynolds number is small (i.e., Re = 500 to 2000). Additionally, the effect of porosity of the barrier is examined. While the pressure plots display no distinct trend based on Reynolds number, the porosity has a marked effect on the flowfield structure and endwall pressure, with the pressure increasing as porosity decreases until a maximum value is reached.      

激波聚焦诱导点火和爆轰的数值研究

以二维轴对称多组分Euler方程为基础，采用非正交结构化网格和改进的波传播算法，模拟了激波在抛物形反射壁面聚焦反射诱导点火和爆轰的过程，描述了其流场形态。讨论了预混气组成、入射激波强度及反射壁面形状对点火和爆轰的影响。结果表明，激波在抛物形反射壁面顶点处聚焦反射可形成局部高温高压区域，该区域在一定条件下可点燃预混气甚至形成爆轰，其中低稀释剂浓度的预混气、较大的入射激波Mach数和较深的反射壁面有利于可燃预混气形成爆轰。     

Interaction of a centered isentropic compression wave with the bow shock ahead of a body in a rarefied gas

Rarefied gas flow with a centered isentropic compression wave is investigated using direct Monte Carlo simulation of the solution of the Boltzmann equation. For monatomic gas flow the pattern of formation of a suspended compression shock near the geometric center of the compression wave is considered. The flow pattern is compared with the results obtained within the framework of gas dynamics. For a diatomic gas the interference of a centered compression wave with the bow shock ahead of a cylinder is investigated. The dependence of the pressure and the heat transfer to the surface on the Reynolds number and the wave center position relative to the cylinder center is analyzed. The results are compared with those of numerical simulation of the Euler and boundary-layer equations.     

Numerical investigations of shock waves in gas-particle mixtures

The propagation of shock waves in gas-particle mixtures in one- and two-dimensional geometries is numerically investigated. Two schemes for approximating conservation laws for particles, which are collectively treated as a continuum medium, are compared and discussed. Different models of the drag coefficient and Nusselt number, directly affecting the interaction between the gas and particle phases, are used for obtaining shock profiles, and the results are compared. The oblique shock reflections at a solid wedge in a gas-particle mixture are simulated. The results demonstrate that the reflection pattern changes as the shock propagates along the wedge, revealing strong non-selfsimilarity of the phenomenon.Received: 22 May 2003, Accepted: 28 August 2003, Published online: 12 November 2003 Correspondence to:T. Saito     

RESEARCH ON PRESSURE WAVE PROPAGATION CHARACTERISTICS IN THREE-PHASE FLOW DURING MANAGED PRESSURE DRILLING

考虑虚拟质量力、相间阻力、气相溶解度及滑脱速度等因素,在双流体模型基础上,建立了控压钻井中油-气-钻井液三相流体压力波速模型. 将溢流气体视为气相,将溢流油相及钻井液相视为液相,液相弹性模量及密度等参数为油相及钻井液相中各参数的加权和,利用半隐式差分及小扰动理论等数学方法,借助计算机编程对其求解. 结果表明,当井底气侵量从0.36m³/h 增至3.6m³/h,波速减小峰值为498.59m/s,而相同的油侵增加量,波速呈缓慢减小趋势,波速减小峰值为19.21m/s;当回压从0.1MPa 增至9.0MPa,波速呈增大趋势,波速增大峰值为233.15m/s;不考虑虚拟质量力,在低频段引起的波速误差呈增大趋势,在高频段引起的波速误差峰值稳定于10.03%.